Project-team positioning:

Some topics of the INRIA project teams (STATIFY, CELESTE, MODAL, SEQUEL, CLASSIC) are close to the ASTRAL objectives such as non parametric view of high dimensional data, statistical/machine learning, model selection, clustering, sequential learning algorithms, or multivariate data analysis for complex data. While certain ASTRAL objectives are similar to those of these teams, our approaches are significantly different. For example, in multivariate data analysis of complex data including clustering, our team mainly focuses on a geometric approach for mixed data. We also consider the case of successive arrivals of information in SIR both from the theoretical and numerical point of view. Currently there is no direct competition between our team and other INRIA project teams. However, interactions between ASTRAL and other INRIA teams exist. For instance, ASTRAL and STATIFY collaborations are fruitful with common publications, in particular with S. Girard (STATIFY project team).

In the field of multivariate data analysis, the team have interesting discussions with Agrocampus Ouest (Rennes, France) and with H.A.L. Kiers (Groningen University) on a mixed data approach for dimension reduction. Conditional and regression quantiles are very active research fields in France (University of Toulouse, Toulouse School of Economics, University of Montpellier) and around the world (ULB, Belgium; University of Illinois Urbana-Champaign, USA; Open University, UK; Brunel University, UK). The ASTRAL team has for the last four-year period collaborated with D. Paindaveine (ULB, Belgium). In the dimension reduction framework, there is a large international community in Europe, America or Asia working on SIR and related methods. However, to our knowledge, the ASTRAL team was the first to introduce importance of variables and recursive methods in SIR, and the first to adapt the SIR approach to data stream.

Project-team positioning:

In the last three decades, the use of Feynman-Kac type particle models has been developed in variety of scientific disciplines, including in molecular chemistry, risk analysis, biology, signal processing, Bayesian inference and data assimilation.

The design and the mathematical analysis of Feynman-Kac particle methodologies has been one of the main research topics of P. Del Moral since the late 1990's  46, 43, 41, see also the books  45, 40, 44, 47 and references therein. These mean field particle sampling techniques encapsulate particle filters, sequential Monte Carlo methods, spatial branching and evolutionary algorithms, Fleming-Viot genetic type particles methods arising in the computation of quasi-invariant measures and simulation of non absorbed processes, as well as diffusion Monte Carlo methods arising in numerical physics and molecular chemistry. The term "particle filters" was first coined in the article  46 published in 1996 in reference to branching and mean field interacting particle methods used in fluid mechanics since the beginning of the 1960s. This article presents the first rigorous analysis of these mean field type particle algorithms.

The INRIA project teams applying the particle methodology developed by ASTRAL include the INRIA project team SIMSMART (rare event simulation as well as particle filters) and the INRIA project team Matherials (applications in molecular chemistry). The project team ASTRAL also has several collaborative research projects with these, teams as well as with researchers from international universities working in this subject, including Oxford, Cambridge, New South Wales Sydney, UTS, Bath, Warwick and Singapore Universities.

Discrete-time models

In this framework, the basic model can be described by a state space where the system evolves, an action space, a stochastic kernel governing the dynamic and, depending on the state and action variables, a one-step cost (reward) function. The distribution of the controlled stochastic process is defined through the control policy which is then selected in order to optimize the objective function. This is a very general model for dynamic optimization in discrete-time, which also goes by the name of stochastic dynamic programming. For references, the interested reader may consult the following books 34, 36, 49, 50, 52, 53, 54, 55, 59, 58, 61 and the references therein (this list of references is, of course, not exhaustive).

Continuous-time models

Most of the continuous-time stochastic processes consist of a combination of the following three different ingredients: stochastic jumps, diffusion and deterministic motions. In this project, we will focus on non-diffusive models, in other words, stochastic models for which the randomness appears only at fixed or random times, i.e. those combining deterministic motions and random jumps. These stochastic processes are the so-called piecewise deterministic Markov processes (PDMPs) 35, 37, 38, 51, 56, 57, 60. This family of models plays a central role in applied probability because it forms the bulk of models in many research fields such as, e.g. operational research, management science and economy and covers an enormous variety of applications.

These models can be framed in several different forms of generality, depending on their mathematical properties such as the type of performance criterion, full or incomplete state information, with or without constraints, adaptative or not, but more importantly, the nature of the boundary of the state space, the type of dynamic between two jumps and on the number of decision-makers. These last three characteristics make the analysis of the controlled process much more involved.

Part of this project will cover both theoretical and numerical aspects of stochastic optimal control. It is clear that stochastic problems and control games have been extensively studied in the literature. Nevertheless, important challenges remain to be addressed. From the theoretical side, there are still many technical issues that are, for the moment, still unanswered or at most have received partial answers. This is precisely what makes them difficult and requires either the creative transposition of pre-existing methodologies or the development of new approaches. It is interesting to note that one of the feature of these theoretical problems is that they are closely related to practical issues. Solving such problems not only gives rise to challenging mathematical questions, but also allow a better insight into the structure and properties of real practical problems. Theory for applications will be for us the thrust that will guide us in this project. From the numerical perspective, solving a stochastic decision model remains a critical issue. Indeed, except for very few specific models, the determination of an optimal policy and the associated value function is an extremely difficult problem to tackle. The development of computational and numerical methods to get quasi-optimal solutions is, therefore, of crucial importance to demonstrate the practical interest of stochastic decision model as a powerful modeling tool. During the International Conference on Dynamic Programming and Its Applications held at the University of British Columbia, Canada in April 1977, Karl Hinderer, a pioneer in the field of stochastic dynamic programming emphasized that "whether or not our field will have a lasting impact on science beyond academic circles depends heavily on the success of implemented applications". We believe that this statement is still in force some forty years later.

The objective of this project is to address these important challenges. They are mainly related to models with general state/action spaces and with continuous time variables covering a large field of applications. Here is a list of topics we would like to study: games, constrained control problems, non additive types of criteria, numerical and computational challenges, analysis of partially observed/known stochastic decision processes. This list is not necessarily exhaustive and may of course evolve over time.

Our research agenda on optimal stochastic control is developed around the applied mathematical axis as well as the numerical perspective, including concrete industrial transfers with a special focus on Naval Group. Our mid-term objectives will focus on the following themes described above: properties of control policies in continuous-time control problems, non additive types of criteria, numerical and computational challenges. Our long-term objectives will focus on the analysis of partially observed/known stochastic control problems, constrained control problems and games.

Project-team positioning:

There exists a large national/international community working on PDMPs and MDPs both on the theoretical, numerical and practical aspects. One may cite A. Almudevar (University of Rochester, USA), E. Altman (INRIA Team NEO, France), K. Avrachenkov (INRIA Team NEO, France), N. Bauerle (Karlsruhe University, Germany), D. Bertsekas (Massachusetts Institute of Technology, USA), O. Costa (Sao Paulo University, Brazil), M. Davis (Imperial College London, England), E. Feinberg (Stony Brook University, USA), D. Goreac (Université Paris-Est Marne-la-Vallée, France), X. Guo (Zhongshan University, China), O. Hernandez-Lerma (National Polytechnic Institute, Mexico), S. Marcus (University of Maryland, USA), T. Prieto-Rumeau (Facultad de Ciencias, UNED, Spain), A. Piunovskiy (University of Liverpool, England), U. Rieder (Universität Ulm, Germany), J. Tsitsiklis (Massachusetts Institute of Technology, USA), B. Van Roy (Stanford University, USA), O. Vega-Amaya (Universidad de Sonora, Mexico), Y. Zhang (University of Liverpool, England) to name just a few. Many of the colleagues cited above are at the head of research groups which have not been described in detail due to space limitation and so, this list is far from being exhaustive.

To some extent, our team is in competition wit the colleagues and teams mentioned above. We emphasize that there exists a long standing collaboration between our group and O. Costa (Sao Paulo University, Brazil) since 1998. In the last 10 years, we have established very fruitful collaborations with T. Prieto-Rumeau (Facultad de Ciencias, UNED, Spain) and A. Piunovskiy (University of Liverpool, England).

Inside INRIA, the team NEO and in particular E. Altman and K. Avrachenkov work on discrete-time MDPs but they are mainly focused on the case of countable (finite) state/action spaces MDPs. From this point of view, our results on this theme may appear complementary to theirs.

6.1.1 FracLab

• Keyword:
  Stochastic process
• Functional Description:

  FracLab is a general purpose signal and image processing toolbox based on fractal, multifractal and local regularity methods. FracLab can be approached from two different perspectives: - (multi-) fractal and local regularity analysis: A large number of procedures allow to compute various quantities associated with 1D or 2D signals, such as dimensions, Hölder and 2-microlocal exponents or multifractal spectra.

  - Signal/Image processing: Alternatively, one can use FracLab directly to perform many basic tasks in signal processing, including estimation, detection, denoising, modeling, segmentation, classification, and synthesis.

• URL:
  https://­project.­inria.­fr/­fraclab/
• Contact:
  Jacques Lévy Véhel
• Participants:
  Antoine Echelard, Christian Choque-Cortez, Jacques Lévy Véhel, Khalid Daoudi, Olivier Barrière, Paulo Goncalves, Pierrick Legrand
• Partners:
  Centrale Paris, Mas

6.1.2 PCAmixdata

• Keyword:
  Statistic analysis
• Functional Description:
  Mixed data type arise when observations are described by a mixture of numerical and categorical variables. The R package PCAmixdata extends standard multivariate analysis methods to incorporate this type of data. The key techniques included in the package are PCAmix (PCA of a mixture of numerical and categorical variables), PCArot (rotation in PCAmix) and MFAmix (multiple factor analysis with mixed data within a dataset). The MFAmix procedure handles a mixture of numerical and categorical variables within a group - something which was not possible in the standard MFA procedure. We also included techniques to project new observations onto the principal components of the three methods in the new version of the package.
• URL:
  https://­cran.­r-project.­org/­web/­packages/­PCAmixdata/­index.­html
• Contact:
  Marie Chavent

6.1.3 vimplclust

• Keywords:
  Clustering, Fair and ethical machine learning
• Functional Description:
  vimpclust is an R package that implements methods related to sparse clustering and variable importance. The package currently allows to perform sparse k-means clustering with a group penalty, so that it automatically selects groups of numerical features. It also allows to perform sparse clustering and variable selection on mixed data (categorical and numerical features), by preprocessing each categorical feature as a group of numerical features. Several methods for visualizing and exploring the results are also provided.
• URL:
  https://­CRAN.­R-project.­org/­package=vimpclust
• Contact:
  Marie Chavent

6.1.4 divdiss

• Name:
  divisive monothetic clustering on dissimilarity matrix
• Keywords:
  Clustering, Machine learning
• Functional Description:
  The div_diss function implements a divisive monotopic hierarchical classification algorithm.
• URL:
  https://­github.­com/­chavent/­divdiss
• Contact:
  Marie Chavent

7.1.1 Has breed any effect on beef sensory quality?

A total of 436 young cattle from 15 cattle breeds were reared in as similar conditions as possible to evaluate the impact of breed on sensory quality of beef from longissimus muscle determined by sensory analysis. In 10, two statistical methods for processing the sensory data were compared. The analysis of variance with or without the panelist effect gave similar conclusions indicating that the robustness of the results was not dependent on the method chosen. The 4 meat descriptors (tenderness, juiciness, beef flavor and off-flavor) placed breeds into 5 groups using an unsupervised classification (hierarchical ascending classification). Aberdeen Angus, Highland and Jersey, that have a high lipid content in the muscle studied, differed from the other breeds in that they had a higher beef flavour. The dual-purpose and rustic breeds, Simmental, Casina and Marchigiana, produced significantly less juicy and less tender meat than that from breeds selected for meat production. Overall, despite significant differences previously identified for animal, carcass, muscle and beef traits for the same animals, differences in sensory scores between most of the breeds were small, with only significant differences between the few breeds that had extreme sensory profiles (such as Simmental and Pirenaica).

Authors: A. Conanec; M. D. M. Campo; I. Richardson; P. Ertbjerg; S. Failla, B. Panea; M. Chavent (ASTRAL); J. Saracco (ASTRAL); J. L. Williams; M.-P. Ellies-Oury and J.-F. Hocquette.

7.1.2 Certain relationships between Animal Performance, Sensory Quality and Nutritional Quality can be generalized between various experiments on animal of similar types

In the beef sector, one of the major challenges is to early predict carcass and meat quality and to jointly satisfy the multiple expectations of the various stakeholders. Thus, the objective of this study 13 was to determine if the relationships among carcass, nutritional and sensory qualities established previously by Ellies-Oury et al. (2016) might be generalized to different type of animals.

The Longissimus thoracis muscles of 32 young Charolais bulls were analyzed in terms of sensory and nutritional quality (lipid content and fatty acid composition). These parameters of interest were linked together and to animal performances by using a clustering of variables.

Longissimus thoracis sensory and nutritional qualities appear sometimes antagonistic. Indeed, some “positive” sensory descriptors (juiciness, overall appreciation, overall flavor and overall odor) are negatively related to PUFA proportions. PUFA proportions are positively associated with carcass weight but in the same time with rancid/fish flavors. Moreover, CLA and trans MUFA proportions are positively associated with the “negative” descriptors of greasy feel and residues. To finish, carcass weight and ADG are negatively associated with some “positive” sensory descriptors except tenderness.

It can be concluded from this work that these relationships, that were already established in previous works, are robust between experiments.

In order to highlight robust and generalizable relationships in different contexts, it is now appropriate to apply this method to a larger database containing different traits and various characteristics of breed, slaughter ages, animal types, fattening practices.

Authors: M.-P. Ellies-Oury; D. Durand; A, Listrat; M. Chavent (ASTRAL); J. Saracco (ASTRAL) and D. Gruffat.

