{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# First time here?\n", "Please see our [demo](ReadMeFirst.ipynb) on how to use the notebooks.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Timescales of measurement and why they matter\n", "\n", "The purpose of this demo is to get you thinking about how the timescale of your measurement technique affects the answer you get. Every physical process has one or more timescales associated with it. \n", "\n", "For example, an enzyme is synthesized and degraded on the timescale of minutes, performs a single enzymatic reaction on the timescale of microseconds to seconds, and fluctuates on timescales down to picoseconds. What properties you measure will depend on *how* you perform the measurement, because each experimental technique has its own timescales as well. \n", "\n", "For example, think of a camera. We think of a photograph as capturing an instant in time, but in reality a camera has a finite shutter-speed: the shutter is open for a period of time, and the image recorded is the sum of the signal that enters the lens during that time. If motion is much slower than that shutter-speed, then effectively no averaging takes place, and we get a single sharp image. However, motion faster than that shutter speed blurs the image. The other relevant time scale is the cycle time: how fast can we record new images? Varying these two times will have very different effects on the data we measure.\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll start the demo by importing a few packages we'll need." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "from ipywidgets import interact, interactive, fixed, interact_manual\n", "import ipywidgets as widgets\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we're importing a time series we've previously created. You can think of this as the true underlying behavior of the system, if we had an infinitely fast camera with an infinitesimal shutter speed." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "all_data = np.loadtxt(\"double_well.asc\")\n", "all_histogram,bin_edges = np.histogram(all_data, 235, [-2.35,2.35], density=True)\n", "time = np.arange(len(all_data))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what we get if we simply plot the time series and histogram it. We can see that there are 2 primary states (centered roughly around -1.1 and 1.1), but that each state has several substates associated with it." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(time, all_data, \"-k\", linewidth=0.1)\n", "plt.figtext(0.5, 0.0, \"Time\")\n", "plt.figtext(-0.1, 0.5, \"Value\")\n", "plt.show()\n", "\n", "plt.plot(bin_edges[:-1], all_histogram, \"-k\")\n", "plt.figtext(0.5, 0.0, \"Value\")\n", "plt.figtext(-0.1, 0.5, \"Prob Density\")\n", "plt.show()" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "Now, suppose our camera is a bit slower (perhaps because we have to manually push the button to take an image), but we still have the same infinitesimal shutter speed. The result would be that we would have fewer data points (the time series is downsampled), but still no averaging. What is the effect on the time series and histogram? Play with the downsample factor and find out." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def downsample_both(downsample_factor):\n", " reshaped = np.reshape(all_data, (int(len(all_data)/downsample_factor),\n", " downsample_factor))\n", " time_reshaped = np.reshape(time, (int(len(all_data)/downsample_factor),\n", " downsample_factor))\n", " downsampled = reshaped[:,0]\n", " time_downsampled = time_reshaped[:,0]\n", " down_histogram,bin_edges = np.histogram(downsampled, 235, [-2.35,2.35], density=True)\n", " \n", " plt.plot(time_downsampled, downsampled, \"-r\")\n", " plt.figtext(0.5, 0.0, \"Time\")\n", " plt.figtext(-0.1, 0.5, \"Value\")\n", " plt.ylim(-2.2, 2.2)\n", " plt.show()\n", " \n", " plt.plot(bin_edges[:-1], down_histogram, \"-k\")\n", " plt.figtext(0.5, 0.0, \"Value\")\n", " plt.figtext(-0.1, 0.5, \"Prob Density\")\n", " plt.show()\n", " " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c5f9f4e64e454a199180bfeeca679436", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(Dropdown(description='Downsample Factor', options=(1, 100, 1000, 2500, 5000, 10000, 5000…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "downscale_options = (1,100,1000,2500, 5000,10000, 50000, 100000)\n", "interact(downsample_both, downsample_factor=widgets.Dropdown(options=downscale_options, description=\"Downsample Factor\" ) );" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that as we reduce the number of data points, the time series gets coarser and the histogram gets noisier (so we can't see the finer features). However, the width of the distribution stays more or less the same; any changes are just the result of it being noisier." ] }, { "cell_type": "raw", "metadata": {}, "source": [ "Now, imagine instead that we are changing the shutter speed of our camera. As with downsampling, a slower shutter means fewer data points, but now each data point is the *average* of the signal over that time period. What will happen to the time series and histogram? Play with the averaging time to find out. For comparison purposes, the histogram plot will continue to show the unaveraged histogram as well." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def average_both(average_factor):\n", " reshaped = np.reshape(all_data, (int(len(all_data)/average_factor),\n", " average_factor))\n", " time_reshaped = np.reshape(time, (int(len(all_data)/average_factor),\n", " average_factor))\n", " averaged = np.add.reduce(reshaped, 1) / average_factor\n", " ave_histogram,bin_edges = np.histogram(averaged, 235, [-2.35,2.35], density=True)\n", " time_downsampled = time_reshaped[:,0]\n", " plt.plot(time_downsampled, averaged, \"-r\")\n", " plt.ylim(-2.2, 2.2)\n", " plt.figtext(0.5, 0.0, \"Time\")\n", " plt.figtext(-0.1, 0.5, \"Value\")\n", " plt.show()\n", " \n", " plt.plot(bin_edges[:-1], all_histogram, \"-k\", bin_edges[:-1], ave_histogram, \"-r\")\n", " plt.figtext(0.5, 0.0, \"Value\")\n", " plt.figtext(-0.1, 0.5, \"Prob Density\")\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "1a7dd84976644dcf8e3f0171470d715a", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(Dropdown(description='Averaging Time', options=(1, 10, 100, 1000, 10000, 100000), value=…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "average_options = (1,10, 100, 1000, 10000, 100000)\n", "interact(average_both, average_factor=widgets.Dropdown(options=average_options, description=\"Averaging Time\" ) );\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When you move the averaging time from 1 to 10, very little changes in either the time series or the histogram. That tells us that the timescale to move between the substates is probably less than or comparable to 10. \n", "\n", "When the averaging time goes to 100, the variance of the time series is noticeably smaller, and the substructure within the two main states largely disappears. This means that during 100 time counts, the system is hopping repeatedly from one substate to another, so that each \"measurement\" records an average of one or more substates. Also, the peaks have gotten a little narrower, for the same reason.\n", "\n", "Now look at an averaging time of 1000. The variance in the time series is much smaller, and the histogram peaks have gotten significantly narrower and have moved toward the middle. This is because now each \"measurement\" likely has contributions from both major states. The histograms have also started to get noisy, because we have a lot less data.\n", "\n", "Finally, look at averaging times of 10000 and 100000. This time is longer than the time to exchange between the two major states, and ** __as a result we no longer see 2 states at all__ **. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.1" } }, "nbformat": 4, "nbformat_minor": 2 }