相关论文: Short introduction to Nonstandard Analysis

These lecture notes cover advanced topics in linear regression, with an in-depth exploration of the existence, uniqueness, relations, computation, and non-asymptotic properties of the most prominent estimators in this setting. The covered…

In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…

The purpose of these lecture notes is to give a quick and introductory overview of holographic superconductors. Besides the actual description of the standard holographic superconductor, attention is paid to the motivations and the relation…

While there are numerous linear algebra teaching tools, they tend to be focused on the basics, and not handle the more advanced aspects. This project aims to fill that gap, focusing specifically on methods like Strassen's fast matrix…

We give a general approach to infinite dimensional non-Gaussian Analysis for measures which need not have a logarithmic derivative. This framework also includes the possibility to handle measures of Poisson type.

In his remarkable paper Formalism64, Robinson defends his philsophocal position as follows: (i) Any mention of infinite totalities is literally meaningless. (ii) We should act as if infinite totalities really existed. Being the originator…

The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…

The differences between the $N=0$ and $N=1$ standard models are emphasized in formulating their short distance extension. We sketch methods to reproduce many of the small numbers in the model in terms of scale ratios, applying see-saw like…

Logical relations (LR) have been around for many years, and today they are used in many formal results. However, it can be difficult to LR beginners to find a good place to start to learn. Papers often use highly specialized LRs that use…

This is a survey of some recent applications of Boolean valued analysis to operator theory and harmonic analysis. Under consideration are pseudoembedding operators, the noncommutative Wickstead problem, the Radon-Nikodym Theorem for…

Reverse Mathematics (RM) is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson. The aim of RM is finding the minimal axioms needed to prove a theorem of ordinary (i.e. non-set theoretical)…

In this paper we provide a survey on the framework of abstract non-interference. In particular, we describe a general formalization of abstract non-interference by means of three dimensions (observation, protection and semantics) that can…

We present a suite of experiments that allow us to understand the underlying challenges of language model adaptation to nonstandard text. We do so by designing interventions that approximate core features of user-generated text and their…

These informal notes are concerned with sums and averages in various situations in analysis.

A generalization of Passing-Bablok regression is proposed for comparing multiple measurement methods simultaneously. Possible applications include assay migration studies or interlaboratory trials. When comparing only two methods, the…

Abductive reasoning aims to find plausible explanations for an event. This style of reasoning is critical for commonsense tasks where there are often multiple plausible explanations. Existing approaches for abductive reasoning in natural…

As suggested by the title, the aim of this paper is to uncover the vast computational content of classical Nonstandard Analysis. To this end, we formulate a template $\mathfrak{CI}$ which converts a theorem of 'pure' Nonstandard Analysis,…

In many modern applications, a carefully designed primary study provides individual-level data for interpretable modeling, while summary-level external information is available through black-box, efficient, and nonparametric…

Reliability of machine learning evaluation -- the consistency of observed evaluation scores across replicated model training runs -- is affected by several sources of nondeterminism which can be regarded as measurement noise. Current…

In a recent letter [Phys. Rev. Lett. {\bf 100}, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of…