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1. The Facial Weak Order on Hyperplane Arrangements

Author

Vincent Pilaud, Thomas McConville, Christophe Hohlweg, Aram Dermenjian, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Massachusetts Institute of Technology (MIT), Centre National de la Recherche Scientifique (CNRS), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), ANR-15-CE40-0004,SC3A,Surfaces, Catégorification et Combinatoire des Algèbres Amassées(2015), ANR-17-CE40-0018,CAPPS,Analyse Combinatoire de Polytopes et de Subdivisions Polyédrales(2017), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Pilaud, Vincent, Surfaces, Catégorification et Combinatoire des Algèbres Amassées - - SC3A2015 - ANR-15-CE40-0004 - AAPG2015 - VALID, and Analyse Combinatoire de Polytopes et de Subdivisions Polyédrales - - CAPPS2017 - ANR-17-CE40-0018 - AAPG2017 - VALID

Subjects
Hyperplane arrangements, zonotopes, 0102 computer and information sciences, Lattice (discrete subgroup), poset of regions, 01 natural sciences, Theoretical Computer Science, Combinatorics, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, 52C35, 03G10, Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, Order (group theory), 0101 mathematics, Mathematics, Homotopy, 010102 general mathematics, Coxeter group, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Oriented matroid, Computational Theory and Mathematics, Cover (topology), Hyperplane, 010201 computation theory & mathematics, Combinatorics (math.CO), Geometry and Topology, Partially ordered set
Abstract

We extend the facial weak order from finite Coxeter groups to central hyperplane arrangements. The facial weak order extends the poset of regions of a hyperplane arrangement to all its faces. We provide four non-trivially equivalent definitions of the facial weak order of a central arrangement: (1) by exploiting the fact that the faces are intervals in the poset of regions, (2) by describing its cover relations, (3) using covectors of the corresponding oriented matroid, and (4) using certain sets of normal vectors closely related to the geometry of the corresponding zonotope. Using these equivalent descriptions, we show that when the poset of regions is a lattice, the facial weak order is a lattice. In the case of simplicial arrangements, we further show that this lattice is semidistributive and give a description of its join-irreducible elements. Finally, we determine the homotopy type of all intervals in the facial weak order., 34 pages, 12 figures

Published
2021

2. INPUT OF DEEP PHENOTYPING IN THE METABOLIC SYNDROME STRATIFICATION

Author

Monnerie, Stéphanie, Pétéra, Mélanie, Canlet, Cécile, Castelli, Florence, Colsch, Benoit, Fenaille, Francois, Joly, Charlotte, Jourdan, Fabien, Lenuzza, Natacha, Lyan, Bernard, Martin, Jean-Francois, Migné, Carole, Morais, José A, Poupin, Nathalie, Vinson, Florence, Thevenot, Etienne, Junot, Christophe, Gaudreau, Pierrette, Comte, Blandine, Pujos-Guillot, Estelle, Unité de Nutrition Humaine - Clermont Auvergne (UNH), Institut National de la Recherche Agronomique (INRA)-Université Clermont Auvergne (UCA), Plateforme d’Exploration du Métabolisme, Institut National de la Recherche Agronomique (INRA), ToxAlim (ToxAlim), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Ecole Nationale Vétérinaire de Toulouse (ENVT), Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Ecole d'Ingénieurs de Purpan (INPT - EI Purpan), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National de la Recherche Agronomique (INRA), MetaboHUB, Service de Pharmacologie et Immunoanalyse (SPI), Laboratoire d'Etude du Métabolisme des Médicaments (LEMM), Commissariat à l'Energie Atomique et aux Energies Alternatives (CEA), Institut National de Recherche en Agriculture, Alimentation et Environnement (INRAE), Université Paris Saclay (COMUE), Laboratoire d'Intégration des Systèmes et des Technologies (LIST), Division de Gériatrie, Centre de recherche du Centre universitaire de santé McGill, McGill University, Département de médecine, Centre de Recherche du Centre hospitalier de l’Université de Montréal, Université de Montréal (UdeM), Unité de Nutrition Humaine (UNH), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Plateforme Exploration du Métabolisme (PFEM), MetaboHUB-Clermont, MetaboHUB-MetaboHUB-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Université Clermont Auvergne (UCA), Institut National de la Recherche Agronomique (INRA)-Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-MetaboHUB-Clermont, MetaboHUB-MetaboHUB, MetaToul AXIOM (E20), Institut National de la Recherche Agronomique (INRA)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Ecole Nationale Vétérinaire de Toulouse (ENVT), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Ecole d'Ingénieurs de Purpan (INP - PURPAN), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National de la Recherche Agronomique (INRA)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-MetaboHUB-MetaToul, MetaboHUB-Génopole Toulouse Midi-Pyrénées [Auzeville] (GENOTOUL), Université de Toulouse (UT)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-MetaboHUB-Génopole Toulouse Midi-Pyrénées [Auzeville] (GENOTOUL), Université de Toulouse (UT)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Médicaments et Technologies pour la Santé (MTS), Université Paris-Saclay-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Université Paris-Saclay-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Métabolisme et Xénobiotiques (ToxAlim-MeX), Université de Toulouse (UT)-Université de Toulouse (UT), Laboratoire Sciences des Données et de la Décision (LS2D), Département Métrologie Instrumentation & Information (DM2I), Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, McGill University = Université McGill [Montréal, Canada], Centre de Recherche du Centre Hospitalier de l’Université de Montréal (CR CHUM), Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Analyse de Xénobiotiques, Identification, Métabolisme (E20 Metatoul-AXIOM), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National de la Recherche Agronomique (INRA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National de la Recherche Agronomique (INRA)-MetaToul-MetaboHUB, Génopole Toulouse Midi-Pyrénées [Auzeville] (GENOTOUL), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Ecole Nationale Vétérinaire de Toulouse (ENVT), Université Fédérale Toulouse Midi-Pyrénées-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Génopole Toulouse Midi-Pyrénées [Auzeville] (GENOTOUL), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Laboratoire d'Intégration des Systèmes et des Technologies (LIST), Plateforme d'Exploration du Métabolisme PFEM, Université Fédérale Toulouse Midi-Pyrénées-Ecole d'Ingénieurs de Purpan (INPT - EI Purpan), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-MetaToul-MetaboHUB, Université Fédérale Toulouse Midi-Pyrénées-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées

Subjects
[SDV.OT]Life Sciences [q-bio]/Other [q-bio.OT], [CHIM.ANAL]Chemical Sciences/Analytical chemistry
Abstract

IntroductionMetabolic syndrome (MetS), defined as a cluster of cardiometabolic factors, is a public health challenge because of its growing prevalence. In the context of personalized medicine, new tools are necessary to bring additional knowledge about MetS etiology, better stratify populations and customise strategies for prevention. The objective of this study was to characterize the MetS phenotypic spectrum using complementary untargeted metabolomics platforms (HRMS, RMN).Technological and methodological innovationA case-control study was designed within the Quebec NuAge cohort1. Six complementary untargetedmetabolomic/lipidomic approaches were performed on serum samples collected at recruitment and 3 years later. Procedures were set up to guaranty the inter-laboratory standardisation from sample preparation to data processing, performed using reproducible online Galaxy workflows. A full feature selection strategy was developed to build a comprehensive molecular MetS signature, stable over time.Results and impactA wide range of metabolites (lipids, carbohydrates, amino-acids, peptides…) reflecting subject stability and providing new insights about underlying mechanisms, were found to be modulated. An optimized reduced signature was proposed, allowing good prediction performances (12% misclassification, AUC=0.95, CI:[0.92-0.98]). These results demonstrated the interest of a multidimensional molecular phenotyping as part of the next generation of medicine tools in the frame of noncommunicable diseases.References[1] Gaudreau P et al., 2007. Rejuvenation Res.10(3):377-386.

Published
2020

3. Evaluation of upconverting nanoparticles towards heart theranostics

Author

Céline Galés, Kermorgant Marc, Francis Beaudry, Dina N. Arvanitis, Jennifer Ben Salem, Olivier Lairez, Christophe Coudret, Robert Mauricot, Calise Denis, Clément Roux, Marc Verelst, Julien Santelli, Anne Pavy-Le Traon, Jean-Michel Senard, Anne-Cécile Oster, Institut des Maladies Métaboliques et Cardiovasculaires (I2MC), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National de la Santé et de la Recherche Médicale (INSERM), Groupe de Recherche en Pharmacologie Animale du Québec [Saint-Hyacinthe, QC, Canada] (GREPAQ), Département de Biomédecine Vétérinaire [Saint-Hyacinthe, QC, Canada], Faculté de Médecine Vétérinaire [Saint-Hyacinthe, QC, Canada], Université de Montréal (UdeM)-Université de Montréal (UdeM)-Faculté de Médecine Vétérinaire [Saint-Hyacinthe, QC, Canada], Université de Montréal (UdeM)-Université de Montréal (UdeM), Centre d'élaboration de matériaux et d'études structurales (CEMES), 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 de Toulouse (UT)-Institut de Chimie de Toulouse (ICT), Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Service de Microchirurgie [CHU Toulouse], Centre Hospitalier Universitaire de Toulouse (CHU Toulouse), Fédération de Cardiologie [CHU Toulouse], Service Cardiologie [CHU Toulouse], Pôle Cardiovasculaire et Métabolique [CHU Toulouse], Centre Hospitalier Universitaire de Toulouse (CHU Toulouse)-Centre Hospitalier Universitaire de Toulouse (CHU Toulouse)-Pôle Cardiovasculaire et Métabolique [CHU Toulouse], Centre Hospitalier Universitaire de Toulouse (CHU Toulouse)-Centre Hospitalier Universitaire de Toulouse (CHU Toulouse), Interactions moléculaires et réactivité chimique et photochimique (IMRCP), Institut de Chimie de Toulouse (ICT), Université de Toulouse (UT)-Institut Ecologie et Environnement (INEE), Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Fluides, Energie, Réacteurs, Matériaux et Transferts (FERMAT), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), 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)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), IDeAS - Interfaces Dynamiques et Assemblages Stimulables (IDeAS), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie de Toulouse (ICT), CHROMALYS SAS [Toulouse], Service Pharmacologie Clinique [CHU Toulouse], Pôle Santé publique et médecine publique [CHU Toulouse], The authors acknowledge core support from Animal facility ANEXPLO, CREFRE US06 Rangueil. This work was funded by the CNRS (Défi IMAG’IN -AAP 2017). JBS was supported by the Fondation de France, Grant number RAF18002BBA (https://www.fondationdefrance.org/en) awarded to DA. JS was supported by grants from CHROMALYS, INSERM (www.inserm.fr) and the 'Région Midi-Pyrénées' (https://www.laregion.fr/). ANR is acknowledged for funding project 'BLINK': ANR-15-CE09-0020 (https://anr.fr/)., ANR-15-CE09-0020,BLINK,Nanohybrides multi-luminescents à scintillation contrôlée pour la microscopie en super résolution, et le suivi de particule unique(2015), Bodescot, Myriam, Nanohybrides multi-luminescents à scintillation contrôlée pour la microscopie en super résolution, et le suivi de particule unique - - BLINK2015 - ANR-15-CE09-0020 - AAPG2015 - VALID, Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National de la Santé et de la Recherche Médicale (INSERM), Institut National des Sciences Appliquées (INSA)-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées (INSA)-Université Fédérale Toulouse Midi-Pyrénées-Institut de Chimie de Toulouse (ICT-FR 2599), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Fédération des services de cardiologie [Rangueil], Institut de Chimie de Toulouse (ICT-FR 2599), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie de Toulouse (ICT-FR 2599), Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut de Chimie du CNRS (INC)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Institut de Chimie du CNRS (INC)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Service de Microchirurgie [Rangueil], Centre Régional d'Exploration Fonctionnelle et Ressources Expérimentales (CREFRE), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Toulouse III - Paul Sabatier (UT3), Hôpital de Rangueil, CHU Toulouse [Toulouse]-CHU Toulouse [Toulouse], Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Institut de Chimie de Toulouse (ICT-FR 2599), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD), Service de Pharmacologie Clinique, and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Hôpital Purpan [Toulouse]

Subjects
Male, Theranostic Nanomedicine, Physiology, 02 engineering and technology, 030204 cardiovascular system & hematology, Cardiovascular Physiology, 01 natural sciences, Electrocardiography, 0302 clinical medicine, Medicine and Health Sciences, Medicine, Nanotechnology, Upconverting nanoparticles, media_common, Multidisciplinary, Pharmaceutics, Heart, Pericardial space, 021001 nanoscience & nanotechnology, 3. Good health, [SDV.MHEP.CSC] Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Bioassays and Physiological Analysis, Optical Equipment, [SDV.SP.PHARMA] Life Sciences [q-bio]/Pharmaceutical sciences/Pharmacology, Drug delivery, Heart Function Tests, Engineering and Technology, Anatomy, 0210 nano-technology, Pericardium, Preclinical imaging, Research Article, Drug, Heart Diseases, media_common.quotation_subject, Science, Equipment, 010402 general chemistry, Research and Analysis Methods, 03 medical and health sciences, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Animals, Targeted release, business.industry, Myocardium, Lasers, Electrophysiological Techniques, Body Weight, Biology and Life Sciences, 0104 chemical sciences, Mice, Inbred C57BL, Time course, Cardiovascular Anatomy, [SDV.SP.PHARMA]Life Sciences [q-bio]/Pharmaceutical sciences/Pharmacology, Nanoparticles, Cardiac Electrophysiology, business, Drug Delivery
Abstract

Restricted and controlled drug delivery to the heart remains a challenge giving frequent off-target effects as well as limited retention of drugs in the heart. There is a need to develop and optimize tools to allow for improved design of drug candidates for treatment of heart diseases. Over the last decade, novel drug platforms and nanomaterials were designed to confine bioactive materials to the heart. Yet, the research remains in its infancy, not only in the development of tools but also in the understanding of effects of these materials on cardiac function and tissue integrity. Upconverting nanoparticles are nanomaterials that recently accelerated interest in theranostic nanomedicine technologies. Their unique photophysical properties allow for sensitive in vivo imaging that can be combined with spatio-temporal control for targeted release of encapsulated drugs.Here we synthesized upconverting NaYF4:Yb,Tm nanoparticles and show for the first time their innocuity in the heart, when injected in the myocardium or in the pericardial space in mice. Nanoparticle retention and upconversion in the cardiac region did not alter heart rate variability, nor cardiac function as determined over a 15-day time course ensuing the sole injection. Altogether, our nanoparticles show innocuity primarily in the pericardial region and can be safely used for controlled spatiotemporal drug delivery.Our results support the use of upconverting nanoparticles as potential theranostics tools overcoming some of the key limitations associated with conventional experimental cardiology.

