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  • 1.
    Berglund, Martin
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Drewes, Frank
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    On the complexity of variants of the k Best strings problem2010In: Proceedings of the Prague stringology conference 2010, dblp , 2010, p. 76-88Conference paper (Refereed)
    Abstract [en]

    We investigate the problem of extracting the k best strings from a nondeterministic weighted automaton over a semiring S. This problem, which has been considered earlier in the literature, is more difficult than extracting the k best runs, since distinct runs may not correspond to distinct strings. Unsurprisingly, the computational complexity of the problem depends on the semiring S used. We study three different cases, namely the tropical and complex tropical semirings, and the semiring of positive real numbers. For the first case, we establish a polynomial algorithm. For the second and third cases, NP-completeness and undecidability results are shown.

  • 2.
    Bondesson, Lennart
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Traat, Imbi
    Institute of Mathematical Statistics , University of Tartu , 50409 Tartu, Estonia.
    A non-symmetric matrix with integer eigenvalues2007In: Linear and Multilinear Algebra, ISSN 0308-1087, 1563-5139, Vol. 55, no 3, p. 239-247Article in journal (Refereed)
    Abstract [en]

    A nonsymmetric N × N matrix with elements as certain simple functions of N distinct real or complex numbers r 1, r 2, …, rN is presented. The matrix is special due to its eigenvalues − the consecutive integers 0,1,2, …, N−1. Theorems are given establishing explicit expressions of the right and left eigenvectors and formulas for recursive calculation of the right eigenvectors. A special case of the matrix has appeared in sampling theory where its right eigenvectors, if properly normalized, give the inclusion probabilities of the conditional Poisson sampling design.

  • 3.
    Ciegis, Raimondas
    et al.
    Vilnius Gediminas Technical University, Lithuania.
    Henty, David
    University of Edingburg, UK.
    Kågström, Bo
    Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).
    Zilinskas, Julius
    Vilnius Gediminas Technical University, Lithuania.
    Parallel Scientific Computing and Optimization: Advances with Applications2009Book (Other academic)
  • 4.
    Dmytryshyn, Andrii
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Structure preserving stratification of skew-symmetric matrix polynomials2017In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 532, p. 266-286Article in journal (Refereed)
    Abstract [en]

    We study how elementary divisors and minimal indices of a skew-symmetric matrix polynomial of odd degree may change under small perturbations of the matrix coefficients. We investigate these changes qualitatively by constructing the stratifications (closure hierarchy graphs) of orbits and bundles for skew-symmetric linearizations. We also derive the necessary and sufficient conditions for the existence of a skew-symmetric matrix polynomial with prescribed degree, elementary divisors, and minimal indices.

  • 5.
    Dmytryshyn, Andrii
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Dopico, Froilán
    Universidad Carlos III de Madrid.
    Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade2018In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 536, p. 1-18Article in journal (Refereed)
    Abstract [en]

    We show that the set of m×m complex skew-symmetric matrix polynomials of odd grade d, i.e., of degree at most d, and (normal) rank at most 2r is the closure of the single set of matrix polynomials with the certain, explicitly described, complete eigenstructure. This complete eigenstructure corresponds to the most generic m×m complex skew-symmetric matrix polynomials of odd grade d and rank at most 2r. In particular, this result includes the case of skew-symmetric matrix pencils (d=1).

  • 6.
    Jäger, Gerold
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Climer, Sharlee
    Zhang, Weixiong
    The complete parsimony haplotype inference problem and algorithms based on integer programming, branch-and-bound and Boolean satisfiability2016In: Journal of Discrete Algorithms, ISSN 1570-8667, E-ISSN 1570-8675, Vol. 37, p. 68-83Article in journal (Refereed)
    Abstract [en]

    Haplotype inference by pure parsimony (HIPP) is a well-known paradigm for haplotype inference. In order to assess the biological significance of this paradigm, we generalize the problem of HIPP to the problem of finding all optimal solutions, which we call CHIPP. We study intrinsic haplotype features, such as backbone haplotypes and fat genotypesas well as equal columns and decomposability. We explicitly exploit these features in three computational approaches that are based on integer linear programming, depth-first branch-and-bound, and Boolean satisfiability. Further we introduce two hybrid algorithms that draw upon the diverse strengths of the approaches. Our experimental analysis shows that our optimized algorithms are significantly superior to the baseline algorithms, often with orders of magnitude faster running time. Finally, our experiments provide some useful insights into the intrinsic features of this important problem.

