Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Random walk”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9Linked to original sources
PubMed2002

Multifractal stationary random measures and multifractal random walks with log infinitely divisible scaling laws.

We define a large class of continuous time multifractal random measures and processes with arbitrary log infinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal multifractal random walk [J.F. Muzy, J. Delour, and E. Bacry, Eur. J. Phys. B 17, 537 (2000), E. Bacry, J. Delour, and J.F. Muzy, Phys. Rev. E 64, 026103 (2001)] and the log-Poisson "product of cylindrical pulses" [J. Barral and B.B. Mandelbrot, Cowles Foundation Discussion Paper No. 1287, 2001 (unpublished)]. Our construction is based on some "continuous stochastic multiplication" [as introduced in F. Schmitt and D. Marsan, Eur. J. Phys. B. 20, 3 (2001)] from coarse to fine scales that can be seen as a continuous interpolation of discrete multiplicative cascades. We prove the stochastic convergence of the defined processes and study their main statistical properties. The question of genericity (universality) of limit multifractal processes is addressed within this new framework. We finally provide a method for numerical simulations and discuss some specific examples.

Journal Article↗
PubMed2003

Random-walk-based estimates of transport properties in small specimens of composite materials.

A method based on random walks is developed for estimating the dc conductance and similar transport properties in small specimens of composite materials. The method is valid over a much wider range of material structures than are asymptotic methods, and requires only that the internal structure of the material be known. The error in its estimates is limited primarily by CPU speed. It is found to work best for composites consisting of a bulk conducting phase and inclusions of lower conductivity.

Journal Article↗
PubMed2003

Scaling properties of random walks on small-world networks.

Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These properties include the average number of distinct sites visited by the random walker, the mean-square displacement of the walker, and the distribution of first-return times. The scaling form has three characteristic time regimes. At short times, the walker does not see the small-world shortcuts and effectively probes an ordinary Euclidean network in d dimensions. At intermediate times, the properties of the walker shows scaling behavior characteristic of an infinite small-world network. Finally, at long times, the finite size of the network becomes important, and many of the properties of the walker saturate. We propose general analytical forms for the scaling properties in all three regimes, and show that these analytical forms are consistent with our numerical simulations.

Journal Article↗
PubMed2001

Dissipative Abelian sandpiles and random walks.

We show that the dissipative Abelian sandpile on a graph L can be related to a random walk on a graph that consists of L extended with a trapping site. From this relation it can be shown, using exact results and a scaling assumption, that the correlation length exponent nu of the dissipative sandpiles always equals 1/d(w), where d(w) is the fractal dimension of the random walker. This leads to a new understanding of the known result that nu=1/2 on any Euclidean lattice. Our result is, however, more general, and as an example we also present exact data for finite Sierpinski gaskets, which fully confirm our predictions.

Journal Article↗
PubMed2026

RCoxNet: A Deep Learning Framework Integrating Random Walk with Restart, Mutation, and Clinical Data for Cancer Survival Prediction.

Accurate survival prediction in cancer remains challenging due to the sparsity of somatic mutation profiles and the failure of existing models to capture higher-order gene-gene dependencies. Network diffusion methods such as Random Walk with Restart (RWR) can propagate mutation signals across protein-protein interaction (PPI) networks to address sparsity, yet their integration within a deep learning Cox survival framework has not been comprehensively benchmarked across multiple cancer cohorts. We present RCoxNet, a deep learning framework that maps somatic mutation profiles onto a ConsensusPathDB-derived PPI network via RWR, selects prognostic genes by log-rank filtering, and processes network-informed mutation scores through three fully connected hidden layers feeding into a Cox proportional hazards output. RCoxNet was evaluated on The Cancer Genome Atlas (TCGA) cohorts for four cancer types (breast invasive carcinoma [BRCA], lung adenocarcinoma [LUNG], glioblastoma multiforme [GBM], and ovarian serous cystadenocarcinoma [OV]) using 20 independent random splits. The model achieved mean C-index values of 0.807 ± 0.044 (BRCA), 0.750 ± 0.039 (LUNG), 0.704 ± 0.041 (GBM), and 0.668 ± 0.036 (OV), consistently outperforming DeepSurv, Cox-nnet, SurvivalNet, Cox Elastic-Net (Cox-EN), and DeepHit, with statistically significant gains over Cox-EN, Cox-nnet, SurvivalNet, and DeepHit across the majority of cohorts. RCoxNet demonstrates that embedding sparse mutation profiles into a PPI network context substantially improves cancer survival prediction and yields biologically interpretable prognostic features relevant to precision oncology.

