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In this work, we consider a class of $n$-dimensional, $n\geq2$, piecewise linear discontinuous maps that can exhibit a new type of attractor, called a weird quasiperiodic attractor. While the dynamics associated with these attractors may…
Graph convolutional networks (GCNs) is a class of artificial neural networks for processing data that can be represented as graphs. Since financial transactions can naturally be constructed as graphs, GCNs are widely applied in the…
Graph neural networks (GNNs) have emerged as a powerful tool for nonlinear processing of graph signals, exhibiting success in recommender systems, power outage prediction, and motion planning, among others. GNNs consists of a cascade of…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver…
We characterize the connectivity structure of feed-forward, deep neural networks (DNNs) using network motif theory. To address whether a particular motif distribution is characteristic of the training task, or function of the DNN, we…
Asynchronous Boolean networks are a type of discrete dynamical system in which each variable can take one of two states, and a single variable state is updated in each time step according to pre-selected rules. Boolean networks are popular…
Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network…
Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in…
Recent studies have shown that Graph Convolutional Networks (GCNs) are vulnerable to adversarial attacks on the graph structure. Although multiple works have been proposed to improve their robustness against such structural adversarial…
This research addresses the challenge of characterizing the complexity and unpredictability of basins within various dynamical systems. The main focus is on demonstrating the efficiency of convolutional neural networks (CNNs) in this field.…
The local structure of unweighted networks can be characterized by the number of times a subgraph appears in the network. The clustering coefficient, reflecting the local configuration of triangles, can be seen as a special case of this…
In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear…
Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original…
This paper deals with identifiability of undirected dynamical networks with single-integrator node dynamics. We assume that the graph structure of such networks is known, and aim to find graph-theoretic conditions under which the state…
We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph…
Anomaly detection on attributed networks attracts considerable research interests due to wide applications of attributed networks in modeling a wide range of complex systems. Recently, the deep learning-based anomaly detection methods have…
Temporal Graph Neural Networks (TGNNs) are widely used to model dynamic systems where relationships and features evolve over time. Although TGNNs demonstrate strong predictive capabilities in these domains, their complex architectures pose…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
A unified approach to studying convergence and stochastic stability of continuous time consensus protocols (CPs) is presented in this work. Our method applies to networks with directed information flow; both cooperative and noncooperative…