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Gillespie Algorithm
In probability theory, the Gillespie algorithm (or the Doob–Gillespie algorithm or stochastic simulation algorithm, the SSA) generates a statistically correct trajectory (possible solution) of a stochastic equation system for which the reaction rates are known. It was created by Joseph L. Doob and others (circa 1945), presented by Dan Gillespie in 1976, and popularized in 1977 in a paper where he uses it to simulate chemical or biochemical systems of reactions efficiently and accurately using limited computational power (see stochastic simulation). As computers have become faster, the algorithm has been used to simulate increasingly complex systems. The algorithm is particularly useful for simulating reactions within cells, where the number of reagents is low and keeping track of every single reaction is computationally feasible. Mathematically, it is a variant of a dynamic Monte Carlo method and similar to the kinetic Monte Carlo methods. It is used heavily in computational system ... [...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] |
William Feller
William "Vilim" Feller (July 7, 1906 – January 14, 1970), born Vilibald Srećko Feller, was a Croatian–American mathematician specializing in probability theory. Early life and education Feller was born in Zagreb to Ida Oemichen-Perc, a Croatian–Austrian Catholic, and Eugen Viktor Feller, son of a Polish–Jewish father (David Feller) and an Austrian mother (Elsa Holzer). Eugen Feller was a famous chemist and created ''Elsa fluid'' named after his mother. According to Gian-Carlo Rota, Eugen Feller's surname was a "Slavic tongue twister", which William changed at the age of twenty. This claim appears to be false. His forename, Vilibald, was chosen by his Catholic mother for the saint day of his birthday. Career and later life Feller held a docent position at the University of Kiel beginning in 1928. Because he refused to sign a Nazi oath, he fled the Nazis and went to Copenhagen, Denmark in 1933. He also lectured in Sweden (Stockholm and Lund). As a refugee in Sweden, Fe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Chemistry
Computational chemistry is a branch of chemistry that uses computer simulations to assist in solving chemical problems. It uses methods of theoretical chemistry incorporated into computer programs to calculate the structures and properties of molecules, groups of molecules, and solids. The importance of this subject stems from the fact that, with the exception of some relatively recent findings related to the hydrogen molecular ion (dihydrogen cation), achieving an accurate quantum mechanical depiction of chemical systems analytically, or in a closed form, is not feasible. The complexity inherent in the many-body problem exacerbates the challenge of providing detailed descriptions of quantum mechanical systems. While computational results normally complement information obtained by chemical experiments, it can occasionally predict unobserved chemical phenomena. Overview Computational chemistry differs from theoretical chemistry, which involves a mathematical description of chem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Kinetics
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is different from chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction. History The pioneering work of chemical kinetics was done by German chemist Ludwig Wilhelmy in 1850. He experimentally studied the rate of inversion of sucrose and he used integrated rate law for the determination of the reaction kinetics of this reaction. His work was noticed 34 years later by Wilhelm Ostwald. In 1864, Peter Waage and Cato Guldberg published the law ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Example Calculation Illustrating The Gillespie Algorithm For Reversible Dimerising Molecules
Example may refer to: * ''exempli gratia'' (e.g.), usually read out in English as "for example" * .example, reserved as a domain name that may not be installed as a top-level domain of the Internet ** example.com, example.net, example.org, and example.edu: second-level domain names reserved for use in documentation as examples * HMS ''Example'' (P165), an Archer-class patrol and training vessel of the Royal Navy Arts * ''The Example'', a 1634 play by James Shirley * ''The Example'' (comics), a 2009 graphic novel by Tom Taylor and Colin Wilson * Example (musician), the British dance musician Elliot John Gleave (born 1982) * ''Example'' (album), a 1995 album by American rock band For Squirrels See also * Exemplar (other), a prototype or model which others can use to understand a topic better * Exemplum, medieval collections of short stories to be told in sermons * Eixample The Eixample (, ) is a district of Barcelona between the old city (Ciutat Vella) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tau-leaping
