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We study the kernel estimator of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that this estimator is consistent and asymptotically normal. Next, in the numerical studies, we propose two data-driven methods to choose the bandwidth parameters. These methods are based on the so-called two bandwidths approach., Comment: 27 pages, 24 figures. arXiv admin note: text overlap with arXiv:2012.04741

The main objective of this article is to establish a central limit theorem for additive three-variable functionals of bifurcating Markov chains. We thus extend the central limit theorem under point-wise ergodic conditions studied in Bitseki-Delmas (2022) and to a lesser extent, the results of Bitseki-Delmas (2022) on central limit theorem under $L^{2}$ ergodic conditions. Our results also extend and complement those of Guyon (2007) and Delmas and Marsalle (2010). In particular, when the ergodic rate of convergence is greater than $1/\sqrt{2}$, we have, for certain class of functions, that the asymptotic variance is non-zero at a speed faster than the usual central limit theorem studied by Guyon and Delmas-Marsalle., Comment: 14 pages. arXiv admin note: text overlap with arXiv:2012.04741

Defect engineering is applied to hybrid (CH$_3$NH$_3$)PbI$_3$ organic-inorganic perovskites. These materials have become one of the most promising low-cost alternatives to traditional semiconductors in the field of photovoltaics and light emitting devices. We use here Helium ion irradiation at low energy as a tool for the controlled introduction of point defects in both single crystals and polycrystalline thin films. The irradiation defects modify the opto-electronic properties as probed using photoluminescence spectroscopy from 10K to room-temperature. 2 Contrary to usual semiconductors, we observe a very good resilience of the PL properties with irradiation, even associated to an enhancement of the optical emission at low temperature. We discuss these results in relation with the tetragonal to orthorhombic low-temperature phase transition below T=160 K. A comparison between spectra from single crystals and polycrystalline films, both with and without irradiation defects, allow a better understanding of the light emission mechanisms in both kinds of samples. We thereby evidence radiation hardness of these materials and the specificity of defects and their impact over light emission properties.

Bitseki and Delmas (2021) have studied recently the central limit theorem for kernel estimator of invariant density in bifurcating Markov chains models. We complete their work by proving a moderate deviation principle for this estimator. Unlike the work of Bitseki and Gorgui (2021), it is interesting to see that the distinction of the two regimes disappears and that we are able to get moderate deviation principle for large values of the ergodic rate. It is also interesting and surprising to see that for moderate deviation principle, the ergodic rate begins to have an impact on the choice of the bandwidth for values smaller than in the context of central limit theorem studied by Bitseki and Delmas (2021)., Comment: 27

Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. Motivated by the functional estimation of the density of the invariant probability measure which appears as the asymptotic distribution of the trait, we prove the consistence and the Gaussian fluctuations for a kernel estimator of this density based on late generations. In this setting, it is interesting to note that the distinction of the three regimes on the ergodic rate identified in a previous work (for fluctuations of average over large generations) disappears. This result is a first step to go beyond the threshold condition on the ergodic rate given in previous statistical papers on functional estimation., Comment: 40 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:2012.04741; text overlap with arXiv:2106.07711

Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for additive functionals of BMC under $L^2$-ergodic conditions with three different regimes. This completes the pointwise approach developed in a previous work. As application, we study the elementary case of symmetric bifurcating autoregressive process, which justify the non-trivial hypothesis considered on the kernel transition of the BMC. We illustrate in this example the phase transition observed in the fluctuations., Comment: 39 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:2012.04741

The main purpose of this article is to establish moderate deviation principles for additive functionals of bifurcating Markov chains. Bifurcating Markov chains are a class of processes which are indexed by a regular binary tree. They can be seen as the models which represent the evolution of a trait along a population where each individual has two offsprings. Unlike the previous results of Bitseki, Djellout \& Guillin (2014), we consider here the case of functions which depend only on one variable. So, mainly inspired by the recent works of Bitseki \& Delmas (2020) about the central limit theorem for general additive functionals of bifurcating Markov chains, we give here a moderate deviation principle for additive functionals of bifurcating Markov chains when the functions depend on one variable. This work is done under the uniform geometric ergodicity and the uniform ergodic property based on the second spectral gap assumptions. The proofs of our results are based on martingale decomposition recently developed by Bitseki \& Delmas (2020) and on results of Dembo (1996), Djellout (2001) and Puhalski (1997)., Comment: 23 pages, 4 figures

