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  • 1.
    Berglund, Martin
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Drewes, Frank
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    On the complexity of variants of the k Best strings problem2010Ingår i: Proceedings of the Prague stringology conference 2010, dblp , 2010, s. 76-88Konferensbidrag (Refereegranskat)
    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 universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Traat, Imbi
    Institute of Mathematical Statistics , University of Tartu , 50409 Tartu, Estonia.
    A non-symmetric matrix with integer eigenvalues2007Ingår i: Linear and Multilinear Algebra, ISSN 0308-1087, 1563-5139, Vol. 55, nr 3, s. 239-247Artikel i tidskrift (Refereegranskat)
    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 universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Zilinskas, Julius
    Vilnius Gediminas Technical University, Lithuania.
    Parallel Scientific Computing and Optimization: Advances with Applications2009Bok (Övrigt vetenskapligt)
  • 4.
    Daghighi, Abtin
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Gauthier, Paul M.
    Université de Montréal, Montréal, Canada.
    An algebra of polyanalytic functions2021Ingår i: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 165, nr 2, s. 225-240Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The most important uniform algebra is the family of continuous functions on a compact subset K of the complex plane C which are analytic on the interior int(K). For polyanalytic functions and compact sets K which are regular (i.e. K = int(K)), we introduce analogous spaces, which are Banach spaces with respect to the sup-norm, but are not closed with respect to the usual pointwise multiplication. We introduce a multiplication on these spaces and investigate the resulting algebras.

  • 5.
    Dmytryshyn, Andrii
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Structure preserving stratification of skew-symmetric matrix polynomials2017Ingår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 532, s. 266-286Artikel i tidskrift (Refereegranskat)
    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.

  • 6.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Dopico, Froilán
    Universidad Carlos III de Madrid.
    Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade2018Ingår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 536, s. 1-18Artikel i tidskrift (Refereegranskat)
    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).

  • 7.
    Hellström, Lars
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Quantifiers and n-ary Binders: An OpenMath Standard Enhancement Proposal2013Ingår i: CICM-WS-WiP 2013: Workshops and Work in Progress at CICM, 2013, artikel-id 21Konferensbidrag (Refereegranskat)
    Abstract [en]

    It is proposed that the restriction in the OpenMath standard that an OMBIND element must have exactly three children should be lifted, to support more general binder symbols. The case of logics with generalised quantifiers is described in some detail, since these turn out to not have a natural encoding within OpenMath 2.0, because of precisely this restriction. That restricting quantifiers to a single body should have such consequences is not trivial, but follows from a theorem in the Logic branch of Philosophy.

  • 8.
    Jäger, Gerold
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Climer, Sharlee
    Zhang, Weixiong
    The complete parsimony haplotype inference problem and algorithms based on integer programming, branch-and-bound and Boolean satisfiability2016Ingår i: Journal of Discrete Algorithms, ISSN 1570-8667, E-ISSN 1570-8675, Vol. 37, s. 68-83Artikel i tidskrift (Refereegranskat)
    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.

  • 9.
    Lindström, Sten
    Umeå universitet, Humanistiska fakulteten, Institutionen för idé- och samhällsstudier.
    A semantic approach to nonmonotonic reasoning: inference operations and choice2022Ingår i: Theoria, ISSN 0040-5825, E-ISSN 1755-2567, Vol. 88, nr 3, s. 494-528Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premisses. The semantics is formulated in terms of selection functions and is a generalisation of the preferential semantics of Shoham, Kraus et al., and Makinson. A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred ones. A proposition α is a nonmonotonic consequence of a set of propositions Γ iff α holds in all the most preferred Γ-states. In the literature on revealed preference theory, there are a number of well-known theorems concerning the representability of selection functions, satisfying certain properties, in terms of underlying preference relations. Such theorems are utilised here to give corresponding representation theorems for nonmonotonic inference operations. At the end of the paper, the connection between nonmonotonic inference and belief revision, in the sense of Alchourrón, Gärdenfors, and Makinson, is explored. In this connection, infinitary belief revision operations, that allow for the revision of a theory with a possibly infinite set of propositions, are introduced and characterised axiomatically. Several semantic representation theorems are proved for operations of this kind.

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  • 10.
    Lindström, Sten
    Umeå universitet, Humanistiska fakulteten, Institutionen för idé- och samhällsstudier.
    Introduction2012Ingår i: 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, s. vii-xivKapitel i bok, del av antologi (Refereegranskat)
    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?

