Kinetic Simulation Algorithm Ontology (KiSAO)
type: Ontology
default language: en
rights: Artistic License 2.0
comment: This is a core version which contains all but deprecated classes.
version info: 2.34
definition: The Kinetic Simulation Algorithm Ontology (KiSAO) classifies algorithms available for the simulation and analysis of models in biology, and their characteristics and the parameters required for their use.

has characteristic
type: ObjectProperty
inverse of: is characteristic of
domain: modelling and simulation algorithm
range: modelling and simulation algorithm characteristic
definition: 'has characteristic' links algorithms to the characteristics they possess.

is hybrid of
type: ObjectProperty
sub property of: uses
domain: Class
  intersection of: modelling and simulation algorithm
  intersection of: Restriction
    on property: has characteristic
    some values from: hybridity
range: modelling and simulation algorithm
definition: The basic idea of hybrid simulation methods is to combine the advantages of complementary simulation approaches: the whole system is subdivided into appropriate parts and different simulation methods operate on these parts at the same time. 'is hybrid of' is a relation between the complex simulation method and algorithms it applies to the different parts of the system.

Axiom
annotated source: is hybrid of
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1093/bib/bbn050
comment: Biochemical simulations: stochastic, approximate stochastic and hybrid approaches. Pahle J. Brief Bioinform. 2009 Jan;10(1):53-64. Epub 2009 Jan 16.

is parameter of
type: ObjectProperty
inverse of: has parameter
domain: modelling and simulation algorithm parameter
range: modelling and simulation algorithm
definition: 'is parameter of' is an inverse of 'has parameter' and links parameters to the algorithms which use them.

has parameter
type: ObjectProperty
domain: modelling and simulation algorithm
range: modelling and simulation algorithm parameter
definition: 'has parameter' links algorithms to the parameters they use.

is characteristic of
type: ObjectProperty
domain: modelling and simulation algorithm characteristic
range: modelling and simulation algorithm
definition: 'is characteristic of' is an inverse of 'has characteristic' and links characteristics to the algorithms which possess them.

is similar to
type: ObjectProperty
type: SymmetricProperty
type: ReflexiveProperty
created: 2011-06-10
creator: AZ
definition: A relationship indicating that two entities are similar to each other.

uses
type: ObjectProperty
inverse of: is used by
domain: modelling and simulation algorithm
range: modelling and simulation algorithm
created: 2011-06-10
creator: AZ
definition: A relation between algorithms indicating that one algorithm uses another one (for example, if the algorithm switches between several algorithms).

is generalization of
type: ObjectProperty
sub property of: is similar to
domain: modelling and simulation algorithm
range: modelling and simulation algorithm
created: 2011-06-10
creator: AZ
definition: A relation between kinetic simulation algorithms, indicating that one is a generalization of another (e.g.if one extends another to suit systems with more general characteristics ).

is used by
type: ObjectProperty
created: 2011-07-19
creator: AZ
definition: A relation between algorithms indicating that one algorithm is used by another one (for example, if the algorithm switches between several algorithms). 'is used by' is inverse of 'uses'.

has type
type: DatatypeProperty
type: FunctionalProperty
domain: modelling and simulation algorithm parameter
definition: Indicates the type of algorithm parameter value, such as, for example, xsd:double for 'absolute tolerance'.

has Runge-Kutta method order
type: DatatypeProperty
domain: Runge-Kutta based method
range: int
definition: Indicates the order of a 'Runge-Kutta based method' [urn.miriam.biomodels.kisao:KISAO_0000064]. A 'Runge-Kutta based method' has order p if for sufficiently smooth initial value problems (y'=f(x,y), y(x0)=y0), ||y(x0 + h)-y1||<=Kh^(p+h).

modelling and simulation algorithm
type: Class
created: 2008-05-26
creator: dk
is organizational: true
alternative label: modeling and simulation algorithm
definition: Algorithm used to instantiate a simulation from a mathematical model.

weighted stochastic simulation algorithm
type: Class
subclass of: accelerated stochastic simulation algorithm
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
created: 2009-01-24
creator: NLN
alternative label: weighted SSA
definition: The weighted stochastic simulation algorithm manipulates the probabilities measure of biochemical systems by sampling, in order to increase the fraction of simulation runs exhibiting rare events.

Axiom
annotated source: weighted stochastic simulation algorithm
annotated property: altLabel
annotated target: weighted SSA
comment: EXACT

Axiom
annotated source: weighted stochastic simulation algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/19045316
comment: Kuwahara H, Mura I. (2008) An efficient and exact stochastic simulation method to analyse rare events in biochemical systems. J Chem Phys. 129(16):165101.

Gillespie first reaction algorithm
type: Class
subclass of: Gillespie-like method
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
created: 2007-11-09
creator: NLN
is implemented in: Cain
alternative label: Gillespie's first reaction method
definition: Stochastic simulation algorithm using the reaction probability density function (next-reaction density function), giving the probability that the next reaction will happen in a given time interval. To choose the next reaction to fire, the algorithm calculates a tentative reaction time for each reaction and then select the smallest.

Axiom
annotated source: Gillespie first reaction algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/0021-9991(76)90041-3
comment: Gillespie DT. A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions. Journal of Computational Physics, Volume 2 , pages 403-434 (1976).

Axiom
annotated source: Gillespie first reaction algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1021/j100540a008
comment: Gillespie DT. Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry, Vol. 81, No. 25. (1977), pp. 2340-2361.

Axiom
annotated source: Gillespie first reaction algorithm
annotated property: altLabel
annotated target: Gillespie's first reaction method
comment: EXACT

multi-state agent-based simulation method
type: Class
subclass of: rule-based simulation method
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: stochastic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with adaptive time step
is implemented in: StochSim
alternative label: Morton-Firth
definition: The agent-based simulation method instantiates each molecule as an individual software object. The interactions between those objects are determined by interaction probabilities according to experimental data. The probability is depended on the state the molecule is in at that specific time (molecules have multiple-state). Additionally, ''pseudo-molecules'' are introduced to the system in order to simulate unimolecular reactions. For simulation, continuous time is broken down into discrete, independent ''slices''. During each time slice one molecule is selected randomly, a second molecule or pseudo-molecule is selected afterwards (leading to either a unimolecular or a bimolecular reaction). The reaction will only take place if a produced random number exceeds the reaction probability calculated beforehand. In that case, the system is updated after that reaction.

Axiom
annotated source: multi-state agent-based simulation method
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/9628844
comment: Morton-Firth, C.J, Bray, D. Predicting temporal fluctuations in an intracellular signalling pathway. Journal of Theoretical Biology, volume 192, pages 117-128 (1998).

Axiom
annotated source: multi-state agent-based simulation method
annotated property: altLabel
annotated target: Morton-Firth
comment: EXACT

CVODE
type: Class
subclass of: CVODE-like method
subclass of: Restriction
  on property: is similar to
  some values from: PVODE
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: relative tolerance
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: absolute tolerance
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: maximum number of steps
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: integration method
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: iteration type
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: linear solver
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: preconditioner
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: upper half-bandwidth
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: lower half-bandwidth
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: interpolate solution
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: stability limit detection flag
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: auto reduce tolerances
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: absolute tolerance adjustment factor
disjoint with: DASPK
created: 2007-11-30
creator: dk
is implemented in: SBML-SAT
is implemented in: SUNDIALS
is implemented in: libRoadRunner
is implemented in: http://identifiers.org/biosimulators/bionetgen
is implemented in: http://identifiers.org/biosimulators/jsim
is implemented in: http://identifiers.org/biosimulators/opencor
is implemented in: http://identifiers.org/biosimulators/pysces
is implemented in: http://identifiers.org/biosimulators/tellurium
is implemented in: http://identifiers.org/biosimulators/vcell
alternative label: VODE
alternative label: VODEPK
alternative label: code value ordinary differential equation solver
definition: The CVODE is a package written in C that solves ODE initial value problems, in real N-space, written as y'=f(t,y), y(t0)=y0. It is capable for stiff and non-stiff systems and uses two different linear multi-step methods, namely the Adam-Moulton [http://identifiers.org/biomodels.kisao/KISAO_0000280] method and the backward differentiation formula [http://identifiers.org/biomodels.kisao/KISAO_0000288].

Axiom
annotated source: CVODE
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/bionetgen
comment: BioNetGen @end

Axiom
annotated source: CVODE
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/jsim
comment: JSim @end

Axiom
annotated source: CVODE
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/opencor
comment: OpenCOR @end

Axiom
annotated source: CVODE
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/pysces
comment: PySCeS @end

Axiom
annotated source: CVODE
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium @end

Axiom
annotated source: CVODE
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell @end

Axiom
annotated source: CVODE
annotated property: seeAlso
annotated target: citeulike:1832863
comment: Cohen S, Hindmarsh C. Cvode, A Stiff/nonstiff Ode Solver In C. Computers in Physics, Vol. 10 (2), pages 138-143 (1996).

Axiom
annotated source: CVODE
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/1089014.1089020
comment: Hindmarsh, A. C., et al., SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Trans. Math. Softw., 31:363-396, 2005.

Axiom
annotated source: CVODE
annotated property: altLabel
annotated target: VODE
comment: RELATED

Axiom
annotated source: CVODE
annotated property: altLabel
annotated target: VODEPK
comment: RELATED

Axiom
annotated source: CVODE
annotated property: altLabel
annotated target: code value ordinary differential equation solver
comment: EXACT

PVODE
type: Class
subclass of: CVODE-like method
subclass of: Class
  union of: Class
    intersection of: Restriction
      on property: uses
      some values from: backward differentiation formula
    intersection of: Restriction
      on property: uses
      some values from: generalized minimal residual algorithm
  union of: Restriction
    on property: uses
    some values from: Adams-Moulton method
subclass of: Restriction
  on property: is similar to
  some values from: CVODE
disjoint with: IDA
disjoint with: DASSL
is implemented in: SUNDIALS
alternative label: parallel code value ordinary differential equation solver
definition: PVODE is a general-purpose solver for ordinary differential equation (ODE) systems that implements methods for both stiff and nonstiff systems. [...] In the stiff case, PVODE uses a backward differentiation formula method [http://identifiers.org/biomodels.kisao/KISAO_0000288] combined with preconditioned GMRES [http://identifiers.org/biomodels.kisao/KISAO_0000253] iteration. Parallelism is achieved by distributing the ODE solution vector into user-specified segments and parallelizing a set of vector kernels accordingly. For PDE-based ODE systems, we provide a module that generates a band block-diagonal preconditioner for use with the GMRES [http://identifiers.org/biomodels.kisao/KISAO_0000253] iteration. PVODE is based on CVODE [http://identifiers.org/biomodels.kisao/KISAO_0000019].

Axiom
annotated source: PVODE
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/1089014.1089020
comment: Hindmarsh, A. C., et al., SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Trans. Math. Softw., 31:363-396, 2005.

Axiom
annotated source: PVODE
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1177/109434209901300405
comment: Byrne GD, Hindmarsh AC. PVODE, an ODE Solver for Parallel Computers. International Journal of High Performance Computing Applications, Vol. 13 (4), pages 354-365 (1999).

Axiom
annotated source: PVODE
annotated property: altLabel
annotated target: parallel code value ordinary differential equation solver
comment: EXACT

StochSim nearest-neighbour algorithm
type: Class
subclass of: rule-based simulation method
subclass of: Restriction
  on property: has characteristic
  some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: stochastic system behaviour
subclass of: Restriction
  on property: is similar to
  some values from: cellular automata update method
subclass of: Restriction
  on property: uses
  some values from: multi-state agent-based simulation method
is implemented in: Stochsim 1.2 and more recent versions
definition: The nearest-neighbour algorithm allows for the representation of spatial information, by adding a two-dimensional lattice in the form of a probabilistic cellular automata. That way, nearest neighbour interactions do additionally influence reactions taking place in the systems. Reactions between entities are calculated using the agent-based simulation algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000017].

Axiom
annotated source: StochSim nearest-neighbour algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/11395441
comment: Le Novere N, Shimizu TS. STOCHSIM: modelling of stochastic biomolecular processes. Bioinformatics, volume 17 (6), pages 575-576 (2001).

Elf and Ehrenberg method
type: Class
subclass of: sub-volume stochastic reaction-diffusion algorithm
subclass of: Restriction
  on property: uses
  some values from: Gibson-Bruck next reaction algorithm
subclass of: Restriction
  on property: uses
  some values from: Gillespie direct algorithm
disjoint with: Stundzia and Lumsden method
is implemented in: MesoRD
is implemented in: SmartCell
alternative label: Elf algorithm
alternative label: NSM
alternative label: next-subvolume method
definition: Sub-volume stochastic reaction-diffusion method that is a combination of the Direct Method [http://identifiers.org/biomodels.kisao/KISAO_0000029] for sampling the time for a next reaction or diffusion event in each subvolume, with Gibson and Bruck's Next Reaction Method [http://identifiers.org/biomodels.kisao/KISAO_0000027], which is used to keep track of in which subvolume an event occurs next. The subvolumes are kept sorted in a queue, implemented as a binary tree, according to increasing time of the next event. When an event has occurred in the subvolume at the top of the queue, new event times need to be sampled only for one (the event is a chemical reaction) or two (the event is a diffusion jump) subvolume(s).

Axiom
annotated source: Elf and Ehrenberg method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1049/sb:20045021
comment: Elf J, Ehrenberg M. Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases. Systems Biology, IEE Proceedings, volume 1 (2), pages 230-236 (2004).

Axiom
annotated source: Elf and Ehrenberg method
annotated property: altLabel
annotated target: Elf algorithm
comment: EXACT

Axiom
annotated source: Elf and Ehrenberg method
annotated property: altLabel
annotated target: NSM
comment: EXACT

Axiom
annotated source: Elf and Ehrenberg method
annotated property: altLabel
annotated target: next-subvolume method
comment: EXACT

Gibson-Bruck next reaction algorithm
type: Class
subclass of: accelerated stochastic simulation algorithm
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
subclass of: Restriction
  on property: is similar to
  some values from: Gillespie first reaction algorithm
created: 2007-11-10
creator: dk
is implemented in: Cain
is implemented in: SmartCell
is implemented in: http://identifiers.org/biosimulators/ecell4
is implemented in: http://identifiers.org/biosimulators/vcell
alternative label: Gibson and Bruck algorithm
alternative label: Gibson-Bruck's next reaction algorithm
alternative label: Gillespie-Gibson stochastic simulation algorithm
alternative label: SSA-GB
alternative label: next reaction method
definition: As with the first reaction method [http://identifiers.org/biomodels.kisao/KISAO_0000015], a putative reaction time is calculated for each reaction, and the reaction with the shortest reaction time will be realized. However, the unused calculated reaction times are not wasted. The set of reactions is organized in a priority queue to allow for the efficient search for the fastest reaction. In addition, by using a so-called dependency graph only those reaction times are recalculated in each step, that are dependent on the reaction, which has been realized.

Axiom
annotated source: Gibson-Bruck next reaction algorithm
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ecell4
comment: E-Cell @end

Axiom
annotated source: Gibson-Bruck next reaction algorithm
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell @end

Axiom
annotated source: Gibson-Bruck next reaction algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1021/jp993732q
comment: Gibson MA, Bruck J. Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels. Journal of Physical Chemistry A, Vol. 104, pages 1876-1889 (2000).

Axiom
annotated source: Gibson-Bruck next reaction algorithm
annotated property: altLabel
annotated target: Gibson and Bruck algorithm
comment: EXACT

Axiom
annotated source: Gibson-Bruck next reaction algorithm
annotated property: altLabel
annotated target: Gibson-Bruck's next reaction algorithm
comment: EXACT

Axiom
annotated source: Gibson-Bruck next reaction algorithm
annotated property: altLabel
annotated target: Gillespie-Gibson stochastic simulation algorithm
comment: EXACT

Axiom
annotated source: Gibson-Bruck next reaction algorithm
annotated property: altLabel
annotated target: SSA-GB
comment: EXACT

Axiom
annotated source: Gibson-Bruck next reaction algorithm
annotated property: altLabel
annotated target: next reaction method
comment: EXACT

slow-scale stochastic simulation algorithm
type: Class
subclass of: accelerated stochastic simulation algorithm
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
alternative label: slow-scale stochastic SSA
alternative label: ssSSA
definition: Attempt to overcome the problem of stiff systems by developing an ''approximate theory that allows one to stochastically advance the system in time by simulating the firings of only the slow reaction events''.

Axiom
annotated source: slow-scale stochastic simulation algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/15638651
comment: Cao Y, Gillespie DT, Petzold LR. The slow-scale stochastic simulation algorithm. Journal of Chemical Physics, Vol. 122, No. 1. (1 January 2005).

Axiom
annotated source: slow-scale stochastic simulation algorithm
annotated property: altLabel
annotated target: slow-scale stochastic SSA
comment: EXACT

Axiom
annotated source: slow-scale stochastic simulation algorithm
annotated property: altLabel
annotated target: ssSSA
comment: EXACT

Gillespie direct algorithm
type: Class
subclass of: Gillespie-like method
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
subclass of: Restriction
  on property: is similar to
  some values from: Bortz-Kalos-Lebowitz algorithm
created: 2007-11-10
creator: dk
is implemented in: BetaWB
is implemented in: ByoDyn
is implemented in: Cain
is implemented in: http://identifiers.org/biosimulators/bionetgen
is implemented in: http://identifiers.org/biosimulators/ibiosim
alternative label: DM
alternative label: Doob-Gillespie method
alternative label: Gillespie's algorithm
alternative label: Gillespie's direct method
alternative label: SSA
alternative label: stochastic simulation algorithm
definition: Stochastic simulation algorithm using the reaction probability density function (next-reaction density function), giving the probability that the next reaction will happen in a given time interval. To choose the next reaction to fire, the algorithm directly and separately calculates the identity of the reaction and the time it will fire.

Axiom
annotated source: Gillespie direct algorithm
annotated property: altLabel
annotated target: Gillespie's algorithm
comment: EXACT

Axiom
annotated source: Gillespie direct algorithm
annotated property: altLabel
annotated target: Gillespie's direct method
comment: EXACT

Axiom
annotated source: Gillespie direct algorithm
annotated property: altLabel
annotated target: SSA
comment: EXACT

Axiom
annotated source: Gillespie direct algorithm
annotated property: altLabel
annotated target: stochastic simulation algorithm
comment: EXACT

Axiom
annotated source: Gillespie direct algorithm
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/bionetgen
comment: BioNetGen @end

Axiom
annotated source: Gillespie direct algorithm
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim @end

Axiom
annotated source: Gillespie direct algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/0021-9991(76)90041-3
comment: Gillespie DT. A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions. Journal of Computational Physics, Volume 2 , pages 403-434 (1976).

Axiom
annotated source: Gillespie direct algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1021/j100540a008
comment: Gillespie DT. Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry, Vol. 81, No. 25. (1977), pp. 2340-2361.

Axiom
annotated source: Gillespie direct algorithm
annotated property: altLabel
annotated target: DM
comment: EXACT

Axiom
annotated source: Gillespie direct algorithm
annotated property: altLabel
annotated target: Doob-Gillespie method
comment: EXACT

Euler forward method
type: Class
subclass of: Euler method
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
disjoint with: Euler backward method
created: 2007-11-10
creator: dk
is implemented in: http://identifiers.org/biosimulators/ibiosim
is implemented in: http://identifiers.org/biosimulators/vcell
alternative label: explicit Euler method
alternative label: explicit Gaussian first order Runge-Kutta
definition: The Euler method is an explicit one-step method for the numerical integration of ODES with a given initial value. The calculation of the next integration step at time t+1 is based on the state of the system at time point t.

Axiom
annotated source: Euler forward method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim @end

Axiom
annotated source: Euler forward method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell @end

Axiom
annotated source: Euler forward method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/052143064X
comment: Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes. Cambridge University Press, New York, 2nd edition (1992).

Axiom
annotated source: Euler forward method
annotated property: altLabel
annotated target: explicit Euler method
comment: EXACT

Axiom
annotated source: Euler forward method
annotated property: altLabel
annotated target: explicit Gaussian first order Runge-Kutta
comment: EXACT

Euler backward method
type: Class
subclass of: Euler method
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
created: 2007-11-02
creator: dk
is implemented in: GSL
alternative label: implicit Euler method
alternative label: implicit Gaussian first order Runge-Kutta
definition: The Euler backward method is an implicit one-step method for the numerical integration of ODES with a given initial value. The next state of a system is calculated by solving an equation that considers both, the current state of the system and the later one.

Axiom
annotated source: Euler backward method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/052143064X
comment: Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes in Fortran 77. Cambridge University Press (2001).

Axiom
annotated source: Euler backward method
annotated property: altLabel
annotated target: implicit Euler method
comment: EXACT

Axiom
annotated source: Euler backward method
annotated property: altLabel
annotated target: implicit Gaussian first order Runge-Kutta
comment: EXACT

explicit fourth-order Runge-Kutta method
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has Runge-Kutta method order
  has value: 4
created: 2007-11-12
creator: dk
is implemented in: GSL
is implemented in: http://identifiers.org/biosimulators/jsim
is implemented in: http://identifiers.org/biosimulators/vcell
alternative label: ERK4
alternative label: RK4
alternative label: Runge-Kutta method
definition: The Runge-Kutta method is a method for the numerical integration of ODES with a given initial value. The calculation of the next integration step at time t+1 is based on the state of the system at time point t, plus the product of the size of the interval and an estimated slope. The slope is a weighted average of 4 single slope points (beginning of interval-midpoint-midpoint-end of interval).

Axiom
annotated source: explicit fourth-order Runge-Kutta method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/jsim
comment: JSim @end

Axiom
annotated source: explicit fourth-order Runge-Kutta method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell @end

Axiom
annotated source: explicit fourth-order Runge-Kutta method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0-471-91046-5
comment: Butcher JC. The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods (1987).

Axiom
annotated source: explicit fourth-order Runge-Kutta method
annotated property: altLabel
annotated target: ERK4
comment: EXACT

Axiom
annotated source: explicit fourth-order Runge-Kutta method
annotated property: altLabel
annotated target: RK4
comment: EXACT

Axiom
annotated source: explicit fourth-order Runge-Kutta method
annotated property: altLabel
annotated target: Runge-Kutta method
comment: EXACT

Rosenbrock method
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2007-11-12
creator: dk
is implemented in: http://identifiers.org/biosimulators/ecell4
alternative label: Kaps-Rentrop method
alternative label: generalized fourth order Runge-Kutta method
definition: Some general implicit processes are given for the solution of simultaneous first-order differential equations. These processes, which use successive substitution, are implicit analogues of the (explicit) Runge-Kutta processes. They require the solution in each time step of one or more set of simultaneous linear equations, usually of a special and simple form. Processes of any required order can be devised, and they can be made to have a wide margin of stability when applied to a linear problem.

Axiom
annotated source: Rosenbrock method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ecell4
comment: E-Cell @end

Axiom
annotated source: Rosenbrock method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1093/comjnl/5.4.329
comment: Rosenbrock HH. Some general implicit processes for the numerical solution of differential equations. The Computer Journal, pages 329-330 (1963).

Axiom
annotated source: Rosenbrock method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/052143064X
comment: Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes. Cambridge University Press, New York, 2nd edition, pages 742-746 (1992).

Axiom
annotated source: Rosenbrock method
annotated property: altLabel
annotated target: Kaps-Rentrop method
comment: EXACT

Axiom
annotated source: Rosenbrock method
annotated property: altLabel
annotated target: generalized fourth order Runge-Kutta method
comment: EXACT

sorting stochastic simulation algorithm
type: Class
subclass of: accelerated stochastic simulation algorithm
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
alternative label: sorting SSA
alternative label: sorting direct method
definition: In order to overcome the problem of high complexity of the stochastic simulation algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000029] when simulating large systems, the sorting direct method maintains a loosely sorted order of the reactions as the simulation executes.

Axiom
annotated source: sorting stochastic simulation algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/j.compbiolchem.2005.10.007
comment: McCollum J M, Peterson G D, Cox C D, Simpson M L, Samatova N F. The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behaviour. Computational Biology and Chemistry, Volume 30 (1), pages 39-49 (2006).

Axiom
annotated source: sorting stochastic simulation algorithm
annotated property: altLabel
annotated target: sorting SSA
comment: EXACT

Axiom
annotated source: sorting stochastic simulation algorithm
annotated property: altLabel
annotated target: sorting direct method
comment: EXACT

tau-leaping method
type: Class
subclass of: stochastic simulation leaping method
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: tau-leaping epsilon
created: 2008-07-08
creator: NLN
is implemented in: ByoDyn
is implemented in: Cain
is implemented in: SmartCell
alternative label: tauL
definition: Approximate acceleration procedure of the stochastic simulation algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000029] that divides the time into subintervals and ''leaps'' from one to another, firing all the reaction events in each subinterval.

Axiom
annotated source: tau-leaping method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.1378322
comment: Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of Chemical Physics, Vol. 115 (4), pages 1716-1733 (2001). Section V.

Axiom
annotated source: tau-leaping method
annotated property: altLabel
annotated target: tauL
comment: EXACT

Poisson tau-leaping method
type: Class
subclass of: tau-leaping method
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
is implemented in: ByoDyn
alternative label: explicit tau-leaping
alternative label: explicit tau-leaping method with basic pre-leap check
alternative label: explicit tau-leaping method with basic preleap check
alternative label: poisson tau-leaping
definition: Explicit tau-leaping method with basic pre leap check.

Axiom
annotated source: Poisson tau-leaping method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.1378322
comment: Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of Chemical Physics, Vol. 115 (4), pages 1716-1733 (2001). Section V.

Axiom
annotated source: Poisson tau-leaping method
annotated property: altLabel
annotated target: explicit tau-leaping
comment: EXACT

Axiom
annotated source: Poisson tau-leaping method
annotated property: altLabel
annotated target: explicit tau-leaping method with basic preleap check
comment: EXACT

Axiom
annotated source: Poisson tau-leaping method
annotated property: altLabel
annotated target: poisson tau-leaping
comment: EXACT

implicit tau-leaping method
type: Class
subclass of: tau-leaping method
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: tau-leaping delta
created: 2007-10-12
creator: dk
definition: Contrary to the explicit tau-leaping [http://identifiers.org/biomodels.kisao/KISAO_0000039 and http://identifiers.org/biomodels.kisao/KISAO_0000245 some http://identifiers.org/biomodels.kisao/KISAO_0000239] , the implicit tau-leaping allows for much larger time-steps when simulating stiff systems.

Axiom
annotated source: implicit tau-leaping method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.1627296
comment: Rathinam M, Petzold L R, Cao Y, Gillespie D T. Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method. The Journal of Chemical Physics, Volume 119 (24), pages 12784-12794 (2003).

trapezoidal tau-leaping method
type: Class
subclass of: tau-leaping method
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
created: 2007-10-16
creator: dk
alternative label: trapezoidal implicit tau-leaping method
definition: Formula for accelerated discrete efficient stochastic simulation of chemically reacting system [which] has better accuracy and stiff stability properties than the explicit and implicit [http://identifiers.org/biomodels.kisao/KISAO_0000045] tau-leaping formulas for discrete stochastic systems, and it limits to the trapezoidal rule in the deterministic regime.

Axiom
annotated source: trapezoidal tau-leaping method
annotated property: seeAlso
annotated target: citeulike:1755561
comment: Cao Y, Petzold L. Trapezoidal tau-leaping formula for the stochastic simulation of biochemical systems. Foundations of Systems Biology in Engineering (FOSBE), pages 149-152 (2005).

Axiom
annotated source: trapezoidal tau-leaping method
annotated property: altLabel
annotated target: trapezoidal implicit tau-leaping method
comment: EXACT

adaptive explicit-implicit tau-leaping method
type: Class
subclass of: tau-leaping method
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
definition: Modification of the original tau-selection strategy [http://identifiers.org/biomodels.kisao/KISAO_0000040], designed for explicit tau-leaping, is modified to apply to implicit tau-leaping, allowing for longer steps when the system is stiff. Further, an adaptive strategy is proposed that identifies stiffness and automatically chooses between the explicit and the (new) implicit tau-selection methods to achieve better efficiency.

Axiom
annotated source: adaptive explicit-implicit tau-leaping method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.2745299
comment: Cao Y, Gillespie DT, Petzold LR. Adaptive explicit-implicit tau-leaping method with automatic tau selection. The Journal of Chemical Physics, Vol. 126 (22) (2007).

Bortz-Kalos-Lebowitz algorithm
type: Class
subclass of: generalized stochastic simulation algorithm
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: is similar to
  some values from: Gillespie direct algorithm
alternative label: BKL
alternative label: DMC
alternative label: KMC
alternative label: dynamic Monte Carlo
alternative label: dynamic Monte Carlo method
alternative label: kinetic Monte Carlo
alternative label: kinetic Monte Carlo method
alternative label: n-fold way
definition: The Bortz-Kalos-Lebowitz (or: kinetic Monte-Carlo-) method is a stochastic method for the simulation of time evolution of processes using (pseudo-)random numbers.

Axiom
annotated source: Bortz-Kalos-Lebowitz algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/0021-9991(75)90060-1
comment: Bortz AB, Kalos MH, Lebowitz JL. A new algorithm for Monte Carlo simulation of Ising spin systems. Journal of Computational Physics, Vol. 17 (1), pages 10-18 (1975).

Axiom
annotated source: Bortz-Kalos-Lebowitz algorithm
annotated property: altLabel
annotated target: BKL
comment: EXACT

Axiom
annotated source: Bortz-Kalos-Lebowitz algorithm
annotated property: altLabel
annotated target: DMC
comment: EXACT

Axiom
annotated source: Bortz-Kalos-Lebowitz algorithm
annotated property: altLabel
annotated target: KMC
comment: EXACT

Axiom
annotated source: Bortz-Kalos-Lebowitz algorithm
annotated property: altLabel
annotated target: dynamic Monte Carlo
comment: EXACT

Axiom
annotated source: Bortz-Kalos-Lebowitz algorithm
annotated property: altLabel
annotated target: dynamic Monte Carlo method
comment: EXACT

Axiom
annotated source: Bortz-Kalos-Lebowitz algorithm
annotated property: altLabel
annotated target: kinetic Monte Carlo
comment: EXACT

Axiom
annotated source: Bortz-Kalos-Lebowitz algorithm
annotated property: altLabel
annotated target: kinetic Monte Carlo method
comment: EXACT

Axiom
annotated source: Bortz-Kalos-Lebowitz algorithm
annotated property: altLabel
annotated target: n-fold way
comment: EXACT

Smoluchowski equation based method
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: stochastic system behaviour
created: 2007-10-29
creator: dk
is organizational: true
definition: Method based on the Smoluchowski equation.

Axiom
annotated source: Smoluchowski equation based method
annotated property: seeAlso
annotated target: urn:issn:0942-9352
comment: Smoluchowski M. Mathematical theory of the kinetics of the coagulation of colloidal solutions. Z. Phys. Chem, Vol. 92, No. 129. (1917).

Brownian diffusion Smoluchowski method
type: Class
subclass of: Smoluchowski equation based method
subclass of: Restriction
  on property: has characteristic
  some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: discrete variable
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: Brownian diffusion accuracy
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: surface-bound epsilon
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: neighbour distance
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: virtual box size
disjoint with: Greens function reaction dynamics
is implemented in: Smoldyn
definition: In the Brownian diffusion Smoluchowski method, ''each molecule is treated as a point-like particle that diffuses freely in three-dimensional space. When a pair of reactive molecules collide, such as an enzyme and its substrate, a reaction occurs and the simulated reactants are replaced by products. [..] Analytic solutions are presented for some simulation parameters while others are calculated using look-up tables''. Supported chemical processes include molecular diffusion, treatment of surfaces, zeroth-order-, unimolecular-, and bimolecular reactions.

Axiom
annotated source: Brownian diffusion Smoluchowski method
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/16204833
comment: Andrews SS, Bray D. Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Phys Biol, volume 1 (3-4), pages 137-151 (December 2004).

Greens function reaction dynamics
type: Class
subclass of: Smoluchowski equation based method
subclass of: Restriction
  on property: has characteristic
  some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: discrete variable
subclass of: Restriction
  on property: has characteristic
  some values from: progression with adaptive time step
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
alternative label: GFRD
alternative label: Green's function reaction dynamics
definition: Method that simulates biochemical networks on particle level. It considers both changes in time and space by ''exploiting both the exact solution of the Smoluchowski Equation to set up an event-driven algorithm'' which allows for large jumps in time when the considered particles are far away from each other [in space] and thus cannot react. GFRD combines the propagation of particles in space with the reactions taking place between them in one simulation step.

Axiom
annotated source: Greens function reaction dynamics
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.2137716
comment: Van Zon JS, Ten Wolde PR. Green's-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space. Journal of Chemical Physics, Volume 123 (23) (2005).

Axiom
annotated source: Greens function reaction dynamics
annotated property: altLabel
annotated target: GFRD
comment: EXACT

Axiom
annotated source: Greens function reaction dynamics
annotated property: altLabel
annotated target: Green's function reaction dynamics
comment: EXACT

Runge-Kutta based method
type: Class
subclass of: one-step method
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: is generalization of
  some values from: Euler method
subclass of: Restriction
  on property: has Runge-Kutta method order
  some values from: integer
created: 2007-11-12
creator: dk
is implemented in: ByoDyn
is organizational: true
alternative label: modified Euler method
definition: A method of numerically integrating ordinary differential equations, which uses a sampling of slopes through an interval and takes a weighted average to determine the right end point. This averaging gives a very accurate approximation.

Axiom
annotated source: Runge-Kutta based method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0-471-91046-5
comment: Butcher JC. The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods (1987).

Axiom
annotated source: Runge-Kutta based method
annotated property: altLabel
annotated target: modified Euler method
comment: RELATED

deterministic cellular automata update algorithm
type: Class
subclass of: cellular automata update method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
created: 2007-11-30
creator: dk
definition: A cellular automaton is a discrete model of a regular grid of cells with a finite number of dimensions. Each cell has a finite number of defined states. The automaton changes its state in a discrete manner, meaning that the state of a cell at time t is determined by a function of the states of its neighbours at time t - 1. These neighbours are a selection of cells relative to the specified cell. Famous examples for deterministic cellular automata are Conway's game of life or Wolfram's elementary cellular automata.

Axiom
annotated source: deterministic cellular automata update algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-0252000232
comment: Burks, Arthur W (Editor). Essays on Cellular Automata. University of Illinois Press (1970).

LSODE
type: Class
subclass of: Livermore solver
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
subclass of: Restriction
  on property: uses
  some values from: backward differentiation formula
subclass of: Restriction
  on property: uses
  some values from: Adams predictor-corrector method
created: 2007-11-16
creator: dk
alternative label: Livermore solver for ordinary differential equations
definition: LSODE solves stiff and nonstiff systems of the form dy/dt = f. In the stiff case, it treats the Jacobian matrix sf/dy as either a dense (full) or a banded matrix, and as either user-supplied or internally approximated by difference quotients. It uses Adams methods (predictor-corrector) [http://identifiers.org/biomodels.kisao/KISAO_0000364] in the nonstiff case, and Backward Differentiation Formula (BDF) methods (the Gear methods) [http://identifiers.org/biomodels.kisao/KISAO_0000288] in the stiff case.

Axiom
annotated source: LSODE
annotated property: seeAlso
annotated target: citeulike:1774586
comment: Radhakrishnan K, Hindmarsh AC. Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations. Lawrence Livermore National Laboratory Report, Vol. UCRL-ID-113855 (1993).

Axiom
annotated source: LSODE
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/1218052.1218054
comment: Hindmarsh AC. LSODE and LSODI, two new initial value ordinary differential equation solvers. SIGNUM Newsletter, Volume 15 (4), pages 10-11 (1980).

Axiom
annotated source: LSODE
annotated property: altLabel
annotated target: Livermore solver for ordinary differential equations
comment: EXACT

binomial tau-leaping method
type: Class
subclass of: tau-leaping method
subclass of: Restriction
  on property: is similar to
  some values from: sub-volume stochastic reaction-diffusion algorithm
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: coarse-graining factor
created: 2007-10-16
creator: dk
alternative label: BtauL
alternative label: binomial tau-leap spatial stochastic simulation algorithm
definition: Coarse grained modified version of the next subvolume method [http://identifiers.org/biomodels.kisao/KISAO_0000022] that allows the user to consider both diffusion and reaction events in relatively long simulation time spans as compared with the original method and other commonly used fully stochastic computational methods.

Axiom
annotated source: binomial tau-leaping method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.2771548
comment: Marquez-Lago T., Burrage K. Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics. The Journal of Chemical Physics, Vol. 127 (10) (2007).

Axiom
annotated source: binomial tau-leaping method
annotated property: altLabel
annotated target: BtauL
comment: EXACT

Axiom
annotated source: binomial tau-leaping method
annotated property: altLabel
annotated target: binomial tau-leap spatial stochastic simulation algorithm
comment: EXACT

Gillespie multi-particle method
type: Class
subclass of: generalized stochastic simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: spatial description
subclass of: Restriction
  on property: uses
  some values from: Gillespie direct algorithm
subclass of: Restriction
  on property: uses
  some values from: multiparticle lattice gas automata
alternative label: GMP
alternative label: Gillespie's multi-particle method
alternative label: particle-based spatial stochastic method
definition: Combination of the multiparticle method for diffusion [http://identifiers.org/biomodels.kisao/KISAO_0000334] and the SSA [http://identifiers.org/biomodels.kisao/KISAO_0000029].

Axiom
annotated source: Gillespie multi-particle method
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/16731694
comment: Rodriguez VJ, Kaandorp JA, Dobrzynski M, Blom JG. Spatial stochastic modelling of the phosphoenolpyruvate-dependent phosphotransferase (PTS) pathway in Escherichia coli. Bioinformatics, Vol. 22 (15), pages 1895-1901 (2006).

Axiom
annotated source: Gillespie multi-particle method
annotated property: altLabel
annotated target: GMP
comment: EXACT

Axiom
annotated source: Gillespie multi-particle method
annotated property: altLabel
annotated target: Gillespie's multi-particle method
comment: EXACT

Axiom
annotated source: Gillespie multi-particle method
annotated property: altLabel
annotated target: particle-based spatial stochastic method
comment: EXACT

Stundzia and Lumsden method
type: Class
subclass of: sub-volume stochastic reaction-diffusion algorithm
alternative label: RD SSA
alternative label: reaction-diffusion stochastic simulation algorithm
definition: Sub-volume stochastic reaction-diffusion method that using Green's function to link the bulk diffusion coefficient D in Fick's differential law to the corresponding transition rate probability for diffusion of a particle between finite volume elements. This generalized stochastic algorithm enables to numerically calculate the time evolution of a spatially inhomogeneous mixture of reaction-diffusion species in a finite volume. The time step is stochastic and is generated by a probability distribution determined by the intrinsic reaction kinetics and diffusion dynamics.

