In probability theory, a branching process is a type of mathematical object known as a stochastic process, which consists of collections of random variables. The random variables of a stochastic process are indexed by the natural numbers. The original purpose of branching processes was to serve as a mathematical model of a population in which each individual in generation produces some random number of individuals in generation , according, in the simplest case, to a fixed probability distribution that does not vary from individual to individual. Branching processes are used to model reproduction; for example, the individuals might correspond to bacteria, each of which generates 0, 1, or 2 offspring with some probability in a single time unit. Branching processes can also be used to model other systems with similar dynamics, e.g., the spread of surnames in genealogy or the propagation of neutrons in a nuclear reactor. A central question in the theory of branching processes is the probability of ultimate extinction, where no individuals exist after some finite number of generations. Using Wald's equation, it can be shown that starting with one individual in generation zero, the expected size of generation n equals μn where μ is the expected number of children of each individual. If μ < 1, then the expected number of individuals goes rapidly to zero, which implies ultimate extinction with probability 1 by Markov's inequality. Alternatively, if μ > 1, then the probability of ultimate extinction is less than 1 (but not necessarily zero; consider a process where each individual either has 0 or 100 children with equal probability. In that case, μ = 50, but probability of ultimate extinction is greater than 0.5, since that's the probability that the first individual has 0 children). If μ = 1, then ultimate extinction occurs with probability 1 unless each individual always has exactly one child. In theoretical ecology, the parameter μ of a branching process is called the basic reproductive rate. (Wikipedia).
Follow updates on Twitter: https://twitter.com/eigensteve This series discusses exponential growth, which is a ubiquitous phenomenon in science and engineering. This video will provide a high-level overview. Website: https://www.eigensteve.com/
From playlist Intro to Data Science
Compare Linear and Exponential Growth Using Recursive and Explicit Equations
This video explains the different between linear and exponential growth. Both recursive and explicit equations are discussed. Site: http://mathispower4u.com
From playlist Linear, Exponential, and Logistic Growth: Recursive/Explicit
Using two multipliers when solving a system of equations using the addition method
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Follow updates on Twitter: https://twitter.com/eigensteve This video discusses how all exponential growth eventually tapers off, through one mechanism or another. Website: https://www.eigensteve.com/
From playlist Intro to Data Science
👉 Learn how to solve multi-step equations with parenthesis. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-step equation with parenthes
From playlist How to Solve Multi Step Equations with Parenthesis
Using a Multiplier to Solve the System of Equations Using Elimination
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Medium
Solving an equation with a variable on both sides infinite solutions
👉 Learn how to solve multi-step equations with parenthesis and variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To
From playlist Solve Multi-Step Equations......Help!
Branching Random Walk and Regular variation by Rajat Subhra Hazra
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
2020.05.21 Jason Schweinsberg - A Gaussian particle distribution for branching Brownian motion [...]
A Gaussian particle distribution for branching Brownian motion with an inhomogeneous branching rate Motivated by the goal of understanding the evolution of populations undergoing selection, we consider branching Brownian motion in which particles independently move according to one-dime
From playlist One World Probability Seminar
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
Understanding the basic reproduction number via branching process by Sujit Kumar Nath
Seminar Understanding the basic reproduction number via branching process Speaker: Sujit Kumar Nath (University of Leeds) Date: Wed, 30 September 2020, 15:00 to 16:30 Venue: Online seminar Abstract Branching process is a random process having many applications in physics, biology a
From playlist Seminar Series
From playlist Contributed talks One World Symposium 2020
8.4: Recursion with Transformations - The Nature of Code
This video looks at what happens when you need to translate() and rotate() in a recursive function. The class "branching tree" fractal is demonstrated. (If I reference a link or project and it's not included in this description, please let me know!) Read along: http://natureofcode.com/b
From playlist The Nature of Code: Simulating Natural Systems
DevOps with AWS Tutorial | AWS DevOps for Beginners | Edureka | AWS Live - 3
🔥Edureka AWS Training: https://www.edureka.co/aws-certification-training In this Edureka video, you will be understanding the various DevOps Tools and their deployment on AWS Cloud. Towards the end, we'll also be doing a hands-on to put all this knowledge into action! Amazon AWS Video Tut
From playlist Edureka Live Classes 2020
From playlist Contributed talks One World Symposium 2020
Julia Komjathy: Weighted distances in scale free random graph models
Abstract: In this talk I will review the recent developments on weighted distances in scale free random graphs as well as highlight key techniques used in the proofs. We consider graph models where the degree distribution follows a power-law such that the empirical variance of the degrees
From playlist Probability and Statistics
Jim Nolen: "A free boundary problem from Brownian bees in the infinite swarm limit in R^d"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop IV: Stochastic Analysis Related to Hamilton-Jacobi PDEs "A free boundary problem from Brownian bees in the infinite swarm limit in R^d" Jim Nolen - Duke University Abstract: I will discuss a stochastic interacting particle system in R^d
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
Rajat Subhra Hazra: Branching Random Walk with innite progeny mean
In this talk we discuss the extremes of branching random walks under the assumption that the underlying Galton-Watson tree has in nite progeny mean. It is assumed that the displacements are either regularly varying or they have lighter tails. In the regularly varying case, it is shown that
From playlist Probability and Statistics
Solving an equation with parentheses
👉 Learn how to solve multi-step equations with parenthesis. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-step equation with parenthes
From playlist How to Solve Multi Step Equations with Parenthesis