{ "metadata": { "name": "", "signature": "sha256:2bed684893bd98141976ea918a0449cbc9df53fcd78f3976632f9ac0cc89e9c6" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "# Dynamic Control for Purchasing of Online Advertisements\n", "\n", "\n", "### By Michael Els\n", "\n", "\n", "### 10/07/2014\n", "\n", "\n", "\n", "\n", "\n", "![logo](maxpoint.png)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Focus of this talk\n", "\n", "1. Not Math\n", "2. Not Programming\n", "3. Problem Solving\n", "4. Under-utilized methods\n", "5. Showcase Ipython Notebooks" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 4, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Background \u2013 What we do as a company\n", "\n", "1. Programmatic Advertising\n", "2. Custom ad campaigns for agencies and large companies\n", "3. Targeting Platform\n", " - Hyper local geo targeting\n", " - Cookie and cookieless user targeting\n", " - Contextual and Performance based media targeting" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "![overview](rtb_overview.jpg)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 4, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Background \u2013 What does our system do\n", "\n", "- Real Time Bidding with 12B-15B ad requests\n", "- We want to serve several hundred million ads\n", "- Data intelligence paltform\n", "- Offline and online models to create scored lists\n", " - Users\n", " - Media\n", " - Geography\n", " - Time\n", " - Auction theory\n", "- Score every ad request\n", "- Bidders execute on scores in under 50ms roundtrip\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 4, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Background \u2013 What we do as data scientists\n", "\n", "1. Focus\n", " - Machine learning\n", " - Automation\n", " - Scale\n", "2. Process\n", " - Prototype examples\n", " - Implement in production if possible" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 4, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Background \u2013 The pacing problem\n", "\n", "For each campaign we have a target for the number of ads to serve every minute. We would like to serve the best quality ads at every opportunity. " ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_number": 7, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "source": [ "### Why?\n", "1. Best time to influence people\n", "2. Always serve the best ads possible\n", "3. Smooth serving accross the day (hedging)\n", "4. To beat competition" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 7, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Problem 1: How do I control the speed of ad serving?" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 9, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "source": [ "![logo](requests_by_hour.png)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 9, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## PID Control\n", "\n", "A proportional-integral-derivative controller is a control loop feedback mechanism.\n", "\n", "- $SP$ : Set point (target you would like your process to hit)\n", "- $PV$ : Process value (where your process currently is)\n", "- $e$ : Error\u00a0($SP - PV$)\n", "- $K_p$ : Proportional gain, a tuning parameter\n", "- $K_i$ : Integral gain, a tuning parameter\n", "- $K_d$ : Derivative gain, a tuning parameter\n", "- $t$ : Time or instantaneous time (the present)\n", "- $\\tau$ : Variable of integration; takes on values from time 0 to the present\n", "- $u(t)$ : PID Controller output at time $t$\n", "\n", "$$\n", "u(t) = K_pe(t) + K_i\\int_0^te(\\tau)d\\tau + K_d\\cfrac{d}{dt}e(t)\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 9, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## PID Tuning\n", "\n", "- PID loops are very sensitive to tuning the parameters\n", "- Tuning parameters are also specific to each implementation\n", "- Tuning is made easier through dimension reduction of parameter space via Ziegler-Nichols transformation\n", "\n", "\n", "| | $K_p$ | $K_i$ | $K_d$ |\n", "| -------- | -------- | -------- | -------- |\n", "| PID | $0.6K_u$ | $2K_p/P_u$ | $K_pP_u/8$|" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pandas as pd\n", "from pandas import Series\n", "import matplotlib.pyplot as plt\n", "import numpy.random as rand\n", "import numpy as np\n", "%matplotlib inline\n", "pd.set_option('display.width',200)\n", "\n", "import time\n", "from bokeh.plotting import *\n", "from bokeh.objects import Glyph\n", "from bokeh.objects import Range1d \n", "output_notebook(url=\"default\")" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 9, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "skip" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Using saved session configuration for http://localhost:5006/\n", "To override, pass 'load_from_config=False' to Session\n" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "class PID: \n", " def __init__(self):\n", " self.Kp = 0\n", " self.Kd = 0\n", " self.Ki = 0\n", " self.Ku = 0\n", " self.Pu = 0\n", " self.previous_error = 0\n", " self.cumulative_error = 0\n", " \n", " def update_params(self):\n", " self.Kp = 0.6*self.Ku\n", " self.Ki = 2*0.2*self.Ku/self.Pu\n", " self.Kd = 0.6*self.Ku*self.Pu/8\n", " \n", " def set_zn_params(self,Ku, Pu):\n", " ''' Ziegler-Nichols Parameters '''\n", " self.Pu = Pu\n", " self.Ku = Ku\n", " self.update_params()\n", "\n", " def set_pid_params(self,Kp, Ki, Kd):\n", " self.Kp = Kp\n", " self.Kd = Ki\n", " self.Ki = Kd\n", " \n", " def step(self, error, time_delta):\n", " \n", " error_delta = error - self.previous_error \n", " \n", " self.p_contribution = self.Kp * error\n", " self.cumulative_error += error * time_delta \n", " self.i_contribution = self.Ki * self.cumulative_error\n", " self.d_contribution = 0\n", " if time_delta > 0: \n", " self.d_contribution = self.Kd * error_delta/time_delta \n", " \n", " self.previous_error = error \n", " \n", " return self.p_contribution + self.i_contribution + self.d_contribution" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 9, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "def pid_plot(res):\n", " fig = plt.figure()\n", " ax = res.process_value.plot(figsize=(12,6), label = 'Process Value' )\n", " res.set_point.plot(secondary_y=False, style='y', label = 'Setpoint Target' )\n", " ax2 = res.controller_output.plot(secondary_y=True, style='r', label = 'Controller Output' )\n", " \n", " ax.set_xlabel('Iteration', fontsize=16)\n", " ax.set_ylabel('Target Values', fontsize=16)\n", " ax2.set_ylabel('Controller Output', fontsize=16)\n", " \n", " handles, labels = ax.get_legend_handles_labels()\n", " handles2, labels2 = ax2.get_legend_handles_labels()\n", " \n", " handles.extend(handles2)\n", " labels.extend(labels2)\n", " \n", " ax.legend(handles, labels)\n", " plt.show()" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 9 }, "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "def pid_stream_plot1(res):\n", " N = len(res.iteration)\n", "\n", " figure(tools=\"\", \n", " title = 'PID Process',\n", " x_axis_label = 'Iteration',\n", " y_axis_label = 'Process Value',\n", " y_range=Range1d(start=0, end=15))\n", "\n", " hold()\n", "\n", " line(res.iteration,res.set_point, color=\"#DF7401\", plot_width=800, plot_height=500, legend='Set Point')\n", " line(res.iteration[:1],res.process_value[:1], color=\"#013ADF\", plot_width=800, plot_height=500, legend='Process Value')\n", " line(res.iteration[:1],res.controller_output[:1], color=\"#FF0000\", plot_width=800, plot_height=500, legend='Controller Output')\n", "\n", " grid().grid_line_alpha=0.3\n", "\n", " renderer1 = [r for r in