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"hide_input": true,
"slideshow": {
"slide_type": "slide"
},
"tags": [
"hide_input"
]
},
"outputs": [
{
"data": {
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"\n",
" \n",
" \n",
" \n",
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"source": [
"### BEGIN hide_toggle\n",
"### Update 30/10-'20\n",
"def hide_toggle_code(off=0):\n",
" \"\"\"This function generates HTML code to toggle the display of an input\n",
" cell.\n",
" \n",
" The output of the cell will still be displayed. This can be used\n",
" to hide (from immediate view) some code to generate data or the\n",
" like. It can also be used to hide other notebook explicit\n",
" implementations - e.g., C++ processing, or the like.\n",
" \n",
" Note, calling this function alone will not enable toggling.\n",
" Instead, we must wrap the generated code in an\n",
" `IPython.display.HTML` object and return that as the cell value.\n",
" This will let IPython evaluate the HTML code and pass it on to the\n",
" browser.\n",
" \n",
" If all one wants is to toggle a cell one can use the function\n",
" `hide_toggle` below. However, we can also combine the code\n",
" generated here with other HTML code - for example _style_\n",
" declarations and pass that along embedded in an HTML object.\n",
" \n",
" Parameters\n",
" ----------\n",
" off : int \n",
" Offset of cell to hide relative to the cell calling this function \n",
" \n",
" Returns\n",
" -------\n",
" code : str \n",
" HTML code to enable toggling of the cell\n",
"\n",
" \"\"\"\n",
" from random import randint \n",
" from IPython.display import HTML \n",
" \n",
" jp_cell = 'document.getElementsByClassName(\"jp-Cell jp-mod-selected\")[0]'\n",
" jq_cell = '$(\"div.cell.code_cell.rendered.selected\")'\n",
" toggle_text = 'Please close'\n",
" cell_id = str(randint(1,2**64))\n",
" func_name = f'code_toggle_{cell_id}'\n",
" \n",
" scr1 = f'''\n",
" \n",
" '''\n",
" but = f'''\n",
" \n",
" >
\n",
" \n",
" '''\n",
" scr2 = f'''\n",
" \n",
" '''\n",
" return scr1+but+scr2 \n",
"\n",
"def hide_toggle(off=0,cnt=None):\n",
" \"\"\"This will wrap the HTML code returned from the above function\n",
" in an `IPython.display.HTML` object so that the notebook will \n",
" evaluate the HTML code. \n",
" \n",
" This function is what we will use most of the time. However, \n",
" the function `hide_toggle_code` can be combined with other code \n",
" and then be put into an HTML object to let the notebook evaluate\n",
" all the code. \n",
"\n",
" Parameters \n",
" ----------\n",
" off : int \n",
" Cell offset relative to calling cell which we should toggle \n",
" cnt : int or None \n",
" If not None, set the execution count to this number \n",
" (currently broken)\n",
" \n",
" Returns\n",
" -------\n",
" object : IPython.display.HTML \n",
" HTML object wrapping code to toggle cell \n",
" \"\"\"\n",
" from IPython.display import HTML\n",
" if cnt is not None:\n",
" get_ipython().execution_count = cnt\n",
" return HTML(hide_toggle_code(off))\n",
"### END hide_toggle\n",
"\n",
"\n",
"### BEGIN setup_matplotlib\n",
"### Update 30/10-'20\n",
"def _setup_matplotlib():\n",
" \"\"\"Set-up Matplotlib parameters. \n",
" \n",
" We specify that we want both PDF and PNG images, and \n",
" that the default image size should be 8 by 8 inches \n",
" \n",
" We also disable warnings about too many open figures \n",
" \"\"\"\n",
" %matplotlib inline \n",
" from matplotlib import rcParams \n",
" \n",
" rcParams['figure.max_open_warning'] = 0\n",
" rcParams['font.serif'] = ['Palatino'] + rcParams['font.serif']\n",
" rcParams['font.family'] = ['serif']\n",
" rcParams['mathtext.fontset'] = 'dejavuserif'\n",
" rcParams['axes.formatter.use_mathtext'] = True\n",
"\n",
" f = None\n",
" try:\n",
" # IPython >= 7.23 depcrates set_matplotlib_formats\n",
" from matplotlib_inline.backend_inline import set_matplotlib_formats\n",
" f = set_matplotlib_formats\n",
" \n",
" except Exception as e:\n",
" try:\n",
" from IPython.display import set_matplotlib_formats\n",
" f = set_matplotlib_formats\n",
" except Exception as e:\n",
" pass \n",
"\n",
" if f is not None:\n",
" set_matplotlib_formats('png','pdf')\n",
" \n",
"_setup_matplotlib()\n",
"### END setup_matplotlib\n",
"_setup_matplotlib()\n",
"\n",
"### BEGIN css_styling\n",
"### Update 30/10-'20\n",
"def css_styling_code():\n",
" \"\"\"This function returns HTML code to customize the CSS \n",
