Related papers: On Three Alternative Characterizations of Combined…

The main goal of this article is to introduce new quantitative characteristics of cycles in finite simple connected graphs and to establish relations of these characteristics with the stretch and spanning tree congestion of graphs. The main…

Proofs of coherence in category theory, starting from Mac Lane's original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what one finds in the lambda calculus, or in term-rewriting…

In this paper we present a new approach to data modelling, called the concept-oriented model (CoM), and describe its main features and characteristics including data semantics and operations. The distinguishing feature of this model is that…

We study algebraic K-theory and topological Hochschild homology in the setting of bimodules over a stable category, a datum we refer to as a laced category. We show that in this setting both K-theory and THH carry universal properties, the…

Cooperative perception aims to address the inherent limitations of single-vehicle autonomous driving systems through information exchange among multiple agents. Previous research has primarily focused on single-frame perception tasks.…

The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…

Graphs provide a natural representation of relational structure that arises across diverse domains. Despite this ubiquity, graph structure is typically learned in a modality- and task-isolated manner, where graph representations are…

As a follow-up to a paper of D. Petz and J. Zem\'anek [4], a number of equivalent conditions which characterize the trace among linear functionals on matrix algebras, finite rank operators and the socle elements of semisimple Banach…

The generic trace format GenTra4CP has been defined in 2004 with the goal of becoming a standard trace format for the observation of constraint solvers over finite domains. It has not been used since. This paper defines the concept of…

Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…

Concept relatedness estimation (CRE) aims to determine whether two given concepts are related. Existing methods only consider the pairwise relationship between concepts, while overlooking the higher-order relationship that could be encoded…

We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total…

This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…

We study an invariant, the secondary trace, attached to two commuting endomorphisms of a 2-dualizable object in a symmetric monoidal higher category. We establish a secondary trace formula which encodes the natural symmetries of this…

Mazurkiewicz traces describe concurrent behaviors of distributed systems. Trace-closed word languages, which are "linearizations" of trace languages, constitute a weaker notion of concurrency but still give us tools to investigate the…

The concept of sum labelling was introduced in 1990 by Harary. A graph is a sum graph if its vertices can be labelled by distinct positive integers in such a way that two vertices are connected by an edge if and only if the sum of their…

This paper considers the problem of inferring the structure of a network from indirect observations. Each observation (a "trace") is the unordered set of nodes which are activated along a path through the network. Since a trace does not…

Framed combinatorial topology is a recent approach to tame geometry which expresses higher-dimensional stratified spaces via tractable combinatorial data. The resulting theory of spaces is well-behaved and computable. In this paper we…

This article contains an overview of the results of the author in a field of algebraic topology used in computer science. The relationship between the cubical homology groups of generalized tori and homology groups of partial trace monoid…

Trace theory is a principled framework for defining equivalence relations for concurrent program runs based on a commutativity relation over the set of atomic steps taken by individual program threads. Its simplicity, elegance, and…