Related papers: Measure Theory and Integration By and For the Lear…
Accumulating evidence indicates that the capacity to integrate information in the brain is a prerequisite for consciousness. Integrated Information Theory (IIT) of consciousness provides a mathematical approach to quantifying the…
A meaningful and deep understanding of the human aspects of software engineering (SE) requires psychological constructs to be considered. Psychology theory can facilitate the systematic and sound development as well as the adoption of…
Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic…
Expressing physics problems in the form of a mathematical model is one of the most important stages in the problem-solving process. Particularly in algebraic symbolization, understanding the meanings of signs and being able to manipulate…
The book gives a detailed exposition of basic concepts and results of a theory of processes. The presentation of theoretical concepts and results is accompanied with illustrations of their application to solving various problems of…
We characterize a notion of confidence that arises in learning or updating beliefs: the amount of trust one has in incoming information and its impact on the belief state. This learner's confidence can be used alongside (and is easily…
Previous theoretical results pertaining to meta-learning on sequences build on contrived assumptions and are somewhat convoluted. We introduce new information-theoretic tools that lead to an elegant and very general decomposition of error…
This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…
It is well-known (at least in the education research literature) that primary school students face considerable difficulties in the understanding of negative integers (and numbers), related operations and their visualizations. In the…
The integrated information theory of consciousness (IIT) is uniquely ambitious in proposing a mathematical formula, derived from apparently fundamental properties of conscious experience, to describe the quantity and quality of…
Information theory is widely accepted as a powerful tool for analyzing complex systems and it has been applied in many disciplines. Recently, some central components of information theory - multivariate information measures - have found…
The research presented in this thesis was motivated by the need to improve introductory physics courses. Introductory physics courses are generally the first courses in which students learn to create models to solve complex problems.…
The progress of machine learning over the past decade is undeniable. In retrospect, it is both remarkable and unsettling that this progress was achievable with little to no rigorous theory to guide experimentation. Despite this fact,…
We define an integral of real-valued functions with respect to a measure that takes its values in the extended positive cone of a partially ordered vector space $E$. The monotone convergence theorem, Fatou's lemma, and the dominated…
Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle…
Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea of…
We describe a course designed to help future educators build an integrated understanding of the different elements of physics education research (PER), including: research into student learning, content knowledge from the perspective of how…
In the theory of belief functions, many measures of uncertainty have been introduced. However, it is not always easy to understand what these measures really try to represent. In this paper, we re-interpret some measures of uncertainty in…
Ensemble learning is a method that leverages weak learners to produce a strong learner. However, obtaining a large number of base learners requires substantial time and computational resources. Therefore, it is meaningful to study how to…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…