cancer survival prediction↗
PubMed1997

Excitation of arbitrary shapes by gradient optimized random walk in discrete k-space.

A new technique for the excitation of arbitrary shapes is proposed. It is based on a parallel sequence of small tip angle RF pulses and gradient pulses. The small tip angle rotations co-add yielding a 90 degrees excitation pulse within the selected excitation profile while outside the profile, the rotations cancel each other. A full theory of the completely arbitrary regional volume excitation (CARVE) method is presented and experimentally verified. In CARVE, k-space is discrete because the RF is applied in pulses. The discrete character of k-space permits an arbitrary trajectory for the k-space walk. The optimal random trajectory is found by minimizing the gradient load using simulated annealing. It is shown, both theoretically and experimentally, that such a trajectory is much better than any other systematic or random trajectory in k-space.

Image Processing, Computer-Assisted↗
PubMed2002

Random-walk simulations of NMR dephasing effects due to uniform magnetic-field gradients in a pore.

A random-walk simulation program was developed to study the effect of dephasing spins in a uniform magnetic-field gradient in a porous material. It is shown that this simulation program correctly reproduces basic nuclear magnetic resonance behavior, such as the formation of a spin echo. The spin-echo decay due to dephasing in a nonrestricted medium gives the well-known exponential relation containing the cube of time, whereas the spin-echo decay due to dephasing in a porous material gives a monoexponential decay. By varying the pore size and magnetic-field gradient, the motional averaging regime and the localization regime can be simulated. Moreover, the unknown intermediate regime is investigated. By choosing the right scaling parameters, the spin-echo decay due to dephasing in a pore can be described by one master curve for all pore sizes and gradient strengths. This master curve reveals a small intermediate regime, perfectly symmetrical around the gradient for which the dephasing length is exactly equal to the structural length of the pore.

Journal Article↗
PubMed2002

Exact multifractal spectra for arbitrary laplacian random walks.

Iterated conformal mappings are used to obtain exact multifractal spectra of the harmonic measure for arbitrary Laplacian random walks in two dimensions. Separate spectra are found to describe scaling of the growth measure in time, of the measure near the growth tip, and of the measure away from the growth tip. The spectra away from the tip coincide with those of conformally invariant equilibrium systems with arbitrary central charge c < or = 1, with c related to the particular walk chosen, while the scaling in time and near the tip cannot be obtained from the equilibrium properties.

Journal Article↗
PubMed2004

Quantum random walks and piecewise deterministic evolutions.

In the continuous space and time limit, we show that the probability density to find the quantum random walk (QRW) driven by the Hadamard "coin" solves a hyperbolic evolution equation similar to the one obtained for a random two-velocity evolution with spatially inhomogeneous transition rates between the velocity states. In spite of the presence of a nonlinear drift term, it is remarkable that the QRW position can easily be described in simple analytical terms. This allows us to derive the quadratic time dependence of the variance typical for the QRW.

Journal Article↗
PubMed2005

Random walks for interactive organ segmentation in two and three dimensions: implementation and validation.

A new approach to interactive segmentation based on random walks was recently introduced that shows promise for allowing physicians more flexibility to segment arbitrary objects in an image. This report has two goals: To introduce a novel computational method for applying the random walker algorithm in 2D/3D using the Graphics Processing Unit (GPU) and to provide quantitative validation studies of this algorithm relative to different targets, imaging modalities and interaction strategies.