" of the notebook \n",
" \n",
" - The text font to be Palatino (serif)\n",
" - Headers are oblique (italic)\n",
" - Extra spacing below H1 headers \n",
" - Extra spacing spacing above H1 headers \n",
" - Headers have larger fonts, and is set in normal weight\n",
" - Remove padding around code cells \n",
" - Code uses the fint \"Source Code Pro\" (or monospace)\n",
" - Code background is changed to light yellow \n",
" - Output background is set to lavender\n",
" \n",
" The function combines these CSS declarations with the HTML \n",
" code from `hide_toggle_code` above so what we automatically \n",
" hide this code from the user. \n",
" \"\"\"\n",
" styles = '''\n",
" \n",
" \n",
" '''\n",
" return styles\n",
"\n",
"def css_styling():\n",
" from IPython.display import HTML \n",
" \n",
" return HTML(hide_toggle_code()+css_styling_code())\n",
"### END css_styling\n",
"css_styling()"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "-"
},
"tags": [
"title"
]
},
"source": [
"### Christian Holm Christensen \n",
"\n",
"# Statistik\n",
"## Introduktion med Python \n",
"## Version 0.1 - September 2019 (Dansk)\n",
"\n",
"> Vi kigger på statistik og data behandling. \n",
">\n",
"> This document is available in many formats at https://cholmcc.gitlab.io/nbi-python\n",
"\n",
"### Niels Bohr Institutet "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-14T19:40:05.680232Z",
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"shell.execute_reply": "2021-11-14T19:40:05.682438Z"
},
"slideshow": {
"slide_type": "skip"
},
"tags": [
"hide_input",
"hide_output",
"nolatex"
]
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/tmp/ipykernel_454209/406809543.py:5: DeprecationWarning: `set_matplotlib_formats` is deprecated since IPython 7.23, directly use `matplotlib_inline.backend_inline.set_matplotlib_formats()`\n",
" set_matplotlib_formats('png', 'pdf')\n"
]
}
],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"plt.rcParams['figure.figsize'] = [10, 10]"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Data og statistik\n",
"\n",
"- Vi måler $x$\n",
"- Hver gang vi gentager målingen får vi et lidt anderledes resultat\n",
"- Hvad er vores måleresultat? "
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Svaret er bestemt via _statistik_"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Citat:\n",
"\n",
"> Statistics is the science of learning from data, and of measuring, controlling, and communicating uncertainty; \n",
"> and it thereby provides the navigation essential for controlling the course of scientific and societal advances.\n",
"> This field will become ever more critical as academia, businesses, and governments rely increasingly on data\n",
">-driven decisions, expanding the demand for statistics expertise.\n",
"\n",
"[Science, Vol. 336, Issue 6077, pp. 12](https://doi.org/10.1126/science.1218685)"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Tankeeksperiment\n",
"\n",
"Tre menesker ved en moterveejsbro tæller røde biler \n",
"\n",
"- Én er farveblind og tæller alle grønne og røde biler \n",
"- Én har festet natten før og sover halvdelen af tiden, og resten af tiden tæller kun halvdelen af alle røde biler \n",
"- Den sidste har sovet dårligt (pga. ovenover) og tæller kun halvdelen af alle røde biler "
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Antag $N=100$ røde biler passerer, så har vi at "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-14T19:40:05.690685Z",
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"shell.execute_reply": "2021-11-14T19:40:05.692282Z"
},
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
"N=100\n",
"NN=np.array([2*N, 1/2*1/2*N, 1/2*N])"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Hvad er svaret?"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Præcision \n",
"\n",
"Usikkerhed på tælletal $n$: $\\delta_n=\\sqrt{n}$, så "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-14T19:40:05.699003Z",
"iopub.status.busy": "2021-11-14T19:40:05.696234Z",
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"shell.execute_reply": "2021-11-14T19:40:05.702864Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Obs 1: 200.0 +/- 14.142135623730951\n",
"Obs 2: 25.0 +/- 5.0\n",
"Obs 3: 50.0 +/- 7.0710678118654755\n"
]
}
],
"source": [
"dNN = np.sqrt(NN)\n",
"for i,(n,dn) in enumerate(zip(NN,dNN)):\n",
" print('Obs {}: {} +/- {}'.format(i+1,n,dn))"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Relativt"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-14T19:40:05.709240Z",
