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At least 613 records · Page 34Linked to original sources
PubMed1999

Effect of lateral boundaries on contrast functions in time-resolved transillumination measurements.

The method of images is employed to insert the effects of the presence of a single lateral boundary on contrast functions previously derived for an infinite slab using a random walk model of photon transport. The predictions of the model for zero and extrapolated boundary conditions are compared with Monte Carlo (MC) simulations and with experimental results obtained using a homogenous phantom with tissue-like optical properties. As expected, the extrapolated boundary condition yields better agreement between the theoretical predictions and results obtained from MC and experiments. This indicates that the random walk model has potential as a forward model in iterative imaging schemes developed for optical tomography.

Biophysical Phenomena↗
PubMed2006

Single- versus dual-process models of lexical decision performance: insights from response time distributional analysis.

This article evaluates 2 competing models that address the decision-making processes mediating word recognition and lexical decision performance: a hybrid 2-stage model of lexical decision performance and a random-walk model. In 2 experiments, nonword type and word frequency were manipulated across 2 contrasts (pseudohomophone-legal nonword and legal-illegal nonword). When nonwords became more wordlike (i.e., BRNTA vs. BRANT vs. BRANE), response latencies to nonwords were slowed and the word frequency effect increased. More important, distributional analyses revealed that the Nonword Type = Word Frequency interaction was modulated by different components of the response time distribution, depending on the specific nonword contrast. A single-process random-walk model was able to account for this particular set of findings more successfully than the hybrid 2-stage model.

Adult↗
PubMed2005

Scale-free networks from self-organization.

We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of parameters. The growth mechanism is based on using local graph information only, so this is a process of self-organization. The standard mean-field equations are an excellent approximation for network growth using these rules. We discuss the effects of finite size on the degree distribution, and compare analytical results to simulated networks. Finally, we generalize the random walk algorithm to produce weighted networks with power-law distributions of both weight and degree.

Journal Article↗
PubMed2003

Autonomous T cell trafficking examined in vivo with intravital two-photon microscopy.

The recirculation of T cells between the blood and secondary lymphoid organs requires that T cells are motile and sensitive to tissue-specific signals. T cell motility has been studied in vitro, but the migratory behavior of individual T cells in vivo has remained enigmatic. Here, using intravital two-photon laser microscopy, we imaged the locomotion and trafficking of naive CD4(+) T cells in the inguinal lymph nodes of anesthetized mice. Intravital recordings deep within the lymph node showed T cells flowing rapidly in the microvasculature and captured individual homing events. Within the diffuse cortex, T cells displayed robust motility with an average velocity of approximately 11 microm x min(-1). T cells cycled between states of low and high motility roughly every 2 min, achieving peak velocities >25 microm x min(-1). An analysis of T cell migration in 3D space revealed a default trafficking program analogous to a random walk. Our results show that naive T cells do not migrate collectively, as they might under the direction of pervasive chemokine gradients. Instead, they appear to migrate as autonomous agents, each cell taking an independent trafficking path. Our results call into question the role of chemokine gradients for basal T cell trafficking within T cell areas and suggest that antigen detection may result from a stochastic process through which a random walk facilitates contact with antigen-presenting dendritic cells.

Adoptive Transfer↗
PubMed2005

Interpreting two-photon imaging data of lymphocyte motility.

Recently, using two-photon imaging it has been found that the movement of B and T cells in lymph nodes can be described by a random walk with persistence of orientation in the range of 2 minutes. We interpret this new class of lymphocyte motility data within a theoretical model. The model considers cell movement to be composed of the movement of subunits of the cell membrane. In this way movement and deformation of the cell are correlated to each other. We find that, indeed, the lymphocyte movement in lymph nodes can best be described as a random walk with persistence of orientation. The assumption of motility induced cell elongation is consistent with the data. Within the framework of our model the two-photon data suggest that T and B cells are in a single velocity state with large stochastic width. The alternative of three different velocity states with frequent changes of their state and small stochastic width is less likely. Two velocity states can be excluded.

Algorithms↗
PubMed1999

Effects of similarity and practice on speeded classification response times and accuracies: further tests of an exemplar-retrieval model.

Observers were tested in a perceptual category-learning experiment in which they were instructed to make classification decisions as rapidly as possible without making errors. Nosofsky and Palmeri's (1997b) exemplar-based random walk (EBRW) model of speeded classification was tested for its ability to fit the classification response times and accuracies. The authors demonstrated that the EBRW model provided good quantitative fits to the mean response times and accuracies associated with individual objects as a function of their locations in a multidimensional similarity space and as a function of practice in the task. Preliminary evidence was also obtained that stimulus-specific adjustments in the random walk response criteria may have occurred during the course of learning.