curplot().renderers if isinstance(r, Glyph)][1]\n", " ds1 = renderer1.data_source\n", " renderer2 = [r for r in curplot().renderers if isinstance(r, Glyph)][2]\n", " ds2 = renderer2.data_source\n", " \n", " #xaxis().axis_label='Iteration'\n", " #yaxis().axis_label='Values'\n", " show()\n", "\n", " for i in range(N):\n", " ds1.data[\"x\"] = res.iteration[:i]\n", " ds1.data[\"y\"] = res.process_value[:i]\n", " ds2.data[\"x\"] = res.iteration[:i]\n", " ds2.data[\"y\"] = res.controller_output[:i]\n", " ds1._dirty = True\n", " ds2._dirty = True\n", " cursession().store_objects(ds1)\n", " cursession().store_objects(ds2)\n", " time.sleep(0.01)" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 9 }, "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "def run_pid(Ku = 0.2, Pu = 5):\n", " pid = PID()\n", " pid.set_zn_params(Ku, Pu)\n", "\n", " res = pd.DataFrame(columns=('iteration', 'set_point', 'process_value', \n", " 'controller_output', 'controller_change', 'error'))\n", " iteration = 0\n", " set_point = 5\n", " process_value = 0\n", " controller_output = 1\n", " controller_change = 0\n", " error = 0\n", " time_delta = 1\n", "\n", " row = pd.DataFrame([dict(iteration = iteration, \n", " set_point = set_point,\n", " process_value = process_value, \n", " controller_output = controller_output,\n", " controller_change = controller_change,\n", " error = error)])\n", " res = res.append(row, ignore_index=True)\n", "\n", " for i in range(1, 250):\n", " process_value = 1.7*(controller_output + 1)\n", " error = set_point - process_value\n", " controller_change = pid.step(error,time_delta)\n", " controller_output += controller_change \n", " controller_output = min(max(controller_output,1),30)\n", "\n", " #arbitrary set_point changes \n", " if (i==50):\n", " set_point = 8\n", " if (i==100):\n", " set_point = 12\n", " if (i==150):\n", " set_point = 4\n", "\n", " row = pd.DataFrame([dict(iteration = i, \n", " set_point = set_point, \n", " process_value = process_value, \n", " error = error,\n", " controller_output = controller_output,\n", " controller_change = controller_change)])\n", " res = res.append(row, ignore_index=True) \n", " \n", " return res" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 9, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 9, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## PID Toy Example" ] }, { "cell_type": "code", "collapsed": false, "input": [ "res = run_pid(Ku = 0.2, Pu = 5)\n", "pid_plot(res)\n", "#pid_stream_plot1(res)\n" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 18, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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9+/fn7rvvZunSpTRp0sR5rsNHH33El19+SWJiIps3b+aWW25h1qxZpKWl8dpr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\nNrqe6VYJIpLbVBIjIj6RdQm7Rtgl2rH9+ql+XRpQParEoxp2iUX3DPG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"text": [ "" ] } ], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 18, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Some Lessons\n", "\n", "1. So this kind of works!\n", "2. Tuning is important\n", "3. Build in safeguards" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 18, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Problem 2: But my process value is not nearly that smooth\n", "\n", "We need some kind of time series smoothing." ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 21 }, "slideshow": { "slide_type": "fragment" } }, "source": [ "Anything ARIMA or moving average based is a really bad idea:\n", "1. It's slow changing\n", "2. Has a built in lag\n", "3. Entirely backwards looking\n", "4. Offline Algorithm" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 22, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "source": [ "What we really need is a **Dynamic Linear Model**$^1$\n", "\n", "1. Forward looking\n", "2. Online Algorithm\n", "4. Certainty estimates about current state\n", "3. Bayesian\n", "\n", "$ $\n", "\n", "$^1$ We run about 3B DLMs a day, pacing is only 4-5M of those" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 22, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Kalman Filter\n", "\n", "Kalman filter is a very basic DLM$^2$\n", "\n", "The general problem is to estimate the state $x \\in \\mathbb{R}^n$ of a discrete-time controlled process that is governed by the linear stochastic difference equation:\n", "\n", "$$\n", "x_k = Ax_{k-1} + Bu_{k-1} + w_{k}\n", "$$\n", "\n", "with measurement $z \\in \\mathbb{R}^m$ that is\n", "\n", "$$\n", "z_k = Hx_k + v_k\n", "$$\n", "\n", "where $w_k$ and $v_k$ are the process and measurement noise with\n", "\n", "$$ p(w) \\backsim N(0,Q) $$\n", "$$ p(v) \\backsim N(0,R) $$\n", "\n", "$A$ is $n \\times n$ is the difference equation relating state $k$ to state $k-1$.\n", "\n", "$B$ relates to the optional control input $u \\in \\mathbb{R}^l$ to state $x$.\n", "\n", "$H$ is an $m \\times n$ matrix in the measurement equation relating to the observed measurements $z_k$.\n", "\n", "$ $\n", "\n", "\n", "$^2$ (2006) Welch and Bishop - 'An Introduction to the Kalman Filter'" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 22, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Kalman Filter continued\n", "\n", "We can define $\\hat{x}^-_k \\in \\mathbb{R}^n$ as a priori estimate a step $k$ given all our knowledge up to step $k$, and $\\hat{x}_k \\in \\mathbb{R}^n$ is the a posteriori state estimate at step $k$ given measurement $z_k$. \n", "\n", "Thus a priori and a posteriori errors are:\n", "\n", "$$e^-_k \\equiv x_k - \\hat{x}^-_k $$\n", "$$e_k \\equiv x_k - \\hat{x}_k $$\n", "\n", "With covariances:\n", "\n", "$$ P^-_k = E[e^-_ke^{-T}_k]\n", "\\\\\n", "P_k = E[e_ke^{T}_k]$$\n", "\n", "We eventually end up with something called *blending factor*\n", "\n", "$$K_k = P^-_kH^t(HP^-_kH^T+R)^{-1} $$\n", "\n", "So as the measurement error covariance $R$ approaches $0$, $K$ weights the process residual more heavily. \n", "\n", "Conversely, as the a priori estimate error covariance $P^-_k$ approaches $0$, $K$ weights the process residual less heavily." ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 22, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Kalman Filter Algorithm\n", "\n", "Get initial estimates for $\\hat{x}_k$ and $P_{k-1}$\n", "\n", "###Time update step (Predict)\n", "Project the new state\n", "\n", "$$\\hat{x}^-_k = A \\hat{x}_{k-1} + Bu_{k-1}$$\n", "\n", "Project the new error covariance\n", "\n", "$$P^-_k=AP_{k-1}A^T+Q$$\n", "\n", "\n", "###Measurement Update (Correct)\n", "Compute blending factor\n", "\n", "$$K_k = P^-_kH^T(HP^-_kH^T+R)^{-1}$$\n", "\n", "Update process estimate with new measurement\n", "\n", "$$\\hat{x}_k = \\hat{x}^-_k + K_k(z_k-H\\hat{x}^-_k)$$\n", "\n", "Update error covariance\n", "\n", "$$P_k = (I-K_kH)P^-_k$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "class KalmanFilter:\n", " def __init__(self, x, A, B, P, Q, H, R):\n", " self.x_aposteriori = x # Starting state\n", " self.A = A # State transition matrix\n", " self.B = B # Control matrix\n", " self.covariance_aposteriori = P # Starting covariance\n", " self.Q = Q # Process Error\n", " self.H = H # Observation matrix\n", " self.R = R # Measurement Error\n", " \n", " def update(self, measurement, control = 0):\n", " # Time update\n", " x_apriori = self.A * self.x_aposteriori + self.B * control\n", " covariance_apriori = self.A * self.covariance_aposteriori * self.A.T + self.Q\n", " \n", " # Measurement Update\n", " kalman_gain = covariance_apriori * self.H.T * np.linalg.inv((self.H * covariance_apriori * self.H.T + self.R))\n", " self.x_aposteriori = x_apriori + kalman_gain * (measurement - self.H * x_apriori)\n", " dimension = self.covariance_aposteriori.size\n", " self.covariance_aposteriori = (np.eye(dimension) - kalman_gain * self.H) * covariance_apriori" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 22, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_kf(df):\n", " fig = plt.figure()\n", " ax = df.measurement.plot(figsize=(12,6), label = 'Measurement' )\n", " df.smoothed_measurement.plot(secondary_y=False, style='g', label = 'Smoothed Measurement' )\n", "\n", " ax.set_xlabel('Iteration', fontsize=16)\n", " ax.set_ylabel('Measured Values', fontsize=16)\n", "\n", " handles, labels = ax.get_legend_handles_labels()\n", "\n", " ax.legend(handles, labels)\n", " plt.show()\n", " \n", "def kf_stream_plot1(df):\n", " N = len(df.iteration)\n", "\n", " figure(tools=\"\", \n", " title = 'Kalman Filter Toy Example',\n", " x_axis_label = 'Iteration',\n", " x_range=Range1d(start=0, end=N),\n", " y_range=Range1d(start=0, end=df.measurement.max() + 1))\n", "\n", " hold()\n", "\n", " line(res.iteration[:1],df.measurement[:1], color=\"#013ADF\", plot_width=800, plot_height=500, legend='Measurement Value')\n", " line(res.iteration[:1],df.smoothed_measurement[:1], color=\"#088A08\", plot_width=800, plot_height=500, legend='Smoothed Measurement')\n", "\n", " grid().grid_line_alpha=0.3\n", "\n", " renderer1 = [r for r in curplot().renderers if isinstance(r, Glyph)][0]\n", " ds1 = renderer1.data_source\n", " renderer2 = [r for r in curplot().renderers if isinstance(r, Glyph)][1]\n", " ds2 = renderer2.data_source\n", " \n", " xaxis().axis_label='Iteration'\n", " yaxis().axis_label='Values'\n", " show()\n", "\n", " for i in range(N):\n", " ds1.data[\"x\"] = df.iteration[:i]\n", " ds1.data[\"y\"] = df.measurement[:i]\n", " ds2.data[\"x\"] = df.iteration[:i]\n", " ds2.data[\"y\"] = df.smoothed_measurement[:i]\n", " ds1._dirty = True\n", " ds2._dirty = True\n", " cursession().store_objects(ds1)\n", " cursession().store_objects(ds2)\n", " time.sleep(0.01)" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 22, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 22, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Kalman Filter Toy Example\n", "\n", "Create some noisy series which has a clear underlying mean that will never clearly be measured.\n", "\n", "Generate $z \\backsim \\sum\\limits^n I(Uniform(0,10)>5)$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = np.matrix(1)\n", "A = np.matrix(1)\n", "B = np.matrix(0)\n", "P = np.matrix(1)\n", "Q = np.matrix(0.05)\n", "H = np.matrix(1)\n", "R = np.matrix(2)\n", "\n", "kf = KalmanFilter(x, A, B, P, Q, H, R)\n", "\n", "df = pd.DataFrame(columns=('iteration','measurement','smoothed_measurement'))\n", "smoothed_measurement = 0\n", "measurement = 0\n", "\n", "row = pd.DataFrame([dict(iteration = 0,\n", " measurement = measurement, \n", " smoothed_measurement = smoothed_measurement)])\n", "\n", "df = df.append(row, ignore_index=True)" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 29, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "trials = 20\n", "\n", "for i in range(1,100):\n", " measurement = 1*(np.random.uniform(0,10,trials)>5).sum()\n", " kf.update(measurement)\n", " smoothed_measurement = kf.x_aposteriori[(0,0)]\n", " row = pd.DataFrame([dict(iteration = i,\n", " measurement = measurement, \n", " smoothed_measurement = smoothed_measurement)])\n", " df = df.append(row, ignore_index=True)\n", " if i == 50:\n", " trials += 10\n", " \n", "#plot_kf(df)\n", "kf_stream_plot1(df)" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 29, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "outputs": [ { "html": [ "" ], "metadata": {}, "output_type": "display_data" } ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 29, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Some more Lessons\n", "\n", "1. So this also kind of works!\n", "2. Tuning is also important\n", "3. We don't want a smooth filter" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def pid_plot2(res):\n", " fig = plt.figure()\n", " ax = res.process_value.plot(figsize=(12,6), label = 'Process Value' )\n", " res.set_point.plot(secondary_y=False, style='y', label = 'Setpoint Target' )\n", " res.smoothed.plot(secondary_y=False, style='g', label = 'Smoothed Process Value' )\n", " ax2 = res.controller_output.plot(secondary_y=True, style='r', label = 'Controller Output' )\n", " \n", " ax.set_xlabel('Iteration', fontsize=16)\n", " ax.set_ylabel('Target Values', fontsize=16)\n", " ax2.set_ylabel('Controller Output', fontsize=16)\n", " \n", " handles, labels = ax.get_legend_handles_labels()\n", " handles2, labels2 = ax2.get_legend_handles_labels()\n", " \n", " handles.extend(handles2)\n", " labels.extend(labels2)\n", " \n", " ax.legend(handles, labels)\n", " plt.show()\n", " \n", "def pid_stream_plot2(res):\n", " N = len(res.iteration)\n", "\n", " figure(tools=\"pan,wheel_zoom,box_zoom,reset,previewsave\", \n", " title = 'PID Process with noisy data',\n", " y_range = Range1d(start=0, end=res.controller_output.max()+1),\n", " x_axis_label = 'Iteration')\n", "\n", " hold()\n", "\n", " line(res.iteration,res.set_point, color=\"#DF7401\", plot_width=800, plot_height=500, legend='Set Point')\n", " line(res.iteration[:1],res.process_value[:1], color=\"#013ADF\", plot_width=800, plot_height=500, legend='Process Value')\n", " line(res.iteration[:1],res.controller_output[:1], color=\"#FF0000\", plot_width=800, plot_height=500, legend='Controller Output')\n", " line(res.iteration[:1],res.smoothed[:1], color=\"#088A08\", plot_width=800, plot_height=500, legend='Smoothed Process Value')\n", " \n", " grid().grid_line_alpha=0.3\n", "\n", " renderer1 = [r for r in curplot().renderers if isinstance(r, Glyph)][1]\n", " ds1 = renderer1.data_source\n", " renderer2 = [r for r in curplot().renderers if isinstance(r, Glyph)][2]\n", " ds2 = renderer2.data_source\n", " renderer3 = [r for r in curplot().renderers if isinstance(r, Glyph)][3]\n", " ds3 = renderer3.data_source\n", " \n", " xaxis().axis_label='Iteration'\n", " yaxis().axis_label='Values'\n", " show()\n", "\n", " for i in range(N):\n", " ds1.data[\"x\"] = res.iteration[:i]\n", " ds1.data[\"y\"] = res.process_value[:i]\n", " ds2.data[\"x\"] = res.iteration[:i]\n", " ds2.data[\"y\"] = res.controller_output[:i]\n", " ds3.data[\"x\"] = res.iteration[:i]\n", " ds3.data[\"y\"] = res.smoothed[:i]\n", " ds1._dirty = True\n", " ds2._dirty = True\n", " ds3._dirty = True\n", " cursession().store_objects(ds1)\n", " cursession().store_objects(ds2)\n", " cursession().store_objects(ds3)\n", " time.sleep(0.01)" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 29, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 29, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Putting it together" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def init_system(Ku = 0.3,Pu = 25):\n", " res = pd.DataFrame(columns=('iteration', 'set_point', 'process_value', 'smoothed',\n", " 'controller_output', 'controller_change', 'error'))\n", " iteration = 0\n", " set_point = 5\n", " process_value = 0\n", " controller_output = 1\n", " controller_change = 0\n", " error = 0\n", " smoothed = 0\n", "\n", " row = pd.DataFrame([dict(iteration = iteration, \n", " set_point = set_point,\n", " process_value = process_value, \n", " smoothed = smoothed,\n", " controller_output = controller_output,\n", " controller_change = controller_change,\n", " error = error)])\n", " res = res.append(row, ignore_index=True)\n", "\n", " #initialise PID\n", " pid = PID()\n", " pid.set_zn_params(Ku, Pu)\n", "\n", " #initialise Kalman Filter\n", " x = np.matrix(1)\n", " A = np.matrix(1)\n", " B = np.matrix(0)\n", " P = np.matrix(1)\n", " Q = np.matrix(0.5)\n", " H = np.matrix(1)\n", " R = np.matrix(10)\n", " kf = KalmanFilter(x, A, B, P, Q, H, R)\n", " \n", " return res, pid, kf " ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 29, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "outputs": [], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "def exec_system(res, pid, kf):\n", " controller_output = res.controller_output[0]\n", " set_point = res.set_point[0]\n", " time_delta = 1\n", " for i in range(1, 250):\n", " process_value = 1*(rand.uniform(0,10,controller_output)>5).sum()\n", " kf.update(process_value)\n", " smoothed = kf.x_aposteriori[(0,0)]\n", " error = set_point - smoothed.item()\n", " controller_change = pid.step(error,time_delta)\n", " controller_output += controller_change \n", " controller_output = min(max(controller_output,1),30)\n", "\n", " #arbitrary set_point changes \n", " if (i==50):\n", " set_point = 8\n", " if (i==100):\n", " set_point = 12\n", " if (i==150):\n", " set_point = 4\n", "\n", "\n", " row = pd.DataFrame([dict(iteration = i, \n", " set_point = set_point, \n", " process_value = process_value, \n", " smoothed = smoothed,\n", " error = error,\n", " controller_output = controller_output,\n", " controller_change = controller_change)])\n", " res = res.append(row, ignore_index=True) \n", " \n", " return res" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 29, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "res, pid, kf = init_system(Ku = 0.3,Pu = 5)\n", "res = exec_system(res, pid, kf)\n", "pid_plot2(res)\n", "#pid_stream_plot2(res)" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 29, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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At+gou4uLC0uWLKF58+b4+fnxxBNPAHD48GEef/xxdu3ahbe3N/7+/mW+TmMdCQkJ3HPP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\nUx2rpES+ZvyN3bOn73uhHo8xMfqvfcAAOVmIjZXGZuvWSUGuQ4fEVjS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JyPfuLUK+EUqn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LgZNQq2bfPc7n//g1mz4IbRN3BMl2OYOncqpVWl/FKwkO7Vp9SXX2zdGtoUTAha7cYqtKUnw60j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"text": [ "" ] } ], "prompt_number": 34 }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 29, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Even more Lessons\n", "\n", "1. So this still also kind of works!\n", "2. Tuning is also important but all ad campaigns are different\n", "3. Movements of the PID controller output is not smooth" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 38, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "source": [ "![domain_requests](requests_by_domain.png)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 38, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Particle Swarm Optimization\n", "\n", "1. Create a population (called a swarm) of candidate solutions (called particles). \n", "2. These particles are moved around in the search-space according to a few simple formulae. \n", "3. The movements of the particles are guided by their own best known position in the search-space as well as the entire swarm's best known position. \n", "4. When improved positions are being discovered these will then come to guide the movements of the swarm.\n" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 38, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Na\u00efve Particle Swarm Optimization\n", "\n", "1. Pick a safe starting point (the system has to start somewhere)\n", "2. After each iteration spawn $k$ new particles around the previous used particle\n", "3. Validate retroactively which particle would have performed the best in the last iteration\n", "4. Update used particle to be the optimal back tested particle\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def pid_neighbours(pid, w):\n", " \n", " # create neighbouring PIDs\n", " pidKminus = copy(pid)\n", " pidKminus.set_params(max(pid.Ku*(1-w),ku_floor), pid.Pu) \n", " \n", " pidKplus = copy(pid)\n", " pidKplus.set_params(min(pid.Ku*(1+w),ku_ceiling), pid.Pu) \n", " \n", " pidPminus = copy(pid)\n", " pidPminus.set_params(pid.Ku, max(pid.Pu*(1-w), pu_floor))\n", " \n", " pidPplus = copy(pid)\n", " pidPplus.set_params(pid.Ku, min(pid.Pu*(1+w), pu_ceiling))\n", " \n", " return pidKminus, pidKplus, pidPminus, pidPplus" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 38, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "outputs": [], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "df3 = pd.read_csv('test_dat.csv')\n", "\n", "pacing_all = pd.DataFrame(columns=('thour','tmin','imps'))\n", "for i in range(7,23):\n", " for j in range(2,58):\n", " impressions = df3[(df3.thour==i) & (df3.tminute==j)]['dirretargetingflag'].notnull().sum()\n", " row = pd.DataFrame([dict(thour = i,tmin = j,imps = impressions), ])\n", " pacing_all = pacing_all.append(row, ignore_index=True)\n", "\n", "def score_plot(df3):\n", " plt.figure()\n", " ax = df3['final_score'].hist(bins=100, range = (0,10),figsize=(12,6))\n", " ax.set_xlabel('Score', fontsize=16) \n", " ax.set_ylabel('Available ads', fontsize=16)\n", " handles, labels = ax.get_legend_handles_labels()\n", "\n", "def ts_plot(pacing_all):\n", " plt.figure()\n", " ax = pacing_all.imps.plot(figsize=(12,6), label = 'Ads Available')\n", " ax.set_xlabel('Minute', fontsize=16) \n", " ax.set_ylabel('Available ads', fontsize=16)\n", " handles, labels = ax.get_legend_handles_labels()" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 38, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 38, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## So let's try some real data" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 44 }, "slideshow": { "slide_type": "fragment" } }, "source": [ "### Skew and variable score distributions" ] }, { "cell_type": "code", "collapsed": false, "input": [ "score_plot(df3)" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 45, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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W2CGXJEm1RDrkniHvqEEGBgZq3oaHZxc9OUmSJBXABXlHrSGdRV3/1vgKKlJv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\nCFhCepGpJEmS1JM2AvYHPg1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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 45, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "### Highly volatile stream of ad requests" ] }, { "cell_type": "code", "collapsed": false, "input": [ "ts_plot(pacing_all)" ], "language": "python", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 47, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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VUV3LgYrtoNz0jQD+AOD7oOofhl1YLL4I4EkATwD4BYAuADNBE888\nBeAeACEeiiAIacV2oCJAAkSlo8POaeFMNaNPvGByqllUT5kC7L+/O0KfM9VTppSK6nnzap+pVh23\nOPGPjg43h8zO4oMP+r/nlFNI1PH3kAanWhXVXA1k2rTS1/s51Wr1D74crF4tUfuTc9Y8mURUpzqJ\n+MfnPw/ccYf962tFvTjVUd9XK1GdRqfaVP2j1k61Gv/g3+fAgNmp5t97rZzq/UGC9wcATgcwF8A7\nAPyw+Pj+ZbZjPoCPAzgWwFEgoX4eaBbHewEcAuD+4n0hJmnM3qUV6St7bPrKVELMlKlmYbTfft73\n8wDGMDhTzaxeDWzY4A5IMjnV27e7meq5c92ppDk3O22at/rH1q3x4x9JZqrV+Ednp72onpigde7o\ncCtm7N5Nz23fHvy+oSH34JxEOTh1G9A/O6xOdWurN/7BB3bOUuptB0oz1ab4B1/K1k8aRkdpG+F+\n1isSBA1U5Izn2Jgr7ONU/xgfLxXzldxXOU7wNuFHFBFZTbhONRDdqQ7K/wcRVVQnkal2HBKTTKUz\n1ZUaqOjnVNsMVFRr05sy1bV2qq8DMBXAmwHsB+A40EyKJwOYXny+HHYCmATQC3LEewFsBvC3AH5S\nfM1PAJxZ5ucIglADeKS9KiKCMtW6qOaYQhgc/2De+lbgXe9yne+g+Mfb3w68/vWuwGSnetq05OIf\nSVGOU/2rXwGf/jT1aVcXHXyGh8l9Vw/EOoUCCcKkRTVPIT57tutwMlGqf/AJmakP+AAb5FTzMnn7\n0Q+4IyN0wsZVVrit/Hm28Y9LLgF+9rN41T9Y/FeL5cuB9743+vvqwamOKpDLcap1URj2OeWK6iVL\ngLPPdu9X0qnm20D1nGqbgYr67Ik88yNAfcwl9Wolqk8F8CUA2jw/eBgU2zi1zHYMAPgvABtAYnoQ\n5FDPBVAcNoQtxftCTNKYvUsr0lf23Hdf1nPfTwSxiOCdnSn+wTvPmTO977d1qnVRDZBQZPcyKP5x\n2WXA617nHnw4N8uimgVNOfGPJDPVulNtGyXYuZPcdnaqJyboRGK//aKJ6iTjH3x1QP2Os9msrxgI\nylSbthNexvi4WVSPj7vOMS8nyKkuFEqFo238Y2SE+jlO/MMk7Cq5rxoZcU8yo74PsBNYLHCqgZqp\njioy457QjIxUP/4xMuI9QY3jVKvblf6bCiqpV8k61fl88GeYnGq+r1YEMQ1UDIuh2RJU/UNlN1xx\nq7MVwLDPc7YcBOAiUAxkCMCvAPy99hoHPqX7Fi5ciPnz5wMA+vv7sWDBglcvXfCGIfflfpT7TFra\nk+b7H/nICixenMG++wK/+U0WF18MrF/vff1JJ2XQ0gIMDGRx9tnAM89kioIqi2wWKBQyaG0Fli2j\n17e0eN/f2UlRgLD2TE5msXMnANB9IFsUNHR/8eIspk2j17e1AStXZrFhAzBrFj2/fHm2+L4MCgVg\nzZps8YCUKYrsLMbHgdmz6fmo/bVixYpE+j+Xo/Zks1msWwe85jW0Pps3U38GvX/VKnp/Zyfw5JNZ\nvPIKMDycwX77AatX+7+/UAAeeSRbjAPQ561bF/55QfcffzyLsTFgYMB9vr/f/bxCIYv16+nz1PcX\nCvT5ExPZ4olApuhUZ7FyJXDeed7XT0zQfSBbrMtN99eto+fHxzNob6fXb9xIz7e3A5s2ues3MkLt\n2b0byOczRbGZxQMPAO98p7t9mPojn8+gr4/6O5cDZs6k7X1wMIvly4G3v92uv7ZuzWLNGm9/rFix\nomK/78ceyxbLJ0Z7//Cw+/5CIfj1N98MHH10Bv/yL5XfX61YsaJ4ZcBuf6Lez+eBp56Kvr3v2kW/\nNwBYsiSLoaHg12/Y4G6v6vYeZX+Ty3nXL5fLYGIifv9deWUG114LbNtG98fHM8XxGFls2QIcdRS9\nfteubPF3EW35QdsfAIyO0v2XXsqirc3tT/31zzxD9/P5TFFUZ/GmNwFLl2aKA5Hd/sjngbVr3eNF\nZydw661ZzJzpbc9jjwGf+xxw+eVZrKedUSJ8G4BpeERL8fH/KnP554Ly2syHAVwPYA2APYuP7QVg\nreG9jiAItWP+fMdZtYpuP/WU4+y1V+lrxsYcp7PTcd7zHscBHGfNGvoPOE4+7zg/+IHjnH++45xx\nBj2mc++9jnPqqeFt6ehwnI9+1F32EUfQ/yOPdJzWVscZGnJfe845jrNokePMnes4mzfTYzt2uO/9\n8pcd53Ofc5yzz3ac445znP32o8f7+hznkUcc5/jjo/dVUvzDPzjOoYfS7UsucZyvfc1xfvELxzn3\n3PD3fu1rtB7nnOM4S5c6zoIF9NjFFztOWxt9HyZ6ex3npz+lzwUcZ599HOe//7u89fj1r+l7WbqU\nlrlpk/vc2Bg99vGPl77v5z93nPPOc5zXvtZxzjyTHvvkJ+n1N91U+vr/+R/3ez3lFPfxyy6jx26+\n2XF6euix73+fHjvtNOpnZvFix3nDGxznxBMd589/dpzLL6fXDQzQ86ed5jhz5pjXc599HOcb36Dv\n55xzHOcf/9Fx9tiDtvc777TuLuf00x3n29+2f3253H+/4xx8cPT3vfWt9L3+8Y/hr/3c5xzniiui\nf0Zc7r2Xvrdly6K9721vc5yvfCX657W3u9ve4sXhr//EJ2i/pXLddY7T1WX/mXfe6V3GOec4zgkn\n2L9f5+ijHefhh937b3ub49xzD+37jzmGvkPAcd79bseZNy/+5+g89BAt91vfovvnnec4s2Y5zjXX\nmF9/ySX0+scfd5wbbnCcCy5wnIkJ2q8dfLDjHH44PX/ffbQ/v/tuxznkEHov4Djr15cu84YbSo9J\nCJibpTVA6H4MVO3jfABPAzgGwCoAVwD4JIAri/ePKT5fDmsBnACgByTU/wbAagC/A/CR4ms+AuD2\nMj9HEISEUS/Rj4+bL3FyvIMnDeGBgxzr4Off9CbKNetEiX+oAxU/8Qn3/a97nXdSEI5/DA66tZnV\n6AgPRpsxw81UA3QJsbU1mSxeJkP55qiUU1KP4w9c/YMz1f39lPvduZNK6335y973FQr0nJ6pfsMb\n4kUEAPeyNk8Nr16i5u9bv2x9ww3A1Vf7Z6qD4h+AuU712Jibt7eJf+Tz7jpzn9vUqeYSj7t3Jxf/\nqCRxYgMA/W6mTbNrqzq2Iine9Cbgs581P1fNTLUeGSknUx0lIqMPqoz7PTL6fr1WAxULBfpc2/gH\n7xe5+sfBB7uv4yiJOsBYnx8BiL6dBInqG0Hu8Q9ArvE+AA4HcFnx/qUADis+fn20jy3hcQA/BfAY\ngJXFx74P4OsA3g4qqXdq8b4QE75UIoQjfWXPyEi2ZKS1TqFAQloVT62tpaL6ssuAxx4rfX9nZ/hB\ngSdX4B38Cy8An/kM3W5vB5YtM4tqrtkMeJ8vFEgcTJ/uXa8pU+KLan27evBB4L77oi9HzVTz7Ii2\nopq/q85Ob6Z6yhSqgjIwAGzaROXzVEyZascB1q0rHWBoC7f35Zfpv3oAe+CBbMljALXtxRfjZaoB\nc53qsTE3b69W/1D7Ux2oGDdTPTbmCvLW1ujVP0y53kruq8JKHvoxPEy/G1tRneQgOoBmB/3tb0sf\nz2bj16mOU/3DNOtmGKaa0lEHKprqMpeTqdb367UqqWebqeaBil1d9BtzHOqP664D3vEO97fKywqq\n4R11fYJE9YER/g6K9rFGvgngCFBJvY+AqoEMgFzrQwCcBhrAKAhCilAPin5OteOQiOAa0FzzVxfV\nfqhO9e23k1NpakdLiyuQOzpomT095pnTKJvn/eyWFldUsVPd3++dYphnElPX8xOfIHEZh6lTo7+n\nEk71lCk0YHP79tJJcwBatqn6h+30yyb4fTyLpXrg58/XxQAPNtRnVOTBrVGcanWgIrtUqqhetAj4\netHKGRnxOtW6qFaFz403Am97m3c9WVTncuT4c9ujVP8IcktXrSqdnr1c4laNiOJUxxXuYfi1u5p1\nqkdH3aty6meHfU65AxVtnOq773ad2zCiONVJimr+baiiOqpT3dLiDpDv6KDfte5U8z7B9P1E3TaD\nBiquj7YoIe1w+F4IR/rKntbWzKs7bK6SocPClUX1+HipqDbNhMd0dro7t6efBp57rvQ1+by31rU6\nkYzpsh4NdKP/6oGPp+5mp7q/37teJqd65UpyUF/7Wv91AMzblamuchi6Ux1HVOtOdV8fCdOBAVpv\n/Xv0K6mnCvyoBInqN74xA6D0oDY25lbrUJ3qz32OqppEcarV+Advf+rscABw553AF77gxj927qT1\n5viHeiBnEfDtbwNrlRFAuZwb/+jpIWd+6tRk4h+8TT38cPKOb9zYAJdotHWqK1H9w9TuTCaD24sh\n0jhOdRxRPXUqioPh7NbTr0414JYmtVmG7lTrbuxvfws8+6z/MtR9VVqcao5/+H13uqjmKCCLap4x\nlfef3N4kRXWQUy0IQhOycCFwZoSK8OqBNyhTrR4MWFSzqOMSaX6oMyqOj/sLd5Oo7u31d6q5HSq8\nI2Y3Uo1/tLSYRbXpkq3OxATwwQ+WPp6EU83xDxuBxu00OdWzZ1PsQ3eqeaiVHv9gkRf3QMrv4/iH\nKVNtEtUsglVR3drqf1BXv5tdu9zvYXKSvlM/pxoADjmE/nP8w8+pVt3EtdqQet2pfukl2q6iiuqg\nvuYT1iSxcZE/+MHSdYiaqU76ZADwb7fJqf7ud4NnE+X3Rd3OR0a8v+9ynGrAflvRhblpmTt22C0L\nCHeq405T/uijwH8FlLkwxT9snGo+ieDfMhsoqqg2OdWm/k0y/qFzOmig4GoAzyl/zxf/CylHcsL2\nNGtf5XLAT34SLec7Pp71ONVB8Q+GM9V9fSRyosQ//EQ1O9UsoFVRbXKq29u9YorhHbHuVPMOneMf\n6g44LJcHUMZ70aJsycEtjqhWIxfsVLe2Ro9/dHa6orqvjybAueMOs6gGSp1qtaZ3HIIy1Q89lH11\n/VT4AN/aWnqVwW9A68SE+7rt2ynWwdGVnh5zppprds+eTf/ZqWYhrDvVeu71Na/xridP/sIxmjii\n2iTseF8VZ+ZDm88LEry5HPWl2ueOEz1TXYn4h2mZfpnqxYspPhNEnJNH3n8w5QxUVP+HYXKq9WUG\n1aQHomWq4w5UXLcOeOgh/+d5fdXfWJCoVmfoVcW+Kf6hOtVBk/NUyql+J4C7QNU5DgVV69gIml2x\nACDkHE8QhHrg6aeBOXOCoxg6NplqXTRz7KK/n6a+DhPV6kDF8fHgqavLdaqDMtXd3a5Tra6njaje\nsIH+88GMhSrP9hgF0+QvceIfVGvWHah41lnAAw+Uxih4uTt3ugc0PilRn4/C9de7OXSTU82fY3Kq\ngVKnmtvkJ6r1fh4bo8d7e83VP1g08zr6OdV69Q+eyEadFZQnnlBPVqZPtx+oePrpVKUmaLBcpZzq\noHiG6ftnR7C7u7ZOdVimWu3HiQn/qa/V90UV1bt3xxfVata+XFEdx6nO54GTT6Z2+DnVbW30vO5U\n244TmJwM7ndeX/U3ZjNQ8cYbgb/+1W0X7+Pb292xNJXKVNuK6ktBFT7epdx/C6gaSCtIcAspR3LC\n9jRrX61cCRxzTDSR5DiZUKea4x8vvQQcd5wrZqdPtxPVUZxqFtUskvycavWSoEqQU93dbS6pZxP/\neOEFAMi8KqpZfMVBjX9EzVSr8Q8+KA4NkeicPp1Oqp5/3tvHvK6qG1quU/2737nu4I4dpRVejjkm\nA8BfVOuZal4nW1E9PBzsVH/2s1RWkD+PByryCdW2bVRuUc9UDw3RfX376OnxZvP7++0HKt5zD7B6\ndXCmulKiGvAXqLwtqW0aHnZ/c7V0qv0y1aZ1mpgI//3GcaqHhykGw1dJbDPV6n/1fbai2qb6R5io\nPuGEDB56yCw4WVTzVTY1MhXl6svkZHC/66LatqTe735HVaRUp5rbx7E1U6a6mvGPQwH8FuRKOwDY\n23kKVLf60mgfKwhC2njmGeCb3wQWLIh+SVp1kYHS93P8Y889aUfMTjWLahbEfuii2m8qdI5/dHS4\nB7IpU+Jnqk3xjylT4sU/dKea/8dx6ZJyqnla7oEBV3ROnUpOdVRRfcst5gGkQevAbeFa4bbVP/jz\n1eofQLCo7uujgz+fRI2MuE61GgPiA3FPD3Dgge7n8SBD7udXXvEOxuP4B38+P86lHlkMqE51FAHC\nJ1J+B/lKxD/8rhYwJsHF+XxbUW3Kba9ZA/zwh3Zt/O533RMZJugEPa5THaekHg8A5m3L1qnmNj36\nKHD//fGcajWOZHK/bZxqwC2Dms8Df/oTsGSJK6pnzaLnVPFq+70DlXOqeVpzbhcfC/jqlu5U1yL+\nUQCQL/5/BRT7YF4CYFmYRaglzZoTjkMz9tXy5bTT+fSn7Z1HEgzeOtVA6ftVJ7q93SuqBwejxz/C\nnGpVRAfFP2yc6r4+ej8LI3aq1XW0d6qzr4ppFkFxXLqknGqA+mv7dvouAHLWtmwxO2WqG6rHP37+\nc2DpUvt1UPtsdNSN2TCLF2eNIjnMqTZtGxMTdLLQ1eV+vyMjwU51a6tbCYbbyE719u10u7e3dKAi\nb6fcbt62uYJNOaLa5JbyvqoWTjX3jdomdvSjONX68t//fuAf/9GujddeS4aACl+t0lEz1VGd6jjx\nDz7B4N9aFFE9Pk5RrD/8Id5ARcB7guc43s8PE9UPPpgFQCfY3K7f/x6491663dHhlrFURTXHK2wI\nO5nxc6rDqn/wyQO3Sz2ZSEv1j6fg1qJ+DMBFAOYB2APAxZDye4JQ9+TzwAEHkPtmK6rVsm6Af8ZW\nrf7BDnFrq32mOmr8QxfVfvGPoIGK7FT39pLwammh5aqZ6u99j15r61Tz5CpAZZ3qXA742c/o9uSk\nexugA8jUqW4fdXXR+1hUT51a2sf8WeokL9x//Hl+34sf+omI7lTz4D71se99L1xUv/wycNtt3s9i\npzpIVOvVP1pb6fUjI8BPf0qiurub1nvzZmCPPbzCkUW17lTnct7ykfwd1YNTbRv/KMep1uMfN98M\nPPkkXdWygUssqphOoplynOo4meq4onpiwnWbbZzqoSF3u9dFtf498tWToPEc/B5VVE9M0PfLV7lY\nVKu/Ga7vbjMhlE38QzUw+GphkFOtzorLolrtNxunemSErrxxG6NgK6p/DoArsF4O4EgAmwC8DJrp\n8LJoHyvUgmbNCcehGfuK4xO2jifAO7dMqKhWq3/oTrXtQMWw+Ic6UDGKU22Kf3AbczlaHl/2b293\nRfX4OPBP/+RWdAgT1WvXAqecknlV/OzeTQemuKJadbR0p3rTJuDii+n2c88B//qv7nvHxkjcs5vH\n69gUSREAACAASURBVMd9xDlJXVSrByug1Kn2q1EetA5qn3HpQubIIzPo7XW/a8eh/uaTEb/4xy23\n0IBLFc5Ud3W5B1o1/mEaqMhO9YsvAp/8pFvloK2NxgbMneuddZEz1bqo5pM9FtVxnWp+r1+mWo9A\nJIFJgKok5VSry//KV4BzzwUOspxSbnS09Dfk51SrmepqDFTkqjpR4h9q7IlP1HTH1sSKFcBVV3mX\noW+L+lWUoMjdCSdkAJSK6tFRt3/9RPWll9KJURg28Y+OjvJFtToXgDrpV3s77YM5LsL9vGYNbYe8\nzCjYiurrAPxb8fZS0KyHFwD4LIAFAH4V7WMFQUgbfPBnR9nmYK87ILbxD32gYlimmgfUsXg17ej0\nTDUTx6nu6qKBhL291B8stNvb3ZJ6LAgHBsKd6m3bSEQfc4zXoe7rCxfVq1YBGzd6H+MJc3g5nZ1e\ngTY+7h4ohobcShb83KxZXqeaXWrAX1TrM1OqfRBHVIc51ZOT8IhqXjeOOZicaq46AdDBf2iI6g+b\nnGoeqMiiWp/8hWfX3LaNlsWZ6tZWcqpZVKuZasCtj6u6hHxCpuaH+/tLq3/88Y/+wolPpEwCl/sx\n6RkVbeMf5TrVvPxCgbb1Cy6wdwhNTrWfqFbbqk8IVImBiuU61SyqbeIfXMWH2wr4O9VhWXn1NWqm\nmkU17zP9RPXu3d59jh82olo9cVUjG0w+TwN5eXnqb4Bvz5vnPqZWCGppcdvLy+Ll6CcgtsSd/GUj\ngBsBXAOqWy3UAc2YE45LM/aVKmxtJxKhnVA21KlWRbXqENtmqgHX6Us6U20qqdfZSTva3l56jJ1q\nNf6hiuowp/qJJ4CjjgIGBtxM9fg4CdiwnfZ3vwv85jfex8KcahbVXI1iZMT9PsfGgH/5F+DUU+l+\nV5e37BeLar0kV2urt6Y2u/n8fBynWj2g6pnqpUuz6O0tFQI8O52ppF5Hh/s9rF5NNbczGdcx7O72\nxj+4nrJ6csXbA7ti27e7