Axiom
annotated source: Stundzia and Lumsden method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1006/jcph.1996.0168
comment: Stundzia AB, Lumsden CJ. Stochastic simulation of coupled reaction-diffusion processes. J Comput Phys, Vol. 127 (1), pages 196-207 (1996).

Axiom
annotated source: Stundzia and Lumsden method
annotated property: altLabel
annotated target: RD SSA
comment: EXACT

Axiom
annotated source: Stundzia and Lumsden method
annotated property: altLabel
annotated target: reaction-diffusion stochastic simulation algorithm
comment: EXACT

estimated midpoint tau-leaping method
type: Class
subclass of: tau-leaping method
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
alternative label: explicit tau-leaping method with estimated-mid point technique
definition: Estimated-Midpoint tau-Leap Method: For the selected leaping time tau which satisfies the Leap Condition, compute the expected state change lambda' = tau sumj( aj(x)vj ) during [t, t + tau). Then, with x' =x + [lambda'/2], generate for each j = 1,...,M a sample value kj of the Poisson random variable P(aj(x'), tau). Compute the actual state change, lambda = sumj( kjvj ), and effect the leap by replacing t by t + tau and x by x + lambda.

Axiom
annotated source: estimated midpoint tau-leaping method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.1378322
comment: Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of Chemical Physics, Vol. 115 (4), pages 1716-1733 (2001). Section VI.

Axiom
annotated source: estimated midpoint tau-leaping method
annotated property: altLabel
annotated target: explicit tau-leaping method with estimated-mid point technique
comment: EXACT

k-alpha leaping method
type: Class
subclass of: stochastic simulation leaping method
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: is similar to
  some values from: tau-leaping method
definition: Alternative to the tau-leaping [http://identifiers.org/biomodels.kisao/KISAO_0000039], where one leaps a fixed number of reaction-events.

Axiom
annotated source: k-alpha leaping method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.1378322
comment: Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of Chemical Physics, Vol. 115 (4), pages 1716-1733 (2001). Section VIII.

nonnegative Poisson tau-leaping method
type: Class
subclass of: tau-leaping method
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
subclass of: Restriction
  on property: is similar to
  some values from: Poisson tau-leaping method
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: critical firing threshold
alternative label: modified poisson tau-leaping
definition: The explicit tau-leaping procedure attempts to speed up the stochastic simulation of a chemically reacting system by approximating the number of firings of each reaction channel during a chosen time increment Tau as a Poisson random variable. Since the Poisson random variable can have arbitrarily large sample values, there is always the possibility that this procedure will cause one or more reaction channels to fire so many times during Tau that the population of some reactant species will be driven negative. Two recent papers have shown how that unacceptable occurrence can be avoided by replacing the Poisson random variables with binomial random variables, whose values are naturally bounded. This paper describes a modified Poisson tau-leaping procedure that also avoids negative populations, but is easier to implement than the binomial procedure. The new Poisson procedure also introduces a second control parameter, whose value essentially dials the procedure from the original Poisson tau-leaping at one extreme to the exact stochastic simulation algorithm at the other; therefore, the modified Poisson procedure will generally be more accurate than the original Poisson procedure [http://identifiers.org/biomodels.kisao/KISAO_0000040].

Axiom
annotated source: nonnegative Poisson tau-leaping method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.1992473
comment: Cao Y, Gillespie DT, Petzold LR. Avoiding negative populations in explicit Poisson tau-leaping. Journal of Chemical Physics, Vol. 123, 4104 (2005).

Fehlberg method
type: Class
subclass of: embedded Runge-Kutta 5(4) method
is implemented in: GSL
is implemented in: http://identifiers.org/biosimulators/ecell4
is implemented in: http://identifiers.org/biosimulators/ibiosim
is implemented in: http://identifiers.org/biosimulators/jsim
is implemented in: http://identifiers.org/biosimulators/vcell
alternative label: RKF45
alternative label: Runge-Kutta-Fehlberg method
definition: The method was developed by the German mathematician Erwin Fehlberg and is based on the class of Runge-Kutta methods. The Runge-Kutta-Fehlberg method uses an O(h4) method together with an O(h5) method that uses all of the points of the O(h4) method, and hence is often referred to as an RKF45 method. Similar schemes with different orders have since been developed. By performing one extra calculation that would be required for an RK5 method, the error in the solution can be estimated and controlled and an appropriate step size can be determined automatically, making this method efficient for ordinary problems of automated numerical integration of ordinary differential equations.

Axiom
annotated source: Fehlberg method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ecell4
comment: E-Cell @end

Axiom
annotated source: Fehlberg method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim @end

Axiom
annotated source: Fehlberg method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/jsim
comment: JSim @end

Axiom
annotated source: Fehlberg method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell @end

Axiom
annotated source: Fehlberg method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/BF02241732
comment: Erwin Fehlberg (1970). Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme, Computing (Arch. Elektron. Rechnen), vol. 6, pp. 61-71. @de

Axiom
annotated source: Fehlberg method
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/14990450
comment: Takahashi K, Kaizu K, Hu B, Tomita M. A multi-algorithm, multi-timescale method for cell simulation. Bioinformatics volume 20(4), pages 538-46 (2004).

Axiom
annotated source: Fehlberg method
annotated property: altLabel
annotated target: RKF45
comment: EXACT

Axiom
annotated source: Fehlberg method
annotated property: altLabel
annotated target: Runge-Kutta-Fehlberg method
comment: EXACT

Dormand-Prince method
type: Class
subclass of: embedded Runge-Kutta 5(4) method
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: safety factor on new step selection
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: minimum factor to change step size by
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: maximum factor to change step size by
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: beta parameter for stabilized step size control
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: initial step size
created: 2007-11-12
creator: dk
is implemented in: ECell3
is implemented in: GSL
is implemented in: Matlab
is implemented in: http://identifiers.org/biosimulators/ibiosim
is implemented in: http://identifiers.org/biosimulators/jsim
alternative label: DOPRI
alternative label: Prince-Dormand method
definition: Dormand-Prince is an explicit method for the numerical integration of ODES with a given initial value. It is an 'embedded Runge-Kutta method' [http://identifiers.org/biomodels.kisao/KISAO_0000302] RK5 (4) which (a) has a 'small' principal truncation term in the Fifth order and (b) has an extended region of absolute stability.

Axiom
annotated source: Dormand-Prince method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim @end

Axiom
annotated source: Dormand-Prince method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/jsim
comment: JSim @end

Axiom
annotated source: Dormand-Prince method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/0771-050X(80)90013-3
comment: Dormand J, Prince P. A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics, Volume 6, pages 19-26 (1980).

Axiom
annotated source: Dormand-Prince method
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/14990450
comment: Takahashi K, Kaizu K, Hu B, Tomita M. A multi-algorithm, multi-timescale method for cell simulation. Bioinformatics volume 20(4), pages 538-46 (2004).

Axiom
annotated source: Dormand-Prince method
annotated property: altLabel
annotated target: Prince-Dormand method
comment: EXACT

LSODA
type: Class
subclass of: Livermore solver
subclass of: Restriction
  on property: is similar to
  some values from: LSODE
subclass of: Restriction
  on property: uses
  some values from: backward differentiation formula
subclass of: Restriction
  on property: uses
  some values from: Adams method
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: relative tolerance
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: absolute tolerance
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: maximum Adams order
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: maximum BDF order
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: initial step size
created: 2007-11-30
creator: dk
alternative label: Livermore solver for ordinary differential equations with automatic method switching
definition: LSODA solves systems dy/dt = f with a dense or banded Jacobian when the problem is stiff, but it automatically selects between non-stiff (Adams [http://identifiers.org/biomodels.kisao/KISAO_0000289]) and stiff (BDF [http://identifiers.org/biomodels.kisao/KISAO_0000288]) methods. It uses the non-stiff method initially, and dynamically monitors data in order to decide which method to use.

Axiom
annotated source: LSODA
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0904010
comment: Petzold LR. Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations. SIAM Journal on Scientific and Statistical Computing, Vol. 4 (1), pages 136-148 (1983).

Axiom
annotated source: LSODA
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-0444866073
comment: A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.

Axiom
annotated source: LSODA
annotated property: seeAlso
annotated target: http://www.nea.fr/abs/html/uscd1227.html
comment: Petzold LR, Hindmarsh, AC. LSODAR: Livermore solver of ordinary differential equations with automatic method switching and root finding, Computing and Mathematics Research Division, 1-316 Lawerence Livermore National Laboratory (1987).

Axiom
annotated source: LSODA
annotated property: altLabel
annotated target: Livermore solver for ordinary differential equations with automatic method switching
comment: EXACT

LSODAR
type: Class
subclass of: Livermore solver
subclass of: Restriction
  on property: is similar to
  some values from: LSODA
created: 2007-10-27
creator: dk
alternative label: Livermore solver for ordinary differential equations with automatic method switching and root finding
alternative label: ordinary differential equation solver for stiff or non-stiff systems with root finding
definition: LSODAR is a variant of LSODA [http://identifiers.org/biomodels.kisao/KISAO_0000088] with a root finding capability added. Thus it solves problems dy/dt = f with dense or banded Jacobian and automatic method selection, and at the same time, it finds the roots of any of a set of given functions of the form g(t,y). This is often useful for finding stop conditions, or for finding points at which a switch is to be made in the function f.

Axiom
annotated source: LSODAR
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-0444866073
comment: A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.

Axiom
annotated source: LSODAR
annotated property: seeAlso
annotated target: http://www.nea.fr/abs/html/uscd1228.html
comment: Petzold LR, Hindmarsh, AC. LSODAR: Livermore solver of ordinary differential equations with automatic method switching and root finding, Computing and Mathematics Research Division, 1-316 Lawerence Livermore National Laboratory (1987).

Axiom
annotated source: LSODAR
annotated property: altLabel
annotated target: Livermore solver for ordinary differential equations with automatic method switching and root finding
comment: EXACT

Axiom
annotated source: LSODAR
annotated property: altLabel
annotated target: ordinary differential equation solver for stiff or non-stiff systems with root finding
comment: EXACT

LSODI
type: Class
subclass of: Livermore solver
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: is similar to
  some values from: LSODE
alternative label: Livermore solver for ordinary differential equations, implicit version
definition: LSODI solves systems given in linearly implicit form, including differential-algebraic systems.

Axiom
annotated source: LSODI
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/1218052.1218054
comment: Hindmarsh AC. LSODE and LSODI, two new initial value ordinary differential equation solvers. SIGNUM Newsletter, Volume 15 (4), pages 10-11 (1980).

Axiom
annotated source: LSODI
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-0444866073
comment: A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.

Axiom
annotated source: LSODI
annotated property: altLabel
annotated target: Livermore solver for ordinary differential equations, implicit version
comment: EXACT

LSODIS
type: Class
subclass of: Livermore solver
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: is similar to
  some values from: LSODE
created: 2007-11-30
creator: dk
alternative label: Livermore solver for ordinary differential equations, implicit sparse version
definition: LSODIS is a set of general-purpose FORTRAN routines solver for the initial value problem for ordinary differential equation systems. It is suitable for both stiff and nonstiff systems. LSODIS treat systems in the linearly implicit form A(t,y) dy/dt = g(t,y), A = a square matrix, i.e. with the derivative dy/dt implicit, but linearly so.

Axiom
annotated source: LSODIS
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-0444866073
comment: A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.

Axiom
annotated source: LSODIS
annotated property: seeAlso
annotated target: http://www.nea.fr/abs/html/uscd1225.html
comment: Seager M, Balsdon S. LSODIS - A sparse implicit ODE solver. 10th World Congress on System Simulation and Scientific Computation, pages 437-439 (1983).

Axiom
annotated source: LSODIS
annotated property: altLabel
annotated target: Livermore solver for ordinary differential equations, implicit sparse version
comment: EXACT

LSODPK
type: Class
subclass of: Livermore solver
subclass of: Restriction
  on property: is similar to
  some values from: LSODE
subclass of: Restriction
  on property: uses
  some values from: Krylov subspace projection method
created: 2008-07-08
creator: NLN
alternative label: Livermore solver for ordinary differential equations for stiff and nonstiff systems with krylov corrector iteration
definition: LSODPK is a set of FORTRAN subroutines for solving the initial value problem for stiff and nonstiff systems of ordinary differential equations. In solving stiff systems, LSODPK uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods [http://identifiers.org/biomodels.kisao/KISAO_0000354]. The user must select the desired Krylov method and supply a pair of routine to evaluate, preprocess, and solve the (left and/or right) preconditioner matrices. Aside from preconditioning, the implementation is matrix-free, meaning that explicit storage of the Jacobian (or related) matrix is not required. The method is experimental because the scope of problems for which it is effective is not well-known, and users are forewarned that LSODPK may or may not be competitive with traditional methods on a given problem. LSODPK also includes an option for a user-supplied linear system solver to be used without Krylov iteration.

Axiom
annotated source: LSODPK
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-0444866073
comment: A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.

Axiom
annotated source: LSODPK
annotated property: altLabel
annotated target: Livermore solver for ordinary differential equations for stiff and nonstiff systems with krylov corrector iteration
comment: EXACT

Livermore solver
type: Class
subclass of: ODE solver
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: progression with adaptive time step
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2008-07-08
creator: NLN
is organizational: true
definition: Method to solve ordinary differential equations developed at the Lawrence Livermore National Laboratory.

sub-volume stochastic reaction-diffusion algorithm
type: Class
subclass of: generalized stochastic simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: spatial description
disjoint with: D-leaping method
created: 2008-07-08
creator: NLN
is organizational: true
definition: Stochastic method using a combination of discretisation of compartment volumes into voxels and Gillespie-like algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000241] to simulate the evolution of the system.

modelling and simulation algorithm characteristic
type: Class
creator: AZ
is organizational: true
alternative label: modeling and simulation algorithm characteristic
definition: Simulation algorithm property, which can, for example, describe the model, such as the type of variables (discrete or continuous), and information on the treatment of spatial descriptions, or can be a numerical characteristic, such as the system's behaviour (deterministic or stochastic) as well as the progression mechanism (fixed or adaptive time steps).

type of variable
type: Class
subclass of: modelling and simulation algorithm characteristic
creator: AZ
is organizational: true
definition: Type of variables used for the simulation.

type of system behaviour
type: Class
subclass of: modelling and simulation algorithm characteristic
creator: AZ
is organizational: true
definition: A characteristic describing the rules the algorithm uses to simulate the temporal evolution of a system, specifically whether or not the final state is uniquely determined from a precise initial state.

type of progression time step
type: Class
subclass of: modelling and simulation algorithm characteristic
creator: AZ
is organizational: true
definition: Type of time steps used by the algorithm.

spatial description
type: Class
subclass of: modelling and simulation algorithm characteristic
created: 2008-07-08
creator: NLN
definition: Algorithm, possessing this characteristic, takes into account the location of the reacting components.

deterministic system behaviour
type: Class
subclass of: type of system behaviour
disjoint with: stochastic system behaviour
created: 2008-07-08
creator: NLN
definition: Algorithm, possessing this characteristic, simulates the temporal evolution of a system deterministically, so that from a precise initial state the algorithm will always end up in the same final state.

stochastic system behaviour
type: Class
subclass of: type of system behaviour
created: 2008-07-08
creator: NLN
definition: Algorithm, possessing this characteristic, simulates the temporal evolution of a system using probabilistic rules, so that between two simulations, the same precise initial state may result in a different final state.

discrete variable
type: Class
subclass of: type of variable
disjoint with: continuous variable
created: 2008-07-08
creator: NLN
definition: Algorithm, possessing this characteristic, allows values of system's variables to change by discrete (integral) amounts.

continuous variable
type: Class
subclass of: type of variable
subclass of: Restriction
  on property: has characteristic
  some values from: stochastic system behaviour
created: 2008-07-08
creator: NLN
definition: Algorithm, possessing this characteristic, allows the values of a system's variables to change by continuous (non-integral) amounts.

progression with adaptive time step
type: Class
subclass of: type of progression time step
disjoint with: progression with fixed time step
created: 2008-07-08
creator: NLN
definition: Algorithm, possessing this characteristic, does not use fixed time steps to update the state of a system during the whole simulation, but on the contrary adapts the length of the time steps to the local situation.

progression with fixed time step
type: Class
subclass of: type of progression time step
created: 2008-07-08
creator: NLN
definition: Algorithm, possessing this characteristic, uses time steps of constant length to update the state of a system during the whole simulation.

modelling and simulation algorithm parameter
type: Class
subclass of: Restriction
  on property: is parameter of
  some values from: modelling and simulation algorithm
creator: AZ
is organizational: true
alternative label: modeling and simulation algorithm parameter
definition: Parameter that can be used in the simulation experiment settings.

particle number lower limit
type: Class
subclass of: partitioning control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: Pahle hybrid method
subclass of: Restriction
  on property: has type
  some values from: double
definition: This parameter of 'Pahle hybrid method' [http://identifiers.org/biomodels.kisao/KISAO_0000231] is a double value specifying the lower limit for particle numbers. Species with a particle number below this value are considered as having a low particle number. The 'particle number lower limit' cannot be higher than the 'particle number upper limit' [http://identifiers.org/biomodels.kisao/KISAO_0000204].

particle number upper limit
type: Class
subclass of: partitioning control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: Pahle hybrid method
subclass of: Restriction
  on property: has type
  some values from: double
definition: This parameter of 'Pahle hybrid method' [http://identifiers.org/biomodels.kisao/KISAO_0000231] is a double value specifying the upper limit for particle numbers. Species with a particle number above this value are considered as having a high particle number. The 'particle number upper limit' cannot be lower than the 'particle number lower limit' [http://identifiers.org/biomodels.kisao/KISAO_0000203].

partitioning interval
type: Class
subclass of: partitioning control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: Class
    intersection of: modelling and simulation algorithm
    intersection of: Restriction
      on property: has characteristic
      some values from: hybridity
subclass of: Restriction
  on property: has type
  some values from: integer
definition: This positive integer value specifies after how many steps the internal partitioning of the system should be recalculated.

relative tolerance
type: Class
subclass of: tolerance
subclass of: Restriction
  on property: is parameter of
  all values from: Restriction
    on property: has characteristic
    some values from: approximate solution
subclass of: Restriction
  on property: has type
  some values from: double
alternative label: RTOL
definition: This parameter is a numeric value specifying the desired relative tolerance the user wants to achieve. A smaller value means that the trajectory is calculated more accurately.

Axiom
annotated source: relative tolerance
annotated property: altLabel
annotated target: RTOL
comment: EXACT

absolute tolerance
type: Class
subclass of: tolerance
subclass of: Restriction
  on property: is parameter of
  all values from: Restriction
    on property: has characteristic
    some values from: approximate solution
subclass of: Restriction
  on property: has type
  some values from: double
alternative label: ATOL
definition: This parameter is a positive numeric value specifying the desired absolute tolerance the user wants to achieve.

Axiom
annotated source: absolute tolerance
annotated property: altLabel
annotated target: ATOL
comment: EXACT

use reduced model
type: Class
subclass of: method switching control parameter
subclass of: Restriction
  on property: is parameter of
  some values from: LSODA
subclass of: Restriction
  on property: has type
  some values from: boolean
alternative label: integrate reduced model
definition: Boolean value which indicates whether the simulation/analysis should be performed using the complete model or an equivalent reduced model. Reduced models can be determined in many ways such as using mass conservation laws.

Axiom
annotated source: use reduced model
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/14990466
comment: Jacek Puchałka, Andrzej M Kierzek. Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys J. 2004, 86(3):1357-1372.

maximum Adams order
type: Class
subclass of: maximum order
subclass of: Restriction
  on property: has type
  some values from: integer
disjoint with: maximum BDF order
alternative label: Adams max order
alternative label: maximum non-stiff order
definition: This parameter is a positive integer value specifying the maximal order the non-stiff Adams integration method [http://identifiers.org/biomodels.kisao/KISAO_0000289] shall attempt before switching to the stiff BDF method [http://identifiers.org/biomodels.kisao/KISAO_0000288].

maximum BDF order
type: Class
subclass of: maximum order
subclass of: Restriction
  on property: has type
  some values from: integer
alternative label: BDF max order
alternative label: maximum stiff order
definition: This parameter is a positive integer value specifying the maximal order the stiff BDF integration method [http://identifiers.org/biomodels.kisao/KISAO_0000288] shall attempt before switching to smaller internal step sizes.

number of history bins
type: Class
subclass of: granularity control parameter
subclass of: Restriction
  on property: is parameter of
  some values from: Class
    intersection of: modelling and simulation algorithm
    intersection of: Restriction
      on property: has characteristic
      some values from: delay differential equation problem
subclass of: Restriction
  on property: has type
  some values from: integer
definition: The 'number of history bins' is only enabled for models that contain delayed or multistep reactions for specifying the granularity with which the delayed reaction solver should retain the history of species values, for species that participate in delayed reactions.

tau-leaping epsilon
type: Class
subclass of: error control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: tau-leaping method
subclass of: Restriction
  on property: has type
  some values from: double
alternative label: epsilon
alternative label: tolerance
definition: The leap condition is chosen such that the expected change in the propensity function aj(x) is bounded by Epsilon * a0 where Epsilon is an error control parameter between 0 and 1. This parameter is the basic error control mechanism for the Tau-Leaping algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000039]. As Epsilon decreases the leaps become shorter and the simulation is more accurate.

Axiom
annotated source: tau-leaping epsilon
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.1378322
comment: Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of Chemical Physics, Vol. 115 (4), pages 1716-1733 (2001). Section V.

Axiom
annotated source: tau-leaping epsilon
annotated property: altLabel
annotated target: epsilon
comment: EXACT

minimum reactions per leap
type: Class
subclass of: method switching control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: Class
    intersection of: Restriction
      on property: is hybrid of
      some values from: Gillespie direct algorithm
    intersection of: Restriction
      on property: is hybrid of
      some values from: tau-leaping method
subclass of: Restriction
  on property: has type
  some values from: integer
alternative label: threshold
definition: 'minimum reactions per leap' parameter is used in hybrid methods, which adaptively switch between the tau-leaping algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000039] to the SSA Direct Method [http://identifiers.org/biomodels.kisao/KISAO_0000029] when the number of reactions in a single tau-leaping leap step is less than the threshold.

Pahle hybrid method
type: Class
subclass of: hybrid method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: stochastic system behaviour
subclass of: Restriction
  on property: is hybrid of
  some values from: Gibson-Bruck next reaction algorithm
subclass of: Restriction
  on property: is hybrid of
  some values from: Class
    intersection of: Gibson-Bruck next reaction algorithm
    intersection of: Restriction
      on property: has characteristic
      some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: particle number lower limit
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: particle number upper limit
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
is organizational: true
definition: The hybrid method combines the stochastic 'Gibson-Bruck's next reaction method' [http://identifiers.org/biomodels.kisao/KISAO_0000027] with different algorithms for the numerical integration of ODEs [http://identifiers.org/biomodels.kisao/KISAO_0000245 some http://identifiers.org/biomodels.kisao/KISAO_0000374]. The biochemical network is dynamically partitioned into a deterministic and a stochastic subnet depending on the current particle numbers in the system. The user can define limits for when a particle number should be considered low or high. The stochastic subnet contains reactions involving low numbered species as substrate or product. All the other reactions form the deterministic subnet. The two subnets are then simulated in parallel using the stochastic and deterministic solver, respectively. The reaction probabilities in the stochastic subnet are approximated as constant between two stochastic reaction events.

Axiom
annotated source: Pahle hybrid method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: Pahle hybrid method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1093/bioinformatics/btl485
comment: COPASI--a COmplex PAthway SImulator. Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U. Bioinformatics. 2006 Dec 15;22(24):3067-74. Epub 2006 Oct 10.

LSOIBT
type: Class
subclass of: Livermore solver
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: is similar to
  some values from: LSODE
alternative label: Livermore solver for ordinary differential equations given in implicit form, with block-tridiagonal Jacobian treatment
definition: LSOIBT solves linearly implicit systems in which the matrices involved are all assumed to be block-tridiagonal. Linear systems are solved by the LU method.

Axiom
annotated source: LSOIBT
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-0444866073
comment: A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.

Axiom
annotated source: LSOIBT
annotated property: altLabel
annotated target: Livermore solver for ordinary differential equations given in implicit form, with block-tridiagonal Jacobian treatment
comment: EXACT

LSODES
type: Class
subclass of: Livermore solver
subclass of: Restriction
  on property: is similar to
  some values from: LSODE
alternative label: Livermore solver for ordinary differential equations with general sparse Jacobian matrix
definition: LSODES solves systems dy/dt = f and in the stiff case treats the Jacobian matrix in general sparse form. It determines the sparsity structure on its own, or optionally accepts this information from the user. It then uses parts of the Yale Sparse Matrix Package (YSMP) to solve the linear systems that arise, by a sparse (direct) LU factorization/backsolve method.

Axiom
annotated source: LSODES
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-0444866073
comment: A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.

Axiom
annotated source: LSODES
annotated property: altLabel
annotated target: Livermore solver for ordinary differential equations with general sparse Jacobian matrix
comment: EXACT

LSODKR
type: Class
subclass of: Livermore solver
subclass of: Restriction
  on property: is similar to
  some values from: LSODE
subclass of: Restriction
  on property: is similar to
  some values from: LSODPK
subclass of: Restriction
  on property: uses
  some values from: Krylov subspace projection method
alternative label: Livermore solver for ordinary differential equations, with preconditioned Krylov iteration methods for the Newton correction linear systems, and with root finding.
definition: LSODKR is an initial value ODE solver for stiff and nonstiff systems. It is a variant of the LSODPK [http://identifiers.org/biomodels.kisao/KISAO_0000093] and LSODE [http://identifiers.org/biomodels.kisao/KISAO_0000071] solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE [http://identifiers.org/biomodels.kisao/KISAO_0000071] are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fixpoint) iteration and modified Newton iteration, c) LSODKR includes the ability to find roots of given functions of the solution during the integration.

Axiom
annotated source: LSODKR
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-0444866073
comment: A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.

Axiom
annotated source: LSODKR
annotated property: altLabel
annotated target: Livermore solver for ordinary differential equations, with preconditioned Krylov iteration methods for the Newton correction linear systems, and with root finding.
comment: EXACT

type of solution
type: Class
subclass of: modelling and simulation algorithm characteristic
creator: AZ
is organizational: true
definition: A characteristic describing the type of the solution produced by the method, specifically whether it is exact or approximate.

exact solution
type: Class
subclass of: type of solution
disjoint with: approximate solution
definition: Algorithm, possessing this characteristic, provides an exact solution to the initial problem.

approximate solution
type: Class
subclass of: type of solution
definition: Approximation algorithms are algorithms used to find approximate solutions to optimization problems. Approximation algorithms are often associated with NP-hard problems; since it is unlikely that there can ever be efficient polynomial time exact algorithms solving NP-hard problems, one settles for polynomial time sub-optimal solutions. Unlike heuristics, which usually only find reasonably good solutions reasonably fast, one wants provable solution quality and provable run time bounds. Ideally, the approximation is optimal up to a small constant factor (for instance within 5% of the optimal solution). Approximation algorithms are increasingly being used for problems where exact polynomial-time algorithms are known but are too expensive due to the input size.

type of method
type: Class
subclass of: modelling and simulation algorithm characteristic
creator: AZ
is organizational: true
definition: A characteristic describing the way the method finds a solution, specifically whether it solves an equation involving only the current state of the system (explicit) or both the current and the later one (implicit).

explicit method type
type: Class
subclass of: type of method
disjoint with: implicit method type
creator: AZ
definition: Explicit methods calculate the state of a system at a later time from the state of the system at the current time. Mathematically, if Y(t) is the current system state and Y((t+delta t) is the state at the later time (delta t is a small time step), then, for an explicit method Y(t+delta t) = F(Y(t)), to find Y(t+delta t).

implicit method type
type: Class
subclass of: type of method
creator: AZ
definition: Implicit methods find a solution by solving an equation involving both the current state of the system and the later one. Mathematically, if Y(t) is the current system state and Y((t+delta t) is the state at the later time (delta t is a small time step), then, for an implicit method one solves an equation G(Y(t), Y(t+delta t))=0, to find Y(t+delta t).

Gillespie-like method
type: Class
subclass of: Monte Carlo method
subclass of: Restriction
  on property: has characteristic
  some values from: discrete variable
subclass of: Restriction
  on property: has characteristic
  some values from: progression with adaptive time step
is organizational: true
definition: Stochastic simulation algorithm using an approach alike the one described in Gillespie's papers of 1976 and 1977.

error control parameter
type: Class
subclass of: modelling and simulation algorithm parameter
creator: AZ
is organizational: true
definition: Parameter controlling method accuracy.

method switching control parameter
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: is parameter of
  all values from: Restriction
    on property: uses
    some values from: modelling and simulation algorithm
creator: AZ
is organizational: true
definition: Parameters describing threshold conditions for algorithms that switch between different methods.

granularity control parameter
type: Class
subclass of: modelling and simulation algorithm parameter
creator: AZ
is organizational: true
definition: Parameter controlling granularity.

tau-leaping delta
type: Class
subclass of: partitioning control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: implicit tau-leaping method
subclass of: Restriction
  on property: has type
  some values from: double
definition: Tau-leaping delta specifies how close two symmetric transition rates must be before we classify them as in partial-equilibrium. Only applies to the implicit tau routine [http://identifiers.org/biomodels.kisao/KISAO_0000045].

critical firing threshold
type: Class
subclass of: partitioning control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: nonnegative Poisson tau-leaping method
subclass of: Restriction
  on property: has type
  some values from: integer
alternative label: nonnegative tau-leaping second control parameter
definition: The 'nonnegative Poisson tau-leaping method' [http://identifiers.org/biomodels.kisao/KISAO_0000084] is based on the fact that negative populations typically arise from multiple firings of reactions that are only a few firings away from consuming all the molecules of one of their reactants. To focus on those reaction channels, the modified tau-leaping algorithm introduces a second control parameter nc, a positive integer that is usually set somewhere between 5 and 20. Any reaction channel with a positive propensity function that is currently within nc firings of exhausting one of its reactants is then classified as a critical reaction. The modified algorithm chooses tau in such a way that no more than one firing of all the critical reactions can occur during the leap.

Axiom
annotated source: critical firing threshold
annotated property: altLabel
annotated target: nonnegative tau-leaping second control parameter
comment: EXACT

partitioning control parameter
type: Class
subclass of: modelling and simulation algorithm parameter
creator: Parameter describing partitioning of the system.
is organizational: true

coarse-graining factor
type: Class
subclass of: granularity control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: binomial tau-leaping method
subclass of: Restriction
  on property: has type
  some values from: double
definition: The time in each Monte-Carlo iteration of 'binomial tau-leaping method' [http://identifiers.org/biomodels.kisao/KISAO_0000074] is updated with the time increments tau=f/(a1+a2+...+aM). Here 1/(a1+a2+...+aM) is the averaged microscopic increment of the SSA [http://identifiers.org/biomodels.kisao/KISAO_0000029] and f is a coarse-graining factor, controlling the speed-up.

Axiom
annotated source: coarse-graining factor
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/15638577
comment: Chatterjee A, Vlachos DG, Katsoulakis MA. Binomial distribution based tau-leap accelerated stochastic simulation. J Chem Phys. 2005;122(2):024112.

Brownian diffusion accuracy
type: Class
subclass of: error control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: Brownian diffusion Smoluchowski method
subclass of: Restriction
  on property: has type
  some values from: integer
is implemented in: Smoldyn
definition: Accuracy code of 'Brownian diffusion Smoluchowski method' [http://identifiers.org/biomodels.kisao/KISAO_0000057], which sets which neighbouring boxes are checked for potential bi-molecular reactions. Consider the reaction A + B -> C and suppose that A and B are within a binding radius of each other. This reaction will always be performed if A and B are in the same virtual box. If accuracy is set to at least 3, then it will also occur if A and B are in nearest-neighbour virtual boxes. If it is at least 7, then the reaction will happen if they are in nearest-neighbour boxes that are separated by periodic boundary conditions. And if it is 9 or 10, then all edge and corner boxes are checked for reactions, which means that no potential reactions are overlooked.

molecules per virtual box
type: Class
subclass of: virtual box size
subclass of: Restriction
  on property: has type
  some values from: integer
disjoint with: virtual box side length
is implemented in: Smoldyn
definition: Target molecules per virtual box is a parameter of 'Brownian diffusion Smoluchowski method' [http://identifiers.org/biomodels.kisao/KISAO_0000057], which sets the box sizes so that the average number of molecules per box, at simulation initiation, is close to the requested number.

virtual box side length
type: Class
subclass of: virtual box size
subclass of: Restriction
  on property: has type
  some values from: double
is implemented in: Smoldyn
definition: The 'virtual box side length' is a parameter of 'Brownian diffusion Smoluchowski method' [http://identifiers.org/biomodels.kisao/KISAO_0000057]. It requests the length of one side of a box.

surface-bound epsilon
type: Class
subclass of: partitioning control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: Brownian diffusion Smoluchowski method
subclass of: Restriction
  on property: has type
  some values from: double
definition: A parameter of 'Brownian diffusion Smoluchowski method' [http://identifiers.org/biomodels.kisao/KISAO_0000057]. Molecules that are bound to a surface are given locations that are extremely close to that surface. However, this position does not need to be exactly at the surface, and in fact it usually cannot be exactly at the surface due to round-off error. The tolerance for how far a surface-bound molecule is allowed to be away from the surface can be set with the epsilon statement.

neighbour distance
type: Class
subclass of: partitioning control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: Brownian diffusion Smoluchowski method
subclass of: Restriction
  on property: has type
  some values from: double
definition: A parameter of 'Brownian diffusion Smoluchowski method' [http://identifiers.org/biomodels.kisao/KISAO_0000057]. When a surface-bound molecule diffuses off of one surface panel, it can sometimes diffuse onto the neighbouring surface tile. It does so only if the neighbouring panel is declared to be a neighbour and also the neighbour is within a distance that is set with the neighbour distance statement.

virtual box size
type: Class
subclass of: partitioning control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: Brownian diffusion Smoluchowski method
definition: Target size of virtual boxes for 'Brownian diffusion Smoluchowski method' [http://identifiers.org/biomodels.kisao/KISAO_0000057].

Euler method
type: Class
subclass of: one-step method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has characteristic
  some values from: linearity of equation
subclass of: Restriction
  on property: is similar to
  some values from: Class
    intersection of: Runge-Kutta based method
    intersection of: Restriction
      on property: has Runge-Kutta method order
      has value: 1
creator: AZ
is implemented in: ByoDyn
is implemented in: http://identifiers.org/biosimulators/jsim
definition: The Euler method, named after Leonhard Euler, is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.

Axiom
annotated source: Euler method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/jsim
comment: JSim @end

Axiom
annotated source: Euler method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/052143064X
comment: Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes in Fortran 77. Cambridge University Press (2001).

NFSim agent-based simulation method
type: Class
subclass of: multi-state agent-based simulation method
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
subclass of: Restriction
  on property: is generalization of
  some values from: Gillespie direct algorithm
disjoint with: implicit-state Doob-Gillespie algorithm
created: 2011-04-07
creator: AZ
is implemented in: http://identifiers.org/biosimulators/bionetgen
definition: A generalization a rule-based version of 'Gillespie's direct method' (SSA) [http://identifiers.org/biomodels.kisao/KISAO_0000029]. The method is guaranteed to produce the same results as the exact SSA [http://identifiers.org/biomodels.kisao/KISAO_0000029] by cycling over three primary steps. First, NFsim calculates the probability or propensity for each rule to take effect given the current molecular states. Second, it samples the time to the next reaction event and selects the corresponding reaction rule. Finally, NFsim executes the selected reaction by applying the rule and updating the molecular agents accordingly.

Axiom
annotated source: NFSim agent-based simulation method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/bionetgen
comment: NFSim @end

Axiom
annotated source: NFSim agent-based simulation method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1038/nmeth.1546
comment: Sneddon MW, Faeder JR and Emonet T. Efficient modelling, simulation and coarse-graining of biological complexity with NFsim. Nature Methods (2011) 8(2):177-83.

cellular automata update method
type: Class
subclass of: rule-based simulation method
subclass of: Restriction
  on property: has characteristic
  some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
created: 2011-04-07
creator: AZ
alternative label: CA
alternative label: cellular automata
alternative label: cellular spaces
alternative label: cellular structures
alternative label: homogeneous structures
alternative label: iterative arrays
alternative label: tessellation automata
alternative label: tessellation structures
definition: Cellular automata are mathematical idealizations of physical systems in which space and time are discrete, and physical quantities take on a finite set of discrete values. A cellular automaton consists of a regular uniform lattice (or ''array''), usually infinite in extent, with a discrete variable at each site (''cell''). A cellular automaton evolves in discrete time steps, with the value of the variable at one site being affected by the values of variables at sites in its ''neighbourhood'' on the previous time step. The neighbourhood of a site is typically taken to be the site itself and all immediately adjacent sites. The variables at each site are updated simultaneously (''synchronously''), based on the values of the variables in their neighbourhood at the preceding time step, and according to a definite set of ''local rules''.

Axiom
annotated source: cellular automata update method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1103/RevModPhys.55.601
comment: Wolfram, Stephen (1983) Statistical mechanics of cellular automata. Reviews of Modern Physics 55 (3): 601-644.

Axiom
annotated source: cellular automata update method
annotated property: altLabel
annotated target: CA
comment: EXACT

Axiom
annotated source: cellular automata update method
annotated property: altLabel
annotated target: cellular automata
comment: EXACT

Axiom
annotated source: cellular automata update method
annotated property: altLabel
annotated target: cellular spaces
comment: EXACT

Axiom
annotated source: cellular automata update method
annotated property: altLabel
annotated target: cellular structures
comment: EXACT

Axiom
annotated source: cellular automata update method
annotated property: altLabel
annotated target: homogeneous structures
comment: EXACT

Axiom
annotated source: cellular automata update method
annotated property: altLabel
annotated target: iterative arrays
comment: EXACT

Axiom
annotated source: cellular automata update method
annotated property: altLabel
annotated target: tessellation automata
comment: EXACT

Axiom
annotated source: cellular automata update method
annotated property: altLabel
annotated target: tessellation structures
comment: EXACT

hard-particle molecular dynamics
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: progression with adaptive time step
created: 2011-05-05
creator: AZ
definition: A collision-driven molecular dynamics algorithm for a system of non-spherical particles.

