title: A model of macroevolution with a natural system size

abstract:
  We describe a simple model of evolution which incorporates the branching and
extinction of species lines, and also includes abiotic influences. A first
principles approach is taken in which the probability for speciation and
extinction are defined purely in terms of the fitness landscapes of each
species. Numerical simulations show that the total diversity fluctuates around
a natural system size $N_{\rm nat}$ which only weakly depends upon the number
of connections per species. This is in agreement with known data for real
multispecies communities. The numerical results are confirmed by approximate
mean field analysis.

categories: adap-org cond-mat.stat-mech nlin.AO q-bio


title:
Renormalization group of probabilistic cellular automata with one
  absorbing state

abstract:
  We apply a recently proposed dynamically driven renormalization group scheme
to probabilistic cellular automata having one absorbing state. We have found
just one unstable fixed point with one relevant direction. In the limit of
small transition probability one of the cellular automata reduces to the
contact process revealing that the cellular automata are in the same
universality class as that process, as expected. Better numerical results are
obtained as the approximations for the stationary distribution are improved.


title: Analysis of the Effective Degrees of Freedom in Genetic Algorithms

abstract:
  An evolution equation for a population of strings evolving under the genetic
operators: selection, mutation and crossover is derived. The corresponding
equation describing the evolution of schematas is found by performing an exact
coarse graining of this equation. In particular exact expressions for schemata
reconstruction are derived which allows for a critical appraisal of the
``building-block hypothesis'' of genetic algorithms. A further coarse-graining
is made by considering the contribution of all length-l schematas to the
evolution of population observables such as fitness growth. As a test function
for investigating the emergence of structure in the evolution the increase per
generation of the in-schemata fitness averaged over all schematas of length l,
$\Delta_l$, is introduced. In finding solutions of the evolution equations we
concentrate more on the effects of crossover, in particular we consider
crossover in the context of Kauffman Nk models with k=0,2. For k=0, with a
random initial population, in the first step of evolution the contribution from
schemata reconstruction is equal to that of schemata destruction leading to a
scale invariant situation where the contribution to fitness of schematas of
size l is independent of l. This balance is broken in the next step of
evolution leading to a situation where schematas that are either much larger or
much smaller than half the string size dominate over those with $l \approx
N/2$. The balance between block destruction and reconstruction is also broken
in a k>0 landscape. It is conjectured that the effective degrees of freedom for
such landscapes are landscape connective trees that break down into effectively
fit smaller blocks, and not the blocks themselves. Numerical simulations
confirm this ``connective tree hypothesis'' by showing that correlations drop
off with connective distance and not with intrachromosomal distance.


title: The selection of altruistic behaviour

abstract:
  Altruistic behaviour is disadvantageous for the individual while is
advantageous for its group. If the target of the selection is the individual,
one would expect the selection process to lead to populations formed by wholly
homogeneous groups, made up of either altruistic or egoistic individuals, where
the winning choice depends on the balance beetwen group advantage and
individual disadvantage. We show in a simple model that populations formed by
inhomogeneous groups can be stabilized in some circumstances. We argue that
this condition is realized when there is a relative advantage conferred by the
presence of a few altruists to all the members of the group.


title: Dynamical Equilibrium of Interacting Ant Societies

abstract:
  The sustainable biodiversity associated with a specific ecological niche as a
function of land area is analysed computationally by considering the
interaction of ant societies over a collection of islands. A power law
relationship between sustainable species and land area is observed. We will
further consider the effect a perturbative inflow of ants has upon the model.


title: Coevolution of Symbiotic Species

abstract:
  This paper will consider the coevolution of species which are symbiotic in
their interaction. In particular, we shall analyse the interaction of squirrels
and oak trees, and develop a mathematical framework for determining the
coevolutionary equilibrium for consumption and production patterns.


title: Quasi-Linear Cellular Automata

abstract:
  Simulating a cellular automaton (CA) for t time-steps into the future
requires t^2 serial computation steps or t parallel ones. However, certain CAs
based on an Abelian group, such as addition mod 2, are termed ``linear''
because they obey a principle of superposition. This allows them to be
predicted efficiently, in serial time O(t) or O(log t) in parallel.
  In this paper, we generalize this by looking at CAs with a variety of
algebraic structures, including quasigroups, non-Abelian groups, Steiner
systems, and others. We show that in many cases, an efficient algorithm exists
even though these CAs are not linear in the previous sense; we term them
``quasilinear.'' We find examples which can be predicted in serial time
proportional to t, t log t, t log^2 t, and t^a for a < 2, and parallel time log
t, log t log log t and log^2 t.
  We also discuss what algebraic properties are required or implied by the
existence of scaling relations and principles of superposition, and exhibit
several novel ``vector-valued'' CAs.


title: Comment on "Self-organized criticality in living systems" by C. Adami

abstract:
  Following extensive numerical experiments, it has been suggested that the
evolution of competing computer programs in artificial life simulations shows
signs of being a self-organized critical process. The primary evidence for this
claim comes from the distribution of the lifetimes of species in the
simulations, which appears to follow a power law. We argue that, for a number
of reasons, it is unlikely that the system is in fact at a critical point and
suggest an alternative explanation for the power-law lifetime distribution.


title: Evolution on a Rugged Landscape:Pinning and Aging

abstract:
  Population dynamics on a rugged landscape is studied analytically and
numerically within a simple discrete model for evolution of N individuals in
one-dimensional fitness space. We reduce the set of master equations to a
single Fokker-Plank equation which allows us to describe the dynamics of the
population in terms of thermo-activated Langevin diffusion of a single particle
in a specific random potential. We found that the randomness in the mutation
rate leads to pinning of the population and on average to a logarithmic
slowdown of the evolution, resembling aging phenomenon in spin glass systems.
In contrast, the randomness in the replication rate turns out to be irrelevant
for evolution in the long-time limit as it is smoothed out by increasing
``evolution temperature''. The analytic results are in a good agreement with
numerical simulations.


title: A model of mass extinction

abstract:
  A number of authors have in recent years proposed that the processes of
macroevolution may give rise to self-organized critical phenomena which could
have a significant effect on the dynamics of ecosystems. In particular it has
been suggested that mass extinction may arise through a purely biotic mechanism
as the result of so-called coevolutionary avalanches. In this paper we first
explore the empirical evidence which has been put forward in favor of this
conclusion. The data center principally around the existence of power-law
functional forms in the distribution of the sizes of extinction events and
other quantities. We then propose a new mathematical model of mass extinction
which does not rely on coevolutionary effects and in which extinction is caused
entirely by the action of environmental stresses on species. In combination
with a simple model of species adaptation we show that this process can account
for all the observed data without the need to invoke coevolution and critical
processes. The model also makes some independent predictions, such as the
existence of ``aftershock'' extinctions in the aftermath of large mass
extinction events, which should in theory be testable against the fossil
record.


title: Mass Extinction in a Simple Mathematical Biological Model

abstract:
  Introducing the effect of extinction into the so-called replicator equations
in mathematical biology, we construct a general model of ecosystems. The
present model shows mass extinction by its own extinction dynamics when the
system initially has a large number of species ( diversity). The extinction
dynamics shows several significant features such as a power law in basin size
distribution, induction time, etc. The present theory can be a mathematical
foundation of the species-area effect in the paleontologic theory for mass
extinction.


title:
Car accidents and number of stopped cars due to road blockage on a
  one-lane highway

abstract:
  Within the framework of a simple model of car traffic on a one-lane highway,
we study the probability for car accidents to occur when drivers do not respect
the safety distance between cars, and, as a result of the blockage during the
time $T$ necessary to clear the road, we determine the number of stopped cars
as a function of car density. We give a simple theory in good agreement with
our numerical simulations.


title: Cellular Automata Models for Diffusion of Innovations

abstract:
  We propose a probabilistic cellular automata model for the spread of
innovations, rumors, news, etc. in a social system. The local rule used in the
model is outertotalistic, and the range of interaction can vary. When the range
R of the rule increases, the takeover time for innovation increases and
converges toward its mean-field value, which is almost inversely proportional
to R when R is large. Exact solutions for R=1 and $R=\infty$ (mean-field) are
presented, as well as simulation results for other values of R. The average
local density is found to converge to a certain stationary value, which allows
us to obtain a semi-phenomenological solution valid in the vicinity of the
fixed point n=1 (for large t).


title: The Study of Correlation Structures of DNA Sequences: A Critical Review

abstract:
  The study of correlation structure in the primary sequences of DNA is
reviewed. The issues reviewed include: symmetries among 16 base-base
correlation functions, accurate estimation of correlation measures, the
relationship between $1/f$ and Lorentzian spectra, heterogeneity in DNA
sequences, different modeling strategies of the correlation structure of DNA
sequences, the difference of correlation structure between coding and
non-coding regions (besides the period-3 pattern), and source of broad
distribution of domain sizes. Although some of the results remain
controversial, a body of work on this topic constitutes a good starting point
for future studies.


