Related papers: The Evolution of Lattice Field Theory: a Statistic…
Let $\mathcal{T}$ be a collection of 3-element subsets $S$ of $\{1, \ldots,n\}$ with the property that if $i<j<k$ and $a<b<c$ are two 3-element subsets in $S$, then there exists an integer sequence $x_1 < x_2 < \cdots < x_n$ such that $x_i,…
This study is intended to find an answer for the question on which national "shoulders" the worldwide top-level research stands. Traditionally, national scientific standings are evaluated in terms of the number of citations to their papers.…
Lattice gauge theory was formulated by Kenneth Wilson in 1974. In the ensuing decades, improvements in actions, algorithms, and computers have enabled tremendous progress in QCD, to the point where lattice calculations can yield sub-percent…
The empirical and theoretical justification of Gartner hype curves is a very relevant open question in the field of Technological Life Cycle analysis. The scope of the present paper is to introduce a simple model describing the growth of…
Stochastic evolutions of classical field theories have recently become popular in the study of problems such as determination of the rates of topological transitions and the statistical mechanics of nonlinear coherent structures. To obtain…
This White Paper has been prepared as a planning document for the Division of High Energy Physics of the U. S. Department of Energy. Recent progress in lattice-based studies of physics beyond the standard model is summarized, and major…
Machine learning (ML) has transformed numerous fields, but understanding its foundational research is crucial for its continued progress. This paper presents an overview of the significant classical ML algorithms and examines the…
The world's collective knowledge is evolving through research and new scientific discoveries. It is becoming increasingly difficult to objectively rank the impact research institutes have on global advancements. However, since the funding,…
Scientific publications form the cornerstone of innovation and have maintained a stable growth trend over the years. However, in recent years, there has been a significant surge in retractions, driven largely by the proliferation of…
The statistics community, which has traditionally lacked a transparent and open peer-review system, faces a challenge of inconsistent paper quality, with some published work containing substantial errors. This problem resonates with…
Finite fields form an important chapter in abstract algebra, and mathematics in general. We aim to provide a geometric and intuitive model for finite fields, involving algebraic numbers, in order to make them accessible and interesting to a…
We collected and cleaned a large data set on publications in statistics. The data set consists of the coauthor relationships and citation relationships of 83, 331 papers published in 36 representative journals in statistics, probability,…
Over the last four decades, the way knowledge is created in academia has transformed dramatically: research teams have grown larger, scholars draw from ever-wider pools of prior work, and the most influential discoveries increasingly emerge…
The emergence of intellectual property as an academic issue opens a big gate to a cross-disciplinary field. Different disciplines start a dialogue in the framework of the international multilateral treaties in the early 90's. As global…
We present an alternative domain concerning mathematics to investigate universal evolution mechanisms by focusing on large cycles theory (LCT) - a simplified version of well-known hamiltonian graph theory. LCT joins together a number of…
Understanding the dynamics of research production and collaboration may reveal better strategies for scientific careers, academic institutions and funding agencies. Here we propose the use of a large and multidisciplinar database of…
In this paper, we proposed an evolving model via the hypergraph to illustrate the evolution of the citation network. In the evolving model, we consider the mechanism combined with preferential attachment and the aging influence. Simulation…
Industry involvement in the machine learning (ML) community seems to be increasing. However, the quantitative scale and ethical implications of this influence are rather unknown. For this purpose, we have not only carried out an informed…
This is an evolving document. It is devoted to summarizing patterns and laws of knowledge growth. By examining a variety of parameters in data sources such as Wikipedia and Microsoft Academic Graph, we can get deeper insights of how…
In this paper, we study growth rate of product of sets in the Heisenberg group over finite fields and the complex numbers. More precisely, we will give improvements and extensions of recent results due to Hegyv\'{a}ri and Hennecart (2018).