arXiv research

The paper generalizes Cartan Geometry using Polacek and Siegel's approach.

Develops a new Bayesian inference method for discrete data.

Study generalised Einstein metrics on Lie groups, classifying various types.

We survey briefly the definition of the Rozansky-Witten invariants, and review their relevance to the study of compact hyperkahler manifolds. We consider how various generalisations of the invariants might prove useful for the study of non-compact hyperkahler manifolds, of quaternionic-Kahler manifolds, and of relation…

Weighted Lie algebroids were recently introduced as Lie algebroids equipped with an additional compatible non-negative grading, and represent a wide generalisation of the notion of a VB -algebroid. There is a close relation between two term representations up to homotopy of Lie algebroids and VB - algebroids. In this p…

We prove that, for M theory or type II, generic Minkowski flux backgrounds preserving $\mathcal{N}$ supersymmetries in dimensions $D\geq4$ correspond precisely to integrable generalised $G_{\mathcal{N}}$ structures, where $G_{\mathcal{N}}$ is the generalised structure group defined by the Killing spinors. In other word…

We define additional gradings on two generalisations of Khovanov homology (one due to the first author, the other due to the second), and use them to define invariants of various kinds of embeddings. These include invariants of links in thickened surfaces and of surfaces embedded in thickened $3$-manifolds. In particul…

Defines a new process for financial modeling.

The paper improves generalization bounds using interpolation between various divergences.

We come up with infinite-dimensional prequantum line bundles and moment map interpretations of three different sets of equations - the generalised Monge-Amp`ere equation, the almost Hitchin system, and the Calabi-Yang-Mills equations. These are all perturbations of already existing equations. Our construction for the g…

A generalised notion of connection on a fibre bundle E over a manifold M is presented. These connections are characterised by a smooth distribution on E which projects onto a (not necessarily integrable) distribution on M and which, in addition, is `parametrised' in some specific way by a vector bundle map from a presc…

The paper connects DNN generalization to node SNR using information theory.

Decouples homotopy quotients of generalised configuration spaces on surfaces.

The study shows symmetry improves machine learning generalization.

Study on approximability and generalization in machine learning.

This paper explains double descent in linear neural networks, identifying new factors.

We generalise the expansion formulae of Musiker, Schiffler and Williams, obtained for cluster algebras from orientable surfaces, to a larger class of coefficients which we call principal laminations. In doing so, for any quasi-cluster algebra from a non-orientable surface, we are able to obtain expansion formulae for e…

Diffusion models adapt to data geometry through log-domain smoothing.

Introduces a new phase space for 2D supersymmetric sigma models.

This review compares GAMs and neural networks on real-world tabular data.

We define $(p,q)$ hermitian geometry as the target space geometry of the two dimensional $(p,q)$ supersymmetric sigma model. This includes generalised Kähler geometry for $(2,2)$, generalised hyperkähler geometry for $(4,2)$, strong Kähler with torsion geometry for $(2,1)$ and strong hyperkähler with torsion geometry f…

Novel GLMMNet model tackles high-cardinality categorical features in actuarial applications.

This work uncovers algorithm-dependent regularisation in diffusion models.

In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel representation for the solution of the optimal stopping problem. In particular, we …

Paper proves non-zero generalization boost for equivariant models.

A census is presented of all closed non-orientable 3-manifold triangulations formed from at most seven tetrahedra satisfying the additional constraints of minimality and P^2-irreducibility. The eight different 3-manifolds represented by these 41 different triangulations are identified and described in detail, with part…

This paper presents a cross-country comparison of significant predictors of small business failure between Italy and the UK. Financial measures of profitability, leverage, coverage, liquidity, scale and non-financial information are explored, some commonalities and differences are highlighted. Several models are consid…

Motivated by the definition of the smooth manifold structure on a suitable mapping space, we consider the general problem of how to transfer local properties from a smooth space to an associated mapping space. This leads to the notion of smoothly local properties. In realising the definition of a local property at a pa…

Strong Kähler with Torsion is the target space geometry of $(2,1)$ and $(2,0)$ supersymmetric nonlinear sigma models. We discuss how it can be represented in terms of Generalised Complex Geometry in analogy to the Gualtieri map from the geometry of $(2,2)$ supersymmetric nonlinear sigma models to Generalised Kähler Geo…

This paper uses results on the classification of minimal triangulations of 3-manifolds to produce additional results, using covering spaces. Using previous work on minimal triangulations of lens spaces, it is shown that the lens space $L(4k, 2k-1)$ and the generalised quaternionic space $S^3/Q_{4k}$ have complexity $k,…

New link groups are derived from torus necklaces, connecting braid groups to reflection groups.

In this paper we introduce distinct approaches to loop braid groups, a generalisation of braid groups, and unify all the definitions that have appeared so far in literature, with a complete proof of the equivalence of these definitions. These groups have in fact been an object of interest in different domains of mathem…

Study on generalisation in random feature learning and hidden manifold models.

Geometry-aware noise improves model generalization on complex manifolds.

Generalizes beam models to include curvature and torsion.

Cross validation residuals are well known for the ordinary least squares model. Here leave-M-out cross validation is extended to generalised least squares. The relationship between cross validation residuals and Cook's distance is demonstrated, in terms of an approximation to the difference in the generalised residual …

mcanalysis quantifies menstrual cycle effects in health data.

Learning with auxiliary tasks can improve the ability of a primary task to generalise. However, this comes at the cost of manually labelling auxiliary data. We propose a new method which automatically learns appropriate labels for an auxiliary task, such that any supervised learning task can be improved without requiri…

Constructs a unique Levi-Civita connection for generalised metrics.

In the geometry of generic 2-plane fields on 5-manifolds, the local equivalence problem was solved by Cartan who also constructed the fundamental curvature invariant. For generic 2-plane fields or $(2,3,5)$-distributions determined by a single function of the form $F(q)$, the vanishing condition for the curvature invar…

Global existence and convergence of heat flow for p-harmonic maps.

New method improves policies by combining Markov and non-Markov strategies.

The paper applies generalised geometry to semi-Riemannian immersions and hypersurfaces.

New bounds link flat minima to good generalisation in overparameterized models.

Paper uses SLT to improve model selection for SHM.

New approach to T-duality using Courant algebroids.

Introduces Conditional Action Trees to simplify RL action spaces.

We define and examine the notion of a Killing section of a Riemannian Lie algebroid as a natural generalisation of a Killing vector field. We show that the various expression for a vector field to be Killing naturally generalise to the setting of Lie algebroids. As an application we examine the internal symmetries of a…