  • 11. Pikhurko, Oleg
    et al.
    Sliačan, Jakub
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Tyros, Konstantinos
    Strong forms of stability from flag algebra calculations2019Ingår i: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 135, s. 129-178Artikel i tidskrift (Refereegranskat)
    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.

  • 12.
    Psarras, Christos
    et al.
    RWTH Aachen University, Aachen, Germany.
    Barthels, Henrik
    RWTH Aachen University, Aachen, Germany.
    Bientinesi, Paolo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    The linear algebra mapping problem: Current state of linear algebra languages and libraries2022Ingår i: ACM Transactions on Mathematical Software, ISSN 0098-3500, E-ISSN 1557-7295, Vol. 48, nr 3, artikel-id 3549935Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We observe a disconnect between developers and end-users of linear algebra libraries. On the one hand, developers invest significant effort in creating sophisticated numerical kernels. On the other hand, end-users are progressively less likely to go through the time consuming process of directly using said kernels; instead, languages and libraries, which offer a higher level of abstraction, are becoming increasingly popular. These languages offer mechanisms that internally map the input program to lower level kernels. Unfortunately, our experience suggests that, in terms of performance, this translation is typically suboptimal.

    In this paper, we define the problem of mapping a linear algebra expression to a set of available building blocks as the "Linear Algebra Mapping Problem"(LAMP); we discuss its NP-complete nature, and investigate how effectively a benchmark of test problems is solved by popular high-level programming languages and libraries. Specifically, we consider Matlab, Octave, Julia, R, Armadillo (C++), Eigen (C++), and NumPy (Python); the benchmark is meant to test both compiler optimizations, as well as linear algebra specific optimizations, such as the optimal parenthesization of matrix products. The aim of this study is to facilitate the development of languages and libraries that support linear algebra computations.

  • 13.
    Sjöblom, Axel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The Abel-Ruffini Theorem: The insolvability of the general quintic equation by radicals2024Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Den här uppsatsen utforskar Galoisteorin för att bevisa Abel-Ruffinis sats. I den första delen är algebraiska strukturer i fokus: Grupper, ringar, kroppar, etc. Efter detta intrduceras polynom-ringar, och fokuset vänds sedan till ändliga kropps-utvidgningar. I den sista delen av huvudtexten så studeras lösbara förvidgningar och Abel-Ruffini's sats bevisas. Diskusionen ger en översikt över analytiska lösningar av polynom-ekvationer.

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  • 14.
    Säfström, Anna Ida
    Department of Mathematical Sciences, University of Gothenburg, Gothenburg, Sweden.
    Exercising mathematical competence: practising representation theory and representing mathematical practice2013Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
  • 15.
    Säfström, Anna Ida
    Institutionen för matematiska vetenskaper, Göteborgs universitet, Göteborg, Sverige.
    Tensor products of highest weight representations and skew-symmetric matrix equations A+B+C=02010Licentiatavhandling, monografi (Övrigt vetenskapligt)
  • 16. Tropp, Joel A.
    et al.
    Yurtsever, Alp
    Udell, Madeleine
    Cevher, Volkan
    Streaming Low-Rank Matrix Approximation with an Application to Scientific Simulation2019Ingår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 41, nr 4, s. A2430-A2463Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm for constructing an accurate low-rank approximation of a matrix from streaming data. This method is accompanied by an a priori analysis that allows the user to set algorithm parameters with confidence and an a posteriori error estimator that allows the user to validate the quality of the reconstructed matrix. In comparison to previous techniques, the new method achieves smaller relative approximation errors and is less sensitive to parameter choices. As concrete applications, the paper outlines how the algorithm can be used to compress a Navier--Stokes simulation and a sea surface temperature dataset.

  • 17.
    Trygg, Johan
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Kemiska institutionen.
    Wold, Svante
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Kemiska institutionen. Umetrics AB.
    Eriksson, Lennart
    Umetrics AB.
    Hierarchically Organizing Data Using a Partial Least Squares Analysis (PLS-Trees)2009Patent (Övrig (populärvetenskap, debatt, mm))
    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.

  • 18.
    Verdier, Olivier
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Department of Computing, Mathematics and Physics, Western Norway University of Applied Sciences, Bergen, Norway.
    Extension of matrix pencil reduction to abelian categories2018Ingår i: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 17, nr 4, artikel-id 1850062Artikel i tidskrift (Refereegranskat)
    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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