Relevant bibliographies by topics / Random walk numerical methods

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Random walk numerical methods'

Author: Grafiati
Published: 4 June 2021
Last updated: 12 February 2022

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Journal articles on the topic "Random walk numerical methods"

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Suciu, N., L. Schüler, S. Attinger, C. Vamoș, and P. Knabner. "Consistency issues in PDF methods." Analele Universitatii "Ovidius" Constanta - Seria Matematica 23, no. 3 (November 1, 2015): 187–208. http://dx.doi.org/10.1515/auom-2015-0055.

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Abstract Concentrations of chemical species transported in random environments need to be statistically characterized by probability density functions (PDF). Solutions to evolution equations for the one-point one-time PDF are usually based on systems of computational particles described by Itô equations. We establish consistency conditions relating the concentration statistics to that of the Itô process and the solution of its associated Fokker-Planck equation to that of the PDF equation. In this frame, we use a recently proposed numerical method which approximates PDFs by particle densities obtained with a global random walk (GRW) algorithm. The GRW-PDF approach is illustrated for a problem of contaminant transport in groundwater.
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HARA, TAKASHI, and GORDON SLADE. "THE LACE EXPANSION FOR SELF-AVOIDING WALK IN FIVE OR MORE DIMENSIONS." Reviews in Mathematical Physics 04, no. 02 (June 1992): 235–327. http://dx.doi.org/10.1142/s0129055x9200008x.

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This paper is a continuation of the companion paper [14], in which it was proved that the standard model of self-avoiding walk in five or more dimensions has the same critical behaviour as the simple random walk, assuming convergence of the lace expansion. In this paper we prove the convergence of the lace expansion, an upper and lower infrared bound, and a number of other estimates that were used in the companion paper. The proof requires a good upper bound on the critical point (or equivalently a lower bound on the connective constant). In an appendix, new upper bounds on the critical point in dimensions higher than two are obtained, using elementary methods which are independent of the lace expansion. The proof of convergence of the lace expansion is computer assisted. Numerical aspects of the proof, including methods for the numerical evaluation of simple random walk quantities such as the two-point function (or lattice Green function), are treated in an appendix.
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Nie, Da-Cheng, Zi-Ke Zhang, Qiang Dong, Chongjing Sun, and Yan Fu. "Information Filtering via Biased Random Walk on Coupled Social Network." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/829137.

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The recommender systems have advanced a great deal in the past two decades. However, most researchers focus their attentions on mining the similarities among users or objects in recommender systems and overlook the social influence which plays an important role in users’ purchase process. In this paper, we design a biased random walk algorithm on coupled social networks which gives recommendation results based on both social interests and users’ preference. Numerical analyses on two real data sets,EpinionsandFriendfeed, demonstrate the improvement of recommendation performance by taking social interests into account, and experimental results show that our algorithm can alleviate the user cold-start problem more effectively compared with the mass diffusion and user-based collaborative filtering methods.
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Yang, Fan, Dongfang Liang, Xuefei Wu, and Yang Xiao. "On the application of the depth-averaged random walk method to solute transport simulations." Journal of Hydroinformatics 22, no. 1 (May 24, 2019): 33–45. http://dx.doi.org/10.2166/hydro.2019.015.

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Abstract Most numerical studies on solute mixing rely on mesh-based methods, and complicated schemes have been developed to enhance numerical stability and reduce artificial diffusion. This paper systematically studies the depth-averaged random walk scheme, which is a meshfree method with the merits of being highly robust and free of numerical diffusion. First, the model is used to solve instantaneous release problems in uniform flows. Extensive parametric studies are carried out to investigate the influences of the number of particles and the size of time steps. The predictions are shown to be independent of time steps but are sensitive to the particle numbers. Second, the model is applied to the solute transport problem along an estuary subject to extensive wetting and drying during tidal oscillations. Finally, the model is used to investigate the wind-induced chaotic mixing in a shallow basin. The effect of diffusion on the chaotic mixing is investigated. This study proposes a generic sampling method to interpret the output of the random walk method and highlights the importance of accurately taking diffusion into account in analysing the transport phenomena. The sampling technique also offers a guideline for estimating the total number of particles needed in the application.
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Nan, Tongchao, Jichun Wu, Kaixuan Li, and Jianguo Jiang. "Permeability Estimation Based on the Geometry of Pore Space via Random Walk on Grids." Geofluids 2019 (January 8, 2019): 1–10. http://dx.doi.org/10.1155/2019/9240203.

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In the literature, the mean penetration depth (MPD) calculated by “walk on spheres” or “walk on cubes” was used to quickly estimate the intrinsic permeability of digitized porous media. However, these two methods encounter difficulties such as irregular boundaries and the determination of arrivals at a boundary. In this study, an MPD method that is based on a more flexible “random walk on grid” (WOG) is explored. Moreover, the accurate MPDs for the pores of simple shapes are derived with Green’s functions to validate the WOG-based MPD. The results suggested that MPDs based on Green’s functions and WOG are consistent with each other; the factor C in the permeability expression is slightly dependent on roundness of the cross sections and is approximately 1.125 on average, according to analytical and numerical results. In a synthetic complex pore, the permeability estimated by WOG is comparable to, but greater than, the estimate based on the pore-scale dynamics simulation in COMSOL.
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Novak, Miroslav M. "Correlations in Computer Programs." Fractals 06, no. 02 (June 1998): 131–38. http://dx.doi.org/10.1142/s0218348x9800016x.