  • 7.
    Lindström, Sten
    Umeå University, Faculty of Arts, Department of historical, philosophical and religious studies.
    Introduction2012In: Epistemology versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf / [ed] Dybjer, P.; Lindström, S.; Palmgren, E.; Sundholm, G., Dordrecht: Springer, 2012, p. vii-xivChapter in book (Refereed)
    Abstract [en]

    This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?

  • 8. Pikhurko, Oleg
    et al.
    Sliačan, Jakub
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Tyros, Konstantinos
    Strong forms of stability from flag algebra calculations2019In: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 135, p. 129-178Article in journal (Refereed)
    Abstract [en]

    Given a hereditary family g of admissible graphs and a function lambda(G) that linearly depends on the statistics of order-k subgraphs in a graph G, we consider the extremal problem of determining lambda(n, g), the maximum of lambda(G) over all admissible graphs G of order n. We call the problem perfectly B-stable for a graph B if there is a constant C such that every admissible graph G of order n >= C can be made into a blow-up of B by changing at most C(lambda(n, g) - lambda(G)) (n 2) adjacencies. As special cases, this property describes all almost extremal graphs of order n within o(n(2)) edges and shows that every extremal graph of order n >= C is a blow-up of B. We develop general methods for establishing stability-type results from flag algebra computations and apply them to concrete examples. In fact, one of our sufficient conditions for perfect stability is stated in a way that allows automatic verification by a computer. This gives a unifying way to obtain computer-assisted proofs of many new results.

  • 9.
    Trygg, Johan
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Wold, Svante
    Umeå University, Faculty of Science and Technology, Department of Chemistry. Umetrics AB.
    Eriksson, Lennart
    Umetrics AB.
    Hierarchically Organizing Data Using a Partial Least Squares Analysis (PLS-Trees)2009Patent (Other (popular science, discussion, etc.))
    Abstract [en]

    Abstract: A method and system for partitioning (clustering) large amounts of data in a relatively short processing time. The method involves providing a first data matrix and a second data matrix where each of the first and second data matrices includes one or more variables, and a plurality of data points. The method also involves determining a first score from the first data matrix using a partial least squares (PLS) analysis or orthogonal PLS (OPLS) analysis and partitioning the first and second data matrices (e.g., row-wise) into a first group and a second group based on the sorted first score, the variance of the first data matrix, and a variance of the first and second groups relative to the variances of the first and second data matrices.

  • 10.
    Verdier, Olivier
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Department of Computing, Mathematics and Physics, Western Norway University of Applied Sciences, Bergen, Norway.
    Extension of matrix pencil reduction to abelian categories2018In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 17, no 4, article id 1850062Article in journal (Refereed)
    Abstract [en]

    Matrix pencils, or pairs of matrices, are used in a variety of applications. By the Kronecker decomposition theorem, they admit a normal form. This normal form consists of four parts, one part based on the Jordan canonical form, one part made of nilpotent matrices, and two other dual parts, which we call the observation and control part. The goal of this paper is to show that large portions of that decomposition are still valid for pairs of morphisms of modules or abelian groups, and more generally in any abelian category. In the vector space case, we recover the full Kronecker decomposition theorem. The main technique is that of reduction, which extends readily to the abelian category case. Reductions naturally arise in two flavors, which are dual to each other. There are a number of properties of those reductions which extend remarkably from the vector space case to abelian categories. First, both types of reduction commute. Second, at each step of the reduction, one can compute three sequences of invariant spaces (objects in the category), which generalize the Kronecker decomposition into nilpotent, observation and control blocks. These sequences indicate whether the system is reduced in one direction or the other. In the category of modules, there is also a relation between these sequences and the resolvent set of the pair of morphisms, which generalizes the regular pencil theorem. We also indicate how this allows to define invariant subspaces in the vector space case, and study the notion of strangeness as an example.

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