"iopub.status.busy": "2021-11-14T19:40:05.708331Z",
"iopub.status.idle": "2021-11-14T19:40:05.712149Z",
"shell.execute_reply": "2021-11-14T19:40:05.713088Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Obs 1 relativ usikkerhed: 7.07%\n",
"Obs 2 relativ usikkerhed: 20.00%\n",
"Obs 3 relativ usikkerhed: 14.14%\n"
]
}
],
"source": [
"for i,(n,dn) in enumerate(zip(NN,dNN)):\n",
" print('Obs {} relativ usikkerhed: {:6.2f}%'.format(i+1,100*dn/n))"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Observatør 1 har den bedst bestemte værdi - eller mest _præcise_ (engl. _precise_) værdi"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Nøjagtighed\n",
"\n",
"Lad os sammenligne med den \"sande\" værdi"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-14T19:40:05.728975Z",
"iopub.status.busy": "2021-11-14T19:40:05.726979Z",
"iopub.status.idle": "2021-11-14T19:40:05.731355Z",
"shell.execute_reply": "2021-11-14T19:40:05.727968Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Obs 1 måling 200.0 +/- 14.1 er cirka 7 usikkerheder fra N=200.0\n",
"Obs 2 måling 25.0 +/- 5.0 er cirka 15 usikkerheder fra N=25.0\n",
"Obs 3 måling 50.0 +/- 7.1 er cirka 7 usikkerheder fra N=50.0\n"
]
}
],
"source": [
"for i,(n,dn) in enumerate(zip(NN,dNN)):\n",
" print('Obs {} måling {:5.1f} +/- {:4.1f} er cirka {:2.0f} usikkerheder fra N={}'\n",
" .format(i+1, n, dn, np.abs(N-n)/dn, n))"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Observatørene 1 og 3 er altså _lige_ tætte på den \"sande\" værdi, mens Observatør 2 er langt fra.\n",
"\n",
"De er mere _nøjagtige_ (engl. _accurate_) end Observatør 2 "
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Præcision og Nøjagtighed \n",
"\n",
"(engl. _precision and accuracy_) \n",
"\n",
"- _Præcision_ er hvor godt vi kender vores resultat og kan beregnes statistisk \n",
"- _Nøjagtighed_ er hvor tæt vi er på den \"sande\" resultat og kan oftes kun anslås "
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"_Statistik_ handler om præcision, mens det er en kunstform at være nøjagtig. \n",
"\n",
"_Eller_: Statistik fortæller os ikke hvor tæt vi er på den \"sande\" værdi"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Middelværdi\n",
"\n",
"Anne har lavet 10 målinger "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-14T19:40:05.739779Z",
"iopub.status.busy": "2021-11-14T19:40:05.738515Z",
"iopub.status.idle": "2021-11-14T19:40:05.740923Z",
"shell.execute_reply": "2021-11-14T19:40:05.741776Z"
}
},
"outputs": [],
"source": [
"data = np.array([2, 5, 2, 5, 1, 1, 3, 7, 2, 7])"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"Hvad er hendes result?"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Gennemsnittet (eller middelværdi)\n",
"\n",
"$$\\overline{x} = \\frac1N\\sum_{i=1}^N x_i\\quad.$$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-14T19:40:05.751340Z",
"iopub.status.busy": "2021-11-14T19:40:05.749575Z",
"iopub.status.idle": "2021-11-14T19:40:05.754698Z",
"shell.execute_reply": "2021-11-14T19:40:05.753793Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3.5\n"
]
}
],
"source": [
"resultat = data.mean()\n",
"print(resultat)"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Middelværdi som funktion af data størrelse\n",
"\n",
"Lad os varierer data størrelsen (engl. _sample size_). \n",
"\n",
"- 1000 prøver \n",
"- af tilfældig størrelse mellem 10 og 9999 ($N\\sim U(10,9999)$)\n",
"- af tilfældige heltal mellem 0 og 9 ($X\\sim U(0,9)$)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-14T19:40:05.764796Z",
"iopub.status.busy": "2021-11-14T19:40:05.763742Z",
"iopub.status.idle": "2021-11-14T19:40:08.209774Z",
"shell.execute_reply": "2021-11-14T19:40:08.210597Z"
}
},
"outputs": [
{
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\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"np.random.seed(123456)\n",
"data = np.array([(n,np.random.randint(0,10,size=n).mean()) \n",
" for n in np.random.randint(10,10000,size=1000)])\n",
"plt.scatter(data[:,0],data[:,1],label='Samples',s=16)\n",
"plt.axhline(4.5,label='Expectation value',color='tab:orange')\n",
"plt.xlabel('Sample size')\n",
"plt.ylabel(r'$\\overline{x}$')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Anne får mere og mere præcise målinger jo større data størrelse"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Usikkerheder \n",
"\n",
