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At least 1,243 records · Page 69Linked to original sources
PubMed2007

Correlation in a Gaussian chain with the ends fixed.

We consider an ideal chain whose ends are fixed without fluctuation at different points, possibly by optical tweezers. We derive a two-point probability distribution of a corresponding random walk and explicitly calculate the scattering function. We find that the contour plot of the resulting function shows a kind of normal butterfly pattern, contaminated by wavy texture. These results are compared with some representative previous models.

Biophysics↗
PubMed2006

Manifold learning for robot navigation.

In this paper we introduce methods to build a SOM that can be used as an isometric map for mobile robots. That is, given a dataset of sensor readings collected at points uniformly distributed with respect to the ground, we wish to build a SOM whose neurons (prototype vectors in sensor space) correspond to points uniformly distributed on the ground. Manifold learning techniques have already been used for dimensionality reduction of sensor space in navigation systems. Our focus is on the isometric property of the SOM. For reliable path-planning and information sharing between several robots, it is desirable that the robots build an internal representation of the sensor manifold, a map, that is isometric with the environment. We show experimentally that standard Non-Linear Dimensionality Reduction (NLDR) algorithms do not provide isometric maps for range data and bearing data. However, the auxiliary low dimensional manifolds created can be used to improve the distribution of the neurons of a SOM (that is, make the neurons more evenly distributed with respect to the ground). We also describe a method to create an isometric map from a sensor readings collected along a polygonal line random walk.

Artificial Intelligence↗
PubMed2004

Identifying uniformly mutated segments within repeats.

Given a long string of characters from a constant size alphabet we present an algorithm to determine whether its characters have been generated by a single i.i.d. random source. More specifically, consider all possible n-coin models for generating a binary string S, where each bit of S is generated via an independent toss of one of the n coins in the model. The choice of which coin to toss is decided by a random walk on the set of coins where the probability of a coin change is much lower than the probability of using the same coin repeatedly. We present a procedure to evaluate the likelihood of a n-coin model for given S, subject a uniform prior distribution over the parameters of the model (that represent mutation rates and probabilities of copying events). In the absence of detailed prior knowledge of these parameters, the algorithm can be used to determine whether the a posteriori probability for n=1 is higher than for any other n>1. Our algorithm runs in time O(l4logl), where l is the length of S, through a dynamic programming approach which exploits the assumed convexity of the a posteriori probability for n. Our test can be used in the analysis of long alignments between pairs of genomic sequences in a number of ways. For example, functional regions in genome sequences exhibit much lower mutation rates than non-functional regions. Because our test provides means for determining variations in the mutation rate, it may be used to distinguish functional regions from non-functional ones. Another application is in determining whether two highly similar, thus evolutionarily related, genome segments are the result of a single copy event or of a complex series of copy events. This is particularly an issue in evolutionary studies of genome regions rich with repeat segments (especially tandemly repeated segments).

Algorithms↗
PubMed2006

Structure prediction of helical transmembrane proteins at two length scales.

As the first step toward a multi-scale, hierarchical computational approach for membrane protein structure prediction, the packing of transmembrane helices was modeled at the residue and atom levels, respectively. For predictions at the residue level, the helix-helix and helix-membrane interactions were described by a set of knowledge-based energy functions. For predictions at the atom level, CHARMM19 force field was used. To facilitate the system to overcome energy barriers, the Wang-Landau method was employed, where a random walk is performed in the energy space with a uniform probability. Native-like structures were predicted at both levels for two model systems, each of which consists of two transmembrane helices. Interestingly, consistent results were obtained from simulations at the residue and atom levels for the same system, strongly suggesting the feasibility of a hierarchical approach for membrane protein structure predictions.

Amino Acid Sequence↗
PubMed2006

Empirical and theoretical analysis of the extremely low frequency arterial blood pressure power spectrum in unanesthetized rat.

