2025Activity reportProject-Team​​SIMBA

3.1.1 Links‌ between macroscopic models and‌​‌ stochastic microscopic processes

For​​ multiscale models, it is​​​‌ often relevant to distinguish‌ what could be called‌​‌ the microscopic level (i.e.​​ the level of single​​​‌ individuals), the macroscopic level‌ (i.e. the level of‌​‌ large population densities) or​​ the intermediate mesoscopic level​​​‌ (i.e. a level of‌ population densities, but where‌​‌ demographic stochasticity cannot be​​ neglected). Microscopic models can​​​‌ be for example stochastic,‌ individual-based models, mesoscopic models‌​‌ can be SDEs and​​ macroscopic models are usually​​​‌ models of population densities,‌ such as ODEs, PDEs‌​‌ or PDMPs. Many biological​​ questions are stated at​​​‌ the macroscopic level, and‌ the main modeling issue‌​‌ lies in the appropriate​​ way to incorporate meso-​​​‌ or microscopic features in‌ the description of the‌​‌ macroscopic scale.

Typically, individual-based​​ models are models where​​​‌ the population state at‌ time $t$ is described‌​‌ as a counting measure​​ ${\nu }_t={\sum ‌}_{i=1}^{{\mathrm{N‌}}_t}{\delta }_{x_{\mathrm{i‌‌}}\left(t\right)}$ where​​ $N_t$ is the​​​‌ number of individuals alive‌ at time $t$,‌​‌ and $x_i(t)$ is the​​​‌ characteristic of the $\mathrm{i‌}$-th individual (e.g. phenotype,‌​‌ mass, size, length of​​​‌ telomeres, age...), belonging to​ some set $𝒳$.​‌ The dynamics is strongly​​ dependent on the precise​​​‌ phenomenon to be modeled,​ but in the simplest​‌ cases, ${\left({\nu }_{\mathrm{t}}\right)}_{t\ge \mathrm{0‌}}$ is a Markov jump​ process on point measures​‌ on $𝒳$ whose infinitesimal​​ generator has the following​​​‌ form:

where $b(‌x,\nu ;dy)$ is​​​‌ the infinitesimal birth rate​ of an individual $\mathrm{y‌}$ from an individual $\mathrm{x}$ in the population $\mathrm{\nu ‌}$ and $d(\mathrm{x},\nu )$ is​‌ the death rate of​​ an individual $x$ in​​​‌ the population $\nu$.​

We have developed a​‌ strong expertise in the​​ derivation of simplified macroscopic​​​‌ models from complex microscopic​ effects when there is​‌ a strong separation between​​ time and/or space scales.​​​‌ Mathematically, this requires us​ to encode the scale​‌ separation through scaling parameters​​ and to solve an​​​‌ asymptotic analysis problem, which​ can be averaging (slow-fast​‌ dynamics, singular perturbation) 57​​, 2, homogeneization​​​‌ 48, 65,​ concentration limits 52,​‌ 55, 56 or​​ more generally parameter scaling​​​‌ problems where the scaling​ parameter has a biological​‌ meaning 54, 49​​. For individual-based models,​​​‌ the simplest parameter scaling​ that can be considered​‌ is a large population​​ asymptotic encoded with a​​​‌ parameter $K$, where​ the state of the​‌ population is modified as​​ ${\nu }_t^K=‌\frac{1}{K}{\sum }_{\mathrm{i}=1}^{N_{\mathrm{t‌}}}{\delta }_{x_i(t)}$ and the​​​‌ generator (1)​ as

leading to mean-field​​​‌ macroscopic models when $\mathrm{K}\to \infty$ 54.​‌ More complex scalings can​​ involve rare or small​​​‌ mutations combined with long-time​ scalings, complex local interactions​‌ as in 48 or​​ multiscale phenomena (e.g. within​​​‌ cell dynamics combined with​ the dynamics of populations​‌ of cells, like for​​ telomeres). Each problem usually​​​‌ requires new methodological development.​

3.1.2 Numerical analysis

Sometimes,​‌ it is not possible​​ to construct a simplified​​​‌ macroscopic description of complex,​ multiscale biological phenomena. In​‌ such cases, we need​​ to rely on numerical​​​‌ simulations. More generally, numerical​ simulations are very helpful​‌ to supply a priori​​ information on phenomena that​​ are difficult to reproduce​​​‌ in laboratory experiments or‌ on large-scale models that‌​‌ involve several interacting elements.​​

Despite increasing computing facilities,​​​‌ existing numerical schemes are‌ rarely adapted to individual-based‌​‌ models. Better numerical approaches​​ based on a deeper​​​‌ understanding of their multiscale‌ features would significantly reduce‌​‌ computational costs and yield​​ reliable error estimates. This​​​‌ is one of our‌ motivations in studying model‌​‌ reduction through asymptotic analysis​​ as described above. We​​​‌ propose to design numerical‌ schemes taking into account‌​‌ local extinction or local​​ deterministic approximation, or develop​​​‌ hybrid methods relying on‌ duality methods based e.g.‌​‌ on the Poisson representation​​ of birth and death​​​‌ processes, which allows to‌ switch between microscopic and‌​‌ mesoscopic models when the​​ population size crosses a​​​‌ threshold.

3.2.1 Statistical learning, regression‌

We want to develop‌​‌ methodologies that take into​​ account the specificities of​​​‌ biological data: they are‌ often high dimensional and‌​‌ correlated (for instance multiomics​​ data, such as genome,​​​‌ proteome or transcriptome) but‌ with few observations (patients)‌​‌ and with missing data.​​ Variable selection is of​​​‌ particular interest to study‌ the link between an‌​‌ outcome (the occurence of​​ an illness for instance)​​​‌ with covariates or to‌ infer partial correlations between‌​‌ several variables for instance​​ to study quantitative microbiome​​​‌ data. For instance, in‌ variable selection, we propose‌​‌ to study the theoretical​​ guarantees of our methods​​​‌ 42, 72 and‌ to extend them to‌​‌ other models of dependencies​​ such as mixtures of​​​‌ quantitative or qualitative covariates‌ with dependencies between the‌​‌ covariates. In regression, we​​ wish to tackle the​​​‌ challenge not only to‌ select the covariates related‌​‌ to an event (illness,​​ death...), but also to​​​‌ understand which configuration of‌ these covariates triggers its‌​‌ occurrence.

We also develop​​ goodness-of-fit tests to assess​​​‌ the different assumptions of‌ a (possibly heteroscedastic) regression‌​‌ model. Most of them​​ are “directional” in that​​​‌ they detect departures from‌ a given assumption of‌​‌ the model. Other tests​​ are “omnibus” in that​​​‌ they assess whether a‌ model fits a dataset‌​‌ on all its assumptions.​​ We focus on the​​​‌ task of choosing the‌ structural part of the‌​‌ regression function because it​​ contains easily interpretable information​​​‌ about the studied relationship.‌ Among the large number‌​‌ of existing tests, we​​ consider nonparametric tests which​​​‌ are all based on‌ generalizations of the Cramér-von‌​‌ Mises statistic. To perform​​​‌ these goodness-of-fit tests, we​ develop the R package​‌ cvmgof41, 1​​, an easy-to-use tool​​​‌ which allows practitioners to​ compare the implemented tests.​‌ In the future, we​​ plan to enrich the​​​‌ cvmgof package with tests​ concerning the other assumptions​‌ of a regression model​​ such as the functional​​​‌ form of the variance​ or the additivity of​‌ the random error term,​​ using directional tests such​​​‌ as 67. Another​ perspective is to develop​‌ a similar tool for​​ other statistical models widely​​​‌ used in biostatistics such​ as generalized linear models.​‌

3.2.2 Signal or online​​ data analysis

We develop​​​‌ tools for the analysis​ of online data, which​‌ are now very frequent​​ in the health domain​​​‌ (recording of cardiac signals,​ physiological measurements via connected​‌ objects...). The purpose is​​ either the update of​​​‌ estimation parameters for models​ with sequential arrival of​‌ new data, or the​​ online detection of change-points​​​‌ in temporal signals. For​ the first purpose, stochastic​‌ algorithms are essential tools​​ 50, which allow​​​‌ one to approximate eigenvectors​ in a stepwise manner​‌ 83, 82,​​ 86. We focus​​​‌ on several incremental procedures​ for regression and data​‌ analysis like PCA (Principal​​ Component Analysis) 84 and​​​‌ linear and logistic regressions​ on standardised data in​‌ order to avoid numerical​​ explosion 78. Our​​​‌ aim is to apply​ these results to other​‌ methods related to PCA,​​ such as multiple factorial​​​‌ analyses, partial PCA, and​ to learning (classification, regression,​‌ event scores).

Change-point detection​​ is of particular interest​​​‌ in e-health, for example​ for detecting changes in​‌ the health status of​​ the elderly or people​​​‌ at risk of a​ disease. We plan to​‌ develop tools for online​​ change-point detection using score-based​​​‌ CUSUM statistics. Our aim​ is to use the​‌ beginning of the signal​​ to build simulation-based thresholds​​​‌ that have to be​ crossed for the detection​‌ of the change-point. We​​ also want to propose​​​‌ new stopping rules adapted​ to the characteristics of​‌ the signal. These questions​​ may be relevant for​​​‌ a large part of​ the applications we shall​‌ develop with physicians.

3.2.3​​ Network inference

Inferring networks​​​‌ from data is often​ a crucial step for​‌ understanding biological interactions, such​​ as regulatory links between​​​‌ genes within individual cells​ 73, 47 or​‌ communication relationships between bacteria​​ within a population.