"- Statistisk usikkerhed: Variation i fundne værdier \n",
"- Kvantiseret som _varians_ (engl. _variance_)\n",
"\n",
"Hvis $\\hat{x}$ er en _estimator_ af den \"sande\" værdi $x$, så er den kvadratiske usikkerhed givet ved _variansen_ af $\\hat{x}$:\n",
"\n",
"$$s_{\\hat{x}}^2 = \\frac{1}{N}\\sum_{i=1}^N (x_i - \\overline{x})^2\\quad,$$\n",
"\n",
"og _standard afvigelsen_ er givet ved \n",
"\n",
"$$s_{\\hat{x}} = \\sqrt{s_{\\hat{x}}^2}\\quad,$$ \n",
"\n",
"så at usikkerheden er \n",
"\n",
"$$\\delta_{\\hat{x}} = s_{\\hat{x}} = \\sqrt{s_{\\hat{x}}^2}\\quad.$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Variantion af middelværdi \n",
"\n",
"Vi beregner variansen \n",
"\n",
"$$s^2_{\\overline{x}} = \\frac1N\\sum_{i=1}^N \\left(\\overline{x}_i - \\overline{\\overline{x}}\\right)^2\\quad,$$\n",
"\n",
"af _middelværdierne_ $\\overline{x}_i$ i 30 intervaller af data størrelse "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-14T19:40:08.223844Z",
"iopub.status.busy": "2021-11-14T19:40:08.222760Z",
"iopub.status.idle": "2021-11-14T19:40:09.222078Z",
"shell.execute_reply": "2021-11-14T19:40:09.221605Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
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oWAqP77sSch+6Pd/zIDryXiNH4LrM2Mfm9xn+/gMBxoBHCmVuZHN0cmVhbQplbmRvYmoKMTkgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxMDAgPj4Kc3RyZWFtCnicLY25DcAwDAN7T6ERrId+9glSJfu3oRUVMg48E8QI6WI8gKdbLm2Zvc35Ps3cxGKTVKfEmCR4wfDs0O0o8m7iemSsVRnYL2sQmzg22LUjVQu65qIP/Mvg354zkcH9AUOnIVEKZW5kc3RyZWFtCmVuZG9iagoxNSAwIG9iago8PCAvQmFzZUZvbnQgL0RlamFWdVNlcmlmLUl0YWxpYyAvQ2hhclByb2NzIDE2IDAgUgovRW5jb2RpbmcgPDwgL0RpZmZlcmVuY2VzIFsgNzggL04gMTE1IC9zIDEyMCAveCBdIC9UeXBlIC9FbmNvZGluZyA+PgovRmlyc3RDaGFyIDAgL0ZvbnRCQm94IFsgLTg0MCAtMzQ3IDE2NDUgMTExMCBdIC9Gb250RGVzY3JpcHRvciAxNCAwIFIKL0ZvbnRNYXRyaXggWyAwLjAwMSAwIDAgMC4wMDEgMCAwIF0gL0xhc3RDaGFyIDI1NSAvTmFtZSAvRGVqYVZ1U2VyaWYtSXRhbGljCi9TdWJ0eXBlIC9UeXBlMyAvVHlwZSAvRm9udCAvV2lkdGhzIDEzIDAgUiA+PgplbmRvYmoKMTQgMCBvYmoKPDwgL0FzY2VudCA5MjkgL0NhcEhlaWdodCAwIC9EZXNjZW50IC0yMzYgL0ZsYWdzIDk2Ci9Gb250QkJveCBbIC04NDAgLTM0NyAxNjQ1IDExMTAgXSAvRm9udE5hbWUgL0RlamFWdVNlcmlmLUl0YWxpYwovSXRhbGljQW5nbGUgMCAvTWF4V2lkdGggMTM0MiAvU3RlbVYgMCAvVHlwZSAvRm9udERlc2NyaXB0b3IgL1hIZWlnaHQgMCA+PgplbmRvYmoKMTMgMCBvYmoKWyA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMAo2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDMxOCA0MDIgNDYwIDgzOCA2MzYKOTUwIDg5MCAyNzUgMzkwIDM5MCA1MDAgODM4IDMxOCAzMzggMzE4IDMzNyA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2CjYzNiA2MzYgMzM3IDMzNyA4MzggODM4IDgzOCA1MzYgMTAwMCA3MjIgNzM1IDc2NSA4MDIgNzMwIDY5NCA3OTkgODcyIDM5NQo0MDEgNzQ3IDY2NCAxMDI0IDg3NSA4MjAgNjczIDgyMCA3NTMgNjg1IDY2NyA4NDMgNzIyIDEwMjggNzEyIDY2MCA2OTUgMzkwCjMzNyAzOTAgODM4IDUwMCA1MDAgNTk2IDY0MCA1NjAgNjQwIDU5MiAzNzAgNjQwIDY0NCAzMjAgMzEwIDYwNiAzMjAgOTQ4IDY0NAo2MDIgNjQwIDY0MCA0NzggNTEzIDQwMiA2NDQgNTY1IDg1NiA1NjQgNTY1IDUyNyA2MzYgMzM3IDYzNiA4MzggNjAwIDYzNiA2MDAKMzE4IDM3MCA1MTggMTAwMCA1MDAgNTAwIDUwMCAxMzQyIDY4NSA0MDAgMTEzNyA2MDAgNjk1IDYwMCA2MDAgMzE4IDMxOCA1MTEKNTExIDU5MCA1MDAgMTAwMCA1MDAgMTAwMCA1MTMgNDAwIDk4OSA2MDAgNTI3IDY2MCAzMTggNDAyIDYzNiA2MzYgNjM2IDYzNgozMzcgNTAwIDUwMCAxMDAwIDQ3NSA2MTIgODM4IDMzOCAxMDAwIDUwMCA1MDAgODM4IDQwMSA0MDEgNTAwIDY1MCA2MzYgMzE4CjUwMCA0MDEgNDcwIDYxMiA5NjkgOTY5IDk2OSA1MzYgNzIyIDcyMiA3MjIgNzIyIDcyMiA3MjIgMTAwMSA3NjUgNzMwIDczMAo3MzAgNzMwIDM5NSAzOTUgMzk1IDM5NSA4MDcgODc1IDgyMCA4MjAgODIwIDgyMCA4MjAgODM4IDgyMCA4NDMgODQzIDg0MyA4NDMKNjYwIDY3NiA2NjggNTk2IDU5NiA1OTYgNTk2IDU5NiA1OTYgOTQwIDU2MCA1OTIgNTkyIDU5MiA1OTIgMzIwIDMyMCAzMjAgMzIwCjYwMiA2NDQgNjAyIDYwMiA2MDIgNjAyIDYwMiA4MzggNjAyIDY0NCA2NDQgNjQ0IDY0NCA1NjUgNjQwIDU2NSBdCmVuZG9iagoxNiAwIG9iago8PCAvTiAxNyAwIFIgL3MgMTggMCBSIC94IDE5IDAgUiA+PgplbmRvYmoKMjQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzNDkgPj4Kc3RyZWFtCnicNZK5cSQxDEX9jgIJqIq4yXhmay1t/u4+sCVj6mPIBv4B1k5ZskO+1KXUpMPkjz7HxVP+DdpS+X40zm+VSzRStEp0hehp6S2fx6wlVaxDfIt7DXweP/d/zO9I1JY2juNsOUkDE+y82M7FVLa2JLMNEbFLLGNa6DWag+/tqHgv8XWGejgh+H6MLs8jmsOKSisJbb6BL2KP16AXyJhjimKGrpLKlnFX3H8eRXdbwp03FfcXcVTnVkFPj60YnJ7R2uaSKGwSzU6mjcKpMgKFaeu3wmmSQZBgud1sCjbm+JEiVD/Tj0vvizjd74nBWU0Oype5r15jCg44rfVi1li8FfN1gwtH+I2dd2WzkXxTZaeTYZAYCmzYDypj9jcTgsQTT7h3u5tCtw0r78bY/KBet7diQsL4YzzWz9IpyWrem5PhIImut7Li5jX1dXfQ+BYleeW13Df5ef7+B/I+gc4KZW5kc3RyZWFtCmVuZG9iagoyNSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDk1ID4+CnN0cmVhbQp4nE2OQQ6AMAgE77yCD5gAtWz6H+MJ/38VxZpeyITJssCMhbeRAw0MG3woKTo7wBe1IawKDnKpXVC3ttATCZrhorLu/tEungVB7W1LMw9k8Q8Vt+4LlZzvBJ03rykiOQplbmRzdHJlYW0KZW5kb2JqCjI2IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzExID4+CnN0cmVhbQp4nD1SSW7EMAy75xX8QAHttt+ToqeZ/19LKZ0eAhK2ZFJU8hQEKfhSR9ZGuuNbLz8bWo73MFuO12XbPszXMJOAsUr7JgL3pSUwCyif1JMPZvVNM+NXiqNscSzhuUkiKOEJf5QI9+UqTTwEceAUWdbHu8Bnx579Ie/uKzaLKfwelkaXM86HCLGrP0hPJKub4EmjQUah1hDHVw9ok4rRRiNH2E9O6hwbKtLN91WFss5QGcf/vCQmB3Vgc8XZds+rUejhTJTtOTKN99hq9hh05vSwaCHOHU6kUuQkQVux6JqisfkO6xuZqOUwPYsVBeUXNdrJWu5Jg7W9C6eX3XEfGfJqEqd3rKYcht1JVOImWsdgdJ/MyvzM72K1BtvTc+J8IZUunDrr9HqYQ4Rj1nQMn3Xd188vfnp35QplbmRzdHJlYW0KZW5kb2JqCjI3IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjM4ID4+CnN0cmVhbQp4nD1RSXIEMQi7+xX6QKrACGy/p1Nzmvz/GuGp5NLIoMW4swyGNHx5IJ3ICHz7aOhZ+BlpDjcD10JukI4wPIOWEFSrpSFW12fMmRd5aS6pH5Srv9TSWVHeToZZbSMQnNCUti+bsnxGy1Odtus7dUDXZ4S+t1OFnAdxjmpHMMRRNEt72ATPAvfqiVAk8R5k/qHYV8spRYjdS+ZN0AW5qItRevHbS1XLad5oeiml4EeT+bmvEo6WS/GDt342bORbHTFc3NacHrRJTrSnBB2ionTaPS/XY8uTqG7TF+TC6HdMjeb9Qc//r3qP1y/wn1WSCmVuZHN0cmVhbQplbmRvYmoKMjggMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNDQgPj4Kc3RyZWFtCnicRVExbkUxCNtzCl+gUgyEJOf5Vaff+681vFadcCywDVnXMLEmPuhYYVju+OQoaKK/B9dq9H5Q5C/iTjAPaA7ewNl4DTOJUf0XHnCyymu45ut9DBGIeZBLdMjrLIQmyESk6iqZClHoPRYvOCdCOUXECtitUSoBPKOD+7SuFSAbUQYs2QupvsYWpbdycO8qlrOMKpdhW4cijxyOeKauIcbsuYjd7KpVdjQKX90RkotHS15B9ccj+nfC2jM74reQrpByM7ajX037bV1pZp1Ny+oo5VhVK2nnZpSlOnjl6p1y1zG3lp2tWt9SPv+O7/H1AwOOWW0KZW5kc3RyZWFtCmVuZG9iagoyOSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDM4MSA+PgpzdHJlYW0KeJw1UkGSBCEIu88r+MBWCYLoe2Zrb/P/6yax59BFWiEJ4JrLhq22H59W61hn2K+/ci3zc+wjFOWWNS0OYrTNGPZ+5XCbeWyuvJ9vxfcr2oViljJinKfG92XxHmJlpA5uiLKNGT6WarpJBpLcJs5HhBpSTKMJ3NKVsmmT5WoAdN9GcJPLCrefiw7uUL9mWHrYKlbPfWxtCNW2da4aI1u6KFDLjIh8agIOyOJniFUROmiJaMA6PfZUTSa9kCXxR1aqU4cRDuo5gRNmEN8auiWL3IP12w9qzkT+VmeYzh6WhwuAeoAp6LK0vrtjDp7xzkVo4gTTgp0akKGTZL3Ns/U26JCR+7ivxbtw75wf06HPEbW4GEQOQLUdEncSyY5nyqDvluHI2wKHBnSwtMKInAJoJ7kCp7MOQ2+Fx8Gg9gGW4ynh40YcegtnpHLrKJC33jV7aJmlFBGJmZE7n5p69lpZYmW8MkLQremyUaMeY9lHVjNd1r/7eL/+/gHaP6EQCmVuZHN0cmVhbQplbmRvYmoKMzAgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxOTAgPj4Kc3RyZWFtCnicTZBLcsQwCET3OgVH4A8+z6Sy8tx/O41UE2fjfga1BG3FxGSJjxtTJdOPrMG0oveytk03SClTyCooezz4v4xey7ypOMj0ohIlY9v6Wpqnop44ATV42qcjjduSFN002xqduwOSa16M+keeM8V0HwqdptYDPJpf2WVRfeB40fqD88I+9BBmPJSuJNg/O0hgKQnMKBfIA3vJjsz4RIcs4NkVRwbRSCmgs7E1PIGYGWm5n7htNv6mfa/fD6JjS10KZW5kc3RyZWFtCmVuZG9iagozMSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEwNSA+PgpzdHJlYW0KeJxFjrsRwDAIQ3umYASbn5N9cqnw/m2A+OwG3gFCMjZsyD2KXoZDCJ8OLDeSDJxFxooOvbWa+d46qEkIJxBTdK+utE429Dv14bGB5ErQVoYOEt8Ord8R59Avze2hMsgIGzLD+wGqbCiwCmVuZHN0cmVhbQplbmRvYmoKMzIgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNTggPj4Kc3RyZWFtCnicRU/BEcMwCPtnCo2AsI3jedrrK93/W0F8zcOWDoRAzQ2GFvp8TUyxNw+xOA3fImuA5ph2gmyYXHgd9C6xge0e4miF6sSuyKAUi3vGt4vrpWuhVNkRi45UxKBmhJ3pdhKRLiGFj9qTqI42V0WXlEK37ZntksfLdIfRFjqGK1UmFbmKmLDyF1SZ7g/pylOtPxlKc91uD0v55weyHD68CmVuZHN0cmVhbQplbmRvYmoKMzMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA2OSA+PgpzdHJlYW0KeJwzNjJQMFAwsgQTBgrmZgYKKYZcRgamCqZGCrlcIDEgIwfMMADTMAosbGhoimCYG1hApBAMM7BioGkIFlh5GgBOoxbhCmVuZHN0cmVhbQplbmRvYmoKMzQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyODkgPj4Kc3RyZWFtCnicRZJLlsUgCETnWQVLQL66nvTp0ev9T7tAXzIwVUqUC7psEpMGPksGuSr9jMvHJMP4u1ydzIPck2waeQ02uq8Y+F2UwqS3Rc7W+0rdK5lKPoImM/YKIlOCDBmnIec6qlwROBf6XE3xNQyNlEc7kM6vUeGvQzzBYoMpK89mwczcKSbqiATtagU/b+fgNh+7QuS8UXOArjCglq0yV0XgOnWgBY8pAvX5aAdM4zWKPh2X4JDqruyh1Utd0V3WHM2k6odS1nYS1pRieihFpCkFpxRl6aYs16ll8WuKzsZXenmIvMZiFn+8xseqvXXa40yyXFUQRYMezkmCqpyjKuE62/pW6w1o6HkVxtvtxkArwh1Z9T5qVjeBxp7Xd1+//5lxfkYKZW5kc3RyZWFtCmVuZG9iagozNSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE5MSA+PgpzdHJlYW0KeJxNkDEWwzAIQ3efgiNggbF9nvR1Su+/VtC06RCjPIH1TbiLigWP6CHDTB69eef/K8uAnK0Dt/CYVJz4idE3BTr+lCNNYLGtC4aKryWY7NaQo5nmlS7GwAy12FWP5vhgeCzex5g9OOt0RqYPMmW4alUzTScpErDe8BVaeOtXy3CPWyTFpYIpRlrllzmGZCGrD7pzF4+5Vj0a9iqFyA4IuMeco8PTNt/MLZjPqlg7nX6tEVtvkXS177M93z8RSuoKZW5kc3RyZWFtCmVuZG9iagozNiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIxNiA+PgpzdHJlYW0KeJw1UMltxDAM/KsKNhBAPCXV42B/2/83M5QDGOBY5BxkTZMpOeVHXTJN0l1+dfhU8ZDv8DgEvhMtCZ1yVJ4ReFM7ErFE0WO1muwAObqc8DObErbRoUZUCSUDmB6szzBKA5lWT+ixl6O1WkUzW5X1+hDRmRNMQk5Howj0qMkId5GnN+KS32GWjbTAVnxHisSFJ/zjGLoWyzUC8DBZiDQ3JrZE3miBoS2U49VowAor0oHCV0/E9peTPBleeGmKsr4uQG3LVVSbU/fSiympydD/azzj8wdFYFIZCmVuZHN0cmVhbQplbmRvYmoKMzcgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA4MyA+PgpzdHJlYW0KeJxNzbENwDAIBMCeKRgBY/zE+0Sp7P3bAIqSNHBC+gcdLNxUY9o0dlM+GzXLw649lBcp5geMI5Shgf4I6qEuUhUh+E8Vzf4Xkrn6sui6AayDGa0KZW5kc3RyZWFtCmVuZG9iagozOCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI2NSA+PgpzdHJlYW0KeJxVkU1uxTAIhPc5BReIZP6CfZ5Ub/V6/21ncKq+SpH4HPAw4CuGDLElp42SXEPSXb70sJFiM+V7k4e8m7RUTEvUXCxUlsp92JWSEzJLwsQjGe7DkQSEpVxDIpaswu8oF0WXgLzO2dFQgAzIHTdQ4fPqK2GUokagRUtW7R5FtW4KooeACk2FdQY2fYXQtkfJ70j3ocra4nCr4U1IXc+QfxQ+SUZP1A4JKpahZjzd0+jae3NeO8KxV1NMVHC3bJX0lRfo2bbDLeOen6Q1hRWq1neuHh8iOFPz1N2FESv2TfRxZhtbtAWjho++Zw8++50Ap2b2vOMf8vl7Cx+001zWB+51vX4ARWtqkQplbmRzdHJlYW0KZW5kb2JqCjM5IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTI0ID4+CnN0cmVhbQp4nC1OyQ3DMAz7ZwouEECU7Tiap0V/3f9bUilggAYvcfBGoCZODmROkBfePMQs4mu8CozAbS1RG6+DNob4GR3gqkYpez9MZTsy1hNJblf4hAoN6hetz9BlqXp2L7cofZrZvcv1Rgk62IxiNmhQ+7VPcY0difpXf35oOihXCmVuZHN0cmVhbQplbmRvYmoKNDAgMCBvYmoKPDwgL0JCb3ggWyAtNzcwIC0zNDcgMjEwNiAxMTEwIF0gL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMzAKL1N1YnR5cGUgL0Zvcm0gL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnicRZJJjiQxCEX3cQqOYCYbnyelWlXff9sPIqVahEBg4A/xeB1xS/n3+FHxdD4TPynuS7yufB5fJbFcrEJCVSzPxM9j9lb0UllL9Gxmi44mG3KLBtHuRLvZnc62iWaIeTJDVO/OdTaxX49oLbHYE7lz7K1cKhdcWryyxuaXLSHORmsGXz6fJzdXdcEsudhZGkj1SoBWvVHG4WKziZq9YWzx3XtvDRYHnWaJx/3OOJy17zcWlLGdE1sNnUyLrUYXNXU3SrVmVu/7iDfe0YnMUUKZHQVBEoNA8SBOq0EHHwxFY/ywejNHtThEcEWOU1wLFGkVYu3xxncrGM7bhVt4Ek637DuT7S7aZldh3Lp1fBUMmP4+2bfJ5s06korP1SrHbe19kDqcIw4+tJtB1YJOwQF22X8Qs+zFn/Y6o33ec7Hjn2e/z89//ad8LAplbmRzdHJlYW0KZW5kb2JqCjQxIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTc0ID4+CnN0cmVhbQp4nEWQMbIDMQhD+z0FRzBCNvZ5kkmVf//2CzLZFF69MVhoYW4bFksfCmeEPf1qxLC/pjjD3hexbqLRl04aYxqHDrc9rjgwLvllSNOCp1WV6hEh3TjdQL2FqwJE+8Kh/tWKfaoimtDA0LAbOoF/pa8d+AHXrs71g+lH0G43EVmEyhcGJaJmIo/N8cmbsqQSeS8l9kfrH2cTvW68nSYqLxmi7A3U2+8WH9frH2weQ5EKZW5kc3RyZWFtCmVuZG9iago0MiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDM0MSA+PgpzdHJlYW0KeJw9kktuxDAMQ/c5hS4wgPWL7fNM0dX0/ts+OkUXAQUplkhK7WnD+rYXQd1hnWlffpGJbT9C72Gfy8f6j7a5u3m4rTCvsjvtffk9rdJiuGVZ1C14X7FOkE6VSi7rSTp72wzLOWzXAQ91OVG1JVz8plLTfC5Vkpk74LUZMpkAnje+NK/FLcnR2VWf09Y8v78vuGUMjVZDwXLSBBXLZqG9TcqKCXREVPs+8+RIdB2UHD9ROt2wKEsYf8zb22rwZoCorq0pihINnytX/EcDPzDkZmY+tAq36RO8nQ1xcIEiCTIbRop885YuPv3whm8T8XkF3f5wnApRriQDV2mUp3000iHlF5vNYN9k048SXI2tXScrCrkjPxs+KI7UP5oW8kt7kpb7OQUqRKy0uAX0iEWc9bGCwYDn1IJTEkrUk9ESXzgOi9dZKutKW6gse67xfX3/AmOMf3oKZW5kc3RyZWFtCmVuZG9iago0MyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMzMCA+PgpzdHJlYW0KeJw1UsttJTEMu7sKNbCA9bfrmUVOSf/XkJoXYABx9KUol5dsqZZ/6pLt0mHyX5dbi4f8LIcPIPaR3BLuckKeFdmieiR6i1aNNd+MEF0XZnjolHgnI+gR+wpbhpVwBu2z7OxBFjEZZhtZjYhe5MGrmGq3X+usIdJWYYaaokblTLNISfwfJfHPIsgvTlespJfTUkxTAr0tyHZK0S+Q59uwEYr9jAV33YMYjTQM2KPJsxJ/XjHi+c6xrxJEir4J4UA9GfTR7gpUuHdEd/OxJK6DFJsrPgjXnHAu8OWRDMvUK+uzAMgGUiegYuvyV7KW3kjGMrymI0r7LL/vfQPyNjpGHNg5TRfQHo4NQglvDymiRN33Chzpg5BdEDDKpfgq0LOKVANHqJPCSXUhIB4BLZb7eCxQyycC8cvsc8iEtDxQ7i1/h3rW1y8JfnzrCmVuZHN0cmVhbQplbmRvYmoKNDQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNyA+PgpzdHJlYW0KeJwzNrRQMIDDFEMuABqUAuwKZW5kc3RyZWFtCmVuZG9iago0NSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIyMiA+PgpzdHJlYW0KeJxFUblxBDEMy1UFShB/qp7zODr3nxrUes7BLjAiBQJUWmIjm7+wRrniS5ZoIyLws8oueQ/JHiK7UNsgbC0pSPGaFl5LxVBWUH+EtPXia1k8Jy7Ta/BUqs2d2IkMDufE3A+G3QqZZ8Cpb71hRG0ZtdpQ+jFWldYtheisSBXY+l7Oxg+RGjbx/tlgfiCMqH0o62RGA6bKkfyS/NDybg5wcbgfuNLY0YuP3cs6GZHR1Gl5gt3wOQtmAHbk8RtikAszv0wOw3NZMkuOM0G8kHwaMaptRvh7kNf6/gVtdFHbCmVuZHN0cmVhbQplbmRvYmoKNDYgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA4NSA+PgpzdHJlYW0KeJxNzbERACEIBMDcKigB9EDt5+cj7T99zw804ZZhAM9VVKAsXcWty2Np95OBLCOVcEHUJdN2qVTK44D7I6HZJeyhccpjKO3AENT6fKTMP94PbeMejQplbmRzdHJlYW0KZW5kb2JqCjQ3IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjExID4+CnN0cmVhbQp4nDVQyXHEMAz7qwo0kBlRvKR6nNnf9v8NQTkvwSYuMjQwEYEfUXhOpC38ylDZUMN3aDSw6QiB6YRI4BnmBim+RWK59qthnBSyLEkx3LM1IYsTmlQWPeMYGML3Gev9s8gtxprxamRLu0icduV7c4iYTAabUHO7tYtg3ervKk/vxDW/RbhIklEQXdgU7g3xxXMsM3RTCgvYVtTUS0B2WHerr5wbtOPdGJA90ZONzE8zfOqrcct24a1pyvemEDGWDLagZt9TH7akJ0v/r/GMzx9qilMaCmVuZHN0cmVhbQplbmRvYmoKMjIgMCBvYmoKPDwgL0Jhc2VGb250IC9EZWphVnVTZXJpZiAvQ2hhclByb2NzIDIzIDAgUgovRW5jb2RpbmcgPDwKL0RpZmZlcmVuY2VzIFsgMzIgL3NwYWNlIDQ2IC9wZXJpb2QgNDggL3plcm8gL29uZSAvdHdvIDUyIC9mb3VyIDU0IC9zaXggNTYgL2VpZ2h0IDgzIC9TCjg2IC9WIDk3IC9hIDk5IC9jIDEwMSAvZSAvZiAxMDUgL2kgMTA4IC9sIC9tIC9uIC9vIC9wIDExNCAvciAvcyAxMjIgL3ogXQovVHlwZSAvRW5jb2RpbmcgPj4KL0ZpcnN0Q2hhciAwIC9Gb250QkJveCBbIC03NzAgLTM0NyAyMTA2IDExMTAgXSAvRm9udERlc2NyaXB0b3IgMjEgMCBSCi9Gb250TWF0cml4IFsgMC4wMDEgMCAwIDAuMDAxIDAgMCBdIC9MYXN0Q2hhciAyNTUgL05hbWUgL0RlamFWdVNlcmlmCi9TdWJ0eXBlIC9UeXBlMyAvVHlwZSAvRm9udCAvV2lkdGhzIDIwIDAgUiA+PgplbmRvYmoKMjEgMCBvYmoKPDwgL0FzY2VudCA5MjkgL0NhcEhlaWdodCAwIC9EZXNjZW50IC0yMzYgL0ZsYWdzIDMyCi9Gb250QkJveCBbIC03NzAgLTM0NyAyMTA2IDExMTAgXSAvRm9udE5hbWUgL0RlamFWdVNlcmlmIC9JdGFsaWNBbmdsZSAwCi9NYXhXaWR0aCAxMzQyIC9TdGVtViAwIC9UeXBlIC9Gb250RGVzY3JpcHRvciAvWEhlaWdodCAwID4+CmVuZG9iagoyMCAwIG9iagpbIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwCjYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgMzE4IDQwMiA0NjAgODM4IDYzNgo5NTAgODkwIDI3NSAzOTAgMzkwIDUwMCA4MzggMzE4IDMzOCAzMTggMzM3IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYKNjM2IDYzNiAzMzcgMzM3IDgzOCA4MzggODM4IDUzNiAxMDAwIDcyMiA3MzUgNzY1IDgwMiA3MzAgNjk0IDc5OSA4NzIgMzk1CjQwMSA3NDcgNjY0IDEwMjQgODc1IDgyMCA2NzMgODIwIDc1MyA2ODUgNjY3IDg0MyA3MjIgMTAyOCA3MTIgNjYwIDY5NSAzOTAKMzM3IDM5MCA4MzggNTAwIDUwMCA1OTYgNjQwIDU2MCA2NDAgNTkyIDM3MCA2NDAgNjQ0IDMyMCAzMTAgNjA2IDMyMCA5NDggNjQ0CjYwMiA2NDAgNjQwIDQ3OCA1MTMgNDAyIDY0NCA1NjUgODU2IDU2NCA1NjUgNTI3IDYzNiAzMzcgNjM2IDgzOCA2MDAgNjM2IDYwMAozMTggMzcwIDUxOCAxMDAwIDUwMCA1MDAgNTAwIDEzNDIgNjg1IDQwMCAxMTM3IDYwMCA2OTUgNjAwIDYwMCAzMTggMzE4IDUxMQo1MTEgNTkwIDUwMCAxMDAwIDUwMCAxMDAwIDUxMyA0MDAgOTg5IDYwMCA1MjcgNjYwIDMxOCA0MDIgNjM2IDYzNiA2MzYgNjM2CjMzNyA1MDAgNTAwIDEwMDAgNDc1IDYxMiA4MzggMzM4IDEwMDAgNTAwIDUwMCA4MzggNDAxIDQwMSA1MDAgNjUwIDYzNiAzMTgKNTAwIDQwMSA0NzAgNjEyIDk2OSA5NjkgOTY5IDUzNiA3MjIgNzIyIDcyMiA3MjIgNzIyIDcyMiAxMDAxIDc2NSA3MzAgNzMwCjczMCA3MzAgMzk1IDM5NSAzOTUgMzk1IDgwNyA4NzUgODIwIDgyMCA4MjAgODIwIDgyMCA4MzggODIwIDg0MyA4NDMgODQzIDg0Mwo2NjAgNjc2IDY2OCA1OTYgNTk2IDU5NiA1OTYgNTk2IDU5NiA5NDAgNTYwIDU5MiA1OTIgNTkyIDU5MiAzMjAgMzIwIDMyMCAzMjAKNjAyIDY0NCA2MDIgNjAyIDYwMiA2MDIgNjAyIDgzOCA2MDIgNjQ0IDY0NCA2NDQgNjQ0IDU2NSA2NDAgNTY1IF0KZW5kb2JqCjIzIDAgb2JqCjw8IC9TIDI0IDAgUiAvViAyNSAwIFIgL2EgMjYgMCBSIC9jIDI3IDAgUiAvZSAyOCAwIFIgL2VpZ2h0IDI5IDAgUgovZiAzMCAwIFIgL2ZvdXIgMzEgMCBSIC9pIDMyIDAgUiAvbCAzMyAwIFIgL20gMzQgMCBSIC9uIDM1IDAgUiAvbyAzNiAwIFIKL29uZSAzNyAwIFIgL3AgMzggMCBSIC9wZXJpb2QgMzkgMCBSIC9yIDQxIDAgUiAvcyA0MiAwIFIgL3NpeCA0MyAwIFIKL3NwYWNlIDQ0IDAgUiAvdHdvIDQ1IDAgUiAveiA0NiAwIFIgL3plcm8gNDcgMCBSID4+CmVuZG9iagozIDAgb2JqCjw8IC9GMSAyMiAwIFIgL0YyIDE1IDAgUiA+PgplbmRvYmoKNCAwIG9iago8PCAvQTEgPDwgL0NBIDAgL1R5cGUgL0V4dEdTdGF0ZSAvY2EgMSA+PgovQTIgPDwgL0NBIDEgL1R5cGUgL0V4dEdTdGF0ZSAvY2EgMSA+PgovQTMgPDwgL0NBIDAuOCAvVHlwZSAvRXh0R1N0YXRlIC9jYSAwLjggPj4gPj4KZW5kb2JqCjUgMCBvYmoKPDwgPj4KZW5kb2JqCjYgMCBvYmoKPDwgPj4KZW5kb2JqCjcgMCBvYmoKPDwgL0YxLURlamFWdVNlcmlmLXByb3BvcnRpb25hbCA0MCAwIFIgL00wIDEyIDAgUiA+PgplbmRvYmoKMTIgMCBvYmoKPDwgL0JCb3ggWyAtOCAtOCA4IDggXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEzMSAvU3VidHlwZSAvRm9ybQovVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJxtkEEOhCAMRfc9RS/wSUtFZevSa7iZTOL9twNxQEzdNNC+PH5R/pLwTqXA+CQJS06z5HrTkNK6TIwY5tWyKMegUS3WznU4qM/QcGN0i7EUptTW6Hijm+k23pM/+rBZIUY/HA6vhHsWQyZcKTEGh98LL9vD/xGeXtTAH6KNfmNaQ/0KZW5kc3RyZWFtCmVuZG9iagoyIDAgb2JqCjw8IC9Db3VudCAxIC9LaWRzIFsgMTAgMCBSIF0gL1R5cGUgL1BhZ2VzID4+CmVuZG9iago0OCAwIG9iago8PCAvQ3JlYXRpb25EYXRlIChEOjIwMjExMTE2MTA1MjQzKzAyJzAwJykKL0NyZWF0b3IgKE1hdHBsb3RsaWIgdjMuMy40LCBodHRwczovL21hdHBsb3RsaWIub3JnKQovUHJvZHVjZXIgKE1hdHBsb3RsaWIgcGRmIGJhY2tlbmQgdjMuMy40KSA+PgplbmRvYmoKeHJlZgowIDQ5CjAwMDAwMDAwMDAgNjU1MzUgZiAKMDAwMDAwMDAxNiAwMDAwMCBuIAowMDAwMDE0OTYwIDAwMDAwIG4gCjAwMDAwMTQ0MTEgMDAwMDAgbiAKMDAwMDAxNDQ1NCAwMDAwMCBuIAowMDAwMDE0NTk2IDAwMDAwIG4gCjAwMDAwMTQ2MTcgMDAwMDAgbiAKMDAwMDAxNDYzOCAwMDAwMCBuIAowMDAwMDAwMDY1IDAwMDAwIG4gCjAwMDAwMDAzOTQgMDAwMDAgbiAKMDAwMDAwMDIwOCAwMDAwMCBuIAowMDAwMDAzMTgyIDAwMDAwIG4gCjAwMDAwMTQ3MDYgMDAwMDAgbiAKMDAwMDAwNDUwOSAwMDAwMCBuIAowMDAwMDA0MzAyIDAwMDAwIG4gCjAwMDAwMDM5NzQgMDAwMDAgbiAKMDAwMDAwNTU2NCAwMDAwMCBuIAowMDAwMDAzMjAzIDAwMDAwIG4gCjAwMDAwMDMzOTUgMDAwMDAgbiAKMDAwMDAwMzgwMSAwMDAwMCBuIAowMDAwMDEzMDc5IDAwMDAwIG4gCjAwMDAwMTI4NzkgMDAwMDAgbiAKMDAwMDAxMjQ0MSAwMDAwMCBuIAowMDAwMDE0MTM0IDAwMDAwIG4gCjAwMDAwMDU2MTYgMDAwMDAgbiAKMDAwMDAwNjAzOCAwMDAwMCBuIAowMDAwMDA2MjA1IDAwMDAwIG4gCjAwMDAwMDY1ODkgMDAwMDAgbiAKMDAwMDAwNjkwMCAwMDAwMCBuIAowMDAwMDA3MjE3IDAwMDAwIG4gCjAwMDAwMDc2NzEgMDAwMDAgbiAKMDAwMDAwNzkzNCAwMDAwMCBuIAowMDAwMDA4MTEyIDAwMDAwIG4gCjAwMDAwMDgzNDMgMDAwMDAgbiAKMDAwMDAwODQ4NCAwMDAwMCBuIAowMDAwMDA4ODQ2IDAwMDAwIG4gCjAwMDAwMDkxMTAgMDAwMDAgbiAKMDAwMDAwOTM5OSAwMDAwMCBuIAowMDAwMDA5NTU0IDAwMDAwIG4gCjAwMDAwMDk4OTIgMDAwMDAgbiAKMDAwMDAxMDA4OSAwMDAwMCBuIAowMDAwMDEwNTUyIDAwMDAwIG4gCjAwMDAwMTA3OTkgMDAwMDAgbiAKMDAwMDAxMTIxMyAwMDAwMCBuIAowMDAwMDExNjE2IDAwMDAwIG4gCjAwMDAwMTE3MDUgMDAwMDAgbiAKMDAwMDAxMjAwMCAwMDAwMCBuIAowMDAwMDEyMTU3IDAwMDAwIG4gCjAwMDAwMTUwMjAgMDAwMDAgbiAKdHJhaWxlcgo8PCAvSW5mbyA0OCAwIFIgL1Jvb3QgMSAwIFIgL1NpemUgNDkgPj4Kc3RhcnR4cmVmCjE1MTc3CiUlRU9GCg==\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"bins = np.linspace(10,10000,30)\n",
