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Monte Carlo method

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	NationMaster - Encyclopedia: Monte Carlo method
		Monte Carlo methods are methods for solving various kinds of computational problems by using random numbers (or more often pseudo-random numbers), as opposed to deterministic algorithms.
		Monte Carlo methods are extremely important in computational physics and related applied fields, and have diverse applications from esoteric quantum chromodynamics calculations, to use by engineers in designing heat shields and aerodynamic forms.
		Monte Carlo simulations are distinguished from other types of simulation techniques by their extensive use of random numbers and repeated trials.
	www.nationmaster.com /encyclopedia/Monte_Carlo_method (650 words)

	Monte Carlo method - Wikipedia, the free encyclopedia
		Monte Carlo methods are extremely important in computational physics and related applied fields, and have diverse applications from esoteric quantum chromodynamics calculations to designing heat shields and aerodynamic forms.
		Monte Carlo methods were central to the simulations required for the Manhattan Project, though were strongly limited by the computational tools at the time.
		Uses of Monte Carlo methods require large amounts of random numbers, and it was their use that spurred the development of pseudorandom number generators, which were far quicker to use than the tables of random numbers which had been previously used for statistical sampling.
	en.wikipedia.org /wiki/Monte_Carlo_method (1313 words)

	Reference.com/Encyclopedia/Monte Carlo method
		Monte Carlo simulation methods are especially useful in studying systems with a large number of coupled degrees of freedom, such as liquids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model).
		Monte Carlo methods were central to the simulations required for the Manhattan Project, though were severely limited by the computational tools at the time.
		Uses of Monte Carlo methods require large amounts of random numbers, and it was their use that spurred the development of pseudorandom number generators, which were far quicker to use than the tables of random numbers which had been previously used for statistical sampling.
	www.reference.com /browse/wiki/Monte_Carlo_method (2637 words)

	Monte Carlo method Summary
		Although crude Monte Carlo methods were employed in studies that predate that of the development of the atomic bomb the systematic development of Monte Carlo ideas emerged in 1948 when a group of scientists obtained Monte Carlo estimates for the eigenvalues of the Schrödinger equation.
		Monte Carlo methods are very important in computational physics and related applied fields, and have diverse applications from esoteric quantum chromodynamics calculations to designing heat shields and aerodynamic forms.
		Monte Carlo methods were central to the simulations required for the Manhattan Project, though were strongly limited by the computational tools at the time.
	www.bookrags.com /Monte_Carlo_method (2780 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		In chemistry, dynamic Monte Carlo (DMC) is a method for modeling the dynamic behaviors of molecules by comparing the rates of individual steps with random numbers.
		Unlike the Metropolis Monte Carlo method, which has been employed to study systems at equilibrium, the DMC method is used to investigate non-equilibrium systems such as a reaction, diffusion, and so-forth.
		The DMC method is very similar to the kinetic Monte Carlo method.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Dynamic_Monte_Carlo_method (297 words)

	Monte Carlo Lv The Venetian Lv (Site not responding. Last check: )
		Monte Carlo Lv The Venetian Lv Monte Carlo Lv Monte Carlo or Bust - Monte Carlo or Bust is a 1969 comedy film based around the Monte Carlo Rally.
		Dynamic Monte Carlo method - In chemistry, Dynamic Monte Carlo (DMC) is a method for modeling the dynamic behaviors of molecules by comparing the rates of individual steps with random numbers.
		Monte Carlo Masters - The Monte Carlo Masters is an annual tennis tournament for male professional players held in Monte Carlo, Monaco.
	www.capitalbanklv.com /montecarlolv.html (545 words)

	DFSS for Thermal Management: Introduction to the Monte Carlo Method (Site not responding. Last check: )
		The goal of the Monte Carlo method is to simulate an existing model (which can be an equation, simulation, or physical hardware) by randomly sampling from the input parameter distributions and then performing the necessary calculations (experiments) to predict (measure) the output response.
		The layout of a typical Excel-based Monte Carlo simulation worksheet is shown in Figure 3 where the maximum number of Monte Carlo trials is dictated by the maximum number of rows in the worksheet (65,536 trials in Excel 2002).
		Monte Carlo methods can be applied to extremely complex computational fluid dynamic and finite element models as well, but the execution time for each trial may be hours instead of milliseconds for a spreadsheet model.
	www.coolingzone.com /Guest/News/NL_JAN_2004/Garron/Garron_Jan_04.html (1334 words)

