相关论文: Widening Operators for Weakly-Relational Numeric A…

Let $R$ be an associative algebra over a field $K$ generated by a vector subspace $V$. The polynomial $f(x_1,\ldots,x_n)$ of the free associative algebra $K\langle x_1,x_2,\ldots\rangle$ is a weak polynomial identity for the pair $(R,V)$ if…

We introduce a method for calculating the stationary state of a translation invariant array of weakly coupled cavities in the presence of dissipation and coherent as well as incoherent drives. Instead of computing the full density matrix…

The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…

Due to the heterogeneity of the global distribution of ecological and hydrological ground-truth observations, machine learning models can have limited adaptability when applied to unknown locations, which is referred to as weak…

We address the problem of modulating a parameter onto a power-limited signal, transmitted over a discrete-time Gaussian channel and estimating this parameter at the receiver. Continuing an earlier work, where the optimal trade-off between…

In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly…

Neural networks are surprisingly good at interpolating and perform remarkably well when the training set examples resemble those in the test set. However, they are often unable to extrapolate patterns beyond the seen data, even when the…

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…

In this work we analyze convergence of solutions for the Laplace operator with Neumann boundary conditions in a two-dimensional highly oscillating domain which degenerates into a segment (thin domains) of the real line. We consider the case…

We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.

In this paper, we point out that the definition of weak tracial approximation can be improved and strengthened. An example of weak tracial approximation is also provided.

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

We show that the variational representations for f-divergences currently used in the literature can be tightened. This has implications to a number of methods recently proposed based on this representation. As an example application we use…

We associate to an integral operator a discrete one which is conceptually simpler, and study the relations between them.

We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these…

Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.

Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…

In this paper we perform the rigorous derivation of the topological derivative for optimization problems constrained by a class of quasi-linear elliptic transmission problems. In the case of quasi-linear constraints, techniques using…

We present a novel framework for deriving integral constraints for correlators on conformal line defects. These constraints emerge from the non-linearly realized ambient-space conformal symmetry. To validate our approach, we examine several…

Spectral problem for the Dirac operator with regular but not strongly regular boundary conditions and complex-valued potential summable over a finite interval is considered. The purpose of this paper is to find conditions under which the…