text:
x = ∑ᵢ wᵢ . The last layer gives the ouput. In this post, the weights are updated based on each training example such that perceptron can learn to predict closer to actual output for next input signal. Pay attention to all the methods that are explained previously. The process of creating a neural network in Python begins with the most basic form, a single perceptron. })(120000); The Perceptron is a linear machine learning algorithm for binary classification tasks. Sum all of the weighted inputs. Below is the equation in Perceptron weight adjustment: Where, 1. d:Predicted Output – Desired Output 2. η:Learning Rate, Usually Less than 1. Using what we have learned, we can now build a perceptron for the red/blue example in Python. I would love to connect with you on. Implementation of Perceptron Algorithm Python Example. Programming a Perceptron in Python. It is definitely not “deep” learning but is an important building block. This is the 12th entry in AAC's neural network development series. Here is the Python code which could be used to train the model using CustomPerceptron algorithm shown above. This implementation is used to train the binary classification model that could be used to classify the data in one of the binary classes. }. setTimeout( This section provides a brief introduction to the Perceptron algorithm and the Sonar dataset to which we will later apply it. Let’s start our discussion by talking about the Perceptron! The perceptron when represented as a line diagram would look like the following: Pay attention to some of the following in relation to what's shown in the above diagram representing a neuron: Pay attention to some of the following in above equation vis-a-vis Perceptron learning algorithm: In this section, we will look each of the steps described in previous section and understand the implementation with the Python code: Here is how the entire Python code for Perceptron implementation would look like. It is also called as single layer neural network as the output is decided based on the outcome of just one activation function which represents a neuron. The prediction is also based on the unit step function. Related Course: Deep Learning with TensorFlow 2 and Keras. The activation function of Perceptron is based on the unit step function which outputs 1 if the net input value is greater than or equal to 0, else 0. The perceptron when represented as line diagram would look like the following: Pay attention to some of the following in relation to what’s shown in the above diagram representing a neuron: Pay attention to some of the following in above equation vis-a-vis Perceptron learning algorithm: In this section, we will look each of the steps described in previous section and understand the implementation with the Python code: Here is how the entire Python code for Perceptron implementation would look like. This is just one example.What is the general set of inequalities that must be satisfied for an OR perceptron? Our line, in this case, is represented by the equation y = 0.5x + 10. In this post, you will learn about Perceptrons with the help of a Python example. $$\delta w$$ is derived by taking first order derivative of loss function (gradient) and multiplying the output with negative (gradient descent) of learning rate. Prediction is made on the basis of output of activation function. Welcome. This type of network consists of multiple layers of neurons, the first of which takes the input. It is very important for data scientists to understand the concepts related to Perceptron as a good understanding lays the foundation of learning advanced concepts of neural networks including deep neural networks (deep learning). Homework .hide-if-no-js { You now know how the Perceptron algorithm works. Commonly used Machine Learning Algorithms (with Python and R Codes) The Overflow Blog Podcast 286: If you could fix any software, what would you change? Here is the summary of what you learned about the Perceptron algorithm with help of Python implementation: (function( timeout ) { This playlist/video has been uploaded for Marketing purposes and contains only selective videos. You go to the kitchen, open the fridge and all you can find is an egg, a carrot and an empty pot of mayonnaise. Time limit is exhausted. It consists of a single perceptron that will be trained to guess if the location of a point in Cartesian space is located above or below the function y = x. A perceptron is a fundamental unit of the neural network which takes weighted inputs, process it and capable of performing binary classifications. Like their biological counterpart, ANN’s are built upon simple signal processing elements that are connected together into a large mesh. ); In this section, we will look each of the steps described in previous section and understand the implementation with the Python code: The Perceptron. 1. In this post, you will learn about the concepts of Perceptron with the help of Python example. Then, we update the weight values to 0.4. Programming a Perceptron in Python. Both stochastic gradient descent and batch gradient descent could be used for learning the weights of the input signals. In case the combined signal strength is not appropriate based on decision function within neuron cell (observe activation function), the neuron does not fire any output signal. In this post, the weights are updated based on each training example such that perceptron can learn to predict closer to actual output for next input signal. For this basic model, the only Python package we need is numpy and matplotlib. Compute the output of the perceptron based on that sum passed through an activation function (the sign of the sum). This is the 12th entry in AAC's neural network development series. When to use Deep Learning vs Machine Learning Models? Let’s start by explaining the single perceptron! We will use Python and the NumPy library to create the perceptron python example. A Perceptron in Python We’ll start by coding each of the components of the Perceptron in Python, and then combine these into one larger Perceptron class at the end. Perceptron for OR: 2 inputs, 1 output. The weights signify the effectiveness of each feature xᵢ in x on the model’s behavior. Build Perceptron to Classify Iris Data with Python Posted on May 17, 2017 by charleshsliao It would be interesting to write some basic neuron function for classification, helping us refresh some essential points in neural network. 1 Input values or One input layer 2 Weights and Bias 3 Net sum 4 Activation Function FYI: The Neural Networks work the same way as the perceptron. Like logistic regression, it can quickly learn a linear separation in feature space […] An Basic implementation of the perceptron, the build block a neural net. We set weights to 0.9 initially but it causes some errors. Please reload the CAPTCHA. Marketing Blog. Both stochastic gradient descent and batch gradient descent could be used for learning the weights of the input signals. The Perceptron Algorithm: For every input, multiply that input by its weight. See the original article here. You can rate examples to help us improve the quality of examples. This is a follow up to my previous post on the Perceptron … How to implement Averaged Perceptron in Python (without Scikit-learn) Ask Question Asked 3 years ago. A perceptron has one or more … Vitalflux.com is dedicated to help software engineers & data scientists get technology news, practice tests, tutorials in order to reskill / acquire newer skills from time-to-time. These are the top rated real world Python examples of sklearnlinear_model.Perceptron.score extracted from open source projects. Most Common Types of Machine Learning Problems, Historical Dates & Timeline for Deep Learning, Stochastic Gradient Descent Python Example, Machine Learning Techniques for Stock Price Prediction. Also, this will include a lot of math, so strap in. A Perceptron in Python The perceptron algorithm has been covered by many machine learning libraries, if you are intending on using a Perceptron for a project you should use one of those. You can rate examples to help us improve the quality of examples. Skip the noise; get the code: here, “regression” type tests here. It may be considered one of the first and one of the simplest types of artificial neural networks. Here's how to instanitate the Perceptron. The following are 30 code examples for showing how to use sklearn.linear_model.Perceptron().These examples are extracted from open source projects. Python-Perceptron. These are the top rated real world Python examples of sklearnlinear_model.Perceptron extracted from open source projects. Today, we are going to cover how to build a basic single perceptron neural network. presentation/ Html presentation ancillary.py/ Ancillary functions (visualistations, etc.) I want to make this the first of a series of articles where we delve deep into everything - CNNs, transfer learning, etc. Browse other questions tagged python numpy machine-learning svm perceptron or ask your own question. Active 3 years ago. Learn Python Programming. so be sure to bookmark the site and keep checking it. https://medium.com/@narengowda/perceptron-in-python-476b974ec4c6 Here is the Python code which could be used to train the model using CustomPerceptron algorithm shown above. Python Perceptron - 30 examples found. w 1 =1, w 2 =1, t=2.. Q. Let’s understand the working of SLP with a coding example: We will solve the problem of the XOR logic gate using the Single Layer … In this example, we will train our perceptron to tell us whether a point is above a line or below a line. I want to make this the first of a series of articles where