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Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order…
A reaction system exhibits "absolute concentration robustness" (ACR) in some species if the positive steady-state value of that species does not depend on initial conditions. Mathematically, this means that the positive part of the variety…
This article offers a brief overview of the current research topics concerning strategies to mitigate the adverse effects of perturbations in complex networks. It addresses the issue of an unclear use of Robustness and Resilience…
Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…
The sensitivity (i.e. dynamic response) of complex networked systems has not been well understood, making difficult to predict whether new macroscopic dynamic behavior will emerge even if we know exactly how individual nodes behave and how…
We study stationary distributions in the context of stochastic reaction networks. In particular, we are interested in complex balanced reaction networks and reduction of such networks by assuming a set of species (called non-interacting…
In a recent article [1] we surveyed advances related to adaptation, learning, and optimization over synchronous networks. Various distributed strategies were discussed that enable a collection of networked agents to interact locally in…
In our previous work we have shown how Bayesian networks can be used for adaptive testing of student skills. Later, we have taken the advantage of monotonicity restrictions in order to learn models fitting data better. This article provides…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…
In this paper, we propose a new framework for synchronization of heterogeneous multi agent system which we refer to as weak synchronization. This new framework of synchronization is based on achieving the network stability in the absence of…
The capacity to resist attacks from the environment is crucial to the survival of all organisms. We quantitatively analyze the susceptibility of protein interaction networks of numerous organisms to random and malicious attacks. We find for…
Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an…
Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…
We present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of…
We consider damped elastodynamic networks where the damping matrix is assumed to be a non-negative linear combination of the stiffness and mass matrices (also known as Rayleigh or proportional damping). We give here a characterization of…
In systems and synthetic biology, much research has focused on the behavior and design of single pathways, while, more recently, experimental efforts have focused on how cross-talk (coupling two or more pathways) or inhibiting molecular…
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…