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Numerical and statistical methods are used to analyze and classify computer programs. Both computer source code and object files are examined. The results of the application of the Pearson and Spearman correlation methods to the source code are coupled with the random walk model applied to the binary code. One of the practical consequences of the analysis is the ability to quantify the degree of similarity between different computer programs and, hence, identify cases of plagiarism.
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ZHAO, XIAOJUN, JIE SUN, NA ZHANG, and PENGJIAN SHANG. "EXTREME EVENTS ANALYSIS OF NON-STATIONARY TIME SERIES BY USING HORIZONTAL VISIBILITY GRAPH." Fractals 28, no. 05 (August 2020): 2050089. http://dx.doi.org/10.1142/s0218348x20500899.

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In this paper, we analyze the extreme events of non-stationary time series in the framework of horizontal visibility graph (HVG). We give a new definition of extreme events, which incorporates the temporal structure of the series and the degree of the nodes in the HVG. An advantage of the new concept is that it does not require ad hoc treatment even when the non-stationarity arises in time series. We also use the information-theoretic methods to analyze the degree of nodes in the HVG. In the numerical analysis, we study the statistical characterizations of the extreme events of synthetic time series, including the random noises, periodic time series, random walk processes, and the long-range auto-correlated time series. Then, we study 9 time series in stock markets to identify the extreme events evolving in these non-stationary systems. Interestingly, we find that the daily closing price series perform rather close to the random walk processes, while the daily trading volume series behave quite similar to the random noises.
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Mainardi, Francesco. "On the Advent of Fractional Calculus in Econophysics via Continuous-Time Random Walk." Mathematics 8, no. 4 (April 21, 2020): 641. http://dx.doi.org/10.3390/math8040641.

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In this survey article, at first, the author describes how he was involved in the late 1990s on Econophysics, considered in those times an emerging science. Inside a group of colleagues the methods of the Fractional Calculus were developed to deal with the continuous-time random walks adopted to model the tick-by-tick dynamics of financial markets Then, the analytical results of this approach are presented pointing out the relevance of the Mittag-Leffler function. The consistence of the theoretical analysis is validated with fitting the survival probability for certain futures (BUND and BTP) traded in 1997 at LIFFE, London. Most of the theoretical and numerical results (including figures) reported in this paper were presented by the author at the first Nikkei symposium on Econophysics, held in Tokyo on November 2000 under the title “Empirical Science of Financial Fluctuations” on behalf of his colleagues and published by Springer. The author acknowledges Springer for the license permission of re-using this material.
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Burmeister, Louis C. "The Effect of Space-Dependent Thermal Conductivity on the Steady Central Temperature of a Cylinder." Journal of Heat Transfer 124, no. 1 (July 10, 2001): 195–97. http://dx.doi.org/10.1115/1.1418701.

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A transformation is presented that enables the center temperature of a cylinder to be expressed in terms of an integral of the peripheral temperature distribution for heat conduction with space-dependent thermal conductivity. Its predictions agree with exact answers and with numerical solutions obtained with finite difference methods for four test cases. The new result can be applied to a two-dimensional floating random-walk Monte Carlo procedure which previously was restricted to the case of constant thermal conductivity.
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Wang, Jingnan, and Ralf Korn. "Numerical Algorithms for Reflected Anticipated Backward Stochastic Differential Equations with Two Obstacles and Default Risk." Risks 8, no. 3 (July 1, 2020): 72. http://dx.doi.org/10.3390/risks8030072.

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We study numerical algorithms for reflected anticipated backward stochastic differential equations (RABSDEs) driven by a Brownian motion and a mutually independent martingale in a defaultable setting. The generator of a RABSDE includes the present and future values of the solution. We introduce two main algorithms, a discrete penalization scheme and a discrete reflected scheme basing on a random walk approximation of the Brownian motion as well as a discrete approximation of the default martingale, and we study these two methods in both the implicit and explicit versions respectively. We give the convergence results of the algorithms, provide a numerical example and an application in American game options in order to illustrate the performance of the algorithms.
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Dissertations / Theses on the topic "Random walk numerical methods"

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Gjetvaj, Filip. "Experimental characterization and modeling non-Fickian dispersion in aquifers." Thesis, Montpellier, 2015. http://www.theses.fr/2015MONTS204/document.

