An Information-Based Neural Approach to Constraint Satisfaction

A novel artificial neural network approach to constraint satisfaction problems is presented. Based on information-theoretical considerations, it differs from a conventional mean-field approach in the form of the resulting free energy. The method, implemented as an annealing algorithm, is numerically explored on a testbed of K-SAT problems. The performance shows a dramatic improvement to that of a conventional mean-field approach, and is comparable to that of a state-of-the-art dedicated heuristic (Gsat+Walk). The real strength of the method, however, lies in its generality -- with minor modifications it is applicable to arbitrary types of discrete constraint satisfaction problems.Comment: 13 pages, 3 figures,(to appear in Neural Computation

Airline Crew Scheduling with Potts Neurons

A Potts feedback neural network approach for finding good solutions to resource allocation problems with a non-fixed topology is presented. As a target application the airline crew scheduling problem is chosen. The topological complication is handled by means of a propagator defined in terms of Potts neurons. The approach is tested on artificial random problems tuned to resemble real-world conditions. Very good results are obtained for a variety of problem sizes. The computer time demand for the approach only grows like \mbox{(number of flights)}^3. A realistic problem typically is solved within minutes, partly due to a prior reduction of the problem size, based on an analysis of the local arrival/departure structure at the single airportsComment: 9 pages LaTeX, 3 postscript figures, uufiles forma

Perturbing General Uncorrelated Networks

This paper is a direct continuation of an earlier work, where we studied Erd\"os-R\'enyi random graphs perturbed by an interaction Hamiltonian favouring the formation of short cycles. Here, we generalize these results. We keep the same interaction Hamiltonian but let it act on general graphs with uncorrelated nodes and an arbitrary given degree distribution. It is shown that the results obtained for Erd\"os-R\'enyi graphs are generic, at the qualitative level. However, scale-free graphs are an exception to this general rule and exhibit a singular behaviour, studied thoroughly in this paper, both analytically and numerically.Comment: 7 pages, 7 eps figures, 2-column revtex format, references adde

A Potts Neuron Approach to Communication Routing

A feedback neural network approach to communication routing problems is developed with emphasis on Multiple Shortest Path problems, with several requests for transmissions between distinct start- and endnodes. The basic ingredients are a set of Potts neurons for each request, with interactions designed to minimize path lengths and to prevent overloading of network arcs. The topological nature of the problem is conveniently handled using a propagator matrix approach. Although the constraints are global, the algorithmic steps are based entirely on local information, facilitating distributed implementations. In the polynomially solvable single-request case the approach reduces to a fuzzy version of the Bellman-Ford algorithm. The approach is evaluated for synthetic problems of varying sizes and load levels, by comparing with exact solutions from a branch-and-bound method. With very few exceptions, the Potts approach gives legal solutions of very high quality. The computational demand scales merely as the product of the numbers of requests, nodes, and arcs.Comment: 10 pages LaTe

Scaling and Scale Breaking in Polyelectrolyte

We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy with the chain-length divided by the temperature. This scaling is broken at low temperatures by the ultraviolet divergence of the Coulomb potential. By introducing a renormalization of the strength of the nearest- neighbour interaction the scaling is restored, making possible an efficient blocking method for emulating very large polyelectrolytes using small systems. The high temperature behaviour is well reproduced by the analytical high-$T$ expansions even for fairly low temperatures and system sizes. In addition, results from low-$T$ expansions, where the coefficients have been computed numerically, are presented. These results approximate well the corresponding Monte Carlo results at realistic temperatures. A corresponding analysis of screened chains is performed. The situation here is complicated by the appearance of an additional parameter, the screening length. A window is found in parameter space, where scaling holds for the end-to-end distance. This window corresponds to situations where the range of the potential interpolates between the bond length and the size of the chain. This scaling behaviour, which is verified by Monte Carlo results, is consistent with Flory scaling. Also for the screened chain a blocking approach can be devised, that performs well for low temperatures, whereas the low-$T$ expansion is inaccurate at realistic temperatures.Comment: 18 pages, latex, 6 figure

Central obesity as a precursor to the metabolic syndrome in the AusDiab study and Mauritius

Evidence from epidemiologic studies that central obesity precedes future metabolic change and does not occur concurrently with the appearance of the blood pressure, glucose, and lipid abnormalities that characterize the metabolic syndrome (MetS) has been lacking. Longitudinal surveys were conducted in Mauritius in 1987, 1992, and 1998, and in Australia in 2000 and 2005 (AusDiab). This analysis included men and women (aged 25 years) in three cohorts: AusDiab 2000&ndash;2005 (n = 5,039), Mauritius 1987&ndash;1992 (n = 2,849), and Mauritius 1987&ndash;1998 (n = 1,999). MetS components included waist circumference, systolic blood pressure, fasting and 2-h postload plasma glucose, high-density lipoprotein (HDL) cholesterol, triglycerides, and homeostasis model assessment of insulin sensitivity (HOMA-S) (representing insulin sensitivity). Linear regression was used to determine which baseline components predicted deterioration in other MetS components over 5 years in AusDiab and 5 and 11 years in Mauritius, adjusted for age, sex, and ethnic group. Baseline waist circumference predicted deterioration (P &lt; 0.01) in four of the other six MetS variables tested in AusDiab, five of six in Mauritius 1987&ndash;1992, and four of six in Mauritius 1987&ndash;1998. In contrast, an increase in waist circumference between baseline and follow-up was only predicted by insulin sensitivity (HOMA-S) at baseline, and only in one of the three cohorts. These results suggest that central obesity plays a central role in the development of the MetS and appears to precede the appearance of the other MetS components.<br /

Properties of Random Graphs with Hidden Color

We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub-coloring, with or without the restriction to nondegenerate graphs. The calculability of local and global structural properties of graphs from the resulting ensembles is demonstrated. Cluster size statistics are derived with generating function techniques, yielding a well-defined percolation threshold. Explicit rules are derived for the enumeration of small subgraphs. Duality and redundancy is discussed, and subclasses corresponding to commonly studied models are identified.Comment: 14 pages, LaTeX, no figure

Local atomic arrangement and martensitic transformation in Ni50_{50}Mn35_{35}In15_{15}: An EXAFS Study

Heusler alloys that undergo martensitic transformation in ferromagnetic state are of increasing scientific and technological interest. These alloys show large magnetic field induced strains upon martensitic phase change thus making it a potential candidate for magneto-mechanical actuation. The crystal structure of martensite is an important factor that affects both the magnetic anisotropy and mechanical properties of such materials. Moreover, the local chemical arrangement of constituent atoms is vital in determining the overall physical properties. Ni$_{50}$Mn$_{35}$In$_{15}$ is one such ferromagnetic shape memory alloy that displays exotic properties like large magnetoresistance at moderate field values. In this work, we present the extended x-ray absorption fine-structure measurements (EXAFS) on the bulk Ni$_{50}$Mn$_{35}$In$_{15}$ which reveal the local structural change that occurs upon phase transformation. The change in the bond lengths between different atomic species helps in understanding the type of hybridization which is an important factor in driving such Ni-Mn based systems towards martensitic transformation

Analysis of complex contagions in random multiplex networks

We study the diffusion of influence in random multiplex networks where links can be of $r$ different types, and for a given content (e.g., rumor, product, political view), each link type is associated with a content dependent parameter $c_i$ in $[0,\infty]$ that measures the relative bias type-$i$ links have in spreading this content. In this setting, we propose a linear threshold model of contagion where nodes switch state if their "perceived" proportion of active neighbors exceeds a threshold \tau. Namely, a node connected to $m_i$ active neighbors and $k_i-m_i$ inactive neighbors via type-$i$ links will turn active if $\sum{c_i m_i}/\sum{c_i k_i}$ exceeds its threshold \tau. Under this model, we obtain the condition, probability and expected size of global spreading events. Our results extend the existing work on complex contagions in several directions by i) providing solutions for coupled random networks whose vertices are neither identical nor disjoint, (ii) highlighting the effect of content on the dynamics of complex contagions, and (iii) showing that content-dependent propagation over a multiplex network leads to a subtle relation between the giant vulnerable component of the graph and the global cascade condition that is not seen in the existing models in the literature.Comment: Revised 06/08/12. 11 Pages, 3 figure