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At least 523 records · Page 29Linked to original sources
PubMed1978

A stochastic model for cell populations with circadian rhythms.

A mathematical model for cell kinetics, based on a random walk, is developed. The model allows variations with time of the rates of passage of proliferating cells through the four phases of the mitotic cycle. Circadian variations in the mitotic and labelling indices of the Syrian hamster cheek pouch epithelium have previously been observed, and the random walk model has been used to simulate this phenomenon. Assuming that all basal cells are proliferative and that these cells leave the basal layer randomly throughout the mitotic cycle to become differentiated cells, it was found that the experimentally observed circadian rhythms of the mitotic and labelling indices could be reproduced in the model by postulating a circadian rhythm in the rate of passage of cells through the G1 and S phases only. Moreover, the growth activity of cells in both the G1 and S phases appears to reach a peak during the dark hours of the light-dark cycle, and to fall off rapidly in the early hours of daylight. The postulate of Møller, Larsen & Faber (1974) that injection of the animals with tritiated thymidine causes a shortening of the G2 phase duration has been qualitatively confirmed by using the random walk model to simulate the FLM and MI curves after injection with tritiated thymidine.

Animals↗
PubMed1999

The gambler's ruin problem, genetic algorithms, and the sizing of populations.

This paper presents a model to predict the convergence quality of genetic algorithms based on the size of the population. The model is based on an analogy between selection in GAs and one-dimensional random walks. Using the solution to a classic random walk problem-the gambler's ruin-the model naturally incorporates previous knowledge about the initial supply of building blocks (BBs) and correct selection of the best BB over its desired quality of the solution, as well as the problem size and difficulty. The accuracy of the model is verified with experiments using additively decomposable functions of varying difficulty. The paper demonstrates how to adjust the model to account for noise present in the fitness evaluation and for different tournament sizes.

Algorithms↗
PubMed1997

Stepped versus continuous rotatory motors at the molecular scale.

Nature invented molecular rotatory devices such as the flagellar motor and ATP synthase. Photoselection techniques have been frequently used to detect the rotational random walk of proteins but only rarely for the rotational drift of subunits in proteins. Pertinent theories predict an oscillatory behavior of the polarization anisotropy, r, for unidirectional rotational drift, as opposed to a monotonic relaxation of r for bidirectional random walk. The underlying assumption of an angular continuum is questionable for intersubunit rotation in proteins. We developed a theory for stepped rotatory devices. It predicts the damped oscillation of r under unidirectional drift. Damping increases with decreasing number of steps. For only three steps a quasi-monotonic relaxation of r is predicted for both random walk and drift. In photoselection experiments with active F-ATPase we observed the relaxation of r when a spectroscopic probe was attached to the central beta-subunit. This behavior is compatible with the expectation for a three-stepped rotatory device.

Flagella↗
PubMed2002

Application of the moment condition to noise simulation and to stability analysis.

It is well-known that low frequency noises (flicker FM and random walk FM) are not stationary; it is not possible to define either the mean value or the (true) variance. Therefore, the use of a stationary approach yields convergence problems unless a low cut-off frequency is introduced, the physical meaning of which is not clear. As an example, in the case of random walk FM, the mean frequency of an oscillator does not converge if the analysis duration tends toward infinity. However, linear drifts appear if a phase sequence of random walk FM is observed over a duration smaller than the inverse of its low cut-off frequency. Moreover, the estimators, which are devoted to these non-stationary processes (i.e., the Hadamard variance), are insensitive to linear frequency drifts and converge for lower frequency noises (f(-4) FM). The moment condition explains the link between insensitivity to drifts and convergence for low frequency noises in a stationary approach. This condition may be summarized by the following consideration: the divergence effect of a low frequency noise for the lowest frequencies induces a false drift with random drift coefficients; the lower the low cut-off frequency, the higher the variance of the coefficients of this drift. These variances may be known by theoretical calculations. The order of the drift is directly linked to the power law of the noise. The moment condition will be demonstrated and applied for creating new estimators (new variances) and for simulating low frequency noises with a very low cut-off frequency.

Journal Article↗
PubMed2005

Self-avoiding walks on scale-free networks.

Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAW's) are expected to be more suitable than unrestricted random walks to explore various kinds of real-life networks. Here we study long-range properties of random SAW's on scale-free networks, characterized by a degree distribution P(k) approximately k(-gamma). In the limit of large networks (system size N-->infinity), the average number sn of SAW's starting from a generic site increases as mu(n) , with mu = k2/k-1 . For finite N, sn is reduced due to the presence of loops in the network, which causes the emergence of attrition of the paths. For kinetic growth walks, the average maximum length L increases as a power of the system size: L approximately Nalpha, with an exponent alpha increasing as the parameter gamma is raised. We discuss the dependence of alpha on the minimum allowed degree in the network. A similar power-law dependence is found for the mean self-intersection length of nonreversal random walks. Simulation results support our approximate analytical calculations.

Journal Article↗
PubMed1996

Approximate scaling properties of RNA free energy landscapes.

RNA free energy landscapes are analysed by means of "time-series" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and the scaling of the curve length measured with different yard stick lengths are used to describe the structure of these "time series". Although they are stationary by construction, we find that their local behavior is consistent with both AR(1) and self-affine processes. Random walks confined to excursion sets (i.e., with the restriction that the fitness value exceeds a certain threshold at each step) exhibit essentially the same statistics as free random walks. We find that an AR(1) time series is in general approximately self-affine on timescales up to approximately the correlation length. We present an empirical relation between the correlation parameter rho of the AR(1) model and the exponents characterizing self-affinity.

Animals↗
PubMed2003

Effects of anisotropic optical properties on photon migration in structured tissues.

It is often adequate to model photon migration in human tissue in terms of isotropic diffusion or random walk models. A nearly universal assumption in earlier analyses is that anisotropic tissue optical properties are satisfactorily modelled by using a transport-corrected scattering coefficient which then allows one to use isotropic diffusion-like models. In the present paper we introduce a formalism, based on the continuous-time random walk, which explicitly allows the diffusion coefficients to differ along the three axes. The corrections necessitated by this form of anisotropy are analysed in the case of continuous-wave and time-resolved measurements and for both reflectance and transmission modes. An alternate model can be developed in terms of a continuous-time random walk in which the times between successive jumps differ along the three axes, but is not included here.

Anisotropy↗
PubMed1994

Single-particle tracking: models of directed transport.

Single-particle tracking techniques make it possible to measure motion of individual particles on the cell surface. In these experiments, individual trajectories are observed, so the data analysis must take into account the randomness of individual random walks. Methods of data analysis are discussed for models combining diffusion and directed motion. In the uniform flow model, a tracer simultaneously diffuses and undergoes directed motion. In the conveyor belt model, a tracer binds and unbinds to a uniform conveyor belt moving with constant velocity. If a tracer is bound, it moves at the velocity of the conveyor belt; if it is unbound, it diffuses freely. Trajectories are analyzed using parameters that measure the extent and asymmetry of the trajectory. A method of assessing the usefulness of such parameters is presented, and pitfalls in data analysis are discussed. Joint probability distributions of pairs of extent and asymmetry parameters are obtained for a pure random walk. These distributions can be used to show that a trajectory is not likely to have resulted from a pure random walk.

Biological Transport, Active↗
PubMed1994

Is global motion really based on spatial integration of local motion signals?

Previous studies have shown that a random-dot kinematogram (RDK) comprising dots, each of which takes a random walk in direction or speed over time, can appear to flow in a single direction. This has been interpreted as evidence for the existence of a co-operative network linking neurons sensitive to different directions/speeds and different spatial locations. We have investigated the possibility that global motion perception in such patterns might simply reflect motion energy detection at a coarse spatial scale (such that many dots fall in the receptive field of one energy detector) without the need to encode local dot motions on a fine spatial scale and then integrate their motions over space. We created random-walk RDKs and then spatially high-pass filtered them to remove low spatial frequencies. Perception of global motion was unimpaired for both direction and speed random walks, showing that the phenomenon is not reliant on low spatial frequencies and must, therefore, involve integration of local motion signals across space, as originally postulated.

Discrimination, Psychological↗
PubMed2001

Modeling translocation of particles on one-dimensional polymer lattices.

We introduce a general random walk model that is an extension of the random walk model proposed by Berg. The model can be used to describe a particle's translocation along a polymeric lattice with a nonuniform distribution of obstacles. These obstacles are representative of DNA-bound proteins, of drugs, and of a DNA packing environment. Using this model in the bacteriophage replication process, we show the effects of random obstacles on an ATP-driven particle's translocation along single-stranded DNA. The principal finding is that the average statistical time of the translocation process decreases with the increase of an obstacle's strength. We also find an interesting relation between the average statistical time and the DNA chain length. Our results can be used to explain some physiological phenomena. They show the usefulness of our model in an analysis of the effect of random obstacles on particles' translocation along one-dimensional polymer lattices.

Adenosine Triphosphate↗
PubMed1993

Mutation models and quantitative genetic variation.

Analyses of evolution and maintenance of quantitative genetic variation depend on the mutation models assumed. Currently two polygenic mutation models have been used in theoretical analyses. One is the random walk mutation model and the other is the house-of-cards mutation model. Although in the short term the two models give similar results for the evolution of neutral genetic variation within and between populations, the predictions of the changes of the variation are qualitatively different in the long term. In this paper a more general mutation model, called the regression mutation model, is proposed to bridge the gap of the two models. The model regards the regression coefficient, gamma, of the effect of an allele after mutation on the effect of the allele before mutation as a parameter. When gamma = 1 or 0, the model becomes the random walk model or the house-of-cards model, respectively. The additive genetic variances within and between populations are formulated for this mutation model, and some insights are gained by looking at the changes of the genetic variances as gamma changes. The effects of gamma on the statistical test of selection for quantitative characters during macroevolution are also discussed. The results suggest that the random walk mutation model should not be interpreted as a null hypothesis of neutrality for testing against alternative hypotheses of selection during macroevolution because it can potentially allocate too much variation for the change of population means under neutrality.

Biological Evolution↗
PubMed2000

A statistical mechanical analysis of postural sway using non-Gaussian FARIMA stochastic models.

In this paper, postural sway is modeled using a fractional autoregressive integrated moving average (FARIMA) family of models: the center-of-pressure (COP) motion is viewed in terms of a self-similar, anti-persistent random-walk process, obtained by fractionally summating non-Gaussian random variables, whose correlation structure for small time lags is shaped by a linear time-invariant low-pass filter. The model parameters are: the strength of the stochastic driving, e.g., the root mean square (rms) value of the time-difference COP motion; the DC gain, damping ratio and natural frequency of the filter; the Hurst exponent, which measures the random-walk antipersistence magnitude. In the proposed modeling procedure, a graphical estimator for determining the Hurst exponent is cascaded to a method for matching autoregressive (AR) models to fractionally difference COP motion via higher order cumulants. The effect of the presence or absence of vision on the model parameter values is discussed with regard to data from experiments on healthy young adults.

Adult↗
PubMed1991

The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells.

Simulated neural impulse trains were generated by a digital realization of the integrate-and-fire model. The variability in these impulse trains had as its origin a random noise of specified distribution. Three different distributions were used: the normal (Gaussian) distribution (no skew, normokurtic), a first-order gamma distribution (positive skew, leptokurtic), and a uniform distribution (no skew, platykurtic). Despite these differences in the distribution of the variability, the distributions of the intervals between impulses were nearly indistinguishable. These inter-impulse distributions were better fit with a hyperbolic gamma distribution than a hyperbolic normal distribution, although one might expect a better approximation for normally distributed inverse intervals. Consideration of why the inter-impulse distribution is independent of the distribution of the causative noise suggests two putative interval distributions that do not depend on the assumed noise distribution: the log normal distribution, which is predicated on the assumption that long intervals occur with the joint probability of small input values, and the random walk equation, which is the diffusion equation applied to a random walk model of the impulse generating process. Either of these equations provides a more satisfactory fit to the simulated impulse trains than the hyperbolic normal or hyperbolic gamma distributions. These equations also provide better fits to impulse trains derived from the maintained discharges of ganglion cells in the retinae of cats or goldfish. It is noted that both equations are free from the constraint that the coefficient of variation (CV) have a maximum of unity.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed2000

Static and dynamic properties of the backbone network for the irreversible kinetic gelation model

We study by Monte Carlo simulations the fractal nature of the backbone network for the irreversible kinetic gelation model in both two and three dimensions. The fractal dimension of the backbone network generated at the gel point is measured by various methods, and results are found to be consistent with that of the standard percolation backbone. Our observation is different from the previous work in three dimensions, where a distinctly larger value was observed. We also measure the spectral dimension d(B)(s) and the fractal dimension d(B)(w) of random walks on a backbone, defined by, respectively, the probability of random walks returning to the starting point and the rms displacements after t time steps. Results are also found to be consistent with the corresponding percolation values. We therefore conclude that the backbone network of the kinetic gelation model exhibits the same static and dynamic properties as those of the standard percolation backbone.

Journal Article↗
PubMedDate not supplied

Treatment of intermittent claudication with pentoxifylline: a 12-month, randomized trial--walking distance and microcirculation.

