Related papers: Set Theory and the Analyst
Convexity is an important notion in non linear optimization theory as well as in infinite dimensional functional analysis. As will be seen below, very simple and powerful tools will be derived from elementary duality arguments (which are…
We study some measures which are related to the notion of the $\e$-complexity. We prove that measure of $\e$-complexity defined on the base of the notion of $\e$-separability is equivalent to the dual measure that is defined through…
When developing and assessing density functional theory methods, a finite basis set is usually employed. In most cases, however, the issue of basis set dependency is neglected. Here, we assess several basis sets and functionals. In…
This article presents a Bayesian approach for predicting and identifying the factors which most influence an individual's propensity to fall into the category of Not in Employment Education or Training (NEET). The approach partitions the…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
In this paper we give a detailed measure theoretical analysis of what we call sum-level sets for regular continued fraction expansions. The first main result is to settle a recent conjecture of Fiala and Kleban, which asserts that the…
To enable the study of open sets in computational approaches to mathematics, lots of extra data and structure on these sets is assumed. For both foundational and mathematical reasons, it is then a natural question, and the subject of this…
Starting with the Brezis-Browder principle, we give stronger versions of many variational principles and minimal element theorems which appeared in the recent literature. Relationships among the elements of different sets of assumptions are…
Whether explicit or implicit, sets are a critical part of many pieces of software. As a result, it is necessary to develop abstractions of sets for the purposes of abstract interpretation, model checking, and deductive verification.…
Style is an integral part of natural language. However, evaluation methods for style measures are rare, often task-specific and usually do not control for content. We propose the modular, fine-grained and content-controlled similarity-based…
We use an information-theoretic measure of linguistic similarity to investigate the organization and evolution of scientific fields. An analysis of almost 20M papers from the past three decades reveals that the linguistic similarity is…
Linear theory provides a reasonable description of the velocity correlations of biased tracers both perpendicular and parallel to the line of separation, provided one accounts for the fact that the measurement is almost always made using…
We give an overview of statistical models and likelihood, together with two of its variants: penalized and hierarchical likelihood. The Kullback-Leibler divergence is referred to repeatedly, for defining the misspecification risk of a…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…
Research on computational argumentation is currently being intensively investigated. The goal of this community is to find the best pro and con arguments for a user given topic either to form an opinion for oneself, or to persuade others to…
Marketing analytics is a diverse field, with both academic researchers and practitioners coming from a range of backgrounds including marketing, expert systems, statistics, and operations research. This paper provides an integrative review…
What can be more fascinating than {\it experimental metaphysics}, to quote one of Abner Shimony's enlightening expressions? Bell inequalities are at the heart of the study of nonlocality. I present a list of open questions, organised in…
The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…
A dual action is obtained for a general non-abelian and non-supersymmetric gauge theory at the classical level. The construction follows steps similar to those used in pure abelian gauge theory. As an example we study the spontaneously…
This is the written version of a series of lectures reviewing the basics of duality as applied to p-forms and sigma-models. The ideas are introduced by way of worked examples, often quite detailed. Our approach is very pedestrian and the…