Search results for "Random walk"
showing 10 items of 132 documents
Detection and visualization of physical knots in macromolecules
2010
Abstract This manuscript provides a pedagogical introduction on how to determine and visualize simple physical knots occurring in polymers, proteins and DNA. We explain how the Alexander polynomial is computed and implemented in a simulation code, and how the structure can be simplified beforehand to save computer time. The concept of knottedness can also be extended in a statistical framework to chains which are not closed. The latter is exemplified by comparing statistics of knots in open random walks and closed random loops.
Guide to Practical Work with the Monte Carlo Method
2002
The guide is structured such that we proceed from the “easy” simulation methods and algorithms to the more sophisticated. For each method the algorithms are presented by the technique of stepwise refinement. We first present the idea and the basic outline. From then on we proceed by breaking up the larger logical and algorithmic structures into smaller ones, until we have reached the level of single basic statements. Sometimes we may elect not to go to such a depth and the reader is asked to fill in the gaps.
A New Tool for the Modeling of AI and Machine Learning Applications: Random Walk-Jump Processes
2011
Published version of an article from the book: Hybrid artificial intelligent systems, Lecture notes in computer science. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/978-3-642-21219-2_2 There are numerous applications in Artificial Intelligence (AI) and Machine Learning (ML) where the criteria for decisions are based on testing procedures. The most common tools used in such random phenomena involve Random Walks (RWs). The theory of RWs and its applications have gained an increasing research interest since the start of the last century. [1]. In this context, we note that a RW is, usually, defined as a trajectory involving a series of successive ran…
Geometric characterization and simulation of planar layered elastomeric fibrous biomaterials
2015
An important class of biomaterials is composed of layered networks of elastomeric fibers. While there is a growing interest in modeling and simulation of the mechanical response of these biomaterials, a theoretical foundation for such simulations has yet to be firmly established. The present work addresses this issue in two ways. First, using methods of geometric probability we develop theoretical estimates for the linear and areal fiber intersection densities for two-dimensional fibrous networks. These are expressed in terms of the fiber density and orientation distribution function, both of which are relatively easy to measure properties. Secondly, we develop a random walk algorithm for g…
Stochastic reconstruction of sandstones
2000
A simulated annealing algorithm is employed to generate a stochastic model for a Berea and a Fontainebleau sandstone with prescribed two-point probability function, lineal path function, and ``pore size'' distribution function, respectively. We find that the temperature decrease of the annealing has to be rather quick to yield isotropic and percolating configurations. A comparison of simple morphological quantities indicates good agreement between the reconstructions and the original sandstones. Also, the mean survival time of a random walker in the pore space is reproduced with good accuracy. However, a more detailed investigation by means of local porosity theory shows that there may be s…
Secular Mean Reversion and Long-Run Predictability of the Stock Market
2013
Empirical financial literature documents the evidence of mean reversion in stock prices and the absence of out-of-sample return predictability over periods shorter than 10 years. The goal of this paper is to test the random walk hypothesis in stock prices and return predictability over periods longer than 10 years. Specifically, using 141 years of data, this paper begins by performing formal tests of the random walk hypothesis in the prices of the real S&P Composite Index over increasing time horizons up to 40 years. Even though our results cannot support the conventional wisdom which says that the stock market is safer for long-term investors, our findings speak in favor of the mean revers…
EXACT SOLUTIONS FOR A CLASS OF FRACTAL TIME RANDOM WALKS
1995
Fractal time random walks with generalized Mittag-Leffler functions as waiting time densities are studied. This class of fractal time processes is characterized by a dynamical critical exponent 0<ω≤1, and is equivalently described by a fractional master equation with time derivative of noninteger order ω. Exact Greens functions corresponding to fractional diffusion are obtained using Mellin transform techniques. The Greens functions are expressible in terms of general H-functions. For ω<1 they are singular at the origin and exhibit a stretched Gaussian form at infinity. Changing the order ω interpolates smoothly between ordinary diffusion ω=1 and completely localized behavior in the …
Random walks and random numbers from supercontinuum generation
2012
International audience; We report a numerical study showing how the random intensity and phase fluctuations across the bandwidth of a broadband optical supercontinuum can be interpreted in terms of the random processes of random walks and L´evy flights. We also describe how the intensity fluctuations can be applied to physical random number generation. We conclude that the optical supercontinuum provides a highly versatile means of studying and generating a wide class of random processes at optical wavelengths.
Poisson convergence on continuous time branching random walks and multistage carcinogenesis.
1982
A theorem for Poisson convergence on realizations of two-dimensional Branching Random Walks with an underlying continuous time Markov Branching Process is proved. This result can be used to gain an approximation for the number of cells having sustained a certain deficiency after a long time in multistage carcinogenesis.
Thermal relaxation of colour centres in LiBaF3crystals
2001
Abstract Processes in LiBaF3 crystals caused by the thermal decay of F-type centres created by X-irradiation at room temperature have been examined. It is shown that the thermal decay of F-type centres results in the formation of two kinds of electron centres peaking at 630 nm and 740 nm differing in thermal stability. Weak TSL intensity, accompanying the decay of F-centres, also observed as well as the low value of the process activation energy suggest that due to the presence of moving anion vacancies a random walk of the F-centres occur. We propose that in course of the random walk of the F-centres both the aggregate F-centres are created and the annihilation with some complementary radi…