title:
Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform
  Computations

abstract:
  We present results from an experiment similar to one performed by Packard
(1988), in which a genetic algorithm is used to evolve cellular automata (CA)
to perform a particular computational task. Packard examined the frequency of
evolved CA rules as a function of Langton's lambda parameter (Langton, 1990),
and interpreted the results of his experiment as giving evidence for the
following two hypotheses: (1) CA rules able to perform complex computations are
most likely to be found near ``critical'' lambda values, which have been
claimed to correlate with a phase transition between ordered and chaotic
behavioral regimes for CA; (2) When CA rules are evolved to perform a complex
computation, evolution will tend to select rules with lambda values close to
the critical values. Our experiment produced very different results, and we
suggest that the interpretation of the original results is not correct. We also
review and discuss issues related to lambda, dynamical-behavior classes, and
computation in CA. The main constructive results of our study are identifying
the emergence and competition of computational strategies and analyzing the
central role of symmetries in an evolutionary system. In particular, we
demonstrate how symmetry breaking can impede the evolution toward higher
computational capability.


title: Antichaos in a Class of Random Boolean Cellular Automata

abstract:
  A variant of Kauffman's model of cellular metabolism is presented. It is a
randomly generated network of boolean gates, identical to Kauffman's except for
a small bias in favor of boolean gates that depend on at most one input. The
bias is asymptotic to 0 as the number of gates increases. Upper bounds on the
time until the network reaches a state cycle and the size of the state cycle,
as functions of the number of gates $n$, are derived. If the bias approaches 0
slowly enough, the state cycles will be smaller than $n^c$ for some $c<1$. This
lends support to Kauffman's claim that in his version of random network the
average size of the state cycles is approximately $n^{1/2}$.


title: A Criterion for Stability in Random Boolean Cellular Automata

abstract:
  Random boolean cellular automata are investigated, where each gate has two
randomly chosen inputs and is randomly assigned a boolean function of its
inputs. The effect of non-uniform distributions on the choice of the boolean
functions is considered. The main results are that if the gates are more likely
to be assigned constant functions than non-canalyzing functions, then with very
high probability, the automaton will exhibit very stable behavior: most of the
gates will stabilize, and the state cycles will be bounded in size.


title:
Biased Random-Walk Learning: A Neurobiological Correlate to
  Trial-and-Error

abstract:
  Neural network models offer a theoretical testbed for the study of learning
at the cellular level. The only experimentally verified learning rule, Hebb's
rule, is extremely limited in its ability to train networks to perform complex
tasks. An identified cellular mechanism responsible for Hebbian-type long-term
potentiation, the NMDA receptor, is highly versatile. Its function and efficacy
are modulated by a wide variety of compounds and conditions and are likely to
be directed by non-local phenomena. Furthermore, it has been demonstrated that
NMDA receptors are not essential for some types of learning. We have shown that
another neural network learning rule, the chemotaxis algorithm, is
theoretically much more powerful than Hebb's rule and is consistent with
experimental data. A biased random-walk in synaptic weight space is a learning
rule immanent in nervous activity and may account for some types of learning --
notably the acquisition of skilled movement.


title:
A nonequilibrium statistical field theory of swarms and other spatially
  extended complex systems

abstract:
  A class of models with applications to swarm behavior as well as many other
types of spatially extended complex biological and physical systems is studied.
Internal fluctuations can play an active role in the organization of the phase
structure of such systems. Consequently, it is not possible to fully understand
the behavior of these systems without explicitly incorporating the
fluctuations. In particular, for the class of models studied here the effect of
internal fluctuations due to finite size is a renormalized decrease in the
temperature near the point of spontaneous symmetry breaking. We briefly outline
how these models can be applied to the behavior of an ant swarm.


title: Swarms, Phase Transitions, and Collective Intelligence

abstract:
  A spacially extended model of the collective behavior of a large number of
locally acting organisms is proposed in which organisms move probabilistically
between local cells in space, but with weights dependent on local morphogenetic
substances, or morphogens. The morphogens are in turn are effected by the
passage of an organism. The evolution of the morphogens, and the corresponding
flow of the organisms constitutes the collective behavior of the group. Such
models have various types of phase transitions and self-organizing properties
controlled both by the level of the noise, and other parameters.
  The model is then applied to the specific case of ants moving on a lattice.
The local behavior of the ants is inspired by the actual behavior observed in
the laboratory, and analytic results for the collective behavior are compared
to the corresponding laboratory results.
  It is hoped that the present model might serve as a paradigmatic example of a
complex cooperative system in nature. In particular swarm models can be used to
explore the relation of nonequilibrium phase transitions to at least three
important issues encountered in artificial life. Firstly, that of emergence as
complex adaptive behavior. Secondly, as an exploration of continuous phase
transitions in biological systems. Lastly, to derive behavioral criteria for
the evolution of collective behavior in social organisms.


title: Dynamics, Computation, and the "Edge of Chaos": A Re-Examination

abstract:
  In this paper we review previous work and present new work concerning the
relationship between dynamical systems theory and computation. In particular,
we review work by Langton \cite{Langton90} and Packard \cite{Packard88} on the
relationship between dynamical behavior and computational capability in
cellular automata (CA). We present results from an experiment similar to the
one described in \cite{Packard88}, that was cited there as evidence for the
hypothesis that rules capable of performing complex computations are most
likely to be found at a phase transition between ordered and chaotic behavioral
regimes for CA (the ``edge of chaos''). Our experiment produced very different
results from the original experiment, and we suggest that the interpretation of
the original results is not correct. We conclude by discussing general issues
related to dynamics, computation, and the ``edge of chaos'' in cellular
automata.


title: Exact solutions for a mean-field Abelian sandpile

abstract:
  We introduce a model for a sandpile, with N sites, critical height N and each
site connected to every other site. It is thus a mean-field model in the
spin-glass sense. We find an exact solution for the steady state probability
distribution of avalanche sizes, and discuss its asymptotics for large N.


title: Prediction and Adaptation in an Evolving Chaotic Environment

abstract:
  We describe the results of analytic calculations and computer simulations of
adaptive predictors (predictive agents) responding to an evolving chaotic
environment and to one another. Our simulations are designed to quantify
adaptation and to explore co-adaptation for a simple calculable model of a
complex adaptive system. We first consider the ability of a single agent,
exposed to a chaotic environment, to model, control, and predict the future
states of that environment. We then introduce a second agent which, in
attempting to model and control both the chaotic environment and the first
agent, modifies the extent to which that agent can identify patterns and
exercise control. We find that (i) optimal adaptive predictors have an optimal
memory and an optimal complexity, which are small for a rapidly changing map
dynamics and (ii) that the predictive power can be increased by imposing chaos
or random noise onto the map dynamics. The competition between the two
predictive agents can lead either to chaos, or to metastable emergent behavior,
best described as a leader-follower relationship. Our results suggest a
correlation between optimal adaptation, optimal complexity, and emergent
behavior, and provide preliminary support for the concept of optimal
co-adaptation near the edge of chaos.


title: Dynamics of Earthquake Faults

abstract:
  We present an overview of our ongoing studies of the rich dynamical behavior
of the uniform, deterministic Burridge--Knopoff model of an earthquake fault.
We discuss the behavior of the model in the context of current questions in
seismology. Some of the topics considered include: (1) basic properties of the
model, such as the magnitude vs. frequency distribution and the distinction
between small and large events; (2) dynamics of individual events, including
dynamical selection of rupture propagation speeds; (3) generalizations of the
model to more realistic, higher dimensional models; (4) studies of
predictability, in which artificial catalogs generated by the model are used to
test and determine the limitations of pattern recognition algorithms used in
seismology.

categories: adap-org chao-dyn nlin.AO nlin.CD nlin.PS patt-sol


title: On the Threshold of Chaos in Random Boolean Cellular Automata

abstract:
  A random boolean cellular automaton is a network of boolean gates where the
inputs, the boolean function, and the initial state of each gate are chosen
randomly. In this article, each gate has two inputs. Let $a$ (respectively $c$)
be the probability the the gate is assigned a constant function (respectively a
non-canalyzing function, i.e., {\sc equivalence} or {\sc exclusive or}).
Previous work has shown that when $a > c$, with probability asymptotic to 1,
the random automaton exhibits very stable behavior: almost all of the gates
stabilize, almost all of them are weak, i.e., they can be perturbed without
affecting the state cycle that is entered, and the state cycle is bounded in
size. This article gives evidence that the condition $a = c$ is a threshold of
chaotic behavior: with probability asymptotic to 1, almost all of the gates are
still stable and weak, but the state cycle size is unbounded. In fact, the
average state cycle size is superpolynomial in the number of gates.


title: Cell Division, Differentiation and Dynamic Clustering

abstract:
  A novel mechanism for cell differentiation is proposed, based on the dynamic
clustering in a globally coupled chaotic system. A simple model with metabolic
reaction, active transport of chemicals from media, and cell division is found
to show three successive stages with the growth of the number of cells;
coherent growth, dynamic clustering, and fixed cell differentiation. At the
last stage, disparity in activities, germ line segregation, somatic cell
differentiation, and homeochaotic stability against external perturbation are
found. Our results, in consistency with the experiments of the preceding paper,
imply that cell differentiation can occur without a spatial pattern. From
dynamical systems viewpoint, the new concept of ``open chaos" is proposed, as a
novel and general scenario for systems with growing numbers of elements, also
seen in economics and sociology.A


title: Imitation Games

abstract:
  Mutual imitation games among artificial birds are studied. By employing a
variety of mappings and game rules, the evolution to the edge between chaos and
windows is universally confirmed. Some other general features are observed,
including punctuated equilibria, and successive alternations of dominant
species with temporal complexity. Diversity of species aided by the
symbolization of artificial birds' song are also shown.


