Search results for " Random walks"

showing 4 items of 4 documents

One-dimensional random walks with self-blocking immigration

2017

We consider a system of independent one-dimensional random walkers where new particles are added at the origin at fixed rate whenever there is no older particle present at the origin. A Poisson ansatz leads to a semi-linear lattice heat equation and predicts that starting from the empty configuration the total number of particles grows as $c \sqrt{t} \log t$. We confirm this prediction and also describe the asymptotic macroscopic profile of the particle configuration.

Statistics and Probability60G50Particle numbervacant timeInteracting random walksPoisson distributionPoisson comparison01 natural sciences010104 statistics & probabilitysymbols.namesakeLattice (order)FOS: Mathematicsdensity-dependent immigrationStatistical physics0101 mathematicsAnsatzMathematics010102 general mathematicsProbability (math.PR)Random walk60K35symbolsHeat equationStatistics Probability and Uncertainty60F99Mathematics - Probability
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Coalescing directed random walks on the backbone of a 1 +1-dimensional oriented percolation cluster converge to the Brownian web

2018

We consider the backbone of the infinite cluster generated by supercritical oriented site percolation in dimension 1 +1. A directed random walk on this backbone can be seen as an "ancestral line" of an individual sampled in the stationary discrete-time contact process. Such ancestral lineages were investigated in [BCDG13] where a central limit theorem for a single walker was proved. Here, we consider infinitely many coalescing walkers on the same backbone starting at each space-time point. We show that, after diffusive rescaling, the collection of paths converges in distribution to the Brownian web. Hence, we prove convergence to the Brownian web for a particular system of coalescing random…

Probability (math.PR)FOS: MathematicsOriented percolation coalescing random walks Brownian webMathematics - Probability
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On the analysis of a random walk-jump chain with tree-based transitions and its applications to faulty dichotomous search

2018

Random Walks (RWs) have been extensively studied for more than a century [1]. These walks have traditionally been on a line, and the generalizations for two and three dimensions, have been by extending the random steps to the corresponding neighboring positions in one or many of the dimensions. Among the most popular RWs on a line are the various models for birth and death processes, renewal processes and the gambler’s ruin problem. All of these RWs operate “on a discretized line”, and the walk is achieved by performing small steps to the current-state’s neighbor states. Indeed, it is this neighbor-step motion that renders their analyses tractable. When some of the transitions are to non-ne…

Statistics and ProbabilityCurrent (mathematics)Learning systemsRandom walk jumpsDichotomous searches02 engineering and technologyState (functional analysis)Random walkTime reversibilityBirth–death process020202 computer hardware & architectureChain (algebraic topology)020204 information systemsModeling and SimulationLine (geometry)Controlled random walks0202 electrical engineering electronic engineering information engineeringJumpStatistical physicsTime reversibilitiesMathematics
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An enhanced random walk algorithm for delineation of head and neck cancers in PET studies

2017

An algorithm for delineating complex head and neck cancers in positron emission tomography (PET) images is presented in this article. An enhanced random walk (RW) algorithm with automatic seed detection is proposed and used to make the segmentation process feasible in the event of inhomogeneous lesions with bifurcations. In addition, an adaptive probability threshold and a k-means based clustering technique have been integrated in the proposed enhanced RW algorithm. The new threshold is capable of following the intensity changes between adjacent slices along the whole cancer volume, leading to an operator-independent algorithm. Validation experiments were first conducted on phantom studies:…

Similarity (geometry)Computer sciencePET imagingBiomedical EngineeringRandom walk030218 nuclear medicine & medical imaging03 medical and health sciences0302 clinical medicinemedicineImage Processing Computer-AssistedHumansSegmentationComputer visionCluster analysisEvent (probability theory)Settore ING-INF/05 - Sistemi Di Elaborazione Delle Informazionimedicine.diagnostic_testbusiness.industryPhantoms ImagingBiological target volume; Head and neck cancer segmentation; PET imaging; Random walksComputer Science ApplicationPattern recognitionRandom walkComputer Science ApplicationsBiological target volumeHausdorff distancePositron emission tomographyHead and Neck Neoplasms030220 oncology & carcinogenesisPositron-Emission TomographyArtificial intelligenceHead and neck cancer segmentationComputer Vision and Pattern RecognitionbusinessAlgorithmsBiological target volume Head and neck cancer segmentation PET imaging Random walks Algorithms Head and Neck Neoplasms Humans Image Processing Computer-Assisted Phantoms Imaging Positron-Emission TomographyVolume (compression)
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