7.2.1 Integro-differential optimality equations for the risk-sensitive control of piecewise deterministic Markov processes

In this paper 12 we study the minimization problem of the infinite-horizon expected exponential utility total cost for continuous-time piecewise deterministic Markov processes with the control acting continuously on the jump intensity $\lambda$ and on the transition measure $Q$ of the process. The action space is supposed to depend on the state variable and the state space is considered to have a frontier such that the process jumps whenever it touches this boundary. We characterize the optimal value function as the minimal solution of an integro-differential optimality equation satisfying some boundary conditions, as well as the existence of a deterministic stationary optimal policy. These results are obtained by using the so-called policy iteration algorithm, under some continuity and compactness assumptions on the parameters of the problem, as well as some non-explosive conditions for the process.

Authors: F. Dufour (ASTRAL) and O. Costa.

7.2.2 On the equivalence of the integral and differential Bellman equations in impulse control problems

When solving optimal impulse control problems, one can use the dynamic programming approach in two different ways: at each time moment, one can make the decision whether to apply a particular type of impulse, leading to the instantaneous change of the state, or apply no impulses at all; or, otherwise, one can plan an impulse after a certain interval, so that the length of that interval is to be optimised along with the type of that impulse. The first method leads to the differential Bellman equation, while the second method leads to the integral Bellman equation. The target of the current article 28 is to prove the equivalence of those Bellman equations in many specific models. Those include abstract dynamical systems, controlled ordinary differential equations, piece-wise deterministic Markov processes and continuous-time Markov decision processes.

Authors: F. Dufour (ASTRAL); A. Piunovskiy and A. Plakhov.

7.2.3 Maximizing the probability of visiting a set infinitely often for a countable state space Markov decision process

In 29, we consider a Markov decision process with countable state space and Borel action space. We are interested in maximizing the probability that the controlled Markov chain visits some subset of the state space infinitely often. We provide sufficient conditions, based on continuity and compactness requirements, together with a stability condition on a parametrized family of auxiliary control models, which imply the existence of an optimal policy that is deterministic and stationary. We compare our hypotheses with those existing in the literature.

Authors: F. Dufour (ASTRAL) and T. Prieto-Rumeau

7.2.4 Stationary Markov Nash equilibria for nonzero-sum constrained ARAT Markov games

In 30, we consider a nonzero-sum Markov game on an abstract measurable state space with compact metric action spaces. The goal of each player is to maximize his respective discounted payoff function under the condition that some constraints on a discounted payoff are satisfied. We are interested in the existence of a Nash or noncooperative equilibrium. Under suitable conditions, which include absolute continuity of the transitions with respect to some reference probability measure, additivity of the payoffs and the transition probabilities (ARAT condition), and continuity in action of the payoff functions and the density function of the transitions of the system, we establish the existence of a constrained stationary Markov Nash equilibrium, that is, the existence of stationary Markov strategies for each of the players yielding an optimal profile within the class of all history-dependent profiles.

Authors: F. Dufour (ASTRAL) and T. Prieto-Rumeau

7.3.1 Advanced topics in Sliced Inverse Regression

Since its introduction in the early 90s, the Sliced Inverse Regression (SIR) methodology has evolved adapting to increasingly complex data sets in contexts combining linear dimension reduction with non linear regression. The assumption of dependence of the response variable with respect to only a few linear combinations of the covariates makes it appealing for many computational and real data application aspects. This work 14 proposes an overview of the most active research directions in SIR modeling from multivariate regression models to regularization and variable selection.

Authors: S. Girard; H. Lorenzo (ASTRAL) and J. Saracco (ASTRAL).

7.3.2 Computational outlier detection methods in sliced inverse regression

Sliced inverse regression (SIR) focuses on the relationship between a dependent variable $y$ and a p-dimensional explanatory variable $x$ in a semiparametric regression model, in which, the link relies on an index $x^{\text{'}}\beta$ and link function $f$. SIR allows estimating the direction of $\beta$ that forms the effective dimension reduction (EDR) space. Based on the estimated index, the link function $f$ can then be nonparametrically estimated using kernel estimator. This two-step approach is sensitive to the presence of outliers in the data. The aim of this paper 22 is to propose computational methods to detect outliers in that kind of single-index regression model. Three outlier detection methods are proposed and their numerical behaviors are illustrated on a simulated sample. To discriminate outliers from "normal" observations, they use IB (in-bags) or OOB (out-of-bags) prediction errors from subsampling or resampling approaches. These methods, implemented in $R$, are compared with each other in a simulation study. An application on a real data is also provided.

Authors: H. Lorenzo (ASTRAL) and J. Saracco (ASTRAL).

7.3.3 Data-Driven Sparse Partial Least Squares

In the supervised high dimensional settings with a large number of variables and a low number of individuals, variable selection allows a simpler interpretation and more reliable predictions. That subspace selection is often managed with supervised tools when the real question is motivated by variable prediction. In 17 we propose a Partial Least Square (PLS) based method, called data-driven sparse PLS (ddsPLS), allowing variable selection both in the covariate and the response parts using a single hyper-parameter per component. The subspace estimation is also performed by tuning a number of underlying parameters. The ddsPLS method is compared to existing methods such as classical PLS and two well established sparse PLS methods through numerical simulations. The observed results are promising both in terms of variable selection and prediction performance. This methodology is based on new prediction quality descriptors associated with the classical R 2 and Q 2 and uses bootstrap sampling to tune parameters and select an optimal regression model.

Authors: H. Lorenzo (ASTRAL); O. Cloarec; R. Thiébaut and J. Saracco (ASTRAL).

7.3.4 Handling Correlations in Random Forests: which Impacts on Variable Importance and Model Interpretability?

The present manuscript 19 tackles the issues of model interpretability and variable importance in random forests, in the presence of correlated input variables. Variable importance criteria based on random permutations are known to be sensitive when input variables are correlated, and may lead for instance to unreliability in the importance ranking. In order to overcome some of the problems raised by correlation, an original variable importance measure is introduced. The proposed measure builds upon an algorithm which clusters the input variables based on their correlations, and summarises each such cluster by a synthetic variable. The effectiveness of the proposed criterion is illustrated through simulations in a regression context, and compared with several existing variable importance measures.

Authors: M. Chavent (ASTRAL); J. Lacaille; A. Mourer and M. Olteanu.

7.4.1 A note on Riccati matrix difference equations

Discrete algebraic Riccati equations and their fixed points are well understood and arise in a variety of applications, however, the time-varying equations have not yet been fully explored in the literature. In this article 24 we provide a self-contained study of discrete time Riccati matrix difference equations. In particular, we provide a novel Riccati semigroup duality formula and a new Floquet-type representation for these equations. Due to the aperiodicity of the underlying flow of the solution matrix, conventional Floquet theory does not apply in this setting and thus further analysis is required. We illustrate the impact of these formulae with an explicit description of the solution of time-varying Riccati difference equations and its fundamental-type solution in terms of the fixed point of the equation and an invertible linear matrix map, as well as uniform upper and lower bounds on the Riccati maps. These are the first results of this type for time varying Riccati matrix difference equations.

Authors: P. Del Moral (ASTRAL) and E. Horton (ASTRAL).

