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There is a very important problem that has not attracted sufficient attention in academia, i.e., nonlinear field normalization citation counts at the paper level obtained using nonlinear field normalization methods cannot be added or…
Summing or averaging nonlinearly field-normalized citation counts is a common but methodologically problematic practice, as it violates mathematical principles. The issue originates from the nonlinear transformation, which disrupts the…
To quantify the mechanism of a complex network growth we focus on the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely,…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
Citation numbers are extensively used for assessing the quality of scientific research. The use of raw citation counts is generally misleading, especially when applied to cross-disciplinary comparisons, since the average number of citations…
Bibliometric studies often rely on field-normalized citation impact indicators in order to make comparisons between scientific fields. We discuss the connection between field normalization and the choice of a counting method for handling…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
The large amount of information contained in bibliographic databases has recently boosted the use of citations, and other indicators based on citation numbers, as tools for the quantitative assessment of scientific research. Citations…
In 1960s, Dana Scott gave a recursion theoretic characterization of standard systems of countable non-standard models of arithmetic, i.e., collections of sets of standard natural numbers coded in non-standard models. Later, Knight and Nadel…
Citation count is a popular index for assessing scientific papers. However, it depends on not only the quality of a paper but also various factors, such as conventionality, team size, and gender. Here, we examine the extent to which the…
The purpose of this paper is to update the review of Bornmann and Daniel (2008) presenting a narrative review of studies on citations in scientific documents. The current review covers 41 studies published between 2006 and 2018. Bornmann…
The aim of this paper is to highlight a hitherto unknown computational aspect of Nonstandard Analysis. Recently, a number of nonstandard versions of Goedel's system T have been introduced ([2,9,12]), and it was shown in [26] that the…
Articles are cited for different purposes and differentiating between reasons when counting citations may therefore give finer-grained citation count information. Although identifying and aggregating the individual reasons for each citation…
Generalized contextuality is a possible indicator of non-classical behaviour in quantum information theory. In finite-dimensional systems, this is justified by the fact that noncontextual theories can be embedded into some simplex, i.e.…
Citation count is a quantifiable measure to indicate the number of times an article is cited by other articles. It is believed that if an article is cited often then it must be an important or influential article; however, there is no…
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…
If we want to assess whether the paper in question has had a particularly high or low citation impact compared to other papers, the standard practice in bibliometrics is to normalize citations in respect of the subject category and…
The problem of linearization by point transformations is solved for equations in the generalized Riccati and Abel chain of order not exceeding the fourth. It is shown in particular that nonlinear third order and fourth order equations from…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie `non-computational' proofs from the mainstream mathematical…