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At least 667 records · Page 37Linked to original sources
PubMed1997

Direction discrimination of cyclopean (stereoscopic) and luminance motion.

This study compared direction discrimination of cyclopean (stereoscopic) and luminance motion involving stimuli equated for effective strength. The stimuli were random-walk cinematogram (RWC) displays whose signal and noise discs were created from binocular disparity differences embedded in a dynamic random-dot stereogram or from luminance differences. Experiment 1 measured global motion detection thresholds for cyclopean and luminance stimuli by manipulating the proportion of signal to noise discs. Detection thresholds for cyclopean motion were about 25% whereas detection thresholds for luminance motion were 5%, thus five times more cyclopean motion events than luminance events were necessary to elicit threshold responding. Experiment 2 measured thresholds for discriminating the direction of cyclopean and luminance motion under conditions of equal stimulus strength by presenting the motion displays at equal multiples of detection threshold. Direction discrimination thresholds (ranging from about 5-30 deg, depending upon conditions) were similar for cyclopean and luminance motion, thus the precision with which the pooling of local motion events in one direction can be discriminated from the pooling of events in a slightly different direction is the same for cyclopean and luminance stimuli. The finding that cyclopean motion information is pooled is consistent with the idea that the direction of cyclopean motion is coded in the responses of a population of directionally selective mechanisms.

Depth Perception↗
PubMed2002

A reaction-diffusion model for interference in meiotic crossing over.

One crossover point between a pair of homologous chromosomes in meiosis appears to interfere with occurrence of another in the neighborhood. It has been revealed that Drosophila and Neurospora, in spite of their large difference in the frequency of crossover points, show very similar plots of coincidence-a measure of the interference-against the genetic distance of the interval, defined as one-half the average number of crossover points within the interval. We here propose a simple reaction-diffusion model, where a "randomly walking" precursor becomes immobilized and matures into a crossover point. The interference is caused by pair-annihilation of the random walkers due to their collision and by annihilation of a random walker due to its collision with an immobilized point. This model has two parameters-the initial density of the random walkers and the rate of its processing into a crossover point. We show numerically that, as the former increases and/or the latter decreases, plotted curves of the coincidence vs. the genetic distance converge on a unique curve. Thus, our model explains the similarity between Drosophila and Neurospora without parameter values adjusted finely, although it is not a "genetic model" but is a "physical model," specifying explicitly what happens physically.

Crossing Over, Genetic↗
PubMed1995

Detection of temporary lateral confinement of membrane proteins using single-particle tracking analysis.

Techniques such as single-particle tracking allow the characterization of the movements of single or very few molecules. Features of the molecular trajectories, such as confined diffusion or directed transport, can reveal interesting biological interactions, but they can also arise from simple Brownian motion. Careful analysis of the data, therefore, is necessary to identify interesting effects from pure random movements. A method was developed to detect temporary confinement in the trajectories of membrane proteins that cannot be accounted for by Brownian motion. This analysis was applied to trajectories of two lipid-linked members of the immunoglobulin superfamily, Thy-1 and a neural cell adhesion molecule (NCAM 125), and the results were compared with those for simulated random walks. Approximately 28% of the trajectories for both proteins exhibited periods of transient confinement, which were < 0.07% likely to arise from random movements. In contrast to these results, only 1.5% of the simulated trajectories showed confined periods. Transient confinement for both proteins lasted on average 8 s in regions that were approximately 280 nm in diameter.

Animals↗
PubMed2001

Hitch-hiking: a parallel heuristic search strategy, applied to the phylogeny problem.

The article introduces a parallel heuristic search strategy ("Hitch-hiking") which can be used in conjunction with other random-walk heuristic search strategies. It is applied to an artificial phylogeny problem, in which character sequences are evolved using pseudo-random numbers from a hypothetical ancestral sequence. The objective function to be minimized is the minimum number of character-state changes required on a binary tree that could account for the sequences observed at the tips (leaves) of the tree -- the Maximum Parsimony criterion. The Hitch-hiking strategy is shown to be useful in that it is robust and that on average the solutions found using the strategy are better than those found without. Also the strategy can dynamically provide information on the characteristics of the landscape of the problem. I argue that Hitch-hiking as a scheme for parallelization of existing heuristic search strategies is of potentially very general use, in many areas of combinatorial optimization.

Algorithms↗
PubMed2000

Descriptive parameter for photon trajectories in a turbid medium.

