Search results for "Random walk"
showing 10 items of 132 documents
Optimal Resource Discovery Paths of Gnutella2
2008
This paper shows that the performance of peer-to-peer resource discovery algorithms is upper bounded by a k-Steiner minimum tree and proposes an algorithm locating near-optimal query paths for the peer-to-peer resource discovery problem. Global knowledge of the topology and the resources from the peer-to-peer network are required as an input to the algorithm. The algorithm provides an objective measure for defining how good local search algorithms are. The performance is evaluated in simulated peer-to-peer scenarios and in the measured Gnutella2 P2P network topology with four local search algorithms: breadth-first search, self-avoiding random walker, highest degree search and Dynamic Query …
On the analysis of a new Markov chain which has applications in AI and machine learning
2011
Accepted version of an article from the conference: 2011 24th Canadian Conference on Electrical and Computer Engineering. Published version available from IEEE: http://dx.doi.org/10.1109/CCECE.2011.6030727 In this paper, we consider the analysis of a fascinating Random Walk (RW) that contains interleaving random steps and random "jumps". The characterizing aspect of such a chain is that every step is paired with its counterpart random jump. RWs of this sort have applications in testing of entities, where the entity is never allowed to make more than a pre-specified number of consecutive failures. This paper contains the analysis of the chain, some fascinating limiting properties, and some i…
Annealed Invariance Principle for Random Walks on Random Graphs Generated by Point Processes in R-d
2016
International audience; We consider simple random walks on random graphs embedded in R-d and generated by point processes such as Delaunay triangulations, Gabriel graphs and the creek-crossing graphs. Under suitable assumptions on the point process, we show an annealed invariance principle for these random walks. These results hold for a large variety of point processes including Poisson point processes, Matern cluster and Matern hardcore processes which have respectively clustering and repulsiveness properties. The proof relies on the use the process of the environment seen from the particle. It allows to reconstruct the original process as an additive functional of a Markovian process und…
Movement patterns of Tenebrio beetles demonstrate empirically that correlated-random-walks have similitude with a Lévy walk.
2013
AbstractCorrelated random walks are the dominant conceptual framework for modelling and interpreting organism movement patterns. Recent years have witnessed a stream of high profile publications reporting that many organisms perform Lévy walks; movement patterns that seemingly stand apart from the correlated random walk paradigm because they are discrete and scale-free rather than continuous and scale-finite. Our new study of the movement patterns of Tenebriomolitor beetles in unchanging, featureless arenas provides the first empirical support for a remarkable and deep theoretical synthesis that unites correlated random walks and Lévy walks. It demonstrates that the two models are complemen…
Probability and algorithmics: a focus on some recent developments
2017
Jean-François Coeurjolly, Adeline Leclercq-Samson Eds.; International audience; This article presents different recent theoretical results illustrating the interactions between probability and algorithmics. These contributions deal with various topics: cellular automata and calculability, variable length Markov chains and persistent random walks, perfect sampling via coupling from the past. All of them involve discrete dynamics on complex random structures.; Cet article présente différents résultats récents de nature théorique illustrant les interactions entre probabilités et algorithmique. Ces contributions traitent de sujets variés : automates cellulaires et calculabilité, chaînes de Mark…
Variable Length Markov Chains, Persistent Random Walks: a close encounter
2020
This is the story of the encounter between two worlds: the world of random walks and the world of Variable Length Markov Chains (VLMC). The meeting point turns around the semi-Markov property of underlying processes.
Persistent random walks, variable length Markov chains and piecewise deterministic Markov processes *
2013
A classical random walk $(S_t, t\in\mathbb{N})$ is defined by $S_t:=\displaystyle\sum_{n=0}^t X_n$, where $(X_n)$ are i.i.d. When the increments $(X_n)_{n\in\mathbb{N}}$ are a one-order Markov chain, a short memory is introduced in the dynamics of $(S_t)$. This so-called "persistent" random walk is nolonger Markovian and, under suitable conditions, the rescaled process converges towards the integrated telegraph noise (ITN) as the time-scale and space-scale parameters tend to zero (see Herrmann and Vallois, 2010; Tapiero-Vallois, Tapiero-Vallois2}). The ITN process is effectively non-Markovian too. The aim is to consider persistent random walks $(S_t)$ whose increments are Markov chains with…
Polymer solutions confined in slit-like pores with attractive walls: An off-lattice Monte Carlo study of static properties and chain dynamics
1996
Using a bead spring model of flexible polymer chains, the density profiles and chain configurational properties of polymer solutions confined between parallel plates were studied. A wide range of density ϕ, chain length N, and strength e of a short-range attractive wall potential was investigated. Both a temperature T in the good solvent regime (T > θ, θ being the Theta temperature where a chain in unconfined bulk three-dimensional solution would behave ideally) and a temperature in the bad solvent regime (T θ) show a crossover from two-dimensional excluded volume behavior (Rg ∝ N2ν with ν = 3/4) to ideal random walk behavior (ν = 1/2), the relaxation times show effective exponents Zeff (τ …
Mapping onto ideal chains overestimates self-entanglements in polymer melts
2017
In polymer physics it is typically assumed that excluded volume interactions are effectively screened in polymer melts. Hence, chains could be described by an effective random walk without excluded volume interactions. In this letter, we show that this mapping is problematic by analyzing the occurrence of knots, their spectrum and sizes in polymer melts, corresponding random walks and chains in dilute solution. The effective random walk severely overrates the occurrence of knots and their complexity, particularly when compared to melts of flexible chains, indicating that non-trivial effects due to remnants of self-avoidance still play a significant role for the chain lengths considered in t…
Structure of Polymers
2014
The structure and thermodynamics of polymers are discussed both with an adapted version of Flory’s regular solution theory and the concept of scaling and random walks. The salient properties of polymers like segregation and elasticity are discussed in terms of these concept. The Flory-Stockmayer theory of gelation is introduced and related to the percolation concept.