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Ces travaux ont pour objectif de modéliser les mécanismes de dispersion dans les aquifères. L’hétérogénéité du champ de vitesse et le transfert de masse entre zones immobiles et mobiles sont deux origines possibles du comportement non-Fickéen, jusqu’alors étudiées de façon séparée. Notre hypothèse de départ est que ces deux mécanismes coexistent. Nos travaux comprennent : 1) des expériences de traçage sur colonnes de billes de verre et carottes de grès de Berea, en mode flow-through et push-pull, et 2) des simulations numériques réalisées à partir d’images en microtomographie RX segmentées en trois phases : solide, vide et microporosité. L’analyse du champ de vitesse (Stokes) montre l’importance de la discrétisation spatiale et de la prise en compte de la microporosité. Les résultats des simulations de transport (en utilisant la méthode time domain random walk) permettent de quantifier l’effet combiné de l’hétérogénéité du champ de vitesse et des transferts diffusifs dans la fraction micro-poreuse de la roche sur la dispersion non-Fickéenne, caractérisée à partir des courbes de restitution (BTC). Ces résultats sont cohérents avec les observations expérimentales. Nous concluons que ces deux effets doivent être pris en compte même si leur identification à partir de la forme des BTCs issues des traçages des milieux naturels (souvent caractérisés par de faible valeurs du nombre de Peclet ) reste difficile. Enfin, un modèle moyen macroscopique 1D est proposé dans le cadre d’une approche de type continuous time random walk dans laquelle des distributions spécifiques du temps de transfert des particules sont construites pour chacun des deux mécanismes de transport
His work aims at modeling hydrodynamic dispersion mechanisms in aquifers. So far both flow field heterogeneity and mobile-immobile mass transfer have been studied separately for explaining the ubiquitously observed non-Fickian behaviors, but we postulate that both mechanisms contribute simultaneously. Our investigations combine laboratory experiments and pore scale numerical modeling. The experimental rig was designed to enable push-pull and flow through tracer tests on glass bead columns and Berea sandstone cores. Modeling consists in solving Stokes flow and solute transport on 3D X-ray microtomography images segmented into three phases: solid, void and microporosity. Transport is modeled using time domain random walk. Statistical analysis of the flow field emphasizes the importance of the mesh resolution and the inclusion of the microporosity. Results from the simulations show that both the flow field heterogeneity and the diffusive transport in the microporous fraction of the rock contribute to the overall non-Fickian transport behavior observed, for instance, on the breakthrough curves (BTC). These results are supported by our experiments. We conclude that, in general, this dual control must be taken into account, even if these different influences can hardly be distinguished from a qualitative appraisal of the BTC shape, specifically for the low values of the Peclet number that occurs in natural conditions. Finally, a 1D up-scaled model is developed in the framework of the continuous time random walk, where the influences of the flow field heterogeneity and mobile-immobile mass transfer are both taken into account using distinct transition time distributions
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Wu, Tao. "Higher-order Random Walk Methods for Data Analysis." Thesis, Purdue University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10790747.

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Markov random walk models are powerful analytical tools for multiple areas in machine learning, numerical optimizations and data mining tasks. The key assumption of a first-order Markov chain is memorylessness, which restricts the dependence of the transition distribution to the current state only. However in many applications, this assumption is not appropriate. We propose a set of higher-order random walk techniques and discuss their applications to tensor co-clustering, user trails modeling, and solving linear systems. First, we develop a new random walk model that we call the super-spacey random surfer, which simultaneously clusters the rows, columns, and slices of a nonnegative three-mode tensor. This algorithm generalizes to tensors with any number of modes. We partition the tensor by minimizing the exit probability between clusters when the super-spacey random walk is at stationary. The second application is user trails modeling, where user trails record sequences of activities when individuals interact with the Internet and the world. We propose the retrospective higher-order Markov process as a two-step process by first choosing a state from the history and then transitioning as a first-order chain conditional on that state. This way the total number of parameters is restricted and thus the model is protected from overfitting. Lastly we propose to use a time-inhomogeneous Markov chain to approximate the solution of a linear system. Multiple simulations of the random walk are conducted to approximate the solution. By allowing the random walk to transition based on multiple matrices, we decrease the variance of the simulations, and thus increase the speed of the solver.

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Fakhereddine, Rana. "Méthodes de Monte Carlo stratifiées pour l'intégration numérique et la simulation numériques." Thesis, Grenoble, 2013. http://www.theses.fr/2013GRENM047/document.

