Multi shocks in Reaction-diffusion models

It is shown, concerning equivalent classes, that on a one-dimensional lattice with nearest neighbor interaction, there are only four independent models possessing double-shocks. Evolution of the width of the double-shocks in different models is investigated. Double-shocks may vanish, and the final state is a state with no shock. There is a model for which at large times the average width of double-shocks will become smaller. Although there may exist stationary single-shocks in nearest neighbor reaction diffusion models, it is seen that in none of these models, there exist any stationary double-shocks. Models admitting multi-shocks are classified, and the large time behavior of multi-shock solutions is also investigated.Comment: 17 pages, LaTeX2e, minor revisio

Finite-dimensional representation of the quadratic algebra of a generalized coagulation-decoagulation model

The steady-state of a generalized coagulation-decoagulation model on a one-dimensional lattice with reflecting boundaries is studied using a matrix-product approach. It is shown that the quadratic algebra of the model has a four-dimensional representation provided that some constraints on the microscopic reaction rates are fulfilled. The dynamics of a product shock measure with two shock fronts, generated by the Hamiltonian of this model, is also studied. It turns out that the shock fronts move on the lattice as two simple random walkers which repel each other provided that the same constraints on the microscopic reaction rates are satisfied.Comment: Minor revision

Exact Solution of a Reaction-Diffusion Model with Particle Number Conservation

We analytically investigate a 1d 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 decay on three different length scales which depend on total density of particles.Comment: 7 pages, REVTEX4, Contents updated and new references added, to appear in Physical Review

Repelling Random Walkers in a Diffusion-Coalescence System

We have shown that the steady state probability distribution function of a diffusion-coalescence system on a one-dimensional lattice of length L with reflecting boundaries can be written in terms of a superposition of double shock structures which perform biased random walks on the lattice while repelling each other. The shocks can enter into the system and leave it from the boundaries. Depending on the microscopic reaction rates, the system is known to have two different phases. We have found that the mean distance between the shock positions is of order L in one phase while it is of order 1 in the other phase.Comment: 5 pages, 1 EPS figure, Accepted for publication in PRE (2008

Familiarity expands space and contracts time

When humans draw maps, or make judgments about travel-time, their responses are rarely accurate and are often systematically distorted. Distortion effects on estimating time to arrival and the scale of sketch-maps reveal the nature of mental representation of time and space. Inspired by data from rodent entorhinal grid cells, we predicted that familiarity to an environment would distort representations of the space by expanding the size of it. We also hypothesized that travel-time estimation would be distorted in the same direction as space-size, if time and space rely on the same cognitive map. We asked international students, who had lived at a college in London for 9 months, to sketch a south-up map of their college district, estimate travel-time to destinations within the area, and mark their everyday walking routes. We found that while estimates for sketched space were expanded with familiarity, estimates of the time to travel through the space were contracted with familiarity. Thus, we found dissociable responses to familiarity in representations of time and space. © 2016 The Authors Hippocampus Published by Wiley Periodicals, Inc

Discontinuous Phase Transition in an Exactly Solvable One-Dimensional Creation-Annihilation System

An exactly solvable reaction-diffusion model consisting of first-class particles in the presence of a single second-class particle is introduced on a one-dimensional lattice with periodic boundary condition. The number of first-class particles can be changed due to creation and annihilation reactions. It is shown that the system undergoes a discontinuous phase transition in contrast to the case where the density of the second-class particles is finite and the phase transition is continuous.Comment: Revised, 8 pages, 1 EPS figure. Accepted for publication in Journal of Statistical Mechanics: theory and experimen

Relaxation time in a non-conserving driven-diffusive system with parallel dynamics

We introduce a two-state non-conserving driven-diffusive system in one-dimension under a discrete-time updating scheme. We show that the steady-state of the system can be obtained using a matrix product approach. On the other hand, the steady-state of the system can be expressed in terms of a linear superposition Bernoulli shock measures with random walk dynamics. The dynamics of a shock position is studied in detail. The spectrum of the transfer matrix and the relaxation times to the steady-state have also been studied in the large-system-size limit.Comment: 10 page

Microbial and biochemical characteristics of fermented fish sausage from common carp (Cyprinus carpio) mince by application of Pediococcus pentasaceus at different incubation temperatures

Fermented sausage is a favorite kind of meat-product that has allocated great proportions of meat consumption in the world. For the first time in Iran in this study the production of Fermented sausage from minced meat of common carp was assessed by means of lactic acid bacteria at different incubating temperatures as 15, 25, and 35˚C. To prepare the fish sausage, common carp mince was grounded and mixed with NaCl (3%), glucose (3%) and lactic acid bacteria at 5 log CFU/g and afterward were incubated for 48 h. During the incubation of fish sausage, microbiological tests, moisture and protein content, and TVB-N were measured. According to the results, the higher temperature of 35˚C stimulated the rapid growth of lactic acid bacteria, resulting in a rapid decline in pH, and consequently suppressed the growth of pseudomonas, Micrococcaceae and Enterobacteriacea

Decoding oscillatory representations of visual stimuli in episodic memory and working memory

Theories inspired by electrophysiological studies in animals suggest that the replay of past experiences plays an important role in episodic memory as well as working memory; yet very little is known about the neural characteristics of such replay in the human brain. This thesis consists of neuroimaging experiments for studying the temporal characteristics of the replay in the human brain and analytical methods for decoding replay. To that end, oscillatory neural activity patterns were recorded from healthy young adults via a non-invasive electrophysiological technique (Magnetoencephalography, MEG). Firstly, a pipeline for decoding MEG data using machine learning algorithms was eveloped and proposed. Then using an associative recognition experiment, we marked the neural signature for categorical visual information (about faces and scenes) during encoding. These markers of encoding-related experiences were then used for detecting the replay during retrieval - triggered by an associative memory cue. As a result, replay was detected at about 500 ms from onset of the cue. The results suggest that episodic recollection and replay are accomplished within 500 ms. Next, in a working memory experiment, I used item speci c visual information for tracking the replay of oscillatory activity while maintaining that information. Three visual stimuli with presumably distinct cortical representations were selected (types: a face, a banana, and a chair) and presented in a sequential order. Event-related responses during encoding showed a main e ect of item type and working memory load at 400-500 ms from onset of the stimuli. Using a decoding approach, it was possible to categorize oscillatory patterns related to each of the three stimulus types. These decoders are now used as markers of item speci c replay in working memory during the maintenance phase. This analysis is ongoing. Finally, we proposed a pipeline for detecting an optimal feature space for decoding MEG data at a group level because the previous pipeline relied on di erent features across subjects for decoding. Here the Canonical Variates Analysis of beamformer reconstructed MEG data in source space was used. Canonical Variates Analysis stimated the dependency of the selected features of MEG data to the experimental conditions and enabled multivariate decoding of MEG signal in the source space. Thus this proposed method was an optimal way for group level inference of MEG multivariate analysis. Overall, the MEG based decoding of the representation of visual stimuli was shown in source and sensor spaces. Also, our results revealed the temporal characteristic of replay in an episodic memory experiment

One-transit paths and steady-state of a non-equilibrium process in a discrete-time update

We have shown that the partition function of the Asymmetric Simple Exclusion Process with open boundaries in a sublattice-parallel updating scheme is equal to that of a two-dimensional one-transit walk model defined on a diagonally rotated square lattice. It has been also shown that the physical quantities defined in these systems are related through a similarity transformation.Comment: 8 pages, 2 figure