The efficacy, safety and cost of pentoxifylline (PXF) in severe intermittent claudication was studied comparing PXF and placebo in a 12-month study. A treadmill test and microcirculatory evaluation with laser Doppler flowmetry were performed at inclusion and at the end of 6 and 12 months. A physical training plan (based on walking) and reduction in risk factor levels plan was used in both groups. Of the 120 included patients, 101 completed the study: 56 in the PXF group and 45 in the placebo group. There were 19 dropouts (due to low compliance). The two groups were comparable for age, sex distribution, walking distance, and the presence of risk factors and smoking. Intention-to-treat analysis indicated a 268% increase in walking distance in the PXF group (vs 198% in the placebo group; p<0.05) at 6 months and an increase of 404% (vs 280% in the placebo group; p<0.02) at 12 months. The absolute and percent increase in pain-free walking distance (PFWD) was greater in the PXF group (p<0.05). Treatment was well tolerated. No serious drug-related side effects were observed. Microcirculatory evaluation indicated an increase in flux (p < 0.05) in the PXF group (not significant in the placebo group); the after-exercise flux (AEF) was increased (p<0.05) in both groups at 6 months but the increase in AEF was greater in the PXF group at 12 month. In conclusion, between-group analysis favors PXF considering walking distance and microcirculatory parameters. Results indicate good efficacy and tolerability.

Aged↗
PubMed1997

Common effects of touch and vision on postural parameters.

Subjects stood upright with the index finger of the right hand either touching a nearby surface gently or not touching it at all and with the eyes either open or closed. Trajectories of the center of pressure (COP) were analyzed as fractional Brownian motion. The extracted parameters were the effective diffusion (D) coefficients and Hurst (H) exponents for short-term time intervals (corresponding to positively correlated random walks) and long-term time intervals (corresponding to negatively correlated random walks). Gentle tactile contact reduced the effective stochastic activity measured by D to the same extent as the availability of vision. Further, touch interacted with time interval in the same way as vision, with the correlated activity closer to H = 0.5 at both time scales when the finger contacted the nearby surface. The results corroborate and extend major features of recent investigations of haptic influences on posture and recent analyses of vision's influence on the fractional Brownian motions of the COP. Discussion focused on (a) the equivalence of expropriospecific information (about the body's orientation to the environment) registered haptically and visually and (b) the possibility that postural sway may reflect exploratory motions in the short term (obtaining information about the postural system) and performatory motions in the long term (using this information).

Adolescent↗
PubMed2004

Two-dimensional Langevin approach to the human stabilogram.

Two-dimensional Langevin equation is considered as a model of the center of pressure (COP) random walk at quiet standing condition. The matrix of the mean square displacement describes quantitatively the COP random walk. Twenty-six young subjects were included in the study. Elements of the matrix of the mean square displacement derived from experimental data are well approximated by theoretical expressions derived from the Langevin equation, in the short-term regime. We have studied statistical properties of the COP displacements. Non-Gaussian behaviour of the displacements is indicated by the characteristic functions. New coordinate system constituted and utilised by the postural control system (PCS) was found for every subject. This new coordinate system is turned with respect to the system defined by the anatomy of the body. In this new coordinate system the matrix of the mean square displacement takes the form close to diagonal. The status of PCS in this new coordinate system can be quantified by the elements of the diffusion matrix, which are the measure of the stochastic activity of that system, rotation angle of new coordinate system and the friction coefficient. We have applied this analysis to examine how the visual inputs affect the PCS. We have found that the stochastic activity of the PCS increases after exclusion of the visual inputs. We have also shown that the visual system does not affect the friction coefficient. Furthermore, we have found that orientation of the new coordinate system chosen by PCS at included visual inputs differs from the orientation at excluded visual inputs.

Adult↗
PubMed1999

Migration of lymphocytes on fibronectin-coated surfaces: temporal evolution of migratory parameters.

Lymphocytes typically interact with implanted biomaterials through adsorbed exogenous proteins. To provide a more complete characterization of these interactions, analysis of lymphocyte migration on adsorbed extracellular matrix proteins must accompany the commonly performed adhesion studies. We report here a comparison of the migratory and adhesion behavior of Jurkat cells (a T lymphoblastoid cell line) on tissue culture treated and untreated polystyrene surfaces coated with various concentrations of fibronectin. The average speed of cell locomotion showed a biphasic response to substrate adhesiveness for cells migrating on untreated polystyrene and a monotonic decrease for cells migrating on tissue culture-treated polystyrene. A modified approach to the persistent random walk model was implemented to determine the time dependence of cell migration parameters. The random motility coefficient showed significant increases with time when cells migrated on tissue culture-treated polystyrene surfaces, while it remained relatively constant for experiments with untreated polystyrene plates. Finally, a cell migration computer model was developed to verify our modified persistent random walk analysis. Simulation results suggest that our experimental data were consistent with temporally increasing random motility coefficients.

Adsorption↗