Algorithms↗
PubMed2004

Analysis of a one-dimensional random walk with irreversible losses at each step: applications for protein movement on DNA.

We analysed a one-dimensional random walk between two points when the migrating particle could be irreversibly lost (dissociated) from the system at each step of the process. We show that in the case of losses at each step the average number of steps made by the particle that reaches the final point does not obey quadratic dependence on the distance between the starting and the final points: for long distances this dependence is linear. This is because losses "select" for shorter pathways between the starting and the final points. We applied this analysis to protein translocations within long DNA molecules.

Animals↗
PubMed1977

Random walks and generalized master equations with internal degrees of freedom.

We present an extension of the continuous-time random walk formalism to include internal states and to establish the connection to generalized master equations with internal states. The theory allows us to calculate physical observables from which we can extract the characteristic parameters of the internal states of the system under study.

Journal Article↗
PubMed2005

Random walk of polarized light in turbid media.

We study the propagation of polarized light in turbid media as a random walk of vector photons. Both propagation and polarization directions of light are found to isotropize, following a power law of the number of scattering events. The characteristic length scale governing light isotropization and linear depolarization, the isotropization length , is derived using the exact Mie scattering for spherical particles. A simple relation is obtained for Rayleigh-Gans scatterers where is the transport mean free path and is the mean cosine of scattering angles.

Journal Article↗
PubMed2002

Patterns of particle distribution in multiparticle systems by random walks with memory enhancement and decay.

We investigate the pattern of particle distribution and its evolution with time in multiparticle systems using the model of random walks with memory enhancement and decay. This model describes some biological intelligent walks. With decrease in the memory decay exponent alpha, the distribution of particles changes from a random dispersive pattern to a locally dense one, and then returns to the random one. Correspondingly, the fractal dimension D(f,p) characterizing the distribution of particle positions increases from a low value to a maximum and then decreases to the low one again. This is determined by the degree of overlap of regions consisting of sites with remanent information. The second moment of the density rho(2) was introduced to investigate the inhomogeneity of the particle distribution. The dependence of rho(2) on alpha is similar to that of D(f,p) on alpha. rho(2) increases with time as a power law in the process of adjusting the particle distribution, and then rho(2) tends to a stable equilibrium value.

Journal Article↗
PubMed2005

Relationships between the folding rate constant and the topological parameters of small two-state proteins based on general random walk model.

In this paper, we propose an analytically tractable model of protein folding based on one-dimensional general random walk. A second-order differential equation for the mean folding time of a single protein is constructed which can be used to derive the observed relationship between the folding rate constant and the number of native contacts. The parameters appearing in the model can be determined by fitting the theoretical prediction to the experimental result. In addition, taking into account the fact that the number of native contacts is almost proportional to the relative contact order, we can also explain the observed relationship between the folding rate constant and the relative contact order.

Animals↗
PubMed2001

Autocatalytic polymerization generates persistent random walk of crawling cells.

The autocatalytic polymerization kinetics of the cytoskeletal actin network provides the basic mechanism for a persistent random walk of a crawling cell. It is shown that network remodeling by branching processes near the cell membrane is essential for the bimodal spatial stability of the network which induces a spontaneous breaking of isotropic cell motion. Details of the phenomena are analyzed using a simple polymerization model studied by analytical and simulation methods.

Actins↗
PubMed2003

Time-dependent random walks and the theory of complex adaptive systems.

Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are time dependent. We determine the survival probability in the presence of an absorbing boundary. For an unbiased walk, the survival probability is maximized in the case of large temporal oscillations in the jumping probabilities. On the other hand, a random walker who is drifted towards the absorbing boundary performs best with a constant jumping probability. We use the results to reveal the underlying dynamics responsible for the phenomenon of self-segregation and clustering observed in the evolutionary minority game.

Adaptation, Biological↗