mirror of https://github.com/jlizier/jidt
230 lines
38 KiB
Plaintext
230 lines
38 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "87e17b68-7539-4539-aeab-9df6fc819f22",
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"metadata": {},
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"source": [
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"# Conditional mutual information between successive letters in written English\n",
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"\n",
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"Author: J. Lizier, Isabelle De Backer, 2022-; based on the original Matlab tutorials.\n",
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"\n",
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"The following block aims to import all the relevant libraries to analyse data"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "55ca6967-2ca7-45e8-9858-6bb0356c2bee",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"import math\n",
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"\n",
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"# Specifics required for the text processing here:\n",
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"import string\n",
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"import re"
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]
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},
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{
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"cell_type": "markdown",
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"id": "bc5119d3-c9d3-4139-ad43-3346098ea85d",
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"metadata": {},
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"source": [
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"# Preparing your environment\n",
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"\n",
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"As per `Module_2_notebook.ipynb` etc. we need to use the functions we have defined in our previous work in other notebooks. So gather the new functions you wrote in this module into your `simpleinfotheory.py` script, and make sure it is referencable from here (you may need to change the folder referenced below) before you run the import line in the next cell:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "8df5b524-117e-4a02-989e-9647b336dcc5",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Option 3: edit simpleinfotheory.py and past your functions into that as you write them\n",
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"import sys\n",
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"sys.path.append('../../Module1-IntroToInfoTheory/PythonCode/completed/')\n",
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"import simpleinfotheory"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4ecca927-eb6b-4840-8ea5-d4ea2bf79869",
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"metadata": {},
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"source": [
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"# 7. (Optional Extension) Conditional mutual information between successive letters in written English\n",
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"\n",
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"In this extension activity, we will continue our analysis of written English extracted from the [Seinfeld](https://en.wikipedia.org/wiki/Seinfeld) scripts as begun in the previous modules.\n",
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"\n",
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"1. Download the scripts from the links on Module 2 on Canvas, load into Python and preprocess as per steps 1-4 of the activity from module 2, such that we have the characters stored in the numpy array `processedStr`:<br/>\n",
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"_Note:_ you may need to alter the filename/path to match your own --"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "0cebd6af-93fe-4377-9bdf-adfc995bcd10",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([' ', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l',\n",
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" 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y',\n",
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" 'z'], dtype='<U1')"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"filename = './Seinfeld-scripts-textOnly.txt'\n",
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"with open(filename, 'rt') as f:\n",
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" str = f.read()\n",
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"p = re.compile('[!\"#\\$%&\\'\\(\\)\\*\\+\\,-\\.\\/:;<=>\\?@\\[\\]\\\\\\^_`{\\|}~0-9]*');\n",
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"processedStr = p.sub('', str); # Remove punctuation characters and digits\n",
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"processedStr = ' '.join(processedStr.split('\\n')); # Replace newline characters with spaces\n",
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"processedStr = processedStr.lower(); # Convert all upper case into lower case\n",
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"processedStr = np.array(list(processedStr)); # Finally convert this into a numpy array so we can work with it\n",
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"np.unique(processedStr)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4e6b1195-3c3b-4570-ac49-742810f94025",
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"metadata": {},
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"source": [
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"2. We previously computed the mutual information between characters over several lags between these characters. In particular, we examined the mutual information between characters separated by a lag of 2, and posed the question of whether the information carried by the earlier character about the later one is also included in the character in between them. Think about how you could investigate this question using conditional mutual information?\n",
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"3. Calculate the mutual information between characters separated by another character, conditioned on the character in the middle. Use our function `simpleinfotheory.conditionalmutualinformationempirical()`.<br/>\n",
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" _Hint_: You should create vectors of samples for each of: the earlier character, the middle character, and the later character; and pass these through to the function. Recall that to select all but the last two items in a numpy array `x`, you can refer to `x[:-2]`, and similarly to select all but the first and last items in an array you can refer to `x[1:-1]`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "f1225213-86e2-49f3-9ff9-dfe0f6d34876",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0.739076942492698"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# Compute the mutual information between successive characters conditioned on the character in between:\n",
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"simpleinfotheory.conditionalmutualinformationempirical(processedStr[:-2],processedStr[2:],processedStr[1:-1])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ab60c5ec-592a-4e15-97c7-280f7ce91253",
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"metadata": {},
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"source": [
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"4. Compare this conditional mutual information to the mutual information between the two characters separated by another character as computed in the previous module (see the result for a lag of 2 on the sample plot in that activity). Is the conditional mutual information here larger or smaller than that? What does this tell us about the structure of the relationships in sequences of characters in English text?\n",
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"5. _Challenge_: Can you compute such conditional mutual information over lags of up to 5 characters, conditioning on all intervening characters, and then plot these? Alternatively, you could compute the joint mutual information from sets of consecutive characters (up to 5 of them) to the next character. (How are these two quantities related?).<br/>\n",
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" Note that the calculations here will take _significantly_ longer than previous ones since we are dealing with higher and higher order multivariate spaces (not so long for a lag of 2, but ~1 minute for lag 5). What is the size of the probability space we are estimating once we are looking at a lag of 5 (i.e. 4 characters in between the previous and next)? Do you think we can properly estimate the joint probabilities here from the amount of data that we have?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "c9a980f0-ad8a-4aea-9fbe-5d0a78282db8",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"cond MI over lag 1 is 0.7196\n",
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"\n",
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"cond MI over lag 2 is 0.7391\n",
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"\n",
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"cond MI over lag 3 is 0.5251\n",
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"\n",
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"cond MI over lag 4 is 0.3197\n",
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"\n",
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"cond MI over lag 5 is 0.2474\n",
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"\n"
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]
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},
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Compute the mutual information between successive characters conditioned on up to 5 characters in between:\n",
|
|
"maxLag = 5;\n",
|
|
"\n",
|
|
"condMisVsLag = np.zeros(maxLag);\n",
|
|
"conditionalCharacters = None;\n",
|
|
"\n",
|
|
"nextChar = processedStr[maxLag:];\n",
|
|
"for lag in range(1,maxLag+1): # To go from 1 up to maxLag\n",
|
|
" sourceChar = processedStr[maxLag-lag:-lag];\n",
|
|
" if (lag == 1):\n",
|
|
" # Nothing to condition on, just compute MI\n",
|
|
" condMisVsLag[lag-1] = simpleinfotheory.mutualinformationempirical(sourceChar,nextChar)[0];\n",
|
|
" conditionalCharacters = sourceChar; # Initialise the characters to now be conditioned on\n",
|
|
" else:\n",
|
|
" condMisVsLag[lag-1] = simpleinfotheory.conditionalmutualinformationempirical(sourceChar,nextChar,conditionalCharacters);\n",
|
|
" conditionalCharacters = np.column_stack( (conditionalCharacters,sourceChar) ); # Add to the characters to be conditioned on\n",
|
|
" print('cond MI over lag %d is %.4f\\n' % (lag, condMisVsLag[lag-1]));\n",
|
|
"\n",
|
|
"plt.scatter(range(1,maxLag+1), condMisVsLag, c=\"red\", marker=\"x\");\n",
|
|
"plt.xlabel('Lag')\n",
|
|
"plt.ylabel('Cond MI (bits)');\n",
|
|
"plt.title('Average MI between characters separated by the\\ngiven lag conditioned on intervening chars');\n",
|
|
"plt.savefig('CondMIversusLag.png')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "498d4c88-23f4-4544-922d-e812255fd914",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3 (ipykernel)",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
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"name": "ipython",
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},
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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}
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}
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