18,732 research outputs found

    A Symbolic Computational Approach to a Problem Involving Multivariate Poisson Distributions

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    Multivariate Poisson random variables subject to linear integer constraints arise in several application areas, such as queuing and biomolecular networks. This note shows how to compute conditional statistics in this context, by employing WF Theory and associated algorithms. A symbolic computation package has been developed and is made freely available. A discussion of motivating biomolecular problems is also provided.Comment: 19 pages, accompanied by a maple package MVPoisson downloadable from http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/mvp.htm

    On Balanced k-coverage in Visual Sensor Network

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    Given a set of directional visual sensors, the kk-coverage problem determines the orientation of minimal directional sensors so that each target is covered at least kk times. As the problem is NP-complete, a number of heuristics have been devised to tackle the issue. However, the existing heuristics provide imbalance coverage of the targets--some targets are covered kk times while others are left totally uncovered or singly covered. The coverage imbalance is more serious in under-provisioned networks where there do not exist enough sensors to cover all the targets kk times. Therefore, we address the problem of covering each target at least kk times in a balanced way using minimum number of sensors. We study the existing Integer Linear Programming (ILP) formulation for single coverage and extend the idea for kk-coverage. However, the extension does not balance the coverage of the targets. We further propose Integer Quadratic Programming (IQP) and Integer Non-Linear Programming (INLP) formulations that are capable of addressing the coverage balancing. As the proposed formulations are computationally expensive, we devise a faster Centralized Greedy kk-Coverage Algorithm (CGkCA) to approximate the formulations. Finally, through rigorous simulation experiments we show the efficacy of the proposed formulations and the CGkCA

    Computing the Line Index of Balance Using Integer Programming Optimisation

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    An important measure of signed graphs is the line index of balance which has several applications in many fields. However, this graph-theoretic measure was underused for decades because of the inherent complexity in its computation which is closely related to solving NP-hard graph optimisation problems like MAXCUT. We develop new quadratic and linear programming models to compute the line index of balance exactly. Using the Gurobi integer programming optimisation solver, we evaluate the line index of balance on real-world and synthetic datasets. The synthetic data involves Erd\H{o}s-R\'{e}nyi graphs, Barab\'{a}si-Albert graphs, and specially structured random graphs. We also use well known datasets from the sociology literature, such as signed graphs inferred from students' choice and rejection as well as datasets from the biology literature including gene regulatory networks. The results show that exact values of the line index of balance in relatively large signed graphs can be efficiently computed using our suggested optimisation models. We find that most real-world social networks and some biological networks have small line index of balance which indicates that they are close to balanced.Comment: Accepted author copy, 20 pages, 4 tables and 3 figures. This work is followed up in another study with more focus on Operations Research aspects of the topic that can be found in arXiv:1611.0903

    Structured Projection-Based Model Reduction with Application to Stochastic Biochemical Networks

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    The Chemical Master Equation (CME) is well known to provide the highest resolution models of a biochemical reaction network. Unfortunately, even simulating the CME can be a challenging task. For this reason more simple approximations to the CME have been proposed. In this work we focus on one such model, the Linear Noise Approximation. Specifically, we consider implications of a recently proposed LNA time-scale separation method. We show that the reduced order LNA converges to the full order model in the mean square sense. Using this as motivation we derive a network structure preserving reduction algorithm based on structured projections. We present convex optimisation algorithms that describe how such projections can be computed and we discuss when structured solutions exits. We also show that for a certain class of systems, structured projections can be found using basic linear algebra and no optimisation is necessary. The algorithms are then applied to a linearised stochastic LNA model of the yeast glycolysis pathway.Comment: 13 pages; 7 figures; submitted to IEEE Transaction on Automatic Contro

    Towards balanced clustering - part 1 (preliminaries)

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    The article contains a preliminary glance at balanced clustering problems. Basic balanced structures and combinatorial balanced problems are briefly described. A special attention is targeted to various balance/unbalance indices (including some new versions of the indices): by cluster cardinality, by cluster weights, by inter-cluster edge/arc weights, by cluster element structure (for element multi-type clustering). Further, versions of optimization clustering problems are suggested (including multicriteria problem formulations). Illustrative numerical examples describe calculation of balance indices and element multi-type balance clustering problems (including example for design of student teams).Comment: 21 pages, 17 figures, 14 table

    mplrs: A scalable parallel vertex/facet enumeration code

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    We describe a new parallel implementation, mplrs, of the vertex enumeration code lrs that uses the MPI parallel environment and can be run on a network of computers. The implementation makes use of a C wrapper that essentially uses the existing lrs code with only minor modifications. mplrs was derived from the earlier parallel implementation plrs, written by G. Roumanis in C++. plrs uses the Boost library and runs on a shared memory machine. In developing mplrs we discovered a method of balancing the parallel tree search, called budgeting, that greatly improves parallelization beyond the bottleneck encountered previously at around 32 cores. This method can be readily adapted for use in other reverse search enumeration codes. We also report some preliminary computational results comparing parallel and sequential codes for vertex/facet enumeration problems for convex polyhedra. The problems chosen span the range from simple to highly degenerate polytopes. For most problems tested, the results clearly show the advantage of using the parallel implementation mplrs of the reverse search based code lrs, even when as few as 8 cores are available. For some problems almost linear speedup was observed up to 1200 cores, the largest number of cores tested.Comment: Revision incorporating additional suggested change

