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Topic: Random walk Monte Carlo

Related Topics

Monte Carlo method

Gibbs sampling

Metropolis algorithm

Importance sampling

Rejection sampling

VEGAS algorithm

Stratified sampling

Random number

Stochastic tunneling

Markov chain

Simulated annealing

Genetic algorithm

Monte Carlo

Hamiltonian dynamics

Hidden Markov model

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	TreeAge Software - Monte Carlo Simulation
		Monte Carlo simulation allows analysts to examine the potential impact of all parameter uncertainties in the model.
		Monte Carlo simulation refers to the use of random numbers in evaluating a model.
		Monte Carlo simulation can update any number of parameters between model recalculations, assigning values that are randomly sampled from probability distributions.
	www.treeage.com /learnMore/MonteCarloSimulation.html (991 words)

	Random walk - Wikipedia, the free encyclopedia
		This is a random walk on a graph.
		In physics, random walks are used as simplified models of physical Brownian motion and the random movement of molecules in liquids and gases.
		Random walk can be used to sample from a state space which is unknown or very large, for example to pick a random page off the internet or, for research of working conditions, a random illegal worker in a given country.
	en.wikipedia.org /wiki/Random_walk (2508 words)

	Markov chain Monte Carlo - Wikipedia, the free encyclopedia
		Markov chain Monte Carlo (MCMC) methods (which include random walk Monte Carlo methods), are a class of algorithms for sampling from probability distributions based on constructing a Markov chain that has the desired distribution as its stationary distribution.
		Random walk methods are a kind of random simulation or Monte Carlo method.
		However, whereas the random samples of the integrand used in a conventional Monte Carlo integration are statistically independent, those used in MCMC are correlated.
	en.wikipedia.org /wiki/Random_walk_Monte_Carlo (745 words)

	Learn more about Monte Carlo method in the online encyclopedia. (Site not responding. Last check: 2007-11-01)
		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.
		The "Monte Carlo" designation is a reference to the famous casino in that area, and was popularized by early pioneers in the field such as Stanislaw Marcin Ulam, Enrico Fermi, John von Neumann and Nick Metropolis.
	www.onlineencyclopedia.org /m/mo/monte_carlo_method.html (707 words)

	Monte Carlo Techniques
		The method calls for a random walk, or a guided random walk, in phase space during which the integrand is evaluated at each step and averaged over.
		The Monte Carlo approach is implemented by enclosing the circle in a square of side 2 and using random numbers in the interval x = (-1,1) and y = (-1,1).
		A parallel implementation of the Monte Carlo integration must have the random sequence distributed to the different nodes, either by communication or by a local generation of the sequence.
	einstein.drexel.edu /courses/PHYS405/Monte_Carlo/index.html (1885 words)

	Web Site for Perfectly Random Sampling with Markov Chains:
		Another problem is that of generating a random spanning tree of a graph or spanning arborescence of a directed graph in accordance with the uniform distribution, or more generally in accordance with a distribution given by weights on the edges of the graph or digraph.
		However, the running time of their algorithm is an unbounded random variable whose order of magnitude is typically unknown a priori and which is not independent of the state sampled, so a naive user with limited patience who aborts a long run of the algorithm will introduce bias.
		A random walk example is used to illustrate the multistage generalization and to compare it with Propp and Wilson's single-stage scheme.
	dbwilson.com /exact (14686 words)

	Citations: Error and complexity of random walk Monte-Carlo radiosity - Sbert (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		Random walks are generated by sampling their origin ## corresponding to a light source patch, with birth density # # # # # ###, # # # # # # # the selfemitted power.
		In figure 7 we compare the three methods with a reference solution (generated with a Phi T local Monte Carlo method [Sbert97] with 16 million rays) All the presented results are the average of 6 executions.
		....finite path length estimators and an infinite path length one are characterized for both shooting and gathering random walk.
	citeseer.ist.psu.edu /context/194268/0 (2325 words)