The Ariel mission will observe spectroscopically around 1000 exoplanets to further characterise their atmospheres. For the mission to be as efficient as possible, a good knowledge of the planets' ephemerides is needed before its launch in 2028. While ephemerides for some planets are being refined on a per-case basis, an organised effort to collectively verify or update them when necessary does not exist. In this study, we introduce the ExoClock project, an open, integrated and interactive platform with the purpose of producing a confirmed list of ephemerides for the planets that will be observed by Ariel. The project has been developed in a manner to make the best use of all available resources: observations reported in the literature, observations from space instruments and, mainly, observations from ground-based telescopes, including both professional and amateur observatories. To facilitate inexperienced observers and at the same time achieve homogeneity in the results, we created data collection and validation protocols, educational material and easy to use interfaces, open to everyone. ExoClock was launched in September 2019 and now counts over 140 participants from more than 15 countries around the world. In this release, we report the results of observations obtained until the 15h of April 2020 for 119 Ariel candidate targets. In total, 632 observations were used to either verify or update the ephemerides of 83 planets. Additionally, we developed the Exoplanet Characterisation Catalogue (ECC), a catalogue built in a consistent way to assist the ephemeris refinement process. So far, the collaborative open framework of the ExoClock project has proven to be highly efficient in coordinating scientific efforts involving diverse audiences. Therefore, we believe that it is a paradigm that can be applied in the future for other research purposes, too., Comment: 33 pages, 3 figures, 3 tables, accepted for publication in Experimental Astronomy, data available through OSF at DOI: 10.17605/OSF.IO/3W7HM

Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for general additive functionals of BMC, and prove the existence of three regimes. This corresponds to a competition between the reproducing rate (each individual has two children) and the ergodicity rate for the evolution of the trait. This is in contrast with the work of Guyon (2007), where the considered additive functionals are sums of martingale increments, and only one regime appears. Our result can be seen as a discrete time version, but with general trait evolution, of results in the time continuous setting of branching particle system from Adamczak and Mi\l{}o\'{s} (2015), where the evolution of the trait is given by an Ornstein-Uhlenbeck process., Comment: 32

The amount of user generated contents from various social medias allows analyst to handle a wide view of conversations on several topics related to their business. Nevertheless keeping up-to-date with this amount of information is not humanly feasible. Automatic Summarization then provides an interesting mean to digest the dynamics and the mass volume of contents. In this paper, we address the issue of tweets summarization which remains scarcely explored. We propose to automatically generated summaries of Micro-Blogs conversations dealing with public figures E-Reputation. These summaries are generated using key-word queries or sample tweet and offer a focused view of the whole Micro-Blog network. Since state-of-the-art is lacking on this point we conduct and evaluate our experiments over the multilingual CLEF RepLab Topic-Detection dataset according to an experimental evaluation process., Comment: 8 pages, 4 tables

We describe the asymptotic behavior of the number $Z_n[a_n,\infty)$ of individuals with a large value in a stable bifurcating autoregressive process. The study of the associated first moment $\mathbb{E}(Z_n[a_n,\infty))$ is equivalent to the annealed large deviation problem $\mathbb{P}(Y_n\geq a_n)$, where $Y$ is an autoregressive process in a random environment and $a_n\rightarrow \infty$. The population with large values and the trajectorial behavior of $Z_n[a_n,\infty)$ is obtained from the ancestral paths associated to the large deviations of $Y$ together with its environment. The study of large deviations of autoregressive processes in random environment is of independent interest and achieved first in this paper. The proofs of trajectorial estimates for bifurcating autoregressive process involves then a law of large numbers for non-homogenous trees. Two regimes appear in the stable case, depending on the fact that one of the autoregressive parameter is greater than one or not. It yields two different asymptotic behaviors for the large local densities and maximal value of the bifurcating autoregressive process., Comment: 28 pages

We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain on $\mathbb R^d$. Bifurcating Markov chains (BMC for short) are a class of stochastic processes indexed by regular binary trees. A kernel estimator is proposed whose bandwidth is selected by a method inspired by the works of Goldenshluger and Lepski [18]. Drawing inspiration from dimension jump methods for model selection, we also provide an algorithm to select the best constant in the penalty., Comment: 18 pages, 2 figures

Elections unleash strong political views on Twitter, but what do people really think about politics? Opinion and trend mining on micro blogs dealing with politics has recently attracted researchers in several fields including Information Retrieval and Machine Learning (ML). Since the performance of ML and Natural Language Processing (NLP) approaches are limited by the amount and quality of data available, one promising alternative for some tasks is the automatic propagation of expert annotations. This paper intends to develop a so-called active learning process for automatically annotating French language tweets that deal with the image (i.e., representation, web reputation) of politicians. Our main focus is on the methodology followed to build an original annotated dataset expressing opinion from two French politicians over time. We therefore review state of the art NLP-based ML algorithms to automatically annotate tweets using a manual initiation step as bootstrap. This paper focuses on key issues about active learning while building a large annotated data set from noise. This will be introduced by human annotators, abundance of data and the label distribution across data and entities. In turn, we show that Twitter characteristics such as the author's name or hashtags can be considered as the bearing point to not only improve automatic systems for Opinion Mining (OM) and Topic Classification but also to reduce noise in human annotations. However, a later thorough analysis shows that reducing noise might induce the loss of crucial information., Comment: Journal of Interdisciplinary Methodologies and Issues in Science - Vol 3 - Contextualisation digitale - 2017

The 2013 D\'efi de Fouille de Textes (DEFT) campaign is interested in two types of language analysis tasks, the document classification and the information extraction in the specialized domain of cuisine recipes. We present the systems that the LIA has used in DEFT 2013. Our systems show interesting results, even though the complexity of the proposed tasks., Comment: 12 pages, 3 tables, (Paper in French)

Twitter is now a gold marketing tool for entities concerned with online reputation. To automatically monitor online reputation of entities , systems have to deal with ambiguous entity names, polarity detection and topic detection. We propose three approaches to tackle the first issue: monitoring Twitter in order to find relevant tweets about a given entity. Evaluated within the framework of the RepLab-2013 Filtering task, each of them has been shown competitive with state-of-the-art approaches. Mainly we investigate on how much merging strategies may impact performances on a filtering task according to the evaluation measure.

Many works related to Twitter aim at characterizing its users in some way: role on the service (spammers, bots, organizations, etc.), nature of the user (socio-professional category, age, etc.), topics of interest , and others. However, for a given user classification problem, it is very difficult to select a set of appropriate features, because the many features described in the literature are very heterogeneous, with name overlaps and collisions, and numerous very close variants. In this article, we review a wide range of such features. In order to present a clear state-of-the-art description, we unify their names, definitions and relationships, and we propose a new, neutral, typology. We then illustrate the interest of our review by applying a selection of these features to the offline influence detection problem. This task consists in identifying users which are influential in real-life, based on their Twitter account and related data. We show that most features deemed efficient to predict online influence, such as the numbers of retweets and followers, are not relevant to this problem. However, We propose several content-based approaches to label Twitter users as Influencers or not. We also rank them according to a predicted influence level. Our proposals are evaluated over the CLEF RepLab 2014 dataset, and outmatch state-of-the-art methods.

In a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and Bitseki Penda, Djellout and Guillin. These preliminary results are the key ingredient to implement nonparametric wavelet thresholding estimation procedures: in a second part, we construct nonparametric estimators of the transition density of a BMC, of its mean transition density and of the corresponding invariant density, and show smoothness adaptation over various multivariate Besov classes under $L^p$-loss error, for $1 \leq p < \infty$. We prove that our estimators are (nearly) optimal in a minimax sense. As an application, we obtain new results for the estimation of the splitting size-dependent rate of growth-fragmentation models and we extend the statistical study of bifurcating autoregressive processes.

Bifurcating autoregressive processes, which can be seen as an adaptation of au-toregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify any a priori form for the two autoregressive functions and we use nonparametric techniques. We investigate both nonasymp-totic and asymptotic behavior of the Nadaraya-Watson type estimators of the autoregressive functions. We build our estimators observing the process on a finite subtree denoted by Tn, up to the depth n. Estimators achieve the classical rate |Tn| --$\beta$/(2$\beta$+1) in quadratic loss over H{\"o}lder classes of smoothness. We prove almost sure convergence, asymptotic normality giving the bias expression when choosing the optimal bandwidth and a moderate deviations principle. Our proofs rely on specific techniques used to study bifurcating Markov chains. Finally, we address the question of asymmetry and develop an asymptotic test for the equality of the two autoregressive functions.