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Hybrid Stochastic Simulation
Hybrid stochastic simulations are a sub-class of stochastic simulations. These simulations combine existing stochastic simulations with other stochastic simulations or algorithms. Generally they are used for physics and physics-related research. The goal of a hybrid stochastic simulation varies based on context, however they typically aim to either improve accuracy or reduce computational complexity. The first hybrid stochastic simulation was developed in 1985. History The first hybrid stochastic simulation was developed by Simon Duane at the University of Illinois at Urbana-Champaign in 1985. It combined the Langevin equation with microcanonical ensembles. Duane's hybrid stochastic simulation was based upon the idea that the two algorithms complemented each other. The Langevin equation excelled at simulating long-time properties, but the addition of noise into the system created inefficient exploration of short-time properties. The microcanonical ensemble approach meanwhile e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Simulation
A stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities.DLOUHÝ, M.; FÁBRY, J.; KUNCOVÁ, M.. Simulace pro ekonomy. Praha : VŠE, 2005. Realizations of these random variables are generated and inserted into a model of the system. Outputs of the model are recorded, and then the process is repeated with a new set of random values. These steps are repeated until a sufficient amount of data is gathered. In the end, the distribution of the outputs shows the most probable estimates as well as a frame of expectations regarding what ranges of values the variables are more or less likely to fall in. Often random variables inserted into the model are created on a computer with a random number generator (RNG). The U(0,1) uniform distribution outputs of the random number generator are then transformed into random variables with probability distributions that are used in the system model. Etymology ''Stoc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Cambridge
, mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Scholars of the University of Cambridge , type = Public research university , endowment = £7.121 billion (including colleges) , budget = £2.308 billion (excluding colleges) , chancellor = The Lord Sainsbury of Turville , vice_chancellor = Anthony Freeling , students = 24,450 (2020) , undergrad = 12,850 (2020) , postgrad = 11,600 (2020) , city = Cambridge , country = England , campus_type = , sporting_affiliations = The Sporting Blue , colours = Cambridge Blue , website = , logo = University of Cambridge log ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Random Variable
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma is its standard deviation. The variance of the distribution is \sigma^2. A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal distrib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler–Maruyama Method
In Itô calculus, the Euler–Maruyama method (also called the Euler method) is a method for the approximate numerical solution of a stochastic differential equation (SDE). It is an extension of the Euler method for ordinary differential equations to stochastic differential equations. It is named after Leonhard Euler and Gisiro Maruyama. Unfortunately, the same generalization cannot be done for any arbitrary deterministic method. Consider the stochastic differential equation (see Itô calculus) :\mathrm X_t = a(X_t, t) \, \mathrm t + b(X_t, t) \, \mathrm W_t, with initial condition ''X''0 = ''x''0, where ''W''''t'' stands for the Wiener process, and suppose that we wish to solve this SDE on some interval of time , ''T'' Then the Euler–Maruyama approximation to the true solution ''X'' is the Markov chain ''Y'' defined as follows: * partition the interval , ''T''into ''N'' equal subintervals of width \Delta t>0: ::0 = \tau_ float: """ Sample a ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Receptor (biochemistry)
In biochemistry and pharmacology, receptors are chemical structures, composed of protein, that receive and transduce signals that may be integrated into biological systems. These signals are typically chemical messengers which bind to a receptor and cause some form of cellular/tissue response, e.g. a change in the electrical activity of a cell. There are three main ways the action of the receptor can be classified: relay of signal, amplification, or integration. Relaying sends the signal onward, amplification increases the effect of a single ligand, and integration allows the signal to be incorporated into another biochemical pathway. Receptor proteins can be classified by their location. Transmembrane receptors include ligand-gated ion channels, G protein-coupled receptors, and enzyme-linked hormone receptors. Intracellular receptors are those found inside the cell, and include cytoplasmic receptors and nuclear receptors. A molecule that binds to a receptor is called a li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinite Space
is a 2009 role-playing video game co-developed by Nude Maker and PlatinumGames for the Nintendo DS. It was published by Sega in 2009 in Japan, and 2010 in Western territories. The science fiction storyline, set across the Small Magellanic Cloud, Small and Large Magellanic Clouds, follows the life and growth of Yuri as he first confronts the aggressive expansion of the Lugovalian Empire, then a greater alien threat. Gameplay involves Yuri's fleet travelling across the galaxies, fighting in both scripted battles and random encounters, with the battle system featuring real-time commands and both ships and crew being customizable. The project emerged when producer Atsushi Inaba contacted Nude Maker to produce a title together, as Inaba had enjoyed working with them on ''Steel Battalion''. The story, created by director Hifumi Kono, drew inspiration from numerous Western and Japanese science fiction works, particularly the work of authors Arthur C. Clarke and Greg Egan, and anime c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brownian Motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such a fluid, there exists no preferential direction of flow (as in transport phenomena). More specifically, the fluid's overall linear and angular momenta remain null over time. The kinetic energies of the molecular Brownian motions, together with those of molecular rotations and vibrations, sum up to the caloric component of a fluid's internal energy (the equipartition theorem). This motion is named after the botanist Robert Brown, who first described the phenomenon in 1827, while looking th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Oxford
The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the world's second-oldest university in continuous operation. It grew rapidly from 1167 when Henry II banned English students from attending the University of Paris. After disputes between students and Oxford townsfolk in 1209, some academics fled north-east to Cambridge where they established what became the University of Cambridge. The two English ancient universities share many common features and are jointly referred to as ''Oxbridge''. Both are ranked among the most prestigious universities in the world. The university is made up of thirty-nine semi-autonomous constituent colleges, five permanent private halls, and a range of academic departments which are organised into four divisions. All the colleges are self-governing institutions within the university, each controlling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Holcman
David Holcman is an applied mathematician, biophysicist and computational biologist at École Normale Supérieure in Paris. He is known for his work on the narrow escape problem, based on analysis of the Laplace equation, the redundancy principle in biology based on extreme statistics, the modeling of molecular trafficking in neurobiology, of diffusion and electrodiffusion in nanodomains such as dendritic spines, the modeling of neuronal networks dynamics such as Up and Down states in electrophysiology. He developed multiscale methods and simulations to analyse large amount of molecular super-resolution trajectories, and polymer physics modeling and analysis to study cell nucleus organization. These computational approaches led to several verified predictions in the life sciences such as nanocolumn organization of synapses or astrocytic protrusion penetrating neuronal synapses, molecular ER organization in dendritic spines and many more. The narrow escape theory was recently ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm can be expressed within a finite amount of spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called ''color''. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years. QCD exhibits three salient properties: * Color confinement. Due to the force between two color charges remaining constant as they are separated, the energy grows until a quark–antiquark pair is spontaneously produced, turning the initial hadron into a pair of hadrons instead of isolating a color charge. Al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microcanonical Ensemble
In statistical mechanics, the microcanonical ensemble is a statistical ensemble that represents the possible states of a mechanical system whose total energy is exactly specified. The system is assumed to be isolated in the sense that it cannot exchange energy or particles with its environment, so that (by conservation of energy) the energy of the system does not change with time. The primary macroscopic variables of the microcanonical ensemble are the total number of particles in the system (symbol: ), the system's volume (symbol: ), as well as the total energy in the system (symbol: ). Each of these is assumed to be constant in the ensemble. For this reason, the microcanonical ensemble is sometimes called the ensemble. In simple terms, the microcanonical ensemble is defined by assigning an equal probability to every microstate whose energy falls within a range centered at . All other microstates are given a probability of zero. Since the probabilities must add up to 1, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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