From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code

We regularize compact and non-compact Abelian Chern–Simons–Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group R, each local Hilbert space is analogous to the one of a charged “particle” moving in the link-pair group space R2 in a constant “magnetic” background field. In the compact case, the link-pair group space is a torus U(1)2 threaded by k units of quantized “magnetic” flux, with k being the level of the Chern–Simons theory. The holonomies of the torus U(1)2 give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry from U(1) to Z(k). The local Hilbert space of a link-pair then decomposes into representations of a magnetic translation group. In the pure Chern–Simons limit of a large “photon” mass, this results in a Z(k)-symmetric variant of Kitaev’s toric code, self-adjointly extended by the two non-dynamical background lattice gauge fields. Electric charges on the original lattice and on the dual lattice obey mutually anyonic statistics with the statistics angle . Non-Abelian U(k) Berry gauge fields that arise from the self-adjoint extension parameters may be interesting in the context of quantum information processing.

Bringing results to fruition through publication: An analysis of a peer-reviewed, open access and context-focused journal's editorial practice

When it comes to helping to shape sustainable development, research is most useful when it bridges the science–implementation/management gap and when it brings development specialists and researchers into a dialogue (Hurni et al. 2004); can a peer-reviewed journal contribute to this aim? In the classical system for validation and dissemination of scientific knowledge, journals focus on knowledge exchange within the academic community and do not specifically address a ‘life-world audience’. Within a North-South context, another knowledge divide is added: the peer review process excludes a large proportion of scientists from the South from participating in the production of scientific knowledge (Karlsson et al. 2007). Mountain Research and Development (MRD) is a journal whose mission is based on an editorial strategy to build the bridge between research and development and ensure that authors from the global South have access to knowledge production, ultimately with a view to supporting sustainable development in mountains. In doing so, MRD faces a number of challenges that we would like to discuss with the td-net community, after having presented our experience and strategy as editors of this journal. MRD was launched in 1981 by mountain researchers who wanted mountains to be included in the 1992 Rio process. In the late 1990s, MRD realized that the journal needed to go beyond addressing only the scientific community. It therefore launched a new section addressing a broader audience in 2000, with the aim of disseminating insights into, and recommendations for, the implementation of sustainable development in mountains. In 2006, we conducted a survey among MRD’s authors, reviewers, and readers (Wymann et al. 2007): respondents confirmed that MRD had succeeded in bridging the gap between research and development. But we realized that MRD could become an even more efficient tool for sustainability if development knowledge were validated: in 2009, we began submitting ‘development’ papers (‘transformation knowledge’) to external peer review of a kind different from the scientific-only peer review (for ‘systems knowledge’). At the same time, the journal became open access in order to increase the permeability between science and society, and ensure greater access for readers and authors in the South. We are currently rethinking our review process for development papers, with a view to creating more space for communication between science and society, and enhancing the co-production of knowledge (Roux 2008). Hopefully, these efforts will also contribute to the urgent debate on the ‘publication culture’ needed in transdisciplinary research (Kueffer et al. 2007).

Mapping Individual Variation in Male Mating Preference Space: Multiple Choice in a Color Polymorphic Cichlid Fish

Sexual selection theory largely rests on the assumption that populations contain individual variation in mating preferences and that individuals are consistent in their preferences. However, there are few empirical studies of within-population variation and even fewer have examined individual male mating preferences. Here, we studied a color polymorphic population of the Lake Victoria cichlid fish Neochromis omnicaeruleus, a species in which color morphs are associated with different sex-determining factors. Wild-caught males were tested in three-way choice trials with multiple combinations of different females belonging to the three color morphs. Compositional log-ratio techniques were applied to analyze individual male mating preferences. Large individual variation in consistency, strength, and direction of male mating preferences for female color morphs was found and hierarchical clustering of the compositional data revealed the presence of four distinct preference groups corresponding to the three color morphs in addition to a no-preference class. Consistency of individual male mating preferences was higher in males with strongest preferences. We discuss the implications of these findings for our understanding of the mechanisms underlying polymorphism in mating preferences.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