title: Chaos as a Source of Complexity and Diversity in Evolution

abstract:
  The relevance of chaos to evolution is discussed in the context of the origin
and maintenance of diversity and complexity. Evolution to the edge of chaos is
demonstrated in an imitation game. As an origin of diversity, dynamic
clustering of identical chaotic elements, globally coupled each to other, is
briefly reviewed. The clustering is extended to nonlinear dynamics on
hypercubic lattices, which enables us to construct a self-organizing genetic
algorithm. A mechanism of maintenance of diversity, ``homeochaos", is given in
an ecological system with interaction among many species. Homeochaos provides a
dynamic stability sustained by high-dimensional weak chaos. A novel mechanism
of cell differentiation is presented, based on dynamic clustering. Here, a new
concept -- ``open chaos" -- is proposed for the instability in a dynamical
system with growing degrees of freedom. It is suggested that studies based on
interacting chaotic elements can replace both top-down and bottom-up
approaches.


title: Scaling behaviour in daily air humidity fluctuations

abstract:
  We show that the daily average air humidity fluctuations exhibit non-trivial
$1/f^{\alpha}$ behaviour which different from the spectral properties of other
meteorological quantities. This feature and the fractal spatial strucure found
in clouds make it plausible to regard air humidity fluctuations as a
manifestation of self-organized criticality. We give arguments why the dynamics
in air humidity can be similar to those in sandpile models of SOC.


title: Parametric ordering of complex systems

abstract:
  Cellular automata (CA) dynamics are ordered in terms of two global
parameters, computable {\sl a priori} from the description of rules. While one
of them (activity) has been used before, the second one is new; it estimates
the average sensitivity of rules to small configurational changes. For two
well-known families of rules, the Wolfram complexity Classes cluster
satisfactorily. The observed simultaneous occurrence of sharp and smooth
transitions from ordered to disordered dynamics in CA can be explained with the
two-parameter diagram.


title: Soft Turbulence in the Atmospheric Boundary Layer

abstract:
  In this work we compare the spectral properties of the daily medium
temperature fluctuations with the experimental results of the Chicago Group, in
which the local temperature fluctuations were measured in a helium cell. The
results suggest that the dynamics of the daily temperature fluctuations is
determined by the oft turbulent state of the atmospheric boundary layer, which
state is significantly different from low dimensional chaos.


title: Self-organized Criticality in Living Systems

abstract:
  We suggest that ensembles of self-replicating entities such as biological
systems naturally evolve into a self-organized critical state in which
fluctuations, as well as waiting-times between phase transitions are
distributed according to a 1/f power law. We demonstrate these concepts by
analyzing a population of self-replicating strings (segments of computer-code)
subject to mutation and survival of the fittest.


title: Learning and Complexity in Genetic Auto-Adaptive Systems

abstract:
  We describe and investigate the learning capablities displayed by a
population of self-replicating segments of computer-code subject to random
mutation: the tierra environment. We find that learning is achieved through
phase transitions that adapt the population to whichever environment it
encounters, with a learning rate characterized by the environmental variables.
Our results suggest that most effective learning is achieved close to the edge
of chaos.


title: Training and Turnover in Organizations

abstract:
  We present a two-level model of organizational training and agent production.
Managers decide whether or not to train based on both the costs of training
compared to the benefits and on their expectations and observations of the
number of other firms that also train. Managers also take into account the sum
of their employees' contributions and the average tenure length within their
organization. Employees decide whether or not to contribute to production based
on their expectations as to how other employees will act. Trained workers learn
over time and fold their increased productivity into their decision whether or
not to contribute. We find that the dynamical behavior at the two levels is
closely coupled: the evolution of the industry over time depends not only on
the characteristics of training programs, learning curves, and cost-benefit
analyses, but on the vagaries of chance as well. For example, in one case, the
double dilemma can be resolved for the industry as a whole and productivity
then increases steadily over time. In another, the organizational level dilemma
may remain unresolved and workers may contribute at fluctuating levels. In this
case the overall productivity stays low. We also find a correlation between
high productivity and low turnover and show that a small increase in training
rates can lead to explosive growth in productivity.


title:
Like Sparrows on a Clothes Line: The Self-Organization of Random Number
  Sequences

abstract:
  We study sequences of random numbers {Z[1],Z[2],Z[3],...,Z[n]} -- which can
be considered random walks with reflecting barriers -- and define their "types"
according to whether Z[i] > Z[i+1], (a down-movement), or Z[i] < Z[i+1]
(up-movement). This paper examines the means, xi, to which the Zi converge,
when a large number of sequences of the same type is considered. It is shown
that these means organize themselves in such a way that, between two turning
points of the sequence, they are equidistant from one another. We also show
that m steps in one direction tend to offset one step in the other direction,
as m -> infinity. Key words:random number sequence, self-organization, random
walk, reflecting barriers.


title: Cellular Games

abstract:
  A cellular game is a dynamical system in which cells, placed in some discrete
structure, are regarded as playing a game with their immediate neighbors.
Individual strategies may be either deterministic or stochastic. Strategy
success is measured according to some universal and unchanging criterion.
Successful strategies persist and spread; unsuccessful ones disappear. In this
thesis, two cellular game models are formally defined, and are compared to
cellular automata. Computer simulations of these models are presented.
Conditions providing maximal average cell success, on one and two-dimensional
lattices, are examined. It is shown that these conditions are not necessarily
stable; and an example of such instability is analyzed. It is also shown that
Nash equilibrium strategies are not necessarily stable. Finally, a particular
kind of zero-depth, two-strategy cellular game is discussed; such a game is
called a simple cellular game. It is shown that if a simple cellular game is
left/right symmetric, and if there are initially only finitely many cells using
one strategy, the zone in which this strategy occurs has probability 0 of
expanding arbitrarily far in one direction only. With probability 1, it will
either expand in both directions or disappear. Computer simulations of such
games are presented.


title: Beliefs and Cooperation

abstract:
  Individuals in groups must often choose between acting selfishly and
cooperating for the common good. The choices they make are based on their
beliefs on how they expect their actions to affect others. We show that for a
broad set of beliefs and group characteristics cooperation can appear
spontaneously in non-cooperative groups after very long periods of time. When
delays in information are unavoidable the group dynamics acquires a wide
repertoire of behaviors, ranging from opportunistic oscillations to bursty
chaos, thus excluding the possibility of sustained cooperation.


title: On Modelling Life

abstract:
  We present a theoretical as well as experimental investigation of a
population of self-replicating segments of code subject to random mutation and
survival of the fittest. Under the assumption that such a system constitutes a
minimal system with characteristics of life, we obtain a number of statements
on the evolution of complexity and the trade-off between entropy and
information.


title: Evolutionary Learning in the 2D Artificial Life System "Avida"

abstract:
  We present a new tierra-inspired artificial life system with local
interactions and two-dimensional geometry, based on an update mechanism akin to
that of 2D cellular automata. We find that the spatial geometry is conducive to
the development of diversity and thus improves adaptive capabilities. We also
demonstrate the adaptive strength of the system by breeding cells with simple
computational abilities, and study the dependence of this adaptability on
mutation rate and population size.


title: Nonlinear Dynamics in Distributed Systems

abstract:
  We build on a previous statistical model for distributed systems and
formulate it in a way that the deterministic and stochastic processes within
the system are clearly separable. We show how internal fluctuations can be
analysed in a systematic way using Van Kanpen's expansion method for Markov
processes. We present some results for both stationary and time-dependent
states. Our approach allows the effect of fluctuations to be explored,
particularly in finite systems where such processes assume increasing
importance.


title: Study of a New Neuron

abstract:
  We study a modular neuron alternative to the McCulloch-Pitts neuron that
arises naturally in analog devices in which the neuron inputs are represented
as coherent oscillatory wave signals. Although the modular neuron can compute
$XOR$ at the one neuron level, it is still characterized by the same
Vapnik-Chervonenkis dimension as the standard neuron. We give the formulas
needed for constructing networks using the new neuron and training them using
back-propagation. A numerical study of the modular neuron on two data sets is
presented, which demonstrates that the new neuron performs at least as well as
the standard neuron.


title: Constructive Complexity and Artificial Reality: An Introduction

abstract:
  Basic problems of complex systems are outlined with an emphasis on
irreducibility and dynamic many-to-many correspondences. We discuss the
importance of a constructive approach to artificial reality and the
significance of an internal observer.


title: Dynamics of a stochastically driven running sandpile

abstract:
  We analyze in detail a one-dimensional stochastically driven running
sandpile. The dynamics shows three different phases, depending on the on-site
relaxation rate and stochastic driving rate. Two phases are characterized by
the presence of travelling waves. The third shows algebraic relaxation.


title: Asymptotic Exit Location Distributions in the Stochastic Exit Problem

abstract:
  Consider a two-dimensional continuous-time dynamical system, with an
attracting fixed point $S$. If the deterministic dynamics are perturbed by
white noise (random perturbations) of strength $\epsilon$, the system state
will eventually leave the domain of attraction $\Omega$ of $S$. We analyse the
case when, as $\epsilon\to0$, the exit location on the boundary
$\partial\Omega$ is increasingly concentrated near a saddle point $H$ of the
deterministic dynamics. We show that the asymptotic form of the exit location
distribution on $\partial\Omega$ is generically non-Gaussian and asymmetric,
and classify the possible limiting distributions. A key role is played by a
parameter $\mu$, equal to the ratio $|\lambda_s(H)|/\lambda_u(H)$ of the stable
and unstable eigenvalues of the linearized deterministic flow at $H$. If
$\mu<1$ then the exit location distribution is generically asymptotic as
$\epsilon\to0$ to a Weibull distribution with shape parameter $2/\mu$, on the
$O(\epsilon^{\mu/2})$ length scale near $H$. If $\mu>1$ it is generically
asymptotic to a distribution on the $O(\epsilon^{1/2})$ length scale, whose
moments we compute. The asymmetry of the asymptotic exit location distribution
is attributable to the generic presence of a `classically forbidden' region: a
wedge-shaped subset of $\Omega$ with $H$ as vertex, which is reached from $S$,
in the $\epsilon\to0$ limit, only via `bent' (non-smooth) fluctuational paths
that first pass through the vicinity of $H$. We deduce from the presence of
this forbidden region that the classical Eyring formula for the
small-$\epsilon$ exponential asymptotics of the mean first exit time is
generically inapplicable.