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

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


title: Autonomous Traffic Signal Control Model with Neural Network Analogy

abstract:
  We propose here an autonomous traffic signal control model based on analogy
with neural networks. In this model, the length of cycle time period of traffic
lights at each signal is autonomously adapted. We find a self-organizing
collective behavior of such a model through simulation on a one-dimensional
lattice model road: traffic congestion is greatly diffused when traffic signals
have such autonomous adaptability with suitably tuned parameters. We also find
that effectiveness of the system emerges through interactions between units and
shows a threshold transition as a function of proportion of adaptive signals in
the model.


title:
Individual Adaption in a Path-Based Simulation of the Freeway Network of
  Northrhine-Westfalia

abstract:
  Traffic simulations are made more realistic by giving individual drivers
intentions, i.e. an idea of where they want to go. One possible implementation
of this idea is to give each driver an exact pre-computed path, that is, a
sequence of roads this driver wants to follow. This paper shows, in a realistic
road network, how repeated simulations can be used so that drivers can explore
different paths, and how macroscopic quantities such as locations of jams or
network throughput change as a result of this.


title:
Experiences with a simplified microsimulation for the Dallas/Fort Worth
  area

abstract:
  We describe a simple framework for micro simulation of city traffic. A medium
sized excerpt of Dallas was used to examine different levels of simulation
fidelity of a cellular automaton method for the traffic flow simulation and a
simple intersection model. We point out problems arising with the granular
structure of the underlying rules of motion.


title: Generalized Deterministic Traffic Rules

abstract:
  We study a family of deterministic models for highway traffic flow which
generalize cellular automaton rule 184. This family is parametrized by the
speed limit $m$ and another parameter $k$ that represents a ``degree of
aggressiveness'' in driving, strictly related to the distance between two
consecutive cars. We compare two driving strategies with identical maximum
throughput: ``conservative'' driving with high speed limit and ``aggressive''
driving with low speed limit. Those two strategies are evaluated in terms of
accident probability. We also discuss fundamental diagrams of generalized
traffic rules and examine limitations of maximum achievable throughput.
Possible modifications of the model are considered.


title: Modeling diffusion of innovations with probabilistic cellular automata

abstract:
  We present a family of one-dimensional cellular automata modeling the
diffusion of an innovation in a population. Starting from simple deterministic
rules, we construct models parameterized by the interaction range and
exhibiting a second-order phase transition. We show that the number of
individuals who eventually keep adopting the innovation strongly depends on
connectivity between individuals.


title: Adaptation and Optimal Chemotactic Strategy for E. Coli

abstract:
  Extending the classic works of Berg and Purcell on the biophysics of
bacterial chemotaxis, we find the optimal chemotactic strategy for the
peritrichous bacterium E. Coli in the high and low signal to noise ratio
limits. The optimal strategy depends on properties of the environment and
properties of the individual bacterium and is therefore highly adaptive. We
review experiments relevant to testing both the form of the proposed strategy
and its adaptability and propose extensions of them which could test the limits
of the adaptability in this simplest sensory processing system.

categories: adap-org cond-mat.soft nlin.AO q-bio.CB q-bio.MN


title:
Using microsimulation feedback for trip adaptation for realistic traffic
  in Dallas

abstract:
  This paper presents a day-to-day re-routing relaxation approach for traffic
simulations. Starting from an initial planset for the routes, the route-based
microsimulation is executed. The result of the microsimulation is fed into a
re-router, which re-routes a certain percentage of all trips. This approach
makes the traffic patterns in the microsimulation much more reasonable.
Further, it is shown that the method described in this paper can lead to strong
oscillations in the solutions.


title:
Analysis of a dissipative model of self-organized criticality with
  random neighbors

abstract:
  We analyze a random neighbor version of the OFC stick-slip model. We find
that the mean avalanche size is finite as soon as dissipation exists in the
bulk but that this size grows exponentially fast when dissipation tends to
zero.


title:
First Order Nonequilibrium Phase Transition in a Spatially Extended
  System

abstract:
  We investigate a system of harmonically coupled identical nonlinear
constituents subject to noise in different spatial arrangements. For global
coupling we find for infinitely many constituents the coexistence of several
ergodic components and a bifurcation behaviour like in first order phase
transitions. These results are compared with simulations for finite systems
both for global coupling and for nearest neighbour coupling on two- and
three-dimensional cubic lattices. The mean-field type results for global
coupling provide a better understanding of the more complex behaviour in the
latter case.


title: The Bak-Chen-Tang Forest Fire Model Revisited

abstract:
  We reconsider a model introduced by Bak, Chen, and Tang (Phys. Rev. A 38, 364
(1988)) as a supposedly self-organized critical model for forest fires. We
verify again that the model is not critical in 2 dimensions, as found also by
previous authors. But we find that the model does show anomalous scaling (i.e.,
is critical in the sense of statistical mechanics) in 3 and 4 dimensions. We
relate these results to recent claims by A. Johansen.


title:
Domain formation in transitions with noise and time-dependent
  bifurcation parameter

abstract:
  The characteristic size for spatial structure, that emerges when the
bifurcation parameter in model partial differential equations is slowly
increased through its critical value, depends logarithmically on the size of
added noise. Numerics and analysis are presented for the real Ginzburg-Landau
and Swift-Hohenberg equations.

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


title: Noise and slow-fast dynamics in a three-wave resonance problem

abstract:
  Recent research on the dynamics of certain fluid dynamical instabilities
shows that when there is a slow invariant manifold subject to fast timescale
instability the dynamics are extremely sensitive to noise. The behaviour of
such systems can be described in terms of a one-dimensional map, and previous
work has shown how the effect of noise can be modelled by a simple adjustment
to the map. Here we undertake an in depth investigation of a particular set of
equations, using the methods of stochastic integration. We confirm the
prediction of the earlier studies that the noise becomes important when
mu|log(epsilon)| = O(1), where mu is the small timescale ratio and \epsilon is
the noise level. In addition, we present detailed information about the
statistics of the solution when the noise is a dominant effect; the analytical
results show excellent agreement with numerical simulations.


title: Random Neighbor Theory of the Olami-Feder-Christensen Earthquake Model

abstract:
  We derive the exact equations of motion for the random neighbor version of
the Olami-Feder-Christensen earthquake model in the infinite-size limit. We
solve them numerically, and compare with simulations of the model for large
numbers of sites. We find perfect agreement. But we do not find any scaling or
phase transitions, except in the conservative limit. This is in contradiction
to claims by Lise & Jensen (Phys. Rev. Lett. 76, 2326 (1996)) based on
approximate solutions of the same model. It indicates again that scaling in the
Olami-Feder-Christensen model is only due to partial synchronization driven by
spatial inhomogeneities. Finally, we point out that our method can be used also
for other SOC models, and treat in detail the random neighbor version of the
Feder-Feder model.


title:
Stochastic calculus: application to dynamic bifurcations and threshold
  crossings

abstract:
  For the dynamic pitchfork bifurcation in the presence of white noise, the
statistics of the last time at zero are calculated as a function of the noise
level and the rate of change of the parameter. The threshold crossing problem
used, for example, to model the firing of a single cortical neuron is
considered, concentrating on quantities that may be experimentally measurable
but have so far received little attention. Expressions for the statistics of
pre-threshold excursions, occupation density and last crossing time of zero are
compared with results from numerical generation of paths.


title:
Condensation in Globally Coupled Populations of Chaotic Dynamical
  Systems

abstract:
  The condensation transition, leading to complete mutual synchronization in
large populations of globally coupled chaotic Roessler oscillators, is
investigated. Statistical properties of this transition and the cluster
structure of partially condensed states are analyzed.


title: Coherence and clustering in ensembles of neural networks

abstract:
  Large ensembles of globally coupled chaotic neural networks undergo a
transition to complete synchronization for high coupling intensities. The onset
of this fully coherent behavior is preceded by a regime where clusters of
networks with identical activity are spontaneously formed. In these regimes of
coherent collective evolution the dynamics of each neural network is still
chaotic. These results may be relevant to the study of systems where
interaction between elements is able to give rise to coherent complex behavior,
such as in cortex activity or in insect societies.


title: Learning from Mistakes

abstract:
  A simple model of self-organised learning with no classical (Hebbian)
reinforcement is presented. Synaptic connections involved in mistakes are
depressed. The model operates at a highly adaptive, probably critical, state
reached by extremal dynamics similar to that of recent evolution models. Thus,
one might think of the mechanism as synaptic Darwinism.


title: Noise and dynamic transitions

abstract:
  A parabolic stochastic PDE is studied analytically and numerically, when a
bifurcation parameter is slowly increased through its critical value. The aim
is to understand the effect of noise on delayed bifurcations in systems with
spatial degrees of freedom. Realisations of the nonautonomous stochastic PDE
remain near the unstable configuration for a long time after the bifurcation
parameter passes through its critical value, then jump to a new configuration.
The effect of the nonlinearity is to freeze in the spatial structure formed
from the noise near the critical value.


title: A noise-controlled dynamic bifurcation

abstract:
  We consider a slow passage through a point of loss of stability. If the
passage is sufficiently slow, the dynamics are controlled by additive random
disturbances, even if they are extremely small. We derive expressions for the
`exit value' distribution when the parameter is explicitly a function of time
and the dynamics are controlled by additive Gaussian noise. We derive a new
expression for the small correction introduced if the noise is coloured
(exponentially correlated). There is good agreement with results obtained from
simulation of sample paths of the appropriate stochastic differential
equations. Multiplicative noise does not produce noise-controlled dynamics in
this fashion.


title: Emergence of Algorithmic Languages in Genetic Systems

abstract:
  In genetic systems there is a non-trivial interface between the sequence of
symbols which constitutes the chromosome, or ``genotype'', and the products
which this sequence encodes --- the ``phenotype''. This interface can be
thought of as a ``computer''. In this case the chromosome is viewed as an
algorithm and the phenotype as the result of the computation. In general only a
small fraction of all possible sequences of symbols makes any sense for a given
computer. The difficulty of finding meaningful algorithms by random mutation is
known as the brittleness problem. In this paper we show that mutation and
crossover favour the emergence of an algorithmic language which facilitates the
production of meaningful sequences following random mutations of the genotype.
We base our conclusions on an analysis of the population dynamics of a variant
of Kitano's neurogenetic model wherein the chromosome encodes the rules for
cellular division and the phenotype is a 16-cell organism interpreted as a
connectivity matrix for a feedforward neural network. We show that an
algorithmic language emerges, describe this language in extenso, and show how
it helps to solve the brittleness problem.


title: Self-Adaptation in Evolving Systems

abstract:
  A theoretical and experimental analysis is made of the effects of
self-adaptation in a simple evolving system. Specifically, we consider the
effects of coding the mutation and crossover probabilities of a genetic
algorithm evolving in certain model fitness landscapes. The resultant
genotype-phenotype mapping is degenerate, there being no direct selective
advantage for one probability versus another. We show that the action of
mutation and crossover breaks this degeneracy leading to an induced symmetry
breaking among the genotypic synonyms. We demonstrate that this induced
symmetry breaking allows the system to self-adapt in a time dependent
environment.


title: Codon Bias and Mutability in HIV Sequences

abstract:
  A survey of the patterns of synonymous codon preferences in the HIV env gene
reveals a relation between the codon bias and the mutability requirements in
different regions in the protein. At hypervariable regions in $gp120$, one
finds a greater proportion of codons that tend to mutate non-synonymously, but
to a target that is similar in hydrophobicity and volume. We argue that this
strategy results from a compromise between the selective pressure placed on the
virus by the induced immune response, which favours amino acid substitutions in
the complementarity determining regions, and the negative selection against
missense mutations that violate structural constraints of the env protein.


title: Symmetry Breaking and Adaptation: Evidence from a Toy Model of a Virus

abstract:
  We argue that the phenomenon of symmetry breaking in genetics can enhance the
adaptability of a species to changes in the environment. In the case of a
virus, the claim is that the codon bias in the neutralization epitope improves
the virus' ability to generate mutants that evade the induced immune response.
We support our claim with a simple ``toy model'' of a viral epitope evolving in
competition with the immune system. The effective selective advantage of a
higher mutability leads to a dominance of codons that favour non-synonymous
mutations. The results in this paper suggest the possibility of emergence of an
algorithmic language in more complicated systems.


title: Dynamics controlled by additive noise

abstract:
  Analysis is presented of a system whose dynamics are dramatically simplified
by tiny amounts of additive noise.
  The dynamics divide naturally into two phases. In the slower phase,
trajectories are close to an invariant manifold; this allows small random
disturbances to exert a controlling influence. A map is derived which provides
an accurate description of the trajectories.


title: Emergence of Cooperation and Organization in an Evolutionary Game

abstract:
  A binary game is introduced and analysed. N players have to choose one of the
two sides independently and those on the minority side win. Players uses a
finite set of ad hoc strategies to make their decision, based on the past
record. The analysing power is limited and can adapt when necessary.
Interesting cooperation and competition pattern of the society seem to arise
and to be responsive to the payoff function.


title:
High-Speed Network Traffic Management Analysis and Optimization: Models
  and Methods

abstract:
  The main steps of automatic control methodology include the hierarchical
representation of management system and the formal definitions of input
variables, object and goal of control of each management level. A Petri net
model of individual traffic source is presented. It is noted that the current
set of traffic parameters recommended by ATM-forum is not enough to synthesize
optimal traffic control system. The feature of traffic self-similarity can be
used to effectively solve optimal control task. An example of an optimal
control scheme for cell discarding algorithm is presented.


title: Theoretical approach to biological aging

abstract:
  We present a model for biological aging that considers the number of
individuals whose (inherited) genetic charge determines the maximum age for
death: each individual may die before that age due to some external factor, but
never after that limit. The genetic charge of the offspring is inherited from
the parent with some mutations, described by a transition matrix. The model can
describe different strategies of reproduction and it is exactly soluble. We
applied our method to the bit-string model for aging and the results are in
perfect agreement with numerical simulations.


title:
Search for an unitary mortality law through a theoretical model for
  biological ageing

abstract:
  In this work we check the occurrence of the Azbel assumption of mortality
within the framework of a bit string model for biological ageing. We reproduced
the observed feature of linear correspondence between the fitting parameters of
the death rate as obtained by Azbel with demographic data.


title:
Classifying Rational Densities Using Two One-Dimensional Cellular
  Automata

abstract:
  Given a (finite) string of zeros and ones, we report a way to determine if
the number of ones is less than, greater than, or equal to a prescribed number
by applying two sets of cellular automaton rules in succession. Thus, we solve
the general density classification problem using cellular automaton.


title:
Coevolution of membranes and channels: A possible step in the origin of
  life

abstract:
  We propose a scenario for the origin of life based on the coevolution of
lipid bilayer vesicles and protein channels.


title:
Conservation laws in coupled multiplicative random arrays lead to $1/f$
  noise

abstract:
  We consider the dynamic evolution of a coupled array of N multiplicative
random variables. The magnitude of each is constrained by a lower bound w_0 and
their sum is conserved. Analytical calculation shows that the simplest case,
N=2 and w_0=0, exhibits a Lorentzian spectrum which gradually becomes fractal
as w_0 increases. Simulation results for larger $N$ reveal fractal spectra for
moderate to high values of w_0 and power-law amplitude fluctuations at all
values. The results are applied to estimating the fractal exponents for
cochlear-nerve-fiber action-potential sequences with remarkable success, using
only two parameters.


title:
Analysis, Synthesis, and Estimation of Fractal-Rate Stochastic Point
  Processes

abstract:
  Fractal and fractal-rate stochastic point processes (FSPPs and FRSPPs)
provide useful models for describing a broad range of diverse phenomena,
including electron transport in amorphous semiconductors, computer-network
traffic, and sequences of neuronal action potentials. A particularly useful
statistic of these processes is the fractal exponent $\alpha$, which may be
estimated for any FSPP or FRSPP by using a variety of statistical methods.
Simulated FSPPs and FRSPPs consistently exhibit bias in this fractal exponent,
however, rendering the study and analysis of these processes non-trivial. In
this paper, we examine the synthesis and estimation of FRSPPs by carrying out a
systematic series of simulations for several different types of FRSPP over a
range of design values for $\alpha$. The discrepancy between the desired and
achieved values of $\alpha$ is shown to arise from finite data size and from
the character of the point-process generation mechanism. In the context of
point-process simulation, reduction of this discrepancy requires generating
data sets with either a large number of points, or with low jitter in the
generation of the points. In the context of fractal data analysis, the results
presented here suggest caution when interpreting fractal exponents estimated
from experimental data sets.


title:
The Measure of Compositional Heterogeneity in DNA Sequences Is Related
  to Measures of Complexity

abstract:
  This commentary discusses a recently proposed measure of heterogeneity of DNA
sequences and compares with the measures of complexity.


title: Evolution and extinction dynamics in rugged fitness landscapes

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


title:
Self-Organized Criticality with Complex Scaling Exponents in the Train
  Model

abstract:
  The train model which is a variant of the Burridge-Knopoff earthquake model
is investigated for a velocity-strengthening friction law. It shows
self-organized criticality with complex scaling exponents. That is, the
probability density function of the avalanche strength is a power law times a
log-periodic function. Exact results (scaling exponent: $3/2+2\pi i/\ln 4$) are
found for a nonlocal cellular automaton which approximates the overdamped train
model. Further the influence of random static friction is discussed.


title: TRANSIMS traffic flow characteristics

abstract:
  Knowledge of fundamental traffic flow characteristics of traffic simulation
models is an essential requirement when using these models for the planning,
design, and operation of transportation systems. In this paper we discuss the
following: a description of how features relevant to traffic flow are currently
under implementation in the TRANSIMS microsimulation, a proposition for
standardized traffic flow tests for traffic simulation models, and the results
of these tests for two different versions of the TRANSIMS microsimulation.


title: A condition for the genotype-phenotype mapping: Causality

abstract:
  The appropriate choice of the genotype-phenotype mapping in combination with
the mutation operator is important for a successful evolutionary search
process. We suggest a measure to quantify the quality of this combination by
addressing the question whether the relation among distances is carried over
from one space to the other. Search processes which do not destroy the
neighbourhood structure are termed strongly causal. We apply the proposed
measure to parameter and structure optimisation problems in order to assess the
combination (mapping, mutation operator) and at the same time to be able to
propose improved settings.


title:
Absence of self-organized criticality in a random-neighbor version of
  the OFC stick-slip model

abstract:
  We report some numerical simulations to investigate the existence of a
self-organized critical (SOC) state in a random-neighbor version of the OFC
model for a range of parameters corresponding to a non-conservative case. In
contrast to a recent work, we do not find any evidence of SOC. We use a more
realistic distribution of energy among sites to perform some analytical
calculations that agree with our numerical conclusions.


title:
Multiresolution wavelet analysis of heartbeat intervals discriminates
  healthy patients from those with cardiac pathology

abstract:
  We applied multiresolution wavelet analysis to the sequence of times between
human heartbeats (R-R intervals) and have found a scale window, between 16 and
32 heartbeats, over which the widths of the R-R wavelet coefficients fall into
disjoint sets for normal and heart-failure patients. This has enabled us to
correctly classify every patient in a standard data set as either belonging to
the heart-failure or normal group with 100% accuracy, thereby providing a
clinically significant measure of the presence of heart-failure from the R-R
intervals alone.
  Comparison is made with previous approaches, which have provided only
statistically significant measures.

categories: adap-org chao-dyn nlin.AO nlin.CD physics.med-ph q-bio


title: Experiences with iterated traffic microsimulations in Dallas

abstract:
  This paper reports experiences with iterated traffic microsimulations in the
context of a Dallas study. ``Iterated microsimulations'' here means that the
information generated by a microsimulation is fed back into the route planner
so that the simulated individuals can adjust their routes to circumvent
congestion. This paper gives an overview over what has been done in the Dallas
context to better understand the relaxation process, and how to judge the
robustness of the results.


title: Early-time critical dynamics of lattices of coupled chaotic maps

abstract:
  The early-time critical dynamics of continuous, Ising-like phase transitions
is studied numerically for two-dimensional lattices of coupled chaotic maps.
Emphasis is laid on obtaining accurate estimates of the dynamic critical
exponents \theta' and z. The critical points of five different models are
investigated, varying the mode of update, the coupling, and the local map. Our
results suggest that the nature of update is a relevant parameter for dynamic
universality classes of extended dynamical systems, generalizing results
obtained previously for the static properties. They also indicate that the
universality observed for the static properties of Ising-like transitions of
synchronously-updated systems does not hold for their dynamic critical
properties.


title: Cellular automaton rules conserving the number of active sites

abstract:
  This paper shows how to determine all the unidimensional two-state cellular
automaton rules of a given number of inputs which conserve the number of active
sites. These rules have to satisfy a necessary and sufficient condition. If the
active sites are viewed as cells occupied by identical particles, these
cellular automaton rules represent evolution operators of systems of identical
interacting particles whose total number is conserved. Some of these rules,
which allow motion in both directions, mimic ensembles of one-dimensional
pseudo-random walkers. Numerical evidence indicates that the corresponding
stochastic processes might be non-Gaussian.


title: Sentient Networks

abstract:
  In this paper we consider the question whether a distributed network of
sensors and data processors can form "perceptions" based on the sensory data.
Because sensory data can have exponentially many explanations, the use of a
central data processor to analyze the outputs from a large ensemble of sensors
will in general introduce unacceptable latencies for responding to dangerous
situations. A better idea is to use a distributed "Helmholtz machine"
architecture in which the collective state of the network as a whole provides
an explanation for the sensory data.


title: Effects of neutral selection on the evolution of molecular species

abstract:
  We introduce a new model of evolution on a fitness landscape possessing a
tunable degree of neutrality. The model allows us to study the general
properties of molecular species undergoing neutral evolution. We find that a
number of phenomena seen in RNA sequence-structure maps are present also in our
general model. Examples are the occurrence of "common" structures which occupy
a fraction of the genotype space which tends to unity as the length of the
genotype increases, and the formation of percolating neutral networks which
cover the genotype space in such a way that a member of such a network can be
found within a small radius of any point in the space. We also describe a
number of new phenomena which appear to be general properties of neutrally
evolving systems. In particular, we show that the maximum fitness attained
during the adaptive walk of a population evolving on such a fitness landscape
increases with increasing degree of neutrality, and is directly related to the
fitness of the most fit percolating network.


title:
Adaptive Competition, Market Efficiency, Phase Transitions and
  Spin-Glasses

abstract:
  We analyze a simple model of adaptive competition which captures essential
features of a variety of adaptive competitive systems in the social and
biological sciences. Each of N agents, at each time step of a game, joins one
of two groups. The agents in the minority group are awarded a point, while the
agents in the majority group get nothing. Each agent has a fixed set of
strategies drawn at the beginning of the game from a common pool, and chooses
his current best-performing strategy to determine which group to join. For a
fixed N, the system exhibits a phase change as a function of the size of the
common strategy pool from which the agents initially draw their strategies. For
small pool sizes, the system is in an efficient market phase. All information
that can be used by the agents' strategies is traded away, no agent can
accumulate more points than would an agent making random guesses, and thus the
commons suffer,since relatively few points are awarded to the agents in total.
For large initial strategy pool sizes, the system is in an inefficient market
phase, in which there is predictive information available to the agents'
strategies, and some agents can do better than random at accumulating points.
In this phase, the total number of points awarded to the agents is greater than
in a game in which all agents guess randomly, and so the commons do relatively
well. At a critical size of the strategy pool marking the cross-over from the
efficient market to the inefficient market phases, the commons do best. This
critical size of the pool grows monotonically with N. The behavior of this
system has some features reminiscent of a spin-glass.


title: Geometric statistical inference

abstract:
  Finite sample size corrections to the reparametrization-invariant solution of
the inverse problem of probability are computed, and shown to converge
uniformly to the correct distribution.


title: Probabilistic Analysis of the Number Partitioning Problem

abstract:
  Given a sequence of $N$ positive real numbers $\{a_1,a_2,..., a_N \}$, the
number partitioning problem consists of partitioning them into two sets such
that the absolute value of the difference of the sums of $a_j$ over the two
sets is minimized. In the case that the $a_j$'s are statistically independent
random variables uniformly distributed in the unit interval, this NP-complete
problem is equivalent to the problem of finding the ground state of an
infinite-range, random anti-ferromagnetic Ising model. We employ the annealed
approximation to derive analytical lower bounds to the average value of the
difference for the best constrained and unconstrained partitions in the large
$N$ limit. Furthermore, we calculate analytically the fraction of metastable
states, i.e. states that are stable against all single spin flips, and found
that it vanishes like $N^{-3/2}$.

categories: adap-org cond-mat.stat-mech math-ph math.MP nlin.AO


title: Modelling coevolution in multispecies communities

abstract:
  We introduce the Webworld model, which links together the ecological
modelling of food web structure with the evolutionary modelling of speciation
and extinction events. The model describes dynamics of ecological communities
on an evolutionary timescale. Species are defined as sets of characteristic
features, and these features are used to determine interaction scores between
species. A simple rule is used to transfer resources from the external
environment through the food web to each of the species, and to determine mean
population sizes. A time step in the model represents a speciation event. A new
species is added with features similar to those of one of the existing species
and a new food web structure is then calculated. The new species may (i) add
stably to the web, (ii) become extinct immediately because it is poorly
adapted, or (iii) cause one or more other species to become extinct due to
competition for resources. We measure various properties of the model webs and
compare these with data on real food webs. These properties include the
proportions of basal, intermediate and top species, the number of links per
species and the number of trophic levels. We also study the evolutionary
dynamics of the model ecosystem by following the fluctuations in the total
number of species in the web. Extinction avalanches occur when novel organisms
arise which are significantly better adapted than existing ones. We discuss
these results in relation to the observed extinction events in the fossil
record, and to the theory of self-organized criticality.


title: Invariant closure for the Fokker-Planck equation

abstract:
  We develop the principle of dynamic invariance to obtain closed moment
equations from the Fokker-Planck kinetic equation. The analysis is carried out
to explicit formulae for computation of the lowest eigenvalue and of the
corresponding eigenfunction for arbitrary potentials.


title:
Conditional exponents, entropies and a measure of dynamical
  self-organization

abstract:
  In dynamical systems composed of interacting parts, conditional exponents,
conditional exponent entropies and cylindrical entropies are shown to be well
defined ergodic invariants which characterize the dynamical selforganization
and statitical independence of the constituent parts. An example of interacting
Bernoulli units is used to illustrate the nature of these invariants.


title:
Emergence of Rules in Cell Society: Differentiation, Hierarchy, and
  Stability

abstract:
  A dynamic model for cell differentiation is studied, where cells with
internal chemical reaction dynamics interact with each other and replicate. It
leads to spontaneous differentiation of cells and determination, as is
discussed in the isologous diversification. Following features of the
differentiation are obtained: (1)Hierarchical differentiation from a ``stem''
cell to other cell types, with the emergence of the interaction-dependent rules
for differentiation; (2)Global stability of an ensemble of cells consisting of
several cell types, that is sustained by the emergent, autonomous control on
the rate of differentiation; (3)Existence of several cell colonies with
different cell-type distributions. The results provide a novel viewpoint on the
origin of complex cell society, while relevance to some biological problems,
especially to the hemopoietic system, is also discussed.


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

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


title:
Large-scale evolution and extinction in a hierarchically structured
  environment

abstract:
  A class of models for large-scale evolution and mass extinctions is
presented. These models incorporate environmental changes on all scales, from
influences on a single species to global effects. This is a step towards a
unified picture of mass extinctions, which enables one to study coevolutionary
effects and external abiotic influences with the same means. The generic
features of such models are studied in a simple version, in which all
environmental changes are generated at random and without feedback from other
parts of the system.


title:
Generic Emergence of Power Law Distributions and L\'evy-Stable
  Intermittent Fluctuations in Discrete Logistic Systems

abstract:
  The dynamics of generic stochastic Lotka-Volterra (discrete logistic) systems
of the form \cite{Solomon96a} $w_i (t+1) = \lambda(t) w_i (t) + a {\bar w (t)}
- b w_i (t) {\bar w(t)}$ is studied by computer simulations. The variables
$w_i$, $i=1,...N$, are the individual system components and ${\bar w (t)} =
{1\over N} \sum_i w_i (t)$ is their average. The parameters $a$ and $b$ are
constants, while $\lambda(t)$ is randomly chosen at each time step from a given
distribution. Models of this type describe the temporal evolution of a large
variety of systems such as stock markets and city populations. These systems
are characterized by a large number of interacting objects and the dynamics is
dominated by multiplicative processes. The instantaneous probability
distribution $P(w,t)$ of the system components $w_i$, turns out to fulfill a
(truncated) Pareto power-law $P(w,t) \sim w^{-1-\alpha}$. The time evolution of
${\bar w (t)} $ presents intermittent fluctuations parametrized by a truncated
L\'evy distribution of index $\alpha$, showing a connection between the
distribution of the $w_i$'s at a given time and the temporal fluctuations of
their average.


title: Critical Exponent of Species-Size Distribution in Evolution

abstract:
  We analyze the geometry of the species- and genotype-size distribution in
evolving and adapting populations of single-stranded self-replicating genomes:
here programs in the Avida world. We find that a scale-free distribution (power
law) emerges in complex landscapes that achieve a separation of two fundamental
time scales: the relaxation time (time for population to return to equilibrium
after a perturbation) and the time between mutations that produce fitter
genotypes. The latter can be dialed by changing the mutation rate. In the
scaling regime, we determine the critical exponent of the distribution of sizes
and strengths of avalanches in a system without coevolution, described by
first-order phase transitions in single finite niches.


title:
Collective Behaviour and Diversity in Economic Communities: Some
  Insights from an Evolutionary Game

abstract:
  Many complex adaptive systems contain a large diversity of specialized
components. The specialization at the level of the microscopic degrees of
freedom, and diversity at the level of the system as a whole are phenomena that
appear during the course of evolution of the system. We present a mathematical
model to describe these evolutionary phenomena in economic communities. The
model is a generalization of the replicator equation. The economic motivation
for the model and its relationship with some other game theoretic models
applied to ecology and sociobiology is discussed. Some results about the
attractors of this dynamical system are described. We argue that while the
microscopic variables -- the agents comprising the community -- act locally and
independently, time evolution produces a collective behaviour in the system
characterized by individual specialization of the agents as well as global
diversity in the community. This occurs for generic values of the parameters
and initial conditions provided the community is sufficiently large, and can be
viewed as a kind of self-organization in the system. The context dependence of
acceptable innovations in the community appears naturally in this framework.


title:
Dynamics of Individual Specialization and Global Diversification in
  Communities

abstract:
  We discuss a model of an economic community consisting of $N$ interacting
agents. The state of each agent at any time is characterized, in general, by a
mixed strategy profile drawn from a space of $s$ pure strategies. The community
evolves as agents update their strategy profiles in response to payoffs
received from other agents. The evolution equation is a generalization of the
replicator equation. We argue that when $N$ is sufficiently large and the
payoff matrix elements satisfy suitable inequalities, the community evolves to
retain the full diversity of available strategies even as individual agents
specialize to pure strategies.


title: Statistics of extinction and survival in Lotka-Volterra systems

abstract:
  We analyze purely competitive many-species Lotka-Volterra systems with random
interaction matrices, focusing the attention on statistical properties of their
asymptotic states. Generic features of the evolution are outlined from a
semiquantitative analysis of the phase-space structure, and extensive numerical
simulations are performed to study the statistics of the extinctions. We find
that the number of surviving species depends strongly on the statistical
properties of the interaction matrix, and that the probability of survival is
weakly correlated to specific initial conditions.

categories: adap-org cond-mat.soft nlin.AO physics.bio-ph q-bio


title: Extinction events and species lifetimes in a simple ecological model

abstract:
  A model for large-scale evolution recently introduced by Amaral and Meyer is
studied analytically and numerically. Species are located at different trophic
levels and become extinct if their prey becomes extinct. It is proved that this
model is self-organized critical in the thermodynamic limit, with an exponent 2
characterizing the size distribution of extinction events. The lifetime
distribution of species, cutoffs due to finite-size effects, and other
quantities are evaluated. The relevance of this model to biological evolution
is critically assessed.


title:
Neural network design for J function approximation in dynamic
  programming

abstract:
  This paper shows that a new type of artificial neural network (ANN) -- the
Simultaneous Recurrent Network (SRN) -- can, if properly trained, solve a
difficult function approximation problem which conventional ANNs -- either
feedforward or Hebbian -- cannot. This problem, the problem of generalized maze
navigation, is typical of problems which arise in building true intelligent
control systems using neural networks. (Such systems are discussed in the
chapter by Werbos in K.Pribram, Brain and Values, Erlbaum 1998.) The paper
provides a general review of other types of recurrent networks and alternative
training techniques, including a flowchart of the Error Critic training design,
arguable the only plausible approach to explain how the brain adapts
time-lagged recurrent systems in real-time. The C code of the test is appended.
As in the first tests of backprop, the training here was slow, but there are
ways to do better after more experience using this type of network.


title: On the 1/f fluctuations in the nonlinear systems affected by noise

abstract:
  We investigate a problem of the necessary and sufficient conditions for
appearance of the 1/f fluctuations in the simple systems affected by the
external random perturbations, i.e. the power spectral density of the flux of
particles moving in some contours and perturbed by the external forces. In some
cases we observe the 1/f behavior but only in some range of frequencies and
parameters of the systems.


title: How fast do structures emerge in hypercycle-systems?

abstract:
  A general framework for the simulation of reaction-diffusion systems with
probabilistic cellular automata is presented. The basic reaction probabilities
of the chemical model translate directly into the transition rules of the
automaton, thus allowing a clear comparison between simulation results and
analytic calculations. This framework is then applied to simulations of
hypercycle-systems in up to three dimensions. Furthermore, a new measurement
quantity is introduced and applied to the hypercycle-systems in two and three
dimensions. It can be shown that this quantity can be interpreted as a measure
for the macroscopic order of the hypercycle systems.


title: Simple model of 1/f noise

abstract:
  Simple analytically solvable model of 1/f noise is proposed. The model
consists of one or few particles moving in the closed contour. The drift period
of the particle round the contour fluctuates about some average value, e.g. due
to the external random perturbations of the system's parameters. The model
contains only one relaxation rate, however, the power spectral density of the
current of particles reveals an exact 1/f spectrum in any desirable wide range
of frequency and can be expressed by the Hooge formula. It is likely that the
analysis and the generalizations of the model can strongly influence on the
understanding of the origin of 1/f noise.


title:
Nondecay probability of a metastable state: almost exact analytical
  description in wide range of noise intensity

abstract:
  This paper presents a complete description of noise-induced decay of a
metastable state in a wide range of noise intensity. Recurrent formulas of
exact moments of decay time valid for arbitrary noise intensity have been
obtained. The nondecay probability of a metastable state was found to be really
close to the exponent even for the case when the potential barrier height is
comparable or smaller than the noise intensity.


title: Coupled Oscillators with Chemotaxis

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


title: Development and Evolution of Neural Networks in an Artificial Chemistry

abstract:
  We present a model of decentralized growth for Artificial Neural Networks
(ANNs) inspired by the development and the physiology of real nervous systems.
In this model, each individual artificial neuron is an autonomous unit whose
behavior is determined only by the genetic information it harbors and local
concentrations of substrates modeled by a simple artificial chemistry. Gene
expression is manifested as axon and dendrite growth, cell division and
differentiation, substrate production and cell stimulation. We demonstrate the
model's power with a hand-written genome that leads to the growth of a simple
network which performs classical conditioning. To evolve more complex
structures, we implemented a platform-independent, asynchronous, distributed
Genetic Algorithm (GA) that allows users to participate in evolutionary
experiments via the World Wide Web.


title: Dynamics of Internal Models in Game Players

abstract:
  A new approach for the study of social games and communications is proposed.
Games are simulated between cognitive players who build the opponent's internal
model and decide their next strategy from predictions based on the model. In
this paper, internal models are constructed by the recurrent neural network
(RNN), and the iterated prisoner's dilemma game is performed. The RNN allows us
to express the internal model in a geometrical shape. The complicated
transients of actions are observed before the stable mutually defecting
equilibrium is reached. During the transients, the model shape also becomes
complicated and often experiences chaotic changes. These new chaotic dynamics
of internal models reflect the dynamical and high-dimensional rugged landscape
of the internal model space.


title: A dynamical theory of speciation on holey adaptive landscapes

abstract:
  The metaphor of holey adaptive landscapes provides a pictorial representation
of the process of speciation as a consequence of genetic divergence. In this
metaphor, biological populations diverge along connected clusters of well-fit
genotypes in a multidimensional adaptive landscape and become reproductively
isolated species when they come to be on opposite sides of a ``hole'' in the
adaptive landscape. No crossing of any adaptive valleys is required. I
formulate and study a series of simple models describing the dynamics of
speciation on holey adaptive landscapes driven by mutation and random genetic
drift. Unlike most previous models that concentrate only on some stages of
speciation, the models studied here describe the complete process of speciation
from initiation until completion. The evolutionary factors included are
selection (reproductive isolation), random genetic drift, mutation,
recombination, and migration. In these models, pre- and post-mating
reproductive isolation is a consequence of cumulative genetic change. I study
possibilities for speciation according to allopatric, parapatric, peripatric
and vicariance scenarios. The analytic theory satisfactorily matches results of
individual-based simulations reported by Gavrilets et al. (1998). It is
demonstrated that rapid speciation including simultaneous emergence of several
new species is a plausible outcome of the evolutionary dynamics of subdivided
populations. I consider effects of population size, population subdivision, and
local adaptation on the dynamics of speciation. I briefly discuss some
implications of the dynamics on holey adaptive landscapes for molecular
evolution.


title: Rapid parapatric speciation on holey adaptive landscapes

abstract:
  A classical view of speciation is that reproductive isolation arises as a
by-product of genetic divergence. Here, individual-based simulations are used
to evaluate whether the mechanisms implied by this view may result in rapid
speciation if the only source of genetic divergence are mutation and random
genetic drift. Distinctive features of the simulations are the consideration of
the complete process of speciation (from initiation until completion), and of a
large number of loci, which was only one order of magnitude smaller than that
of bacteria. It is demonstrated that rapid speciation on the time scale of
hundreds of generations is plausible without the need for extreme founder
events, complete geographic isolation, the existence of distinct adaptive peaks
or selection for local adaptation. The plausibility of speciation is enhanced
by population subdivision. Simultaneous emergence of more than two new species
from a subdivided population is highly probable. Numerical examples relevant to
the theory of centrifugal speciation and to the conjectures about the fate of
``ring species'' and ``sexual continuums'' are presented.


title: Life as Complex Systems --- Viewpoint from Intra-Inter Dynamics

abstract:
  Basic problems in complex systems are surveyed in connection with Life. As a
key issue for complex systems, complementarity between syntax/rule/parts and
semantics/behavior/whole is stressed. To address the issue, a constructive
approach for a biological system is proposed. As a construction in a computer,
intra-inter dynamics is presented for cell biology, where the following five
general features are drawn from our model experiments; intrinsic
diversification, recursive type formation, rule generation, formation of
internal representation, and macroscopic robustness. Significance of the
constructed logic to the biology of existing organisms is also discussed.


title: Memory Effects and Macroscopic Manifestation of Randomness

abstract:
  It is shown that due to memory effects the complex behaviour of components in
a stochastic system can be transmitted to macroscopic evolution of the system
as a whole. Within the Markov approximation widely using in ordinary
statistical mechanics, memory effects are neglected. As a result, a time-scale
separation between the macroscopic and the microscopic level of description
exists, the macroscopic differential picture is no a consequence of microscopic
non-differentiable dynamics. On the other hand, the presence of complete memory
in a system means that all its components have the same behaviour. If the
memory function has no characteristic time scales, the correct description of
the macroscopic evolution of such systems have to be in terms of the fractional
calculus.


title: Cooperative mechanism of self-regulation in hierarchical living systems

abstract:
  We study the problem of how a ``living'' system complex in structure can
respond perfectly to local changes in the environment. Such a system is assumed
to consist of a distributed ``living'' medium and a hierarchical ``supplying''
network that provides this medium with ``nutritious'' products. Because of the
hierarchical organization each element of the supplying network has to behave
in a self-consistent way for the system can adapt to changes in the
environment.
  We propose a cooperative mechanism of self-regulation by which the system as
a whole can react perfectly. This mechanism is based on an individual response
of each element to the corresponding small piece of the information on the
state of the ``living'' medium. The conservation of flux through the supplying
network gives rise to a certain processing of information and the
self-consistent behavior of the elements, leading to the perfect
self-regulation. The corresponding equations governing the ``living'' medium
state are obtained.


title: Wavelet Based Fractal Analysis of Airborne Pollen

abstract:
  The most abundant biological particles in the atmosphere are pollen grains
and spores. Self protection of pollen allergy is possible through the
information of future pollen contents in the air. In spite of the importance of
airborne pol len concentration forecasting, it has not been possible to predict
the pollen concentrations with great accuracy, and about 25% of the daily
pollen forecasts have resulted in failures. Previous analysis of the dynamic
characteristics of atmospheric pollen time series indicate that the system can
be described by a low dimensional chaotic map. We apply the wavelet transform
to study the multifractal characteristics of an a irborne pollen time series.
We find the persistence behaviour associated to low pollen concentration values
and to the most rare events of highest pollen co ncentration values. The
information and the correlation dimensions correspond to a chaotic system
showing loss of information with time evolution.


title: The Evolutionary Design of Collective Computation in Cellular Automata

abstract:
  We investigate the ability of a genetic algorithm to design cellular automata
that perform computations. The computational strategies of the resulting
cellular automata can be understood using a framework in which ``particles''
embedded in space-time configurations carry information and interactions
between particles effect information processing. This structural analysis can
also be used to explain the evolutionary process by which the strategies were
designed by the genetic algorithm. More generally, our goals are to understand
how machine-learning processes can design complex decentralized systems with
sophisticated collective computational abilities and to develop rigorous
frameworks for understanding how the resulting dynamical systems perform
computation.

categories: adap-org cond-mat.dis-nn math.DS nlin.AO nlin.PS patt-sol physics.bio-ph


title: Dynamics of clade diversification on the morphological hypercube

abstract:
  Understanding the relationship between taxonomic and morphological changes is
important in identifying the reasons for accelerated morphological
diversification early in the history of animal phyla. Here, a simple general
model describing the joint dynamics of taxonomic diversity and morphological
disparity is presented and applied to the data on the diversification of
blastozoans. I show that the observed patterns of deceleration in clade
diversification can be explicable in terms of the geometric structure of the
morphospace and the effects of extinction and speciation on morphological
disparity without invoking major declines in the size of morphological
transitions or taxonomic turnover rates. The model allows testing of hypotheses
about patterns of diversification and estimation of rates of morphological
evolution. In the case of blastozoans, I find no evidence that major changes in
evolutionary rates and mechanisms are responsible for the deceleration of
morphological diversification seen during the period of this clade's expansion.
At the same time, there is evidence for a moderate decline in overall rates of
morphological diversification concordant with a major change (from positive to
negative values) in the clade's growth rate.


title: Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model

abstract:
  A model of $s$ interacting species is considered with two types of dynamical
variables. The fast variables are the populations of the species and slow
variables the links of a directed graph that defines the catalytic interactions
among them. The graph evolves via mutations of the least fit species. Starting
from a sparse random graph, we find that an autocatalytic set (ACS) inevitably
appears and triggers a cascade of exponentially increasing connectivity until
it spans the whole graph. The connectivity subsequently saturates in a
statistical steady state. The time scales for the appearance of an ACS in the
graph and its growth have a power law dependence on $s$ and the catalytic
probability. At the end of the growth period the network is highly non-random,
being localized on an exponentially small region of graph space for large $s$.


title: Decline in extinction rates and scale invariance in the fossil record

abstract:
  We show that the decline in the extinction rate during the Phanerozoic can be
accurately parameterized by a logarithmic fit to the cumulative total
extinction. This implies that extinction intensity is falling off approximately
as the reciprocal of time. We demonstrate that this observation alone is
sufficient to explain the existence of the proposed power-law forms in the
distribution of the sizes of extinction events and in the power spectrum of
Phanerozoic extinction, results which previously have been explained by
appealing to self-organized critical theories of evolutionary dynamics.


title: Stable Adaptive Control Using New Critic Designs

abstract:
  Classical adaptive control proves total-system stability for control of
linear plants, but only for plants meeting very restrictive assumptions.
Approximate Dynamic Programming (ADP) has the potential, in principle, to
ensure stability without such tight restrictions. It also offers nonlinear and
neural extensions for optimal control, with empirically supported links to what
is seen in the brain. However, the relevant ADP methods in use today -- TD,
HDP, DHP, GDHP -- and the Galerkin-based versions of these all have serious
limitations when used here as parallel distributed real-time learning systems;
either they do not possess quadratic unconditional stability (to be defined) or
they lead to incorrect results in the stochastic case. (ADAC or Q-learning
designs do not help.) After explaining these conclusions, this paper describes
new ADP designs which overcome these limitations. It also addresses the
Generalized Moving Target problem, a common family of static optimization
problems, and describes a way to stabilize large-scale economic equilibrium
models, such as the old long-term energy model of DOE.


title:
Nonlinear theory of autooscillations of quasiplanar interface during
  directional solidification

abstract:
  Within the framework of the frozen temperature approximation we develop a
strongly-nonlinear theory of one-dimensional pattern formation during
directional solidification of binary mixture under nonequilibrium segregation.
In the case of small partition coefficient the full problem is reduced to the
system of two ordinary differential equations describing the interface motion
in terms of its velocity and position coordinate. The type of the oscillatory
instability bifurcation is studied in detail in different limits. For the
subcrytical bifurcaton relaxation interface oscillations are analyzed
analytically and numerically. We show that these oscillation exibit a number of
anomalous properies. In particular, such oscillations can be weakly- or
strongly-dissipative depending on the physical parameters and the amplitude of
the strongly-dissipative oscillations is determined not only by the form of the
corresponding nullcline but also by the behavior of the system for small values
of the interface velocity. Characteristic parameters of the superlattice
occuring in the growing crystal are estimated.


title:
Optimizing Epochal Evolutionary Search: Population-Size Independent
  Theory

abstract:
  Epochal dynamics, in which long periods of stasis in population fitness are
punctuated by sudden innovations, is a common behavior in both natural and
artificial evolutionary processes. We use a recent quantitative mathematical
analysis of epochal evolution to estimate, as a function of population size and
mutation rate, the average number of fitness function evaluations to reach the
global optimum. This is then used to derive estimates of and bounds on
evolutionary parameters that minimize search effort.


title: Optimizing Epochal Evolutionary Search: Population-Size Dependent Theory

abstract:
  Epochal dynamics, in which long periods of stasis in an evolving population
are punctuated by a sudden burst of change, is a common behavior in both
natural and artificial evolutionary processes. We analyze the population
dynamics for a class of fitness functions that exhibit epochal behavior using a
mathematical framework developed recently. In the latter the approximations
employed led to a population-size independent theory that allowed us to
determine optimal mutation rates. Here we extend this approach to include the
destabilization of epochs due to finite-population fluctuations and show that
this dynamical behavior often occurs around the optimal parameter settings for
efficient search. The resulting, more accurate theory predicts the total number
of fitness function evaluations to reach the global optimum as a function of
mutation rate, population size, and the parameters specifying the fitness
function. We further identify a generalized error threshold, smoothly bounding
the two-dimensional regime of mutation rates and population sizes for which
evolutionary search operates efficiently.


title: Emergence and Growth of Complex Networks in Adaptive Systems

abstract:
  We consider the population dynamics of a set of species whose network of
catalytic interactions is described by a directed graph. The relationship
between the attractors of this dynamics and the underlying graph theoretic
structures like cycles and autocatalytic sets is discussed. It is shown that
when the population dynamics is suitably coupled to a slow dynamics of the
graph itself, the network evolves towards increasing complexity driven by
autocatalytic sets. Some quantitative measures of network complexity are
described.


title:
One Dimensional $n$ary Density Classification Using Two Cellular
  Automaton Rules

abstract:
  Suppose each site on a one-dimensional chain with periodic boundary condition
may take on any one of the states $0,1,..., n-1$, can you find out the most
frequently occurring state using cellular automaton? Here, we prove that while
the above density classification task cannot be resolved by a single cellular
automaton, this task can be performed efficiently by applying two cellular
automaton rules in succession.


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

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

categories: adap-org cond-mat nlin.AO physics.optics


title:
Distributed Self-regulation Induced by Negative Feedbacks in Ecological
  and Economic Systems

abstract:
  We consider an ecological system governed by Lotka-Volterra dynamics and an
example of an economic system as a mesomarket with perfect competition. We
propose a mechanism for cooperative self-regulation that enables the system
under consideration to respond properly to changes in the environment. This
mechanism is based on (1) active individual behavior of the system elements at
each hierarchical level and (2) self-processing of information caused by the
hierarchical organization. It is shown how the proposed mechanism suppresses
nonlocal interaction of elements belonging to a particular level as mediated by
higher levels.


abstract:
  A simple model for the formation of a complex organism is introduced.
Individuals can communicate and specialize, leading to an increase in
productivity. If there are limits to the capacity of individuals to communicate
with other individuals, the individuals form groups that interact with each
other, leading to a complex organism that has interacting units on all scales.


title: Extinction, diversity and survivorship of taxa in the fossil record

abstract:
  Using data drawn from large-scale databases, a number of interesting trends
in the fossil record have been observed in recent years. These include the
average decline in extinction rates throughout the Phanerozoic, the average
increase in standing diversity, correlations between rates of origination and
extinction, and simple laws governing the form of survivorship curves and the
distribution of the lifetimes of taxa. In this paper we derive mathematically a
number of relations between these quantities and show how these different
trends are inter-related. We also derive a variety of constraints on the
possible forms of these trends, such as limits on the rate at which extinction
may decline and limits on the allowed difference between extinction and
origination rates at any given time.


title: Time evolution of averages in dynamical systems driven by noise

abstract:
  This paper presents description of time evolution of averages of Markov
process in wide range of noise intensity. Exact expression of time scale of
average evolution has been obtained. It has been demonstrated numerically that
for purely noise-induced transitions (transitions over potential barriers) the
time evolution of mean coordinate is a simple exponent with a good precision
even for the case when the potential barrier height is comparable or smaller
than the noise intensity. Also it has been demonstrated that nonlinear system
may be "linearized" by a strong noise.


title: The Structure of Adaptive Competition in Minority Games

abstract:
  In this paper we present results and analyses of a class of games in which
heterogeneous agents are rewarded for being in a minority group. Each agent
possesses a number of fixed strategies each of which are predictors of the next
minority group. The strategies use a set of aggregate, publicly available
information (reflecting the agents' collective previous decisions) to make
their predictions. An agent chooses which group to join at a given moment by
using one of his strategies. These games are adaptive in that agents can
choose, at different points of the game, to exercise different strategies in
making their choice of which group to join. We find, rather generally, that
such systems evidence a phase change from a maladaptive, informationally
efficient phase in which the system performs poorly at generating resources, to
an inefficient phase in which there is an emergent cooperation among the
agents, and the system more effectively generates resources. The best emergent
coordination is achieved in a transition region between these two phases. This
transition occurs when the dimension of the strategy space is of the order of
the number of agents playing the game. We present explanations for this general
behavior, based in part on an information theoretic analysis of the system and
its publicly available information. We also propose a mean-field like model of
the game which is most accurate in the maladaptive, efficient phase. In
addition, we show that the best individual agent performance in the two
different phases is achieved by sets of strategies with markedly different
characteristics. We discuss implications of our results for various aspects of
the study of complex adaptive systems.


title: Power spectra of extinction in the fossil record

abstract:
  Recent Fourier analyses of fossil extinction data have indicated that the
power spectrum of extinction during the Phanerozoic may take the form of 1/f
noise, a result which, it has been suggested, could be indicative of the
presence of "critical dynamics" in the processes giving rise to extinction. In
this paper we examine extinction power spectra in some detail, using
family-level data from a variety of different sources. We find that although
the average form of the power spectrum roughly obeys the 1/f law, the spectrum
can be represented more accurately by dividing it into two regimes: a
low-frequency one which is well fit by an exponential, and a high-frequency one
in which it follows a power law with a 1/f^2 form. We give explanations for the
occurrence of each of these behaviours and for the position of the cross-over
between them.


title:
Reproductive Tradeoffs In Uncertain Environments: Explaining The
  Evolution Of Cultural Elaboration

abstract:
  Dunnell's (1989) explanation for cultural elaboration proposed that
elaboration could be a consequence of selection within uncertain environments.
He developed the theory to the extent that it performed well explaining the
distribution of elaboration at regional scales within eastern North America.
More detailed studies require more detailed development of the theory, so that
additional hypotheses and implications can be deduced. We draw upon theories of
selection in fluctuating environments and portions of life history theory to
propose a formal model of selection for "waste" in uncertain environments. We
use agent-based simulation to explore the sufficiency of the theory for
explaining the maintenance of high levels of elaboration within populations,
and deduce novel implications for archaeological evidence usable by others to
test the utility of Dunnell's model in specific localities.


title: Modeling 1/f noise

abstract:
  The noise of signals or currents consisting from a sequence of pulses,
elementary events or moving discrete objects (particles) is analyzed. A simple
analytically solvable model is investigated in detail both analytically and
numerically. It is shown that 1/f noise may result from the statistics of the
pulses transit times with random increments of the time intervals between the
pulses. The model also serves as a basis for revealing parameter dependences of
1/f noise and allows one to make some generalizations. As a result the
intensity of 1/f noise is expressed through the distribution and characteristic
functions of the time intervals between the subsequent transit times of the
pulses. The conclusion that 1/f noise may result from the clustering of the
signal pulses, elementary events or particles can be drawn from the analysis of
the model systems.

categories: adap-org cond-mat.stat-mech cond-mat.str-el math.DS math.SP nlin.AO


title: Clustering and synchronization with positive Lyapunov exponents

abstract:
  Clustering and correlation effects are frequently observed in chaotic systems
in situations where, because of the positivity of the Lyapunov exponents, no
dimension reduction is to be expected. In this paper, using a globally coupled
network of Bernoulli units, one finds a general mechanism by which strong
correlations and slow structures are obtained at the synchronization edge. A
structure index is defined, which diverges at the transition points. Some
conclusions are drawn concerning the construction of an ergodic theory of
self-organization.


title: Market force, ecology and evolution

abstract:
  Markets have internal dynamics leading to excess volatility and other
phenomena that are difficult to explain using rational expectations models.
This paper studies these using a nonequilibrium price formation rule, developed
in the context of trading with market orders. Because this is so much simpler
than a standard inter-temporal equilibrium model, it is possible to study
multi-period markets analytically. There price dynamics have second order
oscillatory terms.
  Value investing does not necessarily cause prices to track values. Trend
following causes short term trends in prices, but also causes longer-term
oscillations. When value investing and trend following are combined, even
though there is little linear structure, there can be boom-bust cycles,excess
and temporally correlated volatility, and fat tails in price fluctuations. The
long term evolution of markets can be studied in terms of flows of money.
  Profits can be decomposed in terms of aggregate pairwise correlations.
  Under reinvestment of profits this leads to a capital allocation model that
is equivalent to a standard model in population biology. An investigation of
market efficiency shows that patterns created by trend followers are more
resistant to efficiency than those created by value investors, and that profit
maximizing behavior slows the progression to efficiency. Order of magnitude
estimates suggest that the timescale for efficiency is years to decades.


