The Impact and Embedding of an Established Resource: British History Online as a Case Study: final report

The final report of this JISC-funded project, April 2011

Tensor product categorifications and the super Kazhdan-Lusztig conjecture

We give a new proof of the "super Kazhdan-Lusztig conjecture" for the Lie super algebra $\mathfrak{gl}_{n|m}(\mathbb{C})$ as formulated originally by the first author. We also prove for the first time that any integral block of category O for $\mathfrak{gl}_{n|m}(\mathbb{C})$ (and also all of its parabolic analogs) possesses a graded version which is Koszul. Our approach depends crucially on an application of the uniqueness of tensor product categorifications established recently by the second two authors.Comment: 58 pages; v2: relatively minor changes, a few adjustments to wording and references; v3: final version, more minor changes, to appear in IMR

On the definition of quantum Heisenberg category

We introduce a diagrammatic monoidal category $\mathcal{H}eis_k(z,t)$ which we call the quantum Heisenberg category, here, $k \in \mathbb{Z}$ is "central charge" and $z$ and $t$ are invertible parameters. Special cases were known before: for central charge $k=-1$ and parameters $z = q-q^{-1}$ and $t = -z^{-1}$ our quantum Heisenberg category may be obtained from the deformed version of Khovanov's Heisenberg category introduced by Licata and the second author by inverting its polynomial generator, while $\mathcal{H}eis_0(z,t)$ is the affinization of the HOMFLY-PT skein category. We also prove a basis theorem for the morphism spaces in $\mathcal{H}eis_k(z,t)$.Comment: v1: preliminary version; v2: minor corrections, published versio

Diet and identity:being a good parent in the face of contradictions presented by the ketogenic diet

The ketogenic diet is a high‐fat diet used to treat drug‐resistant childhood epilepsy. Given that negative meanings tend to be attached to fatty foods and children's food consumption is seen to be the responsibility of parents, the ketogenic diet may be problematic for parenting identity. This article draws upon in‐depth semi‐structured interviews with 12 parents from 10 families that have a child whose epilepsy is being treated with the ketogenic diet. The main focus of the article is the meanings these parents attached to foods and how they were drawn upon or altered to overcome some of the contradictions presented by the diet. It will be argued that the diet was medicalised and parents came to view food as medicine. When viewing food in this way, negative associations with fat were reversed. Furthermore, parents also used food as a symbol of inclusion and prioritised portion size or the child's enjoyment of food in order to use food as a symbol of love. In turn this enabled parents to feel they were being good parents. Overall, it seems that diet can be medicalised and the identity of the good parent maintained if dietary treatment is successful

Robust Singular Smoothers For Tracking Using Low-Fidelity Data

Tracking underwater autonomous platforms is often difficult because of noisy, biased, and discretized input data. Classic filters and smoothers based on standard assumptions of Gaussian white noise break down when presented with any of these challenges. Robust models (such as the Huber loss) and constraints (e.g. maximum velocity) are used to attenuate these issues. Here, we consider robust smoothing with singular covariance, which covers bias and correlated noise, as well as many specific model types, such as those used in navigation. In particular, we show how to combine singular covariance models with robust losses and state-space constraints in a unified framework that can handle very low-fidelity data. A noisy, biased, and discretized navigation dataset from a submerged, low-cost inertial measurement unit (IMU) package, with ultra short baseline (USBL) data for ground truth, provides an opportunity to stress-test the proposed framework with promising results. We show how robust modeling elements improve our ability to analyze the data, and present batch processing results for 10 minutes of data with three different frequencies of available USBL position fixes (gaps of 30 seconds, 1 minute, and 2 minutes). The results suggest that the framework can be extended to real-time tracking using robust windowed estimation.Comment: 9 pages, 9 figures, to be included in Robotics: Science and Systems 201

Computations in cubic function fields of characteristic three

This paper contains an account of arbitrary cubic function fields of characteristic three.  We define a standard form for an arbitrary cubic curve and consider its function field.  By considering an integral basis for the maximal order of these function fields, we are able to calculate the field discriminant and the genus.  We also give explicit algorithms for ideal arithmetic which for certain cubic function fields give rise to composition and reduction algorithms for computing in the associated ideal class group