Based on their properties, stochastic processes can be divided into various categories, which include random walks, martingales, Markov processes, L�vy processes, Gaussian processes, and random fields, renewal processes and branching processes.
22.
In the early 1960s Edgar Gilbert then used concepts and techniques from the probability subject of branching processes to show that a threshold value existed for the infinite or " giant " component.
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"' Harry Kesten "'( born 19 November 1931, Germany ) is an American mathematician best known for his work in probability, most notably on random walks on random matrices, branching processes, and percolation theory.
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Hi, I take a lecture in Evolutionary Dynamics ( I am a biologists, thats why I am asking in the first place ) and there was a lecture about Branching processes, specifically the Galton Watson process.
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A "'resource-dependent branching process ( RDBP ) "'is a discrete-time BP which models the development of a population in which individuals are supposed to have to work in order to be able to live and to reproduce.
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With his Los Alamos colleague Robert Schrandt he published a report, " Some Elementary Attempts at Numerical Modeling of Problems Concerning Rates of Evolutionary Processes ", which applied his earlier ideas on branching processes to biological inheritance.
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The trophoblast, which is a collection of cells that invades the maternal endometrium to gain access to nutrition for the fetus, proliferates rapidly and forms a network of branching processes which cover the entire embryo and invade and destroy the maternal tissues.
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According to this hypothesis, the activity of the brain would be continuously transitioning between two phases, one in which activity will rapidly reduce and die, and another where activity will build up and amplify over time . so subcritical, critical and slightly supercritical branching process of thoughts could describe how human and animal minds function.
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This method allowed them to study in exquisite detail the branching processes of nerve cells ( axons and dendrites ) and how they seemed to interconnect among themselves, forming chains and neural networks which could explain the synaptic transmission, and ultimately Cajal won over Golgi on their dispute of the neuron doctrine vs . the syncytium theory.
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When the graph is uniformly random except for the degree distribution, these critical vertices are the ones with the highest degree, and have thus been implicated in the spread of disease ( natural and artificial ) in social and communication networks, and in the spread of fads ( both of which are modeled by a percolation or branching process ).
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