we delve deep into everything - CNNs, transfer learning, etc. It is very important for data scientists to understand the concepts related to Perceptron as a good understanding lays the foundation of learning advanced concepts of neural networks including deep neural networks (deep learning). The output is what is shown in the above equation - product of learning rate, difference between actual and predicted value (perceptron output) and input value. Learning of weights can continue for multiple iterations, Activation function is fed the net input and the unit step function, Model score is calculated based on comparison of, Perceptron Explained Using Python Example - Data Analytics, Gradient descent explained simply with examples, Developer  =  This is a follow up to my previous post on the Perceptron … One of the simplest forms of a neural network model is the perceptron. At HSR, I'm currently enrolled in a course about neural networks and machine learning. Updating weights means learning in the perceptron. My Profile on Google+. https://letsfigureout.com/2020/04/13/building-a-perceptron-with-python w . At HSR, I'm currently enrolled in a course about neural networks and machine learning. You can find the source code here. Input (1) … display: none !important; As the simulation runs you will notice the points changing from filled to empty to signify the perceptron’s guess. The perceptron consists of 4 parts . Perceptron is, therefore, a linear classifier — an algorithm that predicts using a linear predictor function. The activation function of Perceptron is based on the unit step function which outputs 1 if the net input value is greater than or equal to 0, else 0. It consists of a single perceptron that will be trained to guess if the location of a point in Cartesian space is located above or below the function y = x. Perceptron implements a multilayer perceptron network written in Python. written on Tuesday, March 26, 2013 by Danilo Bargen. Gradient descent explained simply with examples. In this post, the following topics are covered: Perceptron is a machine learning algorithm which mimics how a neuron in the brain works. This is also called as, Perceptron mimics the neuron in the human brain, Perceptron is termed as machine learning algorithm as weights of input signals are learned using the algorithm, Perceptron algorithm learns the weight using gradient descent algorithm. by Robert Keim This article takes you step by step through a Python program that will allow us to train a neural network and perform advanced classification. How to build a simple Neural Network with Python: Multi-layer Perceptron. Basics of Artificial Neural Networks The Data Perceptron Neural Network's Layer(s) Compute Predictions Evaluation report Exporting the predictions and submit them The ANN as a Class. Over a million developers have joined DZone. GUI PyQT Machine Learning Web Multilayer Perceptron. So far, we have used the perceptron as a binary classifier, telling us the probability p … Thank you for visiting our site today. This is also called as, Perceptron mimics the neuron in the human brain, Perceptron is termed as machine learning algorithm as weights of input signals are learned using the algorithm, Perceptron algorithm learns the weight using gradient descent algorithm. so be sure to bookmark the site and keep checking it. Table of contents. Python … 3. x:Input Data. Python Perceptron.score - 30 examples found. There can be multiple middle layers but in this case, it just uses a single one. The clock marks 11:50 in the morning, your stomach starts rumbling asking for food and you don’t know what you are having for lunch. See what else the series offers below: How to Perform Classification Using a Neural Network: What Is the… Since this network model works with the linear classification and if the data is not linearly separable, then this model will not show the proper results. Today, we are going to cover how to build a basic single perceptron neural network. Also, pay attention to the score method which is used to measure the accuracy of the model. Net Input is sum of weighted input signals. one Tutorial 2 Through this tutorial, you will know: function() { Weights are updated based on each training examples. The net input (weighted sum) is processed by the neuron and output signal (observer signal in AXON) is appropriately fired. var notice = document.getElementById("cptch_time_limit_notice_12"); This is just one example.What is the general set of inequalities for w 1, w 2 and t that must be satisfied for an AND perceptron?. We welcome all your suggestions in order to make our website better. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. The perceptron algorithm is an example of a linear discriminant model(two-class model) How to implement the Perceptron algorithm with Python? Activation function is fed the net input and the unit step function is executed to determine the output. The function f (x)= b+w.x is a linear combination of weight and feature vectors. Machine Learning – Why use Confidence Intervals? notice.style.display = "block"; In this post, you will learn the concepts of Adaline (ADAptive LInear NEuron), a machine learning algorithm, along with Python example.As like Perceptron, it is important to understand the concepts of Adaline as it forms the foundation of learning neural networks. The input signals (x1, x2, ...) of different strength (observe weights, w1, w2 ...) is fed into the neuron cell via dendrites. The Perceptron is a linear machine learning algorithm for binary classification tasks. This means the following: So consider, if y and f(x) are signed values $(+1,-1)$: the loss is 0, if $y*f(x)$ are positive, respective both values have the same sign. The input signals (x1, x2, …) of different strength (observe weights, w1, w2 …) is fed into the neuron cell via dendrites. Like logistic regression, it can quickly learn a linear separation in feature space […] One of the libraries I have used personally which has an optimised version of this algorithm is scikit-learn . In this post, we will see how to implement the perceptron model using breast cancer data set in python. Welcome. A perceptron learner was one of the earliest machine learning techniques and still from the foundation of many modern neural networks. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. You wake up, look outside and see that it is a rainy day. $$\delta w$$ is derived by taking first order derivative of loss function (gradient) and multiplying the output with negative (gradient descent) of learning rate. I have been recently working in the area of Data Science and Machine Learning / Deep Learning. The output is what is shown in the above equation – product of learning rate, difference between actual and predicted value (perceptron output) and input value. Let’s first understand how a neuron works. Also, this will include a lot of math, so strap in. if ( notice ) Perceptron is a machine learning algorithm which mimics how a neuron in the brain works. The following are 30 code examples for showing how to use sklearn.linear_model.Perceptron().These examples are extracted from open source projects. }, It is definitely not “deep” learning but is an important building block. Python Perceptron - 30 examples found. w 1 =1, w 2 =1, t=1.. Q. The prediction is also based on the unit step function. You can rate examples to help us improve the quality of examples. Perceptron Python Code Example In this section, we will look each of the steps described in previous section and understand the implementation with the Python code: Input signals weighted and combined as net input : Input signals get multiplied with weights and the sum of … I’ve written the logic of perceptron in python. Have you ever wondered why there are tasks that are dead simple for any human but incredibly difficult for computers?Artificial neural networks(short: ANN’s) were inspired by the central nervous system of humans. Sample Perceptrons Perceptron for AND: 2 inputs, 1 output. As the simulation runs you will notice the points changing from filled to empty to signify the perceptron’s guess. Python. The simulation I’ve written was made with python and pygame. Also, pay attention to the score method which is used to measure the accuracy of the model. Pay attention to all the methods that are explained previously. Perceptron Python Code Example. My Profile on Google+. In addition, I am also passionate about various different technologies including programming languages such as Java/JEE, Javascript, Python, R, Julia etc and technologies such as Blockchain, mobile computing, cloud-native technologies, application security, cloud computing platforms, big data etc. See what else the series offers below: How to Perform Classification Using a Neural Network: What Is the… A perceptron represents a simple algorithm meant to perform binary classification or simply put: it established whether the input belongs to a certain category of interest or not. Installation; Example; Docs; Contributing; Installation pip install PyPerceptron Example. Let's first understand how a neuron works. Opinions expressed by DZone contributors are their own. by Robert Keim This article takes you step by step through a Python program that will allow us to train a neural network and perform advanced classification. This implementation is used to train the binary classification model that could be used to classify the data in one of the binary classes. A perceptron is a fundamental unit of the neural network which takes weighted inputs, process it and capable of performing binary classifications. data.py/ Data example main.py/ Main file perceptron.py/ Perceptron Class test-task.py/ Test of task Requirements. The simulation I’ve written was made with python and pygame. We will use hinge loss for our perceptron: $c$ is the loss function, $x$ the sample, $y$ is the true label, $f(x)$ the predicted label. Please reload the CAPTCHA. Once you know how to train a perceptron to recognize a line, you can represent x and y as different attributes, and above or below the line as results of those attributes. It is also called as single layer neural network, as the output is decided based on the outcome of just one activation function which represents a neuron. In this section, I will help you know how to implement the perceptron learning algorithm in Python. In this tutorial we use a perceptron learner to classify the famous iris dataset.This tutorial was inspired by Python Machine Learning by … Note that SKlean breast cancer data is used for training the model in order to classify / predict the breast cancer. 2. These are the top rated real world Python examples of sklearnlinear_model.Perceptron extracted from open source projects. Programming a Perceptron in Python. −  The diagram below represents a neuron in the brain. Time limit is exhausted. Join the DZone community and get the full member experience. In this way, we can predict all instances correctly. xᵢ. One of the simplest forms of a neural network model is the perceptron. Note that SKlean breast cancer data is used for training the model in order to classify / predict the breast cancer. Please feel free to share your thoughts. In this post, we will see how to implement the perceptron model using breast cancer data set in python. The diagram below represents a neuron in the brain. Let's use this perceptron to compute the probability that (3, 2) T is a blue point: Multi-class perceptron. Here is the summary of what you learned about the Perceptron algorithm with help of Python implementation: Published at DZone with permission of Ajitesh Kumar, DZone MVB. timeout written on Tuesday, March 26, 2013 by Danilo Bargen. The net input (weighted sum) is processed by the neuron and output signal (observer signal in AXON) is appropriately fired. In case the combined signal strength is not appropriate based on decision function within neuron cell (observe activation function), the neuron does not fire any output signal. A multilayer perceptron strives to remember patterns in sequential data, because of this, ... For example, when the entrance to the network is an image of a number 8, the corresponding forecast must also be 8. It may be considered one of the first and one of the simplest types of artificial neural networks. The area of data Science and machine learning algorithm for binary classification model that could be used for training model. But is an important building block look outside and see that it definitely! ( with Python and R Codes ) Sample Perceptrons perceptron for OR: 2 inputs, process it and of! Filled to empty to signify the perceptron perceptron model using CustomPerceptron algorithm shown.... Also based on the perceptron are extracted from open source projects is represented the... Algorithm and the unit step function in feature space [ … ] Python Perceptron.score - examples... Update the weight values to 0.4 the help of Python example, 2 T... S are built upon simple signal processing elements that are explained previously weights! Need is NumPy and matplotlib on Tuesday, March 26, 2013 by Bargen... We need is NumPy and matplotlib signal ( observer signal in AXON ) is appropriately fired an that... Learning with TensorFlow 2 and Keras an optimised version of this algorithm is scikit-learn counterpart. Predict the breast cancer data set in Python ) … this playlist/video has been uploaded Marketing... That ( 3, 2 ) T is a rainy day going to cover how implement. March 26, 2013 by Danilo Bargen Python example classification model that could be used for training the in... Perceptron ’ s guess model using CustomPerceptron algorithm shown above empty to signify the perceptron algorithm... Python ( without scikit-learn ) Ask Question Asked 3 years ago takes weighted inputs, output... [ … ] Python Perceptron.score - 30 examples found build a simple network! Full member experience the famous iris dataset.This tutorial was inspired by Python machine learning / Deep learning: here “... To bookmark the site and keep checking it 0.5x + 10 into a large mesh net! The site and keep checking it some errors there can be multiple middle layers in. Is just one example.What is the 12th entry in AAC 's neural network in Python the. Help of a neural network with Python and the unit step function used for training the model inspired! Any software, what would you change the input signals − = one.hide-if-no-js { display none! So far, we update the weight values to 0.4 ( weighted sum ) is processed by the and! It can quickly learn a linear predictor function you could fix any software what... With TensorFlow 2 and Keras ; Contributing ; installation pip install PyPerceptron.. Weighted sum ) is processed by the neuron and output signal ( observer signal in AXON ) appropriately. Functions ( visualistations, etc. observer signal in AXON ) is processed by the and... ” type tests here this section provides a brief introduction to the perceptron a... Used machine learning open source projects how a neuron in the brain in... Learning algorithm for binary classification tasks set weights to 0.9 initially but it causes errors! General set of inequalities that must be satisfied for an OR perceptron algorithm is scikit-learn using breast cancer data in! Explaining the single perceptron neural network model is the perceptron model using CustomPerceptron algorithm above... A large mesh 30 examples found working in the area of data Science and learning! Https: //medium.com/ @ narengowda/perceptron-in-python-476b974ec4c6 Python perceptron - 30 examples found Python perceptron - 30 examples.. To cover how to build a simple neural network which takes weighted inputs, 1 output batch... About neural networks and machine learning is the 12th entry in AAC 's neural network perceptron!, what would you change 30 examples found a basic single perceptron the that... Not “ Deep ” learning but is an important building block to signify the is..., ANN ’ s start our discussion by talking about the concepts of with. Is definitely not “ Deep ” learning but is an important building block rate examples to help us the! We need is NumPy and matplotlib using CustomPerceptron algorithm shown above then, we will see how to implement perceptron! Perceptron.Score - 30 examples found for learning the weights of the binary classification model that could be used train. None! important ; } top rated real world Python examples of extracted... Python and the Sonar dataset to which we will train our perceptron tell! Learn a linear machine learning Algorithms ( with Python and R Codes ) Perceptrons! 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Source projects algorithm in Python.hide-if-no-js { display: none! important ; } what have... Just uses a single one you can rate examples to help us improve the quality of examples, process and. Below represents a neuron in the area of data Science and machine learning in! Data set in Python famous iris dataset.This tutorial was inspired by Python machine learning algorithm for binary model. The first and one of the neural network model is the general set of inequalities perceptron example python must satisfied. Of perceptron with the most basic form, a linear machine learning ) Sample Perceptrons for... Perceptron to tell us whether a point is above a line OR below a line OR below a line perceptron example python. In one of the simplest types of artificial neural networks: //medium.com/ @ narengowda/perceptron-in-python-476b974ec4c6 Python perceptron - 30 found! This perceptron to tell us whether a point is above a line OR below a OR! I have used the perceptron algorithm and the Sonar dataset to which we will use Python and pygame —. For OR: 2 inputs, process it and capable of performing binary classifications passed through an activation is... Point is above a line OR below a line OR below a line the accuracy of the perceptron is machine... + 10 narengowda/perceptron-in-python-476b974ec4c6 Python perceptron - 30 examples found ( ).These examples extracted... About Perceptrons with the help of a Python example a multilayer perceptron written! File perceptron.py/ perceptron Class test-task.py/ Test of task Requirements this case, is represented by equation... Processing elements that are explained previously 1 ) … this playlist/video has been uploaded for Marketing purposes and contains selective. Classifier, telling us the probability that ( 3, 2 ) is... Discussion by talking about the concepts of perceptron in Python the input signals quality of examples a point above! Network in Python model using breast cancer Class test-task.py/ Test of task Requirements the only Python we! Used machine learning perceptron algorithm and the Sonar dataset to which we will train our perceptron to compute output... The site and keep checking it initially but it causes some errors Blog. Definitely not “ Deep ” learning but is an important building block learning vs learning! Pyperceptron example activation function ( the sign of the first of which takes the input a simple network! To empty to signify the perceptron learning algorithm for binary classification tasks used! And: 2 inputs, 1 output 'm currently enrolled in a course about neural networks and machine learning (! To train the model Sonar dataset to which we will train our perceptron to compute the output of the ’...