title: A Network of Oscillators for Retrieving Phase Information

abstract:
  We propose a network of oscillators to retrieve given patterns in which the
oscillators keep a fixed phase relationship with one another. In this
description, the phase and the amplitude of the oscillators can be regarded as
the timing and the strength of the neuronal spikes, respectively. Using the
amplitudes for encoding, we enable the network to realize not only oscillatory
states but also non-firing states. In addition, it is shown that under suitable
conditions the system has a Lyapunov function ensuring a stable retrieval
process. Finally, the associative memory capability of the network is
demonstrated numerically.


title: Bubbles and Market Crashes

abstract:
  We present a dynamical theory of asset price bubbles that exhibits the
appearance of bubbles and their subsequent crashes. We show that when
speculative trends dominate over fundamental beliefs, bubbles form, leading to
the growth of asset prices away from their fundamental value. This growth makes
the system increasingly susceptible to any exogenous shock, thus eventually
precipitating a crash. We also present computer experiments which in their
aggregate behavior confirm the predictions of the theory.


title:
Secondary Image Synthesis In Electronic Computer Photography (Vtorichnyj
  Sintez Izobrazhenij V Elektronnoj Komp'Yuternoj Fotografii)

abstract:
  The principal scheme of the secondary image synthesis in electronic computer
photography is described. The crucial role of the Clebsch-Gordan coefficient
calculus is pointed out.


title:
Towards A Description Of Interactive Psychoinformation Systems.
  Preliminary Remarks. (K Opisaniyu Interaktivnyh Psihoinformatsionnyh Sistem.
  Predvaritel'Nye Zamechaniya)

abstract:
  An approach to description of interactive psychoinformation systems, based on
the concept of "virtualization" and essentially using the technique of the
"secondary image synthesis" (adap-org/9409002), is sketched. The article has a
rather discussional character and maybe considered as a comment to some
statements of the introduction to the author's paper "Complex projective
geometry and quantum projective field theory" (Theor. Math. Phys., 1994).


title: A New Look at Broken Ergodicity

abstract:
  We study the nature and mechanisms of broken ergodicity (BE) in specific
random walk models corresponding to diffusion on random potential surfaces, in
both one and high dimension. Using both rigorous results and nonrigorous
methods, we confirm several aspects of the standard BE picture and show that
others apply in one dimension, but need to be modified in higher dimensions.
These latter aspects include the notions that at fixed temperature confining
barriers increase logarithmically with time, that ``components'' are
necessarily bounded regions of state space which depend on the observational
timescale, and that the system continually revisits previously traversed
regions of state space. We examine our results in the context of several
experiments, and discuss some implications of our results for the dynamics of
disordered and/or complex systems.


title:
Belavkin-Kolokoltsov Watch-Dog Effects in Interactively Controlled
  Stochastic Computer-Graphic Dynamical Systems. A Summary of Mathematical
  Researches

abstract:
  This paper contains a summary of mathematical researches of stochastic
properties of the long time behavior of a continuously observed (and
interactively controlled) quantum--field top. Applications to interactively
controlled stochastic computer-graphic dynamical systems are also discussed.

categories: adap-org dg-ga math.DG nlin.AO nlin.SI solv-int


title: On The Avalanche-finiteness Of Abelian Sandpiles

abstract:
  We prove a necessary and sufficient condition for an Abelian Sandpile Model
(ASM) to be avalanche-finite, namely: all unstable states of the system can be
brought back to stability in finite number of topplings. The method is also
computationally feasible since it involves no greater than $\mbox{O} \left( N^3
\right)$ arithmetic computations where $N$ is the total number of sites of the
system. Key words: Abelian sandpile model; avalanche-finiteness; self-organized
criticality


title:
Random Walks on a Fluctuating Lattice: A Renormalization Group Approach
  Applied in One Dimension

abstract:
  We study the problem of a random walk on a lattice in which bonds connecting
nearest neighbor sites open and close randomly in time, a situation often
encountered in fluctuating media. We present a simple renormalization group
technique to solve for the effective diffusive behavior at long times. For
one-dimensional lattices we obtain better quantitative agreement with
simulation data than earlier effective medium results. Our technique works in
principle in any dimension, although the amount of computation required rises
with dimensionality of the lattice.


title:
Mass-extinction: Evolution and the effects of external influences on
  unfit species

abstract:
  We present a new model for extinction in which species evolve in bursts or
`avalanches', during which they become on average more susceptible to
environmental stresses such as harsh climates and so are more easily rendered
extinct. Results of simulations and analytic calculations using our model show
a power-law distribution of extinction sizes which is in reasonable agreement
with fossil data. e also see a number of features qualitatively similar to
those seen in the fossil record. For example, we see frequent smaller
extinctions in the wake of a large mass extinction, which arise because there
is reduced competition for resources in the aftermath of a large extinction
event, so that species which would not normally be able to compete can get a
foothold, but only until the next cold winter or bad attack of the flu comes
along to wipe them out.


title: Kinetic Theory of Anomalous Transport of SupraThermal Particles

abstract:
  The plasma turbulence as is well known plays crucial role in the processes of
plasma dynamics and transport phenomena. It affects both macroscopic plasma
behaviour and distribution of particles, and besides suprathermal component of
particle ensemble is even more sensitive to turbulent processes. We have
performed investigation of behaviour of fast particles in turbulent
inhomogeneous magnetized plasma. The general kinetic equation describing
evolution of fast particle distribution at the presence of MHD plasma
turbulence has been derived and analyzed. We constructed semi-analytical
solution of the kinetic equation into suprathermal energy region. Several
factors have been examined among them like turbulence else are nonuniform
external electric and magnetic field, and inhomogeneity of the plasma. It was
shown that last one is essential and may lead to some unexpected effects.


title: Communities of Practice: Performance and Evolution

abstract:
  We present a detailed model of collaboration in communities of practice and
we examine its dynamical consequences for the group as a whole. We establish
the existence of a novel mechanism that allows the community to naturally adapt
to growth, specialization, or changes in the environment without the need for
central controls. This mechanism relies on the appearance of a dynamical
instability that initates an exploration of novel interactions, eventually
leading to higher performance for the community as a whole.


title: The covariance matrix of the potts model: A random cluster analysis

abstract:
  We consider the covariance matrix $G^{mn}(x-y)$ of the d-dimensional q-states
Potts model, rewriting it in terms of the connectivity, the finite-cluster
connectivity and the infinite-cluster covariance in the random cluster repre-
sentation of Fortuin and Kasteleyn. In any of the $q$ ordered phases, we show
that the matrix $G^{mn}(x-y)$ has one tivial eigenvalue 0, one simple eigen-
value $G_{\wir}^{(1)}(x-y)$ and one ($q-2$)-fold degenerate eigenvalue
$G_{\wir}^{(2)}(x-y)$. Furthermore, we identify the eigenvalues both in terms
of representations of the unbroken symmetry group of the model, and in terms of
connectivities and cluster covariances, thereby attributing algebraic signifi-
cance to these stochastic geometric quantities. In addition to establishing the
existence of the correlation lengths $\xi_{\wir}^{(1)}$ and $\xi_{\wir}^{(2)}$
corresponding to $G_{\wir}^{(1)}(x-y)$ and $G_{\wir}^{(2)}(x-y)$, we show that
$\xi_{\wir}^{(1)}(\beta)\geq \xi_{\wir}^{(2)}(\beta)$ for all inverse tempera-
tures $\beta$. For dimension $d=2$ and $q \geq 1$, we establish a duality
relation between $\xi_{\wir}^{(2)}$ and $\xi_{\free}$, the correlation length
of the two-point function with free boundary conditions: We show
$\xi_{\wir}^{(2)}(\beta) = \frac{1}{2} \xi_{\free}(\beta^\ast)$ for all $\beta
\geq \beta_o$, where $\beta^\ast$ is the dual inverse temperature and $\beta_o$
is the self-dual point. In order to prove the above results, we introduce two
new inequalities. The first is similar to the FKG inequality, but holds for
events which are neither increasing nor decreasing, and replaces independence
in the standard percolation model; the second replaces the van den Berg -
Kesten inequality.


title: Mapping Self-Organized Criticality onto Criticality

abstract:
  We present a general conceptual framework for self-organized criticality
(SOC), based on the recognition that it is nothing but the expression,
''unfolded'' in a suitable parameter space, of an underlying {\em unstable}
dynamical critical point. More precisely, SOC is shown to result from the
tuning of the {\em order parameter} to a vanishingly small, but {\em positive}
value, thus ensuring that the corresponding control parameter lies exactly at
its critical value for the underlying transition. This clarifies the role and
nature of the {\em very slow driving rate} common to all systems exhibiting
SOC. This mechanism is shown to apply to models of sandpiles, earthquakes,
depinning, fractal growth and forest-fires, which have been proposed as
examples of SOC.


title:
An Evolutionary Approach to Associative Memory in Recurrent Neural
  Networks

abstract:
  In this paper, we investigate the associative memory in recurrent neural
networks, based on the model of evolving neural networks proposed by Nolfi,
Miglino and Parisi. Experimentally developed network has highly asymmetric
synaptic weights and dilute connections, quite different from those of the
Hopfield model. Some results on the effect of learning efficiency on the
evolution are also presented.


title:
Preferential Partner Selection in an Evolutionary Study of Prisoner's
  Dilemma

abstract:
  Partner selection is an important process in many social interactions,
permitting individuals to decrease the risks associated with cooperation. In
large populations, defectors may escape punishment by roving from partner to
partner, but defectors in smaller populations risk social isolation. We
investigate these possibilities for an evolutionary prisoner's dilemma in which
agents use expected payoffs to choose and refuse partners. In comparison to
random or round-robin partner matching, we find that the average payoffs
attained with preferential partner selection tend to be more narrowly confined
to a few isolated payoff regions. Most ecologies evolve to essentially full
cooperative behavior, but when agents are intolerant of defections, or when the
costs of refusal and social isolation are small, we also see the emergence of
wallflower ecologies in which all agents are socially isolated. In between
these two extremes, we see the emergence of ecologies whose agents tend to
engage in a small number of defections followed by cooperation thereafter. The
latter ecologies exhibit a plethora of interesting social interaction patterns.
Keywords: Evolutionary Game; Iterated Prisoner's Dilemma; Partner Choice and
Refusal; Artificial Life; Genetic Algorithm; Finite Automata.


title:
Scaling and singularities in the entrainment of globally-coupled
  oscillators

abstract:
  The onset of collective behavior in a population of globally coupled
oscillators with randomly distributed frequencies is studied for phase
dynamical models with arbitrary coupling. The population is described by a
Fokker-Planck equation for the distribution of phases which includes the
diffusive effect of noise in the oscillator frequencies. The bifurcation from
the phase-incoherent state is analyzed using amplitude equations for the
unstable modes with particular attention to the dependence of the nonlinearly
saturated mode $|\alpha_\infty|$ on the linear growth rate $\gamma$. In general
we find $|\alpha_\infty|\sim \sqrt{\gamma(\gamma+l^2D)}$ where $D$ is the
diffusion coefficient and $l$ is the mode number of the unstable mode. The
unusual $(\gamma+l^2D)$ factor arises from a singularity in the cubic term of
the amplitude equation.


title:
Analyzing Social Network Structures in the Iterated Prisoner's Dilemma
  with Choice and Refusal

abstract:
  The Iterated Prisoner's Dilemma with Choice and Refusal (IPD/CR) is an
extension of the Iterated Prisoner's Dilemma with evolution that allows players
to choose and to refuse their game partners. From individual behaviors,
behavioral population structures emerge. In this report, we examine one
particular IPD/CR environment and document the social network methods used to
identify population behaviors found within this complex adaptive system. In
contrast to the standard homogeneous population of nice cooperators, we have
also found metastable populations of mixed strategies within this environment.
In particular, the social networks of interesting populations and their
evolution are examined.


title:
A set of hard spheres with tangential inelastic collision as a model of
  granular matter: $1/f^\alpha$ fluctuation, non-Gaussian distribution, and
  convective motion

abstract:
  A set of hard spheres with tangential inelastic collision is found to
reproduce observations of real and numerical granular matter. After time is
scaled so as to cancel energy dissipation due to inelastic collisions out,
inelastically colliding hard spheres in two dimensional space come to have
$1/f^\alpha$ fluctuation of total energy, non-Gaussian distribution of
displacement vectors, and convective motion of spheres, which hard spheres with
elastic collision, a conventional model of granular matter, cannot reproduce.


title: A Pinned Polymer Model of Posture Control

abstract:
  A phenomenological model of human posture control is posited. The dynamics
are modelled as an elastically pinned polymer under the influence of noise. The
model accurately reproduces the two-point correlation functions of experimental
posture data and makes predictions for the response function of the postural
control system. The physiological and clinical significance of the model is
discussed.


title: Proportion Regulation in Globally Coupled Nonlinear Systems

abstract:
  As a model of proportion regulation in differentiation process of biological
system, globally coupled activator-inhibitor systems are studied. Formation and
destabilization of one and two cluster state are predicted analytically.
Numerical simulations show that the proportion of units of clusters is chosen
within a finite range and it is selected depend on the initial condition.


title: The Fight Against the Second Law of Thermodynamics

abstract:
  After presenting possible motives for fighting against the second law of
thermodynamics, several attempts to beat this law are analyzed. The second law
wins, but an interesting interpretation of it emerges. This interpretation uses
the notion of ``encoded order'' and claims that whether a system is or is not
in thermodynamic equilibrium depends on the coordinates which the observer
decides to measure. This interpretation may not be new, but most present day
physicists seem to be unaware of it. The question of subjectivity of entropy
and the connection between the present interpretation and ``algorithmic
randomness'' are addressed.
  Key words: Maxwell's demon, perpetuum mobile, subjectivity, entropy,
H-theorem, randomness, complexity, information.


title: Upper Bounds for the Critical Car Densities in Traffic Flow Problems

abstract:
  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.


title: Statistical Theory of Sedimentation of Disordered Suspensions

abstract:
  An analytical treatment for the sedimentation rate of disordered suspensions
is presented in the context of a resistance problem.
  From the calculation it is confirmed that the lubrication effect is important
in contrast to the suggestion by Brady and Durlofsky (Phys.Fluids Vol.31, 717
(1988)). The calculated sedimentation rate agrees well with the experimental
results in all range of the volume fraction.


title: Emergent Traffic Jams

abstract:
  We study a single-lane traffic model that is based on human driving behavior.
The outflow from a traffic jam self-organizes to a critical state of maximum
throughput. Small perturbations of the outflow far downstream create emergent
traffic jams with a power law distribution $P(t) \sim t^{-3/2}$ of lifetimes,
$t$. On varying the vehicle density in a closed system, this critical state
separates lamellar and jammed regimes, and exhibits $1/f$ noise in the power
spectrum. Using random walk arguments, in conjunction with a cascade equation,
we develop a phenomenological theory that predicts the critical exponents for
this transition and explains the self-organizing behavior. These predictions
are consistent with all of our numerical results.


title: Traffic at the Edge of Chaos

abstract:
  We use a very simple description of human driving behavior to simulate
traffic. The regime of maximum vehicle flow in a closed system shows
near-critical behavior, and as a result a sharp decrease of the predictability
of travel time. Since Advanced Traffic Management Systems (ATMSs) tend to drive
larger parts of the transportation system towards this regime of maximum flow,
we argue that in consequence the traffic system as a whole will be driven
closer to criticality, thus making predictions much harder. A simulation of a
simplified transportation network supports our argument.


title: Clustered Volatility in Multiagent Dynamics

abstract:
  Large distributed multiagent systems are characterized by vast numbers of
agents trying to gain access to limited resources in an unpredictable
environment. Agents in these system continuously switch strategies in order to
opportunistically find improvements in their utilities. We have analyzed the
fluctuations around equilibrium that arise from strategy switching and
discovered the existence of a new phenomenon. It consists of the appearance of
sudden bursts of activity that punctuate the fixed point, and is due to an
effective random walk consistent with overall stability. This clustered
volatility is followed by relaxation to the fixed point but with different
strategy mixes from the previous one. This phenomenon is quite general for
systems in which agents explore strategies in search of local improvements.


title:
Self-Organized Critical Models Without Local Particle Conservation Laws
  On Superlattices

abstract:
  We consider simple examples of self-organized critical systems on
  one-dimensional superlattices without local particle conservation laws. The
  set of all recurrence states are also found in these examples using a
  method similar to the burning algorithm.


title: Comment on "Linguistic Features of Noncoding DNA Sequences"

abstract:
  In a recent Physical Review Letter, Mantegna et. al., report that certain
statistical signatures of natural language can be found in non-coding DNA
sequences. In this comment we show that random noise with power-law correlation
similar to $1/f$ noise, exhibits the same "linguistic" signature as those found
in non-coding DNA. We conclude that these signatures cannot distinguish
languages from noise.


title: Strong Ordering by Non-uniformity of Thresholds in a Coupled Map Lattice

abstract:
  The coupled map lattice by Olami {\it et al.} [Phys. Rev. Lett. {\bf 68},
1244 (1992)] is ``doped'' by letting just {\it one} site have a threshold,
$T^{*}_{\rm max}$, bigger than the others. On an $L \times L$ lattice with
periodic boundary conditions this leads to a transition from avalanche sizes of
about one to exactly $L^2$, and after each avalanche stresses distributes among
only five distinct values, $\tau_{k}$, related to the parameters $\alpha $ and
$T^{*}_{\rm max}$ by $\tau_{k}= k\alpha T^{*}_{\rm max}$ where $k=0,1,2,3,4$.
This result is independent of lattice size. The transient times are inversely
proportional to the amount of doping and increase linearly with $L$.


title:
Abundance Distributions in Artificial Life and Stochastic Models: "Age
  and Area" revisited

abstract:
  Using an artificial system of self-replicating strings, we show a correlation
between the age of a genotype and its abundance that reflects a punctuated
rather than gradual picture of evolution, as suggested long ago by Willis. In
support of this correlation, we measure genotype abundance distributions and
find universal coefficients. Finally, we propose a simple stochastic model
which describes the dynamics of equilibrium periods and which correctly
predicts most of the observed distributions.


title: A Theory of Differentiation with Dynamic Clustering

abstract:
  A novel theory for cell differentiation is proposed, based on simulations
with interacting artificial cells which have metabolic networks within, and
divide into two when the final product is accumulated. Results of simulations
with coupled chemical networks and division process lead to the following
scenario of the differentiation: Up to some numbers of cells, divisions bring
about almost identical cells with synchronized metabolic oscillations. As the
number is increased the oscillations lose the synchrony, leading to groups of
cells with different phases of oscillations. At later stage this
differentiation is fixed in time, and cells spilt into groups with different
chemical constituents spontaneously, which are transmitted to daughter cells by
cell divisions. Hierarchical differentiation, origin of stem cells, and
anomalous differentiation by transplantations are also discussed with relevance
to real biological experimental results. (Keywords: differentiation, metabolic
network, cell division, clustering, open chaos)


title:
Evolution of Cooperation, Differentiation, Complexity, and Diversity in
  an Iterated Three-person Game

abstract:
  A non-zero-sum 3-person coalition game is presented, to study the evolution
of complexity and diversity in cooperation, where the population dynamics of
players with strategies is given according to their scores in the iterated game
and mutations. Two types of differentiations emerge initially; biased one to
classes and temporal one to change their roles for coalition. Rules to change
the hands are self-organized in a society through evolution. The co-evolution
of diversity and complexity of strategies and interactions (or communications)
are found at later stages of the simulation. Relevance of our results to the
biological society is briefly discussed.