7.4.2 On the Stability of Positive Semigroups

In 26, the stability and contraction properties of positive integral semigroups on locally compact Polish spaces are investigated. We provide a novel analysis based on an extension of V-norm, Dobrushin-type, contraction techniques on functionally weighted Banach spaces for Markov operators. These are applied to a general class of positive and possibly time-inhomogeneous bounded integral semigroups and their normalised versions. Under mild regularity conditions, the Lipschitz-type contraction analysis presented in this article simplifies and extends several exponential estimates developed in the literature. The spectraltype theorems that we develop can also be seen as an extension of Perron-Frobenius and Krein-Rutman theorems for positive operators to time-varying positive semigroups. We review and illustrate in detail the impact of these results in the context of positive semigroups arising in transport theory, physics, mathematical biology and advanced signal processing.

Authors: P. Del Moral (ASTRAL); E. Horton (ASTRAL) and A. Jasra.

7.4.3 Quantum harmonic oscillators and Feynman-Kac path integrals for linear diffusive particles

In 27, we propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked controllability conditions, the ground state and the zero-point energy are explicitly computed in terms of a positive fixed point of a continuous time algebraic Riccati matrix equation. We also present an explicit solution of normalized and time dependent Feynman-Kac measures in terms of a time varying linear dynamical system coupled with a differential Riccati matrix equation. A refined non asymptotic analysis of the stability of these models is developed based on a recently developed Floquet-type representation of time varying exponential semigroups of Riccati matrices. We provide explicit and non asymptotic estimates of the exponential decays to equilibrium of Feynman-Kac semigroups in terms of Wasserstein distances or Boltzmann-relative entropy. For reversible models we develop a series of functional inequalities including de Bruijn identity, Fisher's information decays, log-Sobolev inequalities, and entropy contraction estimates. In this context, we also provide a complete and explicit description of all the spectrum and the excited states of the Hamiltonian, yielding what seems to be the first result of this type for this class of models. We illustrate these formulae with the traditional harmonic oscillator associated with real time Brownian particles and Mehler's formula. The analysis developed in this article can also be extended to solve time dependent Schrodinger equations equipped with time varying linear diffusions and quadratic potential functions.

Authors: P. Del Moral (ASTRAL) and E. Horton (ASTRAL).

7.5.1 Asymptotic moments of spatial branching processes

Suppose that $X=(X_t,t\ge 0)$ is either a superprocess or a branching Markov process on a general space E, with non-local branching mechanism and probabilities $P_{{\delta }_x}$ , when issued from a unit mass at $x\in E$. For a general setting in which the first moment semigroup of $X$ displays a Perron-Frobenius type behaviour, we show that 31, for $k\ge 2$ and any positive bounded measurable function $f$ on $E$, ${lim}_{t\to \infty }g\left(t\right)E_{{\delta }_x}\left[{(f,X_t)}^k\right]=C_k(x,f)$ where the constant $C_k(x,f)$ can be identified in terms of the principal right eigenfunction and left eigen-measure and $g\left(t\right)$ is an appropriate determinisitic normalisation, which can be identified explicitly as either polynomial in $t$ or exponential in $t$, depending on whether $X$ is a critical, supercritical or subcritical process. The method we employ is extremely robust and we are able to extract similarly precise results that additionally give us the moment growth with time of ${\int }_0^t(g,X_t)ds$, for bounded measurable $g$ on $E$.

Authors: I. Gonzalez; E. Horton (ASTRAL) and A. E. Kyprianou.

7.5.2 Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes

Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon compensating for this, the distribution of cell sizes converges to an asymptotic profile. However, the long-term stochastic behaviour of the system is more delicate, and its almost sure asymptotics have been so far largely unexplored. In this article 33 , we study a growth-fragmentation process whose cell sizes are bounded above, and prove the existence of regimes with differing almost sure long-term behaviour.

Authors: E. Horton (ASTRAL) and A. R. Watson.

7.5.3 Stochastic Methods for Neutron Transport Equation III: Generational many-to-one and k-eff

The neutron transport equation (NTE) describes the flux of neutrons over time through an inhomogeneous fissile medium. In the recent articles, [A. M. G. Cox et al., J. Stat. Phys., 176 (2019), pp. 425–455; E. Horton, A. E. Kyprianou, and D. Villemonais, Ann. Appl. Probab., 30 (2020), pp. 2573–2612] a probabilistic solution of the NTE is considered in order to demonstrate a Perron–Frobenius type growth of the solution via its projection onto an associated leading eigenfunction. In [S. C. Harris, E. Horton, and A. E. Kyprianou, Ann. Appl. Probab., 30 (2020), pp. 2815–2845; A. M. G. Cox et al., Monte Carlo Methods for the Neutron Transport Equation, arxiv (2020)], further analysis is performed to understand the implications of this growth both in the stochastic sense as well as from the perspective of Monte Carlo simulation. Such Monte Carlo simulations are prevalent in industrial applications, in particular where regulatory checks are needed in the process of reactor core design. In that setting, however, it turns out that a different notion of growth takes center stage, which is otherwise characterized by another eigenvalue problem. In that setting, the eigenvalue, sometimes called $k$-effective (written $k_{\mathrm{𝚎𝚏𝚏}}$), has the physical interpretation as being the ratio of neutrons produced (during fission events) to the number lost (due to absorption in the reactor or leakage at the boundary) per typical fission event. In this article 11, we aim to supplement [J. Stat. Phys., 176 (2019), pp. 425–455; Ann. Appl. Probab., 30 (2020), pp. 2573–2612; Ann. Appl. Probab., 30 (2020), pp. 2815–2845; Monte Carlo Methods for the Neutron Transport Equation, arxiv (2020)] by developing the stochastic analysis of the NTE further to the setting where a rigorous probabilistic interpretation of $k_{\mathrm{𝚎𝚏𝚏}}$ is given, both in terms of a Perron–Frobenius type analysis as well as via classical operator analysis. To our knowledge, despite the fact that an extensive engineering literature and industrial Monte Carlo software are concentrated around the estimation of $k_{\mathrm{𝚎𝚏𝚏}}$ and its associated eigenfunction, we believe that our work is the first rigorous treatment in the probabilistic sense (which underpins some of the aforesaid Monte Carlo simulations).

Authors: A. M. G. Cox; E. Horton (ASTRAL); A. E. Kyprianou and D. Villemonais

Read More: SIAM

7.5.4 Yaglom limit for critical neutron transport

In 32, we consider the classical Yaglom limit theorem for the Neutron Branching Process (NBP) in the setting that the mean semigroup is critical, i.e. its leading eigenvalue is zero. We show that the law of the process conditioned on survival is asymptotically equivalent to an exponential distribution. As part of the proof, we also show that the probability of survival decays inversely proportionally to time. Although Yaglom limit theorems have recently been handled in the setting of spatial branching processes and superprocesses, as well as in the setting of isotropic homogeneous Neutron Branching Processes, our approach and the main novelty of this work is based around a precise result for the scaled asymptotics for the k-th martingale moments of the NBP (rather than the Yaglom limit itself). Our proof of the asymptotic martingale moments turns out to offer a general approach to asymptotic martingale moments of critical branching Markov processes with a non-local branching mechanism. Indeed this is the context in which we give both our moment proofs and the Yaglom limit.

