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Resource-dependent Branching Process
A branching process (BP) (see e.g. Jagers (1975)) is a mathematical model to describe the development of a population. Here population is meant in a general sense, including a human population, animal populations, bacteria and others which reproduce in a biological sense, cascade process, or particles which split in a physical sense, and others. Members of a BP-population are called individuals, or particles. If the times of reproductions are discrete (usually denoted by 1,2, ...) then the totality of individuals present at time and living to time excluded are thought of as forming the generation. Simple BPs are defined by an initial state (number of individuals at time 0) and a law of reproduction, usually denoted by . 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. The population decides on a society form which det ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Branching Process
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 n produces some random number of individuals in generation n+1, 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 the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convergence Of Random Variables
In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied. The different possible notions of convergence relate to how such a behavior can be characterized: two readily understood behaviors are that the sequence eventually takes a constant value, and that values in the sequence continue to change but can be described by an unchanging probability distribution. Background "Stochastic convergence" formalizes the idea that a sequence of essentially rando ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Controlled Branching Process
Control may refer to: Basic meanings Economics and business * Control (management), an element of management * Control, an element of management accounting * Comptroller (or controller), a senior financial officer in an organization * Controlling interest, a percentage of voting stock shares sufficient to prevent opposition * Foreign exchange controls, regulations on trade * Internal control, a process to help achieve specific goals typically related to managing risk Mathematics and science * Control (optimal control theory), a variable for steering a controllable system of state variables toward a desired goal * Controlling for a variable in statistics * Scientific control, an experiment in which "confounding variables" are minimised to reduce error * Control variables, variables which are kept constant during an experiment * Biological pest control, a natural method of controlling pests * Control network in geodesy and surveying, a set of reference points of known geospatia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bisexual Galton–Watson Process
Bisexuality is a romantic or sexual attraction or behavior toward both males and females, or to more than one gender. It may also be defined to include romantic or sexual attraction to people regardless of their sex or gender identity, which is also known as ''pansexuality.'' The term ''bisexuality'' is mainly used in the context of human attraction to denote romantic or sexual feelings toward both men and women, and the concept is one of the three main classifications of sexual orientation along with heterosexuality and homosexuality, all of which exist on the heterosexual–homosexual continuum. A bisexual identity does not necessarily equate to equal sexual attraction to both sexes; commonly, people who have a distinct but not exclusive sexual preference for one sex over the other also identify themselves as bisexual. Scientists do not know the exact cause of sexual orientation, but they theorize that it is caused by a complex interplay of genetic, hormonal, and envir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bruss–Duerinckx Theorem
The theorem of the envelopment of societies for resource-dependent populations, also called the Bruss–Duerinckx theorem, is a mathematical result on the behavior of populations which choose their society form according to only two hypotheses, namely those which are seen as most "natural": * Hypothesis 1 (H1): Individuals want to survive and see a future for their descendants, * Hypothesis 2 (H2): The average individual prefers a higher standard of living to a lower one, where H1 is supposed to precede H2 in the case of incompatibility of H1 with H2. Here populations with a society structure are modeled by so-called resource-dependent branching processes (RDBPs). The objective of RDBPs is to model different society structures and to compare the advantages and disadvantages of different societies, with the focus being on human societies. A RDBP is a discrete time branching process (BP) in which individuals are supposed to have to work in order to be able to live and to reproduce. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
