Related papers: Past and future of the cap set problem
Today's QCD problems, prospects and achievements are reviewed.
This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a prior-free assessment of {\it confidence} is, in…
It is well-known that an algorithm exists which approximates the NP-complete problem of Set Cover within a factor of ln(n), and it was recently proven that this approximation ratio is optimal unless P = NP. This optimality result is the…
The aim of this paper is to review the state-of-the-art of recent research concerning the numerical index of Banach spaces, by presenting some of the results found in the last years and proposing a number of related open problems.
We discuss the past and future of set theory, axiom systems and independence results. We deal in particular with cardinal arithmetic.
We consider the future causal boundary as a tool to find obstructions to conformal extensions, the latter being a slight generalization to conformal compactifications.
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…
This paper focuses on the superset model problem that arises in the context of regression. To address this problem, we take the Bayesian approach to measure its uncertainty. An illustrative example with the real dataset is provided.
We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
Deep learning's recent history has been one of achievement: from triumphing over humans in the game of Go to world-leading performance in image classification, voice recognition, translation, and other tasks. But this progress has come with…
In this paper, we study a free boundary problem for a class of nonlinear nonautonomous size structured population model. Using the comparison principle and upper lower solution methods, we establish the existence of the solution for such…
We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog…
In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Building on recent advances showing infinite sumsets can be found,…
In a recent paper, one of us posed three open problems concerning squarefree arithmetic progressions in infinite words. In this note we solve these problems and prove some additional results.
In this paper we consider convergence of approximate solutions of conservation laws. We start with an overview over the historical developments since the 1950s, and the analytical tools used in this context. Then we present some of our own…
The aim of this survey article is to cover most of the recent research on preopen sets. I try to present majority of the results on preopen sets that I am aware of.
We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.
This is a survey of old and recent results about the asymptotic Plateau problem. Our aim is to give a fairly complete picture of the field, and present the current situation.