Authors: S. C. Harris; E. Horton (ASTRAL); A. E. Kyprianou and M. Wang.

7.5.5 A theoretical analysis of one-dimensional discrete generation ensemble Kalman particle filters

Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type particle filters (a.k.a. sequential Monte Carlo), this ensemble-type methodology can also be interpreted as mean-field particle approximations of the Kalman-Bucy filtering equation. In contrast with conventional mean-field type interacting particle methods equipped with a globally Lipschitz interacting drift-type function, Ensemble Kalman filters depend on a nonlinear and quadratic-type interaction function defined in terms of the sample covariance of the particles. Most of the literature in applied mathematics and computer science on these sophisticated interacting particle methods amounts to designing different classes of useable observer-type particle methods. These methods are based on a variety of inconsistent but judicious ensemble auxiliary transformations or include additional inflation/localisationtype algorithmic innovations, in order to avoid the inherent time-degeneracy of an insufficient particle ensemble size when solving a filtering problem with an unstable signal. To the best of our knowledge, the first and the only rigorous mathematical analysis of these sophisticated discrete generation particle filters is developed in the pioneering articles by Le Gland-Monbet-Tran and by Mandel-Cobb-Beezley, which were published in the early 2010s. Nevertheless, besides the fact that these studies prove the asymptotic consistency of the Ensemble Kalman filter, they provide exceedingly pessimistic meanerror estimates that grow exponentially fast with respect to the time horizon, even for linear Gaussian filtering problems with stable one dimensional signals. In the present article 25 we develop a novel self-contained and complete stochastic perturbation analysis of the fluctuations, the stability, and the long-time performance of these discrete generation ensemble Kalman particle filters, including time-uniform and non-asymptotic mean-error estimates that apply to possibly unstable signals. To the best of our knowledge, these are the first results of this type in the literature on discrete generation particle filters, including the class of genetic-type particle filters and discrete generation ensemble Kalman filters. The stochastic Riccati difference equations considered in this work are also of interest in their own right, as a prototype of a new class of stochastic rational difference equation.

Authors: P. Del Moral (ASTRAL) and E. Horton (ASTRAL)

7.5.6 Interacting Weighted Ensemble Kalman Filter applied to Underwater Terrain Aided Navigation

Terrain Aided Navigation (TAN) provides a driftfree navigation approach for Unmanned Underwater Vehicles. This paper 21 focuses on an improved version of the Weighted Ensemble Kalman Filter (WEnKF) to solve the TAN problem. We analyze some theoretical limitations of the WEnKF and derive an improved version which ensures that the asymptotic variance of weights remains bounded. This improvement results in an enhanced robustness to nonlinearities in practice. Numerical results are presented and the robustness is demonstrated with respect to conventional WEnKF, yielding twice as less nonconvergence cases.

Authors: C. Palmier (ASTRAL); K. Dahia; N. Merlinge; D. Laneuville (ASTRAL) and P. Del Moral (ASTRAL).

7.6.1 Definition of the fluctuation function in the detrendred fluctuation analysis and its variant

The detrended fluctuation analysis (DFA) and its variants are popular methods to analyze the self-similarity of a signal. Two steps characterize them: firstly, the trend of the centered integrated signal is estimated and removed. Secondly, the properties of the so-called fluctuation function which is an approximation of the standard deviation of the resulting process is analyzed. However, it appears that the statistical mean was assumed to be equal to zero to obtain it. As there is no guarantee that this assumption is true a priori, this hypothesis is debatable. The purpose of this paper 9 is to propose two alternative definitions of the fluctuation function. Then, we compare all of them based on a matrix formulation and the filter-based interpretation we recently proposed. This analysis will be useful to show that the approach proposed in the original paper remains a good compromise in terms of accuracy and computational cost.

Authors: B. Berthelot; E. Grivel; P. Legrand (ASTRAL) and A. Giremus.

7.6.2 A matrix approach to get the variance of the square of the fluctuation function of the DFA

The fluctuation analysis (FA) and the detrended fluctuation analysis (DFA) make it possible to estimate the Hurst exponent H, which characterizes the self-similarity of a signal. Both are based on the fact that the so-called fluctuation function, which can be seen as an approximation of the standard deviation of the process scaled in time by multiplying the time variable by a positive constant, depends on H. The main novelty of the paper 15 is to provide the expression of the variance of the square of the fluctuation function, by using a matrix formulation. We show that it depends on the correlation function of the signal under study when it is zero-mean and Gaussian. Illustrations are given when dealing with a zero-mean white Gaussian noise. Moving average processes and first-order autoregressive processes are also addressed.

Authors: E. Grivel; B. Berthelot and P. Legrand (ASTRAL).

7.6.3 DFA-based abacuses providing the Hurst exponent estimate for short-memory processes

The detrended fluctuation analysis (DFA) and its higher-order variant make it possible to estimate the Hurst exponent and therefore to quantify the long-range dependence of a random process. These methods are popular and used in a wide range of applications where they have been proven to be discriminative to characterize or classify processes. Nevertheless, in practice, the signal may be short-memory. In addition, depending on the number of samples available, there is no guarantee that these methods provide the true value of the Hurst exponent, leading the user to draw erroneous conclusions on the long-range dependence of the signal under study. In this paper 16, using a matrix formulation and making no approximation, we first propose to analyze how the DFA and its higher-order variant behave with respect to the number of samples available. Illustrations dealing with short-memory data that can be modeled by a white noise, a moving-average process and a random process whose autocorrelation function exponentially decays are given. Finally, to avoid any wrong conclusions, we propose to derive abacuses linking the value provided by the DFA or its variant with the properties of the signal and the number of samples available.

Authors: E. Grivel; B. Berthelot; P. Legrand (ASTRAL) and A. Giremus

7.6.4 New variants of DFA based on loess and lowess methods: generalization of the detrending moving average

Proposed early in the 90ies, the detrended fluctuation analysis (DFA) can be used to estimate the Hurst exponent and has been proven relevant in various applications, from economics to biomedical. For the last years, variants have been proposed. They differ in the way to estimate the trend of the centered integrated signal. In this paper 18, we recall the main principles of some of these methods, provide explanations on the behaviours of the algorithms and analyze the relevance of new variants based on the Savitzky-Golay filter, also known as the LOESS approach, and the LOWESS. They bridge the gap between the DFA and the detrending moving average (DMA). We hence show that the LOESS-based method is a generalization of the DMA.

Authors: B. Berthelot; E. Grivel and P. Legrand (ASTRAL).

