1,051 research outputs found
A linear construction for certain Kerdock and Preparata codes
The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre\- parata codes
are shown to be linear over \ZZ_4, the integers . The Kerdock and
Preparata codes are duals over \ZZ_4, and the Nordstrom-Robinson code is
self-dual. All these codes are just extended cyclic codes over \ZZ_4. This
provides a simple definition for these codes and explains why their Hamming
weight distributions are dual to each other. First- and second-order
Reed-Muller codes are also linear codes over \ZZ_4, but Hamming codes in
general are not, nor is the Golay code.Comment: 5 page
Modeling two-language competition dynamics
During the last decade, much attention has been paid to language competition
in the complex systems community, that is, how the fractions of speakers of
several competing languages evolve in time. In this paper we review recent
advances in this direction and focus on three aspects. First we consider the
shift from two-state models to three state models that include the possibility
of bilingual individuals. The understanding of the role played by bilingualism
is essential in sociolinguistics. In particular, the question addressed is
whether bilingualism facilitates the coexistence of languages. Second, we will
analyze the effect of social interaction networks and physical barriers.
Finally, we will show how to analyze the issue of bilingualism from a game
theoretical perspective.Comment: 15 pages, 5 figures; published in the Special Issue of Advances in
Complex Systems "Language Dynamics
Topological reversibility and causality in feed-forward networks
Systems whose organization displays causal asymmetry constraints, from
evolutionary trees to river basins or transport networks, can be often
described in terms of directed paths (causal flows) on a discrete state space.
Such a set of paths defines a feed-forward, acyclic network. A key problem
associated with these systems involves characterizing their intrinsic degree of
path reversibility: given an end node in the graph, what is the uncertainty of
recovering the process backwards until the origin? Here we propose a novel
concept, \textit{topological reversibility}, which rigorously weigths such
uncertainty in path dependency quantified as the minimum amount of information
required to successfully revert a causal path. Within the proposed framework we
also analytically characterize limit cases for both topologically reversible
and maximally entropic structures. The relevance of these measures within the
context of evolutionary dynamics is highlighted.Comment: 9 pages, 3 figure
A lattice model for the line tension of a sessile drop
Within a semi--infinite thre--dimensional lattice gas model describing the
coexistence of two phases on a substrate, we study, by cluster expansion
techniques, the free energy (line tension) associated with the contact line
between the two phases and the substrate. We show that this line tension, is
given at low temperature by a convergent series whose leading term is negative,
and equals 0 at zero temperature
Link Prediction Based on Local Random Walk
The problem of missing link prediction in complex networks has attracted much
attention recently. Two difficulties in link prediction are the sparsity and
huge size of the target networks. Therefore, the design of an efficient and
effective method is of both theoretical interests and practical significance.
In this Letter, we proposed a method based on local random walk, which can give
competitively good prediction or even better prediction than other
random-walk-based methods while has a lower computational complexity.Comment: 6 pages, 2 figure
Red Queen Coevolution on Fitness Landscapes
Species do not merely evolve, they also coevolve with other organisms.
Coevolution is a major force driving interacting species to continuously evolve
ex- ploring their fitness landscapes. Coevolution involves the coupling of
species fit- ness landscapes, linking species genetic changes with their
inter-specific ecological interactions. Here we first introduce the Red Queen
hypothesis of evolution com- menting on some theoretical aspects and empirical
evidences. As an introduction to the fitness landscape concept, we review key
issues on evolution on simple and rugged fitness landscapes. Then we present
key modeling examples of coevolution on different fitness landscapes at
different scales, from RNA viruses to complex ecosystems and macroevolution.Comment: 40 pages, 12 figures. To appear in "Recent Advances in the Theory and
Application of Fitness Landscapes" (H. Richter and A. Engelbrecht, eds.).
Springer Series in Emergence, Complexity, and Computation, 201
Signatures of currency vertices
Many real-world networks have broad degree distributions. For some systems,
this means that the functional significance of the vertices is also broadly
distributed, in other cases the vertices are equally significant, but in
different ways. One example of the latter case is metabolic networks, where the
high-degree vertices -- the currency metabolites -- supply the molecular groups
to the low-degree metabolites, and the latter are responsible for the
higher-order biological function, of vital importance to the organism. In this
paper, we propose a generalization of currency metabolites to currency
vertices. We investigate the network structural characteristics of such
systems, both in model networks and in some empirical systems. In addition to
metabolic networks, we find that a network of music collaborations and a
network of e-mail exchange could be described by a division of the vertices
into currency vertices and others.Comment: to appear in Journal of the Physical Society of Japa
The shape of ecological networks
We study the statistics of ecosystems with a variable number of co-evolving
species. The species interact in two ways: by prey-predator relationships and
by direct competition with similar kinds. The interaction coefficients change
slowly through successful adaptations and speciations. We treat them as
quenched random variables. These interactions determine long-term topological
features of the species network, which are found to agree with those of
biological systems.Comment: 4 pages, 2 figure
Statistics of Certain Models of Evolution
In a recent paper, Newman surveys the literature on power law spectra in
evolution, self-organised criticality and presents a model of his own to arrive
at a conclusion that self-organised criticality is not necessary for evolution.
Not only did he miss a key model (Ecolab) that has a clear self-organised
critical mechanism, but also Newman's model exhibits the same mechanism that
gives rise to power law behaviour as does Ecolab. Newman's model is, in fact, a
``mean field'' approximation of a self-organised critical system. In this
paper, I have also implemented Newman's model using the Ecolab software,
removing the restriction that the number of species remains constant. It turns
out that the requirement of constant species number is non-trivial, leading to
a global coupling between species that is similar in effect to the species
interactions seen in Ecolab. In fact, the model must self-organise to a state
where the long time average of speciations balances that of the extinctions,
otherwise the system either collapses or explodes. In view of this, Newman's
model does not provide the hoped-for counter example to the presence of
self-organised criticality in evolution, but does provide a simple, almost
analytic model that can used to understand more intricate models such as
Ecolab.Comment: accepted in Phys Rev E.; RevTeX; See
http://parallel.hpc.unsw.edu.au/rks/ecolab.html for more informatio
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