Axiom
annotated source: hard-particle molecular dynamics
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/j.jcp.2004.08.014
comment: Aleksandar Donev, Salvatore Torquato, Frank H. Stillinger, Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles. I. Algorithmic details, Journal of Computational Physics, v.202 n.2, p.737-764, 20 January 2005

first-passage Monte Carlo algorithm
type: Class
subclass of: Monte Carlo method
subclass of: Restriction
  on property: has characteristic
  some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: progression with adaptive time step
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
created: 2011-05-05
creator: AZ
alternative label: AED DKMC
alternative label: AED diffusion kinetic Monte Carlo method
alternative label: asynchronous event-driven diffusion Monte Carlo
definition: We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green's functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions.

Axiom
annotated source: first-passage Monte Carlo algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1103/PhysRevLett.97.230602
comment: T. Oppelstrup, V. V. Bulatov, G. H. Gilmer, M. H. Kalos, and B. Sadigh. First-passage Monte- Carlo algorithm: Diffusion without all the hops. Physical Review Letters, 97(23):230602, 2006.

Axiom
annotated source: first-passage Monte Carlo algorithm
annotated property: altLabel
annotated target: AED DKMC
comment: EXACT

Axiom
annotated source: first-passage Monte Carlo algorithm
annotated property: altLabel
annotated target: AED diffusion kinetic Monte Carlo method
comment: EXACT

Axiom
annotated source: first-passage Monte Carlo algorithm
annotated property: altLabel
annotated target: asynchronous event-driven diffusion Monte Carlo
comment: EXACT

Gill method
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has Runge-Kutta method order
  has value: 4
created: 2011-05-09
creator: AZ
alternative label: Gill's method
alternative label: Runge-Kutta-Gill method
definition: Gill's fourth order method is a Runge-Kutta method for approximating the solution of the initial value problem y'(x) = f(x,y); y(x0) = y0 which evaluates the integrand,f(x,y), four times per step. This method is a fourth order procedure for which Richardson extrapolation can be used.

Axiom
annotated source: Gill method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1017/S0305004100026414
comment: Gill, S. 1951. A process for the step-by-step integration of differential equations in an automatic digital computing machine. Proc. Cambridge Philos. Soc., 47, pp 96-108.

Axiom
annotated source: Gill method
annotated property: altLabel
annotated target: Gill's method
comment: EXACT

Axiom
annotated source: Gill method
annotated property: altLabel
annotated target: Runge-Kutta-Gill method
comment: EXACT

Metropolis Monte Carlo algorithm
type: Class
subclass of: Monte Carlo method
subclass of: Restriction
  on property: has characteristic
  some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
created: 2011-05-09
creator: AZ
is implemented in: CompuCell3D
alternative label: Metropolis algorithm
alternative label: Metropolis-Hastings algorithm
definition: A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration [http://identifiers.org/biomodels.kisao/KISAO_0000051] over configuration space.

Axiom
annotated source: Metropolis Monte Carlo algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.1699114
comment: Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, M.N.; Teller, A.H.; Teller, E. (1953). Equations of State Calculations by Fast Computing Machines. Journal of Chemical Physics 21 (6): 1087-1092.

Axiom
annotated source: Metropolis Monte Carlo algorithm
annotated property: altLabel
annotated target: Metropolis algorithm
comment: EXACT

Axiom
annotated source: Metropolis Monte Carlo algorithm
annotated property: altLabel
annotated target: Metropolis-Hastings algorithm
comment: EXACT

Adams-Bashforth method
type: Class
subclass of: Adams method
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
created: 2011-05-09
creator: AZ
alternative label: explicit Adams method
definition: Given an initial value problem: y' = f(x,y), y(x0) = y0 together with additional starting values y1 = y(x0 + h), . . . , yk-1 = y(x0 + (k-1) h) the k-step Adams-Bashforth method is an explicit linear multistep method that approximates the solution, y(x) at x = x0+kh, of the initial value problem by yk = yk - 1 + h * ( a0 f(xk - 1,yk - 1) + a1 f(xk - 2,yk - 2) + . . . + ak - 1 f(x0,y0) ), where a0, a1, . . . , ak - 1 are constants.

Axiom
annotated source: Adams-Bashforth method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-3-540-56670-0
comment: Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag

Axiom
annotated source: Adams-Bashforth method
annotated property: altLabel
annotated target: explicit Adams method
comment: EXACT

Adams-Moulton method
type: Class
subclass of: Adams method
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
created: 2011-05-09
creator: AZ
is implemented in: http://identifiers.org/biosimulators/vcell
alternative label: implicit Adams method
definition: The (k-1)-step Adams-Moulton method is an implicit linear multistep method that iteratively approximates the solution, y(x) at x = x0+kh, of the initial value problem by yk = yk - 1 + h * ( b0 f(xk,yk) + b1 f(xk - 1,yk - 1) + . . . + bk - 1 f(x1,y1) ), where b1, . . . , bk - 1 are constants.

Axiom
annotated source: Adams-Moulton method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell @end

Axiom
annotated source: Adams-Moulton method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-3-540-56670-0
comment: Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag

Axiom
annotated source: Adams-Moulton method
annotated property: altLabel
annotated target: implicit Adams method
comment: EXACT

multistep method
type: Class
subclass of: modelling and simulation algorithm
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
created: 2011-05-09
creator: AZ
is organizational: true
alternative label: multi-value method
definition: A numerical method for differential equations which is based on several values of the solution.

Axiom
annotated source: multistep method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-3-540-56670-0
comment: Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag

Axiom
annotated source: multistep method
annotated property: altLabel
annotated target: multi-value method
comment: EXACT

KINSOL
type: Class
subclass of: Newton-type method
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: linearity of equation
subclass of: Restriction
  on property: uses
  some values from: Krylov subspace projection method
created: 2011-05-09
creator: AZ
is implemented in: SUNDIALS
alternative label: FKINSOL
alternative label: NKSOL
alternative label: Newton-Krylov solver for nonlinear algebraic systems
definition: KINSOL solves algebraic systems in real N-space, written as F(u)=0, F:RN->RN, given an initial guess u0. The basic method is either a modified or an inexact Newton iteration [http://identifiers.org/biomodels.kisao/KISAO_0000408]. The linear systems that arise are solved with either a direct (dense or banded) solver (serial version only), or one of the Krylov iterative solvers [http://identifiers.org/biomodels.kisao/KISAO_0000354]. In the Krylov case, the user can (optionally) supply a right preconditioner.

Axiom
annotated source: KINSOL
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0911026
comment: BROWN, P. N. AND SAAD, Y. 1990. Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Stat. Comput. 11, 450-481.

Axiom
annotated source: KINSOL
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/1089014.1089020
comment: Hindmarsh, A. C., et al., SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Trans. Math. Softw., 31:363-396, 2005.

Axiom
annotated source: KINSOL
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.4249/scholarpedia.2860
comment: Alan C. Hindmarsh and Radu Serban (2007) Sundails equation solvers, Scholarpedia, 2(3):2860.

Axiom
annotated source: KINSOL
annotated property: altLabel
annotated target: FKINSOL
comment: RELATED

Axiom
annotated source: KINSOL
annotated property: altLabel
annotated target: NKSOL
comment: RELATED

Axiom
annotated source: KINSOL
annotated property: altLabel
annotated target: Newton-Krylov solver for nonlinear algebraic systems
comment: RELATED

IDA
type: Class
subclass of: IDA-like method
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: linearity of equation
subclass of: Restriction
  on property: has characteristic
  some values from: differential-algebraic equation problem
subclass of: Restriction
  on property: is similar to
  some values from: DASPK
subclass of: Restriction
  on property: uses
  some values from: backward differentiation formula
subclass of: Restriction
  on property: uses
  some values from: Krylov subspace projection method
subclass of: Restriction
  on property: uses
  some values from: scaled preconditioned generalized minimal residual method
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: linear solver
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: upper half-bandwidth
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: lower half-bandwidth
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: interpolate solution
created: 2011-05-09
creator: AZ
is implemented in: SUNDIALS
is implemented in: http://identifiers.org/biosimulators/opencor
is implemented in: http://identifiers.org/biosimulators/vcell
alternative label: implicit differential-algebraic solver
alternative label: solver for differential-algebraic equation systems
definition: IDA solves real differential-algebraic systems in N-space, in the general form F(t,y,y')=0, y(t0)=y0, y'(t0)=y'0. At each step, a Newton iteration [http://identifiers.org/biomodels.kisao/KISAO_0000408] leads to linear systems Jx=b, which are solved by one of five methods - two direct (dense or band; serial version only) and three Krylov [http://identifiers.org/biomodels.kisao/KISAO_0000354] (GMRES [http://identifiers.org/biomodels.kisao/KISAO_0000353], BiCGStab [http://identifiers.org/biomodels.kisao/KISAO_0000392], or TFQMR [http://identifiers.org/biomodels.kisao/KISAO_0000396]). IDA is written in C, but derived from the package DASPK [http://identifiers.org/biomodels.kisao/KISAO_0000355] which is written in Fortran.

Axiom
annotated source: IDA
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/opencor
comment: OpenCOR @end

Axiom
annotated source: IDA
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell @end

Axiom
annotated source: IDA
annotated property: label
annotated target: IDA
comment: Alan C. Hindmarsh and Radu Serban (2007) Sundails equation solvers, Scholarpedia, 2(3):2860.

Axiom
annotated source: IDA
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0915088
comment: BROWN, P. N., HINDMARSH, A. C., AND PETZOLD, L. R. 1994. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15, 1467-1488.

Axiom
annotated source: IDA
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/1089014.1089020
comment: Hindmarsh, A. C., et al., SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Trans. Math. Softw., 31:363-396, 2005.

Axiom
annotated source: IDA
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.4249/scholarpedia.2860
comment: Alan C. Hindmarsh and Radu Serban (2007) Sundails equation solvers, Scholarpedia, 2(3):2860.

Axiom
annotated source: IDA
annotated property: altLabel
annotated target: implicit differential-algebraic solver
comment: EXACT

Axiom
annotated source: IDA
annotated property: altLabel
annotated target: solver for differential-algebraic equation systems
comment: RELATED

finite volume method
type: Class
subclass of: partial differential equation discretization method
subclass of: Restriction
  on property: has characteristic
  some values from: mesh-based geometry handling
created: 2011-05-09
creator: AZ
is implemented in: http://identifiers.org/biosimulators/vcell
alternative label: FVM
definition: The finite volume method is a method for representing and evaluating partial differential equations in the form of algebraic equations, which attempts to emulate continuous conservation laws of physics.

Axiom
annotated source: finite volume method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell @end

Axiom
annotated source: finite volume method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0898715342
comment: Y. Saad. 2003. Iterative Methods for Sparse Linear Systems (2nd ed.). Soc. for Industrial and Applied Math., Philadelphia, PA, USA.

Axiom
annotated source: finite volume method
annotated property: altLabel
annotated target: FVM
comment: EXACT

Euler-Maruyama method
type: Class
subclass of: SDE solver
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: has parameter
  some values from: step size
subclass of: Restriction
  on property: is generalization of
  some values from: Euler method
created: 2011-05-09
creator: AZ
alternative label: stochastic Euler scheme
definition: The Euler-Maruyama method is a method for the approximate numerical solution of a stochastic differential equation, which truncates the Ito and Stratonovich Taylor series of the exact solution after the first order stochastic terms. This converges to the Ito solution with strong global order accuracy 1/2 or weak global order accuracy 1. It is a simple generalization of the Euler method [http://identifiers.org/biomodels.kisao/KISAO_0000261] for ordinary differential equations to stochastic differential equations.

Axiom
annotated source: Euler-Maruyama method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1098/rspa.2003.1247
comment: Burrage, K., Burrage, P.M. and Tian, T. (2004) Numerical methods for strong solutions of stochastic differential equations: an overview. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 460 (2041). pp. 373-402.

Axiom
annotated source: Euler-Maruyama method
annotated property: altLabel
annotated target: stochastic Euler scheme
comment: EXACT

Milstein method
type: Class
subclass of: SDE solver
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
created: 2011-05-10
creator: AZ
definition: The Milstein method is a technique for the approximate numerical solution of a stochastic differential equation.

Axiom
annotated source: Milstein method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/079233213X
comment: Milstein M. G. Numerical Integration of Stochastic Differential Equations (Mathematics and Its Applications) Springer, 2004.

backward differentiation formula
type: Class
subclass of: multistep method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has characteristic
  some values from: linearity of equation
disjoint with: Adams method
created: 2011-05-10
creator: AZ
is implemented in: ByoDyn
is implemented in: GSL
is implemented in: http://identifiers.org/biosimulators/ibiosim
alternative label: BDF
alternative label: Gear method
alternative label: Gear's method
definition: The backward differentiation formulas (BDF) are implicit multistep methods based on the numerical differentiation of a given function and are wildly used for integration of stiff differential equations.

Axiom
annotated source: backward differentiation formula
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim @end

Axiom
annotated source: backward differentiation formula
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0136266061
comment: C. William Gear. 1971. Numerical Initial Value Problems in Ordinary Differential Equations. Prentice Hall PTR, Upper Saddle River, NJ, USA.

Axiom
annotated source: backward differentiation formula
annotated property: altLabel
annotated target: BDF
comment: EXACT

Axiom
annotated source: backward differentiation formula
annotated property: altLabel
annotated target: Gear method
comment: EXACT

Axiom
annotated source: backward differentiation formula
annotated property: altLabel
annotated target: Gear's method
comment: EXACT

Adams method
type: Class
subclass of: multistep method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has characteristic
  some values from: linearity of equation
created: 2011-05-10
creator: AZ
is implemented in: ByoDyn
definition: Adams' methods are multi-step methods used for the numerical integration of initial value problems in Ordinary Differential Equations (ODE's). Adams' algorithm consists of two parts: firstly, a starting procedure which provides y1, ... , yk-1 ( approximations to the exact solution at the points x0 + h, ... , x0 + (k - 1)h ) and, secondly, a multistep formula to obtain an approximation to the exact solution y(x0 + kh). This is then applied recursively, based on the numerical approximation of k successive steps, to compute y(x0 + (k + 1)h).

Axiom
annotated source: Adams method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-3-540-56670-0
comment: Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag

Merson method
type: Class
subclass of: embedded Runge-Kutta method
subclass of: Restriction
  on property: has Runge-Kutta method order
  has value: 4
created: 2011-05-10
creator: AZ
is implemented in: http://identifiers.org/biosimulators/jsim
alternative label: KM
alternative label: Kutta-Merson method
alternative label: Merson's method
alternative label: Runge-Kutta-Merson method
definition: A five-stage Runge-Kutta method with fourth-order accuracy.

Axiom
annotated source: Merson method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/jsim
comment: JSim @end

Axiom
annotated source: Merson method
annotated property: seeAlso
annotated target: http://nla.gov.au/nla.cat-vn870866
comment: R.H. Merson, An operational method for the study of integration processes, in: Proceedings of the Symposium on Data Processing, Weapons Research Establishment, Salisbury, Australia, 1957, pp. 110-1-110-25.

Axiom
annotated source: Merson method
annotated property: altLabel
annotated target: KM
comment: EXACT

Axiom
annotated source: Merson method
annotated property: altLabel
annotated target: Kutta-Merson method
comment: EXACT

Axiom
annotated source: Merson method
annotated property: altLabel
annotated target: Merson's method
comment: EXACT

Axiom
annotated source: Merson method
annotated property: altLabel
annotated target: Runge-Kutta-Merson method
comment: EXACT

Hammer-Hollingsworth method
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2011-05-10
creator: AZ
definition: The numerical integration of ordinary differential equations by the use of Gaussian quadrature methods.

Axiom
annotated source: Hammer-Hollingsworth method
annotated property: seeAlso
annotated target: urn:issn:0891-6837
comment: P. C. Hammer & J. W. Hollingsworth, Trapezoidal methods of approximating solutions of differential equations, MTAC, v. 9, 1955, pp. 92-96. MR 17, 302.

Lobatto method
type: Class
subclass of: Runge-Kutta based method
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: symplecticness
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2011-05-10
creator: AZ
alternative label: implicit Runge-Kutta method based on Lobatto quadrature
definition: There are three families of Lobatto methods, called IIIA, IIIB and IIIC. These are named after Rehuel Lobatto. All are implicit Runge-Kutta methods, have order 2s − 2 and they all have c1 = 0 and cs = 1.

Axiom
annotated source: Lobatto method
annotated property: seeAlso
annotated target: urn:issn:1088-6842(e)
comment: J. C. Butcher, Integration processes based on Radau quadrature formulas, Math. Comp., v. 18, 1964, pp. 233-244.

Axiom
annotated source: Lobatto method
annotated property: altLabel
annotated target: implicit Runge-Kutta method based on Lobatto quadrature
comment: EXACT

Butcher-Kuntzmann method
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: symplecticness
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2011-05-10
creator: AZ
alternative label: Gauss method
definition: From a theoretical point of view, the Butcher-Kuntzmann Runge-Kutta methods belong to the best step-by-step methods for nonstiff problems. These methods integrate first-order initial-value problems by means of formulas based on Gauss-Legendre quadrature, and combine excellent stability features with the property of superconvergence at the step points.

Axiom
annotated source: Butcher-Kuntzmann method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1002/zamm.19660460519
comment: F. Ceschin, J. Kuntzmann, Problèmes différentiels de conditions initiales. Paris 1963. Dunod. @fr

Axiom
annotated source: Butcher-Kuntzmann method
annotated property: seeAlso
annotated target: urn:issn:1088-6842(e)
comment: Butcher, J. C. (1964) Implicit Runge-Kutta processes. Math. Comput. 18, 50-64.

Axiom
annotated source: Butcher-Kuntzmann method
annotated property: altLabel
annotated target: Gauss method
comment: EXACT

Heun method
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has Runge-Kutta method order
  has value: 2
created: 2011-05-10
creator: AZ
alternative label: Heun's method
definition: The method is named after Karl L. W. M. Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It can be seen as extension of the Euler method [http://identifiers.org/biomodels.kisao/KISAO_0000261] into two-stage second-order Runge-Kutta method.

Axiom
annotated source: Heun method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-3-540-56670-0
comment: Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag

Axiom
annotated source: Heun method
annotated property: altLabel
annotated target: Heun's method
comment: EXACT

embedded Runge-Kutta method
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with adaptive time step
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2011-05-10
creator: AZ
is organizational: true
alternative label: embedded RK
definition: An embedded Runge-Kutta method is a method in which two Runge-Kutta estimates are obtained using the same auxiliary functions ki but with a different linear combination of these functions so that one estimate has an order one greater than the other.

Axiom
annotated source: embedded Runge-Kutta method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-3-540-56670-0
comment: Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag

Axiom
annotated source: embedded Runge-Kutta method
annotated property: altLabel
annotated target: embedded RK
comment: EXACT

Zonneveld method
type: Class
subclass of: embedded Runge-Kutta method
subclass of: Restriction
  on property: uses
  some values from: Class
    intersection of: Runge-Kutta based method
    intersection of: Restriction
      on property: has Runge-Kutta method order
      has value: 3
subclass of: Restriction
  on property: uses
  some values from: Class
    intersection of: Runge-Kutta based method
    intersection of: Restriction
      on property: has Runge-Kutta method order
      has value: 4
created: 2011-05-10
creator: AZ
definition: An embedded Runge-Kutta method [http://identifiers.org/biomodels.kisao/KISAO_0000302] of order 4(3), proposed by J.A. Zonneveld in 1964.

Axiom
annotated source: Zonneveld method
annotated property: seeAlso
annotated target: http://trove.nla.gov.au/work/21424455
comment: Zonneveld, J. A (1970). Automatic numerical integration Mathematisch Centrum, Amsterdam

Radau method
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has parameter
  some values from: maximum order
subclass of: Restriction
  on property: has parameter
  some values from: minimum order
subclass of: Restriction
  on property: has parameter
  some values from: initial order
created: 2011-05-11
creator: AZ
is implemented in: http://identifiers.org/biosimulators/jsim
alternative label: implicit Runge-Kutta method based on Radau quadrature
definition: Implicit Runge-Kutta methods based on Radau quadrature.

Axiom
annotated source: Radau method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/jsim
comment: JSim @end

Axiom
annotated source: Radau method
annotated property: seeAlso
annotated target: urn:issn:1088-6842(e)
comment: J. C. Butcher, Integration processes based on Radau quadrature formulas, Math. Comput., 18(1964), 233-244.

Axiom
annotated source: Radau method
annotated property: altLabel
annotated target: implicit Runge-Kutta method based on Radau quadrature
comment: EXACT

Verner method
type: Class
subclass of: embedded Runge-Kutta method
subclass of: Restriction
  on property: uses
  some values from: Class
    intersection of: Runge-Kutta based method
    intersection of: Restriction
      on property: has Runge-Kutta method order
      has value: 5
subclass of: Restriction
  on property: uses
  some values from: Class
    intersection of: Runge-Kutta based method
    intersection of: Restriction
      on property: has Runge-Kutta method order
      has value: 6
created: 2011-05-10
creator: AZ
alternative label: Verner's method
definition: The first high order (6(5)) embedded Runge-Kutta formulas that avoid the drawback of giving identically zero error estimates for quadrature problems y' = f(x) were constructed by Verner in 1978.

Axiom
annotated source: Verner method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0728027
comment: J.H. Verner, Some Runge-Kutta formula pairs, SIAM J. Numer. Anal 28 (1991) 496-511

Axiom
annotated source: Verner method
annotated property: altLabel
annotated target: Verner's method
comment: EXACT

Lagrangian sliding fluid element algorithm
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has characteristic
  some values from: partial differential equation problem
created: 2011-05-11
creator: AZ
is implemented in: http://identifiers.org/biosimulators/jsim
alternative label: BTEX
alternative label: LSFEA
alternative label: blood-tissue exchange method
definition: Because the analytic solutions to the partial differential equations require convolution integration, solutions are obtained relatively efficiently by a fast numerical method. Our approach centers on the use of a sliding fluid element algorithm for capillary convection, with the time step set equal to the length step divided by the fluid velocity. Radial fluxes by permeation between plasma, interstitial fluid, and cells and axial diffusion exchanges within each time step are calculated analytically. The method enforces mass conservation unless there is regional consumption.

Axiom
annotated source: Lagrangian sliding fluid element algorithm
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/jsim
comment: JSim @end

Axiom
annotated source: Lagrangian sliding fluid element algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/1449234
comment: Bassingthwaighte JB, Chan IS, and Wang CY. Computationally efficient algorithms for capillary convection-permeation-diffusion models for blood-tissue exchange. Ann Biomed Eng 20: 687-725, 1992.

Axiom
annotated source: Lagrangian sliding fluid element algorithm
annotated property: altLabel
annotated target: BTEX
comment: EXACT

Axiom
annotated source: Lagrangian sliding fluid element algorithm
annotated property: altLabel
annotated target: LSFEA
comment: EXACT

Axiom
annotated source: Lagrangian sliding fluid element algorithm
annotated property: altLabel
annotated target: blood-tissue exchange method
comment: EXACT

finite difference method
type: Class
subclass of: partial differential equation discretization method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has characteristic
  some values from: mesh-based geometry handling
created: 2011-05-11
creator: AZ
alternative label: FDM
definition: The finite difference method is based on local approximations of the partial derivatives in a Partial Differential Equation, which are derived by low order Taylor series expansions.

Axiom
annotated source: finite difference method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0898715342
comment: Y. Saad. 2003. Iterative Methods for Sparse Linear Systems (2nd ed.). Soc. for Industrial and Applied Math., Philadelphia, PA, USA.

Axiom
annotated source: finite difference method
annotated property: altLabel
annotated target: FDM
comment: EXACT

MacCormack method
type: Class
subclass of: finite difference method
disjoint with: Crank-Nicolson method
created: 2011-05-11
creator: AZ
is implemented in: http://identifiers.org/biosimulators/jsim
definition: In computational fluid dynamics, the MacCormack method is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method [http://identifiers.org/biomodels.kisao/KISAO_0000307] is introduced by R. W. MacCormack in 1969.

Axiom
annotated source: MacCormack method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/jsim
comment: JSim @end

Axiom
annotated source: MacCormack method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.2514/2.6901
comment: MacCormack, R. W., The Effect of viscosity in hypervelocity impact cratering, AIAA Paper, 69-354 (1969).

Crank-Nicolson method
type: Class
subclass of: finite difference method
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
created: 2011-05-11
creator: AZ
definition: In numerical analysis, the Crank-Nicolson method is a finite difference method [http://identifiers.org/biomodels.kisao/KISAO_0000307] used for numerically solving the heat equation and similar partial differential equations. It is a second-order method in time, implicit in time, and is numerically stable. The method was developed by John Crank and Phyllis Nicolson in the mid 20th century.

Axiom
annotated source: Crank-Nicolson method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/BF02127704
comment: Crank, J.; Nicolson, P. (1947). A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type. Proc. Camb. Phil. Soc. 43 (1): 50-67.

method of lines
type: Class
subclass of: partial differential equation discretization method
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: progression with adaptive time step
subclass of: Restriction
  on property: has characteristic
  some values from: mesh-based geometry handling
created: 2011-05-11
creator: AZ
alternative label: MOL
alternative label: NMOL
alternative label: NUMOL
definition: The method of lines is a general technique for solving partial differential equations (PDEs) by typically using finite difference relationships for the spatial derivatives and ordinary differential equations for the time derivative.

Axiom
annotated source: method of lines
annotated property: label
annotated target: method of lines
comment: EXACT

Axiom
annotated source: method of lines
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0126241309
comment: Schiesser, W. E. (1991). The Numerical Method of Lines. Academic Press.

Axiom
annotated source: method of lines
annotated property: altLabel
annotated target: MOL
comment: EXACT

Axiom
annotated source: method of lines
annotated property: altLabel
annotated target: NMOL
comment: EXACT

Axiom
annotated source: method of lines
annotated property: altLabel
annotated target: NUMOL
comment: EXACT

type of domain geometry handling
type: Class
subclass of: modelling and simulation algorithm characteristic
creator: AZ
is organizational: true

S-System power-law canonical differential equations solver
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with adaptive time step
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2011-05-20
creator: AZ
is implemented in: http://identifiers.org/biosimulators/ecell4
alternative label: ESSYNS GMA
definition: Ordinary differential equations can be recast into a nonlinear canonical form called an S-system. Evidence for the generality of this class comes from extensive empirical examples that have been recast and from the discovery that sets of differential equations and functions, recognized as among the most general, are special cases of S-systems. Identification of this nonlinear canonical form suggests a radically different approach to numerical solution of ordinary differential equations. By capitalizing on the regular structure of S-systems, efficient formulas for a variable-order, variable-step Taylor-series method are developed.

Axiom
annotated source: S-System power-law canonical differential equations solver
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ecell4
comment: E-Cell @end

Axiom
annotated source: S-System power-law canonical differential equations solver
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0727042
comment: Irvine, D.H. and Savageau, M.A., Efficient solution of nonlinear ordinary differential equations expressed in S-System canonical form, Siam. J. Numer. Anal., 27:704-735, 1990.

Axiom
annotated source: S-System power-law canonical differential equations solver
annotated property: altLabel
annotated target: ESSYNS GMA
comment: EXACT

lattice gas automata
type: Class
subclass of: deterministic cellular automata update algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
disjoint with: multiparticle lattice gas automata
created: 2011-05-23
creator: AZ
alternative label: LGA
alternative label: LGCA
alternative label: lattice gas cellular automata
definition: Lattice gas automata methods are a series of cellular automata methods used to simulate fluid flows. From the LGCA, it is possible to derive the macroscopic Navier-Stokes equations.

Axiom
annotated source: lattice gas automata
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/3-540-66973-6
comment: Dieter A. Wolf-Gladrow (2000). Lattice-Gas Cellular Automata and Lattice Boltzmann Models. Springer.

Axiom
annotated source: lattice gas automata
annotated property: altLabel
annotated target: LGA
comment: EXACT

Axiom
annotated source: lattice gas automata
annotated property: altLabel
annotated target: LGCA
comment: EXACT

Axiom
annotated source: lattice gas automata
annotated property: altLabel
annotated target: lattice gas cellular automata
comment: EXACT

enhanced Greens function reaction dynamics
type: Class
subclass of: Smoluchowski equation based method
subclass of: Restriction
  on property: has characteristic
  some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: discrete variable
subclass of: Restriction
  on property: has characteristic
  some values from: progression with adaptive time step
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
subclass of: Restriction
  on property: is similar to
  some values from: Greens function reaction dynamics
created: 2011-05-23
creator: AZ
alternative label: eGFRD
definition: GFRD [http://identifiers.org/biomodels.kisao/KISAO_0000058] decomposes the multi­body reaction diffusion problem to a set of single and two body problems. Analytical solutions for two body reaction diffusion are available via Smoluchowski equation. eGFRD allows to solve each sub­problem asynchronously by introducing the concept of first passage processes.

Axiom
annotated source: enhanced Greens function reaction dynamics
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/978-3-540-88562-7_3
comment: K. Takahashi, An exact Brownian dynamics method for cell simulation, in Computational Methods in Systems Biology, vol. 5307/2008.

Axiom
annotated source: enhanced Greens function reaction dynamics
annotated property: altLabel
annotated target: eGFRD
comment: EXACT

Axiom
annotated source: enhanced Greens function reaction dynamics
annotated property: altLabel
annotated target: enhanced Greens function reaction dynamics
comment: EXACT

E-Cell multi-algorithm simulation method
type: Class
subclass of: hybrid method
created: 2011-05-23
creator: AZ
is implemented in: http://identifiers.org/biosimulators/ecell4
definition: A modular meta-algorithm with a discrete event scheduler that can incorporate any type of time-driven simulation algorithm. It was shown that this meta-algorithm can efficiently drive simulation models with different simulation algorithms with little intrusive modification to the algorithms themselves. Only a few additional methods to handle communications between computational modules are required.

Axiom
annotated source: E-Cell multi-algorithm simulation method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ecell4
comment: E-Cell @end

Axiom
annotated source: E-Cell multi-algorithm simulation method
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/14990450
comment: Takahashi, K., Kaizu, K., Hu, B., and Tomita, M., A multi-algorithm, multi-timescale method for cell simulation. Bioinformatics, in press.

Gauss-Legendre Runge-Kutta method
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2011-05-26
creator: AZ
is implemented in: http://identifiers.org/biosimulators/ibiosim
alternative label: Open Formula
definition: So called 'Open Formula', two points formula, three points formula, four points formula, five points formula and six points formula of the Runge-Kutta method to solve the initial value problem of the ordinary differential equation. These formulas use the points and weights from the Gauss-Legendre Quadrature formulas for finding the value of the definite integral.

Axiom
annotated source: Gauss-Legendre Runge-Kutta method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim @end

Axiom
annotated source: Gauss-Legendre Runge-Kutta method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/960-8457-54-8
comment: Maitree Podisuk, Sirirat Khuntidilokwongsa, and Witchaya Rattanametawee. 2006. Gauss-Legendre Quadrature formula in Runge-Kutta method with modified model of Newton cooling law. In Proceedings of the 8th WSEAS international conference on Mathematical methods and computational techniques in electrical engineering (MMACTEE'06). World Scientific and Engineering Academy and Society (WSEAS), Stevens Point, Wisconsin, USA, 312-317.

Axiom
annotated source: Gauss-Legendre Runge-Kutta method
annotated property: altLabel
annotated target: Open Formula
comment: EXACT

Monte Carlo method
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: stochastic system behaviour
created: 2011-05-26
creator: AZ
is organizational: true
alternative label: MC
definition: Monte Carlo methods (or Monte Carlo experiments) are a class of computational algorithms that rely on repeated random sampling to compute their results.

Axiom
annotated source: Monte Carlo method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.2307/2280232
comment: Metropolis, N.; Ulam, S. (1949). "The Monte Carlo Method". Journal of the American Statistical Association (American Statistical Association) 44 (247): 335-341.

Axiom
annotated source: Monte Carlo method
annotated property: altLabel
annotated target: MC
comment: EXACT

BioRica hybrid method
type: Class
subclass of: hybrid method
subclass of: Restriction
  on property: has characteristic
  some values from: progression with adaptive time step
created: 2011-05-26
creator: AZ
is implemented in: BioRica
definition: The simulation schema for a given BioRica node is given by a hybrid algorithm that deals with continuous time and allows for discrete events that roll back the time according to these discrete interruptions.

Axiom
annotated source: BioRica hybrid method
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/19425152
comment: Cvijovic M, Soueidan H, Sherman DJ, Klipp E, Nikolski M. Exploratory simulation of cell ageing using hierarchical models. Genome Inform. 2008;21:114-25.

Cash-Karp method
type: Class
subclass of: embedded Runge-Kutta 5(4) method
created: 2011-05-26
creator: AZ
is implemented in: Cain
is implemented in: GSL
definition: An family of explicit Runge-Kutta formulas, which are very efficient for problems with smooth solution as well as problems having rapidly varying solutions. Each member of this family consists of a fifty-order formula that contains embedded formulas of all orders 1 through 4. By computing solutions at several different orders, it is possible to detect sharp fronts or discontinuities before all the function evaluations defining the full Runge-Kutta step have been computed.

Axiom
annotated source: Cash-Karp method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/79505.79507
comment: J. R. Cash, A. H. Karp. "A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides", ACM Transactions on Mathematical Software 16: 201-222, 1990.

hybridity
type: Class
subclass of: modelling and simulation algorithm characteristic
created: 2011-05-27
creator: AZ
definition: The basic idea of hybrid simulation methods is to combine the advantages of complementary simulation approaches: the whole system is subdivided into appropriate parts and different simulation methods operate on these parts at the same time.

equation-free probabilistic steady-state approximation
type: Class
subclass of: accelerated stochastic simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has parameter
  some values from: minimum fast/discrete reaction occurrences number
subclass of: Restriction
  on property: has parameter
  some values from: number of samples
subclass of: Restriction
  on property: has parameter
  some values from: maximum discrete number
subclass of: Restriction
  on property: has parameter
  some values from: minimum fast rate
created: 2011-06-02
creator: AZ
definition: We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. <...> The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.

Axiom
annotated source: equation-free probabilistic steady-state approximation
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.2131050
comment: Salis H, Kaznessis YN. An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks. J Chem Phys. 2005 Dec 1;123(21):214106.

nested stochastic simulation algorithm
type: Class
subclass of: accelerated stochastic simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: uses
  some values from: Gillespie direct algorithm
created: 2011-06-02
creator: AZ
alternative label: nested SSA
definition: This multiscale method is a small modification of the Gillespie's direct method [http://identifiers.org/biomodels.kisao/KISAO_0000029], in the form of a nested SSA, with inner loops for the fast reactions, and outer loop for the slow reactions. The number of groups can be more than two, and the grouping into fast and slow variables can be done dynamically in an adaptive version of the scheme.

Axiom
annotated source: nested stochastic simulation algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/16321076
comment: E W., Liu D. and Vanden-Eijnden E. Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates. J Chem Phys. 2005 Nov 15;123(19):194107.

Axiom
annotated source: nested stochastic simulation algorithm
annotated property: altLabel
annotated target: nested SSA
comment: EXACT

minimum fast/discrete reaction occurrences number
type: Class
subclass of: error control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: equation-free probabilistic steady-state approximation
subclass of: Restriction
  on property: has type
  some values from: integer
created: 2011-06-02
creator: AZ
definition: Parameter of 'equation-free probabilistic steady-state approximation' method [http://identifiers.org/biomodels.kisao/KISAO_0000323], which describes the minimum number of fast/discrete reaction occurrences before their effects cause convergence to a quasi-steady-state distribution.

Axiom
annotated source: minimum fast/discrete reaction occurrences number
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.2131050
comment: Salis H, Kaznessis YN. An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks. J Chem Phys. 2005 Dec 1;123(21):214106.

number of samples
type: Class
subclass of: error control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: equation-free probabilistic steady-state approximation
subclass of: Restriction
  on property: has type
  some values from: integer
created: 2011-06-02
creator: AZ
definition: Parameter of 'equation-free probabilistic steady-state approximation' method [http://identifiers.org/biomodels.kisao/KISAO_0000323], which determines the number of samples taken from the distribution.

Axiom
annotated source: number of samples
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.2131050
comment: Salis H, Kaznessis YN. An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks. J Chem Phys. 2005 Dec 1;123(21):214106.

maximum discrete number
type: Class
subclass of: partitioning control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: equation-free probabilistic steady-state approximation
subclass of: Restriction
  on property: has type
  some values from: integer
created: 2011-06-02
creator: AZ
definition: Parameter of 'equation-free probabilistic steady-state approximation' method [http://identifiers.org/biomodels.kisao/KISAO_0000323], which controls the maximum number of molecules of some reactant species in order for the reaction to be considered discrete.

Axiom
annotated source: maximum discrete number
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.2131050
comment: Salis H, Kaznessis YN. An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks. J Chem Phys. 2005 Dec 1;123(21):214106.

minimum fast rate
type: Class
subclass of: partitioning control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: equation-free probabilistic steady-state approximation
subclass of: Restriction
  on property: has type
  some values from: double
created: 2011-06-02
creator: AZ
definition: Parameter of 'equation-free probabilistic steady-state approximation' method [http://identifiers.org/biomodels.kisao/KISAO_0000323], which controls the minimum rate of the reaction in order for it to be considered fast.

Axiom
annotated source: minimum fast rate
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.2131050
comment: Salis H, Kaznessis YN. An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks. J Chem Phys. 2005 Dec 1;123(21):214106.

constant-time kinetic Monte Carlo algorithm
type: Class
subclass of: accelerated stochastic simulation algorithm
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
created: 2011-06-03
creator: AZ
alternative label: SSA-CR
definition: The computational cost of the original SSA [http://identifiers.org/biomodels.kisao/KISAO_0000029] scaled linearly with the number of reactions in the network. Gibson and Bruck developed a logarithmic scaling version of the SSA which uses a priority queue or binary tree for more efficient reaction selection [http://identifiers.org/biomodels.kisao/KISAO_0000027]. More generally, this problem is one of dynamic discrete random variate generation which finds many uses in kinetic Monte Carlo and discrete event simulation. We present here a constant-time algorithm, whose cost is independent of the number of reactions, enabled by a slightly more complex underlying data structure.

Axiom
annotated source: constant-time kinetic Monte Carlo algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/18513044
comment: Slepoy A, Thompson AP, Plimpton SJ. A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networks. J Chem Phys. 2008 May 28;128(20):205101.

Axiom
annotated source: constant-time kinetic Monte Carlo algorithm
annotated property: altLabel
annotated target: SSA-CR
comment: EXACT

R-leaping algorithm
type: Class
subclass of: stochastic simulation leaping method
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
created: 2011-06-03
creator: AZ
alternative label: R-leap method
definition: A novel algorithm is proposed for the acceleration of the exact stochastic simulation algorithm by a predefined number of reaction firings (R-leaping) that may occur across several reaction channels. In the present approach, the numbers of reaction firings are correlated binomial distributions and the sampling procedure is independent of any permutation of the reaction channels. This enables the algorithm to efficiently handle large systems with disparate rates, providing substantial computational savings in certain cases.

