Application Of Random Walks Research Articles

Random walk with Brownian motion: Theory and application

While physical models are classical, random walks are statistical models. Historically, Karl Pearson was the first to propose the random walk. This study will focus on the essential of the random walk, and additionally, this essay will offer some application guidelines and explain when the random walk is applicable. The random walk means that the performance of an event is based on the past, as people cannot predict the future development steps and directions. The random walk, which dates to the 16th century, is a significant area of probability with many applications. The random walk and Brownian motion are the main topics of this paper. The four applications of random walks that are highlighted in this paper are the following. They include the multi-particle random walk immune algorithm, the density peak clustering algorithm, a review of random walk-based community discovery techniques, and interactive image segmentation that combines random walk and random forest. This work paves the way to unravel the importance of random walk.

Analysis of the Principle and Applications of Random Walk: Finance, Diffusion Equations and Game Design

Analysis of the Principle and Applications of Random Walk: Finance, Diffusion Equations and Game Design

Principle and application of random walk simulation: Multilayer networks, predation and stock market

Given the probabilities (which remain unchanged at each step) of travelling a certain distance in a certain direction, a random walk is a method used in probability theory to determine the likely position of a point depending on random movements. Markov processes, in which future behavior is independent of previous behavior, include random walks as an illustration. This study will mainly pay attention to three different applications of random walks in aspects of multilayer networks, predation and stock market. A real and intricate network could be solved by a mathematical equation depending on a random walk model. There are totally four different types of random walks that properly represent the motion of an animal searching for preys. Among these four types, CCRW is the best explanation for the route of a predator. Nevertheless, by analyzing the panel unit root tests, random walks fail to simulation the variability of share prices. This study promotes scholars to come up with an idea of the principle and application of random walks, and therefore realize the significance of such simulations.

Application of Random Walks in Data Processing

A random walk is known as a process that a random walker makes consecutive steps in space at equal intervals of time and the length and direction of each step is determined independently. It is an example of Markov processes, meaning that future movements of the random walker are independent of the past. The applications of random walks are quite popular in the field of mathematics, probability and computer science. Random walk related models can be used in different areas such as prediction, recommendation algorithm to recent supervised learning and networks. It is noticeable that there are few reviews about randoms for the beginners and how random walks are used nowadays in distinctive areas. Hence, the aim of the article is to provide a brief review of classical random walks, including basic concepts and models of the algorithm and then some applications in the field of computer science for the beginners to understand the significance and future of random walks.

Three-dimensional random walk models of individual animal movement and their application to trap counts modelling

Random walks (RWs) have proved to be a powerful modelling tool in ecology, particularly in the study of animal movement. An application of RW concerns trapping which is the predominant sampling method to date in insect ecology and agricultural pest management. A lot of research effort has been directed towards modelling ground-dwelling insects by simulating their movement in 2D, and computing pitfall trap counts, but comparatively very little for flying insects with 3D elevated traps. We introduce the mathematics behind 3D RWs and present key metrics such as the mean squared displacement (MSD) and path sinuosity, which are already well known in 2D. We develop the mathematical theory behind the 3D correlated random walk (CRW) which involves short-term directional persistence and the 3D Biased random walk (BRW) which introduces a long-term directional bias in the movement so that there is an overall preferred movement direction. In this study, we focus on the geometrical aspects of the 3D trap and thus consider three types of shape; a spheroidal trap, a cylindrical trap and a rectangular cuboidal trap. By simulating movement in 3D space, we investigated the effect of 3D trap shapes and sizes and of movement diffusion on trapping efficiency. We found that there is a non-linear dependence of trap counts on the trap surface area or volume, but the effect of volume appeared to be a simple consequence of changes in area. Nevertheless, there is a slight but clear hierarchy of trap shapes in terms of capture efficiency, with the spheroidal trap retaining more counts than a cylinder, followed by the cuboidal type for a given area. We also showed that there is no effect of short-term persistence when diffusion is kept constant, but trap counts significantly decrease with increasing diffusion. Our results provide a better understanding of the interplay between the movement pattern, trap geometry and impacts on trapping efficiency, which leads to improved trap count interpretations, and more broadly, has implications for spatial ecology and population dynamics.

Application of random walk to model temperature in 60 African cities for the 20th century

The 20th century is marked with climate change led by global warming. So far, many models have been applied to analyze the temperature change. However, a simple but interesting model, a random walk is hardly used in his regard. In this study, we use the random walk to model the temperature in the format of random walk that is the conversion of recorded temperature and the real recorded temperature in 60 African cities including 53 capitals for the 20th century. The results show that the random walk can satisfyingly model either temperature in the format of random walk or real recorded temperature although the fitted results from other climate models are unavailable for comparison in these 60 cities. As nothing else besides random numbers is involved in this modelling, the results seem somewhat counter-intuitively.

