In mathematics, Ingleton's inequality is an inequality that is satisfied by the rank function of any representable matroid. In this sense it is a necessary condition for representability of a matroid over a finite field. Let M be a matroid and let ρ be its rank function, Ingleton's inequality states that for any subsets X1, X2, X3 and X4 in the support of M, the inequality ρ(X1)+ρ(X2)+ρ(X1∪X2∪X3)+ρ(X1∪X2∪X4)+ρ(X3∪X4) ≤ ρ(X1∪X2)+ρ(X1∪X3)+ρ(X1∪X4)+ρ(X2∪X3)+ρ(X2∪X4) is satisfied. Aubrey William Ingleton, an English mathematician, wrote an important paper in 1969 in which he surveyed the representability problem in matroids. Although the article is mainly expository, in this paper Ingleton stated and proved Ingleton's inequality, which has found interesting applications in information theory, matroid theory, and network coding. (Wikipedia).
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
Nexus trimester - Nigel Boston (University of Wisconsin)
Ingleton-violating Points in the Entropy Region Nigel Boston (University of Wisconsin) February 22, 2016 Abstract: After recalling the entropy region and Ingleton inequalities, I shall describe ways to obtain points in the entropy region for 4 discrete random variables that violate this
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Nexus Trimester - László Csirmaz (Central European University, Budapest) 1/3
Geometry of the entropy region László Csirmaz (Central European University, Budapest) February 16, 2016 Abstract: A three-lecture series covering some recent research on the geometry of the entropy region. The lectures will cover: 1) Shannon inequalities; the case of one, two and three v
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Nexus Trimester - László Csirmaz (Central European University, Budapest) 3/3
Geometry of the entropy region László Csirmaz (Central European University, Budapest) February 16, 2016 Abstract: A three-lecture series covering some recent research on the geometry of the entropy region. The lectures will cover: 1) Shannon inequalities; the case of one, two and three va
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Nexus Trimester - László Csirmaz (Central European University, Budapest) 2/3
Geometry of the entropy region László Csirmaz (Central European University, Budapest) February 16, 2016 Abstract: A three-lecture series covering some recent research on the geometry of the entropy region. The lectures will cover: 1) Shannon inequalities; the case of one, two and three va
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Nexus Trimester - Terence Chan (University of South Australia) - 2
Fundamental aspects of information inequalities 2/3 Terence Chan (University of South Australia) February 25, 2016 Abstract: Information inequalities are very important tools and are often needed to characterise fundamental limits and bounds in many communications problems such as data t
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
M. Debbah, E. Ullmo, J.C. Belfiore, F. Otto, F. Baccelli - Where are we 100 years after Shannon?
Panel: Mathematical Theories for Information and Communication Technologies: Where are we 100 years after Shannon?
From playlist 2nd Huawei-IHES Workshop on Mathematical Theories for Information and Communication Technologies
Nexus Trimester - John Walsh (Drexel University)
Rate Regions for Network Coding: Computation, Symmetry, and Hierarchy John Walsh (Drexel University) February 17, 2016 Abstract: This talk identifies a number of methods and algorithms we have created for determining fundamental rate regions and efficient codes for network coding proble
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
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
Mark Burgess interviewed at Velocity 2011
Mark Burgess CTO, Cfengine Mark Burgess is the founder, CTO and principal author of Cfengine. He is Professor of Network and System Administration at Oslo University College and has led the way in theory and practice of automation and policy based management for 20 years. In the 1990s h
From playlist Velocity 2011
Solving a multi-step inequality and then graphing
👉 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 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 an inequality with a parenthesis on both sides
👉 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 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
Solving and graphing an 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 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 an inequality with infinite many solutions
👉 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 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
How to Solve Inequalities (NancyPi)
MIT grad explains solving inequalities. This video focuses on solving linear inequalities. It shows when to switch the sign of the inequality, if you divide or multiply by a negative number, and is an introduction to how to solve inequalities in algebra. To skip ahead: 1) For a basic examp
From playlist Algebra
Graphing an inequality with variables and parenthesis on both sides
👉 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