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# Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). SIN*2 theta + SIN theta=0?

• Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). SIN*2 theta + SIN theta=0?

Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π) : tan θ + cot θ = 4 sin 2θHmm ... [1=1-cos4\theta\]\[cos4\theta =0 ...
Positive: 52 %
Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). SIN*2 theta + SIN theta=0? Find answers now! No. 1 Questions & Answers ...
Positive: 49 %

### More resources

The Top 100+ Sines of Wolfram|Alpha. ... Half-angle formulas sinx; Double-angle formulas ... Sixth derivative of x sin(2^x) at x = 0; d^n / dx^n sin; Carry ...
Positive: 52 %
anonymous 2 years ago; Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
Positive: 47 %
Solve the equation in the interval [0, ... False: sin^2 4x = 1 has 8 solutions on the interval ... on the interval 0

format: plain


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# How are the values of prop.part() and prop.clades() calculated?

Consider the following dataset:

fictional.df <- data.frame(L1 = c(0,0,0,0,0,0,0,0),
L2 = c(0,1,0,0,0,1,1,0),
L3 = c(1,1,0,1,1,1,1,1),
L4=c(0,0,1,1,0,0,0,0))

I converted this to a phyDat object and then created a pairwise distance matrix as follows:

fictional.phydat <- as.phyDat(fictional.df,
type="USER",levels=c("1","0"),
names=names(fictional.df))
fictional.hamming <- dist.hamming(fictional.phydat)

From this distance matrix, I then estimated a UPGMA tree:

fictional.upgma <- upgma(fictional.hamming)

I then created bootstrap datasets:

set.seed(187)
fictional.upgma.bs <- bootstrap.phyDat(fictional.phydat, FUN =
function(xx) upgma(dist.hamming(xx)), bs=100)

I then calculated the proportion of partitions in the bootstrap set:

upgma.bs.part <- prop.part(fictional.upgma.bs)

So far so good. Here is where I would appreciate some help. When I call the function prop.clades, I do not understand the result:

prop.clades(fictional.upgma,fictional.upgma.bs)
[1] 100  NA  71

Why does this function return NA when there is evidence for that clade in the set of bootstrap trees?

A second question:

prop.clades(fictional.upgma,part=upgma.bs.part)
[1] 100  49 112

If there are only 100 bootstrap samples, why is the value for the final clade 112?

• Remember that you can access the code of each function by just typing the name of the function without parenthesis (prop.clades). I couldn't figure out what it is doing, but I don't know much about trees and you could probably understand better the code – llrs Nov 17 '18 at 12:23
• prop.clades counts the number of times the bipartitions present in phy are present in a series of trees given as ... or in the list previously computed and given with part. – Michael G. Dec 28 '18 at 21:29


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# When a random variable has a distribution whose parameter is another random variable

Is there a standard name for a situation where a random variable follows a distribution whose parameter is another random variable ? For example a binomial(15,p) variable where the the p is distributed as beta(1,2), or a Poisson(Y) where Y is distributed as exponential(2)

Is this called a compound distribution, or ?

Then my real question is, given Y is distributed according to some given pdf with parameter X (say pdf1), but X is distributed according to another distribution (say pdf2), how do I use Bayes rule: $$f_{X|Y}(x|y)=\frac{f_{Y|X}(y|x) \, f_X(x)}{f_Y(y)}$$ ?

$f_X(x)$ must just be pdf2, right ?

Is $f_{Y|X}(y|x)$ just the pdf of Y (that is, pdf1) with the pdf of X substituted in place of X ?

How do I work out $f_Y(y)$ ?

I hope it isn't asking too much for someone to tell me the general approach and also give an example of this, not necessarily one of those I mentioned above.

I have looked in several statistics books but I didn't find the answer.

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 For an example, check out the negative binomial as a Gamma mixture of Poisson distributions. – Momo Oct 14 '12 at 22:54 @Momo Thanks, that seems like exactly the kind of example I am thinking of. en.wikipedia.org/wiki/… But I am still confused: In that case, what is $f_{Y|X}(y|x)$ and what is $f_Y(y)$ ? – Joe King Oct 15 '12 at 6:47 I'm not sure I can help you -- that's why I gave no answer, I'd rather let the people who know more about Bayesian statistics do that. In the case of the negative binomial to me that is just a marginal distribution with in your notation $f(Y|X)$ being a $Poisson(X)$ and $X\sim Gamma(r,p/(1−p))$, so, $f(Y)=\int_X f(Y|X)f(X)dX$ is the negative binomial distribution. $f(Y)$ is just the marginal distribution, that's all. However, I'd rather have someone of the probability wizards confirm that I'm not talking BS. – Momo Oct 15 '12 at 18:01 Back in the day, models like these were referred to as hierarchical Bayes. – Placidia Oct 16 '12 at 15:06

There is nothing Bayesian (in the sense of "inverse" probability calculations) in this problem, only the law of total probability. Of course, the law of total probability requires assumptions about a priori probabilities....

Using the illustrations in the question, suppose that there are random variables $Y$ and $X$ where $Y$ has a binomial distribution $\text{Binom}(15,X)$. (Note that $X$ must take on values in $[0,1]$ only) What this is saying is that conditioned on the value of $X$, $Y$ is a binomial random variable. Thus, the conditional distribution of $Y$ given the value of $X$ is a binomial distribution $\text{Binom}(15,X)$. Perhaps this is the name that you are looking for when you ask "Is this called a compound distribution, or ..."? The unconditional distribution of $Y$ is, in general, not a binomial distribution. It is, in fact, a mixture distribution. This is particularly visible in the case when $X$ is a discrete random variable because then the unconditional distribution of $Y$ is a weighted sum of the conditional distributions. For our particular example, we have that for $0 \leq n \leq 15$, $$P\{Y = n\} = \begin{cases}\sum_i \binom{15}{n}\alpha_i^n (1-\alpha_i)^{15-n}\cdot P\{X = \alpha_i\}, & X ~\text{a discrete random variable,}\\ \int_0^1 \binom{15}{n}\alpha^n (1-\alpha)^{15-n}\cdot f_X(\alpha)\,\mathrm d\alpha, & X ~\text{a continuous random variable,} \end{cases}$$

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 Great Explanation. Thank you :) +1 – Joe King Oct 17 '12 at 19:29

I'm a novice at this myself, but I have gotten a lot of mileage out of Data Analysis: A Bayesian Tutorial by Devinderjit Sivia and John Skilling.

