This document provides an overview of entropy and conditional entropy in information theory. It begins with examples of encoding variables with different probabilities to minimize the number of bits needed. It then defines entropy as the average number of bits needed to encode events from a probability distribution. Several example distributions are provided, along with their entropies. Finally, it defines conditional entropy as the expected entropy of a variable given knowledge of another variable.
The closed interval method tells us how to find the extreme values of a continuous function defined on a closed, bounded interval: we check the end points and the critical points.
We define what it means for a function to have a maximum or minimum value, and explain the Extreme Value Theorem, which indicates these maxima and minima must be there under certain conditions.
Fermat's Theorem says that at differentiable extreme points, the derivative should be zero, and thus we arrive at a technique for finding extrema: look among the endpoints of the domain of definition and the critical points of the function.
There's also a little digression on Fermat's Last theorem, which is not related to calculus but is a big deal in recent mathematical history.
We define what it means for a function to have a maximum or minimum value, and explain the Extreme Value Theorem, which indicates these maxima and minima must be there under certain conditions.
Fermat's Theorem says that at differentiable extreme points, the derivative should be zero, and thus we arrive at a technique for finding extrema: look among the endpoints of the domain of definition and the critical points of the function.
There's also a little digression on Fermat's Last theorem, which is not related to calculus but is a big deal in recent mathematical history.
The closed interval method tells us how to find the extreme values of a continuous function defined on a closed, bounded interval: we check the end points and the critical points.
We define what it means for a function to have a maximum or minimum value, and explain the Extreme Value Theorem, which indicates these maxima and minima must be there under certain conditions.
Fermat's Theorem says that at differentiable extreme points, the derivative should be zero, and thus we arrive at a technique for finding extrema: look among the endpoints of the domain of definition and the critical points of the function.
There's also a little digression on Fermat's Last theorem, which is not related to calculus but is a big deal in recent mathematical history.
We define what it means for a function to have a maximum or minimum value, and explain the Extreme Value Theorem, which indicates these maxima and minima must be there under certain conditions.
Fermat's Theorem says that at differentiable extreme points, the derivative should be zero, and thus we arrive at a technique for finding extrema: look among the endpoints of the domain of definition and the critical points of the function.
There's also a little digression on Fermat's Last theorem, which is not related to calculus but is a big deal in recent mathematical history.
New Bounds on the Size of Optimal MeshesDon Sheehy
The theory of optimal size meshes gives a method for analyzing the output size (number of simplices) of a Delaunay refinement mesh in terms of the integral of a sizing function over the input domain.
The input points define a maximal such sizing function called the feature size.
This paper presents a way to bound the feature size integral in terms of an easy to compute property of a suitable ordering of the point set.
The key idea is to consider the pacing of an ordered point set, a measure of the rate of change in the feature size as points are added one at a time.
In previous work, Miller et al.\ showed that if an ordered point set has pacing $\phi$, then the number of vertices in an optimal mesh will be $O(\phi^dn)$, where $d$ is the input dimension.
We give a new analysis of this integral showing that the output size is only $\Theta(n + n\log \phi)$.
The new analysis tightens bounds from several previous results and provides matching lower bounds.
Moreover, it precisely characterizes inputs that yield outputs of size $O(n)$.
An introduction to Google's AI Engine, look deeper into Artificial Networks and Machine Learning. Appreciate how our simplest neural network be codified and be used to data analytics.
Multimodal pattern matching algorithms and applicationsXavier Anguera
In this presentation I focus on 3 projects I have been working in the last year. The first one is a novel pattern matching algorithm, based on the well known Dynamic Time Warping. The presented algorithm can be used to find real-valued subsequences within a longer sequence, without prior knowledge of their start-end points. I have applied the algorithm for the task of acoustic matching, for which I will show some preliminary results. Then I will continue to explain a second DTW-based algorithm, this one being able do an online of two musical pieces. One of the music pieces can be input life or be retrieved from an audio file, while the second one is extracted from an online music video. The online alignment allows for the music video to be played in total synchrony with the corresponding ambient/recorded audio. Finally, I will talk about video copy detection, which is the task of finding video duplicate segments within a big database. I will explain our multimodal approach, based on audio-visual change-based features.