    Load Balancing in Mobility-on-Demand Systems: Reallocation Via Parametric Control Using Concurrent Estimation

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    Mobility-on-Demand (MoD) systems require load balancing to maintain consistent service across regions with uneven demand subject to time-varying traffic conditions. The load-balancing objective is to jointly minimize the fraction of lost customer requests due to vehicle unavailability and the fraction of time when vehicles drive empty during load balancing operations. In order to bypass the intractability of a globally optimal solution to this stochastic dynamic optimization problem, we propose a parametric threshold-based control driven by the known relative abundance of vehicles available in and en route to each region. This is still a difficult parametric optimization problem for which one often resorts to trial-and-error methods where multiple sample paths are generated through simulation or from actual data under different parameter settings. In contrast, this paper utilizes concurrent estimation methods to simultaneously construct many sample paths from a single nominal sample path. The performance of the parametric controller for intermediate size systems is compared to that of a simpler single-parameter controller, a state-blind static controller, a policy of no control, and a theoretically-derived lower bound. Simulation results show the value of state information in improving performance

    Multi-Dimensional Balanced Graph Partitioning via Projected Gradient Descent

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    Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the multi-dimensional variant when balance according to multiple weight functions is required. As we demonstrate by experimental evaluation, such multi-dimensional balance is important for achieving performance improvements for typical distributed graph processing workloads. We propose a new scalable technique for the multidimensional balanced graph partitioning problem. The method is based on applying randomized projected gradient descent to a non-convex continuous relaxation of the objective. We show how to implement the new algorithm efficiently in both theory and practice utilizing various approaches for projection. Experiments with large-scale social networks containing up to hundreds of billions of edges indicate that our algorithm has superior performance compared with the state-of-the-art approaches

    Data-Driven Robust Taxi Dispatch under Demand Uncertainties

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    In modern taxi networks, large amounts of taxi occupancy status and location data are collected from networked in-vehicle sensors in real-time. They provide knowledge of system models on passenger demand and mobility patterns for efficient taxi dispatch and coordination strategies. Such approaches face new challenges: how to deal with uncertainties of predicted customer demand while fulfilling the system's performance requirements, including minimizing taxis' total idle mileage and maintaining service fairness across the whole city; how to formulate a computationally tractable problem. To address this problem, we develop a data-driven robust taxi dispatch framework to consider spatial-temporally correlated demand uncertainties. The robust vehicle dispatch problem we formulate is concave in the uncertain demand and convex in the decision variables. Uncertainty sets of random demand vectors are constructed from data based on theories in hypothesis testing, and provide a desired probabilistic guarantee level for the performance of robust taxi dispatch solutions. We prove equivalent computationally tractable forms of the robust dispatch problem using the minimax theorem and strong duality. Evaluations on four years of taxi trip data for New York City show that by selecting a probabilistic guarantee level at 75%, the average demand-supply ratio error is reduced by 31.7%, and the average total idle driving distance is reduced by 10.13% or about 20 million miles annually, compared with non-robust dispatch solutions.Comment: Accepted as a regular paper, IEEE Transactions on Control Systems Technology; 15 pages. This version updated as of Oct 201

    Characterization of SINR Region for Multiple Interfering Multicast in Power-Controlled Systems

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    This paper considers a wireless communication network consisting of multiple interfering multicast sessions. Different from a unicast system where each transmitter has only one receiver, in a multicast system, each transmitter has multiple receivers. It is a well known result for wireless unicast systems that the feasibility of an signal-to-interference-plus-noise power ratio (SINR) without power constraint is decided by the Perron-Frobenius eigenvalue of a nonnegative matrix. We generalize this result and propose necessary and sufficient conditions for the feasibility of an SINR in a wireless multicast system with and without power constraint. The feasible SINR region as well as its geometric properties are studied. Besides, an iterative algorithm is proposed which can efficiently check the feasibility condition and compute the boundary points of the feasible SINR region.Comment: 25 pages, 4 figures, submitted to IEEE Trans. Inform. Theor
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