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The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based…
Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…
Synthesis automatically generates a process model from a behavioural specification. When the target model is a Petri net, we address synthesis through region theory. Researchers have studied region-based synthesis extensively for…
Boolean combinations allow combining given combinatorial objects to obtain new, potentially more complicated, objects. In this paper, we initiate a systematic study of this idea applied to graphs. In order to understand expressive power and…
Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact…
We show that some natural problems that are XNLP-hard (which implies W[t]-hardness for all t) when parameterized by pathwidth or treewidth, become FPT when parameterized by stable gonality, a novel graph parameter based on optimal maps from…
This paper presents the benefits of formal modelling and verification techniques for self-stabilising distributed algorithms. An algorithm is studied, that takes a set of processes connected by a tree topology and converts it to a ring…
Many physical systems can be best understood as sets of discrete data with associated relationships. Where previously these sets of data have been formulated as series or image data to match the available machine learning architectures,…
Petri nets are an established graphical formalism for modeling and analyzing the behavior of systems. An important consideration of the value of Petri nets is their use in describing both the syntax and semantics of modeling formalisms.…
This paper discusses the complexity of graph pebbling, dealing with both traditional pebbling and the recently introduced game of cover pebbling. Determining whether a configuration is solvable according to either the traditional definition…
Given a graph $G$ and a real number $0\le p\le 1$, we define the random set $B_p(G)\subset V(G)$ by including each vertex independently and with probability $p$. We investigate the probability that the random set $B_p(G)$ is a zero forcing…
This paper aims to develop a mathematical foundation to model knitting with graphs. We provide a precise definition for knit objects with a knot theoretic component and propose a simple undirected graph, a simple directed graph, and a…
Recently, progress has been made towards improving relational reasoning in machine learning field. Among existing models, graph neural networks (GNNs) is one of the most effective approaches for multi-hop relational reasoning. In fact,…
In many complex systems that can be modeled using Petri nets time can be a very important factor which should be taken into account during creation and analysis of the model. Time data can describe starting moments of some actions or their…
Knowledge graphs are structured representations of facts in a graph, where nodes represent entities and edges represent relationships between them. Recent research has resulted in the development of several large KGs. However, all of them…
Graph convolutional networks have been successful in addressing graph-based tasks such as semi-supervised node classification. Existing methods use a network structure defined by the user based on experimentation with fixed number of layers…
Let $G$ be a graph of order $n$. For a positive integer $p$, $G$ is said to be a $\mathbf{W}_{p}$ graph if $n\geq p$ and every $p$ pairwise disjoint independent sets of $G$ are contained within $p$ pairwise disjoint maximum independent…
In geographic information systems and in the production of digital maps for small devices with restricted computational resources one often wants to round coordinates to a rougher grid. This removes unnecessary detail and reduces space…
The theory of Petri Nets provides a general framework to specify the behaviors of real-time reactive systems and Time Petri Nets were introduced to take also temporal specifications into account. We present in this paper a forward…
We prove that certain problems naturally arising in knot theory are NP--hard or NP--complete. These are the problems of obtaining one diagram from another one of a link in a bounded number of Reidemeister moves, determining whether a link…