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In this paper we study Cartesian products of graphs and their divisorial gonality, which is a tropical version of the gonality of an algebraic curve. We present an upper bound on the gonality of the Cartesian product of any two graphs, and…

The characteristic feature of the adeles is that they involve localizations of products (or equivalently restricted products of localizations). The point of this paper is to introduce an adelic style cohomological invariant of a partially…

For any hereditary graph class $F$, we construct optimal adjacency labeling schemes for the classes of subgraphs and induced subgraphs of Cartesian products of graphs in $F$. As a consequence, we show that, if $F$ admits efficient adjacency…

One of the consequences of persistent technological change is that it force individuals to make decisions under extreme uncertainty. This means that traditional decision-making frameworks cannot be applied. To address this issue we…

Graph Neural Networks have revolutionized many machine learning tasks in recent years, ranging from drug discovery, recommendation systems, image classification, social network analysis to natural language understanding. This paper shows…

This paper aims to establish theoretical foundations of graph product multilayer networks (GPMNs), a family of multilayer networks that can be obtained as a graph product of two or more factor networks. Cartesian, direct (tensor), and…

Fine localization in autonomous driving platforms is a task of broad interest, receiving much attention in recent years. Some localization algorithms use the Euclidean distance as a similarity measure between the local image acquired by a…

The operation of zig-zag products of graphs is the analogue of the semidirect product of groups. Using this observation, we present a categorical description of zig-zag products in order to generalize the construction for the category of…

In an affiliation network vertices are linked to attributes and two vertices are declared adjacent whenever they share a common attribute. For example, two customers of an internet shop are called adjacent if they have purchased the same or…

We give a survey on classical and recent results on dual spaces of topological tensor products as well as some examples where these are used.

Image analysis in the field of digital pathology has recently gained increased popularity. The use of high-quality whole slide scanners enables the fast acquisition of large amounts of image data, showing extensive context and microscopic…

We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…

Humans inevitably develop a sense of the relationships between objects, some of which are based on their appearance. Some pairs of objects might be seen as being alternatives to each other (such as two pairs of jeans), while others may be…

We consider classes T of topological spaces (referred to as T-spaces) that are stable under continuous images and frequently under arbitrary products. A local T-space has for each point a neighborhood base consisting of subsets that are…

Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…

User opinions expressed in the form of ratings can influence an individual's view of an item. However, the true quality of an item is often obfuscated by user biases, and it is not obvious from the observed ratings the importance different…

The aim of this paper is to generalize some of the properties and results regarding both the coincidence point set and the common fixed point set of any two digitally continuous maps to the case of several (more than two) digitally…

Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that objects close in each of these measures have some similar…

Topological algebras have properties that extend naturally to those of topological groups [8, 9], but is it the case that semi-direct products exist as in the category of groups? Firstly, we express concepts in categorical language that…

Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…