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We collect novel data in the public service domain to evaluate the capability of the state-of-the-art automatic speech recognition (ASR) models in capturing regional differences in accents in the United Kingdom (UK), specifically focusing on two accents from Scotland with distinct dialects. This study addresses real-world problems where biased ASR models can lead to miscommunication in public services, disadvantaging individuals with regional accents particularly those in vulnerable populations. We first examine the out-of-the-box performance of the Whisper large-v3 model on a baseline dataset and our data. We then explore the impact of fine-tuning Whisper on the performance in the two UK regions and investigate the effectiveness of existing model evaluation techniques for our real-world application through manual inspection of model errors. We observe that the Whisper model has a higher word error rate (WER) on our test datasets compared to the baseline data and fine-tuning on a given data improves performance on the test dataset with the same domain and accent. The fine-tuned models also appear to show improved performance when applied to the test data outside of the region it was trained on suggesting that fine-tuned models may be transferable within parts of the UK. Our manual analysis of model outputs reveals the benefits and drawbacks of using WER as an evaluation metric and fine-tuning to adapt to regional dialects.

A Skyrme type energy functional for maps $\varphi$ from an oriented Riemannian 3-manifold $M$ to a contact 3-manifold $N$ is defined, generalizing the BPS Skyrme energy of Ferreira and Zakrzewski. This energy has a topological lower bound, attained by solutions of a first order self-duality equation which we call (strong) Beltrami maps. In the case where $N$ is the 3-sphere, we show that the original Ferreira-Zakrzewski model (which has $N=S^3$ with the standard contact structure) can have no BPS solutions on $M=S^3$ with $|\mathrm{deg}(\varphi)|>1$ if the coupling constant has the lowest admissible value., Comment: 14 pages

The Skyrme model is extended with the Maxwell action and a source term for the gauge field. We consider the specialized case of vanishing isospin states, such that only an electric potential is turned on and study the backreaction onto the Skyrme fields. In particular, we study Skyrmions with baryon numbers B=4,8,12,16 and 40. We find, in agreement with physical expectations, that the Coulomb backreaction is most pronounced for large Skyrmions and find furthermore that the dynamics of the theory is more sensitive to the backreaction than the ground states (global minimizers of the energy). Calibrating the model to Carbon-12, we find excellent agreement of the masses of the studied Skyrmions - within 1.86% of experimental data. The Coulomb energies are slightly larger than phenomenological fits suggest, but only by about 3-22%, whereas the radii are within 15% errors, with the largest errors on the smallest baryon number (B=4) and the smallest errors on the large baryon numbers., Comment: LaTeX: 40+20 pages, 49 figures; V2: comment added and typos corrected

A method is developed to compute minimal energy vortex lattices in a general Ginzburg-Landau model of a superconductor subjected to an applied magnetic field. The model may have any number of components and may be spatially anisotropic. Both the period vectors of the vortex lattice, and the orientation of its vortex lines, are determined dynamically; no assumptions are made about them. Methods to compute the first and second critical magnetic fields, $H_{c_1}$ and $H_{c_2}$, in this class of models are also developed. These methods are applied to a simple anisotropic single-component model, and to an anisotropic two-component model of strong current theoretical interest (a so-called $s+id$ model). It is found, in both cases, that at low applied field the vortex lines can tilt very significantly away from the direction of the applied field (by as much as $40^o$ for the single-component and $30^o$ for the $s+id$ model). The optimal lattice in the $s+id$ model is qualitatively very different from the conventional triangular Abrikosov lattice, exhibiting a phase transition from a system of Skyrmion chains when the external field is orthogonal to the basal plane to a deformed Abrikosov lattice when applied in the basal plane., Comment: 35 pages, 15 figures

We show that there exists a family of mutually singular doubling measures on Laakso space with respect to which real-valued Lipschitz functions are almost everywhere differentiable. This implies that there exists a measure zero universal differentiability set in Laakso space. Additionally, we show that each of the measures constructed supports a Poincar\'e inequality., Comment: arXiv admin note: text overlap with arXiv:2208.03361

