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51. Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model

Author

Dmitry Kramkov, Sergio Pulido, Carnegie Mellon University [Pittsburgh] (CMU), Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), The research of the first author was supported in part by the Carnegie Mellon-Portugal Program and by the Oxford-Man Institute for Quantitative Finance at the University of Oxford. The research of the second author was supported by the Chair Markets in Transition, under the aegis of Louis Bachelier laboratory, a joint initiative of Ecole Polytechnique, Université d'Evry-Val-d'Essonne and Fédération Bancaire Française, Labex ANR 11-LABX-0019, and the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n.~307465-POLYTE., ANR-11-LABX-0019,LABEX FCD,LABEX Finance & Croissance Durable(2011), European Project: 307465,EC:FP7:ERC,ERC-2012-StG_20111012,POLYTE(2012), Carnegie Mellon University (CMU), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Chair Markets in Transition, under the aegis of Louis Bachelier laboratory, a joint initiative of Ecole Polytechnique, Université d'Evry-Val-d'Essonne and Fédération Bancaire Française. This research has also received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n.~307465-POLYTE., Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), ANR-11-LABX-0019/11-LABX-0019,LABEX FCD,LABEX Finance & Croissance Durable(2011), and Laboratoire de Mathématiques et Modélisation d'Evry

Subjects
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], multi-dimensional quadratic BSDEs,stability of quadratic BSDEs,asymptotic behavior of quadratic BSDEs,liquidity,price impact, Process (engineering), [QFIN.PM]Quantitative Finance [q-fin]/Portfolio Management [q-fin.PM], JEL: D - Microeconomics/D.D5 - General Equilibrium and Disequilibrium/D.D5.D53 - Financial Markets, Stability (learning theory), 01 natural sciences, [QFIN.PM] Quantitative Finance [q-fin]/Portfolio Management [q-fin.PM], [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], JEL: C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C62 - Existence and Stability Conditions of Equilibrium, JEL : G.G1.G12, FOS: Economics and business, asymptotic behavior of quadratic BSDEs, 010104 statistics & probability, Quadratic equation, Portfolio Management (q-fin.PM), Impact model, FOS: Mathematics, Econometrics, JEL : C.C6.C62, 0101 mathematics, [QFIN.TR]Quantitative Finance [q-fin]/Trading and Market Microstructure [q-fin.TR], Quantitative Finance - Portfolio Management, Mathematics, Numerical Analysis, Quantitative Finance - Trading and Market Microstructure, liquidity, Risk aversion, multi-dimensional quadratic BSDEs, Applied Mathematics, [QFIN.CP] Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], Probability (math.PR), 010102 general mathematics, [QFIN.TR] Quantitative Finance [q-fin]/Trading and Market Microstructure [q-fin.TR], Mathematical Finance (q-fin.MF), Trading and Market Microstructure (q-fin.TR), Market liquidity, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], JEL : D.D5.D53, Quantitative Finance - Mathematical Finance, Financial modeling, 60H10, 91B24, 91G80, stability of quadratic BSDEs, Finance, Mathematics - Probability, price impact, JEL: G - Financial Economics/G.G1 - General Financial Markets/G.G1.G12 - Asset Pricing • Trading Volume • Bond Interest Rates
Abstract

We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices are stable under the demand process and derive their analytic expansions for small risk aversion coefficients of the dealer., Final version, 28 pages

Published
2016
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52. CLASSIFICATION OF RANDOM TIMES AND APPLICATIONS

Author

Aksamit, Anna, Choulli, Tahir, Jeanblanc, Monique, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), University of Oxford [Oxford], University of Alberta, Université d'Évry-Val-d'Essonne (UEVE), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), University of Alberta [Edmonton], Université d'Evry-Val d'Essonne, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), University of Oxford, JEANBLANC, Monique, and Laboratoire de Mathématiques et Modélisation d'Evry

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
Abstract

The paper gathers together ideas related to thin random time, i.e., random time whose graph is contained in a thin set. The concept naturally completes the studies of random times and progressive enlargement of filtrations. We develop classification and (*)-decomposition of random times, which is analogous to the decomposition of a stopping time into totally inaccessible and accessible parts, and we show applications to the hypothesis (H ′), honest times and informational drift via entropy.

Published
2016

53. No evidence for TSLP pathway activity in human breast cancer

Author

Alix Scholer-Dahirel, Fabien Reyal, Carolina Martinez-Cingolani, Vassili Soumelis, Maude Guillot-Delost, Benjamin Sadacca, Lucia Pattarini, Paula Michea, Philémon Sirven, André Nicolas, Raphaël Zollinger, Cristina Ghirelli, Immunité et cancer (U932), Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut Curie-Université Paris Descartes - Paris 5 (UPD5), Institut National de la Santé et de la Recherche Médicale (INSERM), Department of Immunology, University of Toronto, IGR Curie CIC 1428 - Center of Clinical Investigations, Institut Curie, Residual Tumor & Response to Treatment Laboratory (RT2Lab) - Translational Research Department, UMR 1152 - Statistiques and Génome du Laboratoire de Mathématiques et Modélisation d’Évry, Institut National de la Recherche Agronomique (INRA), Centre National de la Recherche Scientifique (CNRS), Université d'Evry Val d'Essonne, Department of Surgery, Columbia University College of Physicians and Surgeons, Platform of Investigative Pathology of Biopathology Department, Institut National de la Sante et de la Recherche Medicale [BIO2012-02, BIO2014-08], Fondation pour la Recherche Medicale, Association de la Recherche Contre le Cancer [PJA 20131200436], INCA [2011-1-PL BIO-12-IC-1, 2012-1-GYN-04-IC-1], CIC IGR-Curie [1428], [ANR-13-BSV1-0024-02], [ANR-10-IDEX-0001-02 PSL], [ANR-11-LABX-0043], Institut Curie-Université Paris Descartes - Paris 5 (UPD5)-Institut National de la Santé et de la Recherche Médicale (INSERM), Université Paris Descartes - Paris 5 (UPD5)-Institut Curie [Paris]-Institut National de la Santé et de la Recherche Médicale (INSERM), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université Paris Descartes - Paris 5 (UPD5)-Institut Curie-Institut National de la Santé et de la Recherche Médicale (INSERM), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), and Université d'Évry-Val-d'Essonne (UEVE)

Subjects
0301 basic medicine, Stromal cell, Thymic stromal lymphopoietin, medicine.medical_treatment, [SDV]Life Sciences [q-bio], Immunology, Biology, 03 medical and health sciences, Breast cancer, thymic stromal lymphopoietin, medicine, Immunology and Allergy, tumor microenvironment, dendritic cells, Original Research, Tumor microenvironment, Cancer, medicine.disease, Primary tumor, cytokines, 3. Good health, 030104 developmental biology, Cytokine, Oncology, Tumor progression
Abstract

Thymic stromal lymphopoietin (TSLP) is an epithelial cell-derived cytokine that primes dendritic cells for Th2 induction. It has been implicated in different types of allergic diseases. Recent work suggested that TSLP could play an important role in the tumor microenvironment and influence tumor progression, in particular in breast cancer. In this study we systematically assessed the production of TSLP at the mRNA and protein levels in several human breast cancer cell lines, large-scale public transcriptomics data sets, and primary human breast tumors. We found that TSLP production was marginal, and concerned less than 10% of the tumors, with very low mRNA and protein levels. In most cases TSLP was undetectable and found to be expressed at lower levels in breast cancer as compared to normal breast tissue. Last, we could not detect any functional TSLP receptor (TSLPR) expression neither on hematopoietic cells nor on stromal cells within the primary tumor microenvironment. We conclude that TSLP-TSLPR pathway activity is not significantly detected within human breast cancer. Taken together, these observations do not support TSLP targeting in breast cancer.

Published
2016
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54. A system of quadratic BSDEs arising in a price impact model

Author

Dmitry Kramkov, Sergio Pulido, Carnegie Mellon University [Pittsburgh] (CMU), Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Carnegie Mellon University (CMU), and Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, [MATH] Mathematics [math], multi-dimensional quadratic BSDE, 01 natural sciences, Market maker, JEL: G - Financial Economics, FOS: Economics and business, 010104 statistics & probability, Quadratic equation, Portfolio Management (q-fin.PM), JEL : G, 91G80, 0502 economics and business, FOS: Mathematics, JEL : C, Uniqueness, JEL : D, 0101 mathematics, [MATH]Mathematics [math], Quantitative Finance - Portfolio Management, Mathematics, Quadratic growth, JEL: C - Mathematical and Quantitative Methods, 050208 finance, liquidity, JEL: D - Microeconomics, [QFIN]Quantitative Finance [q-fin], Probability (math.PR), 05 social sciences, 91B24, Mathematical Finance (q-fin.MF), [QFIN] Quantitative Finance [q-fin], Market liquidity, Quantitative Finance - Mathematical Finance, Norm (mathematics), Bounded function, Financial modeling, 60H10, Statistics, Probability and Uncertainty, liquidity,price impact,multi-dimensional quadratic BSDE, Mathematical economics, Mathematics - Probability, price impact
Abstract

We consider a financial model where the prices of risky assets are quoted by a representative market maker who takes into account an exogenous demand. We characterize these prices in terms of a system of BSDEs with quadratic growth. We show that this system admits a unique solution for every bounded demand if and only if the market maker's risk-aversion is sufficiently small. The uniqueness is established in the natural class of solutions, without any additional norm restrictions. To the best of our knowledge, this is the first study that proves such (global) uniqueness result for a system of fully coupled quadratic BSDEs., Comment: Published at http://dx.doi.org/10.1214/15-AAP1103 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Published
2016

55. Adaptive estimation of the baseline hazard function in the Cox model by model selection, with high-dimensional covariates

Author

Agathe Guilloux, Sarah Lemler, Marie-Luce Taupin, Laboratoire de Statistique Théorique et Appliquée (LSTA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Université Pierre et Marie Curie - Paris 6 (UPMC), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), INRA - Mathématiques et Informatique Appliquées (Unité MIAJ), Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), ENSIIE-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS), Unité MaIAGE, and INRAE

Subjects
FOS: Computer and information sciences, Statistics and Probability, Statistics::Theory, Mathematics - Statistics Theory, Statistics Theory (math.ST), 02 engineering and technology, Semi-parametric model, Model selection, Statistics - Applications, 01 natural sciences, Non-asymptotic oracle inequalities, 010104 statistics & probability, Statistics::Machine Learning, Lasso (statistics), [STAT.AP] Statistics [stat]/Applications [stat.AP], [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Covariate, Statistics, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Statistics::Methodology, Applications (stat.AP), High-dimensional covariates, 0101 mathematics, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], ComputingMilieux_MISCELLANEOUS, Mathematics, [STAT.AP]Statistics [stat]/Applications [stat.AP], Proportional hazards model, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Applied Mathematics, Estimator, Contrast (statistics), 020206 networking & telecommunications, Right-censored data, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Cox's proportional hazards model, Nonparametric model, Survival analysis, Regression, Statistics::Computation, Adaptive estimator, Concentration inequalities, Statistics, Probability and Uncertainty, Conditional hazard rate function
Abstract

International audience; The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via a Lasso procedure based on the partial log-likelihood, secondly, we plug this Lasso estimator into a least-squares type criterion and then perform a model selection procedure to obtain an adaptive penalized contrast estimator of the baseline function. Using non-asymptotic estimation results stated for the Lasso estimator of the regression parameter , we establish a non-asymptotic oracle inequality for this penalized contrast estimator of the baseline function, which highlights the discrepancy of the rate of convergence when the dimension of the covariates increases.