Concerning​​​‌ gene regulatory networks, we​ are interested in so-called​‌ single-cell data, where mRNA​​ levels are measured individually​​​‌ in many cells rather​ than being population-averaged, revealing​‌ the intrinsically stochastic “transcriptional​​ bursting” phenomenon. In previous​​​‌ work 73, we​ described a promising strategy​‌ in which the network​​ inference problem is seen​​​‌ as a calibration procedure​ for a PDMP model​‌ that is able to​​ fit real single-cell data​​​‌ 10. In the​ simplest version of this​‌ model, the state of​​ each gene $i\in ‌\{1,...,n\}$ at​‌ time $t$ is described​​ by its promoter state​​​‌ $E_i\left(\mathrm{t}\right)\in \{\mathrm{0‌},1\}$,​​ the quantity of transcribed​​ RNA $Y_i(‌t)\in {\mathrm{ℝ‌}}_{+}$ and of translated‌​‌ proteins $X_i(t)\in {\mathrm{ℝ‌}}_{+}$, where

Interactions between genes in​​​‌ the network are encoded‌ in functions $k_{\text{on‌‌},i}\left(\mathrm{x}\right)\ll k_{\text{off‌},i}$ which correspond‌ to burst frequencies. We‌​‌ plan to develop dynamical​​ models that fully exploit​​​‌ the particular time structure‌ of the data: as‌​‌ cells have to be​​ killed for measurements, such​​​‌ data do not consist‌ of cell trajectories but‌​‌ rather independent samples of​​ time-varying multivariate distributions. As​​​‌ the number of genes‌ can be large (‌​‌$\approx 2\times {\mathrm{10}}^5$ in humans), we​​​‌ will also investigate variational‌ methods, which generalize the‌​‌ usual expectation-maximization (EM) algorithm,​​ as a relevant way​​​‌ to make the inference‌ procedure both robust and‌​‌ scalable.

We also develop​​ methods to infer gene​​​‌ networks from dynamic gene‌ expression data within a‌​‌ collaboration with CHRU Strasbourg.​​ The goal here is​​​‌ to design new models‌ and inference methods adapted‌​‌ to the prediction of​​ the outcome of biological​​​‌ intervention experiments such as‌ “gene knock-down”, in order‌​‌ to identify therapeutic targets​​ that could be experimentally​​​‌ studied.

3.2.4 Inference for‌ stochastic processes

In our‌​‌ collaborations with practitioners, we​​ are led to infer​​​‌ specific quantities of interest‌ for stochastic dynamical models‌​‌ of various classes, such​​ as the speed of​​​‌ telomere shortening using multitype‌ branching processes; the growth‌​‌ rate of clonal populations​​ and their phylogenetic tree​​​‌ using heterogeneous population growth‌ models in cancer; links‌​‌ between gene expressions using​​ PDMPs or the speed​​​‌ of propagation of fungi‌ using stochastic models with‌​‌ latent variables given by​​ the solution of a​​​‌ partial differential equation (see‌ our main applications in‌​‌ Section 4). For​​ all these sophisticated stochastic​​​‌ processes, statistical inference raises‌ many open, difficult questions.‌​‌ In particular, we plan​​ to develop inference tools​​​‌ for general classes of‌ models such as PDMP,‌​‌ bifurcating Markov processes or​​ branching processes. More generally,​​​‌ the inference of dynamical‌ models relies strongly on‌​‌ their long-time behavior, for​​ which the team has​​​‌ a strong expertise (see‌ Section 3.3). Most‌​‌ often in biology, models​​ rely on latent variables,​​​‌ that may follow complex‌ dynamics as in the‌​‌ examples above. The inference​​ of this kind of​​​‌ models requires us to‌ develop efficient Bayesian algorithms,‌​‌ EM like algorithms and​​ variational methods.

3.3.1 Links between macroscopic​‌ and microscopic eco-evolutionary models​​

We develop here similar​​​‌ ideas as in Section​ 3.1.1, but the​‌ mathematical questions are of​​ different nature for models​​​‌ of tumor growth in​ medicine than for population​‌ models in ecology or​​ evolution, because in the​​​‌ first case one wants​ to capture transitory behavior​‌ (e.g., in growing populations​​ for tumor growth), whereas​​​‌ in the second case,​ one usually models long​‌ term evolution assuming that​​ the ecological dynamics is​​​‌ in a stationary (quasi-equilibrium)​ state and that evolution​‌ acts slowly.

In addition​​ to the various classes​​​‌ of models described in​ Section 3.1.1, which​‌ are also relevant for​​ ecology and evolution, some​​​‌ other types of models​ are well-developed in these​‌ domains, such as Dawson–Watanabe​​ processes 62, Fleming–Viot​​​‌ processes 68 or a​ particular class of PDMPs​‌ called switched dynamical systems​​ used to model abruptly​​​‌ changing environments. The general​ goal of designing macroscopic​‌ models from complex multiscale​​ models through parameter scalings​​​‌ extends to these new​ classes of models. For​‌ example, Fleming-Viot processes appear​​ as the fast dynamics​​​‌ in the long term​ evolution of biological populations​‌ under assumptions of small​​ mutations and large population​​​‌ 2.

In ecology,​ our motivations are to​‌ highlight the biological assumptions​​ underlying different classes of​​​‌ macroscopic models, or to​ take into account at​‌ the macroscopic scale complex​​ local interactions between individuals.​​​‌ In evolutionary biology, the​ time scales involved are​‌ so long that it​​ is hard to observe​​​‌ experimentally evolutionary phenomena such​ as diversification. Mathematical analysis​‌ of models is therefore​​ of great importance, e.g.​​​‌ to construct approximate models​ allowing to predict long​‌ term evolution of biological​​ populations.

3.3.2 Adaptive dynamics:​​​‌ concentration limits

Asymptotic analysis​ is particularly useful in​‌ the branch of evolutionary​​ biology called adaptive dynamics​​​‌. This biological theory​ which studies the interplay​‌ between ecological interactions and​​ long term evolution was​​​‌ developed in the mid​ 90's 80, 63​‌ and provides theoretical ecologists​​ with useful tools to​​​‌ deduce evolutionary patterns from​ ecological parameters (directional evolution​‌ through canonical equations and​​ diversification through evolutionary branching​​​‌).

So far, two​ mathematical approaches to justify,​‌ study and improve these​​ tools have been developed:​​​‌ a deterministic one, based​ on PDE models 64​‌, 88, 79​​ and a probabilistic one,​​​‌ based on individual-based models​ 52, 56.​‌ Both approaches are concentration​​ limits, aiming to construct​​​‌ approximate models where population​ densities are replaced by​‌ Dirac masses representing coexisting​​ sub-populations. They both can​​ be seen as particular​​​‌ parameter scalings on individual-based‌ models of the form‌​‌ (2), combining​​ large population scaling with​​​‌ scalings of rare mutations‌ and/or small mutations.

However,‌​‌ the adaptive dynamics toolbox​​ and the existing mathematical​​​‌ approaches are criticized because‌ they are based on‌​‌ unrealistic biological assumptions on​​ the scales involved in​​​‌ the process 92,‌ 89. Mathematical analysis‌​‌ is needed both to​​ quantify the underlying assumptions​​​‌ on scales and to‌ propose alternative models based‌​‌ on more realistic assumptions.​​ For example, we plan​​​‌ to design PDE models‌ of adaptive dynamics allowing‌​‌ for local extinctions of​​ populations 74, 81​​​‌. Similarly, the actual‌ occurrence of evolutionary branching‌​‌ in sexual populations is​​ debated 92 and our​​​‌ goal is to shed‌ light on these questions‌​‌ using asymptotic analysis starting​​ from individual-based models.

3.3.3​​​‌ Population dynamics with absorption‌ and quasi-stationary distributions

In‌​‌ conservation biology, it is​​ fundamental to quantify the​​​‌ chances of survival of‌ species in a given‌​‌ environment. In addition, the​​ observed biological populations are​​​‌ intrinsically conditioned to be‌ non-extinct, which introduces an‌​‌ observation bias that is​​ rarely taken into account.​​​‌ For a given model‌ of population dynamics, it‌​‌ is therefore important to​​ develop tools allowing to​​​‌ study the population size‌ before extinction and to‌​‌ quantify its extinction probability​​ in a given time​​​‌ window. When the population‌ size is stable during‌​‌ long time intervals before​​ extinction, it can be​​​‌ described by a quasi-stationary‌ distribution (QSD), defined as‌​‌ a stationary distribution conditionally​​ on non-extinction. The QSD​​​‌ also allows to quantify‌ the population extinction rate.‌​‌

Our research program on​​ this topic builds on​​​‌ recent works of the‌ team 59, 4‌​‌, where we developed​​ probabilistic criteria for the​​​‌ large time convergence of‌ conditional distributions of stochastic‌​‌ population processes, that proved​​ to apply to a​​​‌ wide range of stochastic‌ processes. These works open‌​‌ many perspectives. We focus​​ here on the methodological​​​‌ ones and will mention‌ some numerical issues in‌​‌ Section 3.3.4 below. A​​ first question is to​​​‌ obtain criteria for the‌ convergence of conditional distributions‌​‌ for weaker distances than​​ in 59, 4​​​‌: instead of the‌ total variation distance, we‌​‌ study convergence in Wasserstein​​ distances. This is particularly​​​‌ relevant for PDMPs or‌ for infinite dimensional processes‌​‌ such as individual-based models,​​ where coupling properties are​​​‌ not strong enough to‌ expect convergence in total‌​‌ variation. We also want​​ to study other questions​​​‌ related to QSDs: Can‌ we characterize the speed‌​‌ of convergence of conditional​​ distributions to a QSD?​​​‌ Is it possible to‌ study the path to‌​‌ extinction of a stochastic​​ population process, in order​​​‌ to characterize the parameters‌ improving their survival (e.g.‌​‌ for protected species) or​​ their extinction (e.g. for​​​‌ pests in agronomy)? What‌ can be said about‌​‌ the genealogy of populations​​ before extinction?

3.3.4 Numerical​​​‌ analysis

The challenges detailed‌ here are related to‌​‌ those described in Section​​ 3.1.2. Ecological or​​​‌ evolutionary models pose specific‌ numerical problems that we‌​‌ want to tackle. For​​​‌ example, in the numerical​ simulation of individual-based models​‌ like (1),​​ when the population size​​​‌ is small, randomness cannot​ be neglected and exact​‌ algorithms have to be​​ used; when the population​​​‌ size is large, such​ algorithms become too costly​‌ and one would like​​ to take advantage of​​​‌ deterministic approximations like those​ we developed in 53​‌, 70. The​​ error analysis of such​​​‌ hybrid numerical schemes is​ difficult 40, 76​‌ and the case of​​ spatially or trait-structured individual-based​​​‌ models is still largely​ open.

