Related papers: Bernstein polynomials: a bibliometric data analysi…
The three and five-dimensional convex sets of two-level complex and quaternionic quantum systems are studied in the Bayesian thermostatistical framework introduced by Lavenda. Associated with a given parameterization of each such set is a…
Biomarker discovery is vital in advancing personalized medicine, offering insights into disease diagnosis, prognosis, and therapeutic efficacy. Traditionally, the identification and validation of biomarkers heavily depend on extensive…
In the social sciences, researchers search for information on the Web, but this is most often distributed on different websites, search portals, digital libraries, data archives, and databases. In this work, we present an integrated search…
In 1869, the first draft of the periodic table was published by Russian chemist Dmitri Mendeleev. In terms of data science, his achievement can be viewed as a successful example of feature embedding based on human cognition: chemical…
Binary data are highly common in many applications, however it is usually modelled with the assumption that the data are independently and identically distributed. This is typically not the case in many real-world examples and such the…
Sergey Pinchuk discovered a class of pairs of real polynomials in two variables that have a nowhere vanishing Jacobian determinant and define maps of the real plane to itself that are not one-to-one. This paper describes the asymptotic…
Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the rigorous definitions,…
Materials informatics, data-enabled investigation, is a "fourth paradigm" in materials science research after the conventional empirical approach, theoretical science, and computational research. Materials informatics has two essential…
During recent years, bibliometric studies have become increasingly important in evaluating individual scientists, institutes, and entire observatories. In astronomy, often librarians are involved in maintaining publication databases and…
Although deep learning has historical roots going back decades, neither the term "deep learning" nor the approach was popular just over five years ago, when the field was reignited by papers such as Krizhevsky, Sutskever and Hinton's now…
Bayesian approaches to learn the graphical structure of Bayesian Belief Networks (BBNs) from databases share the assumption that the database is complete, that is, no entry is reported as unknown. Attempts to relax this assumption involve…
In 1970, Donald Ornstein proved a landmark result in dynamical systems, viz., two Bernoulli systems with the same entropy are isomorphic except for a measure 0 set. Keane and Smorodinsky gave a finitary proof of this result. They also…
Onomastics is "the science or study of the origin and forms of proper names of persons or places." ["Onomastics". Merriam-Webster.com, 2013. http://www.merriam-webster.com (11 February 2013)]. Especially personal names play an important…
In this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming Y is a random variable satisfying moment conditions, we use the generating function of these…
Social Network Analysis is a way of studying agents embedded in contexts. In about 1998, physicists discovered social networks as representations of complex systems. Small-world and scale-free networks are the paradigmatic models of this…
Quaternions, discovered by Sir William Rowan Hamilton in the 19th century, are a significant extension of complex numbers and a profound tool for understanding three-dimensional rotations. This work explores the quaternion's history,…
Making sense of a dataset in an automatic and unsupervised fashion is a challenging problem in statistics and AI. Classical approaches for {exploratory data analysis} are usually not flexible enough to deal with the uncertainty inherent to…
Spatial transcriptomics assays are rapidly increasing in scale and complexity, making computational analysis a major bottleneck in biological discovery. Although frontier AI agents have improved dramatically at software engineering and…
Let $K$ be a number field and $f_1,\ldots,f_s\in K[x_1,\ldots,x_n]$ forms of odd degrees. In 1957, Birch proved that if $n$ is sufficiently large then the forms always have a nontrivial zero in $K^n$. Apart from some small degrees, the…
The two Journal Citation Reports of the Science Citation Index 2004 and the Social Science Citation Index 2004 were combined in order to analyze and map journals and specialties at the edges and in the overlap between the two databases. For…