The entropic vector or entropic function is a concept arising in information theory. It represents the possible values of Shannon's information entropy that subsets of one set of random variables may take. Understanding which vectors are entropic is a way to represent all possible inequalities between entropies of various subsets. For example, for any two random variables , their joint entropy (the entropy of the random variable representing the pair ) is at most the sum of the entropies of and of : Other information-theoretic measures such as conditional information, mutual information, or total correlation can be expressed in terms of joint entropy and are thus related by the corresponding inequalities.Many inequalities satisfied by entropic vectors can be derived as linear combinations of a few basic ones, called Shannon-type inequalities.However, it has been proven that already for variables, no finite set of linear inequalities is sufficient to characterize all entropic vectors. (Wikipedia).
This shows an small game that illustrates the concept of a vector. The clip is from the book "Immersive Linear Algebra" at http://www.immersivemath.com
From playlist Chapter 2 - Vectors
Vector Calculus 1: What Is a Vector?
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Vector Calculus
What is a vector? We gently introduce the i and j basis vectors and the idea of a column vector is presented. The algebra of addition, subtraction and scalar multiplication is discussed. Free ebook Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Take a sh
From playlist Introduction to Vectors
A short refresher on vectors. Before I introduce vector-based functions, it's important to look at vectors themselves and how they are represented in python™ and the IPython Notebook using SymPy.
From playlist Life Science Math: Vectors
This shows an interactive illustration that shows vector subtraction. The clip is from the book "Immersive Linear Algebra" at http://www.immersivemath.com.
From playlist Chapter 2 - Vectors
Nexus trimester - Tarik Kaced (Université de Paris-Est, LACL, UPEC)
Dual Information Inequalities Tarik Kaced (Université de Paris-Est, LACL, UPEC) february 24, 2016 Abstract: The duality for entropic matroids and polymatroids is discussed under the lens of information inequalities. We define the dual of an information inequality and ask whether the new d
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Radek Adamczak: Functional inequalities and concentration of measure III
Concentration inequalities are one of the basic tools of probability and asymptotic geo- metric analysis, underlying the proofs of limit theorems and existential results in high dimensions. Original arguments leading to concentration estimates were based on isoperimetric inequalities, whic
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
Nexus Trimester - Randall Dougherty (Center for Communications Research)
Entropy inequalities and linear rank inequalities Randall Dougherty (Center for Communications Research) February 16, 2016 Abstract: Entropy inequalities (Shannon and non-Shannon) have been used to obtain bounds on the solutions to a number of problems. When the problems are restricted t
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Entropic and metric uncertainty relations (...) - R. Adamczak - Workshop 2 - CEB T3 2017
Radosław Adamczak / 24.10.17 Entropic and metric uncertainty relations for random unitary matrices I will discuss recent results concerning almost optimal entropic and metric (total-variation and Hellinger) uncertainty relations which hold with high probability for measurements given by
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Nexus Trimester - František Matúš (Institute of Information Theory and Automation) 2/3
Entropy region and convolution František Matúš (Institute of Information Theory and Automation) February 19, 2016 Abstract: The entropy region is constructed from vectors of random variables by collecting Shannon entropies of all subvectors. We will review results on its shape using poly
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
Quadratically regularized optimal transport - Lorenz - Workshop 1 - CEB T1 2019
Lorenz (Univ. Braunschweig) / 07.02.2019 Quadratically regularized optimal transport Among regularization techniques for optimal transport, entropic regularization has played a pivotal rule. The main reason may be its computational simplicity: the Sinkhorn-Knopp iteration can be impleme
From playlist 2019 - T1 - The Mathematics of Imaging
Cartesian to parametric form of line
How to transform a Cartesian form of a line to a parametric form of a line. An example is discussed. Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/OsY1rkt1al
From playlist Introduction to Vectors
Multivariable Calculus | The notion of a vector and its length.
We define the notion of a vector as it relates to multivariable calculus and define its length. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Vectors for Multivariable Calculus
Organic Chemistry Practice Exam 10
While I'm in quarantine with no access to YouTube studios to shoot my regular content, I thought I might as well give everyone some organic chemistry review! Pause the video if you want to try a question on your own, and then listen to the explanation. Happy studying! Try all of the organ
From playlist Organic Chemistry Practice Problems
Optimal Transportation and Applications - 12 November 2018
http://crm.sns.it/event/436 It is the ninth edition of this "traditional'' meeting in Pisa, after the ones in 2001, 2003, 2006, 2008, 2010, 2012, 2014 and 2016. Organizing Committee Luigi Ambrosio, Scuola Normale Superiore, Pisa Giuseppe Buttazzo, Dipartimento di Matematica, Università
From playlist Centro di Ricerca Matematica Ennio De Giorgi
Niles Weed :Weak limits for entropic optimal transport I
CONFERENCE Recording during the thematic meeting : "Meeting in Mathematical Statistics " the December 16, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIRM's Au
From playlist Probability and Statistics
Calculus 3: Vector Calculus in 2D (17 of 39) What is the Position Vector?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the position vector. The position vector indicates the position of a particle relative to the origin. The position usually depends on, or is a function of, a parametric variable (ex. t
From playlist CALCULUS 3 CH 3 VECTOR CALCULUS