相关论文: Metrics and Ambits and Sprawls, Oh My
Suppose we have just performed searches in a self-index for two patterns $A$ and $B$ and now we want to search for their concatenation \A B); how can we best make use of our previous computations? In this paper we consider this problem and,…
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
In continuous logic, there are plenty of examples of interesting stable metric structures. However, on the other side of the SOP line, there are only a few metric structures where order is relevant, and orders often appear in different…
This thesis covers several developments performed in metric-affine gravity. This alternative framework extends General Relativity by considering a more general connection than the one induced by the metric (i.e., arbitrary torsion and…
The present work is dedicated to searching parameters, alternative to entropy, applicable for description of highly organized systems. The general concept has been offered, in which the system complexity and order are functions of the order…
In this article, we introduce the notions of sequentially compactness and boundedly compactness in the framework of a newly defined $b_v(s)$-metric space which is a generalization of usual metric spaces and several other abstract spaces. We…
In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
Trusses, defined as sets with a suitable ternary and a binary operations, connected by the distributive laws, are studied from a ring and module theory point of view. The notions of ideals and paragons in trusses are introduced and several…
Database indexes facilitate data retrieval and benefit broad applications in real-world systems. Recently, a new family of index, named learned index, is proposed to learn hidden yet useful data distribution and incorporate such information…
In the early 80's, Alain Quilliot presented an approach of ordered sets and graphs in terms of metric spaces, where instead of positive real numbers, the values of the distance are elements of an ordered monoid equipped with an involution.…
With the expansion of scientific research, the number of scientific research is increasing. A new urgent problem is raised that how to keep these researches in a proper way. Therefore, knowledge mapping methods come into being, providing a…
This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics;…
We investigate structure that describes physical data in gravitational systems that is, to one degree or another, independent of the metric and affine structure. We dub such structure surplus structure and seek to incorporate it into our…
Artificial intelligence (AI) in its various forms finds more and more its way into complex distributed systems. For instance, it is used locally, as part of a sensor system, on the edge for low-latency high-performance inference, or in the…
This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.
Background: In view of the growth of published papers, there is an increasing need for studies that summarise scientific research. An increasingly common review is a 'Methodology scoping review', which provides a summary of existing…
We study the structure of cubic matrix mechanics based on three-index objects. It is shown that there exists a counterpart of canonical structure in classical mechanics.
Comtraces (combined traces) are extensions of Mazurkiewicz traces that can model the "not later than" relationship. In this paper, we first introduce the novel notion of generalized comtraces, extensions of comtraces that can additionally…