The consensus that complexity begets stability in ecosystems was challenged the seventies, a result recently extended to ecologically-inspired networks. approaches assume existence of feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show equilibrium feasibility vanishes species rich systems. This leaves us uncomfortable situation assumed local criteria is far from granted....

Calcium ions (Ca2+) are important mediators of a great variety cellular activities e.g. in response to an agonist activation receptor. The magnitude is often encoded by frequency modulation Ca2+ oscillations and correlated with the stimulation intensity. intensity highly depends on sensitivity cell certain agonist. In some cases, it essential that neighboring cells produce similar synchronized despite their different sensitivity. order decipher presumed function waves spreading among...

The topic of this thesis is the study several stochastic control problems motivated by sailing races. goal to minimize travel time between two locations, selecting fastest route in face randomly changing weather conditions, such as wind direction. When a sailboat travelling upwind, key decide when tack. Since maneuver slows down yacht, it natural model lost tacking penalty which places problem context optimal with switching costs. An objective work propose and mathematical models that...

This work studies the ultrasensitivity of multisite binding processes where ligand molecules can bind to several sites. It considers more particularly recent models involving complex chemical reactions in allosteric phosphorylation and for transcription factors nucleosomes competing on DNA. New statistics-based formulas Hill coefficient effective are provided necessary conditions a system be ultrasensitive exhibited. is first shown that approached using sharp-threshold theorems which have...

We formulate the optimal control problem for a sailboat that seeks to reach an upwind buoy, under hypothesis wind speed is constant and direction Brownian motion. The yacht moves in $\mathbb{R}^2$ target ball of radius $\eta \geq 0$ centered at origin. can be subject tacking cost $c\geq 0$. consider three problems depending on value parameters: first one corresponds case =0$, $c=0$, second >0$, third 0$, $c>0$. define problems, prove their function finite. guess strategy $A^\star$ $c=0$....

The consensus that complexity begets stability in ecosystems was challenged the seventies, a result recently extended to ecologically-inspired networks. approaches assume existence of feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show equilibrium feasibility vanishes species rich systems. This leaves us uncomfortable situation assumed local criteria is far from granted....

We study the ultrasensitivity of multisite binding processes where ligand molecules can bind to several sites, considering more particularly recent models involving complex chemical reactions in phosphorylation systems such as allosteric processes, or substrate-catalyst chain and nucleosome mediated cooperativity. New statistics based formulas for Hill coefficient effective are provided necessary conditions a system be ultrasensitive exhibited. then assume that process is described by...