The slope of the log of power versus the log of frequency in the arterial blood pressure (BP) power spectrum is classically considered constant over the low-frequency range (i.e., "fractal" behavior), and is quantified by beta in the relationship "1/f(beta)." In practice, the fractal range cannot extend to indefinitely low frequencies, but factor(s) that terminate this behavior, and determine beta, are unclear. We present 1) data in rats (n = 8) that reveal an extremely low frequency spectral region (0.083-1 cycle/h), where beta approaches 0 (i.e., the "shoulder"); and 2) a model that 1) predicts realistic values of beta within that range of the spectrum that conforms to fractal dynamics (approximately 1-60 cycles/h), 2) offers an explanation for the shoulder, and 3) predicts that the "successive difference" in mean BP (mBP) is an important parameter of circulatory function. We recorded BP for up to 16 days. The absolute difference between successive mBP samples at 0.1 Hz (the successive difference, or Delta) was 1.87 +/- 0.21 mmHg (means +/- SD). We calculated beta for three frequency ranges: 1) 0.083-1; 2) 1-6; and 3) 6-60 cycles/h. The beta for all three regions differed (P < 0.01). For the two higher frequency ranges, beta indicated a fractal relationship (beta(6-60/h) = 1.27 +/- 0.01; beta(1-6/h) = 1.80 +/- 0.16). Conversely, the slope of the lowest frequency region (i.e., the shoulder) was nearly flat (beta(0.083-1 /h) = 0.32 +/- 0.28). We simulated the BP time series as a random walk about 100 mmHg with ranges above and below of 10, 30, and 50 mmHg and with Delta from 0.5 to 2.5. The spectrum for the conditions mimicking actual BP time series (i.e., range, 85-115 mmHg; Delta, 2.00) resembled the observed spectra, with beta in the lowest frequency range = 0.207 and fractal-like behavior in the two higher frequency ranges (beta = 1.707 and 2.057). We suggest that the combined actions of mechanisms limiting the excursion of arterial BP produce the shoulder in the spectrum and that Delta contributes to determining beta.

Animals↗
PubMed1998

A nonlinear explanation of aging-induced changes in heartbeat dynamics.

The possibility of computing a cardiac age on the basis of spectral analysis of healthy individual tachograms was confirmed and facilitated by the use of a nonlinear technique: recurrence quantification analysis. The age of 112 subjects was predicted by this technique in terms of a progressive increase in the deterministic character of the heartbeat. This result confirms the "random-walk" character of the heartbeat as predicted by the terminal dynamics paradigm, thus allowing for a simple and comprehensive model of the effect of aging on cardiac dynamics: as age progresses, heart rate dynamics become increasingly predictable (constrained) on a beat-to-beat basis. This implies a basically stochastic nature of heart rate dynamics, probably reflecting the continuous adjustments to an unpredictable internal environment.

Adult↗
PubMed2006

Long-range negative correlation of glucose dynamics in humans and its breakdown in diabetes mellitus.

Diurnal fluctuations in glucose levels continuously monitored during normal daily life are investigated using an extended random walk analysis, referred to as detrended fluctuation analysis (DFA), in 12 nondiabetic subjects and 15 diabetic patients. The DFA exponent alpha = 1.25 +/- 0.29 for healthy individuals in the "long-range" (>2 h) regime is shown to be significantly (P < 0.01) smaller than the reference "uncorrelated" value of alpha = 1.5, suggesting that the instantaneous net effects of the dynamical balance of glucose flux and reflux, causing temporal changes in glucose concentration, are long-range negatively correlated. By contrast, in diabetic patients, the DFA exponent alpha = 1.65 +/- 0.30 is significantly (P < 0.05) higher than that in nondiabetic subjects, evidencing a breakdown of the long-range negative correlation. It is suggested that the emergence of such positive long-range glucose correlations in diabetic patients-indicating that the net effects of the flux and reflux persist for many hours-likely reflects pathogenic mechanisms of diabetes, i.e., the lack of long-term stability of blood glucose and that the long-range negatively correlated glucose dynamics are functional in maintaining normal glucose homeostasis.

Adaptation, Physiological↗
PubMed1996

Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics.