"vm = np.array([data[np.logical_and(data[:,0]>=l,data[:,0] For en prøve \n",
">\n",
"> $$\\{x_1,\\ldots,x_N\\}$$\n",
">\n",
"> af størrelse $N$ er gennemsnittet \n",
">\n",
"> $$\\overline{x} = \\frac{1}{N}\\sum_{i=1}^{N}x_i\\quad,$$\n",
">\n",
"> et estimat af den \"sande\" værdi, og \n",
">\n",
"> $$\\delta_{\\overline{x}} = \\frac{s_x}{\\sqrt{N}}=\\sqrt{\\frac{s_x^2}{N}}\\quad\\text{med}\\quad s_x^2 = \\frac1N\\sum_{i=1}^N \\left(x_i-\\overline{x}\\right)^2\\quad,$$ \n",
"> \n",
"> præcisionen (el. usikkerheden) med hvilken vi har bestemt $\\overline{x}$ "
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Eksempel \n",
"\n",
"Lad os gentage vores tidligere forsøg "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-14T19:40:09.230110Z",
"iopub.status.busy": "2021-11-14T19:40:09.229219Z",
"iopub.status.idle": "2021-11-14T19:40:10.408972Z",
"shell.execute_reply": "2021-11-14T19:40:10.409777Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"np.random.seed(123456)\n",
"def me(sample):\n",
" return len(sample), sample.mean(), sample.std()/np.sqrt(len(sample))\n",
"data = np.array([me(np.random.randint(0,10,size=n)) \n",
" for n in np.random.randint(10,10000,size=100)])\n",
"plt.errorbar(data[:,0],data[:,1],data[:,2],fmt='o',label=r'$\\overline{x}$ with uncer.',ms=4)\n",
"plt.axhline(4.5,label='Expectation value',color='tab:orange')\n",
"plt.xlabel('Sample size')\n",
"plt.ylabel(r'$\\overline{x}$')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"_Avanceret_: Hvorfor overlapper ikke alle fejl med forventningsværdien? Hvor mange af disse kan vi forvente? "
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Afledte værdier \n",
"\n",
"Lad $y(x_1,\\ldots,x_n)$ være en _afledt_ værdi af de _uafhængige_ målingerne $x_1,\\ldots,x_n$, hver med usikkerhed $\\delta_{x_i}$\n",
"\n",
"- Hvad er usikkerheden på $y$? "
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Husk, usikkerheden er kvadratroden af variansen. \n",
"\n",
"- Dvs. hvis $x_i$ varierer, så giver det ophav til variation i $y$. \n",
"- Hvordan bestemmer vi variation af en funktion $y(x_1,\\ldots,x_n)$? "
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Partiel afledt af $y$ med hensyn til $x_i$ giver variationen af $y$ når $x_i$ varierer \n",
"\n",
"Kæderegel for usikkerheder \n",
"\n",
"$$s_{y}^2 \\approx \\left(\\frac{\\partial y}{\\partial x_1}\\right)^2s_{x_1}^2+\\cdots+\\left(\\frac{\\partial y}{\\partial x_n}\\right)^2s_{x_n}^2\\quad.$$\n",
"\n",
"(Tayler udvikling til anden orden)"
]
},
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"source": [
"## Eksempel $y=a+b$"
]
},
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"metadata": {
"lang": "da"
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"source": [
"Lad os sige vi har målt "
]
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"source": [
"a, b, da, db = 10, 20, 1, 0.5"
]
},
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"cell_type": "markdown",
"metadata": {
"lang": "da"
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"source": [
"og vi vil bestemme $y=a+b$ med tilhørende usikkerhed. Vi har \n",
"\n",
"$$\\frac{\\partial y}{\\partial a} = 1\\quad\\frac{\\partial y}{\\partial b}=1\\quad,$$ \n",
"\n",
"så "
]
},
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"outputs": [
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"name": "stdout",
"output_type": "stream",
"text": [
"y = 30 +/- 1\n"
]
}
],
"source": [
"y = a+b\n",
"dy = np.sqrt(1**2 * da**2 + 1**2 * db**2)\n",
"print('y = {:.0f} +/- {:.0f}'.format(y,dy))"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "da",
"slideshow": {
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"source": [
"Med samme værdier af $a,b$, hvad er usikkerheden på $ab$? $a/b$? "
]
},
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"outputs": [
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"name": "stdout",
"output_type": "stream",
"text": [
"d(a*b)=21 d(a/b)=0.1\n"
]
}
],
"source": [
"dprod = np.sqrt(b**2 * da**2 + a**2 * db**2)\n",
"drat = np.sqrt(1/b**2 * da**2 + a**2 / b**4 * db**2)\n",
"print('d(a*b)={:.0f} d(a/b)={:.1f}'.format(dprod,drat))"
]
}
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