Published
2016
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56. Modeling the Dynamics of Gonadotropin-Releasing Hormone (GnRH) Secretion in the Course of an Ovarian Cycle

Author

Clément, Frédérique, Vidal, Alexandre, Multiscale dYnamiCs in neuroENdocrine AxEs (Mycenae), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Duncan J MacGregor, Gareth Leng, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria) - Institut National de Recherche en Informatique et en Automatique (Inria), and Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS)

Subjects
010101 applied mathematics, 0103 physical sciences, [SDV.BDLR]Life Sciences [q-bio]/Reproductive Biology, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [SDV.NEU] Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], 0101 mathematics, 01 natural sciences, [SDV.BDLR] Life Sciences [q-bio]/Reproductive Biology, ComputingMilieux_MISCELLANEOUS, 010305 fluids & plasmas
Abstract

International audience

Published
2016

57. Jump filtering and efficient drift estimation for lévy-driven sde's

Author

Gloter, Arnaud, Loukianova, Dasha, Mai, Hilmar, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Économie et Statistique (CREST), Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI)-École polytechnique (X)-École Nationale de la Statistique et de l'Administration Économique (ENSAE ParisTech )-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI)-École polytechnique (X)-École Nationale de la Statistique et de l'Administration Économique (ENSAE Paris)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), INSEE - École Nationale de la Statistique et de l'Administration Économique, and loukianova, dasha

Subjects
maximum-likelihood estimation, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], 62M, 62F, Lévy-driven SDE, efficient drift estimation, [MATH] Mathematics [math], ergodic properties, [MATH]Mathematics [math], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], high frequency data
Abstract

The problem of drift estimation for thesolution $X$ of a stochastic differential equation with L\'evy-type jumpsis considered under discrete high-frequency observations with a growing observation window.An efficient and asymptotically normal estimator for the drift parameter is constructed under minimal conditions on the jump behavior and the sampling scheme. In the case of a bounded jump measure density these conditions reduce to$n\Delta_n^{3-\eps}\to 0,$ where $n$ is the number of observations and $\Delta_n$ is the maximal sampling step. This result relaxes the condition $n\Delta_n^2 \to 0$ usually required for joint estimation of drift and diffusion coefficient for SDE's with jumps. The main challenge in this estimation problem stems from the appearance of the unobserved continuous part $X^c$ in the likelihood function. In order to construct the drift estimator we recover this continuous part from discrete observations. More precisely, we estimate, in a nonparametric way,stochastic integrals with respect to $X^c$.Convergence results of independent interest are proved for these nonparametric estimators. Finally, we illustrate the behavior of our drift estimator for a number of popular L\'evy--driven models from finance.

Published
2016

58. Capital Valuation Adjustment and Funding Valuation Adjustment

Author

Stéphane Crépey, Claudio Albanese, Simone Caenazzo, CASS Business School - London, UK, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), and Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS)

Subjects
Financial economics, Collateral, Retained earnings, media_common.quotation_subject, counterparty risk, Computational Finance (q-fin.CP), [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], FOS: Economics and business, Quantitative Finance - Computational Finance, Incomplete markets, Debt, 0502 economics and business, Economics, 050207 economics, Valuation (finance), media_common, 050208 finance, [QFIN.CP] Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], 05 social sciences, initial margin, KVA, MVA, FVA, variation margin, Market incompleteness, Cost of capital, 8. Economic growth, Financial crisis, Dividend, cost of funding, cost of capital
Abstract

In the aftermath of the 2007 global financial crisis, banks started reflecting into derivative pricing the cost of capital and collateral funding through XVA metrics. Here XVA is a catch-all acronym whereby X is replaced by a letter such as C for credit, D for debt, F for funding, K for capital and so on, and VA stands for valuation adjustment. This behaviour is at odds with economies where markets for contingent claims are complete, whereby trades clear at fair valuations and the costs for capital and collateral are both irrelevant to investment decisions. In this paper, we set forth a mathematical formalism for derivative portfolio management in incomplete markets for banks. A particular emphasis is given to the problem of finding optimal strategies for retained earnings which ensure a sustainable dividend policy.

Published
2016

59. The role of the pressure in the partial regularity theory for weak solutions of the Navier–Stokes equations

Author

Diego Chamorro, Pierre Gilles Lemarié-Rieusset, Kawther Mayoufi, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Generalization, Kohn and Nirenberg theory, Complex system, Mathematics::Analysis of PDEs, 01 natural sciences, Caffarelli, Navier–Stokes equations, Mathematics - Analysis of PDEs, Mathematics (miscellaneous), FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics, Mathematical physics, Serrin criterion, Mechanical Engineering, 010102 general mathematics, Partial regularity, Connection (mathematics), 010101 applied mathematics, Dissipative system, Nirenberg and Matthaei experiment, Analysis, Analysis of PDEs (math.AP)
Abstract

We study the role of the pressure in the partial regularity theory for weak solutions of the Navier--Stokes equations. By introducing the notion of dissipative solutions, due to Duchon \& Robert, we will provide a generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach gives a new enlightenment of the role of the pressure in this theory in connection to Serrin's local regularity criterion.

Published
2016

60. NON-ARBITRAGE UNDER ADDITIONAL INFORMATION FOR THIN SEMIMARTINGALE MODELS

Author

Aksamit, Anna, Choulli, Tahir, Deng, Jun, Jeanblanc, Monique, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), University of Oxford [Oxford], University of Alberta, College of Engineering [Beijing], China Agricultural University (CAU), Université d'Évry-Val-d'Essonne (UEVE), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), University of Alberta [Edmonton], Université d'Evry-Val d'Essonne, JEANBLANC, Monique, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), University of Oxford, and Laboratoire de Mathématiques et Modélisation d'Evry

Subjects
FOS: Economics and business, Random horizon, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Arbitrage, Local martingale deflator, Progressive enlargement of filtration, Honest time, Quantitative Finance - Mathematical Finance, and phrases: Unbounded-profit-with-bounded-risk, Mathematical Finance (q-fin.MF), Thin semimartingales
Abstract

This paper completes the two studies undertaken in \cite{aksamit/choulli/deng/jeanblanc2} and \cite{aksamit/choulli/deng/jeanblanc3}, where the authors quantify the impact of a random time on the No-Unbounded-Risk-with-Bounded-Profit concept (called NUPBR hereafter) when the stock price processes are quasi-left-continuous (do not jump on predictable stopping times). Herein, we focus on the NUPBR for semimartingales models that live on thin predictable sets only and the progressive enlargement with a random time. For this flow of information, we explain how far the NUPBR property is affected when one stops the model by an arbitrary random time or when one incorporates fully an honest time into the model. This also generalizes \cite{choulli/deng} to the case when the jump times are not ordered in anyway. Furthermore, for the current context, we show how to construct explicitly local martingale deflator under the bigger filtration from those of the smaller filtration., This paper develops the part of thin and single jump processes mentioned in our earlier version: "Non-arbitrage up to random horizon and after honest times for semimartingale models", Available at: arXiv:1310.1142v1. arXiv admin note: text overlap with arXiv:1404.0410

Published
2016

61. An application of the KMT construction to the pathwise weak error in the Euler approximation of one-dimensional diffusion process with linear diffusion coefficient

Author

Emmanuelle Clément, Arnaud Gloter, Clément, Emmanuelle, Mathématiques et Informatique pour la Complexité et les Systèmes (MICS), CentraleSupélec, Fédération de Mathématiques de l'Ecole Centrale Paris (FR3487), Ecole Centrale Paris-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), and Centre National de la Recherche Scientifique (CNRS)-Ecole Centrale Paris-CentraleSupélec

Subjects
Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Wasserstein metric, Euler scheme, Space (mathematics), 01 natural sciences, Euler method, Komlós -Major- Tusnády construction, 010104 statistics & probability, symbols.namesake, Uniform norm, Mathematics::Probability, Diffusion process, Order (group theory), 65C30, Wasserstein couplings, 0101 mathematics, Diffusion (business), quantile coupling technique, Mathematics, 010102 general mathematics, Mathematical analysis, Binary logarithm, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], symbols, 60H35, Statistics, Probability and Uncertainty
Abstract

It is well known that the strong error approximation in the space of continuous paths equipped with the supremum norm between a diffusion process, with smooth coefficients, and its Euler approximation with step $1/n$ is $O(n^{-1/2})$ and that the weak error estimation between the marginal laws at the terminal time $T$ is $O(n^{-1})$. An analysis of the weak trajectorial error has been developed by Alfonsi, Jourdain and Kohatsu-Higa [Ann. Appl. Probab. 24 (2014) 1049–1080], through the study of the $p$-Wasserstein distance between the two processes. For a one-dimensional diffusion, they obtained an intermediate rate for the pathwise Wasserstein distance of order $n^{-2/3+\varepsilon}$. Using the Komlós, Major and Tusnády construction, we improve this bound assuming that the diffusion coefficient is linear and we obtain a rate of order $\log n/n$.

Published
2016
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62. Non-asymptotic oracle inequalities for the Lasso and Group Lasso in high dimensional logistic model

Author

Marius Kwemou, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Université d'Evry Val d'Essonne, Centre National de la Recherche Scientifique (CNRS), LERSTAD, Université Gaston Berger de Saint-Louis Sénégal (UGB), Laboratoire Statistique et Génome (SG), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), laboratoire d'Etudes et de recherches en Statistiques et Développement (LERSTAD), Université Gaston Bergé Sénégal, Research partially supported by IRD/DSF Département Soutien et Formation des communautés scientifiques du Sud, Laboratoire de Mathématiques et Modélisation d'Evry, and Université d'Évry-Val-d'Essonne (UEVE)

Subjects
FOS: Computer and information sciences, 0301 basic medicine, Statistics and Probability, Elastic net regularization, Logistic model, Lasso, Group Lasso, high-dimensional, oracle inequality, Statistics::Theory, [SDV]Life Sciences [q-bio], Mathematics - Statistics Theory, Context (language use), Statistics Theory (math.ST), Statistics - Applications, 01 natural sciences, 010104 statistics & probability, 03 medical and health sciences, Statistics::Machine Learning, Lasso (statistics), Statistics, FOS: Mathematics, Applied mathematics, Statistics::Methodology, Applications (stat.AP), 0101 mathematics, Linear combination, Eigenvalues and eigenvectors, Mathematics, [STAT.AP]Statistics [stat]/Applications [stat.AP], [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Sparse approximation, Function (mathematics), State (functional analysis), Statistics::Computation, oracle, 030104 developmental biology
Abstract

We consider the problem of estimating a function $f_{0}$ in logistic regression model. We propose to estimate this function $f_{0}$ by a sparse approximation build as a linear combination of elements of a given dictionary of $p$ functions. This sparse approximation is selected by the Lasso or Group Lasso procedure. In this context, we state non asymptotic oracle inequalities for Lasso and Group Lasso under restricted eigenvalues assumption as introduced in \cite{BRT}. Those theoretical results are illustrated through a simulation study.