Published
2019

4. Rigidity and Substitutive Dendric Words

Author

Fabien Durand, Dominique Perrin, Francesco Dolce, Julien Leroy, Valérie Berthé, Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 (LAMFA), Université de Picardie Jules Verne (UPJV)-Centre National de la Recherche Scientifique (CNRS), Université de Liège, Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Université du Québec à Montréal (UQAM), Laboratoire d'Informatique Gaspard-Monge (ligm), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Laboratoire Amiénois de Mathématique Fondamentale et Appliquée (LAMFA), Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM)

Subjects
Left and right, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 010102 general mathematics, Substitution (logic), Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing), Rigidity (psychology), 0102 computer and information sciences, Extension (predicate logic), S-adic word, 01 natural sciences, Combinatorics, 010201 computation theory & mathematics, Rigidity, Computer Science (miscellaneous), Bipartite graph, Topological eigenvalue, Dendric word, 0101 mathematics, Substitution, Computer Science::Formal Languages and Automata Theory, Mathematics
Abstract

International audience; Received (Day Month Year) Accepted (Day Month Year) Communicated by (xxxxxxxxxx) Dendric words are infinite words that are defined in terms of extension graphs. These are bipartite graphs that describe the left and right extensions of factors. Dendric words are such that all their extension graphs are trees. They are also called tree words. This class of words includes classical families of words such as Sturmian words, codings of interval exchanges, or else, Arnoux-Rauzy words. We investigate here the properties of substitutive dendric words and prove some rigidity properties, that is, algebraic properties on the set of substitutions that fix a dendric word. We also prove that aperiodic minimal dendric subshifts (generated by dendric words) cannot have rational topological eigenvalues, and thus, cannot be generated by constant length substitutions.

Published
2018

5. Routine repeated echocardiographic monitoring of fetuses exposed to maternal anti-SSA antibodies: time to question the dogma

Author

Munther A. Khamashta, Nathalie Morel, N. Costedoat-Chalumeau, Alice Maltret, Rebecca Fischer-Betz, K. Levesque, Antonio Brucato, Centre de Recherche Épidémiologie et Statistique Sorbonne Paris Cité (CRESS (U1153 / UMR_A_1125 / UMR_S_1153)), Institut National de la Recherche Agronomique (INRA)-Université Paris Diderot - Paris 7 (UPD7)-Université Paris Descartes - Paris 5 (UPD5)-Université Sorbonne Paris Cité (USPC)-Institut National de la Santé et de la Recherche Médicale (INSERM), Referral Center for Rare Autoimmune and Systemic Diseases, Internal Medicine Department, AP-HP - Hôpital Cochin Broca Hôtel Dieu [Paris]-AP-HP - Hôpital Cochin Broca Hôtel Dieu [Paris], AP-HP - Hôpital Cochin Broca Hôtel Dieu [Paris], Policlinic of Rheumatology and Hiller Research Unit Rheumatology, Medical Faculty, Heinrich-Heine-Universität Düsseldorf [Düsseldorf]-Heinrich-Heine-Universität Düsseldorf [Düsseldorf], Heinrich Heine University Düsseldorf, Service Médecine Interne Gynéco-obstétricale, Centre Hospitalier Universitaire Sainte-Justine, Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Centre Hospitalier Universitaire Sainte Justine (CHU Sainte Justine), Service de Cardiologie, CHU Necker - Enfants Malades [AP-HP], Lupus Clinic Rheumatology Department, Dubai Hospital, Dipartimento di Scienze Biomediche e Cliniche, Università degli studi di Milano [Milano], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-AP-HP - Hôpital Cochin Broca Hôtel Dieu [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), Heinrich Heine Universität Düsseldorf = Heinrich Heine University [Düsseldorf]-Heinrich Heine Universität Düsseldorf = Heinrich Heine University [Düsseldorf], Heinrich Heine Universität Düsseldorf = Heinrich Heine University [Düsseldorf], CHU Sainte Justine [Montréal], Università degli Studi di Milano = University of Milan (UNIMI), CCSD, Accord Elsevier, Université Paris Diderot - Paris 7 (UPD7)-Université Sorbonne Paris Cité (USPC)-Université Paris Descartes - Paris 5 (UPD5)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut National de la Recherche Agronomique (INRA), and Università degli Studi di Milano [Milano] (UNIMI)

Subjects
Pediatrics, medicine.medical_specialty, Immunology, Ro/ssa Antibodies, Context (language use), 030204 cardiovascular system & hematology, 03 medical and health sciences, 0302 clinical medicine, Every other week, Rheumatology, medicine, Congenital Heart-block, Immunology and Allergy, Cardiac Manifestations, 030203 arthritis & rheumatology, Fetus, Pregnancy, Fluorinated Steroids, [SDV.MHEP] Life Sciences [q-bio]/Human health and pathology, biology, business.industry, medicine.disease, Neonatal Lupus, 3. Good health, Risk-factors, biology.protein, Gestation, Staff time, Complete Atrioventricular-block, Systemic-lupus-erythematosus, Intravenous Immunoglobulin, Antibody, Research Registry, business, [SDV.MHEP]Life Sciences [q-bio]/Human health and pathology, Anti-SSA/Ro autoantibodies
Abstract

Summary In around 1% of exposed pregnancies, anti-Ro/SSA and anti-La/SSB antibodies lead to congenital heart block, the main feature of neonatal lupus syndrome. As such, echocardiographic screening to detect congenital heart block, done every other week from 16 weeks to at least 24 weeks gestation, is widely recommended for anti-SSA-positive pregnant women. Such screening is now routinely done in many centres worldwide. In this Viewpoint, we call this dogma into question for several reasons. Even if congenital heart block is discovered (which is rare), the usefulness of treatment with fluorinated steroids has not been shown, whereas the associated side-effects are well known. The discovery of congenital heart block very early in the pregnancy does not modify obstetric management, and at least 500 ultrasounds are needed to find one case of congenital heart block, which would ultimately be found by other means. Finally, this screening strategy misses most cases of congenital heart block because most affected women are not known to have anti-SSA antibodies, and thus are not screened. Accordingly, except in the context of research protocols, which are certainly needed and are outside the scope of this Viewpoint, overturning the dogma of routine repeated screenings for congenital heart block could save money and health-care staff time and prevent maternal stress without substantial clinical consequences.

Published
2019

6. Braid moves in commutation classes of the symmetric group

Author

Nathan Williams, Anne Schilling, Nicolas M. Thiry, Graham White, Graphes, Algorithmes et Combinatoire (LRI) (GALaC - LRI), Laboratoire de Recherche en Informatique (LRI), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Davis], University of California [Davis] (UC Davis), University of California-University of California, Department of Mathematics [Stanford], Stanford University, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)

Subjects
Mathematics::Combinatorics, 05E45 (Primary), 20F55, 13F60 (Secondary), Group (mathematics), 010102 general mathematics, Braid group, 0102 computer and information sciences, Braid theory, 01 natural sciences, Combinatorics, 010201 computation theory & mathematics, Symmetric group, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Physical Sciences and Mathematics, FOS: Mathematics, Braid, Bijection, Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, Combinatorics (math.CO), math.CO, 0101 mathematics, Abelian group, Word (group theory), Mathematics
Abstract

We prove that the expected number of braid moves in the commutation class of the reduced word $(s_1 s_2 \cdots s_{n-1})(s_1 s_2 \cdots s_{n-2}) \cdots (s_1 s_2)(s_1)$ for the long element in the symmetric group $\mathfrak{S}_n$ is one. This is a variant of a similar result by V. Reiner, who proved that the expected number of braid moves in a random reduced word for the long element is one. The proof is bijective and uses X. Viennot's theory of heaps and variants of the promotion operator. In addition, we provide a refinement of this result on orbits under the action of even and odd promotion operators. This gives an example of a homomesy for a nonabelian (dihedral) group that is not induced by an abelian subgroup. Our techniques extend to more general posets and to other statistics., Comment: 24 pages; 5 figures; v3: version to appear in European J. Combinatorics

Published
2017

7. Can generic knee joint models improve the measurement of osteoarthritic knee kinematics during squatting activity?

Author

Nicola Hagemeister, Jacques A. de Guise, Julien Clément, Raphaël Dumas, Département de génie de la production automatisée, Ecole de Technologie Supérieure [Montréal] (ETS), Laboratoire de Biomécanique et Mécanique des Chocs (LBMC UMR T9406), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR), Laboratoire de recherche en imagerie et orthopédie, Centre de Recherche du Centre Hospitalier de l’Université de Montréal (CR CHUM), Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre Hospitalier de l'Université de Montréal (CHUM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)

Subjects
Male, musculoskeletal diseases, Knee Joint, MULTI-BODY, Computer science, Posture, 0206 medical engineering, Biomedical Engineering, Hinge, Bioengineering, Knee kinematics, 02 engineering and technology, Kinematics, KNEE OSTEOARTHRITIS, Models, Biological, VALIDATION, Body Mass Index, Stereoradiography, BIOMECANIQUE, 03 medical and health sciences, 0302 clinical medicine, Osteoarthritis, Image Processing, Computer-Assisted, Humans, Osteoarthritic knee, Range of Motion, Articular, Joint (geology), Aged, Orthodontics, OPTIMISATION, Reproducibility of Results, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], General Medicine, Anatomy, Middle Aged, musculoskeletal system, 020601 biomedical engineering, Biomechanical Phenomena, Computer Science Applications, Human-Computer Interaction, SOFT TISSUE ARTEFACT, STEREORADIOGRAPHY, Squatting position, Female, human activities, 030217 neurology & neurosurgery
Abstract

Knee joint kinematics derived from multi-body optimisation (MBO) still requires evaluation. The objective of this study was to corroborate model-derived kinematics of osteoarthritic knees obtained using four generic knee joint models used in musculoskeletal modelling – spherical, hinge, degree-of-freedom coupling curves and parallel mechanism – against reference knee kinematics measured by stereo-radiography. Root mean square errors ranged from 0.7° to 23.4° for knee rotations and from 0.6 to 9.0 mm for knee displacements. Model-derived knee kinematics computed from generic knee joint models was inaccurate. Future developments and experiments should improve the reliability of osteoarthritic knee models in MBO and musculoskeletal modelling.

Published
2016

8. Apport d’un phénotypage multidimensionnel dans la stratification du syndrome métabolique

Author

Pujos-Guillot, Estelle, Monnerie, Stéphanie, Thévenot, E., Junot, Christophe, Morais, José A, Payette, Héléne, Gaudreau, Pierrette, Comte, Blandine, Unité de Nutrition Humaine (UNH), Institut National de la Recherche Agronomique (INRA)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020]), MetaboHUB, Laboratoire d'analyse des données et d'intelligence des systèmes (LADIS), Département Métrologie Instrumentation & Information (DM2I), Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Laboratoire d'Etude du Métabolisme des Médicaments (LEMM), Service de Pharmacologie et Immunoanalyse (SPI), Médicaments et Technologies pour la Santé (MTS), Université Paris-Saclay-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Université Paris-Saclay-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Médicaments et Technologies pour la Santé (MTS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Département de Gériatrie, Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier), Centre de recherche sur le vieillissement, Université de Sherbrooke (UdeS), Département de médecine, Centre de Recherche du Centre Hospitalier de l’Université de Montréal (CR CHUM), Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Université Montréal, Unité de Nutrition Humaine - Clermont Auvergne (UNH), Institut National de la Recherche Agronomique (INRA)-Université Clermont Auvergne (UCA), Laboratoire d'Intégration des Systèmes et des Technologies (LIST), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Laboratoire d'Intégration des Systèmes et des Technologies (LIST), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Médicaments et Technologies pour la Santé (MTS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Université de Sherbrooke, Centre de Recherche du Centre hospitalier de l' Université de Montréal, Unité de Nutrition Humaine - Clermont Auvergne ( UNH ), Université Clermont Auvergne ( UCA ) -Institut national de la recherche agronomique [Auvergne/Rhône-Alpes] ( INRA Auvergne/Rhône-Alpes ), LIST/LADIS, Laboratoire d'Intégration de Systèmes et des technologies, Commissariat à l'Energie Atomique et aux Energies Alternatives, Laboratoire d'Etude du Métabolisme des Médicaments ( LEMM ), Service de Pharmacologie et Immunoanalyse ( SPI ), Département Médicaments et Technologies pour la Santé ( DMTS ), Direction de Recherche Fondamentale (CEA) ( DRF (CEA) ), Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay-Direction de Recherche Fondamentale (CEA) ( DRF (CEA) ), Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay-Département Médicaments et Technologies pour la Santé ( DMTS ), Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay, Centre Hospitalier Régional Universitaire [Montpellier] ( CHRU Montpellier ), Université Paris-Saclay-Direction de Recherche Technologique (CEA) (DRT (CEA)), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Laboratoire d'Intégration des Systèmes et des Technologies (LIST)

Subjects
[CHIM.ANAL]Chemical Sciences/Analytical chemistry, [ SDV.AEN ] Life Sciences [q-bio]/Food and Nutrition, [ SDV.SPEE ] Life Sciences [q-bio]/Santé publique et épidémiologie, [ CHIM.ANAL ] Chemical Sciences/Analytical chemistry, [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie, [SDV.AEN]Life Sciences [q-bio]/Food and Nutrition
Abstract

BIEN VIEILLIR AU 21ème SIÈCLE SYMPOSIUM SCIENTIFIQUE 109 - SYNDROME MÉTABOLIQUE ET VIEILLISEMENT BIEN VIEILLIR AU 21ème SIÈCLE SYMPOSIUM SCIENTIFIQUE 109 - SYNDROME MÉTABOLIQUE ET VIEILLISEMENTBIEN VIEILLIR AU 21ème SIÈCLE SYMPOSIUM SCIENTIFIQUE 109 - SYNDROME MÉTABOLIQUE ET VIEILLISEMENT; Introduction: Dans le contexte du développement d’une médecine/nutrition de précision, de nouveaux outils sont nécessaires afin d’approfondir nos connaissances sur l’étiologie du SMet et de personnaliser les stratégies de prévention ou de traitement.Méthodologie: Une étude cas/témoin nichée au sein de l’étude longitudinale québécoise NuAge a été réalisée sur 61 cas et 62 témoins d’âge similaire (68-82 ans), sélectionnés parmi 853 hommes. Des échantillons de sérum, collectés au recrutement (2003-2005) et trois ans plus tard, ont été analysés par dix méthodes métabolomiques/lipidomiques complémentaires de l’infrastructure française metaboHUB. L’ensemble des données ont été traitées grâce à des workflows Galaxy garantissant leur reproductibilité.Résultats: Des signatures spécifiques du SMet et de ses composantes ont été identifiées et leur stabilité évaluée au cours du temps. Ces données permettront une reclassification moléculaire du syndrome. De plus, les données phénotypiques et nutritionnelles des sujets ont été intégrées aux données «omiques» afin de mieux comprendre et caractériser les sous-phénotypes mis en évidence.Conclusion: Cette approche ouvre la porte à une meilleure compréhension des phénotypes métaboliques, résultant des relations complexes entre facteurs intrinsèques et extrinsèques, et au développement de nouveaux outils prédictifs ou diagnostics permettant un meilleur vieillissement.

