Combinatorics | Graph theory | Algebra | Dynamical systems
In mathematics, the concept of graph dynamical systems can be used to capture a wide range of processes taking place on graphs or networks. A major theme in the mathematical and computational analysis of GDSs is to relate their structural properties (e.g. the network connectivity) and the global dynamics that result. The work on GDSs considers finite graphs and finite state spaces. As such, the research typically involves techniques from, e.g., graph theory, combinatorics, algebra, and dynamical systems rather than differential geometry. In principle, one could define and study GDSs over an infinite graph (e.g. cellular automata or probabilistic cellular automata over or interacting particle systems when some randomness is included), as well as GDSs with infinite state space (e.g. as in coupled map lattices); see, for example, Wu. In the following, everything is implicitly assumed to be finite unless stated otherwise. (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
Graph Data Structure 1. Terminology and Representation (algorithms)
This is the first in a series of videos about the graph data structure. It mentions the applications of graphs, defines various terminology associated with graphs, and describes how a graph can be represented programmatically by means of adjacency lists or an adjacency matrix.
From playlist Data Structures
Graphing the system of two linear inequalities with two horizontal line
👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of
From playlist Solve a System of Inequalities by Graphing
Graph the system of three linear inequalities and determine the feasible region ex 15
http://www.freemathvideos.com In this video series you will learn how to graph a system of linear inequalities. When graphing a system of linear inequalities you will graph just like a system of linear equations except you will use test points to shade. #systemsofequations #solvesystemofi
From playlist Graph a System of Inequalities (3 or More) #System
Graphing a linear system of linear inequalities
👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of
From playlist Solve a System of inequalities by Graphing | Standard Form
Learn how to graph a system of linear inequalities of two vertical boundary lines
👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of
From playlist Solve a System of Inequalities by Graphing
Topics in Dynamical Systems: Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos
This video provides a high-level overview of dynamical systems, which describe the changing world around us. Topics include nonlinear dynamics, linearization at fixed points, eigenvalues and eigenvectors, bifurcations, invariant manifolds, and chaos!! @eigensteve on Twitter eigensteve.co
From playlist Dynamical Systems (with Machine Learning)
The Anatomy of a Dynamical System
Dynamical systems are how we model the changing world around us. This video explores the components that make up a dynamical system. Follow updates on Twitter @eigensteve website: eigensteve.com
From playlist Research Abstracts from Brunton Lab
Christian Kuehn (7/25/22): Dynamical Systems for Deep Neural Networks
Abstract: In this talk, I am going to explain several approaches to explain the geometry and dynamics of neural networks. First, I will show, why neural networks should always be viewed within the framework of dynamical systems. Then I am going to show how to employ rigorous validated comp
From playlist Applied Geometry for Data Sciences 2022
Step by step tutorial for graphing a system of two variable inequalities
👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of
From playlist Solve a System of inequalities by Graphing | Standard Form
Networks: Part 5 - Oxford Mathematics 4th Year Student Lecture
Network Science provides generic tools to model and analyse systems in a broad range of disciplines, including biology, computer science and sociology. This course (we are showing the whole course over the next few weeks) aims at providing an introduction to this interdisciplinary field o
From playlist Oxford Mathematics Student Lectures - Networks
Carina Curto - Graph rules and topological insights for inhibitory network dynamics
---------------------------------- Institut Henri Poincaré, 11 rue Pierre et Marie Curie, 75005 PARIS http://www.ihp.fr/ Rejoingez les réseaux sociaux de l'IHP pour être au courant de nos actualités : - Facebook : https://www.facebook.com/InstitutHenriPoincare/ - Twitter : https://twitter
From playlist Workshop "Workshop on Mathematical Modeling and Statistical Analysis in Neuroscience" - January 31st - February 4th, 2022
Daniela Egas Santander (6/30/21): Nerve theorems for fixed points of neural networks
A fundamental question in computational neuroscience is to understand how the network’s connectivity shapes neural activity. A popular framework for modeling neural activity are a class of recurrent neural networks called threshold linear networks (TLNs). A special case of these are comb
From playlist AATRN 2021
Konstantin Mischaikow (1/27/21): Nonlinear Dynamics in an Age of Heuristic Science
Title: Nonlinear Dynamics in an Age of Heuristic Science Abstract: Motivated by problems in systems and synthetic biology (but I believe the problems are common to multiscale systems and data driven science) I will argue the need for a new framework in which to discuss nonlinear dynamics
From playlist AATRN 2021
Marian Mrozek (8/30/21): Combinatorial vs. Classical Dynamics: Recurrence
The study of combinatorial dynamical systems goes back to the seminal 1998 papers by Robin Forman. The main motivation to study combinatorial dynamics comes from data science. Combinatorial dynamics also provides very concise models of dynamical phenomena. Moreover, some topological invari
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Network dynamics (Lecture 01) by Sandeep Krishna
ORGANIZERS: Abhishek Dhar and Sanjib Sabhapandit DATE: 27 June 2018 to 13 July 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore This advanced level school is the ninth in the series. This is a pedagogical school, aimed at bridging the gap between masters-level courses and topics in
From playlist Bangalore School on Statistical Physics - IX (2018)
AQS-automata, state transition graphs, return-point by Muhittin Mungan
Program Entropy, Information and Order in Soft Matter  ORGANIZERS Bulbul Chakraborty, Pinaki Chaudhuri, Chandan Dasgupta, Marjolein Dijkstra, Smarajit Karmakar, Vijaykumar Krishnamurthy, Jorge Kurchan, Madan Rao, Srikanth Sastry and Francesco Sciortino DATE & TIME 27 August 2018 to
From playlist Entropy, Information and Order in Soft Matter
Networks: Part 7 - Oxford Mathematics 4th Year Student Lecture
Network Science provides generic tools to model and analyse systems in a broad range of disciplines, including biology, computer science and sociology. This course (we are showing the whole course over the next few weeks) aims at providing an introduction to this interdisciplinary field o
From playlist Oxford Mathematics Student Lectures - Networks
How to graph the system of linear inequalities of one horizontal and one vertical
👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of
From playlist Solve a System of Inequalities by Graphing
The mathematics of natural algorithms - Bernard Chazelle
Computer Science/Discrete Mathematics Seminar Topic: The mathematics of natural algorithms Speaker: Bernard Chazelle Affiliation:Princeton University Date: November 14, 2016 For more video, visit http://video.ias.edu
From playlist Mathematics