We are also​‌ interested in numerical methods​​ to approximate QSDs, among​​​‌ which the most developed​ are particle methods 91​‌, 58 and stochastic​​ algorithms such as self-interacting​​​‌ processes 44, 43​. The analysis of​‌ these algorithms relies on​​ long-time analysis of particle​​​‌ or nonlinear systems and​ our research project on​‌ QSDs detailed above will​​ be of great help.​​​‌ In particular, Wasserstein distances​ are known to be​‌ well adapted to the​​ study of convergence of​​​‌ particle systems thanks to​ their tensorization properties. We​‌ also plan to develop​​ new numerical approaches based​​​‌ on the stationary distribution​ of approximating processes, such​‌ as those obtained by​​ central limit theorems for​​​‌ stochastic processes 60.​

4.1.1​​​‌ Reconstruction of tumor heterogeneity​

Targeted therapies represent a​‌ real advance in the​​ treatment of patients with​​​‌ cancer. Most of these​ therapies are kinase inhibitors​‌ and require precise analysis​​ of tumor DNA mutations​​​‌ to ensure the absence​ of primary resistance. Indeed,​‌ tumors are often genetically​​ heterogeneous with the presence​​​‌ of many subclones, but​ they release “circulating” cell-free​‌ DNA (cfDNA) that can​​ be directly extracted from​​​‌ basic blood samples: as​ measurement sensitivity improves, such​‌ liquid biopsies increasingly appear​​ as a mirror of​​​‌ tumor heterogeneity. In this​ context, we are taking​‌ a promising statistical approach​​ to analyze longitudinal cfDNA​​​‌ data, with the purpose​ of gaining a deeper​‌ understanding of the mechanism​​ by which resistance develops​​​‌ in individual patients. While​ addressing the standard problem​‌ of reconstructing the associated​​ phylogenetic tree, this approach​​​‌ also describes the production​ of cfDNA from the​‌ temporal dynamics of cells,​​ in order to best​​​‌ exploit the longitudinal structure​ of the data. This​‌ is a project in​​ collaboration with physicians Jean-Louis​​​‌ Merlin (Institut de Cancérologie​ de Lorraine), Alexandre Harlé​‌ (Institut de Cancérologie de​​ Lorraine) and Erwan Pencreac'h​​ (CHRU Strasbourg). We currently​​​‌ also have another ongoing‌ project on a tumor‌​‌ heterogeneity reconstruction for chronic​​ lymphocytic leukemia in collaboration​​​‌ with Laurent Vallat (CHRU‌ Strasbourg).

4.1.2 Evolution of‌​‌ low-grade gliomas

We have​​ an ongoing collaboration with​​​‌ the Centre de Recherche‌ en Automatique de Nancy‌​‌ CRAN (Jean-Marie Moureaux) and​​ neuro-oncologist and surgeon from​​​‌ CHRU Nancy (Luc Taillandier,‌ Fabien Rech) about diffuse‌​‌ low-grade gliomas (DLGG). These​​ are slow-growing tumors that​​​‌ are often asymptomatic for‌ a long period of‌​‌ time. They progress to​​ a higher grade, resulting​​​‌ in the patient's death.‌ The current treatment strategy‌​‌ aims to surgically reduce​​ tumor volume as soon​​​‌ as possible. As DLGGs‌ infiltrate functional areas, surgery‌​‌ is performed in an​​ awake state, with active​​​‌ patient participation, while electrical‌ brain stimulations are done,‌​‌ to identify functional structures.​​ At CHRU Nancy, surgeries​​​‌ are filmed, but the‌ patient's responses are recorded‌​‌ manually. We aim to​​ develop an automatic tool​​​‌ to detect, analyse and‌ register the patients responses.‌​‌ We use deep learning​​ algorithms for motion and​​​‌ speech detection. In perspective,‌ the fine anomalies that‌​‌ can be identified are​​ likely to be correlated​​​‌ with the patient's short-‌ and long-term cognitive outcome.‌​‌

4.3.1​‌ Modeling gene expression at​​ single-cell level

Gene expression​​​‌ in cells has long​ been only observable through​‌ averaged quantities over cell​​ populations. The development of​​​‌ single-cell transcriptomics has enabled​ gene expression to be​‌ measured in individual cells:​​ it turns out that​​​‌ even for an isogenic​ population located in a​‌ homogeneous medium, molecular variability​​ can be large. An​​​‌ average description is therefore​ not sufficient to account​‌ for fundamental phenomena such​​ as cell differentiation. Recently,​​​‌ a view emerged that​ the dynamics governing the​‌ switching of cells from​​ one differentiation state to​​​‌ another could be characterized​ by a peak in​‌ gene expression variability at​​ the point of fate​​​‌ commitment 90. We​ are continuing on this​‌ path, working on the​​ link between PDMP models​​​‌ and notions of entropy​ and epigenetic landscape.

4.3.2​‌ Transcriptional bursting in regulatory​​ networks

Working in the​​​‌ active field of single-cell​ dynamics and gene regulatory​‌ networks provides opportunities to​​ interact with biologists such​​​‌ as Olivier Gandrillon from​ ENS Lyon 90,​‌ 77, and potentially​​ also physicians such as​​​‌ Erwan Pencreac'h in CHRU​ Strasbourg. The biological literature​‌ increasingly highlights gene regulatory​​ networks as playing an​​​‌ important role (independent of​ genetic mutations) in the​‌ acquisition of resistance to​​ cancer treatments, hence this​​​‌ topic might become soon​ also relevant to the​‌ application area of oncology.​​

4.3.3 Prediction and identification​​​‌ of therapeutic targets for​ chronic lymphocytic leukemia

In​‌ an ongoing collaboration with​​ Laurent Vallat (CHRU Strasbourg),​​​‌ we develop new models​ and inference methods for​‌ gene regulation networks allowing​​ to make prediction of​​​‌ biological intervention experiments (such​ as gene knock-down). Inference​‌ is performed on gene​​ expression data from cells​​ of patients suffering from​​​‌ different forms of chronic‌ lymphocytic leukemia. The goal‌​‌ is to use prediction​​ to identify therapeutic targets​​​‌ which could be knocked-down‌ to reduce the cells'‌​‌ proliferation. Biological experiments will​​ be performed by Laurent​​​‌ Vallat and his group‌ to assess the therapeutic‌​‌ potential of the new​​ targets.

6.1.1 cvmgof

• Keywords:
  Regression,‌​‌ Test, Estimators
• Scientific Description:​​
  Many goodness-of-fit tests have​​​‌ been developed to assess‌ the different assumptions of‌​‌ a (possibly heteroscedastic) regression​​ model. Most of them​​​‌ are "directional" in that‌ they detect departures from‌​‌ a given assumption of​​ the model. Other tests​​​‌ are "global" (or "omnibus")‌ in that they assess‌​‌ whether a model fits​​ a dataset on all​​​‌ its assumptions. cvmgof focuses‌ on the task of‌​‌ choosing the structural part​​ of the regression function​​​‌ because it contains easily‌ interpretable information about the‌​‌ studied relationship. It implements​​ 2 nonparametric "directional" tests​​​‌ and one nonparametric "global"‌ test, all based on‌​‌ generalizations of the Cramer-von​​ Mises statistic.
• Functional Description:​​​‌
  cvmgof is an R‌ library devoted to Cramer-von‌​‌ Mises goodness-of-fit tests. It​​ implements three nonparametric statistical​​​‌ methods based on Cramer-von‌ Mises statistics to estimate‌​‌ and test a regression​​ model.
• URL:
  https://­cran.­r-project.­org/­web/­packages/­cvmgof/­index.­html
• Publication:​​​‌
  hal-03101612
• Contact:
  Romain Azais‌
• Participants:
  Sandie Ferrigno, Marie-Jose‌​‌ Martinez, Romain Azais

6.1.2​​ Harissa

• Name:
  Hartree approximation​​​‌ for inference along with‌ a stochastic simulation algorithm‌​‌
• Keywords:
  Gene regulatory networks,​​ Reverse engineering, Molecular simulation​​​‌
• Functional Description:
  Harissa is‌ a Python package for‌​‌ both inference and simulation​​ of gene regulatory networks,​​​‌ based on stochastic gene‌ expression with transcriptional bursting.‌​‌ It was implemented in​​ the context of a​​​‌ mechanistic approach to gene‌ regulatory network inference from‌​‌ single-cell data.
• URL:
  https://­github.­com/­ulysseherbach/­harissa​​​‌
• Publications:
  hal-04208601, hal-04071033​, hal-01646910
• Contact:
  Ulysse​‌ Herbach

6.1.3 MultiRNAflow

• Name:​​
  An R package for​​​‌ the analysis of RNAseq​ raw counts with multiple​‌ biological conditions and time​​ points
• Keywords:
  RNA-seq, Gene​​​‌ regulatory networks, Integrated data​ analysis, Complex experimental design,​‌ Multiple temporal and biological​​ conditions, Differential expression
• Functional​​​‌ Description:
  The R package​ MultiRNAflow provides an easy​‌ to use unified framework​​ allowing to make both​​​‌ unsupervised and supervised analysis​ (differential expression analysis) for​‌ RNAseq datasets with an​​ arbitrary number of biological​​​‌ conditions and time points.​ In particular, this package​‌ makes a deep downstream​​ analysis of differential expression​​​‌ information, e.g. identifying temporal​ patterns across biological conditions​‌ and differentially expresses genes​​ which are specific to​​​‌ a biological condition for​ each time.
• Release Contributions:​‌
  First version
• URL:
  https://­bioconductor.­org/­packages/­release/­bioc/­html/­MultiRNAflow.­html​​
• Contact:
  Nicolas Champagnat
• Participants:​​​‌
  Rodolphe Loubaton, Nicolas Champagnat,​ Pierre Vallois, Laurent Vallat​‌
• Partner:
  CHRU de Strasbourg​​

6.1.4 quantCurves

• Keyword:
  Statistical​​​‌ modeling
• Functional Description:
  Non-parametric​ methods as local normal​‌ regression, polynomial local regression​​ and penalized cubic B-splines​​​‌ regression are used to​ estimate quantiles curves.
• URL:​‌
  https://­cran.­r-project.­org/­web/­packages/­quantCurves/­quantCurves.­pdf
• Contact:
  Sandie Ferrigno​​

6.1.5 PEOC

• Name:
  Parameters​​​‌ Estimation Of Chalara model​
• Keywords:
  Statistical inference, Iterative​‌ algorithm, Monte Carlo estimation,​​ Python, Statistical modeling
• Functional​​​‌ Description:
  PEOC is Python​ software which aims to​‌ simulate and estimate the​​ parameters of the chalara​​​‌ model of the article​ 'Mechanistic-statistical model for the​‌ expansion of ash dieback'​​ by Coralie Fritsch, Marie​​​‌ Grosdidier, Anne Gégout-Petit and​ Benoît Marçais. It allows​‌ to reproduce the simulations​​ made in this article,​​​‌ which is available at​ the following url https://hal.science/hal-04690647.​‌
• URL:
  https://­github.­com/­coraliefritsch/­peoc
• Contact:
  Coralie​​ Fritsch

7.1.1 Gene regulatory networks​​

7.1.2 Parameter‌ scalings in population dynamics‌​‌

7.1.3 Individual-based modeling in​​ medicine, ecology and evolution​​​‌

7.1.4 Quasi-stationary distributions​‌

Participants: Nicolas Champagnat,​​ Edouard Strickler, Denis​​​‌ Villemonais.

