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Two distinct structures of aggregates of atoms connected by anisotropic bonds with a network configuration are discussed from the viewpoint of a point set topology. A specific topological space connects the two types of topological…

Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant topological signals across distinct systems. In geometry and…

Homomorphisms between relational structures play a central role in finite model theory, constraint satisfaction and database theory. A central theme in quantum computation is to show how quantum resources can be used to gain advantage in…

Ontologies provide a formal description of concepts and their relationships in a knowledge domain. The goal of ontology alignment is to identify semantically matching concepts and relationships across independently developed ontologies that…

Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…

In this article, we study holomorphic isometric embeddings between bounded symmetric domains. In particular, we show the total geodesy of any holomorphic isometric embedding between reducible bounded symmetric domains with the same rank.

There are many methodologies and techniques for easing the task of ontology building. Here we describe the intersection of two of these: ontology normalisation and fully programmatic ontology development. The first of these describes a…

It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…

Self-organizing maps (SOMs) are a technique that has been used with high-dimensional data vectors to develop an archetypal set of states (nodes) that span, in some sense, the high-dimensional space. Noteworthy applications include weather…

This paper studies the homotopy theory of algebras and homotopy algebras over an operad. It provides an exhaustive description of their higher homotopical properties using the more general notion of morphisms called infinity-morphisms. The…

The study of homonymy is vital to resolving fundamental problems in lexical semantics. In this paper, we propose four hypotheses that characterize the unique behavior of homonyms in the context of translations, discourses, collocations, and…

Increasing inhomogeneity due to gravitational clumping reflects increasing gravitational entropy in a time evolving universe. Starting from an ensemble of uniformly distributed particles it is demonstrated that gravitational clustering is…

The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity…

The interactions between the Sun, interplanetary space, near Earth space environment, the Earth's surface, and the power grid are, perhaps unsurprisingly, very complicated. The study of such requires the collaboration between many different…

In a context of constant evolution and proliferation of AI technology,Hybrid Intelligence is gaining popularity to refer a balanced coexistence between human and artificial intelligence. The term has been extensively used in the past two…

The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…

Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…

Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…

Recent advances in operator learning theory have improved our knowledge about learning maps between infinite dimensional spaces. However, for large-scale engineering problems such as concurrent multiscale simulation for mechanical…

We interpret mathematically the pair (master equation, solution of master equation) up to equivalence, as the pair (a presentation of a free triangular dga T over a combination operad O, dga map of T into C, a dga over O) up to homotopy…