Related papers: Extrapolation: Stories and Problems
The paper suggests a method of extrapolation of notion of one-sided semi-infinite sequences representing traces of two-sided band-limited sequences; this features ensure uniqueness of this extrapolation and possibility to use this for…
Among many efforts to facilitate timely access to safe and effective medicines to children, increased attention has been given to extrapolation. Loosely, it is the leveraging of conclusions or available data from adults or older age groups…
A modestly revised version of lecture notes that were distributed to accompany my four lectures at the 2017 Spring School of Analysis at Paseky, sponsored by Charles University, Prague. They are an introductory survey of Rubio de Francia…
We give an alternate proof of three versions of the theorem on extrapolation of Carleson measures.
This is a survey of old and new problems and results in additive number theory.
Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.
In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.
Theoretical and experimental studies of high multiplicity events are analyzed. Some interesting phenomena can be revealed at high multiplicities. Preliminary results of project "Thermalization" are reported.
We present the theory of hard exclusive processes, at medium and asymptotical energies, illustrated through some selected examples.
The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…
This expository thesis contains a study of four interpolation theorems, the requisite background material, and a few applications. The materials introduced in the first three sections of Chapter 1 are used to motivate and prove the…
The right to AI explainability has consolidated as a consensus in the research community and policy-making. However, a key component of explainability has been missing: extrapolation, which describes the extent to which AI models can be…
The first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \cite{I} and numerous applications in \cite{RS} and \cite{Y2}.…
We provide a detailed overview of the various approaches that were proposed to date to solve the task of Open Information Extraction. We present the major challenges that such systems face, show the evolution of the suggested approaches…
This article gives a brief survey of the theory and applications of anomalies.
Extrapolation is defined as making predictions beyond the range of the data used to estimate a statistical model. In ecological studies, it is not always obvious when and where extrapolation occurs because of the multivariate nature of the…