Laboratoire de Mathématiques et Modélisation d'Évry

The use of comparative genomics for functional, evolutionary, and epidemiological studies requires methods to classify gene families in terms of occurrence in a given species. These methods usually lack multivariate statistical models to infer the partitions and the optimal number of classes and don't account for genome organization. We introduce a graph structure to model pangenomes in which nodes represent gene families and edges represent genomic neighborhood. Our method, named PPanGGOLiN, partitions nodes using an Expectation-Maximization algorithm based on multivariate Bernoulli Mixture Model coupled with a Markov Random Field. This approach takes into account the topology of the graph and the presence/absence of genes in pangenomes to classify gene families into persistent, cloud, and one or several shell partitions. By analyzing the partitioned pangenome graphs of isolate genomes from 439 species and metagenome-assembled genomes from 78 species, we demonstrate that our method is effective in estimating the persistent genome. Interestingly, it shows that the shell genome is a key element to understand genome dynamics, presumably because it reflects how genes present at intermediate frequencies drive adaptation of species, and its proportion in genomes is independent of genome size. The graph-based approach proposed by PPanGGOLiN is useful to depict the overall genomic diversity of thousands of strains in a compact structure and provides an effective basis for very large scale comparative genomics. The software is freely available at https://github.com/labgem/PPanGGOLiN.

This paper is devoted mainly to the global existence problem for the two-dimensional parabolic-parabolic Keller-Segel system in the full space. We derive a critical mass threshold below which global existence is ensured. Carefully using energy methods and ad hoc functional inequalities, we improve and extend previous results in this direction. The given threshold is thought to be the optimal criterion, but this question is still open. This global existence result is accompanied by a detailed discussion on the duality between the Onofri and the logarithmic Hardy-Littlewood-Sobolev inequalities that underlie the following approach.

Many traditional methods for identifying changepoints can struggle in the presence of outliers, or when the noise is heavy-tailed. Often they will infer additional changepoints to fit the outliers. To overcome this problem, data often needs to be preprocessed to remove outliers, though this is difficult for applications where the data needs to be analyzed online. We present an approach to changepoint detection that is robust to the presence of outliers. The idea is to adapt existing penalized cost approaches for detecting changes so that they use loss functions that are less sensitive to outliers. We argue that loss functions that are bounded, such as the classical biweight loss, are particularly suitable—as we show that only bounded loss functions are robust to arbitrarily extreme outliers. We present an efficient dynamic programming algorithm that can find the optimal segmentation under our penalized cost criteria. Importantly, this algorithm can be used in settings where the data needs to be analyzed online. We show that we can consistently estimate the number of changepoints, and accurately estimate their locations, using the biweight loss function. We demonstrate the usefulness of our approach for applications such as analyzing well-log data, detecting copy number variation, and detecting tampering of wireless devices. Supplementary materials for this article are available online.

We consider a simple model arising in modeling angiogenesis and more specifically the development of capillary blood vessels due to an exogenous chemo-attractive signal (solid tumors for instance). It is given as coupled system of parabolic equations through a nonlinear transport term. We show that, by opposition to some classical chemotaxis model, this system admits a positive energy. This allows us to develop an existence theory for weak solutions. We also show that, in two dimensions, this system admits a family of self-similar waves.

In this paper, we give relations involving values of q-Bernoulli, q-Euler, and Bernstein polynomials. Using these relations, we obtain some interesting identities on the q-Bernoulli, q-Euler, and Bernstein polynomials.

Structural variation is a major source of genetic diversity and an important substrate for selection. In allopolyploids, homoeologous exchanges (i.e. between the constituent subgenomes) are a very frequent type of structural variant. However, their direct impact on gene content and gene expression had not been determined. Here, we used a tissue-specific mRNA-Seq dataset to measure the consequences of homoeologous exchanges (HE) on gene expression in Brassica napus, a representative allotetraploid crop. We demonstrate that expression changes are proportional to the change in gene copy number triggered by the HEs. Thus, when homoeologous gene pairs have unbalanced transcriptional contributions before the HE, duplication of one copy does not accurately compensate for loss of the other and combined homoeologue expression also changes. These effects are, however, mitigated over time. This study sheds light on the origins, timing and functional consequences of homeologous exchanges in allopolyploids. It demonstrates that the interplay between new structural variation and the resulting impacts on gene expression, influences allopolyploid genome evolution.

Antimicrobial resistance is a major global health threat and its development is promoted by antibiotic misuse. While disk diffusion antibiotic susceptibility testing (AST, also called antibiogram) is broadly used to test for antibiotic resistance in bacterial infections, it faces strong criticism because of inter-operator variability and the complexity of interpretative reading. Automatic reading systems address these issues, but are not always adapted or available to resource-limited settings. We present an artificial intelligence (AI)-based, offline smartphone application for antibiogram analysis. The application captures images with the phone's camera, and the user is guided throughout the analysis on the same device by a user-friendly graphical interface. An embedded expert system validates the coherence of the antibiogram data and provides interpreted results. The fully automatic measurement procedure of our application's reading system achieves an overall agreement of 90% on susceptibility categorization against a hospital-standard automatic system and 98% against manual measurement (gold standard), with reduced inter-operator variability. The application's performance showed that the automatic reading of antibiotic resistance testing is entirely feasible on a smartphone. Moreover our application is suited for resource-limited settings, and therefore has the potential to significantly increase patients' access to AST worldwide.

in English). Importantly, the findings provide a crucial constraint on, and resource for, future work that seeks to understand the effect of color on cognition and behavior, enabling stronger a priori predictions about universal as well as culturally relative effects of conceptual color associations on cognition and behavior to be systematically tested. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

In this paper we investigate special generalized Bernoulli polynomials that generalize classical Bernoulli polynomials and numbers. We call them poly-Bernoulli polynomials. We prove a collection of extremely important and fundamental identities satisfied by our poly-Bernoulli polynomials and numbers. These properties are of arithmetical nature.

We present a selective review on probabilistic modeling of heterogeneity in\nrandom graphs. We focus on latent space models and more particularly on\nstochastic block models and their extensions that have undergone major\ndevelopments in the last five years.\n

TNBC is a highly heterogeneous and aggressive breast cancer subtype associated with high relapse rates, and for which no targeted therapy yet exists. Protein arginine methyltransferase 5 (PRMT5), an enzyme which catalyzes the methylation of arginines on histone and non-histone proteins, has recently emerged as a putative target for cancer therapy. Potent and specific PRMT5 inhibitors have been developed, but the therapeutic efficacy of PRMT5 targeting in TNBC has not yet been demonstrated. Here, we examine the expression of PRMT5 in a human breast cancer cohort obtained from the Institut Curie, and evaluate the therapeutic potential of pharmacological inhibition of PRMT5 in TNBC. We find that PRMT5 mRNA and protein are expressed at comparable levels in TNBC, luminal breast tumors, and healthy mammary tissues. However, immunohistochemistry analyses reveal that PRMT5 is differentially localized in TNBC compared to other breast cancer subtypes and to normal breast tissues. PRMT5 is heterogeneously expressed in TNBC and high PRMT5 expression correlates with poor prognosis within this breast cancer subtype. Using the small-molecule inhibitor EPZ015666, we show that PRMT5 inhibition impairs cell proliferation in a subset of TNBC cell lines. PRMT5 inhibition triggers apoptosis, regulates cell cycle progression and decreases mammosphere formation. Furthermore, EPZ015666 administration to a patient-derived xenograft model of TNBC significantly deters tumor progression. Finally, we reveal potentiation between EGFR and PRMT5 targeting, suggestive of a beneficial combination therapy. Our findings highlight a distinctive subcellular localization of PRMT5 in TNBC, and uphold PRMT5 targeting, alone or in combination, as a relevant treatment strategy for a subset of TNBC.

In gene therapy with human hematopoietic stem and progenitor cells (HSPCs), each gene-corrected cell and its progeny are marked in a unique way by the integrating vector. This feature enables lineages to be tracked by sampling blood cells and using DNA sequencing to identify the vector integration sites. Here, we studied 5 cell lineages (granulocytes, monocytes, T cells, B cells, and natural killer cells) in patients having undergone HSPC gene therapy for Wiskott-Aldrich syndrome or β hemoglobinopathies. We found that the estimated minimum number of active, repopulating HSPCs (which ranged from 2000 to 50 000) was correlated with the number of HSPCs per kilogram infused. We sought to quantify the lineage output and dynamics of gene-modified clones; this is usually challenging because of sparse sampling of the various cell types during the analytical procedure, contamination during cell isolation, and different levels of vector marking in the various lineages. We therefore measured the residual contamination and corrected our statistical models accordingly to provide a rigorous analysis of the HSPC lineage output. A cluster analysis of the HSPC lineage output highlighted the existence of several stable, distinct differentiation programs, including myeloid-dominant, lymphoid-dominant, and balanced cell subsets. Our study evidenced the heterogeneous nature of the cell lineage output from HSPCs and provided methods for analyzing these complex data.

Abstract In this paper, we first present a sufficient condition(a variant) for the large deviation criteria of Budhiraja, Dupuis and Maroulas for functionals of Brownian motions. The sufficient condition is particularly more suitable for stochastic differential/partial differential equations with reflection. We then apply the sufficient condition to establish a large deviation principle for obstacle problems of quasi-linear stochastic partial differential equations. It turns out that the backward stochastic differential equations will also play an important role.

The Anthropocene epoch is associated with the spreading of metals in the environment increasing oxidative and genotoxic stress on organisms. Interestingly, c. 520 plant species growing on metalliferous soils acquired the capacity to accumulate and tolerate a tremendous amount of nickel in their shoots. The wide phylogenetic distribution of these species suggests that nickel hyperaccumulation evolved multiple times independently. However, the exact nature of these mechanisms and whether they have been recruited convergently in distant species is not known. To address these questions, we have developed a cross-species RNA-Seq approach combining differential gene expression analysis and cluster of orthologous group annotation to identify genes linked to nickel hyperaccumulation in distant plant families. Our analysis reveals candidate orthologous genes encoding convergent function involved in nickel hyperaccumulation, including the biosynthesis of specialized metabolites and cell wall organization. Our data also point out that the high expression of IREG/Ferroportin transporters recurrently emerged as a mechanism involved in nickel hyperaccumulation in plants. We further provide genetic evidence in the hyperaccumulator Noccaea caerulescens for the role of the NcIREG2 transporter in nickel sequestration in vacuoles. Our results provide molecular tools to better understand the mechanisms of nickel hyperaccumulation and study their evolution in plants.