title: Elements of a Theory of Simulation

abstract:
  Unlike computation or the numerical analysis of differential equations,
simulation does not have a well established conceptual and mathematical
foundation. Simulation is an arguable unique union of modeling and computation.
However, simulation also qualifies as a separate species of system
representation with its own motivations, characteristics, and implications.
This work outlines how simulation can be rooted in mathematics and shows which
properties some of the elements of such a mathematical framework has. The
properties of simulation are described and analyzed in terms of properties of
dynamical systems. It is shown how and why a simulation produces emergent
behavior and why the analysis of the dynamics of the system being simulated
always is an analysis of emergent phenomena. A notion of a universal simulator
and the definition of simulatability is proposed. This allows a description of
conditions under which simulations can distribute update functions over system
components, thereby determining simulatability. The connection between the
notion of simulatability and the notion of computability is defined and the
concepts are distinguished. The basis of practical detection methods for
determining effectively non-simulatable systems in practice is presented. The
conceptual framework is illustrated through examples from molecular
self-assembly end engineering.


title:
Numerical investigation of surface level instability due to tube in
  vibrating bed of powder

abstract:
  Surface level instability when tube is injected into vibrating bed of powder,
which was originally found in experiments, is investigated numerically. We find
that thicker (thiner) tube makes surface level inside tube higher (lower) than
surface level outside tube. With fixed acceleration amplitude of vibration,
surface level inside tube becomes higher as amplitude of vibration increases,
which can be explained by considering the dependence upon strength of
convective flow.


title: Hydrodynamic Description of Granular Convection

abstract:
  We present a hydrodynamic model that captures the essence of granular
dynamics in a vibrating bed. We carry out the linear stability analysis and
uncover the instability mechanism that leads to the appearance of the
convective rolls via a supercritical bifurcation of a bouncing solution. We
also explicitly determine the onset of convection as a function of control
parameters and confirm our picture by numerical simulations of the continuum
equations.


title: Hierarchical Crossover and Probability Landscapes of Genetic Operators

abstract:
  The time evolution of a simple model for crossover is discussed. A variant of
this model with an improved exploration behavior in phase space is derived as a
subset of standard one- and multi-point crossover operations. This model is
solved analytically in the flat fitness case. Numerical simulations compare the
way of phase space exploration of different genetic operators. In the case of a
non-flat fitness landscape, numerical solutions of the evolution equations
point out ways to estimate premature convergence.


title: The Distributed Genetic Algorithm Revisited

abstract:
  This paper extends previous work done by Tanese on the distributed genetic
algorithm (DGA). Tanese found that the DGA outperformed the canonical serial
genetic algorithm (CGA) on a class of difficult, randomly-generated Walsh
polynomials. This left open the question of whether the DGA would have similar
success on functions that were more amenable to optimization by the CGA. In
this work, experiments were done to compare the DGA's performance on the Royal
Road class of fitness functions to that of the CGA. Besides achieving
superlinear speedup on KSR parallel computers, the DGA again outperformed the
CGA on the functions R3 and R4 with regard to the metrics of best fitness,
average fitness, and number of times the optimum was reached. Its performance
on R1 and R2 was comparable to that of the CGA. The effect of varying the DGA's
migration parameters was also investigated. The results of the experiments are
presented and discussed, and suggestions for future research are made.


title: A Statistical Approach to Vehicular Traffic

abstract:
  A two--dimensional cellular automaton is introduced to model the flow and
jamming of vehicular traffic in cities. Each site of the automaton represents a
crossing where a finite number of cars can wait approaching the crossing from
each of the four directions. The flow of cars obeys realistic traffic rules. We
investigate the dependence of the average velocity of cars on the global
traffic density. At a critical threshold for the density the average velocity
reduces drastically caused by jamming. For the low density regime we provide
analytical results which agree with the numerical results.


title:
Evolutionary Dynamics and Optimization: Neutral Networks as
  Model-Landscapes for RNA Secondary-Structure Folding-Landscapes

abstract:
  We view the folding of RNA-sequences as a map that assigns a pattern of base
pairings to each sequence, known as secondary structure. These preimages can be
constructed as random graphs (i.e. the neutral networks associated to the
structure $s$). By interpreting the secondary structure as biological
information we can formulate the so called Error Threshold of Shapes as an
extension of Eigen's et al. concept of an error threshold in the single peak
landscape. Analogue to the approach of Derrida & Peliti for a of the population
on the neutral network. On the one hand this model of a single shape landscape
allows the derivation of analytical results, on the other hand the concept
gives rise to study various scenarios by means of simulations, e.g. the
interaction of two different networks. It turns out that the intersection of
two sets of compatible sequences (with respect to the pair of secondary
structures) plays a key role in the search for ''fitter'' secondary structures.


title:
Exact Results for Spatio-Temporal Correlations in a Self-Organized
  Critical Model of Punctuated Equilibrium

abstract:
  We introduce a self-organized critical model of punctuated equilibrium with
many internal degrees of freedom ($M$) per site. We find exact solutions for
$M\rightarrow \infty$ of cascade equations describing avalanche dynamics in the
steady state. This proves the existence of simple power laws with critical
exponents that verify general scaling relations for nonequilibrium phenomena.
Punctuated equilibrium is described by a Devil's staircase with a
characteristic exponent, $\tau_{FIRST}=2-d/4$ where $d$ is the spatial
dimension.


title: Hydrodynamic effects in density waves of granular flows

abstract:
  Granular flows in a narrow pipe are studied numerically by the model taking
account of hydrodynamic effects of fluid surrounding particles. In the
simulations density waves are observed over the wide range of the Stokes
number, which represents the inertial effect of particles. The mechanisms of
formation of the density waves are considered and two types of density waves,
which are observed in the systems with zero and finite Stokes numbers, are
presented. Power spectra of density waves obtained from the simulations with
non-zero Stokes number show $1/f^\alpha$ power law which is similar to that in
experiments.


title: Ground State Structure in a Highly Disordered Spin Glass Model

abstract:
  We propose a new Ising spin glass model on $Z^d$ of Edwards-Anderson type,
but with highly disordered coupling magnitudes, in which a greedy algorithm for
producing ground states is exact. We find that the procedure for determining
(infinite volume) ground states for this model can be related to invasion
percolation with the number of ground states identified as $2^{\cal N}$, where
${\cal N} = {\cal N}(d)$ is the number of distinct global components in the
``invasion forest''. We prove that ${\cal N}(d) = \infty$ if the invasion
connectivity function is square summable. We argue that the critical dimension
separating ${\cal N} = 1$ and ${\cal N} = \infty$ is $d_c = 8$. When ${\cal
N}(d) = \infty$, we consider free or periodic boundary conditions on cubes of
side length $L$ and show that frustration leads to chaotic $L$ dependence with
{\it all} pairs of ground states occuring as subsequence limits. We briefly
discuss applications of our results to random walk problems on rugged
landscapes.


title:
How birds fly together: Long-range order in a two-dimensional dynamical
  XY model

abstract:
  We propose a non-equilibrium continuum dynamical model for the collective
motion of large groups of biological organisms (e.g., flocks of birds, slime
molds, etc.) Our model becomes highly non-trivial, and different from the
equilibrium model, for $d<d_c=4$; nonetheless, we are able to determine its
scaling exponents {\it exactly} in $d=2$, and show that, unlike equilibrium
systems, our model exhibits a broken continuous symmetry even in $d=2$. Our
model describes a large universality class of microscopic rules, including
those recently simulated by Viscek et. al.

categories: adap-org cond-mat nlin.AO nlin.PS patt-sol


title: Kolmogorov turbulence in a random-force-driven Burgers equation

abstract:
  The dynamics of velocity fluctuations, governed by the one-dimensional
Burgers equation, driven by a white-in-time random force with the spatial
spectrum $\overline{|f(k)|^2}\proptok^{-1}$, is considered. High-resolution
numerical experiments conducted in this work give the energy spectrum
$E(k)\propto k^{-\beta}$ with $\beta =5/3\pm 0.02$. The observed two-point
correlation function $C(k,\omega)$ reveals $\omega\propto k^z$ with the
"dynamical exponent" $z\approx 2/3$. High-order moments of velocity differences
show strong intermittency and are dominated by powerful large-scale shocks. The
results are compared with predictions of the one-loop renormalized perturbation
expansion.


title:
Self-Organization in Models of Populations with Two-Parent Reproduction
  on a Rugged Fitness Landscape

abstract:
  The two-parent reproduction model of Derrida and Peliti is simulated on a
rugged fitness landscape. Fixed fitness values for each possible genotype are
assigned randomly, with all fit individuals having the same probability of
reproduction. The previously observed transition to a self-organized state of
the population with less recombinational load, implies an abrupt change of
genetic overlap distributions, showing up characteristics of a phase
transition. A crossover variant of the model has a smoother transition to the
adapted regime, with a residual collective adaptation for small values of the
threshold in fitness. When a geographical constraint (shortest possible
distance) on pairwise reproduction in a population arranged one-dimensionally
is imposed, a poised state results, suggestive of self-organized criticality.


title: Chromosome mapping: radiation hybrid data and stochastic spin models

abstract:
  This work approaches human chromosome mapping by developing algorithms for
ordering markers associated with radiation hybrid data. Motivated by recent
work of Boehnke et al. [1], we formulate the ordering problem by developing
stochastic spin models to search for minimum-break marker configurations. As a
particular application, the methods developed are applied to 14 human
chromosome-21 markers tested by Cox et al. [2]. The methods generate
configurations consistent with the best found by others. Additionally, we find
that the set of low-lying configurations is described by a Markov-like ordering
probability distribution. The distribution displays cluster correlations
reflecting closely linked loci.


