mdh.sePublications
Change search
Refine search result
1 - 16 of 16
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1.
    Andren, Daniel
    et al.
    Umeå University.
    Hellström, Lars
    Umeå University.
    Markström, Klas
    Umeå University.
    Fast multiplication of matrices over a finitely generated semiring2008In: Information Processing Letters, ISSN 0020-0190, E-ISSN 1872-6119, Vol. 107, no 6, p. 230-234Article in journal (Refereed)
  • 2.
    Hellström, Lars
    Mälardalen University, School of Education, Culture and Communication. Umeå University.
    A Rewriting Approach to Graph Invariants2009In: Generalized Lie Theory in Mathematics, Physics and Beyond / [ed] Sergei Silvestrov, Eugen Paal, Viktor Abramov, Alexander Stolin, Berlin, Heidelberg: Springer, 2009, p. 47-67Chapter in book (Refereed)
    Abstract [en]

    Diagrammatic calculation is a powerful tool that gets near indispensable when one tries to manage some of the newer algebraic structures that have been popping up in the last couple of decades. Concretely, it generalises the underlying structure of expressions to being general graphs, where traditional algebraic notation only supports path- or treelike expressions. This paper demonstrates how to apply the author's Generic Diamond Lemma in diagrammatic calculations, by solving through elementary rewriting techniques the problem of classifying all multigraph invariants satisfying a linear contract—delete recursion. (As expected, this leads one to rediscover the Tutte polynomial, along with some more degenerate invariants.) In addition, a concept of “semigraph” is defined which formalises the concept of a graph-theoretical “gadget”.

  • 3.
    Hellström, Lars
    Mälardalen University, School of Education, Culture and Communication. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Critical Pairs in Network Rewriting2014In: IWC 2014: 3rd International Workshop on Confluence / [ed] Takahito Aoto & Delia Kesner, 2014, p. 9-13Conference paper (Refereed)
    Abstract [en]

    This extended abstract breifly introduces rewriting of networks (directed acyclic graphs with the extra structure needed to serve as expressions for PROducts and Permutations categories) and describes the critical pairs aspects of this theory. The author's interest in these comes from wanting to do equational reasoning in algebraic theories (such as Hopf algebras) that mix ordinary operations with co-operations; networks then serve as a formalism for expressions.

    The main message is to point out two phenomena that arise in network rewriting. The first is that of non-convexity of rules, wherein the left hand side of a rule need not be syntactically similar to a symbol in any extension of the underlying signature. The second is one of critical pairs potentially arising where two redexes wrap around each other even when they do not intersect.

  • 4.
    Hellström, Lars
    Umeå universitet.
    Literate sources for content dictionaries2013In: MathUI, OpenMath, PLMMS and ThEdu Workshops and Work in Progress at the Conference on Intelligent Computer Mathematics, Aachen: Redaktion Sun SITE, Informatik V, RWTH Aachen , 2013Conference paper (Refereed)
    Abstract [en]

    It is suggested that a LaTeX document could be used as the Literate Programming source of an OpenMath content dictionary. Several approaches to literate programming are reviewed and a possible implementation is sketched.

  • 5.
    Hellström, Lars
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Literate Sources for Content Dictionaries: a Progress Report2014In: CICM-WS-WiP 2014: Workshop and Work in Progress Papers at CICM 2014 / [ed] Matthew England et al., Aachen: CEUR-WS.org , 2014Conference paper (Refereed)
    Abstract [en]

    At OM2013, the author suggested and sketched a system that would use LaTeX documents as Literate Programming sources for content dictionaries. This paper reports on the progress that has since been made with this system. One important milestone that has been reached is that valid .ocd files with CDDefinitions, FMPs, CMPs, and Examples are being generated.

  • 6.
    Hellström, Lars
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Mathematical Formulae Beyond the Tree Paradigm2016Conference paper (Other academic)
    Abstract [en]

    A restriction in the traditional language of mathematics is that every formula has an underlying tree structure, wherein an expression decomposes into subexpressions that each contribute one result to the whole. Some modern mathematics (especially in higher algebra and differential geometry) is however not so well catered for by this tree paradigm, and would be much better off if this restriction was lifted; it is not that the mathematics requires a generalised formula language, but it becomes a whole lot easier to state and do when you use one.

    This poster shows the formula language of networks that arises when one relaxes the tree restriction to instead allow an underlying directed acyclic graph (DAG) structure. Evaluation of networks is non-obvious, but can be carried out in any PROP/symocat; conversely, evaluation of networks characterises PROPs in much the same way as evaluation of words characterises monoids. Networks are isomorphic to the abstract index interpretation of Einstein convention tensor expressions, and demonstrate that these can in fact be given a coordinate-free interpretation. Special cases of the network notation that have been invented independently include the Penrose graphical notation and quantum gate arrays.

