Related papers: Stability of Boolean Multilevel Networks
It has recently been suggested \cite{Radicchi2013} that in a two-level multiplex network, a gradual change in the value of the "interlayer" strength $p$ can provoke an abrupt structural transition. The critical point $p^*$ at which this…
In the analysis of the robustness of multiplex networks, it is commonly assumed that a node is functioning only if its interdependent nodes are simultaneously functioning. According to this model, a multiplex network becomes more and more…
We present a rigorous mathematical framework for analyzing dynamics of a broad class of Boolean network models. We use this framework to provide the first formal proof of many of the standard critical transition results in Boolean network…
Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…
The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…
The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability…
We propose a concept to generate and stabilize diverse partial synchronization patterns (phase clusters) in adaptive networks which are widespread in neuro- and social sciences, as well as biology, engineering, and other disciplines. We…
The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy…
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…
Our current world is linked by a complex mesh of networks where information, people and goods flow. These networks are interdependent each other, and present structural and dynamical features different from those observed in isolated…
We investigate the optimization of synchronizability in multiplex networks and demonstrate that the interlayer coupling strength is the deciding factor for the efficiency of optimization. The optimized networks have homogeneity in the…
Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…
Complex diseases can be modeled as damage to intracellular networks that results in abnormal cell behaviors. Network-based dynamic models such as Boolean models have been employed to model a variety of biological systems including those…
Recent developments in complex systems have witnessed that many real-world scenarios, successfully represented as networks are not always restricted to binary interactions but often include higher-order interactions among the nodes. These…
During the last few years an area of active research in the field of complex systems is that of their information storing and processing abilities. Common opinion has it that the most interesting beaviour of these systems is found ``at the…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
Inter-layer synchronization is a dynamical state occurring in multi-layer networks composed of identical nodes. The state corresponds to have all layers synchronized, with nodes in each layer which do not necessarily evolve in unison. So…
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…
For years, we have been building models of gene regulatory networks, where recent advances in molecular biology shed some light on new structural and dynamical properties of such highly complex systems. In this work, we propose a novel…