title:
Word Processors with Line-Wrap: Cascading, Self-Organized Criticality,
  Random Walks, Diffusion, Predictability

abstract:
  We examine the line-wrap feature of text processors and show that adding
characters to previously formatted lines leads to the cascading of words to
subsequent lines and forms a state of self-organized criticality. We show the
connection to one-dimensional random walks and diffusion problems, and we
examine the predictability of catastrophic cascades.


title: The Instability of Markets

abstract:
  Recent developments in the global liberalization of equity and currency
markets, coupled to advances in trading technologies, are making markets
increasingly interdependent. This increased fluidity raises questions about the
stability of the international financial system. In this paper, we show that as
couplings between stable markets grow, the likelihood of instabilities is
increased, leading to a loss of general equilibrium as the system becomes
increasingly large and diverse.


title: Pattern Formation and Functionality in Swarm Models

abstract:
  We explore a simplified class of models we call swarms, which are inspired by
the collective behavior of social insects. We perform a mean-field stability
analysis and perform numerical simulations of the model. Several interesting
types of behavior emerge in the vicinity of a second-order phase transition in
the model, including the formation of stable lines of traffic flow, and memory
reconstitution and bootstrapping. In addition to providing an understanding of
certain classes of biological behavior, these models bear a generic resemblance
to a number of pattern formation processes in the physical sciences.


title: Mutation Accumulation and the Catastrophic Senescence of Pacific Salmon

abstract:
  The bit-string model of biological aging is used to simulate the catastrophic
senescence of Pacific Salmon. We have shown that reproduction occuring only
once and at a fixed age is the only ingredient needed to explain the
catastrophic senescence according the mutation accumulation theory. Several
results are presented, some of them with up to $10^8$ fishes, showing how the
survival rates in catastrophic senescence are affected by changes in the
parameters of the model.


title: Long Range Anticorrelations and Non-Gaussian Behavior of a Leaky Faucet

abstract:
  We find that intervals between successive drops from a leaky faucet display
scale-invariant, long-range anticorrelations characterized by the same
exponents of heart beat-to-beat intervals of healthy subjects. This behavior is
also confirmed by numerical simulations on lattice and it is faucet-width- and
flow-rate-independent. The histogram for the drop intervals is also well
described by a L\'evy distribution with the same index for both histograms of
healthy and diseased subjects. This additional result corroborates the evidence
for similarities between leaky faucets and healthy hearts underlying dynamics.


title:
Kolmogorov turbulence in a random-force-driven Burgers equation:
  anomalous scaling and probability density functions

abstract:
  High-resolution numerical experiments, described in this work, show that
velocity fluctuations governed by the one-dimensional Burgers equation driven
by a white-in-time random noise with the spectrum $\overline{|f(k)|^2}\propto
k^{-1}$ exhibit a biscaling behavior: All moments of velocity differences
$S_{n\le 3}(r)=\overline{|u(x+r)-u(x)|^n}\equiv\overline{|\Delta u|^n}\propto
r^{n/3}$, while $S_{n>3}\propto r^{\zeta_n}$ with $\zeta_n\approx 1$ for real
$n>0$ (Chekhlov and Yakhot, Phys. Rev. E {\bf 51}, R2739, 1995). The
probability density function, which is dominated by coherent shocks in the
interval $\Delta u<0$, is ${\cal P}(\Delta u,r)\propto (\Delta u)^{-q}$ with
$q\approx 4$.


title:
Dynamic Entropies, Long--Range Correlations and Fluctuations in Complex
  Linear Structures

abstract:
  We investigate symbolic sequences and in particular information carriers as
e.g. books and DNA--strings. First the higher order Shannon entropies are
calculated, a characteristic root law is detected. Then the algorithmic entropy
is estimated by using Lempel--Ziv compression algorithms. In the third section
the correlation function for distant letters, the low frequency Fourier
spectrum and the characteristic scaling exponents are calculated. We show that
all these measures are able to detect long--range correlations. However, as
demonstrated by shuffling experiments, different measures operate on different
length scales. The longest correlations found in our analysis comprise a few
hundreds or thousands of letters and may be understood as long--wave
fluctuations of the composition.


title:
Evolving Neural Networks with Iterative Learning Scheme for Associative
  Memory

abstract:
  A locally iterative learning (LIL) rule is adapted to a model of the
associative memory based on the evolving recurrent-type neural networks
composed of growing neurons. There exist extremely different scale parameters
of time, the individual learning time and the generation in evolution. This
model allows us definite investigation on the interaction between learning and
evolution. And the reinforcement of the robustness against the noise is also
achieved in the evolutional scheme.


title: Onsager reciprocity relations without microscopic reversibility

abstract:
  In this paper we show that Onsager--Machlup time reversal properties of
thermodynamic fluctuations and Onsager reciprocity relations for transport
coefficients can hold also if the microscopic dynamics is not reversible. This
result is based on the explicit construction of a class of conservative models
which can be analysed rigorously.


title: Molecular dynamics of arbitrarily shaped granular particles}

abstract:
  We propose a new model for the description of complex granular particles and
their interaction in molecular dynamics simulations of granular material in two
dimensions. The grains are composed of triangles which are connected by
deformable beams. Particles are allowed to be convex or concave. We present
first results of simulations using this particle model.


title: A model for evolution and extinction

abstract:
  We present a model for evolution and extinction in large ecosystems. The
model incorporates the effects of interactions between species and the
influences of abiotic environmental factors. We study the properties of the
model by approximate analytic solution and also by numerical simulation, and
use it to make predictions about the distribution of extinctions and species
lifetimes that we would expect to see in real ecosystems. It should be possible
to test these predictions against the fossil record. The model indicates that a
possible mechanism for mass extinction is the coincidence of a large
coevolutionary avalanche in the ecosystem with a severe environmental
disturbance.


title:
Smoothing representation of fitness landscapes - the genotype-phenotype
  map of evolution

abstract:
  We investigate an simple evolutionary game of sequences and demonstrate on
this example the structure of fitness landscapes in discrete problems. We show
the smoothing action of the genotype-phenotype mapping which still makes it
feasible for evolution to work. Further we propose the density of sequence
states as a classifying measure of fitness landscapes.


title:
Analytic Investigations of Random Search Strategies for Parameter
  Optimization

abstract:
  Several standard processes for searching minima of potential functions, such
as thermodynamical strategies (simulated annealing) and biologically motivated
selfreproduction strategies, are reduced to Schr\"odinger problems. The
properties of the landscape are encoded in the spectrum of the Hamiltonian. We
investigate this relation between landscape and spectrum by means of
topological methods which lead to a possible classification of landscapes in
the framework of the operator theory. The influence of the dimension $d$ of the
search space is discussed. The connection between thermodynamical strategies
and biologically motivated selfreproduction strategies is analyzed and
interpreted in the above context. Mixing of both strategies is introduced as a
new powerful tool of optimization.


title: Ergodic Properties of the Spin - Boson System

abstract:
  We investigate the dynamics of a 2-level atom (or spin-1/2) coupled to a
mass-less bosonic field at positive temperature. We prove that, at small
coupling, the combined quantum system approaches thermal equilibrium. Moreover
we establish that this approach is exponentially fast in time. We first reduce
the question to a spectral problem for the Liouvillean, a self-adjoint operator
naturally associated with the system. To compute this operator, we invoke
Tomita-Takesaki theory. Once this is done we use complex deformation techniques
to study its spectrum. The corresponding zero temperature model is also
reviewed and compared.


title:
Reproducible noise in a macroscopic system: magnetic avalanches in
  Perminvar

abstract:
  A study of magnetic avalanches in Perminvar, an Fe-Ni-Co alloy, shows that
some avalanches are almost exactly reproducible from one magnetic field cycle
to the next, while others show significant variability. Averaging over many
cycles produces a fingerprint reflecting the reproducibility of the noise. The
fingerprint is not strongly temperature or driving-rate dependent, indicating
that the variability is a consequence of dynamical effects. We also find that
the slope of the cycle-averaged magnetization, d<M>/dH, is correlated with the
cycle-to-cycle variations in magnetization, suggesting an analogy with the
fluctuation-dissipation relationship from equilibrium thermodynamics.


title: Non-Mean-Field Behavior of Realistic Spin Glasses

abstract:
  We provide rigorous proofs which show that the main features of the Parisi
solution of the Sherrington-Kirkpatrick spin glass are not valid for more
realistic spin glass models in any dimension and at any temperature.


title: Scalings of Pitches in Music

abstract:
  We investigate correlations among pitches in several songs and pieces of
piano music by mapping them to one-dimensional walks. Two kinds of correlations
are studied, one is related to the real values of frequencies while they are
treated only as different symbols for another. Long-range power law behavior is
found in both kinds. The first is more meaningful. The structure of music, such
as beat, measure and stanza, are reflected in the change of scaling exponents.
Some interesting features are observed. Our results demonstrate the viewpoint
that the fundamental principle of music is the balance between repetition and
contrast.


title: Exact Results of the Bit-String Model for Catastrophic Senescence

abstract:
  We succeeded in obtaining exact results of the bit-string model of biological
aging for populations whose individuals breed only once. These results are in
excellent agreement with those obtained through computer simulations. In
addition, we obtain an expression for the minimum birth needed to avoid
mutational meltdown.


title:
Self-organization, ergodicity breaking, phase transition and
  synchronization in two-dimensional traffic-flow model

abstract:
  Analytical investigation is made on the two-dimensional traffic-flow model
with alternative movement and exclude-volume effect between right and up arrows
[Phys. Rev. {\bf A} 46 R6124 (1992)]. Several exact results are obtained,
including the upper critical density above which there are only jamming
configurations, and the lower critical density below which there are only
moving configurations. The observed jamming transition takes place at another
critical density $p_{c}(N)$, which is in the intermidiate region between the
lower and upper critical densities. It is derived that
$p_{c}(N)\,=\,CN^{\alpha}$, where $C$ and $\alpha$ are determined to be
respectively $0.76$ and $-0.14$ from previous numerical simulation. This
transition is suggested to be a second-order phase transition, the order
parameter is found. The nature of self-organization, ergodicity breaking and
synchronization are discussed, Comparison with the sandpile model is made.


