arXiv research

Equivalent bicategories constructed from action Lie groupoids.

The paper applies $S^1$-localization to symplectic cohomology.

New approach to $Z$-stability and critical metrics on Kähler manifolds.

The equivariant coarse index is well-understood and widely used for actions by discrete groups. We extend the definition of this index to general locally compact groups. We use a suitable notion of admissible modules over $C^*$-algebras of continuous functions to obtain a meaningful index. Inspired by work by Roe, we t…

Formula for fixed points on noncompact spaces.

In this paper we introduce exotic twisted $\mathbb T$-equivariant K-theory of loop space $LZ$ depending on the (typically non-flat) holonomy line bundle ${\mathcal L}^B$ on $LZ$ induced from a gerbe with connection $B$ on $Z$. We also define exotic twisted $\mathbb T$-equivariant Chern character that maps the exotic tw…

Develops a new theory of localization in algebraic geometry.

We define exotic twisted $S^1$-equivariant cohomology for the loop space $LZ$ of a smooth manifold $Z$ via the invariant differential forms on $LZ$ with coefficients in the (typically non-flat) holonomy line bundle of a gerbe, with differential an equivariantly flat superconnection. We introduce the twisted Bismut-Cher…

Equivariant cohomology simplifies symplectic manifold integrals with group actions.

Consider a proper, isometric action by a unimodular, locally compact group $G$ on a complete Riemannian manifold $M$. For equivariant elliptic operators that are invertible outside a cocompact subset of $M$, we show that a localised index in the $K$-theory of the maximal group $C^*$-algebra of $G$ is well-defined. The …

Researchers compute the index of a specific operator on contact manifolds.

We present homotopy theoretic and geometric interpretations of the Kane-Mele invariant for gapped fermionic quantum systems in three dimensions with time-reversal symmetry. We show that the invariant is related to a certain 4-equivalence which lends it an interpretation as an obstruction to a block decomposition of the…

Study of Seiberg-Witten invariants for 4-manifolds with group actions.

We generalise the Atiyah-Segal-Singer fixed point theorem to noncompact manifolds. Using $KK$-theory, we extend the equivariant index to the noncompact setting, and obtain a fixed point formula for it. The fixed point formula is the explicit cohomological expression from Atiyah-Segal-Singer's result. In the noncompact …

Researchers compute mod 2 Seiberg-Witten invariants for spin structures and families.

The problem of spoofing attacks is increasingly relevant as digital systems are becoming more ubiquitous. Thus the detection of such attacks and the localisation of attackers have been objects of recent study. After an attack has been detected, various algorithms have been proposed in order to localise the attacker. In…

Convolutional neural network localizes OD and fovea in UWFoV-SLO images.

Solves open problem on Lie groupoids equivalence.

We solve 6-DoF localisation and 3D reconstruction using deep state-space models.

We investigate whether ResNet architectures can outperform more traditional Convolutional Neural Networks on the task of fine-grained vehicle classification. We train and test ResNet-18, ResNet-34 and ResNet-50 on the Comprehensive Cars dataset without pre-training on other datasets. We then modify the networks to use …

CNNs help diagnose diabetic retinopathy by localizing lesions.

We propose a method that performs anomaly detection and localisation within heterogeneous data using a pairwise undirected mixed graphical model. The data are a mixture of categorical and quantitative variables, and the model is learned over a dataset that is supposed not to contain any anomaly. We then use the model o…

Analytic torsion defined for non-compact Lie groups and discrete subgroups.

New ensemble methods improve time series forecasting accuracy.

As sensor networks for health monitoring become more prevalent, so will the need to control their usage and consumption of energy. This paper presents a method which leverages the algorithm's performance and energy consumption. By utilising Reinforcement Learning (RL) techniques, we provide an adaptive framework, which…

Meta-models predict model hyperparameters for NDT experiments.

This paper explores estimating chaotic dynamics and parameters using local ensemble Kalman filters.

Study $SL(2,\mathbb{C})$ connections on Seifert-fibered spaces using gauge theory.

Paper establishes loop space T-duality formulae and refines earlier work.

While facial biometrics has been widely used for identification purpose, it has recently been researched as medical biometrics for a range of diseases. In this chapter, we investigate the facial landmark detection for atypical 3D facial modelling in facial palsy cases, while potentially such modelling can assist the me…

This article is a first step in establishing a link between the Donaldson polynomials and Seiberg-Witten invariants of a smooth 4-manifold.

We present a simple one-parameter model for spatially localised evolving agents competing for spatially localised resources. The model considers selling agents able to evolve their pricing strategy in competition for a fixed market. Despite its simplicity, the model displays extraordinarily rich behavior. In addition t…

Localizes smooth spaces to study their homotopy properties.

In this paper, we show the spooky effect at a distance that arises in optimal estimation of multiple targets with the optimal sub-pattern assignment (OSPA) metric. This effect refers to the fact that if we have several independent potential targets at distant locations, a change in the probability of existence of one o…

ALP outperforms other data descriptors in one-class classification.

We study a variational problem whose critical point determines the Reeb vector field for a Sasaki-Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein-Hilbert action, restricted to a space of Sasakian metrics on a link L …

Optimizes one-class classification methods for better performance.

A localisation of the category of n-manifolds is introduced by formally inverting the connected sum construction with a chosen n-manifold Y. On the level of automorphism groups, this leads to the stable diffeomorphism groups of n-manifolds. In dimensions 0 and 2, this is connected to the stable homotopy groups of spher…

Advocates against over-smoothing and over-squashing in GNNs, suggesting they are less critical than previously thought.

The paper extends localisation technique to multiple constraints in Euclidean spaces.

Clients are increasingly looking for fast and effective means to quickly and frequently survey and communicate the condition of their buildings so that essential repairs and maintenance work can be done in a proactive and timely manner before it becomes too dangerous and expensive. Traditional methods for this type of …

We record various properties of twisted Becker-Gottlieb transfer maps and study their multiplicative properties analogous to Becker-Gottlieb transfer. We show these twisted transfer maps factorise through Becker-Schultz-Mann-Miller-Miller transfer; some of these might be well known. We apply this to show that $BSO(2n+1…

Improved likelihood-free inference by localizing and refining low-dimensional approximations.

Mutual information is widely applied to learn latent representations of observations, whilst its implication in classification neural networks remain to be better explained. We show that optimising the parameters of classification neural networks with softmax cross-entropy is equivalent to maximising the mutual informa…

On a five dimensional simply connected Sasaki-Einstein manifold, one can construct Yang-Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however the contact instanton equations are not elliptic. It turns out that these equa…

A number of recent approaches to policy learning in 2D game domains have been successful going directly from raw input images to actions. However when employed in complex 3D environments, they typically suffer from challenges related to partial observability, combinatorial exploration spaces, path planning, and a scarc…

In four-dimensional gauge theory there exists a well-known correspondence between instantons and holomorphic curves, and a similar correspondence exists between certain octonionic instantons and triholomorphic curves. We prove that this latter correspondence stems from the dynamics of various dimensional reductions of …

Improved trading strategy using deep learning and changepoint detection for market changes.