6,716 research outputs found
Study of near consensus complex social networks using Eigen theory
This paper extends the definition of an exact consensus complex social network to that of a near consensus complex social network. A near consensus complex social network is a social network with nontrivial topological features and steady state values of the decision certitudes of the majority of the nodes being either higher or lower than a threshold value. By using eigen theories, the relationships among the vectors representing the steady state values of the decision certitudes of the nodes, the influence weight matrix and the set of vectors representing the initial state values of the decision certitudes of the nodes that satisfies a given near consensus specification are characterized
Connections between the Sznajd Model with General Confidence Rules and graph theory
The Sznajd model is a sociophysics model, that is used to model opinion
propagation and consensus formation in societies. Its main feature is that its
rules favour bigger groups of agreeing people. In a previous work, we
generalized the bounded confidence rule in order to model biases and prejudices
in discrete opinion models. In that work, we applied this modification to the
Sznajd model and presented some preliminary results. The present work extends
what we did in that paper. We present results linking many of the properties of
the mean-field fixed points, with only a few qualitative aspects of the
confidence rule (the biases and prejudices modelled), finding an interesting
connection with graph theory problems. More precisely, we link the existence of
fixed points with the notion of strongly connected graphs and the stability of
fixed points with the problem of finding the maximal independent sets of a
graph. We present some graph theory concepts, together with examples, and
comparisons between the mean-field and simulations in Barab\'asi-Albert
networks, followed by the main mathematical ideas and appendices with the
rigorous proofs of our claims. We also show that there is no qualitative
difference in the mean-field results if we require that a group of size q>2,
instead of a pair, of agreeing agents be formed before they attempt to convince
other sites (for the mean-field, this would coincide with the q-voter model).Comment: 15 pages, 18 figures. To be submitted to Physical Revie
Naturalism, Theism, and the Origin of Life
Alvin Plantinga and Phillip E. Johnson strongly attack "metaphysical naturalism", a doctrine based, in part, on Darwinian concepts. They claim that this doctrine dominates American academic, educational, and legal thought, and that it is both erroneous and pernicious. Stuart Kauffman claims that currently accepted versions of Darwinian evolutionary theory are radically incomplete, that they should be supplemented by explicit recognition of the importance of coherent structures — the prevalence of "order for free". Both of these developments are here interpreted in relation to some contemporary theistic notions of "creation", including those of Lewis Ford, Robert Neville, and Robert Sokolowski. Kaufmann’s approach is consistent with the approach of process theism, and is not invalidated by the attacks of Plantinga and Johnson
Collective Relaxation Dynamics of Small-World Networks
Complex networks exhibit a wide range of collective dynamic phenomena,
including synchronization, diffusion, relaxation, and coordination processes.
Their asymptotic dynamics is generically characterized by the local Jacobian,
graph Laplacian or a similar linear operator. The structure of networks with
regular, small-world and random connectivities are reasonably well understood,
but their collective dynamical properties remain largely unknown. Here we
present a two-stage mean-field theory to derive analytic expressions for
network spectra. A single formula covers the spectrum from regular via
small-world to strongly randomized topologies in Watts-Strogatz networks,
explaining the simultaneous dependencies on network size N, average degree k
and topological randomness q. We present simplified analytic predictions for
the second largest and smallest eigenvalue, and numerical checks confirm our
theoretical predictions for zero, small and moderate topological randomness q,
including the entire small-world regime. For large q of the order of one, we
apply standard random matrix theory thereby overarching the full range from
regular to randomized network topologies. These results may contribute to our
analytic and mechanistic understanding of collective relaxation phenomena of
network dynamical systems.Comment: 12 pages, 10 figures, published in PR
First-passage distributions for the one-dimensional Fokker-Planck equation
We present an analytical framework to study the first-passage (FP) and
first-return (FR) distributions for the broad family of models described by the
one-dimensional Fokker-Planck equation in finite domains, identifying general
properties of these distributions for different classes of models. When in the
Fokker-Planck equation the diffusion coefficient is positive (nonzero) and the
drift term is bounded, as in the case of a Brownian walker, both distributions
may exhibit a power-law decay with exponent -3/2 for intermediate times. We
discuss how the influence of an absorbing state changes this exponent. The
absorbing state is characterized by a vanishing diffusion coefficient and/or a
diverging drift term. Remarkably, the exponent of the Brownian walker class of
models is still found, as long as the departure and arrival regions are far
enough from the absorbing state, but the range of times where the power law is
observed narrows. Close enough to the absorbing point, though, a new exponent
may appear. The particular value of the exponent depends on the behavior of the
diffusion and the drift terms of the Fokker-Planck equation. We focus on the
case of a diffusion term vanishing linearly at the absorbing point. In this
case, the FP and FR distributions are similar to those of the voter model,
characterized by a power law with exponent -2. As an illustration of the
general theory, we compare it with exact analytical solutions and extensive
numerical simulations of a two-parameter voter-like family models. We study the
behavior of the FP and FR distributions by tuning the importance of the
absorbing points throughout changes of the parameters. Finally, the possibility
of inferring relevant information about the steady-sate probability
distribution of a model from the FP and FR distributions is addressed.Comment: 17 pages, 8 figure
Weighted random--geometric and random--rectangular graphs: Spectral and eigenfunction properties of the adjacency matrix
Within a random-matrix-theory approach, we use the nearest-neighbor energy
level spacing distribution and the entropic eigenfunction localization
length to study spectral and eigenfunction properties (of adjacency
matrices) of weighted random--geometric and random--rectangular graphs. A
random--geometric graph (RGG) considers a set of vertices uniformly and
independently distributed on the unit square, while for a random--rectangular
graph (RRG) the embedding geometry is a rectangle. The RRG model depends on
three parameters: The rectangle side lengths and , the connection
radius , and the number of vertices . We then study in detail the case
which corresponds to weighted RGGs and explore weighted RRGs
characterized by , i.e.~two-dimensional geometries, but also approach
the limit of quasi-one-dimensional wires when . In general we look for
the scaling properties of and as a function of , and .
We find that the ratio , with , fixes the
properties of both RGGs and RRGs. Moreover, when we show that
spectral and eigenfunction properties of weighted RRGs are universal for the
fixed ratio , with .Comment: 8 pages, 6 figure
Open problems in artificial life
This article lists fourteen open problems in artificial life, each of which is a grand challenge requiring a major advance on a fundamental issue for its solution. Each problem is briefly explained, and, where deemed helpful, some promising paths to its solution are indicated
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