title:
Mean Switching Frequency Locking in Stochastic Bistable Systems Driven
  by Periodical Force

abstract:
  The nonlinear response of noisy bistable systems driven by strong amplitude
periodical force is investigated by physical experiment. The new phenomenon of
locking of the mean switching frequency between states of bistable system is
found. It is shown that there is an interval of noise intensities in which the
mean switching frequency remains constant and coincides with the frequency of
external periodic force. The region on the parameter plane ``noise intensity -
amplitude of periodic excitation'' which corresponds to this phenomenon is
similar to the synchronization (phase-locking) region (Arnold's tongue) in
classical oscillatory systems.


title: Avalanche Dynamics in Evolution, Growth, and Depinning Models

abstract:
  The dynamics of complex systems in nature often occurs in terms of
punctuations, or avalanches, rather than following a smooth, gradual path. A
comprehensive theory of avalanche dynamics in models of growth, interface
depinning, and evolution is presented. Specifically, we include the Bak-Sneppen
evolution model, the Sneppen interface depinning model, the Zaitsev flux creep
model, invasion percolation, and several other depinning models into a unified
treatment encompassing a large class of far from equilibrium processes. The
formation of fractal structures, the appearance of $1/f$ noise, diffusion with
anomalous Hurst exponents, Levy flights, and punctuated equilibria can all be
related to the same underlying avalanche dynamics. This dynamics can be
represented as a fractal in $d$ spatial plus one temporal dimension. We develop
a scaling theory that relates many of the critical exponents in this broad
category of extremal models, representing different universality classes, to
two basic exponents characterizing the fractal attractor. The exact equations
and the derived set of scaling relations are consistent with numerical
simulations of the above mentioned models.


title: Spatial Inhomogeneity and Thermodynamic Chaos

abstract:
  We present a coherent approach to the competition between thermodynamic
states in spatially inhomogeneous systems, such as the Edwards-Anderson spin
glass with a fixed coupling realization. This approach explains and relates
chaotic size dependence, ``dispersal of the metastate'', and for replicas:
non-independence, symmetry breaking, and overlap (non-)self-averaging.


title: Octonionic binocular mobilevision. An overview

abstract:
  This paper is a compact overview of the heuristic approach to the recently
elaborated octonionic binocular mobilevision.


title:
Reconstruction of a first-order phase transition from computer
  simulations of individual phases and subphases

abstract:
  We present a new method for investigating first-order phase transitions using
Monte Carlo simulations. It relies on the multiple-histogram method and uses
solely histograms of individual phases. In addition, we extend the method to
include histograms of subphases. The free energy difference between phases,
necessary for attributing the correct statistical weights to the histograms, is
determined by a detour in control parameter space via auxiliary systems with
short relaxation times. We apply this method to a recently introduced model for
structure formation in polypeptides for which other methods fail.


title: Dynamical Model for Virus Spread

abstract:
  The steady state properties of the mean density population of infected cells
in a viral spread is simulated by a general forest fire like cellular automaton
model with two distinct populations of cells ( permissive and resistant ones)
and studied in the framework of the mean field approximation. Stochastic
dynamical ingredients are introduced in this model to mimic cells regeneration
(with probability {\it p}) and to consider infection processes by other means
than contiguity (with probability {\it f}). Simulations are carried on a $L
\times L$ square lattice considering the eigth first neighbors. The mean
density population of infected cells ($D_i$) is measured as function of the
regeneration probability {\it p}, and analized for small values of the ratio
{\it f/p } and for distinct degrees of the cell resistance. The results
obtained by a mean field like approach recovers the simulations results. The
role of the resistant parameter $R$ ($R \geq 2)$ on the steady state properties
is investigated and discussed in comparision with the $R=1$ monocell case which
corresponds to the {\em self organized critical} forest fire model. The fractal
dimension of the dead cells ulcers contours were also estimated and analised as
function of the model parameters.


title: Scaling and universality in binary fragmenting with inhibition

abstract:
  We investigate a new model of binary fragmentation with inhibition, driven by
the white noise. In a broad range of fragmentation probabilities, the power-law
spatiotemporal correlations are found to arise due to self-organized
criticality (SOC). We find in the SOC phase a non-trivial power spectrum of the
temporal sequence of the fragmentation events. The $1/f$~ behaviour is
recovered in the irreversible, near-equilibrium part of this phase.


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

abstract:
  In the paper by J.\L uczka {\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).


title:
A Geometric Formulation of Occam's Razor for Inference of Parametric
  Distributions

abstract:
  I define a natural measure of the complexity of a parametric distribution
relative to a given true distribution called the {\it razor} of a model family.
The Minimum Description Length principle (MDL) and Bayesian inference are shown
to give empirical approximations of the razor via an analysis that
significantly extends existing results on the asymptotics of Bayesian model
selection. I treat parametric families as manifolds embedded in the space of
distributions and derive a canonical metric and a measure on the parameter
manifold by appealing to the classical theory of hypothesis testing. I find
that the Fisher information is the natural measure of distance, and give a
novel justification for a choice of Jeffreys prior for Bayesian inference. The
results of this paper suggest corrections to MDL that can be important for
model selection with a small amount of data. These corrections are interpreted
as natural measures of the simplicity of a model family. I show that in a
certain sense the logarithm of the Bayesian posterior converges to the
logarithm of the {\it razor} of a model family as defined here. Close
connections with known results on density estimation and ``information
geometry'' are discussed as they arise.


title: Self-organized criticality and the lattice topology

abstract:
  We examine exhaustively the behavior of avalanches in critical height
sandpile models based in two- and three-dimensional lattices of various
topologies. We get that for two-dimensional lattices the spatial and temporal
distributions characterizing bulk avalanches do not depend on the lattice
topology. For the three-dimensional case, we detect a small dependence of the
topology for the temporal distribution, while the spatial ones are independent.
The two-dimensional lattices studied are: the plane ($R^2$), the cylinder
($S^1\times R$), and the M\"obius-strip ($M$); and the three-dimensional are:
$R^3$, $S^1\times R^2$, $S^1\times S^1\times R$, $M\times R$, $S^2\times R$,
$K\times R$, and $RP\times R$, where $K$ and $RP$ are respectively the Klein
bottle and the real projective plane.


title: Infinite Hierarchy of Exact Equations in the Bak-Sneppen Model

abstract:
  We derive an infinite hierarchy of exact equations for the Bak-Sneppen model
in arbitrary dimensions. These equations relate different moments of temporal
duration and spatial size of avalanches. We prove that the exponents of the BS
model are the same above and below the critical point and express the universal
amplitude ratio of the avalanche spatial size in terms of the critical
exponents. The equations uniquely determine the shape of the scaling function
of the avalanche distribution. It is suggested that in the BS model there is
only one independent critical exponent.

categories: adap-org cond-mat nlin.AO nlin.SI solv-int


title: Self-Organized Critical Directed Percolation

abstract:
  We introduce and study a dynamic transport model exhibiting Self-Organized
Criticality. The novel concepts of our model are the probabilistic propagation
of activity and unbiased random repartition of energy among the active site and
its nearest neighbors. For space dimensionality $d\geq 2$ we argue that the
model is related to $d+1$ dimensional directed percolation, with time
interpreted as the preferred direction.


title: Phase Structure of Systems with Multiplicative Noise

abstract:
  The phase diagrams and transitions of nonequilibrium systems with
multiplicative noise are studied theoretically. We show the existence of both
strong and weak-coupling critical behavior, of two distinct active phases, and
of a nonzero range of parameter values over which the susceptibility is
infinite in any dimension. A scaling theory of the strong-coupling transition
is constructed.


title:
Response to Parisi's Comment on ``Non-mean-field behavior of realistic
  spin glasses''

abstract:
  We expand on why our recent results rule out the standard SK picture of
realistic spin glasses.


title: Learning from Minimum Entropy Queries in a Large Committee Machine

abstract:
  In supervised learning, the redundancy contained in random examples can be
avoided by learning from queries. Using statistical mechanics, we study
learning from minimum entropy queries in a large tree-committee machine. The
generalization error decreases exponentially with the number of training
examples, providing a significant improvement over the algebraic decay for
random examples. The connection between entropy and generalization error in
multi-layer networks is discussed, and a computationally cheap algorithm for
constructing queries is suggested and analysed.


title:
Comment on `Avalanche Dynamics in Evolution, Growth and Depinning
  Models'

abstract: This paper is withdrawn.


title: Propagation of Information in Populations of Self-Replicating Code

abstract:
  We observe the propagation of information in a system of self-replicating
strings of code (``Artificial Life'') as a function of fitness and mutation
rate. Comparison with theoretical predictions based on the reaction-diffusion
equation shows that the response of the artificial system to fluctuations (\eg
velocity of the information wave as a function of relative fitness) closely
follows that of natural systems. We find that the relaxation time of the system
depends on the speed of propagation of information and the size of the system.
This analysis offers the possibility of determining the minimal system size for
observation of non-equilibrium effects at fixed mutation rate.


title: Physical Complexity of Symbolic Sequences

abstract:
  A practical measure for the complexity of sequences of symbols (``strings'')
is introduced that is rooted in automata theory but avoids the problems of
Kolmogorov-Chaitin complexity. This physical complexity can be estimated for
ensembles of sequences, for which it reverts to the difference between the
maximal entropy of the ensemble and the actual entropy given the specific
environment within which the sequence is to be interpreted. Thus, the physical
complexity measures the amount of information about the environment that is
coded in the sequence, and is conditional on such an environment. In practice,
an estimate of the complexity of a string can be obtained by counting the
number of loci per string that are fixed in the ensemble, while the volatile
positions represent, again with respect to the environment, randomness. We
apply this measure to tRNA sequence data.