In many applications of laser techniques for diagnostic or therapeutic purposes it is necessary to be able to characterize photon trajectories to know which parts of the tissue are being interrogated. In this paper, we consider the cw reflectance experiment on a semi-infinite medium with uniform optical parameters and having a planar interface. The analysis is carried out in terms of a continuous-time random walk and the relation between the occupancy of a plane parallel to the surface to the maximum depth reached by the random walker is studied. The first moment of the ratio of average depth to the average maximum depth yields information about the volume of tissue interrogated as well as giving some indication of the region of tissue that gets the most light. We have also calculated the standard deviation of this random variable. It is not large enough to qualitatively affect information contained in the first moment.

Lasers↗
PubMed2000

Impact of correlated synaptic input on output firing rate and variability in simple neuronal models.

Cortical neurons are typically driven by thousands of synaptic inputs. The arrival of a spike from one input may or may not be correlated with the arrival of other spikes from different inputs. How does this interdependence alter the probability that the postsynaptic neuron will fire? We constructed a simple random walk model in which the membrane potential of a target neuron fluctuates stochastically, driven by excitatory and inhibitory spikes arriving at random times. An analytic expression was derived for the mean output firing rate as a function of the firing rates and pairwise correlations of the inputs. This stochastic model made three quantitative predictions. (1) Correlations between pairs of excitatory or inhibitory inputs increase the fluctuations in synaptic drive, whereas correlations between excitatory-inhibitory pairs decrease them. (2) When excitation and inhibition are fully balanced (the mean net synaptic drive is zero), firing is caused by the fluctuations only. (3) In the balanced case, firing is irregular. These theoretical predictions were in excellent agreement with simulations of an integrate-and-fire neuron that included multiple conductances and received hundreds of synaptic inputs. The results show that, in the balanced regime, weak correlations caused by signals shared among inputs may have a multiplicative effect on the input-output rate curve of a postsynaptic neuron, i.e. they may regulate its gain; in the unbalanced regime, correlations may increase firing probability mainly around threshold, when output rate is low; and in all cases correlations are expected to increase the variability of the output spike train.

Action Potentials↗
PubMed2000

Endothelial cell migration on surfaces modified with immobilized adhesive peptides.

Endothelial cell (EC) migration has been studied on aminophase surfaces with covalently bound RGDS and YIGSRG cell adhesion peptides. The fluorescent marker dansyl chloride was used to quantify the spatial distribution of the peptides on the modified surfaces. Peptides appeared to be distributed in uniformly dispersed large clusters separated by areas of lower peptide concentrations. We employed digital time-lapse video microscopy and image analysis to monitor EC migration on the modified surfaces and to reconstruct the cell trajectories. The persistent random walk model was then applied to analyze the cell displacement data and compute the mean root square speed, the persistence time, and the random motility coefficient of EC. We also calculated the time-averaged speed of cell locomotion. No differences in the speed of cell locomotion on the various substrates were noted. Immobilization of the cell adhesion peptides (RGDS and YIGSRG), however, significantly increased the persistence of cell movement and, thus, the random motility coefficient. These results suggest that immobilization of cell adhesion peptides on the surface of implantable biomaterials may lead to enhanced endothelization rates.

Amino Acid Sequence↗
PubMed1997

Torsional directed walks, entropic elasticity, and DNA twist stiffness.

DNA and other biopolymers differ from classical polymers because of their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the "torsional directed walk." Motivated by a recent experiment on single lambda-DNA molecules [Strick, T. R., Allemand, J.-F., Bensimon, D., Bensimon, A. & Croquette, V. (1996) Science 271, 1835-1837], we formulate the torsional directed walk problem and solve it analytically in the appropriate force regime. Our technique affords a direct physical determination of the microscopic twist stiffness C and twist-stretch coupling D relevant for DNA functionality. The theory quantitatively fits existing experimental data for relative extension as a function of overtwist over a wide range of applied force; fitting to the experimental data yields the numerical values C = 120 nm and D = 50 nm. Future experiments will refine these values. We also predict that the phenomenon of reduction of effective twist stiffness by bend fluctuations should be testable in future single-molecule experiments, and we give its analytic form.

Animals↗
PubMed2002

Percolation in a random environment.

We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the system with varying degree of disorder is governed by new, random fixed points with anisotropic scaling properties. For weaker disorder both the magnetization and the anisotropy exponents are nonuniversal, whereas for strong enough disorder the system scales into an infinite randomness fixed point in which the critical exponents are exactly known.

Journal Article↗
PubMed2001

Monte Carlo predictions of DNA fragment-size distributions for large sizes after HZE particle irradiation.

