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# Bigram Python

This will change in a future version of Python. Tags: bigram, bigram in python, bigram trigram in python, ngram, ngrams, ngrams python, trigram in python, trigrams Comments Leave a Comment Categories python , Tech. input_fp ‑‑ file pointer with input text frequencies ‑‑ mapping from each bigram to its counted. Quite the opposite. BigramCollocationFinder. User-defined table-generating functions (Advanced) A user-defined table generating function ( UDTF ) has the ability to output any number of fields and any number of rows for each row of input. Need Python code : select five words from a. This model has a sim-ilar predictive distribution to models based on equa-tion (1), with one key di erence: the bigram statistics f ijj in MacKay and Peto’s model are not smoothed with marginal statistics f i, but are smoothed with a. SmartDeploy’s unique layered approach enables single image management of Windows OS and applications. Define a function train_bigram_tagger(train_sents) that calls train_nltk_taggers and returns only the bigram tagger. The bigram TH is by far the most common bigram, accounting for 3. We can actually perform simple analysis of text without NLTK. I need an advice about gensim phrases extraction. Zobacz pełny profil użytkownika Dominika Ratajczak i odkryj jego(jej) kontakty oraz pozycje w podobnych firmach. Adrianogba / bigram-trigram-python Star 0 Code Issues Pull requests This is an simple artificial intelligence program to predict the next word based on a informed. The likelihood ratio code was adapted from. Although the term is often associated with sentiment classification of documents, broadly speaking it refers to the use of text analytics approaches applied to the set of problems related to identifying and extracting subjective material in text sources. The next () function returns the next item in an iterator. There’s even a huge example plot gallery right on the matplotlib web site, so I’m not going to bother covering the basics here. A bigram is an n-gram for n=2. Using the Code. In this guide, I will explain how to cluster a set of documents using Python. Below is the full code of sentiment analysis on movie review polarity data-set using tf-idf features. 359–394, 1999. symspellpy symspellpy is a Python port of SymSpell v6. The following are code examples for showing how to use nltk. Preface This book provides an overview of the important issues in information retrieval, and how those issues aﬀect the design and implementation of search engines. zip (*iterators) Python iterables or containers ( list, string etc ) Returns a single iterator object, having mapped values from all the. Python has a bigram function as part of NLTK library which helps us generate these pairs. word (if linear. Since words are by definition expressed by sound, factoring. Here are the examples of the python api nltk. A bigram or digram is a sequence of two adjacent elements from a string of tokens, which are typically letters, syllables, or words. python - NLTK-Counting Frequency of Bigram. LionKimbro, IanBicking, lwickjr. If you are aspiring to start your career in the NLP programming language, then you must know the Frequently Asked Questions in any NLP Interview to help you out, we have gathered a list. """ with zipfile. Emoticon Scores Search for Emoticons in the given text using RegEx or find. (The history is whatever words in the past we are conditioning on. Search Engines Information Retrieval in Practice ©W. Each of these layers has a number of units defined by the parameter num_units. While not particularly fast to process, Python's dict has the advantages of being convenient to use, being sparse (absent features need not be stored) and storing feature. A bigram is formed by creating a pair of words from every two consecutive words from a given sentence. TextBlob is a Python (2 and 3) library for processing textual data. The question was as follows: Suppose I want to generate bigrams for the word single  Then the output should be a list ['si','in','ng','gl','le']. def get_list_phrases (text): tweet_phrases = [] for tweet in text: tweet_words = tweet. Spam Classifier in Python from scratch. In LDA models, each document is composed of multiple topics. Let's change that. Example import nltk word_data = "The best performance can bring in sky high success. split()) return lst I processed the following code through jythonc compiler to form a JAR file. bigrams) and networks of words using Python. This is the second part of a series of articles about data mining on Twitter. You can vote up the examples you like or vote down the ones you don't like. Second Attempt At Querying The Data: PyTables To The Rescue. These are the top rated real world C# (CSharp) examples of Bigram extracted from open source projects. This is described in Topic Modeling: Beyond Bag-of-Words by Hanna Wallach et al. 29th Use Perl or Java reg-ex package xHW focus is on writing the "grammar" or FSA for dates and times Add 1 to every bigram c(w. We collected more than 300,000 marijuana related tweets during November 2016 in our study. running redis as daemon on osx; ERROR 1071 (42000): Specified key was too long; max key length is 767 bytes;. The text files containing the counts can be used with ngram_score. Sentences as probability models. Please practice hand-washing and social distancing, and check out our resources for adapting to these times. Phrases(texts) example this gives lda output of - Indi. For example, if a random bigram 'abc xyz' appears, and neither 'abc' nor 'xyz' appeared anywhere else in the text, 'abc xyz' will be identified as highly significant bigram when it. a guest raw download clone embed report print Python 3. Use MathJax to format equations. The authors of that paper used text mining to examine a corpus. A model is built by observing some samples generated by the phenomenon to be modelled. { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Linguist 278: Programming for Linguists ", "Stanford Linguistics, Fall 2019. mymod as mymod1 mymod1. txt using a smoothed unigram model and a smoothed bigram model. 나는 문서 - 용어 행렬을 구할 수 있지만, 단어 - 단어 행렬의 동시 발생 (co-occurenc. I need to write a regex that will read another text string. Drawing a simple Pie Chart using Python Matplotlib. We all face the problem of spams in our inboxes. One of the major forms of pre-processing is to filter out useless data. Quantum Computer Programming. pdf), Text File (. RegEx can be used to check if the string contains the specified search pattern. Let's take advantage of python's zip builtin to build our bigrams. Hi bhargav Its was informative notebook about topic modeling and spacy. In this article, I will be using the accuracy result data obtained from that evaluation. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. This is by far the most simplistic way of modelling the human language. A command-line program to encrypt/decrypt a message using a random reciprocal bigram table and write a bigram table to a text file. Chris Fotache. Use the NLTK Bigram Collocation finder to determine the frequency of each bigram (explained below) Stuff a Python dictionary with the bigram and bigram measure raw frequency score; Render a word cloud of bigrams; Note: I added an underscore to link bigrams together to make the word cloud easier to read. 673502 27 description machine learning 0. Making statements based on opinion; back them up with references or personal experience. I then wrote the following program in java to access this python class: import org. I want to find frequency of bigrams which occur more than 10 times together and have the highest PMI. An iterable object. They are from open source Python projects. Spark examples: batch logistic regression foreground bigram model and background unigram model. I need to write a regex that will read another text string. In this article, we'll understand the simplest model that assigns probabilities to sentences and sequences of words, the n-gram. GitHub Gist: instantly share code, notes, and snippets. (bigram_tf_idf <-series %>% count (book, bigram, sort = TRUE) %>% bind_tf_idf (bigram, book, n) %>% arrange (desc (tf_idf))) ## Source: local data frame [523,420 x 6] ## Groups: book [7] ## ## book bigram n tf idf ## ## 1 Goblet of Fire mr crouch 152 0. As you type in this text box, the graph below will update automatically, (assuming you have javascript enabled in your browser). 16 NLP Programming Tutorial 2 - Bigram Language Model Exercise Write two programs train-bigram: Creates a bigram model test-bigram: Reads a bigram model and calculates entropy on the test set Test train-bigram on test/02-train-input. Deques are a generalization of stacks and queues (the name is pronounced "deck" and is short for "double-ended queue"). """Print most frequent N-grams in given file. In this post I am going to talk about N-grams, a concept found in Natural Language Processing ( aka NLP). étudier les types de données et leurs utilisations courantes, à l’aide d’algorithmes adaptés et optimisés. mypack2 import mymod as mymod2 mymod2. It supports non-English languages, especially south east Asian languages. Based on the add-1 smoothing equation, the probability function can be like this:. Document/Text classification is one of the important and typical task in supervised machine learning (ML). The likelihood ratio code was adapted from. java] The First Step In Building An N-gram Model Is To Create A Dictionary That Maps Words To Java Map Or Python Dictionary (which. And if we don't have enough information to calculate the bigram, we can use the unigram probability P(w n). Dominika Ratajczak ma 7 pozycji w swoim profilu. next ( iterable, default ) Parameter Values. You can rate examples to help us improve the quality of examples. 16 NLP Programming Tutorial 2 - Bigram Language Model Exercise Write two programs train-bigram: Creates a bigram model test-bigram: Reads a bigram model and calculates entropy on the test set Test train-bigram on test/02-train-input. ! Perplexity = 1/0 = ∞. #If not, then we change the format. The data was pre-processed and Naïve Bayes classifier on unigram and bigram word model gave accuracy of 74%. It can be used to measure how similar two strings are in terms of the number of common bigrams (a bigram is a pair of adjacent letters in the string). The texts consist of sentences and also sentences consist of words. This is the second part of a series that explores letter correlation and simple language statistics for AI. The Markov Property states that the probability of future states depends only on the present state, not on the sequence of events that preceded it. php on line 38 Notice: Undefined index: HTTP_REFERER in /var/www/html/destek. Separate out unrelated code from the problematic code into a small runnable example that illustrates your problem For a full detail see the Help Docs. étudier les types de données et leurs utilisations courantes, à l’aide d’algorithmes adaptés et optimisés. Bigram frequency python. There are 481318 word in the pdf file. This article shows how you can perform sentiment analysis on movie reviews using Python and Natural Language Toolkit (NLTK). San Francisco (is a 2-gram). I want to find frequency of bigrams which occur more than 10 times together and have the highest PMI. py and used for breaking ciphers, see this page for details. bigrams function. This is a Python and NLTK newbie question. next ( iterable, default ) Parameter Values. """ return BigramCollocationFinder (self. x package that encapsulates a large trigram library for Icelandic. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. split()) return lst I processed the following code through jythonc compiler to form a JAR file. Below is the full code of sentiment analysis on movie review polarity data-set using tf-idf features. In order to look for ngram relationships at multiple scales, you will use the ngram_range parameter as Peter discussed in the video. I tried using nltk. White and black scrabble tiles on black surface by Pixabay Bag of Words (BOW) is a method to extract features from text documents. an n-gram of size 1 is referred to as a "unigram"; size 2 is a "bi. I'm trying to easily implement this idea using the current LDA packages (for example python lda. Abstractive techniques revisited Pranay, Aman and Aayush 2017-04-05 gensim , Student Incubator , summarization It describes how we, a team of three students in the RaRe Incubator programme , have experimented with existing algorithms and Python tools in this domain. 단어 - 단어 동시 발생 매트릭스 나는 당신이 낱말 낱말 co-ocurrence 모체를 파생하게하는 sklearn에있는 단위를 찾고있다. So it appears that the bigram hypothesis is correct, and including significant bigrams can increase classifier effectiveness. 