Published
2018

9. Two Plane-Probing Algorithms for the Computation of the Normal Vector to a Digital Plane

Author

Xavier Provençal, Tristan Roussillon, Jacques-Olivier Lachaud, Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Geometry Processing and Constrained Optimization (M2DisCo), Laboratoire d'InfoRmatique en Image et Systèmes d'information (LIRIS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École Centrale de Lyon (ECL), Université de Lyon-Université Lumière - Lyon 2 (UL2)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Université Lumière - Lyon 2 (UL2), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL)

Subjects
Statistics and Probability, Applied Mathematics, Computation, Regular polygon, Discrete geometry, 0102 computer and information sciences, 02 engineering and technology, Condensed Matter Physics, 01 natural sciences, Combinatorics, 010201 computation theory & mathematics, Modeling and Simulation, 0202 electrical engineering, electronic engineering, information engineering, Digital geometry, 020201 artificial intelligence & image processing, [INFO]Computer Science [cs], Geometry and Topology, Computer Vision and Pattern Recognition, Lattice reduction, Algorithm, Normal, Time complexity, Saddle, Mathematics
Abstract

Digital planes are sets of integer points located between two parallel planes. We present a new algorithm that computes the normal vector of a digital plane given only a predicate “is a point x in the digital plane or not”. In opposition to classical recognition algorithm, this algorithm decides on-the-fly which points to test in order to output at the end the exact surface characteristics of the plane. We present two variants: the H-algorithm, which is purely local, and the R-algorithm which probes further along rays coming out from the local neighborhood tested by the H-algorithm. Both algorithms are shown to output the correct normal to the digital planes if the starting point is a lower leaning point. The worst-case time complexity is in $$O(\omega )$$ for the H-algorithm and $$O(\omega \log \omega )$$ for the R-algorithm, where $$\omega $$ is the arithmetic thickness of the digital plane. In practice, the H-algorithm often outputs a reduced basis of the digital plane while the R-algorithm always returns a reduced basis. Both variants perform much better than the theoretical bound, with an average behavior close to $$O(\log \omega )$$ . Finally, we show how this algorithm can be used to analyze the geometry of arbitrary digital surfaces, by computing normals and identifying convex, concave or saddle parts of the surface. This paper is an extension of Lachaud et al. (Proceedings of 19th IAPR international conference discrete geometry for computer imagery (DGCI’2016), Nantes, France. Springer, Cham, 2016).

Published
2017

10. Return words of linear involutions and fundamental groups

Author

Valérie Berthé, Francesco Dolce, Dominique Perrin, Giuseppina Rindone, Vincent Delecroix, Christophe Reutenauer, Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), ESIEE Paris, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université Sciences et Technologies - Bordeaux 1-Université Bordeaux Segalen - Bordeaux 2, Laboratoire d'Informatique Gaspard-Monge (ligm), and Université du Québec à Montréal (UQAM)

Subjects
Pure mathematics, General Mathematics, Geometric representation, Dynamical Systems (math.DS), 0102 computer and information sciences, 68R15, 01 natural sciences, Set (abstract data type), symbols.namesake, FOS: Mathematics, Mathematics - Combinatorics, [INFO]Computer Science [cs], 0101 mathematics, Mathematics - Dynamical Systems, [MATH]Mathematics [math], Mathematics, Basis (linear algebra), Applied Mathematics, 010102 general mathematics, Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing), Index (publishing), 010201 computation theory & mathematics, Poincaré conjecture, Free group, symbols, Combinatorics (math.CO), Alphabet, Word (group theory), Computer Science::Formal Languages and Automata Theory
Abstract

We investigate the shifts associated with natural codings of linear involutions. We deduce, from the geometric representation of linear involutions as Poincaré maps of measured foliations, a suitable definition of return words which yields that the set of return words to a given word is a symmetric basis of the free group on the underlying alphabet,$A$. The set of return words with respect to a subgroup of finite index$G$of the free group on$A$is also proved to be a symmetric basis of$G$.

Published
2017

11. The enumeration of generalized Tamari intervals

Author

Wenjie Fang, Louis-François Préville-Ratelle, Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université Sciences et Technologies - Bordeaux 1-Université Bordeaux Segalen - Bordeaux 2, Université du Québec à Montréal (UQAM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)

Subjects
Path (topology), Discrete mathematics, Mathematics::Combinatorics, 010102 general mathematics, Lattice (group), 0102 computer and information sciences, 01 natural sciences, Combinatorics, 010201 computation theory & mathematics, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Bijection, Enumeration, Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, Combinatorics (math.CO), 0101 mathematics, Tamari lattice, Mathematics
Abstract

Let $v$ be a grid path made of north and east steps. The lattice $\rm{T{\scriptsize AM}}(v)$, based on all grid paths weakly above $v$ and sharing the same endpoints as $v$, was introduced by Pr\'eville-Ratelle and Viennot (2014) and corresponds to the usual Tamari lattice in the case $v=(NE)^n$. Our main contribution is that the enumeration of intervals in $\rm{T{\scriptsize AM}}(v)$, over all $v$ of length $n$, is given by $\frac{2 (3n+3)!}{(n+2)! (2n+3)!}$. This formula was first obtained by Tutte(1963) for the enumeration of non-separable planar maps. Moreover, we give an explicit bijection from these intervals in $\rm{T{\scriptsize AM}}(v)$ to non-separable planar maps., Comment: 19 pages, 11 figures. Title changed, originally titled "From generalized Tamari intervals to non-separable planar maps (extended abstract)", submitted

Published
2017

12. The Fourier expansion of $\eta(z)\eta(2z)\eta(3z)/\eta(6z)$

Author

Kassel, Christian, Reutenauer, Christophe, Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)

Subjects
Mathematics - Number Theory, High Energy Physics::Experiment, 11F11, 11F20, 14C05, 14G15, 14N10, Nuclear Experiment, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Abstract

We compute the Fourier coefficients of the weight one modular form $\eta(z)\eta(2z)\eta(3z)/\eta(6z)$ in terms of the number of representations of an integer as a sum of two squares. We deduce a relation between this modular form and translates of the modular form $\eta(z)^4/\eta(2z)^2$. In the last section we use our main result to give an elementary proof of an identity by Victor Kac., Comment: 10 pages. Version 2: Section 4 was added

Published
2017

13. Recent results on syntactic groups of prefix codes

Author

Clelia De Felice, Jean Berstel, Giuseppina Rindone, Dominique Perrin, Christophe Reutenauer, Perrin, Dominique, Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Dipartimento Informatica ed Applicazioni 'Renato M. Capocelli' (DIA), Università degli Studi di Salerno (UNISA), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Università degli Studi di Salerno = University of Salerno (UNISA), Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM)

Subjects
Prefix code, Discrete mathematics, Class (set theory), Group (mathematics), 010102 general mathematics, Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing), 0102 computer and information sciences, Permutation group, 16. Peace & justice, 01 natural sciences, Transformation (music), Theoretical Computer Science, Prefix, TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, Computational Theory and Mathematics, [INFO.INFO-FL]Computer Science [cs]/Formal Languages and Automata Theory [cs.FL], 010201 computation theory & mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, 0101 mathematics, Arithmetic, Computer Science::Formal Languages and Automata Theory, [INFO.INFO-FL] Computer Science [cs]/Formal Languages and Automata Theory [cs.FL], Mathematics
Abstract

International audience; We give a simplified presentation of groups in transformation monoids. We use this presentation to describe two recent results on syntactic groups of prefix codes. The first one uses Sturmian words to build finite bifix codes with a given permutation group as syntactic group. The second one describes a class of prefix codes such that all their syntactic groups are cyclic.

Published
2012

14. The Tyrosine Phosphatase STEP Is Involved in Age-Related Memory Decline

Author

Paul J. Lombroso, Christopher M. Norris, Guylaine Ferland, Manavi Chatterjee, Bruno Bontempi, Angus C. Nairn, Julien Dufort-Gervais, Jonathan Brouillette, David Castonguay, Rémi Quirion, Caroline Menard, Jay S. Schneider, Amy F.T. Arnsten, Erwan Bezard, Pierrette Gaudreau, Université de Montréal (UdeM), Department of Psychiatry [Montréal], McGill University = Université McGill [Montréal, Canada], Institut des Maladies Neurodégénératives [Bordeaux] (IMN), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Yale University School of Medicine, Hôpital du Sacré-Cœur, Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Département de médecine, Centre de Recherche du Centre Hospitalier de l’Université de Montréal (CR CHUM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre Hospitalier de l'Université de Montréal (CHUM)

Subjects
Male, 0301 basic medicine, medicine.medical_specialty, [SDV.NEU.NB]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Neurobiology, Phosphatase, Morris water navigation task, Hippocampus, Protein tyrosine phosphatase, CREB, Article, General Biochemistry, Genetics and Molecular Biology, Rats, Sprague-Dawley, Mice, 03 medical and health sciences, 0302 clinical medicine, Neurotrophic factors, Internal medicine, medicine, Animals, Humans, Memory impairment, Phosphorylation, ComputingMilieux_MISCELLANEOUS, Aged, 80 and over, Memory Disorders, biology, Cognition, Protein Tyrosine Phosphatases, Non-Receptor, Macaca mulatta, Rats, Mice, Inbred C57BL, 030104 developmental biology, Endocrinology, Case-Control Studies, biology.protein, Tyrosine, Female, General Agricultural and Biological Sciences, 030217 neurology & neurosurgery
Abstract

Cognitive disabilities that occur with age represent a growing and expensive health problem. Age-associated memory deficits are observed across many species, but the underlying molecular mechanisms remain to be fully identified. Here, we report elevations in the levels and activity of the striatal-enriched phosphatase (STEP) in the hippocampus of aged memory-impaired mice and rats, in aged rhesus monkeys, and in people diagnosed with amnestic mild cognitive impairment (aMCI). The accumulation of STEP with aging is related to dysfunction of the ubiquitin-proteasome system that normally leads to the degradation of STEP. Higher level of active STEP is linked to enhanced dephosphorylation of its substrates GluN2B and ERK1/2, CREB inactivation, and a decrease in total levels of GluN2B and brain-derived neurotrophic factor (BDNF). These molecular events are reversed in aged STEP knockout and heterozygous mice, which perform similarly to young control mice in the Morris water maze (MWM) and Y-maze tasks. In addition, administration of the STEP inhibitor TC-2153 to old rats significantly improved performance in a delayed alternation T-maze memory task. In contrast, viral-mediated STEP overexpression in the hippocampus is sufficient to induce memory impairment in the MWM and Y-maze tests, and these cognitive deficits are reversed by STEP inhibition. In old LOU/C/Jall rats, a model of healthy aging with preserved memory capacities, levels of STEP and GluN2B are stable, and phosphorylation of GluN2B and ERK1/2 is unaltered. Altogether, these data suggest that elevated levels of STEP that appear with advancing age in several species contribute to the cognitive declines associated with aging.

Published
2018

15. Lyndon Christoffel digitally convex

Author

Christophe Reutenauer, Jacques-Olivier Lachaud, Xavier Provençal, Srečko Brlek, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Arithmétique informatique (ARITH), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), NSERC (Canada) and Canada Research Chair., Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)

Subjects
Convex hull, Computer science, Discrete geometry, Lyndon words, Christoffel words, 0102 computer and information sciences, 02 engineering and technology, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], 01 natural sciences, Convexity, Factorization, Artificial Intelligence, Euclidean geometry, 0202 electrical engineering, electronic engineering, information engineering, Point (geometry), Time complexity, Discrete mathematics, Christoffel symbols, Regular polygon, Digital convexity, 010201 computation theory & mathematics, Signal Processing, 020201 artificial intelligence & image processing, Computer Vision and Pattern Recognition, Software, Word (computer architecture)
Abstract

International audience; Discrete geometry redefines notions borrowed from Euclidean geometry creating a need for new algorithmical tools. The notion of convexity does not translate trivially, and detecting if a discrete region of the plane is convex requires a deeper analysis. To the many different approaches of digital convexity, we propose the combinatorics on words point of view, unnoticed until recently in the pattern recognition community. In this paper, we provide first a fast optimal algorithm checking digital convexity of polyominoes coded by their contour word. The result is based on linear time algorithms for both computing the Lyndon factorization of the contour word and the recognition of Christoffel factors that are approximations of digital lines. By avoiding arithmetical computations the algorithm is much simpler to implement and much faster in practice. We also consider the convex hull computation and relate previous work in combinatorics on words with the classical Melkman algorithm.

Published
2009

16. Codings of rotations on two intervals are full

Author

Alexandre Blondin Massé, Sébastien Labbé, Laurent Vuillon, Srečko Brlek, Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM)

Subjects
Applied Mathematics, 010102 general mathematics, Palindrome, 0102 computer and information sciences, 01 natural sciences, Pseudorandom binary sequence, Upper and lower bounds, Combinatorics, Combinatorics on words, Number theory, Unit circle, 010201 computation theory & mathematics, Bounded function, Discrete Mathematics and Combinatorics, Partition (number theory), 0101 mathematics, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

Codings of rotations are transformations taking a point x on the unit circle and translating it by an angle α, so that a symbolic sequence is built by coding iterations of this translation on x according to a partition of the unit circle [P. Alessandri and V. Berthe, Three distance theorems and combinatorics on words, Enseig. Math. 44 (1998) 103–132]. If the partition consists of two intervals, the resulting coding is a binary sequence. In particular, it yields the famous Sturmian sequences if the size of one interval is exactly α with α irrational [J. Berstel and P. Seebold, Sturmian words, in: Lothaire, Combinatorics on Words, Cambridge University Press, 2002]. Otherwise, the coding is a Rote sequence if the length of the intervals are rationally independent of α [G. Rote, Sequences with subword complexity 2n, J. Number Theory 46 (1994) 196–213] and quasi-Sturmian in the other case [G. Didier, Codages de rotations et fractions continues, J. Number Theory 71 (1998) 275–306]. Many studies show properties of sequences constructed by codings of rotation in terms of their subword complexity [P. Alessandri and V. Berthe, Three distance theorems and combinatorics on words, Enseig. Math. 44 (1998) 103–132], continued fractions and combinatorics on words [G. Didier, Codages de rotations et fractions continues, J. Number Theory 71 (1998) 275–306] or discrepancy and substitutions [B. Adamczewski, Codages de rotations et phenomenes d'autosimilarite, J. Theor. nombres Bordeaux 14 (2002) 351–386]. Our goal is to link properties of the sequence given by coding of rotations with the palindromic structure of its subwords. The palindromic complexity | Pal ( w ) | of a finite word w is bounded by | w | + 1 , and finite Sturmian (and even episturmian) words realize the upper bound [X. Droubay, J. Justin and G. Pirillo, Episturmian words and some constructions of de Luca and Rauzy, Theoret. Comput. Sci. 255 (2001) 539–553]. The palindromic defect of a finite word w is defined in [S. Brlek, S. Hamel, M. Nivat and C. Reutenauer, On the palindromic complexity of infinite words, Int. J. Found. Comput. Sci. 15: 2 (2004) 293–306] by D ( w ) = | w | + 1 − | Pal ( w ) | . Words for which D ( w ) = 0 are called full [S. Brlek, S. Hamel, M. Nivat and C. Reutenauer, On the palindromic complexity of infinite words, Int. J. Found. Comput. Sci. 15: 2 (2004) 293–306] or rich [A. Glen, J. Justin, S. Widmer and L.Q. Zamboni, Palindromic richness, Eur. J. Comb. 30 (2009) 510–531] and an infinite word is full if all its prefixes are full. Moreover, the case of periodic words is completely characterized in [S. Brlek, S. Hamel, M. Nivat and C. Reutenauer, On the palindromic complexity of infinite words, Int. J. Found. Comput. Sci. 15: 2 (2004) 293–306]. Our main result is the following.