A L\xe9vy expansion strategy optimizes early dune building by beach grasses

Lifeforms ranging from bacteria to humans employ specialized random movement patterns. Although effective as optimization strategies in many scientific fields, random walk application in biology has remained focused on search optimization by mobile organisms. Here, we report on the discovery that heavy-tailed random walks underlie the ability of clonally expanding plants to self-organize and dictate the formation of biogeomorphic landscapes. Using cross-Atlantic surveys, we show that congeneric beach grasses adopt distinct heavy-tailed clonal expansion strategies. Next, we demonstrate with a spatially explicit model and a field experiment that the Lévy-type strategy of the species building the highest dunes worldwide generates a clonal network with a patchy shoot organization that optimizes sand trapping efficiency. Our findings demonstrate Lévy-like movement in plants, and emphasize the role of species-specific expansion strategies in landscape formation. This mechanistic understanding paves the way for tailor-made planting designs to successfully construct and restore biogeomorphic landscapes and their services.

Review of Random Walk in Image Processing

The random walk, proposed in 1905, was applied into the field of computer vision in 1979. Subsequently, more and more researchers paid their attention to this new method. Recently it has become prevailing as to be widely applied in image processing, e.g. image segmentation, image fusion, image enhancement and so on. Until now there is no comprehensive review on random walk in image processing yet. Therefore, almost important references are reviewed in the paper, and six representative random walk models have been listed and explained in detail. And then their applications of random walk in image processing are introduced. At last, some existed problems and future work are pointed out.

Random Walk Methods for Modeling Hydrodynamic Transport in Porous and Fractured Media from Pore to Reservoir Scale

Random walk (RW) or Continuous Time Random Walk (CTRW) are recurring Monte Carlo methods used to model convective and diffusive transport in complex heterogeneous media. Many applications can be found, including fluid mechanic, hydrology, and chemical reactors modeling. These methods are easy to implement, very versatile and flexible enough to become appealing for many applications because they generally overlook of deeply simplify the building of explicit complex meshes required by deterministic methods. RW and CTRW provide a good physical understanding of the interactions between the space scales of het-erogeneities and the transport phenomena under consideration. In addition, they can result in efficient up-scaling methods, especially in context of flow and transport in fractured media. In the present study, we review the applications of RW or CTRW for several situations coping with various spatial scales, and different insights into up-scaling applications. RW and CTRW advantages and downsides are also discussed, thus providing a few avenues for further works and applications.

Applications of random walks on graphs to gibbs samplers

We view the Gibbs sampler as a random walk on a graph and show that ergodic properties in the Gibbs sampler are implied by the connectivity of some appropriately defined directed graph.

Applications of random walks on graphs to gibbs samplers

We view the Gibbs sampler as a random walk on a graph and show that ergodic properties in the Gibbs sampler are implied by the connectivity of some appropriately defined directed graph.

An Application of Random Walk to a Problem in Population Genetics

An Application of Random Walk to a Problem in Population Genetics

An Application of Random Walk to a Problem in Population Genetics

An Application of Random Walk to a Problem in Population Genetics

A bibliography on applications of random walks in theoretical chemistry and physics

A bibliography on applications of random walks in theoretical chemistry and physics

Level Touchings in a Random Walk.

Previous article Next article Level Touchings in a Random Walk.Herbert B. RosenstockHerbert B. Rosenstockhttps://doi.org/10.1137/0116093PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Level Touchings in a Random Walk.." SIAM Journal on Applied Mathematics, 16(6), pp. 1130–1131[1] A. H. Gray, Jr., Level touchings in a restricted random walk, SIAM J. Appl. Math., 16 (1968), 1123–1129 10.1137/0116092 MR0235621 0254.60048 LinkISIGoogle Scholar[2] William Feller, An introduction to probability theory and its applications. Vol. I, John Wiley and Sons, Inc., New York, 1957xv+461 MR0088081 0077.12201 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails New Poisson inequality for the Radon transform of infinitely differentiable functionsJournal of Inequalities and Applications, Vol. 2018, No. 1 | 17 August 2018 Cross Ref A bibliography on applications of random walks in theoretical chemistry and physicsAdvances in Molecular Relaxation and Interaction Processes, Vol. 22, No. 1 | 1 Jan 1982 Cross Ref Volume 16, Issue 6| 1968SIAM Journal on Applied Mathematics1123-1403 History Submitted:14 February 1968Published online:12 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0116093Article page range:pp. 1130-1131ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics