{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction\n", "\n", "In this notebook you find the code developed for the experimental section of our paper [1].\n", "\n", "The reminder of this notebook goes as follows:\n", "1. download dataset;\n", "2. parse dataset;\n", "3. observed user behaviour (Table 1);\n", "4. sDCG and sRBP discount functions;\n", "5. fit discount functions on the observed user behaviour (Figure 3, Table 2, 3, 4 and 5);\n", "6. correlation analysis (Figure 4 and 5, Table 6 and 7)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import sys, os, math, re, gzip, xml.etree.ElementTree, urllib.request, plotly\n", "import pandas as pd\n", "import numpy as np\n", "import scipy.stats as stats\n", "import plotly.graph_objs as go\n", "from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n", "from tqdm import tqdm_notebook\n", "from scipy import signal\n", "from bs4 import BeautifulSoup as bs\n", "\n", "plotly.offline.init_notebook_mode(connected=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Download Dataset \n", "\n", "From TREC ([trec.nist.gov](http://trec.nist.gov)) we download the dataset. This dataset consists of: \n", "1. a qrels file; \n", "2. a session-topic mapping file;\n", "2. sessions files, and; \n", "4. search results.\n", "\n", "However, in order to download the search results you need to request username and password following the instructions you find on this [link](https://trec.nist.gov/results.html).\n", "\n", "## QRels" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "https://trec.nist.gov/data/session/2014/judgments.txt\n" ] } ], "source": [ "if not os.path.isfile('qrels.txt'):\n", " url_qrels = \"https://trec.nist.gov/data/session/2014/judgments.txt\"\n", " urllib.request.urlretrieve(url_qrels, \"qrels.txt\")\n", " print(url_qrels)\n", "else:\n", " print('qrels.txt file exists')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Session-topic Mapping" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "https://trec.nist.gov/data/session/2014/session-topic-mapping.txt\n" ] } ], "source": [ "if not os.path.isfile('session_to_topic.txt'):\n", " url_session_to_topic = \"https://trec.nist.gov/data/session/2014/session-topic-mapping.txt\"\n", " !rm -f session_to_topic.txt\n", " urllib.request.urlretrieve(url_session_to_topic, \"session_to_topic.txt\")\n", " print(url_session_to_topic)\n", "else:\n", " print('session_to_topic.txt file exists')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sessions" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "https://trec.nist.gov/data/session/2014/sessiontrack2014.xml.gz\n" ] } ], "source": [ "if not os.path.isfile('sessions.xml'):\n", " url_sessions = \"https://trec.nist.gov/data/session/2014/sessiontrack2014.xml.gz\"\n", " urllib.request.urlretrieve(url_sessions, \"sessions.xml.gz\")\n", " !gunzip sessions.xml.gz\n", " print(url_sessions)\n", "else:\n", " print('sessions.xml file exists')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Search Results\n", "\n", "To execute the following code you need to first obtain username and password using this [link](https://trec.nist.gov/results.html). Then, replace the strings \"username\" and \"password\" with the correct ones." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "https://trec.nist.gov/results/trec23/./session/input-ECxCGxPRF.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ECxCGxPRF.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ECxCGxPRF.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ECxSRMxOS.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ECxSRMxOS.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ECxSRMxOS.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ECxSRMxPRF.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ECxSRMxPRF.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ECxSRMxPRF.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-GUS14Run1.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-GUS14Run1.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-GUS14Run1.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-GUS14Run2.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-GUS14Run2.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-GUS14Run2.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-GUS14Run3.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-GUS14Run3.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-GUS14Run3.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ICTNET14SER1.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ICTNET14SER1.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ICTNET14SER1.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ICTNET14SER2.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ICTNET14SER2.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ICTNET14SER2.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ICTNET14SER3.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ICTNET14SER3.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ICTNET14SER3.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-RAMA.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-RAMA.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-RAMA.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-SCIAITeamC.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-SCIAITeamC.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-SCIAITeamF.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-SCIAITeamF.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-SCIAITeamL.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-SCIAITeamL.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-UMASS1.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-UMASS1.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-UMASS1.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-UMASS2.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-UMASS2.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-UMASS2.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-UMASS3.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-UMASS3.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-UMASS3.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-UMASS4.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-UMASS4.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-UMASS4.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-WLZNTJU.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-WLZNTJU.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-WLZNTJU.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ecnusession1.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ecnusession1.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ecnusession1.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ecnusession2.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ecnusession2.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ecnusession2.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ecnusession3.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ecnusession3.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-ecnusession3.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-uclbaseline.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-udel14Run1.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-udel14Run1.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-udelitu.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-webis2014act.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-webis2014act.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-webis2014act.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-webis2014db.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-webis2014db.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-webis2014db.RL3.gz\n", "https://trec.nist.gov/results/trec23/./session/input-webisSt14ax.RL1.gz\n", "https://trec.nist.gov/results/trec23/./session/input-webisSt14ax.RL2.gz\n", "https://trec.nist.gov/results/trec23/./session/input-webisSt14ax.RL3.gz\n" ] } ], "source": [ "username = \"username\"\n", "password = \"password\"\n", "\n", "if not os.path.isdir('session') or len(os.listdir('session')) == 0:\n", " password_mgr = urllib.request.HTTPPasswordMgrWithDefaultRealm()\n", " top_level_url = \"https://trec.nist.gov/results\"\n", " password_mgr.add_password(None, top_level_url, username, password)\n", " handler = urllib.request.HTTPBasicAuthHandler(password_mgr)\n", " opener = urllib.request.build_opener(handler)\n", " urllib.request.install_opener(opener)\n", "\n", " !rm -f -r session\n", " !mkdir session\n", "\n", " runs_page = opener.open(\"https://trec.nist.gov/results/trec23/session.input.html\")\n", " soup = bs(runs_page)\n", " for link in soup.findAll('a', attrs={'href': re.compile(\".