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arXiv1996

On Self-Organized Criticality and Synchronization in Lattice Models of Coupled Dynamical Systems

Lattice models of coupled dynamical systems lead to a variety of complex behaviors. Between the individual motion of independent units and the collective behavior of members of a population evolving synchronously, there exist more complicated attractors. In some cases, these states are identified with self-organized critical phenomena. In other situations, with clusterization or phase-locking. The conditions leading to such different behaviors in models of integrate-and-fire oscillators and stick-slip processes are reviewed.

cond-mat↗

arXiv1998

Diversity, Stability, Recursivity, and Rule Generation in Biological System: Intra-inter Dynamics Approach

Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction among the units, and the dynamics to change the dynamics itself, for example by replication (and death) of units according to their internal states. Applying the dynamics to cell differentiation, isologous diversification theory is proposed. According to it, orbital instability leads to diversified cell behaviors first. At the next stage, several cell types are formed, first triggered by clustering of oscillations, and then as attracting states of internal dynamics stabilized by the cell-to-cell interaction. At the third stage, the differentiation is determined as a recursive state by cell division. At the last stage, hierarchical differentiation proceeds, with the emergence of stochastic rule for the differentiation to sub-groups, where regulation of the probability for the differentiation provides the diversity and stability of cell society. Relevance of the theory to cell biology is discussed.

adap-org↗

arXiv1997

Evolution and extinction dynamics in rugged fitness landscapes

Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness landscapes. As a consequence, the average fitness in the system increases logarithmically with time, while the rate of extinction steadily decreases. This dynamics is studied by numerical simulations and, in a simpler mean field version, analytically. We also study the effect of externally added `mass' extinctions. The predictions for various quantities of paleontological interest (life-time distributions, distribution of event sizes and behavior of the rate of extinction) are robust and in good agreement with available data. Brief version of parts of this work have been published as Letters. (PRL 75, 2055, (1995) and PRL, 79, 1413, (1997))

adap-org↗

arXiv1998

Coherence and synchronization in diode-laser arrays with delayed global coupling

The dynamics of a semiconductor-laser array whose individual elements are coupled in a global way through an external mirror is numerically analysed. A coherent in-phase solution is seen to be preferred by the system at intermediate values of the feedback coupling strength. At low values of this parameter, a strong amplification of the spontaneous emission noise is observed. A tendency towards chaos synchronization is also observed at large values of the feedback strength.

adap-org↗

arXiv1999

Physicists attempt to scale the ivory towers of finance

Physicists have recently begun doing research in finance, and even though this movement is less than five years old, interesting and useful contributions have already emerged. This article reviews these developments in four areas, including empirical statistical properties of prices, random-process models for price dynamics, agent-based modeling, and practical applications.

adap-org↗

arXiv1995

Upper Bounds for the Critical Car Densities in Traffic Flow Problems

In most models of traffic flow, the car density $p$ is the only free parameter in determining the average car velocity $\langle v \rangle$. The critical car density $p_c$, which is defined to be the car density separating the jamming phase (with $\langle v \rangle = 0$) and the moving phase (with $\langle v \rangle > 0$), is an important physical quantity to investigate. By means of simple statistical argument, we show that $p_c < 1$ for the Biham-Middleton-Levine model of traffic flow in two or higher spatial dimensions. In particular, we show that $p_{c} \leq 11/12$ in 2 dimension and $p_{c} \leq 1 - \left( \frac{D-1}{2D} \right)^D$ in $D$ ($D > 2$) dimensions.

adap-org↗

arXiv1996

Density Fluctuations in Traffic Flow

Density fluctuations in traffic current are studied by computer simulations using the deterministic coupled map lattice model on a closed single-lane circuit. By calculating a power spectral density of temporal density fluctuations at a local section, we find a power-law behavior, $\sim 1/f^{1.8}$, on the frequency $f$, in non-congested flow phase. The distribution of the headway distance $h$ also shows the power law like $\sim 1/h^{3.0} $ at the same time. The power law fluctuations are destroyed by the occurence of the traffic jam.

chao-dyn↗

arXiv1997

Brownian Motors driven by Particle Exchange

We extend the Langevin dynamics so that particles can be exchanged with a particle reservoir. We show that grand canonical ensembles are realized at equilibrium and derive the relations of thermodynamics for processes between equilibrium states. As an application of the proposed evolution rule, we devise a simple model of Brownian motors driven by particle exchange. KEYWORDS: Langevin Dynamics, Thermodynamics, Open Systems

cond-mat.stat-mech↗

arXiv1998

Coupled Oscillators with Chemotaxis

A simple coupled oscillator system with chemotaxis is introduced to study morphogenesis of cellular slime molds. The model successfuly explains the migration of pseudoplasmodium which has been experimentally predicted to be lead by cells with higher intrinsic frequencies. Results obtained predict that its velocity attains its maximum value in the interface region between total locking and partial locking and also suggest possible roles played by partial synchrony during multicellular development.

