相关论文: Majorization and Inequalities among Complete Homog…
Large Language Models (LLMs) have demonstrated impressive generalization capabilities across various tasks, but their claim to practical relevance is still mired by concerns on their reliability. Recent works have proposed examining the…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.
Motivated by recent best case analyses for some sorting algorithms and based on the type of complexity we partition the algorithms into two classes: homogeneous and non homogeneous algorithms. Although both classes contain algorithms with…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
We use machine learning methods to search for parity violations in the Large-Scale Structure (LSS) of the Universe, motivated by recent claims of chirality detection using the 4-Point Correlation Function (4PCF), which would suggest new…
In many neural models, new features as polynomial functions of existing ones are used to augment representations. Using the natural language inference task as an example, we investigate the use of scaled polynomials of degree 2 and above as…
In this paper, we develop a theory of symmetrization on the one dimensional integer lattice. More precisely, we associate a radially decreasing function $u^*$ with a function $u$ defined on the integers and prove the corresponding…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
We consider divergence form elliptic operators in dimension $n\geq 2$ with $L^\infty$ coefficients. Although solutions of these operators are only H\"{o}lder continuous, we show that they are differentiable ($C^{1,\alpha}$) with respect to…
It has been well-observed that an inequality of the type $\pi(x;q,a) > \pi(x;q,b)$ is more likely to hold if $a$ is a non-square modulo $q$ and $b$ is a square modulo $q$ (the so-called ``Chebyshev Bias''). For instance, each of…
In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show on a few examples, both in partial differential and partial difference equations when this happens. Moreover…
In this series of papers we study subspaces of de Branges spaces of entire functions which are generated by majorization on subsets $D$ of the closed upper half-plane. The present, first, part is addressed to the question which subspaces of…
Recent work shows that a new family of norms on Hermitian matrices arise by evaluating the even degree complete homogeneous symmetric (CHS) polynomials on the eigenvalues of a Hermitian matrix. The CHS norm of a graph is then defined by…
This paper studies the magnitude homology of graphs focusing mainly on the relationship between its diagonality and the girth. Magnitude and magnitude homology are formulations of the Euler characteristic and the corresponding homology,…
Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…
This paper introduces a unified framework for Bohr-type inequalities by incorporating multiple Schwarz functions into the majorant series for $K$-quasiconformal harmonic mappings in the unit disk $\mathbb{D} := \{z\in\mathbb{C} : |z| <…
The symmetric difference in Boolean lattices can be defined in two different but equivalent forms. However, it can be introduced also in every bounded lattice with complementation where these two forms need not coincide. We study lattices…
We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…
We present consistent algorithms for multiclass learning with complex performance metrics and constraints, where the objective and constraints are defined by arbitrary functions of the confusion matrix. This setting includes many common…