  • 7.
    Hellström, Lars
    Mälardalen University, School of Education, Culture and Communication.
    Network Rewriting I: The Foundation2012Report (Other academic)
    Abstract [en]

    A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and Permutations category'), and conversely that the PROP axioms are implicit in the concept of evaluating a network. Ordinary terms and operads constitute the special case that the graph underlying the network is a rooted tree. Furthermore a rewriting theory for networks is developed. Included in this is a subexpression concept for which is given both algebraic and effective graph-theoretical characterisations, a construction of reduction maps from rewriting systems, and an analysis of the obstructions to confluence that can occur. Several Diamond Lemmas for this rewriting theory are given. In addition there is much supporting material on various related subjects. In particular there is a "toolbox" for the construction of custom orders on the free PROP, so that an order can be tailored to suit a specific rewriting system. Other subjects treated are the abstract index notation in a general PROP context and the use of feedbacks (sometimes called traces) in PROPs.

  • 8.
    Hellström, Lars
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Network Rewriting II: Bi- and Hopf Algebras2015In: Leibniz International Proceedings in Informatics, LIPIcs, Volume 36 / [ed] Maribel Fernández, Dagstuhl, Germany: Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik , 2015, Vol. 36, p. 194-208Conference paper (Refereed)
    Abstract [en]

    Bialgebras and their specialisation Hopf algebras are algebraic structures that challenge traditional mathematical notation, in that they sport two core operations that defy the basic functional paradigm of taking zero or more operands as input and producing one result as output. On the other hand, these peculiarities do not prevent studying them using rewriting techniques, if one works within an appropriate network formalism rather than the traditional term formalism. This paper restates the traditional axioms as rewriting systems, demonstrating confluence in the case of bialgebras and finding the (infinite) completion in the case of Hopf algebras. A noteworthy minor problem solved along the way is that of constructing a quasi-order with respect to which the rules are compatible.

  • 9.
    Hellström, Lars
    Mälardalen University, School of Education, Culture and Communication.
    Network Rewriting II: Bi- and Hopf AlgebrasManuscript (preprint) (Other academic)
    Abstract [en]

    Bialgebras and their specialisation Hopf algebras are algebraic structures that challenge traditional mathematical notation, in that they sport two core operations that defy the basic functional paradigm of taking zero or more operands as input and producing one result as output. On the other hand, these peculiarities do not prevent studying them using rewriting techniques, if one works within an appropriate network formalism. This paper restates the traditional axioms as rewriting systems, demonstrating confluence in the case of bialgebras and finding the (infinite) completion in the case of Hopf algebras. A noteworthy minor problem solved along the way is that of constructing a quasi-order with respect to which the rules are compatible.

  • 10.
    Hellström, Lars
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ordered and Combinatorial Structures for Higher-Dimensional Rewriting2016In: / [ed] Samuel Mimram, 2016Conference paper (Refereed)
    Abstract [en]

    In principle, rewriting is the logically pure activity of transforming abstract expressions according to fully formalised rules, but in practice there is a significant interplay between abstract rules, more-or-less concrete interpretations, and a variety of book-keeping devices that all need to fit together if the rewriting process is to yield results. This paper presents elementary realisations of book-keeping and other formalising devices that are useful in higher-dimensional rewriting, with a focus on the "2-dimensional" case (PROPs and other types of monoidal category). In particular, it explains how one may construct a variety of ordering relations on these object that are sensitive to differences in the underlying graph structure of the objects being rewritten. It also shows how the formal feedback operation can be used to handle nonconvex redexes, which is a phenomenon of higher-dimensional rewriting that lacks a counterpart in word or term rewriting.

  • 11.
    Hellström, Lars
    Mälardalen University, School of Education, Culture and Communication. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ordering Networks2014Conference paper (Refereed)
    Abstract [en]

    This extended abstract discusses the problem of defining quasi-orders that are suitable for use with network rewriting. The author’s primary interest is in using network rewriting as a tool for equational reasoning in algebraic theories with both operations and co-operations.

  • 12.
    Hellström, Lars
    Umeå universitet.
    Quantifiers and n-ary binders: an OpenMath standard enhancement proposal2013In: Proceedings of the MathUI, OpenMath, PLMMS and ThEdu Workshops and Work in Progress at CICMco-located with Conferences on Intelligent Computer Mathematics (CICM 2013), Aachen: Redaktion Sun SITE, Informatik V, RWTH Aachen , 2013Conference paper (Refereed)
    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.