Published
2009

17. A description of the Zeta map on Dyck paths area sequences

Author

Pons, Viviane, Laboratoire Interdisciplinaire des Sciences du Numérique (LISN), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Graphes, Algorithmes et Combinatoire (GALaC), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Algorithmes, Apprentissage et Calcul (AAC), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Centre de recherches mathématiques (CRM), Centre National de la Recherche Scientifique (CNRS), International Research Lab (IRL CRM-CNRS), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre National de la Recherche Scientifique (CNRS), and ANR-21-CE48-0020,PAGCAP,Au delà du Permutoèdre et de l'Associaèdre : Géométrie, Combinatoire, Algèbre et Probabilité(2021)

Subjects
Mathematics::Combinatorics, Zeta map, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], Dyck paths, Computer Science::Formal Languages and Automata Theory
Abstract

We give a description of the well known Zeta map on Dyck paths which sends the dinv,area statistics to the area,bounce statistics. Our description uses Dyck paths area sequences and can be implemented easily., 12 pages

Published
2023

18. Rigidity and Substitutive Dendric Words

Author

Berthé, V., Durand, F., Berthe, Valerie, De Felice, Clelia, Delecroix, Vincent, Dolce, Francesco, leroy, julien, Perrin, Dominique, Reutenauer, Christophe, Rindone, Giuseppina, Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Dipartimento Informatica ed Applicazioni 'Renato M. Capocelli' (DIA), Università degli Studi di Salerno (UNISA), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Fonds National de la Recherche Scientifique (FNRS), Université de Liège, ESIEE Paris, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Université Le Havre Normandie (ULH), Normandie Université (NU), Physiologie intégrative, cellulaire et moléculaire (PICM), Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Groupe Sociétés, Religions, Laïcités (GSRL), École pratique des hautes études (EPHE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique Gaspard-Monge (ligm), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Université du Québec à Montréal (UQAM), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université Sciences et Technologies - Bordeaux 1-Université Bordeaux Segalen - Bordeaux 2, Università degli Studi di Salerno = University of Salerno (UNISA), and Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)

Subjects
FOS: Computer and information sciences, General Computer Science, Combinatorics on words, Discrete Mathematics (cs.DM), Bifix codes, Free groups, 010102 general mathematics, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 68R15, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], 01 natural sciences, Theoretical Computer Science, 010101 applied mathematics, 0103 physical sciences, [INFO]Computer Science [cs], 010307 mathematical physics, 0101 mathematics, [MATH]Mathematics [math], ComputingMilieux_MISCELLANEOUS, Computer Science - Discrete Mathematics
Abstract

We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract generalization of the natural codings of linear involutions. We prove several results concerning the subgroups generated by return words and by maximal bifix codes in these sets., arXiv admin note: substantial text overlap with arXiv:1405.3529

Published
2015

19. Higher-Order Pushdown Trees are Circularly Computable

Author

Fortier, Jérôme, Laboratoire d'informatique Fondamentale de Marseille - UMR 6166 (LIF), Université de la Méditerranée - Aix-Marseille 2-Université de Provence - Aix-Marseille 1-Centre National de la Recherche Scientifique (CNRS), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), David Baelde, Jade Alglave, Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), and Baelde, David

Subjects
[INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, Computer Science::Logic in Computer Science, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], [INFO]Computer Science [cs], [INFO] Computer Science [cs], Computer Science::Formal Languages and Automata Theory
Abstract

National audience; We are interested in the problem of expressiveness of the following operations in the category of sets: finite products and coproducts, initial algebras (induction) and final coalgebras (coinduction). These operations are the building blocks of a logical system that allows circularity in Gentzen-style proofs. Proofs in this system are seen as simple programs, while the cut-elimination process is viewed as a running automaton with a memory device. In this paper, we show that higher-order trees, those accepted by higher-order pushdown automata, are computable in this setting, by providing an explicit simulation of the automata by cut-elimination.

Published
2015

20. Card-Shuffling via Convolutions of Projections on Combinatorial Hopf Algebras

Author

C. Y. Amy Pang, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), James Haglund, Jiang Zeng, Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM)

Subjects
Vertex (graph theory), combinatorial Hopf algebras, Pure mathematics, General Computer Science, Distribution (number theory), [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], shuffling, Theoretical Computer Science, Operator (computer programming), dual graded graphs, FOS: Mathematics, Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, noncommutative symmetric functions, Connection (algebraic framework), Eigenvalues and eigenvectors, Mathematics, Markov chains, Shuffling, Markov chain, hyperplane walks, Probability (math.PR), Hopf algebra, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Combinatorics (math.CO), Mathematics - Probability
Abstract

Recently, Diaconis, Ram and I created Markov chains out of the coproduct-then-product operator on combinatorial Hopf algebras. These chains model the breaking and recombining of combinatorial objects. Our motivating example was the riffle-shuffling of a deck of cards, for which this Hopf algebra connection allowed explicit computation of all the eigenfunctions. The present note replaces in this construction the coproduct-then-product map with convolutions of projections to the graded subspaces, effectively allowing us to dictate the distribution of sizes of the pieces in the breaking step of the previous chains. An important example is removing one “vertex” and reattaching it, in analogy with top-to-random shuffling. This larger family of Markov chains all admit analysis by Hopf-algebraic techniques. There are simple combinatorial expressions for their stationary distributions and for their eigenvalues and multiplicities and, in some cases, the eigenfunctions are also calculable., Récemment, avec Diaconis et Ram, nous avons construit des chaines de Markov à partir de l’opérateur “coproduit-puis-produit” défini sur un algèbre de Hopf combinatoire. Ces chaines modélisent la déconstruction et la construction d’objets combinatoires. La motivation était le “mélange à l’américaine”, une méthode populaire pour mélanger un jeu de cartes, pour lequel les liens avec les algèbres de Hopf combinatoires nous a permis de calculer explicitement toutes les fonctions propres. Ici, on généralise cette construction en remplaçant l’opérateur “coproduit-puis-produit” par les convolutions de projections sur les composantes graduées de l’algèbre. Ceci nous permet de stipuler les tailles des pièces dans la décomposition des objets combinatoires. Un exemple important est la suppression et l’insertion d’un “sommet”, par analogie avec la bibliothèque de Tsetlin. On constate que toutes ces chaines peuvent être analysées par des techniques provenant de la théorie des algèbres de Hopf combinatoires. On prouve des expressions combinatoires simples pour les distributions stationnaires ainsi que pour les valeurs propres et leurs multiplicités. Dans certains cas, il est possible de calculer les fonctions propres associées.

Published
2015
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21. Bifix codes and interval exchanges

Author

Clelia De Felice, Christophe Reutenauer, Valérie Berthé, Giuseppina Rindone, Dominique Perrin, Francesco Dolce, Julien Leroy, Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Dipartimento Informatica ed Applicazioni 'Renato M. Capocelli' (DIA), Università degli Studi di Salerno = University of Salerno (UNISA), Laboratoire d'Informatique Gaspard-Monge (LIGM), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Fonds National de la Recherche Scientifique (FNRS), Université de Liège, ESIEE Paris, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Università degli Studi di Salerno (UNISA), Laboratoire d'Informatique Gaspard-Monge (ligm), Université du Québec à Montréal (UQAM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)

Subjects
Discrete mathematics, Class (set theory), Algebra and Number Theory, Combinatorics on words, Bifix codes, Interval exchange transformations, 010102 general mathematics, 0102 computer and information sciences, 01 natural sciences, Combinatorics, 010201 computation theory & mathematics, FOS: Mathematics, Mathematics - Combinatorics, Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], Interval (graph theory), [INFO]Computer Science [cs], Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Combinatorics (math.CO), 0101 mathematics, [MATH]Mathematics [math], Decoding methods, Computer Science::Formal Languages and Automata Theory, Mathematics
Abstract

We investigate the relation between bifix codes and interval exchange transformations. We prove that the class of natural codings of regular interval echange transformations is closed under maximal bifix decoding., Comment: arXiv admin note: substantial text overlap with arXiv:1305.0127, arXiv:1308.5396

Published
2015

22. The zeta function of the Hilbert scheme of $n$ points on a two-dimensional torus

Author

Kassel, Christian, Reutenauer, Christophe, Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), and Kassel, Christian

Subjects
[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA], MSC: 05A17, 14C05, 14G10, 14N10, 16S34, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA], [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Abstract

We compute the zeta function of the Hilbert scheme of $n$ points on a two-dimensional torus and show it satisfies a remarkable functional equation. To this end we establish an explicit formula for the number $C_n(q)$ of ideals of codimension $n$ of the algebra $\textbf{F}_q[x,y,x^{-1}, y^{-1}]$ of Laurent polynomials in two variables over a finite field of cardinality $q$. This number is a palindromic polynomial of degree $2n$ in $q$. Moreover, $C_n(q) = (q-1)^2 P_n(q)$, where $P_n(q)$ is another palindromic polynomial, whose integer coefficients turn out to be non-negative and which is a $q$-analogue of the sum of divisors of $n$. Each coefficient of $P_n(q)$ counts the divisors of $n$ in a certain interval. We also give arithmetical interpretations of the values of $C_n(q)$ and of $P_n(q)$ at $q = -1$ and at roots of unity of order $3$, $4$, $6$.

Published
2015

23. Star-cumulants of free unitary Brownian motion

Author

Nizar Demni, Alexandru Nica, Mathieu Guay-Paquet, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Department of Pure Mathematics [Waterloo], University of Waterloo [Waterloo], ANR-11-LABEX-0020-01, ANR, NSERC, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de combinatoire et d'informatique mathématique [Montréal] ( LaCIM ), and Université du Québec à Montréal ( UQAM )

Subjects
Free probability, Infinitesimal, media_common.quotation_subject, [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], Mathematics::Analysis of PDEs, [ MATH.MATH-CO ] Mathematics [math]/Combinatorics [math.CO], 01 natural sciences, Unitary state, Free cumulants, 010104 statistics & probability, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Mathematics - Combinatorics, [ MATH.MATH-OA ] Mathematics [math]/Operator Algebras [math.OA], 0101 mathematics, Operator Algebras (math.OA), Free unitary Brownian motion, Cumulant, Brownian motion, Mathematics, Mathematical physics, media_common, Sequence, 46L54, Applied Mathematics, 010102 general mathematics, Probability (math.PR), Mathematics - Operator Algebras, R-diagonal element, non-crossing partitions, 16. Peace & justice, Infinity, Connection (mathematics), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Nonlinear Sciences::Exactly Solvable and Integrable Systems, infinetisimal determining sequence, Combinatorics (math.CO), [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Mathematics - Probability
Abstract

We study joint free cumulants of u_t and u_t^{*}, where u_t is a free unitary Brownian motion at time t. We determine explicitly some special families of such cumulants. On the other hand, for a general joint cumulant of u_t and u_t^{*}, we "calculate the derivative" for t going to infinity, when u_t approaches a Haar unitary. In connection to the latter calculation we put into evidence an "infinitesimal determining sequence" which naturally accompanies an arbitrary R-diagonal element in a tracial *-probability space., 35 pages. This version has added details in Sections 5 and 6

Published
2015

24. Subwords and Plane Partitions

Author

Nathan Williams, Zachary Hamaker, Institute for Mathematics and its Applications [Minneapolis] (IMA), University of Minnesota [Twin Cities] (UMN), University of Minnesota System-University of Minnesota System, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), James Haglund, Jiang Zeng, Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)

Subjects
plane partition, Mathematics::Combinatorics, linear extension, General Computer Science, Plane (geometry), Plane partition, Little bump, centrally symmetric $k$-triangulation, Type (model theory), [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], Computer Science::Computational Geometry, Square (algebra), Theoretical Computer Science, insertion, Combinatorics, subword complex, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Linear extension, Bijection, Discrete Mathematics and Combinatorics, reduced word, Mathematics
Abstract

Using the powerful machinery available for reduced words of type $B$, we demonstrate a bijection between centrally symmetric $k$-triangulations of a $2(n + k)$-gon and plane partitions of height at most $k$ in a square of size $n$. This bijection can be viewed as the type $B$ analogue of a bijection for $k$-triangulations due to L. Serrano and C. Stump., En utilisant la machinerie puissante pour mots réduits de type $B$, nous démontrons une bijection entre les $k$-triangulations centralement symétriques d’un $2(n + k)$-gon et les partitions de plans de hauteur inférieure ou égale à $k$ dans un carré de taille $n$. Cette bijection peut être considérée comme l’analogue de type $B$ d’une bijection de $k$-triangulations due à L. Serrano et C. Stump.