000000 79 oral written communication 0. python natural-language-processing smoothing bigrams unigram Updated Feb 17, 2020. English Letter Frequency Counts: Mayzner Revisited or ETAOIN SRHLDCU Introduction On December 17th 2012, I got a nice letter from Mark Mayzner, a retired 85-year-old researcher who studied the frequency of letter combinations in English words in the early 1960s. For above file, the bigram set and their count will be : (the, quick) = 2 (quick, person) = 2 (person, did) = 1 (did, not) = 1 (not, realize) = 1 (realize, his) = 1 (his, speed) = 1 (speed, and) = 1 (and, the) = 1 (person, bumped) = 1. pmi, 5) finder3 = TrigramCollocationFinder. word is a sequence for which close matches are desired (typically a string), and possibilities is a list of sequences against which to match word (typically a list of strings). I'm trying to implement Latent Dirichlet Allocation (LDA) on a bigram language model. Based on the given python code, I am assuming that bigrams[N] and unigrams[N] will give the frequency (counts) of combination of words and a single word respectively. Some researchers created this condition by testing baboons with no obvious experience with spelling and speech stimuli. 5 NLTK is a leading platform for building Python programs to work with human language data. py $あ あい いう うえ えお お$ 他にもたくさん機能があるので、上記リンク先のチュートリアルなどを読むべし 検索もできるようだ. ConditionalFreqDist() method. Generate Unigrams Bigrams Trigrams Ngrams Etc In Python - Arshad Mehmood. Question D-2: Draw from bigram distribution (15 points) Please implement draw_next_word_bigram_model. Then we used static_rnn method to construct the network and generate the predictions. Learn Python programming with this Python tutorial for beginners!. I have doubt how to do trigram and trigram topic modeling texts = metadata['cleandata'] bigram = gensim. py] Now, you’ll create an MLE bigram model, in much the same way as you created an MLE unigram model. " These are phrases of one or more words that contain a noun, maybe some descriptive words, maybe a verb, and maybe something like an adverb. How To Train Dataset Using Svm. The Natural Language Toolkit, or NLTK for short, is a Python library written for working and modeling text. One of the major forms of pre-processing is to filter out useless data. They are from open source Python projects. This module allows both LDA model estimation from a training corpus and inference of topic distribution on new, unseen documents. sub − This is the substring to be searched. Source code is tracked on GitHub. ((The(raw_freq(measure(returns(frequency(as(the(ratio. PdfReadWarning: Xref table not zero-indexed. You can vote up the examples you like or vote down the ones you don't like. { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Linguist 278: Programming for Linguists ", "Stanford Linguistics, Fall 2019. bigram_fd). Leave a Comment. join(str(i. Upon receiving the input parameters, the generate_ngrams function declares a list to keep track of the generated n-grams. With 4-gram, the test result received 0. Although the term is often associated with sentiment classification of documents, broadly speaking it refers to the use of text analytics approaches applied to the set of problems related to identifying and extracting subjective material in text sources. Said another way, the probability of the bigram heavy rain is larger than the probability of the bigram large rain. If we are dealing with text documents and want to perform machine learning on text, we can't directly work with raw text. Collocations are expressions of multiple words which commonly co-occur. Advanced Text processing is a must task for every NLP programmer. Python: NLTK bigram and trigram filter example. People read texts. Getting started All les that are necessary to do the ass…. Do you mean that my general idea of computing each feature value in terms of bigram (N-gram) is correct? In other words, there is no big difference in computing the feature values between bag-of-words and N-gram model. Related courses. search(), re. Use N-gram for prediction of the next word, POS tagging to do sentiment analysis or labeling the entity and TF-IDF to find the uniqueness of the document. There’s even a huge example plot gallery right on the matplotlib web site, so I’m not going to bother covering the basics here. The first line of text is from the nltk website. I am trying to build a bigram model and to calculate the probability of word occurrence. Bigram frequency python Without going into too much detail (you can find many tutorials about tf-idf on the web), documents that have similar content will have similar tf-idf vectors. py, except that the words proposed should be the homophones deemed most probable by the bigram model with plus-one smoothing (section 3 above). lda implements latent Dirichlet allocation (LDA) using collapsed Gibbs sampling. # bigram-spam-classifier # A bigram approach for classifying Spam and Ham messages # install with pip pip install bigram-spam-classifier # import in your python file from bigram_spam_classifier import spamclassifier # create an object of the classifier and pass your message as the parameter. Mastering Natural Language Processing with Python by Deepti Chopra, Nisheeth Joshi, Iti Mathur Get Mastering Natural Language Processing with Python now with O'Reilly online learning. The challenge, however, is how to extract good quality of topics that are clear, segregated and meaningful. python - perplexity - write a program to compute unsmoothed unigrams and bigrams Ngram model and perplexity in NLTK (1) To put my question in context, I would like to train and test/compare several (neural) language models. I’ve personally found ratio and token_set_ratio to be the most useful. Example Analysis: Be + words Forget my previous posts on using the Stanford NLP engine via command and retreiving information from XML files in R…. count(sub, start= 0,end=len(string)) Parameters. This points to the idea that including only. " These are phrases of one or more words that contain a noun, maybe some descriptive words, maybe a verb, and maybe something like an adverb. Then we used static_rnn method to construct the network and generate the predictions. Please purchase one to access all content. This process is called creating bigrams. Graphs are used by tf. Text Mining with R by Julia Silge, David Robinson Get Text Mining with R now with O’Reilly online learning. This module does just that. For this we represent text as word graph. The(result(fromthe(score_ngrams(function(is(a(list(consisting(of(pairs,(where(each(pair(is(a(bigramand(its(score. Executing the program without any command-line arguments starts bigram in message encryption/decryption mode. TextBlob - Easy to use nl p tools API, built on top of NLTK and Pattern. b) Write a function to compute bigram unsmoothed and smoothed models. There are 53212 keyword in the pdf file. It has easy-to-use functions to assist with splitting data into training and testing sets, as well as training a model, making predictions, and evaluating the model. You can rate examples to help us improve the quality of examples. First, split the file into. , "Keywords in Context (Using n-grams) with. Create your free Platform account to download ActivePython or customize Python with the packages you require and Recent Python Packages matching "bigram" Sort by:. Based on code from the chapter "Natural Language Corpus Data" by Peter Norvig from the book "Beautiful Data" (Segaran and Hammerbacher, 2009). There are already tons of tutorials on how to make basic plots in matplotlib. " These are phrases of one or more words that contain a noun, maybe some descriptive words, maybe a verb, and maybe something like an adverb. - Java implementation coming soon. f = open('a_text_file') raw = f. More precisely, we can use n-gram models to derive a probability of the sentence ,W, as the joint probability of each individual word in the sentence, wi. Making statements based on opinion; back them up with references or personal experience. Let's start building some models. That is, you create the word cloud with Python. You can add a default return value, to return if the iterable has reached to its end. What perplexity does the bigram model give to this sentence? P(sentence) = 0. 2 Accuracies of Various Approaches (Accuracies are calculated using 5-fold cross-validation) Unigram Bigram Unigram + Bigram Recurrent Neural Networks 69. After I get the corpus with bigram phrases detected, I went through the same process of Doc2Vec I did with unigram. The top bigrams are shown in the scatter plot to the left. Context is very important to understand the meaning of words. LionKimbro, IanBicking, lwickjr. The interface follows conventions found in scikit-learn. I tried using nltk. Getting Python. The below Python code describes the process:. Learn Python programming with this Python tutorial for beginners!. We created two LSTM layers using BasicLSTMCell method. Since B has already happened, the sam. Python Desktop Apps with Tkinter. Building an MLE bigram model [Coding only: use starter code problem3. By voting up you can indicate which examples are most useful and appropriate. Mapping of (bigram, count) pairs. Turns out that is the simplest bit, an N-gram is simply a sequence of N words. The Natural Language Toolkit has data types and functions that make life easier for us when we want to count bigrams and compute their probabilities. Click to enlarge the graph. Stay safe and healthy. The essential concepts in text mining is n-grams, which are a set of co-occurring or continuous sequence of n items from a sequence of large text or sentence. ZipFile(filename) as f: data = tf. 大学の課題で出たので，簡易に実装してみた． N-gramとは 自然言語処理の素性として良く使われる数量． 1-gram(uni-gram)だと，単語の頻度．2-gram(bi-gram)だと連続する二つの単語の出現頻度，3-gram(tri-gram)だと連続する三つの単語の出現頻度である． Web文書を対象として，解析してみる． クローラー. # Python code to demonstrate the working of. It also normalizes the text, lowercasing, replacing. def calculate_bigram (sentence_lst): """ - bigram을 만들고, 단어가 나왔을 때, 그 다음에 어떤 단어가 나올 condition prob을 만든다 - Counter말고 dictionary로 만들어도 되는데, most_common이 있기 때문에 Counter을 사용함 - 만약 tri-gram을 만들 경우에는 nested Counter가 3개가 나오게 된다. Use MathJax to format equations. LionKimbro, IanBicking, lwickjr. ConditionalFreqDist() method. Syntax str. (I am working on fuzzy plagiarism detection. Abstractive techniques revisited Pranay, Aman and Aayush 2017-04-05 gensim , Student Incubator , summarization It describes how we, a team of three students in the RaRe Incubator programme , have experimented with existing algorithms and Python tools in this domain. A common method of reducing the complexity of n-gram modeling is using the Markov Property. Although nltk is used, it is just for the construction of ngrams. – Make use only of the raw frequency of an n-gram ! But there is an additional source of knowledge we can draw on --- the n-gram “hierarchy” – If there are no examples of a particular trigram,w n-2w n-1w n, to compute P(w n|w n-2w n-1), we can estimate its probability by using the bigram probability P(w n|w n-1 ). The Python code for everything in the chapter. Based on the given python code, I am assuming that bigrams[N] and unigrams[N] will give the frequency (counts) of combination of words and a single word respectively. Technology used :Python , Beautiful Soup, Sqlite. Here are the examples of the python api nltk. A Python program called lab4c. pdf), Text File (. Natural Language Processing in Python: Part 3. The standard split() can use only one delimiter. py filename: Problem description: Build a tool which receives a corpus of text, analyses it and reports the top 10 most frequent bigrams, trigrams,. RegEx can be used to check if the string contains the specified search pattern. Python import mypack1. I am trying to use BigramAssocMeasures PMI to find the most import bigrams however it's giving all Bigrams the same score, so I end up with a list in alphabetical order when I use. That is, you create the word cloud with Python. Loading features from dicts¶. in their 2002 paper “BLEU: a Method for Automatic Evaluation of Machine Translation“. an n-gram of size 1 is referred to as a "unigram"; size 2 is a "bi. 3 Windows X86-64 Installer. Typically, bigrams encode the probability of particular word pairs. 1, font=(None, 14), variable=var, value=myvalue). Hello, world! 