	Randomwalk
		This is just one of an infinite variety of random walk possibilities, many of which have interesting physics applications.
		In mathematics and physics, a random walk is a formalization of the intuitive idea of taking successive steps, each in a random direction.
		In this case the exponent is a parameter that will be determined by the fit, but we have an expectation that it should be p= 0.5, since theory says that 2-dim random walks should have a distance that depends on the sqrt(number of steps).
	www2.hawaii.edu /~spiek/Randomwalk.html (2357 words)

	A random walk through time and space
		Einstein's work on Brownian motion also was the first practical application of random processes for understanding physical phenomena, because he related the random walk of a single particle to the diffusion of many particles.
		This randomness was the source of the irreversibility of many macroscopic processes and, hence, the second law of thermodynamics.
		However, random fluctuations and statistical mechanics are fundamental to the most elemental building blocks of the physical world and are called on to explain the mysterious processes of protein folding, cell-membrane function, evolution, and even stock market behavior.
	www.eurekalert.org /features/doe/2005-08/drnl-arw082205.php (3133 words)

	Monte Carlo Examples - GNU Scientific Library -- Reference Manual
		The integral gives the mean time spent at the origin by a random walk on a body-centered cubic lattice in three dimensions.
		The Monte Carlo routines only select points which are strictly within the integration region and so no special measures are needed to avoid these singularities.
		With 500,000 function calls the plain Monte Carlo algorithm achieves a fractional error of 0.6%.
	www.gnu.org /software/gsl/manual/html_node/Monte-Carlo-Examples.html (448 words)

	Stanford Probability Seminar
		The phase transition in random K-satisfiability problems is a very important phenomenon both from the point of view of physics and from that of computational complexity.
		The entropy of a random variable with density f is defined as the integral of -f log f.
		At each unit of time the walk picks one of its 2d neighbors at random and attempts to move to it, but the move is suppressed if the respective edge is not present in C_\infty.
	www-stat.stanford.edu /~amir/prob-seminar/y2005 (3655 words)

	99C-21 Monte Carlo approach as a tool for mass transfer analysis in food systems. (Site not responding. Last check: 2007-11-01)
		Monte Carlo simulation has been increasingly used in life science and engineering, however, few articles are found in food processing, especially mass transfer.
		Diffusion in two dimensions was modeled as a random walk process in which a diffusing particle, dextran, of known molecular weight and diffusivity in water, moves within a space lattice that was restricted to a circular shape with point source and constant boundary conditions.
		Monte Carlo simulation can be a useful tool to help clarify mass transfer phenomena in food systems.
	ift.confex.com /ift/2005/techprogram/paper_29262.htm (398 words)

	HISTORY OF MONTE CARLO METHOD
		The Monte Carlo method provides approximate solutions to a variety of mathematical problems by performing statistical sampling experiments on a computer.
		Among all numerical methods that rely on N-point evaluations in M-dimensional space to produce an approximate solution, the Monte Carlo method has absolute error of estimate that decreases as N superscript -1/2 whereas, in the absence of exploitable special structure all others have errors that decrease as N superscript -1/M at best.
		The real use of Monte Carlo methods as a research tool stems from work on the atomic bomb during the second world war.
	www.geocities.com /CollegePark/Quad/2435/history.html (603 words)

	Advanced Monte Carlo Methods
		Monte Carlo methods are numerical methods that use random numbers to compute quantities of interest.
		There are few areas of science and technology where Monte Carlo methods are not used, and understanding how they are used in applications, with an eye on cross-domain fertilization, is a very important way to motivate and reinforce interest in Monte Carlo Methods.
		Thus, Monte Carlo methods themselves are a fruitful source of research problems, and when combined with deterministic methods have the promise to provide many improved numerical methods.
	www.cs.fsu.edu /~mascagni/Advanced_Monte_Carlo_Methods.html (2914 words)

