Related papers: Mathematical proof concerning the additivity probl…
Analogy has received attention as a form of inductive reasoning in the empirical sciences. However, its role in pure mathematics has received less consideration. This paper provides an account of how an analogy with a more familiar…
Field normalization plays a crucial role in scientometrics to ensure fair comparisons across different disciplines. In this paper, we revisit the effectiveness of several widely used field normalization methods. Our findings indicate that…
Fractional counting of citations can improve on ranking of multi-disciplinary research units (such as universities) by normalizing the differences among fields of science in terms of differences in citation behavior. Furthermore,…
A common question from students on the usual diagonalization proof for the uncountability of the set of real numbers is: when a representation of real numbers, such as the decimal expansions of real numbers, allows us to use the…
We address the question how citation-based bibliometric indicators can best be normalized to ensure fair comparisons between publications from different scientific fields and different years. In a systematic large-scale empirical analysis,…
Many questions in experimental mathematics are fundamentally inductive in nature. Here we demonstrate how Bayesian inference --the logic of partial beliefs-- can be used to quantify the evidence that finite data provide in favor of a…
Describing real-world entities can vary across different sources, posing a challenge when integrating or exchanging data. We study the problem of joinability under syntactic transformations, where two columns are not equi-joinable but can…
We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for…
The ISI-Impact Factors suffer from a number of drawbacks, among them the statistics-why should one use the mean and not the median?-and the incomparability among fields of science because of systematic differences in citation behavior among…
We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting bottom is strongly normalising provided all its `stratified approximations'…
Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often…
Citations are the cornerstone of knowledge propagation and the primary means of assessing the quality of research, as well as directing investments in science. Science is increasingly becoming "data-intensive", where large volumes of data…
Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
We prove various extensions of the Tennenbaum phenomenon to the case of computable quotient presentations of models of arithmetic and set theory. Specifically, no nonstandard model of arithmetic has a computable quotient presentation by a…
In the case of the scientometric evaluation of multi- or interdisciplinary units one risks to compare apples with oranges: each paper has to assessed in comparison to an appropriate reference set. We suggest that the set of citing papers…
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…
Citation networks have fed numerous works in scientific evaluation, science mapping (and more recently large-scale network studies) for decades. The variety of citation behavior across scientific fields is both a research topic in sociology…
Coinduction refers to both a technique for the definition of infinite streams, so-called codata, and a technique for proving the equality of coinductively specified codata. This article first reviews coinduction in declarative programming.…
We provide a proof of strong normalisation for lambda+, a recently introduced, explicitly typed, non-deterministic lambda-calculus where isomorphic propositions are identified. Such a proof is a non-trivial adaptation of the reducibility…