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Les méthodes de Monte Carlo (MC) sont des méthodes numériques qui utilisent des nombres aléatoires pour résoudre avec des ordinateurs des problèmes des sciences appliquées et des techniques. On estime une quantité par des évaluations répétées utilisant N valeurs et l'erreur de la méthode est approchée par la variance de l'estimateur. Le présent travail analyse des méthodes de réduction de la variance et examine leur efficacité pour l'intégration numérique et la résolution d'équations différentielles et intégrales. Nous présentons d'abord les méthodes MC stratifiées et les méthodes d'échantillonnage par hypercube latin (LHS : Latin Hypercube Sampling). Parmi les méthodes de stratification, nous privilégions la méthode simple (MCS) : l'hypercube unité Is := [0; 1)s est divisé en N sous-cubes d'égale mesure, et un point aléatoire est choisi dans chacun des sous-cubes. Nous analysons la variance de ces méthodes pour le problème de la quadrature numérique. Nous étudions particulièrment le cas de l'estimation de la mesure d'un sous-ensemble de Is. La variance de la méthode MCS peut être majorée par O(1=N1+1=s). Les résultats d'expériences numériques en dimensions 2,3 et 4 montrent que les majorations obtenues sont précises. Nous proposons ensuite une méthode hybride entre MCS et LHS, qui possède les propriétés de ces deux techniques, avec un point aléatoire dans chaque sous-cube et les projections des points sur chacun des axes de coordonnées également réparties de manière régulière : une projection dans chacun des N sousintervalles qui divisent I := [0; 1) uniformément. Cette technique est appelée Stratification Sudoku (SS). Dans le même cadre d'analyse que précédemment, nous montrons que la variance de la méthode SS est majorée par O(1=N1+1=s) ; des expériences numériques en dimensions 2,3 et 4 valident les majorations démontrées. Nous présentons ensuite une approche de la méthode de marche aléatoire utilisant les techniques de réduction de variance précédentes. Nous proposons un algorithme de résolution de l'équation de diffusion, avec un coefficient de diffusion constant ou non-constant en espace. On utilise des particules échantillonnées suivant la distribution initiale, qui effectuent un déplacement gaussien à chaque pas de temps. On ordonne les particules suivant leur position à chaque étape et on remplace les nombres aléatoires qui permettent de calculer les déplacements par les points stratifiés utilisés précédemment. On évalue l'amélioration apportée par cette technique sur des exemples numériques Nous utilisons finalement une approche analogue pour la résolution numérique de l'équation de coagulation, qui modélise l'évolution de la taille de particules pouvant s'agglomérer. Les particules sont d'abord échantillonnées suivant la distribution initiale des tailles. On choisit un pas de temps et, à chaque étape et pour chaque particule, on choisit au hasard un partenaire de coalescence et un nombre aléatoire qui décide de cette coalescence. Si l'on classe les particules suivant leur taille à chaque pas de temps et si l'on remplace les nombres aléatoires par des points stratifiés, on observe une réduction de variance par rapport à l'algorithme MC usuel
Monte Carlo (MC) methods are numerical methods using random numbers to solve on computers problems from applied sciences and techniques. One estimates a quantity by repeated evaluations using N values ; the error of the method is approximated through the variance of the estimator. In the present work, we analyze variance reduction methods and we test their efficiency for numerical integration and for solving differential or integral equations. First, we present stratified MC methods and Latin Hypercube Sampling (LHS) technique. Among stratification strategies, we focus on the simple approach (MCS) : the unit hypercube Is := [0; 1)s is divided into N subcubes having the same measure, and one random point is chosen in each subcube. We analyze the variance of the method for the problem of numerical quadrature. The case of the evaluation of the measure of a subset of Is is particularly detailed. The variance of the MCS method may be bounded by O(1=N1+1=s). The results of numerical experiments in dimensions 2,3, and 4 show that the upper bounds are tight. We next propose an hybrid method between MCS and LHS, that has properties of both approaches, with one random point in each subcube and such that the projections of the points on each coordinate axis are also evenly distributed : one projection in each of the N subintervals that uniformly divide the unit interval I := [0; 1). We call this technique Sudoku Sampling (SS). Conducting the same analysis as before, we show that the variance of the SS method is bounded by O(1=N1+1=s) ; the order of the bound is validated through the results of numerical experiments in dimensions 2,3, and 4. Next, we present an approach of the random walk method using the variance reduction techniques previously analyzed. We propose an algorithm for solving the diffusion equation with a constant or spatially-varying diffusion coefficient. One uses particles, that are sampled from the initial distribution ; they are subject to a Gaussian move in each time step. The particles are renumbered according to their positions in every step and the random numbers which give the displacements are replaced by the stratified points used above. The improvement brought by this technique is evaluated in numerical experiments. An analogous approach is finally used for numerically solving the coagulation equation ; this equation models the evolution of the sizes of particles that may agglomerate. The particles are first sampled from the initial size distribution. A time step is fixed and, in every step and for each particle, a coalescence partner is chosen and a random number decides if coalescence occurs. If the particles are ordered in every time step by increasing sizes an if the random numbers are replaced by statified points, a variance reduction is observed, when compared to the results of usual MC algorithm
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Yu, Wei, and 余韡. "Reverse Top-k search using random walk with restart." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/197515.

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With the increasing popularity of social networking applications, large volumes of graph data are becoming available. Large graphs are also derived by structure extraction from relational, text, or scientific data (e.g., relational tuple networks, citation graphs, ontology networks, protein-protein interaction graphs). Nodeto-node proximity is the key building block for many graph based applications that search or analyze the data. Among various proximity measures, random walk with restart (RWR) is widely adapted because of its ability to consider the global structure of the whole network. Although RWR-based similarity search has been well studied before, there is no prior work on reverse top-k proximity search in graphs based on RWR. We discuss the applicability of this query and show that the direct application of existing methods on RWR-based similarity search to solve reverse top-k queries has very high computational and storage demands. To address this issue, we propose an indexing technique, paired with an on-line reverse top-k search algorithm. In the indexing step, we compute from the graph G a graph index, which is based on a K X |V| matrix, containing in each column v the K largest approximate proximity values from v to any other node in G. K is application-dependent and represents the highest value of k in a practical reverse top-k query. At each column v of the index, the approximate values are lower bounds of the K largest proximity values from v to all other nodes. Given the graph index and a reverse top-k query q (k _ K), we prove that the exact proximities from any node v to query q can be efficiently computed by applying the power method. By comparing these with the corresponding lower bounds taken from the k-th row of the graph index, we are able to determine which nodes are certainly not in the reverse top-k result of q. For some of the remaining nodes, we may also be able to determine that they are certainly in the reverse top-k result of q, based on derived upper bounds for the k-th largest proximity value from them. Finally, for any candidate that remains, we progressively refine its approximate proximities, until based on its lower or upper bound it can be determined not to be or to be in the result. The proximities refined during a reverse top-k are used to update the graph index, making its values progressively more accurate for future queries. Our experimental evaluation shows that our technique is efficient and has manageable storage requirements even when applied on very large graphs. We also show the effectiveness of the reverse top-k search in the scenarios of spam detection and determining the popularity of authors.
published_or_final_version
Computer Science
Master
Master of Philosophy
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Costaouec, Ronan, and Ronan Costaouec. "Numerical methods for homogenization : applications to random media." Phd thesis, Université Paris-Est, 2011. http://pastel.archives-ouvertes.fr/pastel-00674957.