*\\.gz\")}):\n", " run_path = link.get(\"href\")\n", " url_run = \"https://trec.nist.gov/results/trec23/\"+run_path\n", " print(url_run)\n", " urllib.request.urlretrieve(url_run, run_path)\n", "else:\n", " print('a session folder exists and is not empty')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Parse Dataset\n", "\n", "With the following code we parse the downloaded files into data-structures needed for the experiments below. \n", "\n", "## QRels" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "159d45cc68c4472994a80821fc71c4b3", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(IntProgress(value=0, max=16949), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "qrels = {}\n", "with open(\"qrels.txt\") as file:\n", " for line in tqdm_notebook(file.readlines()):\n", " elem = line.split(\" \")\n", " topic = int(elem[0])\n", " document = elem[2]\n", " rel = int(elem[3])\n", " if not topic in qrels:\n", " qrels[topic] = {}\n", " if not document in qrels[topic]:\n", " qrels[topic][document] = {}\n", " qrels[topic][document][0] = rel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Session-topic Mapping" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "ff2f4054803544be85cc34432a1ceb53", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(IntProgress(value=0, max=101), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "session_qrels_remap = {}\n", "with open(\"session_to_topic.txt\") as file:\n", " for line in tqdm_notebook(file.readlines()):\n", " elem = re.split(\"\\s+\", line.strip())\n", " if not elem[0].startswith('#') and len(elem) >= 2:\n", " session = int(elem[0])\n", " topic = int(elem[1])\n", " session_qrels_remap[session] = topic" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sessions\n", "\n", "Each session is represented by a list of strings having the following meaning:\n", "\n", "* **q-{n}:** The session has started. n is the number of judged relevant documents for the topic associated to this session;\n", "\n", "* **r:** The user has reformulated the query;\n", "\n", "* **e-{r}:** The user has examined the snippet or clicked on the document link. r is 1 when the document is relevant to the topic and 0 otherwise;\n", "\n", "* **n-{r}:** The user has not examined the snippet or clicked on the document link. r is 1 when the document is relevant to the topic and 0 otherwise;\n", "\n", "* **f:** The end of the session." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "71b22b1816e74d1ab922c8169e260254", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(IntProgress(value=0, max=1257), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "xml_sessions = xml.etree.ElementTree.parse(\"sessions.xml\").getroot()\n", "\n", "sessions = {}\n", "for xml_session in tqdm_notebook(xml_sessions.findall('session')):\n", " session = int(xml_session.get('num'))\n", " \n", " topic = 0\n", " if session in session_qrels_remap:\n", " topic = session_qrels_remap[session]\n", " \n", " max_reformulate = 0\n", " rels_found = set()\n", " sessions[session] = []\n", " for xml_interaction in xml_session.findall('interaction'):\n", " interaction = int(xml_interaction.get(\"num\"))\n", " interaction_type = xml_interaction.get(\"type\")\n", " \n", " if interaction == 1:\n", " if topic > 0:\n", " n_rel = 0\n", " for doc in qrels[topic]:\n", " if qrels[topic][doc][0] > 0:\n", " n_rel += 1\n", " sessions[session].append(\"q-\"+str(n_rel))\n", " else:\n", " sessions[session].append(\"q\")\n", " max_reformulate = 0\n", " elif interaction_type == \"reformulate\":\n", " sessions[session].append(\"r\")\n", " max_reformulate +=1\n", " \n", " rels = {}\n", " if topic > 0:\n", " for xml_result in xml_interaction.find(\"results\").findall(\"result\"):\n", " rank = int(xml_result.get(\"rank\"))\n", " document = xml_result.find(\"clueweb12id\").text\n", " \n", " rels[rank] = 0\n", " if document in qrels[topic] and document not in rels_found and qrels[topic][document][0] > 0:\n", " #rels_found.add(document)\n", " rels[rank] = 1\n", " \n", " max_rank = -1\n", " for xml_result in xml_interaction.find(\"results\").findall(\"result\"):\n", " max_rank = int(xml_result.get(\"rank\"))\n", " break\n", " \n", " if xml_interaction.find(\"clicked\"):\n", " for xml_click in xml_interaction.find(\"clicked\").findall(\"click\"):\n", " max_rank = int(xml_click.find(\"rank\").text)\n", " \n", " for xml_result in xml_interaction.find(\"results\").findall(\"result\"):\n", " rank = int(xml_result.get(\"rank\"))\n", " if topic > 0:\n", " if rank <= max_rank:\n", " if rels[rank] > 0:\n", " sessions[session].append(\"e-1\")\n", " else:\n", " sessions[session].append(\"e-0\")\n", " else:\n", " if rels[rank] > 0:\n", " sessions[session].append(\"n-1\")\n", " else:\n", " sessions[session].append(\"n-0\")\n", " else:\n", " if rank <= max_rank:\n", " sessions[session].append(\"e\")\n", " else:\n", " sessions[session].append(\"n\")\n", " \n", " is_e = False\n", " i = len(sessions[session]) - 1\n", " while i >= 0:\n", " if sessions[session][i] == \"q\" or sessions[session][i] == \"r\":\n", " break\n", " elif sessions[session][i].startswith(\"e\"):\n", " is_e = True\n", " elif is_e:\n", " sessions[session][i] = sessions[session][i].replace(\"n\", \"e\")\n", " i-=1\n", " \n", " sessions[session].append(\"f\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Search Results" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "8e7cb003720c4e38bd0f0bf1780f9100", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(IntProgress(value=0, max=73), HTML(value='')))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "runs = {}\n", "\n", "for path, dirs, files in os.walk('./session'):\n", " for run_name in tqdm_notebook(files):\n", " run_path = \"session/\"+run_name\n", " with gzip.open(run_path, \"rb\") as file:\n", " runs[run_name] = {}\n", " for line in file:\n", " elem = str(line).split(\" \")[0:4]\n", " session = int(elem[0].split(\"'\")[1])\n", " topic = 0\n", " if session in session_qrels_remap:\n", " topic = session_qrels_remap[session]\n", " if topic > 0 and topic in qrels:\n", " if session not in runs[run_name]:\n", " runs[run_name][session] = []\n", "\n", " document = elem[2]\n", " rank = elem[3]\n", " rel = 0\n", " if document in qrels[topic] and qrels[topic][document][0] > 0:\n", " rel = 1\n", " if rank == 1:\n", " runs[run_name][session].append(\"r\")\n", " runs[run_name][session].append(\"n-\" + str(rel))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Observed User Behaviours (Table 1)\n", "\n", "With this code we compute the observed user behaviours.\n", "\n", "## Over Sessions\n", "\n", "This generates a dataframe representing the observed examination probability distribution over queries, reformulations and ranks." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
\n", " | 0 | \n", "1 | \n", "2 | \n", "3 | \n", "4 | \n", "5 | \n", "6 | \n", "7 | \n", "8 | \n", "9 | \n", "10 | \n", "11 | \n", "12 | \n", "13 | \n", "14 | \n", "
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1 | \n", "0.042890 | \n", "0.028976 | \n", "0.015445 | \n", "0.009574 | \n", "0.005489 | \n", "0.002553 | \n", "0.001149 | \n", "0.000638 | \n", "0.000255 | \n", "0.000128 | \n", "0.000000 | \n", "0.000128 | \n", "0.000128 | \n", "0.000128 | \n", "0.000128 | \n", "
2 | \n", "0.032550 | \n", "0.021828 | \n", "0.012254 | \n", "0.008042 | \n", "0.004468 | \n", "0.001915 | \n", "0.000894 | \n", "0.000638 | \n", "0.000255 | \n", "0.000128 | \n", "0.000000 | \n", "0.000128 | \n", "0.000128 | \n", "0.000128 | \n", "0.000128 | \n", "
3 | \n", "0.024636 | \n", "0.017871 | \n", "0.009701 | \n", "0.006255 | \n", "0.003829 | \n", "0.001532 | \n", "0.000766 | \n", "0.000511 | \n", "0.000255 | \n", "0.000128 | \n", "0.000000 | \n", "0.000000 | \n", "0.000128 | \n", "0.000000 | \n", "0.000000 | \n", "
4 | \n", "0.019403 | \n", "0.014680 | \n", "0.008552 | \n", "0.004978 | \n", "0.003319 | \n", "0.001404 | \n", "0.000638 | \n", "0.000383 | \n", "0.000255 | \n", "0.000128 | \n", "0.000000 | \n", "0.000000 | \n", "0.000128 | \n", "0.000000 | \n", "0.000000 | \n", "
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61 rows × 1 columns
\n", "\n", " | 0 | \n", "1 | \n", "2 | \n", "3 | \n", "4 | \n", "5 | \n", "6 | \n", "7 | \n", "8 | \n", "9 | \n", "10 | \n", "11 | \n", "12 | \n", "13 | \n", "14 | \n", "
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0 | \n", "1.405216e-01 | \n", "9.676489e-02 | \n", "6.663348e-02 | \n", "4.588462e-02 | \n", "3.159670e-02 | \n", "2.175787e-02 | \n", "1.498273e-02 | \n", "1.031729e-02 | \n", "7.104612e-03 | \n", "4.892322e-03 | \n", "3.368912e-03 | \n", "2.319874e-03 | \n", "1.597493e-03 | \n", "1.100053e-03 | \n", "7.575098e-04 | \n", "
1 | \n", "7.734311e-02 | \n", "5.325940e-02 | \n", "3.667507e-02 | \n", "2.525489e-02 | \n", "1.739083e-02 | \n", "1.197553e-02 | \n", "8.246497e-03 | \n", "5.678638e-03 | \n", "3.910379e-03 | \n", "2.692734e-03 | \n", "1.854249e-03 | \n", "1.276858e-03 | \n", "8.792602e-04 | \n", "6.054692e-04 | \n", "4.169334e-04 | \n", "
