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o,a,s,u,l,f,p,d,y=[r||v],m=c.call(t,\"type\")?t.type:t,x=c.call(t,\"namespace\")?t.namespace.split(\".\"):[];if(a=d=s=r=r||v,3!==r.nodeType&&8!==r.nodeType&&!xt.test(m+b.event.triggered)&&(m.indexOf(\".\")>-1&&(x=m.split(\".\"),m=x.shift(),x.sort()),l=m.indexOf(\":\")<0&&\"on\"+m,(t=t[b.expando]?t:new b.Event(m,\"object\"==typeof t&&t)).isTrigger=i?2:3,t.namespace=x.join(\".\"),t.rnamespace=t.namespace?new RegExp(\"(^|\\\\.)\"+x.join(\"\\\\.(?:.*\\\\.|)\")+\"(\\\\.|$)\"):null,t.result=void 0,t.target||(t.target=r),n=null==n?[t]:b.makeArray(n,[t]),p=b.event.special[m]||{},i||!p.trigger||!1!==p.trigger.apply(r,n))){if(!i&&!p.noBubble&&!g(r)){for(u=p.delegateType||m,xt.test(u+m)||(a=a.parentNode);a;a=a.parentNode)y.push(a),s=a;s===(r.ownerDocument||v)&&y.push(s.defaultView||s.parentWindow||e)}for(o=0;(a=y[o++])&&!t.isPropagationStopped();)d=a,t.type=o>1?u:p.bindType||m,(f=(G.get(a,\"events\")||Object.create(null))[t.type]&&G.get(a,\"handle\"))&&f.apply(a,n),(f=l&&a[l])&&f.apply&&X(a)&&(t.result=f.apply(a,n),!1===t.result&&t.preventDefault());return t.type=m,i||t.isDefaultPrevented()||p._default&&!1!==p._default.apply(y.pop(),n)||!X(r)||l&&h(r[m])&&!g(r)&&((s=r[l])&&(r[l]=null),b.event.triggered=m,t.isPropagationStopped()&&d.addEventListener(m,bt),r[m](),t.isPropagationStopped()&&d.removeEventListener(m,bt),b.event.triggered=void 0,s&&(r[l]=s)),t.result}},simulate:function(e,t,n){var r=b.extend(new b.Event,n,{type:e,isSimulated:!0});b.event.trigger(r,null,t)}}),b.fn.extend({trigger:function(e,t){return this.each((function(){b.event.trigger(e,t,this)}))},triggerHandler:function(e,t){var n=this[0];if(n)return b.event.trigger(e,t,n,!0)}}),d.focusin||b.each({focus:\"focusin\",blur:\"focusout\"},(function(e,t){var n=function(e){b.event.simulate(t,e.target,b.event.fix(e))};b.event.special[t]={setup:function(){var r=this.ownerDocument||this.document||this,i=G.access(r,t);i||r.addEventListener(e,n,!0),G.access(r,t,(i||0)+1)},teardown:function(){var r=this.ownerDocument||this.document||this,i=G.access(r,t)-1;i?G.access(r,t,i):(r.removeEventListener(e,n,!0),G.remove(r,t))}}}));var wt=e.location,Tt={guid:Date.now()},Ct=/\\?/;b.parseXML=function(t){var n;if(!t||\"string\"!=typeof t)return null;try{n=(new e.DOMParser).parseFromString(t,\"text/xml\")}catch(e){n=void 0}return n&&!n.getElementsByTagName(\"parsererror\").length||b.error(\"Invalid XML: \"+t),n};var 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" \"\"\"Create RGB image with cyan channel saturated via segmentation mask.\"\"\"\n",
" # Make float and normalized image\n",
" im = np.copy(im).astype(float)\n",
"\n",
" # Build RGB image by stacking grayscale images\n",
" im_rgb = np.dstack(3 * [im / im.max()])\n",
"\n",
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" im_rgb[im_bw, 0] = 1.0\n",
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" return im_rgb\n",
"\n",
"\n",
"im_rgb = make_overlay(phase_im, phase_seg > 0)\n",
"\n",
"hv.RGB(im_rgb).opts(\n",
" frame_width=300, frame_height=phase_im.shape[0] * 300 // phase_im.shape[0]\n",
")"
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"metadata": {},
"source": [
"That looks pretty great to me, let's see how many cells we were actually able to measure. "
]
},
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"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Segmented and analyzed 92 cells!\n"
]
}
],
"source": [
"# Print the total number of cells. \n",
