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Publications (10 of 15) Show all publications
Hellström, L., Carlsson, L., Falster, D. S., Westoby, M. & Brannstrom, A. (2018). Branch Thinning and the Large-Scale, Self-Similar Structure of Trees. American Naturalist, 192(1), E37-E47
Open this publication in new window or tab >>Branch Thinning and the Large-Scale, Self-Similar Structure of Trees
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2018 (English)In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 192, no 1, p. E37-E47Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
UNIV CHICAGO PRESS, 2018
Keywords
branching structure, self-similarity, tree architecture, wood litter
National Category
Mathematics
Identifiers
urn:nbn:se:mdh:diva-40104 (URN)10.1086/697429 (DOI)000435128300004 ()29897799 (PubMedID)
Available from: 2018-06-28 Created: 2018-06-28 Last updated: 2018-06-28Bibliographically approved
Hellström, L. (2016). Mathematical Formulae Beyond the Tree Paradigm. In: : . Paper presented at 27th Nordic Congress of Mathematicians, Stockholm.
Open this publication in new window or tab >>Mathematical Formulae Beyond the Tree Paradigm
2016 (English)Conference paper, Poster (with or without abstract) (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.

Keywords
coarity, PROP, network, monoidal category, directed acyclic graph, tensor product, entanglement, Penrose graphical notation, abstract index notation
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-31315 (URN)
Conference
27th Nordic Congress of Mathematicians, Stockholm
Available from: 2016-03-18 Created: 2016-03-18 Last updated: 2016-10-11Bibliographically approved
Hellström, L. (2016). Ordered and Combinatorial Structures for Higher-Dimensional Rewriting. In: Samuel Mimram (Ed.), : . Paper presented at Second edition of the workshop on Higher-Dimensional Rewriting and Applications 22-26 June 2016, Porto, Portugal http://hdra.gforge.inria.fr/ Co-located with the FSCD conference.
Open this publication in new window or tab >>Ordered and Combinatorial Structures for Higher-Dimensional Rewriting
2016 (English)In: / [ed] Samuel Mimram, 2016Conference paper, Published 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.

Keywords
rewriting, network rewriting, PROP, monoidal category, order relation, biaffine PROP, PROP with formal feedback
National Category
Algebra and Logic Discrete Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-33075 (URN)
Conference
Second edition of the workshop on Higher-Dimensional Rewriting and Applications 22-26 June 2016, Porto, Portugal http://hdra.gforge.inria.fr/ Co-located with the FSCD conference
Note

These proceedings were distributed (electronically on USB stick) to all participants at the FSCD conference and associated workshops.

Available from: 2016-09-07 Created: 2016-09-06 Last updated: 2017-09-28Bibliographically approved
Hellström, L. (2015). Network Rewriting II: Bi- and Hopf Algebras. In: Maribel Fernández (Ed.), Leibniz International Proceedings in Informatics, LIPIcs, Volume 36: . Paper presented at 26th International Conference on Rewriting Techniques and Applications (RTA 2015), June 29 to July 1, 2015 - Warsaw, Poland (pp. 194-208). Dagstuhl, Germany: Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 36
Open this publication in new window or tab >>Network Rewriting II: Bi- and Hopf Algebras
2015 (English)In: 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, Published 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.

Place, publisher, year, edition, pages
Dagstuhl, Germany: Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2015
Series
Leibniz International Proceedings in Informatics (LIPIcs), ISSN 1868-8969
Keywords
confluence, network, PROP, Hopf algebra, bialgebra, rewriting
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-29884 (URN)10.4230/LIPIcs.RTA.2015.194 (DOI)2-s2.0-84958953312 (Scopus ID)978-3-939897-85-9 (ISBN)
Conference
26th International Conference on Rewriting Techniques and Applications (RTA 2015), June 29 to July 1, 2015 - Warsaw, Poland
Available from: 2015-12-09 Created: 2015-12-09 Last updated: 2017-09-28Bibliographically approved
Hellström, L. (2014). Critical Pairs in Network Rewriting. In: Takahito Aoto & Delia Kesner (Ed.), IWC 2014: 3rd International Workshop on Confluence. Paper presented at IWC 2014 (3rd International Workshop on Confluence), part of Vienna Summer of Logic 2014, Vienna, 13 July 2014 (pp. 9-13).
Open this publication in new window or tab >>Critical Pairs in Network Rewriting
2014 (English)In: IWC 2014: 3rd International Workshop on Confluence / [ed] Takahito Aoto & Delia Kesner, 2014, p. 9-13Conference paper, Published 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.

Keywords
network, PROP, critical pair, ambiguity, confluence, wrap ambiguity
National Category
Algebra and Logic Discrete Mathematics Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-26109 (URN)
Conference
IWC 2014 (3rd International Workshop on Confluence), part of Vienna Summer of Logic 2014, Vienna, 13 July 2014
Available from: 2014-10-15 Created: 2014-10-15 Last updated: 2014-11-06Bibliographically approved
Hellström, L. (2014). Literate Sources for Content Dictionaries: a Progress Report. In: Matthew England et al. (Ed.), CICM-WS-WiP 2014: Workshop and Work in Progress Papers at CICM 2014. Paper presented at The 26th OpenMath Workshop. Aachen: CEUR-WS.org
Open this publication in new window or tab >>Literate Sources for Content Dictionaries: a Progress Report
2014 (English)In: CICM-WS-WiP 2014: Workshop and Work in Progress Papers at CICM 2014 / [ed] Matthew England et al., Aachen: CEUR-WS.org , 2014Conference paper, Published 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.