  • 13.
    Hellström, Lars
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    The eval symbol for axiomatising variadic functions2014In: CICM-WS-WiP 2014: Workshop and Work in Progress Papers at CICM 2014 / [ed] Matthew England et al., Aachen: CEUR-WS.org , 2014Conference paper (Refereed)
    Abstract [en]

    This paper describes (and constitutes the source for!) the proposed list4 OpenMath content dictionary. The main feature in this content dictionary is the eval symbol, which treats a list of values as the list of children of an application element. This may, among other things, be employed to state properties of variadic functions.

  • 14.
    Hellström, Lars
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Valued Custom Skew Fields with Generalised PBW Property from Power Series Construction2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, p. 33-55Chapter in book (Refereed)
    Abstract [en]

    This chapter describes a construction of associative algebras that, despite starting from a commutation relation that the user may customize quite considerably, still manages to produce algebras with a number of useful properties: they have a Poincaré–Birkhoff–Witt type basis, they are equipped with a norm (actually an ultranorm) that is trivial to compute for basis elements, they are topologically complete, and they satisfy their given commutation relation. In addition, parameters can be chosen so that the algebras will in fact turn out to be skew fields and the norms become valuations. The construction is basically that of a power series algebra with given commutation relation, stated to be effective enough that the other properties can be derived. What is worked out in detail here is the case of algebras with two generators, but only the analysis of the commutation relation is specific for that case.

  • 15.
    Hellström, Lars
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Umea Univ, Dept Math & Math Stat, SE-90187 Umeå, Sweden.
    Carlsson, Linus
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Umea Univ, Dept Math & Math Stat, SE-90187 Umea, Sweden.
    Falster, Daniel S.
    Univ New South Wales, Evolut & Ecol Res Ctr, Sydney, NSW 2052, Australia.;Univ New South Wales, Sch Biol Earth & Environm Sci, Sydney, NSW 2052, Australia.;Macquarie Univ, Dept Biol Sci, Sydney, NSW 2109, Australia..
    Westoby, Mark
    Macquarie Univ, Dept Biol Sci, Sydney, NSW 2109, Australia..
    Brannstrom, Ake
    Umea Univ, Dept Math & Math Stat, SE-90187 Umea, Sweden.;Int Inst Appl Syst Anal, Evolut & Ecol Program, A-2361 Laxenburg, Austria..
    Branch Thinning and the Large-Scale, Self-Similar Structure of Trees2018In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 192, no 1, p. E37-E47Article in journal (Refereed)
    Abstract [en]

    Branch formation in trees has an inherent tendency toward exponential growth, but exponential growth in the number of branches cannot continue indefinitely. It has been suggested that trees balance this tendency toward expansion by also losing branches grown in previous growth cycles. Here, we present a model for branch formation and branch loss during ontogeny that builds on the phenomenological assumption of a branch carrying capacity. The model allows us to derive approximate analytical expressions for the number of tips on a branch, the distribution of growth modules within a branch, and the rate and size distribution of tree wood litter produced. Although limited availability of data makes empirical corroboration challenging, we show that our model can fit field observations of red maple (Acer rubrum) and note that the age distribution of discarded branches predicted by our model is qualitatively similar to an empirically observed distribution of dead and abscised branches of balsam poplar (Populus balsamifera). By showing how a simple phenomenological assumptionthat the number of branches a tree can maintain is limitedleads directly to predictions on branching structure and the rate and size distribution of branch loss, these results potentially enable more explicit modeling of woody tissues in ecosystems worldwide, with implications for the buildup of flammable fuel, nutrient cycling, and understanding of plant growth.

  • 16.
    Hellström, Lars
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Makhlouf, Abdenacer
    University of Haute Alsace, LMIA.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Universal Algebra Applied to Hom-Associative Algebras, and More2014In: Algebra, Geometry, and Mathematical Physics: AGMP, Mulhouse, France, October 2011, Springer Berlin/Heidelberg, 2014, p. 157-199Conference paper (Refereed)
    Abstract [en]

    The purpose of this paper is to discuss the universal algebra theory of hom-algebras. This kind of algebra involves a linear map which twists the usual identities. We focus on hom-associative algebras and hom-Lie algebras for which we review the main results. We discuss the envelopment problem, operads, and the Diamond Lemma; the usual tools have to be adapted to this new situation. Moreover we study Hilbert series for the hom-associative operad and free algebra, and describe them up to total degree equal 8 and 9 respectively.

1 - 16 of 16
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf