179 research outputs found

    Density functional theory for nearest-neighbor exclusion lattice gasses in two and three dimensions

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    To speak about fundamental measure theory obliges to mention dimensional crossover. This feature, inherent to the systems themselves, was incorporated in the theory almost from the beginning. Although at first it was thought to be a consistency check for the theory, it rapidly became its fundamental pillar, thus becoming the only density functional theory which possesses such a property. It is straightforward that dimensional crossover connects, for instance, the parallel hard cube system (three-dimensional) with that of squares (two-dimensional) and rods (one-dimensional). We show here that there are many more connections which can be established in this way. Through them we deduce from the functional for parallel hard (hyper)cubes in the simple (hyper)cubic lattice the corresponding functionals for the nearest-neighbor exclusion lattice gases in the square, triangular, simple cubic, face-centered cubic, and body-centered cubic lattices. As an application, the bulk phase diagram for all these systems is obtained.Comment: 13 pages, 13 figures; needs revtex

    A note on Condorcet consistency and the median voter

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    We discuss to which extent the median voter theorem extends to the domain of single-peaked preferences on median spaces. After observing that on this domain a Condorcet winner need not exist, we show that if a Condorcet winner does exist, then it coincides with the median alternative ('the median voter'). Based on this result, we propose two non-cooperative games that implement the unique strategy-proof social choice rule on this domain. --

    A Distributed algorithm to find Hamiltonian cycles in Gnp random graphs

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    In this paper, we present a distributed algorithm to find Hamiltonian cycles in random binomial graphs Gnp. The algorithm works on a synchronous distributed setting by first creating a small cycle, then covering almost all vertices in the graph with several disjoint paths, and finally patching these paths and the uncovered vertices to the cycle. Our analysis shows that, with high probability, our algorithm is able to find a Hamiltonian cycle in Gnp when p_n=omega(sqrt{log n}/n^{1/4}). Moreover, we conduct an average case complexity analysis that shows that our algorithm terminates in expected sub-linear time, namely in O(n^{3/4+epsilon}) pulses.Postprint (published version

    Stochastic Analysis of a Churn-Tolerant Structured Peer-to-Peer Scheme

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    We present and analyze a simple and general scheme to build a churn (fault)-tolerant structured Peer-to-Peer (P2P) network. Our scheme shows how to "convert" a static network into a dynamic distributed hash table(DHT)-based P2P network such that all the good properties of the static network are guaranteed with high probability (w.h.p). Applying our scheme to a cube-connected cycles network, for example, yields a O(logN)O(\log N) degree connected network, in which every search succeeds in O(logN)O(\log N) hops w.h.p., using O(logN)O(\log N) messages, where NN is the expected stable network size. Our scheme has an constant storage overhead (the number of nodes responsible for servicing a data item) and an O(logN)O(\log N) overhead (messages and time) per insertion and essentially no overhead for deletions. All these bounds are essentially optimal. While DHT schemes with similar guarantees are already known in the literature, this work is new in the following aspects: (1) It presents a rigorous mathematical analysis of the scheme under a general stochastic model of churn and shows the above guarantees; (2) The theoretical analysis is complemented by a simulation-based analysis that validates the asymptotic bounds even in moderately sized networks and also studies performance under changing stable network size; (3) The presented scheme seems especially suitable for maintaining dynamic structures under churn efficiently. In particular, we show that a spanning tree of low diameter can be efficiently maintained in constant time and logarithmic number of messages per insertion or deletion w.h.p. Keywords: P2P Network, DHT Scheme, Churn, Dynamic Spanning Tree, Stochastic Analysis

    Compact routing in fault-tolerant distributed systems

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    A compact routing algorithm is a routing algorithm which reduces the space complexity of all-pairs shortest path routing. Compact routing protocols in distributed systems have been studied extensively as an attractive alternative to the traditional method of all-pairs shortest path routing. The use of compact routing protocols have several advantages. Compact routing schemes are not only more memory-efficient, but provide faster routing table lookup, more efficient broadcast scheme, and allow for a more scalable network. These routing schemes still maintain optimal or near-optimal routing paths. However, most of the compact routing protocols are not fault-tolerant. This thesis will first report the recent developments in the compact routing research. Several new methods for compact routing in fault-tolerant distributed systems will be presented and analyzed. The most important feature of the algorithms presented in this thesis is that they are self-stabilizing. The self-stabilization paradigm has been shown to be the most unified and all-inclusive approach to the design of fault-tolerant system. Additionally, these algorithms will address and solve several problems left unsolved by previous works. Relabelable and non-relabelable networks will be considered for both specific and arbitrary topologies

    Selective naive Bayes predictor with mixtures of truncated exponentials

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    Naive Bayes models have been successfully used in classification problems where the class variable is discrete. Naive Bayes models have been applied to regression or prediction problems, i.e. classification problems with continuous class, but usually under the assumption that the joint distribution of the feature variables and the class is multivariate Gaussian. In this paper we are interested in regres- sion problems where some of the feature variables are discrete while the others are continuous. We propose a Naive Bayes predictor based on the approximation of the joint distribution by a Mixture of Truncated Exponentials (MTE). We have designed a procedure for selecting the variables that should be used in the construction of the model. This scheme is based on the mutual information between each of the candidate variables and the class. Since the mutual information can not be computed exactly for the MTE distribution, we introduce an unbiased estimator of it, based on Monte Carlo methods. We test the performance of the proposed model in three real life problems, related to higher education management
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