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In this thesis we investigate numerical methods for the homogenization of materials the structures of which, at fine scales, are characterized by random heterogenities. Under appropriate hypotheses, the effective properties of such materials are given by closed formulas. However, in practice the computation of these properties is a difficult task because it involves solving partial differential equations with stochastic coefficients that are additionally posed on the whole space. In this work, we address this difficulty in two different ways. The standard discretization techniques lead to random approximate effective properties. In Part I, we aim at reducing their variance, using a well-known variance reduction technique that has already been used successfully in other domains. The works of Part II focus on the case when the material can be seen as a small random perturbation of a periodic material. We then show both numerically and theoretically that, in this case, computing the effective properties is much less costly than in the general case
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Costaouec, Ronan. "Numerical methods for homogenization : applications to random media." Thesis, Paris Est, 2011. http://www.theses.fr/2011PEST1012/document.

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Le travail de cette thèse a porté sur le développement de techniques numériques pour l'homogénéisation de matériaux présentant à une petite échelle des hétérogénéités aléatoires. Sous certaines hypothèses, la théorie mathématique de l'homogénéisation stochastique permet d'expliciter les propriétés effectives de tels matériaux. Néanmoins, en pratique, la détermination de ces propriétés demeure difficile. En effet, celle-ci requiert la résolution d'équations aux dérivées partielles stochastiques posées sur l'espace tout entier. Dans cette thèse, cette difficulté est abordée de deux manières différentes. Les méthodes classiques d'approximation conduisent à approcher les propriétés effectives par des quantités aléatoires. Réduire la variance de ces quantités est l'objectif des travaux de la Partie I. On montre ainsi comment adapter au cadre de l'homogénéisation stochastique une technique de réduction de variance déjà éprouvée dans d'autres domaines. Les travaux de la Partie II s'intéressent à des cas pour lesquels le matériau d'intérêt est considéré comme une petite perturbation aléatoire d'un matériau de référence. On montre alors numériquement et théoriquement que cette simplification de la modélisation permet effectivement une réduction très importante du coût calcul
In this thesis we investigate numerical methods for the homogenization of materials the structures of which, at fine scales, are characterized by random heterogenities. Under appropriate hypotheses, the effective properties of such materials are given by closed formulas. However, in practice the computation of these properties is a difficult task because it involves solving partial differential equations with stochastic coefficients that are additionally posed on the whole space. In this work, we address this difficulty in two different ways. The standard discretization techniques lead to random approximate effective properties. In Part I, we aim at reducing their variance, using a well-known variance reduction technique that has already been used successfully in other domains. The works of Part II focus on the case when the material can be seen as a small random perturbation of a periodic material. We then show both numerically and theoretically that, in this case, computing the effective properties is much less costly than in the general case
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Van, Vleck Erik S. "Random and numerical aspects of the shadowing lemma." Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/29357.

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Coskun, Mustafa Coskun. "ALGEBRAIC METHODS FOR LINK PREDICTIONIN VERY LARGE NETWORKS." Case Western Reserve University School of Graduate Studies / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=case1499436242956926.

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Kolgushev, Oleg. "Influence of Underlying Random Walk Types in Population Models on Resulting Social Network Types and Epidemiological Dynamics." Thesis, University of North Texas, 2016. https://digital.library.unt.edu/ark:/67531/metadc955128/.

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Epidemiologists rely on human interaction networks for determining states and dynamics of disease propagations in populations. However, such networks are empirical snapshots of the past. It will greatly benefit if human interaction networks are statistically predicted and dynamically created while an epidemic is in progress. We develop an application framework for the generation of human interaction networks and running epidemiological processes utilizing research on human mobility patterns and agent-based modeling. The interaction networks are dynamically constructed by incorporating different types of Random Walks and human rules of engagements. We explore the characteristics of the created network and compare them with the known theoretical and empirical graphs. The dependencies of epidemic dynamics and their outcomes on patterns and parameters of human motion and motives are encountered and presented through this research. This work specifically describes how the types and parameters of random walks define properties of generated graphs. We show that some configurations of the system of agents in random walk can produce network topologies with properties similar to small-world networks. Our goal is to find sets of mobility patterns that lead to empirical-like networks. The possibility of phase transitions in the graphs due to changes in the parameterization of agent walks is the focus of this research as this knowledge can lead to the possibility of disruptions to disease diffusions in populations. This research shall facilitate work of public health researchers to predict the magnitude of an epidemic and estimate resources required for mitigation.
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Matteuzzi, Tommaso. "Network diffusion methods for omics big bio data analytics and interpretation with application to cancer datasets." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13660/.