/WhyqlVHGqBl6VlrdsTa291LzdOnlw6sPOMM/1y6X/wjm6VtasYM+ytM\nttjGP3SnOm78Y+tWyvTrVy2C4NKIKn7xD7861Wlyqk2i2ib+wdEMdRm6U83fF8eegvqY68SrTvXk\nJG2/3L9+AxWHh5OLf4Q51c88A3z84+56mpzqvfd2H1OvlAL0XxfVExPVF9WCIDQYuqgOOgAsW+Z1\nUExOteO4AkHNVPNOLUqmGnAHKwbFP0yiOmiacpNT3dNDO2N2mQASSSzieKBiFKf6iSeAo48mURrV\nqVYFtPqY7lTrotpxSChwLICd67ExEm8HHED3OzvtnOq2tmiiOmzQonoiwicreqZadap1QcODonRR\nzYOSVq50TxYefth1qru6KA89MkKCee5cr1PNTEzQAZpLHw4M0H3VqW5ro4P6tm3+opoz1dxnLN6m\nT6dtjUU2v94v5+o3UJHbtscelRPVUat/hMU/Nm1ya5PztgPQYN799vPGvYLgbTxOplofqJh0pnrd\nOjr5Up3qqFf/KuVUs6jm5Qe1wxT/4H3mjBn0Xx+o6DjRnGr1WKHiOF5RbRqoODLiPbmzcap5TA/f\n57ZyX6hOdZLxD7XiR9hfwj9loRI0Y044Ls3YV1FE9XnnUUY4KFO9bBnVpAa8s1uZ4h9JOdWtraXx\nj7e/HXj3u0tfzwLH5FSr8Q/AdarPPx943eu879m+PdypfuEFErFvelPmVZE7Pm4vqvX1ZVHNEzOY\nnGqADjiDg3SbnSN+PWMb/9Cd6rD4x1vfGjxrm9pnfDVB7YtDD/VmqvXt0c+pZtavp+XPmAF86EPA\nkUfSul5wAXDSSdQ3LEZNJ1dcVYXZscPdDrZvp+W2t1OO9eabvfEPvd28vXR00DZ3ySWUGVari/Bl\ndj+R4+dUZzKU058zxx2AlhR+ZQ0ZU6baJv5xww1uyTzVqX7hBWD//Uu3BT/0qkNMnEy1TfWPKK7l\noYcC//u/0eMfuZw71iLKQEXVqTZlqru7vaKaZ1T1W6fjjssAMItqXp9p0+g//3bYqQbsneqxMTr5\neNe7Sp+3caqHh6OL6jCnupz4h8G/eZWvRFiO5fw5giCkFRalQPiU17kciZIgp1o9kAwMuJcK9fgH\ni+qwWRz5AOB38PNzqo8/3vx6jgqYMtUc/+CdMYupj36U7qvlqGyc6rEx1wFX+4qnaQ8inzc71YCb\nRzU51QB9Ryzi+SCnTisM0HtN8Q89txgkqnM5r6jmqaqD+kTts97e0slfJie97rXJqQ4S1TwQ8Ywz\ngJ/8hEqTdXUBn/gERUM41jF1qvnkanLS2087drhONWc32eUaHCx1qtUDtSqqBwdp4OiUKV6nessW\n93P9+ivIqZ45090Gwk5QbbGNf6jbp81ARa5YA3hF9YYNrqg29cP69cD8+e597ruomeqWlupU/wDi\nxT84muEX/+BxKJxp5nWYmPAOhlVP7NS4hyqqn3ySlssGyPPPkwHAbVUz1Sw2dVGtHjeiiup8nn4r\npm1MF9WmyV90p9oU/7B1qpOIfwSJ6iuiLUpIO9lstikd2Dg0Y19FyVTncnRAczPVGQDegyzv+LZt\ncw/6gNepnj2bdto2QoDdK9OELYArzA88EDjnnPD15XyrvqyTT6ZL07/6lbuDZlHNqG21yVSzqH7y\nSW9fTZ0aXgrNz6kGXPcoyKlmUb17N/VRLucVn1Gdav6cIKeaB1IGuY2q88eiWj2ArVyZRW9vxjf+\n4Vf9A6BtjUU1C6zDDgPOPNP9vI0b3QGbavUPhuMfzO7dbqaa+40PyCxyAOqTnh6voOFlc71zXkZP\nj3uCxqLar8+CM9UZzJzpCtmg+EMUbAcqRnWq1W1F3U62bKFSeiYHddcumpiKr7yonx8tU50pyRNX\nqk41EG+goi6q9fjH975H+52vf927DgD1v8mp1scntLdTuz70Ibrq6Dj0/BFH0G/nkUeyADKB8Y99\n96UxCyZRbRv/AOj34zehl+5U6wMVR0bcCEku51b6uPBCugoFAO98J3D22XRbH0vT1uaeAJjiH5Kp\nFgQhFurBPiz+kc+rorr0MqwqMrds8TrVaqZ6r71IVI+NJTdQcc4c4N//PXx9/cTUaacB73mPN7IS\nJKq3b/d3qgcHaWfPNY7VgXTlxj94GSws+WCxc6e/U83RD863A6WZanaf/DLVHIkJylSzgxgmqhmT\nU53LUb/ncqUTVwD+1T8A2tZYVPN3eOCBwD//s/t5GzeS+ObtwORU69U0uPoHQO3lygQ82BagZfll\nqllccTujOtV+wm77dlrnKOUwbYiTqbZxqtlRBVynenDQPfk0xT/Gx0uFGn++/tsLcobzeW91lsFB\n16menPQXg1Gdaj6ZC3Oq9UlYWACPj/s71cPD7hgJhvtg9+7S2A6PTzA51RzR4hPu0VFvjIhFNZ/8\nqPGP7m6aoKYcpxqgfZZfRScbp5oFtXp16eqr3X3VvHnAr39Nt7n6R5hTzeNSksxUXwaa4AWg2tSX\nhfwJKafZnNdyaMa+ipKp5p1vUKaaD3hbttBBn51q1SlobydhvXFjcgMVbenoMDvV3MbxcffgoZfl\n0zPVhYJZVL/nPTRTJUcuTjwx4zkBsRHVpvgHr79aM7atjfpx/ny3LcPDXqdaj34A/k612seqU80D\n6bj/uI1RRbV6sDJlqg86KIPOTlo/04lUUKZ69uxSp1qlt5cGy7G7q8eAFiwA3vjG0r7SnWq+rTvV\nevUPP1GtZqrDnGq+rK9v+5lM5tUrQWr5sSSwjX+U61QPDblTwnd1mZ1qPqlQ188v/qHm21U4U81O\n8DPPUDZ+fJy+h1//mirj6PDyoggsrjgR5FRzhEMV1mr72KXWnWpur4rqVOsnQ7pTrYpqdv7Vk4bJ\nSWDBgsyrn8Xt0p1qRhXVvK1X06nmdnL8o6PD/3iixz/8MtWA+fcWRlj8424Am0GiOowoGWxBEFJG\nFFGtO9WmTLUqFvziHwCN9n/+ebfEmx+qU22q5hE1S+rnVANeNxIIdqo5c2jKZA4NkQvDDpw+3Xpf\nX/hO28+pbmuj70Adec/oAxVbWrxOtYopU80OMW8TaqaaRfWUKW4evFJONVdb2bXLvvoH4HWqTaJ6\nyhQ6ATn5ZPOA1eXL6b8uyjhTDbhONWAW1aaBivz6KE41VzPh/Klfpnr//d2JLZLCNv6hO9VTpgS7\nfGruN593S7AND7uiSO8HdfIndiD94h/cHp5aXoWFl1ojmU/WBwdLHWB+j/rfhON4J7naay/ar7Go\nVsUhw9Or61VvpkxxxbTJqQ4T1ab4hylTrZ7IqrN98m11++S41uioezWLScKpzuep/1pa3N8+i2pu\no1/1D+4THqionwyr6AMV/epUA95sNbfNtH2oBB2CWgEsUW6H/QkppxlrL8elGftKPfiHDVT0iuqs\n0akOin+oonr//engY+NUB8U/bAY7qvhd9gfcx2xENU9GYnKqeVIJjn8sX571ONVTp8aPf3R2ep1q\ndphPPLE0/jF3rr9TfcQRwGtf697fe2/gzW+mzzjySFo/U/yjt9d1wfn75nbygcfGqe7uJhGhu5Nr\n1mTR0UGfuWuXuz2q9aT9nOowUd3b60Ym2tvpgGk6udLfq24HnKkG3MG2vG2b6lSr7VMz1SxaeDvy\nE9Wm/DJA+6rBQToxSjr+oYszHT+n2ib+oTrVDNcCN8U/1MgT4xf/4D7QhSfXqWZRzb+FQoFe6159\nMy8v6AT45pvdWUwBWoeuLoqj8aRE+nezciX910U1T58dJKr1deZlqPEP9cTOz6lm1P1MLgc8+mjW\nU99Zdar1zHrcTDW3h/cjuRxVAjn4YDeCElb9QxXV/J0GTYJkcqr1TLVqEuknjjfcELxOIoYFQQBQ\nzkDFYKd661avU60PFNlvPxJNUQYqJhH/YIcyjlOt3va7BA24NXRZzKo5ZNtMtX7Jm/PFXV1ep7q/\nnypcqCc0LKr33psOHGpOnLnsMio7yOyxB3D77fQdv/yyd3KeadNcUT1livfgrR6UozjV3d3m+AcP\nuGNRzcvmkwc+gKv58CiiGnAjE4B52+FZFfm2elnZ5FTzAVvNgpsy1aqo5t8JixC9z/h3qNezVuEr\nELYTrtgSx6mOE/9ghoZoPdipdpS6YqpTzfhtZ36imp9TM9UMn/ya2mzjVG/c6F614tfeey9trx0d\n9qKa3Va+UmQaqFiuU81OsJr7NjnVc+e6y2dRbdpnlutUq6L6mWeotOLLL0cX1ePjtO1FdapHRryf\nozrVvL3pgtsPEdVNRDPmhOPSjH2lxids4x9+mepczlt/V81UqwMVAXKqATtRzYI6aKCiLWGZan4N\n4O9Us1sMAEuWlF4W5YMfxz/e+tbomWrdqeb15PiHKhr1soMsqufNc+MfQQcchgURu3csqvff3/2+\n1MvquuCLIqp7erzxD54oaM89M0ZRzaP729qoUgSP8Ae8onp42F9U77kn/T/ggNKcs05XF617dze1\ny+RUc0k93kZ52ng+IVK3p7Y290Sgu9vtq+Fh8wybYaI6k8m8up6VGqgYpfqHzUBF9Tesimq1bKEe\nZTGJ6jCnWr9Uz5lqVbQC9Hk2TnWQqB4Y8H6eeoXCz6let47+6051V5fZqVYjRjZO9Tnn0HwB7FTz\ne1SnurWVhKheiu+oozKe346NU82zhgLR4x98f8MGur1yZfhAxUsuARYtcvtkbIzWJcipZlNHPdaN\njrqT4ajtiiOqgzLVOhcA+CSAQwDwbtkB0FL8H+FwJghC2oiaqQ6rU82XwScmzPEP3vnut5/7mUF0\ndpZObqC3KWqmmh0bnTCnmkVRb68rdoDSmtO6U82D7oD4mWpuc2ur16nmdVIPBDzByX77+cc/TPAI\neb4iwULnvPOAN7wBuOUW78x/fqI6rE414BXVk5NutpgnZpk2jfqVHWrVqf7kJ0vbDXgHKqp5ceak\nk1wH+aGH6DG/7Y+/N97W1WiQOlBRjX9wrXQ1lw7QY+r2psY/RkZo0JyfU82CzbTtT056q5Ekhe1A\nRZNTPThoX/2DGRx0t2feHljABcU/TH3W12fOv6pONbd76lT6fahX31RsnOrt272fp1+hMIlqfr26\nD1BFPwvquAMVd++mAbmFgjlTzQMY+bZaUk49KeB2TU7SX9hAxdbW6AMV+f4LL9DtlSvdkzO/gYrP\nP+/m0st1qnt6zPEPfRsPK71oewj6BwDXAngUJKhvAnAzgF0AnoUMUqwLmjEnHJdm7KsomWpv/MOb\nqeb3jo3RgS2XIweKxY0e/4jiVO/e7Qo+nTiZam6Pjp6p1qt/8GumTPGKaubxxylfqWeqFy/29lVv\nr/eg+dGP0mVkFT3+wQe1tjY6GKhukjqYEyAHaNeu4PiHidZW+uNygGrfcj/YiGobp3rWLBLB7FSz\nU7V6dRY9PaVONTvTpu/NtvqH+n6ufBLkVM+Z4x6oeTtVnWoWJOxUs3hmUa06ln6ieniYfiNhTrX+\nfDab9TjVScc/9IlSVGyd6rvvpooqjF/8Y3DQ7Wd9sGJQ/MPkVE+bVirsOFOtO9W9vbStmwbEqusX\n16nu76crdbffDnznO+5rdDOC3+fnVNuIanaqeTvlaJ068ZTqVPNASt2pXrYs6/mNsVMNhGeqZ860\nd6q7urzxjw0bgNe/HnjiCf9pyvX9DOCaPN3d4aJaz1Tz/ll3qsfH3e+0UKBZH8Mm67IV1RcB+BrI\nqQaAGwB8BMABAEYBhExfIAhC2tHrVPtlqnkACYtq3kkBrlDURbUaO9CdAnaqbQYq7trlzfKqxIl/\ncHt0uC1+8Q9+je5UM889Bzz6qNep7ulx150nWlDzowDw2GPA5s3eZZmcas726k61Wnawtxd48UUS\njezE2cY/1H4ZGfFOI28jqqMMVLzwQsp1s8vOTtWuXfCI6nyeZn27+2563rS92GaqVdSTPRPd3STS\nud9M8Q/1AD025rrGLFT0+AejZqrDRHWQUz0x4S47aadanyhFxTZT/aMf0Ymm2l51IKf6XlVU61lj\noNSpVscpqO2ePt0s7ExOdVcX/fm566Ysr44uqtXv/Qc/oPKaa9fSDIZqP6j/+X16ptp2oCKvM2eo\nATqxbmvzVtdRRbV6AqSePPCVF7UP+P36PpOv3LGonjXL3qmeOtUb/3jhBeorU/yDnWq1pCizc6c7\nbiVsoKLuVE9MuMct7kuAnPC+PjpBKxQoIx82WZetqH4NgAcBFIp/vJvaAeCrAAyVHYW00Yw54bg0\nY1/Zxj/4cc4fTpmSeVUosujl+AeLajVmoTsFfX3kbNg41aqoVgcx6e23QS9vphJW/QPwimpduHEp\nO8Ab/zj11IzHTeaavOoAIpNA0EW1X6ZaXfbMmXTpd9Ys98Bl61Sr/cInT7ai+qab3ElWbJxqFoPc\nDyyqgUyJU80VFXj9dXRRzVGMIMKc6mnTKJPOIsU0UHH2bPc5dqpt4h96prq/n/rg+uuBRx6hx3k7\nV/v4pz8FPvvZYi9lMhWLf+gD3HRM1T+4pJ4qqjk7zPhlqoHS+If6HvUzAdqep0+3d6o5U62L6s5O\nemzHjlLh/KlPkWDu7vYX1UcfTYI5KFPN4k3ty4mJ0pMCFo6qU63HP3ichsrEBP3m2almobtrlzso\nUR+o2NHhxj/0gYqHHZZBWxuwzz5uu/yc6pYW+lNF9fAw8OMfkxD1g0W16lRv3AicfjptM/xbyueB\nz3yGvgf15Ebtb64c09YW3akGvPEP1eQ4+mh6bS5HjyflVI+C8tcFAC8DOEh5bjeAvU1vEgShfogj\nqnkAzMQEOQttbVQOiZ1qdQCMGrdQnQKA3OowUd3T414eNsVT4jrVpveEZar5NVyPmAWm6u7yTGVq\n/IOXOT7uOtWqeOCTERX1MjXguq9+TjWL6hkz3AlODj4YeOop+0y1ui56/EOdEIdRBd8117jl4fzE\nmDpDonoCow5UGhhAiahW2xDkVE+fTm0eHg4X1TzwUa0ionLXXd6JYExO9fz59F8V1Wr8wyZTrTrV\n//d/wOrV9LjqVHMN369/nWaMYyoZ/1CnXNfh7Ul3m/Us7FNPed/nF/8A/J1qv/hHf7958pdp04Kd\navV31dlJ36dJVN96K22Ten1klSeeCM5UA+5t/URBH1ehx1OixD+mTaPHOZ4H2DvVevyDTwrWrgWu\nusrNVAPmaeA5MqY61Q895FY4MaGL6slJ6sM99qBjwpo1rqj+7W9pv2GKf3R3u5Vjwpxq/fijTsSk\nxz9UUc3fbVKiehVogCIA/BnAFwGcCOB4AFcCWGu5HKGGNGNOOC7N2FdxRTVAtZd/+UvgAx9wD6Zq\n/EMd3KLXqQa8VRj8mDKFDnocmVAPfu96Fx1Aow5U5Pbo6E51X1+pOGtr85aXA9wSVKqoHh11s4PZ\nbBZdXcB//AcJXp4xMMip1uMf7HD7OdUc/5g5k8TAzJlUb/rJJ73iPgxdVAc51Wo0QR0Y6CeqVSGl\n9vX4uCuqt2zJorfXG/9Q6z