7.7.1 Quina metodologia per despolhar l'enquèsta Bourciez ?

An astonishing team of researchers, teachers and, above all, lovers of the Langue d'Oc with diverse and varied skills, has been carrying out a systematic analysis of the Bourciez survey for just over a year. In 1894, Edouard Bourciez, then a professor at the University of Bordeaux, asked teachers in the Bordeaux and Toulouse academies to translate a reworked version of the parable of the prodigal son into the idiom of the commune where they taught. The results of this investigation undoubtedly exceeded the professor's expectations, since more than 4400 parables were returned to him. These manuscripts are now kept at the University of Bordeaux and form a corpus of 17 volumes of about 1000 manuscript pages each. We are very grateful to the university library for allowing us to have them. For reasons that are not easy to explain, a systematic analysis of this survey has never been carried out, except for the Basque part corresponding to 150 municipalities, i.e. less than 4 percent of the corpus. We are proceeding with the analysis of this survey 20 according to the following four points, not in series, but in parallel: - Computer transcription of the manuscripts ; - Creation of the database; - Data mining and statistical analysis of the database; - Formatting of the results in a format accessible to the greatest number of people.

Author: Alexandre Genadot (ASTRAL)

7.7.2 Hierarchical Agglomerative Clustering under contiguity constraint for Hi-C data analysis

The spatial organisation of the genome within the cell nucleus has a major impact on the regulation of gene expression, with important implications for foetal development, cell differentiation and disease development. This is the initial motivation for this work 23, which aims to study the three-dimensional structure of genetic material and its variations using Hi-C data. First, the modelling of the hierarchical structure of the genome from Hi-C data is investigated. Extensions of a natural statistical tool for examining hierarchical structures, Hierarchical Ascending Classification (HAC), are studied to justify its application to Hi-C. This allows us to justify the modelling of structures by binary trees (derived from HAC). We then develop a method for comparing two samples of trees to be able to identify significant differences.

Authors: N. Randriamihamison (ASTRAL).

Naval Group

Participants: P. Del Moral, F. Dufour, A. Genadot, E. Horton, D. Laneuville, O. Marceau, R. Namyst, A. Nègre, H. Zhang, R. Zhang.

In the applicative domain, an important research focus of the team is the tracking of passive underwater targets in the context of passive underwater acoustic warfare. This is a very complicated practical problem that combines both filtering and stochastic control issues. This research topic is addressed in collaboration with Naval Group. We refer the reader to the section 4.1 for a more detailed description of this theme.

Thales Optronique

Participants: Benoîte de Saporta, François Dufour, Tiffany Cerchi.

Maintenance, optimization, fleet of industrial equipements. The topic of this collaboration with Université de Montpellier and Thales Optronique is the application of Markov decision processes to the maintenance optimization of a fleet of industrial equipments.

Thales AVS

Participants: Bastien Berthelot, Pierrick Legrand.

The collaboration is centered around some contributions to the estimation of the Hurst coefficient and his application on biosignals in the domain of crew monitoring.

Case Law Analytics

Participant: Pierrick Legrand.

Pierrick Legrand is a consultant for the startup Case Law Analytics. The object of the consulting is confidential.

Sartorius

Participants: Hadrien Lorenzo Jérôme Saracco.

The team is currently initiating a scientific collaboration with the Advanced Data Analytics Group of Sartorius Corporate Research which is an international pharmaceutical and laboratory equipment supplier, covering the segments of Bioprocess Solutions and Lab Products and Services. The current work concerns the development of a PLS (Partial Least Squares) inspired method in the context of multiblock of covariates (corresponding to different technologies and/or different sampling, statistical natures...) and high dimensional datasets (with the sample size n much smaller than the number of variables in the different blocks). The proposed method, called ddsPLS for data-driven sparse PLS, allows variable selection in the X and in the Y parts thanks to interpretable parameters associate with the soft-thresolding of the empirical correlation matrices (between the X's blocks and the Y block) decomposed in SVD (Singular Values Decomposition) ways. In addition a methodology to handle specific missing values (i.e. missing samples in some covariate blocks) is also under investigation.

Safran Aircraft Engines

Participants: Marie Chavent, Jérôme Lacaille, Alex Mourer, Madalina Olteanou

The collaboration is centered around an applied mathematics thesis defining a formalism and a methodology for processing and interpretation by the importance of variables (from measurements and calculated indicators) in the case of unsupervised problems. This methodology is accompanied by code programming and a demonstration on an example data set from Safran Aircraft Engines.

Orosys

Participants: Tara Vanhatalo, Pierrick Legrand

Within the framework of Tara Vanhatalo's cifre thesis, a collaboration contract has been signed between Inria, Univiersité de Bordeaux and the company Orosys.

The collaboration is oriented around the modeling of amplifiers by AI.

9.1.1 Participation in other International Programs

Emma Horton and her collaborator Ellen Powell (University of Durham, UK) have been awarded a PHC Alliance 2022 grant.

9.2.1 Visits of international scientists

9.2.2 Visits to international teams

9.3.1 Visits of national scientists

9.3.2 Visits to national teams

Naval Group

Astral is a joint INRIA team project with Naval Group. The topic of this collaboration is described in section 4.1.

QuAMProcs of the program Project Blanc of the ANR

The mathematical analysis of metastable processes started 75 years ago with the seminal works of Kramers on Fokker-Planck equation. Although the original motivation of Kramers was to « elucidate some points in the theory of the velocity of chemical reactions », it turns out that Kramers’ law is observed to hold in many scientific fields: molecular biology (molecular dynamics), economics (modelization of financial bubbles), climate modeling, etc. Moreover, several widely used efficient numerical methods are justified by the mathematical description of this phenomenon.

Recently, the theory has witnessed some spectacular progress thanks to the insight of new tools coming from Spectral and Partial Differential Equations theory.

Semiclassical methods together with spectral analysis of Witten Laplacian gave very precise results on reversible processes. From a theoretical point of view, the semiclassical approach allowed to prove a complete asymptotic expansion of the small eigen values of Witten Laplacian in various situations (global problems, boundary problems, degenerate diffusions, etc.). The interest in the analysis of boundary problems was rejuvenated by recent works establishing links between the Dirichlet problem on a bounded domain and the analysis of exit event of the domain. These results open numerous perspectives of applications. Recent progress also occurred on the analysis of irreversible processes (e.g. on overdamped Langevin equation in irreversible context or full (inertial) Langevin equation).

The above progresses pave the way for several research tracks motivating our project: overdamped Langevin equations in degenerate situations, general boundary problems in reversible and irreversible case, non-local problems, etc.

Mission pour les initiatives transverses et interdisciplinaires, Défi Modélisation du Vivant, projet MISGIVING

The aim of MISGIVING (MathematIcal Secrets penGuins dIVING) is to use mathematical models to understand the complexity of the multiscale decision process conditioning not only the optimal duration of a dive but also the diving behaviour of a penguin inside a bout. A bout is a sequence of succesive dives where the penguin is chasing prey. The interplay between the chasing period (dives) and the resting period due to the physiological cost of a dive (the time spent at the surface) requires some kind of optimization.

10.1.1 Scientific events: organisation

• Pierrick Legrand started the organisation of EA2022 in Exeter, England.
• Pierrick Legrand participated to the organisation of the GIS Albatros Techno Days.