2 | \n", "4.256965e-02 | \n", "2.931397e-02 | \n", "2.018596e-02 | \n", "1.390029e-02 | \n", "9.571910e-03 | \n", "6.591333e-03 | \n", "4.538872e-03 | \n", "3.125522e-03 | \n", "2.152272e-03 | \n", "1.482081e-03 | \n", "1.020579e-03 | \n", "7.027829e-04 | \n", "4.839448e-04 | \n", "3.332502e-04 | \n", "2.294801e-04 | \n", "
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39 | \n", "1.081936e-11 | \n", "7.450346e-12 | \n", "5.130398e-12 | \n", "3.532854e-12 | \n", "2.432766e-12 | \n", "1.675232e-12 | \n", "1.153585e-12 | \n", "7.943727e-13 | \n", "5.470147e-13 | \n", "3.766809e-13 | \n", "2.593870e-13 | \n", "1.786170e-13 | \n", "1.229979e-13 | \n", "8.469782e-14 | \n", "5.832394e-14 | \n", "
40 | \n", "5.954978e-12 | \n", "4.100670e-12 | \n", "2.823771e-12 | \n", "1.944483e-12 | \n", "1.338994e-12 | \n", "9.220478e-13 | \n", "6.349333e-13 | \n", "4.372227e-13 | \n", "3.010769e-13 | \n", "2.073252e-13 | \n", "1.427666e-13 | \n", "9.831082e-14 | \n", "6.769802e-14 | \n", "4.661768e-14 | \n", "3.210150e-14 | \n", "
41 | \n", "3.277620e-12 | \n", "2.257009e-12 | \n", "1.554204e-12 | \n", "1.070243e-12 | \n", "7.369826e-13 | \n", "5.074951e-13 | \n", "3.494673e-13 | \n", "2.406474e-13 | \n", "1.657127e-13 | \n", "1.141118e-13 | \n", "7.857875e-14 | \n", "5.411028e-14 | \n", "3.726099e-14 | \n", "2.565837e-14 | \n", "1.766866e-14 | \n", "
42 | \n", "1.804002e-12 | \n", "1.242258e-12 | \n", "8.554337e-13 | \n", "5.890620e-13 | \n", "4.056352e-13 | \n", "2.793253e-13 | \n", "1.923468e-13 | \n", "1.324523e-13 | \n", "9.120827e-14 | \n", "6.280712e-14 | \n", "4.324974e-14 | \n", "2.978230e-14 | \n", "2.050845e-14 | \n", "1.412237e-14 | \n", "9.724833e-15 | \n", "
43 | \n", "9.929228e-13 | \n", "6.837386e-13 | \n", "4.708307e-13 | \n", "3.242197e-13 | \n", "2.232616e-13 | \n", "1.537406e-13 | \n", "1.058677e-13 | \n", "7.290176e-14 | \n", "5.020103e-14 | \n", "3.456904e-14 | \n", "2.380466e-14 | \n", "1.639218e-14 | \n", "1.128785e-14 | \n", "7.772951e-15 | \n", "5.352548e-15 | \n", "
44 | \n", "5.465047e-13 | \n", "3.763297e-13 | \n", "2.591452e-13 | \n", "1.784505e-13 | \n", "1.228832e-13 | \n", "8.461885e-14 | \n", "5.826957e-14 | \n", "4.012513e-14 | \n", "2.763065e-14 | \n", "1.902680e-14 | \n", "1.310208e-14 | \n", "9.022254e-15 | \n", "6.212833e-15 | \n", "4.278232e-15 | \n", "2.946042e-15 | \n", "
45 | \n", "3.007962e-13 | \n", "2.071319e-13 | \n", "1.426335e-13 | \n", "9.821917e-14 | \n", "6.763491e-14 | \n", "4.657422e-14 | \n", "3.207157e-14 | \n", "2.208487e-14 | \n", "1.520791e-14 | \n", "1.047235e-14 | \n", "7.211387e-15 | \n", "4.965848e-15 | \n", "3.419543e-15 | \n", "2.354739e-15 | \n", "1.621502e-15 | \n", "
46 | \n", "1.655582e-13 | \n", "1.140054e-13 | \n", "7.850549e-14 | \n", "5.405983e-14 | \n", "3.722625e-14 | \n", "2.563445e-14 | \n", "1.765219e-14 | \n", "1.215551e-14 | \n", "8.370433e-15 | \n", "5.763982e-15 | \n", "3.969147e-15 | \n", "2.733203e-15 | \n", "1.882117e-15 | \n", "1.296048e-15 | \n", "8.924745e-16 | \n", "
47 | \n", "9.112324e-14 | \n", "6.274857e-14 | \n", "4.320942e-14 | \n", "2.975453e-14 | \n", "2.048933e-14 | \n", "1.410920e-14 | \n", "9.715766e-15 | \n", "6.690394e-15 | \n", "4.607086e-15 | \n", "3.172495e-15 | \n", "2.184619e-15 | \n", "1.504355e-15 | \n", "1.035917e-15 | \n", "7.133450e-16 | \n", "4.912180e-16 | \n", "
48 | \n", "5.015423e-14 | \n", "3.453681e-14 | \n", "2.378247e-14 | \n", "1.637689e-14 | \n", "1.127733e-14 | \n", "7.765704e-15 | \n", "5.347558e-15 | \n", "3.682393e-15 | \n", "2.535740e-15 | \n", "1.746142e-15 | \n", "1.202414e-15 | \n", "8.279969e-16 | \n", "5.701687e-16 | \n", "3.926251e-16 | \n", "2.703664e-16 | \n", "
49 | \n", "2.760489e-14 | \n", "1.900906e-14 | \n", "1.308987e-14 | \n", "9.013842e-15 | \n", "6.207041e-15 | \n", "4.274244e-15 | \n", "2.943296e-15 | \n", "2.026789e-15 | \n", "1.395672e-15 | \n", "9.610763e-16 | \n", "6.618088e-16 | \n", "4.557295e-16 | \n", "3.138209e-16 | \n", "2.161008e-16 | \n", "1.488097e-16 | \n", "
50 | \n", "1.519373e-14 | \n", "1.046259e-14 | \n", "7.204664e-15 | \n", "4.961219e-15 | \n", "3.416355e-15 | \n", "2.352544e-15 | \n", "1.619990e-15 | \n", "1.115545e-15 | \n", "7.681776e-16 | \n", "5.289764e-16 | \n", "3.642595e-16 | \n", "2.508335e-16 | \n", "1.727270e-16 | \n", "1.189419e-16 | \n", "8.190483e-17 | \n", "