Published
2015

25. The finite index basis property

Author

Giuseppina Rindone, Francesco Dolce, Clelia De Felice, Julien Leroy, Christophe Reutenauer, Dominique Perrin, Valérie Berthé, Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Dipartimento Informatica ed Applicazioni 'Renato M. Capocelli' (DIA), Università degli Studi di Salerno (UNISA), Laboratoire d'Informatique Gaspard-Monge (ligm), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Fonds National de la Recherche Scientifique (FNRS), Université de Liège, ESIEE Paris, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal (UQAM), Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Università degli Studi di Salerno = University of Salerno (UNISA), Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM)

Subjects
FOS: Computer and information sciences, Class (set theory), Discrete Mathematics (cs.DM), Dynamical systems theory, Interval (mathematics), Bifix codes, Combinatorics on words, Free groups, Set (abstract data type), Tree (descriptive set theory), FOS: Mathematics, Mathematics - Combinatorics, [INFO]Computer Science [cs], [MATH]Mathematics [math], Mathematics, Discrete mathematics, Algebra and Number Theory, Basis (linear algebra), 16. Peace & justice, Free group, Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], Combinatorics (math.CO), Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Word (group theory), Computer Science::Formal Languages and Automata Theory, Computer Science - Discrete Mathematics
Abstract

We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems corresponding to Sturmian words. We introduce a class of sets of factors of an infinite word with linear factor complexity containing Sturmian sets and regular interval exchange sets, namemly the class of tree sets. We prove as a main result that for a uniformly recurrent tree set $F$, a finite bifix code $X$ on the alphabet $A$ is $F$-maximal of $F$-degree $d$ if and only if it is the basis of a subgroup of index $d$ of the free group on $A$., Comment: arXiv admin note: text overlap with arXiv:1011.5369, arXiv:1305.0120

Published
2015

26. Generalized Polarization Modules (extended abstract)

Author

Héctor Blandin, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), James Haglund, Jiang Zeng, Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)

Subjects
Algebraic combinatorics, Conjecture, General Computer Science, diagonally symmetric polynomials, polarization operators, representation theory, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], Vandermonde matrix, Representation theory, Theoretical Computer Science, Combinatorics, Symmetric function, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Operator (computer programming), Algebraic Combinatorics, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, symmetric functions, Combinatorics (math.CO), Representation Theory (math.RT), Direct product, Mathematics - Representation Theory, Mathematics, Vector space
Abstract

This work enrols the research line of M. Haiman on the Operator Theorem (the old operator conjecture). This theorem states that the smallest $\mathfrak{S}_n$-module closed under taking partial derivatives and closed under the action of polarization operators that contains the Vandermonde determinant is the space of diagonal harmonics polynomials. We start generalizing the context of this theorem to the context of polynomials in $\ell$ sets of $n$ variables $x_{ij}$ with $1\le i \le \ell$ and $1 \le j \le n$. Given a $\mathfrak{S}_n$-stable family of homogeneous polynomials in the variables $x_{ij}$ the smallest vector space closed under taking partial derivatives and closed under the action of polarization operators that contains $F$ is the polarization module generated by the family $F$. These polarization modules are all representation of the direct product $\mathfrak{S}_n \times GL_\ell(\mathbb{C})$. In order to study the decomposition into irreducible submodules, we compute the graded Frobenius characteristic of these modules. For several cases of $\mathfrak{S}_n$-stable families of homogeneous polynomials in n variables, for every $n \ge 1$, we show general formulas for this graded characteristic in a global manner, independent of the value of $\ell$., Ce travail s'inscrit dans la lignée de recherche des travaux de M. Haiman sur le théorème de l'opérateur (ex-conjecture de l'opérateur). Ce théorème affirme que le plus petit $\mathfrak{S}_n$-module clos par dérivation partielle et clos par l'action des opérateurs de polarisation qui contient le déterminant de Vandermonde est l'espace des polynômes harmoniques diagonaux. On commence par généraliser le contexte du théorème de l'opérateur au contexte de polynômes à ensembles de $n$ variables $x_{ij}$ avec $1\le i \le \ell$ et $1 \le j \le n$. Étant donnée une famille $\mathfrak{S}_n$-stable $F$ des polynômes homogènes en les variables $x_{ij}$, le plus petit espace vectoriel $\mathcal{M}_F$ clos par dérivation partielle et clos par léaction des opérateurs de polarisation contenant $F$ est le module de polarisation engendré par la famille $F$. Les modules $\mathcal{M}_F$ sont tous des représentations du produit direct $\mathfrak{S}_n \times GL_\ell(\mathbb{C})$. Dans le but d'étudier la décomposition en sous-modules irréductibles on calcule la caractéristique de Frobenius graduée de ces modules. Pour plusieurs cas de familles homogènes $\mathfrak{S}_n$-stables constituées des polynômes homogènes à $n$ variables, pour tout $n \ge 1$, on démontre des formules générales pour cette caractéristique graduée de façon globale, indépendante de la valeur de $\ell$.

Published
2015

27. Random walk speed is a proper function on Teichm\'uller space

Author

Azemar, Aitor, Gadre, Vaibhav, Gouëzel, Sébastien, Haettel, Thomas, Lessa, Pablo, Uyanik, Caglar, University of Glasgow, Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut Montpelliérain Alexander Grothendieck (IMAG), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), International Research Lab (IRL CRM-CNRS), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre National de la Recherche Scientifique (CNRS), Centro de Matemática [Montevideo] (CMAT), Universidad de la República [Montevideo] (UDELAR), and University of Wisconsin-Madison

Subjects
Mathematics - Geometric Topology, [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT], 05C81, 60B20, 20F67, 30F45, 20E08, Mathematics - Group Theory, Mathematics - Probability
Abstract

Consider a closed surface $M$ with negative Euler characteristic, and an admissible probability measure on the fundamental group of $M$ with finite first moment. Corresponding to each point in the Teichm\"uller space of $M$, there is an associated random walk on the hyperbolic plane. We show that the speed of this random walk is a proper function on the Teichm\"uller space of $M$, and we relate the growth of the speed to the Teichm\"uller distance to a basepoint. One key argument is an adaptation of Gou\"ezel's pivoting techniques to actions of a fixed group on a sequence of hyperbolic metric spaces., Comment: 14 pages. Comments welcome!

Published
2022

28. Hepatitis A and B vaccine uptake and immunisation among men who have sex with men seeking PrEP: a substudy of the ANRS IPERGAY trial

Author

Paul, Le Turnier, Isabelle, Charreau, Audrey, Gabassi, Diane, Carette, Laurent, Cotte, Gilles, Pialoux, Cécile, Tremblay, Bruno, Spire, Marie-Laure, Chaix, Laurence, Meyer, Catherine, Capitant, Constance, Delaugerre, François, Raffi, Jean-Michel, Molina, N, Lorente, Centre Hospitalier Andrée Rosemon [Cayenne, Guyane Française], Institut National de la Santé et de la Recherche Médicale (INSERM), Laboratoire de Virologie [CHU Saint-Louis], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Groupe Hospitalier Saint Louis - Lariboisière - Fernand Widal [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), Université Paris Descartes - Paris 5 (UPD5), Centre de Recherche en Cancérologie de Lyon (UNICANCER/CRCL), Centre Léon Bérard [Lyon]-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), CHU Tenon [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU), Centre de Recherche du Centre Hospitalier de l’Université de Montréal (CR CHUM), Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Université de Montréal (UdeM), CRSN/Faculté de médecine Université de Montréal, Sciences Economiques et Sociales de la Santé & Traitement de l'Information Médicale (SESSTIM - U1252 INSERM - Aix Marseille Univ - UMR 259 IRD), Institut de Recherche pour le Développement (IRD)-Aix Marseille Université (AMU)-Institut National de la Santé et de la Recherche Médicale (INSERM), Observatoire régional de la santé Provence-Alpes-Côte d'Azur [Marseille] (ORS PACA), Génétique et Ecologie des Virus, Génétique des Virus et Pathogénèse des Maladies Virales, Université Paris Diderot - Paris 7 (UPD7)-Institut National de la Santé et de la Recherche Médicale (INSERM), Centre de recherche en épidémiologie et santé des populations (CESP), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Sud - Paris 11 (UP11)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital Paul Brousse-Institut National de la Santé et de la Recherche Médicale (INSERM), Service de maladies infectieuses et tropicales [Saint-Louis], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Université Paris Cité (UPCité), Génomes, biologie cellulaire et thérapeutiques (GenCellDi (U944 / UMR7212)), Collège de France (CdF (institution))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Centre d’Investigation Clinique de Nantes (CIC Nantes), Université de Nantes (UN)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre hospitalier universitaire de Nantes (CHU Nantes), Hopital Saint-Louis [AP-HP] (AP-HP), and Université Sorbonne Paris Cité (USPC)

Subjects
Infectious Diseases, [SDV]Life Sciences [q-bio], Dermatology
Abstract

Vaccination against hepatitis A virus (HAV) and hepatitis B virus (HBV) is recommended in men who have sex with men (MSM). We assessed HAV and HBV vaccine uptake in the non-immune participants and their immunisation during follow-up of the ANRS IPERGAY (Intervention Préventive de l'Exposition aux Risques avec et pour les Gays) pre-exposure prophylaxis (PrEP) trial.During the ANRS IPERGAY trial among MSM (NCT 01473472), vaccination against HAV and HBV was offered free of charge to all non-immune participants at baseline. We assessed anti-HAV IgGs and anti-hepatitis B surface (HBs) antibodies (Abs) at baseline, 1–3 months after each vaccine dose and on the last follow-up visit. Vaccination uptake and immunisation were analysed in non-immune participants with at least 6 months of follow-up after the 1st vaccine dose.A total of 427 MSM with a median age of 34.8 years were analysed. Median follow-up was 2.2 years (Q1–Q3, 1.6–2.9). Absence of anti-HAV IgG at baseline (50.4%, 215/427) was associated with younger age (p=0.0001). Among HAV non-immune participants, 96.1% (197/205) received one or more vaccine doses and 91.0% (172/189) received two vaccine doses. Among HBV non-immune participants, 97.6 % (81/83) received one or more vaccine doses and 78.4% (58/74) received three doses. On the last-visit sample, anti-HAV IgG and anti-HBs Abs were respectively detected in 94.8% (95% CI 90.0% to 97.7%) and 79.6% (95% CI 66.5% to 89.4%) of participants with complete vaccination and in 80.0% (95% CI 51.9% to 95.7%) and 40.0% (95% CI 16.3% to 67.7%) of participants with incomplete vaccination.Vaccine acceptability against HAV and HBV infections was very high in MSM starting PrEP. Immunisation was high in participants with a full vaccination scheme. Physicians must consider PrEP visits as major opportunities to propose and complete HAV and HBV vaccination in at-risk non-immune subjects.

Published
2022

29. Last-Iterate Convergence of Optimistic Gradient Method for Monotone Variational Inequalities

Author

Gorbunov, Eduard, Taylor, Adrien, Gidel, Gauthier, Montreal Institute for Learning Algorithms [Montréal] (MILA), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Statistical Machine Learning and Parsimony (SIERRA), Département d'informatique - ENS Paris (DI-ENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), This work was partially supported by a grant for research centers in the field of artificial intelligence, provided by the Analytical Center for the Government of the Russian Federation in accordance with the subsidy agreement (agreement identifier 000000D730321P5Q0002) and the agreement with the Moscow Institute of Physics and Technology dated November 1, 2021 No. 70-2021-00138. A. Taylor acknowledges support from the French 'Agence Nationale de la Recherche' as part of the 'Investissements d’avenir' program, reference ANR-19-P3IA-0001 (PRAIRIE 3IA Institute), as well as support from the European Research Council (grrant SEQUOIA 724063)., ANR-19-P3IA-0001,PRAIRIE,PaRis Artificial Intelligence Research InstitutE(2019), and European Project: 724063,ERC-2016-COG,SEQUOIA(2017)

Subjects
[INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Optimization and Control (math.OC), FOS: Mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control
Abstract

The Past Extragradient (PEG) [Popov, 1980] method, also known as the Optimistic Gradient method, has known a recent gain in interest in the optimization community with the emergence of variational inequality formulations for machine learning. Recently, in the unconstrained case, Golowich et al. [2020] proved that a $O(1/N)$ last-iterate convergence rate in terms of the squared norm of the operator can be achieved for Lipschitz and monotone operators with a Lipschitz Jacobian. In this work, by introducing a novel analysis through potential functions, we show that (i) this $O(1/N)$ last-iterate convergence can be achieved without any assumption on the Jacobian of the operator, and (ii) it can be extended to the constrained case, which was not derived before even under Lipschitzness of the Jacobian. The proof is significantly different from the one known from Golowich et al. [2020], and its discovery was computer-aided. Those results close the open question of the last iterate convergence of PEG for monotone variational inequalities., NeurIPS 2022. 21 pages, 2 figures. Changes in v2: few typos were fixed, more clarifications were added. Code: https://github.com/eduardgorbunov/potentials_and_last_iter_convergence_for_VIPs

Published
2022

30. StarPU profiling interface

Author

Aumage, Olivier, Coti, Camille, Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), STatic Optimizations, Runtime Methods (STORM), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Inria & Labri, Université de Bordeaux, and Université du Québec à Montréal

Subjects
Runtime system, [INFO.INFO-PF]Computer Science [cs]/Performance [cs.PF], performance monitoring, Task parallelism, trace collection, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC]
Abstract

This document introduces the programming interface exposed by the StarPU task-based parallel runtime system for performance monitoring tools to collect performance-related metrics on the execution of StarPU applications. It defines the entry point, the callback methods, the performance counters available. It also presents the usage of the mechanisms.

Published
2022

31. An extension of Tamari lattices

Author

Louis-François Préville-Ratelle, Xavier Gérard Viennot, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Instituto de Matemática y Física - Universidad de Talca, Universidad de Talca, Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), James Haglund, Jiang Zeng, Viennot, Xavier Gérard, Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM)

Subjects
$m$-Tamari lattice, General Computer Science, Tamari lattice, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], 01 natural sciences, Theoretical Computer Science, Combinatorics, Symmetric group, Lattice (order), [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, 0101 mathematics, Mathematics, rational Catalan combinatorics, Binary tree, Mathematics::Combinatorics, Coprime integers, 010102 general mathematics, diagonal coinvariant spaces, Square lattice, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Bijection, Combinatorics (math.CO), Partially ordered set
Abstract

For any finite path $v$ on the square lattice consisting of north and east unit steps, we construct a poset Tam$(v)$ that consists of all the paths lying weakly above $v$ with the same endpoints as $v$. For particular choices of $v$, we recover the traditional Tamari lattice and the $m$-Tamari lattice. In particular this solves the problem of extending the $m$-Tamari lattice to any pair $(a; b)$ of relatively prime numbers in the context of the so-called rational Catalan combinatorics.For that purpose we introduce the notion of canopy of a binary tree and explicit a bijection between pairs $(u; v)$ of paths in Tam$(v)$ and binary trees with canopy $v$. Let $(\overleftarrow{v})$ be the path obtained from $v$ by reading the unit steps of $v$ in reverse order and exchanging east and north steps. We show that the poset Tam$(v)$ is isomorphic to the dual of the poset Tam$(\overleftarrow{v})$ and that Tam$(v)$ is isomorphic to the set of binary trees having the canopy $v$, which is an interval of the ordinary Tamari lattice. Thus the usual Tamari lattice is partitioned into (smaller) lattices Tam$(v)$, where the $v$’s are all the paths of length $n-1$ on the square lattice.We explain possible connections between the poset Tam$(v)$ and (the combinatorics of) the generalized diagonal coinvariant spaces of the symmetric group., Pour tout chemin $v$ sur le réseau carré formé de pas Nord et Est, nous construisons un ensemble partiellement ordonné Tam $(v)$ dont les éléments sont les chemins au dessus de $v$ et ayant les mêmes extrémités. Pour certains choix de $v$ nous retrouvons le classique treillis de Tamari ainsi que son extension $m$-Tamari. En particulier nous résolvons le problème d’étendre le treillis $m$-Tamari à toute paire $(a; b)$ d’entiers premiers entre eux dans le contexte de la combinatoire rationnelle de Catalan.Pour ceci nous introduisons la notion de canopée d’un arbre binaire et explicitons une bijection entre les paires $(u; v)$ de chemins dans Tam$(v)$ et les arbres binaires ayant la canopée $v$. Soit $(\overleftarrow{v})$ le chemin obtenu en lisant les pas en ordre inverse et en échangeant les pas Est et Nord. Nous montrons que Tam$(v)$ est isomorphe au dual de Tam$(\overleftarrow{v})$ et que Tam$(v)$ est isomorphe à l’ensemble des arbres binaires ayant la canopée $v$, qui est un intervalle du treillis de Tamari ordinaire. Ainsi le traditionnel treillis de Tamari admet une partition en plus petits treillis Tam$(v)$, où les $v$ sont tous les chemins de longueur $n-1$ sur le réseau carré. Enfin nous explicitons les liens possibles entre l’ensemble ordonné Tam$(v)$ et (la combinatoire des) espaces diagonaux coinvariants généralisés du groupe symétrique.