A Nonstationary Space-Time Gaussian Process Model for Partially Converged Simulations

In the context of expensive numerical experiments, a promising solution for alleviating the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at the price of precision in the response. This work addresses the issue of fitting a Gaussian process model to partially converged simulation data for further use in prediction. The main challenge consists of the adequate approximation of the error due to partial convergence, which is correlated in both design variables and time directions. Here, we propose fitting a Gaussian process in the joint space of design parameters and computational time. The model is constructed by building a nonstationary covariance kernel that reflects accurately the actual structure of the error. Practical solutions are proposed for solving parameter estimation issues associated with the proposed model. The method is applied to a computational fluid dynamics test case and shows significant improvement in prediction compared to a classical kriging model.

Chern-Simons theory on Seifert 3-manifolds

We study Chern-Simons theory on 3-manifolds M that are circle-bundles over 2-dimensional orbifolds Σ by the method of Abelianisation. This method, which completely sidesteps the issue of having to integrate over the moduli space of non-Abelian flat connections, reduces the complete partition function of the non-Abelian theory on M to a 2-dimensional Abelian theory on the orbifold Σ, which is easily evaluated.

Space, diffusion and mobility

Given its origins in traditional dialectology, and given advances in our understanding of the social embedding of language variation, it is paradoxical that space should be one of the categories that has received least attention of all in variationist sociolinguistics. Until recently, space has largely been treated as an empty stage on which sociolinguistic processes are enacted. It has been unexamined, untheorized, and its role in shaping and being shaped by variation and change untested. One function of this chapter, therefore, is to assert that space makes a difference, and to begin, in a very hesitant way, to map out what a geographically informed variation analysis might need to address. It also examines variationist interactions with the related concept of mobility. It might be reasonable to think that human geographers would provide some clues on how to proceed. As we will see, they have engaged in a great deal of soul searching about the goals of their discipline, its very existence as a separate field of enquiry, and the directions it should take. Indeed there are remarkable parallels between the recent history of human geographic thought, and interest in language variation across space. Although space has been undertheorized in variation studies, a number of researchers, from the traditional dialectologists through to those interested in the dialectology of mobility and contact, have, of course, been actively engaged in research on geographical variation and language use. Their work will be contextualized here to highlight both the parallels with theory-building in human geography, but also some of the criticisms of earlier approaches which have fed through to human geography, but remain largely unquestioned in variationist practice. The chapter therefore presents a brief theoretical background to space and mobility, before exemplifying these concepts in variationist research through an examination of, for example, the spatial diffusion of linguistic innovations, the spatial configuration of linguistic boundaries and initial steps to examine the consequences of mobility for variationist research.

Exploring double field theory

We consider a flux formulation of Double Field Theory in which fluxes are dynamical and field-dependent. Gauge consistency imposes a set of quadratic constraints on the dynamical fluxes, which can be solved by truly double configurations. The constraints are related to generalized Bianchi Identities for (non-)geometric fluxes in the double space, sourced by (exotic) branes. Following previous constructions, we then obtain generalized connections, torsion and curvatures compatible with the consistency conditions. The strong constraint-violating terms needed to make contact with gauged supergravities containing duality orbits of non-geometric fluxes, systematically arise in this formulation.

Light-cone Wilson loop in classical lattice gauge theory

The transverse broadening of an energetic jet passing through a non-Abelian plasma is believed to be described by the thermal expectation value of a light-cone Wilson loop. In this exploratory study, we measure the light-cone Wilson loop with classical lattice gauge theory simulations. We observe, as suggested by previous studies, that there are strong interactions already at short transverse distances, which may lead to more efficient jet quenching than in leading-order perturbation theory. We also verify that the asymptotics of the Wilson loop do not change qualitatively when crossing the light cone, which supports arguments in the literature that infrared contributions to jet quenching can be studied with dimensionally reduced simulations in the space-like domain. Finally we speculate on possibilities for full four-dimensional lattice studies of the same observable, perhaps by employing shifted boundary conditions in order to simulate ensembles boosted by an imaginary velocity.