	Monte Carlo method -- Facts, Info, and Encyclopedia article (Site not responding. Last check: )
		Because of the repetition of algorithms and the large number of calculations involved, Monte Carlo is a method suited to calculation using a (A machine for performing calculations automatically) computer, utilizing many techniques of ((computer science) the technique of representing the real world by a computer program) computer simulation.
		Monte Carlo methods were central to the ((computer science) the technique of representing the real world by a computer program) simulations required for the (A former United States executive agency that was responsible for developing atomic bombs during World War II) Manhattan Project.
		Most Monte Carlo optimisation methods are based on (A stochastic process consisting of a sequence of changes each of whose characteristics (as magnitude or direction) is determined by chance) random walks.
	www.absoluteastronomy.com /encyclopedia/M/Mo/Monte_Carlo_method.htm (1245 words)

	Dynamic Monte Carlo method - Wikipedia, the free encyclopedia
		In chemistry, Dynamic Monte Carlo (DMC) is a method for modeling the dynamic behaviors of molecules by comparing the rates of individual steps with random numbers.
		Unlike the Metropolis Monte Carlo method, which has been employed to study systems at equilibrium, the DMC method is used to investigate nonequilibrium systems such as reaction, diffusion, etc. This method is mainly applied to analyze the behavior of adsorbates on surfaces.
		This method is efficient in computation time because the reaction always occurs in one event.
	en.wikipedia.org /wiki/Dynamic_Monte_Carlo_method (301 words)

	CSERD Resources: Algorithms: Monte Carlo Modeling
		The most common method (integration of differential equations) is to determine general properties of the system, to specify the rate of change over time, and to track the change in those general quantities over time.
		Monte Carlo modeling attempts to solve dynamic problems by tracking individual elements, in this case, individual predators and prey, and determining the occurence of key events (such as eating and being eaten) by evaluation of the probability of occurence of that event within a given time.
		While more cumbersome computationally, this method not only allows us to deal with the effects of random events on a small population more realistically, but it also allows us to more easily track the change of traits within the population.
	www.shodor.org /refdesk/Resources/Algorithms/MonteCarlo/index.php (487 words)

	Rich Sutton's Publications
		Monte Carlo methods have a natural way of setting the step size: for each state s they use a step size of 1/n_s, where n_s is the number of times state s has been visited.
		Learning methods are used in Dyna both for compiling planning results and for updating a model of the effects of the agent's actions on the world.
		Adaptive methods for problems of the first kind are well known, and include self-tuning regulators and model-reference methods, whereas adaptive methods for optimal-control problems have received relatively little attention.
	web.cs.ualberta.ca /~sutton/publications.html (12459 words)

	NERSC 2000 Annual Report: Science Highlights: Advanced Scientific Computing Research and Other Projects
		Two-dimensional Monte Carlo (cyan squares) and n-fold way (fl circles) simulations with each PE having a block of lattice sites 128 on a side.
		We used our PDES to perform dynamic Monte Carlo simulations for thermal switching of nanoscale magnets and to perform finite-size scaling for a dynamic phase transition for magnetic thin films.
		Our dynamic Monte Carlo algorithms allow simulations that are true to the underlying physical dynamic and span very large time scales, from atomistic times to engineering times.
	www.nersc.gov /news/annual_reports/annrep00/sh_ADV_07.html (581 words)

	5. Monte Carlo Methods
		Monte Carlo methods require only experience--sample sequences of states, actions, and rewards from on-line or simulated interaction with an environment.
		Monte Carlo methods are ways of solving the reinforcement learning problem based on averaging sample returns.
		Monte Carlo methods are thus incremental in an episode-by-episode sense, but not in a step-by-step sense.
	www.cs.ualberta.ca /~sutton/book/ebook/node50.html (344 words)

