In the mathematical theory of matroids, the rank of a matroid is the maximum size of an independent set in the matroid. The rank of a subset S of elements of the matroid is, similarly, the maximum size of an independent subset of S, and the rank function of the matroid maps sets of elements to their ranks. The rank function is one of the fundamental concepts of matroid theory via which matroids may be axiomatized. Matroid rank functions form an important subclass of the submodular set functions. The rank functions of matroids defined from certain other types of mathematical object such as undirected graphs, matrices, and field extensions are important within the study of those objects. (Wikipedia).
From playlist Basic Statistics (Descriptive Statistics)
Working with Matrices in Matlab
This tutorial shows how to define and manipulate matrices in Matlab. Topics and timestamps: 0:00 – Introduction 1:19 – Defining a matrix 6:59 – Matrix multiplication (both standard and elementwise) 14:19 – Extracting submatrices 18:16 – Transpose 19:12 – Concatenation 21:57 – Creating l
From playlist Working with Matlab
This video is one of the cornerstones of our dual space extravaganza. Using just some facts about annihilators (in a video below), I provide a very elegant and neat proof of the fact that the rank of A^T equals to the rank of A. Annihilator: https://www.youtube.com/watch?v=ISs13W6474g Cl
From playlist Dual Spaces
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Introduction to group-level statistical analyses, and implementation in Matlab. The video uses files you can download from https://github.com/mikexcohen/ANTS_youtube_videos For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com
From playlist OLD ANTS #8) Statistics
Nonlinear algebra, Lecture 13: "Polytopes and Matroids ", by Mateusz Michalek
This is the thirteenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Z-Score
From playlist Statistics
Joseph Bonin: Delta-matroids as subsystems of sequences of Higgs lifts
Abstract: Delta-matroids generalize matroids. In a delta-matroid, the counterparts of bases, which are called feasible sets, can have different sizes, but they satisfy a similar exchange property in which symmetric differences replace set differences. One way to get a delta-matroid is to t
From playlist Combinatorics
The Basics: Introduction to Matlab, Part 2
Data Science for Biologists The Basics: Introduction to Matlab Part 2 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton
From playlist Data Science for Biologists
Gyula Pap: Linear matroid matching in the oracle model
Gyula Pap: Linear matroid matching in the oracle model Linear matroid matching is understood as a special case of matroid matching when the matroid is given with a matrix representation. However, for certain examples of linear matroids, the matrix representation is not given, and actuall
From playlist HIM Lectures 2015
Definition of Rank and showing Rank(A) = Dim Col(A) In this video, I define the notion of rank of a matrix and I show that it is the same as the dimension of the column space of that matrix. This is another illustration of the beautiful interplay between linear transformations and matrice
From playlist Linear Equations
Percentiles, Deciles, Quartiles
Understanding percentiles, quartiles, and deciles through definitions and examples
From playlist Unit 1: Descriptive Statistics
James Oxley: A matroid extension result
Abstract: Let (A,B) be a 3-separation in a matroid M. If M is representable, then, in the underlying projective space, there is a line where the subspaces spanned by A and B meet, and M can be extended by adding elements from this line. In general, Geelen, Gerards, and Whittle proved that
From playlist Combinatorics
Gary Gordon and Liz McMahon: Generalizations of Crapo's Beta Invariant
Abstract: Crapo's beta invariant was defined by Henry Crapo in the 1960s. For a matroid M, the invariant β(M) is the non-negative integer that is the coefficient of the x term of the Tutte polynomial. Crapo proved that β(M) is greater than 0 if and only if M is connected and M is not a loo
From playlist Combinatorics
Anna De Mier: Approximating clutters with matroids
Abstract: There are several clutters (antichains of sets) that can be associated with a matroid, as the clutter of circuits, the clutter of bases or the clutter of hyperplanes. We study the following question: given an arbitrary clutter Λ, which are the matroidal clutters that are closest
From playlist Combinatorics
Rico Zenklusen: The Submodular Secretary Problem Goes Linear
During the last decade, the matroid secretary problem (MSP) became one of the most prominent classes of online selection problems. The strong interest in MSPs is due to both its many applications and the fact that matroid constraints have useful properties for the design of strong online a
From playlist HIM Lectures 2015
Jim Lawrence: The concatenation operation for uniform oriented matroids and simplicial...
Abstract: Some problems connected with the concatenation operation will be described. Recording during the meeting "Combinatorial Geometries: Matroids, Oriented Matroids and Applications" the September 24, 2018 at the Centre International de Rencontres Mathématiques (Marseille, France) F
From playlist Combinatorics
Anja Fischer: Polynomial Matroid Optimisation Problems
n this talk we consider polynomial matroid optimisation problems with some non-linear monomials in the objective function. The monomials are linearised and we study the corresponding polytopes. Extending results of Edmonds we present complete descriptions for the linearised polytopes for t
From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"
Whitney numbers via measure concentration in representation varieties - Karim Adiprasito
Karim Adiprasito Member, School of Mathematics March 3, 2015 We provide a simple proof of the Rota--Heron--Welsh conjecture for matroids realizable as c-arrangements in the sense of Goresky--MacPherson: we prove that the coefficients of the characteristic polynomial of the associated matr
From playlist Mathematics
Excel 2010 Preview #1: New Rank Function RANK.AVE
Download Excel file: https://people.highline.edu/mgirvin/YouTubeExcelIsFun/Excel2010NewAwesomeThings1-8.xlsx RANK.AVE will average the rank score when there is a tie!! See the new Excel 2010 RANK.AVE and RANK.EQ functions.
From playlist Excel 2010 Videos