Axiom
annotated source: R-leaping algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/16964997
comment: Auger A, Chatelain P, Koumoutsakos P. R-leaping: accelerating the stochastic simulation algorithm by reaction leaps. J Chem Phys. 2006 Aug 28;125(8):084103.

Axiom
annotated source: R-leaping algorithm
annotated property: altLabel
annotated target: R-leap method
comment: EXACT

exact R-leaping algorithm
type: Class
subclass of: stochastic simulation leaping method
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
subclass of: Restriction
  on property: is similar to
  some values from: R-leaping algorithm
created: 2011-06-03
creator: AZ
alternative label: ER-leap method
alternative label: exact R-leap method
alternative label: exact accelerated stochastic simulation algorithm
definition: We present a SSA which, similar to R-leap [http://identifiers.org/biomodels.kisao/KISAO_0000330], accelerates SSA [http://identifiers.org/biomodels.kisao/KISAO_0000029] by executing multiple reactions per algorithmic step, but which samples the reactant trajectories from the same probability distribution as the SSA. This 'exact R-leap' or 'ER-leap' algorithm is a modification of the R-leap algorithm which is both exact and capable of substantial speed-up over SSA.

Axiom
annotated source: exact R-leaping algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/2852436
comment: Eric Mjolsness, David Orendorff, Philippe Chatelain, and Petros Koumoutsakos. An exact accelerated stochastic simulation algorithm. J Chem Phys. 2009 April 14; 130(14): 144110.

Axiom
annotated source: exact R-leaping algorithm
annotated property: altLabel
annotated target: ER-leap method
comment: EXACT

Axiom
annotated source: exact R-leaping algorithm
annotated property: altLabel
annotated target: exact R-leap method
comment: EXACT

Axiom
annotated source: exact R-leaping algorithm
annotated property: altLabel
annotated target: exact accelerated stochastic simulation algorithm
comment: EXACT

ER-leap initial leap
type: Class
subclass of: granularity control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: exact R-leaping algorithm
subclass of: Restriction
  on property: has type
  some values from: integer
created: 2011-06-03
creator: AZ
alternative label: L
definition: L (initial step) is a parameter of 'exact R-leaping method' [http://identifiers.org/biomodels.kisao/KISAO_0000331]. ''We will assume that the reaction event to be bounded occurs within a run of L events in the SSA algorithm[http://identifiers.org/biomodels.kisao/KISAO_0000029], in order to execute L reactions at once in the manner of the R-leap algorithm[http://identifiers.org/biomodels.kisao/KISAO_0000230]''.

Axiom
annotated source: ER-leap initial leap
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/2852436
comment: Eric Mjolsness, David Orendorff, Philippe Chatelain, and Petros Koumoutsakos. An exact accelerated stochastic simulation algorithm. J Chem Phys. 2009 April 14; 130(14): 144110.

Axiom
annotated source: ER-leap initial leap
annotated property: altLabel
annotated target: L
comment: EXACT

accelerated stochastic simulation algorithm
type: Class
subclass of: Gillespie-like method
subclass of: Restriction
  on property: is similar to
  some values from: Gillespie direct algorithm
created: 2011-06-03
creator: AZ
is organizational: true
alternative label: accelerated SSA
definition: An algorithm, which accelerates SSA [http://identifiers.org/biomodels.kisao/KISAO_0000029] either at the expense of its accuracy or exact.

Axiom
annotated source: accelerated stochastic simulation algorithm
annotated property: altLabel
annotated target: accelerated SSA
comment: EXACT

multiparticle lattice gas automata
type: Class
subclass of: deterministic cellular automata update algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
subclass of: Restriction
  on property: is similar to
  some values from: lattice gas automata
created: 2011-06-03
creator: AZ
alternative label: multiparticle lattice gas cellular automata
definition: An algorithm which allows for an arbitrary number of particles, while keeping the benefits of the cellular automata approach [http://identifiers.org/biomodels.kisao/KISAO_0000315].

Axiom
annotated source: multiparticle lattice gas automata
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1142/S0129183194000052
comment: Chopard B., et al.Multiparticle lattice gas automata for reaction diffusion systems. Int. J. Mod. Phys. C 1994;5:47-63.

Axiom
annotated source: multiparticle lattice gas automata
annotated property: altLabel
annotated target: multiparticle lattice gas cellular automata
comment: EXACT

generalized stochastic simulation algorithm
type: Class
subclass of: Gillespie-like method
subclass of: Restriction
  on property: is generalization of
  some values from: Gillespie direct algorithm
created: 2011-06-03
creator: AZ
is organizational: true
definition: Gillespie direct method [http://identifiers.org/biomodels.kisao/KISAO_0000029] follows unit-by-unit changes in the total numbers of each reactant species, it is especially well suited to the study of systems in which reactant densities are low and the application of methods based on continuum approximations, such as the traditional ordinary differential equations of chemical kinetics, is questionable. The 'generalized stochastic simulation algorithm' branch presents methods, which extend Gillespie direct method [http://identifiers.org/biomodels.kisao/KISAO_0000029] to suit to systems with other characteristics.

D-leaping method
type: Class
subclass of: generalized stochastic simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
created: 2011-06-03
creator: AZ
definition: We propose a novel, accelerated algorithm for the approximate stochastic simulation of biochemical systems with delays. The present work extends existing accelerated algorithms by distributing, in a time adaptive fashion, the delayed reactions so as to minimize the computational effort while preserving their accuracy.

Axiom
annotated source: D-leaping method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/j.jcp.2009.05.004
comment: Bayati B, Chatelain P, Koumoutsakos. D-leaping: Accelerating stochastic simulation algorithms for reactions with delays. Journal of Computational Physics. 2009 Sept;228(16):5909-5918.

finite element method
type: Class
subclass of: partial differential equation discretization method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has characteristic
  some values from: mesh-based geometry handling
created: 2011-06-07
creator: AZ
alternative label: FEA
alternative label: FEM
alternative label: finite element analysis
definition: A numerical technique for finding approximate solutions of partial differential equations (PDE) as well as of integral equations. The solution approach is based either on eliminating the differential equation completely (steady state problems), or rendering the PDE into an approximating system of ordinary differential equations, which are then numerically integrated using standard techniques such as Euler method [http://identifiers.org/biomodels.kisao/KISAO_0000261], Runge-Kutta [http://identifiers.org/biomodels.kisao/KISAO_0000064], etc.

Axiom
annotated source: finite element method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1109/MAP.2007.376627
comment: Pelosi G. The finite-element method, Part I: R. L. Courant: Historical Corner. IEEE Antennas and Propagation Magazine, Vol. 49, No. 2. (April 2007), pp. 180-182.

Axiom
annotated source: finite element method
annotated property: altLabel
annotated target: FEA
comment: EXACT

Axiom
annotated source: finite element method
annotated property: altLabel
annotated target: FEM
comment: EXACT

Axiom
annotated source: finite element method
annotated property: altLabel
annotated target: finite element analysis
comment: EXACT

h-version of the finite element method
type: Class
subclass of: finite element method
created: 2011-06-07
creator: AZ
alternative label: h-FEM
alternative label: h-method
definition: Classical form of the 'finite element method' [http://identifiers.org/biomodels.kisao/KISAO_0000337], in which polynomials of fixed degree p are used and the mesh is refined to increase accuracy. Can be considered as a special case of the h-p version [http://identifiers.org/biomodels.kisao/KISAO_0000340].

Axiom
annotated source: h-version of the finite element method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/0168-874X(94)90003-5
comment: Babuska, I., T. Strouboulis, A. Mathur, C. S. Upadhyay, Pollution error in the h-version of the finite element method and the local quality of a-posteriori error estimators, Finite Elements in Analysis and Design, 17: 273-321, 1994.

Axiom
annotated source: h-version of the finite element method
annotated property: altLabel
annotated target: h-FEM
comment: EXACT

Axiom
annotated source: h-version of the finite element method
annotated property: altLabel
annotated target: h-method
comment: EXACT

p-version of the finite element method
type: Class
subclass of: finite element method
created: 2011-06-07
creator: AZ
alternative label: p-FEM
alternative label: p-method
definition: The p version of 'finite element method' [http://identifiers.org/biomodels.kisao/KISAO_0000337] uses a fixed mesh but increases the polynomial degree p to increase accuracy. Can be considered as a special case of the h-p version [http://identifiers.org/biomodels.kisao/KISAO_0000340].

Axiom
annotated source: p-version of the finite element method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0718033
comment: Babuska, I., B.A. Szabo and I.N. Katz, The p-version of the finite element method, SIAM J. Numer. Anal., 18: 515-545, 1981.

Axiom
annotated source: p-version of the finite element method
annotated property: altLabel
annotated target: p-FEM
comment: EXACT

Axiom
annotated source: p-version of the finite element method
annotated property: altLabel
annotated target: p-method
comment: EXACT

h-p version of the finite element method
type: Class
subclass of: finite element method
subclass of: Restriction
  on property: is generalization of
  some values from: h-version of the finite element method
subclass of: Restriction
  on property: is generalization of
  some values from: p-version of the finite element method
disjoint with: mixed finite element method
created: 2011-06-07
creator: AZ
alternative label: hp-FEM
alternative label: hp-method
definition: In h-p version of 'finite difference method' [http://identifiers.org/biomodels.kisao/KISAO_0000337] the two approaches of mesh refinement and degree enchacement are combined.

Axiom
annotated source: h-p version of the finite element method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/BF00272624
comment: Babuska, I., and B. Guo, The h-p version of the finite element method, Comput. Mech., 1: 203-220, 1986.

Axiom
annotated source: h-p version of the finite element method
annotated property: altLabel
annotated target: hp-FEM
comment: EXACT

Axiom
annotated source: h-p version of the finite element method
annotated property: altLabel
annotated target: hp-method
comment: EXACT

mixed finite element method
type: Class
subclass of: finite element method
created: 2011-06-07
creator: AZ
definition: A 'finite element method' [http://identifiers.org/biomodels.kisao/KISAO_0000337] in which both stress and displacement fields are approximated as primary variables.

Axiom
annotated source: mixed finite element method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/0045-7825(90)90168-L
comment: D. N. Arnold. 1990. Mixed finite element methods for elliptic problems. Comput. Methods Appl. Mech. Eng. 82, 1-3 (September 1990), 281-300.

level set method
type: Class
subclass of: partial differential equation discretization method
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: linearity of equation
created: 2011-06-07
creator: AZ
alternative label: LSM
alternative label: level-set method
definition: An algorithm for moving surfaces under their curvature. This algorithm rely on numerically solving Hamilton-Jacobi equations with viscous terms, using approximation techniques from hyperbolic conservation laws.

Axiom
annotated source: level set method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/0021-9991(88)90002-2
comment: Osher, S.; Sethian, J. A. (1988), "Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations", J. Comput. Phys. 79: 12-49.

Axiom
annotated source: level set method
annotated property: altLabel
annotated target: LSM
comment: EXACT

Axiom
annotated source: level set method
annotated property: altLabel
annotated target: level-set method
comment: EXACT

generalized finite element method
type: Class
subclass of: partial differential equation discretization method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has characteristic
  some values from: meshless geometry handling
subclass of: Restriction
  on property: is generalization of
  some values from: finite element method
created: 2011-06-07
creator: AZ
alternative label: GFEM
alternative label: PUM
alternative label: partition of unity method
definition: The GFEM is a generalization of the classical 'finite element method' [http://identifiers.org/biomodels.kisao/KISAO_0000337] — in its h [http://identifiers.org/biomodels.kisao/KISAO_0000338], p [http://identifiers.org/biomodels.kisao/KISAO_0000339], and h-p versions [http://identifiers.org/biomodels.kisao/KISAO_0000340]— as well as of the various forms of meshless methods used in engineering.

Axiom
annotated source: generalized finite element method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1142/S0219876204000083
comment: Babuska, Ivo; Uday Banerjee, John E. Osborn (June 2004). Generalized Finite Element Methods: Main Ideas, Results, and Perspective. International Journal of Computational Methods 1 (1): 67-103.

Axiom
annotated source: generalized finite element method
annotated property: altLabel
annotated target: GFEM
comment: EXACT

Axiom
annotated source: generalized finite element method
annotated property: altLabel
annotated target: PUM
comment: EXACT

Axiom
annotated source: generalized finite element method
annotated property: altLabel
annotated target: partition of unity method
comment: EXACT

h-p cloud method
type: Class
subclass of: partial differential equation discretization method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has characteristic
  some values from: meshless geometry handling
created: 2011-06-09
creator: AZ
alternative label: h-p clouds
alternative label: method of clouds
definition: A meshless method, which uses a partition of unity to construct the family of h-p cloud functions.

Axiom
annotated source: h-p cloud method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1002/(SICI)1098-2426(199611)12:6<673::AID-NUM3>3.0.CO
comment: Duarte, C. A. and Oden, J. T. (1996), H-p clouds—an h-p meshless method. Numerical Methods for Partial Differential Equations, 12: 673-705.

Axiom
annotated source: h-p cloud method
annotated property: altLabel
annotated target: h-p clouds
comment: EXACT

Axiom
annotated source: h-p cloud method
annotated property: altLabel
annotated target: method of clouds
comment: EXACT

mesh-based geometry handling
type: Class
subclass of: type of domain geometry handling
disjoint with: meshless geometry handling
creator: AZ
definition: In most large-scale numerical simulations of physical phenomena, a large percentage of the overall computational effort is expended on technical details connected with meshing. These details include, in particular, grid generation, mesh adaptation to domain geometry, element or cell connectivity, grid motion and separation to model fracture, fragmentation, free surfaces, etc.

meshless geometry handling
type: Class
subclass of: type of domain geometry handling
creator: AZ
definition: Most meshless methods require a scattered set of nodal points in the domain of interest. In these methods, there may be no fixed connectivities between the nodes, unlike the finite element or finite difference methods. This feature has significant implications in modeling some physical phenomena that are characterized by a continuous change in the geometry of the domain under analysis.

extended finite element method
type: Class
subclass of: partial differential equation discretization method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has characteristic
  some values from: meshless geometry handling
subclass of: Restriction
  on property: is generalization of
  some values from: finite element method
created: 2011-06-09
creator: AZ
alternative label: X-FEM
alternative label: XFEM
definition: A numerical method to model arbitrary discontinuities in continuous bodies that does not require the mesh to conform to the discontinuities nor significant mesh refinement near singularities. In X-FEM the standard finite element approximation [http://identifiers.org/biomodels.kisao/KISAO_0000337] is enriched and the approximation space is extended by an additional family of functions.

Axiom
annotated source: extended finite element method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/s00466-002-0391-2
comment: Stazi, F. L.; Budyn, E.; Chessa, J.; Belytschko, T. An extended finite element method with higher-order elements for curved cracks. Computational Mechanics, Volume 31, Issue 1-2, pp. 38-48 (2003).

Axiom
annotated source: extended finite element method
annotated property: altLabel
annotated target: X-FEM
comment: EXACT

Axiom
annotated source: extended finite element method
annotated property: altLabel
annotated target: XFEM
comment: EXACT

method of finite spheres
type: Class
subclass of: partial differential equation discretization method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has characteristic
  some values from: meshless geometry handling
created: 2011-06-09
creator: AZ
alternative label: MFS
definition: Method of finite spheres is truly meshless in the sense that the nodes are placed and the numerical integration is performed without a mesh. Some of the novel features of the method of finite spheres are the numerical integration scheme and the way in which the Dirichlet boundary conditions are incorporated.

Axiom
annotated source: method of finite spheres
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/s004660050481
comment: S. De and K. J. Bathe. The method of finite spheres. Computational Mechanics, Volume 25, Number 4, 329-345.

Axiom
annotated source: method of finite spheres
annotated property: altLabel
annotated target: MFS
comment: EXACT

probability-weighted dynamic Monte Carlo method
type: Class
subclass of: accelerated stochastic simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
created: 2011-06-09
creator: AZ
alternative label: PW-DMC
alternative label: probability-weighted DMC
definition: We have developed a probability-weighted DMC method by incorporating the weighted sampling algorithm of equilibrium molecular simulations. This new algorithm samples the slow reactions very efficiently and makes it possible to simulate in a computationally efficient manner the reaction kinetics of physical systems in which the rates of reactions vary by several orders of magnitude.

Axiom
annotated source: probability-weighted dynamic Monte Carlo method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1021/jp011404w
comment: Resat H, Wiley HS, Dixon DA. Probability-weighted dynamic Monte Carlo method for reaction kinetics simulations. J Phys Chem B. 2001;105:11026-11034.

Axiom
annotated source: probability-weighted dynamic Monte Carlo method
annotated property: altLabel
annotated target: PW-DMC
comment: EXACT

Axiom
annotated source: probability-weighted dynamic Monte Carlo method
annotated property: altLabel
annotated target: probability-weighted DMC
comment: EXACT

multinomial tau-leaping method
type: Class
subclass of: tau-leaping method
subclass of: Restriction
  on property: is generalization of
  some values from: binomial tau-leaping method
created: 2011-06-09
creator: AZ
alternative label: MtauL
definition: The multinomial tau-leaping method is an extension of the binomial tau-leaping method [http://identifiers.org/biomodels.kisao/KISAO_0000074] to networks with arbitrary multiple-channel reactant dependencies. Improvements were achieved by a combination of three factors: First, tau-leaping steps are determined simply and efficiently using a-priori information and Poisson distribution based estimates of expectation values for reaction numbers. Second, networks are partitioned into closed groups of reactions and corresponding reactants in which no group reactant set is found in any other group. Third, product formation is factored into upper bound estimation of the number of times a particular reaction occurs.

Axiom
annotated source: multinomial tau-leaping method
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/17343434
comment: Pettigrew MF, Resat H. Multinomial tau-leaping method for stochastic kinetic simulations. J Chem Phys. 2007 Feb 28;126(8):084101.

Axiom
annotated source: multinomial tau-leaping method
annotated property: altLabel
annotated target: MtauL
comment: EXACT

hybrid method
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: hybridity
subclass of: Restriction
  on property: is hybrid of
  some values from: modelling and simulation algorithm
created: 2011-06-09
creator: AZ
is organizational: true
definition: A simulation methods which combines the advantages of complementary simulation approaches: the whole system is subdivided into appropriate parts and different simulation methods operate on these parts at the same time.

generalized minimal residual algorithm
type: Class
subclass of: Krylov subspace projection method
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: is generalization of
  some values from: minimal residual method
created: 2011-06-10
creator: AZ
is implemented in: CVODE
alternative label: GMRES
definition: An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. The generalized minimal residual method extends the minimal residual method (MINRES) [http://identifiers.org/biomodels.kisao/KISAO_0000388], which is only applicable to symmetric systems, to non-symmetric systems.

Axiom
annotated source: generalized minimal residual algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0907058
comment: Youcef Saad and Martin H. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems. SIAM J. Sci. and Stat. Comput. 7, 856 (1986).

Axiom
annotated source: generalized minimal residual algorithm
annotated property: altLabel
annotated target: GMRES
comment: EXACT

Krylov subspace projection method
type: Class
subclass of: iterative method for solving a system of linear equations
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
created: 2011-06-10
creator: AZ
alternative label: Krylov subspace method
definition: Krylov subspace method is an iterative linear equation method, which builds up Krylov subspaces and look for good approximations to eigenvectors and invariant subspaces within the Krylov spaces.

Axiom
annotated source: Krylov subspace projection method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0898715342
comment: Y. Saad. 2003. Iterative Methods for Sparse Linear Systems (2nd ed.). Soc. for Industrial and Applied Math., Philadelphia, PA, USA.

Axiom
annotated source: Krylov subspace projection method
annotated property: altLabel
annotated target: Krylov subspace method
comment: EXACT

DASPK
type: Class
subclass of: IDA-like method
subclass of: Restriction
  on property: has characteristic
  some values from: differential-algebraic equation problem
subclass of: Restriction
  on property: is similar to
  some values from: IDA
subclass of: Restriction
  on property: uses
  some values from: generalized minimal residual algorithm
subclass of: Restriction
  on property: uses
  some values from: DASSL
subclass of: Restriction
  on property: uses
  some values from: scaled preconditioned generalized minimal residual method
created: 2011-06-10
creator: AZ
alternative label: DDASPK
alternative label: SDASPK
alternative label: differential algebraic system solver with Krylov preconditioning
definition: In DASPK, we have combined the time-stepping methods of DASSL [http://identifiers.org/biomodels.kisao/KISAO_0000255] with preconditioned iterative method GMRES [http://identifiers.org/biomodels.kisao/KISAO_0000386], for solving large-scale systems of DAEs of the form F(t, y, y') = 0, where F, y, y' are N-dimensional vectors, and a consistent set of initial conditions y(t0) = y0, y'(t0) = y'0 is given. DASPK is written in Fortran.

Axiom
annotated source: DASPK
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0915088
comment: Peter N. Brown, Alan C. Hindmarsh, and Linda R. Petzold. 1994. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15, 6 (November 1994), 1467-1488.

Axiom
annotated source: DASPK
annotated property: altLabel
annotated target: DDASPK
comment: NARROW

Axiom
annotated source: DASPK
annotated property: altLabel
annotated target: SDASPK
comment: NARROW

Axiom
annotated source: DASPK
annotated property: altLabel
annotated target: differential algebraic system solver with Krylov preconditioning
comment: EXACT

DASSL
type: Class
subclass of: IDA-like method
subclass of: Restriction
  on property: has characteristic
  some values from: differential-algebraic equation problem
created: 2011-06-10
creator: AZ
alternative label: DDASSL
alternative label: SDASSL
alternative label: differential algebraic system solver
definition: DASSL is designed for the numerical solution of implicit systems of differential/algebraic equations written in the form F(t,y,y')=0, where F, y, and y' are vectors, and initial values for y and y' are given.

Axiom
annotated source: DASSL
annotated property: seeAlso
annotated target: http://www.nea.fr/abs/html/nesc9918.html
comment: Linda R. Petzold: A Description of DASSL: A Differential/Algebraic System Solver, SAND82-8637 (September 1982).

Axiom
annotated source: DASSL
annotated property: altLabel
annotated target: DDASSL
comment: NARROW

Axiom
annotated source: DASSL
annotated property: altLabel
annotated target: SDASSL
comment: NARROW

Axiom
annotated source: DASSL
annotated property: altLabel
annotated target: differential algebraic system solver
comment: EXACT

conjugate gradient method
type: Class
subclass of: Krylov subspace projection method
subclass of: Restriction
  on property: has characteristic
  some values from: symmetricity of matrix
created: 2011-06-10
creator: AZ
alternative label: CG
definition: Conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite. The conjugate gradient method is an iterative method, so it can be applied to sparse systems that are too large to be handled by direct methods. Such systems often arise when numerically solving partial differential equations.

Axiom
annotated source: conjugate gradient method
annotated property: seeAlso
annotated target: urn:issn:0091-0635
comment: M. R. Hestenes and E. L. Stiefel, Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 49 (1952), p. 409.

Axiom
annotated source: conjugate gradient method
annotated property: altLabel
annotated target: CG
comment: EXACT

biconjugate gradient method
type: Class
subclass of: Krylov subspace projection method
subclass of: Restriction
  on property: is generalization of
  some values from: conjugate gradient method
created: 2011-06-10
creator: AZ
alternative label: BCG
alternative label: Bi-CG
alternative label: BiCG
definition: The biconjugate gradient method provides a generalization of conjugate gradient method [http://identifiers.org/biomodels.kisao/KISAO_0000357] to non-symmetric matrices.

Axiom
annotated source: biconjugate gradient method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/BFb0080109
comment: Fletcher, R. (1976). "Conjugate gradient methods for indefinite systems". Numerical Analysis. Lecture Notes in Mathematics (Springer Berlin / Heidelberg) 506: 73-89.

Axiom
annotated source: biconjugate gradient method
annotated property: altLabel
annotated target: BCG
comment: EXACT

Axiom
annotated source: biconjugate gradient method
annotated property: altLabel
annotated target: Bi-CG
comment: EXACT

Axiom
annotated source: biconjugate gradient method
annotated property: altLabel
annotated target: BiCG
comment: EXACT

implicit-state Doob-Gillespie algorithm
type: Class
subclass of: multi-state agent-based simulation method
subclass of: Restriction
  on property: is similar to
  some values from: StochSim nearest-neighbour algorithm
subclass of: Restriction
  on property: is generalization of
  some values from: Gillespie direct algorithm
created: 2011-06-13
creator: AZ
definition: The algorithm uses a representation of the system together with a super-approximation of its ‘event horizon’ (all events that may happen next), and a specific correction scheme to obtain exact timings. Being completely local and not based on any kind of enumeration, this algorithm has a per event time cost which is independent of (i) the size of the set of generable species (which can even be infinite), and (ii) independent of the size of the system (ie, the number of agent instances). The algorithm can be refined, using concepts derived from the classical notion of causality, so that in addition to the above one also has that the even cost is depending (iii) only logarithmically on the size of the model (ie, the number of rules).

Axiom
annotated source: implicit-state Doob-Gillespie algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/3-540-76636-7 978-3-540-76636-0
comment: V. Danos, J. Feret, W. Fontana, and J. Krivine. 2007. Scalable simulation of cellular signalling networks. In Proceedings of the 5th Asian conference on Programming languages and systems (APLAS'07), Zhong Shao (Ed.). Springer-Verlag, Berlin, Heidelberg, 139-157.

rule-based simulation method
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: discrete variable
created: 2011-06-13
creator: AZ
is organizational: true
definition: Rule-based models provide a powerful alternative to approaches that require explicit enumeration of all possible molecular species of a system. Such models consist of formal rules governing interactive behaviour. Rule-based simulation methods simulate such models.

Adams predictor-corrector method
type: Class
subclass of: Adams method
subclass of: Restriction
  on property: uses
  some values from: Adams-Bashforth method
subclass of: Restriction
  on property: uses
  some values from: Adams-Moulton method
created: 2011-06-16
creator: AZ
is implemented in: GSL
definition: The combination of evaluating a single explicit integration method ('Adams-Bashforth method' [http://identifiers.org/biomodels.kisao/KISAO_0000279]) (the predictor step) in order to provide a good initial guess for the successive evaluation of an implicit method ('Adams-Moulton method' [http://identifiers.org/biomodels.kisao/KISAO_0000280]) (the corrector step) using iteration.

Axiom
annotated source: Adams predictor-corrector method
annotated property: seeAlso
annotated target: urn:asin:B0000EFQ8B
comment: Moulton, Forest R. (1926), New methods in exterior ballistics, University of Chicago Press.

NDSolve method
type: Class
subclass of: hybrid method
subclass of: Restriction
  on property: is hybrid of
  some values from: backward differentiation formula
subclass of: Restriction
  on property: is hybrid of
  some values from: embedded Runge-Kutta method
subclass of: Restriction
  on property: is hybrid of
  some values from: method of lines
subclass of: Restriction
  on property: is hybrid of
  some values from: Adams predictor-corrector method
subclass of: Restriction
  on property: is hybrid of
  some values from: partitioned Runge-Kutta method
subclass of: Restriction
  on property: is hybrid of
  some values from: Class
    intersection of: Runge-Kutta based method
    intersection of: Restriction
      on property: has characteristic
      some values from: implicit method type
created: 2011-06-16
creator: AZ
is implemented in: Mathematica
definition: The Mathematica computation system function NDSolve is a general numerical differential equation solver. It can handle a wide range of ordinary differential equations as well as some partial differential equations. NDSolve can also solve some differential-algebraic equations, which are typically a mix of differential and algebraic equations.

Axiom
annotated source: NDSolve method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-1-57955-058-5
comment: Advanced Numerical Differential Equation Solving in Mathematica, Wolfram Mathematica Tutorial Collection, 2008.

symplecticness
type: Class
subclass of: modelling and simulation algorithm characteristic
created: 2011-06-16
creator: AZ
definition: Roughly speaking, ‘symplecticness’ is a characteristic property possessed by the solutions of Hamiltonian problems. A numerical method is called symplectic if, when applied to Hamiltonian problems, it generates numerical solutions which inherit the property of symplecticness (phase volume preservation).

Axiom
annotated source: symplecticness
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1017/S0962492900002282
comment: J. M. Sanz-Serna (1992). Symplectic integrators for Hamiltonian problems: an overview. Acta Numerica, 1, pp 243-286

partitioned Runge-Kutta method
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: symplecticness
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: uses
  min qualified cardinality: 2
  on class: Runge-Kutta based method
created: 2011-06-16
creator: AZ
alternative label: PRK
alternative label: SPRK
alternative label: symplectic partitioned Runge-Kutta method
definition: If a Hamiltonian system possesses a natural partitioning, it is possible to integrate its certain components using one Runge-Kutta method and other components using a different Runge-Kutta method. The overall s-stage scheme is called a partitioned Runge-Kutta method.

Axiom
annotated source: partitioned Runge-Kutta method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/BF01389456
comment: P. Rentrop (1985): Partitioned Runge-Kutta methods with stiffness detection and stepsize control. Numer. Math., Vol. 47, p.545-564.

Axiom
annotated source: partitioned Runge-Kutta method
annotated property: altLabel
annotated target: PRK
comment: EXACT

Axiom
annotated source: partitioned Runge-Kutta method
annotated property: altLabel
annotated target: SPRK
comment: EXACT

Axiom
annotated source: partitioned Runge-Kutta method
annotated property: altLabel
annotated target: symplectic partitioned Runge-Kutta method
comment: EXACT

partial differential equation discretization method
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: partial differential equation problem
created: 2011-06-27
creator: AZ
is organizational: true
definition: A method which solves partial differential equations by discretizing them, i.e. approximating them by equations that involve a finite number of unknowns.

type of problem
type: Class
subclass of: modelling and simulation algorithm characteristic
created: 2011-06-29
creator: AZ
is organizational: true
definition: A characteristic describing the type of the problems which can be solved by the algorithm.

stochastic differential equation problem
type: Class
subclass of: type of differential equation
creator: AZ
alternative label: SDE problem

Axiom
annotated source: stochastic differential equation problem
annotated property: altLabel
annotated target: SDE problem
comment: EXACT

partial differential equation problem
type: Class
subclass of: type of differential equation
creator: AZ
alternative label: PDE problem

Axiom
annotated source: partial differential equation problem
annotated property: altLabel
annotated target: PDE problem
comment: EXACT

differential-algebraic equation problem
type: Class
subclass of: type of differential equation
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
creator: AZ
alternative label: DAE

Axiom
annotated source: differential-algebraic equation problem
annotated property: altLabel
annotated target: DAE
comment: EXACT

ordinary differential equation problem
type: Class
subclass of: type of differential equation
creator: AZ
alternative label: ODE problem

Axiom
annotated source: ordinary differential equation problem
annotated property: altLabel
annotated target: ODE problem
comment: EXACT

delay differential equation problem
type: Class
subclass of: type of differential equation
creator: AZ
alternative label: DDE problem

linearity of equation
type: Class
subclass of: type of problem
created: 2011-07-19
creator: AZ
definition: Linear differential equations are of the form Ly = f, where the differential operator L is a linear operator, y is the unknown function, and the right hand side f is a given function of the same nature as y.

one-step method
type: Class
subclass of: ODE solver
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has parameter
  some values from: step size
created: 2011-06-30
creator: AZ
is organizational: true
definition: A numerical method for differential equations which uses one starting value at each step.

Axiom
annotated source: one-step method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-3-540-56670-0
comment: Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag

implicit midpoint rule
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has Runge-Kutta method order
  has value: 2
created: 2011-06-30
creator: AZ
is implemented in: GSL
alternative label: implicit Gaussian second order Runge-Kutta method
definition: The implicit midpoint rule is a second-order case of the more general implicit s-stage Runge-Kutta methods [http://identifiers.org/biomodels.kisao/KISAO_0000064 and (http://identifiers.org/biomodels.kisao/KISAO_0000245 some http://identifiers.org/biomodels.kisao/KISAO_0000240)].

Axiom
annotated source: implicit midpoint rule
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-3-540-56670-0
comment: Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag.

Axiom
annotated source: implicit midpoint rule
annotated property: altLabel
annotated target: implicit Gaussian second order Runge-Kutta method
comment: EXACT

Bulirsch-Stoer algorithm
type: Class
subclass of: Richardson extrapolation based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: uses
  some values from: modified midpoint method
created: 2011-07-01
creator: AZ
alternative label: GBS
alternative label: Gragg-Bulirsch-Stoer algorithm
definition: The Bulirsch-Stoer method is an adaptive method which uses Gragg's modified midpoint method [http://identifiers.org/biomodels.kisao/KISAO_0000382] to estimate the solution of an initial value problem for various step sizes. The estimates are fit to a "diagonal" rational function or a polynomial as a function of the step size and the limit as the step size tends to zero is taken as the final estimate.

Axiom
annotated source: Bulirsch-Stoer algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/BF02165234
comment: Bulirsch R. and Stoer J. (1966) Numerical treatment of ordinary differential equations by extrapolation methods, Numerische Mathematik, Volume 8, Number 1, 1-13.

Axiom
annotated source: Bulirsch-Stoer algorithm
annotated property: altLabel
annotated target: GBS
comment: EXACT

Axiom
annotated source: Bulirsch-Stoer algorithm
annotated property: altLabel
annotated target: Gragg-Bulirsch-Stoer algorithm
comment: EXACT

Richardson extrapolation based method
type: Class
subclass of: one-step method
created: 2011-07-01
creator: AZ
is organizational: true
definition: A method based on ideas of Richardson extrapolation, which is a process for obtaining increased accuracy in a discretized approximation by extrapolating results from coarse discretizations to an arbitrarily fine one.

Axiom
annotated source: Richardson extrapolation based method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1098/rsta.1911.0009
comment: Richardson, L. F. (1911). The approximate arithmetical solution by finite differences of physical problems including differential equations, with an application to the stresses in a masonry dam. Philosophical Transactions of the Royal Society of London, Series A 210 (459-470): 307-357.

midpoint method
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has Runge-Kutta method order
  has value: 2
created: 2011-07-01
creator: AZ
definition: The midpoint method is an explicit method for approximating the solution of the initial value problem y' = f(x,y); y(x0) = y0 at x for a given step size h. For the midpoint method the derivative of y(x) is approximated by the symmetric difference y'(x) = ( y(x+h) - y(x-h) ) / 2h + O(h2).

Axiom
annotated source: midpoint method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-3-540-56670-0
comment: Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag.

modified midpoint method
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: explicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2011-07-01
creator: AZ
alternative label: Gragg's method
alternative label: Gragg's modified midpoint method
definition: The modified midpoint method is globally a second order method for approximating the solution of the initial value problem y' = f(x, y), y(x0) = y0, which advances a vector of dependent variables y(x) from a point x to a point x + H by a sequence of n substeps each of size h, h = H/n.

Axiom
annotated source: modified midpoint method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/052143064X
comment: Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes in Fortran 77. Cambridge University Press (2001).

Axiom
annotated source: modified midpoint method
annotated property: altLabel
annotated target: Gragg's method
comment: EXACT

Bader-Deuflhard method
type: Class
subclass of: Richardson extrapolation based method
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: uses
  some values from: semi-implicit midpoint rule
subclass of: Restriction
  on property: is generalization of
  some values from: Bulirsch-Stoer algorithm
created: 2011-07-01
creator: AZ
is implemented in: GSL
definition: The Bader-Deuflhard method is an extrapolation method based on a semi-implicit discretization [http://identifiers.org/biomodels.kisao/KISAO_0000387]. It is a generalization of the Bulirsch-Stoer algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000379] for solving ordinary differential equations.

Axiom
annotated source: Bader-Deuflhard method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/BF01418331
comment: Bader, G. and Deuflhard, P. "A Semi-Implicit Mid-Point Rule for Stiff Systems of Ordinary Differential Equations." Numer. Math. 41, 373-398, 1983.

semi-implicit midpoint rule
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: implicit method type
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2011-07-01
creator: AZ
definition: A semi-implicit version of the midpoint method that has an even error series [http://identifiers.org/biomodels.kisao/KISAO_0000381].

Axiom
annotated source: semi-implicit midpoint rule
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/BF01418331
comment: Bader, G. and Deuflhard, P. "A Semi-Implicit Mid-Point Rule for Stiff Systems of Ordinary Differential Equations." Numer. Math. 41, 373-398, 1983.

scaled preconditioned generalized minimal residual method
type: Class
subclass of: generalized minimal residual algorithm
subclass of: Restriction
  on property: uses
  some values from: preconditioning technique
created: 2011-07-18
creator: AZ
alternative label: SPGMR
definition: A scaled preconditioned version of 'generalized minimal residual algorithm' [http://identifiers.org/biomodels.kisao/KISAO_0000353]. For linear system Ax = b a preconditioner matrix P that approximates A is sought, for which linear system Px = b can be solved easily. Preconditioning is applied on the left only. Scaling is done using diagonal matrix D whose diagonal elements are weights w^i = rtol|y^i| +atol^i, where rtol is 'relative tolerance' [http://identifiers.org/biomodels.kisao/KISAO_0000209] and atol is 'absolute tolerance' [http://identifiers.org/biomodels.kisao/KISAO_0000211].

Axiom
annotated source: scaled preconditioned generalized minimal residual method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0915088
comment: Peter N. Brown, Alan C. Hindmarsh, and Linda R. Petzold. 1994. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15, 6 (November 1994), 1467-1488.

Axiom
annotated source: scaled preconditioned generalized minimal residual method
annotated property: altLabel
annotated target: SPGMR
comment: EXACT

minimal residual method
type: Class
subclass of: Krylov subspace projection method
subclass of: Restriction
  on property: has characteristic
  some values from: symmetricity of matrix
created: 2011-07-18
creator: AZ
alternative label: MINRES
definition: The 'minimal residual method' is an algorithm for the numerical solution of indefinite symmertic systems of linear equations.

Axiom
annotated source: minimal residual method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0712047
comment: Paige C.C., Saunders M.A. Solution of sparse indefinite systems of linear equations, SIAM Journal on Numerical Analysis (1975) Volume: 12, Issue: 4, Publisher: SIAM, Pages: 617-629.

Axiom
annotated source: minimal residual method
annotated property: altLabel
annotated target: MINRES
comment: EXACT

quasi-minimal residual method
type: Class
subclass of: ingenious conjugate gradients-squared method
created: 2011-07-18
creator: AZ
alternative label: QMR
definition: The QMR algorithm is a robust iterative solver for general nonsingular non-Hermitian linear systems. The method uses a robust implementation of the look-ahead Lanczos algorithm to generate basis vectors for the Krylov subspaces Kn(r0, A). The QMR iterates are characterized by a quasi-minimal residual property over Kn(r0, A).

Axiom
annotated source: quasi-minimal residual method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/BF01385726
comment: Roland W. Freund and Noël M. Nachtigal. QMR: a quasi-minimal residual method for non-Hermitian linear systems. NUMERISCHE MATHEMATIK Volume 60, Number 1, 315-339.

Axiom
annotated source: quasi-minimal residual method
annotated property: altLabel
annotated target: QMR
comment: EXACT

biconjugate gradient stabilized method
type: Class
subclass of: improved biconjugate gradient method
disjoint with: ingenious conjugate gradients-squared method
is implemented in: CVODE
alternative label: Bi-CGSTAB
alternative label: BiCGSTAB
definition: An iterative method for the numerical solution of nonsymmetric linear systems. It is a variant of the biconjugate gradient method (BiCG) [http://identifiers.org/biomodels.kisao/KISAO_0000358] and has faster and smoother convergence than the original BiCG.

Axiom
annotated source: biconjugate gradient stabilized method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0913035
comment: Van der Vorst, H. A. (1992). Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems. SIAM Journal on Scientific and Statistical Computing 13: 631-644.

Axiom
annotated source: biconjugate gradient stabilized method
annotated property: altLabel
annotated target: Bi-CGSTAB
comment: EXACT

Axiom
annotated source: biconjugate gradient stabilized method
annotated property: altLabel
annotated target: BiCGSTAB
comment: EXACT

ingenious conjugate gradients-squared method
type: Class
subclass of: improved biconjugate gradient method
created: 2011-07-18
creator: AZ
alternative label: CGS
definition: A Lanczos-type method for nonsymmetric sparse linear systems. The method is based on a polynomial variant of the conjugate gradients algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000357]. Although related to the so-called bi-conjugate gradients (Bi-CG) algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000358], it does not involve adjoint matrix-vector multiplications, and the expected convergence rate is about twice that of the Bi-CG algorithm.

Axiom
annotated source: ingenious conjugate gradients-squared method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0910004
comment: Peter Sonneveld. 1989. CGS, a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 10, 1 (January 1989), 36-52.

Axiom
annotated source: ingenious conjugate gradients-squared method
annotated property: altLabel
annotated target: CGS
comment: EXACT

quasi-minimal residual variant of biconjugate gradient stabilized method
type: Class
subclass of: biconjugate gradient stabilized method
created: 2011-07-19
creator: AZ
alternative label: QMRCGSTAB
definition: QMRCGSTAB is a quasi-minimal residual (QMR) variant of the Bi-CGSTAB algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000394] of van der Vorst for solving nonsymmetric linear systems. The motivation for the QMR variant is to obtain smoother convergence behavior of the underlying method.

Axiom
annotated source: quasi-minimal residual variant of biconjugate gradient stabilized method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0915023
comment: T. F. Chan, E. Gallopoulos, V. Simoncini, T. Szeto, and C. H. Tong. 1994. A quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric systems. SIAM J. Sci. Comput. 15, 2 (March 1994), 338-347.

Axiom
annotated source: quasi-minimal residual variant of biconjugate gradient stabilized method
annotated property: altLabel
annotated target: QMRCGSTAB
comment: EXACT

improved biconjugate gradient method
type: Class
subclass of: Krylov subspace projection method
subclass of: Restriction
  on property: is similar to
  some values from: biconjugate gradient method
created: 2011-07-19
creator: AZ
is organizational: true
definition: An 'improved biconjugate gradient method' branch contains algorithms which can be viewed as improvements over some of drawbacks of BCG [http://identifiers.org/biomodels.kisao/KISAO_0000358], such as (1) the need for matrix-vector multiplications with A^T (which can be inconvenient as well as doubling the number of matrix-vector multiplications compared to CG [http://identifiers.org/biomodels.kisao/KISAO_0000357] for each increase in the degree of the underlying Krylov subspace), (2) the possibility of breakdowns and (3) erratic convergence behavior.

transpose-free quasi-minimal residual algorithm
type: Class
subclass of: quasi-minimal residual method
created: 2011-07-19
creator: AZ
is implemented in: CVODE
alternative label: TFQMR
definition: A version of CGS [http://identifiers.org/biomodels.kisao/KISAO_0000393] which 'quasi-minimizes' the residual in the space spanned by the vectors generated by the CGS iteration.

Axiom
annotated source: transpose-free quasi-minimal residual algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0914029
comment: Roland W. Freund. 1993. A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems. SIAM J. Sci. Comput. 14, 2 (March 1993), 470-482.

Axiom
annotated source: transpose-free quasi-minimal residual algorithm
annotated property: altLabel
annotated target: TFQMR
comment: EXACT

preconditioning technique
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: is used by
  some values from: iterative method for solving a system of linear equations
created: 2011-07-19
creator: AZ
definition: Preconditioning is simply a means of transforming the original linear system into one which has the same solution, but which is likely to be easier to solve with an iterative solver.

Axiom
annotated source: preconditioning technique
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0898715342
comment: Saad, Yousef (2003). Iterative methods for sparse linear systems (2nd ed.). SIAM.

iterative method for solving a system of linear equations
type: Class
subclass of: method for solving a system of linear equations
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
created: 2011-07-19
creator: AZ
is organizational: true

Axiom
annotated source: iterative method for solving a system of linear equations
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0898715342
comment: Saad, Yousef (2003). Iterative methods for sparse linear systems (2nd ed.). SIAM.

homogeneousness of equation
type: Class
subclass of: linearity of equation
created: 2011-07-19
creator: AZ
definition: Homogeneous equations are of the form Ly = 0, where the differential operator L is a linear operator and y is the unknown function.

symmetricity of matrix
type: Class
subclass of: type of problem
created: 2011-07-19
creator: AZ
definition: In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.

type of differential equation
type: Class
subclass of: type of problem
created: 2011-07-19
creator: AZ
is organizational: true

steady state root-finding method
type: Class
subclass of: general steady state method
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: steady state root-finding problem
created: 2012-01-17
creator: AZ
is organizational: false
comment: Requested by Frank T. Bergmann on Sunday, November 27, 2011 4:45:30 PM.
definition: Method for finding the root of a function (f(x) = 0).

Newton-type method
type: Class
subclass of: iterative root-finding method
subclass of: Restriction
  on property: has parameter
  some values from: relative tolerance
subclass of: Restriction
  on property: has parameter
  some values from: absolute tolerance
subclass of: Restriction
  on property: has parameter
  some values from: maximum number of steps
created: 2012-01-18
creator: AZ
comment: Requested by Frank T. Bergmann on Sunday, November 27, 2011 4:45:30 PM.
definition: A method which attacks the solution of a nonlinear problem F(x) = 0 by solving a sequence of liner problems of the same kind. The solution of the system F(x)=0 can be interpreted as a steady state of a dynamic system x'(t)=F(x(t)). The Newton approach will only work if the fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] of the dinamic system is attractive [http://identifiers.org/biomodels.teddy/TEDDY_0000094].

Axiom
annotated source: Newton-type method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/9783540210993
comment: Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, 1st ed. 2004.

ordinary Newton method
type: Class
subclass of: Newton-type method
created: 2012-01-18
creator: AZ
definition: A 'Newton-type method' [http://identifiers.org/biomodels.kisao/KISAO_0000408] which solves the general nonlinear problem F(x)=0 by applying successive linearization F'(x[k])deltax[k]=-F(x[k]), x[k+1]=x[k]+deltax[k], k=0,1,...

Axiom
annotated source: ordinary Newton method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/9783540210993
comment: Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, 1st ed. 2004.

simplified Newton method
type: Class
subclass of: Newton-type method
created: 2012-01-18
creator: AZ
definition: A 'Newton-type method' [http://identifiers.org/biomodels.kisao/KISAO_0000408] which is characterized by keeping the initial derivative throughout the whole iteration: F'(x[0])deltax[k]=-F(x[k]), x[k+1]=x[k]+deltax[k], k=0,1,...

Axiom
annotated source: simplified Newton method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/9783540210993
comment: Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, 1st ed. 2004.

Newton-like method
type: Class
subclass of: Newton-type method
created: 2012-01-18
creator: AZ
definition: A 'Newton-type method' [http://identifiers.org/biomodels.kisao/KISAO_0000408] which is characterized by the fact that, in finite dimension, the Jacodian matrices are either replaced by some fixed 'close by' Jacobian F'(z) with z not equal to the initial guess x[0], or by some approximation so that: M'(x[0])deltax[k]=-F(x[k]), x[k+1]=x[k]+deltax[k], k=0,1,...

Axiom
annotated source: Newton-like method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/9783540210993
comment: Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, 1st ed. 2004.

inexact Newton method
type: Class
subclass of: Newton-type method
subclass of: Restriction
  on property: uses
  some values from: Class
    intersection of: modelling and simulation algorithm
    intersection of: Restriction
      on property: has characteristic
      some values from: approximate solution
created: 2012-01-18
creator: AZ
alternative label: iterative Newton method
alternative label: truncated Newton method
definition: For extremely large scale nonlinear problems the arising linear systems for the Newton corrections can no longer be solved directly ('exactly'), but must be solved iterativly ('inexactly) - which gives the name inexact Newton methods. The whole scheme then consists of an inner iteration (at Newton step k): F'(x[k])deltaxi[k]=-F(x[k])+ri[k], k=0,1,... xi[k+1]=x[k]+deltaxi[k], i=0,1,..,imax[k] in terms of residuals ri[k] and an outer iteration where, given x[0], the iterates are defined as x[k+1]=xi[k+1] for i=imax[k], k=0,1,...

Axiom
annotated source: inexact Newton method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/9783540210993
comment: Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, 1st ed. 2004.

Axiom
annotated source: inexact Newton method
annotated property: altLabel
annotated target: iterative Newton method
comment: EXACT

Axiom
annotated source: inexact Newton method
annotated property: altLabel
annotated target: truncated Newton method
comment: EXACT

exact Newton method
type: Class
subclass of: Newton-type method
subclass of: Restriction
  on property: uses
  some values from: Class
    intersection of: modelling and simulation algorithm
    intersection of: Restriction
      on property: has characteristic
      some values from: exact solution
created: 2012-01-18
creator: AZ
alternative label: direct Newton method
definition: Any of the finite dimensional Newton-type methods [http://identifiers.org/biomodels.kisao/KISAO_0000408] requires the numerical solution of the linear equations F'(x[k])deltax[k]=-F(x[k]). Whenever direct elimination methods are applicable, we speak of exact Newton methods.

Axiom
annotated source: exact Newton method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/9783540210993
comment: Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, 1st ed. 2004.

maximum number of steps
type: Class
subclass of: granularity control parameter
subclass of: Restriction
  on property: is parameter of
  all values from: Newton-type method
subclass of: Restriction
  on property: has type
  some values from: integer
created: 2012-01-18
creator: AZ
alternative label: maximum steps
definition: The limit on number of internal steps before an output point.

partial least squares regression method
type: Class
subclass of: partial least squares regression-like method
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: number of partial least squares components
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: type of validation
created: 2012-01-18
creator: AZ
comment: Requested by Kristin Tøndel on Thursday, October 13, 2011 10:46:04 AM.
alternative label: PLSR
alternative label: PLSR method
definition: Multivariate regression method based on estimated latent variables. Related to Principal Component Analysis (PCA) and Principal Component Regression (PCR).

Axiom
annotated source: partial least squares regression method
annotated property: seeAlso
annotated target: http://identifiers.org/biomodels.kisao/10.1007/BFb0062108
comment: Wold S, Martens H, Wold H (1983) The multivariate calibration method in chemistry solved by the PLS method. In: Lecture notes in Mathematics, Matrix Pencils. Heidelberg: Springer-Verlag. pp. 286-293.

Axiom
annotated source: partial least squares regression method
annotated property: altLabel
annotated target: PLSR
comment: EXACT

Axiom
annotated source: partial least squares regression method
annotated property: altLabel
annotated target: PLSR method
comment: EXACT

hierarchical cluster-based partial least squares regression method
type: Class
subclass of: partial least squares regression-like method
subclass of: Restriction
  on property: has characteristic
  some values from: hybridity
subclass of: Restriction
  on property: has parameter
  some values from: number of partial least squares components
subclass of: Restriction
  on property: has parameter
  some values from: mean-centring of variables
subclass of: Restriction
  on property: has parameter
  some values from: standardising of variables
subclass of: Restriction
  on property: uses
  some values from: partial least squares regression method
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: matrix for clusterization
created: 2012-01-18
creator: AZ
comment: Requested by Kristin Tøndel on Thursday, October 13, 2011 11:13:17 AM.
alternative label: HC-PLSR
alternative label: Multivariate regression method based on separating the observations into clusters and generating Partial Least Squares Regression (PLSR) [http://identifiers.org/biomodels.kisao/KISAO_0000416] models within each cluster. This local regression analysis is suitable for very non-linear systems. PLSR is a regression method based on estimated latent variables, related to Principal Component Analysis (PCA) and Principal Component Regression (PCR). Hierarchical cluster-based partial least squares regression method uses fuzzy C-means clustering, PLSR and Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA) or Naive Bayes for classification of new observations to be predicted.

Axiom
annotated source: hierarchical cluster-based partial least squares regression method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/1752-0509-5-90
comment: Tøndel K, Indahl UG, Gjuvsland AB, Vik JO, Hunter P, et al. (2011) Hierarchical Cluster-based Partial Least Squares Regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Systems Biology 5: 90.

N-way partial least squares regression method
type: Class
subclass of: partial least squares regression-like method
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: number of N-way partial least squares regression factors
created: 2012-01-18
creator: AZ
comment: Requested by Kristin Tøndel on Thursday, October 13, 2011 11:33:06 AM.
alternative label: N-PLS
alternative label: N-way PLSR
alternative label: N-way partial least squares method
definition: Multivariate regression method that can be used on N-way data. Based on Partial Least Squares Regression (PLSR) [http://identifiers.org/biomodels.kisao/KISAO_0000416], which is a regression method based on estimated latent variables. PLSR is related to Principal Component Analysis (PCA) and Principal Component Regression (PCR).

Axiom
annotated source: N-way partial least squares regression method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1002/(SICI)1099-128X(199601)10:1<47::AID-CEM400>3.0.CO
comment: Bro R (1996) Multiway calibration. Multilinear PLS. J. Chemometrics 10: 47-6.

Axiom
annotated source: N-way partial least squares regression method
annotated property: seeAlso
annotated target: http://www.models.life.ku.dk/nwaytoolbox
comment: N-way toolbox website

Axiom
annotated source: N-way partial least squares regression method
annotated property: altLabel
annotated target: N-PLS
comment: EXACT

Axiom
annotated source: N-way partial least squares regression method
annotated property: altLabel
annotated target: N-way PLSR
comment: EXACT

Axiom
annotated source: N-way partial least squares regression method
annotated property: altLabel
annotated target: N-way partial least squares method
comment: EXACT

metamodelling method
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
created: 2012-01-18
creator: AZ
is organizational: true
definition: Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space.

Axiom
annotated source: metamodelling method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/1752-0509-5-90
comment: Tøndel K, Indahl UG, Gjuvsland AB, Vik JO, Hunter P, et al. (2011) Hierarchical Cluster-based Partial Least Squares Regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Systems Biology 5: 90.

number of partial least squares components
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: is parameter of
  all values from: partial least squares regression-like method
subclass of: Restriction
  on property: has type
  some values from: integer
created: 2012-01-18
creator: AZ
definition: Parameter used by 'partial least squares regression method' [http://identifiers.org/biomodels.kisao/KISAO_0000416] describing number of PLS components to include in the regression analysis.

Axiom
annotated source: number of partial least squares components
annotated property: seeAlso
annotated target: http://identifiers.org/biomodels.kisao/10.1007/BFb0062108
comment: Wold S, Martens H, Wold H (1983) The multivariate calibration method in chemistry solved by the PLS method. In: Lecture notes in Mathematics, Matrix Pencils. Heidelberg: Springer-Verlag. pp. 286-293.

type of validation
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: is parameter of
  all values from: partial least squares regression-like method
created: 2012-01-18
creator: AZ
definition: Parameter of 'partial least squares regression method' [http://identifiers.org/biomodels.kisao/KISAO_0000416] describing how validation is performed. Possible values include cross-validation and test set validation.

number of N-way partial least squares regression factors
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: is parameter of
  all values from: N-way partial least squares regression method
subclass of: Restriction
  on property: has type
  some values from: integer
created: 2012-01-18
creator: AZ
alternative label: number of factors
definition: Parameter of 'N-way partial least squares regression method' [http://identifiers.org/biomodels.kisao/KISAO_0000369] describing the number of factors to compute.

Axiom
annotated source: number of N-way partial least squares regression factors
annotated property: altLabel
annotated target: number of factors
comment: EXACT

partial least squares regression-like method
type: Class
subclass of: metamodelling method
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: type of validation
created: 2012-01-18
creator: AZ
is organizational: true
definition: Method for building regression models between independent and dependent variables.

mean-centring of variables
type: Class
subclass of: variables preprocessing parameter
subclass of: Restriction
  on property: is parameter of
  all values from: partial least squares regression-like method
subclass of: Restriction
  on property: has type
  some values from: boolean
disjoint with: standardising of variables
created: 2012-01-18
creator: AZ
definition: A boolean parameter of the 'hierarchical cluster-based partial least squares regression method' [http://identifiers.org/biomodels.kisao/KISAO_0000417] specifying whether the variables were mean-centred prior to the regression analysis.

Axiom
annotated source: mean-centring of variables
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/1752-0509-5-90
comment: Tøndel K, Indahl UG, Gjuvsland AB, Vik JO, Hunter P, et al. (2011) Hierarchical Cluster-based Partial Least Squares Regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Systems Biology 5: 90.

standardising of variables
type: Class
subclass of: variables preprocessing parameter
subclass of: Restriction
  on property: is parameter of
  all values from: partial least squares regression-like method
subclass of: Restriction
  on property: has type
  some values from: boolean
created: 2012-01-18
creator: AZ
definition: A boolean parameter of the 'hierarchical cluster-based partial least squares regression method' [http://identifiers.org/biomodels.kisao/KISAO_0000417] specifying whether the variables were standardised (divided by their standard deviations) prior to the regression analysis.

Axiom
annotated source: standardising of variables
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/1752-0509-5-90
comment: Tøndel K, Indahl UG, Gjuvsland AB, Vik JO, Hunter P, et al. (2011) Hierarchical Cluster-based Partial Least Squares Regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Systems Biology 5: 90.

number of clusters
type: Class
subclass of: clusterization parameter
subclass of: Restriction
  on property: has type
  some values from: integer
disjoint with: matrix for clusterization
created: 2012-01-18
creator: AZ
definition: Parameter specifying the number of clusters used by C-means algorithm.

Axiom
annotated source: number of clusters
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/1752-0509-5-90
comment: Tøndel K, Indahl UG, Gjuvsland AB, Vik JO, Hunter P, et al. (2011) Hierarchical Cluster-based Partial Least Squares Regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Systems Biology 5: 90.

matrix for clusterization
type: Class
subclass of: clusterization parameter
subclass of: Restriction
  on property: is parameter of
  all values from: hierarchical cluster-based partial least squares regression method
created: 2012-01-18
creator: AZ
definition: A matrix to do the clustering in 'hierarchical cluster-based partial least squares regression method' [http://identifiers.org/biomodels.kisao/KISAO_0000417].

Axiom
annotated source: matrix for clusterization
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/1752-0509-5-90
comment: Tøndel K, Indahl UG, Gjuvsland AB, Vik JO, Hunter P, et al. (2011) Hierarchical Cluster-based Partial Least Squares Regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Systems Biology 5: 90.

clusterization parameter
type: Class
subclass of: modelling and simulation algorithm parameter
creator: AZ
is organizational: true
definition: Parameter used by algorithms performing clusterization.

variables preprocessing parameter
type: Class
subclass of: modelling and simulation algorithm parameter
creator: AZ
is organizational: true

IDA-like method
type: Class
subclass of: DAE Solver
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: maximum step size
created: 2012-05-24
creator: AZ
is organizational: true
definition: Solves real differential-algebraic systems in N-space, in the general form F(t,y,y')=0, y(t0)=y0, y'(t0)=y'0. At each step, a Newton iteration [http://identifiers.org/biomodels.kisao/KISAO_0000408] leads to linear systems Jx=b, which are solved by one of five methods - two direct (dense or band; serial version only) and three Krylov [http://identifiers.org/biomodels.kisao/KISAO_0000354] (GMRES [http://identifiers.org/biomodels.kisao/KISAO_0000353], BiCGStab [http://identifiers.org/biomodels.kisao/KISAO_0000392], or TFQMR [http://identifiers.org/biomodels.kisao/KISAO_0000396]).

Axiom
annotated source: IDA-like method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/1089014.1089020
comment: Hindmarsh, A. C., et al., SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Trans. Math. Softw., 31:363-396, 2005.

CVODE-like method
type: Class
subclass of: ODE solver
subclass of: Class
  union of: Restriction
    on property: uses
    some values from: Adams-Moulton method
  union of: Restriction
    on property: uses
    some values from: backward differentiation formula
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: maximum step size
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: initial step size
created: 2012-05-24
creator: AZ
is organizational: true
definition: Solves ODE initial value problems, in real N-space, written as y'=f(t,y), y(t0)=y0. It is capable for stiff and non-stiff systems and uses two different linear multi-step methods, namely the Adam-Moulton [http://identifiers.org/biomodels.kisao/KISAO_0000280] method and the backward differentiation formula [http://identifiers.org/biomodels.kisao/KISAO_0000288].

Axiom
annotated source: CVODE-like method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/1089014.1089020
comment: Hindmarsh, A. C., et al., SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Trans. Math. Softw., 31:363-396, 2005.

Higham-Hall method
type: Class
subclass of: embedded Runge-Kutta 5(4) method
created: 2012-09-25
creator: AZ
alternative label: RK5(4)7FEql
definition: The equilibrium theory of Hall and Higham (1988) can be used to determine whether a Runge-Kutta algorithm will perform smoothly when stability restricts the stepsize. Higham-Hall method is a fifth order embedded Runge-Kutta method [http://identifiers.org/biomodels.kisao/KISAO_0000302], which behaves smoothly with respect to the standard type of stepsize controllers.

Axiom
annotated source: Higham-Hall method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/0377-0427(90)90192-3
comment: Higham, D.J. and Hall, G. (1990) Embedded Runge-Kutta formulae with stable equilibrium states. Journal of Computational and Applied Mathematics, 29 (1). pp. 25-33.

embedded Runge-Kutta 5(4) method
type: Class
equivalent class: Class
  intersection of: embedded Runge-Kutta method
  intersection of: Restriction
    on property: uses
    some values from: Class
      intersection of: Runge-Kutta based method
      intersection of: Restriction
        on property: has Runge-Kutta method order
        has value: 4
  intersection of: Restriction
    on property: uses
    some values from: Class
      intersection of: Runge-Kutta based method
      intersection of: Restriction
        on property: has Runge-Kutta method order
        has value: 5
subclass of: embedded Runge-Kutta method
created: 2012-09-26
creator: AZ
is organizational: true
alternative label: RK5(4)
definition: An embedded Runge-Kutta integrator of order 5(4).

Dormand-Prince 8(5,3) method
type: Class
subclass of: embedded Runge-Kutta method
subclass of: Restriction
  on property: uses
  some values from: Class
    intersection of: Runge-Kutta based method
    intersection of: Restriction
      on property: has Runge-Kutta method order
      has value: 5
subclass of: Restriction
  on property: uses
  some values from: Class
    intersection of: Runge-Kutta based method
    intersection of: Restriction
      on property: has Runge-Kutta method order
      has value: 8
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: safety factor on new step selection
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: minimum factor to change step size by
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: maximum factor to change step size by
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: beta parameter for stabilized step size control
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: initial step size
created: 2012-09-26
creator: AZ
definition: This method is based on an 8(6) method by Dormand and Prince (i.e. order 8 for the integration and order 6 for error estimation) modified by Hairer and Wanner to use a 5th order error estimator with 3rd order correction.

Axiom
annotated source: Dormand-Prince 8(5,3) method
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/978-3-540-56670-0
comment: Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag

flux balance analysis
type: Class
subclass of: flux balance method
subclass of: general steady state method
created: 2012-11-29
creator: AZ
comment: Requested by Frank T. Bergmann on Thursday, November 29, 2012 9:51:58 AM.
alternative label: FBA
definition: Flux balance analysis is a mathematical approach for analyzing the flow of metabolites through a metabolic network.

Axiom
annotated source: flux balance analysis
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1038/nbt.1614
comment: Jeffrey D Orth, Ines Thiele and Bernhard O Palsson (2010) What is flux balance analysis? Nature Biotechnology 28, 245–248

COAST
type: Class
subclass of: hybrid method
subclass of: Restriction
  on property: is hybrid of
  some values from: Class
    intersection of: Gillespie first reaction algorithm
    intersection of: tau-leaping method
subclass of: Restriction
  on property: uses
  some values from: Class
    intersection of: modelling and simulation algorithm
    intersection of: Restriction
      on property: has characteristic
      some values from: deterministic system behaviour
subclass of: Restriction
  on property: has parameter
  qualified cardinality: 1
  on class: absolute tolerance
created: 2013-01-28
creator: AZ
comment: Requested by Mark Moeller on Friday, January 25, 2013 11:11:30 AM.
alternative label: controllable approximative stochastic reaction algorithm
definition: An approximative algorithm for stochastic simulations of chemical reaction systems based on three different modeling levels: for small numbers of particles an exact [http://identifiers.org/biomodels.kisao/KISAO_0000236] stochastic [http://identifiers.org/biomodels.kisao/KISAO_0000104] model; for intermediate numbers an approximative [http://identifiers.org/biomodels.kisao/KISAO_0000237], but computationally more efficient stochastic [http://identifiers.org/biomodels.kisao/KISAO_0000104] model based on discrete Gaussian distributions; and for large numbers the deterministic [http://identifiers.org/biomodels.kisao/KISAO_0000103] reaction kinetics. In every simulation time step, the subdivision of the reaction channels into the three different modeling levels is done automatically, where all approximations applied can be controlled by a single error parameter for which an appropriate value can easily be found.

Axiom
annotated source: COAST
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/17100426
comment: Holger Wagner, Mark Moeller, and Klaus Prank (2006) COAST: Controllable approximative stochastic reaction algorithm. J. Chem. Phys. 125, 174104

logical model simulation method
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: discrete variable
created: 2013-01-28
creator: AZ
is organizational: true
definition: Qualitative (logical) models specify the evolution rules of their components. In each state a number of transitions are enabled. A 'logical model simulation method' guides the choice of the transitions processed at each step.

Axiom
annotated source: logical model simulation method
annotated property: seeAlso
annotated target: http://www.identifiers.org/pubmed/22141422
comment: Daniel Machado et al. Modeling formalisms in Systems Biology. AMB Express 2011, 1:45

synchronous logical model simulation method
type: Class
subclass of: logical model simulation method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: synchronous updating policy
disjoint with: asynchronous logical model simulation method
created: 2013-01-28
creator: AZ
definition: Qualitative (logical) models specify the evolution rules of their components. In the case of a synchronous updating all enabled transitions are processed simultaneously.

asynchronous logical model simulation method
type: Class
subclass of: logical model simulation method
subclass of: Restriction
  on property: has characteristic
  some values from: stochastic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: asynchronous updating policy
subclass of: Restriction
  on property: has parameter
  some values from: species transition probabilities
created: 2013-01-28
creator: AZ
definition: Qualitative (logical) models specify the evolution rules of their components. It the case of an asynchronous updating all enabled transitions are performed independently: a state has as many successors as the number of transitions enabled in this state. An 'asynchronous logical model simulation method' specifies a rule to guide the choice of a unique transition at each step (for example random).

type of updating policy
type: Class
subclass of: modelling and simulation algorithm characteristic
created: 2013-01-28
creator: AZ
is organizational: true
definition: A rule to guide the choice of a unique transition at each step used by an 'asynchronous logical model simulation method' [http://identifiers.org/biomodels.kisao/KISAO_0000450].

random updating policy
type: Class
subclass of: type of updating policy
subclass of: Restriction
  on property: is characteristic of
  some values from: Class
    intersection of: asynchronous logical model simulation method
    intersection of: Restriction
      on property: has characteristic
      some values from: stochastic system behaviour
disjoint with: ordered updating policy
created: 2013-01-28
creator: AZ
definition: An updating policy that chooses a transition randomly.

ordered updating policy
type: Class
subclass of: type of updating policy
subclass of: Restriction
  on property: is characteristic of
  some values from: Class
    intersection of: asynchronous logical model simulation method
    intersection of: Restriction
      on property: has characteristic
      some values from: deterministic system behaviour
created: 2013-01-28
creator: AZ
definition: An updating policy that chooses a transition in a definite way.

constant updating policy
type: Class
subclass of: ordered updating policy
created: 2013-01-28
creator: AZ
definition: An updating policy that chooses a transition in a constant way.

prioritized updating policy
type: Class
subclass of: ordered updating policy
created: 2013-01-28
creator: AZ
definition: An updating policy that chooses a transition in a prioritized way.

maximum step size
type: Class
subclass of: error control parameter
subclass of: Restriction
  on property: has type
  some values from: double
created: 2013-07-05
creator: AZ
comment: Requested by Andrew Miller on Tuesday, June 4, 2013 2:33:51 AM.
definition: An upper limit, in the units of the bound variable over which a numerical integration is being performed, that an adaptive step size numerical integration algorithm should take.

maximal timestep method
type: Class
subclass of: hybrid method
subclass of: Restriction
  on property: has characteristic
  some values from: stochastic system behaviour
subclass of: Restriction
  on property: has parameter
  some values from: maximal timestep
subclass of: Restriction
  on property: uses
  some values from: Gibson-Bruck next reaction algorithm
subclass of: Restriction
  on property: uses
  some values from: tau-leaping method
created: 2014-04-25
creator: AZ
comment: Requested by Andrzej Kierzek on Thursday, April 24, 2014 12:40:35 PM Used to simulate systems involving reactions with propensities varying by many orders of magnitude.
definition: Hybrid simulation algorithm [http://www.biomodels.net/kisao/KISAO#KISAO_0000352] combining Gibson and Bruck algorithm [http://www.biomodels.net/kisao/KISAO#KISAO_0000027] with the Gillespie tau-leap method [http://www.biomodels.net/kisao/KISAO#KISAO_0000039].

Axiom
annotated source: maximal timestep method
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/14990466
comment: Puchalka J, Kierzek AM. Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys J. 2004 Mar;86(3):1357-72.

maximal timestep
type: Class
subclass of: method switching control parameter
created: 2014-04-25
creator: AZ
definition: Key parameter of the 'maximal timestep method' [http://www.biomodels.net/kisao/KISAO#KISAO_0000468]. If Gillespie [http://www.biomodels.net/kisao/KISAO#KISAO_0000027] waiting time is longer than maximal timestep, slow reaction is not fired and tau-leap [http://www.biomodels.net/kisao/KISAO#KISAO_0000039] step is executed for fast reactions. Otherwise, slow reaction is fired and tau-leap [http://www.biomodels.net/kisao/KISAO#KISAO_0000039] is executed with shorter time step.

Axiom
annotated source: maximal timestep
annotated property: seeAlso
annotated target: http://identifiers.org/pubmed/14990466
comment: Puchalka J, Kierzek AM. Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys J. 2004 Mar;86(3):1357-72.

optimization algorithm
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has characteristic
  some values from: mathematical system
created: 2015-04-23
creator: AZ
is organizational: true
alternative label: optimization method
definition: An optimization algorithm tries to find the minumum or maximum of an arbitrary function. It takes a function of one or several variables and determines the values for the variables so that the function value is optimal.

Axiom
annotated source: optimization algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0691102872
comment: Brinkhuis J, Tikhomirov V. Optimization: Insights and Applications Princeton Series in Applied Mathematics (illustrated), Princeton University Press, 2005.

local optimization algorithm
type: Class
subclass of: optimization algorithm
disjoint with: global optimization algorithm
created: 2015-04-23
creator: AZ
alternative label: local optimiation method
definition: A local optimization algorithm is an optimisation algorithm [http://www.biomodels.net/kisao/KISAO#KISAO_0000470] that only finds a local optimum of a function. If several optima exist for the function, it usually depends on the starting values for the variables which optimum is found.

global optimization algorithm
type: Class
subclass of: optimization algorithm
subclass of: Restriction
  on property: has parameter
  some values from: seed
created: 2015-04-23
creator: AZ
alternative label: global optimization method
definition: A global optimization algorithm is an optimization algorithm [http://www.biomodels.net/kisao/KISAO#KISAO_0000470] that tries to find the global optimum of a function. If a function has several minima/maxima with in the allowed range of variable values, the global minimum/maximum is the one with the smallest/largest function value.

Bayesian inference algorithm
type: Class
subclass of: modelling and simulation algorithm
created: 2015-04-23
creator: AZ
definition: A bayesian inference algorithm calculates a posterior probability distribution from a prior probability distribution and some additional evidence in the form of a likelyhood function.

Axiom
annotated source: Bayesian inference algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/111803144X
comment: George E. P. Box, George C. Tiao. Bayesian Inference in Statistical Analysis, Volume 40 of Wiley Classics Library. John Wiley & Sons (reprint, revised), 2011.

integration method
type: Class
subclass of: modelling and simulation algorithm parameter
created: 2015-09-10
creator: AZ
is implemented in: http://identifiers.org/biosimulators/opencor
definition: the integration method used by the solver

Axiom
annotated source: integration method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/opencor
comment: OpenCOR @end

Axiom
annotated source: integration method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.3389/fphys.2015.00026
comment: Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26

iteration type
type: Class
subclass of: modelling and simulation algorithm parameter
created: 2015-09-10
creator: AZ
is implemented in: http://identifiers.org/biosimulators/opencor
comment: Requested in https://sourceforge.net/p/kisao/feature-requests/12/
definition: the type of iteration used by the solver

Axiom
annotated source: iteration type
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/opencor
comment: OpenCOR @end

Axiom
annotated source: iteration type
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.3389/fphys.2015.00026
comment: Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26

linear solver
type: Class
subclass of: modelling and simulation algorithm parameter
created: 2015-09-10
creator: AZ
is implemented in: http://identifiers.org/biosimulators/opencor
comment: Requested in https://sourceforge.net/p/kisao/feature-requests/12/
definition: the linear solver used by the solver during a Newton iteration

Axiom
annotated source: linear solver
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/opencor
comment: OpenCOR @end

Axiom
annotated source: linear solver
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.3389/fphys.2015.00026
comment: Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26

preconditioner
type: Class
subclass of: modelling and simulation algorithm parameter
created: 2015-09-10
creator: AZ
is implemented in: http://identifiers.org/biosimulators/opencor
comment: Requested in https://sourceforge.net/p/kisao/feature-requests/12/
definition: the preconditioner, if any, used by the solver when using a GMRES, BiCGStab or TFQMR linear solver during a Newton iteration.

Axiom
annotated source: preconditioner
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/opencor
comment: OpenCOR @end

Axiom
annotated source: preconditioner
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.3389/fphys.2015.00026
comment: Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26

upper half-bandwidth
type: Class
subclass of: half-bandwith parameter
subclass of: Restriction
  on property: has type
  some values from: integer
disjoint with: lower half-bandwidth
created: 2015-09-10
creator: AZ
is implemented in: http://identifiers.org/biosimulators/opencor
comment: Requested in https://sourceforge.net/p/kisao/feature-requests/12/
definition: the upper half-bandwidth value used by the Banded linear solver or preconditioner (a value between 0 and n-1 with n the number of ODEs/DAEs in the model).

Axiom
annotated source: upper half-bandwidth
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/opencor
comment: OpenCOR @end

Axiom
annotated source: upper half-bandwidth
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.3389/fphys.2015.00026
comment: Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26

lower half-bandwidth
type: Class
subclass of: half-bandwith parameter
subclass of: Restriction
  on property: has type
  some values from: integer
created: 2015-09-10
creator: AZ
is implemented in: http://identifiers.org/biosimulators/opencor
comment: Requested in https://sourceforge.net/p/kisao/feature-requests/12/
definition: the lower half-bandwidth value used by the Banded linear solver or preconditioner (a value between 0 and n-1 with n the number of ODEs/DAEs in the model).

Axiom
annotated source: lower half-bandwidth
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/opencor
comment: OpenCOR @end

Axiom
annotated source: lower half-bandwidth
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.3389/fphys.2015.00026
comment: Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26

interpolate solution
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: has type
  some values from: boolean
created: 2015-09-10
creator: AZ
is implemented in: http://identifiers.org/biosimulators/opencor
comment: Requested in https://sourceforge.net/p/kisao/feature-requests/12/
definition: whether the solver returns an interpolated solution.

Axiom
annotated source: interpolate solution
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/opencor
comment: OpenCOR @end

Axiom
annotated source: interpolate solution
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.3389/fphys.2015.00026
comment: Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26

half-bandwith parameter
type: Class
subclass of: modelling and simulation algorithm parameter
definition: the parameter related to the half-bandwidth value used by the Banded linear solver or preconditioner.

step size
type: Class
subclass of: error control parameter
created: 2015-09-10
creator: AZ
comment: Requested in https://sourceforge.net/p/kisao/feature-requests/13/
definition: the size of every step of the algorithm

maximum order
type: Class
subclass of: order
subclass of: Restriction
  on property: has type
  some values from: integer
creator: AZ
is implemented in: Roadrunner
definition: Maximum order of method. For example, in Roadrunner it can be used for two parameters that one can set for deterministic runs: 'maximum_bdf_order' and 'maximum_adams_order'.

minimum step size
type: Class
subclass of: error control parameter
subclass of: Restriction
  on property: has type
  some values from: double
creator: AZ
definition: A lower limit, in the units of the bound variable over which a numerical integration is being performed, that a numerical integration algorithm with variable step size should take.

maximum iterations
type: Class
subclass of: granularity control parameter
creator: AZ
alternative label: iteration limit
definition: For algorithms that iterate to a solution (steady state finders in particular), a limit on the number of iterations that should be performed.

minimum damping
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: has type
  some values from: double
is implemented in: Roadrunner
comment: The damping factor is a variable for at least some steady state algorithms: roadrunner allows you to set the minimum value for this.

seed
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: is parameter of
  some values from: Class
    intersection of: modelling and simulation algorithm
    intersection of: Restriction
      on property: has characteristic
      some values from: stochastic system behaviour
alternative label: random seed
definition: Random seed of a stochastic algorithm. Setting it allows one to reproduce their results while running the same algorithm on the same computer.

discrete event simulation algorithm
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: discrete variable
alternative label: DES
definition: Discrete Event Simulation algorithm refers to the simulation of systems whose (countable) discrete states change over time and are event-driven.

