Related papers: Binary threshold networks as a natural null model …
A mathematical model for a two-gene regulatory network is derived and several of their properties analyzed. Due to the presence of mixed continuous/discrete dynamics and hysteresis, we employ a hybrid systems model to capture the dynamics…
Random Boolean networks (RBNs) are models of genetic regulatory networks. It is useful to describe RBNs as self-organizing systems to study how changes in the nodes and connections affect the global network dynamics. This article reviews…
We consider a process where a spin hops across a discrete network and at certain sites couples to static spins. While this setting is implementable in various scenarios (e.g quantum dots or coupled cavities) the physics of such processes is…
A dynamical system approaching the first-order transition can exhibit a specific type of critical behavior known as self-organized bistability (SOB). It lies in the fact that the system can permanently switch between the coexisting states…
We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great…
A four-node network consisting of a negative loop controlling a positive one is studied. It models some of the features of the p53 gene network. Using piecewise linear dynamics with thresholds, the allowed dynamical classes are fully…
We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a network's level of dilution and asymmetry. The network…
Neural networks storing multiple discrete attractors are canonical models of biological memory. Previously, the dynamical stability of such networks could only be guaranteed under highly restrictive conditions. Here, we derive a theory of…
We study a neural network model of interacting stochastic discrete two--state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective…
The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links, the average eccentricity and…
A random null model termed the Blind Watchmaker network (BW) has been shown to reproduce the degree distribution found in metabolic networks. This might suggest that natural selection has had little influence on this particular network…
Network structure can have significant effects on the propagation of diseases, memes, and information on social networks. Such effects depend on the specific type of dynamical process that affects the nodes and edges of a network, and it is…
Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…
We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…
The interactions between proteins, DNA, and RNA in living cells constitute molecular networks that govern various cellular functions. To investigate the global dynamical properties and stabilities of such networks, we studied the cell-cycle…
Novel computing hardwares are necessary to keep up with today's increasing demand for data storage and processing power. In this research project, we turn to the brain for inspiration to develop novel computing substrates that are…
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…
In a social network individuals or nodes connect to other nodes by choosing one of the channels of communication at a time to re-establish the existing social links. Since available data sets are usually restricted to a limited number of…
We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the…
We study the dynamics of gene activities in relatively small size biological networks (up to a few tens of nodes), e.g. the activities of cell-cycle proteins during the mitotic cell-cycle progression. Using the framework of deterministic…