Related papers: A nonlinear graph-based theory for dynamical netwo…

We derive conditions for the identifiability of nonlinear networks characterized by additive dynamics at the level of the edges when all the nodes are excited. In contrast to linear systems, we show that the measurement of all sinks is…

Observability of an array of identical LTI systems with incommensurable output matrices is studied, where an array is called observable when identically zero relative outputs imply synchronized solutions for the individual systems. It is…

Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…

Many dynamical systems, including thermal, fluid, and multi-agent systems, can be represented as weighted graphs. In this paper we consider whether the unstable states of such systems can be observed from limited discrete-time measurement,…

Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. There are many aspects of dynamical networks that require statistical considerations. In this…

Features of the Jacobian matrix of the delay coordinates map are exploited for quantifying the robustness and reliability of state and parameter estimations for a given dynamical model using an observed time series. Relevant concepts of…

Inferring graph structure from observations on the nodes is an important and popular network science task. Departing from the more common inference of a single graph and motivated by social and biological networks, we study the problem of…

The Jacobian matrix of a dynamic system and its principal minors play a prominent role in the study of qualitative dynamics and bifurcation analysis. When interpreting the Jacobian as an adjacency matrix of an interaction graph, its…

Biological function arises through the dynamical interactions of multiple subsystems, including those between brain areas, within gene regulatory networks, and more. A common approach to understanding these systems is to model the dynamics…

The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…

In this technical note, we study the controllability of diffusively coupled networks from a graph theoretic perspective. We consider leader-follower networks, where the external control inputs are injected to only some of the agents, namely…

This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…

In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…

Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, it is today possible to produce and analyze social and biological networks with detailed information on the time of occurrence and…

A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…

We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…

The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict…

In this paper we investigate the reachability and observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. More in detail, we provide necessary…

The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…