arXiv research

We study a moduli space of ASD connections over $S^3\times \mathbb{R}$. We consider not only finite energy ASD connections but also infinite energy ones. So the moduli space is infinite dimensional in general. We study the (local) mean dimension of this infinite dimensional moduli space. We show the upper bound on the …

The study finds a positive lower bound for the extra field in Yang-Mills equations on closed 4-manifolds.

Extends ASD connection existence to 4-manifolds with cylindrical ends.

The paper defines ASD connections and constructs families over a 5D Heisenberg group.

We study an infinite dimensional ASD moduli space over the cylinder. Our main result is the formula of its local mean dimension. A key ingredient of the argument is the notion of non-degenerate ASD connections. We develop its deformation theory and show that there exist sufficiently many non-degenerate ASD connections …

We prove a sharp lower bound on the curvatures of non-flat ASD connections over the cylinder.

In this paper we announce a gluing theorem for conformal structures with anti-self-dual (ASD) Weyl tensor that applies in geometrical situations that are more general than those considered by previous authors. By adapting a method proposed by Floer, sufficient conditions are given for the existence of ASD conformal str…

Anti-self-dual (ASD) connections for a compact smooth four manifold arise as critical values for the Yang-Mills action functional. Nahm transform is a nice correspondence between a vector bundle with ASD connections and a vector bundle with ASD connections over Picard torus associated to X. In this talk we propose a no…

Gluing instantons on 4-manifolds with group action.

Study identifies key brain regions and model architectures for ASD diagnosis.

The goal of the present study is to identify autism using machine learning techniques and resting-state brain imaging data, leveraging the temporal variability of the functional connections (FC) as the only information. We estimated and compared the FC variability across brain regions between typical, healthy subjects …

Deep learning aids in autism diagnosis and rehabilitation using neuroimaging data.

We give new and rather general gluing theorems for anti-self-dual (ASD) conformal structures, following the method suggested by Floer. The main result is a gluing theorem for pairs of conformally ASD manifolds `joined' across a common piece (union of connected components) of their boundaries. This theorem genuinely ope…

Machine learning for ASD diagnosis using morphological MRI networks.

This paper develops a local analogue of the ADHM construction, which characterises ASD instantons defined over smooth bounded domains inside Euclidean $\mathbb{R}^4$ diffeomorphic to the 4-ball, in terms of infinite dimensional Hilbert spaces and bounded Hermitian linear operators satisfying an analogue of the ADHM equ…

In this article, we study the Kapustin-Witten equations on a closed, simply-connected, four-dimensional manifold which were introduced by Kapustin and Witten. We use the Taubes' compactness theorem in arXiv:1307.6447v4 to prove that if $(A,φ)$ is a smooth solution of Kapustin-Witten equations and the connection $A$ is …

The article provides conditions for unobstructedness of ASD manifolds.

Study on instantons over product manifolds with a codimension-4 form.

Autism spectrum condition (ASC) or autism spectrum disorder (ASD) is primarily identified with the help of behavioral indications encompassing social, sensory and motor characteristics. Although categorized, recurring motor actions are measured during diagnosis, quantifiable measures that ascertain kinematic physiognom…

Game teaches ASD teenagers to imitate gestures.

Autism Spectrum Disorder (ASD) is a developmental disorder that often impairs a child's normal development of the brain. According to CDC, it is estimated that 1 in 6 children in the US suffer from development disorders, and 1 in 68 children in the US suffer from ASD. This condition has a negative impact on a person's …

Discovering imaging biomarkers for autism spectrum disorder (ASD) is critical to help explain ASD and predict or monitor treatment outcomes. Toward this end, deep learning classifiers have recently been used for identifying ASD from functional magnetic resonance imaging (fMRI) with higher accuracy than traditional lear…

We make some comments on noncommutative $U(N)$-instantons on $\mathbb{R}^4_θ$. We elaborate on the equations for the ASD-connection for free modules. Further we make some remarks on the computation of the topological index of ADHM instantons.

Deep-learning model detects ASD from MRI data with high accuracy.

Study extends Yang-Mills energy gap to Kähler surfaces.

Game aims to improve social interactions for teenagers with ASD.

We study the following question: Let $(X,g)$ be a compact Gauduchon surface, $(E,h)$ be a differentiable rank $r$ vector bundle on $X$, ${\mathcal{D}}$ be a fixed holomorphic structure on $D:=\det(E)$ and $a$ be the Chern connection of the pair $(\mathcal{D},\det(h))$. Does the complex space structure on ${\mathcal{M}}…

Bryant and Salamon gave a construction of metrics of G2 holonomy on the total space of the bundle of anti-self-dual (ASD) 2-forms over a 4-dimensional self-dual Einstein manifold. We generalise it by considering the total space of an SO(3) bundle (with fibers R^3) over a 4-dimensional base, with a connection on this bu…

In this article, we consider the Kapustin-Witten equations on a closed $4$-manifold. We study certain analytic properties of solutions to the equations on a closed manifold. The main result is that there exists an $L^{2}$-lower bound on the extra fields over a closed four-manifold satisfying certain conditions if the c…

An Alexander self-dual complex gives rise to a compactification of $M_{0,n}$, called ASD compactification, which is a smooth algebraic variety. ASD compactifications include (but are not exhausted by) the polygon spaces, or the moduli spaces of flexible polygons. We present an explicit description of the Chow rings of …

Deep model integrates MRI and DTI for autism severity prediction.

Deep learning classifies autism vs controls with high accuracy using large fMRI dataset.

Significant progress has been made using fMRI to characterize the brain changes that occur in ASD, a complex neuro-developmental disorder. However, due to the high dimensionality and low signal-to-noise ratio of fMRI, embedding informative and robust brain regional fMRI representations for both graph-level classificati…

Machine learning improves ASD diagnosis accuracy.

ASD algorithm maximizes model estimates by adaptively labeling points.

Study $\mathrm{G}_2$-instantons on 7-sphere from 4-sphere instantons.

Paper discusses ASD challenge for machine condition monitoring.

DCASE 2021 ASD task tackles domain-shifted anomalous sound detection.

DCASE 2022 Task 2 tackles domain shifts in ASD for machine condition monitoring.

Study the geometry and symmetries of moduli spaces of connections on KT manifolds.

Objective. The paper investigates the presence of autism using the functional brain connectivity measures derived from electro-encephalogram (EEG) of children during face perception tasks. Approach. Phase synchronized patterns from 128-channel EEG signals are obtained for typical children and children with autism spect…

Automated video conferencing system improves user experience with ASD and VC.

Mental disorders such as Autism Spectrum Disorders (ASD) are heterogeneous disorders that are notoriously difficult to diagnose, especially in children. The current psychiatric diagnostic process is based purely on the behavioural observation of symptomology (DSM-5/ICD-10) and may be prone to over-prescribing of drugs …

Study proves uniqueness of Yang-Mills field tangent cones in arbitrary dimensions.

Study on Yang-Mills fields blow-up in 4D, proving certain configurations impossible.

Variant of Seiberg-Witten equations for multiple-spinors connects to stability of holomorphic bundles.

In this paper connections between different gauge-theoretical problems in high and low dimensions are established. In particular it is shown that higher dimensional asd equations on total spaces of spinor bundles over low dimensional manifolds can be interpreted as Taubes-Pidstrygach's generalization of the Seiberg-Wit…

In this expository review we discuss various aspects of gauge theory. While the focus is on mathematics, wherever possible we make contact with theoretical high energy physics. Particular emphasis is placed on instantons and monopoles, which admit physical interpretation, and yield interesting and nontrivial mathematic…