What's up with downward collapse

Previous article Algorithms for the Assignment and Transportation ProblemsJames MunkresJames Munkreshttps://doi.org/10.1137/0105003PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Merrill M. Flood, The traveling-salesman problem, Operations Res., 4 (1956), 61–75 MR0078639 CrossrefISIGoogle Scholar[2] L. R. Ford, Jr. and , D. R. Fulkerson, A simple algorithm for finding maximal network flows and an application to the Hitchcock problem, RAND Corporation, Santa Monica, 1955, P-743, Sept. 26 Google Scholar[3] H. W. Kuhn, The Hungarian method for the assignment problem, Naval Res. Logist. Quart., 2 (1955), 83–97 MR0075510 0143.41905 CrossrefGoogle Scholar Previous article FiguresRelatedReferencesCited byDetails Scalable Semidefinite ProgrammingAlp Yurtsever, Joel A. Tropp, Olivier Fercoq, Madeleine Udell, and Volkan Cevher8 February 2021 | SIAM Journal on Mathematics of Data Science, Vol. 3, No. 1AbstractPDF (2365 KB)A Scalable Approach to Compute Delay Margin of a Class of Neutral-Type Time Delay SystemsAdrián Ramírez, Dimitri Breda, and Rifat Sipahi1 March 2021 | SIAM Journal on Control and Optimization, Vol. 59, No. 2AbstractPDF (802 KB)Closing Gaps in Asymptotic Fair DivisionPasin Manurangsi and Warut Suksompong8 April 2021 | SIAM Journal on Discrete Mathematics, Vol. 35, No. 2AbstractPDF (657 KB)A Privacy-Preserving Method to Optimize Distributed Resource AllocationOlivier Beaude, Pascal Benchimol, Stéphane Gaubert, Paulin Jacquot, and Nadia Oudjane24 August 2020 | SIAM Journal on Optimization, Vol. 30, No. 3AbstractPDF (968 KB)Multilevel Artificial Neural Network Training for Spatially Correlated LearningC. B. Scott and Eric Mjolsness29 October 2019 | SIAM Journal on Scientific Computing, Vol. 41, No. 5AbstractPDF (1559 KB)Index Reduction via Unimodular TransformationsSatoru Iwata and Mizuyo Takamatsu3 July 2018 | SIAM Journal on Matrix Analysis and Applications, Vol. 39, No. 3AbstractPDF (458 KB)Max-Plus Algebraic Statistical Leverage ScoresJames Hook16 November 2017 | SIAM Journal on Matrix Analysis and Applications, Vol. 38, No. 4AbstractPDF (2992 KB)A Seamless Multilevel Ensemble Transform Particle FilterA. Gregory and C. J. Cotter28 November 2017 | SIAM Journal on Scientific Computing, Vol. 39, No. 6AbstractPDF (537 KB)Community Detection in Temporal Multilayer Networks, with an Application to Correlation NetworksMarya Bazzi, Mason A. Porter, Stacy Williams, Mark McDonald, Daniel J. Fenn, and Sam D. Howison6 January 2016 | Multiscale Modeling & Simulation, Vol. 14, No. 1AbstractPDF (1688 KB)Multilevel Ensemble Transform Particle Filtering3 May 2016 | SIAM Journal on Scientific Computing, Vol. 38, No. 3AbstractPDF (479 KB)Algebraic Multilevel Preconditioner for the Helmholtz Equation in Heterogeneous Media9 October 2009 | SIAM Journal on Scientific Computing, Vol. 31, No. 5AbstractPDF (3632 KB)Combinatorial Analysis of Singular Matrix Pencils26 January 2007 | SIAM Journal on Matrix Analysis and Applications, Vol. 29, No. 1AbstractPDF (187 KB)Incremental Processing Applied to Munkres’ Algorithm and Its Application in Steinberg’s Placement ProcedureH. W. Carter, M. A. Breuer, and Z. A. Syed3 August 2006 | SIAM Journal on Algebraic Discrete Methods, Vol. 6, No. 2AbstractPDF (1082 KB)On the Assignment Polytope18 July 2006 | SIAM Review, Vol. 16, No. 4AbstractPDF (1033 KB)Algorithms for Obtaining Shortest Paths Visiting Specified Nodes2 August 2006 | SIAM Review, Vol. 15, No. 2AbstractPDF (772 KB)A Review of the Placement and Quadratic Assignment Problems18 July 2006 | SIAM Review, Vol. 14, No. 2AbstractPDF (2163 KB)Optimal and Suboptimal Algorithms for the Quadratic Assignment Problem13 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 10, No. 2AbstractPDF (867 KB)An Out-of-Kilter Method for Minimal-Cost Flow Problems10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 9, No. 1AbstractPDF (957 KB)The Backboard Wiring Problem: A Placement Algorithm18 July 2006 | SIAM Review, Vol. 3, No. 1AbstractPDF (1020 KB) Volume 5, Issue 1| 1957Journal of the Society for Industrial and Applied Mathematics History Submitted:08 August 1956Published online:10 July 2006 InformationCopyright © 1957 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0105003Article page range:pp. 32-38ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

