Related papers: Generalized neck analysis of harmonic maps from su…

In a recent paper the first and the third authors introduced the notion of horizontal \alpha-harmonic map, with respect to a given C^1 planes distribution P_T on all R^m. The goal of this paper is to investigate compactness and quantization…

The large-scale structure of the Universe is distributed in a cosmic web. Studying the distribution and clustering of dark matter particles and halos may open up a new horizon for studying the physics of the dark Universe. In this work, we…

Recent studies have proven that DNNs, unlike human vision, tend to exploit texture information rather than shape. Such texture bias is one of the factors for the poor generalization performance of DNNs. We observe that the texture bias…

The Teichm\"uller harmonic map flow is a gradient flow for the harmonic map energy of maps from a closed surface to a general closed Riemannian target manifold of any dimension, where both the map and the domain metric are allowed to…

Energy minimizing harmonic maps between manifolds are known to be smooth outside a rectifiable set of codimension $3$, called the singular set. The possibility that this set is not a manifold, but has arbitrarily many small gaps in it, is…

In this article, we show that sequences of $(n+\alpha)$-harmonic maps with a free boundary in $\mathbb S^{d-1}$, where $\alpha$ is a parameter tending to zero, converge to a bubble tree. For such sequences, we prove in detail that the…

We quantise integrable point-particle systems with opposite-sign kinetic terms and nontrivial interactions. Using methods from separability theory, we show that previously determined classical stability conditions also imply discrete…

Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local…

We study the approximation power of Graph Neural Networks (GNNs) on latent position random graphs. In the large graph limit, GNNs are known to converge to certain "continuous" models known as c-GNNs, which directly enables a study of their…

The present paper concerns the invariants of generically nef vector bundles on ruled surfaces. By Mehta - Ramanathan Restriction Theorem and by Miyaoka characterization of semistable vector bundles on a curve, the generic nefness can be…

A magnetic helicity integral is proposed which can be applied to domains which are not magnetically closed, i.e. have a non-vanishing normal component of the magnetic field on the boundary. In contrast to the relative helicity integral,…

For domains of first kind [7,13] we describe the qualitative behavior of the global bifurcation diagram of the unbounded branch of solutions of the Gel'fand problem crossing the origin. At least to our knowledge this is the first result…

A non-trivial spatial topology of the Universe is a potentially observable attribute, which can be probed through the circles-in-the-sky for all locally homogeneous and isotropic universes with no assumptions on the cosmological parameters.…

We present our ongoing work on understanding the limitations of graph convolutional networks (GCNs) as well as our work on generalizations of graph convolutions for representing more complex node attribute dependencies. Based on an analysis…

We study the Generalized Brans-Dicke cosmology in the presence of matter and dark energy. Of particular interest for a constant Brans-Dicke parameter, the de Sitter space has also been investigated.

In [31,32,33] the Gauss-Bonnet formulas for coherent tangent bundles over compact oriented surfaces (without boundary) were proved. We establish the Gauss-Bonnet theorem for coherent tangent bundles over compact oriented surfaces with…

In this paper, we show that if the broad line region clouds are in approximate energy equipartition between the magnetic field and gravity, as hypothesized by Rees, there will be a significant effect on the shape and smoothness of broad…

In this paper, we prove the boundary partial regularity for a class of coupled Dirac-harmonic maps satisfying a certain energy monotonicity inequality near the boundary.

We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose…

The two dark sectors of the universe - dark matter and dark energy - may interact with each other. Background and linear density perturbation evolution equations are developed for a generic coupling. We then establish the general conditions…