Axiom
annotated source: discrete event simulation algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0387333320
comment: C.G. Cassandras & S. Lafortune "Introduction to Discrete Event Systems", Chapt 1 2nd Ed 2008. Springer

asynchronous updating policy
type: Class
subclass of: type of updating policy
disjoint with: synchronous updating policy
definition: An updating policy where all enabled transitions (events) occur independently. Thus a state has as many successors as the number of transitions enabled in this state.

synchronous updating policy
type: Class
subclass of: type of updating policy
definition: An updating policy where all enabled transitions occur simultaneously. Thus a state will have at most one successor.

fully asynchronous updating policy
type: Class
subclass of: asynchronous updating policy
definition: An updating policy where all enabled transitions occur either independently or (partially) simultaneously. (i.e. considering all possible combinations of enabled transitions). Thus a state has as many successors as the number of combinations of transitions enabled in this state.

random asynchronous updating policy
type: Class
subclass of: random updating policy
subclass of: asynchronous updating policy
definition: An updating policy where a single transition is picked randomly from the set of transitions enabled in this state. Thus a state will have at most one successor.

CVODES
type: Class
subclass of: CVODE-like method
subclass of: Restriction
  on property: is similar to
  some values from: CVODE
subclass of: Restriction
  on property: uses
  some values from: KLU
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: stability limit detection flag
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: absolute quadrature tolerance
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: relative quadrature tolerance
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: absolute steady-state tolerance
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: relative steady-state tolerance
is implemented in: SUNDIALS
is implemented in: http://identifiers.org/biosimulators/amici
comment: CVODES is a superset of CVODE [http://identifiers.org/biomodels.kisao/KISAO_0000019] and hence all options available to CVODE (with the exception of the FCVODE interface module) are also available for CVODES. Both integration methods (Adams-Moulton [http://identifiers.org/biomodels.kisao/KISAO_0000280] and BDF [http://identifiers.org/biomodels.kisao/KISAO_0000288]) and the corresponding nonlinear iteration methods, as well as all linear solver and preconditioner modules, are available for the integration of the original ODEs, the sensitivity systems, or the adjoint system.
definition: CVODES is a solver for stiff and nonstiff ODE systems (initial value problem) given in explicit form y’ = f(t,y,p) with sensitivity analysis capabilities (both forward and adjoint modes).

Axiom
annotated source: CVODES
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/amici
comment: AMICI @end

KLU
type: Class
subclass of: modelling and simulation algorithm
created: 2017-01-09
creator: AZ
alternative label: "Clark Kent" LU factorization algorithm
definition: KLU is a software package and an algorithm for solving sparse unsymmetric linear systems of equations that arise in circuit simulation applications. It relies on a permutation to Block Triangular Form (BTF), several methods for finding a fill-reducing ordering (variants of approximate minimum degree and nested dissection), and Gilbert/Peierls’ sparse left-looking LU factorization algorithm to factorize each block. The package is written in C and includes a MATLAB interface.

Axiom
annotated source: KLU
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/1824801.1824814
comment: Davis, Timothy A., and Ekanathan Palamadai Natarajan. "Algorithm 907: KLU, a direct sparse solver for circuit simulation problems." ACM Transactions on Mathematical Software (TOMS) 37.3 (2010): 36.

number of runs
type: Class
subclass of: modelling and simulation algorithm parameter
created: 2017-07-18
creator: AZ
comment: Requested in https://sourceforge.net/p/kisao/feature-requests/31/
definition: The number of runs that a simulation should perform. Typically used to specify the number of runs for a stochastic simulation.

dynamic flux balance analysis
type: Class
subclass of: hybrid method
subclass of: flux balance method
subclass of: Restriction
  on property: has characteristic
  some values from: Class
    intersection of: ordinary differential equation problem
    intersection of: flux balance problem
subclass of: Restriction
  on property: is hybrid of
  some values from: flux balance analysis
created: 2017-09-12
creator: AZ
is organizational: true
comment: Ticket 32
alternative label: DFBA
definition: Dynamic flux balance analysis (DFBA) enables the simulation of dynamic biological systems by assuming organisms reach steady state rapidly in response to changes in the extracellular environment. DFBA couples flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model approaches with dynamic model approaches.

Axiom
annotated source: dynamic flux balance analysis
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/s12859-014-0409-8
comment: DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis. Gomez JA, Höffner K, Barton PI. BMC Bioinformatics. 2014 Dec 18;15:409.

SOA-DFBA
type: Class
subclass of: dynamic flux balance analysis
subclass of: Restriction
  on property: uses
  some values from: Euler forward method
created: 2017-09-12
creator: AZ
is implemented in: DFBAlab
comment: Ticket 32
alternative label: SOA
alternative label: static optimization approach dynamic flux balance analysis
definition: Dynamic Flux Balance Analysis (DFBA) [http://identifiers.org/biomodels.kisao/KISAO_0000499] couples flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model approaches with dynamic model approaches. The static optimization approach (SOA) uses the Euler forward method [http://identifiers.org/biomodels.kisao/KISAO_0000030], solving the embedded LPs at each time step. The FBA fluxes are assumed to be constant during the time step.

Axiom
annotated source: SOA-DFBA
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/s12859-014-0409-8
comment: DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis. Gomez JA, Höffner K, Barton PI. BMC Bioinformatics. 2014 Dec 18;15:409.

DOA-DFBA
type: Class
subclass of: dynamic flux balance analysis
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: linearity of equation
created: 2017-09-12
creator: AZ
is implemented in: DFBAlab
comment: Ticket 32
alternative label: DOA
alternative label: dynamic optimization approach dynamic flux balance analysis
definition: Dynamic Flux Balance Analysis (DFBA) [http://identifiers.org/biomodels.kisao/KISAO_0000499] couples flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model approaches with dynamic model approaches. The dynamic optimization approach (DOA) discretizes the time horizon and optimizes simultaneously over the entire time period of interest by solving a nonlinear programming problem (NLP).

Axiom
annotated source: DOA-DFBA
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/s12859-014-0409-8
comment: DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis. Gomez JA, Höffner K, Barton PI. BMC Bioinformatics. 2014 Dec 18;15:409.

DA-DFBA
type: Class
subclass of: dynamic flux balance analysis
created: 2017-09-12
creator: AZ
is implemented in: DFBAlab
comment: Ticket 32
alternative label: DA
alternative label: direct approach dynamics flux balance analysis
definition: Dynamic Flux Balance Analysis (DFBA) [http://identifiers.org/biomodels.kisao/KISAO_0000499] couples flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model approaches with dynamic model approaches. The direct approach (DA) includes the LP solver in the right-hand side evaluator for the ordinary differential equations (ODEs) and takes advantage of reliable implicit ODE integrators with adaptive step size for error control.

Axiom
annotated source: DA-DFBA
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/s12859-014-0409-8
comment: DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis. Gomez JA, Höffner K, Barton PI. BMC Bioinformatics. 2014 Dec 18;15:409.

simulated annealing
type: Class
subclass of: global optimization algorithm
subclass of: Restriction
  on property: has parameter
  some values from: absolute tolerance
subclass of: Restriction
  on property: has parameter
  some values from: start temperature
subclass of: Restriction
  on property: has parameter
  some values from: cooling factor
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
definition: Simulated annealing is an optimization algorithm first proposed by Kirkpatrick et al. and was inspired by statistical mechanics and the way in which perfect crystals are formed. Perfect crystals are formed by first melting the substance of interest, and then cooling it very slowly. At large temperatures the particles vibrate with wide amplitude and this allows a search for global optimum. As the temperature decreases so do the vibrations until the system settles to the global optimum (the perfect crystal). The simulated annealing optimization algorithm uses a similar concept: the objective function is considered a measure of the energy of the system and this is maintained constant for a certain number of iterations (a temperature cycle). In each iteration, the parameters are changed to a nearby location in parameter space and the new objective function value calculated; if it decreased, then the new state is accepted, if it increased then the new state is accepted with a probability that follows a Boltzmann distribution (higher temperature means higher probability of accepting the new state). After a fixed number of iterations, the stopping criterion is checked; if it is not time to stop, then the system's temperature is reduced and the algorithm continues. Simulated annealing is a stochastic algorithm that is guaranteed to converge if ran for an infinite number of iterations. It is one of the most robust global optimization algorithms, although it is also one of the slowest. (Be warned that simulated annealing can run for hours or even days!).

Axiom
annotated source: simulated annealing
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: simulated annealing
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1126/science.220.4598.671
comment: S. Kirkpatrick, J., C.D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science. 220. 671 - 680. 1983.

random search
type: Class
subclass of: global optimization algorithm
subclass of: Restriction
  on property: has parameter
  some values from: maximum iterations
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
definition: Random search is an optimization method that attempts to find the optimum by testing the objective function's value on a series of combinations of random values of the adjustable parameters. The random values are generated complying with any boundaries selected by the user, furthermore, any combinations of parameter values that do not fulfill constraints on the variables are excluded. This means that the method is capable of handling bounds on the adjustable parameters and fulfilling constraints. For infinite number of iterations this method is guaranteed to find the global optimum of the objective function. In general one is interested in processing a very large number of iterations.

Axiom
annotated source: random search
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

particle swarm
type: Class
subclass of: global optimization algorithm
subclass of: Restriction
  on property: has parameter
  some values from: maximum iterations
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
definition: The particle swarm optimization method suggested by Kennedy and Eberhart is inspired by a flock of birds or a school of fish searching for food. Each particle has a position Xi and a velocity Vi in the parameter space. Additionally, it remembers its best achieved objective value O and position Mi. Dependent on its own information and the position of its best neighbor (a random subset of particles of the swarm) a new velocity is calculated. With this information the position is updated.

Axiom
annotated source: particle swarm
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: particle swarm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1109/ICNN.1995.488968
comment: J. Kennedy and R. Eberhart. Particle Swarm Optimization. Proceedings of the Fourth IEEE International Conference on Neural Networks, Perth, Australia. 1942 - 1948. 1995.

genetic algorithm
type: Class
subclass of: evolutionary algorithm
disjoint with: evolutionary programming
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
alternative label: GA
definition: The genetic algorithm (GA) is a computational technique that mimics evolution and is based on reproduction and selection. A GA is composed of individuals that reproduce and compete, each one is a potential solution to the (optimization) problem and is represented by a "genome" where each gene corresponds to one adjustable parameter. At each generation of the GA, each individual is paired with one other at random for reproduction. Two offspring are produced by combining their genomes and allowing for "cross-over", i.e., the two new individuals have genomes that are formed from a combination of the genomes of their parents. Also each new gene might have mutated, i.e. the parameter value might have changed slightly. At the end of the generation, the algorithm has double the number of individuals. Then each of the individuals is confronted with a number of others to count how many does it outperform (the number of wins is the number of these competitors that represent worse solutions than itself). All the individuals are ranked by their number of wins, and the population is again reduced to the original number of individuals by eliminating those which have worse fitness (solutions).

Axiom
annotated source: genetic algorithm
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: genetic algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/9780750308953
comment: T. Bäck, D.B. Fogel, and Z. Michalewicz. Handbook of evolutionary computation. Oxford: IOP Publishing/Oxford University Press. 1997.

genetic algorithm SR
type: Class
subclass of: genetic algorithm
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
alternative label: genetic algorithm with stochastic ranking

Axiom
annotated source: genetic algorithm SR
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: genetic algorithm SR
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1109/4235.873238
comment: T. Runarsson and X. Yao. Stochastic ranking for constrained evolutionary optimization. EEE Transactions on Evolutionary Computation. 4. 284 - 294. 2000.

evolutionary programming
type: Class
subclass of: evolutionary algorithm
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
alternative label: EP
definition: Evolutionary programming (EP) is a computational technique that mimics evolution and is based on reproduction and selection. An EP algorithm is composed of individuals that reproduce and compete, each one is a potential solution to the (optimization) problem and is represented by a "genome" where each gene corresponds to one adjustable parameter. At each generation of the EP, each individual reproduces asexually, i.e. divides into two individuals. One of these contains exactly the same "genome" as the parent while the other suffers some mutations (the parameter values of each gene change slightly). At the end of the generation, the algorithm has double the number of individuals. Then each of the individuals is confronted with a number of others to count how many does it outperform (the number of wins is the number of these competitors that represent worse solutions than itself). All the individuals are ranked by their number of wins, and the population is again reduced to the original number of individuals by eliminating those which have worse fitness (solutions).

Axiom
annotated source: evolutionary programming
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: evolutionary programming
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/9780750308953
comment: T. Bäck, D.B. Fogel, and Z. Michalewicz. Handbook of evolutionary computation. Oxford: IOP Publishing/Oxford University Press. 1997.

evolutionary strategy
type: Class
subclass of: evolutionary programming
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
alternative label: SRES
alternative label: evolutionary strategies with stochastic ranking
definition: Evolutionary Strategies with Stochastic Ranking (SRES) is similar to Evolutionary Programming. However, a parent has multiple offsprings during each generation. Each offspring will contain a recombination of genes with another parent and additional mutations. The algorithm assures that each parameter value will be within its boundaries. But constraints to the solutions may be violated.

Axiom
annotated source: evolutionary strategy
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: evolutionary strategy
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1109/4235.873238
comment: T. Runarsson and X. Yao. Stochastic ranking for constrained evolutionary optimization. EEE Transactions on Evolutionary Computation. 4. 284 - 294. 2000.

truncated Newton
type: Class
subclass of: local optimization algorithm
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
definition: The Truncated Newton method is a sophisticated variant of the Newton optimization method. The Newton optimization method searches for the minimum of a nonlinear function by following descent directions determined from the function's first and second partial derivatives. The Truncated Newton method does an incomplete (truncated) solution of a system of linear equations to calculate the Newton direction. This means that the actual direction chosen for the descent is between the steepest descent direction and the true Newton direction.

Axiom
annotated source: truncated Newton
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: truncated Newton
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0122839528
comment: P.E. Gill, W. Murray, and M.H. Wright. Practical Optimization. London, Academic Press. 1981.

steepest descent
type: Class
subclass of: local optimization algorithm
subclass of: Restriction
  on property: has parameter
  some values from: relative tolerance
subclass of: Restriction
  on property: has parameter
  some values from: maximum iterations
created: 2019-01-18
creator: AZ
definition: Steepest descent is an optimization method that follows the direction of steepest descent on the hyper-surface of the objective function to find a local minimum. The direction of steepest descent is defined by the negative of the gradient of the objective function.

Axiom
annotated source: steepest descent
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1109/ACSSC.1991.186507
comment: D.B. Fogel, L.J. Fogel, and J.W. Atmar. Meta-evolutionary programming. 25th Asiloma Conference on Signals, Systems and Computers. IEEE Computer Society, Asilomar . 540 - 545. 1992.

praxis
type: Class
subclass of: local optimization algorithm
subclass of: Restriction
  on property: has parameter
  some values from: relative tolerance
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
definition: Praxis is a direct search method that searches for the minimum of a nonlinear function without requiring (or attempting to calculate) derivatives of that function. Praxis was developed by Brent after the method proposed by Powell. The inspiration for Praxis was the well-known method of minimising each adjustable parameter (direction) at a time - the principal axes method. In Praxis directions are chosen that do not coincide with the principal axes, in fact if the objective function is quadratic then these will be conjugate directions, assuring a fast convergence rate.

Axiom
annotated source: praxis
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: praxis
annotated property: seeAlso
annotated target: http://identifiers.org/isbn/0486419983
comment: P.R. Brent. A new algorithm for minimizing a function of several variables without calculating derivatives. In Algorithms for minimization without derivatives, (Englewood Cliffs, NJ: Prentice-Hall, Inc.). 117 - 167. 1973.

NL2SOL
type: Class
subclass of: local optimization algorithm
subclass of: Restriction
  on property: has parameter
  some values from: maximum iterations
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
alternative label: adaptive nonlinear least-squares algorithm
definition: The NL2SOL method is based on an adaptive nonlinear least-squares algorithm, devised by Dennis and colleagues. For problems with large number of residuals, this algorithm is known to be more reliable than Gauss-Newton or Levenberg-Marquardt method and more efficient than the secant or variable metric algorithms that are intended for general function minimization.

Axiom
annotated source: NL2SOL
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: NL2SOL
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/355958.355966
comment: J. E. Dennis, D. M. Gay, and R. E. Welsch. An adaptive nonlinear least-squares algorithm. ACM Trans. Math. Softw.. 7(3). 348 - 368. 1981.

Nelder-Mead
type: Class
subclass of: local optimization algorithm
subclass of: Restriction
  on property: has parameter
  some values from: absolute tolerance
subclass of: Restriction
  on property: has parameter
  some values from: maximum iterations
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
alternative label: simplex method
definition: This method also known as the simplex method is due to Nelder and Mead. A simplex is a polytope of N+1 vertices in N dimensions. The objective function is evaluated at each vertex. Dependent on these calculated values a new simplex is constructed. The simplest step is to replace the worst point with a point reflected through the centroid of the remaining N points. If this point is better than the best current point, then we can try stretching exponentially out along this line. On the other hand, if this new point isn't much better than the previous value then we are stepping across a valley, so we shrink the simplex towards the best point.

Axiom
annotated source: Nelder-Mead
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: Nelder-Mead
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1093/comjnl/7.4.308
comment: J. A. Nelder and R. Mead. A simplex method for function minimization. Computer Journal. 7. 308 - 313. 1965.

Levenberg-Marquardt
type: Class
subclass of: local optimization algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: hybridity
subclass of: Restriction
  on property: has parameter
  some values from: relative tolerance
subclass of: Restriction
  on property: has parameter
  some values from: maximum iterations
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
definition: Levenberg-Marquardt is a gradient descent method. It is a hybrid between the steepest descent and the Newton methods. Levenberg first suggested an improvement to the Newton method in order to make it more robust, i.e. to overcome the problem of non-convergence. His suggestion was to add a factor to the diagonal elements of the Hessian matrix of second derivatives when not close to the minimum (this can be judged by how positive definite the matrix is). The effect when this factor is large compared to the elements of Hessian is that the method then becomes the steepest descent method. Later Marquardt suggested that the factor should be multiplicative rather than additive and also defined a heuristic to make this factor increase or decrease. The method known as Levenberg-Marquardt is thus an adaptive method that effectively changes between the steepest descent to the Newton method.

Axiom
annotated source: Levenberg-Marquardt
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: Levenberg-Marquardt
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1090/qam/10666
comment: K. Levenberg. A method for the solution of certain nonlinear problems in least squares. Quart. Appl. Math.. 2. 164 - 168. 1944.

Axiom
annotated source: Levenberg-Marquardt
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0111030
comment: D.W. Marquardt. An algorithm for least squares estimation of nonlinear parameters. SIAM Journal. 11. 431 - 441. 1963.

Hooke&Jeeves
type: Class
subclass of: local optimization algorithm
subclass of: Restriction
  on property: has parameter
  some values from: relative tolerance
subclass of: Restriction
  on property: has parameter
  some values from: maximum iterations
created: 2019-01-18
creator: AZ
is implemented in: http://identifiers.org/biosimulators/copasi
alternative label: Hooke and Jeeves method
alternative label: Hooke-Jeeves method
alternative label: method of Hooke and Jeeves
definition: The method of Hooke and Jeeves is a direct search algorithm that searches for the minimum of a nonlinear function without requiring (or attempting to calculate) derivatives of the function. Instead it is based on a heuristic that suggests a descent direction using the values of the function calculated in a number of previous iterations.

Axiom
annotated source: Hooke&Jeeves
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: Hooke&Jeeves
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/321062.321069
comment: R. Hooke and T. A. Jeeves. "Direct search" solution of numerical and statistical problems. Journal of the Association for Computing Machinery. 8. 212 - 229. 1961.

number of generations
type: Class
subclass of: evolutionary algorithm parameter
subclass of: Restriction
  on property: has type
  qualified cardinality: 1
  on data range: integer
disjoint with: population size
created: 2019-01-18
creator: AZ
definition: The parameter is a positive integer value to determine the number of generations the evolutionary algorithm shall evolve the population.

evolutionary algorithm parameter
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: is parameter of
  some values from: evolutionary algorithm
created: 2019-01-18
creator: AZ

population size
type: Class
subclass of: evolutionary algorithm parameter
subclass of: Restriction
  on property: has type
  some values from: integer
created: 2019-01-18
creator: AZ
definition: The parameter is a positive integer value to determine the size of the population, i.e., the number of individuals that survive after each generation.

evolutionary algorithm
type: Class
subclass of: global optimization algorithm
subclass of: Restriction
  on property: has parameter
  some values from: number of generations
subclass of: Restriction
  on property: has parameter
  some values from: population size
created: 2019-01-18
creator: AZ
is organizational: true
definition: An optimisation algorithm that mimics evolution and is based on reproduction and selection.

simulated annealing parameter
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: is parameter of
  some values from: simulated annealing
created: 2019-01-18
creator: AZ
is organizational: true

start temperature
type: Class
subclass of: simulated annealing parameter
disjoint with: cooling factor
created: 2019-01-18
creator: AZ
definition: Initial temperature of the system. The higher the temperature, the larger the probability that a global optimum is found. Note that the temperature should be very high in the beginning of the method (the system should be above the "melting" temperature). This value has the same units as the objective function, so what represents "high" is different from problem to problem.

cooling factor
type: Class
subclass of: simulated annealing parameter
subclass of: Restriction
  on property: has type
  some values from: double
created: 2019-01-18
creator: AZ
definition: Rate by which the temperature is reduced from one cycle to the next, given by the formula: Tnew=Told*"Cooling Factor". The simulated annealing algorithm works best if the temperature is reduced at a slow rate, so this value should be close to 1.

partitioned leaping method
type: Class
subclass of: tau-leaping method
subclass of: Restriction
  on property: has parameter
  some values from: seed
created: 2020-05-29
creator: AZ
is implemented in: http://identifiers.org/biosimulators/bionetgen
definition: Multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exact-stochastic and "leaping" methodologies into a single partitioned leaping algorithmic framework. The technique correctly accounts for stochastic noise at significantly reduced computational cost, requires the definition of only three modelindependent parameters and is particularly well-suited for simulating systems containing widely disparate species populations.

Axiom
annotated source: partitioned leaping method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/bionetgen
comment: BioNetGen @end

Axiom
annotated source: partitioned leaping method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.2354085
comment: Harris LA, Clancy P. A "partitioned leaping" approach for multiscale modeling of chemical reaction dynamics. J Chem Phys. 125 (14), 144107 (2006).

stop condition
type: Class
subclass of: modelling and simulation algorithm parameter
created: 2020-05-29
creator: AZ
is implemented in: http://identifiers.org/biosimulators/bionetgen
definition: A condition upon which a simulation should terminate.

Axiom
annotated source: stop condition
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/bionetgen
comment: BioNetGen @end

flux variability analysis
type: Class
subclass of: flux balance method
subclass of: general steady state method
subclass of: Restriction
  on property: has parameter
  some values from: parallelism
subclass of: Restriction
  on property: has parameter
  some values from: fraction of optimum
subclass of: Restriction
  on property: has parameter
  some values from: loopless
subclass of: Restriction
  on property: has parameter
  some values from: reactions
subclass of: Restriction
  on property: has parameter
  some values from: nested algorithm
created: 2020-08-11
creator: AZ
is implemented in: http://identifiers.org/biosimulators/cobrapy
alternative label: FVA
definition: Method for determining the minimum and maximum flux of each reaction that satisfies the flux constraints of the flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model.

Axiom
annotated source: flux variability analysis
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cobrapy
comment: COBRApy @end

Axiom
annotated source: flux variability analysis
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/j.ymben.2003.09.002
comment: Mahadevan R, Schilling CH. The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metab Eng. 2003;5(4):264-276.

geometric flux balance analysis
type: Class
subclass of: flux balance analysis
subclass of: Restriction
  on property: has parameter
  some values from: parallelism
created: 2020-08-11
creator: AZ
is implemented in: http://identifiers.org/biosimulators/cobrapy
alternative label: gFBA
alternative label: geometric FBA
definition: Method for determining the central flux distribution among all flux distributions that satisfy the constraints of the flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model.

Axiom
annotated source: geometric flux balance analysis
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cobrapy
comment: COBRApy @end

Axiom
annotated source: geometric flux balance analysis
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/j.jtbi.2009.01.027
comment: Smallbone K, Simeonidis E. Flux balance analysis: a geometric perspective. J Theor Biol. 2009;258(2):311-315.

parsimonious enzyme usage flux balance analysis (minimum sum of absolute fluxes)
type: Class
subclass of: parsimonius flux balance analysis
subclass of: Restriction
  on property: has parameter
  some values from: fraction of optimum
subclass of: Restriction
  on property: has parameter
  some values from: pFBA factor
disjoint with: parsimonius flux balance analysis (minimum number of active fluxes)
created: 2020-08-11
creator: AZ
is implemented in: http://identifiers.org/biosimulators/cbmpy
is implemented in: http://identifiers.org/biosimulators/cobrapy
alternative label: pFBA
alternative label: parsimonious FBA
alternative label: parsimonious flux balance analysis
definition: Method for determining the smallest flux distribution among all flux distributions that satisfy the constraints of the flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model.

Axiom
annotated source: parsimonious enzyme usage flux balance analysis (minimum sum of absolute fluxes)
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cbmpy
comment: CBMPy @end

Axiom
annotated source: parsimonious enzyme usage flux balance analysis (minimum sum of absolute fluxes)
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cobrapy
comment: COBRApy @end

Axiom
annotated source: parsimonious enzyme usage flux balance analysis (minimum sum of absolute fluxes)
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1038/msb.2010.47
comment: Lewis NE, Hixson KK, Conrad TM, et al. Omic data from evolved E. coli are consistent with computed optimal growth from genome-scale models. Mol Syst Biol. 2010;6:390.

parallelism
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: is parameter of
  some values from: flux variability analysis
subclass of: Restriction
  on property: is parameter of
  some values from: geometric flux balance analysis
subclass of: Restriction
  on property: has type
  some values from: integer
definition: Number of parallel processes to use.

fraction of optimum
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: is parameter of
  some values from: flux variability analysis
subclass of: Restriction
  on property: is parameter of
  some values from: parsimonious enzyme usage flux balance analysis (minimum sum of absolute fluxes)
subclass of: Restriction
  on property: has type
  some values from: float
definition: Fraction of the optimum solution which must be maintained.

loopless
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: is parameter of
  some values from: flux variability analysis
subclass of: Restriction
  on property: has type
  some values from: boolean
definition: Whether to return only loopless flux solutions.

pFBA factor
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: is parameter of
  some values from: parsimonious enzyme usage flux balance analysis (minimum sum of absolute fluxes)
subclass of: Restriction
  on property: has type
  some values from: float
definition: Maximum permissible sum of absolute fluxes.

reactions
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: is parameter of
  some values from: flux variability analysis
definition: FVA algorithm [http://www.biomodels.net/kisao/KISAO#KISAO_0000526] parameter: reactions to compute the variablity of.

VODE
type: Class
subclass of: CVODE-like method
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: correction step should use internally generated full Jacobian
subclass of: Restriction
  on property: is similar to
  max qualified cardinality: 1
  on class: CVODE
created: 2020-10-29
creator: JRK
is implemented in: Odespy
is implemented in: SciPy
is implemented in: deSolve
is implemented in: http://identifiers.org/biosimulators/gillespy2
alternative label: DVODE
alternative label: Real-valued Variable-coefficient Ordinary Differential Equation solver, with fixed-leading-coefficient implementation
alternative label: real-valued variable-coefficient ordinary differential equation solver, with fixed-leading-coefficient implementation
definition: VODE provides implicit Adams method (for non-stiff problems) and a method based on backward differentiation formulas (BDF) (for stiff problems).

Axiom
annotated source: VODE
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/gillespy2
comment: GillesPy2 @end

Axiom
annotated source: VODE
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0910062
comment: Peter N. Brown, George D. Byrne & Alan C. Hindmarsh. VODE: A Variable-Coefficient ODE Solver. SIAM J. Sci. and Stat. Comput., 10(5), 1038–1051 (1988).

Axiom
annotated source: VODE
annotated property: altLabel
annotated target: DVODE
comment: RELATED

Axiom
annotated source: VODE
annotated property: altLabel
annotated target: Real-valued Variable-coefficient Ordinary Differential Equation solver, with fixed-leading-coefficient implementation
comment: EXACT

ZVODE
type: Class
subclass of: CVODE-like method
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: correction step should use internally generated full Jacobian
subclass of: Restriction
  on property: is similar to
  max qualified cardinality: 1
  on class: CVODE
created: 2020-10-29
creator: JRK
is implemented in: Odespy
is implemented in: SciPy
is implemented in: deSolve
is implemented in: http://identifiers.org/biosimulators/gillespy2
alternative label: Complex-valued Variable-coefficient Ordinary Differential Equation solver, with fixed-leading-coefficient implementation
alternative label: complex-valued variable-coefficient ordinary differential equation solver, with fixed-leading-coefficient implementation
definition: ZVODE provides implicit Adams method (for non-stiff problems) and a method based on backward differentiation formulas (BDF) (for stiff problems).

Axiom
annotated source: ZVODE
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/gillespy2
comment: GillesPy2 @end

Axiom
annotated source: ZVODE
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0910062
comment: Peter N. Brown, George D. Byrne & Alan C. Hindmarsh. VODE: A Variable-Coefficient ODE Solver. SIAM J. Sci. and Stat. Comput., 10(5), 1038–1051 (1988).

Axiom
annotated source: ZVODE
annotated property: altLabel
annotated target: Complex-valued Variable-coefficient Ordinary Differential Equation solver, with fixed-leading-coefficient implementation
comment: EXACT

explicit Runge-Kutta method of order 3(2)
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2020-10-29
creator: JRK
is implemented in: MATLAB
is implemented in: Octave
is implemented in: Odespy
is implemented in: SciPy
is implemented in: deSolve
is implemented in: http://identifiers.org/biosimulators/gillespy2
alternative label: RK23
definition: RK23 uses the Bogacki-Shampine pair of formulas [1]. The error is controlled assuming accuracy of the second-order method, but steps are taken using the third-order accurate formula (local extrapolation is done). A cubic Hermite polynomial is used for the dense output.

Axiom
annotated source: explicit Runge-Kutta method of order 3(2)
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/gillespy2
comment: GillesPy2 @end

Axiom
annotated source: explicit Runge-Kutta method of order 3(2)
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/0893-9659(89)90079-7
comment: P. Bogacki & L. F. Shampine. A 3(2) pair of Runge - Kutta formulas. Applied Mathematics Letters 2(4), 321-325 (1989).

Axiom
annotated source: explicit Runge-Kutta method of order 3(2)
annotated property: altLabel
annotated target: RK23
comment: EXACT

safety factor on new step selection
type: Class
subclass of: error control parameter
created: 2020-10-29
creator: JRK
is implemented in: JModelica
is implemented in: Odespy
is implemented in: SciPy
is implemented in: http://identifiers.org/biosimulators/gillespy2
alternative label: safe
alternative label: safety

Axiom
annotated source: safety factor on new step selection
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/gillespy2
comment: GillesPy2 @end

Axiom
annotated source: safety factor on new step selection
annotated property: altLabel
annotated target: safe
comment: EXACT

Axiom
annotated source: safety factor on new step selection
annotated property: altLabel
annotated target: safety
comment: EXACT

minimum factor to change step size by
type: Class
subclass of: error control parameter
created: 2020-10-29
creator: JRK
is implemented in: JModelica
is implemented in: Odespy
is implemented in: SciPy
is implemented in: http://identifiers.org/biosimulators/gillespy2
alternative label: dfactor
alternative label: fac1
definition: Minimum factor to increase/decrease step size by in one step. The new step-size is chosen subject to the restriction fac1 <= current step-size / old step-size <= fac2.

Axiom
annotated source: minimum factor to change step size by
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/gillespy2
comment: GillesPy2 @end

Axiom
annotated source: minimum factor to change step size by
annotated property: altLabel
annotated target: dfactor
comment: EXACT

Axiom
annotated source: minimum factor to change step size by
annotated property: altLabel
annotated target: fac1
comment: EXACT

maximum factor to change step size by
type: Class
subclass of: error control parameter
created: 2020-10-29
creator: JRK
is implemented in: JModelica
is implemented in: Odespy
is implemented in: SciPy
is implemented in: http://identifiers.org/biosimulators/gillespy2
alternative label: fac2
alternative label: ifactor
definition: Maximum factor to increase/decrease step size by in one step. The new step-size is chosen subject to the restriction fac1 <= current step-size / old step-size <= fac2.

Axiom
annotated source: maximum factor to change step size by
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/gillespy2
comment: GillesPy2 @end

Axiom
annotated source: maximum factor to change step size by
annotated property: altLabel
annotated target: fac2
comment: EXACT

Axiom
annotated source: maximum factor to change step size by
annotated property: altLabel
annotated target: ifactor
comment: EXACT

beta parameter for stabilized step size control
type: Class
subclass of: error control parameter
subclass of: method switching control parameter
created: 2020-10-29
creator: JRK
is implemented in: JModelica
is implemented in: Odespy
is implemented in: SciPy
is implemented in: http://identifiers.org/biosimulators/gillespy2
alternative label: beta

Axiom
annotated source: beta parameter for stabilized step size control
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/gillespy2
comment: GillesPy2 @end

Axiom
annotated source: beta parameter for stabilized step size control
annotated property: altLabel
annotated target: beta
comment: EXACT

correction step should use internally generated full Jacobian
type: Class
subclass of: method switching control parameter
created: 2020-10-29
creator: JRK
is implemented in: SciPy
is implemented in: http://identifiers.org/biosimulators/gillespy2
alternative label: MF=22
alternative label: with Jacobian
definition: Specifies whether the iteration method of the ODE solver’s correction step is chord iteration with an internally generated full Jacobian or functional iteration with no Jacobian. Option is only considered when the user has not supplied a Jacobian function and has not indicated (by setting either upper or lower band) that the Jacobian is banded.

Axiom
annotated source: correction step should use internally generated full Jacobian
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/gillespy2
comment: GillesPy2 @end

Axiom
annotated source: correction step should use internally generated full Jacobian
annotated property: altLabel
annotated target: MF=22
comment: EXACT

Axiom
annotated source: correction step should use internally generated full Jacobian
annotated property: altLabel
annotated target: with Jacobian
comment: EXACT

stability limit detection flag
type: Class
subclass of: error control parameter
subclass of: method switching control parameter
created: 2020-10-29
creator: JRK
is implemented in: SUNDIALS
definition: Flag to activate stability limit detection.

IDAS
type: Class
subclass of: IDA-like method
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: include sensitivity variables in error control mechanism
created: 2020-10-29
creator: JRK
is implemented in: SUNDIALS
alternative label: implicit differential-algebraic solver with sensitivity analysis
definition: IDAS solves real differential-algebraic systems in N-space, in the general form F(t,y,y')=0, y(t0)=y0, y'(t0)=y'0 with sensitivity analysis.

Axiom
annotated source: IDAS
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/1089014.1089020
comment: SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. Alan C. Hindmarsh, Peter N. Brown, Keith E. Grant, Steven L. Lee, Radu Serban, Dana E. Shumaker & Carol S. Woodward. ACM Transactions on Mathematical Software 31(3), 363-396 (2005).

Axiom
annotated source: IDAS
annotated property: altLabel
annotated target: implicit differential-algebraic solver with sensitivity analysis
comment: EXACT

include sensitivity variables in error control mechanism
type: Class
subclass of: error control parameter
subclass of: method switching control parameter
created: 2020-10-29
creator: JRK
is implemented in: SUNDIALS
alternative label: errconS
definition: Specifies whether sensitivity variables are included or not in the error control mechanism.

Axiom
annotated source: include sensitivity variables in error control mechanism
annotated property: altLabel
annotated target: errconS
comment: EXACT

convex optimization algorithm
type: Class
subclass of: global optimization algorithm
created: 2020-10-29
creator: JRK
definition: Optimization of a convex function over a convex set. Convex optimization is subclass of global optimization because conveness gaurantees that each local optimum is a global optimum.

linear programming
type: Class
subclass of: convex optimization algorithm
created: 2020-10-29
creator: JRK
is implemented in: CPLEX
is implemented in: CVXOPT
is implemented in: ConvOpt
is implemented in: GLPK
is implemented in: Gurobi
is implemented in: MATLAB
is implemented in: Mosek
is implemented in: OptLang
is implemented in: SciPy
is implemented in: SoPlex
is implemented in: XPRESS
alternative label: LP
definition: Method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.

Axiom
annotated source: linear programming
annotated property: altLabel
annotated target: LP
comment: EXACT

quadratic programming
type: Class
subclass of: non-linear programming
created: 2020-10-29
creator: JRK
is implemented in: CPLEX
is implemented in: CVXOPT
is implemented in: ConvOpt
is implemented in: Gurobi
is implemented in: MATLAB
is implemented in: Mosek
is implemented in: OptLang
is implemented in: XPRESS
alternative label: QP
definition: Process of solving a quadratic optimization problem.

Axiom
annotated source: quadratic programming
annotated property: altLabel
annotated target: QP
comment: EXACT

non-linear programming
type: Class
subclass of: global optimization algorithm
created: 2020-10-29
creator: JRK
definition: Process of solving an optimization problem where some of the constraints or the objective function are nonlinear.

simplex method
type: Class
subclass of: linear programming
created: 2020-10-29
creator: JRK
is implemented in: CPLEX
is implemented in: GLPK
is implemented in: Gurobi
alternative label: Dantzig's simplex algorithm
definition: Approach to solving linear programming models by hand using slack variables, tableaus, and pivot variables as a means to finding the optimal solution of an optimization problem.

Axiom
annotated source: simplex method
annotated property: altLabel
annotated target: Dantzig's simplex algorithm
comment: EXACT

primal-dual interior point method
type: Class
subclass of: linear programming
created: 2020-10-29
creator: JRK
is implemented in: CPLEX
is implemented in: GLPK
is implemented in: Gurobi
definition: The Interior Point method approximates the constraints of a linear programming model as a set of boundaries surrounding a region.

Axiom
annotated source: primal-dual interior point method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/0802028
comment: Sanjay Mehrotra. On the Implementation of a Primal-Dual Interior Point Method. SIAM Journal on Optimization, 2(4), 575–601(1991).

optimization method
type: Class
subclass of: method switching control parameter
created: 2020-10-29
creator: JRK
is implemented in: CPLEX
is implemented in: GLPK
is implemented in: Gurobi
definition: Optimization method such as the revised simplex method [http://identifiers.org/biomodels.kisao/KISAO_0000550] or primal-dual interior point method [http://identifiers.org/biomodels.kisao/KISAO_0000551].

optimization solver
type: Class
subclass of: method switching control parameter
created: 2020-10-29
creator: JRK
is implemented in: ConvOpt
is implemented in: OptLang
is implemented in: http://identifiers.org/biosimulators/cbmpy
is implemented in: http://identifiers.org/biosimulators/cobrapy
is implemented in: http://identifiers.org/biosimulators/raven
definition: Optimization solver such as CPLEX, GLPK, or Gurobi.

