Related papers: Nonstandard Analysis in Topology
The paper begins by exploring the various definitions of norms on semigroups and then presents a new definition of a normed semigroup. The properties of normed semigroups in the new sense are investigated. The new definition of the norm is…
We study varieties defined over nonstandard fields using techniques of nonstandard mathematics.
Boundaries in Hypernetwork Theory (HT) are non-structural tags that restrict visibility without altering the underlying hypernetwork. They attach to hypersimplices as annotations and participate in no identity, typing, or alpha/beta…
The use of nonstandard methods to characterize properties of weak, strong and mixed extensions of congruences to ultrafilters has been the main topic of several recent papers. We show that similar methods can be used to characterize the…
This work proposes an overview of the recent semi-supervised learning approaches and related works. Despite the remarkable success of neural networks in various applications, there exist a few formidable constraints, including the need for…
Inspired by recent advances in coverage-guided analysis of neural networks, we propose a novel anomaly detection method. We show that the hidden activation values contain information useful to distinguish between normal and anomalous…
Given a set of data points sampled from some underlying space, there are two important challenges in geometric and topological data analysis when dealing with sampled data: reconstruction -- how to assemble discrete samples into global…
Tables are an abundant form of data with use cases across all scientific fields. Real-world datasets often contain anomalous samples that can negatively affect downstream analysis. In this work, we only assume access to contaminated data…
We study properties of particular non-redundant sets of if-then rules describing dependencies between graded attributes. We introduce notions of saturation and witnessed non-redundancy of sets of graded attribute implications are show that…
The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well…
Standardness is a popular assumption in the literature on set estimation. It also appears in statistical approaches to topological data analysis, where it is common to assume that the data were sampled from a probability measure that…
We give rigorous foundations for parametrized homotopy theory in this monograph. After preliminaries on point-set topology, base change functors, and proper actions of non-compact Lie groups, we develop the homotopy theory of equivariant…
Normalization is ubiquitous in economics, and a growing literature shows that ``normalizations'' can matter for interpretation, counterfactual analysis, misspecification, and inference. This paper provides a general framework for these…
Modern scientific fields face the challenge of integrating a wealth of data, analyses, and results. We recently showed that a neglect of this integration can lead to circular analyses and redundant explanations. Here, we help advance…
I propose a model of aggregation of intervals relevant to the study of legal standards of tolerance. Seven axioms: responsiveness, anonymity, continuity, strategyproofness, and three variants of neutrality are then used to prove several…
Ensuring that analyses performed on a dataset are representative of the entire population is one of the central problems in statistics. Most classical techniques assume that the dataset is independent of the analyst's query and break down…
In Chapter 8 of the Book, ``Graphs and Networks: Transfinite and Nonstandard'' (published by Birkhauser-Boston in 2004), nonstandard versions of transfinite graphs and of electrical networks having such graphs were defined and examined but…
We investigate the connections between computability theory and Nonstandard Analysis. In particular, we investigate the two following topics and show that they are intimately related. (T.1) A basic property of Cantor space $2^{\mathbb{N}}$…
After an introduction to the Hierarchy Problem and to Supersymmetry we discuss the phenomenology of a motivated non-standard pattern of sparticle masses in the context of extensions of the Minimal Supersymmetric Standard Model.
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…