1から50までの和を計算して表示; 2つの自然数の最大公約数を求める（ユークリッドの互除法）. On a related note, I noticed about half the queries people entered into the LSA. Loading features from dicts¶. Simple bigram letter model. In this article, we'll understand the simplest model that assigns probabilities to sentences and sequences of words, the n-gram. You will find this dataset in my tutorial repo. That doesn’t mean it’s useless and unpopular. Bigram Language Model and Cross-entropy in Python Hello everybody, I want to replicate the language analysis of No Country for Old Members: User lifecycle and linguistic change in online communities and use it on reddit data. You can rate examples to help us improve the quality of examples. The below code extracts this dominant topic for each sentence and shows the weight of the topic and the keywords in a nicely formatted output. There are 481318 word in the pdf file. San Francisco (is a 2-gram). bigram and unigram counts of the words in the sentences. English Letter Frequency Counts: Mayzner Revisited or ETAOIN SRHLDCU by Peter Norvig is an analysis of English letter frequencies using the Google Corpus Data. py:1736] This pdf file contains totally 347 pages. document – a list of words/tokens. NLTK Documentation, Release 3. Unigrams in the resultant phrases are considered as the top level category. The(result(fromthe(score_ngrams(function(is(a(list(consisting(of(pairs,(where(each(pair(is(a(bigramand(its(score. Python: histogram/ binning data from 2 arrays. Getting Started/Processing Text. Chen and J. ngram - A set class that supports lookup by N-gram string similarity¶ class ngram. The frequencies from this page are generated from around 4. Kite is a free autocomplete for Python developers. :param line: line as str :return: preprocessed sentence """ # detect sentences sentences = sentence_detector. python,histogram,large-files. You can vote up the examples you like or vote down the ones you don't like. Making statements based on opinion; back them up with references or personal experience. Common corpus analyses such as the calculation of word and n-gram frequency and range, keyness, and collocation are included. By Marco Bonzanini, Independent Data Science Consultant. We won’t get too much into the details of the algorithms that we are going to look at since they are complex and beyond the scope of this tutorial. Subclass in Python By the name of the topic, it is clear in itself that we are going to deal with subclasses of any class. I now have an object that is a DataFrame. x package that encapsulates a large trigram library for Icelandic. #N#Review of Introduction to Programming. Python wordsegment uses two text files to store unigram and bigram count data. python-docx does not automatically set any of the document core properties other than to add a core properties part to a presentation that doesn’t have one (very uncommon). 大学の課題で出たので，簡易に実装してみた． N-gramとは 自然言語処理の素性として良く使われる数量． 1-gram(uni-gram)だと，単語の頻度．2-gram(bi-gram)だと連続する二つの単語の出現頻度，3-gram(tri-gram)だと連続する三つの単語の出現頻度である． Web文書を対象として，解析してみる． クローラー. If you want to compute the letter frequencies of your own piece of text you can use this page. A common method of reducing the complexity of n-gram modeling is using the Markov Property. The)mainprogram)should)perform)the)following)sequence)of)steps:) i. A question popped up on Stack Overflow today asking using the NLTK library to tokenise text into bigrams. the look of it, but I feel this is already a nice start if you want to play around. { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Linguist 278: Programming for Linguists ", "Stanford Linguistics, Fall 2019. For the canonical definition of interpolated Kneser-Ney smoothing, see S. In other words, you approximate it with the probability: P(the | that). How to generate n-grams with Python and NLTK. BigramCollocationFinder. Interpolation is that you calculate the trigram probability as a weighted sum of the actual trigram, bigram and unigram probabilities. Here are the examples of the python api nltk. Calculating Centrality Score of Words of the Given Text This simple program demonstrate the way to calculate the "Closeness Centrality" score of words of the given text. Define a function train_bigram_tagger(train_sents) that calls train_nltk_taggers and returns only the bigram tagger. The other disadvantage of this approach is that it would have entailed querying each of the many bigram files individually, and what I really wanted was a single database to query. Sentiment Analysis means analyzing the sentiment of a given text or document and categorizing the text/document into a specific class or category (like positive and negative). Even though the Hadoop framework is written in Java, programs for Hadoop need not to be coded in Java but can also be developed in other languages like Python or C++ (the latter since version 0. def bigram_finder (self): """Constructs a bigram collocation finder with the bigram and unigram data from this finder. This week we will revisit mrjob and S3 with a few more hands-on tasks. Print out the probabilities of sentences in Toy dataset using the smoothed unigram and bigram models. 단어 - 단어 동시 발생 매트릭스 나는 당신이 낱말 낱말 co-ocurrence 모체를 파생하게하는 sklearn에있는 단위를 찾고있다. 0 MB: ngrams-test. Hi bhargav Its was informative notebook about topic modeling and spacy. But we can also use the function to tokenize into consecutive sequences of words, called n-grams. function s to represent the function's computations. Natural Language Processing with PythonNLTK is one of the leading platforms for working with human language data and Python, the module NLTK is used for natural language processing. For historians you are most likely to use characters as in the bigram "qu" or words as in the trigram "the dog barked"; however, you could also use phonemes, syllables, or any number of other units depending on your research question. Stanza is a new Python NLP library which includes a multilingual neural NLP pipeline and an interface for working with Stanford CoreNLP in Python. 2 Accuracies of Various Approaches (Accuracies are calculated using 5-fold cross-validation) Unigram Bigram Unigram + Bigram Recurrent Neural Networks 69. share Browse other questions tagged python scikit-learn natural-language or ask your own question. I tried using nltk. BLEU (bilingual evaluation understudy) is an algorithm for evaluating the quality of text which has been machine-translated from one natural language to another. I recommend writing the code again from scratch, however (except for the code initializing the mapping dictionary), so that you can test things as you go. python; 4943; NLP_GDGCairo2013; cairotraffic. Indexing Lists 4. O'Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers. Tool to analyze bigrams in a message. In this article, I will be using the accuracy result data obtained from that evaluation. split tweet_phrases. sub − This is the substring to be searched. Now that we know the parts of speech, we can do what is called chunking, and group words into hopefully meaningful chunks. I am trying to build a bigram model and to calculate the probability of word occurrence. ; A number which indicates the number of words in a text sequence. Shivam Bansal, August 24, 2016. Level up your coding skills and quickly land a job. python - perplexity - write a program to compute unsmoothed unigrams and bigrams Ngram model and perplexity in NLTK (1) To put my question in context, I would like to train and test/compare several (neural) language models. One common way to analyze Twitter data is to identify the co-occurrence and networks of words in Tweets. Return a default value when the iterable has. It will find all the e-mail addresses from the list. Zip takes a list of iterables and constructs a new list of tuples where the first list. Sentences as probability models. You can vote up the examples you like or vote down the ones you don't like. Proceedings of Human Language Technologies: The 2009 Annual Conference of the North American Chapter of the Association for Computational Linguistics, Companion Volume: Short Papers. It can be used to measure how similar two strings are in terms of the number of common bigrams (a bigram is a pair of adjacent letters in the string). mymod import myfunc as myfunc1 myfunc1() from には、. It provides good tools for loading and cleaning text that we can use to get our data ready for working with machine learning and deep learning algorithms. In the same way, a language model is built by observing some text. You can rate examples to help us improve the quality of examples. In this post, we’ll see how easy it is to identify people using their writing style through machine learning. A complementary Domino project is available. ") Part-of-speech Tagging ¶ Part-of-speech tags can be accessed through the tags property. All 3 files use the Viterbi Algorithm with Bigram HMM taggers for predicting Parts of Speech(POS) tags. The final function part4() should call the functions from parts 4a-4e below, with the argument given in the examples. This article shows how you can perform sentiment analysis on movie reviews using Python and Natural Language Toolkit (NLTK). Joe James 2,164 views. The Bag of Words representation¶. csv', 'r') as f: lines = f. This time, I’m going to focus on how you can make beautiful data visualizations in Python with matplotlib. from_documents(). An automatic score calculation algorithm is proposed for n-grams. 采用bigram语言模型实现的拼音串智能转换汉字串更多下载资源、学习资料请访问CSDN下载频道. 7, Tensor Flow 0. Make sure both test cases below run with correct results. See this bug report for more information. More precisely, we can use n-gram models to derive a probability of the sentence ,W, as the joint probability of each individual word in the sentence, wi. The first video included an explanation of n-grams and set a challenge for the viewer to write. collocations. I will try to show you power of python in Machine Learning world. gz is assumed to be a text file. The project is based on neural networks which is used to map the sequences to sequences. 6, both bigram and skip-gram can extract keywords from the comments, like the “emergency room”, “urgent care” and “customer service”. Install cleanNLP and language model 2. Here is the code for retrain bigram t stat similar holds for trigrams. from_documents(). Joe James 2,164 views. D op LinkedIn, de grootste professionele community ter wereld. This article illustrates how to write a Python module that allows for efﬁ-ciently querying such language models directly in Python code. 3 Windows Installer; Python 2. An n-gram is a sequence of N n-gram words: a 2-gram (or bigram) is a two-word sequence of words like “please turn”, “turn your”, or ”your homework”, and a 3-gram (or trigram) is a three-word se- quence of words like “please turn your”, or “turn your homework”. Il s'agit d'une série de TDs d'algorithmique et structure de données I. mypack2 import mymod as mymod2 mymod2. If you’d like to browse the 3M word list in Google’s pre-trained model, you can just look at the text files in the vocabulary folder of that project. Creating The Word Dictionary [Coding Only: Save Code As Problem1. tokenize(line) # process each sentence for sentence in sentences: # replace umlauts if args. I'm trying to create bigrams using nltk which don't cross sentence boundaries. Question D-2: Draw from bigram distribution (15 points) Please implement draw_next_word_bigram_model. Phraser (phrases_model) ¶. I eventually would like to try this out in python as a means of learning that language. There are 481318 word in the pdf file. python - perplexity - write a program to compute unsmoothed unigrams and bigrams Ngram model and perplexity in NLTK (1) To put my question in context, I would like to train and test/compare several (neural) language models. The(result(fromthe(score_ngrams(function(is(a(list(consisting(of(pairs,(where(each(pair(is(a(bigramand(its(score. Print out the perplexity under. Define a function train_bigram_tagger(train_sents) that calls train_nltk_taggers and returns only the bigram tagger. txt: The 1/3 million most frequent words, all lowercase, with counts. # Python code to demonstrate the working of. Hello, world! 1から50までの和を計算して表示; 2つの自然数の最大公約数を求める（ユークリッドの互除法）. We can actually perform simple analysis of text without NLTK. Elements are returned in arbitrary order. Quite the opposite. The purpose of zip () is to map the similar index of multiple containers so that they can be used just using as single entity. Use MathJax to format equations. 