DSBs (double-strand breaks) produced by densely ionizing space radiation are not located randomly in the genome: recent data indicate DSB clustering along chromosomes. DSB clustering at large scales, from >100 Mbp down to approximately 2 kbp, is modeled using a Monte-Carlo algorithm. A random-walk model of chromatin is combined with a track model, that predicts the radial distribution of energy from an ion, and the RLC (randomly-located-clusters) formalism, in software called DNAbreak. This model generalizes the random-breakage model, whose broken-stick fragment-size distribution is applicable to low-LET radiation. DSB induction due to track interaction with the DNA volume depends on the radiation quality parameter Q. This dose-independent parameter depends only weakly on LET. Multi-track, high-dose effects depend on the cluster intensity parameter lambda, proportional to fluence as defined by the RLC formalism. After lambda is determined by a numerical experiment, the model reduces to one adjustable parameter Q. The best numerical fits to the experimental data, determining Q, are obtained. The knowledge of lambda and Q allows us to give biophysically based extrapolations of high-dose DNA fragment-size data to low doses or to high LETs.

Algorithms↗
PubMed1993

Generalized Lévy-walk model for DNA nucleotide sequences.

We propose a generalized Lévy walk to model fractal landscapes observed in noncoding DNA sequences. We find that this model provides a very close approximation to the empirical data and explains a number of statistical properties of genomic DNA sequences such as the distribution of strand-biased regions (those with an excess of one type of nucleotide) as well as local changes in the slope of the correlation exponent alpha. The generalized Lévy-walk model simultaneously accounts for the long-range correlations in noncoding DNA sequences and for the apparently paradoxical finding of long subregions of biased random walks (length lj) within these correlated sequences. In the generalized Lévy-walk model, the lj are chosen from a power-law distribution P(lj) varies as lj(-mu). The correlation exponent alpha is related to mu through alpha = 2-mu/2 if 2 < mu < 3. The model is consistent with the finding of "repetitive elements" of variable length interspersed within noncoding DNA.

Base Sequence↗
PubMed2003

Vibrating insoles and balance control in elderly people.

Somatosensory function declines with age, and such changes have been associated with diminished motor performance. Input noise can enhance sensory and motor function. We asked young and elderly participants to stand quietly on vibrating gel-based insoles, and calculated sway parameters and random-walk variables. In our 27 participants, application of noise resulted in a reduction in seven of eight sway parameters in young participants and all of the sway variables in elderly participants. Elderly participants showed greater improvement than young people in two variables, mediolateral range (p=0.008), and critical mean square displacement (p=0.012). Noise-based devices, such as randomly vibrating insoles, could ameliorate age-related impairments in balance control.

Adult↗
PubMed1997

Stochastic epidemics: the probability of extinction of an infectious disease at the end of a major outbreak.

The aim of this study is to derive an asymptotic expression for the probability that an infectious disease will disappear from a population at the end of a major outbreak ('fade-out'). The study deals with a stochastic SIR-model. Local asymptotic expansions are constructed for the deterministic trajectories of the corresponding deterministic system, in particular for the deterministic trajectory starting in the saddle point. The analytical expression for the probability of extinction is derived by asymptotically solving a boundary value problem based on the Fokker-Planck equation for the stochastic system. The asymptotic results are compared with results obtained by random walk simulations.

Communicable Disease Control↗
PubMed2007

Simulations of chemotaxis and random motility in 2D random porous domains.

We discuss a generic computational model of eukariotic chemotaxis in 2D random porous domains. The model couples the fully time-dependent finite-difference solution of a reaction-diffusion equation for the concentration field of a chemoattractant to biased random walks representing individual chemotactic cells. We focus in particular on the influence of consumption of chemoattractant by the boundaries of obstacles with irregular shapes which are distributed randomly in the domain on the chemotactic response of the cells. Cells are stimulated to traverse a field of obstacles by a line source of chemoattractant. We find that the reactivity of the obstacle boundaries with respect to the chemoattractant strongly determines the transit time of cells through two primary mechanisms. The channeling effect arises because cells are effectively repelled from surfaces which consume chemoattractant, and opposing surfaces therefore act to keep cells in the middle of channels. This reduces traversal times relative to the case with unreactive boundaries, provided that the appropriate Péclet number relating the strength of reactivity to diffusion in governing chemoattractant transport is neither too low nor too high. The dead-zone effect arises due to a realistic threshold on the chemotactic response, which at steady state results in portions of the domain having no detectable gradient. Of these two, the channeling effect is responsible for 90% of the sensitivity of transit times to boundary reactivity. Based on these results, we speculate that it may be possible to tune the rates of cellular penetration into porous domains by engineering the reactivity of the internal surfaces to cytokines.

