Related papers: Continuous Sentences Preserved Under Reduced Produ…
The aim of this paper is to investigate properties preserved and co-preserved by coarsely $n$-to-1 functions, in particular by the quotient maps $X\to X/\sim$ induced by a finite group $G$ acting by isometries on a metric space $X$. The…
We develop a pseudo-metric analogue of bisimulation for generalized semi-Markov processes. The kernel of this pseudo-metric corresponds to bisimulation; thus we have extended bisimulation for continuous-time probabilistic processes to a…
Maintaining information in context is essential in successful real-time language comprehension, but maintenance is cognitively costly and can slow processing. We hypothesize that rational language users selectively maintain information that…
We introduce a notion of weak definability of first order structures, show that various classification-theoretic properties are or are not preserved under it, and that the properties which are preserved can also be characterized in terms of…
Linear approximations to the decision boundary of a complex model have become one of the most popular tools for interpreting predictions. In this paper, we study such linear explanations produced either post-hoc by a few recent methods or…
Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example,…
One proves that any everywhere defined constructive mapping from a complete metric space into a complete metric space which preserves the property of precompacity of subsets is locally uniformly continuous. This fact can be viewed as…
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…
In spoken conversations, spontaneous behaviors like filled pause and prolongations always happen. Conversational partner tends to align features of their speech with their interlocutor which is known as entrainment. To produce human-like…
We investigate the relation between the concentration and the product of metric measure spaces. We have the natural question whether, for two concentrating sequences of metric measure spaces, the sequence of their product spaces also…
The majority of research in computational psycholinguistics has concentrated on the processing of words. This study introduces innovative methods for computing sentence-level metrics using multilingual large language models. The metrics…
We characterize the situations in which certain accumulation properties of topological spaces are preserved under taking products.
The space of constructible functions form a dense subspace of the space of generalized valuations. In this note we prove a somewhat stronger property that the sequential closure, taken sufficiently many (in fact, infinitely many) times, of…
There is a lot of research interest in encoding variable length sentences into fixed length vectors, in a way that preserves the sentence meanings. Two common methods include representations based on averaging word vectors, and…
Materials science literature contains millions of materials synthesis procedures described in unstructured natural language text. Large-scale analysis of these synthesis procedures would facilitate deeper scientific understanding of…
This study re-evaluates the assumption that long-range correlations in sentence length are a fundamental feature of natural language and a marker of literary style. While previous research has suggested that punctuation marks--particularly…
We study properties related to relevance in non-monotonic consequence relations obtained by systems of structured argumentation. Relevance desiderata concern the robustness of a consequence relation under the addition of irrelevant…
The concept of a system has proliferated through natural and social sciences. While myriad theories of systems exist, there is no mathematical general theory of systems. In this thesis, we take a first step towards formulating such a…
The class of $\mu$-compact sets can be considered as a natural extension of the class of compact metrizable subsets of locally convex spaces, to which the particular results well known for compact sets can be generalized. This class…
Functions whose composition with every metric is a metric are said to be metric-preserving. In this article, we investigate a variation of the concept of metric-preserving functions where metrics are replaced by ultrametrics.