categories: adap-org cond-mat.stat-mech nlin.AO physics.data-an q-bio.GN


title:
Two-dimensional cellular automaton model of traffic flow with open
  boundaries

abstract:
  A two-dimensional cellular automaton model of traffic flow with open
boundaries are investigated by computer simulations. The outflow of cars from
the system and the average velocity are investigated. The time sequences of the
outflow and average velocity have flicker noises in a jamming phase. The low
density behavior are discussed with simple jam-free approximation.


title: Isologous Diversification: A Theory of Cell Differentiation

abstract:
  Isologous diversification theory for cell differentiation is proposed, based
on simulations of interacting cells with biochemical networks and cell division
process following consumption of some chemicals. According to the simulations
of the interaction-based dynamical systems model, the following scenario of the
cell differentiation is proposed. (1) Up to some threshold number, divisions
bring about almost identical cells with synchronized biochemical oscillations.
(2)As the number is increased the oscillations lose the synchrony, leading to
groups of cells with different phases of oscillations. (3)Amplitudes of
oscillation and averaged chemical compositions start to differ by groups of
cells. The differentiated behavior of states is transmitted to daughter cells.
(4)Recursivity is formed so that the daughter cells keep the identical chemical
character. This ``memory" is made possible through the transfer of initial
conditions. (5) Successive differentiation proceeds. Mechanism of tumor cell
formation, origin of stem cells, anomalous differentiation by transplantations,
apoptosis and other features of cell differentiation process are also
discussed, with some novel predictions. (Keywords: differentiation, chemical
network, cell division, clustering, open chaos)


title: Self-Annealing Dynamics in a Multistable System

abstract:
  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.


title: Coupled Maps with Growth and Death: An Approach to Cell Differentiation

abstract:
  An extension of coupled maps is given which allows for the growth of the
number of elements, and is inspired by the cell differentiation problem. The
growth of elements is made possible first by clustering the phases, and then by
differentiating roles. The former leads to the time sharing of resources, while
the latter leads to the separation of roles for the growth. The mechanism of
the differentiation of elements is studied. An extension to a model with
several internal phase variables is given, which shows differentiation of
internal states. The relevance of interacting dynamics with internal states
(``intra-inter" dynamics) to biological problems is discussed with an emphasis
on heterogeneity by clustering, macroscopic robustness by partial
synchronization and recursivity with the selection of initial conditions and
digitalization.


title:
Effect of time-correlation of input patterns on the convergence of
  on-line learning

abstract:
  We studied the effects of time correlation of subsequent patterns on the
convergence of on-line learning by a feedforward neural network with
backpropagation algorithm. By using chaotic time series as sequences of
correlated patterns, we found that the unexpected scaling of converging time
with learning parameter emerges when time-correlated patterns accelerate
learning process.


title: Power Laws are Logarithmic Boltzmann Laws

abstract:
  Multiplicative random processes in (not necessaryly equilibrium or steady
state) stochastic systems with many degrees of freedom lead to Boltzmann
distributions when the dynamics is expressed in terms of the logarithm of the
normalized elementary variables. In terms of the original variables this gives
a power-law distribution. This mechanism implies certain relations between the
constraints of the system, the power of the distribution and the dispersion law
of the fluctuations. These predictions are validated by Monte Carlo simulations
and experimental data. We speculate that stochastic multiplicative dynamics
might be the natural origin for the emergence of criticality and scale
hierarchies without fine-tuning.


title: Self-organized criticality, evolution and the fossil extinction record

abstract:
  Statistical analysis indicates that the fossil extinction record is
compatible with a distribution of extinction events whose frequency is related
to their size by a power law with an exponent close to two. This result is in
agreement with predictions based on self-organized critical models of
extinction, and might well be taken as evidence of critical behaviour in
terrestrial evolution. We argue however that there is a much simpler
explanation for the appearance of a power law in terms of extinctions caused by
stresses (either biotic or abiotic) to which species are subjected by their
environment. We give an explicit model of this process and discuss its
properties and implications for the interpretation of the fossil record.


title:
Flame front propagation II: Random Noise and Pole-Dynamics in Unstable
  Front Propagation

abstract:
  The problem of flame propagation is studied as an example of unstable fronts
that wrinkle on many scales is studied. The analytic tool of pole expansion in
the complex plane is emloyed to address the interaction of the unstable growth
process with random initial conditions and perturbations.
  We argue that the effect of random noise is immense and that it can never be
neglected in sufficiently large systems. We present simulations that lead to
scaling laws for the velocity and acceleration of the front as a function of
the system size and the level of noise, and analytic arguments that explain
these results in terms of the noisy pole dynamics.


title:
Systems with Multiplicative Noise: Critical Behavior from KPZ Equation
  and Numerics

abstract:
  We show that certain critical exponents of systems with multiplicative noise
can be obtained from exponents of the KPZ equation. Numerical simulations in 1d
confirm this prediction, and yield other exponents of the multiplicative noise
problem. The numerics also verify an earlier prediction of the divergence of
the susceptibility over an entire range of control parameter values, and show
that the exponent governing the divergence in this range varies continuously
with control parameter.


title: A Simple Learning Algorithm for the Traveling Salesman Problem

abstract:
  We propose a learning algorithm for solving the traveling salesman problem
based on a simple strategy of trial and adaptation: i) A tour is selected by
choosing cities probabilistically according to the ``synaptic'' strengths
between cities. ii) The ``synaptic'' strengths of the links that form the tour
are then enhanced (reduced) if the tour length is shorter (longer) than the
average result of the previous trials. We perform extensive simulations of the
random distance traveling-salesman problem. For sufficiently slow learning
rates, near optimal tours can be obtained with the average optimal tour lengths
close to the lower bounds for the shortest tour lengths.


title: Ecological model of extinctions

abstract:
  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.


title: Spontaneous Scaling Emergence in Generic Stochastic Systems

abstract:
  We extend a generic class of systems which have previously been shown to
spontaneously develop scaling (power law) distributions of their elementary
degrees of freedom.
  While the previous systems were linear and exploded exponentially for certain
parameter ranges, the new systems fulfill nonlinear time evolution equations
similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics
and evolve spontaneously towards "fixed trajectories" indexed by the average
value of their degrees of freedom (which corresponds to the SSB order
parameter). The "fixed trajectories" dynamics evolves on the edge between
explosion and collapse/extinction.
  The systems present power laws with exponents which in a wide range ($\alpha
< -2.$) are universally determined by the ratio between the minimal and the
average values of the degrees of freedom. The time fluctuations are governed by
Levy distributions of corresponding power. For exponents $\alpha > -2$ there is
no "thermodynamic limit" and the fluctuations are dominated by a few, largest
degrees of freedom which leads to macroscopic fluctuations, chaos and
bursts/intermitency.


title:
Symmetry Breaking and Adaptation: The Genetic Code of Retroviral Env
  Proteins

abstract:
  Although several synonymous codons can encode the same aminoacid, this
symmetry is generally broken in natural genetic systems. In this article, we
show that the symmetry breaking can result from selective pressures due to the
violation of the synonym symmetry by mutation and recombination. We conjecture
that this enhances the probability to produce mutants that are well-adapted to
the current environment. Evidence is found in the codon frequencies of the HIV
{\it env} protein: the codons most likely to mutate and lead to new viruses
resistant to the current immunological attack, are found with a greater
frequency than their less mutable synonyms.


title: Emergent spatial correlations in stochastically evolving populations

abstract:
  We study the spatial pattern formation and emerging long range correlations
in a model of three species coevolving in space and time according to
stochastic contact rules. Analytical results for the pair correlation
functions, based on a truncation approximation and supported by computer
simulations, reveal emergent strategies of survival for minority agents based
on selection of patterns. Minority agents exhibit defensive clustering and
cooperative behavior close to phase transitions.


title:
Spontaneous Origin of Topological Complexity in Self-Organizing Neural
  Networks

abstract:
  Attention is drawn to the possibility that self-organizing biological neural
networks could spontaneously acquire the capability to carry out sophisticated
computations. In particular it is shown that the effective action governing the
formation of synaptic connections in models of networks of feature detectors
that encorporate Kohonen-like self-organization can spontaneously lead to
structures that are topologically nontrivial in both a 2-dimensional and
4-dimensional sense. It is suggested that the appearance of biological neural
structures with a nontrivial 4-dimensional topology is the fundamental
organizational principle underlying the emergence of advanced cognitive
capabilities.


title:
Stability of periodic solutions in series arrays of Josephson junctions
  with internal Capacitance

abstract:
  A mystery surrounds the stability properties of the splay-phase periodic
solutions to a series array of N Josephson junction oscillators. Contrary to
what one would expect from dynamical systems theory, the splay state appears to
be neutrally stable for a wide range of system parameters. It has been
explained why the splay state must be neutrally stable when the
Stewart-McCumber parameter beta is zero. In this paper we complete the
explanation of the apparent neutral stability; we show that the splay state is
typically hyperbolic -- either asymptotically stable or unstable -- when beta >
0. We conclude that there is only a single unit Floquet multiplier, based on
accurate and systematic computations of the Floquet multipliers for beta
ranging from 0 to 10. However, N-2 multipliers are extremely close to 1 for
beta larger than about 1. In addition, two more Floquet multipliers approach 1
as beta becomes large. We visualize the global dynamics responsible for these
nearly degenerate multipliers, and then estimate them accurately by a multiple
time-scale analysis. For N=4 junctions the analysis also predicts that the
system converges toward either the in-phase state, the splay state, or two
clusters of two oscillators, depending on the parameters.


title:
Spontaneous symmetry breaking and the formation of columnar structures
  in the primary visual cortex II --- Local organization of orientation modules

abstract:
  Self-organization of orientation-wheels observed in the visual cortex is
discussed from the view point of topology. We argue in a generalized model of
Kohonen's feature mappings that the existence of the orientation-wheels is a
consequence of Riemann-Hurwitz formula from topology. In the same line, we
estimate partition function of the model, and show that regardless of the total
number N of the orientation-modules per hypercolumn the modules are
self-organized, without fine-tuning of parameters, into definite number of
orientation-wheels per hypercolumn if N is large.