A nilpotent group without local functional equations for pro-isomorphic subgroups

The pro-isomorphic zeta function of a torsion-free finitely generated nilpotent group G enumerates finite index subgroups H such that H and G have isomorphic profinite completions. It admits an Euler product decomposition, indexed by the rational primes. We manufacture the first example of a torsion-free finitely generated nilpotent group G such that the local Euler factors of its pro-isomorphic zeta function do not satisfy functional equations. The group G has nilpotency class 4 and Hirsch length 25. It is obtained, via the Malcev correspondence, from a Z-Lie lattice L with a suitable algebraic automorphism group Aut(L).Comment: 16 page

Constructing a polynomial whose nodal set is the three-twist knot 525_2

We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot $5_2$. The construction generalizes a similar approach for lemniscate knots: a braid representation is engineered from finite Fourier series and then considered as the nodal set of a certain complex polynomial which depends on an additional parameter. For sufficiently small values of this parameter, the nodal lines form the three-twist knot. Further mathematical properties of this map are explored, including the relationship of the phase critical points with the Morse-Novikov number, which is nonzero as this knot is not fibred. We also find analogous functions for other knots with six crossings. The particular function we find, and the general procedure, should be useful for designing knotted fields of particular knot types in various physical systems.Comment: 19 pages, 6 figure

The Evolution of Shopping Center Research: A Review and Analysis

Retail research has evolved over the past sixty years. Christaller\u27s early work on central place theory, with its simplistic combination of range and threshold has been advanced to include complex consumer shopping patterns and retailer behavior in agglomerated retail centers. Hotelling\u27s seminal research on competition in a spatial duopoly has been realized in the form of comparison shopping in regional shopping centers. The research that has followed Christaller and Hoteling has been as wide as it has been deep, including literature in geography, economics, finance, marketing, and real estate. In combination, the many extensions of central place theory and retail agglomeration economics have clearly enhanced the understanding of both retailer and consumer behavior. In addition to these two broad areas of shopping center research, two more narrowly focused areas of research have emerged. The most recent focus in the literature has been on the positive effects large anchor tenants have on smaller non-anchor tenant sales. These positive effects are referred to as retail demand externalities. Exploring the theoretical basis for the valuation of shopping centers has been another area of interest to researchers. The primary focus of this literature is based in the valuation of current and expected lease contracts

Cornering sgluons with four-top-quark events

The existence of colour-octet scalar states, often dubbed sgluons, is predicted in many extensions of the Standard Model of particle physics, such as supersymmetric realisations featuring Dirac gauginos. Such states have a large pair-production rate at hadron colliders and mainly decay into pairs of jets and top quarks. Consequently, they represent a primary target for experimental searches for new resonances in the multijet and multitop channels at the Large Hadron Collider. Adopting a phenomenologically-motivated simplified model, we reinterpret the results of a recent experimental search for the four-top-quark Standard Model signal, from which we constrain the sgluon mass to be larger than about 1.06 TeV. We additionally consider how modifications of the existing four-top-quark studies could enhance our ability to unravel the presence of scalar octets in data.Comment: 8 pages, 4 figures. References added, matches published versio

The Semantic Automated Discovery and Integration (SADI) Web service Design-Pattern, API and Reference Implementation

Background. 
The complexity and inter-related nature of biological data poses a difficult challenge for data and tool integration. There has been a proliferation of interoperability standards and projects over the past decade, none of which has been widely adopted by the bioinformatics community. Recent attempts have focused on the use of semantics to assist integration, and Semantic Web technologies are being welcomed by this community.

Description. 
SADI – Semantic Automated Discovery and Integration – is a lightweight set of fully standards-compliant Semantic Web service design patterns that simplify the publication of services of the type commonly found in bioinformatics and other scientific domains. Using Semantic Web technologies at every level of the Web services “stack”, SADI services consume and produce instances of OWL Classes following a small number of very straightforward best-practices. In addition, we provide codebases that support these best-practices, and plug-in tools to popular developer and client software that dramatically simplify deployment of services by providers, and the discovery and utilization of those services by their consumers.

Conclusions.
SADI Services are fully compliant with, and utilize only foundational Web standards; are simple to create and maintain for service providers; and can be discovered and utilized in a very intuitive way by biologist end-users. In addition, the SADI design patterns significantly improve the ability of software to automatically discover appropriate services based on user-needs, and automatically chain these into complex analytical workflows. We show that, when resources are exposed through SADI, data compliant with a given ontological model can be automatically gathered, or generated, from these distributed, non-coordinating resources - a behavior we have not observed in any other Semantic system. Finally, we show that, using SADI, data dynamically generated from Web services can be explored in a manner very similar to data housed in static triple-stores, thus facilitating the intersection of Web services and Semantic Web technologies