6,004 research outputs found

    Pairwise Compatibility Graphs (Invited Talk)

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    Pairwise Compatibility Graphs (PCG) are graphs introduced in relation to the biological problem of reconstructing phylogenetic trees. Without demanding to be exhaustive, in this note we take a quick look at what is known in the literature for these graphs. The evolutionary history of a set of organisms is usually represented by a tree-like structure called phylogenetic tree, where the leaves are the known species and the internal nodes are the possible ancestors that might have led, through evolution, to this set of species. Edges are evolutionary relationships between species, while the edge weights represent evolutionary distances among species (evolutionary times). The phylogenetic tree reconstruction problem consists in finding a fully labeled phylogenetic tree that'best' explains the evolution of given species, where'best' means that it optimizes a specific target function. Tree reconstruction problem is proved to be NP-hard under many criteria of optimality, so the performance of the heuristics for this problem is usually experimentally evaluated by comparing the output trees with the partial trees that are unanimously recognized as sure by biologists. But real data consist of a huge number of species, and it is unfeasible to compare trees with such a number of leaves, so it is common to exploit sample techniques. The idea is to find efficient ways to sample subsets of species from a large set in order to test the heuristics on the smaller sub-trees induced by the sample. The constraints on the sample attempt to ensure that the behavior of the heuristics will not be biased by the fact it is applied on the sample instead of on the whole tree. Since very close or very distant taxa can create problems for phylogenetic reconstruction heuristics [9], the following definition of Pairwise Compatibility Graphs [12] appears natura

    All graphs with at most seven vertices are Pairwise Compatibility Graphs

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    A graph GG is called a pairwise compatibility graph (PCG) if there exists an edge-weighted tree TT and two non-negative real numbers dmind_{min} and dmaxd_{max} such that each leaf lul_u of TT corresponds to a vertex uVu \in V and there is an edge (u,v)E(u,v) \in E if and only if dmindT,w(lu,lv)dmaxd_{min} \leq d_{T,w} (l_u, l_v) \leq d_{max} where dT,w(lu,lv)d_{T,w} (l_u, l_v) is the sum of the weights of the edges on the unique path from lul_u to lvl_v in TT. In this note, we show that all the graphs with at most seven vertices are PCGs. In particular all these graphs except for the wheel on 7 vertices W7W_7 are PCGs of a particular structure of a tree: a centipede.Comment: 8 pages, 2 figure

    Relating threshold tolerance graphs to other graph classes

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    A graph G=(V, E) is a threshold tolerance if it is possible to associate weights and tolerances with each node of G so that two nodes are adjacent exactly when the sum of their weights exceeds either one of their tolerances. Threshold tolerance graphs are a special case of the well-known class of tolerance graphs and generalize the class of threshold graphs which are also extensively studied in literature. In this note we relate the threshold tolerance graphs with other important graph classes. In particular we show that threshold tolerance graphs are a proper subclass of co-strongly chordal graphs and strictly include the class of co-interval graphs. To this purpose, we exploit the relation with another graph class, min leaf power graphs (mLPGs)

    Investigation of commuting Hamiltonian in quantum Markov network

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    Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions,so there are some powerful methods including mean field approximation, belief propagation algorithm and etc. Quantum graphical models have been recently developed in context of quantum information and computation, and quantum statistical physics, which is possible by generalization of classical probability theory to quantum theory. The main goal of this paper is preparing a primary generalization of Markov network, as a type of graphical models, to quantum case and applying in quantum statistical physics.We have investigated the Markov network and the role of commuting Hamiltonian terms in conditional independence with simple examples of quantum statistical physics.Comment: 11 pages, 8 figure

    Distributed data association for multi-target tracking in sensor networks

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    Associating sensor measurements with target tracks is a fundamental and challenging problem in multi-target tracking. The problem is even more challenging in the context of sensor networks, since association is coupled across the network, yet centralized data processing is in general infeasible due to power and bandwidth limitations. Hence efficient, distributed solutions are needed. We propose techniques based on graphical models to efficiently solve such data association problems in sensor networks. Our approach scales well with the number of sensor nodes in the network, and it is well--suited for distributed implementation. Distributed inference is realized by a message--passing algorithm which requires iterative, parallel exchange of information among neighboring nodes on the graph. So as to address trade--offs between inference performance and communication costs, we also propose a communication--sensitive form of message--passing that is capable of achieving near--optimal performance using far less communication. We demonstrate the effectiveness of our approach with experiments on simulated data

    UPGMpp: a Software Library for Contextual Object Recognition

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    Object recognition is a cornerstone task towards the scene understanding problem. Recent works in the field boost their perfor- mance by incorporating contextual information to the traditional use of the objects’ geometry and/or appearance. These contextual cues are usually modeled through Conditional Random Fields (CRFs), a partic- ular type of undirected Probabilistic Graphical Model (PGM), and are exploited by means of probabilistic inference methods. In this work we present the Undirected Probabilistic Graphical Models in C++ library (UPGMpp), an open source solution for representing, training, and per- forming inference over undirected PGMs in general, and CRFs in par- ticular. The UPGMpp library supposes a reliable and comprehensive workbench for recognition systems exploiting contextual information, in- cluding a variety of inference methods based on local search, graph cuts, and message passing approaches. This paper illustrates the virtues of the library, i.e. it is efficient, comprehensive, versatile, and easy to use, by presenting a use-case applied to the object recognition problem in home scenes from the challenging NYU2 dataset.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Spanish grant program FPU-MICINN 2010 and the Spanish projects “TAROTH: New developments toward a robot at home” (Ref. DPI2011-25483) and “PROMOVE: Advances in mobile robotics for promoting independent life of elders” (Ref. DPI2014-55826-R
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