1,852 research outputs found

    Polynomial functors and combinatorial Dyson-Schwinger equations

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    We present a general abstract framework for combinatorial Dyson-Schwinger equations, in which combinatorial identities are lifted to explicit bijections of sets, and more generally equivalences of groupoids. Key features of combinatorial Dyson-Schwinger equations are revealed to follow from general categorical constructions and universal properties. Rather than beginning with an equation inside a given Hopf algebra and referring to given Hochschild 11-cocycles, our starting point is an abstract fixpoint equation in groupoids, shown canonically to generate all the algebraic structure. Precisely, for any finitary polynomial endofunctor PP defined over groupoids, the system of combinatorial Dyson-Schwinger equations X=1+P(X)X=1+P(X) has a universal solution, namely the groupoid of PP-trees. The isoclasses of PP-trees generate naturally a Connes-Kreimer-like bialgebra, in which the abstract Dyson-Schwinger equation can be internalised in terms of canonical B+B_+-operators. The solution to this equation is a series (the Green function) which always enjoys a Fa\`a di Bruno formula, and hence generates a sub-bialgebra isomorphic to the Fa\`a di Bruno bialgebra. Varying PP yields different bialgebras, and cartesian natural transformations between various PP yield bialgebra homomorphisms and sub-bialgebras, corresponding for example to truncation of Dyson-Schwinger equations. Finally, all constructions can be pushed inside the classical Connes-Kreimer Hopf algebra of trees by the operation of taking core of PP-trees. A byproduct of the theory is an interpretation of combinatorial Green functions as inductive data types in the sense of Martin-L\"of Type Theory (expounded elsewhere).Comment: v4: minor adjustments, 49pp, final version to appear in J. Math. Phy

    Reproductive parameters in free-ranging female black rhinoceroses (Diceros bicornis) in Zimbabwe

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    Samples and data were collected from twenty-eight female black rhinoceroses (Diceros bicornis) during translocation efforts carried out by the Department of National Parks and Wildlife Management in Zimbabwe. Biological data were collected, cytological examination of vaginal smears was performed, and serum concentrations of follicle stimulating hormone, luteinizing hormone, progesterone, oestriol, and 17-β-oestradiol were determined by radio-immuno-assay. Prolactin levels were determined for 3 pregnant animals, 1 of which was sampled before and after parturition. Vaginal cytology was not found to be helpful for indicating the oestrous cycle stage for the black rhinoceros, but progesterone and 17-β–oestradiol levels were found to be useful indicators of pregnancy and possibly of oestrous cycle stage as well.The articles have been scanned in colour with a HP Scanjet 5590; 600dpi. Adobe Acrobat XI Pro was used to OCR the text and also for the merging and conversion to the final presentation PDF-format.University of Zimbabwe Research Board.mn201

    State sum construction of two-dimensional open-closed Topological Quantum Field Theories

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    We present a state sum construction of two-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, which generalizes the state sum of Fukuma--Hosono--Kawai from triangulations of conventional two-dimensional cobordisms to those of open-closed cobordisms, i.e. smooth compact oriented 2-manifolds with corners that have a particular global structure. This construction reveals the topological interpretation of the associative algebra on which the state sum is based, as the vector space that the TQFT assigns to the unit interval. Extending the notion of a two-dimensional TQFT from cobordisms to suitable manifolds with corners therefore makes the relationship between the global description of the TQFT in terms of a functor into the category of vector spaces and the local description in terms of a state sum fully transparent. We also illustrate the state sum construction of an open-closed TQFT with a finite set of D-branes using the example of the groupoid algebra of a finite groupoid.Comment: 33 pages; LaTeX2e with xypic and pstricks macros; v2: typos correcte

    Research Ethics in Information Systems: Would a Code of Practice Help?

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    The ethical conduct of research is a mark of integrity in the academic and professional worlds. This paper, which draws upon discussions conducted in a panel at the 21st ICIS conference in Brisbane, examines ethical issues associated with three key components of the research process: design, data collection and analysis; writing; and reviewing. The implications of these issues for the IS research community are discussed. Example scenarios are used to illuminate the issues faced by authors and reviewers. After considering the alternatives of strict guidelines enforced by bureaucratic structures, self regulation without guidelines and self regulation through norms set by a code of practice, the last option is recommended because it can lead to better practice in a constructive fashion without either excessive bureaucratic intervention or a free-for-all where anything goes

    The Impact of Online Social Networks on Decision Support Systems

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    Previous research on this matter had already determined that many concepts are encompassed by both online social networking and decision support systems research. Due to the large number of concepts and using clustering techniques, we were able to determine four concept clusters, namely: the technical infrastructure, online communities, network analysis and knowledge management. Then, we intended to gain further knowledge on how those concepts influenced DSS related research and the contribution of each cluster to the support of the phases of decision-making process. We also wanted to perceive the interconnections among the concept clusters themselves, for which we used structural equation modeling techniques. The obtained results evidence that not only online social networks are being used as a technical infrastructure to support the three decision making phases and to support knowledge management and online communities, but also that the other clusters only regard the intelligence phase of the decision process.info:eu-repo/semantics/publishedVersio

    Neutron radiography study of laboratory ageing and treatment applications with stone consolidants

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    A nano-silica consolidant and nano-titania modified tetraethyl-orthosilicate were applied on two building stones, a carbonate and a silicate, by brush, poultice or capillary absorption. Neutron radiography was used to monitor capillary water absorption, and to analyse changes in physical properties caused by heat treatment of specimens for the purposes of artificially ageing and different treatment applications with stone consolidants. Moreover, ultrasonic pulse velocity and gravimetrically determined water absorption were analysed to cross-validate neutron radiography. The results reveal that reactive systems like tetraethyl-orthosilicates need an unknown period for polymerisation, which makes nano-silica consolidants more favourable for construction follow-up work. While polymerisation is incomplete, hydrophobic behaviour, water trapping and pore clogging are evident. Within the tetraethyl-orthosilicate treatment, poultice and brushing are strongly influenced by the applicant, which results in wide ranging amounts of water absorbed and anomalous water distributions and kinetics. The carbonate lithotype displays polymerisation initiated in the core of the specimen, while the lateral surfaces are still mostly hydrophobic. Reaction time differences can be attributed to the different amounts of consolidants applied, which is a result of the chosen application settings. Artificial ageing of stone specimens is a prerequisite when mechanical strength gain is studied, as demonstrated by sound speed propagation
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