Adult↗
PubMed2004

Quantile estimation following non-parametric phase I clinical trials with ordinal response.

A non-parametric multi-dimensional isotonic regression estimator is developed for use in estimating a set of target quantiles from an ordinal toxicity scale. We compare this estimator to the standard parametric maximum likelihood estimator from a proportional odds model for extremely small data sets. A motivating example is from phase I oncology clinical trials, where various non-parametric designs have been proposed that lead to very small data sets, often with ordinal toxicity response data. Our comparison of estimators is performed in conjunction with three of these non-parametric sequential designs for ordinal response data, two from the literature and a new design based on a random walk rule. We also compare with a non-parametric design for binary response trials, by keeping track of ordinal data for estimation purposes, but dichotomizing the data in the design phase. We find that a multidimensional isotonic regression-based estimator far exceeds the others in terms of accuracy and efficiency. A rule by Simon et al. (J. Natl. Cancer Inst. 1997; 89:1138-1147) yields particularly efficient estimators, more so than the random walk rule, but has higher numbers of dose-limiting toxicity. A small data set from a leukemia clinical trial is analysed using our multidimensional isotonic regression-based estimator.

Antineoplastic Agents↗
PubMed2000

An exemplar-retrieval model of speeded same--different judgments.

R. M. Nosofsky and T. J. Palmeri's (1997) exemplar-based random-walk (EBRW) model of speeded classification is extended to account for speeded same--different judgments among integral-dimension stimuli. According to the model, an important component process of same--different judgments is that people store individual examples of experienced same and different pairs of objects in memory. These exemplar pairs are retrieved from memory on the basis of how similar they are to a currently presented pair of objects. The retrieved pairs drive a random-walk process for making same--different decisions. The EBRW predicts correctly that same responses are faster for objects lying in isolated than in dense regions of similarity space. The model also predicts correctly effects of same-identity versus same-category instructions and is sensitive to observers' past experiences with specific same and different pairs of objects.

Humans↗
PubMed1984

On the Williams-Watts function of dielectric relaxation.

It has been observed over the past 15 years that experimental frequency-dependent dielectric constants of broad classes of materials including polymeric systems and glasses may be interpreted in terms of the Williams-Watts polarization decay function [Formula: see text] The exponent alpha and the time constant T depend on the material and fixed external conditions such as temperature and pressure. We derive this form of varphi(alpha)(t) from the following random-walk model. Suppose that an electric field has been applied for some time to a medium containing many polar molecules (or polar groups in complex molecules) and the direction of their dipole moments remains frozen as the field is removed. Furthermore, suppose that the medium contains mobile defects that on reaching the site of a frozen dipole relax the medium to the degree that the dipole may reorient itself. If the diffusion of defects toward dipoles is executed as a continuous-time random walk composed of an alternation of steps and pauses and the pausing-time distribution function has a long tail of the form psi(t) infinity t(-1-alpha), then the relaxation function has the above fractional exponential form.

Journal Article↗
PubMed1992

Predictive power of various models for longitudinal attachment level change.

Several statistical models that have been suggested in the periodontal literature for describing longitudinal attachment level changes, such as the gradual loss, single-burst, multiple-burst, and random walk models as well as other models introduced in this paper are compared by their power to predict future attachment loss. The data used in this analysis is from 1061 sites of 8 subjects, with moderate to severe periodontal disease, monitored monthly for about a year. This study found that none of the suggested models could significantly outperform the naïve mean predictor, which predicts the future attachment level from the past mean. It was also found that no single model, such as the burst, gradual, or random walk, together with measurement error can fully explain the variation in the data. These results indicate that in the course of one year, the attachment level change may not follow the same model. Consequently, a model that fits well to past data cannot be accurately extended to the future.

Disease Susceptibility↗
PubMed2006

Dynamics of epileptic phenomena determined from statistics of ictal transitions.

In this paper, we investigate the dynamical scenarios of transitions between normal and paroxysmal state in epilepsy. We assume that some epileptic neural network are bistable i.e., they feature two operational states, ictal and interictal that co-exist. The transitions between these two states may occur according to a Poisson process, a random walk process or as a result of deterministic time-dependent mechanisms. We analyze data from animal models of absence epilepsy, human epilepsies and in vitro models. The distributions of durations of ictal and interictal epochs are fitted with a gamma distribution. On the basis of qualitative features of the fits, we identify the dynamical processes that may have generated the underlying data. The analysis showed that the following hold. 1) The dynamics of ictal epochs differ from those of interictal states. 2) Seizure initiation can be accounted for by a random walk process while seizure termination is often mediated by deterministic mechanisms. 3) In certain cases, the transitions between ictal and interictal states can be modeled by a Poisson process operating in a bistable network. These results imply that exact prediction of seizure occurrence is not possible but termination of an ictal state by appropriate counter stimulation might be feasible.

