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At least 469 records · Page 26Linked to original sources
PubMed1999

Correlated random walk: a fractal approach to erythrocyte viscoelastic properties.

A numerical method is proposed to evaluate the fractal correlation coefficient on viscoelastic properties of mammalian erythrocyte membranes from the diffractometric data obtained with the erythrodeformeter [16]. The numerical method is formulated on the basis of the fractal approximation for ordinary Brownian motion (OBM) and fractionary Brownian motion (FBM) [10]. Photometric readings performed on the elliptical diffraction pattern, generated by the shear elongated cells and photometrically recorded curves of creep and recovery of cells, are used in the calculations of self-affine Brownian correlation coefficient, averaged over several millions of cells. The time dependence of the correlation coefficient from different hematological disorders and also from healthy donors was calculated, and significative differences were found between both results. Diffractometric data belonging to healthy donors behaves as white noise, while data series from different disease were found to be chaotic.

Animals↗
PubMed2002

A Levy flight-random walk model for bioturbation.

Levy flights are employed in a lattice model of contaminant migration by bioturbation, the reworking of sediment by benthic organisms. The model couples burrowing, foraging, and conveyor-belt feeding with molecular diffusion. The model correctly predicts a square-root dependence on bioturbation rates over a wide range of biomass densities. The model is used to predict the effect of bioturbation on the redistribution of contaminants in laboratory microcosms containing pyrene-inoculated sediments and the tubificid oligochaete Limnodrilus hoffmeisteri. The model predicts the dynamic flux from the sediment and in-bed concentration profiles that are consistent with observations. The sensitivity of flux and concentration profiles to the specific mechanisms of bioturbation are explored with the model. The flux of pyrene to the overlying water was largely controlled by the simulated foraging activities.

Animals↗
PubMedDate not supplied

[Theory of kinetic schemes. Random walks].

During special selection of self--functions of states methods of the kinetic scheme theory can be extrapolated on some probability processes. General solutions can be obtained with these methods, for the problem of casual wanderings in manymeric lattices for example. The general result of the work--distribution of average lifetime of a population in states is in the general case determined only by the topology of the scheme and is independent of the form of self-functions of states.

Kinetics↗
PubMed1992

Visible persistence is reduced by fixed-trajectory motion but not by random motion.

Despite the sluggish temporal response of the human visual system, moving objects appear clear and without blur, which suggests that visible persistence is reduced when objects move. It has been argued that spatiotemporal proximity alone can account for this modulation of visible persistence and that activation of a motion mechanism per se is not necessary. Experiments are reported which demonstrate that there is a motion-specific influence on visible persistence. Specifically, points moving in constant directions, or fixed trajectories, show less persistence than points moving with the same spatial and temporal displacements but taking random walks, randomly changing direction each frame. Subjects estimated the number of points present in the display for these two types of motion conditions. Under conditions chosen to produce 'good' apparent motion, ie small temporal and spatial increments, the apparent number of points for the fixed-trajectory condition was significantly lower than the apparent number in the random-walk condition. The traditional explanation of the suppression of persistence based on the spatiotemporal proximity of objects cannot account for these results. The enhanced suppression of persistence observed for a target moving in a consistent direction depends upon the activation of a directionally tuned motion mechanism extended over space and time.

Female↗
PubMed1999

Vortex dynamics in a three-state model under cyclic dominance.

The evolution of domain structure is investigated in a two-dimensional voter model with three states under cyclic dominance. The study focus on the dynamics of vortices, defined by the points where the three states (domains) meet. We can distinguish vortices and antivortices which walk randomly and annihilate each other. The domain wall motion can create vortex-antivortex pairs at a rate that is increased by the spiral formation due to cyclic dominance. This mechanism is contrasted with a branching annihilating random walk (BARW) in a particle-antiparticle system with density-dependent pair creation rate. Numerical estimates for the critical indices of the vortex density [beta=0.29(4)] and of its fluctuation [gamma=0.34(6)] improve an earlier Monte Carlo study [K. Tainaka and Y. Itoh, Europhys. Lett. 15, 399 (1991)] of the three-state cyclic model in two dimensions.

Journal Article↗
PubMed2001

Deterministic walks in random media.

Deterministic walks over a random set of N points in one and two dimensions ( d = 1,2) are considered. Points ("cities") are randomly scattered in R(d) following a uniform distribution. A walker ("tourist"), at each time step, goes to the nearest neighbor city that has not been visited in the past tau steps. Each initial city leads to a different trajectory composed of a transient part and a final p-cycle attractor. Transient times (for d = 1,2) follow an exponential law with a tau-dependent decay time but the density of p cycles can be approximately described by D(p)proportional to p(-alpha(tau)). For tau>>1 and tau/N<<1, the exponent is independent of tau. Some analytical results are given for the d = 1 case.

Journal Article↗
PubMed1987

Stochastic model of leukocyte chemosensory movement.

We propose a hypothesis for a unified understanding of the persistent and biased random walk behavior of leukocytes exhibiting random motility and chemotaxis, respectively. This hypothesis is based on a description of the leukocyte as an integrated system sensing and responding to a "noisy" receptor signal: random fluctuations inherent in receptor-sensing of chemo-attractant concentrations underlie the random walk behavior. Noise arises from real fluctuations in the receptor binding process, which translate into perceived fluctuations in receptor-measured concentration. The unbiased random walk characteristic of random motility arises from perceived fluctuating gradients without a mean reference direction and the biased random walk in chemotaxis arises due to the occurrence of perceived concentration fluctuations around the mean gradient. Analysis of a stochastic model based on this hypothesis yields an objective index of directional randomness in random motility, the directional persistence time, in terms of model parameters associated with receptor binding, receptor signal transduction, and the cell turning response. Simulation of the model equations yields cell paths from which the orientation behavior in a chemoattractant gradient is characterized in terms of the same model parameters. Our results provide a theoretical relationship between directional persistence and orientation bias and suggest quantitative answers to the questions: Is there an optimal level of persistence with respect to maximizing orientation bias? Do directional persistence and orientation bias both display the same parametric sensitivity? How does this sensitivity depend on the sensing, transduction, and response components of the cell system?

Cell Membrane↗
PubMed1991

Visual discrimination of fractal borders.

The ideas of fractals and fractal dimension are here translated into the realm of visual psychophysics. Borders between two fields of different luminance were used. Because of the finite grain of the visual system, fractal dimension need be defined only within a certain size range. For a fractal dimension of 1.15, the just-detectable difference in fractal dimension was found to be about 0.0085, rising to about 0.015 for a fractal dimension of 1.25. Reducing exposure duration from 1 s to 0.33 s decreases sensitivity to differences in fractal dimension, but there was no gain in increasing the exposure duration. Good visual observers who are naive to the task require some training before reaching optimal performance. The ability to discriminate fractal dimension differs between fractal edges of the same fractal dimension that were generated with differing statistical programs. Even after considerable training, an observer makes 29% errors when asked to distinguish a fractal edge generated with a Gaussian random walk from one with a rectangular random walk. Gaussian random walk fractals can be more easily distinguished from Poissonian and Cauchy ones.

Differential Threshold↗
PubMed1984

Nonrandom spatial distribution by mammalian cells in culture.

Quadrat analysis was used to investigate the spatial distribution of seven mammalian cell lines in culture. The number of cells in replicate unit areas of the culture was determined, and the variance to mean ratio used as an index of random and nonrandom spatial distribution. Only mouse SV3T3 cells distributed themselves randomly throughout the entire culture growth cycle. The remaining six lines all assumed a nonrandom distribution at some point in their growth cycles. Mouse L929 cells displayed avoidance behavior, and spaced themselves at regular intervals in a uniform spatial distribution. The five remaining lines (mouse S180, rat C6, hamster CHO, canine MDCK, and human BeWo) formed multicellular clusters, and were distributed aggregatively rather than randomly. Random walk migration can account for the random distribution of SV3T3 cells. Random walk combined with contact inhibition of movement provides a satisfactory explanation for the uniform distribution of L929 cells. Random walk and contact inhibition are incompatible with cell clustering, however. Thus other mechanisms of motility or adhesiveness must contribute to cell clustering. It is possible that random walk and contact inhibition may be less common components of cell movement than generally assumed.

Animals↗
PubMed1996

What is noise for the motion system?

Motion coherence thresholds in random-dot patterns have been widely adopted as a measure of performance in visual motion processing. However, there has been diversity in the type of "noise" in which a coherent motion signal has to be detected. Here we compare coherence thresholds for three ways of creating motion noise: dots replotted in random positions in each new frame; dots with a set displacement but following a random walk from frame to frame; or dots moving in random directions which remain constant for a given dot over a sequence of displacements. In each case, the signal dots may either remain the same throughout the display sequence, or the signal dots may be re-selected afresh on each frame ("different"). With our display (3 deg square, 120 msec exposure, velocity = 5 or 10 deg sec-1), all these different noise conditions yielded similar thresholds around 5-8%. There were some small but systematic differences between conditions. Thresholds in random-direction displays were consistently higher than those in random-walk or random-position displays, especially at the lower velocity. However, this effect is much smaller than would be expected from the increased standard error of the noise mean in random direction, perhaps because the motion system integrates information most effectively over a local region of space and/or time. Subjects" performance could not be explained by a strategy of identifying individual signal dots with extended trajectories. The similarity between random-walk and random-position thresholds implies that subjects do not exploit the marked differences in speed distribution between signal and noise dots in the latter case. The practical message for the design and interpretation of experiments using coherence thresholds is that the results are not much affected by the choice of noise, at least within the range of stimuli tested here.

Adult↗