Related papers: Levels of discontinuity, limit-computability, and …

Computability on uncountable sets has no standard formalization, unlike that on countable sets, which is given by Turing machines. Some of the approaches to define computability in these sets rely on order-theoretic structures to translate…

Classical models of computation have been successful in capturing the very essence of individual computing devices. Although they are useful to understand computability power and limitations in the small, such models are not suitable to…

A mathematical concept is identified and analyzed that is implicit in the 2012 paper Turing Incomputable Computation, presented at the Alan Turing Centenary Conference (Turing-100, Manchester). The concept, called dynamic level sets, is…

Every open-system dynamics can be associated to infinitely many stochastic pictures, called unravelings, which have proved to be extremely useful in several contexts, both from the conceptual and the practical point of view. Here, focusing…

Many insights into the quantum world can be found by studying it from amongst more general operational theories of physics. In this thesis, we develop an approach to the study of such theories purely in terms of the behaviour of their…

Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…

A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties…

Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that…

We introduce the notions of kernel map and kernel set of a bounded linear operator on a Hilbert space relative to a subspace lattice. The characterization of the kernel maps and kernel sets of finite rank operators leads to showing that…

We explore in the framework of Quantum Computation the notion of computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm that exploits the quantum adiabatic processes is considered…

Let $H$ be a reflexive, dense, separable, infinite dimensional complex Hilbert space and let $B(H)$ be the algebra of all bounded linear operators on $H$. In this paper, we carry out characterizations of norm-attainable operators in normed…

Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…

Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…

S. Gudder and, later, S. Pulmanova and E. Vincekova, have studied in two recent papers a certain ordering of bounded self-adjoint operators on a Hilbert space. We present some further results on this ordering and show that some structure…

We design various logics for proving hyper properties of iterative programs by application of abstract interpretation principles. In part I, we design a generic, structural, fixpoint abstract interpreter parameterized by an algebraic…

We study band-dominated operators on (subspaces of) $L_p$-spaces over metric measure spaces of bounded geometry satisfying an additional property. We single out core assumptions to obtain, in an abstract setting, definitions of limit…

We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…

Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…

In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm in the unit sphere. We prove important results concerning the characterization of the AN operators, see Definition 1.2. The class of AN…

This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent…