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At least 307 records · Page 17Linked to original sources

arXiv2000

The Ashkin-Teller neural network near saturation

The thermodynamic and retrieval properties of the Ashkin-Teller neural network model storing an infinite number of patterns are examined in the replica-symmetric mean-field approximation. In particular, for linked patterns temperature-capacity phase diagrams are derived for different values of the two-neuron and four-neuron coupling strengths. This model can be considered as a particular non-trivial generalisation of the Hopfield model and exhibits a number of interesting new features. Some aspects of replica-symmetry breaking are discussed.

cond-mat.dis-nn↗

arXiv1999

Thresholds in layered neural networks with variable activity

The inclusion of a threshold in the dynamics of layered neural networks with variable activity is studied at arbitrary temperature. In particular, the effects on the retrieval quality of a self-controlled threshold obtained by forcing the neural activity to stay equal to the activity of the stored paterns during the whole retrieval process, are compared with those of a threshold chosen externally for every loading and every temperature through optimisation of the mutual information content of the network. Numerical results, mostly concerning low activity networks are discussed.

cond-mat.dis-nn↗

arXiv2000

Bi-stability of mixed states in neural network storing hierarchical patterns

We discuss the properties of equilibrium states in an autoassociative memory model storing hierarchically correlated patterns (hereafter, hierarchical patterns). We will show that symmetric mixed states (hereafter, mixed states) are bi-stable on the associative memory model storing the hierarchical patterns in a region of the ferromagnetic phase. This means that the first-order transition occurs in this ferromagnetic phase. We treat these contents with a statistical mechanical method (SCSNA) and by computer simulation. Finally, we discuss a physiological implication of this model. Sugase et al. analyzed the time-course of the information carried by the firing of face-responsive neurons in the inferior temporal cortex. We also discuss the relation between the theoretical results and the physiological experiments of Sugase et al.

cond-mat.dis-nn↗

arXiv2000

Gause's exclusion principle revisited: artificial modified species and competition

Gause's principle of competition between two species is studied when one of them is sterile. We study the condition for total extinction in the niche, namely, when the sterile population exterminates the native one by an optimal use of resources. A mathematical Lotka-Volterra non linear model of interaction between a native and sterile species is proposed. The condition for total extinction is related to the initial number $M_{o}$ of sterile individuals released in the niche. In fact, the existence of a critical sterile-population value $M_{c}$ is conjectured from numerical analysis and an analytical estimation is found. When spatial diffusion (migration) is considered a critical size territory is found and, for small territory, total extinction exist in any case. This work is motived by the extermination agriculture problem of fruit flies in our region.

nlin.AO↗

arXiv2000

Structural Susceptibilities in Toy Models of Proteins

New definitions of the structural susceptibilities based on the fluctuations of distances to the native state of toy protein models are proposed. The calculation of such susceptibilities does not require the basin of native state and the folding temperature can be defined from their peak if the native conformation is compact. The number of peaks in the derivatives of distances to the native state with respect to temperature, when plotted versus temperature, may serve as a criterion for foldability. The thermodynamics quantities are obtained by Monte Carlo and molecular dynamics simulations.

cond-mat.stat-mech↗

arXiv1999

Unzipping DNA - towards the first step of replication

The opening of the Y-fork - the first step of DNA replication - is shown to be a critical phenomenon under an external force at one of its ends. From the results of an equivalent delocalization in a non-hermitian quantum-mechanics problem we show the different scaling behavior of unzipping and melting. The resultant long-range critical features within the unzipped part of Y might play a role in the highly correlated biochemical functions during replication.

cond-mat.stat-mech↗

arXiv2000

Probing the basins of attraction of a recurrent neural network

A recurrent neural network is considered that can retrieve a collection of patterns, as well as slightly perturbed versions of this `pure' set of patterns via fixed points of its dynamics. By replacing the set of dynamical constraints, i.e., the fixed point equations, by an extended collection of fixed-point-like equations, analytical expressions are found for the weights w_ij(b) of the net, which depend on a certain parameter b. This so-called basin parameter b is such that for b=0 there are, a priori, no perturbed patterns to be recognized by the net. It is shown by a numerical study, via probing sets, that a net constructed to recognize perturbed patterns, i.e., with values of the connections w_ij(b) with b unequal zero, possesses larger basins of attraction than a net made with the help of a pure set of patterns, i.e., with connections w_ij(b=0). The mathematical results obtained can, in principle, be realized by an actual, biological neural net.

cond-mat.dis-nn↗

arXiv2000

A recurrent neural network with ever changing synapses

A recurrent neural network with noisy input is studied analytically, on the basis of a Discrete Time Master Equation. The latter is derived from a biologically realizable learning rule for the weights of the connections. In a numerical study it is found that the fixed points of the dynamics of the net are time dependent, implying that the representation in the brain of a fixed piece of information (e.g., a word to be recognized) is not fixed in time.

cond-mat.dis-nn↗

arXiv2000

Application of two-parameter dynamical replica theory to retrieval dynamics of associative memory with non-monotonic neurons

The two-parameter dynamical replica theory (2-DRT) is applied to investigate retrieval properties of non-monotonic associative memory, a model which lacks thermodynamic potential functions. 2-DRT reproduces dynamical properties of the model quite well, including the capacity and basin of attraction. Superretrieval state is also discussed in the framework of 2-DRT. The local stability condition of the superretrieval state is given, which provides a better estimate of the region in which superretrieval is observed experimentally than the self-consistent signal-to-noise analysis (SCSNA) does.

