In combinatorics, a matroid embedding is a set system (F, E), where F is a collection of feasible sets, that satisfies the following properties. 1. * Accessibility property: Every non-empty feasible set X contains an element x such that X \ {x} is feasible. 2. * Extensibility property: For every feasible subset X of a basis (i.e., maximal feasible set) B, some element in B but not in X belongs to the extension ext(X) of X, where ext(X) is the set of all elements e not in X such that X ∪ {e} is feasible. 3. * Closure–congruence property: For every superset A of a feasible set X disjoint from ext(X), A ∪ {e} is contained in some feasible set for either all e or no e in ext(X). 4. * The collection of all subsets of feasible sets forms a matroid. Matroid embedding was introduced by to characterize problems that can be optimized by a greedy algorithm. (Wikipedia).
MATLAB Basics: Get The Most Out of MATLAB
In this livestream, Heather Gorr and Elsie Eigerman will be walking through the fundamentals of programming with MATLAB. This isn’t just for beginners; we’ll show you the latest and greatest tips and tricks to help you get the most out of MATLAB. We’ll also walk-through core concepts for t
From playlist MATLAB and Simulink Livestreams
Word embeddings are one of the coolest things you can do with Machine Learning right now. Try the web app: https://embeddings.macheads101.com Word2vec paper: https://arxiv.org/abs/1301.3781 GloVe paper: https://nlp.stanford.edu/pubs/glove.pdf GloVe webpage: https://nlp.stanford.edu/proje
From playlist Machine Learning
Rasa Algorithm Whiteboard - Understanding Word Embeddings 1: Just Letters
We're making a few videos that highlight word embeddings. Before training word embeddings we figured it might help the intuition if we first trained some letter embeddings. It might suprise you but the idea with an embedding can also be demonstrated with letters as opposed to words. We're
From playlist Algorithm Whiteboard
Word Embedding and Word2Vec, Clearly Explained!!!
Words are great, but if we want to use them as input to a neural network, we have to convert them to numbers. One of the most popular methods for assigning numbers to words is to use a Neural Network to create Word Embeddings. In this StatQuest, we go through the steps required to create W
From playlist StatQuest
Advanced Programming Techniques in MATLAB | Master Class with Loren Shure
In this session, you will gain an understanding of how different MATLAB data types are stored in memory and how you can program in MATLAB to use memory efficiently. In recent versions, MATLAB introduced several new programming concepts, including new function types. We will illustrate and
From playlist MATLAB and Simulink Livestreams
Graph Neural Networks, Session 6: DeepWalk and Node2Vec
What are Node Embeddings Overview of DeepWalk Overview of Node2vec
From playlist Graph Neural Networks (Hands-on)
Using and customizing the MATLAB environment
This is part of an online course on MATLAB. The course includes 5+ hours of video lectures, pdf readers, exercises, and solutions. No prior experience with MATLAB is necessary. The goal is for you to learn high-level, transferrable skills that will help you become a better programmer in a
From playlist MATLAB programming, debugging, and style
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
Connecting tropical intersection theory with polytope algebra in types A and B by Alex Fink
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
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
MATLAB Basics – A Practical Look
Heather Gorr and Connell D’Souza walk through the fundamentals of programming with MATLAB. This isn’t just for beginners; we’ll show you the latest and greatest tips and tricks to help you get the most out of MATLAB. We’ll also walk-through core concepts for things like using apps, live sc
From playlist MATLAB and Simulink Livestreams
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
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
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
Lauren Williams - Combinatorics of the amplituhedron
The amplituhedron is the image of the positive Grassmannian under a map in- duced by a totally positive matrix. It was introduced by Arkani-Hamed and Trnka to compute scattering amplitudes in N=4 super Yang Mills. I’ll give a gentle introduction to the amplituhedron, surveying its connecti
From playlist Combinatorics and Arithmetic for Physics: Special Days 2022
How to Generate Code from MATLAB
MATLAB Coder is a powerful tool to help convert MATLAB algorithms and code into low-level C/C++ code that can be deployed royalty-free. In this video you will learn how to prepare code for code generation and use the MATLAB Coder App to convert MATLAB functions into standalone, readable an
From playlist “How To” with MATLAB and Simulink
Yusuke Kobayashi: A weighted linear matroid parity algorithm
The lecture was held within the framework of the follow-up workshop to the Hausdorff Trimester Program: Combinatorial Optimization. Abstract: The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so gener
From playlist Follow-Up-Workshop "Combinatorial Optimization"
Victor Chepoi: Simple connectivity, local to global, and matroids
Victor Chepoi: Simple connectivity, local-to-global, and matroids A basis graph of a matroid M is the graph G(M) having the bases of M as the vertex-set and the pairs of bases differing by an elementary exchange as edges. Basis graphs of matroids have been characterized by S.B. Maurer, J.
From playlist HIM Lectures 2015
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