117,344 research outputs found
Compressibility, laws of nature, initial conditions and complexity
We critically analyse the point of view for which laws of nature are just a
mean to compress data. Discussing some basic notions of dynamical systems and
information theory, we show that the idea that the analysis of large amount of
data by means of an algorithm of compression is equivalent to the knowledge one
can have from scientific laws, is rather naive. In particular we discuss the
subtle conceptual topic of the initial conditions of phenomena which are
generally incompressible. Starting from this point, we argue that laws of
nature represent more than a pure compression of data, and that the
availability of large amount of data, in general, is not particularly useful to
understand the behaviour of complex phenomena.Comment: 19 Pages, No figures, published on Foundation of Physic
Selective pressures on genomes in molecular evolution
We describe the evolution of macromolecules as an information transmission
process and apply tools from Shannon information theory to it. This allows us
to isolate three independent, competing selective pressures that we term
compression, transmission, and neutrality selection. The first two affect
genome length: the pressure to conserve resources by compressing the code, and
the pressure to acquire additional information that improves the channel,
increasing the rate of information transmission into each offspring. Noisy
transmission channels (replication with mutations) gives rise to a third
pressure that acts on the actual encoding of information; it maximizes the
fraction of mutations that are neutral with respect to the phenotype. This
neutrality selection has important implications for the evolution of
evolvability. We demonstrate each selective pressure in experiments with
digital organisms.Comment: 16 pages, 3 figures, to be published in J. theor. Biolog
Complexity of Networks
Network or graph structures are ubiquitous in the study of complex systems.
Often, we are interested in complexity trends of these system as it evolves
under some dynamic. An example might be looking at the complexity of a food web
as species enter an ecosystem via migration or speciation, and leave via
extinction.
In this paper, a complexity measure of networks is proposed based on the {\em
complexity is information content} paradigm. To apply this paradigm to any
object, one must fix two things: a representation language, in which strings of
symbols from some alphabet describe, or stand for the objects being considered;
and a means of determining when two such descriptions refer to the same object.
With these two things set, the information content of an object can be computed
in principle from the number of equivalent descriptions describing a particular
object.
I propose a simple representation language for undirected graphs that can be
encoded as a bitstring, and equivalence is a topological equivalence. I also
present an algorithm for computing the complexity of an arbitrary undirected
network.Comment: Accepted for Australian Conference on Artificial Life (ACAL05). To
appear in Advances in Natural Computation (World Scientific
Cognitive networks: brains, internet, and civilizations
In this short essay, we discuss some basic features of cognitive activity at
several different space-time scales: from neural networks in the brain to
civilizations. One motivation for such comparative study is its heuristic
value. Attempts to better understand the functioning of "wetware" involved in
cognitive activities of central nervous system by comparing it with a computing
device have a long tradition. We suggest that comparison with Internet might be
more adequate. We briefly touch upon such subjects as encoding, compression,
and Saussurean trichotomy langue/langage/parole in various environments.Comment: 16 page
Sequence alignment, mutual information, and dissimilarity measures for constructing phylogenies
Existing sequence alignment algorithms use heuristic scoring schemes which
cannot be used as objective distance metrics. Therefore one relies on measures
like the p- or log-det distances, or makes explicit, and often simplistic,
assumptions about sequence evolution. Information theory provides an
alternative, in the form of mutual information (MI) which is, in principle, an
objective and model independent similarity measure. MI can be estimated by
concatenating and zipping sequences, yielding thereby the "normalized
compression distance". So far this has produced promising results, but with
uncontrolled errors. We describe a simple approach to get robust estimates of
MI from global pairwise alignments. Using standard alignment algorithms, this
gives for animal mitochondrial DNA estimates that are strikingly close to
estimates obtained from the alignment free methods mentioned above. Our main
result uses algorithmic (Kolmogorov) information theory, but we show that
similar results can also be obtained from Shannon theory. Due to the fact that
it is not additive, normalized compression distance is not an optimal metric
for phylogenetics, but we propose a simple modification that overcomes the
issue of additivity. We test several versions of our MI based distance measures
on a large number of randomly chosen quartets and demonstrate that they all
perform better than traditional measures like the Kimura or log-det (resp.
paralinear) distances. Even a simplified version based on single letter Shannon
entropies, which can be easily incorporated in existing software packages, gave
superior results throughout the entire animal kingdom. But we see the main
virtue of our approach in a more general way. For example, it can also help to
judge the relative merits of different alignment algorithms, by estimating the
significance of specific alignments.Comment: 19 pages + 16 pages of supplementary materia
Approximations of Algorithmic and Structural Complexity Validate Cognitive-behavioural Experimental Results
We apply methods for estimating the algorithmic complexity of sequences to
behavioural sequences of three landmark studies of animal behavior each of
increasing sophistication, including foraging communication by ants, flight
patterns of fruit flies, and tactical deception and competition strategies in
rodents. In each case, we demonstrate that approximations of Logical Depth and
Kolmogorv-Chaitin complexity capture and validate previously reported results,
in contrast to other measures such as Shannon Entropy, compression or ad hoc.
Our method is practically useful when dealing with short sequences, such as
those often encountered in cognitive-behavioural research. Our analysis
supports and reveals non-random behavior (LD and K complexity) in flies even in
the absence of external stimuli, and confirms the "stochastic" behaviour of
transgenic rats when faced that they cannot defeat by counter prediction. The
method constitutes a formal approach for testing hypotheses about the
mechanisms underlying animal behaviour.Comment: 28 pages, 7 figures and 2 table
- …