Related papers: Bernstein polynomials: a bibliometric data analysi…
Bibliometrics has the ambitious goal of measuring science. To this end, it exploits the way science is disseminated trough scientific publications and the resulting citation network of scientific papers. We survey the main historical…
National exercises for the evaluation of research activity by universities are becoming regular practice in ever more countries. These exercises have mainly been conducted through the application of peer-review methods. Bibliometrics has…
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
The days of the lone astronomer with his optical telescope and photographic plates are long gone: Astronomy in 2025 will not only be multi-wavelength, but multi-messenger, and dominated by huge data sets and matching data rates. Catalogues…
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.…
Back in 1755, Euler explored an interesting array of numbers that now frequently appears in polynomial identities, combinatorial problems, and finite calculus, among other places. These numbers share a strong connection with well-known…
The Binomial Theorem has long been essential in mathematics. In one form or another it was known to the ancients and, in the hands of Leibniz, Newton, Euler, Galois, and others, it became an essential tool in both algebra and analysis.…
Einstein's research manuscripts provide important insights into his exceptional creativity. At the same time, they can present difficulties for a publication in the documentary edition of the Collected Papers of Albert Einstein (CPAE). The…
To extract essential information from complex data, computer scientists have been developing machine learning models that learn low-dimensional representation mode. From such advances in machine learning research, not only computer…
Neural Networks (NNs) have provided state-of-the-art results for many challenging machine learning tasks such as detection, regression and classification across the domains of computer vision, speech recognition and natural language…
Bernstein-Sato polynomial of a hypersurface is an important object with numerous applications. It is known, that it is complicated to obtain it computationally, as a number of open questions and challenges indicate. In this paper we propose…
The growth of large, programatically accessible bibliometrics databases presents new opportunities for complex analyses of publication metadata. In addition to providing a wealth of information about authors and institutions, databases such…
Analysing historical patterns of artificial intelligence (AI) adoption can inform decisions about AI capability uplift, but research to date has provided a limited view of AI adoption across various fields of research. In this study we…
Subresultants of two univariate polynomials are one of the most classic and ubiquitous objects in computational algebra and algebraic geometry. In 1948, Habicht discovered and proved interesting relationships among subresultants. Those…
The notion of two-numbers of connected Riemannian manifolds was introduced about 35 years ago in [Un invariant geometrique riemannien, C. R. Acad. Sci. Paris Math. 295 (1982), 389--391] by B.-Y. Chen and T. Nagano. Later, two-numbers have…
Data analysis in space sciences has been performed exclusively visually for years, despite the fact that the largest amount of data belongs to non-visible portions of the electromagnetic spectrum. This, on the one hand, limits the study of…
This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent…
Bibliometric studies are a rare undertaking in the field of English language teaching, especially at a journal level. To celebrate the 30th anniversary of TEFLIN Journal, this study exhibits a bibliometric portrait of its publication,…
The authors have been using a largely algebraic form of ``computational discovery'' in various undergraduate classes at their respective institutions for some decades now to teach pure mathematics, applied mathematics, and computational…