Adolescent↗
PubMed1997

The length distribution of perfect dimer repetitive DNA is consistent with its evolution by an unbiased single-step mutation process.

We have examined the length distribution of perfect dimer repeats, where perfect means uninterrupted by any other base, using data from GenBank on primates and rodents. Virtually no lengths greater than 30 repeats are found, except for rodent AG repeats, which extend to 35. Comparable numbers of long AC and AG repeats suggest that they have not been selected for special functions or DNA structures. We have compared the data with predictions of two models: (1) a Bernoulli Model in which bases are assumed equally likely and distributed at random and (2) an Unbiased Random Walk Model (URWM) in which repeats are permitted to change length by plus or minus one unit, with equal probabilities, and in which base substitutions are allowed to destroy long perfect repeats, producing two shorter perfect repeats. The source of repeats is assumed to be from single base substutions from neighboring sequences, i.e., those differing from the perfect repeat by a single base. Mutation rates either independent of repeat length or proportional to length were considered. An upper limit to the lengths L approximately 30 is assumed and isolated dimers are assumed unable to expand, so that there are absorbing barriers to the random walk at lengths 1 and L + 1, and a steady state of lengths is reached. With these assumptions and estimated values for the rates of length mutation and base substitution, reasonable agreement is found with the data for lengths > 5 repeats. Shorter repeats, of lengths </= 3 are in general agreement with the Bernoulli Model. By reducing the rate of length mutations for n </= 5, it is possible to obtain reasonable agreement with the full range of data. For these reduced rates, the times between length mutations become comparable to those suggested for a bottleneck in the evolution of Homo sapiens, which may be the reason for low heterozygosity of short repeats.

Animals↗
PubMed1992

The relationship between the Gabor elementary function and a stochastic model of the inter-spike interval distribution in the responses of visual cortex neurons.

In a previously reported study (Berger et al. 1990) we analyzed distributions of interspike intervals recorded extracellularly from cat visual cortex under four stimulus conditions. Stimuli were gratings differing in orientation and spatial frequency. The probability density function of first passage time for a random walk with drift process, which is defined by its barrier height and drift coefficient, was used to characterize the generating process of axonal discharge under resting and stimulus conditions. Drift coefficient and barrier height were derived from the sample mean and standard deviation of the measured inter-spike intervals. For cells with simple receptive fields, variations in spatial frequency produced changes only in drift coefficient. Variations in barrier height were produced only by changes in orientation of the stimulus. Currently, the method used to analyze these data was implemented in a simulation which displayed the relationship between the interval distribution of impulses, the random walk which represents the time series characteristic of the spike train model and the Gabor filter function which represents the geometry of the receptive field process.

Animals↗
PubMed2005

Overcoming the slowing down of flat-histogram Monte Carlo simulations: cluster updates and optimized broad-histogram ensembles.

We study the performance of Monte Carlo simulations that sample a broad histogram in energy by determining the mean first-passage time to span the entire energy space of d-dimensional ferromagnetic Ising/Potts models. We first show that flat-histogram Monte Carlo methods with single-spin flip updates such as the Wang-Landau algorithm or the multicanonical method perform suboptimally in comparison to an unbiased Markovian random walk in energy space. For the d = 1, 2, 3 Ising model, the mean first-passage time tau scales with the number of spins N = L(d) as tau proportional N2L(z). The exponent z is found to decrease as the dimensionality d is increased. In the mean-field limit of infinite dimensions we find that z vanishes up to logarithmic corrections. We then demonstrate how the slowdown characterized by z > 0 for finite d can be overcome by two complementary approaches--cluster dynamics in connection with Wang-Landau sampling and the recently developed ensemble optimization technique. Both approaches are found to improve the random walk in energy space so that tau proportional N2 up to logarithmic corrections for the d = 1, 2 Ising model.

Journal Article↗
PubMed2005

Theoretical study of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction by a diffusion quantum Monte Carlo approach.

Ab initio calculations of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction has been carried out by the fixed-node diffusion quantum Monte Carlo method in this study. The Monte Carlo sampling is based on the Ornstein-Uhlenbeck random walks guided by a trial wave function constructed from the floating spherical Gaussian orbitals and spherical Gaussian geminals. The Monte Carlo calculated barrier height of 1.09(16) kcal/mol is consistent with the experimental values, 0.86(10)/1.18(10) kcal/mol, and the calculated value from the multireference-type coupled-cluster (MRCC) calculation with the aug-cc-pVQZ(F)/cc-pVQZ(H) basis set, 1.11 kcal/mol. The Monte Carlo-based calculation also gives a similar value of the reaction enthalpy, -32.00(4) kcal/mol, compared with the experimental value, -32.06(17) kcal/mol, and the calculated value from a MRCC/aug-cc-pVQZ(F)/cc-pVQZ(H) calculation, -31.94 kcal/mol. This study clearly indicates a further application of the random-walk-based approach in the field of quantum chemical calculation.