Place, publisher, year, edition, pages
Aachen: CEUR-WS.org, 2014
Series
CEUR Workshop Proceedings, ISSN 1613-0073 ; 1186
Keywords
OpenMath, literate programming, content dictionary, LaTeX, XML
National Category
Software Engineering
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-26083 (URN)2-s2.0-84924873357 (Scopus ID)
Conference
The 26th OpenMath Workshop
Available from: 2014-10-09 Created: 2014-10-09 Last updated: 2018-01-11Bibliographically approved
Hellström, L. (2014). Ordering Networks. In: : . Paper presented at 14th International Workshop on Termination (WST), Wien, July 17–18, 2014.
Open this publication in new window or tab >>Ordering Networks
2014 (English)Conference paper, Published 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.

Keywords
rewriting, network, PROP, PROP order
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-25103 (URN)
Conference
14th International Workshop on Termination (WST), Wien, July 17–18, 2014
Available from: 2014-06-04 Created: 2014-06-04 Last updated: 2014-06-24Bibliographically approved
Hellström, L. (2014). The eval symbol for axiomatising variadic functions. In: Matthew England et al. (Ed.), CICM-WS-WiP 2014: Workshop and Work in Progress Papers at CICM 2014. Paper presented at The 26th OpenMath Workshop. Aachen: CEUR-WS.org
Open this publication in new window or tab >>The eval symbol for axiomatising variadic functions
2014 (English)In: CICM-WS-WiP 2014: Workshop and Work in Progress Papers at CICM 2014 / [ed] Matthew England et al., Aachen: CEUR-WS.org , 2014Conference paper, Published 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.

Place, publisher, year, edition, pages
Aachen: CEUR-WS.org, 2014
Series
CEUR Workshop Proceedings, ISSN 1613-0073 ; 1186
Keywords
OpenMath, variadic function, content dictionary, formal mathematical property, Tcl, literate programming
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-26076 (URN)2-s2.0-84924912206 (Scopus ID)
Conference
The 26th OpenMath Workshop
Available from: 2014-10-09 Created: 2014-10-08 Last updated: 2015-03-26Bibliographically approved
Hellström, L., Makhlouf, A. & Silvestrov, S. (2014). Universal Algebra Applied to Hom-Associative Algebras, and More. In: Algebra, Geometry, and Mathematical Physics: AGMP, Mulhouse, France, October 2011. Paper presented at Algebra, Geometry and Mathematical Physics Conference, University of Haute Alsace, France, October 2011. (pp. 157-199). Springer Berlin/Heidelberg
Open this publication in new window or tab >>Universal Algebra Applied to Hom-Associative Algebras, and More
2014 (English)In: Algebra, Geometry, and Mathematical Physics: AGMP, Mulhouse, France, October 2011, Springer Berlin/Heidelberg, 2014, p. 157-199Conference paper, Published 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.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2014
Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1009 ; 85
Keywords
hom-Lie algebras, hom-associative algebra, operad, universal algebra, enveloping hom-algebra, diamond lemma, Hilbert series
National Category
Mathematics Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-24088 (URN)10.1007/978-3-642-55361-5_11 (DOI)000347610400011 ()2-s2.0-84939444285 (Scopus ID)978-3-642-55360-8 (ISBN)
Conference
Algebra, Geometry and Mathematical Physics Conference, University of Haute Alsace, France, October 2011.
Available from: 2013-12-31 Created: 2013-12-31 Last updated: 2018-02-27Bibliographically approved
Hellström, L. (2013). Literate sources for content dictionaries. In: MathUI, OpenMath, PLMMS and ThEdu Workshops and Work in Progress at the Conference on Intelligent Computer Mathematics: . Paper presented at MathUI, OpenMath, PLMMS and ThEdu Workshops and Work in Progress at CICMco-located with Conferences on Intelligent Computer Mathematics (CICM 2013), Bath, UK, July 9 - 10. Aachen: Redaktion Sun SITE, Informatik V, RWTH Aachen
Open this publication in new window or tab >>Literate sources for content dictionaries
2013 (English)In: 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, Published 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.

Place, publisher, year, edition, pages
Aachen: Redaktion Sun SITE, Informatik V, RWTH Aachen, 2013
Series
CEUR Workshop Proceedings, ISSN 1613-0073 ; 1010
Keywords
OpenMath, content dictionary, literate programming, notation, XML, LaTeX, end-user development
National Category
Software Engineering
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-21082 (URN)
Conference
MathUI, OpenMath, PLMMS and ThEdu Workshops and Work in Progress at CICMco-located with Conferences on Intelligent Computer Mathematics (CICM 2013), Bath, UK, July 9 - 10
Available from: 2013-08-23 Created: 2013-08-23 Last updated: 2018-01-11
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-6140-180X

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