Related papers: Dynamical Coarse Graining of Large Scale-Free Bool…
Partitioning large networks into stable clusters of synchronized nodes is a challenging task. Recent approaches based on spectral analysis can provide exact results on specific dynamics but remain unfeasible for very large networks.…
In this paper we study the phase transitions of different types of Random Boolean networks. These differ in their updating scheme: synchronous, semi-synchronous, or asynchronous, and deterministic or non-deterministic. It has been shown…
Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In…
We study coarse-grained (group-level) alignment dynamics of individual-based animal group models for {\it heterogeneous} populations consisting of informed (on preferred directions) and uninformed individuals. The orientation of each…
Hybrid multiscale modelling has emerged as a useful framework for modelling complex biological phenomena. However, when accounting for stochasticity in the internal dynamics of agents, these models frequently become computationally…
Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as…
Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…
In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…
Growing evidence suggests that synaptic weights in the brain follow heavy-tailed distributions, yet most theoretical analyses of recurrent neural networks (RNNs) assume Gaussian connectivity. We systematically study the activity of RNNs…
The success of deep neural networks in real-world problems has prompted many attempts to explain their training dynamics and generalization performance, but more guiding principles for the training of neural networks are still needed.…
While previous works have shown that an overwhelming number of scale-free networks are sparse, there still exist some real-world networks including social networks, urban networks, information networks, which are by observation dense. In…
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…
Coarse graining model is a promising way to analyze and visualize large-scale networks. The coarse-grained networks are required to preserve the same statistical properties as well as the dynamic behaviors as the initial networks. Some…
Understanding design principles of molecular interaction networks is an important goal of molecular systems biology. Some insights have been gained into features of their network topology through the discovery of graph theoretic patterns…
Many social, technological, biological, and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most…
Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the dynamics of the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in…
Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however,…
Gene regulatory networks exhibit remarkable stability, maintaining functional phenotypes despite genetic and environmental perturbations. Discrete dynamical models, such as Boolean networks, provide systems biologists with a tractable…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
This short paper presents an abstract, tunable model of genomic structural change within the cell lifecycle and explores its use with simulated evolution. A well-known Boolean model of genetic regulatory networks is extended to include…