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At least 307 records · Page 17Linked to original sources
PubMed2004

Exact solution of a reaction-diffusion model with particle-number conservation.

We analytically investigate a one-dimensional branching-coalescing model with reflecting boundaries in a canonical ensemble where the total number of particles on the chain is conserved. Exact analytical calculations show that the model has two different phases which are separated by a second-order phase transition. The thermodynamic behavior of the canonical partition function of the model has been calculated exactly in each phase. Density profiles of particles have also been obtained explicitly. It is shown that the exponential part of the density profiles decays on three different length scales which depend on the total density of particles.

Journal Article↗
PubMed2001

[Characteristics of information decay in short-term visual memory and a diffusion model].

The effect of exposure duration of test stimulus on the decay rate in short-term visual memory (STVM) was investigated in a same-different task. In the model, it is assumed that memory noise, the variance of each convex value represented in STVM, increases with time, which causes the decay in STVM. In recognition experiments, the results showed that the decay rate is lower for longer exposure duration regardless of pattern complexity. Furthermore, the decay lasted gradually for 16 s with exposure duration of 1,200 ms, which suggests that prolonged exposure largely acts to reduce the decay rate but does not prevent the decay itself. These experimental data were well predicted by the model, which clearly indicates that memory noise increases as a linear function of retention interval and that the rate of increase of memory noise is inversely proportional to exposure duration. These results are interpreted by an extension of the integration model of Signal Detection Theory: The number of mental scanning, N, monotonically increases with an increase in exposure duration, s, and increase of memory noise is inversely proportional to N, so memory sensitivity d' is predicted to be multiplied by square route of s.

Humans↗
PubMed1998

Image matching as a diffusion process: an analogy with Maxwell's demons.

In this paper, we present the concept of diffusing models to perform image-to-image matching. Having two images to match, the main idea is to consider the objects boundaries in one image as semi-permeable membranes and to let the other image, considered as a deformable grid model, diffuse through these interfaces, by the action of effectors situated within the membranes. We illustrate this concept by an analogy with Maxwell's demons. We show that this concept relates to more traditional ones, based on attraction, with an intermediate step being optical flow techniques. We use the concept of diffusing models to derive three different non-rigid matching algorithms, one using all the intensity levels in the static image, one using only contour points, and a last one operating on already segmented images. Finally, we present results with synthesized deformations and real medical images, with applications to heart motion tracking and three-dimensional inter-patients matching.

Algorithms↗
PubMed1999

Numerically exploring habitat fragmentation effects on populations using cell-based coupled map lattices.

We examine habitat size, shape, and arrangement effects on populations using a discrete reaction-diffusion model. Diffusion is modeled passively and applied to a cellular grid of territories forming a coupled map lattice. Dispersal mortality is proportional to the amount of nonhabitat and fully occupied habitat surrounding a given cell, with distance decay. After verifying that our model produces the results expected for single patches of uniform habitat, we investigate heterogeneous and fragmented model landscapes. In heterogeneous single-patch systems near critical patch size, populations approach Gaussian spatial distributions with total population constrained by the capacity of the most limiting cell. In fragmented habitat landscapes, threshold effects are more complex and parametrically sensitive. The results from our experiments suggest the following: the ability to achieve persistence in hyperdispersed patchy habitats by adding similarly fragmented patches requires meeting threshold reproduction rates; persistent metapopulations in which no local population is individually persistent appear when dispersal distances and reproduction rates are both high, but only within narrow parameter ranges that are close to extinction thresholds; successful use of stepping-stone patches to support metapopulation systems appears unlikely for passively diffusing species; elongated patches offer early colonization advantages, but blocky patches offer greater population resilience near extinction thresholds. A common theme running through our findings is that population viability estimates may depend on our ability to determine when population and habitat systems are approaching extinction threshold conditions.

Animals↗
PubMed2003

Stationary diffusion gradients associated with photosynthetic carbon flux-a study of compartmental versus diffusion-reaction models.

Metabolic processes usually involve diffusion of compounds in addition to their metabolic reactions. Such processes are adequately described by reaction-diffusion models (in the form partial differential equations) which are usually difficult and tedious to solve. Compartmental models (ordinary differential equations) are much easier to analyse but may be inadequate since they do not allow for spatial gradients. However, a compartmental model can be considered as the limit of a reaction-diffusion model for very fast diffusion (all diffusion coefficients D(j)--> infinity ). A compartmental model m(c) is termed "associated" to the reaction-diffusion model m(rd) if m(c) is the limit of m(rd) for all D(j)--> infinity. From the analytical solutions of a reaction-diffusion model and its associated compartmental model the extent of a diffusion gradient of m(rd) can be estimated by means of parameters from both m(c) and m(rd). This approach is extended to more complicated models that cannot be solved analytically. Gradients can be neglected and, consequently, the compartmental description be used, if the characteristic length s of the diffusion path is small compared with the distance a particle travels in time T(e), where T(e) is the characteristic time for the compartmental model. This ratio of lengths can also be expressed as the ratio of two times, namely the residence time s(2)/D(X) and the turnover time X(C)/v, where X(C) and v are the steady-state concentration of X and its import rate, respectively, for the associated compartmental model. Characteristic times are given for several simple reaction-diffusion systems in rectangular and spherical geometries. Intracellular gradients of HCO(3)(-) and CO(2) are calculated for some flux situations relevant to photosynthetic carbon fixation in green microalgae.

Biological Transport↗
PubMed1993

Single ion channel models incorporating aggregation and time interval omission.

We present a general theoretical framework, incorporating both aggregation of states into classes and time interval omission, for stochastic modeling of the dynamic aspects of single channel behavior. Our semi-Markov models subsume the standard continuous-time Markov models, diffusion models and fractal models. In particular our models allow for quite general distributions of state sojourn times and arbitrary correlations between successive sojourn times. Another key feature is the invariance of our framework with respect to time interval omission: that is, properties of the aggregated process incorporating time interval omission can be derived directly from corresponding properties of the process without it. Even in the special case when the underlying process is Markov, this leads to considerable clarification of the effects of time interval omission. Among the properties considered are equilibrium behavior, sojourn time distributions and their moments, and auto-correlation and cross-correlation functions. The theory is motivated by ion channel mechanisms drawn from the literature, and illustrated by numerical examples based on these.

Biophysical Phenomena↗