Published
2016
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63. Interlayer coupling through a dimensionality-induced magnetic state

Author

Gibert, M., Viret, M., Zubko, P., Jaouen, N., Tonnerre, J.-M., Torres-Pardo, A., Catalano, S., Gloter, A., Stéphan, O., Triscone, J.-M., Hélium : du fondamental aux applications (HELFA), Institut Néel (NEEL), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), University of Geneva [Switzerland], Laboratoire Nano-Magnétisme et Oxydes (LNO), Service de physique de l'état condensé (SPEC - UMR3680), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut Rayonnement Matière de Saclay (IRAMIS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Synchrotron SOLEIL (SSOLEIL), Centre National de la Recherche Scientifique (CNRS), Surfaces, Interfaces et Nanostructures (SIN ), Departamento de Química Inorgánica, Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique des Solides (LPS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Hélium : du fondamental aux applications (NEEL - HELFA), Université de Genève = University of Geneva (UNIGE), Surfaces, Interfaces et Nanostructures (NEEL - SIN), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), SIN - Surfaces, Interfaces et Nanostructures, Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Universidad Complutense de Madrid [Madrid] (UCM), and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)

Subjects
[PHYS]Physics [physics], Nickelates, Condensed Matter::Materials Science, Condensed Matter::Superconductivity, Science, Magnetism, Interface engineering, Condensed Matter::Strongly Correlated Electrons, ddc:500.2, Exchange bias, Condensed Matter::Mesoscopic Systems and Quantum Hall Effect, Article
Abstract

Dimensionality is known to play an important role in many compounds for which ultrathin layers can behave very differently from the bulk. This is especially true for the paramagnetic metal LaNiO3, which can become insulating and magnetic when only a few monolayers thick. We show here that an induced antiferromagnetic order can be stabilized in the [111] direction by interfacial coupling to the insulating ferromagnet LaMnO3, and used to generate interlayer magnetic coupling of a nature that depends on the exact number of LaNiO3 monolayers. For 7-monolayer-thick LaNiO3/LaMnO3 superlattices, negative and positive exchange bias, as well as antiferromagnetic interlayer coupling are observed in different temperature windows. All three behaviours are explained based on the emergence of a (¼,¼,¼)-wavevector antiferromagnetic structure in LaNiO3 and the presence of interface asymmetry with LaMnO3. This dimensionality-induced magnetic order can be used to tailor a broad range of magnetic properties in well-designed superlattice-based devices., Oxide materials can be combined to create heterostructures exhibiting complex properties not found in either substance individually. Here, the authors observe antiferromagnetic interlayer exchange coupling between ferromagnetic lanthanum manganite and nominally paramagnetic lanthanum nickel oxide.

Published
2016
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64. Solutions H^1 of the steady transport equation in a bounded polygon with a fully non-homogeneous velocity

Author

Bernard, Jean-Marie, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques et Modélisation d'Evry

Subjects
Mathematics - Analysis of PDEs, localization methods, transport equation, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], nonstandard boundary condition, Analysis of PDEs (math.AP)
Abstract

This article studies the solutions in H 1 of a steady transport equation with a divergence-free driving velocity that is W 1,$\infty$ , in a two-dimensional bounded polygon. Since the velocity is assumed fully non-homogeneous on the boundary, existence and uniqueness of the solution require a boundary condition on the open part $\Gamma$ -- where the normal component of u is strictly negative. In a previous article, we studied the solutions in L 2 of this steady transport equation. The methods, developed in this article, can be extended to prove existence and uniqueness of a solution in H 1 with Dirichlet boundary condition on $\Gamma$ -- only in the case where the normal component of u does not vanish at the boundary of $\Gamma$ --. In the case where the normal component of u vanishes at the boundary of $\Gamma$ -- , under appropriate assumptions, we construct local H 1 solutions in the neighborhood of the end-points of $\Gamma$ -- , which allow us to establish existence and uniqueness of the solution in H 1 for the transport equation with a Dirichlet boundary condition on $\Gamma$ -- .

Published
2016

65. Effect of earthworm active protein on fibroblast proliferation and its mechanism

Author

Kai Ji, Yu-Ling Wang, Hao Liang, Aiguo Ji, Shuliang Song, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), China Academy of Chinese Medical Sciences, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)

Subjects
0301 basic medicine, MAPK/ERK pathway, Cell Survival, education, Pharmaceutical Science, Biology, Flow cytometry, Biological Factors, Mice, 03 medical and health sciences, Western blot, Drug Discovery, medicine, Animals, Oligochaeta, Fibroblast, PI3K/AKT/mTOR pathway, ComputingMilieux_MISCELLANEOUS, [SDU.STU.OC]Sciences of the Universe [physics]/Earth Sciences/Oceanography, Cell Proliferation, Pharmacology, Dose-Response Relationship, Drug, medicine.diagnostic_test, Cell growth, General Medicine, Fibroblasts, Cell cycle, Molecular biology, 3. Good health, 030104 developmental biology, medicine.anatomical_structure, Complementary and alternative medicine, [SDU]Sciences of the Universe [physics], NIH 3T3 Cells, Molecular Medicine, Signal transduction
Abstract

Earthworms have been used as a traditional medicine in China from thousands of years. In recent years, research has demonstrated that earthworm extracts might promote wound healing; however, its mechanism is still unknown.The study investigates the mechanism and effects of earthworm active protein (EAP), on mouse embryonic fibroblast (NIH/3T3) proliferation.The effects of earthworm active protein (EAP) in different concentrations (0, 25, 50, 100, 150, and 200 μg/mL) on NIH3T3 cell were detected by the MTT and Brdu incorporation assay (50, 100, and 150 μg/mL). The effects of EAP (37.5, 75, and 150 μg/mL) on the cell cycle were detected by flow cytometry. The cell signaling pathways of EAP-promoting NIH3T3 cell proliferation were studied by the MTT and Western blot by using different signaling pathway inhibitors.The results showed that EAP (50, 100, and 150 μg/mL) could promote NIH3T3 fibroblasts proliferation (36.4 ± 4.4%, 59.1 ± 4.9%, and 71.5 ± 5.7%). The mechanism of EAP promoting NIH3T3 cell proliferation should be as follows: EAP elevated cyclin D1 expression by activating MEK/ERK signaling pathway, and then promoted cell cycle from G1 to S phase, finally caused the proliferation of NIH3T3 cell. PI3K signaling pathway may be the upstream of MEK/ERK signaling pathway.The study demonstrates that EAP is effective in promoting effects on proliferation and migration activity of NIH3T3 cell, and the proliferation activity of EAP on NIH3T3 cell may be achieved through the PI3K→Rac→PAK→MEK signaling pathway.

Published
2016
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66. Beyond support in two-stage variable selection

Author

Jean-Michel Becu, Christophe Ambroise, Yves Grandvalet, Cyril Dalmasso, Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), Université de Technologie de Compiègne - Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Fondation UTC pour l'innovation, programme ToxOnChip, Labex MS2T (ANR-11-IDEX-0004-02), ANR-11-IDEX-0004-02/10-LABX-0071, MS2T, Control of Technological Systems of Systems(2011), Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), UTC foundation for Innovation : ToxOnChip program, ANR-11-IDEX-0004-02/10-LABX-0071,MS2T,Control of Technological Systems of Systems(2011), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), ANR-11-IDEX-0004,SUPER,Sorbonne Universités à Paris pour l'Enseignement et la Recherche(2011), and Laboratoire de Mathématiques et Modélisation d'Evry

Subjects
0301 basic medicine, Statistics and Probability, FOS: Computer and information sciences, Mathematical optimization, Variable selection, Linear model, False discovery rate, Inference, Feature selection, Machine learning, computer.software_genre, 01 natural sciences, Statistics - Applications, Theoretical Computer Science, Methodology (stat.ME), 010104 statistics & probability, 03 medical and health sciences, [STAT.AP] Statistics [stat]/Applications [stat.AP], Lasso (statistics), [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Applications (stat.AP), Sensitivity (control systems), 0101 mathematics, Set (psychology), Selection (genetic algorithm), Statistics - Methodology, Mathematics, [STAT.AP]Statistics [stat]/Applications [stat.AP], [STAT.ME] Statistics [stat]/Methodology [stat.ME], business.industry, Screen and clean, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], [STAT] Statistics [stat], [STAT]Statistics [stat], 030104 developmental biology, Computational Theory and Mathematics, Stage (hydrology), Artificial intelligence, p-values, Statistics, Probability and Uncertainty, Lasso, business, computer, [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract

Numerous variable selection methods rely on a two-stage procedure, where a sparsity-inducing penalty is used in the first stage to predict the support, which is then conveyed to the second stage for estimation or inference purposes. In this framework, the first stage screens variables to find a set of possibly relevant variables and the second stage operates on this set of candidate variables, to improve estimation accuracy or to assess the uncertainty associated to the selection of variables. We advocate that more information can be conveyed from the first stage to the second one: we use the magnitude of the coefficients estimated in the first stage to define an adaptive penalty that is applied at the second stage. We give two examples of procedures that can benefit from the proposed transfer of information, in estimation and inference problems respectively. Extensive simulations demonstrate that this transfer is particularly efficient when each stage operates on distinct subsamples. This separation plays a crucial role for the computation of calibrated p-values, allowing to control the False Discovery Rate. In this setup, the proposed transfer results in sensitivity gains ranging from 50% to 100% compared to state-of-the-art.

Published
2016
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67. A candidate gene study identifies a haplotype of CD2 as novel susceptibility factor for systemic sclerosis

Author

Koumakis, E., Bouaziz, M., Dieude, P., Cauvet, A., Ruiz, B., Airo, P., Cusi, D., Matucci-Cerinic, M., Salvi, E., Cuome, G., Hachulla, E., Diot, E., Caramaschi, P., Valeria RICCIERI, Avouac, J., Allanore, Y., Université Sorbonne Paris Cité (USPC), Departement A de Rhumatologie, Hôpital Cochin [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), Université Paris Descartes - Paris 5 (UPD5), Institut Cochin (IC UM3 (UMR 8104 / U1016)), Centre National de la Recherche Scientifique (CNRS)-Université Paris Descartes - Paris 5 (UPD5)-Institut National de la Santé et de la Recherche Médicale (INSERM), Laboratoire Statistique et Génome (SG), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Université d'Evry Val d'Essonne, Departement de Rhumatologie, Hôpital Bichat - Claude Bernard, Assistance Publique - Hôpitaux de Paris (AP-HP), Université Paris Diderot - Paris 7 (UPD7), UMR 699 Service de Rhumatologie, Institut National de la Santé et de la Recherche Médicale (INSERM), Reumatologia e Immunologia, Spedali Civil Brescia, Biomedical Laboratory Techniques, Università degli Studi di Milano [Milano] (UNIMI), Department of Experimental and Clinical Medicine, Università degli Studi 'Magna Graecia' di Catanzaro [Catanzaro, Italie] (UMG), Department of Health Science, Università del Molise, Department of Internal Medicine, Huntsman Cancer Institute, Hôpital Claude Huriez [Lille], CHU Lille, IFR 618 Service de Pneumologie, Hôpital Bretonneau, Assistance Publique - Hôpitaux de Paris (AP-HP), Unità di Reumatologia, Azienda Ospedaliera, University of Verona (UNIVR), Dipartimento di Medicina Interna e Specialitá Mediche, Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome], Koumakis, Eugenie, Bouaziz, Matthieu, Dieudé, Philippe, Cauvet, Anne, Ruiz, Barbara, Airò, Paolo, Cusi, Daniele, Matucci Cerinic, Marco, Salvi, Erika, Cuomo, Giovanna, Hachulla, Eric, Diot, Elisabeth, Caramaschi, Paola, Riccieri, Valeria, Avouac, Jerome, Allanore, Yannick, Université Sorbonne Paris Cité ( USPC ), CHU Cochin [AP-HP], Université Paris Descartes - Paris 5 ( UPD5 ), Institut Cochin ( UM3 (UMR 8104 / U1016) ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire Statistique et Génome ( SG ), Institut National de la Recherche Agronomique ( INRA ) -Université d'Évry-Val-d'Essonne ( UEVE ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques et Modélisation d'Evry ( LaMME ), Institut National de la Recherche Agronomique ( INRA ) -Université d'Évry-Val-d'Essonne ( UEVE ) -ENSIIE-Centre National de la Recherche Scientifique ( CNRS ), Hôpital Bichat - Claude Bernard, Assistance Publique - Hôpitaux de Paris ( AP-HP ), Université Paris Diderot (Paris 7), Institut National de la Santé et de la Recherche Médicale ( INSERM ), Universita degli Studi di Milano ( UNIMI ), University 'Magna Græcia', Hôpital Claude Huriez, Hôpital Bretonneau, Assistance Publique - Hôpitaux de Paris ( AP-HP ), Università degli Studi di Verona, Università degli Studi di Roma 'La Sapienza', Université Paris Descartes - Paris 5 (UPD5)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Università degli studi di Milano [Milano], Università degli Studi di Roma 'La Sapienza' [Rome], Université d'Évry-Val-d'Essonne (UEVE), Università degli Studi di Milano = University of Milan (UNIMI), Università degli Studi 'Magna Graecia' di Catanzaro = University of Catanzaro (UMG), Università degli Studi del Molise = University of Molise (UNIMOL), Università degli studi di Verona = University of Verona (UNIVR), and Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome] (UNIROMA)

