Mathematics of rigidity | Matroid theory
In the mathematics of structural rigidity, a rigidity matroid is a matroid that describes the number of degrees of freedom of an undirected graph with rigid edges of fixed lengths, embedded into Euclidean space. In a rigidity matroid for a graph with n vertices in d-dimensional space, a set of edges that defines a subgraph with k degrees of freedom has matroid rank dn − k. A set of edges is independent if and only if, for every edge in the set, removing the edge would increase the number of degrees of freedom of the remaining subgraph. (Wikipedia).
Louis Theran: Rigidity of Random Graphs in Higher Dimensions
I will discuss rigidity properties of binomial random graphs G(n,p(n)) in fixed dimension d and some related problems in low-rank matrix completion. The threshold for rigidity is p(n) = Θ(log n / n), which is within a multiplicative constant of optimal. This talk is based on joint work wi
From playlist HIM Lectures 2015
Center of Mass & Center of Rigidity | Reinforced Concrete Design
http://goo.gl/nmipcn for more FREE video tutorials covering Concrete Structural Design The objectives of this video are to briefly discuss about the center of mass and center of rigidity by understanding what their means as well as to talks about combination of center of mass and center o
From playlist SpoonFeedMe: Concrete Structures
Physics - Mechanics: Torsion (11 of 14) Torsion and a Hollow Tube
Visit http://ilectureonline.com for more math and science lectures! In this video I will derive the equation of torque=? of the torsion of a hollow tube. Next video in this series can be found at: https://youtu.be/mQ-wseAfAlc
From playlist PHYSICS 16.6 TORSION
Physics - Mechanics: Torsion (2 of 14) What is Torsional Constant?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is torsional constant or the “second momentum of area”. Next video in this series can be found at: https://youtu.be/Mr29GDA0jLE
From playlist PHYSICS 16.6 TORSION
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
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"
How to Make Amazing Tensegrity Structure - Anti-Gravity Structure
We made a sculpture out of wood batten based on the principle of tensional integrity (tensegrity for short), where all the strings are under continuous tension. The result is the impression that the sculpture levitates. Tensegrity is a design principle that applies when a discontinuous se
From playlist Home Science Videos - Cool Science Experiments
An Introduction to Stress and Strain
This video is an introduction to stress and strain, which are fundamental concepts that are used to describe how an object responds to externally applied loads. Stress is a measure of the distribution of internal forces that develop within a body to resist these applied loads. There are
From playlist Mechanics of Materials / Strength of Materials
Teaching Rigid Body Dynamics, Part 6: Summary of Computational Thinking Implementation
See a quick recap of the key features in MATLAB® that support a computational thinking approach when teaching rigid body dynamics. Get a free product Trial: https://goo.gl/ZHFb5u Learn more about MATLAB: https://goo.gl/8QV7ZZ Learn more about Simulink: https://goo.gl/nqnbLe See What's new
From playlist Teaching Rigid Body Dynamics
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
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
Zoltán Szigeti: Packing of arborescences with matroid constraints via matroid intersection
The lecture was held within the framework of the follow-up workshop to the Hausdorff Trimester Program: Combinatorial Optimization. Abstract: Edmonds characterized digraphs having a packing of k spanning arborescences in terms of connectivity and later in terms of matroid intersection. D
From playlist Follow-Up-Workshop "Combinatorial Optimization"
Michael Falk, Research talk - 9 February 2015
http://www.crm.sns.it/course/4392/ Michael Falk (Northern Arizona University) - Research talk We recall the application of resonance varieties in distinguishing homotopy types of complements of complex line arrangements, and illustrate a new application whereby one reconstructs the underl
From playlist Algebraic topology, geometric and combinatorial group theory - 2015
Sahil Singla: Online Matroid Intersection Beating Half for Random Arrival
We study a variant of the online bipartite matching problem that we call the online matroid intersection problem. For two matroids M1 and M2 defined on the same ground set E, the problem is to design an algorithm that constructs the largest common independent set in an online fashion. At e
From playlist HIM Lectures 2015
Lesson 5.5: Variable Number of Arguments
A video segment from the Coursera MOOC on introductory computer programming with MATLAB by Vanderbilt. Lead instructor: Mike Fitzpatrick. Check out the companion website and textbook: http://cs103.net
From playlist Vanderbilt: Introduction to Computer Programming with MATLAB (CosmoLearning Computer Programming)
Kevin Hendrey - Obstructions to bounded branch-depth in matroids (CMSA Combinatorics Seminar)
Kevin Hendrey (Institute for Basic Science) presents “Obstructions to bounded branch-depth in matroids”, 24 November 2020 (CMSA Combinatorics Seminar).
From playlist CMSA Combinatorics Seminar
Strongly log concave polynomials...Bases of Matroids - Shayan Oveis Gharan
More videos on http://video.ias.edu
From playlist Mathematics