	Dr. Michael Mascagni: Recent Papers
		This paper describes the random walk on the boundary Monte Carlo method, and applies it to the calculation of the capacitance of the unit cube.
		This is accomplished with a new probability that is used to terminate random walks in the linearized Poisson-Boltzmann case.
		In addition, the M-out-of-N strategy is examined to speed Grid Monte Carlo computations in a faulty environment and in using the random number generator to provide the ability to validate a volunteered Monte Carlo computation.
	www.cs.fsu.edu /~mascagni/papers.html (4964 words)

	Financial Risk Management
		arithmetic random walk A random walk with increments that are a Gaussian white noise.
		arithmetic random walk with drift An arithmetic random walk with a constant drift.
		In 2002, accounting firm Arthur Andersen was convicted on a single charge related to its auditing of Enron.
	www.riskglossary.com (519 words)

	SIM: Random Walks (Site not responding. Last check: 2007-11-01)
		He chooses a direction at random, walks to the corner of a block and repeats the process.
		We can easily write a Monte Carlo simulation to model the drunkard's random walk, and, for example, determine the average distance the drunkard is from the pub after walking N blocks.
		A simple function which implements the first N steps of such a walk is included in the example program rwalk1d.C.
	hepwww.ph.qmw.ac.uk /~traynor/sim/week4/randomwalk.html (390 words)

	Gambling - Wikipedia, the free encyclopedia
		In mechanical or electronic gambling such as lotteries, slot machines and bingo, the results are random and unpredictable; no amount of skill or knowledge (assuming machinery is functioning as intended) can give an advantage in predicatability to anyone.
		However, it can usually be used to gain a small win in the short run, given a bankroll large enough to survive a streak of five or six losses.
		Scientists have dubbed certain random-number-based calculation algorithms the "Monte Carlo method".
	en.wikipedia.org /wiki/Gambling (3170 words)

	Monte Carlo sampling (Site not responding. Last check: 2007-11-01)
		Monte Carlo sampling of probability distributions: How to make the computer roll dice.
		Lux, L. Koblinger, "Monte Carlo Particle Transport Methods: Neutron and Photon Calculations," CRC Press (1991).
		A.N. Witt, "Multiple scattering in reflection nebulae I. A Monte Carlo approach," The Astrophysical J. Supp.
	omlc.ogi.edu /news/sep98/montecarlosampling/index.html (353 words)

	The Monte Carlo Method (UNC-CH Computer Science)
		The Monte Carlo method consists of creating a statistical situation (probability space) in which a required answer is the expected value of some random variable; the answer is then estimated by sufficient sampling of this random variable to ensure adequate accuracy.
		In the case of linear algebraic problems, the solution is obtained by computing an estimate obtained from a "random walk" in a suitable space.
		In addition, we explore the development of better and more versatile techniques to solve a wide range of large-scale problems, and we also investigate the random generators (especially quasi-random generators of sequences of numbers and sets of numbers, and parallelizable generators--"random trees") that are used, with a view to improving and to analyzing their efficiency.
	www.cs.unc.edu /Research/MonteCarlo.html (307 words)

	Monte Carlo Analysis (Site not responding. Last check: 2007-11-01)
		Monte Carlo is often the method of choice to solve complex problems in nuclear criticality safety and radiation shielding.
		To use Monte Carlo effectively, the analyst must understand the theoretical and computational fundamentals of the method, as well as the computational options available in particular computer tools.
		To familiarize the student with the basic concepts of the Monte Carlo method in a general (non-transport) context to add to the students’ ability to apply method to a variety of problems in mathematics, physics, and engineering.
	www.engr.utk.edu /nuclear/TIW/REP6.html (428 words)

	random walk (Site not responding. Last check: 2007-11-01)
		In this project formulae are derived to compute the mean number of times a site has been visited in a random walk on a two dimensional lattice.
		Asymmetric random walks are considered, with or without drift, for different boundary conditions.
		First general formulas will be derived, and next they will be applied to simple symmetric random walks on finite and infinite lattices; the dependence of the statistics on the lattices dimensionality will also be studied.
	www.to.infn.it /~zaninett/randomwalk.html (207 words)

