arXiv research

The paper studies stability of domains for the first eigenvalue on Riemannian manifolds.

We investigate the geometry and topology of extremal domains in a manifold with negative sectional curvature. An extremal domain is a domain that supports a positive solution to an overdetermined elliptic problem (OEP for short). We consider two types of OEPs. First, we study narrow properties of such domains in a Hada…

The paper examines geometric properties of domains for the p-Laplacian in Euclidean and hyperbolic spaces.

New approach to extremal hyperbolic surfaces using NEC groups.

We find all extremal Lagrangian tori in symplectic unit balls and some toric domains.

An $n$-dimensional Hartogs domain $D_F$ with strongly pseudoconvex boundary can be equipped with a natural \K metric $g_F$. In this paper we prove that if $g_F$ is an extremal \K metric then $(D_F, g_F)$ is biholomorphically isometric to the $n$-dimensional complex hyperbolic space.

Paper tackles open set domain adaptation by detecting unknown classes.

New framework assesses extreme errors in machine learning models.

We build new examples of extremal domains with small prescribed volume for the first eigenvalue of the Laplace-Beltrami operator in some Riemannian manifold with boundary. These domains are close to half balls of small radius centered at a nondegenerate critical point of the mean curvature function of the boundary of t…

Researchers identify valid auxiliary functions for extreme value distributions and their max-domains of attraction.

The study examines special domains in S^2 supporting specific solutions to a PDE.

We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of the Laplace-Beltrami operator in any compact Riemannian manifold. This result generalizes a results of F. Pacard and the second author where the existence of a nondegenerate critical point of the scalar curvature of the …

Develops deep models to handle nonstationary spatial extremal dependence.

Three distinct 3D components found in local extremal Kähler metrics.

Although much research has been devoted to extremal problems on non-overlapping domains little is known about all solutions of this problems. We generalized some of this problems on the case of more general systems of points. It was solved using separating transformations and learning functions in detail. Methods used …

The paper finds minimum Steklov eigenvalues on combinatorial graphs.

We study one extremal problem on the product of power of generalized inner radii of non-overlapping domains in $\mathbb{C}^{n}$.

Paper studies SERA's effectiveness in optimizing imbalanced regression models.

We prove the existence of extremal domains for the first eigenvalue of the Laplace-Beltrami operator in some compact Riemannian manifolds of dimension $n \geq 2$, with volume close to the volume of the manifold. If the first (positive) eigenfunction $φ_0$ of the Laplace-Beltrami operator over the manifold is a nonconst…

RDLI integrates domain logic and context grounding to detect crypto anomalies under scarce labels.

The paper tackles extrapolation in extreme regions of regression problems.

Discrete analogues of classical spectral geometric inequalities and extremal eigenvalue problems on graphs.

Framework reconstructs missing spatio-temporal data for extreme value prediction.

In this paper we address two problems concerning a family of domains $M_Ω(μ) \subset \C^n$, called Cartan-Hartogs domains, endowed with a natural Kaehler metric $g(μ)$. The first one is determining when the metric $g(μ)$ is extremal (in the sense of Calabi), while the second one studies when the coefficient $a_2$ in th…

We prove that a plane domain which is almost isoperimetric (with respect to the $L^1$ metric) is close to a square whose sides are parallel to the coordinates axis. Closeness is measured either by $L^\infty$ Haussdorf distance or Fraenkel asymmetry. In the first case, we determine the extremal domains.

Using generalized Riemann maps, normal forms for almost complex domains (D, J) with singular foliations by stationary disks are defined. Such normal forms are used to construct counterexamples and to determine intrinsic conditions, under which the stationary disks are extremal disks for the Kobayashi metric or determin…

In this paper, we show that the convex domains of the hyperbolic space which are almost extremal for the Faber-Krahn or the Payne-Polya-Weinberger inequalities are close to geodesic balls. Our proof is also valid in other space forms and allows us to recover known results in Euclidean space and on the sphere.

Surface Electromyography (sEMG/EMG) is to record muscles' electrical activity from a restricted area of the skin by using electrodes. The sEMG-based gesture recognition is extremely sensitive of inter-session and inter-subject variances. We propose a model and a deep-learning-based domain adaptation method to approxima…

In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding $H_{0}^{1}(Ω) \hookrightarrow L^{p}(Ω)$ on bounded convex domain in $\mathbb{R}^{2}$. We estimate the best constant by computing the corresponding extremal function using a verified numerical com…

A novel model combines deep learning and extreme value theory for multivariate cyber risk prediction.

Extremes play a special role in Anomaly Detection. Beyond inference and simulation purposes, probabilistic tools borrowed from Extreme Value Theory (EVT), such as the angular measure, can also be used to design novel statistical learning methods for Anomaly Detection/ranking. This paper proposes a new algorithm based o…

Recent years, transfer learning has attracted much attention in the community of machine learning. In this paper, we mainly focus on the tasks of parameter transfer under the framework of extreme learning machine (ELM). Unlike the existing parameter transfer approaches, which incorporate the source model information in…

We generalize the Riesz potential of a compact domain in $\mathbb{R}^{m}$ by introducing a renormalization of the $r^{α-m}$-potential for $α\le0$. This can be considered as generalization of the dual mixed volumes of convex bodies as introduced by Lutwak. We then study the points where the extreme values of the (renorm…

AI-assisted framework detects and predicts rare extreme events.

Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.

We address the problems of multi-domain and single-domain regression based on distinct and unpaired labeled training sets for each of the domains and a large unlabeled training set from all domains. We formulate these problems as a Bayesian estimation with partial knowledge of statistical relations. We propose a worst-…

Study of harmonic maps with extreme Kerr-like singularities.

In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme values for certain subgroups $α$ $\subset$ {1,. .. , d} of variables Xj. Under th…

For a given lattice, we establish an equivalence involving a closed zone of the corresponding Voronoi polytope, a lamina hyperplane of the corresponding Delaunay partition and a quadratic form of rank 1 being an extreme ray of the corresponding L-type domain.

We establish the convexity of Mabuchi's K-energy functional along weak geodesics in the space of Kahler potentials on a compact Kahler manifold thus confirming a conjecture of Chen and give some applications in Kahler geometry, including a proof of the uniqueness of constant scalar curvature metrics (or more generally …

New conditions ensure Dantzig-Wolfe relaxation matches rank-constrained optimization problems.

CSD learns a common component for domain generalization, outperforming existing methods.

REx tackles distributional shift by reducing risk differences across domains.

In this paper we study a sharp Hardy-Littlewood-Sobolev (HLS) type inequality with Riesz potential on bounded smooth domains. We obtain the inequality for a general bounded domain $Ω$ and show that if the extension constant for $Ω$ is strictly larger than the extension constant for the unit ball $B_1$ then extremal fun…

There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed Extreme Learning Machine (PIELM), a rapid version of PINNs which can be applied to s…

We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for convex curves whose curvatures are bounded from above.

Visual Domain Adaptation is a problem of immense importance in computer vision. Previous approaches showcase the inability of even deep neural networks to learn informative representations across domain shift. This problem is more severe for tasks where acquiring hand labeled data is extremely hard and tedious. In this…

An $n$-dimensional Hartogs domain $D_F$ with strongly pseudoconvex boundary can be equipped with a natural Kaehler metric $g_F$. This paper contains two results. In the first one we prove that if $g_F$ is an extremal Kaehler metric then $(D_F, g_F)$ is holomorphically isometric to an open subset of the $n$-dimensional …