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At least 577 records · Page 32Linked to original sources
PubMed1998

Optical simulations of a noninvasive technique for the diagnosis of diseased salivary glands in situ.

A simulation experiment for three-dimensional (3D) imaging of exogenous fluorescinated antibodies that specifically bind to infiltrating lymphocytes in minor salivary glands was carried out. Small (approximately 1 mm3 volume) rhodamine targets, which mimic diseased minor salivary glands labeled with fluorescent antibodies to infiltrating lymphocytes in Sjøgren's syndrome, were embedded in a highly scattering tissue phantom consisting of a thick Delrin disk covered by index matched Delrin slabs of various thickness. In this way the variation of fluorescence profiles on the surface of tissue could be examined corresponding to the range of depths of the salivary glands in vivo. Surface images were obtained for different target depths and radial distances from laser excitation to target fluorophore. These images were analyzed and compared to calculations based on random walk theory in turbid media, using previously determined scattering and absorption coefficients of the Delrin. Excellent agreement between the surface profiles experimentally measured and those predicted by our random walk theory was obtained. Derivation of these theoretical expressions is a necessary step toward devising an inverse algorithm which may have the potential expressions to perform 3D reconstruction of the concentration distribution of fluorescent labels within tissue.

Diagnostic Imaging↗
PubMed1993

The trajectories of spheres during agarose gel electrophoresis.

To develop a physical description of the gel-induced retardation of spheres during gel electrophoresis, the microscopic motion of single electrically charged latex spheres is statistically quantified here, by digital image analysis. To obtain adequate resolution in space, comparatively large spheres, 240 nm in radius, are used. The following observations are made during electrophoresis in a 0.2% agarose gel at 22 degrees C: (a) When a comparatively high field (3.0 V cm-1) is used, inelastic collisions result in field-induced trapping of spheres; no elastic collisions are observed. (b) Reduction of the field from 3.0 to 0.0 V cm-1 results in reverse migration of previously trapped spheres. (c) In the absence of trapping, the electrical field does not cause an alteration in the tortuosity of motion (i.e. motion in a field-perpendicular direction). (d) When results are obtained for a constant time between images (0.2 s), gel-dependent deviations from a true random walk are not observed in the absence of trapping. (e) When results are obtained as a function of time between images, significant gel-dependent deviation from a random walk is observed. In the absence of trapping, the data presented here indicate that retardation is derived primarily from dissipative processes that are concentrated near gel fibers. However, steric effects have not yet been distinguished from hydrodynamic effects.

Buffers↗
PubMed2001

Mechanism of synchronization in a random dynamical system.

The mechanism of synchronization in the random Zaslavsky map is investigated. From the error dynamics of two particles, the structure of phase space was analyzed, and a transcritical bifurcation between a saddle and a stable fixed point was found. We have verified the structure of on-off intermittency in terms of a biased random walk. Furthermore, for the generalized case of the ensemble of particles, a modified definition of the size of a snapshot attractor was exploited to establish the link with a random walk. As a result, the structure of on-off intermittency in the ensemble of particles was explicitly revealed near the transition.

Journal Article↗
PubMed1992

Conformational transition of an alpha-helix studied by molecular dynamics.

Molecular dynamics simulations were performed on a 20-residue polyalanine helix and a spontaneous transition from a kinked to a straight conformation was observed. The kinetics of the transition was analyzed within the framework of the Kramers model for chemical reactions and within a random walk model. The Kramers model which is based on diffusion along a one-dimensional reaction pathway and the crossing of an energy barrier was found to be inadequate. Instead, a random walk model based on diffusion in the high-dimensional phase space of the system was found to be compatible with the data. The high dimensionality of the phase space permits the system to circumvent high energy barriers and diffuse rapidly at about constant energy, but decelerates the reaction since in the labyrinth of pathways the transition state is reached rarely.

Biophysical Phenomena↗
PubMed2000

River networks on the slope-correlated landscape

We study the morphologies of river networks on various landscapes. In general, the probability density distribution of drainage area a of the river network scales as P(a) approximately a(-tau). We consider a slope-slope correlation function G(r) and define the persistent length R where G(r=R) becomes zero. In our restricted solid on solid network model, R is independent of the system size L and tau is close to 4/3, which is the value of the Scheidegger's river network model with random walk process. We also consider an avalanche model, where R is proportional to L. There is a large slope-slope correlation length and the river network does not follow the directed random walk process with tau approximately 1.42.

Journal Article↗
PubMed2001

Depth dependence of the analytical expression for the width of the point spread function (spatial resolution) in time-resolved transillumination.

