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Theory of differential subordination provides techniques to reduce differential subordination problems into verifying some simple algebraic condition called admissibility condition. We exploit the first order differential subordination…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
The motivation for extending secret sharing schemes to cases when either the set of players is infinite or the domain from which the secret and/or the shares are drawn is infinite or both, is similar to the case when switching to abstract…
The paper concerns the investigation of nonconvex and nondifferentiable integral functionals on general Banach spaces, which may not be reflexive and/or separable. Considering two major subdifferentials of variational analysis, we derive…
Transfer learning has emerged as a highly sought-after and actively pursued research area within the statistical community. The core concept of transfer learning involves leveraging insights and information from auxiliary datasets to…
Systematic Generalization refers to a learning algorithm's ability to extrapolate learned behavior to unseen situations that are distinct but semantically similar to its training data. As shown in recent work, state-of-the-art deep learning…
The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a…
Ultrafunctions are a particular class of generalized functions defined on a hyperreal field $\mathbb{R}^{*}\supset\mathbb{R}$ that allow to solve variational problems with no classical solutions. We recall the construction of ultrafunctions…
Irregularities in the metric tensor of a signature-changing space-time suggest that field equations on such space-times might be regarded as distributional. We review the formalism of tensor distributions on differentiable manifolds, and…
The 'signature method' refers to a collection of feature extraction techniques for multivariate time series, derived from the theory of controlled differential equations. There is a great deal of flexibility as to how this method can be…
The use of charge balance functions in heavy-ion collision studies was initially proposed as a probe of delayed hadronization and two-stage quark production in these collisions. It later emerged that general balance functions can also serve…
One of the basic principles of Approximation Theory is that the quality of approximations increase with the smoothness of the function to be approximated. Functions that are smooth in certain subdomains will have good approximations in…
One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…
A general proposition is proved relating multiplicities (of restriction of a representation of a group to a subgroup) under basechange, and used to calculate some multiplicities for cuspidal representations which become principal series…
Domain shift across crowd data severely hinders crowd counting models to generalize to unseen scenarios. Although domain adaptive crowd counting approaches close this gap to a certain extent, they are still dependent on the target domain…
We develop constructions for exchangeable sequences of point processes that are rendered conditionally-i.i.d. negative binomial processes by a (possibly unknown) random measure called the base measure. Negative binomial processes are useful…
We propose a test for a change in the mean for a sequence of functional observations that are only partially observed on subsets of the domain, with no information available on the complement. The framework accommodates important scenarios,…
This is an exposition of some basic ideas in the realm of Global Inverse Function theorems. We address ourselves mainly to readers who are interested in the applications to Differential Equations. But we do not deal with those applications…
We consider a class of "box-like" statistically self-affine functions, and compute the almost-sure box-counting dimension of their graphs. Furthermore, we consider the differentiability of our functions, and prove that, depending on an…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…