Published
2014
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32. Hopf algebra of permutation pattern functions

Author

Yannic Vargas, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Louis J. Billera and Isabella Novik, Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM)

Subjects
Algebraic combinatorics, Mathematics::Combinatorics, General Computer Science, Partial permutation, shuffle, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], Pattern permutation, Hopf algebra, infiltration, Theoretical Computer Science, Cyclic permutation, Bialgebra, Combinatorics, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Permutation, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], representative function, Permutation pattern, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Discrete Mathematics and Combinatorics, bialgebra, Word (group theory), Mathematics
Abstract

We study permutation patterns from an algebraic combinatorics point of view. Using analogues of the classical shuffle and infiltration products for word, we define two new Hopf algebras of permutations related to the notion of permutation pattern. We show several remarkable properties of permutation patterns functions, as well their occurrence in other domains.

Published
2014

33. Codiversification of gut microbiota with humans

Author

Taichi A. Suzuki, J. Liam Fitzstevens, Victor T. Schmidt, Hagay Enav, Kelsey E. Huus, Mirabeau Mbong Ngwese, Anne Grießhammer, Anne Pfleiderer, Bayode R. Adegbite, Jeannot F. Zinsou, Meral Esen, Thirumalaisamy P. Velavan, Ayola A. Adegnika, Le Huu Song, Timothy D. Spector, Amanda L. Muehlbauer, Nina Marchi, Hyena Kang, Lisa Maier, Ran Blekhman, Laure Ségurel, GwangPyo Ko, Nicholas D. Youngblut, Peter Kremsner, Ruth E. Ley, Montreal Institute for Learning Algorithms [Montréal] (MILA), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), University of British Columbia (UBC), Institut für Tropenmedizin [Tübingen], University of Tübingen, Universitätsklinikum Tübingen - University Hospital of Tübingen, Eberhard Karls Universität Tübingen = Eberhard Karls University of Tuebingen, Vietnamese-German Center for Medical Research, Department of Twin Research and Genetic Epidemiology, King's College London, London, Computational and Molecular Population Genetics Lab (CMPG), University of Bern, Éco-Anthropologie (EA), Muséum national d'Histoire naturelle (MNHN)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Biométrie et Biologie Evolutive - UMR 5558 (LBBE), Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Oxygen, Multidisciplinary, [SDV.GEN.GPO]Life Sciences [q-bio]/Genetics/Populations and Evolution [q-bio.PE], Bacteria, Host Microbial Interactions, Humans, Metagenome, Child, Gastrointestinal Microbiome
Abstract

International audience; The gut microbiomes of human populations worldwide have many core microbial species in common. However, within a species, some strains can show remarkable population specificity. The question is whether such specificity arises from a shared evolutionary history (codiversification) between humans and their microbes. To test for codiversification of host and microbiota, we analyzed paired gut metagenomes and human genomes for 1225 individuals in Europe, Asia, and Africa, including mothers and their children. Between and within countries, a parallel evolutionary history was evident for humans and their gut microbes. Moreover, species displaying the strongest codiversification independently evolved traits characteristic of host dependency, including reduced genomes and oxygen and temperature sensitivity. These findings all point to the importance of understanding the potential role of population-specific microbial strains in microbiome-mediated disease phenotypes.

Published
2022

34. Alix is required for activity-dependent bulk endocytosis at brain synapses

Author

Marine H. Laporte, Kwang Il Chi, Laura C. Caudal, Na Zhao, Yvonne Schwarz, Marta Rolland, José Martinez-Hernandez, Magalie Martineau, Christine Chatellard, Eric Denarier, Vincent Mercier, Florent Lemaître, Béatrice Blot, Eve Moutaux, Maxime Cazorla, David Perrais, Fabien Lanté, Dieter Bruns, Sandrine Fraboulet, Fiona J. Hemming, Frank Kirchhoff, Rémy Sadoul, Perrais, David, [GIN] Grenoble Institut des Neurosciences (GIN), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Grenoble Alpes (UGA), Université de Genève = University of Geneva (UNIGE), Saarland University [Saarbrücken], Universidad de Castilla-La Mancha = University of Castilla-La Mancha (UCLM), Interdisciplinary Institute for Neuroscience [Bordeaux] (IINS), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Institut de biologie structurale (IBS - UMR 5075), Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche Interdisciplinaire de Grenoble (IRIG), Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Grenoble Alpes (UGA), Centre de Recherche du Centre Hospitalier de l’Université de Montréal (CR CHUM), Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Institut de Neurosciences de la Timone (INT), Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS), Institute for Advanced Biosciences / Institut pour l'Avancée des Biosciences (Grenoble) (IAB), Centre Hospitalier Universitaire [Grenoble] (CHU)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Etablissement français du sang - Auvergne-Rhône-Alpes (EFS)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), and ANR-17-CE16-0012,LocalEndoProbes,Contrôle Local de l'Endocytose dans les dendrites neuronales analysé par de nouvelles sondes optiques(2017)

Subjects
Neurons, General Immunology and Microbiology, [SDV]Life Sciences [q-bio], General Neuroscience, Calcium-Binding Proteins, Brain, Clathrin, Endocytosis, General Biochemistry, Genetics and Molecular Biology, [SDV] Life Sciences [q-bio], Mice, Synapses, Animals, General Agricultural and Biological Sciences
Abstract

International audience; In chemical synapses undergoing high frequency stimulation, vesicle components can be retrieved from the plasma membrane via a clathrin-independent process called activity-dependent bulk endocytosis (ADBE). Alix (ALG-2-interacting protein X/PDCD6IP) is an adaptor protein binding to ESCRT and endophilin-A proteins which is required for clathrin-independent endocytosis in fibroblasts. Alix is expressed in neurons and concentrates at synapses during epileptic seizures. Here, we used cultured neurons to show that Alix is recruited to presynapses where it interacts with and concentrates endophilin-A during conditions triggering ADBE. Using Alix knockout (ko) neurons, we showed that this recruitment, which requires interaction with the calcium-binding protein ALG-2, is necessary for ADBE. We also found that presynaptic compartments of Alix ko hippocampi display subtle morphological defects compatible with flawed synaptic activity and plasticity detected electrophysiologically. Furthermore, mice lacking Alix in the forebrain undergo less seizures during kainate-induced status epilepticus and reduced propagation of the epileptiform activity. These results thus show that impairment of ADBE due to the lack of neuronal Alix leads to abnormal synaptic recovery during physiological or pathological repeated stimulations.

Published
2022
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35. Genetic relationship between five psychiatric disorders estimated from genome-wide SNPs