External collaborators​: Michel Benaïm (Univ.​‌ Neuchâtel), Alex Cox (Univ.​​ Bath), Emma Horton (Univ.​​​‌ Warwick).

Denis Villemonais obtained​ in 34 a new​‌ criterion for existence and​​ convergence to a quasi-stationary​​​‌ distribution (QSD) based on​ the spectral theory of​‌ positive operators on Banach​​ lattices, building on domination​​​‌ properties for compactness of​ this type of operators​‌ as exposed in 39​​.

One central question​​​‌ in QSD theory is​ to construct and prove​‌ convergence of numerical schemes​​ for their approximation. In​​​‌ 30, D. Villemonais​ studied a binary branching​‌ model with Moran type​​ interactions introduced in 61​​. In this interacting​​​‌ particle system, particles evolve,‌ reproduce and die independently‌​‌ and, with a probability​​ that may depend on​​​‌ the configuration of the‌ whole system, the death‌​‌ of a particle may​​ trigger the reproduction of​​​‌ another particle, while a‌ branching event may trigger‌​‌ the death of another​​ particle. We prove optimal​​​‌ bounds for the distance‌ between the empirical distribution‌​‌ of the particle system​​ and the quasi-stationray distribution​​​‌ of the associated mean‌ semi-group.

In 16,‌​‌ N. Champagnat, E. Strickler​​ and D. Villemonais studied​​​‌ the convergence of general‌ penalized Markov processes with‌​‌ soft killing in (Monge-Kantorovich)​​ $L^1$ Wasserstein distance.​​​‌ We propose a simple‌ criterion ensuring uniform convergence‌​‌ of conditional distributions to​​ a unique QSD. We​​​‌ give several examples of‌ application where our criterion‌​‌ can be checked, including​​ Bernoulli convolutions and piecewise​​​‌ deterministic Markov processes, for‌ which convergence in total‌​‌ variation is not possible.​​

In 29, N.​​​‌ Champagnat and D. Villemonais‌ characterized large classes of‌​‌ non-irreducible absorbed Markov processes​​ with polynomial speed of​​​‌ convergence to a QSD.‌ They applied their criteria‌​‌ to prove the existence​​ of a QSD for​​​‌ general processes in denumerable‌ state spaces, assuming only‌​‌ aperiodicity, the existence of​​ a Lyapunov function and​​​‌ the existence of a‌ point in the state‌​‌ space from which the​​ return time is finite​​​‌ with positive probability.

N.‌ Champagnat and D. Villemonais‌​‌ obtained in 11 general​​ criteria ensuring existence, uniqueness​​​‌ and/or exponential convergence properties‌ for QSD. The criteria‌​‌ were specifically designed to​​ apply to degenerate processes​​​‌ such as hypoelliptic diffusions‌ and allow to improve‌​‌ existing results in this​​ domain.

7.1.5 Multi-type bisexual​​​‌ and weighted branching process‌

Participants: Coralie Fritsch,‌​‌ Denis Villemonais.

External​​ collaborators: Nicolas Zalduendo-Vidal​​​‌ (INRAE Montpellier).

The quasi-stationary‌ behavior of asexual subcritical‌​‌ multi-type Galton-Watson branching processes​​ is well-known. However, this​​​‌ question was open for‌ bisexual processes, even in‌​‌ the single-type case. C.​​ Fritsch and D. Villemonais​​​‌ studied in 17 the‌ quasi-stationary behavior of the‌​‌ multi-type bisexual branching processes​​ in the subcritical case.​​​‌ We establish the existence‌ of an infinite number‌​‌ of QSDs for the​​ process. Among these distributions,​​​‌ only a finite number‌ has good integrability properties.‌​‌ In addition, when the​​ process is irreducible, its​​​‌ conditonal distributions converge towards‌ a unique QSD. This‌​‌ work is based on​​ our previous work 71​​​‌, which was the‌ first one studying the‌​‌ criticality of general multi-type​​ bisexual branching processes.

It​​​‌ is well-known that super-critical‌ multi-type classical branching processes‌​‌ follow the strong law​​ of large numbers at​​​‌ large times. In 35‌, D. Villemonais studied‌​‌ the long-term behavior of​​ weighted multi-type branching processes,​​​‌ focusing on extending classical‌ laws of large numbers‌​‌ and martingale convergence to​​ settings with infinitely many​​​‌ weighted particles, arbitrary type‌ spaces and non-geometric rescaling.‌​‌ We developed applications to​​ Galton-Watson trees indexed by​​​‌ random weights and by‌ random kernels, convergence in‌​‌ Wasserstein distance of the​​ underlying mean semi-group, and​​​‌ convergence of ergodic averages‌ along lineages.

7.1.6 ODE‌​‌ with semi-Markov switching

Participants:​​​‌ Edouard Strickler.

External​ collaborators: Tobias Hurth​‌ (Université de Neuchâtel, Suisse).​​

In classical PDMP, time​​​‌ durations between random events​ are distributed as exponential​‌ variables. This is made​​ in order to ensure​​​‌ the Markov property of​ the process but can​‌ be debated from a​​ modeling perspective. Indeed, the​​​‌ exponential law allows for​ arbitrarily fast switches, which​‌ is not realistic in​​ most biological or physical​​​‌ models, where a minimum​ time is required between​‌ two environmental changes. Motivated​​ by this question, in​​​‌ collaboration with Tobias Hurth,​ we developed in 32​‌ a framework for PDMP​​ where the times between​​​‌ jumps of the process​ can follow any law.​‌ We show that if​​ the law of jumping​​​‌ time is sufficently regular,​ then certain conditions on​‌ the deterministic dynamics leading​​ to ergodicity of the​​​‌ process in the case​ of exponentially distributed jump​‌ times can still be​​ used in this general​​​‌ context, even though times​ between jumps are not​‌ arbitrarily short—which was a​​ property of the exponential​​​‌ distributions used crucially in​ previous references.

7.1.7 Dispersal​‌ Induced Growth

Participants: Edouard​​ Strickler.

External collaborators​​​‌: Michel Benaïm (Université​ de Neuchâtel, Suisse), Claude​‌ Lobry (Université de Nice)​​ and Tewfik Sari (Inrae​​​‌ Montpellier).

In this collaboration,​ we exhaustively studied the​‌ phenomenon of Dispersal Induced​​ Growth (DIG), a term​​​‌ coined by Katriel in​ 75. In a​‌ population spreading across a​​ finite number of patches,​​​‌ individuals in a patch​ may undergo a time-varying​‌ growth rate which is​​ such that, in the​​​‌ absence of migration between​ the patches, the population​‌ will eventually become extinct​​ in each patch. There​​​‌ is Dispersal Induced Growth​ when adding migration between​‌ such patches leads the​​ whole population to grow​​​‌ and survive. In the​ paper 45 we developed​‌ several tools in order​​ to understand when the​​​‌ DIG phenomenon can happen.​ In case where the​‌ graph of migration is​​ connected at each time,​​​‌ then DIG happens if​ and only if the​‌ mean growth rate of​​ an idealized habitat which​​​‌ would have the maximal​ growth rate at each​‌ time is positive. In​​ 13, we consider​​​‌ the case where migration​ is time dependent and​‌ the graph of migration​​ is globally connected but​​​‌ not necessarily connected at​ each time. In this​‌ situation, we exhibit example​​ where there is no​​​‌ DIG. We also give​ an example of Dispersal​‌ Induced Decay, meaning that,​​ in the absence of​​​‌ migration, the population will​ survive in each patch,​‌ while adding migration may​​ lead the whole population​​​‌ to extinction. The study​ is performed via the​‌ sign of a Lyapunov​​ exponent, leading to necessary​​​‌ and sufficient conditions for​ DIG.

In the recent​‌ paper 51, P.​​ Carmona gives an asymptotic​​​‌ formula for the top​ Lyapunov exponent of a​‌ linear $T$-periodic cooperative​​ differential equation, in the​​​‌ limit $T\to +\infty$. The short​‌ note 12 discusses and​​ extends this result.

7.1.8​​​‌ Modeling of chronic obstructive​ pulmonary disease

Participants: Pierre​‌ Vallois.

External collaborators​​: Isabelle Dupin (Univ.​​ Bordeaux), Élise Maurat (Univ.​​​‌ Bordeaux).

Most of the‌ direct respiratory effects of‌​‌ air pollution result from​​ the disruption of the​​​‌ lungs' natural defense mechanisms.‌ Among the most essential‌​‌ ones is mucociliary clearance,​​ which describes the coordinated​​​‌ effort between mucus produced‌ in the respiratory tract‌​‌ to trap microorganisms and​​ particles and the unidirectional​​​‌ movement of cilia, that‌ propels trapped particles towards‌​‌ the throat. The perturbation​​ of mucociliary clearance can​​​‌ lead to the formation‌ of mucus plugs, abnormally‌​‌ thick mucus accumulations that​​ obstruct the airways. several​​​‌ fundamental aspects of mucus‌ plugs remain poorly understood,‌​‌ particularly how they form,​​ where exactly they localize​​​‌ within the bronchial tree,‌ and how they evolve‌​‌ over time. This year,​​ we have been working​​​‌ on using mathematical modeling‌ to simulate the entire‌​‌ bronchial network and explore​​ plug formation, distribution, and​​​‌ temporal behavior in ways‌ that are currently inaccessible‌​‌ experimentally. A paper is​​ currently being written.

7.1.9​​​‌ Drawdowns of diffusions

Participants:‌ Pierre Vallois.