We postulated that aging is associated with disruption in the fractallike long-range correlations that characterize healthy sinus rhythm cardiac interval dynamics. Ten young (21-34 yr) and 10 elderly (68-81 yr) rigorously screened healthy subjects underwent 120 min of continuous supine resting electrocardiographic recording. We analyzed the interbeat interval time series using standard time and frequency domain statistics and using a fractal measure, detrended fluctuation analysis, to quantify long-range correlation properties. In healthy young subjects, interbeat intervals demonstrated fractal scaling, with scaling exponents (alpha) from the fluctuation analysis close to a value of 1.0. In the group of healthy elderly subjects, the interbeat interval time series had two scaling regions. Over the short range, interbeat interval fluctuations resembled a random walk process (Brownian noise, alpha = 1.5), whereas over the longer range they resembled white noise (alpha = 0.5). Short (alpha s)- and long-range (alpha 1) scaling exponents were significantly different in the elderly subjects compared with young (alpha s = 1.12 +/- 0.19 vs. 0.90 +/- 0.14, respectively, P = 0.009; alpha 1 = 0.75 +/- 0.17 vs. 0.99 +/- 0.10, respectively, P = 0.002). The crossover behavior from one scaling region to another could be modeled as a first-order autoregressive process, which closely fit the data from four elderly subjects. This implies that a single characteristic time scale may be dominating heartbeat control in these subjects. The age-related loss of fractal organization in heartbeat dynamics may reflect the degradation of integrated physiological regulatory systems and may impair an individual's ability to adapt to stress.

Adult↗
PubMed1986

How well mixed is inert gas in tissues?

The washout of inert gas from tissues typically follows multiexponential curves rather than monoexponential curves as would be expected from homogeneous, well-mixed compartment. This implies that the ratio for the square root of the variance of the distribution of transit times to the mean (relative dispersion) must be greater than 1. Among the possible explanations offered for multiexponential curves are heterogeneous capillary flow, uneven capillary spacing, and countercurrent exchange in small veins and arteries. By means of computer simulations of the random walk of gas molecules across capillary beds with parameters of skeletal muscle, we find that heterogeneity involving adjacent capillaries does not suffice to give a relative dispersion greater than one. Neither heterogeneous flow, nor variations in spacing, nor countercurrent exchange between capillaries can account for the multiexponential character of experimental tissue washout curves or the large relative dispersions that have been measured. Simple diffusion calculations are used to show that many gas molecules can wander up to several millimeters away from their entry point during an average transit through a tissue bed. Analytical calculations indicate that an inert gas molecule in an arterial vessel will usually make its first vascular exit from a vessel larger than 20 micron and will wander in and out of tissue and microvessels many times before finally returning to the central circulation. The final exit from tissue will nearly always be into a vessel larger than 20 micron. We propose the hypothesis that the multiexponential character of skeletal muscle tissue inert gas washout curves must be almost entirely due to heterogeneity between tissue regions separated by 3 mm or more, or to countercurrent exchanges in vessels larger than 20 micron diam.

Capillaries↗
PubMed1987

Extrapolation of thermodilution curves obtained during a pause in artificial ventilation.

The feasibility of three mathematical models to extrapolate the tail of thermodilution curves, when flectures are present in the descending limb, was tested in anesthetized pigs. The models were a local random walk model (LDRW), a log-normal distribution, and a two-compartment model. First, the accuracy of the extrapolation of the tail by each model was tested on two undisturbed curves by taking the truncation at five different points on the descending limb. The extrapolated curve area obtained from each model was compared with total area of the undisturbed curve. Next, dilution curves obtained during inspiratory hold maneuvers and characterized by deflection points were analyzed, taking the truncation just before deflection. The estimates of cardiac output by the models were compared with electromagnetically measured flow in the pulmonary artery. The area of the dilution curve was estimated more accurately when more information on the descending limb was available. The LDRW model and the log-normal distribution were superior to the two-compartment model regarding accuracy of cardiac output estimation and root-mean-square errors of the fit. Both models estimated curve area with an error less than 5% when truncation of the descending limb occurred below 60% of the peak value. In circumstances of mechanical ventilation, where only short periods of constant flow will be present, analyses of dilution curves based on the LDRW model or the log-normal distribution are recommended.

Animals↗
PubMed2005

Power-law neuronal fluctuations in a recurrent network model of parametric working memory.