10.1.2 Journal

10.1.3 Invited talks

F. Dufour has been invited to give a talk at the workshop Modern Trends in Controlled Stochastic Processes: Theory and Applications, University of Liverpool, July 2021.

F. Dufour has been invited to give a talk at Symposium on Stochastic Hybrid Systems and Applications, July 2021.

E. Horton was invited to give a mini-course at the 6th Bath-Paris-Beijing Branching Structures Workshop, Septemper 2021.

10.1.4 Leadership within the scientific community

Pierrick Legrand is the president of the association EA.

10.1.5 Scientific expertise

J. Saracco is an elected member of the CNU 26 (National Council of Universities in Applied Mathematics), since 2019.

Emma Horton is a member of the RSS Applied Probability committee.

10.1.6 Research administration

J. Saracco is the leader of the team OptimAl of Institut de Mathématiques de Bordeaux (IMB, UMR CNRS 5251) from 2019.

Marie Chavent is a member appointed to the Council of the Department of Engineering and Digital Sciences (SIN) of the University of Bordeaux.

A. Genadot is member of the Scientific council of the Mathematical Institute of Bordeaux.

A. Genadot is member of the "Commission des emplois de recherche" of Inria BSO.

P. Legrand is member of the CUMI commission.

10.2.1 Teaching

• J. Saracco is the head of the engineering department of ENSC, Graduate School of Cognitics (applied cognitive science and technology) which is a Bordeaux INP engineering school.
• Marie Chavent is in charge of the first year of the MIASHS degree program at Université de Bordeaux.
• Alexandre Genadot is in charge of the first year of the MIASHS degree program at Université de Bordeaux.
• Pierrick Legrand is in charge of the mathematics program for the MIASHS degree at Université de Bordeaux.

• Licence : P. Legrand, Algèbre, 129h, L1, Université de Bordeaux, France.
• Licence : P. Legrand, Espaces Euclidiens, 46,5h, L2, Université de Bordeaux, France.
• Licence : P. Legrand, Informatique pour les mathématiques, 30h, L2, Université de Bordeaux, France.
• DU : P. Legrand, Evolution Artificielle, Big data, 8h, DU, Bordeaux INP, France.
• Engineer School: Signal processing, 54 hours, ENSC, Bordeaux, France.
• Master: Scientific courses, 10 hours, Université de Bordeaux, France.
• Licence : A. Genadot, Bases en Probabilités, 18h, L1, Université de Bordeaux, France.
• Licence : A. Genadot, Projet Professionnel de l'étudiant, 8h, L1, Université de Bordeaux, France.
• Licence : A. Genadot, Probabilité, 30h, L2, Université de Bordeaux, France.
• Licence : A. Genadot, Techniques d'Enquêtes, 10h, L2, Université de Bordeaux, France.
• Licence : A. Genadot, Modélisation Statistiques, 16.5h, L3, Université de Bordeaux, France.
• Licence : A. Genadot, Préparation Stage, 15h, L3, Université de Bordeaux, France.
• Licence : A. Genadot, TER, 5h, L3, Université de Bordeaux, France.
• Licence : A. Genadot, Processus, 16.5h, L3, Université de Bordeaux, France.
• Licence : A. Genadot, Statistiques, 20h, L3, Bordeaux INP, France.
• Master : A. Genadot, Savoirs Mathématiques, 81h, M1, Université de Bordeaux et ESPE, France.
• Master : A. Genadot, Martingales, 29h, M1, Université de Bordeaux, France.
• Licence : F. Dufour, Probabilités et statistiques, 70h, first year of école ENSEIRB-MATMECA, Institut Polytechnique de Bordeaux, France.
• Master : F. Dufour, Approche probabiliste et méthode de Monte Carlo, 24h, third year of école ENSEIRB-MATMECA, Institut Polytechnique de Bordeaux, France.
• Licence : J. Saracco, Probabilités et Statistique, 27h, first year of Graduate Schools of Engineering ENSC-Bordeaux INP, Institut Polytechnique de Bordeaux, France.
• Licence : J. Saracco, Statistique inférentielle et Analyse des données, 45h, first year of Graduate Schools of Engineering ENSC-Bordeaux INP, Institut Polytechnique de Bordeaux, France.
• Licence : J. Saracco, Statistique pour l’ingénieur, 16h, first year of Graduate Schools of Engineering ENSPIMA-Bordeaux INP, Institut Polytechnique de Bordeaux, France.
• Master : J. Saracco, Modélisation statistique, 81h, second year of Graduate Schools of Engineering ENSC-Bordeaux INP, Institut Polytechnique de Bordeaux, France.
• DU : J. Saracco, Statistique et Big data, 45h, DU BDSI (Big data et statistique pour l'ingénieur), Bordeaux INP, France.
• Licence : M. Chavent, Statistique Inférentielle, 18h, L2, Université de Bordeaux, France
• Licence : M. Chavent, Techniques d'Enquêtes, 10h, L2, Université de Bordeaux, France
• Master : M. Chavent, DataMining, 43h, M2, Université de Bordeaux
• Master : M. Chavent, Machine Learning, 58h, Université de Bordeaux,
• DU: M. Chavent, Apprentissage, 12h, DU BDSI, Bordeaux INP, France
• Licence : E. Horton, Probabilités et Statistiques, 32h, ENSEIRB-MATMECA, Institut Polytechnique de Bordeaux, France.
• Licence : E. Horton, Probabilités, 22h, ENSEIRB-MATMECA, Institut Polytechnique de Bordeaux, France.
• Licence : E. Horton, Probabilités, 24h, ENSEIRB-MATMECA, Institut Polytechnique de Bordeaux, France.
• Licence : E. Horton, 30h, Statistique inférentielle et Analyse des données, first year of Graduate Schools of Engineering ENSC-Bordeaux INP, Institut Polytechnique de Bordeaux, France.

10.2.2 Supervision

• PhD in progress (2021-2024): John Albechaalany, "Conception d'un modèle multi-objectifs permettant de piloter les liens entre les pratiques d'élevage et la qualité des viandes bovines", supervised by Jérôme Saracco (ASTRAL) and Marie-Pierre Ellies-Oury (Bordeaux Sciences Agro & Inrae).
• PhD in progress (2021-2024): Romain Namyst, "Contrôle optimal stochastique et application à la trajectographie passive", supervised by F. Dufour and A. Genadot. INRIA fellowship. Collaboration with Naval Group.
• PhD in progress: Alex Mourer, "Variables importance in clustering", CIFRE Safran Aircraft Engines, supervised by Jérôme Lacaille (Safran), Madalina Olteanou (SAMM, Paris1), Alex Mourer (doctorant), Marie Chavent (ASTRAL).
• PhD defended in November 2021 (University of Toulouse): Nathanaël Randriamihamison, "Contiguity Constrained Hierarchical Agglomerative Clustering for Hi-C data analysis", supervised by Nathalie Vialaneix (MIAT, INRA Toulouse), Pierre Neuvial (IMT, CNRS), Marie Chavent (ASTRAL).
• PhD defended in November 2021 (University of Bordeaux): Alexandre Conanec, "Modélisation de l'optimisation du pilotage des qualités et des performances de production de la viande bovine", supervised by Marie Chavent(ASTRAL), Jérôme Saracco (ASTRAL), Marie-Pierre Ellies (Bordeaux Sciences Agro & Inrae).
• PhD defended in December 2021: Tiffany Cherchi, “Automated optimal fleet management policy for airborne equipment”, Montpellier University, supervised by B. De Saporta and F. Dufour.
• PhD defended in March 2021: Bastien Berthelot, “Contributions à l'estimation du coefficient de Hurst et son usage sur des biosignaux dans le domaine du crew monitoring”, CIFRE THALES, supervised by P. Legrand.
• PhD defended in December 2021: Camille Palmier, “Nouvelles approches de fusion multi-capteurs par filtrage particulaire pour le recalage de navigation inertielle par corrélation de cartes”, CIFRE, supervised by P. Del Moral, Dann Laneuville (NavalGroup) and Karim Dahia (ONERA).

