Related papers: Functional Asynchronous Networks: Factorization of…
Within the endeavour of modelling and understanding the propagation of delays in transportation networks, an approach that has attracted increasing interest in the last decade is the creation of functional network representations. These…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
A Boolean network is a function $f:\{0,1\}^n\to\{0,1\}^n$ from which several dynamics can be derived, depending on the context. The most classical ones are the synchronous and asynchronous dynamics. Both are digraphs on $\{0,1\}^n$, but the…
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…
To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean…
Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable…
Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…
A machine learning (ML) feature network is a graph that connects ML features in learning tasks based on their similarity. This network representation allows us to view feature vectors as functions on the network. By leveraging function…
Network interactions that are nonlinear in the state of more than two nodes - also known as higher-order interactions - can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to…
Processes on networks consist of two interdependent parts: the network topology, consisting of the links between nodes, and the dynamics, specified by some governing equations. This work considers the prediction of the future dynamics on an…
The human brain has been studied at multiple scales, from neurons, circuits, areas with well defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed…
Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a…
We consider the problem of maximizing the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. We first extend the well-known master stability formalism to the case of…
Self-organization and pattern formation in network-organized systems emerges from the collective activation and interaction of many interconnected units. A striking feature of these non-equilibrium structures is that they are often…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
In many natural synchronization phenomena, communication between individual elements occurs not directly, but rather through the environment. One of these instances is bacterial quorum sensing, where bacteria release signaling molecules in…
Today, complex networks have attracted increasing attention from various fields of science and engineering. It has been demonstrated that many complex networks display various synchronization phenomena. In this paper, we introduce a…
Different Boolean networks may reveal similar dynamics although their definition differs, then preventing their distinction from the observations. This raises the question about the sufficiency of a particular Boolean network for properly…
Despite their increasing popularity and success in a variety of supervised learning problems, deep neural networks are extremely hard to interpret and debug: Given and already trained Deep Neural Net, and a set of test inputs, how can we…
Funnelling effect, in the context of searching on networks, precisely indicates that the search takes place through a few specific nodes. We define the funnelling capacity $f$ of a node as the fraction of successful dynamic paths through it…