Related papers: Towards the Understanding of Stability Puzzles in …
We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems used in neural modelling.
The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations…
We investigate the equilibria of a random model network exhibiting extensive chaos. In this regime, a large number of equilibria is present. They are all saddles with low-dimensional unstable manifolds. Surprisingly, despite network's…
The concept of robustness of regulatory networks has been closely related to the nature of the interactions among genes, and the capability of pattern maintenance or reproducibility. Defining this robustness property is a challenging task,…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
The propagation of noise through parallel regulatory pathways is a characteristic feature of feed-forward loops in genetic networks. Although the contributions of the direct and indirect regulatory pathways of feed-forward loops to output…
A lack of software reproducibility has become increasingly apparent in the last several years, calling into question the validity of scientific findings affected by published tools. Reproducibility issues may have numerous sources of error,…
Complex evolving systems such as the biosphere, ecosystems and societies exhibit sudden collapses, for reasons that are only partially understood. Here we study this phenomenon using a mathematical model of a system that evolves under…
Based on a recently proposed non-equilibrium mechanism for spatial pattern formation [cond-mat/0312366] we study how morphogenesis can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches,…
Gamma-band rhythmic inhibition is a ubiquitous phenomenon in neural circuits yet its computational role still remains elusive. We show that a model of Gamma-band rhythmic inhibition allows networks of coupled cortical circuit motifs to…
We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare current versus fluctuations driven networks, the former (latter) is…
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…
Phage display is a powerful laboratory technique used to study the interactions between proteins and other molecules, whether other proteins, peptides, DNA or RNA. The under-utilisation of this data in conjunction with deep learning models…
Genetic regulatory networks are defined by their topology and by a multitude of continuously adjustable parameters. Here we present a class of simple models within which the relative importance of topology vs. interaction strengths becomes…
The stability of synchronous states is analysed in the context of two populations of inhibitory and excitatory neurons, characterized by different pulse-widths. The problem is reduced to that of determining the eigenvalues of a suitable…
Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present…