Related papers: Set Theory and the Analyst
Comparing alternatives in pairs is a well-known method of ranking creation. Experts are asked to perform a series of binary comparisons and then, using mathematical methods, the final ranking is prepared. As experts conduct the individual…
Given an analytic equivalence relation, we tend to wonder whether it is Borel. When it is non Borel, there is always the hope it will be Borel on a "large" set -- nonmeager or of positive measure. That has led Kanovei, Sabok and Zapletal to…
Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to…
This paper surveys and organizes research works in an under-studied area, which we call automated evaluation for student argumentative writing. Unlike traditional automated writing evaluation that focuses on holistic essay scoring, this…
Semantic measures are widely used today to estimate the strength of the semantic relationship between elements of various types: units of language (e.g., words, sentences, documents), concepts or even instances semantically characterized…
In this paper a new general approach is developed to construct and study Lebesgue type decompositions of linear operators $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue type…
This document consists of lecture notes for a graduate course, which focuses on the relations between Information Theory and Statistical Physics. The course is aimed at EE graduate students in the area of Communications and Information…
Sentence similarity is considered the basis of many natural language tasks such as information retrieval, question answering and text summarization. The semantic meaning between compared text fragments is based on the words semantic…
Artificial Intelligence federates numerous scientific fields in the aim of developing machines able to assist human operators performing complex treatments -- most of which demand high cognitive skills (e.g. learning or decision processes).…
The increasing ease of data capture and storage has led to a corresponding increase in the choice of data, the type of analysis performed on that data, and the complexity of the analysis performed. The main contribution of this paper is to…
The manifestation and effect of bias in news reporting have been central topics in the social sciences for decades, and have received increasing attention in the NLP community recently. While NLP can help to scale up analyses or contribute…
A mathematical model is a function taking certain arguments and returning a theoretical prediction of a feature of a physical system. The arguments to the mathematical model can be split into two groups; (a) controllable variables of the…
Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…
These notes were originally developed as lecture notes for a category theory course. They should be well-suited to anyone that wants to learn category theory from scratch and has a scientific mind. There is no need to know advanced…
This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…
This is an introduction to the set-theoretic method of forcing, including its application in proving the independence of the Continuum Hypothesis from the Zermelo-Fraenkel axioms of set theory. I presuppose no particular mathematical…
We construct measure which determines a two-variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also…
A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the…
This article introduces tools to analyze set-valued data statistically. The tools were initially developed to analyze results from an interlaboratory comparison made by the Electromagnetic Compatibility Working Group of Eurolab France,…
We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to…