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Applied Probability
Applied probability is the application of probability theory to statistical problems and other scientific and engineering domains. Scope Much research involving probability is done under the auspices of applied probability. However, while such research is motivated (to some degree) by applied problems, it is usually the mathematical aspects of the problems that are of most interest to researchers (as is typical of applied mathematics in general). Applied probabilists are particularly concerned with the application of stochastic processes, and probability more generally, to the natural, applied and social sciences, including biology, physics (including astronomy), chemistry, medicine, computer science and information technology, and economics. Another area of interest is in engineering: particularly in areas of uncertainty, risk management, probabilistic design, and Quality assurance. History Having initially been defined at a symposium of the American Mathematical Society in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Design
Probabilistic design is a discipline within engineering design. It deals primarily with the consideration and minimization of the effects of random variability upon the performance of an engineering system during the design phase. Typically, these effects studied and optimized are related to quality and reliability. It differs from the classical approach to design by assuming a small probability of failure instead of using the safety factor. Probabilistic design is used in a variety of different applications to assess the likelihood of failure. Disciplines which extensively use probabilistic design principles include product design, quality control, systems engineering, machine design, civil engineering (particularly useful in limit state design) and manufacturing. Objective and motivations When using a probabilistic approach to design, the designer no longer thinks of each variable as a single value or number. Instead, each variable is viewed as a continuous random variable wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization (computer Science)
In computer science, program optimization, code optimization, or software optimization is the process of modifying a software system to make some aspect of it work more algorithmic efficiency, efficiently or use fewer resources. In general, a computer program may be optimized so that it executes more rapidly, or to make it capable of operating with less Computer data storage, memory storage or other resources, or draw less power. Overview Although the term "optimization" is derived from "optimum", achieving a truly optimal system is rare in practice, which is referred to as superoptimization. Optimization typically focuses on improving a system with respect to a specific quality metric rather than making it universally optimal. This often leads to trade-offs, where enhancing one metric may come at the expense of another. One popular example is space-time tradeoff, reducing a program’s execution time by increasing its memory consumption. Conversely, in scenarios where memory is l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolution
Evolution is the change in the heritable Phenotypic trait, characteristics of biological populations over successive generations. It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, resulting in certain characteristics becoming more or less common within a population over successive generations. The process of evolution has given rise to biodiversity at every level of biological organisation. The scientific theory of evolution by natural selection was conceived independently by two British naturalists, Charles Darwin and Alfred Russel Wallace, in the mid-19th century as an explanation for why organisms are adapted to their physical and biological environments. The theory was first set out in detail in Darwin's book ''On the Origin of Species''. Evolution by natural selection is established by observable facts about living organisms: (1) more offspring are often produced than can possibly survive; (2) phenotypic variatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ecology
Ecology () is the natural science of the relationships among living organisms and their Natural environment, environment. Ecology considers organisms at the individual, population, community (ecology), community, ecosystem, and biosphere levels. Ecology overlaps with the closely related sciences of biogeography, evolutionary biology, genetics, ethology, and natural history. Ecology is a branch of biology, and is the study of abundance (ecology), abundance, biomass (ecology), biomass, and distribution of organisms in the context of the environment. It encompasses life processes, interactions, and adaptations; movement of materials and energy through living communities; ecological succession, successional development of ecosystems; cooperation, competition, and predation within and between species; and patterns of biodiversity and its effect on ecosystem processes. Ecology has practical applications in fields such as conservation biology, wetland management, natural resource m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Reaction
A chemical reaction is a process that leads to the chemistry, chemical transformation of one set of chemical substances to another. When chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an Gibbs free energy, energy change as new products are generated. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the Atomic nucleus, nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive Chemical element, elements where both electronic and nuclear changes can occur. The substance (or substances) initially involved in a chemical reaction are called reagent, reactants or reagents. Chemical reactions are usually characterized by a chemical change, and they yield one or more Product (c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stoichiometry
