Related papers: $C^*$-Algebraic Machine Learning: Moving in a New …

This is a graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space…

A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…

RNAs play crucial and versatile roles in biological processes. Computational prediction approaches can help to understand RNA structures and their stabilizing factors, thus providing information on their functions, and facilitating the…

Any $C^*$-algebra can be regarded as a generalization of locally compact, Hausdorff topological space $\mathcal X$. From the commutative commutative Gelfand-Na\u{\i}mark theorem it follows that the spectrum of any commutative $C^*$-algebra…

Machine learning (ML) provides a broad spectrum of tools and architectures that enable the transformation of data from simulations and experiments into useful and explainable science, thereby augmenting domain knowledge. Furthermore,…

Let $R$ be a rational function of degree at least two, let $J_R$ be the Julia set of $R$ and let $\mu^L$ be the Lyubich measure of $R$. We study the C$^*$-algebra $\mathcal{MC}_R$ generated by all multiplication operators by continuous…

We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised…

The standard C*-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does…

The article is devoted to investigation of classes of functions monotone as functions on general $C^*$-algebras that are not necessarily the $C^*$-algebras of all bounded linear operators on a Hilbert space as it is in classical case of…

In this paper, we characterize the C*-Algebra generated by partial isometries.

We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…

We provide some background on the category of classifiable $\mathrm{C}^*$-algebras, whose objects are infinite-dimensional, simple, separable, unital $\mathrm{C}^*$-algebras that have finite nuclear dimension and satisfy the universal…

This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…

Let $G=K\ltimes A$ be the semi-direct product group of a compact group $K$ acting on an abelian locally compact group $A$. We describe the $C^*$-algebra $C^*(G)$ of $G$ in terms of an algebra of operator fields defined over the spectrum of…

Sampling from known probability distributions is a ubiquitous task in computational science, underlying calculations in domains from linguistics to biology and physics. Generative machine-learning (ML) models have emerged as a promising…

We introduced and study a family of generalized norm on $C^*$-algebras and the notion of Birkhoff-James orthogonality and norm-parallelism with respect to these family of generalized norms are investigated.

Continual Learning (CL) focuses on maximizing the predictive performance of a model across a non-stationary stream of data. Unfortunately, CL models tend to forget previous knowledge, thus often underperforming when compared with an offline…

Let $\Lambda = \mathbb{Z}^n$ with lexicographic ordering. $\Lambda$ is a totally ordered group. Let $X = \Lambda^+ * \Lambda^+$. Then $X$ is a $\Lambda$-tree. Analogous to the construction of graph $C^*$-algebras, we form a groupoid whose…

We study (von Neumann) regular $^*$-subalgebras of $B(H)$, which we call R$^*$-algebras. The class of R$^*$-algebras coincides with that of "E$^*$-algebras that are pre-C$^*$-algebras" in the sense of Z. Sz\H{u}cs and B. Tak\'acs. We give…

In recent years, machine learning (ML) algorithms have been successfully employed in Astronomy for analyzing and interpreting the data collected from various surveys. The need for new robust and efficient data analysis tools in Astronomy is…