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Time series analysis has witnessed the inspiring development from traditional autoregressive models, deep learning models, to recent Transformers and Large Language Models (LLMs). Efforts in leveraging vision models for time series analysis…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
Machine learning systems have been shown to propagate the societal errors of the past. In light of this, a wealth of research focuses on designing solutions that are "fair." Even with this abundance of work, there is no singular definition…
The problems and solutions contained here, all associated with nonlinear recurrences and long-term trends, are new (as far as is known).
In this paper, we present a new axiomatic system that is a minimal axiomatization of Boolean algebras. Furthermore, the symmetric difference is shown to be algebraically analogous to the modular difference of two numbers. Finally, a new…
Ranks of subspaces of vector spaces satisfy all linear inequalities satisfied by entropies (including the standard Shannon inequalities) and an additional inequality due to Ingleton. It is known that the Shannon and Ingleton inequalities…
Linear vector equations and inequalities are considered defined in terms of idempotent mathematics. To solve the equations, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces. The…
In \cite{PSMA}, Pal et al. introduced some weighted means and gave some related inequalities by using an approach for operator monotone functions. This paper discusses the construction of these weighted means in a simple and nice setting…
Despite the high interest for Machine Learning (ML) in academia and industry, many issues related to the application of ML to real-life problems are yet to be addressed. Here we put forward one limitation which arises from a lack of…
This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…
In addition to reproducing discriminatory relationships in the training data, machine learning systems can also introduce or amplify discriminatory effects. We refer to this as introduced unfairness, and investigate the conditions under…
We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators related to the matrix order and the Jensen inequality.…
Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…
We review the basic ideas lying at the foundation of the recently developed theory of twisted symmetries of differential equations, and some of its developments.
We obtain variational inequalities for some classes of bilinear averages of one variable, generalizing the variational inequalities for averages of R. Jones {\it et al}. As an application we get almost everywhere convergence for the ergodic…
This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical…
Machine learning based systems are reaching society at large and in many aspects of everyday life. This phenomenon has been accompanied by concerns about the ethical issues that may arise from the adoption of these technologies. ML fairness…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
T. Coulhon introduced an interesting reformulation of the usual Sobolev inequalities. We characterize Coulhon type inequalities in terms of rearrangement inequalities.