External‌​‌ collaborators: Paavo Salminen​​ (Åbo Akademi University, Finland).​​​‌

In 22, using‌ the excursion theory of‌​‌ diffusion processes, we provide​​ new proofs of, firstly,​​​‌ Lehoczky's formula for the‌ joint distribution of the‌​‌ first drawdown time and​​ the maximum before this​​​‌ time, and, secondly, of‌ Malyutin's formula for the‌​‌ joint distribution of the​​ first hitting time and​​​‌ the maximum drawdown before‌ this time. It is‌​‌ remarkable that the excursion​​ approach which we developed​​​‌ first for Lehoczky's formula‌ also provides a proof‌​‌ for Malyutin's formula. Moreover,​​ we analyze the pure​​​‌ jump process describing the‌ maximum before the first‌​‌ drawdown time when the​​ size of the drawdown​​​‌ is varying.

7.2.1 Quantifying and​​ predicting the evolution of​​​‌ clonal heterogeneity in chronic‌ lymphocytic leukemia

Participants: Nicolas‌​‌ Champagnat, Coralie Fritsch​​, Ulysse Herbach,​​​‌ Pierre Vallois, Vidhi‌ Vidhi.

External collaborators‌​‌: CHRU Strasbourg

The​​ development of targeted therapies​​​‌ has allowed considerable progress‌ in the treatment of‌​‌ many cancers, but their​​ efficacy is dependent on​​​‌ intra-tumor heterogeneity. In lymphomas‌ and leukemias, the identification‌​‌ of gene alterations by​​ high-throughput sequencing allows the​​​‌ characterization of this heterogeneity.‌ In these hemopathies, the‌​‌ initial leukemic clone has​​ a unique immune repertoire​​​‌ corresponding to specific human‌ immunoglobulin genes called VDJ‌​‌ genes encoding the antigen​​ receptor. The occurrence of​​​‌ additional mutations in VDJ‌ genes may be responsible‌​‌ for the emergence of​​ subclones with increased antigen​​​‌ receptor reactivity further complicating‌ the clonal heterogeneity of‌​‌ these hemopathies. However, this​​ second level of clonal​​​‌ heterogeneity and its evolution‌ remain poorly characterized and‌​‌ is not considered in​​ the management of these​​​‌ cancers.

In collaboration with‌ the group of Laurent‌​‌ Vallat in CHRU Strasbourg,​​ we aim to develop​​​‌ a mathematical model for‌ the evolution of the‌​‌ two levels of clonal​​ heterogeneity in leukemia, allowing​​​‌ to characterize their evolution‌ from longitudinal bulk sequencing‌​‌ data of VDJ and​​ cancer genes mutations using​​​‌ a Bayesian approach. This‌ year, we developed a‌​‌ model of the phylogenetic​​​‌ tree of squences of​ VDJ genes based on​‌ the weighted uniform distribution​​ over trees, with weights​​​‌ related to the Hamming​ distance which counts the​‌ number of mutations between​​ sequences. This model allows​​​‌ us to represent with​ a graph the most​‌ probable phylogenetic trees and​​ the uncertainties of certain​​​‌ parts of the tree.​ We are currently working​‌ on the development of​​ variational methods of inference​​​‌ of the tree in​ the context of unobserved​‌ VDJ sequences.

7.2.2 Promoting​​ physical activity and limiting​​​‌ sedentary behaviors to manage​ pain in endometriosis: analysis​‌ of psychosocial variables

Participants:​​ Ulysse Herbach.

External​​​‌ collaborators: Université de​ Haute-Alsace, Université de Nîmes​‌

Endometriosis is negatively linked​​ to physical activity (PA),​​​‌ as its symptoms and​ psychosocial barriers may hinder​‌ participation in PA. This​​ study compared PA, sedentary​​​‌ behavior (SED), and psychosocial​ variables in women with​‌ and without endometriosis 19​​. Women with endometriosis​​​‌ reported lower specific SED,​ poorer quality of life​‌ (QoL), greater score of​​ kinesiophobia, more health-related barriers​​​‌ to PA, lower physical​ self-concepts, and negative PA-related​‌ stereotypes (beliefs or perceptions).​​ The amount of PA​​​‌ was most related to​ previous PA behavior and​‌ intention in both groups.​​ In endometriosis, PA and​​​‌ SED are correlated to​ barriers related to health,​‌ motivational variables, beliefs about​​ the risks of PA,​​​‌ physical self-concepts and QoL.​ Findings highlight the importance​‌ of motivational variables and​​ self-concepts, which could be​​​‌ targeted to support engagement​ in PA to improve​‌ symptom management and QoL​​ in women with endometriosis.​​​‌ This study is a​ first step towards a​‌ finer multivariate analysis including​​ a specific treatment of​​​‌ the ordinal nature of​ the data, for example​‌ using latent Gaussian variables.​​

7.2.3 Uncovering candidate Nanog-Helper​​​‌ genes in early mouse​ embryo differentiation using differential​‌ entropy and network inference​​

Participants: Ulysse Herbach.​​​‌

External collaborators: Université​ libre de Bruxelles, ENS​‌ Lyon, Université Clermont Auvergne​​

In the preimplantation mammalian​​​‌ embryo, stochastic cell-to-cell expression​ heterogeneity is followed by​‌ signal reinforcement to initiate​​ the specification of Inner​​​‌ Cell Mass (ICM) cells​ into Epiblast (Epi). The​‌ expression of NANOG, the​​ key transcription factor for​​​‌ the Epi fate, is​ necessary but not sufficient:​‌ coincident expression of other​​ factors is required. To​​​‌ identify possible Nanog-helper genes,​ we analyzed gene expression​‌ variability in five time-stamped​​ single-cell transcriptomic datasets using​​​‌ differential entropy, a quantitative​ measure of cell-to-cell heterogeneity​‌ 21. The entropy​​ of Nanog displays a​​​‌ peak-shaped temporal pattern from​ the 16-cell to the​‌ 64-cell stage, consistent with​​ its key role in​​​‌ Epi specification. By estimating​ the entropy profiles of​‌ the 21 genes common​​ to all five datasets,​​​‌ we identified three genes​ - Pecam1, Sox2, and​‌ Hnf4a - whose variability​​ in expression patterns mirrors​​​‌ that of Nanog.

We​ further performed gene regulatory​‌ network inference using CARDAMOM​​ 10, an algorithm​​​‌ that exploits temporal dynamics​ and transcriptional bursting. The​‌ results revealed that these​​ three genes exhibit reciprocal​​​‌ activation with Nanog at​ the 32-cell stage. This​‌ regulatory motif reinforces fate-switching​​ decisions and co-expression states.​​ This analysis of single-cell​​​‌ transcriptomic data thus uncovers‌ a likely role for‌​‌ Pecam1, Sox2, and Hnf4a​​ as key genes that,​​​‌ when coincidentally expressed with‌ Nanog, initiate ICM differentiation.‌​‌

7.2.4 Harnessing ecological niche​​ modeling of Listeria monocytogenes​​​‌ for biopreservation system engineering‌

Participants: Sandie Ferrigno.‌​‌

External collaborators: LIBio​​ - Laboratoire d'Ingénierie des​​​‌ Biomolécules (

In this‌ collaboration with the LIBio‌​‌ - Laboratoire d'Ingénierie des​​ Biomolécules of Lorraine University,​​​‌ we work on the‌ presence of pathogens in‌​‌ food. To reduce this​​ presence, hurdle technology, which​​​‌ is based on the‌ use of a combination‌​‌ of several preservative methods,​​ is used by food​​​‌ business operators. Among the‌ multiple available hurdles, biopreservation‌​‌ consists of using microorganisms​​ as protective cultures and/or​​​‌ their metabolites to improve‌ the microbial quality of‌​‌ food. This study explores​​ the potential of ecological​​​‌ niche modeling to guide‌ the selection of biopreservation‌​‌ candidates. A luminescent strain​​ of Listeria monocytogenes was​​​‌ utilized in a multivariate‌ high-throughput competition assay. The‌​‌ resulting data were analyzed​​ using two parallel methods:​​​‌ k-means clustering and Response‌ Surface Modeling. An article‌​‌ 18 has been published​​ on this work.

7.2.5​​​‌ Nonparametric estimation

Participants: Sandie‌ Ferrigno.

External collaborators‌​‌: R. Azais (MOSAIC​​ INRIA Team, ENS Lyon),​​​‌ M.-J. Martinez (LJK-Grenoble University)‌

Many goodness-of-fit tests have‌​‌ been developed to assess​​ the different assumptions of​​​‌ a (possibly heteroscedastic) regression‌ model. Most of them‌​‌ are `directional' in that​​ they detect departures from​​​‌ a given assumption of‌ the model. Other tests‌​‌ are `global' (or `omnibus')​​ in that they assess​​​‌ whether a model fits‌ a dataset on all‌​‌ its assumptions. We focus​​ on the task of​​​‌ choosing the structural part‌ of the regression and‌​‌ the variance functions because​​ they contain easily interpretable​​​‌ information about the studied‌ relationship. We consider two‌​‌ nonparametric `directional' tests and​​ one nonparametric `global' test,​​​‌ all based on generalizations‌ of the Cramér-von Mises‌​‌ statistic. To perform these​​ goodness-of-fit tests, we have​​​‌ developed the R package‌ cvmgof, an easy-to-use tool‌​‌ for practitioners, available from​​ the Comprehensive R Archive​​​‌ Network (CRAN). The package‌ was updated in 2022‌​‌ (this is its third​​ version)(6.1.1). This​​​‌ latest version currently allows‌ testing the regression function‌​‌ in the model. Since​​ 2025, we worked to​​​‌ enrich the package by‌ allowing the user to‌​‌ test the homoscedasticity/heteroscedasticity of​​ the model. This new​​​‌ version will be submitted‌ to CRAN in 2026‌​‌ and an associated article​​ is currently being written.​​​‌ In parallel, with the‌ aim of obtaining better‌​‌ estimators in the various​​ tests we are studying,​​​‌ we have been working‌ on bandwidth selection choice,‌​‌ a crucial parameter in​​ nonparametric estimation. In particular,​​​‌ we have relied on‌ cross-validation methods and have‌​‌ also proposed new ones.​​ We plan to integrate​​​‌ these methods into the‌ cvmgof package in 2026‌​‌ to offer users choices​​ that will improve the​​​‌ quality of the estimators‌ used. We presented these‌​‌ results during the CMStatistics​​ congress in London in​​​‌ December 2025 36.‌

7.2.6 Online big data‌​‌ analysis and online learning​​​‌

Participants: Jean-Marie Monnez.​

A tool for analyzing​‌ streaming data is stochastic​​ approximation introduced by Robbins​​​‌ and Monro in 1951,​ that can be used​‌ for example to estimate​​ online parameters of a​​​‌ regression function 66 or​ centers of clusters in​‌ unsupervised classification 50.​​ Another type of stochastic​​​‌ approximation process, for estimating​ eigenvectors and eigenvalues of​‌ the unknown $Q$-symmetric​​ expectation $B$ of a​​​‌ random matrix $A$ using​ independent observations of $\mathrm{A‌}$, was introduced by​​ Benzécri in 1969 and​​​‌ studied by several authors,​ like the Oja process​‌ (1985). In this type​​ of process, independent observations​​​‌ of the random matrix​ are observed and one​‌ or a mini-batch of​​ observations per step are​​​‌ taken into account. We​ defined an extended Oja​‌ process where there is​​ a correlation model between​​​‌ the random matrices introduced​ at each step and​‌ where all the observations​​ up to the current​​​‌ step can be taken​ into account without storing​‌ them 85. Firstly,​​ this extends the scope​​​‌ of application of these​ processes, secondly previous experiments​‌ we have conducted show​​ that processes using all​​​‌ the data up to​ the current step generally​‌ converge faster than those​​ using a mini-batch of​​​‌ data.