Time Machine session @ ICME 2012 - DTW's New YouthXavier Anguera
This presentation are the slides I gave at the Time Machine Expert session of ICME 2012. It talks about the renewal of Dynamic Time Warping (DTW) as a feasible algorithm for some of today's applications.
Intro to Deep Learning, TensorFlow, and tensorflow.jsOswald Campesato
This fast-paced session introduces Deep Learning concepts, such gradient descent, back propagation, activation functions, and CNNs. We'll look at creating Android apps with TensorFlow Lite (pending its availability). Basic knowledge of vectors, matrices, and Android, as well as elementary calculus (derivatives), are strongly recommended in order to derive the maximum benefit from this session.
A fast-paced introduction to Deep Learning concepts, such as activation functions, cost functions, back propagation, followed by some TensorFlow features, and then a code sample of training a CNN in tensorflow.js. Basic knowledge of vectors, matrices, and derivatives is helpful in order to derive the maximum benefit from this session.
A fast-paced introduction to Deep Learning (DL) concepts, starting with a simple yet complete neural network (no frameworks), followed by aspects of deep neural networks, such as back propagation, activation functions, CNNs, and the AUT theorem. Next, a quick introduction to TensorFlow and TensorBoard, along with some code samples with TensorFlow. For best results, familiarity with basic vectors and matrices, inner (aka "dot") products of vectors, the notion of a derivative, and rudimentary Python is recommended.
A fast-paced introduction to Deep Learning concepts, such as activation functions, cost functions, back propagation, followed by some TensorFlow features, and then a code sample of training a CNN in tensorflow.js. Basic knowledge of vectors, matrices, and derivatives is helpful in order to derive the maximum benefit from this session.
Continuous function have an important property that small changes in input do not produce large changes in output. The Intermediate Value Theorem shows that a continuous function takes all values between any two values. From this we know that your height and weight were once the same, and right now there are two points on opposite sides of the world with the same temperature!
Lesson 18: Maximum and Minimum Values (Section 021 slides)Matthew Leingang
There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
New Bounds on the Size of Optimal MeshesDon Sheehy
The theory of optimal size meshes gives a method for analyzing the output size (number of simplices) of a Delaunay refinement mesh in terms of the integral of a sizing function over the input domain.
The input points define a maximal such sizing function called the feature size.
This paper presents a way to bound the feature size integral in terms of an easy to compute property of a suitable ordering of the point set.
The key idea is to consider the pacing of an ordered point set, a measure of the rate of change in the feature size as points are added one at a time.
In previous work, Miller et al.\ showed that if an ordered point set has pacing $\phi$, then the number of vertices in an optimal mesh will be $O(\phi^dn)$, where $d$ is the input dimension.
We give a new analysis of this integral showing that the output size is only $\Theta(n + n\log \phi)$.
The new analysis tightens bounds from several previous results and provides matching lower bounds.
Moreover, it precisely characterizes inputs that yield outputs of size $O(n)$.
An introduction to Google's AI Engine, look deeper into Artificial Networks and Machine Learning. Appreciate how our simplest neural network be codified and be used to data analytics.
Multimodal pattern matching algorithms and applicationsXavier Anguera
In this presentation I focus on 3 projects I have been working in the last year. The first one is a novel pattern matching algorithm, based on the well known Dynamic Time Warping. The presented algorithm can be used to find real-valued subsequences within a longer sequence, without prior knowledge of their start-end points. I have applied the algorithm for the task of acoustic matching, for which I will show some preliminary results. Then I will continue to explain a second DTW-based algorithm, this one being able do an online of two musical pieces. One of the music pieces can be input life or be retrieved from an audio file, while the second one is extracted from an online music video. The online alignment allows for the music video to be played in total synchrony with the corresponding ambient/recorded audio. Finally, I will talk about video copy detection, which is the task of finding video duplicate segments within a big database. I will explain our multimodal approach, based on audio-visual change-based features.