10.2.3 Juries

Pierrick Legrand was member of the PhD jurys of Ulviya Abdulkarimova, Nicolas Scalzitti and Pierre-antoine Chantal.

International journals

• 9 articleB.Bastien Berthelot, E.Eric Grivel, P.Pierrick Legrand and A.Audrey Giremus. Definition of the fluctuation function in the detrendred fluctuation analysis and its variant.The European Physical Journal B: Condensed Matter and Complex Systems942021
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• 10 articleA.Alexandre Conanec, M. D.Maria Del Mar Campo, I.Ian Richardson, P.Per Ertbjerg, S.Sebastiana Failla, B.Begoña Panea, M.Marie Chavent, J.Jérôme Saracco, J. L.John L. Williams, M.-P.Marie-Pierre Ellies-Oury and J.-F. J.Jean-François J.-F. Hocquette. Has breed any effect on beef sensory quality?Livestock Science250August 2021, 104548
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• 11 articleA. M.Alexander M. G. Cox, E. L.Emma L. Horton, A. E.Andreas E. Kyprianou and D.Denis Villemonais. Stochastic Methods for Neutron Transport Equation III: Generational many-to-one and $k_{\mathrm{𝚎𝚏𝚏}}$.SIAM Journal on Applied Mathematics813May 2021
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• 12 articleF.François Dufour and O.O. Costa. Integro-differential optimality equations for the risk-sensitive control of piecewise deterministic Markov processes.Mathematical Methods of Operations Research932April 2021, 327-357
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• 13 articleM.-P.Marie-Pierre Ellies-Oury, D.D. Durand, A.Anne Listrat, M.Marie Chavent, J.Jérôme Saracco and D.Dominique Gruffat. Certain relationships between Animal Performance, Sensory Quality and Nutritional Quality can be generalized between various experiments on animal of similar types.Livestock Science250August 2021, 104554
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• 14 articleS.Stéphane Girard, H.Hadrien Lorenzo and J.Jérôme Saracco. Advanced topics in Sliced Inverse Regression.Journal of Multivariate Analysis1882022, 104852
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• 15 articleE.Eric Grivel, B.Bastien Berthelot and P.Pierrick Legrand. A matrix approach to get the variance of the square of the fluctuation function of the DFA.Digital Signal Processing2021
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• 16 articleE.Eric Grivel, B.Bastien Berthelot, P.Pierrick Legrand and A.Audrey Giremus. DFA-based abacuses providing the Hurst exponent estimate for short-memory processes.Digital Signal Processing1162021
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• 17 articleH.Hadrien Lorenzo, O.Olivier Cloarec, R.Rodolphe Thiébaut and J.Jérôme Saracco. Data-Driven Sparse Partial Least Squares.Statistical Analysis and Data MiningDecember 2021
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International peer-reviewed conferences

• 18 inproceedingsB.Bastien Berthelot, E.Eric Grivel and P.Pierrick Legrand. New variants of DFA based on loess and lowess methods: generalization of the detrending moving average.ICASSP 2021 - IEEE International Conference on Acoustics, Speech and Signal ProcessingTotonto, Canada2021
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Conferences without proceedings

• 19 inproceedings M.Marie Chavent, J.Jerome Lacaille, A.Alex Mourer and M.Madalina Olteanu. Handling Correlations in Random Forests: which Impacts on Variable Importance and Model Interpretability? ESANN Bruges, Belgium October 2021
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• 20 inproceedings A.Alexandre Genadot. Quina metodologia per despolhar l'enquèsta Bourciez ? Ièr, deman : diga-m'o dins la lenga Montpellier, France November 2021
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• 21 inproceedingsC.Camille Palmier, K.Karim Dahia, N.Nicolas Merlinge, D.Dann Laneuville and P.Pierre Del Moral. Interacting Weighted Ensemble Kalman Filter applied to Underwater Terrain Aided Navigation.ACC 2021 - American Control ConferenceNew Orleans / Virtual, United StatesMay 2021
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Scientific book chapters

• 22 inbookH.Hadrien Lorenzo and J.Jérôme Saracco. Computational outlier detection methods in sliced inverse regression.Advances in Contemporary Statistics and EconometricsSpringer International PublishingJune 2021, 101-122
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Doctoral dissertations and habilitation theses

• 23 thesisN.Nathanaël Randriamihamison. Hierarchical Agglomerative Clustering under contiguity constraint for Hi-C data analysis.Université Paul Sabatier - Toulouse IIIOctober 2021
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Reports & preprints

• 24 miscP.Pierre Del Moral and E.Emma Horton. A note on Riccati matrix difference equations.July 2021
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• 25 miscP.Pierre Del Moral and E.Emma Horton. A theoretical analysis of one-dimensional discrete generation ensemble Kalman particle filters.July 2021
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• 26 miscP.Pierre Del Moral, E.Emma Horton and A.Ajay Jasra. On the Stability of Positive Semigroups.January 2022
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• 27 miscP.Pierre Del Moral and E.Emma Horton. Quantum harmonic oscillators and Feynman-Kac path integrals for linear diffusive particles.June 2021
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• 28 miscF.François Dufour, A.Alexey Piunovskiy and A.Alexander Plakhov. On the equivalence of the integral and differential Bellman equations in impulse control problems.January 2022
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• 29 miscF.François Dufour and T.Tomás Prieto-Rumeau. Maximizing the probability of visiting a set infinitely often for a countable state space Markov decision process.January 2022
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• 30 miscF.François Dufour and T.Tomás Prieto-Rumeau. Stationary Markov Nash equilibria for nonzero-sum constrained ARAT Markov games.January 2022
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• 31 miscI.Isaac Gonzalez, E.Emma Horton and A. E.Andreas E Kyprianou. Asymptotic moments of spatial branching processes.December 2021
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• 32 miscS. C.Simon C Harris, E.Emma Horton, A. E.Andreas E Kyprianou and M.Minmin Wang. Yaglom limit for critical neutron transport.July 2021
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• 33 miscE.Emma Horton and A. R.Alexander R Watson. Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes.July 2021
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