아래 예제 목록에서 일치하는 bigrams [ 'two', 'three'] 을 반환하는 방법. They selected 500 words with the highest bigram frequency from a database of four-letter words. The next () function returns the next item in an iterator. [login to view URL] In that link, download the dataset and use the "2020-03-12 Coronavirus [login to view URL]" file for processing our project. The Natural Language Toolkit has data types and functions that make life easier for us when we want to count bigrams and compute their probabilities. Pie charts can be drawn using the function pie() in the pyplot module. Bigram frequency python Without going into too much detail (you can find many tutorials about tf-idf on the web), documents that have similar content will have similar tf-idf vectors. Learn the basics and concepts of working with quantum computers and qubits through practical. Using Python 3. It is beneficial for extracting information from text such. Building an MLE bigram model [Coding only: use starter code problem3. In this tutorial I will describe how to write a simple MapReduce program for Hadoop in the Python programming language. Related courses. collocations. The core estimation code is based on the onlineldavb. When we are dealing with text classification, sometimes we need to do certain kind of natural language processing and hence sometimes require to form bigrams of words for processing. The next most frequently occurring bigrams are IN, ER, AN, RE. TextBlob is a Python (2 and 3) library for processing textual data. Pie charts can be drawn using the function pie() in the pyplot module. For example, when developing a language model, n-grams are used to develop not just unigram models but also bigram and trigram models. I am trying to build a bigram model and to calculate the probability of word occurrence. A command-line program to encrypt/decrypt a message using a random reciprocal bigram table and write a bigram table to a text file. For example, if we put N=1, then it is referred to as a uni-gram. ("bigram") in that sentence, identify all texts in which that "bigram" appears within a single sentence. get_close_matches (word, possibilities[, n][, cutoff]) ¶ Return a list of the best “good enough” matches. – Make use only of the raw frequency of an n-gram ! But there is an additional source of knowledge we can draw on --- the n-gram “hierarchy” – If there are no examples of a particular trigram,w n-2w n-1w n, to compute P(w n|w n-2w n-1), we can estimate its probability by using the bigram probability P(w n|w n-1 ). util import ngrams def word_grams(words, min=1, max=4): s = [] for n in range(min, max): for ngram in ngrams(words, n): s. 29th Use Perl or Java reg-ex package xHW focus is on writing the "grammar" or FSA for dates and times Add 1 to every bigram c(w. Zip takes a list of iterables and constructs a new list of tuples where the first list. The second sentence is a random sentence. The bigram TH is by far the most common bigram, accounting for 3. N-gramについて勉強したので、そのメモ。 この記事の最後にはpythonで実装したN-Gramを生成するコードを置いておきます。 はじめに N-gram 文字単位のN-gram unigram bigram trigram 単語単位のN-gram unigram bigram trigram 長所と短所 長所 辞書が必要ない 短所 検索ノイズ 単語数 ソースコード タプルでN-gramを返す. The final function part4() should call the functions from parts 4a–4e below, with the argument given in the examples. bigram_fd). Gensim Tutorial - A Complete. 1-gram is also called as unigrams are the unique words present in the sentence. We will use Python to do the job. 9 MB: count_1w. The Natural Language Toolkit has data types and functions that make life easier for us when we want to count bigrams and compute their probabilities. Here is the idea I thought of: Normally we introduce lda. Bigram frequency python Without going into too much detail (you can find many tutorials about tf-idf on the web), documents that have similar content will have similar tf-idf vectors. Goodman, “An empirical study of smoothing techniques for language modeling,” Computer Speech and Language, vol. Twitter Sentiment Analysis with NLTK Now that we have a sentiment analysis module, we can apply it to just about any text, but preferrably short bits of text, like from Twitter! To do this, we're going to combine this tutorial with the Twitter streaming API tutorial. Text bigrams generator tool What is a text bigrams generator? With this tool, you can create a list of all word or character bigrams from the given text. This article shows how you can perform sentiment analysis on movie reviews using Python and Natural Language Toolkit (NLTK). UnigramTagger does not yield consistent results # between python versions. An overview of file dialogs: Tkinter Open File. """ with zipfile. 1), and support multiple architecture like LSTM+CRF, BiLSTM+CRF, and combination of character-level CNN and BiLSTM+CRF. bigram and unigram counts of the words in the sentences. The core estimation code is based on the onlineldavb. word (if linear. The Python code for everything in the chapter. :param line: line as str :return: preprocessed sentence """ # detect sentences sentences = sentence_detector. This gist contains a program that extracts those bigram frequencies into a easily usable JSON format. This is a Python and NLTK newbie question. bigram synonyms, bigram pronunciation, bigram translation, English dictionary definition of bigram. Python: NLTK part 2/3 | Natural Language Tool Kit - stemmer, tokenizer, POS tagger - Duration: 7:49. How To Train Dataset Using Svm. Understanding NLTK collocation scoring for bigrams and trigrams (1). $python collections_counter_get_values. Bigram frequency python Without going into too much detail (you can find many tutorials about tf-idf on the web), documents that have similar content will have similar tf-idf vectors. Generating Shakespearean Sonnets with Python. You can vote up the examples you like or vote down the ones you don't like. c) Bi-gram extraction and Language model Now, we will use library functions of NLTK to find out list of bi-grams sorted with number of occurrences for each language. Details about these models can be found from various sources and search engines accessible through the internet. While not particularly fast to process, Python's dict has the advantages of being convenient to use, being sparse (absent features need not be stored) and storing feature. Once split it becomes simple to retrieve a subsequence of adjacent words in the list by using a slice, represented as two indexes separated by a colon. That doesn’t mean it’s useless and unpopular. (7 replies) Hello Tutors, I'm trying to write a small scrip to find collocations using chi squared, depending on a fairly big corpus. ((The(raw_freq(measure(returns(frequency(as(the(ratio. CRF++ is a simple, customizable, and open source implementation of Conditional Random Fields (CRFs) for segmenting/labeling sequential data. Python's pickle module is an easy way to save Python objects in a standard format. Graphs are used by tf. In this way if we have accurate numbers of particular bigram we can assume the number of trigrams based on this bigram which will be a more robust method to implement so the equation can be: Both the simple interpolation and conditional winter held-out polation lambdas are learned from a held-out corpus. nRecall that Shakespeare produced 300,000 bigram types out of V2= 844 million possible bigrams nSo, 99. The text files containing the counts can be used with ngram_score. For example - Sky High, do or die, best performance, heavy rain etc. In Python 2, items should be unicode string or a plain ASCII str (bytestring) - do not use UTF-8 or other multi-byte encodings, because multi-byte characters will be split up. Bigram Counts § Bigram counts maintain the same principle as monogram counts , but instead of counting occurances of single characters, bigram counts count the frequency of pairs of characters. An iterable object. However I wonder if it's really as straightforward as just taking the average of the vectors of the two words I want to make a bigram vector of?. Where as when I just bigram_measures. It supports non-English languages, especially south east Asian languages. GitHub Gist: instantly share code, notes, and snippets. Human beings can understand linguistic structures and their meanings easily, but machines are not successful enough on natural language comprehension yet. (Called vocab_common in the chapter, but I changed file names here. Building an MLE bigram model [Coding only: use starter code problem3. Return a default value when the iterable has. 707107 47 good oral written 0. Search Engines Information Retrieval in Practice ©W. bigrams() returns an iterator (a generator specifically) of bigrams. The project is based on neural networks which is used to map the sequences to sequences. python - perplexity - write a program to compute unsmoothed unigrams and bigrams Ngram model and perplexity in NLTK (1) To put my question in context, I would like to train and test/compare several (neural) language models. Thus, to compute this probability we need to collect the count of the trigram OF THE KING in the training data as well as the count of the bigram history OF THE. Dla naszego klienta – Polskiego producenta z branży poligraficznej z siedzibą w Warszawie… Zobacz tę i więcej podobnych ofert pracy na LinkedIn. py$あ あい いう うえ えお お\$ 他にもたくさん機能があるので、上記リンク先のチュートリアルなどを読むべし 検索もできるようだ. Install Java 1. This is described in Topic Modeling: Beyond Bag-of-Words by Hanna Wallach et al. Natural Language Processing with PythonNLTK is one of the leading platforms for working with human language data and Python, the module NLTK is used for natural language processing. Il s'agit d'une série de TDs d'algorithmique et structure de données I. • To validate the score of n-grams with that of human annotators used t-test. This process is called creating bigrams. Print out first 40 characters. Python 读取写入配置文件 —— ConfigParser Python 读取写入配置文件很方便，可使用内置的 configparser 模块；可查看源码，如博主本机地址： “C:/python2. ! Perplexity = 1/0 = ∞. Unit tests from the original project are implemented to ensure the accuracy of the port. Creating The Word Dictionary [Coding Only: Save Code As Problem1. An ngram is different than a bigram because an ngram can treat n amount of words or characters as one token. Bigram frequency python Without going into too much detail (you can find many tutorials about tf-idf on the web), documents that have similar content will have similar tf-idf vectors. 나는 문서 - 용어 행렬을 구할 수 있지만, 단어 - 단어 행렬의 동시 발생 (co-occurenc. The first for loop is designed to open the file and take the first line from it. Loading features from dicts¶. In this article you will learn how to remove stop words with the nltk module. Let's create our first TextBlob. These are the top rated real world C# (CSharp) examples of Bigram extracted from open source projects. Mining Twitter Data with Python (Part 3: Term Frequencies) March 17, 2015 June 16, 2015 Marco This is the third part in a series of articles about data mining on Twitter. BigramAssocMeasures() as a variable. myfunc() from mypack1. Search Engines Information Retrieval in Practice ©W. The next () function returns the next item in an iterator. Report Ask Add Snippet. Increment counts for a combination of word and previous word. Python for NLP: Developing an Automatic Text Filler using N-Grams By Usman Malik • 0 Comments This is the 15th article in my series of articles on Python for NLP. Annotation Using Stanford CoreNLP 3. Print out the perplexities computed for sampletest. Janice Shiu. document – a list of words/tokens. In this tutorial, you will discover the bag-of-words model for feature extraction in natural language processing. 5 billion characters of English text, sourced from Wortschatz. Practiline Source Code Line Counter is a powerful source code line count software for developers and project managers. We used these models provided with NLTK [30] and modified them according to our needs. Please note that the port has not been optimized for speed. Then we used static_rnn method to construct the network and generate the predictions. Context is very important to understand the meaning of words. This module does just that. 5, which provides much higher speed and lower memory consumption. Optional arguments start and end are interpreted as in slice notation. Your bigrams list is a list of tuples of pos tuples in the form ((word1, pos1), (word2, pos2)) and you need to "convert" these tuples to (pos1, pos2). myfunc() from mypack1. An ngram is different than a bigram because an ngram can treat n amount of words or characters as one token. Details about these models can be found from various sources and search engines accessible through the internet. Bi-gram, tri-gram and word network analysis; by Shahin Ashkiani; Last updated over 2 years ago Hide Comments (–) Share Hide Toolbars. Questions can be asked via e-mail. Interpolation is that you calculate the trigram probability as a weighted sum of the actual trigram, bigram and unigram probabilities. Said another way, the probability of the bigram heavy rain is larger than the probability of the bigram large rain. Kite is a free autocomplete for Python developers. And if we don't have enough information to calculate the bigram, we can use the unigram probability P(w n). Bigram frequency python Without going into too much detail (you can find many tutorials about tf-idf on the web), documents that have similar content will have similar tf-idf vectors. When people write text, they do so in their own specific style. You can vote up the examples you like or vote down the ones you don't like. LineSentence:. Even though the Hadoop framework is written in Java, programs for Hadoop need not to be coded in Java but can also be developed in other languages like Python or C++ (the latter since version 0. Use MathJax to format equations. (I am working on fuzzy plagiarism detection. class gensim. • The graph is directed (DAG); hence, no cycles. Quite the opposite. Bigramの意味や使い方 バイグラムnグラムのnが2であるもの。すなわち、2文字単位で1文字づつずらして文字列を分割する方式。. Add-one smoothed bigram probabilites ! Original ! Add-one smoothing Too much probability mass is moved ! Adjusted bigram counts ! AP data, 44million words ! Church and Gale (1991) ! In general, add-one smoothing is a poor method of smoothing ! Much worse than other methods in predicting the actual probability for unseen bigrams r = f.