	The BUGS Project - References (Site not responding. Last check: )
		Our Markov chain Monte Carlo implementation demonstrates that the viraemia time-series observed in two sets of hepatitis B patients on antiviral (lamivudine) therapy chronic carriers and liver transplant patients, are significantly different, overcoming clinical trial design differences that question the validity of non- parametric tests.
		The choice of a suitable MCMC method and further the choice of a proposal distribution is known to be crucial for the convergence of the Markov chain.
		The linear imputation methods and the closely related discrimination analysis method are suitable for continuous risk factors which, together with the errors of measurement, are usually assumed to be normally distributed.
	www.mrc-bsu.cam.ac.uk /bugs/references/bugs-disc-abstracts.shtml (10123 words)

	Parametric Estimates by the Monte Carlo Method
		This monograph is devoted to the further development of parametric weight Monte Carlo estimates for solving linear and nonlinear integral equations, radiation transfer equations, and boundary value problems, including problems with random parameters.
		The use of these estimates leads to the construction of new, effective Monte Carlo methods for calculating parametric multiple derivatives of solutions and for the main eigenvalues.
		Additionally, new Monte Carlo methods for solving stochastic radiation transfer problems are presented, including the estimation of probabilistic moments of corresponding critical parameters.
	www.brill.nl /product_id10708.htm (442 words)

	Applications of Diffusion to Monte Carlo Image Synthesis
		Monte Carlo methods have been applied to this problem in order to reduce the amount of computation (1).
		In the current research we have investigated the utility of diffusion algorithms to the problems of dynamic load balancing and partitioning in Monte Carlo path tracing.
		We have implemented a Monte Carlo algorithm as a message-driven concurrent pipeline, and have employed a diffusion algorithm to perform dynamic load balancing.
	www-fp.mcs.anl.gov /CCST/research/reports_pre1998/algorithm_development/monte_carlo/heinrich.html (505 words)

	Real Options with Monte Carlo Simulation (Site not responding. Last check: )
		The Monte Carlo method solves a problem by simulating directly the physical process, and is not necessary to write down the differential equations that describe the behavior of the system.
		The name "Monte Carlo" appeared in the World War II times, and sometimes is attributed to the researcher Nicholas Metropolis, inspired in the interest of Stanislaw Ulam, his colleague of Manhattan Project at Los Alamos, in the poker game.
		Monte Carlo simulation is considered a good way to face these problems, but there is the difficult problem to optimize.
	www.puc-rio.br /marco.ind/monte-carlo.html (4233 words)

	Monte Carlo 2005 Topical Meeting
		The Monte Carlo method has been used for over forty years to solve almost all problems in radiation transport associated with shielding, nuclear reactors, medical equipment, and other similar applications.
		The success of the method is based on its broad application field, accuracy in modeling complicated geometries, ability to handle complicated data, and flexibility.
		For many years, the widespread implementation of the Monte Carlo method was limited because of the computational requirements and because the early Monte Carlo codes required expert knowledge by a specialist in the technique for successful application to a problem.
	meetingsandconferences.com /MonteCarlo2005/program.html (467 words)

	Polymer Research Center: Main (Site not responding. Last check: )
		An off-lattice dynamic Monte Carlo (MC) method is used to investigate the conformational dynamics of chymotrypsin inhibitor 2 (CI2) and subtilisin in both free and complex forms over two time windows, referring to short and long time scales.
		The conformational dynamics of backbone bonds analysed from several independent trajectories reveal that: Both the inhibitor and the enzyme are restricted in their bond rotations, excluding a few bonds, upon binding; the effect being greatest for the loop regions, and for the inhibitor.
		A cooperativity in the near-neighbor bond rotations are observed on both time scales, whereas the cooperative rotations of the bonds far along the sequence appear only in the long time window, and the latter time window is where most of the interactions between the inhibitor and the enzyme are observed.
	klee.bme.boun.edu.tr /jbsd01.html (272 words)

	System and method for determining three-dimensional structures of proteins (US5265030)
		A computer system and method are disclosed for determining a protein's tertiary structure from a primary sequence of amino acid residues.
		The system uses a dynamic Monte Carlo method with Metropolis sampling criterion, and a selected (2,1,0) lattice model, to simulate protein folding during the transition of the protein from an unfolded (denatured) state to its native, folded state.
		Method of determining a three-dimensional conformation of a globular protein utilizing Monte Carlo dynamics technique with asymmetric Metropolis sampling criterion, the method comprising the steps of:
	www.delphion.com /details?&pn10=US05265030 (635 words)

	WSN: JCP manuscripts on-line
		It is shown that it is possible to blend the numerical and analytical methods to increase the reliability of quantitative results, and, at the same time, to achieve savings on computational expenditure for certain types of calculations.
		The fluid is modelled by a generalisation of the microscopic classical Yvon-Kirkwood equations, which yields the same dynamic response as the much-studied quantum Drude oscillator model.
		We display the absorption spectrum, as implied by the renormalised polarisability and the dynamic dielectric constant, for both hard sphere and Lennard-Jones fluids.
	www.ibiblio.org /water/wsn-archive/msg00136.html (690 words)

	Dynamic Monte Carlo method at AllExperts
		In chemistry, Dynamic Monte Carlo (DMC) is a method for modeling the dynamic behaviors of molecules by comparing the rates of individual steps with random numbers.
		Unlike the Metropolis Monte Carlo method, which has been employed to study systems at equilibrium, the DMC method is used to investigate nonequilibrium systems such as reaction, diffusion, etc. This method is mainly applied to analyze the behavior of adsorbates on surfaces.
		The DMC method is very similar to the Kinetic Monte Carlo method.
	en.allexperts.com /e/d/dy/dynamic_monte_carlo_method.htm (352 words)

	Team-Bunraku:Interactive Global Illumination
		Consequently, Monte Carlo integration is the method of choice for solving it.
		However, Monte Carlo integration requires the computation of many samples, which makes it demanding in terms of computation time.
		By reusing data in several frames, our method yields a significant speedup compared to classical computation in which a new cache is computed for every frame.
	ralyx.inria.fr /2006/Raweb/bunraku/uid92.html (635 words)

	Amazon.ca: Monte Carlo Strategies in Scientific Computing: Books: Jun S. Liu (Site not responding. Last check: )
		There is a fairly thorough coverage of wide variety of Monte Carlo algorithms that have arisen in diverse fields such as physics, chemistry, biology, etc., and the relationship among them.
		This is the reason for the emergence of variance reduction methods, importance sampling, rejection, sequential MC, Metropolis algorithms, Gibbs samplers, Markov Chain MC (MCMC), or hybrid MC with molecular dynamics.
		The Monte Carlo method is a computer-based statistical sampling approach for solving numerical problems concerned with a complex system.
	www.amazon.ca /Monte-Carlo-Strategies-Scientific-Computing/dp/0387952306 (1353 words)

	Basics of the Monte Carlo Method with Application to System Reliability (Site not responding. Last check: )
		Monte Carlo simulation, thanks to the great development of computer power, has become the most effective tool for performing realistic reliability and availability analysis.
		For its properties, Monte Carlo simulation is the prominent method for the solution of dynamic reliability problems and for the numerical evaluation of stochastic Petri nets (see the LiLoLe book "Petri Nets for Reliability Modeling").
		They have been collaborating to the development of PSA methods since the beginning of the nineties and have published internationally with emphasis on the use of soft computing embedded in Monte Carlo simulations.
	www.lilole-verlag.de /lll-0006.html (277 words)

	Quasi-Monte Carlo Simulation
		The essential characteristic of the Monte Carlo method is the use of random sampling techniques to reach a solution of the physical problem.
		The evaluation of an integral using Monte Carlo simulations is the strongest application of quasi-random sequences, and hence was the initial motivation for research in this area.
		First, quasi-Monte Carlo methods are valid for integration problems, but may not be directly applicable to simulations, due to the correlations between the points of a quasi-random sequence.
	www.puc-rio.br /marco.ind/quasi_mc.html (7263 words)

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