cond-mat.dis-nn↗

arXiv2001

Multifractal characterisation of complete genomes

This paper develops a theory for characterisation of DNA sequences based on their measure representation. The measures are shown to be random cascades generated by an infinitely divisible distribution. This probability distribution is uniquely determined by the exponent function in the multifractal theory of random cascades. Curve fitting to a large number of complete genomes of bacteria indicates that the Gamma density function provides an excellent fit to the exponent function, and hence to the probability distribution of the complete genomes.

physics.bio-ph↗

arXiv2001

Mechanical denaturation of DNA: existence of a low temperature denaturation

Recent theoretical predictions on DNA mechanical separation induced by pulling forces are numerically tested within a model in which self-avoidance for DNA strands is fully taken into account. DNA strands are described by interacting pairs of self avoiding walks (SAW) which are pulled apart by a force applied at the two extremities. The whole phase diagram is spanned by extensive Monte Carlo (MC) simulations and the existence of a low temperature denaturation is confirmed. The basic features of the phase diagram and the re-entrant phase boundary are also obtained with a simple heuristic argument based on an energy-entropy estimate.

cond-mat.stat-mech↗

arXiv2002

Transient dynamics for sequence processing neural networks

An exact solution of the transient dynamics for a sequential associative memory model is discussed through both the path-integral method and the statistical neurodynamics. Although the path-integral method has the ability to give an exact solution of the transient dynamics, only stationary properties have been discussed for the sequential associative memory. We have succeeded in deriving an exact macroscopic description of the transient dynamics by analyzing the correlation of crosstalk noise. Surprisingly, the order parameter equations of this exact solution are completely equivalent to those of the statistical neurodynamics, which is an approximation theory that assumes crosstalk noise to obey the Gaussian distribution. In order to examine our theoretical findings, we numerically obtain cumulants of the crosstalk noise. We verify that the third- and fourth-order cumulants are equal to zero, and that the crosstalk noise is normally distributed even in the non-retrieval case. We show that the results obtained by our theory agree with those obtained by computer simulations. We have also found that the macroscopic unstable state completely coincides with the separatrix.

cond-mat.dis-nn↗

arXiv2003

Helicase on DNA: A Phase coexistence based mechanism

We propose a phase coexistence based mechanism for activity of helicases, ubiquitous enzymes that unwind double stranded DNA. The helicase-DNA complex constitutes a fixed-stretch ensemble that entails a coexistence of domains of zipped and unzipped phases of DNA, separated by a domain wall. The motor action of the helicase leads to a change in the position of the fixed constraint thereby shifting the domain wall on dsDNA. We associate this off-equilibrium domain wall motion with the unzipping activity of helicase. We show that this proposal gives a clear and consistent explanation of the main observed features of helicases.

cond-mat.soft↗

arXiv2003

Bubble dynamics in DNA

The formation of local denaturation zones (bubbles) in double-stranded DNA is an important example for conformational changes of biological macromolecules. We study the dynamics of bubble formation in terms of a Fokker-Planck equation for the probability density to find a bubble of size n base pairs at time t, on the basis of the free energy in the Poland-Scheraga model. Characteristic bubble closing and opening times can be determined from the corresponding first passage time problem, and are sensitive to the specific parameters entering the model. A multistate unzipping model with constant rates recently applied to DNA breathing dynamics [G. Altan-Bonnet et al, Phys. Rev. Lett. 90, 138101 (2003)] emerges as a limiting case.

cond-mat.soft↗

arXiv1996

Ecological model of extinctions

We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the others, that reproduces and evolves in time. Each species is simultaneously a predator and a prey in a food chain. Mutations that change the interactions are supposed to occur randomly at a low rate. Extinctions of populations result naturally from the predator-prey dynamics. The model is not pinned in a fitness variable, and natural selection arises from the dynamics.

adap-org↗

arXiv2002

Scaling in DNA unzipping models: denaturated loops and end-segments as branches of a block copolymer network

For a model of DNA denaturation, exponents describing the distributions of denaturated loops and unzipped end-segments are determined by exact enumeration and by Monte Carlo simulations in two and three dimensions. The loop distributions are consistent with first order thermal denaturation in both cases. Results for end-segments show a coexistence of two distinct power laws in the relative distributions, which is not foreseen by a recent approach in which DNA is treated as a homogeneous network of linear polymer segments. This unexpected feature, and the discrepancies with such an approach, are explained in terms of a refined scaling picture in which a precise distinction is made between network branches representing single stranded and effective double stranded segments.

cond-mat.stat-mech↗

arXiv2003

Diffusion limited friendship network: A model for six degrees of separation

A dynamic model of a society is studied where each person is an uncorrelated and non-interacting random walker. A dynamical random graph represents the acquaintance network of the society whose nodes are the individuals and links are the pairs of mutual friendships. This network exhibits a novel percolation like phase transition in all dimensions. On introducing simultaneous death and birth rates in the population we show that the friendship network shows the six degrees of separation for ever after where the precise value of the network diameter depends on the death/birth rate. A SIS type model of disease spreading shows that this society remains always healthy if the population density is less than certain threshold value.

cond-mat.stat-mech↗

arXiv1995

Entropic Barriers, Frustration and Order: Basic Ingredients in Protein Folding

We solve a model that takes into account entropic barriers, frustration, and the organization of a protein-like molecule. For a chain of size $M$, there is an effective folding transition to an ordered structure. Without frustration, this state is reached in a time that scales as $M^λ$, with $λ\simeq 3$. This scaling is limited by the amount of frustration which leads to the dynamical selectivity of proteins: foldable proteins are limited to $\sim 300$ monomers; and they are stable in {\it one} range of temperatures, independent of size and structure. These predictions explain generic properties of {\it in vivo} proteins.

cond-mat↗