"print(\"Segmented and analyzed {num} cells!\".format(num=len(df)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Analyzing 92 cells in only 8 images in about 8 seconds is actually pretty good! That's certainly enough to do some serious boot strapping. Let's look at the ECDFs of the mean intensities and the areas. "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
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intensity\"},\"y\":{\"field\":\"__ECDF\"}},\"id\":\"1153\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"1124\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"1125\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"1207\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1173\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1126\",\"type\":\"HelpTool\"},{\"attributes\":{\"axis_label\":\"ECDF\",\"formatter\":{\"id\":\"1145\"},\"ticker\":{\"id\":\"1118\"}},\"id\":\"1117\",\"type\":\"LinearAxis\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"1127\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"fill_alpha\":0.5,\"fill_color\":\"#1f77b3\",\"line_alpha\":0,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1136\",\"type\":\"Patch\"},{\"attributes\":{\"below\":[{\"id\":\"1113\"}],\"center\":[{\"id\":\"1116\"},{\"id\":\"1120\"},{\"id\":\"1149\"}],\"left\":[{\"id\":\"1117\"}],\"plot_height\":200,\"plot_width\":300,\"renderers\":[{\"id\":\"1138\"},{\"id\":\"1155\"}],\"title\":{\"id\":\"1141\"},\"toolbar\":{\"id\":\"1128\"},\"toolbar_location\":null,\"x_range\":{\"id\":\"1105\"},\"x_scale\":{\"id\":\"1109\"},\"y_range\":{\"id\":\"1107\"},\"y_scale\":{\"id\":\"1111\"}},\"id\":\"1104\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{},\"id\":\"1143\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"axis_label\":\"area (\\u00b5m\\u00b2)\",\"formatter\":{\"id\":\"1207\"},\"ticker\":{\"id\":\"1178\"}},\"id\":\"1177\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1182\",\"type\":\"BasicTicker\"},{\"attributes\":{\"axis\":{\"id\":\"1177\"},\"ticker\":null},\"id\":\"1180\",\"type\":\"Grid\"},{\"attributes\":{\"axis\":{\"id\":\"1181\"},\"dimension\":1,\"ticker\":null},\"id\":\"1184\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"1178\",\"type\":\"BasicTicker\"},{\"attributes\":{\"data_source\":{\"id\":\"1135\"},\"glyph\":{\"id\":\"1136\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1137\"},\"selection_glyph\":null,\"view\":{\"id\":\"1139\"}},\"id\":\"1138\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"items\":[{\"id\":\"1150\"}],\"visible\":false},\"id\":\"1149\",\"type\":\"Legend\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b3\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b3\"},\"x\":{\"field\":\"mean 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\"},\"renderers\":[{\"id\":\"1202\"},{\"id\":\"1219\"}]},\"id\":\"1214\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"1188\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"1186\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1185\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"1169\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"1189\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"1190\",\"type\":\"HelpTool\"},{\"attributes\":{\"items\":[{\"id\":\"1214\"}],\"visible\":false},\"id\":\"1213\",\"type\":\"Legend\"}],\"root_ids\":[\"1259\"]},\"title\":\"Bokeh Application\",\"version\":\"2.1.0\"}};\n",
" var render_items = [{\"docid\":\"dac3ec6d-4b89-4c63-87e1-5fe99b04bf8b\",\"root_ids\":[\"1259\"],\"roots\":{\"1259\":\"c15a9be2-f700-429c-80e0-cbb6c82b093c\"}}];\n",