Subjects
Adult, Genetic Markers, Male, systemic sclerosis, [SDV]Life Sciences [q-bio], CD2 Antigens, Polymorphism, Single Nucleotide, White People, polymorphism, sclérose, polymorphisme génétique, Gene Frequency, Risk Factors, sclerosis, autoimmunité, Odds Ratio, Humans, genetic polymorphism, Genetic Predisposition to Disease, genetics, skin and connective tissue diseases, Genetic Association Studies, Aged, Scleroderma, Systemic, [ SDV ] Life Sciences [q-bio], integumentary system, autoimmunity, Middle Aged, CD2, Phenotype, Haplotypes, Italy, Case-Control Studies, Female, France
Abstract

Systemic sclerosis (SSc) is a rare autoimmune disease (AID) with a complex genetic etiology. Evidence for a shared pathogenesis across AIDs is given by the well-known pleiotropism of autoimmune genes. Recently, several unbiased approaches have identified an association between polymorphisms of the CD2 gene, and rheumatoid arthritis (RA) susceptibility. The objective of this study was to investigate whether CD2 polymorphisms are associated with SSc. Objective. Systemic sclerosis (SSc) is a rare autoimmune disease (AID) with a complex genetic aetiology. Evidence for a shared pathogenesis across AIDs is given by the well-known pleiotropism of autoimmune genes. Recently, several unbiased approaches have identified an association between polymorphisms of the CD2 gene, and rheumatoid arthritis (RA) susceptibility. The objective of this study was to investigate whether CD2 polymorphisms are associated with SSc.Methods. Two SNPs of CD2, rs624988 and rs798036, were genotyped in a total of 1,786 SSc patients and 2,360 healthy individuals from two European populations (France and Italy). Meta analyses were performed to assess whether an association exists between CD2 polymorphisms or haplotypes and SSc or its main subtypes.Results. The combined analyses revealed an association between the rs624988 A allele and SSc susceptibility: p(adj)=0.023, OR=1.14 (95%CI 1.04-1.25). Single marker analysis did not reveal any association between rs798036 and SSc. Haplotype analysis identified that the A-T haplotype, previously described in RA, was associated with higher susceptibility for SSc (p(adj)=0.029, OR=1.14, 95%CI 1.04-1.25) and with the positive anticentromere antibody sub-group of SSc patients (p(adj)=0.009, OR=1 95%CI 1.07-1.32). Genotype-mRNA expression correlations revealed that the CD2 risk haplotype was associated with decreased CD2 mRNA expression in SSc patients.Conclusion. Our study establishes CD2 as a new susceptibility factor for SSc, in a European Caucasian population, confirming the sharing of autoimmune risk factors by SSc and RA.

Published
2016

68. Some existence results for advanced backward stochastic differential equations with a jump time

Author

Monique Jeanblanc, Thomas Lim, Nacira Agram, Lim, Thomas, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE), University of Oslo (UiO), Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Single Jump, 0209 industrial biotechnology, Mathematical optimization, 02 engineering and technology, 01 natural sciences, Stochastic differential equation, 020901 industrial engineering & automation, Mathematics::Probability, Immersion, Immersion (mathematics), QA1-939, 0101 mathematics, Diffusion (business), Brownian motion, Mathematics, T57-57.97, Applied mathematics. Quantitative methods, 010102 general mathematics, Mathematical analysis, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Semimartingale, Advanced Backward Stochastic Differential Equations, Jump, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Jump process, Generator (mathematics)
Abstract

In this paper, we are interested by advanced backward stochastic differential equations (ABSDEs), in a probability space equipped with a Brownian motion and a single jump process, with a jump at time τ. ABSDEs are BSDEs where the driver depends on the future paths of the solution. We show, that under immersion hypothesis between the Brownian filtration and its progressive enlargement with τ, assuming that the conditional law of τ is equivalent to the unconditional law of τ, and a Lipschitz condition on the driver, the ABSDE has a solution.

Published
2016

69. Transformation des organisations culturelles et des métiers : quelles formes de reconnaissance ?

Author

Aubouin, Nicolas, Coblence, Emmanuel, Dalmasso, Cedric, Kletz, Frédéric, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Centre de Gestion Scientifique i3 (CGS i3), MINES ParisTech - École nationale supérieure des mines de Paris-PSL Research University (PSL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut interdisciplinaire de l’innovation (I3), and Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Organisation, métier, [SHS.GESTION]Humanities and Social Sciences/Business administration, ComputingMilieux_MISCELLANEOUS, culture, [SHS]Humanities and Social Sciences
Abstract

International audience

Published
2016

70. About the regularity of degenerate non-local Kolmogorov operators under diffusive perturbations

Author

Marino, Lorenzo, Menozzi, Stéphane, Priola, Enrico, Institut of Mathematics - Polish Academy of Sciences (PAN), Polska Akademia Nauk = Polish Academy of Sciences (PAN), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Dipartimento di Matematica 'Felice Casorati' Department of Mathematics [Univ Pavia] (UNIPV), and Università degli Studi di Pavia = University of Pavia (UNIPV)

Subjects
Schauder estimates, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Analysis of PDEs, Degenerate Ornstein-Uhlenbeck operators, Probability (math.PR), FOS: Mathematics, Lp estimates, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Poisson process, Mathematics - Probability, non-local parabolic equations, Analysis of PDEs (math.AP), MSC: 35K10, 35K15, 60J76
Abstract

We study here the effects of a time-dependent second order perturbation to a degenerate Ornstein-Uhlenbeck type operator whose diffusive part can be either local or non-local. More precisely, we establish that some estimates, such as the Schauder and Sobolev ones, already known for the non-perturbed operator still hold, and with the same constants, when we perturb the Ornstein-Uhlenbeck operator with second order diffusions with coefficients only depending on time in a measurable way. The aim of the current work is twofold: we weaken the assumptions required on the perturbation in the local case which has been considered already in [KP17] and we extend the approach presented therein to a wider class of degenerate Kolmogorov operators with non-local diffusive part of symmetric stable type., Comments are welcome!

Published
2023

71. Some remarks about the stationary Micropolar fluid equations: existence, regularity and uniqueness

Author

Chamorro, Diego, Llerena, David, Vergara-Hermosilla, Gastón, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), and Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
Micropolar fluid equations, Mathematics - Analysis of PDEs, Liouville type theorems, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, Analysis of PDEs (math.AP)
Abstract

We consider here the stationary Micropolar fluid equations which are a particular generalization of the usual Navier-Stokes system where the microrotations of the fluid particles must be taken into account. We thus obtain two coupled equations: one based mainly in the velocity field u and the other one based in the microrotation field $\omega$. We will study in this work some problems related to the existence of weak solutions as well as some regularity and uniqueness properties. Our main result establish, under some suitable decay at infinity conditions for the velocity field only, the uniqueness of the trivial solution.

Published
2023

72. Survival and maximum of spectrally negative branching L{\'e}vy processes with absorption

Author

Profeta, Christophe, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Extreme values, Probability (math.PR), FOS: Mathematics, Branching process, Spectrally negative Lévy process, Mathematics - Probability
Abstract

We consider a spectrally negative branching L{\'e}vy process where the particles undergo dyadic branching and are killed when entering the negative half-plane. The purpose of this short note is to give conditions under which this process dies out a.s., and then study the asymptotics of its all-time maximum.

Published
2023

73. A stochastic lipid structured model for macrophage dynamics in atherosclerotic plaques

Author

Eisenbaum, Nathalie, Meunier, Nicolas, Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), and Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
[SDV]Life Sciences [q-bio], [MATH]Mathematics [math]
Abstract

We construct and analyze a system of stochastic differential equations satisfied by the position and the diffusion coefficient of a Brownian particle whose diffusion coefficient is modified at each crossing of the origin and with a dumping coefficient. This system models the effects of lipid accumulation on macrophage dynamics. The novelty of the model, with respect to [1, 15], is to include offloading of lipids through the dumping term. We obtain non-trivial behaviors of the solution: dynamical transition to an absorbing state for the solution to the stochastic system. With this model, we study how changes in parameters, initial conditions included, predict some characteristic features of plaque pathology, which in our case is described by macrophage aggregation.

Published
2023

74. Longitudinal data analysis, causality and care pathways : application to French nationwide claims database

Author

Nevoret, Camille, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Université Paris-Saclay, Agathe Guilloux, Sandrine Katsahian, and Stéphane Bouée

Subjects
Parcours de soin, Care pathway, Analyse causale, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Longitudinal data, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Snds, Causal analysis, Données longitudinales, Att
Abstract

For several years, the health field has seen a significant increase in the amount of data available. In France, new platforms have been created to centralize health data, starting with data from claims database. Initially collected for pricing purposes, these data are a great opportunity for real-life studies of healthcare consumption and its evolution over time. Treatment effectiveness is a recurrent issue in health data studies. Our first contribution concerns a model for estimating the average treatment effect in treated patients (ATT) in the presence of time-dependent confounders. We proposed an unbiased estimate of ATT based on a generalization of Gran's model in the presence of several continuous, time-dependent confounders and a repeatable outcome, such as rehospitalizations. A simulation study demonstrated the value of the correction and the model was applied to MIMIC-III data. In a second step, a multivariate extension of the INGARCH model was proposed to take into account discrete confounders in Gran's model. The study of care pathways is another issue often studied on real-life data. We propose a process to analysed hospital care pathways in order to assess their association with mortality. Sequence analysis methods taking into account the order of occurrence of hospitalizations have been combined. This analysis process was applied to the study of the association of cardiovascular hospitalisations with death in patients with heart failure.; Le domaine de la santé connaît depuis plusieurs années une augmentation importante des données disponibles. En France, de nouvelles plateformes ont vu le jour pour centraliser les données de santé, en commençant par les données des bases médico-administratives. Initialement recueillies pour des besoins tarifaires, ces données sont une grande opportunité pour l'études en vie réelle des consommations de soin et leur évolution dans le temps. L'efficacité des traitements est une problématique récurrente dans les études sur données de santé. Notre première contribution porte sur un modèle d'estimation de l'effet moyen du traitement chez les patients traités (ATT) en présence de facteurs de confusion dépendants du temps. Nous avons proposé une estimation débiaisée de l'ATT basée sur une généralisation du modèle de Gran en présence de plusieurs facteurs de confusion continus et dépendants du temps et d'un résultat qui peut être répétés dans le temps, comme des réhospitalisations. Dans un second temps, une extension multivariée du modèle INGARCH a été proposée pour prendre en compte des facteurs de confusion discrets dans l'estimation de l'ATT. L'étude des parcours de soin est une autre thématique très souvent étudiée sur les données de vie réelle. Nous proposons dans nos travaux une procédure d'analyse des parcours de soin hospitalier afin d'évaluer leur association avec la mortalité. Des méthodes d'analyse de séquences prenant en compte l'ordre de la survenue des hospitalisations ont été combinées. Cette procédure d'analyse a été appliquée à l'étude de l'association des hospitalisations cardiovasculaires avec le décès chez des patients atteints d'insuffisance cardiaque.