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The correspondence between partial metrics and semivaluations

Detailed microscale simulation is typically too computationally expensive for the long time simulations necessary to explore macroscale dynamics. Projective integration uses bursts of the microscale simulator, on microscale time steps, and then computes an approximation to the system over a macroscale time step by extrapolation. Projective integration has the potential to be an effective method to compute the long time dynamic behaviour of multiscale systems. However, many multiscale systems are significantly influenced by noise. By a maximum likelihood estimation, we fit a linear stochastic differential equation to short bursts of data. The analytic solution of the linear stochastic differential equation then estimates the solution over a macroscale, projective integration, time step. We explore how the noise affects the projective integration in two different methods. Monte Carlo simulation suggests design parameters offering stability and accuracy for the algorithms. The algorithms developed here may be applied to compute the long time dynamic behaviour of multiscale systems with noise and to exploit parallel computation. References Yacine Ait-Sahalia. Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach. Econometrica, 70(1):223--262, 2002. Yacine Ait-Sahalia. Likelihood inference for diffusions: a survey. In Jianqing Fan and Hira L. Koul, editors, Frontiers in Statistics: in Honor of Peter J. Bickel's 65th Birthday, chapter 17, pages 369--405. Imperial College Press, 2006. Yacine Ait-Sahalia and Robert Kimmel. Maximum likelihood estimation of stochastic volatility models. Journal of Financial Economics, 83(2):413--452, 2007. doi:10.1016/j.jfineco.2005.10.006 C. P. Calderon. Local diffusion models for stochastic reacting systems: estimation issues in equation-free numerics. Molecular Simulation, 33(9--10):713--731, August 2007. doi:10.1080/08927020701344740 Radek Erban, Ioannis G. Kevrekidis, and Hans G. Othmer. An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal. Physica D: Nonlinear Phenomena, 215(1):1--24, 2006. doi:10.1016/j.physd.2006.01.008 C. W. Gear, I. G. Kevrekidis, and C. Theodoropoulos. `Coarse' integration/bifurcation analysis via microscopic simulators: micro-Galerkin methods. Computers and Chemical Engrg, 26:941--963, 2002. C. W. Gear and Ioannis G. Kevrekidis. Projective methods for stiff differential equations: Problems with gaps in their eigenvalue spectrum. SIAM Journal on Scientific Computing, 24(4):1091--1106, 2003. doi:10.1137/S1064827501388157 Dror Givon and Ioannis G. Kevrekidis. Coarse-grained projective schemes for certain singularly perturbed stochastic problems. Technical report, Princeton University, 2008. Ioannis G. Kevrekidis and Giovanni Samaey. Equation-free multiscale computation: Algorithms and applications. Annu. Rev. Phys. Chem., 60:321--44, 2009. doi:10.1146/annurev.physchem.59.032607.093610 P. E. Kloeden and E. Platen. Numerical solution of stochastic differential equations, volume 23 of Applications of Mathematics. Springer--Verlag, 1992. C. I. Siettos, M. D. Graham, and I. G. Kevrekidis. Coarse brownian dynamics for nematic liquid crystals: Bifurcation, projective integration, and control via stochastic simulation. J. Chemical Physics, 118(22):10149--10156, 2003. doi:10.1063/1.1572456