Time Machine session @ ICME 2012 - DTW's New YouthXavier Anguera
This presentation are the slides I gave at the Time Machine Expert session of ICME 2012. It talks about the renewal of Dynamic Time Warping (DTW) as a feasible algorithm for some of today's applications.
Intro to Deep Learning, TensorFlow, and tensorflow.jsOswald Campesato
This fast-paced session introduces Deep Learning concepts, such gradient descent, back propagation, activation functions, and CNNs. We'll look at creating Android apps with TensorFlow Lite (pending its availability). Basic knowledge of vectors, matrices, and Android, as well as elementary calculus (derivatives), are strongly recommended in order to derive the maximum benefit from this session.
A fast-paced introduction to Deep Learning concepts, such as activation functions, cost functions, back propagation, followed by some TensorFlow features, and then a code sample of training a CNN in tensorflow.js. Basic knowledge of vectors, matrices, and derivatives is helpful in order to derive the maximum benefit from this session.
A fast-paced introduction to Deep Learning (DL) concepts, starting with a simple yet complete neural network (no frameworks), followed by aspects of deep neural networks, such as back propagation, activation functions, CNNs, and the AUT theorem. Next, a quick introduction to TensorFlow and TensorBoard, along with some code samples with TensorFlow. For best results, familiarity with basic vectors and matrices, inner (aka "dot") products of vectors, the notion of a derivative, and rudimentary Python is recommended.
A fast-paced introduction to Deep Learning concepts, such as activation functions, cost functions, back propagation, followed by some TensorFlow features, and then a code sample of training a CNN in tensorflow.js. Basic knowledge of vectors, matrices, and derivatives is helpful in order to derive the maximum benefit from this session.
Continuous function have an important property that small changes in input do not produce large changes in output. The Intermediate Value Theorem shows that a continuous function takes all values between any two values. From this we know that your height and weight were once the same, and right now there are two points on opposite sides of the world with the same temperature!
Lesson 18: Maximum and Minimum Values (Section 021 slides)Matthew Leingang
There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
Detail Description about Probability Distribution for Dummies. The contents are about random variables, its types(Discrete and Continuous) , it's distribution (Discrete probability distribution and probability density function), Expected value, Binomial, Poisson and Normal Distribution usage and solved example for each topic.
This presentation enables users to understand basics of Information Theory, Entropy, Binary channels, channel capacity and error condition in easy and detailed manner. Concepts are explained properly using derivations and examples.
The presentation gives basic insight into Information Theory, Entropies, various binary channels, and error conditions. It explains principles, derivations and problems in very easy and detailed manner with examples.
I am Joe M. I am an Excel Homework Expert at excelhomeworkhelp.com. I hold a Master's in Statistics, from the Gold Coast, Australia. I have been helping students with their homework for the past 6 years. I solve homework related to Excel.
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I am Joe M. I am a Statistics Homework Expert at statisticshomeworkhelper.com. I hold a Master's in Statistics, from the Gold Coast, Australia. I have been helping students with their homework for the past 6 years. I solve homework related to Statistics.
Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com.You can also call on +1 678 648 4277 for any assistance with Statistics Homework.
I am Josh U. I am a Probabilistic Systems Exam Helper at statisticsexamhelp.com. I hold a Masters' Degree in Statistics, from the University of Southampton, UK. I have been helping students with their exams for the past 5 years. You can hire me to take your exam in Probabilistic Systems.
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Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
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Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
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June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
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The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
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• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
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A Strategic Approach: GenAI in EducationPeter Windle
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Macroeconomics- Movie Location
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