Published
2023

75. A turbulent study for a damped Navier-Stokes equation: turbulence and problems

Author

Chamorro, Diego, Jarrín, Oscar, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), and Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
Kolmogorov's dissipation law, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Turbulence theory, Navier-Stokes equations, Analysis of PDEs (math.AP)
Abstract

In this article we consider a damped version of the incompressible Navier-Stokes equations in the whole three-dimensional space with a divergence-free and time-independent external force. Within the framework of a well-prepared force and with a particular choice of the damping parameter, when the Grashof numbers are large enough, we are able to prove some estimates from below and from above between the fluid characteristic velocity and the energy dissipation rate according to the Kolmogorov dissipation law. Precisely, our main contribution concerns the estimate from below which is not often studied in the existing literature. Moreover, we address some remarks which open the door to a deep discussion on the validity of this theory of turbulence.

Published
2023

76. Hedging Valuation Adjustment for Callable Claims

Author

Bénézet, Cyril, Crépey, Stéphane, Essaket, Dounia, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE), Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Université Paris Cité (UPCité)

Subjects
Callable asset, Model risk, Model calibration, Probability (math.PR), Computational Finance (q-fin.CP), Hedging Valuation Adjustment (HVA), [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], Financial derivatives pricing and hedging, FOS: Economics and business, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Quantitative Finance - Computational Finance, Risk Management (q-fin.RM), FOS: Mathematics, Mathematics - Probability, Quantitative Finance - Risk Management
Abstract

Darwinian model risk is the risk of mis-price-and-hedge biased toward short-to-medium systematic profits of a trader, which are only the compensator of long term losses becoming apparent under extreme scenarios where the bad model of the trader no longer calibrates to the market. The alpha leakages that characterize Darwinian model risk are undetectable by the usual market risk tools such as value-at-risk, expected shortfall, or stressed value-at-risk.Darwinian model risk can only be seen by simulating the hedging behavior of a bad model within a good model. In this paper we extend to callable assets the notion of hedging valuation adjustment introduced in previous work for quantifying and handling such risk. The mathematics of Darwinian model risk for callable assets are illustrated by exact numerics on a stylized callable range accrual example. Accounting for the wrong hedges and exercise decisions, the magnitude of the hedging valuation adjustment can be several times larger than the mere difference, customarily used in banks as a reserve against model risk, between the trader's price of a callable asset and its fair valuation.

Published
2023

77. Spatial Clustering of Linkage Disequilibrium blocks for Genome-Wide Association Studies

Author

Dehman, Alia, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université d'Evry Val d'Essonne, Université Paris-Saclay, Christophe Ambroise(christophe.ambroise@genopole.cnrs.fr), Pierre Neuvial(pierre.neuvial@genopole.cnrs.fr), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), and Dehman, Alia

Subjects
[SDV.GEN]Life Sciences [q-bio]/Genetics, Penalized regression, Classification hiérarchique, [SDV.GEN] Life Sciences [q-bio]/Genetics, Model selection, Linkage Disequilibrium, Hierarchical clustering, Gap statistic, Déséquilibre de liaison, [STAT] Statistics [stat], Sélection de modèle, [STAT]Statistics [stat], Group lasso, Genome-Wide Association Studies, Régression pénalisée
Abstract

With recent development of high-throughput genotyping technologies, the usage of Genome-Wide Association Studies (GWAS) has become widespread in genetic research. By screening large portions of the genome, these studies aim to characterize genetic factors involved in the development of complex genetic diseases.GWAS are also based on the existence of statistical dependencies, called Linkage Disequilibrium (LD) usually observed between nearby loci on DNA. LD is defined as the non-random association of alleles at different loci on the same chromosome or on different chromosomes in a population. This biological feature is of fundamental importance in association studies as it provides a fine location of unobserved causal mutations using adjacent genetic markers. Nevertheless, the complex block structure induced by LD as well as the large volume of genetic data are key issues that have arisen with GWA studies.The contributions presented in this manuscript are in twofold, both methodological and algorithmic. On the methodological part, we propose a three-step approach that explicitly takes advantage of the grouping structure induced by LD in order to identify common variants which may have been missed by single marker analyses. In the first step, we perform a hierarchical clustering of SNPs with an adjacency constraint using LD as a similarity measure. In the second step, we apply a model selection approach to the obtained hierarchy in order to define LD blocks. Finally, we perform Group Lasso regression on the inferred LD blocks. The efficiency of the proposed approach is investigated compared to state-of-the art regression methods on simulated, semi-simulated and real GWAS data.On the algorithmic part, we focus on the spatially-constrained hierarchical clustering algorithm whose quadratic time complexity is not adapted to the high-dimensionality of GWAS data. We then present, in this manuscript, an efficient implementation of such an algorithm in the general context of any similarity measure. By introducing a user-parameter h and using the min-heap structure, we obtain a sub-quadratic time complexity of the adjacency-constrained hierarchical clustering algorithm, as well as a linear space complexity in the number of items to be clustered. The interest of this novel algorithm is illustrated in GWAS applications., Avec le développement récent des technologies de génotypage à haut débit, l'utilisation des études d'association pangénomiques (GWAS) est devenue très répandue dans la recherche génétique. Au moyen de criblage de grandes parties du génome, ces études visent à caractériser les facteurs génétiques impliqués dans le développement de maladies génétiques complexes.Les GWAS sont également basées sur l'existence de dépendances statistiques, appelées déséquilibre de liaison(DL), habituellement observées entre des loci qui sont proches dans l'ADN. Le DL est défini comme l'association non aléatoire d'allèles à des loci différents sur le même chromosome ou sur des chromosomes différents dans unepopulation. Cette caractéristique biologique est d'une importance fondamentale dans les études d'association car elle permetla localisation précise des mutations causales en utilisant les marqueurs génétiques adjacents. Néanmoins, la structure de blocs complexe induite par le DL ainsi que le grand volume de données génétiques constituent les principaux enjeux soulevés par les études GWAS.Les contributions présentées dans ce manuscrit comportent un double aspect, à la fois méthodologique et algorithmique. Sur le plan méthodologie, nous proposons une approche en trois étapes qui tire profit de la structure de groupes induite par le DL afin d'identifier des variants communs qui pourraient avoir été manquées par l'analyse simple marqueur. Dans une première étape, nous effectuons une classification hiérarchique des SNPs avec une contrainte d'adjacence et en utilisant le DL comme mesure de similarité. Dans une seconde étape, nous appliquons une approche de sélection de modèle à la hiérarchie obtenue afin de définir des blocs de DL. Enfin, nous appliquons le modèle de régression Group Lasso sur les blocs de DLinférés. L'efficacité de l'approche proposée est comparée à celle des approches de régression standards sur des données simulées, semi-simulées et réelles de GWAS.Sur le plan algorithmique, nous nous concentrons sur l'algorithme de classification hiérarchique avec contrainte spatiale dont la complexité quadratique en temps n'est pas adaptée à la grande dimension des données GWAS. Ainsi, nous présentons, dans ce manuscrit, une mise en œuvre efficace d'un tel algorithme dans le contexte général de n'importe quelle mesure de similarité. En introduisant un paramètre $h$ défini par l'utilisateur et en utilisant la structure de tas-min, nous obtenons une complexité sous-quadratique en temps de l'algorithme de classification hiérarchie avec contrainte d'adjacence, ainsi qu'une complexité linéaire en mémoire en le nombre d'éléments à classer. L'intérêt de ce nouvel algorithme est illustré dans des applications GWAS.

Published
2015

78. A model for gene deregulation detection using expression data

Author

Julien Chiquet, Pierre Neuvial, Rémy Nicolle, Thomas Picchetti, Etienne Birmelé, Mohamed Elati, Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Institut de biologie systémique et synthétique (ISSB), Université d'Évry-Val-d'Essonne (UEVE)-Génopole-Centre National de la Recherche Scientifique (CNRS), Institut Curie, PEPS CNRS Biologie/Mathématique/Informatique CREPE, Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Université Paris Descartes - Paris 5 (UPD5), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Institut Curie [Paris], Birmelé, Etienne, Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques et Modélisation d'Evry ( LaMME ), Institut National de la Recherche Agronomique ( INRA ) -Université d'Évry-Val-d'Essonne ( UEVE ) -ENSIIE-Centre National de la Recherche Scientifique ( CNRS ), Institut de biologie systémique et synthétique ( ISSB ), and Université d'Évry-Val-d'Essonne ( UEVE ) -Génopole-Centre National de la Recherche Scientifique ( CNRS )

Subjects
FOS: Computer and information sciences, Computer science, modèle, Quantitative Biology - Quantitative Methods, 01 natural sciences, regulatory network, 010104 statistics & probability, Structural Biology, Gene expression, Gene Regulatory Networks, [ SDV.BIBS ] Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], Quantitative Methods (q-bio.QM), Regulation of gene expression, 0303 health sciences, [STAT.AP]Statistics [stat]/Applications [stat.AP], deregulation, Applied Mathematics, Message passing, [SDV.BIBS]Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], Computer Science Applications, Modeling and Simulation, Algorithms, Posterior probability, expression des données, Computational biology, Statistics - Applications, 03 medical and health sciences, Modelling and Simulation, Expectation–maximization algorithm, medicine, Humans, False Positive Reactions, Applications (stat.AP), 0101 mathematics, EM algorithm, Molecular Biology, Gene, 030304 developmental biology, belief propagation, inference, Models, Genetic, Research, gène, [ STAT.AP ] Statistics [stat]/Applications [stat.AP], Cancer, medicine.disease, Data set, Urinary Bladder Neoplasms, FOS: Biological sciences, Transcriptome
Abstract

International audience; In tumoral cells, gene regulation mechanisms are severely altered, and these modifications in the regulations may be characteristic of different subtypes of cancer. However, these alterations do not necessarily induce differential expressions between the subtypes. To answer this question, we propose a statistical methodology to identify the misregulated genes given a reference network and gene expression data. Our model is based on a regulatory process in which all genes are allowed to be deregulated. We derive an EM algorithm where the hidden variables correspond to the status (under/over/normally expressed) of the genes and where the E-step is solved thanks to a message passing algorithm. Our procedure provides posterior probabilities of deregulation in a given sample for each gene. We assess the performance of our method by numerical experiments on simulations and on a bladder cancer data set.