In a working memory system, persistent activity maintains information in the absence of external stimulation, therefore the time scale and structure of correlated neural fluctuations reflect the intrinsic microcircuit dynamics rather than direct responses to sensory inputs. Here we show that a parametric working memory model capable of graded persistent activity is characterized by arbitrarily long correlation times, with Fano factors and power spectra of neural activity described by the power laws of a random walk. Collective drifts of the mnemonic firing pattern induce long-term noise correlations between pairs of cells, with the sign (positive or negative) and amplitude proportional to the product of the gradients of their tuning curves. None of the power-law behavior was observed in a variant of the model endowed with discrete bistable neural groups, where noise fluctuations were unable to cause long-term changes in rate. Therefore such behavior can serve as a probe for a quasi-continuous attractor. We propose that the unusual correlated fluctuations have important implications for neural coding in parametric working memory circuits.

Action Potentials↗
PubMed2006

Short-term adaptation and temporal processing in the cryophilic response of Caenorhabditis elegans.

When navigating spatial thermal gradients, the nematode C. elegans migrates toward colder temperatures until it reaches its previous cultivation temperature, exhibiting cryophilic movement. The strategy for effecting cryophilic movement is the biased random walk: C. elegans extends (shortens) periods of forward movement that are directed down (up) spatial thermal gradients by modulating the probability of reorientation. Here, we analyze the temporal sensory processor that enables cryophilic movement by quantifying the movements of individual worms subjected to defined temperature waveforms. We show that step increases in temperature as small as 0.05 degrees C lead to transient increases in the probability of reorientation followed by gradual adaptation to the baseline level; temperature downsteps leads to similar but inverted responses. Short-term adaptation is a general property of sensory systems, allowing organisms to maintain sensitivity to sensory variations over broad operating ranges. During cryophilic movement C. elegans also uses the temporal dynamics of its adaptive response to compute the time derivative of gradual temperature variations with exquisite sensitivity. On the basis of the time derivative, the worm determines how it is oriented in spatial thermal gradients during each period of forward movement. We show that the operating range of the cryophilic response extends to lower temperatures in ttx-3 mutants, which affects the development of the AIY interneurons. We show that the temporal sensory processor for the cryophilic response is affected by mutation in the EAT-4 glutamate vesicular transporter. Regulating the operating range of the cryophilic response and executing the cryophilic response may have separate neural mechanisms.

Acclimatization↗
PubMed2004

Spatio-temporal dynamics of a neutralized B chromosome in the grasshopper Eyprepocnemis plorans.

Spatial and temporal patterns of frequency variation for a neutralized B chromosome in the grasshopper Eyprepocnemis plorans were analyzed along six transects in the east of Spain to explore possible factors affecting the population dynamics of this polymorphism. Three parameters were employed to quantify B frequency: prevalence, load and mean frequency. Of them, load seemed to be the less sensitive parameter, probably due to its small range of variation. Prevalence, however, shows ample variation, but the mean frequency of B chromosomes per individual is the best parameter to characterize B frequency. Only river transects revealed significant differences among populations, and the use of two geographic explicit approaches (Mantel test and distograms) revealed significant isolation by distance (IBD), especially at the Segura River mouth, presumably due to low gene flow and drift. No temporal trend was found in the Segura River transects, which is consistent with the slow changes in B frequency expected during the random walk for neutralized B chromosomes. But these transects showed a clear spatial pattern, with B1 showing lower frequency in the upper course of this river. The present results provide the first empirical evidence of IBD in the evolution of a neutralized B chromosome, and support the notion that B dynamics at this evolutionary stage is best explained by a metapopulation approach.

Animals↗
PubMed2000

Stationary and integrated autoregressive neural network processes.

We consider autoregressive neural network (AR-NN) processes driven by additive noise and demonstrate that the characteristic roots of the shortcuts-the standard conditions from linear time-series analysis-determine the stochastic behavior of the overall AR-NN process. If all the characteristic roots are outside the unit circle, then the process is ergodic and stationary. If at least one characteristic root lies inside the unit circle, then the process is transient. AR-NN processes with characteristic roots lying on the unit circle exhibit either ergodic, random walk, or transient behavior. We also analyze the class of integrated AR-NN (ARI-NN) processes and show that a standardized ARI-NN process "converges" to a Wiener process. Finally, least-squares estimation (training) of the stationary models and testing for nonstationarity is discussed. The estimators are shown to be consistent, and expressions on the limiting distributions are given.