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Nella attuale ricerca biomedica un passo fondamentale verso una comprensione dei meccanismi alla radice di una malattia è costituito dalla identificazione dei disease modules, cioè quei sottonetwork dell'interattoma, il network delle interazioni tra proteine, con un alto numero di alterazioni geniche. Tuttavia, l'incompletezza del network e l'elevata variabilità dei geni alterati rendono la soluzione di questo problema non banale. I metodi fisici che sfruttano le proprietà dei processi diffusivi su network, dei quali mi sono occupato in questo lavoro di tesi, sono quelli che consentono di ottenere le migliori prestazioni. Nella prima parte del mio lavoro, ho indagato la teoria relativa alla diffusione ed ai random walk su network, trovando interessanti relazioni con le tecniche di clustering e con altri modelli fisici la cui dinamica è descritta dalla matrice laplaciana. Ho poi implementato un tecnica basata sulla diffusione su rete applicandola a dati di espressione genica e mutazioni somatiche di tre diverse tipologie di cancro. Il metodo è organizzato in due parti. Dopo aver selezionato un sottoinsieme dei nodi dell'interattoma, associamo ad ognuno di essi un'informazione iniziale che riflette il "grado" di alterazione del gene. L'algoritmo di diffusione propaga l'informazione iniziale nel network raggiungendo, dopo un transiente, lo stato stazionario. A questo punto, la quantità di fluido in ciascun nodo è utilizzata per costruire un ranking dei geni. Nella seconda parte, i disease modules sono identificati mediante una procedura di network resampling. L'analisi condotta ci ha permesso di identificare un numero consistente di geni già noti nella letteratura relativa ai tipi di cancro studiati, nonché un insieme di altri geni correlati a questi che potrebbero essere interessanti candidati per ulteriori approfondimenti.Attraverso una procedura di Gene Set Enrichment abbiamo infine testato la correlazione dei moduli identificati con pathway biologici noti.
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Books on the topic "Random walk numerical methods"

1

Bouleau, Nicolas. Numerical Methods For Stochastic Processes. New York: Wiley, 1994.

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Srivastava, M. S. Economical on-line quality control procedures based on normal random walk model with measurement error. Toronto, Ont: University of Toronto, Dept. of Statistics, 1993.

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Moryson, Martin. Testing for random walk coefficients in regression and state space models. New York: Physica-Verlag, 1998.

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Sabelfeld, Karl K., and Nikolai A. Simonov. Stochastic Methods for Boundary Value Problems: Numerics for High-Dimensional PDEs and Applications. De Gruyter, Inc., 2016.

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Boudreau, Joseph F., and Eric S. Swanson. Quantum mechanics I–few body systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0021.

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Several techniques for obtaining the eigenspectrum and scattering properties of one- and two-body quantum systems are presented. More unusual topics, such as solving the Schrödinger equation in momentum space or implementing relativistic kinematics, are also addressed. A novel quantum Monte Carlo technique that leverages the similarity between path integrals and random walks is developed. An exploration of the method for simple problems is followed by a survey of methods to obtain ground state matrix elements. A review of scattering theory follows. The momentum space T-matrix formalism for scattering is introduced and an efficient numerical method for solving the relevant equations is presented. Finally, the method is extended to the coupled channel scattering problem.
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Romeijn, H. E. Global Optimization by Random Walk Sampling Methods (Tinbergen Institute Research Series). Thesis Pub, 1992.

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7

Boudreau, Joseph F., and Eric S. Swanson. Monte Carlo methods. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0007.

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Monte Carlo methods are those designed to obtain numerical answers with the use of random numbers . This chapter discusses random engines, which provide a pseudo-random pattern of bits, and their use in for sampling a variety of nonuniform distributions, for both continuous and discrete variables. A wide selection of uniform and nonuniform variate generators from the C++ standard library are reviewed, and common techniques for generating custom nonuniform variates are discussed. The chapter presents the uses of Monte Carlo to evaluate integrals, particularly multidimensional integrals, and then introduces the important method of Markov chain Monte Carlo, suitable for solving a wide range of scientific problems that require the sampling of complicated multivariate distributions. Relevant topics in probability and statistics are also introduced in this chapter. Finally, the topics of thermalization, autocorrelation, multimodality, and Gibbs sampling are presented.
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Mathematical Statistics: Theory and Applications. Berlin, Germany: De Gruyter, 2020.

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Coolen, A. C. C., A. Annibale, and E. S. Roberts. Graphs with hard constraints: further applications and extensions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0007.

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This chapter looks at further topics pertaining to the effective use of Markov Chain Monte Carlo to sample from hard- and soft-constrained exponential random graph models. The chapter considers the question of how moves can be sampled efficiently without introducing unintended bias. It is shown mathematically and numerically that apparently very similar methods of picking out moves can give rise to significant differences in the average topology of the networks generated by the MCMC process. The general discussion in complemented with pseudocode in the relevant section of the Algorithms chapter, which explicitly sets out some accurate and practical move sampling approaches. The chapter also describes how the MCMC equilibrium probabilities can be purposely deformed to, for example, target desired correlations between degrees of connected nodes. The mathematical exposition is complemented with graphs showing the results of numerical simulations.
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Book chapters on the topic "Random walk numerical methods"

1

Vamos, Calin, Nicolae Suciu, Harry Vereecken, Olaf Nitzsche, and Horst Hardelauf. "Global Random Walk Simulations of Diffusion." In Scientific Computing, Validated Numerics, Interval Methods, 343–54. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-6484-0_28.

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Kulkarni, Nilkanth H., and Rajesh Gupta. "Numerical Simulation of Solute Transport in Groundwater Flow System Using Random Walk Method." In Geostatistics Valencia 2016, 821–35. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-46819-8_56.

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Severini, Thomas A. "Random Walk Hypothesis." In Introduction to Statistical Methods for Financial Models, 41–68. Boca Raton, FL : CRC Press, [2018]: Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/b21962-3.

