101 research outputs found
Exact Synchronization for Finite-State Sources
We analyze how an observer synchronizes to the internal state of a
finite-state information source, using the epsilon-machine causal
representation. Here, we treat the case of exact synchronization, when it is
possible for the observer to synchronize completely after a finite number of
observations. The more difficult case of strictly asymptotic synchronization is
treated in a sequel. In both cases, we find that an observer, on average, will
synchronize to the source state exponentially fast and that, as a result, the
average accuracy in an observer's predictions of the source output approaches
its optimal level exponentially fast as well. Additionally, we show here how to
analytically calculate the synchronization rate for exact epsilon-machines and
provide an efficient polynomial-time algorithm to test epsilon-machines for
exactness.Comment: 9 pages, 6 figures; now includes analytical calculation of the
synchronization rate; updates and corrections adde
Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy
We develop information-theoretic measures of spatial structure and pattern in
more than one dimension. As is well known, the entropy density of a
two-dimensional configuration can be efficiently and accurately estimated via a
converging sequence of conditional entropies. We show that the manner in which
these conditional entropies converge to their asymptotic value serves as a
measure of global correlation and structure for spatial systems in any
dimension. We compare and contrast entropy-convergence with mutual-information
and structure-factor techniques for quantifying and detecting spatial
structure.Comment: 11 pages, 5 figures,
http://www.santafe.edu/projects/CompMech/papers/2dnnn.htm
Solution of the Quasispecies Model for an Arbitrary Gene Network
In this paper, we study the equilibrium behavior of Eigen's quasispecies
equations for an arbitrary gene network. We consider a genome consisting of genes, so that each gene sequence may be written as . We assume a single fitness peak (SFP) model
for each gene, so that gene has some ``master'' sequence for which it is functioning. The fitness landscape is then determined by
which genes in the genome are functioning, and which are not. The equilibrium
behavior of this model may be solved in the limit of infinite sequence length.
The central result is that, instead of a single error catastrophe, the model
exhibits a series of localization to delocalization transitions, which we term
an ``error cascade.'' As the mutation rate is increased, the selective
advantage for maintaining functional copies of certain genes in the network
disappears, and the population distribution delocalizes over the corresponding
sequence spaces. The network goes through a series of such transitions, as more
and more genes become inactivated, until eventually delocalization occurs over
the entire genome space, resulting in a final error catastrophe. This model
provides a criterion for determining the conditions under which certain genes
in a genome will lose functionality due to genetic drift. It also provides
insight into the response of gene networks to mutagens. In particular, it
suggests an approach for determining the relative importance of various genes
to the fitness of an organism, in a more accurate manner than the standard
``deletion set'' method. The results in this paper also have implications for
mutational robustness and what C.O. Wilke termed ``survival of the flattest.''Comment: 29 pages, 5 figures, to be submitted to Physical Review
On the influence of noise on chaos in nearly Hamiltonian systems
The simultaneous influence of small damping and white noise on Hamiltonian
systems with chaotic motion is studied on the model of periodically kicked
rotor. In the region of parameters where damping alone turns the motion into
regular, the level of noise that can restore the chaos is studied. This
restoration is created by two mechanisms: by fluctuation induced transfer of
the phase trajectory to domains of local instability, that can be described by
the averaging of the local instability index, and by destabilization of motion
within the islands of stability by fluctuation induced parametric modulation of
the stability matrix, that can be described by the methods developed in the
theory of Anderson localization in one-dimensional systems.Comment: 10 pages REVTEX, 9 figures EP
All Else Being Equal Be Empowered
The original publication is available at www.springerlink.com . Copyright Springer DOI : 10.1007/11553090_75The classical approach to using utility functions suffers from the drawback of having to design and tweak the functions on a case by case basis. Inspired by examples from the animal kingdom, social sciences and games we propose empowerment, a rather universal function, defined as the information-theoretic capacity of an agent’s actuation channel. The concept applies to any sensorimotoric apparatus. Empowerment as a measure reflects the properties of the apparatus as long as they are observable due to the coupling of sensors and actuators via the environment.Peer reviewe
