Attraction Basins as Gauges of Robustness against Boundary Conditions in Biological Complex Systems

One fundamental concept in the context of biological systems on which researches have flourished in the past decade is that of the apparent robustness of these systems, i.e., their ability to resist to perturbations or constraints induced by external or boundary elements such as electromagnetic fields acting on neural networks, micro-RNAs acting on genetic networks and even hormone flows acting both on neural and genetic networks. Recent studies have shown the importance of addressing the question of the environmental robustness of biological networks such as neural and genetic networks. In some cases, external regulatory elements can be given a relevant formal representation by assimilating them to or modeling them by boundary conditions. This article presents a generic mathematical approach to understand the influence of boundary elements on the dynamics of regulation networks, considering their attraction basins as gauges of their robustness. The application of this method on a real genetic regulation network will point out a mathematical explanation of a biological phenomenon which has only been observed experimentally until now, namely the necessity of the presence of gibberellin for the flower of the plant Arabidopsis thaliana to develop normally

A view of Neural Networks as dynamical systems

We consider neural networks from the point of view of dynamical systems theory. In this spirit we review recent results dealing with the following questions, adressed in the context of specific models. 1. Characterizing the collective dynamics; 2. Statistical analysis of spikes trains; 3. Interplay between dynamics and network structure; 4. Effects of synaptic plasticity.Comment: Review paper, 51 pages, 10 figures. submitte

Extensive neurosarcoidosis and optic nerve complications

We present the case of a 35-year-old patient suffering from nasal obstruction and headache for 3 years. The patient was hospitalized for a recent and progressive decline of vision of the right eye associated with afferent pupillary deficit and inferior altitudinal hemianopsia. He was diagnosed with systemic sarcoidosis involving the central nervous system as illustrated by magnetic resonance imaging (MRI) scans showing different type diffuse lesions of meningo-encephalitis. Our case is characterized by severe cerebral pachyleptomeningeal lesions complicated by optic nerve compression and cervical spinal cord damage. MRI value of diagnosis for systemic neurosarcoidosis was supported by histological examination of a biopsy of the sphenoid sinus lesions that showed epithelioid granulomas presence without caseous necrosis. Thus, MRI of the brain and spinal cord is a powerful tool method in monitoring and diagnosing aymptomatic and symptomatic neurosarcoïodosis. MRI is also a powerful tool in monitoring the neurosarcoidosis during therapeutic treatments

Spontaneous vertebral artery dissection presenting as symptomatic spinal subarachnoid haemorrhage

Spontaneous vertebral artery dissection presenting as symptomatic spinal subarachnoid haemorrhag