In probability theory, tau-leaping, or τ-leaping, is an approximate method for the simulation of a stochastic system. It is based on the Gillespie algorithm, performing all reactions for an interval of length tau before updating the propensity functions. By updating the rates less often this sometimes allows for more efficient simulation and thus the consideration of larger systems. Many variants of the basic algorithm have been considered. Algorithm The algorithm is analogous to the Euler method In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical analysis, numerical procedure for solving ordinary differential equations (ODEs) with a given Initial value problem, in ... for deterministic systems, but instead of making a fixed change x(t+\tau)=x(t)+\tau x'(t) the change is x(t+\tau)=x(t)+P(\tau x'(t)) where P(\tau x'(t)) is a Poisson distributed random variable with mean \tau x'(t). Given a state \ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rate Equation
In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an Empirical relationship, empirical Differential equation, differential Expression (mathematics), mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only. For many reactions, the initial rate is given by a power law such as :v_0\; =\; k[\mathrm]^x[\mathrm]^y where and are the molar concentrations of the species and usually in Mole (unit), moles per liter (molarity, ). The exponents and are the partial ''orders of reaction'' for and , respectively, and the ''overall'' reaction order is the sum of the exponents. These are often positive integers, but they may also be zero, fractional, or negative. The order of reaction is a number which quantifies the degree to which the rate of a chemical reaction depends on concentrations of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maurice S
Maurice may refer to: *Maurice (name), a given name and surname, including a list of people with the name Places * or Mauritius, an island country in the Indian Ocean *Maurice, Iowa, a city *Maurice, Louisiana, a village *Maurice River, a tributary of the Delaware River in New Jersey Other uses *Maurice (2015 film), ''Maurice'' (2015 film), a Canadian short drama film *Maurice (horse), a Thoroughbred racehorse *Maurice (novel), ''Maurice'' (novel), a 1913 novel by E. M. Forster, published in 1971 **Maurice (1987 film), ''Maurice'' (1987 film), a British film based on the novel *Maurice (Shelley), ''Maurice'' (Shelley), a children's story by Mary Shelley *Maurice, a List of Madagascar (franchise) characters#Maurice, character from the Madagascar ''franchise'' *Maurices, an American retail clothing chain *Maurice or Maryse, a type of cooking spatula See also *Church of Saint Maurice (other) * *Maurice Debate, a 1918 debate in the British House of Commons *Maurice L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manchester Mark 1
The Manchester Mark 1 was one of the earliest stored-program computers, developed at the Victoria University of Manchester, England from the Manchester Baby (operational in June 1948). Work began in August 1948, and the first version was operational by April 1949; a program written to search for Mersenne primes ran error-free for nine hours on the night of 16/17 June 1949. The machine's successful operation was widely reported in the British press, which used the phrase "electronic brain" in describing it to their readers. That description provoked a reaction from the head of the University of Manchester's Department of Neurosurgery, the start of a long-running debate as to whether an electronic computer could ever be truly creative. The Mark 1 was to provide a computing resource within the university, to allow researchers to gain experience in the practical use of computers, but it very quickly also became a prototype on which the design of Ferranti's commercial version coul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David George Kendall
David George Kendall FRS (15 January 1918 – 23 October 2007) was an English statistician and mathematician, known for his work on probability, statistical shape analysis, ley lines and queueing theory. He spent most of his academic life in the University of Oxford (1946–1962) and the University of Cambridge (1962–1985). He worked with M. S. Bartlett during World War II, and visited Princeton University after the war. Life and career David George Kendall was born on 15 January 1918 in Ripon, West Riding of Yorkshire, and attended Ripon Grammar School before attending Queen's College, Oxford, graduating in 1939. He worked on rocketry at the Ministry of Supply's Projectile Development Establishment during World War II, before moving to Magdalen College, Oxford, in 1946. In 1962 he was appointed the first Professor of Mathematical Statistics in the Statistical Laboratory, University of Cambridge; in which post he remained until his retirement in 1985. He was elected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, 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 lev ..., neuroscience, physics, image processing, signal processing, stochastic control, control theory, information theory, computer scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
