|
Wang And Landau Algorithm
The Wang and Landau algorithm, proposed by Fugao Wang and David P. Landau, is a Monte Carlo method designed to estimate the density of states of a system. The method performs a non-Markovian random walk to build the density of states by quickly visiting all the available energy spectrum. The Wang and Landau algorithm is an important method to obtain the density of states required to perform a multicanonical simulation. The Wang–Landau algorithm can be applied to any system which is characterized by a cost (or energy) function. For instance, it has been applied to the solution of numerical integrals and the folding of proteins. The Wang–Landau sampling is related to the metadynamics algorithm.Christoph Junghans, Danny Perez, and Thomas Vogel. "Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang–Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics." Journal of Chemical Theory and Computation 10.5 (2014): 1843-1847. doibr>10.1021/ct5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David P
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". was, according to the Hebrew Bible, the third king of the United Kingdom of Israel. In the Books of Samuel, he is described as a young shepherd and harpist who gains fame by slaying Goliath, a champion of the Philistines, in southern Canaan. David becomes a favourite of Saul, the first king of Israel; he also forges a notably close friendship with Jonathan, a son of Saul. However, under the paranoia that David is seeking to usurp the throne, Saul attempts to kill David, forcing the latter to go into hiding and effectively operate as a fugitive for several years. After Saul and Jonathan are both killed in battle against the Philistines, a 30-year-old David is anointed king over all of Israel and Judah. Following his rise to power, David ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of ris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Estimator
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean. There are point and interval estimators. The point estimators yield single-valued results. This is in contrast to an interval estimator, where the result would be a range of plausible values. "Single value" does not necessarily mean "single number", but includes vector valued or function valued estimators. ''Estimation theory'' is concerned with the properties of estimators; that is, with defining properties that can be used to compare different estimators (different rules for creating estimates) for the same quantity, based on the same data. Such properties can be used to determine the best rules to use under given circumstances. However, in robust statistics, statistica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Of States
In solid state physics and condensed matter physics, the density of states (DOS) of a system describes the number of modes per unit frequency range. The density of states is defined as D(E) = N(E)/V , where N(E)\delta E is the number of states in the system of volume V whose energies lie in the range from E to E+\delta E. It is mathematically represented as a distribution by a probability density function, and it is generally an average over the space and time domains of the various states occupied by the system. The density of states is directly related to the dispersion relations of the properties of the system. High DOS at a specific energy level means that many states are available for occupation. Generally, the density of states of matter is continuous. In isolated systems however, such as atoms or molecules in the gas phase, the density distribution is discrete, like a spectral density. Local variations, most often due to distortions of the original system, are often referr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Walk
In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer science, physics, chemistry, biology, economics, and sociology. The term ''random walk'' was first introduced by Karl Pearson in 1905. Lattice random walk A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. In a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multicanonical Ensemble
In statistics and physics, multicanonical ensemble (also called multicanonical sampling or flat histogram) is a Markov chain Monte Carlo sampling technique that uses the Metropolis–Hastings algorithm to compute integrals where the integrand has a rough landscape with multiple local minima. It samples states according to the inverse of the density of states, which has to be known a priori or be computed using other techniques like the Wang and Landau algorithm. Multicanonical sampling is an important technique for spin systems like the Ising model or spin glasses. Motivation In systems with a large number of degrees of freedom, like spin systems, Monte Carlo integration is required. In this integration, importance sampling and in particular the Metropolis algorithm, is a very important technique. However, the Metropolis algorithm samples states according to \exp(-\beta E) where beta is the inverse of the temperature. This means that an energy barrier of \Delta E on the energy spect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metadynamics
Metadynamics (MTD; also abbreviated as METAD or MetaD) is a computer simulation method in computational physics, chemistry and biology. It is used to estimate the free energy and other state functions of a system, where ergodicity is hindered by the form of the system's energy landscape. It was first suggested by Alessandro Laio and Michele Parrinello in 2002 and is usually applied within molecular dynamics simulations. MTD closely resembles a number of recent methods such as adaptively biased molecular dynamics, adaptive reaction coordinate forces and local elevation umbrella sampling. More recently, both the original and well-tempered metadynamics were derived in the context of importance sampling and shown to be a special case of the adaptive biasing potential setting. MTD is related to the Wang–Landau sampling. Introduction The technique builds on a large number of related methods including (in a chronological order) the deflation, tunneling, tabu search, local elevation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Object Identifier
A digital object identifier (DOI) is a persistent identifier or handle used to uniquely identify various objects, standardized by the International Organization for Standardization (ISO). DOIs are an implementation of the Handle System; they also fit within the URI system ( Uniform Resource Identifier). They are widely used to identify academic, professional, and government information, such as journal articles, research reports, data sets, and official publications. DOIs have also been used to identify other types of information resources, such as commercial videos. A DOI aims to resolve to its target, the information object to which the DOI refers. This is achieved by binding the DOI to metadata about the object, such as a URL where the object is located. Thus, by being actionable and interoperable, a DOI differs from ISBNs or ISRCs which are identifiers only. The DOI system uses the indecs Content Model for representing metadata. The DOI for a document remains fixed over t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Estimator
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean. There are point and interval estimators. The point estimators yield single-valued results. This is in contrast to an interval estimator, where the result would be a range of plausible values. "Single value" does not necessarily mean "single number", but includes vector valued or function valued estimators. ''Estimation theory'' is concerned with the properties of estimators; that is, with defining properties that can be used to compare different estimators (different rules for creating estimates) for the same quantity, based on the same data. Such properties can be used to determine the best rules to use under given circumstances. However, in robust statistics, statistica ... [...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. 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, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metropolis–Hastings Algorithm
In statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult. This sequence can be used to approximate the distribution (e.g. to generate a histogram) or to compute an integral (e.g. an expected value). Metropolis–Hastings and other MCMC algorithms are generally used for sampling from multi-dimensional distributions, especially when the number of dimensions is high. For single-dimensional distributions, there are usually other methods (e.g. adaptive rejection sampling) that can directly return independent samples from the distribution, and these are free from the problem of autocorrelated samples that is inherent in MCMC methods. History The algorithm was named after Nicholas Metropolis and W.K. Hastings. Metropolis was the first author to appear on the list of authors of the 1953 article ''Equation of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its Mechanical equilibrium, equilibrium position, experiences a restoring force ''F'' Proportionality (mathematics), proportional to the displacement ''x'': \vec F = -k \vec x, where ''k'' is a positive coefficient, constant. If ''F'' is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude). If a frictional force (Damping ratio, damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction coefficient, the system can: * Oscillate with a frequency lower than in the Damping ratio, undamped case, and an amplitude decreasing with time (Damping ratio, underdamped oscillator). * Decay to the equilibrium p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Density Of States")
