Related papers: Partitioned difference families: the storm has not…
New families of composition methods with processing of order 4 and 6 are presented and analyzed. They are specifically designed to be used for the numerical integration of differential equations whose vector field is separated into three or…
The way science is currently practiced shows conclusions but hides how they were reached. Researchers work privately, polish their results, publish a finished paper, and defend it. Errors are punished by retraction rather than corrected by…
In recent literature there are an increasing number of papers where the forbidden sets of difference equations are computed. We review and complete different attempts to describe the forbidden set and propose new perspectives for further…
Probability distributions supported on the simplex enjoy a wide range of applications across statistics and machine learning. Recently, a novel family of such distributions has been discovered: the continuous categorical. This family enjoys…
Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for…
Difference-in-differences is one of the most used identification strategies in empirical work in economics. This chapter reviews a number of important, recent developments related to difference-in-differences. First, this chapter reviews…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
The scientific process is a means to turn the results of experiments into knowledge about the world in which we live. Much research effort has been directed toward automating this process. To do this, one needs to formulate the scientific…
In this paper we provide proofs of two new theorems that provide a broad class of partition inequalities and that illustrate a na\"ive version of Andrews' anti-telescoping technique quite well. These new theorems also put to rest any notion…
Social media is nearly ubiquitous in modern life, raising concerns about its societal impacts -- from mental health and polarization to violence and democratic disruption. Yet research on its causal effects is still inconclusive: Various…
Teams dominate the production of high-impact science and technology. Analyzing teamwork from more than 50 million papers, patents, and software products, 1954-2014, we demonstrate across this period that larger teams developed recent,…
Teams now drive most scientific advances, yet the impact of absolute beginners -- authors with no prior publications -- remains understudied. Analyzing over 29 million articles published between 1941 and 2020 across disciplines and team…
Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their centre. Tests that assess statistical hypotheses of centre implicitly assume a specific centre, e.g.,…
This is the first one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple linear groups.
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
The definition and implementation of fairness in automated decisions has been extensively studied by the research community. Yet, there hides fallacious reasoning, misleading assertions, and questionable practices at the foundations of the…
A growing literature provides evidence on multigenerational inequality -- the extent to which socio-economic advantages persist across three or more generations. This chapter reviews its main findings and implications. Most studies find…
With the explosive growth of online social media, the ancient problem of information disorders interfering with news diffusion has surfaced with a renewed intensity threatening our democracies, public health, and news outlets' credibility.…
Recent research has helped to cultivate growing awareness that machine learning systems fueled by big data can create or exacerbate troubling disparities in society. Much of this research comes from outside of the practicing data science…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…