On the Efficiency of Data Representation on the Modeling and Characterization of Complex Networks

Specific choices about how to represent complex networks can have a substantial effect on the execution time required for the respective construction and analysis of those structures. In this work we report a comparison of the effects of representing complex networks statically as matrices or dynamically as spase structures. Three theoretical models of complex networks are considered: two types of Erdos-Renyi as well as the Barabasi-Albert model. We investigated the effect of the different representations with respect to the construction and measurement of several topological properties (i.e. degree, clustering coefficient, shortest path length, and betweenness centrality). We found that different forms of representation generally have a substantial effect on the execution time, with the sparse representation frequently resulting in remarkably superior performance

The Influence of N14(e-,nu)C14(alpha,gamma)O18 reaction on the He-Ignition in Degenerate Physical Conditions

The importance of NCO chain on the onset of the He-flash in degenerate physical conditions has been reevaluated. We find that low-mass, metal-rich (Z $\ge$ 0.001) structures climbing the Red Giant Branch do never attain the physical conditions suitable for the onset of this chain, while at lower metallicities the energy contribution provided by NCO reaction is too low to affect the onset of the central He-flash. At the same time, our evolutionary models suggest that for a Carbon-Oxygen White Dwarf of mass M_{WD}=0.6 M_sun accreting He-rich matter, directly or as a by-product of an overlying H-burning shell, at rates suitable for a dynamical He-flash, the NCO energy contribution is not able to keep hot enough the He-shell and in turn to avoid the occurrence of a strong electron degeneracy and the ensuing final explosion.Comment: 15 pages, 3 tables, 10 figure, to appear in Ap

Analyzing Trails in Complex Networks

Even more interesting than the intricate organization of complex networks are the dynamical behavior of systems which such structures underly. Among the many types of dynamics, one particularly interesting category involves the evolution of trails left by moving agents progressing through random walks and dilating processes in a complex network. The emergence of trails is present in many dynamical process, such as pedestrian traffic, information flow and metabolic pathways. Important problems related with trails include the reconstruction of the trail and the identification of its source, when complete knowledge of the trail is missing. In addition, the following of trails in multi-agent systems represent a particularly interesting situation related to pedestrian dynamics and swarming intelligence. The present work addresses these three issues while taking into account permanent and transient marks left in the visited nodes. Different topologies are considered for trail reconstruction and trail source identification, including four complex networks models and four real networks, namely the Internet, the US airlines network, an email network and the scientific collaboration network of complex network researchers. Our results show that the topology of the network influence in trail reconstruction, source identification and agent dynamics.Comment: 10 pages, 16 figures. A working manuscript, comments and criticisms welcome

Black-hole horizons as probes of black-hole dynamics I: post-merger recoil in head-on collisions

The understanding of strong-field dynamics near black-hole horizons is a long-standing and challenging prob- lem in general relativity. Recent advances in numerical relativity and in the geometric characterization of black- hole horizons open new avenues into the problem. In this first paper in a series of two, we focus on the analysis of the recoil occurring in the merger of binary black holes, extending the analysis initiated in [1] with Robinson- Trautman spacetimes. More specifically, we probe spacetime dynamics through the correlation of quantities defined at the black-hole horizon and at null infinity. The geometry of these hypersurfaces responds to bulk gravitational fields acting as test screens in a scattering perspective of spacetime dynamics. Within a 3 + 1 approach we build an effective-curvature vector from the intrinsic geometry of dynamical-horizon sections and correlate its evolution with the flux of Bondi linear momentum at large distances. We employ this setup to study numerically the head-on collision of nonspinning black holes and demonstrate its validity to track the qualita- tive aspects of recoil dynamics at infinity. We also make contact with the suggestion that the antikick can be described in terms of a "slowness parameter" and how this can be computed from the local properties of the horizon. In a companion paper [2] we will further elaborate on the geometric aspects of this approach and on its relation with other approaches to characterize dynamical properties of black-hole horizons.Comment: final version published on PR

Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems

In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be given to some methods applied in the analysis and characterization of diffusive regimes through the memory function, the mixing condition (or irreversibility), and ergodicity. Those methods can be used in the study of small-scale systems, ranging in size from single-molecule to particle clusters and including among others polymers, proteins, ion channels and biological cells, whose diffusive properties have received much attention lately.Comment: Review article, 20 pages, 7 figures. arXiv admin note: text overlap with arXiv:cond-mat/0201446 by other author

Intermittent exploration on a scale-free network

We study an intermittent random walk on a random network of scale-free degree distribution. The walk is a combination of simple random walks of duration $t_w$ and random long-range jumps. While the time the walker needs to cover all the nodes increases with $t_w$, the corresponding time for the edges displays a non monotonic behavior with a minimum for some nontrivial value of $t_w$. This is a heterogeneity-induced effect that is not observed in homogeneous small-world networks. The optimal $t_w$ increases with the degree of assortativity in the network. Depending on the nature of degree correlations and the elapsed time the walker finds an over/under-estimate of the degree distribution exponent.Comment: 12 pages, 3 figures, 1 table, published versio

Thermodynamical properties of hairy black holes in n spacetimes dimensions

The issue concerning the existence of exact black hole solutions in presence of non vanishing cosmological constant and scalar fields is reconsidered. With regard to this, in investigating no-hair theorem violations, exact solutions of gravity having as a source an interacting and conformally coupled scalar field are revisited in arbitrary dimensional non asymptotically flat space-times. New and known hairy black hole solutions are discussed. The thermodynamical properties associated with these solutions are investigated and the invariance of the black hole entropy with respect to different conformal frames is proven.Comment: Latex document, 23 pages, references added to section [1] and [3], typos correcte

Prominent effect of soil network heterogeneity on microbial invasion

Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks. The main influence of network topology on invasion is linked to the existence of long channels in soil networks that may act as bridges for transmission of microorganisms between distant parts of soil