In this paper, we introduce a novel approach, called Input Output Kernel Regression (IOKR), for learning mappings between structured inputs and structured outputs. The approach belongs to the family of Output Kernel Regression methods devoted to regression in feature space endowed with some output kernel. In order to take into account structure in input data and benefit from kernels in the input space as well, we use the Reproducing Kernel Hilbert Space theory for vector-valued functions. We first recall the ridge solution for supervised learning and then study the regularized hinge loss-based solution used in Maximum Margin Regression. Both models are also developed in the context of semi-supervised setting. In addition we derive an extension of Generalized Cross Validation for model selection in the case of the least-square model. Finally we show the versatility of the IOKR framework on two different problems: link prediction seen as a structured output problem and multi-task regression seen as a multiple and interdependent output problem. Eventually, we present a set of detailed numerical results that shows the relevance of the method on these two tasks.

Uniqueness of Leray solutions of the 3D Navier-Stokes equations is a challenging open problem. In this article we will study this problem for the 3D stationary Navier-Stokes equations in the whole space \mathbb{R}^{3} . Under some additional hypotheses, stated in terms of Lebesgue and Morrey spaces, we will show that the trivial solution \overrightarrow U= 0 is the unique solution. This type of results are known as Liouville theorems.

High-throughput RNA-sequencing has become the gold standard method for whole-transcriptome gene expression analysis, and is widely used in numerous applications to study cell and tissue transcriptomes. It is also being increasingly used in a number of clinical applications, including expression profiling for diagnostics and alternative transcript detection. However, despite its many advantages, RNA sequencing can be challenging in some situations, for instance in cases of low input amounts or degraded RNA samples. Several protocols have been proposed to overcome these challenges, and many are available as commercial kits. In this study, we systematically test three recent commercial technologies for RNA-seq library preparation (TruSeq, SMARTer and SMARTer Ultra-Low) on human biological reference materials, using standard (1 mg), low (100 ng and 10 ng) and ultra-low (<1 ng) input amounts, and for mRNA and total RNA, stranded and unstranded. The results are analyzed using read quality and alignment metrics, gene detection and differential gene expression metrics. Overall, we show that the TruSeq kit performs well with an input amount of 100 ng, while the SMARTer kit shows decreased performance for inputs of 100 and 10 ng, and the SMARTer Ultra-Low kit performs relatively well for input amounts <1 ng. All the results are discussed in detail, and we provide guidelines for biologists for the selection of an RNA-seq library preparation kit.

Summary Characterizing the natural diversity of gene expression across environments is an important step in understanding how genotype‐by‐environment interactions shape phenotypes. Here, we analyzed the impact of water deficit onto gene expression levels in tomato at the genome‐wide scale. We sequenced the transcriptome of growing leaves and fruit pericarps at cell expansion stage in a cherry and a large fruited accession and their F 1 hybrid grown under two watering regimes. Gene expression levels were steadily affected by the genotype and the watering regime. Whereas phenotypes showed mostly additive inheritance, ~80% of the genes displayed non‐additive inheritance. By comparing allele‐specific expression (ASE) in the F 1 hybrid to the allelic expression in both parental lines, respectively, 3005 genes in leaf and 2857 genes in fruit deviated from 1:1 ratio independently of the watering regime. Among these genes, ~55% were controlled by cis factors, ~25% by trans factors and ~20% by a combination of both types of factors. A total of 328 genes in leaf and 113 in fruit exhibited significant ASE‐by‐watering regime interaction, among which ~80% presented trans ‐by‐watering regime interaction, suggesting a response to water deficit mediated through a majority of trans‐ acting loci in tomato. We cross‐validated the expression levels of 274 transcripts in fruit and leaves of 124 recombinant inbred lines ( RIL s) and identified 163 expression quantitative trait loci (eQTL s) mostly confirming the divergences identified by ASE. Combining phenotypic and expression data, we observed a complex network of variation between genes encoding enzymes involved in the sugar metabolism.

We find Fourier expansions of Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. We give a very simple proof of them.

We obtain general weak existence and stability results for stochastic convolution equations with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients and singular kernels. Our approach relies on weak convergence in Lp spaces. The main tools are new a priori estimates on Sobolev–Slobodeckij norms of the solution, as well as a novel martingale problem that is equivalent to the original equation. This leads to generic approximation and stability theorems in the spirit of classical martingale problem theory. We also prove uniqueness and path regularity of solutions under additional hypotheses. To illustrate the applicability of our results, we consider scaling limits of nonlinear Hawkes processes and approximations of stochastic Volterra processes by Markovian semimartingales.