Related papers: The Modular Structure of Kauffman Networks
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
An important part of the analysis of bio-molecular networks is to detect different functional units. Different functions are reflected in a different evolutionary dynamics, and hence in different statistical characteristics of network…
We study the dynamical properties of small regulatory networks treated as non autonomous dynamical systems called modules when working inside larger networks or, equivalently when subject to external signal inputs. Particular emphasis is…
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in…
Cooperative effects in neural networks appear because a neuron fires only if a minimal number $m$ of its inputs are excited. The multiple inputs requirement leads to a percolation model termed {\it quorum percolation}. The connectivity…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
Biological systems operate under persistent noise, which can alter system states and induce transitions between attractors. Here, we study the attractor dynamics of Boolean networks focusing on the transitions between attractors induced by…
We study experimentally the synchronization patterns in time-delayed directed Boolean networks of excitable systems. We observe a transition in the network dynamics when the refractory time of the individual systems is adjusted. When the…
The spontaneous formation and subsequent growth, dissolution, merger and competition of social groups bears similarities to physical phase transitions in metastable finite systems. We examine three different scenarios, percolation, spinodal…
We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number $b_t$ of nodes with value one, and the network sensitivity $\lambda$, and we…
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. Clustering, community structure and assortative mixing by degree are perhaps among most prominent…
In this paper we present a network model to study the impact of spatial distribution of constituents, coupling between them and diffusive processes in the context of biological situations. The model is in terms of network of mobile elements…
Robustness of two coupled networks system has been studied only for dependency coupling (S. Buldyrev et. al., Nature, 2010) and only for connectivity coupling (E. A. Leicht and R. M. D'Souza, arxiv:09070894). Here we study, using a…
A simple but powerful network model with $n$ nodes and $m$ partly overlapping layers is generated as an overlay of independent random graphs $G_1,\dots,G_m$ with variable sizes and densities. The model is parameterised by a joint…
A large variety of dynamical processes that take place on networks can be expressed in terms of the spectral properties of some linear operator which reflects how the dynamical rules depend on the network topology. Often such spectral…
We investigate structural transitions in adaptive networks where node states remain fixed and only the connections evolve via state-dependent rewiring. Using a general framework characterized by probabilistic rules for disconnection and…