From Finite to Infinite Range Order via Annealing: The Causal Architecture of Deformation Faulting in Annealed Close-Packed Crystals
We analyze solid-state phase transformations that occur in zinc-sulfide
crystals during annealing using a random deformation-faulting mechanism with a
very simple interaction between adjacent close-packed double layers. We show
that, through annealing, infinite-range structures emerge from initially
short-range crystal order. That is, widely separated layers carry structurally
significant information and so layer stacking cannot be completely described by
any finite-range Markov process. We compare our results to two experimental
diffraction spectra, finding excellent agreement.Comment: 7 pages, 6 figures; See
http://www.santafe.edu/projects/CompMech/papers/iro.htm
Coupled Replicator Equations for the Dynamics of Learning in Multiagent Systems
Starting with a group of reinforcement-learning agents we derive coupled
replicator equations that describe the dynamics of collective learning in
multiagent systems. We show that, although agents model their environment in a
self-interested way without sharing knowledge, a game dynamics emerges
naturally through environment-mediated interactions. An application to
rock-scissors-paper game interactions shows that the collective learning
dynamics exhibits a diversity of competitive and cooperative behaviors. These
include quasiperiodicity, stable limit cycles, intermittency, and deterministic
chaos--behaviors that should be expected in heterogeneous multiagent systems
described by the general replicator equations we derive.Comment: 4 pages, 3 figures,
http://www.santafe.edu/projects/CompMech/papers/credlmas.html; updated
references, corrected typos, changed conten
A recent appreciation of the singular dynamics at the edge of chaos
We study the dynamics of iterates at the transition to chaos in the logistic
map and find that it is constituted by an infinite family of Mori's -phase
transitions. Starting from Feigenbaum's function for the diameters
ratio, we determine the atypical weak sensitivity to initial conditions associated to each -phase transition and find that it obeys the form
suggested by the Tsallis statistics. The specific values of the variable at
which the -phase transitions take place are identified with the specific
values for the Tsallis entropic index in the corresponding . We
describe too the bifurcation gap induced by external noise and show that its
properties exhibit the characteristic elements of glassy dynamics close to
vitrification in supercooled liquids, e.g. two-step relaxation, aging and a
relationship between relaxation time and entropy.Comment: Proceedings of: Verhulst 200 on Chaos, Brussels 16-18 September 2004,
Springer Verlag, in pres
Measurement in biological systems from the self-organisation point of view
Measurement in biological systems became a subject of concern as a
consequence of numerous reports on limited reproducibility of experimental
results. To reveal origins of this inconsistency, we have examined general
features of biological systems as dynamical systems far from not only their
chemical equilibrium, but, in most cases, also of their Lyapunov stable states.
Thus, in biological experiments, we do not observe states, but distinct
trajectories followed by the examined organism. If one of the possible
sequences is selected, a minute sub-section of the whole problem is obtained,
sometimes in a seemingly highly reproducible manner. But the state of the
organism is known only if a complete set of possible trajectories is known. And
this is often practically impossible. Therefore, we propose a different
framework for reporting and analysis of biological experiments, respecting the
view of non-linear mathematics. This view should be used to avoid
overoptimistic results, which have to be consequently retracted or largely
complemented. An increase of specification of experimental procedures is the
way for better understanding of the scope of paths, which the biological system
may be evolving. And it is hidden in the evolution of experimental protocols.Comment: 13 pages, 5 figure
Tendency to Maximum Complexity in a Non-Equilibrium Isolated System
The time evolution equations of a simplified isolated ideal gas, the
"tetrahe- dral" gas, are derived. The dynamical behavior of the LMC complexity
[R. Lopez-Ruiz, H. L. Mancini, and X. Calbet, Phys. Lett. A 209, 321 (1995)] is
studied in this system. In general, it is shown that the complexity remains
within the bounds of minimum and maximum complexity. We find that there are
certain restrictions when the isolated "tetrahedral" gas evolves towards
equilibrium. In addition to the well-known increase in entropy, the quantity
called disequilibrium decreases monotonically with time. Furthermore, the
trajectories of the system in phase space approach the maximum complexity.Comment: 22 pages, 0 figures. Published in Phys. Rev. E 63, 066116(9) (2001
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