Related papers: Mathematical Data Science
Data and Science has stood out in the generation of results, whether in the projects of the scientific domain or business domain. CERN Project, Scientific Institutes, companies like Walmart, Google, Apple, among others, need data to present…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
This article presents the theoretical foundation of a new frontier of research-`LP Mixed Data Science'-that simultaneously extends and integrates the practice of traditional and novel statistical methods for nonparametric exploratory data…
Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…
Using the National Academies report, {\em Data Science for Undergraduates: Opportunities and Options}, we connect data science curricula to the more familiar pedagogy used by many mathematical scientists. We use their list of ``data acumen"…
Scientists use a mathematical subject called 'topology' to study the shapes of objects. An important part of topology is counting the numbers of pieces and holes in objects, and people use this information to group objects into different…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
Integrative modeling of macromolecular assemblies allows for structural characterization of large assemblies that are recalcitrant to direct experimental observation. A Bayesian inference approach facilitates combining data from…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
In this paper we suggest how the mathematical concept of hyperstructures may be a useful tool in the study of the higher, hierachical structure of languages.
Statistical Machine Learning (SML) refers to a body of algorithms and methods by which computers are allowed to discover important features of input data sets which are often very large in size. The very task of feature discovery from data…
This review article highlights state-of-the-art data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. Our objective is to provide an…
The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…
Data science is gaining more and more and widespread attention, but no consensus viewpoint on what data science is has emerged. As a new science, its objects of study and scientific issues should not be covered by established sciences. Data…
Data science has arrived, and computational statistics is its engine. As the scale and complexity of scientific and industrial data grow, the discipline of computational statistics assumes an increasingly central role among the statistical…
Mathematica offers, by way of the package Combinatorics, many useful functions to work on graphs and ordered structures, but none of these functions was specific enough to meet the needs of our research group. Moreover, the existing…