399 research outputs found
Synchronous and Asynchronous Recursive Random Scale-Free Nets
We investigate the differences between scale-free recursive nets constructed
by a synchronous, deterministic updating rule (e.g., Apollonian nets), versus
an asynchronous, random sequential updating rule (e.g., random Apollonian
nets). We show that the dramatic discrepancies observed recently for the degree
exponent in these two cases result from a biased choice of the units to be
updated sequentially in the asynchronous version
Stochastic resonance and noise delayed extinction in a model of two competing species
We study the role of the noise in the dynamics of two competing species. We
consider generalized Lotka-Volterra equations in the presence of a
multiplicative noise, which models the interaction between the species and the
environment. The interaction parameter between the species is a random process
which obeys a stochastic differential equation with a generalized bistable
potential in the presence of a periodic driving term, which accounts for the
environment temperature variation. We find noise-induced periodic oscillations
of the species concentrations and stochastic resonance phenomenon. We find also
a nonmonotonic behavior of the mean extinction time of one of the two competing
species as a function of the additive noise intensity.Comment: 11 pages, 6 figures, 17 panels. To appear in Physica
Magic Supergravities, N= 8 and Black Hole Composites
We present explicit U-duality invariants for the R, C, Q, O$ (real, complex,
quaternionic and octonionic) magic supergravities in four and five dimensions
using complex forms with a reality condition. From these invariants we derive
an explicit entropy function and corresponding stabilization equations which we
use to exhibit stationary multi-center 1/2 BPS solutions of these N=2 d=4
theories, starting with the octonionic one with E_{7(-25)} duality symmetry. We
generalize to stationary 1/8 BPS multicenter solutions of N=8, d=4
supergravity, using the consistent truncation to the quaternionic magic N=2
supergravity. We present a general solution of non-BPS attractor equations of
the STU truncation of magic models. We finish with a discussion of the
BPS-non-BPS relations and attractors in N=2 versus N= 5, 6, 8.Comment: 33 pages, references added plus brief outline at end of introductio
Vertex routing models
A class of models describing the flow of information within networks via
routing processes is proposed and investigated, concentrating on the effects of
memory traces on the global properties. The long-term flow of information is
governed by cyclic attractors, allowing to define a measure for the information
centrality of a vertex given by the number of attractors passing through this
vertex. We find the number of vertices having a non-zero information centrality
to be extensive/sub-extensive for models with/without a memory trace in the
thermodynamic limit. We evaluate the distribution of the number of cycles, of
the cycle length and of the maximal basins of attraction, finding a complete
scaling collapse in the thermodynamic limit for the latter. Possible
implications of our results on the information flow in social networks are
discussed.Comment: 12 pages, 6 figure
Stochastic synchronization in globally coupled phase oscillators
Cooperative effects of periodic force and noise in globally Cooperative
effects of periodic force and noise in globally coupled systems are studied
using a nonlinear diffusion equation for the number density. The amplitude of
the order parameter oscillation is enhanced in an intermediate range of noise
strength for a globally coupled bistable system, and the order parameter
oscillation is entrained to the external periodic force in an intermediate
range of noise strength. These enhancement phenomena of the response of the
order parameter in the deterministic equations are interpreted as stochastic
resonance and stochastic synchronization in globally coupled systems.Comment: 5 figure
Statistics of Cycles: How Loopy is your Network?
We study the distribution of cycles of length h in large networks (of size
N>>1) and find it to be an excellent ergodic estimator, even in the extreme
inhomogeneous case of scale-free networks. The distribution is sharply peaked
around a characteristic cycle length, h* ~ N^a. Our results suggest that h* and
the exponent a might usefully characterize broad families of networks. In
addition to an exact counting of cycles in hierarchical nets, we present a
Monte-Carlo sampling algorithm for approximately locating h* and reliably
determining a. Our empirical results indicate that for small random scale-free
nets of degree exponent g, a=1/(g-1), and a grows as the nets become larger.Comment: Further work presented and conclusions revised, following referee
report
Portraits of Complex Networks
We propose a method for characterizing large complex networks by introducing
a new matrix structure, unique for a given network, which encodes structural
information; provides useful visualization, even for very large networks; and
allows for rigorous statistical comparison between networks. Dynamic processes
such as percolation can be visualized using animations. Applications to graph
theory are discussed, as are generalizations to weighted networks, real-world
network similarity testing, and applicability to the graph isomorphism problem.Comment: 6 pages, 9 figure
High Dimensional Apollonian Networks
We propose a simple algorithm which produces high dimensional Apollonian
networks with both small-world and scale-free characteristics. We derive
analytical expressions for the degree distribution, the clustering coefficient
and the diameter of the networks, which are determined by their dimension
Exact eigenvalue spectrum of a class of fractal scale-free networks
The eigenvalue spectrum of the transition matrix of a network encodes
important information about its structural and dynamical properties. We study
the transition matrix of a family of fractal scale-free networks and
analytically determine all the eigenvalues and their degeneracies. We then use
these eigenvalues to evaluate the closed-form solution to the eigentime for
random walks on the networks under consideration. Through the connection
between the spectrum of transition matrix and the number of spanning trees, we
corroborate the obtained eigenvalues and their multiplicities.Comment: Definitive version accepted for publication in EPL (Europhysics
Letters
Languages cool as they expand: Allometric scaling and the decreasing need for new words
We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two scaling regimes characterize the word frequency distributions, with only the more common words obeying the classic Zipf law. Using corpora of unprecedented size, we test the allometric scaling relation between the corpus size and the vocabulary size of growing languages to demonstrate a decreasing marginal need for new words, a feature that is likely related to the underlying correlations between words. We calculate the annual growth fluctuations of word use which has a decreasing trend as the corpus size increases, indicating a slowdown in linguistic evolution following language expansion. This ââcooling patternââ forms the basis of a third statistical regularity, which unlike the Zipf and the Heaps law, is dynamical in nature
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