Canonical components of​ the canonical analysis of​‌ two random vectors are​​ collinear with principal components​​​‌ of a PCA of​ the muldimensional linear regression​‌ function of one vector​​ with respect to the​​​‌ other or projected PCA.​ In the context of​‌ streaming data, we define​​ in 20 processes for​​​‌ estimating online in parallel​ this regression function and​‌ canonical components, possibly taking​​ into account at each​​​‌ step all the data​ up to this step​‌ without storing them and​​ using an extended Oja​​​‌ process 85. We​ deal with the cases​‌ of canonical correlation analysis,​​ factorial correspondence analysis and​​​‌ factorial discriminant analysis.

We​ also considered the canonical​‌ analysis of two random​​ vectors in the context​​​‌ of streaming data or​ big data. In the​‌ work described above, specific​​ stochastic approximation processes of​​​‌ canonical components and of​ couples of canonical components​‌ were defined separately for​​ canonical correlation analysis (CCA),​​​‌ factorial correspondence analysis (FCA)​ and factorial discriminant analysis​‌ (FDA). Here, using an​​ extension of the Oja​​​‌ process, we define general​ stochastic approximation processes of​‌ canonical components and of​​ couples of canonical components​​​‌ of the canonical analysis​ of two random vectors​‌ that can be directly​​ applied to CCA, FCA​​​‌ and FDA. A paper​ is currently being written.​‌

We are also currently​​ working on an extension​​​‌ of the Oja process​ to estimate the general​‌ and canonical components of​​ a generalized canonical analysis.​​​‌ It can be directly​ used in mixed data​‌ canonical analysis, generalized canonical​​ correlation analysis, multiple correspondence​​​‌ analysis and in the​ estimation of couples of​‌ canonical components in canonical​​ analysis of two random​​​‌ vectors.

Given a non-decreasing​ sequence of closed convex​‌ subsets $\left(K_{\mathrm{n}}\right)$ in a separable​​​‌ real Hilbert space $\mathrm{H}$, we are also​‌ currently studying the convergence​​ of a stochastic approximation​​ process in $H$ with​​​‌ correlated observations, projected at‌ step $n$ on ${\mathrm{K‌‌}}_n$, that extends​​ processes of the Robbins-Monro​​​‌ type. We established theorems‌ of almost sure convergence‌​‌ and in quadratic mean​​ and applied them to​​​‌ streaming multidimensional linear regression,‌ using at each step‌​‌ a mini-batch of data​​ or all the data​​​‌ up to this step,‌ and to dynamic generalized‌​‌ linear models when the​​ parameter varies with time.​​​‌

7.2.7 Diffuse low-grade gliomas‌

Participants: Sophie Wantz-Mézières.‌​‌

External collaborators: CRAN​​ BioSIS, CHRU Nancy.

The​​​‌ therapeutic management of patients‌ with diffuse low-grade gliomas‌​‌ (DLGG) is based on​​ monitoring progress through regular​​​‌ MRIs, usually through the‌ reconstructed volume of the‌​‌ tumor (after semiautomatic delineation).​​ But this seems not​​​‌ sufficient. Up to now,‌ the diffuse nature of‌​‌ this kind of tumors​​ has been observed but​​​‌ is not well measured.‌ We designed a new‌​‌ MRI-based variable, the ESVR​​ (ExtraSphere Volume Ratio) to​​​‌ quantify the DLGG brain‌ infiltration and discriminate patterns‌​‌ of patients. A machine​​ learning approach allows us​​​‌ to detect that patients'‌ age and ESVR at‌​‌ diagnosis seem to play​​ an important role, as​​​‌ well as the well-known‌ anatomopathology results. This result‌​‌ has been submitted to​​ Biomedical Signal Processing and​​​‌ Control.

A thesis is‌ currently underway to develop‌​‌ a tool to assist​​ in awake surgery. This​​​‌ tool should make it‌ possible to better identify‌​‌ subtle disorders during surgery​​ that are impossible or​​​‌ difficult for humans to‌ assess, in order to‌​‌ better organize the procedure​​ (detection of possible “tipping​​​‌ points” beyond which the‌ patient is no longer‌​‌ performing) or to stop​​ it (detection of alterations​​​‌ that are generally minor‌ but which, in the‌​‌ patient's socio-professional context will​​ have deleterious consequences on​​​‌ their quality of life).‌ Significant progress has been‌​‌ made up to date.​​ The foundations of this​​​‌ tool have been laid,‌ based on two complementary‌​‌ processes: the detection of​​ motor states through pose​​​‌ recognition, and the transcription‌ of oral responses via‌​‌ speech recognition. In order​​ to identify the most​​​‌ suitable technical configuration for‌ the operating room context,‌​‌ work is currently being​​ carried out on simulated​​​‌ data obtained from volunteers:‌ comparison of voice transcription‌​‌ models on audio recordings,​​ and implementation of a​​​‌ comparative study of pose‌ recognition and motor state‌​‌ classification models, based on​​ videos mimicking the exercises​​​‌ performed in the operating‌ room. Finally, a tool‌​‌ for anonymizing videos from​​ the operating room has​​​‌ been developed, allowing secure‌ access to them without‌​‌ compromising patient identity. This​​ work has been partly​​​‌ presented in congress 37‌, and a communication‌​‌ has been submitted in​​ ICASSP 2026.

8.1.1 Associate Teams in‌​‌ the framework of an​​​‌ Inria International Lab or​ in the framework of​‌ an Inria International Program​​

8.1.2 Visits of​​​‌ international scientists

8.1.3 Visits to international​‌ teams

8.2.1​ H2020 projects

N. Champagnat​‌ is scientific collaborator of​​ the ERC SINGER (AdG​​​‌ 101054787) on Stochastic dynamics​ of sINgle cells, coordinated​‌ by S. Méléard (Ecole​​ Polytechnique). He is involved​​​‌ in the research axes​ “From stochastic processes to​‌ singular Hamilton-Jacobi equations” and​​ “Lineages and time reversed​​​‌ trajectories” of this project.​

9.1.1 Scientific events:‌​‌ organisation

9.1.2 Scientific events:​​ selection

9.1.3 Journal​​​‌

9.1.4​​ Invited talks

• N. Champagnat​​​‌ has been invited to‌ give talks at the‌​‌ Kick-off Programme de recherche​​ Mathématiques en interaction (PEPR​​​‌ Maths Vives) in Montpellier‌ in March, at the‌​‌ 44th Conference on Stochastic​​ Processes and their Applications​​​‌ SPA 2025 in Wroclaw,‌ Poland in July and‌​‌ at the Fall Conference​​​‌ “Model design, optimization &​ control” of the thematic​‌ semester on Population Dynamics​​ in Nice in October.​​​‌ He also gave a​ seminar talk at “Séminaire​‌ du Pôle Probabilités” of​​ CMAP (Ecole Polytechnique) in​​​‌ Palaiseau in April.
• N.​ Champagnat, E. Strickler and​‌ D. Villemonais have been​​ invited to give talks​​​‌ at the Workshop on​ quasi-stationnary distributions held at​‌ CERMICS, Marne-la-Vallée, May 21​​ to 23.
• C. Fritsch​​​‌ has been invited to​ give a talk in​‌ a minisymposium at the​​ 56ème Journées de Statistiques​​​‌ in Marseille in June.​ She also gave a​‌ talk during the scientific​​ meeting between the Pôle​​​‌ AM2I and the Chamber​ of agriculture in Nancy​‌ in June.
• U. Herbach​​ has been invited to​​​‌ give a talk (hands-on​ tutorial session) at the​‌ Advanced Lecture Course on​​ Computational Systems Biology (​​​‌CompSysBio 2025) in​ Aussois in October.
• V.​‌ Vidhi gave poster presentation​​ at the European Mathematical​​​‌ Genetics Meeting organized by​ University of Brest in​‌ April and invited talks​​ at International Conference on​​​‌ Mathematical Methods and Model​ in Biosciences and School​‌ for Young Scientists in​​ Bulgaria in June and​​​‌ at InterDoctoral Conference of​ Lorraine and Luxembourg at​‌ IECL, University of Lorraine​​ in November.
• D. Villemonais​​​‌ gave invited talks at​ the “Séminaire de probabilité​‌ et mathématiques financières” of​​ Laboratoire de Mathématiques et​​​‌ Modélisation d'Évry in June,​ at the Congrès SMF​‌ in Dijon in June,​​ at the 13th Aging​​​‌ Research and Drug Discovery​ Meeting in Copenhagen in​‌ August, at the 12th​​ International Conference on Stochastic​​​‌ Analysis and its Applications​ in Bucarest in September,​‌ and at the “Chilean​​ Probability Seminar” of Santiago​​​‌ (online) in October.

9.1.5​ Scientific expertise

• N. Champagnat​‌ has been a member​​ of the Committee for​​​‌ junior permanent research positions​ of Centre Inria de​‌ Lille.
• N. Champagnat and​​ C. Fritsch were members​​​‌ of the Committee for​ career advancement of Inria​‌ personnel.
• C. Fritsch has​​ been a member of​​​‌ the Committee for junior​ permanent research positions of​‌ Centre Inria de l'Université​​ de Bordeaux and Centre​​​‌ Inria de Paris.
• A.​ Gégout-Petit has been member​‌ of four recruitment committes​​ (Nancy (MCF), Montpellier University​​​‌ (PR), Troyes Technological University​ (PR) and Institut Henri​‌ Poincaré (Director)).
• D. Villemonais​​ has been a member​​​‌ of a recruitment comittee​ (Strasbourg, PU).

