Incorporating Weisfeiler-Leman into algorithms for group isomorphism

In this paper we combine many of the standard and more recent algebraic techniques for testing isomorphism of finite groups (GpI) with combinatorial techniques that have typically b

Efficient Reconstruction of Metabolic Pathways by Bidirectional Chemical Search

One of the main challenges in systems biology is the establishment of the metabolome: a catalogue of the metabolites and biochemical reactions present in a specific organism. Current knowledge of biochemical pathways as stored in public databases such as KEGG, is based on carefully curated genomic evidence for the presence of specific metabolites and enzymes that activate particular biochemical reactions. In this paper, we present an efficient method to build a substantial portion of the artificial chemistry defined by the metabolites and biochemical reactions in a given metabolic pathway, which is based on bidirectional chemical search. Computational results on the pathways stored in KEGG reveal novel biochemical pathways

Rank reduction of string C-group representations

We show that a rank reduction technique for string C-group representations first used in [Adv. Math. 228 (2018), pp. 3207-3222] for the symmetric groups generalizes to arbitrary settings. The technique permits us, among other things, to prove that orthogonal groups defined on d-dimensional modules over fields of even order greater than 2 possess string C-group representations of all ranks 3 ≤ n ≤ d. The broad applicability of the rank reduction technique provides fresh impetus to construct, for suitable families of groups, string C-groups of highest possible rank. It also suggests that the alternating group Alt(11)-the only known group having "rank gaps"-is perhaps more unusual than previously thought.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Orthogonal Groups in Characteristic 2 Acting on Polytopes of High Rank

We show that for all integers m⩾ 2 ,and all integers k⩾ 2 ,the orthogonal groups O±(2m,F2k) act on abstract regular polytopes of rank 2m, and the symplectic groups Sp(2m,F2k) act on abstract regular polytopes of rank 2 m+ 1.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Developing a framework for network and cluster identification for use in economic development policy-making

Drawing on extensive academic research concerning clusters and networks, this paper seeks to create a framework capable of reviewing and monitoring different aspects of clusters and networks on an ongoing basis. The nine-element framework allows evaluation of the structures and processes for the eight basic cluster types identified from the literature. The use of this framework as a complimentary tool to the Multi-sectoral Qualitative Analysis (MSQA) methodology is then demonstrated using three examples (the construction, hardwood timber and higher education sectors). The data was gathered from three sets of key stakeholders (government, institutions and industry) provided from a recent study funded by the Welsh Assembly Government's Small Grants Research Programme. These cases illustrate the use of the framework in helping to generate the initial information necessary for subsequent cluster development policy (within overall regional economic development) by government to occur. The framework provides tools for reviewing and monitoring individual sectors. Information captured within the framework can also help in ameliorating problems in sectors likely to decline further. The need for further development research is also identified. Specifically at the level of the firm and network, there is a need to generate a more detailed framework of analysis of factors that contribute to successful processes of network management, learning and innovation, from which more detailed policy could be enacted in future

Chiral Polytopes and Suzuki Simple Groups

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