title:
The Evolutionary Biology of Ourselves: Unit Requirements and
  Organizational Change in United States History

abstract:
  Researchers have proposed that the distinction between so-called "simple" and
"complex" societies can be expressed by an increase in the number of levels at
which functional organization, interaction, and thus selection, operate. In
spite of the obvious links between this suggestion and research into complex
social organization amongst insects and other social animals, the levels of
selection model has seen little use among anthropologists. We suggest that the
primary reason for lack of research into the evolutionary causes of social
complexity has been the lack of descriptive units with which we can examine
phenotypic variation and heritability of social organization above the level of
the organism. The goal of our paper, therefore, is to begin constructing
descriptive units which map to meaningful models of multi-level selection. In
order to demonstrate how these units are useful in a real dataset, we examine
the functional changes involved in the United States economy over the last 100
years, a period of time characterized, we believe, by significant changes in
the number and kinds of social aggregates functioning as "individuals" with
respect to selection. Our preliminary analysis suggests that it is possible to
measure changes in the scale at which functional integration occurs through
published data, and that the multilevel selection model for complex society may
possess considerable power for describing how selection of culturally
transmitted variation occurs in complex societies.


title:
Autocatalytic closure in a cognitive system: A tentative scenario for
  the origin of culture

abstract:
  This paper presents a speculative model of the cognitive mechanisms
underlying the transition from episodic to mimetic (or memetic) culture with
the arrival of Homo erectus, which Donald [1991] claims paved the way for the
unique features of human culture. The model draws on Kauffman's [1993] theory
of how an information-evolving system emerges through the formation of an
autocatalytic network. Though originally formulated to explain the origin of
life, this theory also provides a plausible account of how discrete episodic
memories become woven into an internal model of the world, or worldview, that
both structures, and is structured by, self-triggered streams of thought.
Social interaction plays a role in (and may be critical to) this process.
Implications for cognitive development are explored.


title:
Towards Behaviorly Realistic Simulations of the Stock Market (Traders
  with a Soul)

abstract:
  The price fluctuations in the financial markets are the result of the
individual operations by many individual investors. However for many decades
the finacial theory did not use directly this "microscopic representation". The
difficulties preventing it were multiple but the main two are being solved
recently with the advent of modern computer technology:
  - massive detailed data on the individual market operations became available.
  - "microscopic simulations" of the stock markets in terms of their individual
participating agents allow a very realistic treatment of the problem.
  Consequently, we are now able to confront real market data with the results
of simulating "microscopic" realistic models which include any desired features
in the investors behavior: departures from rationality, herding effects,
heterogenous investor-specific trading strategies etc. In this way we propose
to understand, explain and may be predict the macroscopic market behavior.


title: Stochastic group selection model for the evolution of altruism

abstract:
  We study numerically and analytically a stochastic group selection model in
which a population of asexually reproducing individuals, each of which can be
either altruist or non-altruist, is subdivided into $M$ reproductively isolated
groups (demes) of size $N$. The cost associated with being altruistic is
modelled by assigning the fitness $1- \tau$, with $\tau \in [0,1]$, to the
altruists and the fitness 1 to the non-altruists. In the case that the
altruistic disadvantage $\tau$ is not too large, we show that the finite $M$
fluctuations are small and practically do not alter the deterministic results
obtained for $M \to \infty$. However, for large $\tau$ these fluctuations
greatly increase the instability of the altruistic demes to mutations. These
results may be relevant to the dynamics of parasite-host systems and, in
particular, to explain the importance of mutation in the evolution of parasite
virulence.


title:
A Mathematical Model with Modified Logistic Approach for Singly-Peaked
  Population Processes

abstract:
  When a small number of individuals of organism of single species is confined
in a closed space with limited amount of indispensable resources, their
breading may start initially under suitable conditions, and after peaking, the
population should go extinct as the resources are exhausted. Starting with the
logistic equation and assuming that the carrying capacity of the environment is
a function of the amount of resources, a mathematical model describing such
pattern of population change is obtained. An application of this model to
typical population records, that of deer herds by Scheffer (1951) and O'Roke
and Hamerstrome (1948), yields estimations of the initial amount of
indispensable food and its availability or nutritional efficiency which were
previously unspecified.


title: The Hamming Distance in the Minority Game

abstract:
  We investigate different versions of the minority game, a toy model for
agents buying and selling a commodity. The Hamming distance between the
strategies used by agents to take decisions is introduced as an analytical tool
to determine several properties of these models. The success rate of the agents
in an adaptive version of the game is compared with the rate from a stochastic
version. It is shown numerically and analytically that the adaptive process is
inefficient, increasing the success rate of the unused strategies while
decreasing the success rate of the strategies used by the agents. The agents do
not do as well as if they were forced to use only one strategy permanently. A
version of the game in which the agents strategies evolve is also analyzed
using the notion of distance. The agents evolve into a state in which they are
all using one strategy, which is again the state that yields the maximum
success rate.


title: A General Approach to the Modelling of Trophic Chains

abstract:
  Based on the law of mass action (and its microscopic foundation) and mass
conservation, we present here a method to derive consistent dynamic models for
the time evolution of systems with an arbitrary number of species. Equations
are derived through a mechanistic description, ensuring that all parameters
have ecological meaning. After discussing the biological mechanisms associated
to the logistic and Lotka-Volterra equations, we show how to derive general
models for trophic chains, including the effects of internal states at fast
time scales. We show that conformity with the mass action law leads to
different functional forms for the Lotka-Volterra and trophic chain models. We
use mass conservation to recover the concept of carrying capacity for an
arbitrary food chain.

categories: adap-org chao-dyn cond-mat.stat-mech math.DS nlin.AO nlin.CD physics.bio-ph physics.chem-ph q-bio.PE


title: The Evolutionary Unfolding of Complexity

abstract:
  We analyze the population dynamics of a broad class of fitness functions that
exhibit epochal evolution---a dynamical behavior, commonly observed in both
natural and artificial evolutionary processes, in which long periods of stasis
in an evolving population are punctuated by sudden bursts of change. Our
approach---statistical dynamics---combines methods from both statistical
mechanics and dynamical systems theory in a way that offers an alternative to
current ``landscape'' models of evolutionary optimization. We describe the
population dynamics on the macroscopic level of fitness classes or phenotype
subbasins, while averaging out the genotypic variation that is consistent with
a macroscopic state. Metastability in epochal evolution occurs solely at the
macroscopic level of the fitness distribution. While a balance between
selection and mutation maintains a quasistationary distribution of fitness,
individuals diffuse randomly through selectively neutral subbasins in genotype
space. Sudden innovations occur when, through this diffusion, a genotypic
portal is discovered that connects to a new subbasin of higher fitness
genotypes. In this way, we identify innovations with the unfolding and
stabilization of a new dimension in the macroscopic state space. The
architectural view of subbasins and portals in genotype space clarifies how
frozen accidents and the resulting phenotypic constraints guide the evolution
to higher complexity.


title: The Origin of the RNA World: a Kinetic Model

abstract:
  The aims of this paper are to propose, construct and analyse microscopic
kinetic models for the emergence of long chains of RNA from monomeric
beta-D-ribonucleotide precursors in prebiotic circumstances. Our theory starts
out from similar but more general chemical assumptions to those of Eigen,
namely that catalytic replication can lead to a large population of long
chains. In particular, our models incorporate the possibility of (i) direct
chain growth, (ii) template-assisted synthesis and (iii) catalysis by RNA
replicase ribozymes, all with varying degrees of efficiency. However, in our
models the reaction mechanisms are kept `open'; we do not assume the existence
of closed hypercycles which sustain a population of long chains. Rather it is
the feasibility of the initial emergence of a self-sustaining set of RNA chains
from monomeric nucleotides which is our prime concern. We confront directly the
central nonlinear features of the problem, which have often been overlooked in
previous studies. Our detailed microscopic kinetic models lead to kinetic
equations which are generalisations of the Becker-Doring system (BD) for the
step-wise growth of clusters or polymer chains; they lie within a general
theoretical framework which has recently been successfully applied to a wide
range of complex chemical problems. In fact, the most accurate model we
consider has BD aggregation terms, together with a general Smoluchowski
fragmentation term to model the competing hydrolysis of RNA polymer chains. We
conclude that, starting from reasonable initial conditions of monomeric
nucleotide concentrations within a prebiotic soup and in an acceptable
timescale, it is possible for a self-replicating subset of polyribonucleotide
chains to be selected, while less efficient replicators become extinct.


title: Evolution of genetic organization in digital organisms

abstract:
  We examine the evolution of expression patterns and the organization of
genetic information in populations of self-replicating digital organisms.
Seeding the experiments with a linearly expressed ancestor, we witness the
development of complex, parallel secondary expression patterns. Using
principles from information theory, we demonstrate an evolutionary pressure
towards overlapping expressions causing variation (and hence further evolution)
to sharply drop. Finally, we compare the overlapping sections of dominant
genomes to those portions which are singly expressed and observe a significant
difference in the entropy of their encoding.