Numerial Methods for Volterra Integral Equations with Singular Kernels

The noise contained in images collected by a charge coupled device camera is predominantly of Poisson type. This motivates the use of the negative logarithm of the Poisson likelihood in place of the ubiquitous least squares fit-to-data. However if the underlying mathematical model is assumed to have the form z = Au, where A is a linear, compact operator, Poisson likelihood estimation is ill-posed, and hence some form of regularization is required. In Bardsley, J.M. and Vogel, C.R., 2004, A nonnegatively constrained convex programming method for image reconstruction. SIAM Journal on Scientific Computing, 25(4), pp. 1326–1343, a numerical method is presented and analyzed for Tikhonov regularized Poisson likelihood estimation, but no theoretical justification of the approach is given. Our primary objective in this article is to provide such a theoretical justification. We then briefly present the computational method of Bardsley, J.M. and Vogel, C.R., 2004, A nonnegatively constrained convex programming method for image reconstruction. SIAM Journal on Scientific Computing, 25(4), pp. 1326–1343, which is very effective and computationally efficient for this problem. The practical validity of the approach is then demonstrated on a synthetic example from astronomical imaging.

Discounting Infinite Games But How and Why?

Polynomial-time safe and unsafe approximations for intractable sets were introduced by Meyer and Paterson [Technical Report TM-126, Laboratory for Computer Science, MIT, Cambridge, MA, 1979] and Yesha [SIAM J. Comput., 12 (1983), pp. 411--425], respectively. The question of which sets have optimal safe and unsafe approximations has been investigated extensively. Duris and Rolim [Lecture Notes in Comput. Sci. 841, Springer-Verlag, Berlin, New York, 1994, pp. 38--51] and Ambos-Spies [Proc. 22nd ICALP, Springer-Verlag, Berlin, New York, 1995, pp. 384--392] showed that the existence of optimal polynomial-time approximations for the safe and unsafe cases is independent. Using the law of the iterated logarithm for p-random sequences (which has been recently proven in [Proc. 11th Conf. Computational Complexity, IEEE Computer Society Press, Piscataway, NJ, 1996, pp. 180--189]), we extend this observation by showing that both the class of polynomial-time $\Delta$-levelable sets and the class of sets which have optimal polynomial-time unsafe approximations have p-measure 0. Hence typical sets in E (in the sense of p-measure) do not have optimal polynomial-time unsafe approximations. We will also establish the relationship between resource bounded genericity concepts and the polynomial-time safe and unsafe approximation concepts.

Animal migration is a mass biological phenomenon indispensable for comprehension and assessment of food-webs. So far, theoretical models to describe decision-making processes inherent in the animal migration have not been well established, which is the motivation of this research. It is natural to formulate the animal migration based on a stochastic control theory, which can describe system dynamics and its optimization in stochastic environment. To address this issue, a conceptual stochastic control model for the decision-making processes in animal migration is introduced and mathematically analysed. Its novelty is mathematical simplicity and the new theoretical, stochastic control viewpoint. Stochastic differential equations govern the animal population dynamics with gradual and radical migrations from the current habitat toward the next one. The population decides the occurrences, magnitudes, and timings of the migrations, so that a heuristic performance index is maximised. I derive a variational inequality that governs the maximised performance index and is exactly solvable. Its free boundaries govern the gradual and radical migrations. Despite the model simplicity, the exact solution is consistent with the empirical observation results of fish migration, implying its potential applicability to animal migration. The present model can be used for assessing fish migration. References S. Bauer and B. J. Hoye. Migratory animals couple biodiversity and ecosystem functioning worldwide. Science, 344, 2014. Article No. 1242552. N. E. Leonaerd. Multi-agent system dynamics: Bifurcation and behavior of animal groups. Annual Reviews in Control, 38(2):171–183, 2014. A. M. Oberman. Convergent difference schemes for degenerate elliptic and parabolic equations: Hamilton–jacobi equations and free boundary problems. SIAM Journal on Numerical Analysis, 44(2):879–895, 2006. B. \T1\O ksendal. Stochastic Differential Equations. Springer Berlin Heidelberg, 2003. B. \T1\O ksendal and A. Sulem. Applied Stochastic Control of Jump Diffusions. Springer Berlin Heidelberg, 2007. Y. Yaegashi, H. Yoshioka, K. Unami, and M. Fujihara. An optimal management strategy for stochastic population dynamics of released \(plecoglossus\) \(altivelis\) in rivers. International Journal of Modeling, Simulation, and Scientific Computing, 8(2), 207. Article No. 1750039. H. Yoshioka, T. Shirai, and D. Tagami. Viscosity solutions of a mathematical model for upstream migration of potamodromous fish. In Proceedings of 12th SDEWES Conference, October 4-8, 2017, Dubrovnik, Croatia, 2017. In press.

