(ML 18.4) Examples of Markov chains with various properties (part 1)
A very simple example of a Markov chain with two states, to illustrate the concepts of irreducibility, aperiodicity, and stationary distributions.
From playlist Machine Learning
RT8.2. Finite Groups: Classification of Irreducibles
Representation Theory: Using the Schur orthogonality relations, we obtain an orthonormal basis of L^2(G) using matrix coefficients of irreducible representations. This shows the sum of squares of dimensions of irreducibles equals |G|. We also obtain an orthonormal basis of Class(G) usin
From playlist Representation Theory
(ML 18.3) Stationary distributions, Irreducibility, and Aperiodicity
Definitions of the properties of Markov chains used in the Ergodic Theorem: time-homogeneous MC, stationary distribution of a MC, irreducible MC, aperiodic MC.
From playlist Machine Learning
Matrix Limits and Markov Chains
In this video I present a cool application of linear algebra in which I use diagonalization to calculate the eventual outcome of a mixing problem. This process is a simple example of what's called a Markov chain. Note: I just got a new tripod and am still experimenting with it; sorry if t
From playlist Eigenvalues
(ML 14.3) Markov chains (discrete-time) (part 2)
Definition of a (discrete-time) Markov chain, and two simple examples (random walk on the integers, and a oversimplified weather model). Examples of generalizations to continuous-time and/or continuous-space. Motivation for the hidden Markov model.
From playlist Machine Learning
(ML 18.5) Examples of Markov chains with various properties (part 2)
More examples of (discrete) Markov chains, to illustrate the concepts of irreducibility, aperiodicity, and stationary distributions.
From playlist Machine Learning
(ML 14.2) Markov chains (discrete-time) (part 1)
Definition of a (discrete-time) Markov chain, and two simple examples (random walk on the integers, and a oversimplified weather model). Examples of generalizations to continuous-time and/or continuous-space. Motivation for the hidden Markov model.
From playlist Machine Learning
We show the connection between the method of adjoints in optimal control to the implicit function theorem ansatz. We relate the costate or adjoint state variable to Lagrange multipliers.
From playlist There and Back Again: A Tale of Slopes and Expectations (NeurIPS-2020 Tutorial)
Dmitry Ioffe: Low temperature interfaces and level lines in the critical prewetting regime
Abstract: Complete wetting in the context of the low temperature two-dimensional Ising model is characterized by creation of a mesoscopic size layer of the "-" phase above an active substrate. Adding a small positive magnetic field h makes "-"-phase unstable, and the layer becomes only mic
From playlist Probability and Statistics
Dynamical large deviations and open quantum systems - J. Garrahan - PRACQSYS 2018 - CEB T2 2018
Juan Garrahan (School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, United Kingdom) / 02.07.2018 Dynamical large deviations and open quantum systems I will explain how, in systems
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
The Rule 54: Exactly solvable deterministic interacting model of transport by Tomaz Prosen
PROGRAM THERMALIZATION, MANY BODY LOCALIZATION AND HYDRODYNAMICS ORGANIZERS: Dmitry Abanin, Abhishek Dhar, François Huveneers, Takahiro Sagawa, Keiji Saito, Herbert Spohn and Hal Tasaki DATE : 11 November 2019 to 29 November 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore How do is
From playlist Thermalization, Many Body Localization And Hydrodynamics 2019
(ML 18.2) Ergodic theorem for Markov chains
Statement of the Ergodic Theorem for (discrete-time) Markov chains. This gives conditions under which the average over time converges to the expected value, and under which the marginal distributions converge to the stationary distribution.
From playlist Machine Learning
Macdonald processes I - Alexei Borodin
Alexei Borodin Massachussetts Institute of Technology October 8, 2013 Our goal is to explain how certain basic representation theoretic ideas and constructions encapsulated in the form of Macdonald processes lead to nontrivial asymptotic results in various `integrable'; probabilistic probl
From playlist Mathematics
Abstract Algebra | Irreducible polynomials
We introduce the notion of an irreducible polynomial over the ring k[x] where k is any field. A proof that p(x) is irreducible if and only if (p(x)) is maximal is also given, along with some examples. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal W
From playlist Abstract Algebra
(ML 18.8) Correctness of the Metropolis algorithm
Conditions under which the Metropolis algorithm is guaranteed to converge to the correct result.
From playlist Machine Learning
Interacting particle systems with kinetic (Lecture 1) by Fabio Martinelli
PROGRAM : ADVANCES IN APPLIED PROBABILITY ORGANIZERS : Vivek Borkar, Sandeep Juneja, Kavita Ramanan, Devavrat Shah and Piyush Srivastava DATE & TIME : 05 August 2019 to 17 August 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore Applied probability has seen a revolutionary growth in r
From playlist Advances in Applied Probability 2019
Zeros of polynomials, decay of correlations, and algorithms by Piyush Srivastava
DISCUSSION MEETING : STATISTICAL PHYSICS OF MACHINE LEARNING ORGANIZERS : Chandan Dasgupta, Abhishek Dhar and Satya Majumdar DATE : 06 January 2020 to 10 January 2020 VENUE : Madhava Lecture Hall, ICTS Bangalore Machine learning techniques, especially “deep learning” using multilayer n
From playlist Statistical Physics of Machine Learning 2020
Gabriela Ciolek - Sharp Bernstein and Hoeffding type inequalities for regenerative Markov chains
The purpose of this talk is to present Bernstein and Hoeffding type functional inequalities for regenerative Markov chains. Furthermore, we generalize these results and show exponential bounds for suprema of empirical processes over a class of functions F which size is controlled by its un
From playlist Les probabilités de demain 2017
Giuseppe Mussardo - 2D Ising Model and its tricritical version, when theory meets experiments
The magnetic deformation of the 2D Ising Model and the thermal deformation of the Tricritical Ising Model are related to the exceptional E_8 and E_7 Lie algebras. The corresponding exact S-matrix theories and the related dynamical structure factors of both models have a rich spectroscopy
From playlist 100…(102!) Years of the Ising Model
Alina Ostafe: Dynamical irreducibility of polynomials modulo primes
Abstract: In this talk we look at polynomials having the property that all compositional iterates are irreducible, which we call dynamical irreducible. After surveying some previous results (mostly over finite fields), we will concentrate on the question of the dynamical irreducibility of
From playlist Number Theory Down Under 9