# Vinckenbosch Laura

### Professeure HES ordinaire, Responsable de la filière Economie d'entreprise (EE)

### Professeure HES ordinaire, Responsable de la filière Economie d'entreprise (EE)

Desktop: S142a

Route de Cheseaux 1, 1400 Yverdon-les-Bains, CH

- Mathématiques
- Statistiques

2018

*PLOS computational biology*,
2018,

**Summary:**

The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium feasibility vanishes in species rich systems. This result leaves us in the uncomfortable situation in which the existence of a feasible equilibrium assumed in local stability criteria is far from granted. We extend our analyses by changing interaction structure and intensity, and find that feasibility and stability is warranted irrespective of species richness with weak interactions. Interestingly, we find that the dynamical behaviour of ecologically inspired architectures is very different and richer than that of unstructured systems. Our results suggest that a general understanding of ecosystem dynamics requires focusing on the interplay between interaction strength and network architecture.

2017

*Journal of physics A: mathematical and theoretical*,
February 2017, vol. 50, no. 7

**Summary:**

This work studies the ultrasensitivity of multisite binding processes where ligand molecules can bind to several binding sites. It considers more particularly recent models involving complex chemical reactions in allosteric phosphorylation processes and for transcription factors and nucleosomes competing for binding on DNA. New statistics-based formulas for the Hill coefficient and the effective Hill coefficient are provided and necessary conditions for a system to be ultrasensitive are exhibited. It is first shown that the ultrasensitivity of binding processes can be approached using sharp-threshold theorems which have been developed in applied probability theory and statistical mechanics for studying sharp threshold phenomena in reliability theory, random graph theory and percolation theory. Special classes of binding process are then introduced and are described as density dependent birth and death process. New precise large deviation results for the steady state distribution of the process are obtained, which permits to show that switch-like ultrasensitive responses are strongly related to the multi-modality of the steady state distribution. Ultrasensitivity occurs if and only if the entropy of the dynamical system has more than one global minimum for some critical ligand concentration. In this case, the Hill coefficient is proportional to the number of binding sites, and the system is highly ultrasensitive. The classical effective Hill coefficient I is extended to a new cooperativity index Iq, for which we recommend the computation of a broad range of values of q instead of just the standard one I=I0.9 corresponding to the 10%–90% variation in the dose-response. It is shown that this single choice can sometimes mislead the conclusion by not detecting ultrasensitivity. This new approach allows a better understanding of multisite ultrasensitive systems and provides new tools for the design of such systems.

2016

**Summary:**

Calcium ions (Ca2+) are important mediators of a great variety of cellular activities e.g. in response to an agonist activation of a receptor. The magnitude of a cellular response is often encoded by frequency modulation of Ca2+ oscillations and correlated with the stimula-tion intensity. The stimulation intensity highly depends on the sensitivity of a cell to a certain agonist. In some cases, it is essential that neighboring cells produce a similar and synchro-nized response to an agonist despite their different sensitivity. In order to decipher the pre-sumed function of Ca2+ waves spreading among connecting cells, a mathematical model was developed. This model allows to numerically modifying the connectivity probability between neighboring cells, the permeability of gap junctions and the individual sensitivity of cells to an agonist. Here, we show numerically that strong gap junctional coupling between neighbors ensures an equilibrated response to agonist stimulation via formation of Ca2+ phase waves, i.e. a less sensitive neighbor will produce the same or similar Ca2+ signal as its highly sensitive neighbor. The most sensitive cells within an ensemble are the wave initia-tor cells. The Ca2+ wave in the cytoplasm is driven by a sensitization wave front in the endo-plasmic reticulum. The wave velocity is proportional to the cellular sensitivity and to the strength of the coupling. The waves can form different patterns including circular rings and spirals. The observed pattern depends on the strength of noise, gap junctional permeability and the connectivity probability between neighboring cells. Our simulations reveal that one highly sensitive region gradually takes the lead within the entire noisy system by generating directed circular phase waves originating from this region.

2015

**Summary:**

Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods in order to estimate the quantity of light that is received by a homogeneous tissue when emitted by an optic fiber. A variance reduction method is studied and implemented, as well as a Markov chain Monte Carlo method based on the Metropolis–Hastings algorithm. The resulting estimating methods are then compared to the so-called Wang–Prahl (or Wang) method. Finally, the formal representation allows to derive a non-linear optimization algorithm close to Levenberg–Marquardt that is used for the estimation of the scattering and absorption coefficients of the tissue from measurements.

2014

**Summary:**

We solve two stochastic control problems in which a player tries to minimize or maximize the exit time from an interval of a Brownian particle, by controlling its drift. The player can change from one drift to another but is subject to a switching cost. In each problem, the value function is written as the solution of a free boundary problem involving second order ordinary differential equations, in which the unknown boundaries are found by applying the principle of smooth fit. For both problems, we compute the value function, we exhibit the optimal strategy and we prove its generic uniqueness.

Achievements