Percolation transition and distribution of connected components in generalized random network ensembles

In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree sequences, non-trivial community structure or specific spatial dependence of the link probability for networks embedded in a metric space. We find the cluster distribution of the networks in these ensembles by mapping the problem to a fully connected Potts model with heterogeneous couplings. We show that the nature of the Potts model phase transition, linked to the birth of a giant component, has a crossover from second to first order when the number of critical colors $q_c = 2$ in all the networks under study. These results shed light on the properties of dynamical processes defined on these network ensembles.Comment: 27 pages, 15 figure

Growing Cayley trees described by Fermi distribution

We introduce a model for growing Cayley trees with thermal noise. The evolution of these hierarchical networks reduces to the Eden model and the Invasion Percolation model in the limit $T\to 0$, $T\to \infty$ respectively. We show that the distribution of the bond strengths (energies) is described by the Fermi statistics. We discuss the relation of the present results with the scale-free networks described by Bose statistics

Quantum statistics in complex networks

In this work we discuss the symmetric construction of bosonic and fermionic networks and we present a case of a network showing a mixed quantum statistics. This model takes into account the different nature of nodes, described by a random parameter that we call energy, and includes rewiring of the links. The system described by the mixed statistics is an inhomogemeous system formed by two class of nodes. In fact there is a threshold energy $\epsilon_s$ such that nodes with lower energy $(\epsilon<\epsilon_s)$ increase their connectivity while nodes with higher energy $(\epsilon>\epsilon_s)$ decrease their connectivity in time.Comment: 5 pages, 2 figure

Final state interaction effects in D(e,e′p)D(e,e'p) scattering

We present a systematic study of the final-state interaction (FSI) effects in $D(e,e'p)$ scattering in the CEBAF energy range with particular emphasis on the phenomenon of the angular anisotropy of the missing momentum distribution. We find that FSI effects dominate at missing momentum p_m \gsim 1.5 fm$^{-1}$. FSI effects in the excitation of the $S$-wave state are much stronger than in the excitation of the $D$-wave.Comment: LATEX, 11 pages, 5 figures available from the authors on request, KFA-IKP(TH)-1994-3

An extended formalism for preferential attachment in heterogeneous complex networks

In this paper we present a framework for the extension of the preferential attachment (PA) model to heterogeneous complex networks. We define a class of heterogeneous PA models, where node properties are described by fixed states in an arbitrary metric space, and introduce an affinity function that biases the attachment probabilities of links. We perform an analytical study of the stationary degree distributions in heterogeneous PA networks. We show that their degree densities exhibit a richer scaling behavior than their homogeneous counterparts, and that the power law scaling in the degree distribution is robust in presence of heterogeneity

Non-neutral theory of biodiversity

We present a non-neutral stochastic model for the dynamics taking place in a meta-community ecosystems in presence of migration. The model provides a framework for describing the emergence of multiple ecological scenarios and behaves in two extreme limits either as the unified neutral theory of biodiversity or as the Bak-Sneppen model. Interestingly, the model shows a condensation phase transition where one species becomes the dominant one, the diversity in the ecosystems is strongly reduced and the ecosystem is non-stationary. This phase transition extend the principle of competitive exclusion to open ecosystems and might be relevant for the study of the impact of invasive species in native ecologies.Comment: 4 pages, 3 figur

Maximal planar scale-free Sierpinski networks with small-world effect and power-law strength-degree correlation

Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski networks, which are induced by the famous Sierpinski fractals and constructed in a simple iterative way. We derive analytical expressions for degree distribution, strength distribution, clustering coefficient, and strength-degree correlation, which agree well with the characterizations of various real-life networks. Moreover, we show that the introduced Sierpinski networks are maximal planar graphs.Comment: 6 pages, 5 figures, accepted by EP

Final state interactions and NNNN correlations: are the latter observable?

Are effects of short range correlations in the ground state of the target nucleus (initial state correlations ISC) observable in experiments on quasielastic $A(e,e'p)$ scattering at large missing momentum $p_{m}$? Will the missing momentum spectrum observed at CEBAF be overwhelmed by final state interactions (FSI) of the struck proton? The recent advances in the theory of FSI and findings of complex interplay and strong quantum-mechanical interference of FSI and ISC contributions to scattering at p_{m}\gsim 1\,fm$^{-1}$ are reviewed. We conclude that for p_m \gsim 1 \, fm$^{-1}$ quasielastic scattering is dominated by FSI effects and the sensitivity to details of the nuclear ground state is lost.Comment: Invited Talk given by N.N.Nikolaev at the Conference on Perspectives in Nuclear Physics at Intermediate Energies (Trieste, Italy, May 1995) 18 pages, uuencoded including all figure

Entropy measures for complex networks: Toward an information theory of complex topologies

The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this paper we propose how to define the Shannon entropy of a network ensemble and how it relates to the Gibbs and von Neumann entropies of network ensembles. The quantities we introduce here will play a crucial role for the formulation of null models of networks through maximum-entropy arguments and will contribute to inference problems emerging in the field of complex networks.Comment: (4 pages, 1 figure