Guest Editorial

Contributors

We propose a new method for designing quantum search algorithms for finding a "marked" element in the state space of a classical Markov chain. The algorithm is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of the Markov chain. The main new idea is to apply quantum phase estimation to the quantum walk in order to implement an approximate reflection operator. This operator is then used in an amplitude amplification scheme. As a result we considerably expand the scope of the previous approaches of Ambainis (2004) and Szegedy (2004). Our algorithm combines the benefits of these approaches in terms of being able to find marked elements, incurring the smaller cost of the two, and being applicable to a larger class of Markov chains. In addition, it is conceptually simple and avoids some technical difficulties in the previous analyses of several algorithms based on quantum walk.

We prove several results about the average-case complexity of problems in the Polynomial Hierarchy (PH). We give a connection among average-case, worst-case, and non-uniform complexity of optimization problems. Specifically, we show that if PNP is hard in the worst-case then it is either hard on the average (in the sense of Levin) or it is non-uniformly hard (i.e. it does not have small circuits).Recently, Gutfreund, Shaltiel and Ta-Shma (IEEE Conference on Computational Complexity, 2005) showed an interesting worst-case to average-case connection for languages in NP, under a notion of average-case hardness defined using uniform adversaries. We show that extending their connection to hardness against quasi-polynomial time would imply that NEXP doesn’t have polynomial-size circuits.Finally we prove an unconditional average-case hardness result. We show that for each k, there is an explicit language in P\(^{\Sigma_2}\) which is hard on average for circuits of size n k.KeywordsPseudorandom GeneratorHard FunctionSmall CircuitCircuit FamilyExplicit LanguageThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Article Free Access Share on Efficient repeating pattern finding in music databases Authors: Jia-Lien Hsu Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan 300, R.O.C Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan 300, R.O.CView Profile , Arbee L. P. Chen Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan 300, R.O.C Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan 300, R.O.CView Profile , C.-C. Liu Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan 300, R.O.C Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan 300, R.O.CView Profile Authors Info & Claims CIKM '98: Proceedings of the seventh international conference on Information and knowledge managementNovember 1998 Pages 281–288https://doi.org/10.1145/288627.288668Online:01 November 1998Publication History 44citation667DownloadsMetricsTotal Citations44Total Downloads667Last 12 Months20Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Judgment aggregation is a collective decision making framework where the opinions of a group of agents is combined into a collective opinion. This can be done using many different judgment aggregation procedures. We study the computational complexity of computing the group opinion for several of the most prominent judgment aggregation procedures. In particular, we show that the complexity of this winner determination problem for analogues of the Kemeny rule, the Slater rule and the Young rule lies at the Θp2-level of the Polynomial Hierarchy (PH). Moreover, we show that the problem has a complexity at the Δp2-level of the PH for the analogue of Tideman's procedure with a fixed tie-breaking rule, and at the Σp2-level of the PH for the analogue of Tideman's procedure without a fixed tie-breaking rule.