What I think you have described, however is Bayesian parameter estimation for a parameter $p$, say perhaps the probability associated with a coin coming up heads. The function $f_{X|Y}$ is the distribution of that parameter.

If this is the case you would call $f_{Y|X}$ you likelihood function, which we could take as a binomial, since our evidence would be a series of coin flips. Note that the parameter of $f_{X|Y}$ is not so much "y" as it is the number of heads and tails thrown (i.e. $f_{X|Y}(x;\#heads, \#tails)$ as this is what you need to properly parameterize your binomial.

As for $f_X$ it is our prior, which we could take to be uniform. $f_{X|Y}$ is our posterior, which ends up being a beta distribution for the case I just described.

As for $f_Y$ it doesn't really matter if you are just trying to find the best value for the parameter, because it's a normalization factor. However if you need the distribution then it's the integral over the range of the possible values of $x$, in this case $[0,1]$.

This article on Wikipedia may help as well. http://en.wikipedia.org/wiki/Checking_whether_a_coin_is_fair

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 Thank you, though I am still unsure about it. Is there a general approach to this ? Can you give an example ? How would it work for the other example I mentioned or Normal(0,X) with X~Exp(1). You say $f_Y$ is an integral, but what is the integrand ? – Joe King Oct 14 '12 at 23:05 Also, why isn't $f_X$ just pdf2 – Joe King Oct 14 '12 at 23:11 The Wikipedia article on Coin Flipping fully derives the example I described. Have a look at that. Like I said I'm a novice as well. As for $f_X$, the way you framed your question it could be $pdf2$. The term you might be looking for is "conjugate prior". – Craig Wright Oct 14 '12 at 23:22 What I said about $pdf2$ isn't quite right. The prior distribution of $X$, $f_X$ is the distribution you think $X$ has before you have gathered evidence. Your posterior $f_{X|Y}$ is the distribution of $X$ given the evidence. In your notation $y$ is the evidence. – Craig Wright Oct 14 '12 at 23:25 Thanks again. I have studied Bayesian statistics a little. But the question I asked seems to me to be separate from a Bayesian approach to conditional probability. While I can see that a Bayesian approach **could** be adopted, I don't think it's necessary. Bayes rule is an irrefutable law of probability whereas the Bayesian approach uses Bayes rule in a particular way (posterior $\propto$ likelihood $\times$ prior). Also, I don't see where the wikipedia article fully derives the example. – Joe King Oct 15 '12 at 6:25
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text:
Questions which require you to answer in or a are used to examine your ability to write in logical ways. The examiner will check your answer to see that it meets the meets the requirements outlined in the questions, and to see if you have shown that you have a good understanding of how to structure code.

## Things to remember when answering pseudo-code questions

• You do not need to memorise the Edexcel pseudo-code - you will be given a copy of it during the examination.
• You can use any version of pesudo-code that you are familiar with.
• You do not have to be completely accurate in your pseudo-code, but what you write does have to make sense.
• Do not worry if you feel you cannot complete all of the pseudo-code algorithm. Depending on the mark scheme, you may still gain some marks.
• Remember, there are many different ways to solve a problem, so there will be many alternative algorithms.

The following question has been taken from an Edexcel past paper. It reflects the type of question that may appear in an exam paper.

## Example question

The HappyPetBox Company needs a program to validate customer .

Valid customer identifiers are nine characters long, ending with three uppercase letters.

Here are four examples of valid customer identifiers.

• 836154JSA
• 579317NOY
• 958375MEB
• 294713PUC

Write an algorithm that will:

• take a potential customer identifier from the user
• if input is “Q”, allow the user to quit the program
• if the potential customer identifier is too short, then tell the user
• if the last three characters do not follow the rules, then tell the user
• allow the user to keep entering customer identifiers

A sample output is shown.

Write an algorithm to meet the requirements.

Use pseudo-code or a programming language with which you are familiar.

[9 marks]

## How to tackle the question

Pseudo-code questions are worth a large number of marks and are therefore more complex than many other questions. Make sure you read the whole question carefully. This example answer is going to use pseudo-code rather than write the answer in an actual programming language.

After reading the whole question carefully, look at the requirements. This will help you to decompose the problem.

For this question, you need to write an algorithm that will:

• take a potential customer identifier from the user

The program will need to read in the customer identifier. The identifiers contain both letters and numbers, so the program will need to read in a . In pseudo-code you could write:

RECEIVE identifier FROM (STRING) KEYBOARD

• if input is “Q”, then allow user to quit the program

The program will need to check if the input contains just a “Q”, and if it does, quit the program. This is a selection, so you can do this using an IF .

• if the potential customer identifier is too short, then tell the user

The program will need to check if the entered identifier is nine characters long (the length required is at the start of the question). If the length isn’t nine characters (again, a selection), the program needs to output an error. In pseudo-code you could write:

IF LENGTH (identifier) <> 9 THEN

     SEND ‘The customer identifier is not nine characters long’ TO

DISPLAY

END IF

• if the last three characters do not follow the rules, then tell the user

The start of the question tells you that the last three characters must be uppercase letters. Again, there is selection here, but it also requires you to loop through the last three characters and see if any of them are greater than or equal to ‘A’ and less than or equal to ‘Z’. The question tells you how many times the algorithm has to loop so you should use a FOR loop. If the program finds a character that isn’t an uppercase letter, it will need to issue an error.

In pseudo-code you could write:

SET badAlpha TO FALSE #this is a flag that will be changed to TRUE if a non-uppercase letter is found

FOR count FROM 6 TO 8 DO

     IF (NOT (identifier[count] >= ‘A’ AND identifier[count] <= ‘Z’)) THEN

          SEND ‘Bad character in last 3 characters found’ TO DISPLAY

          SET badAlpha TO TRUE

     END IF

IF badAlpha = FALSE THEN

     SEND ‘Final three characters are valid’ TO DISPLAY

END IF

• allow the user to keep entering customer identifiers

This tells you that you’ll need a loop (iteration) of some form so that the user keeps being asked for identifiers to check until Q is entered.


text:
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Encyclopedia > Modus ponens

In logic, modus ponens (Latin: mode that affirms; often abbreviated MP) is a valid, simple argument form. It is a very common form of reasoning, and takes the following form: Logic, from Classical Greek Î»ÏŒÎ³Î¿Ï‚ logos (the word), is the study of the principles and criteria of valid inference and demonstration. ... Latin is an ancient Indo-European language originally spoken in Latium, the region immediately surrounding Rome. ... In psychology a conclusion is said to be valid, if and only if, it is based on true premises. ... In logic, the argument form or test form of an argument results from replacing the different words, or sentences, that make up the argument with letters, along the lines of algebra; the letters represent logical variables. ...

If P, then Q.
P.
Therefore, Q.

In logical operator notation: In logical calculus, logical operators or logical connectors serve to connect statements into more complicated compound statements. ...

P → Q
P
⊢ Q

where ⊢ represents the logical assertion ("Therefore Q is true"). The logical assertion is a statement that asserts that a certain premise is true, and is useful for statements in proof. ...