Published
2015
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79. UNIVERSITÉ D'ÉVRY-VAL-D'ESSONNE École doctorale 'du Génome aux Organismes'

Author

Chiquet, Julien, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université d'Évry-val-d'Essonne, Christophe Ambroise, Chiquet, Julien, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Université d'Évry-Val-d'Essonne (UEVE), Université d'Évry-Val-d'Essonne, and Laboratoire de Mathématiques et Modélisation d'Evry

Subjects
Gaussian Graphical Model, [STAT.AP]Statistics [stat]/Applications [stat.AP], régression parcimonieuse, Génomique/méthodes, regularisation, génomique, parcimonie structurée, modèle graphique Gaussien, [SDV]Life Sciences [q-bio], hdr, High Dimension and Sparsity, [STAT.OT]Statistics [stat]/Other Statistics [stat.ML], [STAT.OT] Statistics [stat]/Other Statistics [stat.ML], Modèle graphique gaussien, Genomics/methods, [STAT.AP] Statistics [stat]/Applications [stat.AP], Sparse Regression, Régularisation, Regularization methods, Parcimonie structurée
Abstract

https://hal.archives-ouvertes.fr/tel-01288976v1; This document is organized around three chapters.that summarize my research activity since 2008, that is, after my PhD thesis. The first chapter provides motivations for my research work. I first depict informally the kind of data statisticians have to deal with in recent application problems. I build on the example of genomics, with which I am familiar, in order to extract the most striking characteristics of modern data that strongly jeopardize the common way of doing statistics. I exhibit important statistical challenges associated with such data and motivate the use of particular tools at the heart of my research preoccupations, which are at the edge of statistics, optimization and machine learning. I then briefly present the main themes of my research and set them in the landscape of the statistical learning community. The second chapter proposes an overview of my contributions to Gaussian Graphical Models (GGM), in terms of modeling and more importantly in terms of inference of the conditional structure associated with such models. After a quick outline of the existing literature and an introduction to the most popular methods in the community,I present my contribution to this field. These contributions were motivated by the need to account for some special features characterizing genomics data and biological networks. The third chapter is dedicated to my works on structured sparse methods. After a brief overview of the basic computational and statistical tools related to sparse regularization, I present four of my contributions to this field. I wish to demonstrate the diversity of these contributions, some being related to algorithmic and computational considerations, while some others are focused on the statistical properties of the methods. All emerged from motivations anchored in applications. A comprehensive curriculum vitae is finally given in the appendix.

Published
2015

80. PREDICTABLE REPRESENTATION PROPERTY FOR PROGRESSIVE ENLARGEMENTS OF A POISSON FILTRATION

Author

Aksamit, Anna, Jeanblanc, Monique, Rutkowski, Marek, University of Oxford [Oxford], Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Université d'Evry-Val d'Essonne, The University of Sydney [Sydney], University of Oxford, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université d'Évry-Val-d'Essonne (UEVE), The University of Sydney, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), and JEANBLANC, Monique

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], predictable representation property, Poisson process, random time, progressive enlargement
Abstract

We study problems related to the predictable representation property for a progressive enlargement G of a reference filtration F through observation of a finite random time τ. We focus on cases where the avoidance property and/or the continuity property for F-martingales do not hold and the reference filtration is generated by a Poisson process. Our goal is to find out whether the predictable representation property (PRP), which is known to hold in the Poisson filtration, remains valid for a progressively enlarged filtration G with respect to a judicious choice of G-martingales.

Published
2015

81. Bouncing skew Brownian motions

Author

Arnaud Gloter, Miguel Martinez, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Centre National de la Recherche Scientifique (CNRS)-ENSIIE-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA), Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Fédération de Recherche Bézout - Université Paris-Est Marne-la-Vallée (UPEM) - Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12) - Centre National de la Recherche Scientifique (CNRS), MARTINEZ, Miguel, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM)

Subjects
Statistics and Probability, Geometric Brownian motion, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], General Mathematics, 010102 general mathematics, Hitting time, Skew, Brownian excursion, [MATH] Mathematics [math], 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Stochastic differential equation, Mathematics::Probability, Diffusion process, Local time, Calculus, Statistical physics, 0101 mathematics, Statistics, Probability and Uncertainty, [MATH]Mathematics [math], Brownian motion, Mathematics
Abstract

We consider two skew Brownian motions, driven by the same Brownian motion, with different startingpoints and different skewness coefficients. In [13], the evolution of the distance between the two processes,in local time scale and up to their first hitting time is shown to satisfy a stochastic differential equationwith jumps. The jumps of this S.D.E. are naturally driven by the excursion process of one of the two skewBrownian motions.In this article, we show that the description of the distance of the two processes after this first hittingtime may be studied using the self similarity induced by the previous S.D.E. More precisely, we show that thedistance between the two processes in local time scale may be viewed as the unique continuous markovianself-similar extension of the process described in [13]. This permits us to compute the law of the distanceof the two skew Brownian motions at any time in the local time scale, when both original skew Brownianmotions start from zero. As a by product, we manage to study the markovian dependence on the skewnessparameter and answer an open question formulated initially by C. Burdzy and Z.Q. Chen in [6].

Published
2015

82. Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering

Author

Gilles Pagès, Abass Sagna, Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, Discrete mathematics, Mean squared error, Nonlinear filtering, Applied Mathematics, Quantization (signal processing), Probability (math.PR), 010103 numerical & computational mathematics, Conditional expectation, Lipschitz continuity, 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Stochastic differential equation, Quadratic equation, Robustness (computer science), Modeling and Simulation, FOS: Mathematics, Applied mathematics, 0101 mathematics, Mathematics - Probability, Mathematics
Abstract

We take advantage of recent (see~\cite{GraLusPag1, PagWil}) and new results on optimal quantization theory to improve the quadratic optimal quantization error bounds for backward stochastic differential equations (BSDE) and nonlinear filtering problems. For both problems, a first improvement relies on a Pythagoras like Theorem for quantized conditional expectation. While allowing for some locally Lipschitz functions conditional densities in nonlinear filtering, the analysis of the error brings into playing a new robustness result about optimal quantizers, the so-called distortion mismatch property: $L^r$-quadratic optimal quantizers of size $N$ behave in $L^s$ in term of mean error at the same rate $N^{-\frac 1d}$, $0

Published
2015

83. Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations

Author

Alexandre Vidal, Jonathan Touboul, Jonathan E. Rubin, Justyna Signerska-Rynkowska, Multiscale dYnamiCs in neuroENdocrine AxEs (Mycenae), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Labex MemoLife, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Collège de France (CdF (institution))-Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI Paris), Université Paris sciences et lettres (PSL), Centre interdisciplinaire de recherche en biologie (CIRB), Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), University of Pittsburgh (PITT), Pennsylvania Commonwealth System of Higher Education (PCSHE), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI Paris), Université Paris sciences et lettres (PSL)-Collège de France (CdF (institution)), Université Paris sciences et lettres (PSL)-Collège de France (CdF (institution))-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Collège de France (CdF (institution))-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM), Laboratoire de Mathématiques et Modélisation d'Evry, MemoLife, École normale supérieure - Paris (ENS Paris)-Collège de France (CdF)-ESPCI ParisTech-PSL Research University (PSL), Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Collège de France (CdF)-PSL Research University (PSL), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Collège de France (CdF)-Institut National de la Santé et de la Recherche Médicale (INSERM)-PSL Research University (PSL)-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)

Subjects
Dynamical systems theory, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], nonlinear integrate-and-fire neuron model, Biological neuron model, Dynamical Systems (math.DS), 01 natural sciences, 010305 fluids & plasmas, 03 medical and health sciences, rotation theory, 0302 clinical medicine, 0103 physical sciences, FOS: Mathematics, Discrete Mathematics and Combinatorics, Statistical physics, Invariant (mathematics), Mathematics - Dynamical Systems, ComputingMilieux_MISCELLANEOUS, 34K34, 37E45, 37E05, 37E10, 37N25, 92C20, Physics, Quantitative Biology::Neurons and Cognition, Oscillation, Applied Mathematics, Hybrid dynamical systems, Complex dynamics, Nonlinear system, mixed-mode oscillations, Flow (mathematics), Ordinary differential equation, bursting, 030217 neurology & neurosurgery
Abstract

International audience; This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically display a form of mixed-mode oscillations (MMOs), which are trajectories featuring an alternation of small oscillations with spikes or bursts (multiple consecutive spikes). The mechanism by which these are generated relies fundamentally on the hybrid structure of the flow: invariant manifolds of the continuous dynamics govern small oscillations, while discrete resets govern the emission of spikes or bursts, contrasting with classical MMO mechanisms in ordinary differential equations involving more than three dimensions and generally relying on a timescale separation. The decomposition of mechanisms reveals the geometrical origin of MMOs, allowing a relatively simple classification of points on the reset manifold associated to specific numbers of small oscillations. We show that the MMO pattern can be described through the study of orbits of a discrete a daptation map, which is singular as it features discrete discontinuities with unbounded left-and right-derivatives. We study orbits of the map via rotation theory for discontinuous circle maps and elucidate in detail complex behaviors arising in the case where MMOs display at most one small oscillation between each consecutive pair of spikes.

Published
2015
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84. tmle.npvi: targeted, integrative search of associations between DNA copy number and gene expression, accounting for DNA methylation: Fig. 1

Author

Chambaz, Antoine, Neuvial, Pierre, Modélisation aléatoire de Paris X (MODAL'X), Université Paris Nanterre (UPN), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Centre National de la Recherche Scientifique (CNRS)-ENSIIE-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA), This work was partially supported by the French National Cancer Institute (INCa) via Cancéropôle Île-de-France (INCa Grant 2011-1-LABEL- CNRS 3-1)., Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université Paris Ouest Nanterre La Défense (UPOND), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques et Modélisation d'Evry

Subjects
HUMAN BREAST-TUMORS, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], [INFO.INFO-BI] Computer Science [cs]/Bioinformatics [q-bio.QM]
Abstract

International audience; We describe the implementation of the method introduced by Chambaz et al. (2012). We also demonstrate its genome-wide application to the integrative search of new regions with strong association between DNA copy number and gene expression accounting for DNA methylation in breast cancers. Availability and implementation: An open-source R package tmle.npvi is available from CRAN (http://cran.r-project.org/). Contact: pierre.neuvial@genopole.cnrs.fr

Published
2015
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85. MODEL SELECTION IN LOGISTIC REGRESSION

Author

Kwemou, Marius, Taupin, Marie-Luce, Tocquet, Anne-Sophie, laboratoire d'Etudes et de recherches en Statistiques et Développement (LERSTAD), Université Gaston Bergé Sénégal, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), INRA - Mathématiques et Informatique Appliquées (Unité MIAJ), Institut National de la Recherche Agronomique (INRA), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques et Modélisation d'Evry

Subjects
Statistics::Theory, model selection, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], logistic regression, Secondary 62G05, FOS: Mathematics, Statistics::Methodology, projection AMS 2000 MSC: Primary 62J02, Mathematics - Statistics Theory, Statistics Theory (math.ST), 62F12, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], 62G20
Abstract

This paper is devoted to model selection in logistic regression. We extend the model selection principle introduced by Birg\'e and Massart (2001) to logistic regression model. This selection is done by using penalized maximum likelihood criteria. We propose in this context a completely data-driven criteria based on the slope heuristics. We prove non asymptotic oracle inequalities for selected estimators. Theoretical results are illustrated through simulation studies.