9.1.6 Research​‌ administration

• V. Brodu was​​ an elected representative of​​​‌ doctoral students at the​ doctoral school committee (local​‌ scale), and also at​​ the doctoral college committee​​​‌ (regional scale). He was​ then replaced by M.​‌ Gaillard.
• N. Champagnat is​​ elected member of the​​​‌ Commission d'Evaluation of Inria,​ member of the COMIPERS​‌ (hiring committee for non-permanent​​ positions) of Centre Inria​​​‌ de Nancy, substitute member​ of the Comité de​‌ Centre of Centre Inria​​ de Nancy and local​​​‌ researcher (correspondant local) representing​ the COERLE (Inria's Ethic​‌ Committee) at Centre Inria​​ de Nancy.
• C. Fritsch​​​‌ is elected member of​ the Commission d'Evaluation of​‌ Inria.
• A. Gégout-Petit is​​ director of the research​​​‌ unit IECL (Institut Elie​ Cartan de Lorraine), Mathematics​‌ laboratory of Univ. Lorraine​​ (200 members).
• S. Wantz-Mézières​​ is substitute member of​​​‌ the CNU, section 26,‌ college B.
• D. Villemonais‌​‌ is head of the​​ Probability Team in Strasbourg,​​​‌ member of the MSII‌ doctoral school board in‌​‌ University of Strasbourg, and​​ elected member of the​​​‌ “Conseil de l'UFR de‌ mathématiques et informatique” in‌​‌ University of Strasbourg.

9.2.1 Teaching‌​‌

• S. Ferrigno is in​​ charge of the “DU​​​‌ Big Data & Data‌ Science” in ENSMN, Univ.‌​‌ Lorraine.
• D. Villemonais is​​ head of L3 DUAS​​​‌ (actuarial science) in Univ.‌ Strasbourg.
• Master: V. Brodu,‌​‌ Distribution theory and PDEs,​​ 40h, M1, second year​​​‌ of ENSEM, Univ. Lorraine.‌
• Master: V. Brodu, Monte-Carlo‌​‌ methods, 20h, M1, second​​ year of ENSMN, Univ.​​​‌ Lorraine.
• Master: N. Champagnat,‌ Introduction to Quantitative Finance,‌​‌ 12h, M1, second year​​ of ENSMN, Univ. Lorraine.​​​‌
• Master: N. Champagnat, Introduction‌ to Quantitative Finance, 9h,‌​‌ M2, third year of​​ ENSMN, Univ. Lorraine.
• Master:​​​‌ S. Ferrigno, Experimental designs,‌ 6h, M1, fourth year‌​‌ of EEIGM, Univ. Lorraine.​​
• Master: S. Ferrigno, Data​​​‌ analyzing and mining, 36h,‌ M1, second year of‌​‌ ENSMN, Univ. Lorraine.
• Master:​​ S. Ferrigno, Modeling and​​​‌ forecasting, 32h, M1, second‌ year of ENSMN, Univ.‌​‌ Lorraine.
• Master: S. Ferrigno,​​ Training projects, 18h, M1/M2,​​​‌ second and third year‌ of ENSMN, Univ. Lorraine.‌​‌
• Master: C. Fritsch, Inverse​​ problem, 18h, M1, second​​​‌ year of ENSMN, Univ.‌ Lorraine.
• Master: A. Gégout-Petit,‌​‌ Inferential statistics, 20h, M1​​ IMSD, Univ. Lorraine.
• Master:​​​‌ A. Gégout-Petit, Complex data‌ modelling, 30h, M2 IMSD,‌​‌ Univ. Lorraine.
• Master: D.​​ Villemonais, Probability M1 first​​​‌ and second semester, 56h‌
• Master: D. Villemonais, Tutoring‌​‌ of student in actuarial​​ science (stage d'alternance)
• Agregation​​​‌ of mathematics training: Denis‌ Villemonais, Modelling lesson
• Master:‌​‌ S. Wantz-Mézières, Unsupervised Learning,​​ 25h, M2 IMSD, Univ.​​​‌ Lorraine
• Master: S. Wantz-Mézières,‌ Advanced image analysis and‌​‌ digital optimization, M2 IS-SNIM,​​ 36h, Univ. Lorraine.
• Licence:​​​‌ S. Baland, Applied probabilities,‌ 20h, L2 Informatique, Univ.‌​‌ Lorraine.
• Licence: S. Baland,​​ Mathematical tools for biology,​​​‌ 22h, L1 Sciences de‌ la Vie, Univ. Lorraine.‌​‌
• Licence: S. Baland, Probabilities,​​ 20h, L2 Informatique, Univ.​​​‌ Lorraine.
• Licence: V. Brodu,‌ Probability theory and Statistics,‌​‌ 60h, L3, first year​​ of ENSEM, Univ. Lorraine.​​​‌
• Licence: V. Brodu, Operational‌ Research, 30h, L3, first‌​‌ year of ENSMN, Univ.​​ Lorraine.
• Licence: V. Brodu,​​​‌ Mathematical tools for engineers,‌ 20h, L3, first year‌​‌ of ENSEM, Univ. Lorraine.​​
• Licence: E. Cerf, Complementary​​​‌ Analysis, 70h, L1 Mathématiques,‌ Univ. Lorraine.
• Licence: E.‌​‌ Cerf, Mathematics, 12h, L1​​ Professorat des Ecoles, Univ.​​​‌ Lorraine.
• Licence: E. Cerf,‌ Mathematical tools for biology,‌​‌ 22h, L1 Sciences de​​ la Vie, Univ. Lorraine.​​​‌
• Licence: S. Ferrigno, Descriptive‌ and inferential statistics, 60h,‌​‌ L2, second year of​​ EEIGM, Univ. Lorraine.
• Licence:​​​‌ S. Ferrigno, Statistical modeling,‌ 60h, L2, second year‌​‌ of EEIGM, Univ. Lorraine.​​
• Licence: S. Ferrigno, Mathematical​​​‌ and computational tools, 20h,‌ L3, third year of‌​‌ EEIGM, Univ. Lorraine.
• Licence:​​ S. Ferrigno, Training projects,​​​‌ 40h, L1/L3, first, second‌ and third year of‌​‌ EEIGM, Univ. Lorraine.
• Licence:​​ M. Gaillard, Inférence statistique,​​​‌ 40h, L3, first year‌ of ENSEM, Univ. Lorraine.‌​‌
• Licence: V. Kagan, Probability​​​‌ theory tutorial, 40h, L3,​ first year of ENSMN,​‌ Univ. Lorraine.
• Licence: V.​​ Kagan, Numerical Analysis tutorial,​​​‌ 20h, L3, first year​ of ENSMN, Univ. Lorraine.​‌
• Licence: J. Mardomingo Sanz,​​ Analyse numérique et optimisation,​​​‌ 40h, L3, first year​ of ENSMN, Univ. Lorraine.​‌
• Licence: S. Wantz-Mézières, Applied​​ Mathematics: Probability, 48h, L3,​​​‌ first year of TELECOM-NANCY,​ Univ. Lorraine.
• Licence: S.​‌ Wantz-Mézières, Mathematical tools for​​ management and Finance, 180h,​​​‌ L1/L2 first and second​ year of BUT GEA,​‌ IUT Nancy-Charlemagne, Univ. Lorraine.​​

9.2.2 Supervision

9.2.3‌ Juries

• N. Champagnat was‌​‌ referee for the PhD​​ thesis of Nathanaël Boutillon​​​‌ (Aix-Marseille Univ., 11/06/2025).
• N.‌ Champagnat, C. Fritsch and‌​‌ A. Gégout-Petit were examiners​​ for the PhD thesis​​​‌ of Virgile Brodu (Univ.‌ Lorraine, 27/08/2025).
• N. Champagnat‌​‌ and A. Gégout-Petit were​​ examiners for the PhD​​​‌ thesis of Anouk Rago‌ (Univ. Lorraine, 30/06/2025).
• N.‌​‌ Champagnat and A. Gégout-Petit​​ were examiners for the​​​‌ HDR jury of Coralie‌ Fritsch (Univ. Lorraine, 15/12/2025).‌​‌
• A. Gégout-Petit was president​​ the PhD jury of​​​‌ Trinh Duong (Lorraine University,‌ 06/2025).
• A. Gégout-Petit was‌​‌ referee for the PhD​​ jury of Cristina Chavez​​​‌ (Nanterre University, 04/2025).
• A.‌ Gégout-Petit was referee for‌​‌ the PhD jury of​​ Julie Cartier (PSL University,​​​‌ 11/2025).
• A. Gégout-Petit was‌ referee for the PhD‌​‌ jury of Valentin Portmann​​ (Univ. Bordeaux, 11/2025)
• S.​​​‌ Wantz-Mézières was examiner for‌ the PhD thesis of‌​‌ Ghislain Fievet (NGERE, Univ.​​ Lorraine, 20/11/2025).
• U. Herbach​​​‌ was examiner for the‌ PhD thesis of Emrys‌​‌ Reginato (Univ. Grenoble Alpes,​​ 24/11/2025).
• U. Herbach was​​​‌ examiner for the PhD‌ thesis of Gustavo Magaña‌​‌ Loópez (Univ. Bordeaux, 17/12/2025).​​
• E. Strickler was referee​​​‌ for the PhD thesis‌ of Jérémy Colombo (Univ.‌​‌ Neuchâtel, 20/11/25).
• D. Villemonais​​ was referee for the​​​‌ PhD thesis of Jules‌ Olayé (Ecole Polytechnique, Palaiseau,‌​‌ 04/07/2025)

9.3.1 Specific‌​‌ official responsibilities in science​​ outreach structures

• S. Ferrigno:​​​‌ Advisor of groups of‌ EEIGM students in the‌​‌ context of “La main​​ à la Pâte” projects​​​‌ and “CGénial” projects, at‌ middle schools Paul Verlaine‌​‌ in Malzéville and La​​ Craffe in Nancy, at​​​‌ Institut médico-éducatif (IME) in‌ Commercy and in elementary‌​‌ schools in Nancy.
• S.​​ Ferrigno: Advisor of a​​​‌ group of EEIGM students,‌ “Ateliers expérimentaux : Mécanique‌​‌ et Statistique” project, in​​ various high schools in​​​‌ Nancy.