Author

Laura J. Scott, Bernie Devlin, Steven A. McCarroll, James S. Sutcliffe, Stefan Herms, Yunjung Kim, Richard O. Day, Thomas F. Wienker, Frank Dudbridge, I. Nicol Ferrier, Bettina Konte, Marta Ribasés, C. Robert Cloninger, Brenda W.J.H. Penninx, Detelina Grozeva, Herbert Roeyers, Peter Holmans, Colm O'Dushlaine, Scott D. Gordon, Sarah E. Bergen, Fan Meng, Morten Mattingsdal, Hugh Gurling, Ina Giegling, Gerard van Grootheest, Ania Korszun, Markus J. Schwarz, George Kirov, Sebastian Zöllner, Kenneth S. Kendler, Nicholas G. Martin, Michael Conlon O'Donovan, Michael C. Neale, Jim van Os, Aravinda Chakravarti, Timothy W. Yu, Mikael Landén, Inez Myin-Germeys, Markus M. Nöthen, Kathryn Roeder, James B. Potash, Alan W. McLean, Louise Gallagher, Anna K. Kähler, Thomas Bettecken, Nigel Williams, Frank Bellivier, Joseph D. Buxbaum, Derek W. Morris, Susan L. Smalley, Jung-Ying Tzeng, Martin Schalling, Douglas M. Ruderfer, Caroline M. Nievergelt, T. Scott Stroup, David H. Ledbetter, Jennifer Crosbie, Anita Thapar, Barbara Franke, Jeffrey A. Lieberman, Huda Akil, Miguel Casas, Daniel H. Geschwind, Paul Cormican, Bertram Müller-Myhsok, Lyudmila Georgieva, Robert Krasucki, Martin Hautzinger, Alysa E. Doyle, Cinnamon S. Bloss, Gerard D. Schellenberg, Todd Lencz, Melvin G. McInnis, Catalina Betancur, Josep Antoni Ramos-Quiroga, Stephen Sanders, Eftichia Duketis, Don H. Linszen, Matthew W. State, Richard M. Myers, Soumya Raychaudhuri, Lizzy Rossin, Howard J. Edenberg, Michael E. Goddard, S. Hong Lee, Elisabeth B. Binder, Pablo V. Gejman, William A. Scheftner, Wolfgang Maier, Judith A. Badner, Christel M. Middeldorp, Maria Helena Pinto de Azevedo, Johannes H. Smit, Willem A. Nolen, Lieuwe de Haan, Gonneke Willemsen, Keith Matthews, Ellen M. Wijsman, Jennifer K. Lowe, Rebecca McKinney, Magdalena Gross, Dorothy E. Grice, James A. Knowles, Andrew C. Heath, Jana Strohmaier, Vishwajit L. Nimgaonkar, William Byerley, William E. Bunney, Dan E. Arking, Andrew McQuillin, William M. McMahon, Manuel Mattheisen, Hans-Christoph Steinhausen, Joseph Biederman, Guy A. Rouleau, James J. McGough, Sian Caesar, Edward M. Scolnick, Lefkos T. Middleton, Jack D. Barchas, Ian B. Hickie, Danyu Lin, Patrik K. E. Magnusson, Douglas Blackwood, Francis J. McMahon, Ingrid Agartz, Elena Maestrini, Marian L. Hamshere, Lindsey Kent, Walter J. Muir, Stephan Ripke, Lydia Krabbendam, Christine Fraser, Maria Hipolito, Louise Frisén, Eric Fombonne, Emma M. Quinn, Michael Bauer, Richard P. Ebstein, Michael Steffens, Jordan W. Smoller, Stanley J. Watson, Michael Boehnke, Philip Asherson, Agatino Battaglia, Elliot S. Gershon, Russell Schachar, Marcus Ising, Peng Zhang, Margaret A. Pericak-Vance, Joachim Hallmayer, Sean Ennis, Radhika Kandaswamy, René S. Kahn, Susanne Hoefels, Thomas W. Mühleisen, Pamela Sklar, Paul Lichtenstein, Verneri Anttila, Michael L. Cuccaro, Florian Holsboer, René Breuer, Eric M. Morrow, Vinay Puri, Naomi R. Wray, Szabocls Szelinger, Sabine M. Klauck, John B. Vincent, Shrikant Mane, Aribert Rothenberger, Marion Friedl, Ian Jones, Khalid Choudhury, Michael R. Barnes, Adebayo Anjorin, Edwin H. Cook, William Lawson, Allan H. Young, Lambertus Klei, Bryan J. Mowry, Johannes Schumacher, Michael Gill, James L. Kennedy, Marcella Rietschel, Aiden Corvin, Henrik B. Rasmussen, Susmita Datta, Kimberly Chambert, Daniel Moreno-De-Luca, Benjamin S. Pickard, Stan F. Nelson, Veronica J. Vieland, Stephen W. Scherer, Peter M. Visscher, John Strauss, Andreas Reif, Andrew D. Paterson, Ann Olincy, Phoenix Kwan, Anthony J. Bailey, Patrick F. Sullivan, Pierandrea Muglia, Gunnar Morken, Susanne Lucae, Ayman H. Fanous, Jacob Lawrence, Donald J. MacIntyre, Nancy G. Buccola, Rita M. Cantor, Christina M. Hultman, Weihua Guan, Anthony P. Monaco, Jouke-Jan Hottenga, Elaine Kenny, Jianxin Shi, Dale R. Nyholt, Kevin A. McGhee, Falk W. Lohoff, Jonna Kuntsi, Niklas Långström, John I. Nurnberger, Nelson B. Freimer, Erin N. Smith, John P. Rice, Michael T. Murtha, Thomas H. Wassink, Alexandre A. Todorov, Edmund J.S. Sonuga-Barke, Dan Rujescu, Roy H. Perlis, John S. Witte, Christopher A. Walsh, Matthew C. Keller, Pamela B. Mahon, Patrick J. McGrath, Susan L. Santangelo, Annette M. Hartmann, Ole A. Andreassen, Tatiana Foroud, Shaun Purcell, Josef Frank, Douglas F. Levinson, William Coryell, Ana Miranda, Alan F. Schatzberg, Peter Szatmari, Jun Li, Gerome Breen, Stephen V. Faraone, Anil K. Malhotra, Helena Medeiros, Martin A. Kohli, Nicholas Bass, Catherine Lord, Peter Propping, Wei Xu, Federica Tozzi, Ivan Nikolov, Jan K. Buitelaar, Thomas G. Schulze, Katherine Gordon-Smith, Michele L. Pergadia, Fritz Poustka, Valentina Moskvina, David Curtis, Tobias Banaschewski, Devin Absher, Danielle Posthuma, Stanley Zammit, Gary Donohoe, Ingrid Melle, Karola Rehnström, Thomas Hansen, Myrna M. Weissman, Stanley I. Shyn, Hakon Hakonarson, Christa Lese Martin, Digby Quested, Darina Czamara, Jeremy R. Parr, Pamela A. F. Madden, Jens Treutlein, Aarno Palotie, Robert Freedman, Sandra Meier, Bru Cormand, Nicholas J. Schork, Michele T. Pato, John R. Kelsoe, Vanessa Hus, Frans G. Zitman, Josephine Elia, David St Clair, Roel A. Ophoff, Peter McGuffin, Jonathan Pimm, Jonathan L. Haines, Wiepke Cahn, Matthew Flickinger, Steven P. Hamilton, Michael John Owen, Paul D. Shilling, Jeremy M. Silverman, David Craig, Mark J. Daly, Sarah E. Medland, Robert D. Oades, Marion Leboyer, Alan R. Sanders, Vihra Milanova, Chunyu Liu, Jobst Meyer, Dorret I. Boomsma, Evaristus A. Nwulia, Thomas B. Barrett, Jennifer L. Moran, Donald W. Black, Mònica Bayés, Witte J.G. Hoogendijk, Franziska Degenhardt, Benjamin M. Neale, Daniel L. Koller, Carlos N. Pato, Nicholas John Craddock, Richard Bruggeman, Enda M. Byrne, Edward G. Jones, Eco J. C. de Geus, Stéphane Jamain, Jubao Duan, Anne Farmer, Astrid M. Vicente, Grant W. Montgomery, Thomas Werge, Cathryn M. Lewis, Srdjan Djurovic, Phil Lee, Richard Anney, Elaine K. Green, Wade H. Berrettini, Peter P. Zandi, Susan L. Slager, Stephanie H. Witt, Ian W. Craig, Lisa Jones, Sven Cichon, Bruno Etain, Mark Lathrop, Hilary Coon, Robert C. Thompson, Lena Backlund, A. Jeremy Willsey, Andres Ingason, Christine M. Freitag, Sandra K. Loo, Guiomar Oliveira, Line Olsen, Edwin J. C. G. van den Oord, Geraldine Dawson, Joseph A. Sergeant, David A. Collier, Farooq Amin, Srinivasa Thirumalai, Manfred Uhr, Joseph Piven, Andrew M. McIntosh, Anjali K. Henders, Urban Ösby, Klaus-Peter Lesch, Tiffany A. Greenwood, Interdisciplinary Centre Psychopathology and Emotion regulation (ICPE), Perceptual and Cognitive Neuroscience (PCN), Lee, S Hong, Ripke, Stephan, Neale, Benjamin M, Faraone, Stephen V, Wray, Naomi R, Cross-Disorder Group of the Psychiatric Genomics Consortium, International Inflammatory Bowel Disease Genetics Consortium (IIBDGC), Queensland Brain Institute, University of Queensland [Brisbane], Massachusetts General Hospital [Boston], Harvard Medical School [Boston] (HMS), Broad Institute of MIT and Harvard (BROAD INSTITUTE), Harvard Medical School [Boston] (HMS)-Massachusetts Institute of Technology (MIT)-Massachusetts General Hospital [Boston], SUNY Upstate Medical University, State University of New York (SUNY), Mount Sinai School of Medicine, Department of Psychiatry-Icahn School of Medicine at Mount Sinai [New York] (MSSM), Psychiatric and Neurodevelopmental Genetics Unit, Queensland Centre for Mental Health Research, Institute of Psychological Medicine and Clinical Neurosciences, Cardiff University, MRC Centre for Neuropsychiatric Genetics and Genomics, Medical Research Council (MRC)-School of Medicine [Cardiff], Cardiff University-Institute of Medical Genetics [Cardiff]-Cardiff University-Institute of Medical Genetics [Cardiff], New South Wales Department of Primary Industries (NSW DPI), Faculty of Land and Food Resources, University of Melbourne, HudsonAlpha Institute for Biotechnology [Huntsville, AL], Institute of Clinical Medicine [Oslo], Faculty of Medicine [Oslo], University of Oslo (UiO)-University of Oslo (UiO), Diakonhjemmet Hospital, University of Michigan [Ann Arbor], University of Michigan System, Molecular and Behavioral Neuroscience Institute (MBNI), University of Michigan System-University of Michigan System, Emory University [Atlanta, GA], Oslo University Hospital [Oslo], University College of London [London] (UCL), Trinity College Dublin, Johns Hopkins University School of Medicine [Baltimore], MRC Social Genetic Developmental and Psychiatry Centre, Institute of Psychiatry, King's College London, University of Coimbra [Portugal] (UC), Karolinska Institutet [Stockholm], University of Chicago, University of British Columbia (UBC), Department of Child and Adolescent Psychiatry and Psychotherapy [Mannheim], Universität Heidelberg [Heidelberg] = Heidelberg University, Weill Medical College of Cornell University [New York], GlaxoSmithKline, Glaxo Smith Kline, Portland Veterans Administration Medical Center, Windeyer Institute for Medical Sciences, IRCCS Fondazione Stella Maris [Pisa], University Hospital Carl Gustav Carus [Dresden, Germany], Technische Universität Dresden = Dresden University of Technology (TU Dresden), Centro Nacional de Analisis Genomico [Barcelona] (CNAG), Institut National de la Santé et de la Recherche Médicale (INSERM), Université Paris Diderot - Paris 7 (UPD7), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), European Network of Bipolar Research Expert Centres (ENBREC), ENBREC, Department of Psychiatry [Philadelphia], University of Pennsylvania, Physiopathologie des Maladies du Système Nerveux Central, 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), Unité de recherche Phytopharmacie et Médiateurs Chimiques (UPMC), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Max Planck Institute of Psychiatry, Max-Planck-Gesellschaft, Massachusetts General Hospital [Boston, MA, USA], University of Iowa [Iowa City], University of Edinburgh, Royal Hospital for Sick Children [Edinburgh], The Scripps Research Institute [La Jolla, San Diego], MRC Social, Genetic and Developmental Psychiatry Centre (SGDP), King‘s College London-The Institute of Psychiatry, Institute of Medical Sciences, University of Aberdeen, Social, Genetic and Developmental Psychiatry Centre (SGDP), King‘s College London, Department of Genetic Epidemiology in Psychiatry [Mannhein], Universität Heidelberg [Heidelberg] = Heidelberg University-Central Institute of Mental Health Mannheim, Department of Psychiatry, University of Groningen [Groningen]-University Medical Center Groningen [Groningen] (UMCG), Trinity College Dublin-St. James's Hospital, School of Nursing, Louisiana State University (LSU), Donders Center for Cognitive Neuroimaging, Donders Centre for Cognitive Neuroimaging, Radboud University [Nijmegen]-Radboud University [Nijmegen], Department of Psychiatry and Human Behavior, University of California [Irvine] (UC Irvine), University of California (UC)-University of California (UC), Friedman Brain Institute, Mount Sinai, Icahn School of Medicine at Mount Sinai [New York] (MSSM), Seaver Autism Center for Research and Treatment, Department of Neuroscience, Departments of Psychiatry, Genetics and Genomic Sciences, Icahn School of Medicine at Mount Sinai [New York] (MSSM)-Seaver Autism Center-, The Mindich Child Health & Development Institute, Friedman Brain Institute, The Mindich Child Health and Development Institute, University of California [San Francisco] (UC San Francisco), Department of Psychiatry, School of Clinical and Experimental Medicine, University of Alabama at Birmingham [ Birmingham] (UAB), Department of Human Genetics, Los Angeles, David Geffen School of Medicine [Los Angeles], University of California [Los Angeles] (UCLA), University of California (UC)-University of California (UC)-University of California [Los Angeles] (UCLA), McKusick-Nathans Institute of Genetic Medicine, Johns Hopkins University School of Medicine, Stanley Center for Psychiatric Research, Harvard Medical School [Boston] (HMS)-Massachusetts Institute of Technology (MIT)-Massachusetts General Hospital [Boston]-Harvard Medical School [Boston] (HMS)-Massachusetts Institute of Technology (MIT)-Massachusetts General Hospital [Boston], Mental Health Sciences Unit, Department of Genomics, Life and Brain Center, Universität Bonn = University of Bonn, Institute of Human Genetics, Institute of Neuroscience and Medicine (INM-1), Research Center Juelich, Academic Department of Child and Adolescent Psychiatry, Institute of Psychiatry, Department of Disability and Human Development, University of Illinois [Chicago] (UIC), University of Illinois System-University of Illinois System, Department of Developmental Neuroscience, Neuropsychiatric Genetics Research Group, University of California [San Diego] (UC San Diego), John P. Hussman Institute for Human Genomics, University of Miami [Coral Gables], East London NHS Foundation Trust, Queen Mary University of London (QMUL), Max-Planck-Institut für Psychiatrie, Genetics Institute, Autism Speaks and the Department of Psychiatry, University of North Carolina [Chapel Hill] (UNC), University of North Carolina System (UNC)-University of North Carolina System (UNC), School of Neurology, Neurobiology and Psychiatry, Royal Victoria Infirmary, Medstar Research Institute, KG Jebsen Centre for Psychosis Research, University of Oslo (UiO)-Institute of Clinical Medicine-Oslo University Hospital [Oslo], Deparment of Medical Genetics, Human Genetics Branch, National Institutes of Health [Bethesda] (NIH)-National Institute of Mental Health (NIMH), Harvard Medical School [Boston] (HMS)-Massachusetts General Hospital [Boston], Department of Psychiatry and Behavioral Sciences, University of Chicago-NorthShore University Health System, Department of Non-Communicable Disease Epidemiology, London School of Hygiene and Tropical Medicine (LSHTM), Department of Child and Adolescent Psychiatry, Psychosomatics and Psychotherapy, Goethe-Universität Frankfurt am Main, Psychology Department, National University of Singapore (NUS), Department of Biochemistry and Molecular Biology, Department of Medical and Molecular Genetics, Indiana University School of Medicine, Indiana University System-Indiana University System, Academic Centre on Rare Diseases (ACoRD), University College Dublin [Dublin] (UCD), Institut Mondor de Recherche Biomédicale (IMRB), Institut National de la Santé et de la Recherche Médicale (INSERM)-IFR10-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), Service de psychiatrie, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital Henri Mondor-Hôpital Albert Chenevier, Virginia Institute of Psychiatric and Behavioral Genetics, Virginia Commonwealth University (VCU), University of Dundee School of Medicine, University of Dundee, Department of Biostatistics and Center for Statistical Genetics, University of Michigan System-University of Michigan System-School of public health, The University of Hong Kong (HKU)-The University of Hong Kong (HKU), Department of Child Psychiatry, McGill University = Université McGill [Montréal, Canada]-Montreal Children's Hospital, McGill University Health Center [Montreal] (MUHC)-McGill University Health Center [Montreal] (MUHC), Howard University College of Medicine, University of Colorado [Denver], Center for Neurobehavioral Genetics, Department of Genomics, Department of Molecular Medicine, Department of Neurology, University of California (UC)-University of California (UC)-David Geffen School of Medicine [Los Angeles], Medical Research Council-Cardiff University, Department of Psychiatry [Pittsburgh], University of Pittsburgh School of Medicine, Pennsylvania Commonwealth System of Higher Education (PCSHE)-Pennsylvania Commonwealth System of Higher Education (PCSHE), Fisico-Quimica Biologica, Universidade Federal do Rio de Janeiro (UFRJ), Vanderbilt Brain Institute, Vanderbilt University School of Medicine [Nashville], Department of Pediatrics, Perelman School of Medicine, University of Pennsylvania-University of Pennsylvania-Children’s Hospital of Philadelphia (CHOP ), The Center for Applied Genomics, Children’s Hospital of Philadelphia (CHOP ), Stanford School of Medicine [Stanford], Stanford Medicine, Stanford University-Stanford University, Institute for Human Genetics, Neurosciences Centre of Excellence in Drug Discovery, GlaxoSmithKline Research and Development, Center for Genomic Medicine, Copenhagen University Hospital-Rigshospitalet [Copenhagen], Copenhagen University Hospital, Department of Clinical and Developmental Psychology, Eberhard Karls Universität Tübingen = Eberhard Karls University of Tuebingen, Clinical Research Unit, Brain & Mind Research Institute-The University of Sydney, Functional Genomics, Neuronal Plasticity / Mouse Behaviour, Erasmus University Medical Center [Rotterdam] (Erasmus MC), Department of Medical Epidemiology and Biostatistics (MEB), Autism and Communicative Disorders Centre, Center for Human Genetic Research, Center for neuroscience-University of California [Davis] (UC Davis), Bioinformatics Research Center, North Carolina State University [Raleigh] (NC State), Norwegian University of Science and Technology [Trondheim] (NTNU), Norwegian University of Science and Technology (NTNU)-Norwegian University of Science and Technology (NTNU), Emory University [Atlanta, GA]-Atlanta Veterans Affairs Medical Center, Psychiatric Neurogenetics Section, Centre for Addiction and Mental Health, School of Medicine, University of St Andrews [Scotland], Institute of Human Genetics [Erlangen, Allemagne], Friedrich-Alexander Universität Erlangen-Nürnberg (FAU), Division of Molecular Genome Analysis, German Cancer Research Center - Deutsches Krebsforschungszentrum [Heidelberg] (DKFZ), Department of Ecology and Evolutionary Biology, Insitute of Neuroscience and Physiology, University of Gothenburg (GU), Institut de Génomique d'Evry (IG), Université Paris-Saclay-Institut de Biologie François JACOB (JACOB), Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Developmental Brain and Behaviour Unit, University of Southampton, Division of Psychiatric Genomics, Rheinische Friedrich-Wilhelms-Universität Bonn, Statistical Genetics Group, Department of Human Genetics, Department of Pharmacy and Biotechnology, Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), Department of Psychiatry and Psychotherapy, Department of Mental Health, Johns Hopkins University and Hospital, W.M. Keck Biotechnology Resource Laboratory, Yale University [New Haven], Institutes of Neuroscience and Health and Society, Newcastle University [Newcastle], Genetic Epidemiology Unit, Queensland Institute of Medical Research, Department of Biomedicine and the Centre for Integrative Sequencing, Aarhus University [Aarhus], Sorlandet Hospital HF, Division of Psychiatry, University of Edinburgh-Royal Edinburgh Hospital, Medical Genetics Section, University of Edinburgh-Western General Hospital, Unit on the Genetic Basis of Mood and Anxiety Disorders, National Institutes of Health [Bethesda] (NIH), Unidade de Neurodesenvolvimento e Autismo (UNDA), Hospital Pediatrico de Coimbra, Division of Mental Health and Addiction, Molecular Psychiatry Laboratory, University of Michigan System-University of Michigan System-Molecular and Behavioral Neuroscience Institute, Research and Development, First Psychiatric Clinic-Alexander University Hospital, Registo Oncológico Regional-Sul, Instituto Português de Oncologia de Francisco Gentil, The Wellcome Trust Centre for Human Genetics [Oxford], University of Oxford, St. Olav's Hospital, Brown University, Department of Molecular Biology, Cell Biology and Biochemistry, Translational Centre for Regenerative Medicine (TRM), Department of Cell Therapy, Universität Leipzig-Universität Leipzig, Human Genetics Department, University of Pittsburgh (PITT), Institute for Biomedical Imaging and Life Science, University Medical Center [Utrecht]-Brain Center Rudolf Magnus, Head of Medical Sequencing, Program in Genetics and Genomic Biology, Hospital for Sick Children-University of Toronto McLaughlin Centre, The Centre for Applied Genomics, Toronto, The Hospital for sick children [Toronto] (SickKids)-University of Toronto-Department of Molecular Genetics-McLaughlin Centre, Carolina Institute for Developmental Disabilities, Analytic and Translational Genetics Unit, Rush University Medical Center [Chicago], Julius-Maximilians-Universität Würzburg (JMU), Washington University in Saint Louis (WUSTL), Department of Statistics, Carnegie Mellon University [Pittsburgh] (CMU), Department of Experimental Clinical and Health Psychology, Universiteit Gent = Ghent University (UGENT), Department of Child and Adolescent Psychiatry, Georg-August-University = Georg-August-Universität Göttingen, Department of Medicine, Centre de Recherche du Centre Hospitalier de l’Université de Montréal (CR CHUM), Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Departments of Psychiatry and Genetics, Yale School of Medicine [New Haven, Connecticut] (YSM), Maine Medical Center, Free University of Amsterdam, Department of Psychiatry and Behavioral Sciences [Stanford], Pathology and Laboratory Medicine, The Scripps Translational Science Institute and The Scripps Research Institute, Psychiatric Center Nordbaden, Division of Cancer Epidemiology and Genetics, National Cancer Institute [Bethesda] (NCI-NIH), National Institutes of Health [Bethesda] (NIH)-National Institutes of Health [Bethesda] (NIH), The Scripps Translational Science Institute and Scripps Health, Child and Adolescent Psychiatry, Aarhus University Hospital, Molecular Neuropsychiatry and Development Laboratory, Department of Molecular Physiology & Biophysics and Psychiatry, Vanderbilt University [Nashville]-Centers for Human Genetics Research and Molecular Neuroscience, Department of Psychiatry and Behavioural Neurosciences, McMaster University [Hamilton, Ontario]-Offord Centre for Child Studies, The Translational Genomics Research Institute (TGen), Oxford Health NHS Foundation Trust, Marlborough House Secure Unit, Instituto Nacional de Saùde Dr Ricardo Jorge [Portugal] (INSA), BioFIG, Center for Biodiversity, Functional and Integrative Genomics, Battelle Center for Mathematical Medicine, Ohio State University [Columbus] (OSU)-Nationwide Children's Hospital, University of Toronto, Diamantina Institute, Carver College of Medicine [Iowa City], University of Iowa [Iowa City]-University of Iowa [Iowa City], Departments of Biostatistics and Medicine, University of Washington [Seattle], ArcelorMittal Maizières Research SA, ArcelorMittal, Institute of Mental Health, Johns Hopkins Bloomberg School of Public Health [Baltimore], Johns Hopkins University (JHU)-Johns Hopkins University (JHU), Psychiatrie & Neuropsychologie, Farmacologie en Toxicologie, RS: CARIM School for Cardiovascular Diseases, RS: MHeNs School for Mental Health and Neuroscience, Biological Psychology, Educational Neuroscience, Clinical Neuropsychology, Neuroscience Campus Amsterdam - Brain Mechanisms in Health & Disease, LEARN! - Social cognition and learning, Biophotonics and Medical Imaging, Neuroscience Campus Amsterdam - Neurobiology of Mental Health, LEARN! - Brain, learning and development, EMGO+ - Mental Health, LEARN!, Neuroscience Campus Amsterdam - Brain Imaging Technology, LaserLaB - Biophotonics and Microscopy, State University of New York (SUNY)-State University of New York (SUNY), Department of Neuroscience and Physiology, Faculty of Land and Environment, Biosciences Research Division, Department of Environment and Primary Industries Victoria, Department of Epidemiology and Biostatistics, University of California [San Francisco] (UCSF), University of California-University of California, Universität Heidelberg [Heidelberg], Cornell University [New York]-Weill Medical College of Cornell University [New York], Bioinformatics, Internal Medicine, Portland Va Medical Center : Ganzini Linda MD, Technische Universität Dresden = Dresden University of Technology (TU Dresden)-University Hospital Carl Gustav Carus, Centro Nacional de Análisis Genómico (CNAG), Parc Científic de Barcelona (PCB), University of Pennsylvania [Philadelphia], 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), Clinical and Research Programs in Pediatric Psychopharmacology and Adult ADHD, Division Genetic Epidemiology in Psychiatry, Central Institute of Mental Health [Mannheim], Medical Faculty [Mannheim]-Medical Faculty [Mannheim], Universität Heidelberg [Heidelberg]-Central Institute of Mental Health Mannheim, Radboud university [Nijmegen]-Radboud university [Nijmegen], University of California [Irvine] (UCI), University of California-University of California-University of California [Los Angeles] (UCLA), University of Bonn, University of California-University of California-David Geffen School of Medicine [Los Angeles], Cardiff University-Medical Research Council, University of Pennsylvania [Philadelphia]-University of Pennsylvania [Philadelphia]-Children’s Hospital of Philadelphia (CHOP ), Bureau d'Économie Théorique et Appliquée (BETA), Institut National de la Recherche Agronomique (INRA)-Université de Strasbourg (UNISTRA)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut de Biologie François JACOB (JACOB), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, University of Oxford [Oxford], Universität Leipzig [Leipzig]-Universität Leipzig [Leipzig], University of Toronto-The Hospital for sick children [Toronto] (SickKids)-Department of Molecular Genetics-McLaughlin Centre, Julius-Maximilians-Universität Würzburg [Wurtzbourg, Allemagne] (JMU), Universiteit Gent = Ghent University [Belgium] (UGENT), University of Göttingen - Georg-August-Universität Göttingen, Yale University School of Medicine, Georg-August-University [Göttingen], ANS - Amsterdam Neuroscience, Adult Psychiatry, Child Psychiatry, Psychiatry, Human genetics, NCA - Brain mechanisms in health and disease, NCA - Neurobiology of mental health, EMGO - Mental health, NCA - Brain imaging technology, Lee SH, Ripke S, Neale BM, Faraone SV, Purcell SM, Perlis RH, Mowry BJ, Thapar A, Goddard ME, Witte JS, Absher D, Agartz I, Akil H, Amin F, Andreassen OA, Anjorin A, Anney R, Anttila V, Arking DE, Asherson P, Azevedo MH, Backlund L, Badner JA, Bailey AJ, Banaschewski T, Barchas JD, Barnes MR, Barrett TB, Bass N, Battaglia A, Bauer M, Bayés M, Bellivier F, Bergen SE, Berrettini W, Betancur C, Bettecken T, Biederman J, Binder EB, Black DW, Blackwood DH, Bloss CS, Boehnke M, Boomsma DI, Breen G, Breuer R, Bruggeman R, Cormican P, Buccola NG, Buitelaar JK, Bunney WE, Buxbaum JD, Byerley WF, Byrne EM, Caesar S, Cahn W, Cantor RM, Casas M, Chakravarti A, Chambert K, Choudhury K, Cichon S, Cloninger CR, Collier DA, Cook EH, Coon H, Cormand B, Corvin A, Coryell WH, Craig DW, Craig IW, Crosbie J, Cuccaro ML, Curtis D, Czamara D, Datta S, Dawson G, Day R, De Geus EJ, Degenhardt F, Djurovic S, Donohoe GJ, Doyle AE, Duan J, Dudbridge F, Duketis E, Ebstein RP, Edenberg HJ, Elia J, Ennis S, Etain B, Fanous A, Farmer AE, Ferrier IN, Flickinger M, Fombonne E, Foroud T, Frank J, Franke B, Fraser C, Freedman R, Freimer NB, Freitag CM, Friedl M, Frisén L, Gallagher L, Gejman PV, Georgieva L, Gershon ES, Geschwind DH, Giegling I, Gill M, Gordon SD, Gordon-Smith K, Green EK, Greenwood TA, Grice DE, Gross M, Grozeva D, Guan W, Gurling H, De Haan L, Haines JL, Hakonarson H, Hallmayer J, Hamilton SP, Hamshere ML, Hansen TF, Hartmann AM, Hautzinger M, Heath AC, Henders AK, Herms S, Hickie IB, Hipolito M, Hoefels S, Holmans PA, Holsboer F, Hoogendijk WJ, Hottenga JJ, Hultman CM, Hus V, Ingason A, Ising M, Jamain S, Jones EG, Jones I, Jones L, Tzeng JY, Kähler AK, Kahn RS, Kandaswamy R, Keller MC, Kennedy JL, Kenny E, Kent L, Kim Y, Kirov GK, Klauck SM, Klei L, Knowles JA, Kohli MA, Koller DL, Konte B, Korszun A, Krabbendam L, Krasucki R, Kuntsi J, Kwan P, Landén M, Långström N, Lathrop M, Lawrence J, Lawson WB, Leboyer M, Ledbetter DH, Lee PH, Lencz T, Lesch KP, Levinson DF, Lewis CM, Li J, Lichtenstein P, Lieberman JA, Lin DY, Linszen DH, Liu C, Lohoff FW, Loo SK, Lord C, Lowe JK, Lucae S, MacIntyre DJ, Madden PA, Maestrini E, Magnusson PK, Mahon PB, Maier W, Malhotra AK, Mane SM, Martin CL, Martin NG, Mattheisen M, Matthews K, Mattingsdal M, McCarroll SA, McGhee KA, McGough JJ, McGrath PJ, McGuffin P, McInnis MG, McIntosh A, McKinney R, McLean AW, McMahon FJ, McMahon WM, McQuillin A, Medeiros H, Medland SE, Meier S, Melle I, Meng F, Meyer J, Middeldorp CM, Middleton L, Milanova V, Miranda A, Monaco AP, Montgomery GW, Moran JL, Moreno-De-Luca D, Morken G, Morris DW, Morrow EM, Moskvina V, Muglia P, Mühleisen TW, Muir WJ, Müller-Myhsok B, Murtha M, Myers RM, Myin-Germeys I, Neale MC, Nelson SF, Nievergelt CM, Nikolov I, Nimgaonkar V, Nolen WA, Nöthen MM, Nurnberger JI, Nwulia EA, Nyholt DR, O'Dushlaine C, Oades RD, Olincy A, Oliveira G, Olsen L, Ophoff RA, Osby U, Owen MJ, Palotie A, Parr JR, Paterson AD, Pato CN, Pato MT, Penninx BW, Pergadia ML, Pericak-Vance MA, Pickard BS, Pimm J, Piven J, Posthuma D, Potash JB, Poustka F, Propping P, Puri V, Quested DJ, Quinn EM, Ramos-Quiroga JA, Rasmussen HB, Raychaudhuri S, Rehnström K, Reif A, Ribasés M, Rice JP, Rietschel M, Roeder K, Roeyers H, Rossin L, Rothenberger A, Rouleau G, Ruderfer D, Rujescu D, Sanders AR, Sanders SJ, Santangelo SL, Sergeant JA, Schachar R, Schalling M, Schatzberg AF, Scheftner WA, Schellenberg GD, Scherer SW, Schork NJ, Schulze TG, Schumacher J, Schwarz M, Scolnick E, Scott LJ, Shi J, Shilling PD, Shyn SI, Silverman JM, Slager SL, Smalley SL, Smit JH, Smith EN, Sonuga-Barke EJ, St Clair D, State M, Steffens M, Steinhausen HC, Strauss JS, Strohmaier J, Stroup TS, Sutcliffe JS, Szatmari P, Szelinger S, Thirumalai S, Thompson RC, Todorov AA, Tozzi F, Treutlein J, Uhr M, van den Oord EJ, Van Grootheest G, Van Os J, Vicente AM, Vieland VJ, Vincent JB, Visscher PM, Walsh CA, Wassink TH, Watson SJ, Weissman MM, Werge T, Wienker TF, Wijsman EM, Willemsen G, Williams N, Willsey AJ, Witt SH, Xu W, Young AH, Yu TW, Zammit S, Zandi PP, Zhang P, Zitman FG, Zöllner S, Devlin B, Kelsoe JR, Sklar P, Daly MJ, O'Donovan MC, Craddock N, Sullivan PF, Smoller JW, Kendler KS, Wray NR, Cardiff University-Medical Research Council (MRC), HudsonAlpha Institute for Biotechnology, The Institute of Psychiatry-King‘s College London, Cornell University-Weill Medical College of Cornell University [New York], Stanford University Medical School, Technische Universität Dresden (TUD)-University Hospital Carl Gustav Carus, Assistance publique - Hôpitaux de Paris (AP-HP) (APHP)-Hôpital Henri Mondor-Hôpital Albert Chenevier, McGill University-Montreal Children's Hospital, Universidade Federal do Rio de Janeiro [Rio de Janeiro] (UFRJ), Stanford University School of Medicine [Stanford], Stanford University [Stanford], Eberhard Karls Universität Tübingen, Friedrich Alexander University [Erlangen-Nürnberg], Università di Bologna [Bologna] (UNIBO), University of Toronto-The Hospital for Sick Children-Department of Molecular Genetics-McLaughlin Centre, Washington University School of Medicine, Ghent University [Belgium] (UGENT), University of Goettingen, CHUM Research Center, Psychiatry and Behavioral Science, Stanford University School of Medicine [CA, USA], Aalborg Psychiatric Hospital, Aarhus University Hospital, Washington University in St Louis, Instituto Nacional de Saude Dr Ricardo Jorge, Oades, Robert D., Guellaen, Georges, Medical Oncology, Epidemiology, Child and Adolescent Psychiatry / Psychology, and Hematology