Stoichiometry () is the relationships between the masses of reactants and Product (chemistry), products before, during, and following chemical reactions. Stoichiometry is based on the law of conservation of mass; the total mass of reactants must equal the total mass of products, so the relationship between reactants and products must form a ratio of positive integers. This means that if the amounts of the separate reactants are known, then the amount of the product can be calculated. Conversely, if one reactant has a known quantity and the quantity of the products can be empirically determined, then the amount of the other reactants can also be calculated. This is illustrated in the image here, where the unbalanced equation is: : : However, the current equation is imbalanced. The reactants have 4 hydrogen and 2 oxygen atoms, while the product has 2 hydrogen and 3 oxygen. To balance the hydrogen, a coefficient of 2 is added to the product H2O, and to fix the imbalance of oxygen, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Physics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in a wide variety of fields such as biology, neuroscience, computer science, information theory and sociology. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and heat capacity—in terms of microscopic parameters that fluctuate about average values and are characterized by probability distributions. While classical thermodynamics is primarily concerned with thermodynamic equilibrium, statistical mechanics has been applied in non-equilibrium stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruin Theory
In actuarial science and applied probability, ruin theory (sometimes risk theory or collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such models key quantities of interest are the probability of ruin, distribution of surplus immediately prior to ruin and deficit at time of ruin. Classical model The theoretical foundation of ruin theory, known as the Cramér–Lundberg model (or classical compound-Poisson risk model, classical risk process or Poisson risk process) was introduced in 1903 by the Swedish actuary Filip Lundberg. Lundberg's work was republished in the 1930s by Harald Cramér. The model describes an insurance company who experiences two opposing cash flows: incoming cash premiums and outgoing claims. Premiums arrive a constant rate ''c > 0'' from customers and claims arrive according to a Poisson process N_t with intensity \lambda and are independent and identically distributed non-negative random variables ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Science
''Statistical Science'' is a review journal published by the Institute of Mathematical Statistics. The founding editor was Morris H. DeGroot, who explained the mission of the journal in his 1986 editorial: "A central purpose of ''Statistical Science'' is to convey the richness, breadth and unity of the field by presenting the full range of contemporary statistical thought at a modest technical level accessible to the wide community of practitioners, teachers, researchers and students of statistics and probability." Editors * 2023–2025 Moulinath Banerjee * 2020–2022 Sonia Petrone * 2017–2019 Cun-Hui Zhang * 2014–2016 Peter Green (statistician), Peter Green * 2011–2013 Jon A. Wellner, Jon Wellner * 2008–2010 David Madigan * 2005–2007 Ed George * 2002–2004 George Casella * 2001 Morris Eaton * 2001 Richard Tweedie * 1998–2000 Leon Gleser * 1995–1997 Paul Switzer * 1992–1994 Rob Kass, Robert E. Kass * 1989–1991 Carl Morris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joe Gani
Joe or JOE may refer to: Arts Film and television * ''Joe'' (1970 film), starring Peter Boyle * ''Joe'' (2013 film), starring Nicolas Cage, based on the novel ''Joe'' (1991) by Larry Brown * Joe (2023 film), an Indian film * ''Joe'' (TV series), a British TV series airing from 1966 to 1971 * ''Joe'', a 2002 Canadian animated short about Joe Fortes Music and radio * "Joe" (Inspiral Carpets song) * "Joe" (Red Hot Chili Peppers song) * "Joe", a song by The Cranberries on their album ''To the Faithful Departed'' *"Joe", a song by PJ Harvey on her album '' Dry'' *"Joe", a song by AJR on their album ''OK Orchestra'' * Joe FM (other), any of several radio stations Computing * Joe's Own Editor, a text editor for Unix systems * Joe, an object-oriented Java computing framework based on Sun's Distributed Objects Everywhere project Media * Joe (website), a news website for the UK and Ireland * ''Joe'' (magazine), a defunct periodical developed originally for Kenyan yo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Applied Probability
A journal, from the Old French ''journal'' (meaning "daily"), may refer to: *Bullet journal, a method of personal organization *Diary, a record of personal secretive thoughts and as open book to personal therapy or used to feel connected to oneself. A record of what happened over the course of a day or other period *Daybook, also known as a general journal, a daily record of financial transactions *Logbook, a record of events important to the operation of a vehicle, facility, or otherwise * Transaction log, a chronological record of data processing * Travel journal, a record of the traveller's experience during the course of their journey In publishing, ''journal'' can refer to various periodicals or serials: *Academic journal, an academic or scholarly periodical **Scientific journal, an academic journal focusing on science **Medical journal, an academic journal focusing on medicine **Law review, a professional journal focusing on legal interpretation *Magazine, non-academic or sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