51 | \n", "8.362630e-15 | \n", "5.758608e-15 | \n", "3.965447e-15 | \n", "2.730655e-15 | \n", "1.880362e-15 | \n", "1.294840e-15 | \n", "8.916425e-16 | \n", "6.139958e-16 | \n", "4.228049e-16 | \n", "2.911486e-16 | \n", "2.004885e-16 | \n", "1.380588e-16 | \n", "9.506894e-17 | \n", "6.546562e-17 | \n", "4.508042e-17 | \n", "
52 | \n", "4.602791e-15 | \n", "3.169538e-15 | \n", "2.182582e-15 | \n", "1.502952e-15 | \n", "1.034951e-15 | \n", "7.126799e-16 | \n", "4.907600e-16 | \n", "3.379433e-16 | \n", "2.327118e-16 | \n", "1.602482e-16 | \n", "1.103488e-16 | \n", "7.598755e-17 | \n", "5.232595e-17 | \n", "3.603228e-17 | \n", "2.481226e-17 | \n", "
53 | \n", "2.533376e-15 | \n", "1.744514e-15 | \n", "1.201293e-15 | \n", "8.272250e-16 | \n", "5.696372e-16 | \n", "3.922590e-16 | \n", "2.701143e-16 | \n", "1.860040e-16 | \n", "1.280846e-16 | \n", "8.820060e-17 | \n", "6.073600e-17 | \n", "4.182355e-17 | \n", "2.880020e-17 | \n", "1.983217e-17 | \n", "1.365667e-17 | \n", "
54 | \n", "1.394370e-15 | \n", "9.601803e-16 | \n", "6.611918e-16 | \n", "4.553047e-16 | \n", "3.135283e-16 | \n", "2.158994e-16 | \n", "1.486709e-16 | \n", "1.023766e-16 | \n", "7.049776e-17 | \n", "4.854561e-17 | \n", "3.342910e-17 | \n", "2.301968e-17 | \n", "1.585163e-17 | \n", "1.091562e-17 | \n", "7.516631e-18 | \n", "
55 | \n", "7.674614e-16 | \n", "5.284832e-16 | \n", "3.639200e-16 | \n", "2.505997e-16 | \n", "1.725660e-16 | \n", "1.188310e-16 | \n", "8.182848e-17 | \n", "5.634808e-17 | \n", "3.880197e-17 | \n", "2.671951e-17 | \n", "1.839937e-17 | \n", "1.267003e-17 | \n", "8.724737e-18 | \n", "6.007960e-18 | \n", "4.137154e-18 | \n", "
56 | \n", "4.224108e-16 | \n", "2.908772e-16 | \n", "2.003015e-16 | \n", "1.379301e-16 | \n", "9.498031e-17 | \n", "6.540459e-17 | \n", "4.503839e-17 | \n", "3.101398e-17 | \n", "2.135660e-17 | \n", "1.470642e-17 | \n", "1.012702e-17 | \n", "6.973586e-18 | \n", "4.802095e-18 | \n", "3.306781e-18 | \n", "2.277089e-18 | \n", "
57 | \n", "2.324949e-16 | \n", "1.600988e-16 | \n", "1.102460e-16 | \n", "7.591671e-17 | \n", "5.227716e-17 | \n", "3.599869e-17 | \n", "2.478913e-17 | \n", "1.707010e-17 | \n", "1.175467e-17 | \n", "8.094411e-18 | \n", "5.573909e-18 | \n", "3.838262e-18 | \n", "2.643073e-18 | \n", "1.820052e-18 | \n", "1.253310e-18 | \n", "
58 | \n", "1.279652e-16 | \n", "8.811838e-17 | \n", "6.067938e-17 | \n", "4.178456e-17 | \n", "2.877335e-17 | \n", "1.981368e-17 | \n", "1.364394e-17 | \n", "9.395381e-18 | \n", "6.469773e-18 | \n", "4.455164e-18 | \n", "3.067880e-18 | \n", "2.112579e-18 | \n", "1.454748e-18 | \n", "1.001757e-18 | \n", "6.898218e-19 | \n", "
59 | \n", "7.043204e-17 | \n", "4.850036e-17 | \n", "3.339793e-17 | \n", "2.299822e-17 | \n", "1.583685e-17 | \n", "1.090545e-17 | \n", "7.509624e-18 | \n", "5.171218e-18 | \n", "3.560963e-18 | \n", "2.452122e-18 | \n", "1.688561e-18 | \n", "1.162764e-18 | \n", "8.006931e-19 | \n", "5.513669e-19 | \n", "3.796779e-19 | \n", "
60 | \n", "3.876579e-17 | \n", "2.669460e-17 | \n", "1.838222e-17 | \n", "1.265822e-17 | \n", "8.716604e-18 | \n", "6.002359e-18 | \n", "4.133297e-18 | \n", "2.846238e-18 | \n", "1.959954e-18 | \n", "1.349648e-18 | \n", "9.293840e-19 | \n", "6.399851e-19 | \n", "4.407015e-19 | \n", "3.034724e-19 | \n", "2.089747e-19 | \n", "
61 rows × 15 columns
\n", "\n", " | 0 | \n", "1 | \n", "2 | \n", "3 | \n", "4 | \n", "5 | \n", "6 | \n", "7 | \n", "8 | \n", "9 | \n", "10 | \n", "11 | \n", "12 | \n", "13 | \n", "14 | \n", "
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | \n", "0.044418 | \n", "0.003950 | \n", "0.002577 | \n", "0.002067 | \n", "0.001792 | \n", "0.001616 | \n", "0.001493 | \n", "0.001400 | \n", "0.001327 | \n", "0.001268 | \n", "0.001219 | \n", "0.001177 | \n", "0.001142 | \n", "0.001110 | \n", "0.001083 | \n", "
1 | \n", "0.028025 | \n", "0.002492 | \n", "0.001626 | \n", "0.001304 | \n", "0.001131 | \n", "0.001020 | \n", "0.000942 | \n", "0.000883 | \n", "0.000837 | \n", "0.000800 | \n", "0.000769 | \n", "0.000743 | \n", "0.000720 | \n", "0.000701 | \n", "0.000683 | \n", "
2 | \n", "0.022209 | \n", "0.001975 | \n", "0.001288 | \n", "0.001033 | \n", "0.000896 | \n", "0.000808 | \n", "0.000746 | \n", "0.000700 | \n", "0.000663 | \n", "0.000634 | \n", "0.000609 | \n", "0.000589 | \n", "0.000571 | \n", "0.000555 | \n", "0.000541 | \n", "
3 | \n", "0.019130 | \n", "0.001701 | \n", "0.001110 | \n", "0.000890 | \n", "0.000772 | \n", "0.000696 | \n", "0.000643 | \n", "0.000603 | \n", "0.000571 | \n", "0.000546 | \n", "0.000525 | \n", "0.000507 | \n", "0.000492 | \n", "0.000478 | \n", "0.000466 | \n", "
4 | \n", "0.017183 | \n", "0.001528 | \n", "0.000997 | \n", "0.000800 | \n", "0.000693 | \n", "0.000625 | \n", "0.000577 | \n", "0.000541 | \n", "0.000513 | \n", "0.000490 | \n", "0.000472 | \n", "0.000455 | \n", "0.000442 | \n", "0.000430 | \n", "0.000419 | \n", "
5 | \n", "0.015822 | \n", "0.001407 | \n", "0.000918 | \n", "0.000736 | \n", "0.000638 | \n", "0.000576 | \n", "0.000532 | \n", "0.000499 | \n", "0.000473 | \n", "0.000452 | \n", "0.000434 | \n", "0.000419 | \n", "0.000407 | \n", "0.000395 | \n", "0.000386 | \n", "
6 | \n", "0.014806 | \n", "0.001317 | \n", "0.000859 | \n", "0.000689 | \n", "0.000597 | \n", "0.000539 | \n", "0.000498 | \n", "0.000467 | \n", "0.000442 | \n", "0.000423 | \n", "0.000406 | \n", "0.000392 | \n", "0.000381 | \n", "0.000370 | \n", "0.000361 | \n", "
7 | \n", "0.014012 | \n", "0.001246 | \n", "0.000813 | \n", "0.000652 | \n", "0.000565 | \n", "0.000510 | \n", "0.000471 | \n", "0.000442 | \n", "0.000419 | \n", "0.000400 | \n", "0.000385 | \n", "0.000371 | \n", "0.000360 | \n", "0.000350 | \n", "0.000342 | \n", "
8 | \n", "0.013371 | \n", "0.001189 | \n", "0.000776 | \n", "0.000622 | \n", "0.000539 | \n", "0.000487 | \n", "0.000449 | \n", "0.000421 | \n", "0.000399 | \n", "0.000382 | \n", "0.000367 | \n", "0.000354 | \n", "0.000344 | \n", "0.000334 | \n", "0.000326 | \n", "
9 | \n", "0.012840 | \n", "0.001142 | \n", "0.000745 | \n", "0.000597 | \n", "0.000518 | \n", "0.000467 | \n", "0.000431 | \n", "0.000405 | \n", "0.000384 | \n", "0.000367 | \n", "0.000352 | \n", "0.000340 | \n", "0.000330 | \n", "0.000321 | \n", "0.000313 | \n", "
10 | \n", "0.012390 | \n", "0.001102 | \n", "0.000719 | \n", "0.000577 | \n", "0.000500 | \n", "0.000451 | \n", "0.000416 | \n", "0.000390 | \n", "0.000370 | \n", "0.000354 | \n", "0.000340 | \n", "0.000328 | \n", "0.000318 | \n", "0.000310 | \n", "0.000302 | \n", "
11 | \n", "0.012003 | \n", "0.001067 | \n", "0.000696 | \n", "0.000559 | \n", "0.000484 | \n", "0.000437 | \n", "0.000403 | \n", "0.000378 | \n", "0.000359 | \n", "0.000343 | \n", "0.000329 | \n", "0.000318 | \n", "0.000308 | \n", "0.000300 | \n", "0.000293 | \n", "
12 | \n", "0.011666 | \n", "0.001037 | \n", "0.000677 | \n", "0.000543 | \n", "0.000471 | \n", "0.000425 | \n", "0.000392 | \n", "0.000368 | \n", "0.000349 | \n", "0.000333 | \n", "0.000320 | \n", "0.000309 | \n", "0.000300 | \n", "0.000292 | \n", "0.000284 | \n", "
13 | \n", "0.011369 | \n", "0.001011 | \n", "0.000660 | \n", "0.000529 | \n", "0.000459 | \n", "0.000414 | \n", "0.000382 | \n", "0.000358 | \n", "0.000340 | \n", "0.000325 | \n", "0.000312 | \n", "0.000301 | \n", "0.000292 | \n", "0.000284 | \n", "0.000277 | \n", "
14 | \n", "0.011104 | \n", "0.000988 | \n", "0.000644 | \n", "0.000517 | \n", "0.000448 | \n", "0.000404 | \n", "0.000373 | \n", "0.000350 | \n", "0.000332 | \n", "0.000317 | \n", "0.000305 | \n", "0.000294 | \n", "0.000285 | \n", "0.000278 | \n", "0.000271 | \n", "
15 | \n", "0.010867 | \n", "0.000966 | \n", "0.000630 | \n", "0.000506 | \n", "0.000438 | \n", "0.000395 | \n", "0.000365 | \n", "0.000342 | \n", "0.000325 | \n", "0.000310 | \n", "0.000298 | \n", "0.000288 | \n", "0.000279 | \n", "0.000272 | \n", "0.000265 | \n", "
16 | \n", "0.010652 | \n", "0.000947 | \n", "0.000618 | \n", "0.000496 | \n", "0.000430 | \n", "0.000388 | \n", "0.000358 | \n", "0.000336 | \n", "0.000318 | \n", "0.000304 | \n", "0.000292 | \n", "0.000282 | \n", "0.000274 | \n", "0.000266 | \n", "0.000260 | \n", "
17 | \n", "0.010456 | \n", "0.000930 | \n", "0.000607 | \n", "0.000487 | \n", "0.000422 | \n", "0.000380 | \n", "0.000351 | \n", "0.000329 | \n", "0.000312 | \n", "0.000298 | \n", "0.000287 | \n", "0.000277 | \n", "0.000269 | \n", "0.000261 | \n", "0.000255 | \n", "
18 | \n", "0.010277 | \n", "0.000914 | \n", "0.000596 | \n", "0.000478 | \n", "0.000415 | \n", "0.000374 | \n", "0.000345 | \n", "0.000324 | \n", "0.000307 | \n", "0.000293 | \n", "0.000282 | \n", "0.000272 | \n", "0.000264 | \n", "0.000257 | \n", "0.000251 | \n", "
19 | \n", "0.010113 | \n", "0.000899 | \n", "0.000587 | \n", "0.000471 | \n", "0.000408 | \n", "0.000368 | \n", "0.000340 | \n", "0.000319 | \n", "0.000302 | \n", "0.000289 | \n", "0.000278 | \n", "0.000268 | \n", "0.000260 | \n", "0.000253 | \n", "0.000246 | \n", "