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# Find $\sum_{n=1}^{\infty} x^{\left\lfloor {n \over 2}\right\rfloor} y^{\left\lfloor {n + 1 \over 2}\right\rfloor}$

Let $x,y > 0, xy <1$. Find the sum

$$\sum_{n=1}^{\infty} x^{\left\lfloor {n \over 2}\right\rfloor} y^{\left\lfloor {n + 1 \over 2}\right\rfloor}$$

While I have some ideas how to test convergence, I don't quite know how to get started on the actual sum.

Edit: If we break the sum down to a sum of two infinite series:

$$(y + xy^2 + x^2y^3 + \dots) + (xy + x^2y^2 + \dots)$$

and use the formula for the sum of the first n terms of a geometric series twice, we get:

$$y {1 - (xy)^n \over1 - xy} + xy {1 - (xy)^n \over1 - xy} \to {y \over1 - xy} + {xy \over1 - xy} = {y(1+x) \over 1 - xy}$$ Is this reasoning correct?

• write down the first few terms of the series and look for patterns. – Catalin Zara Nov 28 '16 at 13:38

Note that for $n \in \mathbf N$ we have $$\def\fl#1{\left\lfloor#1\right\rfloor}\fl{\frac n2} + 1 = \fl{\frac{n+2}2}$$ and $$\fl{\frac{n+1}2}+1 = \fl{\frac{n+3}2}$$ So, if we call the sum $s := \sum_{n=1}^\infty x^{\fl{n/2}}y^{\fl{(n+1)/2}}$ and assume it converges we have, \begin{align*} xys &= \sum_{n=1}^\infty x^{\fl{(n+2)/2}}y^{\fl{(n+3)/2}}\\ &= \sum_{k=3}^\infty x^{\fl{k/2}}y^{\fl{(k+1)/2}}\\ &= s - x^0y^1 - x^1y^1\\ &= s - y(1+x) \end{align*} Now solve for $s$, we have
## $$xys = s - y(1+x) \iff s(1-xy) = y(1+x) \iff s = \frac{y(1+x)}{1-xy}$$
• When you write the sum to $\infty$, you are assuming convergence. You have to write the sum to $n$ and let $n\to \infty$. – marty cohen Nov 28 '16 at 14:07
• You are right. I overlooked the assumption that $xy < 1$. – marty cohen Nov 29 '16 at 21:24

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# What does it mean to “interpret the sigmoid $\sigma(\theta^Tx)$ as a probability”? [duplicate]

In Goodfellow's Deep learning text, it is written

Is this way of defining a probability $$p(y=1| x;\theta)$$ even legal?

Recall the definition of a probability given a random variable

where $$p_X$$ is the probability mass function.

Is the logistic function $$\sigma$$ considered to be a probability mass function?

If so, what plausible process is responsible for generating this probability mass function? (i.e., a process similar to how geometric or Bernoulli pmf are defined)

Imagine your data is divided in two classes $$C_{1}$$ and $$C_{2}$$. Regardless of the probability distribution you may assume (I get to that later), using Bayes theorem, you have, $$P(C_{1}|x) = \frac{P(x|C_{1})}{P(x|C_{1})P(C_{1}) + P(x|C_{2})P(C_{2})} = \frac{1}{1+exp(-a)}$$ where, $$a = ln\frac{P(x|C_{1})P(C_{1})}{P(x|C_{2})P(C_{2})}$$ which is the sigmoid. The interesting this now is that, it reduces to linear models when working with generalized linear models (assuming you model all conditional distributions with the same family -Gaussian, binomial, Poisson,...).
• your first equation is incorrect and $a$ is not the sigmoid function. Also, I'm not sure what mentioning Bayes' theorem adds to this. After all, logistic regression does not use Bayes theorem, whereas some of its competitors do, e.g. Naive Bayes, LDA, QDA, etc. – Taylor Jan 20 '19 at 23:06


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# How do you find the center and radius of the circle with equation x^2 + y^2 + 10x +8y = 8?

Dec 29, 2015

There are few ways which can be used to find the center and radius, one of the way is using completion of squares, and is given below in a step by step manner.

#### Explanation:

The given equation
${x}^{2} + {y}^{2} + 10 x + 8 y = 8$

One way to do the problem is to use completing the square to get the problem in the form

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

Where $\left(h , k\right)$ is the center and $r$ is the radius.

${x}^{2} + {y}^{2} + 10 x + 8 y = 8$

Let us group the $x$ and $y$ together.

${x}^{2} + 10 x + {y}^{2} + 8 y = 8$

Divide $x$ coefficient by $2$ square and add on both sides, do the same for $y$ coefficient.

${x}^{2} + 10 x + {\left(5\right)}^{2} + {y}^{2} + 8 y + {\left(4\right)}^{2} = 8 + {5}^{2} + {4}^{2}$
${\left(x + 5\right)}^{2} + {\left(y + 4\right)}^{2} = 8 + 25 + 16$
${\left(x + 5\right)}^{2} + {\left(y + 4\right)}^{2} = 49$
${\left(x - \left(- 5\right)\right)}^{2} + {\left(y - \left(- 4\right)\right)}^{2} = {7}^{2}$

Compare it with
${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

We can see the center $\left(h , k\right)$ is $\left(- 5 , - 4\right)$
Radius $r$ is $7$


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## anonymous 3 years ago I need help with the steps involved to solve the following equation. lim x→−24 (square root(x^2 + 49) − 25)/x + 24 obviously when i plug it in its 0/0 but I'm unsure of the method to solve at this point. if there wasnt a square root i could try factoring and reducing, but with the root in there i don't know how to proceed. thanks!

• This Question is Open
1. ParthKohli

Do you know l'hopital's rule?

2. ParthKohli

That should really be enough, in my opinion.

3. ParthKohli

Or the definition of derivative.

4. ParthKohli

Assume $$h =x + 24$$, then the limit is written as the following:$\lim_{h\to 0} \left(\sqrt{x^2 + 49} - 25 \over h\right)$

5. ParthKohli

Hmm, the definition of derivative doesn't apply here. NVM

6. anonymous

surprisingly enough, we havent covered derivatives yet. or that rule

7. ParthKohli

Darn.

8. anonymous

I haven't had math in years and I'm pretty lost in this class. what we have covered are the limit laws; sum, difference, constant multiple, product, quotient

9. shubhamsrg

You should rationalize the numerator. Must help.

10. ParthKohli

Yay, rationalizing helped me. Shubham, Y U NO REPLY TWO SECONDS LATER?

11. shubhamsrg

I may delete my comment if you ask for it! ;)

12. ParthKohli

13. ParthKohli

:-P

14. anonymous

try $\frac{\sqrt{x^2+49}-25}{x-24}\times \frac{\sqrt{x^2-49}+25}{\sqrt{x^2-49}+25}$

15. ParthKohli

Yes, that's what I did there. Conjugation for the win.

16. anonymous

ok that was wrong!!

17. ParthKohli

No it wasn't?

18. anonymous

$\frac{\sqrt{x^2+49}-25}{x+24}\times \frac{\sqrt{x^2+49}+25}{\sqrt{x^2+49}+25}$ is more like it

19. anonymous

I tried that, which gets me $\frac{ (x^2+49)-625 }{ (x+24) * (\sqrt{x^2+49} +25) }$ Or I think it does. And I'm not sure where to go from there.

20. shubhamsrg

-49+625 = -576 = -(24^2) Does it help ?

21. anonymous

yes! I'm so bad at factoring, I dont ever seem to see stuff like that

22. shubhamsrg


text:
The technical heavy lifting behind this post can be found in this earlier post on generating Munchkin Associator Tokens. Read that one first, or bookmark it for later!

A hard truth about using Marketo is that you won't always use Marketo for email. At some point, you'll use MailChimp or SendGrid for one-off sends, or rent your list (with full opt-in of course) to a partner, or use an in-house mail blaster app for special events.

(On the blaster note, shouts to Gammadyne Mailer, possibly the ugliest best-of-breed app ever created, which did the trick quite well in the pre-MA days.)

You can only dodge this question for so long: Is there any way to track clicks on these emails if they're not sent through Marketo? If the addresses are already in your Marketo instance, yes, there are are a few ways, with varying levels of complexity + client-side slickness (the harder you work on the back end, the more streamlined on the end user side).

Now, let's talk about what you will and won't get without sending through Marketo, even if you adopt the powerful technique below:

• You won't get a literal Clicks Link in Email in the lead's Activity Log, because those activities are only added if you use Marketo's tracking server. However, you will get a Visits Web Page activity logged for the target URL, with (assuming you've added it to the link) utm_medium=email in the query string, which you can interpret in the same way.

• You won't get clicks attributed to email content unless you take pains to embed some kind of additional identifier, like utm_campaign in your URLs. When email is sent via Marketo, the automatically added ?mkt_tok=… param includes a pointer to the lead for later association and a pointer to the email they received.

• We'll be partially emulating the mkt_tok by adding lead info to the URL, but you also need email info that you can decode back to one and only one email or you won't get the specificity you'd get with native Marketo sends. With proper parameters added to the query string, you will get everything you care about, including the partner name, Marketo program, and all that good stuff.

#### Generating the associator token

Reread this for a couple of options for creating tokens.

I'll assume you can export leads from SFDC or Marketo and have a column for MunchkinAssociator. Since it's easiest, I'll be using the prefab token munchkinArgumentsBase64 that's returned from FBMunchkin.getAssociator().

An sample token value is:

WwogICJhc3NvY2lhdGVMZWFkIiwKICB7CiAgICAiRW1haWwiOiAiZW1haWxAZXhhbXBsZS5jb20iCiAgfSwKICAiYjY2NTRlMjQ1OTU4NjBlMmMxYzIzYTE4YjNjODRmM2U1Y2Q1Yzc0NSIKXQ

That's nothing more than the Base64 encoding of this JSON string:

[ "associateLead", {"Email": "email@example.com" }, "b6654e24595860e2c1c23a18b3c84f3e5cd5c745" ]

Which is of course decoded to this simple JS array (carriage returns added):

[
{
"Email": "email@example.com"
},
"b6654e24595860e2c1c23a18b3c84f3e5cd5c745"
]

Having a prepared array means we can smoothly pass it to associateLead later.

(There are other ways to encode and pass the data — a comma-delimited list, whatever — but passing JSON fits most fluently into JavaScript.)

Just put the variable after the # in the URL. I'm using {{variable}} double-curly syntax here, but your ESP templates might use %variable% or something else:

Click here!

That's all on the sending side.

You need one or two simple
<![endif]-->

#### And so…

With associator tokens in hand and all your links tokenized, you can be assured that non-Marketo emails will be as integrated as possible into your MA pipeline.

While the reporting experience won't be as robust as with an all-Marketo campaign, you'll have a lot to go on. Enjoy!


text:
# Supremum of a function as the limit of an integral

I came across a problem and I really don't know where to start from. It states that:

$$\lim_{n\rightarrow\infty} \left(\int_a^b f(x)^n dx\right)^{1/n} = \sup \{ f(x) :a \leq x \leq b \}$$

with $$f : [a,b] \rightarrow \mathbb R$$ being a continuous , nonnegative function.

I tried using the median value theorem, saying that:

$$\int_a^b f(x)^n dx = f(\xi)^n(b-a)$$, for some $$\xi \in [a,b]$$, and then concluded that the limit was $$f(\xi)$$.

However, I couldn?t find any other relationship between it and the other values of $$f$$.

I also tried using the definition of the supremum of a set , but I can't even prove that it is an upper bound.

Let $$M=\sup \{ f(x) :a \leq x \leq b \}$$. Then clearly, $$\left(\int_a^b f(x)^n\,dx\right)^{1/n}\leq M(b-a)^{\frac1n}\to M.$$ Since $$f$$ is continuous, there exists $$x_0\in[a,b]$$ such that $$f(x_0)=M$$ and for any $$0<\epsilon there exists $$(c,d)\subset[a,b]$$ such that $$f(x)>M-\epsilon$$ for $$x\in(c,d)$$. Hence $$\left(\int_a^b f(x)^n\,dx\right)^{1/n}\geq \left(\int_c^d f(x)^n\,dx\right)^{1/n}\geq (M-\epsilon)(d-c)^{\frac1n}\to M-\epsilon.$$ Therefore $$\lim_{n\rightarrow\infty} \left(\int_a^b f(x)^n dx\right)^{1/n} = M=\sup \{ f(x) :a \leq x \leq b \}.$$
• It should be $M(b-a)^{1/n}$ in your first inequality. The proof however, still works. – uniquesolution Aug 23 '19 at 22:41


text:
PeriodicBoundaryCondition

PeriodicBoundaryCondition[u[x1,],pred,f]

represents a periodic boundary condition for all xtarget on the boundary of the region given to NDSolve where pred is True.