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Keller, Alexander. "The Quasi-Random Walk." In Monte Carlo and Quasi-Monte Carlo Methods 1996, 277–91. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1690-2_18.

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Murdoch, D. J. "Random Walk Approximation of Confidence Intervals." In Quality Improvement Through Statistical Methods, 393–404. Boston, MA: Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-1776-3_32.

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Biernacki, Arkadiusz. "Numerical Evaluation of the Random Walk Search Algorithm." In Man-Machine Interactions, 533–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00563-3_56.

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Giordano, Francesco, Marcella Niglio, and Cosimo Damiano Vitale. "Threshold Random Walk Structures in Finance." In Mathematical and Statistical Methods for Actuarial Sciences and Finance, 109–12. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05014-0_25.

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Houghton, Mark, David Head, and Mark Walkley. "A Numerical Model for Random Fibre Networks." In Numerical Methods and Applications, 408–15. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10692-8_46.

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Jordanova, Pavlina, and Milan Stehlík. "P-Thinned Gamma Process and Corresponding Random Walk." In Finite Difference Methods. Theory and Applications, 297–304. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11539-5_33.

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10

Csáki, Endre. "Some Results for Two-Dimensional Random Walk." In Advances in Combinatorial Methods and Applications to Probability and Statistics, 115–24. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-4140-9_8.

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Conference papers on the topic "Random walk numerical methods"

1

Diounou, E., P. Fede, R. Fournier, S. Blanco, and O. Simonin. "Kinetic Approach for Solid Inertial Particle Deposition in Turbulent Near-Wall Region Flow Lattice Boltzmann Based Numerical Resolution." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-12021.

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The purpose of the paper is the deposition on the wall of inertial solid particles suspended in turbulent flow. The modeling of such a system is based on a statistical description using a Probability Density Function. In the PDF transport equation, an original model proposed Aguinaga et al. (2009) is used to close the term representing the fluid-particle interactions. The resulting kinetic equation may be difficult to solve especially in the case of the particle response time is smaller than the integral time scale of the turbulence. In the present paper, the Lattice Boltzmann Method is used in order to overcome such numerical problems. The accuracy of the method and its ability to solve the two-phase kinetic equation is analyzed in the simple case of inertial particles in homogeneous isotropic turbulence for which Lagrangian random walk simulation results are available. The results from LBM are in accordance with the random walk simulations.
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Wang, Xiuling, and Darrell W. Pepper. "A Hybrid Numerical Model for Simulating Atmospheric Dispersion." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80095.

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A hybrid numerical model for simulating atmospheric contaminant dispersion is developed. The hybrid numerical scheme employs an hp-adaptive finite element method coupled with a Lagrangian particle transport technique to solve the governing equations for atmospheric flow and species transport. A random walk/stochastic approach is used to generate Lagrangian particles that define the contaminant dispersion traces. A coarse mesh using low order shape functions is initially generated. Both the mesh and shape function order are subsequently refined and enriched in those regions where high computational error exist. Compared with fine mesh and high order numerical solutions, the hybrid scheme produces highly accurate solutions with reduced computational cost. A general probability distribution is used in the particle transport module for the random component of motion due to turbulent diffusion. Results depicting contaminant transport and dispersion in the atmosphere are presented. The computational efficiency of the hybrid numerical model is also discussed.
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Selent, Bjo¨rn, and Craig Meskell. "Numerical Simulation of Vortex Shedding in Normal Triangular Tube Arrays." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93862.

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The unsteady flow through normal triangular tube arrays is simulated applying the Cloud-in-Element method. The scheme realizes time-stepping via a Langrangian vortex method using random-walk to model diffusion in the flow. The vortex particle velocities are computed on a fixed unstructured grid at each time step. Zero normal velocity on solid boundaries is enforced by a source panel method and zero slip is achieved by introducing vorticity into the flow at each time step. Simulations have been carried out for normal triangular tube arryas with pitch ratios of 1.32, 1.61, 2.08, 2.63 at Reynolds numbers of 1000, 3000, 5000 and 10000. Single vortex shedding frequencies have been observed for the smaller pitch ratios while two Strouhal numbers are obtained for the sparse arrays. This is consistent with experimental data in the literature. Also the overall flow structures were captured successfully.
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Li, Lin, Cun-liang Liu, Xiao-Yu Shi, Hui-ren Zhu, and Bing-ran Li. "Numerical Investigation on Sand Particles Deposition in a U-Bend Ribbed Internal Cooling Passage of Turbine Blade." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-90850.

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Abstract Sand particles impinge the internal cooling passage of the turbine blade and easily deposit, which lead to the decrease of cooling efficiency of the turbine blade and the increase of turbine blade temperature. In order to explore sand particles deposition mechanism in the internal cooling passage of turbine blades, the numerical simulation was performed in a U-bend passage with rib turbulators by means of a commercial CFD code. The fluid phase was modelled employing Reynolds-averaged Navier-Stokes approach. The discrete phase was solved using Lagrangian particle tracking method and a continuous random walk model. A particle deposition model was implemented using user-defined functions. The Reynolds numbers of 30000, 23000 and 15500 are considered. Particles sizes in the range 1–20 microns are considered. Results show that the particles deposition flux decreases gradually along the flow direction. The particles significantly deposit on the rib wall and the bend wall, especially on the windward rib wall and the upstream wall of the bend, with less deposition on the leeward rib wall. This is because the rib wall hinders the movement of fluid and sand particles impact the wall due to inertia, which lead to the energy loss. The particles deposition flux on the windward rib wall increases with the increase of Reynolds number and particles diameter, while the deposition flux on the leeward rib wall decreases. With the increase of the particles diameter, the particles deposition flux increases. The deposition rate increases with the increase of Reynolds number and particles diameter.
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Wang, Yan. "Accelerating Stochastic Dynamics Simulation With Continuous-Time Quantum Walks." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59420.