9.3.2 Participation in‌ Live events

• J. Mardomingo‌​‌ Sanz and V. Brodu​​​‌ volunteered in the popularization​ event “Fête de la​‌ Science” in Univ. Lorraine​​ in October.

International journals

• 11​​​‌ articleM.Michel Benaïm‌, N.Nicolas Champagnat‌​‌, W.William Oçafrain​​ and D.Denis Villemonais​​​‌. Degenerate processes killed‌ at the boundary of‌​‌ a domain.The​​ Annals of Probability53​​​‌2March 2025,‌ 720-752HALDOIback‌​‌ to text
• 12 article​​M.Michel Benaïm,​​​‌ C.Claude Lobry,‌ T.Tewfik Sari and‌​‌ É.Édouard Strickler.​​ A note on the​​​‌ top Lyapunov exponent of‌ linear cooperative systems.‌​‌Annales de la Faculté​​ des Sciences de Toulouse.​​​‌ Mathématiques.341June‌ 2025, 225-241HAL‌​‌DOIback to text​​
• 13 articleM.Michel​​​‌ Benaim, C.Claude‌ Lobry, T.Tewfik‌​‌ Sari and E.Edouard​​ Strickler. Dispersal-induced growth​​​‌ or decay in a‌ time-periodic environment. The case‌​‌ of reducible migration matrices​​.Journal of Mathematical​​​‌ Biology9132025‌, 26HALDOI‌​‌back to text
• 14​​ articleA.Athanase Benetos​​​‌, C.Coralie Fritsch‌, E.Emma Horton‌​‌, L.Lionel Lenotre​​, S.Simon Toupance​​​‌ and D.Denis Villemonais‌. Stochastic branching models‌​‌ for the telomeres dynamics​​ in a model including​​​‌ telomerase activity.Journal‌ of Mathematical Biology91‌​‌8June 2025HAL​​DOIback to text​​​‌
• 15 articleN.Nicolas‌ Champagnat and V.Vincent‌​‌ Hass. Convergence of​​ population processes with small​​​‌ and frequent mutations to‌ the canonical equation of‌​‌ adaptive dynamics.The​​ Annals of Applied Probability​​​‌351February 2025‌, 1-63HALDOI‌​‌back to text
• 16​​ articleN.Nicolas Champagnat​​​‌, É.Édouard Strickler‌ and D.Denis Villemonais‌​‌. Uniform Wasserstein convergence​​ of penalized Markov processes​​​‌.Probability Theory and‌ Related Fields1923-4‌​‌2025, 1031-1069HAL​​DOIback to text​​​‌
• 17 articleC.Coralie‌ Fritsch, D.Denis‌​‌ Villemonais and N.Nicolás​​ Zalduendo. Quasi-limiting behaviour​​​‌ of the sub-critical Multitype‌ Bisexual Galton-Watson Branching Process‌​‌.Bernoulli321​​February 2026, 798​​​‌ -- 822HALDOI‌back to text
• 18‌​‌ articleC.Cécile Mangavel​​, C.Chloé Gapp​​​‌, M.Magda Corgneau‌, A.Alexis Dijamentiuk‌​‌, X.Xincheng Liu​​, A.Annelore Elfassy​​​‌, L.Laurent Guillier‌, G. B.Ghaya‌​‌ Ben Hmidene, S.​​Sandie Ferrigno, M.​​​‌Mickaël Desvaux, A.-M.‌Anne-Marie Revol-Junelles and F.‌​‌Frédéric Borges. Harnessing​​ ecological niche modeling of​​​‌ Listeria monocytogenes for biopreservation‌ system engineering.Food‌​‌ Microbiology133January 2026​​, 104865HALDOI​​​‌back to text
• 19‌ articleT.Tracy Milane‌​‌, U.Ulysse Herbach​​, M.-A.Marie-Anne Jean​​​‌ and G.Géraldine Escriva-Boulley‌. Promoting physical activity‌​‌ and limiting sedentary behaviors​​ to manage pain in​​​‌ endometriosis: What are the‌ psychosocial variables to take‌​‌ into account?Women's Reproductive​​ HealthNovember 2025,​​​‌ 1-21HALDOIback‌ to text
• 20 article‌​‌J.-M.Jean-Marie Monnez.​​ An extended Oja process​​​‌ for streaming canonical analysis‌.Communications in Statistics‌​‌ - Theory and Methods​​2025HALDOIback​​​‌ to text
• 21 article‌F.Francisco Prista von‌​‌ Bonhorst, O.Olivier​​​‌ Gandrillon, U.Ulysse​ Herbach, C.Corentin​‌ Robert, C.Claire​​ Chazaud, Y.Yannick​​​‌ de Decker, D.​Didier Gonze and G.​‌Geneviève Dupont. Uncovering​​ candidate Nanog-Helper genes in​​​‌ early mouse embryo differentiation​ using differential entropy and​‌ network inference.Scientific​​ Reports151June​​​‌ 2025, 19975HAL​DOIback to text​‌
• 22 articleP.Paavo​​ Salminen and P.Pierre​​​‌ Vallois. Drawdowns of​ Diffusions.ESAIM: Probability​‌ and Statistics292025​​, 357-380HALDOI​​​‌back to text

Conferences​ without proceedings

• 23 inproceedings​‌M.Mathilde Gaillard and​​ U.Ulysse Herbach.​​​‌ Efficient Stochastic Simulation of​ Gene Regulatory Networks Using​‌ Hybrid Models of Transcriptional​​ Bursting.Computational Methods​​​‌ in Systems Biology15959​Lecture Notes in Computer​‌ ScienceLyon, FranceSpringer​​ Nature SwitzerlandAugust 2025​​​‌, 109-125HALDOI​back to textback​‌ to text

Doctoral dissertations​​ and habilitation theses

• 24​​​‌ thesisV.Virgile Brodu​. Individual-based stochastic models​‌ with allometric dynamics :​​ branching, convergence, numerical simulations​​​‌.Université de Lorraine​August 2025HALback​‌ to text
• 25 thesis​​C.Coralie Fritsch.​​​‌ Comportement asymptotique de modèles​ probabilistes pour la biologie​‌ : criticité de processus,​​ théorèmes limites, comportement quasi-stationnaire,​​​‌ approximation de modèles.​Université de LorraineDecember​‌ 2025HALback to​​ text

Reports & preprints​​​‌

• 26 miscS.Sylvain​ Billiard, V.Virgile​‌ Brodu, N.Nicolas​​ Champagnat and C.Coralie​​​‌ Fritsch. An individual-based​ stochastic model reveals strong​‌ constraints on allometric relationships​​ with minimal metabolic and​​​‌ ecological assumptions.January​ 2025HALback to​‌ text
• 27 miscN.​​Nicolas Champagnat, R.​​​‌Rodolphe Loubaton, L.​Laurent Vallat and P.​‌Pierre Vallois. Modelling​​ the effects of biological​​​‌ intervention in a dynamical​ gene network.May​‌ 2025HALback to​​ text
• 28 miscN.​​​‌Nicolas Champagnat, P.​Pablo Marquet, C.​‌Cristóbal Quiñinao, R.​​Rolando Rebolledo, M.​​​‌Mauricio Tejo, L.​Leonardo Videla and N.​‌Nicolás Zalduendo Vidal.​​ On ecological models with​​​‌ sublinear growth.July​ 2025, 22 p.​‌HALback to text​​
• 29 miscN.Nicolas​​​‌ Champagnat and D.Denis​ Villemonais. Quasi-stationary distributions​‌ in reducible state spaces​​.October 2025HAL​​​‌back to text
• 30​ miscA. M.A​‌ M G Cox,​​ E.E Horton and​​​‌ D.Denis Villemonais.​ Linear and uniform in​‌ time bound for the​​ binary branching model with​​​‌ Moran type interactions.​January 2025HALback​‌ to text
• 31 misc​​C.Clémence Fournié,​​​‌ E.Elias Ventre,​ U.Ulysse Herbach,​‌ A.Aymeric Baradat,​​ O.Olivier Gandrillon and​​​‌ F.Fabien Crauste.​ Cell Trajectory Inference based​‌ on Schrödinger Problem and​​ a Mechanistic Model of​​​‌ Stochastic Gene Expression.​November 2025HALback​‌ to text
• 32 misc​​T.Tobias Hurth and​​​‌ E.Edouard Strickler.​ Ergodicity and regularity properties​‌ of ODEs with semi-Markov​​ switching.September 2025​​​‌HALback to text​
• 33 miscV.Vincent​‌ Kagan, E.Edouard​​ Strickler and D.Denis​​ Villemonais. Averaging principle​​​‌ for jump processes depending‌ on fast ergodic dynamics‌​‌.October 2025HAL​​back to text
• 34​​​‌ miscD.Denis Villemonais‌. Quasi-compactness for dominated‌​‌ kernels with application to​​ quasi-stationary distribution theory.​​​‌October 2025HALback‌ to text
• 35 misc‌​‌D.Denis Villemonais and​​ N.Nicolas Zalduendo.​​​‌ Convergence of weighted branching‌ processes.December 2025‌​‌HALback to text​​

Other scientific publications

• 36​​​‌ inproceedingsS.Sandie Ferrigno‌ and M.-J.Marie-José Martinez‌​‌. A cross-validation bandwidth​​ choice for nonparametric tests​​​‌ in regression models.‌CMStatistics 2025London, United‌​‌ KingdomDecember 2025HAL​​back to text
• 37​​​‌ inproceedingsL.Léo Gerard‌, L.Laetitia Bau‌​‌, S.Sophie Wantz-Mézières​​, J.-M.Jean-Marie Moureaux​​​‌ and F.Fabien Rech‌. AN ORIGINAL AUTOMATIC‌​‌ SPEECH RECOGNITION DECISION AID​​ TOOL TO FACILITATE AWAKE​​​‌ BRAIN SURGERY.14e‌ Forum du Cancéropôle Est‌​‌Besançon (France), FranceNovember​​ 2025HALback to​​​‌ text

Educational activities

• 38‌ unpublishedJ.-M.Jean-Marie Monnez‌​‌. Streaming data analysis​​ Canonical analysis of two​​​‌ random vectors.March‌ 2025, DoctoralFrance‌​‌HALback to text​​