Journal Article↗
PubMed2006

Building bridges between neural models and complex decision making behaviour.

Diffusion processes, and their discrete time counterparts, random walk models, have demonstrated an ability to account for a wide range of findings from behavioural decision making for which the purely algebraic and deterministic models often used in economics and psychology cannot account. Recent studies that record neural activations in non-human primates during perceptual decision making tasks have revealed that neural firing rates closely mimic the accumulation of preference theorized by behaviourally-derived diffusion models of decision making. This article bridges the expanse between the neurophysiological and behavioural decision making literatures specifically, decision field theory [Busemeyer, J. R. & Townsend, J. T. (1993). Decision field theory: A dynamic-cognitive approach to decision making in an uncertain environment. Psychological Review, 100, 432-459], a dynamic and stochastic random walk theory of decision making, is presented as a model positioned between lower-level neural activation patterns and more complex notions of decision making found in psychology and economics. Potential neural correlates of this model are proposed, and relevant competing models are also addressed.

Action Potentials↗
PubMed1988

Analysis of cell locomotion. Contact guidance of human polymorphonuclear leukocytes.

The methods of statistical physics have been applied to the analysis of cell movement. Human polymorphonuclear leukocytes were exposed to different surfaces possessing parallel oriented physical structures (scratched glass surface, machine drilled aluminum surface, optical grid and stretched polyethylene foil) and cell migration was observed using time-lapse photography. We demonstrate that in cell migration along physical structures, referred to as contact guidance, two subgroups can be distinguished: 1) The nematic type where the cell size is large in relation to the grid distance of the undulate surface. 2) The smectic type where the cell size is small in relation to the grid distance of the substrate. Nematic contact guidance is characterized by an anisotropic random walk. In all substrates investigated the diffusion process parallel to the lines was faster than the diffusion process perpendicular to them. The angular dependent diffusion coefficient was described by an ellipse. Deviation from a circle defined an apolar order parameter, whose value was about 0.3. The amount of information which the cells collected from, the undulate surface was very low, between 0.1 and 0.2 bits. We demonstrate that cells do not recognize all the details of their surroundings and that their migration can be compared to the "groping around" of a short sighted man. The blurred environment can be described by a mean field whose strength is proportional to the apolar order parameter. It is argued that the anisotropic surface tension is the basic source for nematic contact guidance. Smectic contact guidance is characterized by an anisotropic random walk and is quantified by a density order parameter which is 0.28 in the case of the scratched glass surface of a Neubauer counting chamber. The information which the cells collect from their environment is very low (0.03 bits). The lines seen by the cell can be described by a mean field whose strength is proportional to the density oder parameter. Finally, we demonstrate that the locomotion of granulocytes is governed by an internal clock and internal programs. After migrating for a certain time (32 s) in a particular direction, a new direction of locomotion is determined by an internal program. The cell decides basically between left or right, thereby preferring a turn angle such that the cell migrates either parallel or perpendicular to the lines. The angles are nearly equally probable but the cell moves, in the case of nematic guidance, with different velocities in the + or - direction. The cell also has directional memories with characteristic times of 32 s and greater than 100 s.

Cell Movement↗
PubMed2001

Testing Evidence Accrual Models by Manipulating Stimulus Onset.

Many models of response time assume that subjects accrue stimulus "evidence" samples in time (e.g., random walk models, counter models). In this paper, the concept of one stimulus dominating another is used to construct a test of the whole class of evidence accrual models. For an example of dominance, consider stimuli that are presented either virtually instantaneously (stepped) or in a gradually increasing manner (ramped). Ramped stimuli are presented such that the ramped portion precedes the stepped onset of stepped stimuli. In this case ramped stimuli dominate stepped stimuli. In this paper the class of evidence accrual models is formalized. It is shown that under appropriate assumptions evidence accrual models do predict more accurate responses to dominating stimuli. However, this result does not hold for response latencies. There are anomalous cases where an evidence accrual model (the accumulator model of Vickers (1970, Ergonomics 13, 37-58)) predicts slower mean correct response latencies to dominating stimuli. It is shown through extensive computer simulation that these anomalous cases occur only when response criteria are so asymmetric that there are exceedingly extreme response biases. For experiments where response biases are not exceedingly extreme, random walk and accumulator models predict more accurate and quicker correct responses to dominating stimuli. In sum, manipulating the time course of stimuli in accordance with the concept of dominance can provide empirical tests of the class of evidence accrual models. Copyright 2001 Academic Press.

Journal Article↗