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Stochastic diffusion is a general phenomenon observed in various national and engineering systems. It is typically modeled by either stochastic differential equation (SDE) or Fokker-Planck equation (FPE), which are equivalent approaches. Path integral is an accurate and effective method to solve FPEs. Yet, computational efficiency is the common challenge for path integral and other numerical methods, include time and space complexities. Previously, one-dimensional continuous-time quantum walk was used to simulate diffusion. By combining quantum diffusion and random diffusion, the new approach can accelerate the simulation with longer time steps than those in path integral. It was demonstrated that simulation can be dozens or even hundreds of times faster. In this paper, a new generic quantum operator is proposed to simulate drift-diffusion processes in high-dimensional space, which combines quantum walks on graphs with traditional path integral approaches. Probability amplitudes are computed efficiently by spectral analysis. The efficiency of the new method is demonstrated with stochastic resonance problems.
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6

Kang, Zhangyang, Mo Yang, Yuwen Zhang, and Chunsun Guo. "Numerical Investigation of Gas-Solid Two Phase Flow Over Composite Structures of Elbow and Venturi Tube." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62995.

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The Euler-Lagrange method and Dispersed Phase Model (DPM) are adopted in the numerical simulation of gas-solid two-phase flow inside elbow, venturi tube and a new rich-lean pulverized coal burner combined elbow and venturi tube. It is to study the characteristic of coal distribution and the outlet characteristics of rich/lean separation influenced by pulverized coal particle diameter and density. he Detached-eddy-simulation (DES) approach is involved in the calculation of turbulence dispersion of gas phase. The Discrete random walk model (DRW) is used in the turbulence of solid phase. The results show that, for the particles of smaller diameter (10μm), the effect of rich-lean separation of three types of structure is unobvious; for the particles of larger diameter (50μm), this new structure burner can achieve rich-lean separation and the maximum concentration rises as the Stokes number increases; for the particles of more larger diameter 100μm, with the increasing number of St, there will be more than one core of concentration.
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Gutierrez, Gustavo, and Mauricio Giordano. "Study of the Bioheat Equation Using Monte Carlo Simulations for Local Magnetic Hyperthermia." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67460.

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Hyperthermia is a type of cancer treatment in which cancer cells are exposed to high temperatures (up to 44–45°C). Research has shown that high temperatures can damage and kill cancer cells, by a localized and concentrated heating source. By killing cancer cells and damaging proteins and structures within cells, hyperthermia may shrink tumors, with minimal injury to normal tissues. Penne’s bio-heat equation is used to model a heat diffusion process inside a tumor, modeled as a spherical domain with magnetic nanoparticles distributed within the diseased tissue. These magnetic particles are considered as point heat sources. Heat is generated as the result of magnetic relaxation mechanisms (Brownian and Neel relaxation) by the application of alternating magnetic fields. The Bio-Heat equation is solved using Monte Carlo techniques. Monte Carlo simulations are based on departing random walkers from the point where temperature is going to be determined. The probability in each step of the random walk is given by the coefficients of the nodal temperatures after a Finite Difference Discretization of the Penne’s bio-heat diffusion equation. The main advantage of Monte Carlo simulations versus classical numerical methods lies in the possibility of solving the temperature in a specific point without solving for all the points within the domain. This feature and the fact that each random walk is independent from each other results in an easy parallelization of the computer code. Parametric studies of the temperature profiles are carried out to study the effect of different parameters like the heat generation rate, perfusion rate and diameter of the point source on the maximum temperature and on the temperature profile.
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8

Emiris, Ioannis Z., and Vissarion Fisikopoulos. "Efficient Random-Walk Methods for Approximating Polytope Volume." In Annual Symposium. New York, New York, USA: ACM Press, 2014. http://dx.doi.org/10.1145/2582112.2582133.

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Lin, Hsien-Chung, Eugen Solowjow, Masayoshi Tomizuka, and Edwin Kreuzer. "A Data-Driven Exploratory Approach for Level Curve Estimation With Autonomous Underwater Agents." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5118.

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This contribution presents a method to estimate environmental boundaries with mobile agents. The agents sample a concentration field of interest at their respective positions and infer a level curve of the unknown field. The presented method is based on support vector machines (SVMs), whereby the concentration level of interest serves as the decision boundary. The field itself does not have to be estimated in order to obtain the level curve which makes the method computationally very appealing. A myopic strategy is developed to pick locations that yield most informative concentration measurements. Cooperative operations of multiple agents are demonstrated by dividing the domain in Voronoi tessellations. Numerical studies demonstrate the feasibility of the method on a real data set of the California coastal area. The exploration strategy is benchmarked against random walk which it clearly outperforms.
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Wang, Kexiang, Tianyu Liu, Zhifang Sui, and Baobao Chang. "Affinity-Preserving Random Walk for Multi-Document Summarization." In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing. Stroudsburg, PA, USA: Association for Computational Linguistics, 2017. http://dx.doi.org/10.18653/v1/d17-1020.

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