Families of sets | Design of experiments | Combinatorial design
In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t = 2 or (recently) t ≥ 2. A Steiner system with parameters t, k, n, written S(t,k,n), is an n-element set S together with a set of k-element subsets of S (called blocks) with the property that each t-element subset of S is contained in exactly one block. In an alternate notation for block designs, an S(t,k,n) would be a t-(n,k,1) design. This definition is relatively new. The classical definition of Steiner systems also required that k = t + 1. An S(2,3,n) was (and still is) called a Steiner triple (or triad) system, while an S(3,4,n) is called a Steiner quadruple system, and so on. With the generalization of the definition, this naming system is no longer strictly adhered to. Long-standing problems in design theory were whether there exist any nontrivial Steiner systems (nontrivial meaning t < k < n) with t ≥ 6; also whether infinitely many have t = 4 or 5. Both existences were proved by Peter Keevash in 2014. His proof is non-constructive and, as of 2019, no actual Steiner systems are known for large values of t. (Wikipedia).
Discrete-Time Dynamical Systems
This video shows how discrete-time dynamical systems may be induced from continuous-time systems. https://www.eigensteve.com/
From playlist Data-Driven Dynamical Systems
23 Algebraic system isomorphism
Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.
From playlist Abstract algebra
(ML 19.1) Gaussian processes - definition and first examples
Definition of a Gaussian process. Elementary examples of Gaussian processes.
From playlist Machine Learning
Intro to Linear Systems: 2 Equations, 2 Unknowns - Dr Chris Tisdell Live Stream
Free ebook http://tinyurl.com/EngMathYT Basic introduction to linear systems. We discuss the case with 2 equations and 2 unknowns. A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that ar
From playlist Intro to Linear Systems
The Standard Modular System is a system of standard transistorized circuit boards and mounting racks developed by IBM in the late 1950s, originally for the IBM 7030 Stretch. They were used throughout IBM's second-generation computers, peripherals, the 7000 , the 1400 , and the 1620. SMS w
From playlist IBM System/360 Mainframe Computer History
Vector and matrix forms for systems of linear equations | Linear Algebra MATH1141 | N J Wildberger
A system of linear equations may also be viewed in vector form, as an attempt to write one vector as a linear combination of other vectors. Or it more alternatively be viewed in matrix form. We discuss the matrix of coefficients, the vector of variables and the vector of constants. Puttin
From playlist Higher Linear Algebra
The continuation of previous video https://www.youtube.com/watch?v=-42Z-_Kq0QU this video includes 12 types of mechanisms and that not all yet... to be continued.... The idea of this video was taken from the larger work by Ralph Steiner. 🎵 Track Info: Title: Bridge Artist: KV Genre: Dan
From playlist Mechanical principles
Jennifer Tour Chayes (Microsoft Research New England and Microsoft Research New York City) URL: https://www.icts.res.in/lecture/4/details/1644/ Description: Everywhere we turn these days, we find that networks can be used to describe relevant interactions.In the high tech world, we see th
From playlist Distinguished Lectures
Rainbow structures, Latin squares & graph decompositions - Benny Sudakov
Computer Science/Discrete Mathematics Seminar I Topic: Rainbow structures, Latin squares & graph decompositions Speaker: Benny Sudakov Affiliation: ETH Zürich Date: March 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
More designs - P. Keevash - Workshop 1 - CEB T1 2018
Peter Keevash (Oxford) / 01.02.2018 We generalise the existence of combinatorial designs to the setting of subset sums in lattices with coordinates indexed by labelled faces of simplicial complexes. This general framework includes the problem of decomposing hypergraphs with extra edge dat
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
History of science 7: Did Witt discover the Leech lattice?
In about 1970 the German mathematician Witt claimed to have discovered the Leech lattice many years before Leech. This video explains what the Leech lattice is and examines the evidence for Witt's claim. Lieven Lebruyn discussed this question on his blog: http://www.neverendingbooks.org/w
From playlist History of science
Planet, People, and Prosperity: Achim Steiner, Administrator, UNDP
Planet, People, and Prosperity: A Conversation With Achim Steiner, Administrator, United Nations Development Programme On Tuesday, March 30th the Yale Institute for Global Health (YIGH) welcomed Achim Steiner, Administrator of the UN Development Programme, to discuss the nexus of the plane
From playlist YIGH Global Health Conversation Series
Linear Algebra - Lecture 10 - Homogeneous Linear Systems
In this lecture, we define "homogeneous" linear systems, and discuss how to find the solutions to these systems in parametric vector form.
From playlist Linear Algebra Lectures
Jennifer Tour Chayes: Data scientists seeking personalized disease treatments
The study of networks by data scientists is leading to new business models that may someday result in innovative drug therapies keyed to individual patients, said Jennifer Tour Chayes, managing director and distinguished scientist at Microsoft Research. Research into the networks that regu
From playlist Women In Data Science Conference (WiDS)- 2015
Modular Forms | Modular Forms; Section 1 2
We define modular forms, and borrow an idea from representation theory to construct some examples. My Twitter: https://twitter.com/KristapsBalodi3 Fourier Theory (0:00) Definition of Modular Forms (8:02) In Search of Modularity (11:38) The Eisenstein Series (18:25)
From playlist Modular Forms
Sebastian Bubeck: Chasing small sets
I will present an approach based on mirror descent (with a time-varying multiscale entropy functional) to chase small sets in arbitrary metric spaces. This could in particular resolve the randomized competitive ratio of the layered graph traversal problem introduced by Papadimitriou and Ya
From playlist Workshop: Continuous approaches to discrete optimization
Ramamoorthi Ravi: Designing Overlapping Networks for Publish Subscribe Systems
From the publish-subscribe systems of the early days of the Internet to the recent emergence of Web 3.0 and IoT (Internet of Things), new problems arise in the design of networks centered at producers and consumers of constantly evolving information. In a typical problem, each terminal is
From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"
Stephan Held: Mathematik im Chip-Design
Mathematik im Chip-Design wurde von Dr. Stephan Held im Rahmen eines wissenschaftlichen Vortrags am Tag der offenen Tür im Bonner Mathematikzentrum am 15.09.2018 gehalten. uni-bonn.tv hat seinen Vortrag dokumentiert. . (c) Universität Bonn / uni-bonn.tv Videoteam: Ole Lentfer & Christian
From playlist Hausdorff Center goes public
In this section I introduce plane autonomous systems, which form beautiful and useful vector fields.
From playlist A Second Course in Differential Equations
Ramsey classes and sparsity for finite models - J. Nešetřil - Workshop 1 - CEB T1 2018
Jaroslav Nešetřil (Prague) / 31.01.2018 In the talk we relate two notions in the title particularly in the context of sparse dense dichotomy (nowhere and somewhere dense classes and stability) and Ramsey classes of finite models in the context of the characterisation programme. A joint wo
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields