Topics in Combinatorics lecture 11.1 --- Subadditivity of entropy and Shearer's lemma
A useful rule that is satisfied by entropy is that if X_1,...,X_n are random variables, then H[X_1,...,X_n] is at most H[X_1]+...+H[X_n]. Shearer's lemma is a generalization of this, where one compares H[X_1,...,X_n] by a suitable weighted average of joint entropies of the form H[X_i : i i
From playlist Topics in Combinatorics (Cambridge Part III course)
Solving and graphing a linear inequality word problem
Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-step
From playlist Linear Programming
Topics in Combinatorics lecture 11.6 --- Two applications of Shearer's lemma
In the previous video I stated and proved Shearer's entropy lemma. Here I give two applications. The first provides an upper bound for the number of triangles a graph with m edges can have. The second is an upper bound for the size of a family of graphs with vertex set {1,2,...,n} if the i
From playlist Topics in Combinatorics (Cambridge Part III course)
Solving a linear inequality with fractions
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis
New isoperimetric inequalities for convex bodies - Amir Yehudayoff
Computer Science/Discrete Mathematics Seminar I Topic: New isoperimetric inequalities for convex bodies Speaker: Amir Yehudayoff Affiliation: Technion - Israel Institute of Technology Date: November 23, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Nexus Trimester - Mokshay Madiman (University of Delaware)
The Stam region, or the differential entropy region for sums of independent random vectors Mokshay Madiman (University of Delaware) February 25, 2016 Abstract: Define the Stam region as the subset of the positive orthant in [Math Processing Error] that arises from considering entropy powe
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Solving and graphing a linear inequality
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis
Progress on algorithmic versions of the Lovasz Local Lemma - Aravind Srinivasan
Aravind Srinivasan University of Maryland, College Park April 7, 2014 There has been substantial progress on algorithmic versions and generalizations of the Lovasz Local Lemma recently, with some of the main ideas getting simplified as well. I will survey some of the main ideas of Moser &
From playlist Mathematics
Solving and graphing a multi-step inequality
👉 Learn how to solve multi-step linear inequalities having parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-step l
From playlist Solve and Graph Inequalities | Multi-Step With Parenthesis
Solving and graphing a one variable inequality with variable on both sides
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis
Solving and graphing a one variable inequality
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis
Michael Walter: "Quantum Brascamp-Lieb Dualities"
Entropy Inequalities, Quantum Information and Quantum Physics 2021 "Quantum Brascamp-Lieb Dualities" Michael Walter - Universiteit van Amsterdam Abstract: Brascamp-Lieb inequalities are entropy inequalities which have a dual formulation as generalized Young inequalities. In this work, we
From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021
Are These Fish Farting Or Communicating? | ExperiMental | Spark
Welcome to ExperiMental sideshow that gives sheep a hard time and gets snails turned on. Subscribe to Spark for more amazing science, tech and engineering videos - https://goo.gl/LIrlur Follow us on Facebook: https://www.facebook.com/SparkDocs/ Follow us on Instagram: https://www.insta
From playlist The Science Of Nature | Spark X Earth Stories X Real Wild X Pets & Vets
Solving and Graphing an inequality when the solution point is a decimal
👉 Learn how to solve multi-step linear inequalities having parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-step l
From playlist Solve and Graph Inequalities | Multi-Step With Parenthesis
Solving a inequality with a square root
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis
In this brief illustration, the octagon shown is regular. How can we formally prove what is dynamically illustrated here? (Source: Catriona Shearer). GeoGebra resource: https://www.geogebra.org/m/pngwrnzb.
From playlist Geometry: Challenge Problems
One of the things I love about Catriona Shearer's #geometry problems is that they serve as GREAT excuses to procrastinate projects that are way more boring (& don't feel like doing). 🙂https://geogebra.org/m/hqskmkuc #GeoGebra #MTBoS #ITeachMath #EdTech #proof #EdTech #math #maths #MathCha
From playlist Geometry: Challenge Problems
Solving a multi-step inequality with variables on both sides
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis
The adjoint Brascamp-Lieb inequality - Terence Tao
Analysis and Mathematical Physics Topic: The adjoint Brascamp-Lieb inequality Speaker: Terence Tao Affiliation: University of California, Los Angeles Date: March 08, 2023 The Brascamp-Lieb inequality is a fundamental inequality in analysis, generalizing more classical inequalities such a
From playlist Mathematics
Solving a multi step inequality simplify both sides
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis