Local heuristics and the emergence of spanning subgraphs in complex networks

We study the use of local heuristics to determine spanning subgraphs for use in the dissemination of information in complex networks. We introduce two different heuristics and analyze their behavior in giving rise to spanning subgraphs that perform well in terms of allowing every node of the network to be reached, of requiring relatively few messages and small node bandwidth for information dissemination, and also of stretching paths with respect to the underlying network only modestly. We contribute a detailed mathematical analysis of one of the heuristics and provide extensive simulation results on random graphs for both of them. These results indicate that, within certain limits, spanning subgraphs are indeed expected to emerge that perform well in respect to all requirements. We also discuss the spanning subgraphs' inherent resilience to failures and adaptability to topological changes

Probabilistic heuristics for disseminating information in networks

We study the problem of disseminating a piece of information through all the nodes of a network, given that it is known originally only to a single node. In the absence of any structural knowledge on the network other than the nodes' neighborhoods, this problem is traditionally solved by flooding all the network's edges. We analyze a recently introduced probabilistic algorithm for flooding and give an alternative probabilistic heuristic that can lead to some cost-effective improvements, like better trade-offs between the message and time complexities involved. We analyze the two algorithms both mathematically and by means of simulations, always within a random-graph framework and considering relevant node-degree distributions

Corrections to Finite Size Scaling in Percolation

A 1/L-expansion for percolation problems is proposed, where L is the lattice finite length. The square lattice with 27 different sizes L = 18, 22 ... 1594 is considered. Certain spanning probabilities were determined by Monte Carlo simulations, as continuous functions of the site occupation probability p. We estimate the critical threshold pc by applying the quoted expansion to these data. Also, the universal spanning probability at pc for an annulus with aspect ratio r=1/2 is estimated as C = 0.876657(45)

Percolation transition and dissipation in quantum Ising magnets

We study the effects of dissipation on a randomly diluted transverse-field Ising magnet close to the percolation threshold. For weak transverse fields, a novel percolation quantum phase transition separates a superparamagnetic cluster phase from an inhomogeneously ordered ferromagnetic phase. The properties of this transition are dominated by large frozen and slowly fluctuating percolation clusters. This leads to a discontinuous magnetization-field curve and exotic hysteresis phenomena as well as highly singular behavior of magnetic susceptibility and specific heat. We compare our results to the smeared transition in generic dissipative random quantum Ising magnets. We also discuss the relation to metallic quantum magnets and other experimental realizations.Comment: 4 pages, 2 eps figures, final version as publishe

Optimization of hierarchical structures of information flow

The efficiency of a large hierarchical organisation is simulated on Barabasi-Albert networks, when each needed link leads to a loss of information. The optimum is found at a finite network size, corresponding to about five hierarchical layers, provided a cost for building the network is included in our optimization.Comment: Draft of 6 pages including all figure

Model for Cumulative Solar Heavy Ion Energy and Linear Energy Transfer Spectra

A probabilistic model of cumulative solar heavy ion energy and LET spectra is developed for spacecraft design applications. Spectra are given as a function of confidence level, mission time period during solar maximum and shielding thickness. It is shown that long-term solar heavy ion fluxes exceed galactic cosmic ray fluxes during solar maximum for shielding levels of interest. Cumulative solar heavy ion fluences should therefore be accounted for in single event effects rate calculations and in the planning of space missions

Multifractality in a broad class of disordered systems

We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model the angles specifying the directions of the spins) at the percolation threshold. Each of the cumulants has its own independent critical exponent, i.e., there are infinitely many critical exponents involved in the problem. Working out the connection to the random resistor network, we determine these multifractal exponents to two-loop order. Depending on the specifics of the Hamiltonian of each individual model, the amplitudes of the higher cumulants can vanish and in this case, effectively, only some of the multifractal exponents are required.Comment: 4 pages, 1 figur

Influence of lattice distortions in classical spin systems

We investigate a simple model of a frustrated classical spin chain coupled to adiabatic phonons under an external magnetic field. A thorough study of the magnetization properties is carried out both numerically and analytically. We show that already a moderate coupling with the lattice can stabilize a plateau at 1/3 of the saturation and discuss the deformation of the underlying lattice in this phase. We also study the transition to saturation where either a first or second order transition can occur, depending on the couplings strength.Comment: Submitted to Phys. Rev.