PeriodicBoundaryCondition[a+b u[x1,],pred,f]

represents a generalized periodic boundary condition .

Details

• PeriodicBoundaryCondition is used together with differential equations to describe boundary conditions in functions such as NDSolve.
• In NDSolve[eqns,{u1,u2,},{x1,x2,}Ω], xi are the independent variables, uj are the dependent variables, and Ω is the region with boundary Ω.
• Locations where periodic boundary conditions might be specified are shown in blue. They appear on the boundary Ω of the region Ω and specify the relation of the solution at those locations to the locations shown in green. The function f maps from the blue locations to the green locations.
• In the special case of rectangular region Ω, a boundary equation u[,xi,min,]u[,xi,max,] is taken to be equivalent to PeriodicBoundaryCondition[u[,xi,],xixi,max,f] with f=TranslationTransform[{,0,xi,min-xi,max,0,}]. »
• Any logical combination of equalities and inequalities in the independent variables x1, may be used for the predicate pred.
• In PeriodicBoundaryCondition[a+b u[x1,],pred,f], for any point xtarget in the part of Ω where pred is True, then xsource=f[xtarget] should be a point in Ω where pred is not True.
• With PeriodicBoundaryCondition[a+b u[x1,],pred,f], in NDSolve the system matrices are modified so that the solution values u[xtarget] approximately satisfy u[xsource]==a+b u[xtarget] for all xtarget on the boundary of Ω where pred is True.
• Boundary conditions for , including implicit Neumann 0 conditions, will also be mapped to .
• In PeriodicBoundaryCondition[a+b u[x1,],pred,f], both a and b are scalar values that may depend on any of the independent variables xi, including time.
• Antiperiodic boundaries may be specified using PeriodicBoundaryCondition[-u[x1,],pred,f].
• Common values for a and b include:
•  u[x1,…] periodic boundary condition -u[x1,…] anti-periodic boundary condition a u[x1,…] scaled periodic boundary condition u[x1,…]+b offset periodic boundary condition
• For finite element approximations, PeriodicBoundaryCondition operates on nodes in 1D, on edges in 2D and on faces in 3D.

Examples

open allclose all

Basic Examples(2)

Find 5 eigenvalues and eigenvectors of a Laplacian with periodic boundary conditions:

Compare the eigenvalues with the expected analytical eigenvalues:

Visualize the eigenfunctions:

Inspect to see that the bounds are periodic:

Solve a Poisson equation with periodic boundary conditions on curved boundaries:

Visualize the solution:

Visualize the periodic solution:

Scope(15)

1D Eigenvalue Problems(7)

Find 5 eigenvalues and eigenvectors of a Mathieu equation:

Visualize the eigenfunctions:

Inspect to see that the bounds are periodic:

This is equivalent:

Find 5 eigenvalues and eigenvectors of a Laplacian with antiperiodic bounds:

Inspect the eigenvalues:

Visualize the eigenfunctions:

Inspect to see that the eigenvectors add up at the endpoints:

Find 9 eigenvalues and eigenvectors of the Meissner equation on a refined mesh:

Compare the eigenvalues with the expected analytical eigenvalues:

Visualize the eigenfunctions:

Find 5 eigenvalues and eigenvectors of a SturmLiouville operator with a symmetric potential:

Inspect the eigenvalues:

Recompute the eigenvalues with higher resolution:

Visualize the eigenfunctions:

Find 5 periodic eigenvalues and eigenvectors of a SturmLiouville operator with an unsymmetrical potential:

Inspect the eigenvalues:

Visualize the eigenfunctions:

Find 5 antiperiodic eigenvalues and eigenvectors of a SturmLiouville operator with an unsymmetrical potential:

Inspect the eigenvalues:

Visualize the eigenfunctions:

Inspect to see that the eigenvectors add up at the endpoints:

Find 5 relational antiperiodic eigenvalues and eigenvectors of a SturmLiouville operator with an unsymmetrical potential:

Inspect the eigenvalues:

Visualize the eigenfunctions:

Inspect to see that the eigenvectors match the relation at the endpoints:

1D+Time PDE Problems(2)

Solve a 1D Schrödinger equation with periodic boundary conditions:

Visualize the wavefunction:

Solve a 1D wave equation with periodic boundary conditions:

Visualize the periodic wavefunction:

The previous example used as a target. In this case, the target is placed where the flux is entering the periodic domain.

If instead is the target, the wave pulse inverts when reaching and then moves backward. At an implicit Neumann 0 boundary condition imposes a hard boundary condition and the pulse is reflecting off that hard boundary:

Compare the two periodic wavefunctions:

2D PDE Problems(4)

Set up a rectangular region to solve a PDE with a DirichletCondition on the top and bottom:

To implement a periodic boundary condition, specify a mapping f from the target (x==0) to the source (x==2):

Visualize the region Ω and the source of the periodic boundary condition in green and the target in blue:

Specify the periodic boundary condition using the mapping function f:

Solve and visualize the equation:

Find the solution to a Laplace-type equation over a rectangle with a DirichletCondition at the lower-left corner and periodic boundary conditions linking the opposite sides:

Visualize the result:

Inspect the difference of the solution at the boundaries:

Note that the DirichletCondition in the lower-left corner has been propagated to the remaining corners:

Specify a region:

Show the region and the boundaries:

Find a mapping f that maps from the target (blue) to the source (green):

Solve a Poisson equation with internal heat generation and a fixed temperature set on the orange boundaries, and a periodic boundary condition linking the green source and the blue target boundary:

Inspect to see that the periodic boundaries have the same values:

Visualize the solution:

Compare to an antiperiodic solution:

Specify a region:

The lower and upper parts are subject to a DirichletCondition:

The left-hand edge is the target of the relational boundary condition of the right-hand edge (the source):

Solve and visualize the equation:

Inspect to see that the periodic boundaries have the correct relation:

2D+Time PDE Problems(1)

Solve a 2D time-dependent Schrödinger equation with a potential fitting the box and with periodic boundary conditions:

Visualize the wavefunction:

3D Problems(1)

Solve a Poisson equation in a cuboid with periodic boundary conditions:

Visualize the solution:

Applications(1)

Compute eigenvalues of a Laplacian in polar coordinates over a Disk:

Analytically compute the eigenvalues of a Laplacian in Cartesian coordinates over a Disk:

Compare the eigenvalues computed:

Numerically compute the eigenvalues of a Laplacian in Cartesian coordinates over a Disk:

Compare the numerically computed eigenvalues computed in Cartesian coordinates with the analytical solution:

Compare the numerically computed eigenvalues:

Possible Issues(8)

Exclusively specifying periodic boundary condition for stationary PDEs may result in a non-unique solution. In some cases, the system may not be solvable at all:

Specify a DirichletCondition on the source boundary:

The source for the mapping f of the PeriodicBoundaryCondition need not necessarily be on the boundary of a domain:

Visualize the result:

Note that :

Compare to the solution where the source is on the boundary:

Visualize the result:

DirichletCondition cannot be present on the target boundary:

Moving the DirichletCondition to the source boundary works:

Periodic boundary conditions propagate the solution of a PDE from the source to the target boundary. The choice of which boundary is considered source and which is target has an influence on the solution of the PDE.

Consider a rectangular domain and an asymmetric Poisson equation:

The lower and upper parts are subject to a DirichletCondition:

First, the left-hand edge is the target boundary to the right-hand edge (the source):

Solve and visualize the equation:

Inspect the values at the periodic boundaries:

In the second example, the right-hand edge is a target boundary to the left-hand edge (the source):

Solve and visualize the equation:

Inspect the values at the periodic boundaries:

Periodic boundary conditions propagate the solution of a PDE from a source region to the target region. The direction of the mapping has an influence on the solution of the PDE.

Consider a rectangular domain and an asymmetric Poisson equation:

The lower and upper parts are subject to a DirichletCondition:

Map the lower right to the higher left-hand side and the higher right to the lower left-hand side:

The left-hand side is a target boundary to the right-hand side:

Solve and visualize the equation:

Compare to mapping in the same direction but with flipped edges; the lower right to the lower left-hand side and the higher right to the higher left-hand side:

The left-hand side is a target boundary to the right-hand side:

Solve and visualize the equation:

Periodic boundary conditions relate the solution of a PDE from the source to the target boundary. Boundary conditions present, also implicit ones, at the source will affect the solution at the target.

To exemplify the behavior, consider a time-dependent equation discretized with the finite element method. An initial condition u, implicit Neumann zero boundary conditions on both sides and no PeriodicBoundaryCondition are specified:

Visualize the solution at various times:

Note that at both spatial boundaries the implicit Neumann 0 boundary conditions are satisfied.

When a PeriodicBoundaryCondition is used on a source boundary that has an implicit Neumann 0 boundary condition, then that condition will be mapped to the target boundary.

Following is the solution of the same equation and initial condition as previously and an additional periodic boundary condition that has its source on the left and its target on the right:

Visualize the solution at various times:

Note how the solution value at the implicit Neumann 0 boundary condition on the left is mapped to the right.

This is the expected behavior for the finite element method. The tensor product grid method behaves differently, as that method does not have implicit boundary conditions:

Visualize the tensor product grid solution at various times:

A similar behavior can be achieved with the finite element method by specifying a DirichletCondition on the left and a PeriodicBoundaryCondition:

Visualize the difference between the finite element and tensor product grid solutions at various times:

Alternatively, a DirichletCondition could be specified at each side.

Periodic boundary conditions relate the solution of a PDE from the source to the target boundary. Boundary conditions present, including implicit ones, at the source will affect the solution at the target. Multiple periodic boundary conditions can be used to enforce continuous derivatives.

Set up a region and a helper function that takes periodic boundary conditions as arguments:

Set up plotting options and a helper function to create periodic plots:

Solve the PDE with a single periodic boundary condition on the left-hand side:

Visualize a periodic contour plot of the solution:

Visualize a periodic stream density plot of the gradient of the solution:

Note that the gradient is not continuous. This because of the implicit Neumann value that is present at the source location.

Similarly, visualize a periodic density plot of the norm of the gradient of the solution:

Specifying a second periodic boundary condition enforces a continuous derivative. Solve the PDE with periodic boundary conditions on both the left- and right-hand sides:

Visualize a periodic contour plot of the solution. As expected, the solution changes, since the implicit Neumann value is now eliminated:

Visualize a periodic stream density plot of the gradient of the solution. Note that now the gradient is continuous:

Similarly, visualize a periodic density plot of the norm of the gradient of the solution and find that the norm of the gradient is also continuous:

This approach works on unstructured meshes.

Periodic boundary conditions, like Neumann values, operate on edges in 2D and surfaces in 3D. This means that sufficient nodes need to be present in a finite element mesh to make periodic boundary conditions work.

Generate a finite element mesh and visualize the mesh nodes:

Solve a PDE with a periodic boundary condition that maps a single point:

To fix this, specify a predicate for the periodic boundary condition that covers an edge:

Neat Examples(1)

Specify a region to solve a wave equation over a box:

Set up the mapping functions so that the colored edges match. The dashed lines are the respective targets:

Solve the wave equation on a fine mesh:

Visualize the wave propagating on the box:

Wolfram Research (2016), PeriodicBoundaryCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html (updated 2020).