Axiom
annotated source: optimization solver
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cbmpy
comment: CBMPy @end

Axiom
annotated source: optimization solver
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cobrapy
comment: COBRApy @end

Axiom
annotated source: optimization solver
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/raven
comment: RAVEN @end

parsimonius flux balance analysis (minimum number of active fluxes)
type: Class
subclass of: parsimonius flux balance analysis
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/cbmpy
alternative label: pFBA
alternative label: parsimonious FBA
alternative label: parsimonious flux balance analysis
definition: A technique for selecting a parsimonious flux distribution which has a minimal number of active fluxes.

Axiom
annotated source: parsimonius flux balance analysis (minimum number of active fluxes)
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cbmpy
comment: CBMPy @end

absolute quadrature tolerance
type: Class
subclass of: absolute tolerance
created: 2020-10-29
creator: JRK
is implemented in: SUNDIALS
is implemented in: http://identifiers.org/biosimulators/amici
definition: Absolute error tolerance of the adjoint solution.

Axiom
annotated source: absolute quadrature tolerance
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/amici
comment: AMICI @end

relative quadrature tolerance
type: Class
subclass of: relative tolerance
created: 2020-10-29
creator: JRK
is implemented in: SUNDIALS
is implemented in: http://identifiers.org/biosimulators/amici
definition: Relative error tolerance of the adjoint solution.

Axiom
annotated source: relative quadrature tolerance
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/amici
comment: AMICI @end

absolute steady-state tolerance
type: Class
subclass of: absolute tolerance
created: 2020-10-29
creator: JRK
is implemented in: SUNDIALS
is implemented in: http://identifiers.org/biosimulators/amici
definition: Absolute error tolerance of the steady-state.

Axiom
annotated source: absolute steady-state tolerance
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/amici
comment: AMICI @end

relative steady-state tolerance
type: Class
subclass of: relative tolerance
created: 2020-10-29
creator: JRK
is implemented in: SUNDIALS
is implemented in: http://identifiers.org/biosimulators/amici
definition: Relative error tolerance of the steady-state.

Axiom
annotated source: relative steady-state tolerance
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/amici
comment: AMICI @end

initial step size
type: Class
subclass of: error control parameter
created: 2020-10-29
creator: JRK
is implemented in: SUNDIALS
is implemented in: SciPy
is implemented in: libRoadRunner
is implemented in: http://identifiers.org/biosimulators/copasi
is implemented in: http://identifiers.org/biosimulators/gillespy2
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Initial time step size.

Axiom
annotated source: initial step size
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: initial step size
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/gillespy2
comment: GillesPy2 @end

Axiom
annotated source: initial step size
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium @end

LSODA/LSODAR hybrid method
type: Class
subclass of: Livermore solver
subclass of: Restriction
  on property: is hybrid of
  some values from: Class
    intersection of: LSODA
    intersection of: LSODAR
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/copasi
definition: Automatically use LSODA or LSODAR as apropriate for the given problem. Use LSODA if the problem has no roots. Use LSODAR if the problem has roots.

Axiom
annotated source: LSODA/LSODAR hybrid method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: LSODA/LSODAR hybrid method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/978-1-59745-525-1_2
comment: Pedro Mendes, Stefan Hoops, Sven Sahle, Ralph Gauges, Joseph Dada & Ursula Kummer. Computational modeling of biochemical networks using COPASI. Methods in Molecular Biology 500, 17–59 (2009).

Axiom
annotated source: LSODA/LSODAR hybrid method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/j.jbiotec.2017.06.1200
comment: Frank T. Bergmann, Stefan Hoops, Brian Klahn, Ursula Kummer, Pedro Mendes Jürgen Pahle & Sven Sahle. COPASI and its applications in biotechnology. Journal of Biotechnology 261, 215–220 (2017).

Axiom
annotated source: LSODA/LSODAR hybrid method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1093/bioinformatics/btl485
comment: Stefan Hoops, Sven Sahle, Ralph Gauges, Christine Lee, Jürgen Pahle, Natalia Simus, Mudita Singhal, Liang Xu, Pedro Mendes & Ursula Kummer. COPASI—a complex pathway simulator. Bioinformatics 22 (24), 3067–3074 (2006).

Axiom
annotated source: LSODA/LSODAR hybrid method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.5555/1218112.1218421
comment: Sven Sahle, Ralph Gauges, Jürgen Pahle, Natalia Simus, Ursula Kummer, Stefan Hoops, Christine Lee, Mudita Singhal, Liang Xu & Pedro Mendes. Simulation of biochemical networks using COPASI—a complex pathway simulator. Proceedings of the 2006 Winter Simulation Conference, Monterey, CA, USA, 1698–1706 (2006).

Pahle hybrid Gibson-Bruck Next Reaction method/Runge-Kutta method
type: Class
subclass of: Pahle hybrid method
subclass of: Restriction
  on property: is hybrid of
  some values from: Class
    intersection of: Gibson-Bruck next reaction algorithm
    intersection of: explicit fourth-order Runge-Kutta method
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/copasi
definition: Combines a deterministic numerical integration of ODEs with a stochastic simulation algorithm. The whole biochemical network is partitioned into a deterministic and a stochastic subnet internally. The deterministic subnet contains all reactions in which only species with high particle numbers take part. All reactions with at least one low-numbered species are in the stochastic subnet. The partitioning of the biochemical network can change dynamically during the simulation. The reaction probabilities of the stochastic subnet are approximated as constant during one stochastic step. A 4th-order Runge-Kutta method is used to numerically integrate the deterministic part of the system. The stochastic subnet is simulated by the Gibson-Bruck Next Reaction Method.

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/Runge-Kutta method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/Runge-Kutta method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/978-1-59745-525-1_2
comment: Pedro Mendes, Stefan Hoops, Sven Sahle, Ralph Gauges, Joseph Dada & Ursula Kummer. Computational modeling of biochemical networks using COPASI. Methods in Molecular Biology 500, 17–59 (2009).

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/Runge-Kutta method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/j.jbiotec.2017.06.1200
comment: Frank T. Bergmann, Stefan Hoops, Brian Klahn, Ursula Kummer, Pedro Mendes Jürgen Pahle & Sven Sahle. COPASI and its applications in biotechnology. Journal of Biotechnology 261, 215–220 (2017).

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/Runge-Kutta method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1093/bioinformatics/btl485
comment: Stefan Hoops, Sven Sahle, Ralph Gauges, Christine Lee, Jürgen Pahle, Natalia Simus, Mudita Singhal, Liang Xu, Pedro Mendes & Ursula Kummer. COPASI—a complex pathway simulator. Bioinformatics 22 (24), 3067–3074 (2006).

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/Runge-Kutta method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.5555/1218112.1218421
comment: Sven Sahle, Ralph Gauges, Jürgen Pahle, Natalia Simus, Ursula Kummer, Stefan Hoops, Christine Lee, Mudita Singhal, Liang Xu & Pedro Mendes. Simulation of biochemical networks using COPASI—a complex pathway simulator. Proceedings of the 2006 Winter Simulation Conference, Monterey, CA, USA, 1698–1706 (2006).

Pahle hybrid Gibson-Bruck Next Reaction method/LSODA method
type: Class
subclass of: Pahle hybrid method
subclass of: Restriction
  on property: is hybrid of
  some values from: Class
    intersection of: Gibson-Bruck next reaction algorithm
    intersection of: LSODA
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/copasi
definition: Combines a deterministic numerical integration of ODEs with a stochastic simulation algorithm. The whole biochemical network is partitioned into a deterministic and a stochastic subnet internally. The deterministic subnet contains all reactions in which only species with high particle numbers take part. All reactions with at least one low-numbered species are in the stochastic subnet. The partitioning of the biochemical network can change dynamically during the simulation. The reaction probabilities of the stochastic subnet are approximated as constant during one stochastic step. The deterministic subnet is integrated with LSODA. The stochastic subnet is simulated by the Gibson-Bruck Next Reaction Method.

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/LSODA method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/LSODA method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/978-1-59745-525-1_2
comment: Pedro Mendes, Stefan Hoops, Sven Sahle, Ralph Gauges, Joseph Dada & Ursula Kummer. Computational modeling of biochemical networks using COPASI. Methods in Molecular Biology 500, 17–59 (2009).

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/LSODA method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/j.jbiotec.2017.06.1200
comment: Frank T. Bergmann, Stefan Hoops, Brian Klahn, Ursula Kummer, Pedro Mendes Jürgen Pahle & Sven Sahle. COPASI and its applications in biotechnology. Journal of Biotechnology 261, 215–220 (2017).

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/LSODA method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1093/bioinformatics/btl485
comment: Stefan Hoops, Sven Sahle, Ralph Gauges, Christine Lee, Jürgen Pahle, Natalia Simus, Mudita Singhal, Liang Xu, Pedro Mendes & Ursula Kummer. COPASI—a complex pathway simulator. Bioinformatics 22 (24), 3067–3074 (2006).

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/LSODA method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.5555/1218112.1218421
comment: Sven Sahle, Ralph Gauges, Jürgen Pahle, Natalia Simus, Ursula Kummer, Stefan Hoops, Christine Lee, Mudita Singhal, Liang Xu & Pedro Mendes. Simulation of biochemical networks using COPASI—a complex pathway simulator. Proceedings of the 2006 Winter Simulation Conference, Monterey, CA, USA, 1698–1706 (2006).

Pahle hybrid Gibson-Bruck Next Reaction method/RK-45 method
type: Class
subclass of: Pahle hybrid method
subclass of: Restriction
  on property: is hybrid of
  some values from: Class
    intersection of: Gibson-Bruck next reaction algorithm
    intersection of: Fehlberg method
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/copasi
definition: Combines a deterministic numerical integration of ODEs with a stochastic simulation algorithm. The whole biochemical network is partitioned into a deterministic and a stochastic subnet internally. The deterministic subnet contains all reactions in which only species with high particle numbers take part. All reactions with at least one low-numbered species are in the stochastic subnet. The partitioning of the biochemical network can change dynamically during the simulation. The reaction probabilities of the stochastic subnet are approximated as constant during one stochastic step. The deterministic subnet is integrated with RK-45. The stochastic subnet is simulated by the Gibson-Bruck Next Reaction Method.

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/RK-45 method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/RK-45 method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/978-1-59745-525-1_2
comment: Pedro Mendes, Stefan Hoops, Sven Sahle, Ralph Gauges, Joseph Dada & Ursula Kummer. Computational modeling of biochemical networks using COPASI. Methods in Molecular Biology 500, 17–59 (2009).

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/RK-45 method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1016/j.jbiotec.2017.06.1200
comment: Frank T. Bergmann, Stefan Hoops, Brian Klahn, Ursula Kummer, Pedro Mendes Jürgen Pahle & Sven Sahle. COPASI and its applications in biotechnology. Journal of Biotechnology 261, 215–220 (2017).

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/RK-45 method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1093/bioinformatics/btl485
comment: Stefan Hoops, Sven Sahle, Ralph Gauges, Christine Lee, Jürgen Pahle, Natalia Simus, Mudita Singhal, Liang Xu, Pedro Mendes & Ursula Kummer. COPASI—a complex pathway simulator. Bioinformatics 22 (24), 3067–3074 (2006).

Axiom
annotated source: Pahle hybrid Gibson-Bruck Next Reaction method/RK-45 method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.5555/1218112.1218421
comment: Sven Sahle, Ralph Gauges, Jürgen Pahle, Natalia Simus, Ursula Kummer, Stefan Hoops, Christine Lee, Mudita Singhal, Liang Xu & Pedro Mendes. Simulation of biochemical networks using COPASI—a complex pathway simulator. Proceedings of the 2006 Winter Simulation Conference, Monterey, CA, USA, 1698–1706 (2006).

stochastic Runge-Kutta method
type: Class
subclass of: SDE solver
subclass of: Restriction
  on property: has parameter
  some values from: step size
subclass of: Restriction
  on property: is generalization of
  some values from: Euler method
subclass of: Restriction
  on property: has Runge-Kutta method order
  some values from: integer
created: 2020-10-29
creator: JRK
definition: Technique for the approximate numerical solution of a systems of stochastic differential equations (SDEs). The method is a generalisation of the Runge-Kutta method for ordinary differential equations to stochastic differential equations.

absolute tolerance for root finding
type: Class
subclass of: absolute tolerance
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/copasi
definition: Absolute error tolerance for root finding.

Axiom
annotated source: absolute tolerance for root finding
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

stochastic second order Runge-Kutta method
type: Class
subclass of: stochastic Runge-Kutta method
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: absolute tolerance for root finding
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: force physical correctness
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/copasi
alternative label: RI5
definition: Technique for the second order approximate numerical solution of a systems of stochastic differential equations (SDEs). The method is a generalisation of the Runge-Kutta method for ordinary differential equations to stochastic differential equations.

Axiom
annotated source: stochastic second order Runge-Kutta method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

Axiom
annotated source: stochastic second order Runge-Kutta method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1137/060673308
comment: Andreas Rößler. Second order Runge-Kutta methods for Itô stochastic differential equations. SIAM Journal Numerical Analysis 47 (3), 1713–1738 (2009).

Axiom
annotated source: stochastic second order Runge-Kutta method
annotated property: altLabel
annotated target: RI5
comment: EXACT

force physical correctness
type: Class
subclass of: method switching control parameter
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/copasi
definition: Indicates whether to force physical correctness.

Axiom
annotated source: force physical correctness
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/copasi
comment: COPASI @end

NLEQ1
type: Class
subclass of: Newton-type method
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
alternative label: Newton-type method for solveing non-linear (NL) equations (EQ)
alternative label: numerical solution of nonlinear (NL) equations (EQ) especially designed for numerically sensitive problems
definition: Damped Newton-algorithm with rank strategy for systems of highly nonlinear equations. Global Newton method with error oriented convergence criterion; arbitrary selection of direct linear equation solver.

Axiom
annotated source: NLEQ1
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium @end

Axiom
annotated source: NLEQ1
annotated property: seeAlso
annotated target: http://citeseerx.ist.psu.edu/viewdoc/summary
comment: Ulrich Nowak & Lutz Weimann. A family of Newton codes for systems of highly nonlinear equations - algorithm, implementation, application. Konrad-Zuse-Zentrum für Informationstechnik Berlin 91-10 (1991).

Axiom
annotated source: NLEQ1
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/978-3-642-23899-4
comment: Peter Deuflhard. Newton methods for nonlinear problems. Affine Invariance and Adaptive Algorithms (2004).

NLEQ2
type: Class
subclass of: Newton-type method
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
alternative label: Newton-type method for solveing non-linear (NL) equations (EQ)
alternative label: numerical solution of nonlinear (NL) equations (EQ) especially designed for numerically sensitive problems
definition: Damped Newton-algorithm with rank strategy for systems of highly nonlinear equations. Global Newton method with error oriented convergence criterion; QR-decomposition with subcondition number estimate.

Axiom
annotated source: NLEQ2
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium @end

Axiom
annotated source: NLEQ2
annotated property: seeAlso
annotated target: http://citeseerx.ist.psu.edu/viewdoc/summary
comment: Ulrich Nowak & Lutz Weimann. A family of Newton codes for systems of highly nonlinear equations - algorithm, implementation, application. Konrad-Zuse-Zentrum für Informationstechnik Berlin 91-10 (1991).

Axiom
annotated source: NLEQ2
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1007/978-3-642-23899-4
comment: Peter Deuflhard. Newton methods for nonlinear problems. Affine Invariance and Adaptive Algorithms (2004).

auto reduce tolerances
type: Class
subclass of: error control parameter
subclass of: method switching control parameter
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/pysces
definition: Whether to automatically reduce tolerances.

Axiom
annotated source: auto reduce tolerances
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/pysces
comment: PySCeS @end

absolute tolerance adjustment factor
type: Class
subclass of: tolerance
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/pysces
definition: How much to adjust the absolute tolerance.

Axiom
annotated source: absolute tolerance adjustment factor
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/pysces
comment: PySCeS @end

level of superimposed noise
type: Class
subclass of: modelling and simulation algorithm parameter
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/boolnet
alternative label: noise level
definition: Standard deviation of the Gaussian noise which is added to each prediction.

Axiom
annotated source: level of superimposed noise
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/boolnet
comment: BoolNet @end

Axiom
annotated source: level of superimposed noise
annotated property: altLabel
annotated target: noise level
comment: EXACT

probabilistic logical model simulation method
type: Class
subclass of: Monte Carlo method
subclass of: logical model simulation method
subclass of: Restriction
  on property: has characteristic
  some values from: stochastic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: random updating policy
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/boolnet
definition: Qualitative (logical) models specify the evolution rules of their components. Probabilistic networks allow for specifying more than one transition function per variable/gene. Each of these functions has a probability to be chosen, where the probabilities of all functions for one variable sum up to 1. Transitions are performed synchronously by choosing one transition function for each gene according to their probabilities and applying them to the current state.

Axiom
annotated source: probabilistic logical model simulation method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/boolnet
comment: BoolNet @end

species transition probabilities
type: Class
subclass of: modelling and simulation algorithm parameter
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/boolnet
definition: Probability of each species to be chosen for the next state transition.

Axiom
annotated source: species transition probabilities
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/boolnet
comment: BoolNet @end

hybrid tau-leaping method
type: Class
subclass of: tau-leaping method
subclass of: hybrid method
subclass of: Restriction
  on property: is hybrid of
  some values from: Class
    intersection of: tau-leaping method
    intersection of: Class
      union of: Runge-Kutta based method
      union of: LSODA
      union of: multistep method
created: 2020-11-06
creator: BD
creator: JRK
is implemented in: http://identifiers.org/biosimulators/gillespy2
definition: A continuously coupled hybrid deterministic/stochastic simulation algorithm for biochemical networks. Biochemical species are classified as continuous, discrete, or switch. Tau-leaping is used to simulate stochastic species, and LSODA or another ODE integration method is used to simulate continuous species. Switch species are dynamically classified as either continuous or discrete at each timestep depending on a user defined error tolerance.

Axiom
annotated source: hybrid tau-leaping method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/gillespy2
comment: GillesPy2 @end

Axiom
annotated source: hybrid tau-leaping method
annotated property: seeAlso
annotated target: https://github.com/StochSS/GillesPy2
comment: Drawert B et al. GillesPy2

quadratic MOMA
type: Class
subclass of: MOMA
subclass of: Restriction
  on property: has parameter
  some values from: flux minimization weight
disjoint with: linear MOMA
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/cobratoolbox
is implemented in: http://identifiers.org/biosimulators/optflux
is implemented in: http://identifiers.org/biosimulators/raven
alternative label: MOMA
alternative label: Quadratic Minimization of Metabolic Adjustment
alternative label: minimization of metabolic adjustment
alternative label: quadratic minimization of metabolic adjustment
definition: Minimization of metabolic adjustment (MOMA) is an extension of FBA for the prediction of flux distributions in gene knockouts. MOMA employs quadratic programming to identify the closest point (in terms of its Euclidean distance) in the permissible flux space of the knockout to the wild-type flux vector by solving the optimization problem Min sum((fluxAi - fluxBi)^2) + sum(fluxAi)^(fluxMinimizationWeight) + sum(fluxBi)^(fluxMinimizationWeight)

Axiom
annotated source: quadratic MOMA
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cobratoolbox
comment: COBRA Toolbox @end

Axiom
annotated source: quadratic MOMA
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/optflux
comment: Optflux @end

Axiom
annotated source: quadratic MOMA
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/raven
comment: RAVEN @end

Axiom
annotated source: quadratic MOMA
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1073/pnas.232349399
comment: Segre, D., Vitkup, D., & Church, G. M. (2002). Analysis of optimality in natural and perturbed metabolic networks. Proceedings of the National Academy of Sciences, 99(23), 15112-15117.

Axiom
annotated source: quadratic MOMA
annotated property: altLabel
annotated target: Quadratic Minimization of Metabolic Adjustment
comment: EXACT

flux minimization weight
type: Class
subclass of: modelling and simulation algorithm parameter
created: 2020-10-29
creator: JRK
definition: The degree to which minimization of the sum of fluxes should be taken into account in Minimization of Metabolic Adjustment (MOMA) which solvers the optimization problem Min sum((fluxAi - fluxBi)^2) + sum(fluxAi)^(fluxMinimizationWeight) + sum(fluxBi)^(fluxMinimizationWeight)

nested algorithm
type: Class
subclass of: method switching control parameter
created: 2020-10-29
creator: JRK
alternative label: nested method
alternative label: subalgorithm
definition: A nested algorithm of an algorithm

Axiom
annotated source: nested algorithm
annotated property: altLabel
annotated target: nested method
comment: EXACT

Axiom
annotated source: nested algorithm
annotated property: altLabel
annotated target: subalgorithm
comment: EXACT

linear MOMA
type: Class
subclass of: MOMA
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/cobratoolbox
is implemented in: http://identifiers.org/biosimulators/optflux
alternative label: Linear Minimization of Metabolic Adjustment
alternative label: linear minimization of metabolic adjustment
definition: Linear minimization of metabolic adjustment (MOMA) is an extension of FBA for the prediction of flux distributions in gene knockouts. Linear MOMA employs linear programming to identify the closest point (in terms of its L1 norm) in the permissible flux space of the knockout to the wild-type flux vector by solving the optimization problem Min sum(|fluxAi - fluxBi|)

Axiom
annotated source: linear MOMA
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cobratoolbox
comment: COBRA Toolbox @end

Axiom
annotated source: linear MOMA
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/optflux
comment: Optflux @end

Axiom
annotated source: linear MOMA
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1038/ng.846
comment: Szappanos, B., Kovács, K., Szamecz, B., Honti, F., Costanzo, M., Baryshnikova, A., ... & Andrews, B. J. (2011). An integrated approach to characterize genetic interaction networks in yeast metabolism. Nature genetics, 43(7), 656-662.

Axiom
annotated source: linear MOMA
annotated property: altLabel
annotated target: Linear Minimization of Metabolic Adjustment
comment: EXACT

ROOM
type: Class
subclass of: flux balance method
subclass of: general steady state method
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/cobratoolbox
is implemented in: http://identifiers.org/biosimulators/optflux
alternative label: Regulatory on/off minimization of metabolic flux changes
alternative label: regulatory on/off minimization of metabolic flux changes
definition: Constraint-based algorithm for predicting the metabolic steady state after gene knockouts which aims to minimize the number of significant flux changes (hence on/off) with respect to the wild type.

Axiom
annotated source: ROOM
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cobratoolbox
comment: COBRA Toolbox @end

Axiom
annotated source: ROOM
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/optflux
comment: Optflux @end

Axiom
annotated source: ROOM
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1073/pnas.0406346102
comment: Shlomi, T., Berkman, O., & Ruppin, E. (2005). Regulatory on/off minimization of metabolic flux changes after genetic perturbations. Proceedings of the national academy of sciences, 102(21), 7695-7700.

Axiom
annotated source: ROOM
annotated property: altLabel
annotated target: Regulatory on/off minimization of metabolic flux changes
comment: EXACT

BKMC
type: Class
subclass of: Monte Carlo method
subclass of: probabilistic logical model simulation method
subclass of: Restriction
  on property: has characteristic
  some values from: hybridity
subclass of: Restriction
  on property: has characteristic
  some values from: random updating policy
subclass of: Restriction
  on property: is similar to
  some values from: Gillespie direct algorithm
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/maboss
alternative label: Boolean Kinetic Monte-Carlo
alternative label: Boolean kinetic Monte-Carlo
definition: The Boolean kinetic Monte Carlo method (BKMC) is a natural generalization of the asynchronous Boolean simulation method, with a direct probabilistic interpretation. In the BKMC framework, the dynamics is parameterized by a biological time and the order of update is noisy, which is less strict than priority classes introduced in GINsin. A BKMC model is specified by logical rules as in regular Boolean models but with a more precise information: a numerical rate is added for each transition of each node.

Axiom
annotated source: BKMC
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/maboss
comment: MaBoSS @end

Axiom
annotated source: BKMC
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/1752-0509-6-116
comment: Stoll, G., Viara, E., Barillot, E., & Calzone, L. (2012). Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm. BMC systems biology, 6(1), 1-18.

Axiom
annotated source: BKMC
annotated property: altLabel
annotated target: Boolean Kinetic Monte-Carlo
comment: EXACT

Spatiocyte method
type: Class
subclass of: Smoluchowski equation based method
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/ecell4
definition: Lattice-based stochastic particle simulation method for biochemical reaction and diffusion processes.

Axiom
annotated source: Spatiocyte method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ecell4
comment: E-Cell 4 @end

Axiom
annotated source: Spatiocyte method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1038/npre.2009.3845.1
comment: Arjunan, S., & Tomita, M. (2009). A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation. Nature Precedings, 1-1.

minimum order
type: Class
subclass of: order
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/jsim
definition: Minimum order of method.

Axiom
annotated source: minimum order
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/jsim
comment: JSim @end

initial order
type: Class
subclass of: order
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/jsim
definition: Initial order of method.

Axiom
annotated source: initial order
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/jsim
comment: JSim @end

TOMS731
type: Class
subclass of: partial differential equation discretization method
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/jsim
definition: Moving-grid interface for systems of one-dimensional time-dependent partial differential equations.

Axiom
annotated source: TOMS731
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/jsim
comment: JSim @end

Axiom
annotated source: TOMS731
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1145/178365.178391
comment: Blom, J. G., & Zegeling, P. A. (1994). Algorithm 731: a moving-grid interface for systems of one-dimensional time-dependent partial differential equations. ACM Transactions on Mathematical Software (TOMS), 20(2), 194-214.

Gibson-Bruck next reaction algorithm with indexed priority queue
type: Class
subclass of: Gibson-Bruck next reaction algorithm
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/sbscl

Axiom
annotated source: Gibson-Bruck next reaction algorithm with indexed priority queue
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/sbscl
comment: SBSCL @end

IMEX
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/biouml
alternative label: Implicit-Explicit Runge-Kutta method
alternative label: implicit-explicit Runge-Kutta method
definition: Method for solving stiff and imaginary ODE problems

Axiom
annotated source: IMEX
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/biouml
comment: BioUML @end

Axiom
annotated source: IMEX
annotated property: altLabel
annotated target: Implicit-Explicit Runge-Kutta method
comment: EXACT

flux sampling
type: Class
subclass of: flux balance method
subclass of: general steady state method
created: 2020-10-29
creator: JRK
is organizational: true
definition: Method for sampling fluxes from the null space of a flux balance analysis model

ACB flux sampling method
type: Class
subclass of: flux sampling
disjoint with: ACHR flux sampling method
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/cobratoolbox
alternative label: Artificial centering boundary flux sampling method
alternative label: artificial centering boundary flux sampling method

Axiom
annotated source: ACB flux sampling method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cobratoolbox
comment: COBRA Toolbox @end

Axiom
annotated source: ACB flux sampling method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1038/s41596-018-0098-2
comment: Heirendt, L., Arreckx, S., Pfau, T., Mendoza, S. N., Richelle, A., Heinken, A., ... & Magnusdóttir, S. (2019). Creation and analysis of biochemical constraint-based models using the COBRA Toolbox v. 3.0. Nature protocols, 14(3), 639-702.

Axiom
annotated source: ACB flux sampling method
annotated property: altLabel
annotated target: Artificial centering boundary flux sampling method
comment: EXACT

ACHR flux sampling method
type: Class
subclass of: flux sampling
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/cobrapy
is implemented in: http://identifiers.org/biosimulators/cobratoolbox
alternative label: artificial centering hit-and-run flux sampling method

Axiom
annotated source: ACHR flux sampling method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cobrapy
comment: COBRApy @end

Axiom
annotated source: ACHR flux sampling method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cobratoolbox
comment: COBRA Toolbox @end

Axiom
annotated source: ACHR flux sampling method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1287/opre.46.1.84
comment: Kaufman, D. E., & Smith, R. L. (1998). Direction choice for accelerated convergence in hit-and-run sampling. Operations Research, 46(1), 84-95.

mdFBA
type: Class
subclass of: flux balance analysis
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/cobratoolbox
alternative label: metabolic dilution flux balance analysis

Axiom
annotated source: mdFBA
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cobratoolbox
comment: COBRA Toolbox @end

Axiom
annotated source: mdFBA
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/gb-2010-11-4-r43
comment: Benyamini, T., Folger, O., Ruppin, E., & Shlomi, T. (2010). Flux balance analysis accounting for metabolite dilution. Genome biology, 11(4), R43.

dynamic rFBA
type: Class
subclass of: rFBA
disjoint with: srFBA
created: 2020-10-29
creator: JRK
is implemented in: http://identifiers.org/biosimulators/cobratoolbox
alternative label: dynamic regulatory flux balance analysis
alternative label: rFBA
alternative label: regulatory flux balance analysis
definition: Method for predicting the dynamics of metabolic fluxes under patterns of the regulation of gene expression

Axiom
annotated source: dynamic rFBA
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/cobratoolbox
comment: COBRA Toolbox @end

Axiom
annotated source: dynamic rFBA
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1006/jtbi.2001.2405
comment: Covert, M. W., Schilling, C. H., & Palsson, B. (2001). Regulation of gene expression in flux balance models of metabolism. Journal of theoretical biology, 213(1), 73-88.

Axiom
annotated source: dynamic rFBA
annotated property: altLabel
annotated target: dynamic regulatory flux balance analysis
comment: EXACT

MOMA
type: Class
subclass of: flux balance method
subclass of: general steady state method
created: 2020-10-29
creator: JRK
is organizational: true
alternative label: Minimization of Metabolic Adjustment
alternative label: minimization of metabolic adjustment
definition: minimization of metabolic adjustment (MOMA) is an extension of FBA for the prediction of flux distributions in gene knockouts. MOMA identifies the closest point in the permissible flux space of the knockout to the wild-type flux vector by solving an optimization problem.

Axiom
annotated source: MOMA
annotated property: altLabel
annotated target: Minimization of Metabolic Adjustment
comment: EXACT

order
type: Class
subclass of: method switching control parameter
created: 2020-10-29
creator: JRK
definition: Order of method

rFBA
type: Class
subclass of: hybrid method
subclass of: flux balance method
created: 2020-10-29
creator: JRK
is organizational: true
alternative label: regulatory flux balance analysis
definition: Method for predicting metabolic fluxes under patterns of the regulation of gene expression

Axiom
annotated source: rFBA
annotated property: altLabel
annotated target: regulatory flux balance analysis
comment: EXACT

srFBA
type: Class
subclass of: flux balance analysis
subclass of: rFBA
created: 2020-10-29
creator: JRK
alternative label: SR-FBA
alternative label: steady-state regulatory flux balance analysis
definition: Method for predicting steady-state metabolic fluxes under patterns of the regulation of gene expression

Axiom
annotated source: srFBA
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1038/msb4100141
comment: Shlomi, T., Eisenberg, Y., Sharan, R., & Ruppin, E. (2007). A genome‐scale computational study of the interplay between transcriptional regulation and metabolism. Molecular systems biology, 3(1), 101.

Axiom
annotated source: srFBA
annotated property: altLabel
annotated target: SR-FBA
comment: EXACT

tolerance
type: Class
subclass of: error control parameter
created: 2020-10-29
creator: JRK
definition: Numeric value specifying the desired tolerance the user wants to achieve. A smaller value means that the prediction is calculated more accurately.

hybrid Gibson - Milstein method
type: Class
subclass of: hybrid method
subclass of: Restriction
  on property: is hybrid of
  some values from: Class
    intersection of: Gibson-Bruck next reaction algorithm
    intersection of: Milstein method
created: 2021-01-13
creator: JRK
creator: MLB
is implemented in: http://identifiers.org/biosimulators/vcell
definition: A hybrid stochastic method partitions the system into subsets of fast and slow reactions and approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the Gibson algorithm. Fixed time step Milstein is used for approximate numerical solution of CLE.

Axiom
annotated source: hybrid Gibson - Milstein method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell

Axiom
annotated source: hybrid Gibson - Milstein method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/1471-2105-7-93
comment: H.Salis, V. Sotiropoulos and Y. Kaznessis,'Multiscale Hy3S: Hybrid stochastic simulation for supercomputers', BMC Bioinformatics 7:93 (2006).

hybrid Gibson - Euler-Maruyama method
type: Class
subclass of: hybrid method
subclass of: Restriction
  on property: is hybrid of
  some values from: Class
    intersection of: Gibson-Bruck next reaction algorithm
    intersection of: Euler-Maruyama method
created: 2021-01-13
creator: JRK
creator: MLB
is implemented in: http://identifiers.org/biosimulators/vcell
definition: A hybrid stochastic method partitions the system into subsets of fast and slow reactions and approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the Gibson algorithm. Fixed time step Milstein is used for approximate numerical solution of CLE.

Axiom
annotated source: hybrid Gibson - Euler-Maruyama method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell

Axiom
annotated source: hybrid Gibson - Euler-Maruyama method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/1471-2105-7-93
comment: H.Salis, V. Sotiropoulos and Y. Kaznessis,'Multiscale Hy3S: Hybrid stochastic simulation for supercomputers', BMC Bioinformatics 7:93 (2006).

hybrid adaptive Gibson - Milstein method
type: Class
subclass of: hybrid method
subclass of: Restriction
  on property: is hybrid of
  some values from: Class
    intersection of: Gibson-Bruck next reaction algorithm
    intersection of: Milstein method
created: 2021-01-13
creator: JRK
creator: MLB
is implemented in: http://identifiers.org/biosimulators/vcell
definition: A hybrid stochastic method partitions the system into subsets of fast and slow reactions and approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the Gibson algorithm. Fixed time step Milstein is used for approximate numerical solution of CLE.

Axiom
annotated source: hybrid adaptive Gibson - Milstein method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell

Axiom
annotated source: hybrid adaptive Gibson - Milstein method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1186/1471-2105-7-93
comment: H.Salis, V. Sotiropoulos and Y. Kaznessis,'Multiscale Hy3S: Hybrid stochastic simulation for supercomputers', BMC Bioinformatics 7:93 (2006).

number of trials
type: Class
subclass of: granularity control parameter
created: 2021-01-13
creator: JRK
creator: MLB
alternative label: trials
definition: Number of multiple trials (e.g., of a scatter search method).

minimum species threshold for continuous approximation
type: Class
subclass of: granularity control parameter
created: 2021-01-13
creator: JRK
creator: MLB
alternative label: Epsilon
alternative label: epsilon
definition: Minimum number of molecules of both reactant and product species required for approximation as a continuous Markov process.

Axiom
annotated source: minimum species threshold for continuous approximation
annotated property: altLabel
annotated target: Epsilon
comment: EXACT

minimum reaction rate for continuous approximation
type: Class
subclass of: granularity control parameter
created: 2021-01-13
creator: JRK
creator: MLB
alternative label: Lambda
alternative label: lambda
definition: Minimum reaction rate required for approximation as a continuous Markov process.

Axiom
annotated source: minimum reaction rate for continuous approximation
annotated property: altLabel
annotated target: Lambda
comment: EXACT

MSR tolerance
type: Class
subclass of: relative tolerance
created: 2021-01-13
creator: JRK
creator: MLB
alternative label: Multiple slow reactions tolerance
alternative label: multiple slow reactions tolerance
definition: Maximum allowed effect of executing multiple slow reactions per numerical integration of the SDEs.

Axiom
annotated source: MSR tolerance
annotated property: altLabel
annotated target: Multiple slow reactions tolerance
comment: EXACT

SDE tolerance
type: Class
subclass of: relative tolerance
created: 2021-01-13
creator: JRK
creator: MLB
alternative label: Maximum allowed value of the drift and diffusion errors.
alternative label: maximum allowed value of the drift and diffusion errors.
definition: Stochastic differential equation tolerance

Axiom
annotated source: SDE tolerance
annotated property: altLabel
annotated target: Maximum allowed value of the drift and diffusion errors.
comment: EXACT

hierarchical stochastic simulation algorithm
type: Class
subclass of: Gillespie-like method
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
subclass of: Restriction
  on property: is generalization of
  some values from: Gillespie direct algorithm
created: 2021-01-25
creator: JRK
is implemented in: http://identifiers.org/biosimulators/ibiosim
alternative label: hSSA
definition: Fast, memory-efficient method for stochastic simulation of hierarchically organized models, such as a model of a cellular population where each cell in the population is represented by the same species and reactions.

Axiom
annotated source: hierarchical stochastic simulation algorithm
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim

Axiom
annotated source: hierarchical stochastic simulation algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.3389/fbioe.2014.00055
comment: Watanabe, L. H., & Myers, C. J. (2014). Hierarchical stochastic simulation algorithm for SBML models of genetic circuits. Frontiers in bioengineering and biotechnology, 2, 55.

Axiom
annotated source: hierarchical stochastic simulation algorithm
annotated property: altLabel
annotated target: hSSA
comment: EXACT

hierarchical Fehlberg method
type: Class
subclass of: Fehlberg method
created: 2021-01-25
creator: JRK
is implemented in: http://identifiers.org/biosimulators/ibiosim
alternative label: hODE
alternative label: hierarchical ODE integration method
alternative label: hierarchical ordinary differential equation integration method
definition: Method for continuous simulation of hierarchically organized models, such as a model of a cellular population where each cell in the population is represented by the same species and reactions.

Axiom
annotated source: hierarchical Fehlberg method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim

Axiom
annotated source: hierarchical Fehlberg method
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.3389/fbioe.2014.00055
comment: Watanabe, L. H., & Myers, C. J. (2014). Hierarchical stochastic simulation algorithm for SBML models of genetic circuits. Frontiers in bioengineering and biotechnology, 2, 55.

Axiom
annotated source: hierarchical Fehlberg method
annotated property: altLabel
annotated target: hODE
comment: EXACT

hierarchical flux balance analysis
type: Class
subclass of: flux balance analysis
created: 2021-01-25
creator: JRK
is implemented in: http://identifiers.org/biosimulators/ibiosim
alternative label: Hierarchical FBA
alternative label: hFBA
alternative label: hierarchical FBA
definition: Method for constraint-based simulation of hierarchically organized models, such as a model of a cellular population where each cell in the population is represented by the same species and reactions.

Axiom
annotated source: hierarchical flux balance analysis
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim

Axiom
annotated source: hierarchical flux balance analysis
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.3389/fbioe.2014.00055
comment: Watanabe, L. H., & Myers, C. J. (2014). Hierarchical stochastic simulation algorithm for SBML models of genetic circuits. Frontiers in bioengineering and biotechnology, 2, 55.

Axiom
annotated source: hierarchical flux balance analysis
annotated property: altLabel
annotated target: Hierarchical FBA
comment: EXACT

Axiom
annotated source: hierarchical flux balance analysis
annotated property: altLabel
annotated target: hFBA
comment: EXACT

embedded Runge-Kutta Prince-Dormand (8,9) method
type: Class
subclass of: embedded Runge-Kutta method
created: 2021-01-25
creator: JRK
is implemented in: http://identifiers.org/biosimulators/ibiosim
alternative label: RK8PD
definition: An embedded Runge-Kutta integrator of order 8(9).

Axiom
annotated source: embedded Runge-Kutta Prince-Dormand (8,9) method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim

Axiom
annotated source: embedded Runge-Kutta Prince-Dormand (8,9) method
annotated property: altLabel
annotated target: RK8PD
comment: EXACT

composite-rejection stochastic simulation algorithm
type: Class
subclass of: accelerated stochastic simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: exact solution
created: 2021-01-25
creator: JRK
is implemented in: http://identifiers.org/biosimulators/ibiosim
alternative label: SSA-CR

Axiom
annotated source: composite-rejection stochastic simulation algorithm
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim

Axiom
annotated source: composite-rejection stochastic simulation algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1063/1.2919546
comment: Slepoy, A., Thompson, A. P., & Plimpton, S. J. (2008). A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networks. The journal of chemical physics, 128(20), 05B618.

incremental stochastic simulation algorithm
type: Class
subclass of: generalized stochastic simulation algorithm
creator: JRK
is implemented in: https://identifers.org/biosimulators/ibiosim
alternative label: iSSA
definition: Performs local averaging over small time-intervals to compute statistics on typical behavior.

Axiom
annotated source: incremental stochastic simulation algorithm
annotated property: isImplementedIn
annotated target: https://identifers.org/biosimulators/ibiosim
comment: iBioSim

Axiom
annotated source: incremental stochastic simulation algorithm
annotated property: seeAlso
annotated target: http://identifiers.org/doi/10.1109/ISCAS.2010.5537539
comment: Winstead, C., Madsen, C., & Myers, C. (2010, May). iSSA: An incremental stochastic simulation algorithm for genetic circuits. In Proceedings of 2010 IEEE International Symposium on Circuits and Systems (pp. 553-556). IEEE.

Axiom
annotated source: incremental stochastic simulation algorithm
annotated property: altLabel
annotated target: iSSA
comment: EXACT

implicit 4th order Runge-Kutta method at Gaussian points
type: Class
subclass of: Runge-Kutta based method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
created: 2021-01-25
creator: JRK
is implemented in: http://identifiers.org/biosimulators/ibiosim
alternative label: RK4IMP

Axiom
annotated source: implicit 4th order Runge-Kutta method at Gaussian points
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim

Axiom
annotated source: implicit 4th order Runge-Kutta method at Gaussian points
annotated property: altLabel
annotated target: RK4IMP
comment: EXACT

stochastic simulation algorithm with normally-distributed next reaction times
type: Class
subclass of: generalized stochastic simulation algorithm
created: 2021-01-25
creator: JRK
is implemented in: http://identifiers.org/biosimulators/ibiosim
alternative label: NMC

Axiom
annotated source: stochastic simulation algorithm with normally-distributed next reaction times
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim

implementation
type: Class
subclass of: method switching control parameter
created: 2021-01-25
creator: JRK
definition: An implementation of an algorithm. For example, simulation tools can this parameter to differentiate among C, Python, and Java implementations of the same algorithms and allow investigators to select one of these specific implementations through SED-ML.

fully-implicit regular grid finite volume method with a variable time step
type: Class
subclass of: finite volume method
created: 2021-01-30
creator: JRK
is implemented in: http://identifiers.org/biosimulators/vcell

Axiom
annotated source: fully-implicit regular grid finite volume method with a variable time step
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell

semi-implicit regular grid finite volume method with a fixed time step
type: Class
subclass of: finite volume method
created: 2021-01-30
creator: JRK
is implemented in: http://identifiers.org/biosimulators/vcell

Axiom
annotated source: semi-implicit regular grid finite volume method with a fixed time step
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell

IDA-CVODE hybrid method
type: Class
subclass of: hybrid method
created: 2021-01-30
creator: JRK
is implemented in: http://identifiers.org/biosimulators/vcell
definition: Meta algorithm which chooses between IDA and CVODE depending on the problem to be solved. CVODE is used for ordinary differential equation (ODE) systems. IDA is used for differential-algebraic equation (DAE) systems.

Axiom
annotated source: IDA-CVODE hybrid method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/vcell
comment: VCell

bunker
type: Class
subclass of: generalized stochastic simulation algorithm
created: 2021-01-30
creator: JRK
is implemented in: http://identifiers.org/biosimulators/ibiosim
definition: A variant of the stochastic simulation algorithm (SSA) in which the time to the next reaction is equated to the mean inter-event time (inverse of the sum of the propensitites of the reactions) rather than sampled from a distribution parameterized by this mean inter-event time. In this method, the next reaction time is deterministic rather than stochastic as in SSA.

Axiom
annotated source: bunker
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim

emc-sim
type: Class
subclass of: generalized stochastic simulation algorithm
created: 2021-01-30
creator: JRK
is implemented in: http://identifiers.org/biosimulators/ibiosim
definition: A variant of the stochastic simulation algorithm (SSA) in which the time to the next reaction is a constant equal to 1 time unit. In this method, the next reaction time is deterministic rather than stochastic as in SSA.

Axiom
annotated source: emc-sim
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/ibiosim
comment: iBioSim

parsimonius flux balance analysis
type: Class
subclass of: flux balance analysis
created: 2021-04-27
creator: JRK
is organizational: true
alternative label: pFBA
definition: A technique for selecting a flux distribution which is parsimonious by some metric, such as a solution which has the minimal number of active fluxes or a solution which has the smallest sum of active fluxes.

stochastic simulation leaping method
type: Class
subclass of: accelerated stochastic simulation algorithm
created: 2021-04-27
creator: JRK
is organizational: true

flux balance method
type: Class
subclass of: biological state optimization method
subclass of: Restriction
  on property: has characteristic
  some values from: metabolic system
created: 2021-04-27
creator: JRK
is organizational: true

flux balance problem
type: Class
subclass of: type of problem
created: 2021-04-28
creator: JRK

method for solving a system of linear equations
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: linearity of equation
created: 2021-06-01
creator: JRK
is organizational: true
definition: method for solving a system of linear equations Example system of equations: 3x + 2y - z = 0 2x - 2y + 4z = 0 -x + 1/2y - z = 0

dense direct solver
type: Class
subclass of: method for solving a system of linear equations
created: 2021-06-01
creator: JRK
is implemented in: CVODE
alternative label: denese

band direct solver
type: Class
subclass of: method for solving a system of linear equations
created: 2021-06-01
creator: JRK
is implemented in: CVODE
alternative label: banded

diagonal approximate Jacobian solver
type: Class
subclass of: method for solving a system of linear equations
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
created: 2021-06-01
creator: JRK
is implemented in: CVODE
alternative label: diagonal

modelling and simulation algorithm parameter value
type: Class
creator: JRK
creator: 2012-06-01
is organizational: true
definition: A value of a parameter of an algorithm

null
type: Class
subclass of: modelling and simulation algorithm parameter value
created: 2021-06-01
creator: JRK
alternative label: none

general steady state method
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
created: 2021-06-01
creator: JRK
is organizational: true
alternative label: root-finding method
definition: A method looking for a steady state of a dynamic system.

iterative root-finding method
type: Class
subclass of: steady state root-finding method
creator: JRK
creator: 2021-06-01
is organizational: true
definition: Iterative method for finding the root of a function (f(x) = 0).

functional iteration root-finding method
type: Class
subclass of: iterative root-finding method
created: 2021-06-01
creator: JRK
is implemented in: CVODE
definition: Iterative method for finding the root of a function f(x) given by y^{n(m+1)} = h_{n} β_{n,0} f(t_{n}, y^{n(m)}) + a_n This method only involves evaluations of f. This method is suitable for non-stiff functions.

Axiom
annotated source: functional iteration root-finding method
annotated property: seeAlso
annotated target: https://bookdown.org/rdpeng/advstatcomp/functional-iteration.html
comment: Roger Peng. Advanced Statistical Computing.

computational function
type: Class
created: 2021-06-04
creator: JRK
is organizational: true
definition: A mathematical function such as the calculation of a minimum, maximum, or mean of a set of values.

scaled property
type: Class
subclass of: model and simulation property characteristic
created: JRK
created: 2021-06-04

unscaled property
type: Class
subclass of: model and simulation property characteristic
created: 2021-06-04
creator: JRK

primary property
type: Class
subclass of: model and simulation property characteristic
created: 2021-06-04
creator: JRK
definition: A primary output of a simulation.

derived property
type: Class
subclass of: model and simulation property characteristic
created: 2021-06-04
creator: JRK
definition: An output of a simulation which can be derived from its primary outputs.

level
type: Class
subclass of: model and simulation property
subclass of: Restriction
  on property: has characteristic
  some values from: extensive property
created: 2021-06-04
creator: JRK
definition: A level such as of a qualitative variable.

flux
type: Class
subclass of: model and simulation property
subclass of: Restriction
  on property: has characteristic
  some values from: rate
created: 2021-06-04
creator: JRK
definition: A rate through an volume such as of a reaction of a constraint-based models.

lower bound
type: Class
subclass of: bound
created: 2021-06-04
creator: JRK
definition: A lower bound on an estimate of a quantity.

bound
type: Class
subclass of: model and simulation property characteristic
created: 2021-06-04
creator: JRK
is organizational: true
definition: An upper or lower bound on an estimate of a quantity.

minimum flux
type: Class
subclass of: flux
subclass of: Restriction
  on property: has characteristic
  some values from: lower bound
created: 2021-06-04
creator: JRK
definition: Minimum possible flux such as computed by flux variability analysis (FVA, KISAO_0000526).

upper bound
type: Class
subclass of: bound
created: 2021-06-04
creator: JRK
definition: An upper bound on an estimate of a quantity.

maximum flux
type: Class
subclass of: flux
subclass of: Restriction
  on property: has characteristic
  some values from: upper bound
created: 2021-06-04
creator: JRK
definition: Maximum possible flux such as computed by flux variability analysis (FVA, KISAO_0000526).

objective value
type: Class
subclass of: model and simulation property
created: 2021-06-04
creator: JRK
definition: Value of an objective function such as of a constraint-based model.

propensity
type: Class
subclass of: model and simulation property
created: 2021-06-04
creator: JRK
definition: Tendency of an event such as of the firing of a reaction in the stochastic simulation algorithm (SSA, KISAO_0000029).

derivative
type: Class
subclass of: model and simulation property characteristic
subclass of: Restriction
  on property: has characteristic
  some values from: intensive property
created: 2021-06-04
creator: JRK
definition: Rate of change of a variable with respect to another variable.

step
type: Class
subclass of: model and simulation property
created: 2021-06-04
creator: JRK
definition: Iteration such as along a pseudo timecourse of a logical simulation.

shadow price
type: Class
subclass of: sensitivity
created: 2021-06-04
creator: JRK
definition: Change, per infinitesimal unit of the constraint, in the optimal value of the objective function of an optimization problem obtained by relaxing the constraint.

sensitivity
type: Class
subclass of: model and simulation property
subclass of: Restriction
  on property: has characteristic
  some values from: derivative
created: 2021-06-04
creator: JRK
is organizational: true
definition: The sensitivity of a variable to another variable, such as the derivative a variable with respect to another.

reduced costs
type: Class
subclass of: sensitivity
created: 2021-06-04
creator: JRK
definition: The amount by which an objective function coefficient would have to improve before it would be possible for a corresponding variable to assume a positive value in the optimal solution.

concentration rate
type: Class
subclass of: rate of change
subclass of: Restriction
  on property: has characteristic
  some values from: intensive property
created: 2021-06-04
creator: JRK
definition: Rate of a process relative to a volume, such as the rate of a reaction in molar^-1 s^-1.

particle number rate
type: Class
subclass of: rate of change
subclass of: Restriction
  on property: has characteristic
  some values from: extensive property
created: 2021-06-04
creator: JRK
definition: Rate of a process in extensive/absolute units such as mole reactions per second.

amount rate
type: Class
subclass of: rate of change
subclass of: Restriction
  on property: has characteristic
  some values from: extensive property
created: 2021-06-04
creator: JRK
definition: rate of a process in extensive/absolute units such as reactions per second.

rate
type: Class
subclass of: model and simulation property characteristic
created: 2021-06-04
creator: JRK
definition: Speed at which a process is occuring such as the temporal rate of a chemical reaction,

use adaptive time steps
type: Class
subclass of: method switching control parameter
created: 2021-06-05
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Whether an algorithm should use adaptive or fixed time steps.

Axiom
annotated source: use adaptive time steps
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

sequential logical simulation method
type: Class
subclass of: logical model simulation method
subclass of: Restriction
  on property: has characteristic
  some values from: deterministic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: constant updating policy
subclass of: Restriction
  on property: has characteristic
  some values from: synchronous updating policy
created: 2021-07-08
creator: JRK
definition: Qualitative (logical) models specify the evolution rules of their components. In the case of a sequential updating, nodes are updated sequentially in a pre-determined deterministic order.

logical model analysis method
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: discrete variable
created: 2021-07-08
creator: JRK
is organizational: true
definition: A method for analyzing a logical model, such as finding its fixed points.

Naldi MDD logical model stable state search method
type: Class
subclass of: logical model stable state search method
created: 2021-07-08
creator: JRK
alternative label: Naldi Multi-valued Decision Diagram stable state search method
definition: Efficient method for determining the stable states of a regulatory graph using a Multi-valued Decision Diagram (MDD) representation of the logical functions.

Axiom
annotated source: Naldi MDD logical model stable state search method
annotated property: seeAlso
annotated target: http://identifiers.org/doi:10.1007/978-3-540-75140-3_16
comment: Aurélien Naldi, Denis Thieffry and Claudine Chaouiya. Decision Diagrams for the Representation and Analysis of Logical Models of Genetic Networks. Computational Methods in Systems Biology 2007, 4695.

logical model stable state search method
type: Class
subclass of: logical model analysis method
created: 2021-07-08
creator: JRK
is organizational: true
definition: Method for determining the stable states of a regulatory graph.

logical model trap space identification method
type: Class
subclass of: logical model analysis method
created: 2021-07-08
creator: JRK
is organizational: true
definition: Method for determining the trap spaces, or stable motifs or symbolic stable states, of a regulatory graph,

Klarner ASP logical model trap space identification method
type: Class
subclass of: logical model trap space identification method
created: 2021-07-08
creator: JRK
alternative label: Klarner Answer Set Programming logical model trap space identification method
definition: Optimization-based method rooted in answer set programming (ASP) for computing the trap spaces of a regulatory graph.

Axiom
annotated source: Klarner ASP logical model trap space identification method
annotated property: seeAlso
annotated target: http://identifiers.org/doi:10.1007/s11047-015-9520-7
comment: Hannes Klarner, Alexander Bockmayr, and Heike Siebert. Computing maximal and minimal trap spaces of Boolean networks. Natural Computing 14.4 (2015): 535-544.

BDD logical model trap space identification method
type: Class
subclass of: logical model trap space identification method
created: 2021-07-08
creator: JRK
alternative label: Binary Decision Diagram logical model trap space identification method
definition: Method for determining the trap spaces of a regulatory graph using a Binary Decision Diagram (BDD).

Second order backward implicit product Euler scheme
type: Class
subclass of: modelling and simulation algorithm
default language: Method for solving Volterra equations. Uses the trapezoidal rule.
created: 2021-08-07
creator: JRK
is implemented in: http://identifiers.org/biosimulators/xpp

Axiom
annotated source: Second order backward implicit product Euler scheme
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/xpp
comment: XPP

Axiom
annotated source: Second order backward implicit product Euler scheme
annotated property: seeAlso
annotated target: http://identifiers.org/doi:10.1093/comjnl/12.4.393
comment: Peter Linz. Numerical methods for Volterra integral equations of the first kind. Computer Journal 12 (4): 393–397 (1969).

Axiom
annotated source: Second order backward implicit product Euler scheme
annotated property: seeAlso
annotated target: https://doi.org/10.1137/1.9781611970852
comment: Peter Linz. Analytical and Numerical Methods for Volterra Equations. 1985.

maximum number of iterations for root finding
type: Class
subclass of: error control parameter
created: 2021-08-07
creator: JRK
is implemented in: http://identifiers.org/biosimulators/xpp

Axiom
annotated source: maximum number of iterations for root finding
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/xpp
comment: XPP

Jacobian epsilon
type: Class
subclass of: error control parameter
created: 2021-08-07
creator: JRK
is implemented in: http://identifiers.org/biosimulators/xpp

Axiom
annotated source: Jacobian epsilon
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/xpp
comment: XPP

memory size
type: Class
subclass of: error control parameter
created: 2021-08-07
creator: JRK
is implemented in: http://identifiers.org/biosimulators/xpp
definition: Maximum number of points to store in memory, such as in the second order backward implicit product Euler scheme.

Axiom
annotated source: memory size
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/xpp
comment: XPP

Numerical Recipes in C "stiff" Rosenbrock method
type: Class
subclass of: Rosenbrock method
created: 2021-08-08
creator: JRK
is implemented in: http://identifiers.org/biosimulators/xpp
see also: Implementation of the Kaps and Rentrop using the parameters recommended by Shampine and Watts.
see also: Shampine, L.F., and Watts, H.A. 1977, in Mathematical Software III, J.R. Rice, ed. (New York: Academic Press), pp. 257–275; 1979, Applied Mathematics and Computation, vol. 5, pp. 93–121.
alternative label: stiff

Axiom
annotated source: Numerical Recipes in C "stiff" Rosenbrock method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/xpp
comment: XPP

Axiom
annotated source: Numerical Recipes in C "stiff" Rosenbrock method
annotated property: seeAlso
annotated target: https://dl.acm.org/doi/10.5555/148286
comment: William H. Press, Saul A. Teukolsky, William T. Vetterling & Brian P. Flannery. Numerical Recipes in C. The Art of Scientific Computing, 2nd Edition, 1992. Chapter 16. Pages 739-741.

Resource Balance Analysis
type: Class
subclass of: general steady state method
subclass of: biological state optimization method
subclass of: Restriction
  on property: has characteristic
  some values from: cellular system
created: 2021-08-12
creator: JRK
is implemented in: http://identifiers.org/biosimulators/rbapy
alternative label: RBA

Axiom
annotated source: Resource Balance Analysis
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/rbapy
comment: RBApy

Axiom
annotated source: Resource Balance Analysis
annotated property: seeAlso
annotated target: https://doi.org/10.1016/j.automatica.2011.02.038
comment: A. Goelzer, V. Fromion, G. Scorletti. Cell design in bacteria as a convex optimization problem. Automatica, 47(6):1210-1218 (2011).

use multiple steps
type: Class
subclass of: method switching control parameter
created: 2021-08-07
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Whether to perform a multiple time step simulation.

Axiom
annotated source: use multiple steps
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

use stiff method
type: Class
subclass of: method switching control parameter
created: 2021-08-07
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Specifies whether the integrator attempts to solve stiff equations.

Axiom
annotated source: use stiff method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

Numerical Recipes in C "quality-controlled Runge-Kutta" method
type: Class
subclass of: Cash-Karp method
created: 2021-08-18
creator: JRK
is implemented in: http://identifiers.org/biosimulators/xpp
alternative label: rkqs
definition: Cash-Karp method with step size adjustment.

Axiom
annotated source: Numerical Recipes in C "quality-controlled Runge-Kutta" method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/xpp
comment: XPP

Axiom
annotated source: Numerical Recipes in C "quality-controlled Runge-Kutta" method
annotated property: seeAlso
annotated target: https://dl.acm.org/doi/10.5555/148286
comment: William H. Press, Saul A. Teukolsky, William T. Vetterling & Brian P. Flannery. Numerical Recipes in C. The Art of Scientific Computing, 2nd Edition, 1992. Chapter 16. Pages 719.

skip reactions that produce negative species amounts
type: Class
subclass of: method switching control parameter
created: 2021-08-23
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Parameter which instructs a simulation tool to skip reactions that would result in negative amounts of species.

Axiom
annotated source: skip reactions that produce negative species amounts
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

presimulate
type: Class
subclass of: method switching control parameter
created: 2021-08-23
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Whether a model should be presimulated prior to analysis.

Axiom
annotated source: presimulate
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

Broyden method
type: Class
subclass of: method switching control parameter
created: 2021-08-23
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Family of Quasi-Newton methods for finding roots in k variables originally described by C. G. Broyden in 1965.

Axiom
annotated source: Broyden method
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

degree of linearity
type: Class
subclass of: method switching control parameter
created: 2021-08-23
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: The degree of linearity of a system.

Axiom
annotated source: degree of linearity
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

maximum number of steps for presimulation
type: Class
subclass of: maximum number of steps
created: 2021-08-23
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Maximum number of steps to take in presimulating a model prior to analysis.

Axiom
annotated source: maximum number of steps for presimulation
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

maximum number of steps for approximation
type: Class
subclass of: maximum number of steps
created: 2021-08-23
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Maximum number of steps to take in approximating an analysis.

Axiom
annotated source: maximum number of steps for approximation
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

maximum time for approximation
type: Class
subclass of: maximum time
created: 2021-08-23
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Maximum amount of time to spend approximating an analysis.

Axiom
annotated source: maximum time for approximation
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

duration
type: Class
subclass of: modelling and simulation algorithm parameter
created: 2021-08-23
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Length of time to simulate.

Axiom
annotated source: duration
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

maximum time
type: Class
subclass of: granularity control parameter
created: 2021-08-23
creator: JRK
definition: Maximum amount of wall time for an operation.

allow approximation
type: Class
subclass of: method switching control parameter
created: 2021-08-23
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Whether to find an approximate solution if an exact solution could not be found.

Axiom
annotated source: allow approximation
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

relative tolerance for approximation
type: Class
subclass of: relative tolerance
created: 2021-08-23
creator: JRK
is implemented in: http://identifiers.org/biosimulators/tellurium
definition: Relatative tolerance for an alternative approximate solution to an exact solution which could not be found.

Axiom
annotated source: relative tolerance for approximation
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/tellurium
comment: tellurium

number of steps per output
type: Class
subclass of: granularity control parameter
created: 2021-09-22
creator: JRK
is implemented in: http://identifiers.org/biosimulators/bionetgen
definition: Number of simulation steps between each simulation output.

Axiom
annotated source: number of steps per output
annotated property: isImplementedIn
annotated target: http://identifiers.org/biosimulators/bionetgen
comment: BioNetgen

biological state optimization method
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: biological system
created: 2022-03-27
creator: EN
creator: JRK
creator: WL
is organizational: true
definition: A method for computing the optimal state of a biological system according to a particular objective.

Enzyme Cost Minimization
type: Class
subclass of: biological state optimization method
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: metabolic system
created: 2022-03-27
creator: EN
creator: JRK
creator: WL
is implemented in: https://gitlab.com/equilibrator/metabolic-pathway-analysis
alternative label: ECM
definition: For a given metabolic network model, the Enzyme Cost Minimization method determines plausible metabolite and enzyme concentrations (which determine thermodynamic forces and enzyme catalytic rates). Fluxes, enzyme kinetic constants, admissible metabolite concentration ranges, and enzyme cost weights (e.g. enzyme molecular masses) are given as input data. The method applies the principle that high enzyme (or enzyme plus metabolite) concentrations must be avoided, and maximizes a weighted sum of enzyme and metabolite concentrations.

Axiom
annotated source: Enzyme Cost Minimization
annotated property: isImplementedIn
annotated target: https://gitlab.com/equilibrator/metabolic-pathway-analysis
comment: Metabolic Pathway Analysis

Axiom
annotated source: Enzyme Cost Minimization
annotated property: seeAlso
annotated target: http://identifiers.org/doi:10.1371/journal.pcbi.1005167
comment: Elad Noor, Avi Flamholz, Arren Bar-Even, Dan Davidi, Ron Milo & Wolfram Liebermeister. The Protein Cost of Metabolic Fluxes: Prediction from Enzymatic Rate Laws and Cost Minimization. PLoS Comput Biol 12 (11): e1005167 (2016).

Max-min Driving Force method
type: Class
subclass of: biological state optimization method
subclass of: Restriction
  on property: has characteristic
  some values from: continuous variable
subclass of: Restriction
  on property: has characteristic
  some values from: metabolic system
created: 2022-03-27
creator: EN
creator: JRK
creator: WL
is implemented in: https://gitlab.com/equilibrator/metabolic-pathway-analysis
alternative label: MDF
definition: For a given metabolic network model, the MDF method determines plausible metabolite concentrations and thermodynamic forces. Flux directions, equilibrium constants (or equivalently, standard Gibbs free energies of reactions) and admissible metabolite concentration ranges are given as input data. The method applies the principle that low thermodynamic forces must be avoided, and maximizes the minimum thermodynamic force across the entire network.

Axiom
annotated source: Max-min Driving Force method
annotated property: isImplementedIn
annotated target: https://gitlab.com/equilibrator/metabolic-pathway-analysis
comment: Metabolic Pathway Analysis

Axiom
annotated source: Max-min Driving Force method
annotated property: seeAlso
annotated target: http://identifiers.org/doi:10.1371/journal.pcbi.1003483
comment: Elad Noor, Arren Bar-Even, Avi Flamholz, Ed Reznik, Wolfram Liebermeister & Ron Milo. Pathway thermodynamics highlights kinetic obstacles in central metabolism. PLOS Computational Biology 10(2): e1003483 (2014).

type of system described
type: Class
subclass of: modelling and simulation algorithm characteristic
created: 2022-03-29
creator: EN
creator: JRK
creator: WL

mathematical system
type: Class
subclass of: type of system described
created: 2022-03-29
creator: EN
creator: JRK
creator: WL

biological system
type: Class
subclass of: type of system described
created: 2022-03-29
creator: EN
creator: JRK
creator: WL

metabolic system
type: Class
subclass of: biological system
created: 2022-03-29
creator: EN
creator: JRK
creator: WL

cellular system
type: Class
subclass of: biological system
created: 2022-03-29
creator: EN
creator: JRK
creator: WL

biochemical system
type: Class
subclass of: biological system
created: 2022-03-29
creator: EN
creator: JRK
creator: WL

ODE solver
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: relative tolerance
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: absolute tolerance
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: maximum number of steps
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: integration method
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: iteration type
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: linear solver
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: preconditioner
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: upper half-bandwidth
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: lower half-bandwidth
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: interpolate solution
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: stability limit detection flag
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: auto reduce tolerances
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: absolute tolerance adjustment factor
created: 2023-05-19
creator: lps
is organizational: false
alternative label: ordinary differential equation solver
definition: An ODE solver is the general category of packages such as CVODE-like methods [http://identifiers.org/biomodels.kisao/KISAO_0000433] or Livermore solvers [http://identifiers.org/biomodels.kisao/KISAO_0000094] that solve systems of ordinary differential equations.

Axiom
annotated source: ODE solver
annotated property: altLabel
annotated target: ordinary differential equation solver
comment: EXACT

parameters for
type: Class
subclass of: modelling and simulation algorithm parameter
subclass of: Restriction
  on property: has type
  some values from: string
created: 2023/05/19
creator: lps
definition: The children parameters of this term are applied when the parent general term is implented as the more-specific value of this term. For example: a 'parameters for' term might be used as a child of an 'ODE Solver' ([http://identifiers.org/biomodels.kisao/KISAO_0000694]), have a value of 'KISAO_0000019' (CVODE)', and have a child term 'use stiff method' of 'true' ([http://identifiers.org/biomodels.kisao/KISAO_0000671])

steady state root-finding problem
type: Class
subclass of: type of problem
creator: LPS
alternative label: steady state problem

Axiom
annotated source: steady state root-finding problem
annotated property: altLabel
annotated target: steady state problem
comment: EXACT

SDE solver
type: Class
subclass of: modelling and simulation algorithm
subclass of: Class
  complement of: Restriction
    on property: has characteristic
    some values from: spatial description
subclass of: Restriction
  on property: has characteristic
  some values from: stochastic system behaviour
subclass of: Restriction
  on property: has characteristic
  some values from: progression with fixed time step
subclass of: Restriction
  on property: has characteristic
  some values from: approximate solution
subclass of: Restriction
  on property: has characteristic
  some values from: stochastic differential equation problem
created: 2023-06-06
creator: lps
is organizational: false
alternative label: stochastic differential equation solver
definition: An SDE solver is the general category of packages that provide stochastic solutions to a system of differential equations with propensities.

Axiom
annotated source: SDE solver
annotated property: altLabel
annotated target: stochastic differential equation solver
comment: EXACT

particle coordinates
type: Class
subclass of: model and simulation property
subclass of: Restriction
  on property: has characteristic
  some values from: extensive property
created: 12-08-2023
creator: LPS
definition: The set of coordinates for all particles of these entities.

DAE Solver
type: Class
subclass of: modelling and simulation algorithm
subclass of: Restriction
  on property: has characteristic
  some values from: differential-algebraic equation problem
subclass of: Restriction
  on property: has characteristic
  some values from: ordinary differential equation problem
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: relative tolerance
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: absolute tolerance
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: maximum number of steps
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: integration method
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: iteration type
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: linear solver
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: preconditioner
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: upper half-bandwidth
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: lower half-bandwidth
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: interpolate solution
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: stability limit detection flag
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: auto reduce tolerances
subclass of: Restriction
  on property: has parameter
  max qualified cardinality: 1
  on class: absolute tolerance adjustment factor
created: 2024-03-13
creator: lps
is organizational: false
alternative label: differential algebraic equation solver
definition: A DAE solver is the general category of packages such as IDA-like methods [http://identifiers.org/biomodels.kisao/KISAO_0000432] that solve systems of differential algebraic equations (DAEs). DAEs are a superset of ODEs that may additionally contain algebraic equations or 'fast' reactions.

Axiom
annotated source: DAE Solver
annotated property: altLabel
annotated target: differential algebraic equation solver
comment: EXACT

systems property
type: Class
subclass of: model and simulation property
created: 2021-06-03
creator: LPS
is organizational: true
definition: A systems-level property of an entire model or simulation.

concentration control coefficient matrix (unscaled)
type: Class
subclass of: systems property
subclass of: Restriction
  on property: has characteristic
  some values from: unscaled property
created: 2021-06-03
creator: LPS
definition: The unscaled concentration control coefficient matrix. The dimensions are species by reactions.

control coefficient (scaled)
type: Class
subclass of: systems property
subclass of: Restriction
  on property: has characteristic
  some values from: scaled property
created: 2021-06-03
creator: LPS
definition: A scaled control coefficient of any dependent element (such as a reaction or a floating species) with respect to an independent element (such as a global parameter or boundary species).

control coefficient (unscaled)
type: Class
subclass of: systems property
subclass of: Restriction
  on property: has characteristic
  some values from: unscaled property
created: 2021-06-03
creator: LPS
definition: An unscaled control coefficient of any dependent element (such as a reaction or a floating species) with respect to an independent element (such as a global parameter or boundary species).

elasticity matrix (unscaled)
type: Class
subclass of: systems property
subclass of: Restriction
  on property: has characteristic
  some values from: unscaled property
created: 2021-06-03
creator: LPS
definition: The unscaled elasticity matrix. The dimensions are reactions by species.

elasticity coefficient (unscaled)
type: Class
subclass of: systems property
subclass of: Restriction
  on property: has characteristic
  some values from: unscaled property
created: 2021-06-03
creator: LPS
definition: An unscaled elasticity coefficient of any reaction with respect to an independent element (such as a global parameter or boundary species).

elasticity matrix (scaled)
type: Class
subclass of: systems property
subclass of: Restriction
  on property: has characteristic
  some values from: scaled property
created: 2021-06-03
creator: LPS
definition: The scaled elasticity matrix. The dimensions are reactions by species.

elasticity coefficient (scaled)
type: Class
subclass of: systems property
subclass of: Restriction
  on property: has characteristic
  some values from: scaled property
created: 2021-06-03
creator: LPS
definition: A scaled elasticity coefficient of any reaction with respect to an independent element (such as a global parameter or boundary species).

reduced stoichiometry matrix
type: Class
subclass of: systems property
created: 2021-06-03
creator: LPS
definition: The reduced stoichiometry matrix. The dimensions are species by reactions.

reduced Jacobian matrix
type: Class
subclass of: systems property
created: 2021-06-03
creator: LPS
definition: The reduced Jacobian matrix. The dimensions are species by species.

reduced eigenvalue matrix
type: Class
subclass of: systems property
created: 2021-06-03
creator: LPS
definition: The reduced eigenvalue matrix of a model. The dimensions are species by two, where the first column is the real part of the eigenvalues, and the second column is the imaginary part of the eigenvalues.

stoichiometry matrix
type: Class
subclass of: systems property
created: 2021-06-03
creator: LPS
alternative label: full stochiometry matrix
definition: The (full) stoichiometry matrix. The dimensions are species by reactions.

Jacobian matrix
type: Class
subclass of: systems property
created: 2021-06-03
creator: LPS
alternative label: full Jacobian matrix
definition: The (full) Jacobian matrix. The dimensions are species by species.

Eigenvalue matrix
type: Class
subclass of: systems property
created: 2021-06-03
creator: LPS
alternative label: full eigenvalue matrix
definition: The (full) eigenvalue matrix of a model. The dimensions are species by two, where the first column is the real part of the eigenvalues, and the second column is the imaginary part of the eigenvalues.

flux control coefficient matrix (unscaled)
type: Class
subclass of: systems property
subclass of: Restriction
  on property: has characteristic
  some values from: unscaled property
created: 2021-06-03
creator: LPS
definition: The unscaled flux control coefficient matrix. The dimensions are reactions by reactions.

flux control coefficient matrix (scaled)
type: Class
subclass of: systems property
subclass of: Restriction
  on property: has characteristic
  some values from: scaled property
created: 2021-06-03
creator: LPS
definition: The scaled flux control coefficient matrix. The dimensions are reactions by reactions.

link matrix
type: Class
subclass of: systems property
created: 2021-06-03
creator: LPS
definition: The link matrix of a model.

kernel matrix
type: Class
subclass of: systems property
created: 2021-06-03
creator: LPS
definition: The Kernel matrix of a model.

L0 matrix
type: Class
subclass of: systems property
created: 2021-06-03
creator: LPS
definition: The L0 matrix of a model.

Nr matrix
type: Class
subclass of: systems property
created: 2021-06-03
creator: LPS
definition: The Nr matrix of a model.

model and simulation property characteristic
type: Class
created: 2021-06-03
creator: LPS
is organizational: true
definition: A property of a variable of a model or simulation.

intensive property
type: Class
subclass of: model and simulation property characteristic
created: 2021-06-03
creator: LPS
is organizational: true
definition: An intensive variable such as a concentration or temperature.

extensive property
type: Class
subclass of: model and simulation property characteristic
created: 2021-06-03
creator: LPS
definition: An extensive variable such as an amount, particle number, or mass.

aggregation function
type: Class
subclass of: computational function
created: 2021-06-03
creator: LPS
is organizational: true
definition: A function that aggregates a set of results, reducing its dimension(s). Examples include functions that compute minima or maxima of sets of values.

mean ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-06-03
creator: LPS, MK
definition: The mean (average) of a set of values, ignoring NaN entries.

standard deviation ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-06-03
creator: LPS, MK
definition: The standard deviation of a set of values, ignoring NaN entries.

standard error ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-06-03
creator: LPS, MK
definition: The standard error of a set of values, ignoring NaN entries.

maximum ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-06-03
creator: LPS, MK
definition: The maximum value of a set of values, ignoring NaN entries.

minimum ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-06-03
creator: LPS, MK
definition: The minimum value of a set of values, ignoring NaN entries.

maximum
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The maximum of a set of values. If the values contain NaN the maximum is NaN.

model and simulation property
type: Class
created: 2021-06-03
creator: LPS
is organizational: true
definition: A variable of a model or simulation.

time
type: Class
subclass of: model and simulation property
created: 2021-06-03
creator: LPS
definition: The implied time variable of the model state.

rate of change
type: Class
subclass of: model and simulation property
subclass of: Restriction
  on property: has characteristic
  some values from: derivative
subclass of: Restriction
  on property: has characteristic
  some values from: rate
created: 2021-06-03
creator: LPS
alternative label: rate
definition: The rate of change of one variable with respect to a second variable.

concentration control coefficient matrix (scaled)
type: Class
subclass of: systems property
subclass of: Restriction
  on property: has characteristic
  some values from: scaled property
created: 2021-06-03
creator: LPS
definition: The scaled concentration control coefficient matrix. The dimensions are species by reactions.

amount
type: Class
subclass of: model and simulation property
subclass of: Restriction
  on property: has characteristic
  some values from: extensive property
created: 2021-06-03
creator: LPS
definition: The extensive quantity amount.

particle number
type: Class
subclass of: model and simulation property
subclass of: Restriction
  on property: has characteristic
  some values from: extensive property
created: 2021-06-03
creator: LPS
definition: The extensive quantity particle number, or, the molar amount of the entity multiplied by Avogadro's number.

concentration
type: Class
subclass of: model and simulation property
subclass of: Restriction
  on property: has characteristic
  some values from: intensive property
created: 2021-06-03
creator: LPS
definition: The intensive quantity concentration, or, the amount of the entity with respect to the entity in which it resides.

temperature
type: Class
subclass of: model and simulation property
subclass of: Restriction
  on property: has characteristic
  some values from: intensive property
created: 2021-06-03
creator: LPS
definition: The intensive quantity temperature.

minimum
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The minimum of a set of values. If the values contain NaN the minimum is NaN.

mean
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The mean of a set of values. If the values contain NaN the mean is NaN.

standard deviation
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The standard deviation of a set of values. If the values contain NaN the standard deviation is NaN.

standard error
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The standard error of a set of values. If the values contain NaN the standard deviation is NaN.

sum ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The sum of a set of values, ignoring Nan entries.

sum
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The sum of a set of values. If the values contain NaN the sum is NaN.

product ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The product of a set of values, ignoring Nan entries.

product
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The product of a set of values. If the values contain NaN the product is NaN.

cumulative sum ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The cumulative sum of a set of values, ignoring Nan entries.

cumulative sum
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The cumulative sum of a set of values. If the values contain NaN the cumulative sum is NaN.

cumulative product ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The cumulative product of a set of values, ignoring Nan entries.

cumulative product
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The cumulative product of a set of values. If the values contain NaN the cumulative product is NaN.

count ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The number of non-zero elements of a set of values, ignoring Nan entries.

count
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The number of non-zero elements of a set of values. If the values contain NaN the count is NaN.

length ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The number of elements of a set of values, ignoring Nan entries.

length
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The number of elements of a set of values.

median ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The median of a set of values, ignoring Nan entries.

median
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The median of a set of values. If the values contain NaN the median is NaN.

variance ignoring NaN
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The variance of a set of values, ignoring Nan entries.

variance
type: Class
subclass of: aggregation function
created: 2021-10-09
creator: MK
definition: The variance of a set of values. If the values contain NaN the variance is NaN.

Thing
is organizational: true