Related papers: Levels of discontinuity, limit-computability, and …
This work continues the development of an intensional approach to computability initiated in previous work, in which programs and computations, rather than functions, constitute the primary objects of study. In this setting, models of…
In this work it is described all normal extensions of a multipoint minimal operator generated by linear multipoint differential-operator expression for second order in the Hilbert space of vector-functions in terms of boundary values at the…
Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
We introduce a new hierarchical deep learning framework for recursive higher-order meta-learning that enables neural networks (NNs) to construct, solve, and generalise across hierarchies of tasks. Central to this approach is a generative…
We show that there are well separated families of quantum expanders with asymptotically the maximal cardinality allowed by a known upper bound. This has applications to the "growth" of certain operator spaces: It implies asymptotically…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the…
Instantonic theories are quantum field theories where all correlators are determined by integrals over the finite-dimensional space (space of generalized instantons). We consider novel geometrical observables in instantonic topological…
We give an exposition of results from a crossroad between geometric function theory, harmonic analysis, boundary value problems and approximation theory, which characterize quasicircles. We will specifically expose the interplay between the…
Computing is a high-level process of a physical system. Recent interest in non-standard computing systems, including quantum and biological computers, has brought this physical basis of computing to the forefront. There has been, however,…
We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded…
We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of average position and its measurement, we…
We develop a formal model for distributed measurement-based quantum computations, adopting an agent-based view, such that computations are described locally where possible. Because the network quantum state is in general entangled, we need…
The problem of computing spectra of operators is arguably one of the most investigated areas of computational mathematics. However, the problem of computing spectra of general bounded infinite matrices has only recently been solved. We…
BSS RAMs over first-order structures help to characterize algorithms for processing objects by means of useful operations and relations. They are the result of a generalization of several types of abstract machines. We want to discuss…
We define an infinite dimensional modification of lower-semicomputability of density operators by G\'acs with an attempt to fix some problem in the paper. Our attempt is partly achieved by showing the existence of universal operator under…
In 1957, Lacombe initiated a systematic study of the different possible notions of "computable topological spaces". However, he interrupted this line of research, settling for the idea that "computably open sets should be computable unions…
Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the…
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…