Related papers: Levels of discontinuity, limit-computability, and …
We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…
Generally-unbounded infinitesimal generators are studied in the context of operator topology. Beginning with the definition of seminorm, the concept of locally convex topological vector space is introduced as well as the concept of…
We axiomatize and generalize Markov's approach to the continuity problem for Type 1 computable functions, i.e. the problem of finding sufficient conditions on a computable topological space to obtain a theorem of the form "computable…
The cut and join operations play important roles in tensor models in general. We introduce a generalization of the cut operation associated with the higher order variations and demonstrate how they generate operators in the Aristotelian…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
In the setting of modern mathematical logic and model theory, classification theory has been one of the landmark achievements of the field. Likewise, the classification of UHF-algebras and AF-algebras were substantial contributions to the…
We introduce an abstract neural flow framework for neural networks and neural operators. The framework contains two continuous-depth models, namely neural flows with composition and separation structures, and covers both finite-dimensional…
In spite of its fundamental importance, inference has not been an inherent function of multidimensional models and analytical applications. These models are mainly aimed at numeric (quantitative) analysis where the notions of inference and…
The questions of dense definiteness and boundedness of composition operators in $L^2$-spaces are studied by means of inductive limits of operators. Methods based on projective systems of measure spaces and inductive limits of $L^2$-spaces…
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…
To enable the study of open sets in computational approaches to mathematics, lots of extra data and structure on these sets is assumed. For both foundational and mathematical reasons, it is then a natural question, and the subject of this…
One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions…
This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…
The notion of topological entropy can be conceptualized in terms of the number of forward trajectories that are distinguishable at resolution $\varepsilon$ within $T$ time units. It can then be formally defined as a limit of a limit…
We show that separability and second-countability are first-order properties among topological spaces definable in o-minimal expansions of $(\mathbb{R},<)$. We do so by introducing first-order characterizations -- definable separability and…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…
The paper introduces unbounded antilinear operators on Hilbert spaces and develops their fundamental theory. In particular, we establish a closed range theorem, a polar decomposition theorem, and the convexity of the numerical range for…
In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…
We present theoretical and practical results on the order theory of lattices of functions, focusing on Galois connections that abstract (sets of) functions - a topic known as higher-order abstract interpretation. We are motivated by the…