410 research outputs found
Spectral Analysis and the Dynamic Response of Complex Networks
The eigenvalues and eigenvectors of the connectivity matrix of complex
networks contain information about its topology and its collective behavior. In
particular, the spectral density of this matrix reveals
important network characteristics: random networks follow Wigner's semicircular
law whereas scale-free networks exhibit a triangular distribution. In this
paper we show that the spectral density of hierarchical networks follow a very
different pattern, which can be used as a fingerprint of modularity. Of
particular importance is the value , related to the homeostatic
response of the network: it is maximum for random and scale free networks but
very small for hierarchical modular networks. It is also large for an actual
biological protein-protein interaction network, demonstrating that the current
leading model for such networks is not adequate.Comment: 4 pages 14 figure
Statistical mechanics model of angiogenic tumor growth
We examine a lattice model of tumor growth where survival of tumor cells
depends on the supplied nutrients. When such a supply is random, the extinction
of tumors belongs to the directed percolation universality class. However, when
the supply is correlated with distribution of tumor cells, which as we suggest
might mimick the angiogenic growth, the extinction shows different, and most
likely novel critical behaviour. Such a correlation affects also the morphology
of the growing tumors and drastically raise tumor survival probability.Comment: 4 page
Mean-field approximation to a spatial host-pathogen model
We study the mean-field approximation to a simple spatial host-pathogen model that has been shown to display interesting evolutionary properties. We show that previous derivations of the mean-field equations for this model are actually only low-density approximations to the true mean-field limit. We derive the correct equations and the corresponding equations including pair correlations. The process of invasion by a mutant type of pathogen is also discussed.674
Mass enhancement in narrow band systems
A perturbative study of the Holstein Molecular Crystal Model which accounts
for lattice structure and dimensionality effects is presented. Antiadiabatic
conditions peculiar of narrow band materials and an intermediate to strong
electron-phonon coupling are assumed. The polaron effective mass depends
crucially in all dimensions on the intermolecular coupling strengths which also
affect the size of the lattice deformation associated with the small polaron
formation.Comment: Istituto Nazionale di Fisica della Materia - Dipartimento di
Matematica e Fisica, Istituto Nazionale di Fisica della Materia Universita'
di Camerino, 62032 Camerino, Ital
Robustness of spontaneous pattern formation in spatially distributed genetic populations
Spatially distributed genetic populations that compete locally for resources and mate only with sufficiently close neighbors, may give rise to spontaneous pattern formation. Depending on the population parameters, like death rate per generation and size of the competition and mating neighborhoods, isolated groups of individuals, or demes, may appear. The existence of such groups in a population has consequences for genetic diversity and for speciation. In this paper we discuss the robustness of demes formation with respect to two important characteristics of the population: the way individuals recognize the demarcation of the local neighborhoods and the way competition for resources affects the birth rate in an overcrowed situation. Our results indicate that demes are expected to form only for sufficiently sharp demarcations and for sufficiently intense competition.51452
Phase ordering and roughening on growing films
We study the interplay between surface roughening and phase separation during
the growth of binary films. Already in 1+1 dimension, we find a variety of
different scaling behaviors depending on how the two phenomena are coupled. In
the most interesting case, related to the advection of a passive scalar in a
velocity field, nontrivial scaling exponents are obtained in simulations.Comment: 4 pages latex, 6 figure
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