0HOdU8+JEPtEHwevllQGfPpuXpmWoWsS0trqhuaXHd8fZ2+vxLLvG2\nO2ygIk9Kwn2nimoWg6qgUjPVlRio2NPjPziLT5zV7VONf0xOulExdvMB/4GKgL9T7Rf/mD7dfHXH\nJKr1OtU2TjVX0NGd6ldeAc49t/S1ahvU75q3V92pnjLFnKkOG6hoin+ooprfY3KqdVGtXlXh51eu\nzL46boS/Y15/v8gcD1Ts76fXDg4GD+zjkwp1Vkc+Vhx1FEWGeJvmzzaJ6hkz3PiHjVOtV/8AvNU/\nuJ+WLaN28PgV7s8gbA9B3wfAxaIuA9AH4CEAi0HRkH+1XI4gCClFvcTf2uqfqVZ3aHx5eGyMLtsd\ncYQryPX4hypidVF97bXA3/5tcPt6e8kBVZ0V5s47Kf+WtFPNr3nzmynWoL+GhWVPD3D//a7bOTLi\nCp+dO+lAwM91dgI33gg8+6x7gqCKatOlbPVgzg63X/UPdqpf+1q3Pvj06TTYbvXqePGPKJnqGTO8\nbTWhCj/u/xkzqL0vveReutedavXEzHQCxc/39LgnYWFONROUAe3pceMfulPd3e1eItfjH0uWkNvF\n371JVI+NuZfWeTIgk6jm71p1IRk1U520U82D5kwMDZErqYoxHlw2bRpt+yxs1e8hKP4RZaDi2Bh9\njm38Q10n3amePp1qI6vr6jiuqNYz1Q89RFVwVFQR7+dUh4lqzlRHHag4Pu72hboONk61aaCielLA\nJ/BMmFPNEzpt3RocAZucpP0T55S5ukhHB21Xg4OuU83fv1r9QxXVUeIfJqfaFP/YvJmiX7yvBZIT\n1b8EcFXx9tMAjgRwOoC/A3AwgAcslyPUkGbMCcelGfsqrlM9b14GIyPeUf8//zkddExOtV4nFKDq\nFPp0wjq9vbST7usrdaoBOqAlNVBRd6rb28lNV+H4Bz9/+OHuzlg9uPLOHqDtigdE8fIdB7jySrqv\n5hYZPf7BTigf6PwGKh53HD3GpQyPOooGT9o61dw/fplqtaRcEqJ67lz6frdsYee3NFPtN+BPbzNP\nKDM4aC+qg6oV9PaanWqTqFYHKi5bRo9v3Ur/uWqL2t5czh2Uye4sX90AzE61KnDUTHUlBiqaptdm\nuOwh/xbZpW5pIbE0MOA6paoINA1UVC/DA3YDFXnKbNuBikGZ6pkzqY/1E9hCgX7DvB3p1ViYOXNo\nHf/7v+l9Nk41O7X8GE91rjrHUQYqqk41s3OnG4nQRXVHhzf/zv2RywGHHJLx7LPV7y/IqebP6uuj\n7T7MqZ4zx9suPnnm4wRvf35OdVsbfXfqxEFxMtVq/EP9jqZPp9fytpSUqNZ3X7sB3AvgDgDbLJch\nCEKKsRXV6iCRfJ52nmNj5Ar19tJ7f/ITytJxXlB3GfVMtQ29vXTJ1W+2tt274w1UtMlUm1DjH7oT\npF4GHhx0XU59mV1dFAP50Y9cR9+UqTY51WEDFffcE9h3X3fSnb33Btavj+9U685Oa6u7Xqqo5oF/\n6kFcR10fXm5/P/XbSy+5ZRb16h9qjMIvU714sfvdRBHVQU716adTjpnby38sIFRRzUJAFdWbNrnt\nUwVJSwut4/btbmmzIKeaxaDJqa5U/KOz0/+q1fbtJKr5M/nEGnAdyF27XMGptld3qufMof9RBiqO\njtJJnF+m2s+p1jPVXV3uyaceZQFIsPH3rbukPJD09ttpuf/2b3TVziZTzU61OqaChWnQQEV2qtXB\n2iyqx8fNolqtkc9XDoOcarX9cZ3qLVvCnWo1FsQGDP9O+LbuVKvVP+6+Gzj0UNe8OOss4Itf9P/M\nIKdaz1QDtF+qRPzjJQDXADjO8vVCCmnGnHBcmrGv9JJ6tk714GAW3d10AGVRzfT1uVEPvgTe1lYa\n/7BBdarV+AcfWHbtqpxTbUJ3qv1EtepUc6aaUZe/bZtd9Q91xr6ggYpdXTTIhkX11Kl0UlJuprq1\n1R3pz+4qH3BZBADmrKu6Tgz3dUsLCbSuLj7QunWqd+70npj5OdUADSoE6LtJKv4xdSpFmwBab/UK\nRnc3nbzwOqjxDxbVnK/XRTVAfbhtG4kQ/v6CRLW6jfzyl8D99ydbp/rnP3d/U7mcd+IblXyefnOz\nZpU61QB9/yMj9B3MmeMVvnr8o7ubXqM6+Xr8w+RU+02YE5ap5kGHulOtfg4vH6DfMFfw0EU1C+ET\nT3TrzqvT1jN+8Q/Vqeb38OewS21yqguF0pNtk1PN+0U9/sH7LLWknioqV6/OlhX/4Kw0f1+LFwNP\nP+19z8SEV1Srg9r9nGr+DXAN/UzGHajY3U3b42teU9o+Jqj6h7r+/Dw71erYhyBsRfWvAfw9gCUA\nVoMGKu5r+V5BEOoA1akOmvxFFdXsZqh5Z1Xs8OQo6sGFd+DlONVq/IMPNDt3xhuoaJOpNsETKvDg\nHFUE6KI6yKm+6y7gwAPJ1fFzqvXqHzYDFbu6gCuuAP7u7+g5du7i1KlW4x/8HLus3d3eyhR8hVnv\nngAAIABJREFU4ObycCZMTjVAEZC5c93+6ukhob11q3eb8ctUq0yf7s40aINNXV1uL5/IsFN9/PFU\nnUCPf+iiziSq+YRUnYRjdNQ8UFHdHru7qXThwIDX3SvXqV640K0bHJSpHhykbUoV3apT3dJC28CG\nDW4kiL933an+xjeAk082R5kYk1M9MmKu/uEnqvk5v/iH2kZePhDsVKuzPvK6Dw3Fy1Tze9jUCHKq\n9b7gTD6L6l/+kvpVdapN8Y+gTLVqsoyNucZI2EDFri735Io/88c/Bu64w/seP6eaTyz8nGqOyalx\nEx67EgafeAZlqvl7AVxRHSamX+0Hu5fhUwD2AnAWgDWgwYrrQVnqjwKYarmcIPpB4n0NSLi/EcBM\nUMzkKQD3FF8jxKQZc8Jxaca+0neiNgMV83lgzz0zr4rqKVNKnWqeoIEJil0EwcX5daeaDzh84LMl\nCaeaD0xc85XrdevxDz1TzXR2AmecQXntLVv8M9W2TrVeA/u449xoAk/vXW78g59jp5pFdW+vV1Sb\n6gc/+ij1h8mpBkhQ77EHi2rKVO+/P9Wu1p3qMFHNIimJTLWKKqp5UFRrK01YoZfUA6jyCuPnVPNV\nHjX+oWeqOT+qX65+wxsyvk710qWuS+7HkiXe6gvqiR1nqk37goEBcgVVoak61QB9By+8QNted7d3\nWnF1/U47jV6rnvDZDFQcHg52qv3qVJsGKnL8Q902dacaoEHRQLio9nOqTSX1VKdaFe+qsFZPmHg6\nbj1So8Y/DjsMOPZYf6faVFJPdWoPOsibqR4ddb9bW6ea28rL5O1MXf8wp5rXm7fBlhZ6btcut795\nVkYbw0CNr/G68dUndf35yhH/vpMW1QAwAeB2AGeDBPYnAbQD+AGodnW5XAPgTgCHATgaVKbvCyBR\nfQiA+4v3BUGoAFEGKvIMffye3l5XWOmienTUuxO2EawmeIeuZ6r5/+Bg8tU/wjLVfGDiHTO3yy/+\noS+Txdncuf5OtSn+wU61Pk15W5t7WVQXzyyqy41/AK6o5QF8o6NeUX3eeXRZVhc7l18O/OlPwaJa\nd6qnTaO2vPKKXfyDiSKqH3ig1EXzwxT/UJ9TB5ICwK9/DfzhD/7tto1/sLBSB/TxSRiLJP13+5Wv\nAPfcE7w+b3wjcNFFdJuFojpTol/8Y/t26mP1M/U66DNnUo5fFdWOUxr/UE/QGJuBihz/KMepPvJI\n4GMfs4t/7NpFZUO5TCBgFtU8M6OtU60aBCyq9eof7e30n2djnTq11Knm+AcL+t7eYKf67LPpShZf\n+QvLVPPvMsip/sAHgHe8w91fcxsnJtx61AwPVGT4teq+1PRZ/F1we+KIatWp1gf58smOOttqJUS1\nyiCAu0Ei+GUAPcEvD2U6gJMBcNGqHIAh4P+z9+VxclTl2s/0TE/3bJnJTJIJ2SEkLIEQNCyyNgIX\nwUCEeEVQFARFlE+v109BlCsqqBdBvS6ouFyWCyqbIPDJBTRNAE1QyMKOIXtIJpkls+9zvj/eeXNO\nnT5VdXqZme6Z8/x+85uu7dSpt6urnnrqOe+L8wDcOTzvTgAfyHI/ExoT0SecKSZirNIh1bW10ufa\n1JTcfzMxkWo/pXrSJKQFNSe0av/IlFSrAyd1ZKJU8/p9ffICXFbmtX/4eapVUt3S4vUe8s3uj3+k\nlHhBxV+KimTlyWxJdTRK25hItW7/UEl1by/dqA86KJVU9/XJMsoMf1Itz6u5c6n0u+q3zaVSnUiQ\nqmcDk/2DoXqqmXQdcghwzjly/SBPdZD9g/etK9WrViX3fx+6/aO3l+Ld2Eg2jMFBKlSiY/t2+m9L\nqvv6gGeeoRirD7h8bjLq6lKVav13y9aieNw8PoDhZ/9IZ6CimqealeD584Ezz7SzfzC2bs1cqVYz\nfTCpfucd+g54G37joNo/mFSzz7i8PFWpZqLNZJRJtZ9SvXQpnfd6RcWBAeCtt1I91Xx8JqWahYUT\nTqDxB7r9QyfV/HClViNVBRh+W8rtqtBJdTxub/8wKdVMqlX7R2WlHHQ9Uko1QLmqLweQBLAZwPUA\nVgFYlmY7Og4EsBfAfwN4CcAvAVQAqAfQMLxOw/C0g4PDCED1zQZ5qgcG6CJWWip9zHwBNXmq/Uh1\nVZqmMb6g6/YPlVSPtqeabR/64KrOTvpcXU3941ehgMyJq7Y/bZq0fzzyCPBFJfP/wADlz12+HPja\n14KLv3D7bW1eHzeQmf1j8uTUlHoAFTSZPNlLqrlABBMr3RML0DS/4WCo8T/3XFLPysrkAwJA1dU2\nbRo5pTod2CjV0ahZJQ3zVHPMdPuHms5QJ9XqOaDbP3p7Kd6//CVw003AH/5Ag1d1NAzfZZkohtk/\nnnwSuPZaOo/Vfeqk2mT/UP3D6vHF48H2Dz+l2uTd90upx8vUgYp8HoVl/ygpAb76VeD44ymzkR+p\nLiqy81Qz8Y3F6Pu55Ra5jWp54D/+Hvj3H4uZ7R/84MKkGkhVqnUFmB+MwjzVNvYPhm7/6Ovz2j/4\nmsJ+e36rqYsd7NNWkY1Srf5WuC0WKXSleiRJ9bkAfg9SpW8HIAB8EsB0ABeBFOtsUALgXQBuG/7f\niVSrhxj+c8gQE9EnnCkmYqxsPdWsmlRXk69y5szE/ou3Xs57YIAuxib7R6akOldKdZCnOl37h6pU\nv/02EZmpU6Uaz5UW2VM9dy6tywN/6usplRyQWu54cFAqbkxK/Iq/8HG1tHi9rUBm9o+aGrOn+ppr\nqP8mpZr7Z0qpxw8cfqT6xBNJNSwvB8rLE/vjM3cuxVW94YY9QDFJyjWpDlKq1YGKtqRaT6nHDzGq\nUs3EQ1Wq2f6xcGHCQ/JNSvWWLamFTVQwqebzjsmaX/YPJjMvveTdpz4w1GT/8CPVuv3DNFCRH1oY\nJqWacz2zRU2FmqealWA+/3TVndtnklxcDNx4I73V2LBBfr/8EAXQdzh3rlSqTaSaHxRUX3N7u/ze\neaCin1LNpDoe95Z/1wcqqqTaT6lmmAYqzp2b6qlWSboOnVTrSnV/v1ep5j4wcdWtguqgeROpVoWD\nWEzGJQzcL/VBVbd/8BsE7ls69g9DaIx4BMCbAG4E8D8AtlluZ4sdw39/H55+AJRhZDeIuO8G+bj3\nmDa+9NJLMW+4TmxNTQ2WLFmynxTxa3w37abddPD00BDw+utJJJNAcTHdfEzrb9xIy6urgfXrk8Ne\nahpUtmpVcrjQRQIzZwLt7bR9SYnc/rXXaHlVVXr9owt6Etu2UXsDA7ScqnEl0NsL7N5N/bdpjy7U\nSWzdSturyw87jKZffTWJ4mLz9pEIsGVLclhdouVCJIeLriSweDHQ20vr19fL7VtaaBBQIiHbq6tL\nYO9e6k9TE9DdLdenAhQ0vWtXEi+/DJSWUv8bG1P7LwStX1np7S+R6uSwtSQ8PmQpSKKhgdqLRFLX\nX7AgiaEhoKeHvp+dO2m6tJSI3o4d3u+jqSmJV14Bli2jaSCJtWuBpUu9+y8ro/OJpw84IIEdO+T3\ne955CRx8cHD/SalO4u9/B5YvDz9e2+k336TjA4CuriTmz5fx7OxMDr+eTwyTLu/xb9+eHM6sIdvr\n6AB6exOYPh14443kcJl2GnyYTNJ0TU0CTU1Aa2tymHRQfAYGknjhBdmfpqYk1q8HVqyg6cbGJF59\nFWhuTqClhV7pE7zH19hI088+S9M9PTTd3JxEdTVQVeVdv6+PplesoP7NmUPT69bR+c3td3XR8VVV\nJRCPA88/n8S0abScf79dXUAkkhgm3TJe0Sjw8styur8fiMWS2LRJtt/Skhy2RCUgBPDMM8lhBZTO\n95aW1OtBUxMQi1F7L7+cRGMjtTd3LnD22Uk89ZRs/6WXkqiqAlpb6feQTNLvfdOmxHC+4iRWraLv\nGwAOOojO/5YWeiBctUqeP5EIrU9EPzGcvSI5bL2h69dzzyWHs18k9qcrJSsLxWP9+uTwgzSdDxdc\nkMRDDwHnn0/tvfFGctgGQdeHl16i/ZeU0O9xzx6KR38/tcffZ0mJjAdAywcG6Hzl+wFZkmg5H69+\nPXz5ZUqvmkgkhpXq5PADG/Vv507v91lUlMTzz9P9o7KSSqNTOkcm9MnhSrmJ4fOWto9GKf59fTTN\n5ycfX9Dvl+NfXEzTDQ3yerpxo4xPRQX9fpJJItTU1hbkCscELEtAeqGzwSrQgEQAuAHAzcN/1wzP\nuxbAdw3bCQc7rFy5cqy7UDCYiLFavlyIP/yBPp9/vhAPPmhe7x//EOLoo4U47jghPvYxIc49d6W4\n+GIh6upo+RVXkFa0caMQe/bQ5wUL5PZPPknzfv/79Pq3eTNt98gjQpx4ohCrVtH8bdtYmxLic59L\nr81oVIj//M/U+dzvv/3Nf9tDDhHipz8V4tBDhVi2jObNmyf78t73CnH66fT5Jz+h5StXrhSXXirE\n5Zd72/p//0+Ik0+W2y5ZQvPb2oQoLpbzTzhBiB/8QIjPf16I004T4sADhbj9dm9bs2YJUVQkxNCQ\nd/6mTdTGn/5kF5szzqBz4sgjhbjvPiFWrDCv95OfULvvf78QixYJcdJJ9N08/LAQ553nXfeII4T4\nv/9XiFdeodgDQqxfn9rmffcJMXXqyv3Tt95Kcbj6aru+CyHEc89R+21t9tvY4J57hDjlFPOypUtp\nnxs2CFFSQp9VfO97Qpx1lnfeRRdRXK65RognnqDfFiDEBRfQ8tdeo3MMEOLYY4U45xz6fOqp9P+6\n61aKmTNp3Q9/mPrHWLSIfhOHHUbnyuOPp/ZpyhSaNzQkY/bUU0K0t9Nv/OqrhbjwQu82Dz8sxLnn\n0ucbbxTiuuvo8x13CHHJJXI93t/tt9Nv9tlnhdi+nb7LadNonRkzhNixg649p50mt73iCiF+8Qs5\n/c1vCjF9uhCf+IScV1kpRGsrtdfXR/N6e+nc6u8XIhIRYnBQrr9y5Upx0klCPPMM/UbuuEOIj3xE\nLu/qEiIel9M/+pGMPZ/L99xD39lpp9H8NWuEOPxwuc3vf0/rRqPemD3yCK1fU0PTDQ1CTJ0qxPe/\nT/MvvFCIt9+ma8jtt9M1YskSIY46iv7mzKEYbdxI3yVfE55+mtorK6Nr4eTJFNvdu4Xo6ZHXjb/+\nVYjjj6d1r7pKXpOEEOIzn6Hpu++m9X/wAyEuuWSl+MY35PcYidA1obhYiNtuEymYM4fOG8b3vkdt\nHXccTZ96Kh0bo7GR+iqEEAccQOf9TTfRdyyEELfcQtvffLMQkybJ4xWCrnG/+pUQZ55J06tW0bKv\nfS21Xzr6+2nd972Ppj/7WSEWLqR9X3stzVu0iO5tfK4tWSLEZZfJPiDANRHxW6Dh79r0AgDfAtH2\nvwC40LKdIPwfAPcAWA/K/nETiESfCUqp916YSbWDg0MOkM5ARbYGNDXJLBDqq0aAXsWpHlhGtvYP\nvUy5+rq2Js2kmzwoSIfNQEW2f6j+XnX9KVPk68N6ZTRILJZ67OrANoA+t7ZSWiz1e+jpSU2pp/eR\nSw+zdYKRyUDFKVPoFbpu/1Chfp9hnur+fmpvYMBrodBRVuZ9lcv+4XTsPaPhqdbBMefzU++vTZ5q\nrtim2j8iw3fqjg4MK+PefPHcH5P9o6ODBimSIkfz1Up8HOe2Nu9AxY9+FFizxlxRUfVOq55q3f7B\n/m3d/sFWIfX4FiwATjpJbltaak4/x1YPTl1ZXu61GrFXt6SEzhvdAsLnUTSaWoTKZP8gZd1ru+np\nkd+Tnt2oupq+T/271z3VPOCQ49Xbm5r9Q/VU6/aPFSvoXHj5ZYpFb683pR7bGk44AXj3u70VFXX7\nh55ST7fGsB2wtFSOI9ERiaR6quNx/5R6ah+WLaNxE2osgzzVsRhZD9n+MWeOnB8Gbpe/B3Wgomr/\nOPpo4D3vkevk2v4BUI7oCwF8HMDxw/PWAfgOgN+m0Y4f1sOsiJ+Rg7YdMDF9wpliIsZKL/4SlKe6\nuJhuHtu306v7oqJUUs0XYCA3AxX1lHq6NxMAPvjB9No0kRzAzlPNN249+wdjyhRJUlRP9UMPmUm1\nOuiou5s8m+x1BaRfUh+oqN9ISktT/dS8PZDeQMU5c6jwip79QwV/35MmBZNqzlzAnup43L+0fFkZ\nWWIY/CBg+q78wKQ6aLBpJlA91To4Rrxc/x78sn+oAxW58IofqT7oIO/ymTMTRoIL0LmyfbskTUwM\nVPLLA4k7OrykmvtRWpr6gK1urxJ5faDizJn0n6tBqqRar0i4aBGlAGSYBipWVHgHvnE8mTBWVHiv\nY9XV9HBaVUUPPIlEwjMYsKcn1ffM1fqKirykmtfTSbWe1rKmhgif/j2bPNX8O+HvyuSpVuNBVis6\nvx54ALj9dqpUyA9WPDCcj6+oCHj+edr+lVf8ByqaUurNmuX1VAMyp7Wtp7q21vsQ0dYmY6uS6ttv\nB666yjtQMchTPXkyZUxhUj1jhncbG/D555dSb/lyqh/AfeDiS+o5aUKYUl0M4P0A7gOVKv8ZKAPH\nj4aXfwHALwC02R+Kg4NDPiJdpVpVZMKU6lyQar6AcrGE971P5oMF6EJ95JHptelHqtNJqccXZH39\nI46Qpa1VpXrhQuDQQ1P7oSvVatU5QKpQQSn1uC0TqY7FaFk6AxXr6uhG3t7uT6rV79OPVN9/P8WI\nlWrOwACYb4SzZwNHHSWnMyHVPLjPr9+ZYuZMeoNggv4wpn8PfgMVmWhGo8GkurMTOOMM7/LOzmCl\n+vXXKZ719UREAK/q1tND33Nnpzf7B7dvItWssgKp2T/Uh5iiInq4nD9fktH+frNSraO6Wg7eBWRB\nDibVavVGXanmc6qmhkh1JAKsXetdzg+y6vkXiVCfWVDo7JQqKKv7nHWDFXBdqZ40iUi1n1Ld3y/T\n6fmRaj1PtT5QkX8PixZRms32dvr98QBePeMSYDdQUSWVep5qgM5VW6X6oIMoZZ/6EDQ0JONmUstt\nleraWnpY1LOR0PgaO/C5zg/Jeko9tW98reU3j0EIutx8H8BOAI8COAFEqI8HMB/keQZcNo6CApv2\nHcIxEWOlpk0LItWqUt3UBLzzThIVFWalmi9MubB/RCJ0M6moAFatonlcvnrRIn9lPQh+qdk4DmEp\n9fQ81dGovClfdRVw+eU0n0l1MpnE1VcDF1/sbau01EyqVVRXpyrVujLIfVBT+KmoqkpPqY7HSanb\ntStcqWZSzfYU9Sb+/e/TfzVPNRMDU/wXLgQuuyy5f5ofqNJRokpLvTaHXOGEE4Dvfc+8LEyp9iv+\nwuuqbyxMKfU6Ouhhbc0aSVZefz1pJLgArbNjBzB9Op2DO3fSfDUzSW9vKqlWs3SE2T+Csn8AVLTn\nlFPC7R86li8H7rtPfof9/TLjCR8DX3NUa4NqVaqulpaDjg6Zp1q1f+j7Vi0gXV3yzQDfEtjS0NVF\n37NOqvkNjJ9SzcfCMeRtVduGnv1DTanHBBoADjiAsrqo8zhdoH6eBZFqfpOhKtVbtyY9xBagc5Wv\neTp0Un3iicCPf+wl1YDMAKITVxYWdKWaKyiqqKsD3nhDvkVgqG/2wqAr1ZGI/3kcidD5NmlSuJ0s\niFT/G6j8+OcAzAbw7wBesO+yg4NDIcGkVBcVSYVHX49T6rFSzQRCVarVXKAM/pxu8ReAfJe1tcDB\nB9N0c3NqkYV0kI1SrabUU9dX/cxMHMOO1WT/8CPVqlIN2Ns/ABk/G0yfLsnYO+9k5qnmG+rq1fIh\nYO1a4AMfCCbVOjJRqscC/L2XlpLSfu653uXTpnnfWgDy2Nj+AXiVVyadkYi34hwv5xR+QOrDMJ9T\n9fWU4nH3cO3jri5Kx3beebT+5Mmp9o8gpVolHbpS7febUUk1ZS6Rx2c6B44+muZzsRp+EOO+6Eq1\nmlubfxvV1bKQEs/j60VJSaqnGqD527bJVHqVlcDVV8trDh9Hd7csjqST6q4uf6U6HvdWwUxXqVYJ\nNBeNUueZhAwgXKlW7SamPNWAVKpt7B+mfZaUSFJt6kOQUq1eQ2tr6fxVSfWMGem9qVSVatX+ccUV\nFE/1Gsqe6urqcFIddIn6NYAPgaweV4HyVP8ONGjQoQAxEX3CmWIixkq9ualP7S++SDc4hjpQUQjg\nwAMTKfYPNY8wTzMytX8AlB8WoAvq+99PSnl9fXakOkiptrF/6J5qVSWOx71qqd95pds/BgdT8xyz\n/UNVqk19jEZTC78wVq/2Px4dPxo2+f3iF6RUc+UzHTqpBqh/XLqez6OpU+lmxcrhrFne7XWosSoU\nUq0+6Kxbl7r8/e+nPxW6Ug3Qd62T6spKaQ1hKw1A6faam+mzqhrz4DWAfiOsrgL0f9Mm+m3H49R2\nZ6dcbmP/sPFUq1DtH/G4dxCeSakuKiKrDR8bpdST9gGVVKvkTbd/8DWjpwc4/fRE4EBFPh6O81//\nCnz+88DHPiYfmFid7u2lh04TqRbCrFSz/UpVqlVSzdYOflAZGpJvvqJROjaVQFdU0Lo7d8p5/PtK\nV6nu7vYO/q6vT/VUp2P/4FipSnVVlbcP6rlSUkLfqZ+n+rDD5PWrtpa2Vx9Q+S2MLUye6qEheuhf\nudJLqtn+MWNGdko1F3f5CIDtoOqJbwBYC+CLAds5OIxbXH898Hc9F844gV/xF3XENuC1f/C6U6bI\nYhv85M/QL8J8A7a1IZhQVEQX1i9/mSwWmZItP9XF1lPNx6Yr1elCJ9WAjLuqumWrVGcCLkxja//g\n/jGpVrNZqOp7Okp1JvaPsYCa/cMWfGzl5fJzVVWq/UN9WGPVH/B6qlXVWB1QxQ+erFx3dVGlw717\n6fypqPBXqk0VFW091SqYVPNAO7ZZBA2CrayUJJozxqhKNZ/nulKt2j9Y6eZj4z6aBioC3jht3UrW\nMjWTTjxOaiuPUdBJtd9YAfbuMrk1kWo1NqpS7Wf/AOi73bjRO8/0AKySar+BiiyYBCnVQYO7g5Rq\nLv29ahXwjW+kr1Sr6/LbNv2tTzrg75jvVywkbd0qByiqx9bZaadUhw3h6AZl9ngfgLmgXNGlAL46\nvPy7AC4BYDn0xWEsMRF9wpnCL1Zr1lCFsPEIv4GKOqnmC+/UqTS9fXsSF1wA3Hab3FYlejpxtU1N\nFIbaWhqks2FD5mQrG0+1av9QPdVBhNbvvDLth1+TMvmsrKTYs5czSKnONal+5530SXVFBfV13z76\nrrq7vUQvaKAi4I1VoSjV/JtJZ3CkqlTPnk2fN20yK9UMlVRv3Zr0EBHug1plkEm1Oshv2zapGrNS\n3d1NbYfZP9LxVDOYVDc2EulTiZxfvCoq5Bsb3VPtN1BR91SrSvWTTyaxcydVPfRTqouLJQE/+ODU\n31IsRhVLWbX1I9UmpZqJOJNq1Z9sUqrD7B+AJNWqPUL3GgP2nmpW0rdvT+Zcqa6ooIGzL74YPlBR\nV6pzTapNSnV7O51vevzY/pGtp1rHO6BiLIsAHAvgp6BiLXeCKh46OIx7cI7d8Yh0SHVxsbyg8cVU\nVct0pVq9wdhmnwiD6g3Otae6qIiIRtAFNB6XGRtUgus3SDCsHzqYVPNNmksTt7d7SbUp+0cmffDD\ntGnkxU3XU81KdWsrnSu6Eq+eL2EoFFIdlm7LBNVTXVREZdqBVFJ91FFSMVVJNQ8M5fl8fertlYRd\nJ9WdnRiuxCkH/7JSzWW/c+2p5qwZDQ10Ttkq1Y8/DnzkI2almo9P9e/rnmqqVEr73rqViDKTWz+l\nms/VJUtS+xSP03I/Us0E0ETW43GZf9uUUq+nh9ZRlWom1uko1SayyaRaCLNK/LvfAY88Ikk158bm\nvgPBpDoeT70WFRfT/gYHZfaWjg5pAwoaqKgr1epvn9+KZkqqIxF5zqqe6s2b6cFWz/HP9o9ck2oV\n/wAVa5kBYAWAlRm24zCKmIg+4UzhF6vOzsxunIUAPU+1H6nmV4d8QVuwIOFZXlKSqlSrF8+lS+WA\nqWzAF1beRybwU6oB4O23g9v93e+A44/3KtVh1osgTzUg4zZ5splUx2Lk91TtH9One9vKtf2joiKY\n+KgDT5ksRKNSPWxpoe8qEvGeF+w7TcdTne/2j0yuDapSDQCPPebNKcyxv/tu6S9WBypGo9481apS\nXV1N65rsH1QOXdo/WKmePNlOqTap4zb2j4YG2Z8wUl1RQcd9772pSrWaWs4vpR4Tzfe8hwd0JvYX\npAmzfyxZQuMJTMcB+JNq7o+fUm2yf3CqQLZ/qJ5qW6U6jFQzOe3vl+SdEY3S97J6tSTVU6YkUuwf\nLCKYrouPPkqZaVQUFUm1mu0ffJ5lq1RHIvaDrnWoY07U7B+bN9NbDB2cpnAkSTWjD8AfAJyfZTsO\nDjnB734HrF8/cu13dIxvUm1KqdfSkrpecbG0f+hP9bpSbboIZ/PajjGSSjVgfoWqYupUOVgxV0o1\nv86eOjXV/sFKNfs52WvK+ZjVtnKpVDMRtrF/sLpVVIT9BYHeeYfIXTxONzM+RlWVCwPfBPNdqc7k\nLZZOqktL6fehe6pjMVkxVFWqOzrMVgwe0DppEj14mewfPHCOvcuqUs3rhqXU033cYfYPE6n2e1hS\nz2MeqMh9URV6Xanm9tjP/6530bG9/LLMEBE0ULG7m74P/bcFyN9DEKlmC4eK0lLaprSUst/ww3E8\nTr931f6Rrqf67be98xYuNMeT0wGy0q4eM4Mzs6hZlVSlmh/udUyblnov4Hgxqc6VUj1lCu0v04ds\n9dj5eykuphStnJdchfrmI+xNa47T4jvkMyaCp/rxx8mvlS38YsU5dscjdPsHq1r8+pTBAxX5grh+\nfdKz3OSpTmfgli2YVOsX3HQQpJTaQs9TnY2nmglnXZ18Q6CmWYvH5c14xw6ar9/Icq1Uh6nE6g1X\nX49JdU2NfPXNv8+eHuAf//DvayF6qrOxf/B3D3j9ryYlV41xU5M5TzWT6r/9jfIZ66S6pYUysLD9\ngxXEmpr0Uuqlm/1DJdVsMwhSqhm6/UPdl59S/fnPk/rI+37xxeR+JTJIqdarJKrgXPQvMB9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fUAeSGZNo0+T5oUnv1Dx0hm/wC8RVMKGSZSnYubWq6QLamOxUb+xpgPGG2lWq+ux0qwn/2jpISW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\ncLGyh4uVHSZanJyne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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 47, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Finally a realistic simulation\n", "\n", "![sys1](sys1.png)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 47, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## With self-tuning PID paramaters\n", "\n", "![sys2](sys2.png)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 47, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Business Should Shape the Algorithm and its Learning\n", "\n", "1. Self-tuning systems can work well\n", "2. System specific safeguards are needed\n", "3. Slow servers causing data delays\n", "4. Raising and lowering threshold values are not symmetric business decisions\n", "5. Start carefully\n", "6. Check for bad behaviour\n", "7. Monitor systems" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 47, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Our production system\n", "\n", "![real_pid](real_pid.png)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 47, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "# Thank You\n", "![logo](maxpoint.png)\n", "\n", "## #9 on Deloitte 2013 Technology Fast 500\u2122 Rankings\n", "\n", "### michael@maxpoint.com\n", "\n" ] } ], "metadata": {} } ] }