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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…
Applied machine learning (ML) has rapidly spread throughout the physical sciences; in fact, ML-based data analysis and experimental decision-making has become commonplace. We suggest a shift in the conversation from proving that ML can be…
Machine learning encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. We review in a selective way the recent research on…
A theorem prover without an extensive library is much less useful to its potential users. Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic theories also are themselves structured, the study of…
This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…
The increasing data availability and imported analyzing tools from computer science and physical science have sharply changed traditional methodologies of social sciences, leading to a new branch named computational socioeconomics that…
Digital computational outputs are now ubiquitous in the research workflow and the way in which these data are stored and cataloged is becoming more standardized across fields of research. However, even with accessible data and code, the…
Data science and machine learning are the key technologies when it comes to the processes and products with automatic learning and optimization to be used in the automotive industry of the future. This article defines the terms "data…
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,…
Astronomy is increasingly encountering two fundamental truths: (1) The field is faced with the task of extracting useful information from extremely large, complex, and high dimensional datasets; (2) The techniques of astroinformatics and…
We review the role of mathematics from a historical and a conceptual perspective in the light of modern data science.
Simulations play important and diverse roles in statistical workflows, for example, in model specification, checking, validation, and even directly in model inference. Over the past decades, the application areas and overall potential of…
Numerical methods play an ever more important role in astrophysics. This is especially true in theoretical works, but of course, even in purely observational projects, data analysis without massive use of computational methods has become…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
Algorithmic discrimination is an important aspect when data is used for predictive purposes. This paper analyzes the relationships between discrimination and classification, data set partitioning, and decision models, as well as…
Statistical inference is the science of drawing conclusions about some system from data. In modern signal processing and machine learning, inference is done in very high dimension: very many unknown characteristics about the system have to…
Data science has been described as the fourth paradigm for scientific discovery. The latest wave of data science research, pertaining to machine learning and artificial intelligence (AI), is growing exponentially and garnering millions of…
Data science methodologies, which have undergone significant developments recently, provide flexible representational performance and fast computational means to address the challenges faced by traditional scientific methodologies while…
In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that…
Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…