Unsigned state models for the Jones polynomial

It is well a known and fundamental result that the Jones polynomial can be expressed as Potts and vertex partition functions of signed plane graphs. Here we consider constructions of the Jones polynomial as state models of unsigned graphs and show that the Jones polynomial of any link can be expressed as a vertex model of an unsigned embedded graph. In the process of deriving this result, we show that for every diagram of a link in the 3-sphere there exists a diagram of an alternating link in a thickened surface (and an alternating virtual link) with the same Kauffman bracket. We also recover two recent results in the literature relating the Jones and Bollobas-Riordan polynomials and show they arise from two different interpretations of the same embedded graph.Comment: Minor corrections. To appear in Annals of Combinatoric

Using comsumer informedness as an information strategy

__Abstract__ Consumer informedness describes the degree to which consumers are aware of the specific attributes of products or services offered in the marketplace. Understanding how this level of informedness can amplify consumer behaviour provides firms with the opportunity to develop information-based strategies that can encourage their target segment make purchases

A unified Witten-Reshetikhin-Turaev invariant for integral homology spheres

We construct an invariant J_M of integral homology spheres M with values in a completion \hat{Z[q]} of the polynomial ring Z[q] such that the evaluation at each root of unity \zeta gives the the SU(2) Witten-Reshetikhin-Turaev invariant \tau_\zeta(M) of M at \zeta. Thus J_M unifies all the SU(2) Witten-Reshetikhin-Turaev invariants of M. As a consequence, \tau_\zeta(M) is an algebraic integer. Moreover, it follows that \tau_\zeta(M) as a function on \zeta behaves like an ``analytic function'' defined on the set of roots of unity. That is, the \tau_\zeta(M) for all roots of unity are determined by a "Taylor expansion" at any root of unity, and also by the values at infinitely many roots of unity of prime power orders. In particular, \tau_\zeta(M) for all roots of unity are determined by the Ohtsuki series, which can be regarded as the Taylor expansion at q=1.Comment: 66 pages, 8 figure

Baxterization, dynamical systems, and the symmetries of integrability

We resolve the `baxterization' problem with the help of the automorphism group of the Yang-Baxter (resp. star-triangle, tetrahedron, \dots) equations. This infinite group of symmetries is realized as a non-linear (birational) Coxeter group acting on matrices, and exists as such, {\em beyond the narrow context of strict integrability}. It yields among other things an unexpected elliptic parametrization of the non-integrable sixteen-vertex model. It provides us with a class of discrete dynamical systems, and we address some related problems, such as characterizing the complexity of iterations.Comment: 25 pages, Latex file (epsf style). WARNING: Postscript figures are BIG (600kB compressed, 4.3MB uncompressed). If necessary request hardcopy to [email protected] and give your postal mail addres

An Interdisciplinary Perspective on Education Service Systems

Part 3: Finance and Service ScienceInternational audienceThe increased complexity in education systems has given rise to a number of intersecting trends and calling for a discipline to integrate across academic silos. As the concept of service innovation advances more rapidly into education services; industry, government, and academy are awakened to the concept of embedding services innovation. This theoretical paper offers an integrated framework for education systems (IFES) covering two intersecting dimensions where service innovation and service science can take place. As an effort to contribute in the area of service innovation and service sciences, an interdisciplinary approach is applied, interconnecting an array of competences across the different stakeholders. It is hypothesized that to increase productivity in education industries, interconnecting knowledge and resources from diverse areas and across different stakeholders through the co-lineation of four dimensions: (1) information, communications and technology; (2) skills and tools; (3) people and attitudes; (4) systems, processes and management; are essential to creating service innovation. This paper contributes a perspective of interconnectivity balanced with harmony that are crucial for effective productivity and service innovation by adopting a service science approach

String theory and the Kauffman polynomial

We propose a new, precise integrality conjecture for the colored Kauffman polynomial of knots and links inspired by large N dualities and the structure of topological string theory on orientifolds. According to this conjecture, the natural knot invariant in an unoriented theory involves both the colored Kauffman polynomial and the colored HOMFLY polynomial for composite representations, i.e. it involves the full HOMFLY skein of the annulus. The conjecture sheds new light on the relationship between the Kauffman and the HOMFLY polynomials, and it implies for example Rudolph's theorem. We provide various non-trivial tests of the conjecture and we sketch the string theory arguments that lead to it.Comment: 36 pages, many figures; references and examples added, typos corrected, final version to appear in CM

A VALUE PLATFORM ANALYSIS PERSPECTIVE ON CUSTOMER ACCESS INFORMATION TECHNOLOGY

Customer access information technologies (CAITs) provide a link between a firm and its customers. Firms invest in CAITs to reduce costs, increase revenues and market share, lock in existing customers and capture new ones. These benefits, however, are notoriously difficult to measure. This paper proposes an evaluative method for CAlT deployment called value platform analysis, that is based on a conceptual model drawn from the theory of retail outlet deployment in marketing science. The model focuses on the impact of CAIT features and environmental features on transactions generated by the CAIT. Specific econometric models are developed for deployment. Hypotheses regarding the likely impact of automated teller machine (ATM) location design choices and environmental features on ATM transactions are evaluated. The results indicate that there are a number of key features influencing ATM performance. Two distinct ATM deployment scenarios emerge: one for servicing a bank's own customers, and another for providing transaction services for customers for a fee.Information Systems Working Papers Serie

Randomness Increases Order in Biological Evolution

n this text, we revisit part of the analysis of anti-entropy in Bailly and Longo (2009} and develop further theoretical reflections. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in ontogenesis and in evolution. This approach, in particular, focuses on the role of global entropy production and provides a tool for a mathematical understanding of some fundamental observations by Gould on the increasing phenotypic complexity along evolution. Lastly, we analyze the situation in terms of theoretical symmetries, in order to further specify the biological meaning of anti-entropy as well as its strong link with randomness