Simple analytical expressions for the point spread function (PSF) at different depths can save computation time and improve the performance of inverse algorithms for optical imaging. In particular, application of such formulas simplifies quantification of the optical characteristics of tissue abnormalities inside highly scattering media. Earlier it was shown within the random walk theory framework that the PSF for time-resolved transillumination imaging through a highly scattering slab is well represented by a Gaussian. We have experimentally validated a simple formula of the random walk model for the effective width of this Gaussian, as a function of time delay, at different depths of the target. Presented analysis of published experimental data, concerning effective width of the PSF, for a slab of considerably smaller thickness also demonstrates good agreement between the data and predictions of our model. This PSF width determines spatial resolution of the time-resolved imaging and is widely discussed in the literature.

Diagnostic Imaging↗
PubMed1977

The effect of total peripheral resistance on indicator-dilution curves from the central circulation of the dog.

The influence of total peripheral resistance on the dispersion of indicator particles passing through the central circulation was studied in five dogs. The standard deviation of indocyanine green indicator-dilution curves provided a measure of dispersion. The peripheral vascular resistance of the dog was altered during the experiment by the intravenous administration of sodium nitroprusside and methoxamine. We calculated the area of each curve by fitting the first portion of the curve to a random walk function and the cardiac output and the total peripheral resistance were calculated in the usual manner. The mean, standard deviation and area of each of the curves were calculated from the least squares estimate of the random walk function. The relationship of the cardiac output, mean arterial pressure, and total peripheral resistance to the mean and the standard deviation were compared in a multiple stepwise linear regression. For each dog there was a definite linear relationship between total peripheral resistance and standard deviation (p less than 0.01). These results indicate that the dispersion of particles passing through the central circulation is directly related to the total peripheral resistance.

Animals↗
PubMed1983

The probability that related individuals share some section of genome identical by descent.

A formal mathematical framework is presented for the study of linkage in man and the concept of chromosome pedigree is defined for both autosomes and X chromosomes. It is shown that, assuming no interference, all the crossover processes in the pedigree may be viewed jointly as a continuous-time Markov random walk on the vertices of a hypercube, the time parameter being map distance along the chromosome. The event that two individuals have a segment of chromosome in common, thus proving them to be related, corresponds to the random walk hitting a particular set of vertices. The probability of this happening is calculated for various types of relationship, making use of the symmetry of the situation to partition the vertices into a very much smaller number of orbits and render the computation manageable. The probability that an individual with n children passes on all his or her genes to them is also calculated in this way.

Chromosomes, Human↗
PubMed2001

Framework model for single proton conduction through gramicidin.

This paper describes a framework model for proton conduction through gramicidin; a model designed to incorporate information from molecular dynamics and use this to predict conductance properties. The state diagram describes both motion of an excess proton within the pore as well as the reorientation of waters within the pore in the absence of an excess proton. The model is constructed as the diffusion limit of a random walk, allowing control over the boundary behavior of trajectories. Simple assumptions about the boundary behavior are made, which allow an analytical solution for the proton current and conductance. This is compared with corresponding expressions from statistical mechanics. The random walk construction allows diffusing trajectories underlying the model to be simulated in a simple way. Details of the numerical algorithm are described.

Algorithms↗
PubMed2003

Numerical framework models of single proton conduction through gramicidin.

A framework model of single-proton conduction through gramicidin was previously designed to incorporate potentials of mean force and diffusion coefficients computed by the molecular dynamics simulations of Pom s and Roux (1). The resulting diffusion model was solved analytically using the lumped state approximation (LSA), allowing a detailed comparison to be made with conductance data from gramicidin A and two Trp--> Phe analogs (2). The comparison included a sensitivity analysis which required over 1 million current evaluations. A numerical method for constructing framework models is now introduced which involves finding the steady states of random walks using a trapezoid rule closely related to the rule for numerical integration. The method is described and then applied directly to the LSA. Convergence of the results to the analytical solution is seen as the number of random walk sites increase. The numerical method is then used to construct a more elaborate framework model which avoids the LSA. This is also in very good agreement with the analytical solution under the experimental conditions, confirming the accuracy of the LSA. The numerical method remains fast enough to allow an extensive comparison with conductance data.

Computer Simulation↗
PubMed2004

Microsaccades keep the eyes' balance during fixation.

During fixation of a stationary target, small involuntary eye movements exhibit an erratic trajectory-a random walk. Two types of these fixational eye movements are drift and microsaccades (small-amplitude saccades). We investigated fixational eye movements and binocular coordination using a statistical analysis that had previously been applied to human posture control. This random-walk analysis uncovered two different time scales in fixational eye movements and identified specific functions for microsaccades. On a short time scale, microsaccades enhanced perception by increasing fixation errors. On a long time scale, microsaccades reduced fixation errors and binocular disparity (relative to pure drift movements). Thus, our findings clarify the role of oculomotor processes during fixation.

Fixation, Ocular↗
PubMed1990

Eye-movement models for arithmetic and reading performance.

Three stochastic eye-movement models for arithmetic and reading performance have been proposed, one for arithmetic and two for reading. Each model characterizes a real-time stochastic process in terms of fixation durations and saccadic movement, but only direction and length of saccades are considered, not acceleration or velocity. Aspects of the models that are emphasized, partly because of their general neglect in the literature, are the probability distribution of fixation durations and the random walk of saccade directions. The distributions of fixation duration are approximately exponential, but systematic deviations can be accounted for in the models, even though the fit to data is not perfect. In the case of the arithmetic algorithms of addition and subtraction, the random walk of the normative model has only two possible moves. Data are also presented on backtracking, skipping and wandering eye movements, each of which has a significant relative frequency. The first reading model is called a minimal control model, because it does not take account of the effects of many local variables, e.g., word length, that have been extensively studied. The axioms on fixation duration for the minimal control model are the same as for the arithmetic model. Abstracting from the different arrangement of stimuli in arithmetic algorithms and in linear text, the axioms on saccadic motion for the two models are also essentially identical. The stochastic nature of both models is strongly supported by data on the independence of fixation durations from previous fixation durations. Additional detailed evidence is presented for the arithmetic model. To better account for a great variety of experimental results concerning significant effects on eye movements in reading, a text-dependent probabilistic model of reading is introduced. Significant local effects fall into three classes, identified as line, word and grammatical variables. The revised axioms embody five features of text known to be significant: (i) fixation duration depends on the number of letters in a word; (ii) a saccade is longer when a longer word is to the right; (iii) a saccade is longer when the current fixation is on a longer word; (iv) high-frequency fixation words have the highest probability of being skipped; (v) ambiguous or difficult grammatical structures increase backtracking.

Cognition↗
PubMed2004

Advanced fitness landscape analysis and the performance of memetic algorithms.

Memetic algorithms (MAs) have demonstrated very effective in combinatorial optimization. This paper offers explanations as to why this is so by investigating the performance of MAs in terms of efficiency and effectiveness. A special class of MAs is used to discuss efficiency and effectiveness for local search and evolutionary meta-search. It is shown that the efficiency of MAs can be increased drastically with the use of domain knowledge. However, effectiveness highly depends on the structure of the problem. As is well-known, identifying this structure is made easier with the notion of fitness landscapes: the local properties of the fitness landscape strongly influence the effectiveness of the local search while the global properties strongly influence the effectiveness of the evolutionary meta-search. This paper also introduces new techniques for analyzing the fitness landscapes of combinatorial problems; these techniques focus on the investigation of random walks in the fitness landscape starting at locally optimal solutions as well as on the escape from the basins of attractions of current local optima. It is shown for NK-landscapes and landscapes of the unconstrained binary quadratic programming problem (BQP) that a random walk to another local optimum can be used to explain the efficiency of recombination in comparison to mutation. Moreover, the paper shows that other aspects like the size of the basins of attractions of local optima are important for the efficiency of MAs and a local search escape analysis is proposed. These simple analysis techniques have several advantages over previously proposed statistical measures and provide valuable insight into the behaviour of MAs on different kinds of landscapes.

Algorithms↗
PubMed1995

Optokinetic nystagmus (OKN) suppression by fixation of a stabilized target: the effect of OKN-stimulus predictability.

In previous work, subjects looked at a target stabilized at the fovea, superimposed on a sinusiodally moving OKN stimulus. The stabilized target (no retinal-slip) suppressed OKN leaving residual eye movements that were often in counterphase with the OKN stimulus motion. In the present study we explored how this type of suppression of OKN is influenced by OKN stimulus predictability: OKN stimulus motion was either sinusoidal or a random walk of half-sinusoids. During fixation of a stabilized target with sinusoidal stimulus motion, OKN was suppressed leaving residual eye movement whose amplitude was typically less than OKN and with a phase lag of about 180 deg (roughly in counterphase with stimulus motion). With random-walk stimulus motion, the residual movement amplitude was even smaller, and at higher frequencies the phase lag decreased to become the same as for OKN. For both stimulus motions, OKN was suppressed when the target was present, but counterphase residual movements appear to depend on stimulus predictability.

