1,023 research outputs found
Compression-based investigation of the dynamical properties of cellular automata and other systems
A method for studying the qualitative dynamical properties of abstract
computing machines based on the approximation of their program-size complexity
using a general lossless compression algorithm is presented. It is shown that
the compression-based approach classifies cellular automata (CA) into clusters
according to their heuristic behavior, with these clusters showing a
correspondence with Wolfram's main classes of CA behavior. A compression based
method to estimate a characteristic exponent to detect phase transitions and
measure the resiliency or sensitivity of a system to its initial conditions is
also proposed. A conjecture regarding the capability of a system to reach
computational universality related to the values of this phase transition
coefficient is formulated. These ideas constitute a compression-based framework
for investigating the dynamical properties of cellular automata and other
systems.Comment: 28 pages. This version includes the conjecture relating the
transition coefficient to computational universality. Camera ready versio
Causality, Information and Biological Computation: An algorithmic software approach to life, disease and the immune system
Biology has taken strong steps towards becoming a computer science aiming at
reprogramming nature after the realisation that nature herself has reprogrammed
organisms by harnessing the power of natural selection and the digital
prescriptive nature of replicating DNA. Here we further unpack ideas related to
computability, algorithmic information theory and software engineering, in the
context of the extent to which biology can be (re)programmed, and with how we
may go about doing so in a more systematic way with all the tools and concepts
offered by theoretical computer science in a translation exercise from
computing to molecular biology and back. These concepts provide a means to a
hierarchical organization thereby blurring previously clear-cut lines between
concepts like matter and life, or between tumour types that are otherwise taken
as different and may not have however a different cause. This does not diminish
the properties of life or make its components and functions less interesting.
On the contrary, this approach makes for a more encompassing and integrated
view of nature, one that subsumes observer and observed within the same system,
and can generate new perspectives and tools with which to view complex diseases
like cancer, approaching them afresh from a software-engineering viewpoint that
casts evolution in the role of programmer, cells as computing machines, DNA and
genes as instructions and computer programs, viruses as hacking devices, the
immune system as a software debugging tool, and diseases as an
information-theoretic battlefield where all these forces deploy. We show how
information theory and algorithmic programming may explain fundamental
mechanisms of life and death.Comment: 30 pages, 8 figures. Invited chapter contribution to Information and
Causality: From Matter to Life. Sara I. Walker, Paul C.W. Davies and George
Ellis (eds.), Cambridge University Pres
Formal Definitions of Unbounded Evolution and Innovation Reveal Universal Mechanisms for Open-Ended Evolution in Dynamical Systems
Open-ended evolution (OEE) is relevant to a variety of biological, artificial
and technological systems, but has been challenging to reproduce in silico.
Most theoretical efforts focus on key aspects of open-ended evolution as it
appears in biology. We recast the problem as a more general one in dynamical
systems theory, providing simple criteria for open-ended evolution based on two
hallmark features: unbounded evolution and innovation. We define unbounded
evolution as patterns that are non-repeating within the expected Poincare
recurrence time of an equivalent isolated system, and innovation as
trajectories not observed in isolated systems. As a case study, we implement
novel variants of cellular automata (CA) in which the update rules are allowed
to vary with time in three alternative ways. Each is capable of generating
conditions for open-ended evolution, but vary in their ability to do so. We
find that state-dependent dynamics, widely regarded as a hallmark of life,
statistically out-performs other candidate mechanisms, and is the only
mechanism to produce open-ended evolution in a scalable manner, essential to
the notion of ongoing evolution. This analysis suggests a new framework for
unifying mechanisms for generating OEE with features distinctive to life and
its artifacts, with broad applicability to biological and artificial systems.Comment: Main document: 17 pages, Supplement: 21 pages Presented at OEE2: The
Second Workshop on Open-Ended Evolution, 15th International Conference on the
Synthesis and Simulation of Living Systems (ALIFE XV), Canc\'un, Mexico, 4-8
July 2016 (http://www.tim-taylor.com/oee2/
Complexity and Information: Measuring Emergence, Self-organization, and Homeostasis at Multiple Scales
Concepts used in the scientific study of complex systems have become so
widespread that their use and abuse has led to ambiguity and confusion in their
meaning. In this paper we use information theory to provide abstract and
concise measures of complexity, emergence, self-organization, and homeostasis.
The purpose is to clarify the meaning of these concepts with the aid of the
proposed formal measures. In a simplified version of the measures (focusing on
the information produced by a system), emergence becomes the opposite of
self-organization, while complexity represents their balance. Homeostasis can
be seen as a measure of the stability of the system. We use computational
experiments on random Boolean networks and elementary cellular automata to
illustrate our measures at multiple scales.Comment: 42 pages, 11 figures, 2 table
Predictability: a way to characterize Complexity
Different aspects of the predictability problem in dynamical systems are
reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy,
Shannon entropy and algorithmic complexity is discussed. In particular, we
emphasize how a characterization of the unpredictability of a system gives a
measure of its complexity. Adopting this point of view, we review some
developments in the characterization of the predictability of systems showing
different kind of complexity: from low-dimensional systems to high-dimensional
ones with spatio-temporal chaos and to fully developed turbulence. A special
attention is devoted to finite-time and finite-resolution effects on
predictability, which can be accounted with suitable generalization of the
standard indicators. The problems involved in systems with intrinsic randomness
is discussed, with emphasis on the important problems of distinguishing chaos
from noise and of modeling the system. The characterization of irregular
behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports.
Related information at this http://axtnt2.phys.uniroma1.i
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