Artifacts↗
PubMed2004

A solution for two-dimensional mazes with use of chaotic dynamics in a recurrent neural network model.

Chaotic dynamics introduced into a neural network model is applied to solving two-dimensional mazes, which are ill-posed problems. A moving object moves from the position at t to t + 1 by simply defined motion function calculated from firing patterns of the neural network model at each time step t. We have embedded several prototype attractors that correspond to the simple motion of the object orienting toward several directions in two-dimensional space in our neural network model. Introducing chaotic dynamics into the network gives outputs sampled from intermediate state points between embedded attractors in a state space, and these dynamics enable the object to move in various directions. System parameter switching between a chaotic and an attractor regime in the state space of the neural network enables the object to move to a set target in a two-dimensional maze. Results of computer simulations show that the success rate for this method over 300 trials is higher than that of random walk. To investigate why the proposed method gives better performance, we calculate and discuss statistical data with respect to dynamical structure.

Artificial Intelligence↗
PubMed2006

An extension of Geiringer's theorem for a wide class of evolutionary search algorithms.

The frequency with which various elements of the search space of a given evolutionary algorithm are sampled is affected by the family of recombination (reproduction) operators. The original Geiringer theorem tells us the limiting frequency of occurrence of a given individual under repeated application of crossover alone for the classical genetic algorithm. Recently, Geiringer's theorem has been generalized to include the case of linear GP with homologous crossover (which can also be thought of as a variable length GA). In the current paper we prove a general theorem which tells us that under rather mild conditions on a given evolutionary algorithm, call it A, the stationary distribution of a certain Markov chain of populations in the absence of selection is unique and uniform. This theorem not only implies the already existing versions of Geiringer's theorem, but also provides a recipe of how to obtain similar facts for a rather wide class of evolutionary algorithms. The techniques which are used to prove this theorem involve a classical fact about random walks on a group and may allow us to compute and/or estimate the eigenvalues of the corresponding Markov transition matrix which is directly related to the rate of convergence towards the unique limiting distribution.

Algorithms↗
PubMed1997

Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell.

To understand the interspike interval (ISI) variability displayed by visual cortical neurons (Softky & Koch, 1993), it is critical to examine the dynamics of their neuronal integration, as well as the variability in their synaptic input current. Most previous models have focused on the latter factor. We match a simple integrate-and-fire model to the experimentally measured integrative properties of cortical regular spiking cells (McCormick, Connors, Lighthall, & Prince, 1985). After setting RC parameters, the post-spike voltage reset is set to match experimental measurements of neuronal gain (obtained from in vitro plots of firing frequency versus injected current). Examination of the resulting model leads to an intuitive picture of neuronal integration that unifies the seemingly contradictory 1/square root of N and random walk pictures that have previously been proposed. When ISIs are dominated by postspike recovery, 1/square root of N arguments hold and spiking is regular; after the "memory" of the last spike becomes negligible, spike threshold crossing is caused by input variance around a steady state and spiking is Poisson. In integrate-and-fire neurons matched to cortical cell physiology, steady-state behavior is predominant, and ISIs are highly variable at all physiological firing rates and for a wide range of inhibitory and excitatory inputs.

Animals↗
PubMed2005

A random-ray model for speed and accuracy in perceptual experiments.

We present a 'random ray' model to describe Yes/No reaction times (RTs) and errors in perceptual experiments. The ray model is analogous to a random walk, but it is computationally simpler, requiring only elementary geometry. Ray parameters control the drift rates to the Yes and No decision boundaries, bias, and a termination or 'time-out' rule. Rays are normally distributed, but predicted RT distributions are skewed by projection onto the boundaries. Model parameters can be estimated directly from the 16th, 50th, and 84th percentiles of the RT distributions on hit, correct rejection, false alarm, and miss trials, if the data satisfy three easily testable constraints. Examples are given from visual search and object recognition.

Attention↗