Related papers: Set Theory and the Analyst
Few models have been more ubiquitous in their respective fields than Bayesian knowledge tracing and item response theory. Both of these models were developed to analyze data on learners. However, the study designs that these models are…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
I discuss (ontologies_and_ontological_knowledge_bases / formal_methods_and_theories) duality and its category theory extensions as a step toward a solution to Knowledge-Based Systems Theory. In particular I focus on the example of the…
We use a novel type of epistemic logic, employing comparative knowledge assertions, to analyze the relative epistemic powers of individuals or groups of agents. Such comparative assertions can express that a group has the potential to…
We present an overview of the decision-theoretic framework of statistical causality, which is well-suited for formulating and solving problems of determining the effects of applied causes. The approach is described in detail, and is related…
Mathematicians manipulate sets with confidence almost every day, rarely making mistakes. Few of us, however, could accurately quote what are often referred to as "the" axioms of set theory. This suggests that we all carry around with us,…
In this paper we give some new criteria for identifying the components of a probability measure, in its Lebesgue decomposition. This enables us to give new criteria to identify spectral types of self-adjoint operators on Hilbert spaces,…
Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Leibler (KL) divergence, originally introduced in kinetic…
A brief discussion is given of measurement within the context of a theory of "beables", e.g. theories of de Broglie, Bohm, Bell, Vink, and also "modal" theories. It is shown that even in an ideal von Neumann measurement of a beable, the…
In the present paper, we study a set that can be treated as a generalised set of subsums for a geometric series. This object was discovered independently in various mathematical aspects. For instance, it is closely related to various…
Contextuality is a central property in comparative analysis of classical, quantum, and supercorrelated systems. We examine and compare two well-motivated approaches to contextuality. One approach ("contextuality-by-default") is based on the…
NLP researchers regularly invoke abstract concepts like "interpretability," "bias," "reasoning," and "stereotypes," without defining them. Each subfield has a shared understanding or conceptualization of what these terms mean and how we…
In this manuscript, we discuss the substantial importance of Bayesian reasoning in Social Science research. Particularly, we focus on foundational elements to fit models under the Bayesian paradigm. We aim to offer a frame of reference for…
Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective, etc. Each such set is described by a single Set Theory formula with parameters unrelated to other formulas. Exotic expressions involving…
The purpose of this note is to point out analogies between causal analysis in statistics and the correlation-response theory in statistical physics. It is further shown that for some systems the dynamic cavity offers a way to compute the…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
The evoluted set is the set of configurations reached from an initial set via a fixed flow for all times in a fixed interval. We find conditions on the initial set and on the flow ensuring that the evoluted set has negligible boundary (i.e.…
The use of statistical software in academia and enterprises has been evolving over the last years. More often than not, students, professors, workers, and users, in general, have all had, at some point, exposure to statistical software.…
Reading a visualization is like reading a paragraph. Each sentence is a comparison: the mean of these is higher than those; this difference is smaller than that. What determines which comparisons are made first? The viewer's goals and…
Recently, importance of meta-analysis is increasing in the field of dentistry, since it is not easy to settle controversies arising from conflicting studies. Meta-analysis is the statistical method of combining results from two or more…