Gilles Wainrib
Assistant Professor at Département d'Informatiqueteam DATA, Ecole Normale Supérieure (Paris, France).
Email : gilles.wainrib [at]


Recent preprints & publications

Branching random walks on binary strings and application to adaptive immunity
I. Balelli, V. Milisic and G. Wainrib, submitted [arxiv]

During the germinal center reaction, B lymphocytes proliferate, mutate and differentiate, while being submitted to a powerful selection, creating a micro-evolutionary mechanism at the heart of adaptive immunity. We introduce and analyze a simplified mathematical model of the division-mutation process, by considering random walks and branching random walks on graphs, whose structure reflects the associated mutation rules. In particular, we investigate how the combination of various division and mutation models influences the typical time-scales characterizing the efficiency of state space exploration for these processes, such as hitting times and cover times. Beyond the initial biological motivation, this framework is not limited to the modelling of B-cell learning process in germinal centers, as it may be relevant to model other evolutionary systems, but also information propagation in networks, gossip models or epidemic processes.

The real Ginibre ensemble with k=0(n) real eigenvalues
L.C. Garcia del Molino, K. Pakdaman, J.Touboul and G. Wainrib, submitted [arxiv]

We consider the ensemble of Real Ginibre matrices with a positive fraction α > 0 of real eigenvalues. We demonstrate a large deviations principle for the joint eigenvalue density of such matrices and we introduce a two phase log-gas whose stationary distribution coincides with the spectral measure of the ensemble. Using these tools we provide an asymptotic expansion for the probability pnαn that an n × n Ginibre matrix has k = αn real eigenvalues and we characterize the spectral measures of these matrices. 

Mathematical modeling of lymphocytes selection in the germinal center
V.Milisic and G.Wainrib, submitted [arxiv]

Lymphocyte selection is a fundamental operation of adaptive immunity. In order to produce B-lymphocytes with a desired antigenic profile, a process of mutation-selection occurs in the germinal center, which is part of the lymph nodes. We introduce in this article a simplified mathematical model of this process, taking into account the main mechanisms of division, mutation and selection. This model is written as a non-linear, non-local, inhomogeneous second order partial differential equation, for which we develop a mathematical analysis in the case of piecewise-constant coefficients. We assess,  mathematically and numerically, the performance of the biological function by evaluating the duration of this production process as a function of several parameters such as the mutation rate or the selection profile, in various asymptotic regimes.

Network modeling of Crohn's disease
Jean-Marc Victor, Gaëlle Debret, Annick Lesne, Leigh Pascoe, Pascal Carrivain, Gilles Wainrib, Jean-Pierre Hugot, submitted.

Crohn's Disease (CD) is a complex genetic disorder related to genetic and environmental risk factors. We modelled the disease as a modular network of patho-physiological functions, each summarizing gene-environment interactions. The disease resulted from one or few specific combinations of the modules' functional states. Network aging dynamics was able to reproduce age-specific CD incidence curves and their variations over the past century in Western countries. The model allowed translating the Odds Ratios associated to at-risk alleles in terms of disease propensities of the functional modules. Finally, this modelling was successfully applied to other complex genetic disorders including ulcerative colitis, ankylosing spondylarthritis, multiple sclerosis and schizophrenia.

Research Interests

Probability theory / Dynamical systems

- limit theorems
- large deviations
- piecewise-deterministic Markov processes
- singular perturbations
- averaging principles
- stochastic bifurcations
- random matrix theory
- random walk on graphs
- partial differential equations
- random fields

Applications in theoretical biology / computer science

- Hodgkin Huxley models with stochastic ion channels
- Action potential generation and propagation
- Information transmission
- Noise-induced phenomena
- Synchronization
- Synaptic plasticity and learning
- Random neural networks
- Links with machine learning, reservoir computing
- Immune system modeling
- Gene regulatory networks

My collaborators

Vuk Milisic
Hatem Zaag

Contact information

Laboratoire Analyse Géométrie et Applications (LAGA) 
Institut Galilée
Université Paris 13
99, avenue Jean-Baptiste Clément
93430 - Villetaneuse

Bureau D 306
Tel : 01 49 40 35 83
Fax : 01 49 40 35 68

Email : wainrib [at]

Recent Announcements

  • new affiliation -> new email !! my new e-mail adress is wainrib [at]
    Posted Sep 20, 2011, 7:30 AM by Gilles Wainrib
  • New email adress My new email adress is:gwainrib [at]
    Posted Sep 8, 2010, 11:00 AM by Gilles Wainrib
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