相关论文: Domain Theory: An Introduction

Finite collections of point masses contained in some bounded domain produce a unique field in the exterior domain, which means that the associated basis functions (often called ``fundamental solutions'') are independent. A new proof of this…

This article has been withdrawn in 2013. The class of LOTS (linearly ordered topological spaces) contains many important spaces, like the set of real numbers, the set of rational numbers and the ordinals. Such spaces have rich topological…

Arrays are ubiquitous in the context of software verification. However, effective reasoning over arrays is still rare in CP, as local reasoning is dramatically ill-conditioned for constraints over arrays. In this paper, we propose an…

We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to a…

I discuss (ontologies_and_ontological_knowledge_bases / formal_methods_and_theories) duality and its category theory extensions as a step toward a solution to Knowledge-Based Systems Theory. In particular I focus on the example of the…

This paper shows how numerical methods on a regular grid in a box can be used to generate numerical schemes for problems in general smooth domains contained in the box with no need for a domain specific discretization. The focus is mainly…

Relational semigroups with domain and range are a useful tool for modelling nondeterministic programs. We prove that the representation class of domain-range semigroups with demonic composition is not finitely axiomatisable. We extend the…

Deep neural networks learn fragile "shortcut" features, rendering them difficult to interpret (black box) and vulnerable to adversarial attacks. This paper proposes semantic features as a general architectural solution to this problem. The…

Locales have been studied as "topologies without points", mainly by tools of category theory. While traditional topology presents a space as a set of points with specified neighborhoods, localic topology presents a space as a lattice of…

Foundation models (FMs) have revolutionized computer vision, enabling effective learning across different domains. However, their performance under domain shift is yet underexplored. This paper investigates the zero-shot domain adaptation…

This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…

This work is a contribution to the study of set of the representations of integers in a rational base number system. This prefix-closed subset of the free monoid is naturally represented as a highly non regular tree whose nodes are the…

Determining the key elements of interconnected infrastructure and complex systems is paramount to ensure system functionality and integrity. This work quantifies the dominance of the networks' nodes in their respective neighborhoods,…

An n dimensional monomial dynamical system over a finite field K is a nonlinear deterministic time discrete dynamical system with the property that each of the n component functions is a monic nonzero monomial function in n variables. In…

This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…

In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…

This paper contains the results collected so far on polynomial composites in terms of many basic algebraic properties. Since it is a polynomial structure, results for monoid domains come in here and there. The second part of the paper…

The Scott rank of a countable structure is a measure, coming from the proof of Scott's isomorphism theorem, of the complexity of that structure. The Scott spectrum of a theory (by which we mean a sentence of $\mathcal{L}_{\omega_1 \omega}$)…

A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…

While language models are increasingly utilized in materials science, typical models rely on frequency-centric tokenization methods originally developed for natural language processing. However, these methods frequently produce excessive…