Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences...

Deep Learning failure cases are abundant, particularly in the medical area. Recent studies in out-of-distribution generalization have advanced considerably on well-controlled synthetic datasets, but t...

People can acquire knowledge in an unsupervised manner by reading, and compose the knowledge to make novel combinations. In this paper, we investigate whether pretrained language models can perform co...

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In this paper, strongly clean ring defined by W. K. Nicholson in 1999 has been generalized to n-strongly clean, Σ-strongly clean and with the help of example it has been shown that there exists a rin...

For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is cha...

Existing event-centric NLP models often only apply to the pre-defined ontology, which significantly restricts their generalization capabilities. This paper presents CEO, a novel Corpus-based Event Ont...

We define the class of {\it CUSC} rings, that are those rings whose clean elements are uniquely strongly clean. These rings are a common generalization of the so-called {\it USC} rings, introduced by ...

We give a formula for the integral Chow rings of weighted blow-ups. Along the way, we also compute the integral Chow rings of weighted projective stack bundles, a formula for the Gysin homomorphism of...

The jiggling lemma of Thurston shows that any triangulation can be jiggled (read: subdivided and then perturbed) to be in general position with respect to a distribution. Our main result is a generali...

This paper investigates enumerative aspects of permutohedral blades, which provide a generalization of the notion of the tropical hyperplane arrangement. Blade provide the combinatorial underpinning o...

Studying quantum field theories through geometric principles has revealed deep connections between physics and mathematics, including the discovery by Cachazo, Early, Guevara and Mizera (CEGM) of a ge...

In this paper we give some applications of a lemma of Babalola and Opoola \cite{BO}, which is a classical extension of an earlier one by Lewandowski, Miller and Zlotkiewicz \cite{LMZ}. The application...

We find giant graviton solutions in Frolov's three parameter generalization of the Lunin-Maldacena background. The background we study has $\tildeγ_1=0$ and $\tildeγ_2=\tildeγ_3=\tildeγ$. This cla...

In this paper, a general class of regularized $M$-estimators of scatter matrix are proposed which are suitable also for low or insufficient sample support (small $n$ and large $p$) problems. The consi...

The Ichino-Ikeda conjecture, and its generalization to unitary groups by N. Harris, has given explicit formulas for central critical values of a large class of Rankin-Selberg tensor products. Although...

One generalization of ordinary matroids is symplectic matroids. While symplectic matroids were initially defined by their collections of bases, there has been no cryptomorphic definition of symplectic...

In a previous paper we define a Curtis-Tits group as a certain generalization of a Kac-Moody group. We distinguish between orientable and non-orientable Curtis-Tits groups and identify all orientable ...

Nekrashevych algebras of self-similar group actions are natural generalizations of the classical Leavitt algebras. They are discrete analogues of the corresponding Nekrashevych $C^\ast$-algebras. In p...