We develop realizability models of intensional type theory, based on groupoids, wherein realizers themselves carry non-trivial (non-discrete) homotopical structure. In the spirit of realizability, this is intended to formalize a homotopical BHK interpretation, whereby evidence for an identification is a path. Specifically, we study partitioned groupoidal assemblies. Categories of such are parameterised by "realizer categories" (instead of the usual partial combinatory algebras) that come equipped with an interval qua internal cogroupoid. The interval furnishes a notion of homotopy as well as a fundamental groupoid construction. Objects in a base groupoid are realized by points in the fundamental groupoid of some object from the realizer category; isomorphisms in the base groupoid are realized by paths in said fundamental groupoid. The main result is that, under mild conditions on the realizer category, the ensuing category of partitioned groupoidal assemblies models intensional (1-truncated) type theory without function extensionality. Moreover, when the underlying realizer category is "untyped", there exists an impredicative universe of 1-types (the modest fibrations). This is a groupoidal analogue of the traditional situation., Comment: 43 pages, accepted for publication in Mathematical Structures in Computer Science special issue Advances in Homotopy Type Theory

We investigate the ground state crystalline structure of nuclear matter in the $\omega$-meson variant of the Skyrme model. After minimizing energy with respect to variations of both the Skyrme field and the period lattice, we find four distinct periodic solutions which are similar to those found in the standard Skyrme model. We use these crystals to calculate coefficients in the Bethe--Weizs\"acker semi-empirical mass formula and the compression modulus of infinite nuclear matter, and find a significant improvement as compared with other variants of the Skyrme model., Comment: 16 pages, 3 figures, v2: minor revision, journal accepted version

In the setting of horizontal curves in the Heisenberg group, we prove a $C^{m,\omega}$ finiteness principle, a $C^{m,\omega}$ Lusin approximation result, a $C^{\infty}$ Whitney extension result, and a $C^{\infty}$ Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class $C^{m}$, $C^{m,\omega}$, and $C^{\infty}$ in the Heisenberg group., Comment: 27 pages

It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) $B$. Rigid body quantization, in which one quantizes motion on the spin-isospin orbit of just one minimum, is thus an ill-justified approximation. Instead, one should identify a (finite-dimensional) moduli space of configurations containing all local minima (for a given $B$) as well as fields interpolating smoothly between them. This paper proposes a systematic computational scheme for generating such a moduli space: one constructs an energy minimizing path between each pair of local minima, then defines the moduli space to be the union of spin-isospin orbits of points on the union of these curves, a principal bundle over a graph. The energy minimizing curves may be constructed in practice using the nudged elastic band method, a standard tool in mathematical chemistry for analyzing reaction paths and computing activation energies. To illustrate, we apply this scheme to the lightly bound Skyrme model in the point particle approximation, constructing the graphs for $5\leq B\leq 10$. We go on to complete the quantization for $B=7$, in which the graph has two vertices and a single edge. The low-lying quantum states with isospin $1/2$ do not strongly localize around either of the local energy minima (the vertices). Their energies rise monotonically with spin, conflicting with experimental data for Lithium-7.

The crystalline structure of nuclear matter is investigated in the standard Skyrme model with massive pions. A semi-analytic method is developed to determine local minima of the static energy functional with respect to variations of both the field and the period lattice of the crystal. Four distinct Skyrme crystals are found. Two of these were already known -- the cubic lattice of half-skyrmions and the $\alpha$-particle crystal -- but two are new. These new solutions have lower energy per baryon number and less symmetry, being periodic with respect to trigonal but not cubic period lattices. Minimal energy crystals are also constructed under the constraint of constant baryon density, and its shown that the two new non-cubic crystals tend to chain and multi-wall solutions at low densities., Comment: 24 pages, 4 figures

It is proved that the normalized $L^2$ metric on the moduli space of $n$-vortices on a two-sphere, endowed with any Riemannian metric, converges uniformly in the Bradlow limit to the Fubini-Study metric. This establishes, in a rigorous setting, a longstanding informal conjecture of Baptista and Manton., Comment: 19 pages, 0 figures. Minor corrections, accepted version

We investigate the connection between maximal directional derivatives and differentiability for Lipschitz functions defined on Laakso space. We show that maximality of a directional derivative for a Lipschitz function implies differentiability only for a $\sigma$-porous set of points. On the other hand, the distance to a fixed point is differentiable everywhere except for a $\sigma$-porous set of points. This behavior is completely different to the previously studied settings of Euclidean spaces and Carnot groups., Comment: 33 pages