" root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
"\n",
" }\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" } else {\n",
" var attempts = 0;\n",
" var timer = setInterval(function(root) {\n",
" if (root.Bokeh !== undefined) {\n",
" clearInterval(timer);\n",
" embed_document(root);\n",
" } else {\n",
" attempts++;\n",
" if (attempts > 100) {\n",
" clearInterval(timer);\n",
" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
" }\n",
" }\n",
" }, 10, root)\n",
" }\n",
"})(window);"
],
"application/vnd.bokehjs_exec.v0+json": ""
},
"metadata": {
"application/vnd.bokehjs_exec.v0+json": {
"id": "1259"
}
},
"output_type": "display_data"
}
],
"source": [
"p_mean_int = bokeh_catplot.ecdf(\n",
" data=df,\n",
" cats=None,\n",
" val='mean intensity',\n",
" conf_int=True,\n",
" height=200,\n",
" width=300,\n",
" x_axis_label='mean intensity (a.u.)'\n",
")\n",
"\n",
"p_area = bokeh_catplot.ecdf(\n",
" data=df,\n",
" cats=None,\n",
" val='area',\n",
" conf_int=True,\n",
" height=200,\n",
" width=300,\n",
" x_axis_label='area (µm²)'\n",
")\n",
"\n",
"bokeh.io.show(\n",
" bokeh.layouts.gridplot([p_mean_int, p_area], ncols=2)\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The mean and standard deviation of the mean intensities (in arbitrary units) are directly computed."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"mean 0.399901\n",
"std 0.101903\n",
"Name: mean intensity, dtype: float64"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df['mean intensity'].agg(['mean', 'std'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's go ahead and perform 100,000 *in silico* replicates of this experiment to get a confidence interval on our mean and standard deviation of the mean fluorescence intensities."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"95% of our bootstrapped means lie between 0.38 and 0.42.\n",
"95% of our bootstrapped st. devs. lie between 0.06 and 0.14.\n"
]
}
],
"source": [
"def draw_bs_reps(data, func, size=1):\n",
" \"\"\"Draw bootstrap replicates\"\"\"\n",
" return np.array(\n",
" [func(np.random.choice(data, size=len(data))) for _ in range(size)]\n",
" )\n",
"\n",
"\n",
"# Draw bootstrap replicates of mean\n",
"bs_reps_mean = draw_bs_reps(mean_ints, func=np.mean, size=100000)\n",
"\n",
"# Draw bootstrap replicates of standard deviation\n",
"bs_reps_std = draw_bs_reps(mean_ints, func=np.std, size=100000)\n",
"\n",
"# Compute the 97.5% and 2.5% percentiles.\n",
"percs_mean = np.percentile(bs_reps_mean, [2.5, 97.5])\n",
"percs_std = np.percentile(bs_reps_std, [2.5, 97.5])\n",
"\n",
"print(\n",
" \"95% of our bootstrapped means lie between {0:.2f} and {1:.2f}.\".format(\n",
" percs_mean[0], percs_mean[1]\n",
" )\n",
")\n",
"print(\n",
" \"95% of our bootstrapped st. devs. lie between {0:.2f} and {1:.2f}.\".format(\n",
" percs_std[0], percs_std[1]\n",
" )\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Computing environment"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPython 3.7.7\n",
"IPython 7.15.0\n",
"\n",
"numpy 1.18.1\n",
"pandas 0.24.2\n",
"skimage 0.16.2\n",
"bokeh 2.1.0\n",
"bokeh_catplot 0.1.8\n",
"holoviews 1.13.2\n",
"jupyterlab 2.1.4\n"
]
}
],
"source": [
"%load_ext watermark\n",
"%watermark -v -p numpy,pandas,skimage,bokeh,bokeh_catplot,holoviews,jupyterlab"
]
}
],
"metadata": {
"anaconda-cloud": {},
"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": "3.7.7"
}
},
"nbformat": 4,
"nbformat_minor": 4
}