20 | \n", "0.009960 | \n", "0.000886 | \n", "0.000578 | \n", "0.000464 | \n", "0.000402 | \n", "0.000362 | \n", "0.000335 | \n", "0.000314 | \n", "0.000298 | \n", "0.000284 | \n", "0.000273 | \n", "0.000264 | \n", "0.000256 | \n", "0.000249 | \n", "0.000243 | \n", "
21 | \n", "0.009819 | \n", "0.000873 | \n", "0.000570 | \n", "0.000457 | \n", "0.000396 | \n", "0.000357 | \n", "0.000330 | \n", "0.000309 | \n", "0.000293 | \n", "0.000280 | \n", "0.000269 | \n", "0.000260 | \n", "0.000252 | \n", "0.000245 | \n", "0.000239 | \n", "
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61 rows × 15 columns
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61 rows × 1 columns
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61 rows × 1 columns
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2 | \n", "0.033819 | \n", "
3 | \n", "0.029130 | \n", "
4 | \n", "0.026166 | \n", "
5 | \n", "0.024093 | \n", "
6 | \n", "0.022546 | \n", "
7 | \n", "0.021337 | \n", "
8 | \n", "0.020361 | \n", "
9 | \n", "0.019552 | \n", "
10 | \n", "0.018867 | \n", "
11 | \n", "0.018278 | \n", "
12 | \n", "0.017765 | \n", "
13 | \n", "0.017312 | \n", "
14 | \n", "0.016909 | \n", "
15 | \n", "0.016548 | \n", "
16 | \n", "0.016220 | \n", "
17 | \n", "0.015923 | \n", "
18 | \n", "0.015650 | \n", "
19 | \n", "0.015399 | \n", "
20 | \n", "0.015167 | \n", "
21 | \n", "0.014952 | \n", "
22 | \n", "0.014752 | \n", "
23 | \n", "0.014565 | \n", "
24 | \n", "0.014390 | \n", "
25 | \n", "0.014225 | \n", "
26 | \n", "0.014070 | \n", "
27 | \n", "0.013923 | \n", "
28 | \n", "0.013784 | \n", "
29 | \n", "0.013653 | \n", "
... | \n", "... | \n", "
31 | \n", "0.013408 | \n", "
32 | \n", "0.013295 | \n", "
33 | \n", "0.013187 | \n", "
34 | \n", "0.013083 | \n", "
35 | \n", "0.012984 | \n", "
36 | \n", "0.012888 | \n", "
37 | \n", "0.012797 | \n", "
38 | \n", "0.012709 | \n", "
39 | \n", "0.012625 | \n", "
40 | \n", "0.012543 | \n", "
41 | \n", "0.012465 | \n", "
42 | \n", "0.012389 | \n", "
43 | \n", "0.012316 | \n", "
44 | \n", "0.012245 | \n", "
45 | \n", "0.012177 | \n", "
46 | \n", "0.012111 | \n", "
47 | \n", "0.012047 | \n", "
48 | \n", "0.011984 | \n", "
49 | \n", "0.011924 | \n", "
50 | \n", "0.011865 | \n", "
51 | \n", "0.011808 | \n", "
52 | \n", "0.011753 | \n", "
53 | \n", "0.011699 | \n", "
54 | \n", "0.011647 | \n", "
55 | \n", "0.011596 | \n", "
56 | \n", "0.011546 | \n", "
57 | \n", "0.011498 | \n", "
58 | \n", "0.011451 | \n", "
59 | \n", "0.011405 | \n", "
60 | \n", "0.011360 | \n", "
61 rows × 1 columns
\n", "\n", " | 0 | \n", "
---|---|
0 | \n", "0.067638 | \n", "
1 | \n", "0.042675 | \n", "
2 | \n", "0.033819 | \n", "
3 | \n", "0.029130 | \n", "
4 | \n", "0.026166 | \n", "
5 | \n", "0.024093 | \n", "
6 | \n", "0.022546 | \n", "
7 | \n", "0.021337 | \n", "
8 | \n", "0.020361 | \n", "
9 | \n", "0.019552 | \n", "
10 | \n", "0.018867 | \n", "
11 | \n", "0.018278 | \n", "
12 | \n", "0.017765 | \n", "
13 | \n", "0.017312 | \n", "
14 | \n", "0.016909 | \n", "
15 | \n", "0.016548 | \n", "
16 | \n", "0.016220 | \n", "
17 | \n", "0.015923 | \n", "
18 | \n", "0.015650 | \n", "
19 | \n", "0.015399 | \n", "
20 | \n", "0.015167 | \n", "
21 | \n", "0.014952 | \n", "
22 | \n", "0.014752 | \n", "
23 | \n", "0.014565 | \n", "
24 | \n", "0.014390 | \n", "
25 | \n", "0.014225 | \n", "
26 | \n", "0.014070 | \n", "
27 | \n", "0.013923 | \n", "
28 | \n", "0.013784 | \n", "
29 | \n", "0.013653 | \n", "
... | \n", "... | \n", "
31 | \n", "0.013408 | \n", "
32 | \n", "0.013295 | \n", "
33 | \n", "0.013187 | \n", "
34 | \n", "0.013083 | \n", "
35 | \n", "0.012984 | \n", "
36 | \n", "0.012888 | \n", "
37 | \n", "0.012797 | \n", "
38 | \n", "0.012709 | \n", "
39 | \n", "0.012625 | \n", "
40 | \n", "0.012543 | \n", "
41 | \n", "0.012465 | \n", "
42 | \n", "0.012389 | \n", "
43 | \n", "0.012316 | \n", "
44 | \n", "0.012245 | \n", "
45 | \n", "0.012177 | \n", "
46 | \n", "0.012111 | \n", "
47 | \n", "0.012047 | \n", "
48 | \n", "0.011984 | \n", "
49 | \n", "0.011924 | \n", "
50 | \n", "0.011865 | \n", "
51 | \n", "0.011808 | \n", "
52 | \n", "0.011753 | \n", "
53 | \n", "0.011699 | \n", "
54 | \n", "0.011647 | \n", "
55 | \n", "0.011596 | \n", "
56 | \n", "0.011546 | \n", "
57 | \n", "0.011498 | \n", "
58 | \n", "0.011451 | \n", "
59 | \n", "0.011405 | \n", "
60 | \n", "0.011360 | \n", "
61 rows × 1 columns
\n", "