Cleft Extensions and Quotients of Twisted Quantum Doubles

Given a pair of finite groups $F, G$ and a normalized 3-cocycle $\omega$ of $G$, where $F$ acts on $G$ as automorphisms, we consider quasi-Hopf algebras defined as a cleft extension $\Bbbk^G_\omega\#_c\,\Bbbk F$ where $c$ denotes some suitable cohomological data. When $F\rightarrow \overline{F}:=F/A$ is a quotient of $F$ by a central subgroup $A$ acting trivially on $G$, we give necessary and sufficient conditions for the existence of a surjection of quasi-Hopf algebras and cleft extensions of the type $\Bbbk^G_\omega\#_c\, \Bbbk F\rightarrow \Bbbk^G_\omega\#_{\overline{c}} \, \Bbbk \overline{F}$. Our construction is particularly natural when $F=G$ acts on $G$ by conjugation, and $\Bbbk^G_\omega\#_c \Bbbk G$ is a twisted quantum double $D^{\omega}(G)$. In this case, we give necessary and sufficient conditions that Rep($\Bbbk^G_\omega\#_{\overline{c}} \, \Bbbk \overline{G}$) is a modular tensor category.Comment: LaTex; 14 page

Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra

The purpose of this paper is to generalize Zhu's theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights. To recover SL_2(Z)-invariance of the characters it turns out to be necessary to consider twisted modules alongside ordinary ones. It also turns out to be necessary, in describing the space of conformal blocks in the supersymmetric case, to include certain `odd traces' on modules alongside traces and supertraces. We prove that the set of supertrace functions, thus supplemented, spans a finite dimensional SL_2(Z)-invariant space. We close the paper with several examples.Comment: 42 pages. Published versio

Retrospective evaluation of the association between admission blood glucose and l-lactate concentrations in ponies and horses with gastrointestinal disease (2008-2016): 545 cases

A recent study described increased l‐lactate concentrations in ponies with gastrointestinal disease compared to horses, but blood glucose (BG) concentrations were not considered. The study tested the hypothesis that BG and l‐lactate concentrations are correlated in horses and ponies with gastrointestinal disease and that BG concentrations, not equid type (pony vs horse), are an independent predictor of L‐lactate concentrations. It was further hypothesized that equid type was an independent predictor of BG concentrations

Averaging rheological quantities in descriptions of soft glassy materials

Many mean-field models have been introduced to describe the mechanical behavior of glassy materials. They often rely on averages performed over distributions of elements or states. We here underline that averaging is a more intricate procedure in mechanics than in more classical situations such as phase transitions in magnetic systems. This leads us to modify the predictions of the recently proposed SGR model for soft glassy materials, for which we suggest that the viscosity should diverge at the glass transition temperature $T_g$ with an exponential form $\eta \sim \exp(\frac{A}{T-T_g})$.Comment: 4 pages, Latex, 1 eps figur

Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I

We define the partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain a closed formula for the genus two continuous orbifold partition function in terms of an infinite dimensional determinant with entries arising from torus Szeg\"o kernels. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. Using the bosonized formalism, a new genus two Jacobi product identity is described for the Riemann theta series. We compute and discuss the modular properties of the generating function for all $n$-point functions in terms of a genus two Szeg\"o kernel determinant. We also show that the Virasoro vector one point function satisfies a genus two Ward identity.Comment: A number of typos have been corrected, 39 pages. To appear in Commun. Math. Phy

Intrinsic Energy Localization through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic FPU-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and highlight in that the asymmetric nature of the latter interaction potential may lead to a form of hybrid bulk-surface localized solutions

Multiple Reggeon Exchange from Summing QCD Feynman Diagrams

Multiple reggeon exchange supplies subleading logs that may be used to restore unitarity to the Low-Nussinov Pomeron, provided it can be proven that the sum of Feynman diagrams to all orders gives rise to such multiple regge exchanges. This question cannot be easily tackled in the usual way except for very low-order diagrams, on account of delicate cancellations present in the sum which necessitate individual Feynman diagrams to be computed to subleading orders. Moreover, it is not clear that sums of high-order Feynman diagrams with complicated criss-crossing of lines can lead to factorization implied by the multi-regge scenario. Both of these difficulties can be overcome by using the recently developed nonabelian cut diagrams. We are then able to show that the sum of $s$-channel-ladder diagrams to all orders does lead to such multiple reggeon exchanges.Comment: uu-encoded latex file with 11 postscript figures (20 pages

A manifesto for researching entrepreneurial ecosystems

Entrepreneurial ecosystems are the focus of government economic policies around the world for their potential to generate entrepreneur-led economic development. The paper identifies key research questions and challenges to building effective public policy: (i) the limitations of existing data sources, (ii) the need to balance findings from quantitative and qualitative studies, (iii) the danger that entrepreneurial ecosystems will be just a policy fad, (iv) the narrow focus of policy and research on high tech firms and scale-ups, and (v) the need to balance research approaches between simplified models and a complex systems approach. There is a need for a better understanding of the diversity of policy contexts (level of government, country context) and model of ecosystem governance. A more granulated understanding of ecosystem thinking is required, with greater consideration of the diversity of actors and the institutional context, with more attention given to the heterogeneous nature of places and complex interactions between actors and networks. Looking to the future, the potential of new data sources and methodologies is identified. Future research should give greater consideration to the institutional context to understand how policy can better support entrepreneurial activity and the extent to which specific policies can be replicated elsewhere