Text

Wolfram Research (2016), PeriodicBoundaryCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html (updated 2020).

BibTeX

@misc{reference.wolfram_2020_periodicboundarycondition, author="Wolfram Research", title="{PeriodicBoundaryCondition}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html}", note=[Accessed: 18-January-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_periodicboundarycondition, organization={Wolfram Research}, title={PeriodicBoundaryCondition}, year={2020}, url={https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html}, note=[Accessed: 18-January-2021 ]}

CMS

Wolfram Language. 2016. "PeriodicBoundaryCondition." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html.

APA

Wolfram Language. (2016). PeriodicBoundaryCondition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html


text:
##### 2.1.1-3
Multivites
These questions ask us to determine whether given transformation is linear or not. How do we determine that? 2.1.1 $y_{1}=2x_{2}$ $y_{2}=x_{2}+2$ $y_{3}=2x_{2}$
tedallen: April 26, 2015, 9:16 p.m.
Linear transformations will have each row expressed as a sum of scalar multiples of each variable. e.g. x + 3y - 2z. If you see a constant added, like x + 1, then the matrix is another kind of matrix but not linear. another thing that would indicate a matrix is not linear is if variables are exponentiated or multiplied by other varialbes.
jiahengsong: May 1, 2015, 11:39 p.m.
If I understand correctly, though, a nonlinear transformation is not directly representable by matrix multiplication.


text:
# The current measured by an ammeter connected in an a.c. circuit is 20 A, the value of maximum current is

This question was previously asked in
BSF RM Official Paper (Conducted on 22-Sep-2019)
View all BSF RO Papers >
1. 10√2 A
2. 10/√2 A
3. 20√2 A
4. 20 × 1.11 A

Option 3 : 20√2 A
Free
Indian Navy MR 2021 Full Mock Test
16893
50 Questions 50 Marks 30 Mins

## Detailed Solution

CONCEPT:

• An ammeter is an instrument which is used to measure the current flowing through the circuit.

Root mean square value of Alternating Current:

• The root mean square (r.m.s.) value of a.c. is defined as that value of steady current, which would generate the same amount of heat in a given resistance in a given time, as is done by the a.c., when passed through the same resistance for the same time.
• The r.m.s. value is also called an effective value of a.c. or virtual value of a.c. It is represented by Irms or Ieff or Iv.
• The relation between the peak value of a.c. value of current (Io) and r.m.s. value of the current is given as

$${I_{rms}} = \frac{{{I_o}}}{{√ 2 }}$$

CALCULATION:

Given -  r.m.s. current (Irms) = 20 A

• The relation between the peak value of a.c. value of current (Io) and r.m.s. value of the current is given as

$$⇒ {I_{rms}} = \frac{{{I_o}}}{{√ 2 }}$$

⇒ Io = 20 √2


text:
# I Differing first-principle models for Maxwell-Boltzmann statistics?

#### greswd

Let's consider a simple scenario in Maxwell-Boltzmann statistics: 6 identical but distinguishable particles, and 9 quanta of energy, 9 indivisible units, to be distributed among the particles.

The first model is like that of the wheels on a combination lock, or should I say "permutation lock".

There are 6 wheels, one for each particle, and the numbers run from 0 to 9, since there are 9 units of energy available.

The number on each wheel represents the amount of energy each particle possesses. Since there are 6 wheels, there are a total of a million permutations.

However, there are only 9 units of energy in total, so if the 6 numbers do not add up to 9 in total, it is an invalid permutation.

Considering only the valid permutations, the odds of a particle being in the ground state, having zero units of energy, is the highest of all, and it only decreases subsequently for each incremental energy level.

Now for the second model, 9 dice.

One die for each unit of energy, and of course 6 sides, one for each particle.

You can imagine rolling all 9 dice, with the number on each die indicating which particle the unit of energy the die represents belongs to.

This time, there's no need to remove invalid permutations, all are valid.

This model produces quite different results from the first one, as the odds of a particle having one unit of energy is the highest, and the odds of having two units of energy is even higher than the odds of having no energy at all.

Maxwell-Boltzmann statistics follows the first model, and I'm curious as to why nature is of the first model rather than of the second.
Because intuitively, it seems to me like the second model would be more likely to occur. It's simpler in a way, no assumptions need to be made about invalid permutations.

Last edited:
Related Classical Physics News on Phys.org

#### BvU

Homework Helper
You can imagine rolling all 9 dice, with the number on each die indicating which particle the unit of energy the die represents belongs to.
So state 1 1 1 1 1 1 1 1 2 occurs 9 times (any of the other dice can be 2 instead of 1) ?

#### greswd

So state 1 1 1 1 1 1 1 1 2 occurs 9 times (any of the other dice can be 2 instead of 1) ?
yes, so maybe that state should have a statistical weight of 9?

#### BvU

Homework Helper
What would it get in the permutation lock scenario ?

#### greswd

What would it get in the permutation lock scenario ?
It is, as you've mentioned, a state, so I think it's weight is 1, out of 2002.

While for the dice it is 9 out of 10077696.

#### Dale

Mentor
You can imagine rolling all 9 dice, with the number on each die indicating which particle the unit of energy the die represents belongs to.

This time, there's no need to remove invalid permutations, all are valid.
This is not exactly correct. Although all permutations are valid, they are not all distinguishable. For example {1,1,1,1,1,1,1,2,2} refers to the same state as {2,2,1,1,1,1,1,1,1} and {2,1,1,1,1,1,1,1,2}. The particles are distinguishable, but the energy levels are not. If you go through and eliminate all of the invalid permutations of locks and all of the indistinguishable permutations of dice then you are left with 2002 sets in both cases.

The equipartition theorem basically states that all of these 2002 distinguishable/valid sets are equally probable. You could make an arbitrary number of models describing how many indistinguishable sets correspond to each distinguishable set, but that doesn't affect the physics. So physically both scenarios are the same since they both wind up with the same number of sets. In one case you have to remove invalid cases and in the other you have to remove indistinguishable cases.

It is, as you've mentioned, a state, so I think it's weight is 1, out of 2002.

While for the dice it is 9 out of 10077696.
In both cases it is 1 out of 2002.

#### BvU

Homework Helper
Conversely, all 9 energy bits for the first particle gets one out of 10077696 with the dice and 1 out of 2002 with the lock

The energy bits are indistinguishable, so you'd have to divide each of the 10077696 combinations by the number of ways such a combination can occur to get its weight.

(ah, Dale to the rescue while I waste my time trying to get an elegant expression for this dice combination weight )

#### greswd

The equipartition theorem basically states that all of these 2002 distinguishable/valid sets are equally probable. You could make an arbitrary number of models describing how many indistinguishable sets correspond to each distinguishable set, but that doesn't affect the physics.
thanks, so, what's the root, fundamental basis or effect that leads to equipartition probabilities and nature not following the dice distribution?

Is it like some fundamental rule/effect which describes distinguishability affecting probabilities?

Because it seems like the combination lock method isn't a direct, sole logical given, and that there is some fundamental physical principle or effect which makes it so.

#### BvU

Homework Helper
You can't expect nine dice to mimic nine units of energy ...

#### greswd

You can't expect nine dice to mimic nine units of energy ...
But six wheels of a lock demonstrate the mathematics of the phenomenon very well.

I think a more direct, clear and physical visual would be a beer-pong set-up.

Imagine 6 cups representing the 6 particles, and 9 ping-pong balls representing the units of energy, which are hurled at the cups.

Assuming the balls are ghostly and pass through each other instead of bouncing off each other, it will produce the same results as that of the dice.

Last edited:

#### Dale

Mentor
thanks, so, what's the root, fundamental basis or effect that leads to equipartition probabilities and nature not following the dice distribution?
I think that it is called the identity of indiscernibles. Two states that are completely indistinguishable are the same state. I believe that it is simply an assumption that seems to work. Apparently it has a very powerful usage in quantum mechanics where it is the cornerstone of the statistical distributions used to represent particles.

The reason that the combination lock works and the dice does not is that you specified that the particles were distinguishable and the energy levels were not. The combination lock respects that distinction and the dice do not. If you had indistinguishable particles then the combination lock metaphor wouldn't work either.

#### greswd

I think that it is called the identity of indiscernibles. Two states that are completely indistinguishable are the same state.

I believe that it is simply an assumption that seems to work.
wow, that's pretty interesting. I think most would imagine a "beer-pong distribution" as the simplest method of probabilistically distributing energy among particles. but nature appears to have other ideas.

#### Dale

Mentor
I think most would imagine a "beer-pong distribution" as the simplest method of probabilistically distributing energy among particles. but nature appears to have other ideas.
As long as the balls are indistinguishable and the cups are distinguishable it will work fine.

#### greswd

As long as the balls are indistinguishable and the cups are distinguishable it will work fine.
Considering actual, macroscopic ping-pong balls, I'm not sure how indistinguishability would apply.

Whether all 9 balls are white, or each painted with a different color, it would have no effect on the overall distribution. A layer of paint can't change anything.

#### greswd

The energy bits are indistinguishable, so you'd have to divide each of the 10077696 combinations by the number of ways such a combination can occur to get its weight.
As long as the balls are indistinguishable and the cups are distinguishable it will work fine.
Considering actual, macroscopic ping-pong balls, I'm not sure how indistinguishability would apply.

Whether all 9 balls are white, or each painted with a different color, it would have no effect on the overall distribution. A layer of paint can't change anything.
Or, a reverse scenario, if each ping-pong ball is originally of a unique color, we could make them "indistinguishable" by painting all of them white.

And that layer of white paint also can't change anything, the kinematics will remain the same.

Last edited:

#### BvU

Homework Helper
Does someone have a decent expression for the weight of a 9 dice throw ?

#### greswd

Does someone have a decent expression for the weight of a 9 dice throw ?
well, there are 10077696 possible permutations in total.

#### BvU

Homework Helper
I mean: What's the weight if I throw 1 2 3 4 5 6 6 6 6

#### greswd

I mean: What's the weight if I throw 1 2 3 4 5 6 6 6 6
it should be 15120

#### Dale

Mentor
Considering actual, macroscopic ping-pong balls, I'm not sure how indistinguishability would apply.
It doesn’t. But IF it did then the beer pong distribution would work. The observed fact that it doesn’t work is due to the violation of the indistinguishability assumption. Clearly, a layer of paint is not what makes a physical system indistinguishable.

#### BvU

Homework Helper
it should be 15120
So do you have an expression for that ? The number isn't interesting.

#### greswd

It doesn’t. But IF it did then the beer pong distribution would work. The observed fact that it doesn’t work is due to the violation of the indistinguishability assumption. Clearly, a layer of paint is not what makes a physical system indistinguishable.
what do you think makes a physical system indistinguishable?

each ball has tiny imperfections and flaws that distinguish it from the others.

however, even if they are somehow 100% perfect copies of each other, it wouldn't affect the kinematics and wouldn't produce different results.
Their trajectories through the air would not change much.

So energy quanta probably have some other properties in addition to their indistinguishability which make them behave differently and follow the lock model.

#### Dale

Mentor
So energy quanta probably have some other properties
I think it is the opposite. They have fewer properties, not additional ones. That is what makes them indistinguishable. Macroscopic systems have too many properties for the identity of indiscernible to play a role.

#### greswd

So do you have an expression for that ? The number isn't interesting.
$\operatorname{nCr}\left(9,5\right)\cdot5!$

#### greswd

I think it is the opposite. They have fewer properties, not additional ones. That is what makes them indistinguishable. Macroscopic systems have too many properties for the identity of indiscernible to play a role.
The concept of energy quanta is somewhat abstract, but if we replaced all of the ping-pong balls with classical electrons, which behave like tiny ping-pong balls somewhat, I think the result probably wouldn't change.

I think even real electrons in a beer-electron-pong set-up would result in the dice model.

"Differing first-principle models for Maxwell-Boltzmann statistics?"

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text:
# Step response of voltage inverter and RC filter homework question

This is my solution so far:

• Vth would simply be the output of the inverting op amp which is Vth = -(Rf/Ri)Vi
• Rth would simply be R2 || R3.

simulate this circuit – Schematic created using CircuitLab

And now we have a simple RC circuit with a DC source. So at t = inf, its right to assume that the capacitor would just charge to the V of its source. Am I right?

And then the step response would be:

• Using the total response formula of an RC circuit (wouldn't go to all the derivation)

• Tau would just be C x (R2 || R3)

So the step response would look like

V(t) = (0 - Vth)e^(1/(R2||R3)C) + Vth

Did I get this right? I'm having doubts because it's an op-amp and i'm not sure if i'm oversimplifying things.

Well, we are trying to analyze the following circuit (assuming an ideal opamp):

simulate this circuit – Schematic created using CircuitLab

When we use and apply KCL, we can write the following set of equations:

$$\begin{cases} 0=\text{I}_1+\text{I}_2\\ \\ \text{I}_6=\text{I}_2+\text{I}_3\\ \\ \text{I}_3=\text{I}_4+\text{I}_5\\ \\ \text{I}_7=\text{I}_4+\text{I}_5\\ \\ \text{I}_7=\text{I}_1+\text{I}_6 \end{cases}\tag1$$

When we use and apply Ohm's law, we can write the following set of equations:

$$\begin{cases} \text{I}_1=\frac{\text{V}_\text{i}-\text{V}_1}{\text{R}_1}\\ \\ \text{I}_2=\frac{\text{V}_2-\text{V}_1}{\text{R}_2}\\ \\ \text{I}_3=\frac{\text{V}_2-\text{V}_3}{\text{R}_3}\\ \\ \text{I}_4=\frac{\text{V}_3}{\text{R}_4}\\ \\ \text{I}_5=\frac{\text{V}_3}{\text{R}_5} \end{cases}\tag2$$

Substitute $$\(2)\$$ into $$\(1)\$$, in order to get:

$$\begin{cases} 0=\frac{\text{V}_\text{i}-\text{V}_1}{\text{R}_1}+\frac{\text{V}_2-\text{V}_1}{\text{R}_2}\\ \\ \text{I}_6=\frac{\text{V}_2-\text{V}_1}{\text{R}_2}+\frac{\text{V}_2-\text{V}_3}{\text{R}_3}\\ \\ \frac{\text{V}_2-\text{V}_3}{\text{R}_3}=\frac{\text{V}_3}{\text{R}_4}+\frac{\text{V}_3}{\text{R}_5}\\ \\ \text{I}_7=\frac{\text{V}_3}{\text{R}_4}+\frac{\text{V}_3}{\text{R}_5}\\ \\ \text{I}_7=\frac{\text{V}_\text{i}-\text{V}_1}{\text{R}_1}+\text{I}_6 \end{cases}\tag3$$

Now, using an ideal opamp, we know that:

$$\text{V}_+=\text{V}_-=\text{V}_1=0$$

So we can rewrite equation $$\(3)\$$ as follows:

$$\begin{cases} 0=\frac{\text{V}_\text{i}}{\text{R}_1}+\frac{\text{V}_2}{\text{R}_2}\\ \\ \text{I}_6=\frac{\text{V}_2}{\text{R}_2}+\frac{\text{V}_2-\text{V}_3}{\text{R}_3}\\ \\ \frac{\text{V}_2-\text{V}_3}{\text{R}_3}=\frac{\text{V}_3}{\text{R}_4}+\frac{\text{V}_3}{\text{R}_5}\\ \\ \text{I}_7=\frac{\text{V}_3}{\text{R}_4}+\frac{\text{V}_3}{\text{R}_5}\\ \\ \text{I}_7=\frac{\text{V}_\text{i}}{\text{R}_1}+\text{I}_6 \end{cases}\tag4$$

Now, we can solve for:

• $$\text{V}_3=-\frac{\text{R}_2\text{R}_4\text{R}_5\text{V}_\text{i}}{\text{R}_1\text{R}_5\left(\text{R}_3+\text{R}_4\right)+\text{R}_1\text{R}_3\text{R}_4}\tag5$$
• $$\text{I}_5=-\frac{\text{R}_2\text{R}_4\text{V}_\text{i}}{\text{R}_1\text{R}_5\left(\text{R}_3+\text{R}_4\right)+\text{R}_1\text{R}_3\text{R}_4}\tag6$$

Where I used the following Mathematica-code:

In[1]:=V1 = 0;
FullSimplify[
Solve[{0 == I1 + I2, I6 == I2 + I3, I3 == I4 + I5, I7 == I4 + I5,
I7 == I1 + I6, I1 == (Vi - V1)/R1, I2 == (V2 - V1)/R2,
I3 == (V2 - V3)/R3, I4 == V3/R4, I5 == V3/R5}, {I1, I2, I3, I4, I5,
I6, I7, V2, V3}]]

Out[1]={{I1 -> Vi/R1, I2 -> -(Vi/R1),
I3 -> -((R2 (R4 + R5) Vi)/(R1 R3 R4 + R1 (R3 + R4) R5)),
I4 -> -((R2 R5 Vi)/(R1 R3 R4 + R1 (R3 + R4) R5)),
I5 -> -((R2 R4 Vi)/(R1 R3 R4 + R1 (R3 + R4) R5)),
I6 -> -((((R2 + R3) R4 + (R2 + R3 + R4) R5) Vi)/(
R1 R3 R4 + R1 (R3 + R4) R5)),
I7 -> -((R2 (R4 + R5) Vi)/(R1 R3 R4 + R1 (R3 + R4) R5)),
V2 -> -((R2 Vi)/R1),
V3 -> -((R2 R4 R5 Vi)/(R1 R3 R4 + R1 (R3 + R4) R5))}}

In order to calculate the equivalent Thevenin circuit seen by the resistor $$\\text{R}_5\$$, we can write:

• For the Thevenin voltage $$\\text{V}_\text{th}\$$: $$\text{V}_\text{th}=\lim_{\text{R}_5\to\infty}\text{V}_3=-\frac{\text{R}_2\text{R}_4\text{V}_\text{i}}{\text{R}_1\left(\text{R}_3+\text{R}_4\right)}\tag7$$
• For the Thevenin current $$\\text{I}_\text{th}\$$: $$\text{I}_\text{th}=\lim_{\text{R}_5\to0}\text{I}_5=-\frac{\text{R}_2\text{V}_\text{i}}{\text{R}_1\text{R}_3}\tag8$$
• For the Thevenin resistance $$\\text{R}_\text{th}\$$: $$\text{R}_\text{th}=\frac{\text{V}_\text{th}}{\text{I}_\text{th}}=\frac{\text{R}_3\text{R}_4}{\text{R}_3+\text{R}_4}\tag9$$

Where I used Mathematica-code, again:

In[2]:=Limit[-((R2 R4 R5 Vi)/(R1 R3 R4 + R1 (R3 + R4) R5)), R5 -> Infinity]

Out[2]=-((R2 R4 Vi)/(R1 R3 + R1 R4))

In[3]:=Limit[-((R2 R4 Vi)/(R1 R3 R4 + R1 (R3 + R4) R5)), R5 -> 0]

Out[3]=-((R2 Vi)/(R1 R3))

In[4]:=FullSimplify[(-((R2 R4 Vi)/(R1 R3 + R1 R4)))/(-((R2 Vi)/(R1 R3)))]

Out[4]=(R3 R4)/(R3 + R4)

When we want to apply the derivation from above to your circuit we need to use Laplace transform (I will use lower case function names for the functions that are in the (complex) s-domain, so $$\\text{y}\left(\text{s}\right)\$$ is the Laplace transform of the function $$\\text{Y}\left(t\right)\$$):

• $$\text{R}_5=\frac{1}{\text{sC}}\tag{10}$$
• The input voltage, $$\\text{V}_\text{i}\$$, is a Heaviside theta function (because of the step response): $$\text{v}_\text{i}\left(\text{s}\right)=\mathcal{L}_t\left[\theta\left(t\right)\right]_{\left(\text{s}\right)}=\frac{1}{\text{s}}\tag{11}$$

So, we get for $$\\text{V}_3\$$ (using $$\(5)\$$):

$$\text{v}_3\left(\text{s}\right)=-\frac{\text{R}_2\text{R}_4\cdot\frac{1}{\text{sC}}\cdot\frac{1}{\text{s}}}{\text{R}_1\cdot\frac{1}{\text{sC}}\cdot\left(\text{R}_3+\text{R}_4\right)+\text{R}_1\text{R}_3\text{R}_4}\tag{12}$$

Using inverse Laplace transform we get:

$$\text{V}_3\left(t\right)=\frac{\text{R}_2\text{R}_4\left(\exp\left(-\frac{\left(\text{R}_3+\text{R}_4\right)t}{\text{C}\text{R}_3\text{R}_4}\right)-1\right)}{\text{R}_1\left(\text{R}_3+\text{R}_4\right)}\tag{13}$$

Using your values we end up with:

$$\text{V}_3\left(t\right)=\frac{5\left(\exp\left(-75 t\right)-1\right)}{3}=\frac{5}{3}\cdot\left(e^{-75 t}-1\right)\tag{14}$$

Where I used Mathematica-code, again:

In[5]:=Vi = 1/s;
R5 = 1/(s*c);
FullSimplify[
InverseLaplaceTransform[-((R2 R4 R5 Vi)/(
R1 R3 R4 + R1 (R3 + R4) R5)), s, t]]

Out[5]=((-1 + E^(-(((R3 + R4) t)/(c R3 R4)))) R2 R4)/(R1 (R3 + R4))

In[6]:=R1 = 20000;
R2 = 50000;
R3 = 10000;
R4 = 20000;
c = 2*10^(-6);
FullSimplify[((-1 + E^(-(((R3 + R4) t)/(c R3 R4)))) R2 R4)/(
R1 (R3 + R4))]

Out[6]=5/3 (-1 + E^(-75 t))

When analyzing transfer functions, a good way is to break down the system into blocks. The problem is it looks like the analysis for the opamp was done incorrectly The s transfer functions look like this:

Then the total equation would be

K1 is orange
K2 is green
$$\ V_{out} = K_1K_2V_{in}\$$

As s goes to infinity (as c charges) c ends up with the same voltage As r3

• And the voltage at R3 will be Vout, right? Also, what would the relationship be of K1 and K2? And how would they affect the output?
– user263783
Sep 27 '20 at 3:32
• Yes, the voltage at R3 is Vout. K1 and K2 are just gains (from the pic) Sep 27 '20 at 4:03
• Thank you! I understand it now.
– user263783
Sep 27 '20 at 4:53