adap-org↗

arXiv1997

Equilibrium Chemical Engines

An equilibrium reversible cycle with a certain engine to transduce the energy of any chemical reaction into mechanical energy is proposed. The efficiency for chemical energy transduction is also defined so as to be compared with Carnot efficiency. Relevance to the study of protein motors is discussed. KEYWORDS: Chemical thermodynamics, Engine, Efficiency, Molecular machine.

cond-mat.soft↗

arXiv1996

Self-Annealing Dynamics in a Multistable System

A new type of dynamical behavior of a multistable system is reported. We found that a simple non-equilibrium system can reduce its effective temperature autonomously at a global minimum if the residual frustration at a global minimum is small enough, which highlights an unexpected feature of non-equilibrium multistable systems.

adap-org↗

arXiv1999

Fractional Langevin equation to describe anomalous diffusion

A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle, with the power exponent being noninteger. More general equation containing fractional time differential operators instead of usual ones is also proposed to describe anomalous diffusion processes. Such equation can be regarded as corresponding to systems with incomplete Hamiltonian chaos, and depending on the type of the relationship between the speed and coordinate of a particle yields either usual or fractional long-time behavior of diffusion. Correlations with the fractional Fokker-Planck equation are analyzed. Possible applications of the proposed equation beside anomalous diffusion itself are discussed.

chao-dyn↗

arXiv1999

A Complete Enumeration and Classification of Two-Locus Disease Models

There are 512 two-locus, two-allele, two-phenotype, fully-penetrant disease models. Using the permutation between two alleles, between two loci, and between being affected and unaffected, one model can be considered to be equivalent to another model under the corresponding permutation. These permutations greatly reduce the number of two-locus models in the analysis of complex diseases. This paper determines the number of non-redundant two-locus models (which can be 102, 100, 96, 51, 50, or 48, depending on which permutations are used, and depending on whether zero-locus and single-locus models are excluded). Whenever possible, these non-redundant two-locus models are classified by their property. Besides the familiar features of multiplicative models (logical AND), heterogeneity models (logical OR), and threshold models, new classifications are added or expanded: modifying-effect models, logical XOR models, interference and negative interference models (neither dominant nor recessive), conditionally dominant/recessive models, missing lethal genotype models, and highly symmetric models. The following aspects of two-locus models are studied: the marginal penetrance tables at both loci, the expected joint identity-by-descent probabilities, and the correlation between marginal identity-by-descent probabilities at the two loci. These studies are useful for linkage analyses using single-locus models while the underlying disease model is two-locus, and for correlation analyses using the linkage signals at different locations obtained by a single-locus model.

adap-org↗

arXiv1995

Comment on "White-Noise-Induced Transport in Periodic Structures"

In the paper by J.Łuczka {\em et al.} ({\em Europhys. Lett.}, {\bf 31} (1995) 431), the authors reported by rigorous calculation that an additive Poissonian white shot noise can induce a macroscopic current of a dissipative particle in a periodic potential -- even {\em in the absence} of spatial asymmetry of the potential. We argue that their main result is an obvious one caused by the spatially broken symmetry of a probability distribution of the additive noise, unlike the similar result caused by chaotic noise which has a symmetric probability distribution ({\em J.Phys.Soc.Jpn.}, {\bf 63} (1994) 2014).

adap-org↗

arXiv1997

A Prototype Model of Stock Exchange

A prototype model of stock market is introduced and studied numerically. In this self-organized system, we consider only the interaction among traders without external influences. Agents trade according to their own strategy, to accumulate his assets by speculating on the price's fluctuations which are produced by themselves. The model reproduced rather realistic price histories whose statistical properties are also similar to those observed in real markets.

cond-mat.stat-mech↗

arXiv1997

Avalanche Mixing of Granular Solids

Mixing of two fractions of a granular material in a slowly rotating two-dimensional drum is considered. The rotation is around the axis of the upright drum. The drum is filled partially, and mixing occurs only at a free surface of the material. We propose a simple theory of the mixing process which describes a real experiment surprisingly well. A geometrical approach without appealing to ideas of self-organized criticality is used. The dependence of the mixing time on the drum filling is calculated. The mixing time is infinite in the case of the half-filled drum. We describe singular behaviour of the mixing near this critical point.

cond-mat↗

arXiv1997

A general learning algorithm for solving optimization problems and its application to the spin glass problem

We propose a general learning algorithm for solving optimization problems, based on a simple strategy of trial and adaptation. The algorithm maintains a probability distribution of possible solutions (configurations), which is updated continuously in the learning process. As the probability distribution evolves, better and better solutions are shown to emerge. The performance of the algorithm is illustrated by the application to the problem of finding the ground state of the Ising spin glass. A simple theoretical understanding of the algorithm is also presented.

adap-org↗

arXiv1998

A solvable model of the evolutionary loop

A model for the evolution of a finite population in a rugged fitness landscape is introduced and solved. The population is trapped in an evolutionary loop, alternating periods of stasis to periods in which it performs adaptive walks. The dependence of the average rarity of the population (a quantity related to the fitness of the most adapted individual) and of the duration of stases on population size and mutation rate is calculated.

cond-mat.dis-nn↗