Eye Movements↗
PubMed1997

Exemplar similarity and the development of automaticity.

Effects of exemplar similarity on the development of automaticity were investigated with a task in which participants judged the numerosity of random patterns of between 6 and 11 dots. After several days of training, response times were the same at all levels of numerosity, signaling the development of automaticity. In Experiment 1, response times to new patterns were a function of their similarity to old patterns. In Experiment 2, responses to patterns with high within-category similarity became automatized more quickly than responses to patterns with low within-category similarity. In Experiment 3, responses to patterns with high between-category similarity became automatized more slowly than responses to patterns with low between-category similarity. A new theory, the exemplar-based random walk (EBRW) model, was used to explain the results. Combining elements of G. D. Logan's (1988) instance theory of automaticity and R. M. Nosofsky's (1986) generalized context model of categorization, the theory embeds a dynamic similarity-based memory retrieval mechanism within a competitive random walk decision process.

Adult↗
PubMed1994

Drug release from a suspension with a finite dissolution rate: theory and its application to a betamethasone 17-valerate patch.

A random walk method for a diffusion equation is applied to the model for a suspension with a finite dissolution rate developed by Ayres and Lindstrom in 1977. In the method, the diffusion of dissolved drug and dissolution of crystal are calculated separately using a simple BASIC program. The random walk method strictly meets the principle of the conservation of mass as the drug amount in each sublayer rather than the concentration at each subinterval is concerned in the ointment. The model is used to analyze the release of betamethasone 17-valerate from a pressure-sensitive silicone adhesive into a sink. The drug release from the 1.50 mg/mL patch shows no substantial discrepancy from that predicted by the classic suspension model assuming an infinite dissolution rate. However, the classic model overestimates the release from the 3.08 and 5.88 mg/mL patches. The disagreement is lessened when the dissolution rate is assumed to be finite. However, the model does not give a perfect explanation because the drug release from the 3.08 and 5.88 mg/mL patches in the early phase is faster than the model predicts.

Administration, Cutaneous↗
PubMed2002

A mathematical model for the role of cell signal transduction in the initiation and inhibition of angiogenesis.

Neovascular formation can be divided into three main stages (which may be overlapping): (1) changes within the existing vessel, (2) formation of a new channel, (3) maturation of the new vessel. In two previous papers, [Levine, H.A. and Sleeman, B.D. (1997) "A system of reaction diffusion equations arising in the theory of reinforced random walks" SIAM J. AppL Math. 683-730; Levine, H.A., Sleeman, B.D. and Nilsen-Hamilton, M. (2001b) "Mathematical modelling of the onset of capillary formation initiating angiogenesis." J. Math. Biol. 195-238] the authors introduced a new approach to angiogenesis, based on the theory o f reinforced random walks, coupled with a Michaelis-Menten type mechanism which views the endothelial vascular endothelial cell growth factor (VEGF) receptors as the catalyst for transforming into a proteolytic enzyme in order to model the first stage. It is the purpose of this paper to present a more descriptive yet not overly complicated mathematical model of the biochemical events that are initiated when VEGF interacts with endothelial cells and which result in the cell synthesis of proteolytic enzyme. We also delineate via chemical kinetics, three mechanisms by which one may inhibit angiogenesis (inhibition of growth factor, growth factor receptor and protease function).

Animals↗
PubMed2006

Integrating multi-attribute similarity networks for robust representation of the protein space.

MOTIVATION: A global view of the protein space is essential for functional and evolutionary analysis of proteins. In order to achieve this, a similarity network can be built using pairwise relationships among proteins. However, existing similarity networks employ a single similarity measure and therefore their utility depends highly on the quality of the selected measure. A more robust representation of the protein space can be realized if multiple sources of information are used. RESULTS: We propose a novel approach for analyzing multi-attribute similarity networks by combining random walks on graphs with Bayesian theory. A multi-attribute network is created by combining sequence and structure based similarity measures. For each attribute of the similarity network, one can compute a measure of affinity from a given protein to every other protein in the network using random walks. This process makes use of the implicit clustering information of the similarity network, and we show that it is superior to naive, local ranking methods. We then combine the computed affinities using a Bayesian framework. In particular, when we train a Bayesian model for automated classification of a novel protein, we achieve high classification accuracy and outperform single attribute networks. In addition, we demonstrate the effectiveness of our technique by comparison with a competing kernel-based information integration approach.

Algorithms↗