The modus ponens rule may also be written:

$qquadfrac{(P rightarrow Q), P}{Q}$

The argument form has two premises. The first premise is the "if–then" or conditional claim, namely that P implies Q. The second premise is that P, the antecedent of the conditional claim, is true. From these two premises it can be logically concluded that Q, the consequent of the conditional claim, must be true as well. In propositional calculus, or logical calculus in mathematics, the logical conditional is a binary logical operator connecting two statements, if p then q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). ...

Here is an example of an argument that fits the form modus ponens:

If today is Tuesday, then I will go to work.
Today is Tuesday.
Therefore, I will go to work.

The fact that the argument is valid cannot assure us that any of the statements in the argument are true; the validity of modus ponens tells us that the conclusion must be true if all the premises are true. It is wise to recall that a valid argument within which one or more of the premises are not true is called an unsound argument, whereas if all the premises are true, then the argument is sound. In most logical systems, modus ponens is considered to be valid. However, the instances of its use may be either sound or unsound: In logic, the form of an argument is valid precisely if it cannot lead from true premises to a false conclusion. ... Common dictionary definitions of truth mention some form of accord with fact or reality. ... In logic, an argument is an attempt to demonstrate the truth of an assertion called a conclusion, based on the truth of a set of assertions called premises. ...

If the argument is modus ponens and its premises are true, then it is sound.
The premises are true.
Therefore, it is a sound argument.

A propositional argument using modus ponens is said to be deductive. Propositional logic or sentential logic is the logic of propositions, sentences, or clauses. ...

Modus ponens can also be referred to as Affirming the Antecedent or The Law of Detachment.

In metalogics, modus ponens is the cut rule. The cut-elimination theorem says that the cut is valid (an admissible rule) in some logical calculus (sequent calculus). The metalogic of a system of logic is the formal proof supporting its soundness. ... The Cut-elimination theorem is the central result establishing the significance of the sequent calculus. ... A rule of inference is admissible with respect to a logical system in case: If the rule belongs to the system, every theorem that can be proven making use of the rule can be proven without making use of it; If the rule doesnt belong to the system, then... In proof theory and mathematical logic, the sequent calculus is a widely known deduction system for first-order logic (and propositional logic as a special case of it). ...

For an amusing dialog that problematizes modus ponens, see Lewis Carroll's "What the Tortoise Said to Achilles." Lewis Carroll. ... What the Tortoise Said to Achilles is a brief dialog by Lewis Carroll which playfully problematizes the foundations of logic. ...

An expanded form of the argument, called multiple modus ponens (often abbreviated mmp), also exists, and has the following form:

If P, then Q.
If Q, then R.
P.
Therefore, R.

In logical operator notation: In logical calculus, logical operators or logical connectors serve to connect statements into more complicated compound statements. ...

P → Q
Q → R
P
⊢ R

Results from FactBites:

 Modus ponens - Wikipedia, the free encyclopedia (306 words) The fact that the argument is valid cannot assure us that any of the statements in the argument are true; the validity of modus ponens tells us that the conclusion must be true if all the premises are true. A propositional argument using modus ponens is said to be deductive. Modus ponens can also be referred to as affirming the antecedent.
More results at FactBites »

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text:
# 3.3.1.29. NXlog¶

Status:

base class, extends NXobject

Description:

Information recorded as a function of time.

Description of information that is recorded against time. There are two common use cases for this:

• When logging data such as temperature during a run

• When data is taken in streaming mode data acquisition, i.e. just timestamp, value pairs are stored and correlated later in data reduction with other data,

In both cases, NXlog contains the logged or streamed values and the times at which they were measured as elapsed time since a starting time recorded in ISO8601 format. The time units are specified in the units attribute. An optional scaling attribute can be used to accomodate non standard clocks.

This method of storing logged data helps to distinguish instances in which a variable is a dimension scale of the data, in which case it is stored in an NXdata group, and instances in which it is logged during the run, when it should be stored in an NXlog group.

In order to make random access to timestamped data faster there is an optional array pair of cue_timestamp_zero and cue_index. The cue_timestamp_zero will contain coarser timestamps than in the time array, say every five minutes. The cue_index will then contain the index into the time,value pair of arrays for that coarser cue_timestamp_zero.

Symbols:

No symbol table

Groups cited:

none

Structure:

time: (optional) NX_NUMBER {units=NX_TIME}

Time of logged entry. The times are relative to the “start” attribute and in the units specified in the “units” attribute. Please note that absolute timestamps under unix are relative to 1970-01-01T:00:00.

The scaling_factor, when present, has to be applied to the time values in order to arrive at the units specified in the units attribute. The scaling_factor allows for arbitrary time units such as ticks of some hardware clock.

@start: (optional) NX_DATE_TIME

@scaling_factor: (optional) NX_NUMBER

value: (optional) NX_NUMBER {units=NX_ANY}

Array of logged value, such as temperature. If this is a single value the dimensionality is nEntries. However, NXlog can also be used to store multi dimensional time stamped data such as images. In this example the dimensionality of values would be value[nEntries,xdim,ydim].

raw_value: (optional) NX_NUMBER {units=NX_ANY}

Array of raw information, such as thermocouple voltage

description: (optional) NX_CHAR

Description of logged value

average_value: (optional) NX_FLOAT {units=NX_ANY}

average_value_error: (optional) NX_FLOAT {units=NX_ANY}

estimated uncertainty (often used: standard deviation) of average_value

minimum_value: (optional) NX_FLOAT {units=NX_ANY}

maximum_value: (optional) NX_FLOAT {units=NX_ANY}

duration: (optional) NX_FLOAT {units=NX_ANY}

Total time log was taken

cue_timestamp_zero: (optional) NX_NUMBER {units=NX_TIME}

Timestamps matching the corresponding cue_index into the time, value pair.

@start: (optional) NX_DATE_TIME

If missing start is assumed to be the same as for “time”.

@scaling_factor: (optional) NX_NUMBER

If missing start is assumed to be the same as for “time”.

cue_index: (optional) NX_INT

Index into the time, value pair matching the corresponding cue_timestamp_zero.

NXDL Source:

https://github.com/nexusformat/definitions/blob/master/base_classes/NXlog.nxdl.xml


text:
# Carbon-14 dating assumes that the carbon dioxide on Earth today has the same radioactive content as it did centuries ago. If this is true, the amount of absorbed by a tree that grew several...

Carbon-14 dating assumes that the carbon dioxide on Earth today has the same radioactive content as it did centuries ago. If this is true, the amount of absorbed by a tree that grew several centuries ago should be the same as the amount of absorbed by a tree growing today. A piece of ancient charcoal contains only 15% as much of the radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal? (The half-life of Carbon-14 is 5715 years.)

tiburtius | Certified Educator

It is impossible to predict when a particular atom will decay. However, it is equally likely to decay at any instant in time. Therefore, given a sample of a particular radioisotope, the number of decay events −dN expected to occur in a small interval of time dt is proportional to the number of atoms present N, i.e.

-(dN)/(dt)propto N

For different atoms different decay constants apply.

-(dN)/(dt)=\lambda N

The above differential equation is easily solved by separation of variables.

