Related papers: Tensor-Lifted Multivariate Functional Calculus Bey…
Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
The simplest and most natural examples of completely nonunitary contractions on separable complex Hilbert spaces which have polynomial characteristic functions are the nilpotent operators. The main purpose of this paper is to prove the…
The motivation behind this paper is threefold. Firstly, to study, characterize and realize operator concavity along with its applications to operator monotonicity of free functions on operator domains that are not assumed to be matrix…
This work proposes a unified theory of regularity in one hypercomplex variable: the theory of $T$-regular functions. In the special case of quaternion-valued functions of one quaternionic variable, this unified theory comprises…
Task arithmetic, representing downstream tasks through linear operations on task vectors, has emerged as a simple yet powerful paradigm for transferring knowledge across diverse settings. However, maintaining a large collection of task…
Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. The recent surge of transport maps offers a mathematical foundation and new insights for tackling this challenge by…
We are concerned with rigid analytic geometry in the general setting of Henselian fields $K$ with separated analytic structure, whose theory was developed by Cluckers--Lipshitz--Robinson. It unifies earlier work and approaches of numerous…
MINLO (mixed-integer nonlinear optimization) formulations of the disjunction between the origin and a polytope via a binary indicator variable have broad applicability in nonlinear combinatorial optimization, for modeling a fixed cost $c$…
We study the mixed-integer epigraph of a special class of convex functions with non-convex indicator constraints, which are often used to impose logical constraints on the support of the solutions. The class of functions we consider are…
In this paper we use the notion of slice monogenic functions \cite{slicecss} to define a new functional calculus for an $n$-tuple $T$ of not necessarily commuting operators. This calculus is different from the one discussed in…
This paper presents a method for the accurate and efficient computations on scalar, vector and tensor fields in three-dimensional spherical polar coordinates. The methods uses spin-weighted spherical harmonics in the angular directions and…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
This work exploits the logical foundation of session types to determine what kind of type discipline for the pi-calculus can exactly capture, and is captured by, lambda-calculus behaviours. Leveraging the proof theoretic content of the…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
This note is a complement to Pusz--Woronowicz's works on functional calculus for two positive forms from the viewpoint of operator theory. Based on an elementary, self-contained and purely Hilbert space operator explanation of their…
Tensor Ring (TR) decomposition is a powerful tool for high-order data modeling, but is inherently restricted to discrete forms defined on fixed meshgrids. In this work, we propose a TR functional decomposition for both meshgrid and…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
The tensor data recovery task has thus attracted much research attention in recent years. Solving such an ill-posed problem generally requires to explore intrinsic prior structures underlying tensor data, and formulate them as certain forms…