	Random Walks
		That's because multiplying a set of random numbers by D multiplies both the Mean and the Standard Deviation by D.
		If we do a Random Walk a jillion times, each time generating a possible future evolution of the market(s), then analyze these jillion scenarios...
		These 120 gains are chosen, at random, from the 600 monthly gains of the S&P500, in the period Jan 1, 1950 to Jan 1, 2000.
	www.gummy-stuff.org /Random_Walks.htm (1916 words)

	Monte Carlo Methods in Parallel Computing
		Floating Random Walk Solution Algorithm (point.C) The potential at the center of a circle of radius r, which lies entirely within the region is
		In contrast, to achieve 1% accuracy, using the Monte Carlo method, about 10,000 terms must be summed.
		Pick two random integers x and y between 1 and L. Let DelE be the change in energy caused by changing the value of the spin at (x,y).
	www.phy.hr /~laci/para/mc/mc.html (1446 words)

	"3-D Monte Carlo Module for Interactive Trajectory Analysis" (Site not responding. Last check: 2007-11-01)
		t, a random horizontal displacement, of magnitude confined to a length scale proportional to a prescribed constant mesoscale eddy diffusivity, is applied to each particle.
		The random walk particle models predict the same concentration patterns as the more advanced particle models, although some differences in maximum concentrations are evident.
		It should be noted, however, that the random walk particle models with long time steps may not be suitable for use with some physical parameterizations, e.g., plume rise, dry deposition (Uliasz, 1994).
	capita.wustl.edu /capita/CapitaReports/fy95rept/fy95rept.html (9159 words)

	Risk Latte - LearnLatte
		Monte Carlo simulation of multiple assets using Cholesky decomposition;
		It gives the basic quantitative skills required to develop binomial trees and multi-asset Monte Carlo simulation and then simply apply them to pricing and modelling different types and classes of products.
		This programme is targeted at fixed income & equity derivatives traders, structurers and quants who are interested in acquiring the knowledge and tools to significantly enhance their performance and their careers.
	www.risklatte.com /training.php (593 words)

	hemicube_link (Site not responding. Last check: 2007-11-01)
		This paper proposes a new random walk strategy that minimizes the variance of the estimate using statistical estimations of local and global features of the scene.
		Based on the local and global properties, the algorithm decides at each point whether a Russian-roulette like random termination is worth performing, or on the contrary, we should split the path into several child paths.
		In this sense the algorithm is similar to the go-with-the-winners strategy invented in general Monte Carlo context.
	www.iit.bme.hu /~szirmay/gowin_link.htm (178 words)

	An Empirical Comparison of Monte Carlo Radiosity Algorithms (Site not responding. Last check: 2007-11-01)
		Monte Carlo radiosity algorithms are radiosity algorithms in which the radiosity integral equation or system of linear equations is solved using Monte Carlo random walk techniques.
		Since explicit form factor computation and storage is completely avoided in Monte Carlo radiosity algorithms, these algorithms are more reliable and require significantly less storage than other radiosity algorithms, making it feasible to render much more complex scenes.
		This paper presents a comparative study of four main aspects in which proposed Monte Carlo radiosity algorithms differ: whether the discrete or continuous equation is being solved, the random walk state transition simulation technique, sampling order and the sample number generator.
	www.cs.kuleuven.ac.be /cwis/research/graphics/CGRG.PUBLICATIONS/ECMCR (180 words)

	MONTE-CARLO TECHNIQUES (Site not responding. Last check: 2007-11-01)
		Barring random machine error or using undefined variables, you get the same output every time you feed your program the same input.
		Never the less, a popular computer pastime is ``Monte-Carlo'' techniques in which the computer generates what appears to be a series of random numbers.
		These ``pseudo'' random numbers are then used to either simulate naturally random processes, such as the thermal motion of particles or radioactive decay, or to approximate the performance of some mathematical operation.
	www.krellinst.org /UCES/archive/modules/monte/node0.html (142 words)

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