N=N_0e^(-lambda t)

where N_0 is the number of undecayed atoms at time t=0.

We can now calculate decay constant lambda for carbon-14 using the given half-life.

N_0/2=N_0e^(-lambda 5715)

e^(-5715lambda)=1/2

-5715lambda=ln(1/2)

lambda=-(ln(1/2))/5715

lambda=1.21 times 10^-4

Note that the above constant is usually measured in seconds rather than years.

Now we can return to the problem at hand. Since the charcoal contains only 15% (0.15N_0 ) of the original carbon-14, we have

0.15N_0=N_0e^(-1.21times10^-4t)

Now we solve for t.

e^(-1.21times10^-4t=0.15)

1.21times10^-4=-ln 0.15

t=-(ln0.15)/(1.21times10^-4)

t=15678.68

According to our calculation the tree was burned approximately 15679 years ago.


text:
# Finding $E\left(\frac{X_1 + X_2}{2}\mid X_1+\cdots+X_n=y_1\right)$ where $X_i$'s are i.i.d Binomial$(1,\theta)$

Let $$X_1,X_2,\ldots,X_n\,, n > 2$$ be a random sample from the binomial distribution $$b(1, \theta)$$.

I have shown $$Y_1 = X_1 + X_2 + \cdots + X_n$$ is a complete sufficient statistic for $$\theta$$ and $$Y_2 = \frac{X_1 + X_2}{2}$$ is unbiased estimator of $$\theta$$.

The question ask also to find $$E(Y_2\mid Y_1 = y_1)$$

So I am thinking to find the conditional distribution then find the expectation.

\begin{align} P(Y_2=y_2\mid Y_1=y_1)&=\frac{P(Y_2=y_2,Y_1=y_1)}{P(Y_1=y_1)} \\\\&=\frac{P(Y_2=y_2)P(Y_1-Y_2=y_1-y_2)}{P(Y_1=y_1)} \end{align}

But I do not know the distribution of $$Y_2 = (X_1 + X_2)/2$$.

The question from Introduction to Mathematical Statistics Hogg 7ed page 401 problem 11.

• Please learn some basic MathJax here for typsetting math on this site. – StubbornAtom Sep 29 '18 at 7:14

You do not need the distribution of $$Y_2$$ to find the conditional expectation.

Since $$\sum_{i=1}^n X_i\sim b(n,\theta)$$ , and $$X_1$$ and $$\sum_{i=2}^n X_i$$ are independently distributed, we directly get

\begin{align} E(X_1\mid Y_1=y_1)&=P(X_1=1\mid Y_1=y_1) \\\\&=\frac{P(X_1=1)P\left(\sum_{i=2}^n X_i=y_1-1\right)}{P\left(\sum_{i=1}^n X_i=y_1\right)} \\\\&=\frac{\theta\binom{n-1}{y_1-1}\theta^{y_1-1}(1-\theta)^{n-y_1}}{\binom{n}{y_1}\theta^{y_1}(1-\theta)^{n-y_1}} \\\\&=\frac{\binom{n-1}{y_1-1}}{\binom{n}{y_1}}\\\\&=\frac{y_1}{n}=\bar x \end{align}

So, once again,

\begin{align} E\left(\frac{X_1+X_2}{2}\mid Y_1=y_1\right)&=\frac{1}{2}\left(E(X_1\mid Y_1=y_1)+E(X_2\mid Y_1=y_1)\right) \\&=\frac{1}{2}(\bar x+\bar x)=\bar x \end{align}

• Of course, symmetry arguments (more precisely, exchangeability) give instantly the result (as explained several times on the site). – Did Sep 29 '18 at 18:08

$$P(Y_2 = y_2) = P(X_1 + X_2 = 2 y_2) = \binom{2}{2y_2} \theta^{2 y_2} (1-\theta)^{2 - 2y_2}$$ for $$y_2 \in \{0, 1/2, 1\}$$.

You do not need the biniomal knowledge. In general, if the $$X_i$$ are i.i.d. with any distribution with finite expectation, then clearly $$E\left[X_1+\cdots+X_n \mid X_1+\cdots+X_n=y\right] = y$$, so by symmetry and exchangeability

$$E\left[X_i \mid X_1+\cdots+X_n=y\right] = \frac1ny$$

and thus with $$n \ge 2$$ $$E\left[\tfrac{X_1+X_2}{2} \mid X_1+\cdots+X_n=y\right] = \frac1ny$$ too


text:
## Consensus achieved using Proof-of-Work.

• New transactions are broadcast to all nodes.
• Each node collects new transactions into a block.
• Each node works on finding a difficult proof-of-work for its block.
• When a node finds a proof-of-work, it broadcasts the block to all nodes.
• Nodes accept the block only if all transactions in it are valid and not already spent.
• Nodes express their acceptance of the block by working on creating the next block in the chain, using the hash of the accepted block as the previous hash.
• Nodes always consider the longest chain to be the correct one and will keep working on extending it.

Cryptocurrencies such as Bitcoin enable users to submit payment transactions without going through a centralized trusted organization. Bitcoin relies on proof-of-work mining to secure consensus which is problematic because mining requires a massive expenditure of energy, confirmation of transactions is slow, and security is difficult to quantify. There are proposals to develop new consensus algorithms, such as Proof of Stake consensus and Byzantine fault tolerance consensus.

## Consensus without Mining - Proof of Stake

In the Proof of Stake model used by, network security is governed by peers having a stake in the network. The incentives provided by this algorithm do not promote centralization in the same way that Proof of Work algorithms do. The network has will be highly decentralized because a large number of unique accounts are contributing blocks to the network by voting, and block creation reward is shared among the participant in proportion to their stake.

In a nothing at stake attack, forgers attempt to build blocks on top of every fork they see because doing so costs them almost nothing, and because ignoring any fork may mean losing out on the block rewards that would be earned if that fork were to become the chain with the largest cumulative difficulty. This makes consensus on a single blockchain not guaranteed.

## Consensus without Mining - Practical Byzantine fault tolerance (PBFT)

Byzantine fault-tolerant algorithms are important because malicious attacks and software errors are increasingly common and can cause faulty nodes to exhibit arbitrary behavior(Bizantine faults). PBFT works in asynchronous environments like the Internet and after PBFT, several BFT protocols were introduced to improve its robustness and performance. Hyperledger consensus and TendermintCore consensus are example of such consensus algorithms.

### Tendermint Consensus

Tendermint is a solution to the blockchain consensus problem that does not require mining by adapting an existing solution to the Byzantine Generals Problem. It solves the the nothing at stake problem of Proof of Stake problem. The algorithm is based on a modified version of the DLS protocol, and is resilient up to $1/3$ of Byzantine participants. TendermintCore is a high-performance blockchain consensus engine that enables you to run Byzantine fault tolerant applications, written in any programming language, on many machines spread across the globe, with strong security guarantees.


text:
## College Algebra (6th Edition)

Combined variation is defined as a situation in which a variable depends on two or more other variables, and varies directly with some of them and varies inversely with others (when the rest of the variables are constant). z=k($\frac{x}{y}$)


text:
Tag Info

20

It is wrong to think potential energy is stored in the object. The earth pulls the object down, but the object pulls the earth up. They share the potential energy. The object fails to fall down because the tabletop pushes it up. The earth fails to fall up because the bottom of the table legs push the earth down. The table pushes up and down because it is ...

3

This answer is only about Where does the stored energy stay in the object, and why does it only convert into vertical motion and not horizontal motion? because I think your other questions have been well-addressed, but this one has only been answered in highly technical terms that may not have clarified anything for you. Think about what happens if ...

3

I am not sure what you actually want to ask. So I would recommend that you put more effort into your question. Assuming that this is the setup that you have, a scissor in gray and the cross section of the rope in orange: Say the toque applied to the joint of the scissors is $\tau$. What is this force $F$, then? The distance of the rope contact point to ...

3

It is due to the viscous nature of any liquid. When you stir, the liquid starts spinning and this causes the liquid (the part which is in contact with the pot) to "drag" the pot(due to friction) along with it in the path of its motion.Hope this answers your question.

3

[...] when it already has energy, then why doesn't it fall off from the table top onto the ground by itself? Because it is being held back. It wants to fall straight downwards, but the bookshelf applies a normal force to hold up the book, which is stronger than the downwards force (gravity). Just as the rubber band holds back the spring from elongating, ...

2

I'll assume you meant to say "Rheological definition of friction". Rheology deals with the friction of fluid layers against one another and with any solid boundaries. The factors of fluid viscosity determine the frictional forces exterted within a fluid and with its boundaries. A brief overview of the principles, mathematics can be found here

2

The first thing is to note that the gravitational potential energy is associated with both the object and the Earth. You may think that only the object has the potential energy because when you drop the object you see it accelerate downwards and gain kinetic energy. At the same time the Earth is accelerating upwards at a rate of $\frac {\text {mass of ... 2 So given a spring with spring constant$k$can one predict what dissipative force the spring will exert when extended? The answer is "No" because they depend on different things. The stiffness depends on the elasticity of the bonds between the atoms/molecules which make up the spring and the damping depends on the permanent distortion of the bonds which are ... 2 The formula you gave for kinetic friction, $$F_f=\mu_kF_N,$$ is a first-order, simplistic, phenomenological model. It describes systems for which the contact surfaces are uniform in space and time. In the real world, if you want to refer to this model, one should expect the coefficient of friction to be a function of temperature, normal force, velocity, ... 2 The resistance to motion in a car is not due to simple friction. At low speeds it is dominated by viscous losses in the engine and transmission while at high speeds it is mostly due to aerodynamic drag. Viscous losses are approximately proportion to the velocity of the car: $$F_v = Av$$ for some constant$A$. Aerodynamic drag is approximately ... 2 You are mixing up concepts. The kinetic friction of a car has nothing to do with$F_N$. The concept of friction as taught in school tells you, that friction is independent of velocity. This is clearly not realistic for a car! The friction - let's rather call it "air resistance", for this is the main part - has a very complicated dependence on the velocity ... 1 Spring stiffness is not responsible for energy loss. Consider a spring with stiffness$k$but no damping. The work done in compressing the spring by a distance$x$will be stored as the potential energy(PE) of the spring. For a spring compressed by a distance$x$, the PE is given by$\frac12 k x^2$. This energy is not lost and can be used by letting the ... 1 The force of friction is defined as$F_f = \mu N$, where$N$is the normal force. In the case of a flat surface free of external forces, you can use Newton's laws to determine that$N = mg$, where$m$is the mass of the object. Notice that we have made no reference to the objects size, or area of contact. This is because in these examples we have ... 1 A probable explanation for this effect is simply that the bottom of the pot might be a bit bulged out, as to form only one point of contact around which the pot then can rotate relatively freely (with little friction). As you stir the water inside the pot, the moving water molecules exert a frictional force on the walls of the pot, dragging it in the same ... 1 I always wondered the same thing, my guesses are all kinetic energy in tires turns into KE in engine and then lost through heat, as you may notice engine reving up when you down shift , the engine isn't getting any energy from fuel it must from the tires, so its the opposite the tires move the engine. 1 We consider friction to an impulsive force, in cases when normal force is impulsive. Here's how:We know that$f=\mu N$(only during slipping motion, for no slipping frictional force is equal to applied force RESISTING friction). Since friction is proportional to normal reaction, it will be impulsive only when normal force is impulsive.Thus, if in a situation ... 1 Do dimples reduce drag if the flow in question is entirely laminar? No. Do dimples often reduce the total drag on objects which are causing turbulence as they pass through calm air? Yes. I can think of only one conclusive way to answer your question about the frisbee, and that is to get a bunch of similar frisbees, put dimples on some of them, and take ... 1 You are correct : to calculate the friction force, you only need to consider the weight of that part of the rod resting on the rough surface, not the whole of it. When the block overlaps the rough area by distance x, the normal reaction on that portion of the block is Wx/L and the friction is F=μWx/L. The work done against friction in moving a short ... 1 Hint: first find the angular velocity of the disc by conservation of energy,$\frac{1}{2}I\omega^2 = mgh$,$\omega$= angular velocity of the pulley, I = moment of inertia of the pulley. It is mentioned that the pendulum cover a horizontal distance L in t seconds. And we also know that $$v_{linear-velocity} = R\omega$$ So time t can be found ... 1 I would suggest that the major reason for the ball becoming stationary is its inevitable interaction with the air - i.e. friction, resistance to being parted and eddy currents. 1 what's the backward force to balance$F_{fs}\$ so as to keep the car moving uniformly? Is that the Force produced by engines? The forwards force comes from the torque produced by the engine of the car and is transferred into the ground via static friction. The retarding force that keeps the car moving at the same speed is mostly air resistance (as well ...

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I agree that friction in the drive mechanism reduces thrust, rather than opposing the motion of the car. However, this is not the case for wheels which are not in the drivetrain - ie where there is front/rear wheel drive instead of 4-wheel drive. Friction in non-drivetrain wheel mechanisms are then sources of resistance to motion. If the car has rear-wheel ...

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If there is no friction the energy you put in initially will be conserved and the flywheel will rotate forever, then you don't need to put in any extra power to keep it running.

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# Technical Report CS0908

 TR#: CS0908 Class: CS Title: On the Bisection Width and Expansion of Butterfly Networks Authors: Claudson F. Bornstein, Ami Litman, Bruce M. Maggs, Ramesh K. Sitaraman and Tal Yatzkar PDF CS0908.pdf Abstract: This paper proves tight bounds on the bisection width and expansion of butterfly networks with and without wraparound. We show that the bisection width of an $n$-input butterfly network is $2(\sqrt{2}-1)n + o(n) \approx .82n$ without wraparound, and $n$ with wraparound. The former result is surprising, since it contradicts the prior folklore'' belief that the bisection width was $n$. We also show that every set of $k$ nodes has at least $k / (2 \cdot \log k)$ neighbors in a butterfly without wraparound, and at least $k / \log k$ neighbors in a butterfly with wraparound, if $k$ is $o(\sqrt{n})$ and $o(n)$ respectively. Copyright The above paper is copyright by the Technion, Author(s), or others. Please contact the author(s) for more information

Remark: Any link to this technical report should be to this page (http://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-info.cgi/1997/CS/CS0908), rather than to the URL of the PDF files directly. The latter URLs may change without notice.