Published
2015

86. Significance testing for variable selection in high-dimension

Author

Jean-Michel Becu, Christophe Ambroise, Yves Grandvalet, Cyril Dalmasso, Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), ANR-11-IDEX-0004,SUPER,Sorbonne Universités à Paris pour l'Enseignement et la Recherche(2011), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Centre National de la Recherche Scientifique (CNRS) - Université de Technologie de Compiègne, Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Centre de Gestion Scientifique i3 (CGS i3), MINES ParisTech - École nationale supérieure des mines de Paris - PSL Research University (PSL) - Centre National de la Recherche Scientifique (CNRS), ANR-11-IDEX-0004-02/10-LABX-0071, MS2T, Control of Technological Systems of Systems(2011), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), and ANR-11-IDEX-0004-02/10-LABX-0071,MS2T,Control of Technological Systems of Systems(2011)

Subjects
False discovery rate, 0303 health sciences, business.industry, Linear model, Feature selection, Regression analysis, Machine learning, computer.software_genre, 01 natural sciences, [STAT] Statistics [stat], [STAT]Statistics [stat], 010104 statistics & probability, 03 medical and health sciences, Lasso (statistics), Ordinary least squares, Artificial intelligence, Sensitivity (control systems), 0101 mathematics, [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM], business, computer, Selection (genetic algorithm), 030304 developmental biology, Mathematics, [INFO.INFO-BI] Computer Science [cs]/Bioinformatics [q-bio.QM]
Abstract

International audience; Assessing the uncertainty pertaining to the conclusions derived from experimental data is challenging when there is a high number of possible explanations compared to the number of experiments. We propose a new two-stage “screen and clean” procedure for assessing the uncertainties pertaining to the selection of relevant variables in high-dimensional regression problems. In this two-stage method, screening consists in selecting a subset of candidate variables by a sparsity-inducing penalized regression, while cleaning consists in discarding all variables that do not pass a significance test. This test was originally based on ordinary least squares regression. We propose to improve the procedure by conveying more information from the screening stage to the cleaning stage. Our cleaning stage is based on an adaptively penalized regression whose weights are adjusted in the screening stage. Our procedure is amenable to the computation of p-values, allowing to control the False Discovery Rate. Our experiments show the benefits of our procedure, as we observe a systematic improvement of sensitivity compared to the original procedure.

Published
2015
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87. A greedy great approach to learn with complementary structured datasets

Author

Christophe Ambroise, Julien Chiquet, Marie Szafranski, Mathématiques et Informatique Appliquées (MIA-Paris), Institut National de la Recherche Agronomique (INRA)-AgroParisTech, USC INRA, UMR ENSIIE et LaMME, Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), AgroParisTech-Institut National de la Recherche Agronomique (INRA), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - AgroParisTech, Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)

Subjects
compressed representation, numerical simulations, algorithm, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [SDV]Life Sciences [q-bio], complementary structured datasets, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML]
Abstract

HAL Id : hal-01246419, version 1HAL Id : hal-01246419, version 1; We are interested in problems where two hierarchically structured datasets may be complementary for a learning process. This case may arise in biological applications where genomic and metagenomic analyses may be collected for studying the genomic features of an organism along with its environnement. In this work, we propose a model to assess the relevant interactions between the two datasets. We use a compressed representation that of the original data to cope with the high dimensionality of the problem. We show that the collection of models, characterized through the hierarchical structures, forms a partially ordered set and take advantage of this organization to define a greedy approach to solve the problem more efficiently. Finally, we illustrate the behavior of the resulting algorithm on numerical simulations.

Published
2015

88. View and synchronize several genotypes with IGV

Author

Franchinard, Marie-Laure, Sapet, Frederic, Derozier, Sandra, Samson, Franck, Gibrat, Jean-Francois, Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de la Recherche Agronomique (INRA), BIOGEMMA, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques et Modélisation d'Evry

Subjects
[SDV]Life Sciences [q-bio], [INFO]Computer Science [cs], [MATH]Mathematics [math], ComputingMilieux_MISCELLANEOUS
Abstract

Événement(s) lié(s) : - AG France Genomique; Paris (FRA) - (2015-11-24 - 2015-11-25); National audience

Published
2015

89. BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration

Author

Alexandre Popier, Thomas Kruse, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Manceau de Mathématiques (LMM), Le Mans Université (UM), Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, 010102 general mathematics, Mathematical analysis, Probability (math.PR), Poisson random measure, Monotonic function, Poisson distribution, 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, symbols.namesake, Monotone polygon, Modeling and Simulation, Stopping time, Mathematik, symbols, Filtration (mathematics), FOS: Mathematics, Uniqueness, 0101 mathematics, Brownian motion, ComputingMilieux_MISCELLANEOUS, Mathematics - Probability, Mathematics
Abstract

We analyze multidimensional BSDEs in a filtration that supports a Brownian motion and a Poisson random measure. Under a monotonicity assumption on the driver, the paper extends several results from the literature. We establish existence and uniqueness of solutions in $L^p$ provided that the generator and the terminal condition satisfy appropriate integrability conditions. The analysis is first carried out under a deterministic time horizon, and then generalized to random time horizons given by a stopping time with respect to the underlying filtration. Moreover, we provide a comparison principle in dimension one.

Published
2015
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90. Infinite energy solutions for a 1D transport equation with nonlocal velocity

Author

Pierre Gilles Lemarié-Rieusset, Omar Lazar, Instituto de Ciencias Matemáticas (ICMAT), Universidad Carlos III de Madrid [Madrid]-Universidad Complutense de Madrid [Madrid] (UCM)-Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Spain] (CSIC), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Lemarié-Rieusset, Pierre Gilles, Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Universidad Autónoma de Madrid - Consejo Superior de Investigaciones Científicas [Spain] (CSIC) - Universidad Complutense de Madrid - Universidad Carlos III de Madrid [Madrid], Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - Centre National de la Recherche Scientifique (CNRS) - ENSIIE, Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM), and Laboratoire de Mathématiques et Modélisation d'Evry

Subjects
Lebesgue integration, 01 natural sciences, law.invention, non-local transport, symbols.namesake, commutators, Mathematics - Analysis of PDEs, law, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Initial value problem, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Commutator (electric), Muckenhoupt weights, 16. Peace & justice, Functional Analysis (math.FA), 010101 applied mathematics, Sobolev space, Mathematics - Functional Analysis, Norm (mathematics), Dissipative system, symbols, Convection–diffusion equation, Analysis, Analysis of PDEs (math.AP)
Abstract

We study a one dimensional dissipative transport equation with nonlocal velocity and critical dissipation. We consider the Cauchy problem for initial values with infinite energy. The control we shall use involves some weighted Lebesgue or Sobolev spaces. More precisely, we consider the familly of weights given by $w_{\beta}(x)=(1+\vert x \vert^{2})^{-\beta/2}$ where $\beta$ is a real parameter in $(0,1)$ and we treat the Cauchy problem for the cases $\theta_{0} \in H^{1/2} (w_{\beta})$ and $\theta_{0} \in H^{1} (w_{\beta})$ for which we prove global existence results (under smallness assumptions on the $L^\infty$ norm of $\theta_0$). The key step in the proof of our theorems is based on the use of two new commutator estimates involving fractional differential operators and the family of Muckenhoupt weights., Comment: 25 pages. To appear in Dynamics of PDEs

Published
2015

91. The effect of trading futures on short sale constraints

Author

Jarrow, Robert, Protter, Philip, Pulido, Sergio, Cornell University, Columbia University [New York], Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Cornell University [New York], Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)

Subjects
futures contracts, bubbles, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], martingale representation, futures prices, overpricing hypothesis, Short sale constraints, complete markets, [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], supermartingale measures
Abstract

International audience; It is commonly believed that the trading of futures on a commodity enables the market to overcome short selling constraints on the spot commodity itself. This belief is embedded in the notion that trading strategies involving futures contracts enable traders to replicate the payoffs as if they were short the spot commodity. The purpose of this paper is to investigate this common belief in a general arbitrage-free semimartingale financial model with trading in futures and a short selling prohibition on the spot commodity. We show via various examples that, in general, this common belief is incorrect. Furthermore, we provide a set of sufficient conditions, albeit very restrictive, under which the common belief is true.

Published
2015
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92. Complex dynamics for the study of neural activity in the human brain

Author

Garnier, Aurélie, Huneau, Clément, Vidal, Alexandre, Wendling, Fabrice, Benali, Habib, Laboratoire d'Imagerie Biomédicale (LIB), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Génétique et Physiopathologie des Maladies Cérébro-Vasculaires (U1161 / UMR_S 1161), Université Paris Diderot - Paris 7 (UPD7)-Institut National de la Santé et de la Recherche Médicale (INSERM), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Laboratoire Traitement du Signal et de l'Image (LTSI), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de la Santé et de la Recherche Médicale (INSERM), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES), Centre National de la Recherche Scientifique (CNRS) - Institut National de la Santé et de la Recherche Médicale (INSERM) - Université Pierre et Marie Curie - Paris 6 (UPMC), Génétique et Physiopathologie des Maladies Cérébro-Vasculaires, Université Sorbonne Paris Cité (USPC) - Université Paris Diderot - Paris 7 (UP7) - Institut National de la Santé et de la Recherche Médicale (INSERM), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Institut National de la Santé et de la Recherche Médicale (INSERM) - Université de Rennes 1 (UR1), Laboratoire d'Imagerie Biomédicale [Paris] (LIB), Université de Rennes (UR)-Institut National de la Santé et de la Recherche Médicale (INSERM), and Frouin, Frédérique

Subjects
[SDV.IB] Life Sciences [q-bio]/Bioengineering, Quantitative Biology::Neurons and Cognition, Modeling, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Simulation
Abstract

Congrès sous l’égide de la Société Française de Génie Biologique et Médical (SFGBM).; National audience; Neural mass modeling is a part of computational neuroscience that was developed to study the general behavior of interacting neuronal populations. This type of mesoscopic model is able to generate output signals that are comparable with experimental data such as electroencephalograms. Classically, neural mass models consider two interconnected populations. One interaction have been modeled in two differents ways. In this work we propose and analyze a neural mass model embedding both approaches and compare the generated time series to real data.

Published
2015

93. The obstacle problem for semilinear parabolic partial integro-differential equations

Author

Anis Matoussi, Wissal Sabbagh, Chao Zhou, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), National University of Singapore (NUS), Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Variational equation, Differential equation, 010102 general mathematics, Probability (math.PR), Probabilistic logic, Mathematics::Analysis of PDEs, 01 natural sciences, Interpretation (model theory), Connection (mathematics), Sobolev space, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Stochastic differential equation, Modeling and Simulation, Obstacle problem, FOS: Mathematics, Computer Science::Mathematical Software, Applied mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 60H15, 60G46, 35R60, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Mathematics - Probability, Mathematics
Abstract

This paper presents a probabilistic interpretation for the weak Sobolev solution of the obstacle problem for semilinear parabolic partial integro-differential equations (PIDEs). The results of Leandre (1985) concerning the homeomorphic property for the solution of SDEs with jumps are used to construct random test functions for the variational equation for such PIDEs. This results in the natural connection with the associated Reflected Backward Stochastic Differential Equations with jumps (RBSDEs), namely Feynman Kac's formula for the solution of the PIDEs. Moreover it gives an application to the pricing and hedging of contingent claims with constraints in the wealth or portfolio processes in financial markets including jumps., Comment: 31 pages

Published
2015
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94. A neural mass model with direct and indirect excitatory feedback loops: identification of bifurcations and temporal dynamics

Author

Clément Huneau, Alexandre Vidal, Habib Benali, Aurélie Garnier, Laboratoire d'Imagerie Biomédicale (LIB), Centre National de la Recherche Scientifique (CNRS) - Institut National de la Santé et de la Recherche Médicale (INSERM) - Université Pierre et Marie Curie - Paris 6 (UPMC), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Génétique et Physiopathologie des Maladies Cérébro-Vasculaires, Université Sorbonne Paris Cité (USPC) - Université Paris Diderot - Paris 7 (UP7) - Institut National de la Santé et de la Recherche Médicale (INSERM), Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Pierre et Marie Curie - Paris 6 (UPMC), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Génétique et Physiopathologie des Maladies Cérébro-Vasculaires (U1161 / UMR_S 1161), Université Paris Diderot - Paris 7 (UPD7)-Institut National de la Santé et de la Recherche Médicale (INSERM), Laboratoire d'Imagerie Biomédicale [Paris] (LIB), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, and Administateur, HAL Sorbonne Université