Chemotactic Factors↗
PubMed2000

Waiting time to parapatric speciation.

Using a weak migration and weak mutation approximation, I studied the average waiting time to parapatric speciation. The description of reproductive isolation used is based on the classical Dobzhansky model and its recently proposed multilocus generalizations. The dynamics of parapatric speciation are modelled as a biased random walk performed by the average genetic distance between the residents and immigrants. If a small number of genetic changes is sufficient for complete reproductive isolation, mutation and random genetic drift alone can cause speciation on the time-scale of ten to 1,000 times the inverse of the mutation rate over a set of loci underlying reproductive isolation. Even relatively weak selection for local adaptation can dramatically decrease the waiting time to speciation. The actual duration of the parapatric speciation process (that is the duration of intermediate forms in the actual transition to a state of complete reproductive isolation) is shorter by orders of magnitude than the overall waiting time to speciation. For a wide range of parameter values, the actual duration of parapatric speciation is of the order of one over the mutation rate. In general, parapatric speciation is expected to be triggered by changes in the environment.

Animals↗
PubMed1994

Time-continuous branching walk models of unstable gene amplification.

We consider a stochastic mechanism of the loss of resistance of cancer cells to cytotoxic agents, in terms of unstable gene amplification. Two models being different versions of a time-continuous branching random walk are presented. Both models assume strong dependence in replication and segregation of the extrachromosomal elements. The mathematical part of the paper includes the expression for the expected number of cells with a given number of gene copies in terms of modified Bessel functions. This adds to the collection of rare explicit solutions to branching process models. Original asymptotic expansions are also demonstrated. Fitting the model to experimental data yields estimates of the probabilities of gene amplification and deamplification. The thesis of the paper is that purely stochastic mechanisms may explain the dynamics of reversible drug resistance of cancer cells. Various stochastic approaches and their limitations are discussed.

Animals↗
PubMed2005

Elk winter foraging at fine scale in Yellowstone National Park.

The link between landscape properties and foraging decisions by herbivores remains unclear, but such knowledge is central to the understanding of plant-herbivore dynamics. Our goal was to determine whether fine-scale foraging paths of free-ranging elk (Cervus canadensis) respond to spatial structure of habitats in Yellowstone National Park. During winter 2002 we gathered elk-foraging information by following snow tracks in open habitats located on hillsides and flat terrain. The 21 snow paths surveyed were comprised on average of 15 discrete snow craters connected to each other by relatively straight-line movements. Our analyses revealed two levels of selection: elk chose where to dig, and how much search effort to allocate at digging sites based on habitat characteristics. On hillsides, elk preferentially dug in areas of greater biomass of grasses and forbs, and simply walked through poorer sites without digging. Individuals also searched more intensively, creating larger craters, where food biomass was higher. On flat terrain, crater size decreased with snow depth and increased with snow density. Correlated random walk models usually were adequate to characterize elk movement on flat terrain, but not on hillsides. First, as the number of movements between local foraging areas increased, elk displacements on hillsides became shorter than expected from random patterns. This trend on hillsides was strongly influenced by interindividual variation in movement behavior. Second, elk tended to forage perpendicularly to aspect, resulting in horizontal displacements. Our study demonstrates that free-ranging elk adjust their foraging to fine-scale habitat structure.

Animals↗
PubMed1993

Random paths in random arrays of cylinders.

Distributions associated with random tracks in bodies are important to understanding the effects of radiation on objects and their response to it. Results of computer simulations are presented for the distribution densities, average lengths, and relative frequencies of the various types of random tracks resulting from the traversal of random arrays of cylinders by random lines. We consider arrays consisting of freely overlapping long circular cylinders distributed randomly with their axes parallel to a line or a plane, or oriented randomly in the three-dimensional space. The problem of random tracks lying outside the cylinders (external random tracks) is treated analytically, while the distributions of random tracks found within the cylinders (internal random tracks) are determined using a simulation procedure based on a discrete step-by-step random walk mechanism applied in finite samples of the arrays. The numerical results are used to validate various general analytical results for the distribution densities and average lengths of random tracks in structures of arbitrary shape. It is found that the distributions of internal random tracks exhibit strong dependence on the cylinder volume fraction, while the external random tracks are distributed independently of the cylinder volume fraction for all three cases of orientation distribution. At the limit of high cylinder volume fraction, the internal random track distributions approach the distributions of the external random tracks, while at the other extreme, they become, as expected, identical to those determined analytically for a single infinite cylinder.

Computer Simulation↗