Subjects
[SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, Cognitive Neuroscience, Population, Models, Neurological, Parameter space, 03 medical and health sciences, 0302 clinical medicine, Arts and Humanities (miscellaneous), Control theory, medicine, Humans, Computer Simulation, [SDV.NEU] Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], education, Bifurcation, 030304 developmental biology, Mathematics, Feedback, Physiological, Neurons, 0303 health sciences, education.field_of_study, Computational neuroscience, Series (mathematics), Quantitative Biology::Neurons and Cognition, Excitatory Postsynaptic Potentials, Nonlinear system, Range (mathematics), medicine.anatomical_structure, [SDV.IB.IMA] Life Sciences [q-bio]/Bioengineering/Imaging, Nonlinear Dynamics, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], Pyramidal cell, Nerve Net, Biological system, 030217 neurology & neurosurgery
Abstract

International audience; Neural mass modeling is a part of computational neuroscience that was developed to study the general behavior of a neuronal population. This type of mesoscopic model is able to generate output signals that are comparable to experimental data, such as electroencephalograms. Classically, neural mass models consider two interconnected populations: excitatory pyramidal cells and inhibitory interneurons. However, many authors have included an excitatory feedback on the pyramidal cell population. Two distinct approaches have been developed: a direct feedback on the main pyramidal cell population and an indirect feedback via a secondary pyramidal cell population. In this letter, we propose a new neural mass model that couples these two approaches. We perform a detailed bifurcation analysis and present a glossary of dynamical behaviors and associated time series. Our study reveals that the model is able to generate particular realistic time series that were never pointed out in either simulated or experimental data. Finally, we aim to evaluate the effect of balance between both excitatory feedbacks on the dynamical behavior of the model. For this purpose, we compute the codimension 2 bifurcation diagrams of the system to establish a map of the repartition of dynamical behaviors in a direct versus indirect feedback parameter space. A perspective of this work is, from a given temporal series, to estimate the parameter value range, especially in terms of direct versus indirect excitatory feedback.

Published
2015
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95. On the harmonic measure of stable processes

Author

Profeta, Christophe, Simon, Thomas, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé - UMR 8524 (LPP), Laboratoire de Mathématiques et Modélisation d'Evry, Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS) - Université de Lille, Sciences et Technologies, and Université Paris-Sud - Paris 11 (UP11) - Centre National de la Recherche Scientifique (CNRS)

Subjects
Hitting probability, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Martin kernel, 60G51, 60G52, 60J45, Green function, Probability (math.PR), Harmonic measure, FOS: Mathematics, Stable L\'evy process, Hypergeometric function, Mathematics - Probability
Abstract

Using three hypergeometric identities, we evaluate the harmonic measure of a finite interval and of its complementary for a strictly stable real L{\'e}vy process. This gives a simple and unified proof of several results in the literature, old and recent. We also provide a full description of the corresponding Green functions. As a by-product, we compute the hitting probabilities of points and describe the non-negative harmonic functions for the stable process killed outside a finite interval.

Published
2015

96. On an Optional Semimartingale Decomposition and the Existence of a Deflator in an Enlarged Filtration

Author

Aksamit, Anna, Choulli, Tahir, Jeanblanc, Monique, University of Oxford [Oxford], Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université de l'Alberta, Université d'Évry-Val-d'Essonne (UEVE), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), University of Oxford, Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), and Université d'Evry-Val d'Essonne

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
Abstract

International audience; Given a reference filtration F, we consider the cases where an enlarged filtration G is constructed from F in two different ways: progressively with a random time or initially with a random variable. In both situations, under suitable conditions, we present a G-optional semimartingale decomposition for F-local martingales. Our study is then applied to answer the question of how an arbitrage-free semimartingale model is affected when stopped at the random time in the case of progressive enlargement or when the random variable used for initial enlargement satisfies Jacod's hypothesis. More precisely, we focus on the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition. We provide alternative proofs of some results from [5], with a methodology based on our optional semimartingale decomposition, which reduces significantly the length of the proof.

Published
2015
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97. Performance of a blockwise approach in variable selection using linkage disequilibrium information

Author

Dehman, Alia, Ambroise, Christophe, Neuvial, Pierre, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Partially funded by Institut National du Cancer (INCa) and Cancéropôle Ile-de-France, and Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS)

Subjects
Genetic Markers, [STAT.AP]Statistics [stat]/Applications [stat.AP], [SDV.BIBS] Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], Penalized regression, genome wide association studies, linkage disequilibrium, hierarchical clustering, model selection, gap statistic, penalized regression, group lasso, Models, Theoretical, Model selection, Biochemistry, Polymorphism, Single Nucleotide, Genome-wide association studies, [SDV.BIBS]Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], Gap statistic, Hierarchical clustering, Computer Science Applications, Group lasso, Haplotypes, [STAT.AP] Statistics [stat]/Applications [stat.AP], Applications, Linkage disequilibrium, Humans, Molecular Biology, Algorithms, Research Article, Genome-Wide Association Study
Abstract

Background Genome-wide association studies (GWAS) aim at finding genetic markers that are significantly associated with a phenotype of interest. Single nucleotide polymorphism (SNP) data from the entire genome are collected for many thousands of SNP markers, leading to high-dimensional regression problems where the number of predictors greatly exceeds the number of observations. Moreover, these predictors are statistically dependent, in particular due to linkage disequilibrium (LD). We propose a three-step approach that explicitly takes advantage of the grouping structure induced by LD in order to identify common variants which may have been missed by single marker analyses (SMA). In the first step, we perform a hierarchical clustering of SNPs with an adjacency constraint using LD as a similarity measure. In the second step, we apply a model selection approach to the obtained hierarchy in order to define LD blocks. Finally, we perform Group Lasso regression on the inferred LD blocks. We investigate the efficiency of this approach compared to state-of-the art regression methods: haplotype association tests, SMA, and Lasso and Elastic-Net regressions. Results Our results on simulated data show that the proposed method performs better than state-of-the-art approaches as soon as the number of causal SNPs within an LD block exceeds 2. Our results on semi-simulated data and a previously published HIV data set illustrate the relevance of the proposed method and its robustness to a real LD structure. The method is implemented in the R package BALD (Blockwise Approach using Linkage Disequilibrium), available from http://www.math-evry.cnrs.fr/publications/logiciels. Conclusions Our results show that the proposed method is efficient not only at the level of LD blocks by inferring well the underlying block structure but also at the level of individual SNPs. Thus, this study demonstrates the importance of tailored integration of biological knowledge in high-dimensional genomic studies such as GWAS. Electronic supplementary material The online version of this article (doi:10.1186/s12859-015-0556-6) contains supplementary material, which is available to authorized users.

Published
2015
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98. The Landau Equation for Maxwellian molecules and the Brownian Motion on SO_R(N)

Author

Delarue, François, Menozzi, Stephane, Nualart, Eulalia, Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (UNS) - Centre National de la Recherche Scientifique (CNRS), State University Higher School of Economics, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Dept. Economics and Business, Universitat Pompeu Fabra [Barcelona], Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Universitat Pompeu Fabra [Barcelona] (UPF), Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)

Subjects
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Probability (math.PR), 60H30, 60H40, 60H10, Stochastic analysis, Heat kernel estimates on groups, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Analysis of PDEs, Large deviations, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Probability, Analysis of PDEs (math.AP), Landau equation for Maxwellian molecules
Abstract

In this paper we prove that the spatially homogeneous Landau equation for Maxwellian molecules can be represented through the product of two elementary processes. The first one is the Brownian motion on the group of rotations. The second one is, conditionally on the first one, a Gaussian process. Using this representation, we establish sharp multi-scale upper and lower bounds for the transition density of the Landau equation, the multi-scale structure depending on the shape of the support of the initial condition., Comment: 38

Published
2015

99. Continuous time semi-Markov inference of biometric laws associated with a Long-Term Care Insurance portfolio

Author

Biessy, Guillaume, Biessy, Guillaume, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques et Modélisation d'Evry

Subjects
[STAT.AP]Statistics [stat]/Applications [stat.AP], mixture model, Long-Term Care Insurance, [STAT.AP] Statistics [stat]/Applications [stat.AP], parametric model, continuous time semi-Markov process, maximum likelihood, competing risks
Abstract

Unlike the mortality risk on which actuaries have been working for more than a century, the long-term care (LTC) risk is young and as of today hardly mastered. Semi-Markov processes have been identified as an adequate tool to study this risk. Nevertheless, access to data is limited and the associated literature still scarce. Insurers mainly use discrete time methods directly inspired from the study of mortality in order to build experience tables. Those methods however are not perfectly suited for the study of competing risk situations.The present article provides a theoretical framework to estimate biometric laws associated with a long-term care insurance portfolio. The presented method relies on a continuous-time semi-Markov model with three states: autonomy, disability and death. The process describing the state of disability is defined through its transition intensities. We provide a formula to infer the mortality of autonomous people from the mortality of the whole portfolio, on which we have more reliable knowledge. We then propose a parametric expression for the remaining intensities of the model. In particular, incidence in LTC is described by a logistic formula. Under the assumption that the disabled population is a mixture of two latent populations with respect to the category of pathology that caused LTC, we show that the resulting intensity of mortality in LTC takes a very peculiar form and depends on time spent in the LTC state. Estimation of parameters relies on the maximum likelihood method. Our parametric approach, while inducing model uncertainty, eliminates issues related to segmentation in age categories, smoothing or extrapolation at higher ages and thus proves very convenient for the practitioner. Finally, we provide an application using data from a real long-term care insurance portfolio.

Published
2015

100. Utility maximization with random horizon: a BSDE approach

Author

Monique Jeanblanc, Thibaut Mastrolia, Anthony Réveillac, Dylan Possamaï, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Centre National de la Recherche Scientifique (CNRS)-ENSIIE-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA), Université d'Évry-Val-d'Essonne (UEVE), Université Paris Dauphine-PSL, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Université d'Evry-Val d'Essonne, Université Paris-Dauphine, Centre National de la Recherche Scientifique (CNRS) - Université Paris-Dauphine, Université Toulouse 1 Capitole (UT1) - Université Toulouse 2 (UT2) - Université Paul Sabatier - Toulouse 3 (UPS) - PRES Université de Toulouse - Institut National des Sciences Appliquées de Toulouse (INSA de Toulouse) - Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), and Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)

Subjects
Mathematical optimization, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], AMS 2010 subject classification: Primary: 60H10, 91G40 Secondary: 91B16, 91G60, 93E20, 60H20, Mathematics::Probability, credit risk AMS 2010 subject classification: Primary: 60H10, FOS: Mathematics, quadratic BSDEs, enlargement of filtration, Uniqueness, 60H20, ComputingMilieux_MISCELLANEOUS, Mathematics, Horizon (archaeology), Probability (math.PR), Utility maximization, 91G60, 93E20, 91G40, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Secondary: 91B16, Utility maximization problem, Bounded function, Singular coefficients, General Economics, Econometrics and Finance, Mathematical economics, Mathematics - Probability, Finance, Credit risk
Abstract

In this paper, we study a utility maximization problem with random horizon and reduce it to the analysis of a specific backward stochastic differential equation (BSDE), which we call BSDE with singular coefficients, when the support of the default time is assumed to be bounded. We prove existence and uniqueness of the solution for the equation under interest. Our results are illustrated by numerical simulations.

Published
2015
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