Subjects
Netherlands Twin Register (NTR), Medizin, Inheritance Patterns, Social Sciences, AUTISM SPECTRUM DISORDERS, nosology, heritability, COMMON SNPS, 0302 clinical medicine, Crohn Disease, SCHIZOPHRENIA, Child, Psychiatric genetics, Genetics & Heredity, MAJOR DEPRESSIVE DISORDER, RISK, 0303 health sciences, ATTENTION-DEFICIT/HYPERACTIVITY DISORDER, 120 000 Neuronal Coherence, Mental Disorders, Variants, BIPOLAR DISORDER, ASSOCIATION, Genomic disorders and inherited multi-system disorders [DCN PAC - Perception action and control IGMD 3], Psychiatric Disorders, CROHNS-DISEASE, 3. Good health, Schizophrenia, genetic association study, Medical genetics, Major depressive disorder, SNPs, Adult, medicine.medical_specialty, genetic etiology, medical genetics, DEFICIT HYPERACTIVITY DISORDER, Biology, Polymorphism, Single Nucleotide, behavioral disciplines and activities, Article, Genomic disorders and inherited multi-system disorders DCN MP - Plasticity and memory [IGMD 3], Heritability, Genetic Heterogeneity, 03 medical and health sciences, Prevalence of mental disorders, mental disorders, [SDV.BBM] Life Sciences [q-bio]/Biochemistry, Molecular Biology, Genetics, medicine, ddc:61, Humans, Attention deficit hyperactivity disorder, Genetic Predisposition to Disease, [SDV.BBM]Life Sciences [q-bio]/Biochemistry, Molecular Biology, DCN PAC - Perception action and control NCEBP 9 - Mental health, ddc:610, Medizinische Fakultät » Universitätsklinikum Essen » LVR-Klinikum Essen » Klinik für Psychiatrie, Psychosomatik und Psychotherapie des Kindes- und Jugendalters, Bipolar disorder, Psychiatry, 030304 developmental biology, Depressive Disorder, Major, Genome, Human, Genetic heterogeneity, medicine.disease, schizophrenia, Attention Deficit Disorder with Hyperactivity, Child Development Disorders, Pervasive, Perturbações do Desenvolvimento Infantil e Saúde Mental, 030217 neurology & neurosurgery, Genome-Wide Association Study
Abstract

AM Vicente - Cross-Disorder Group of the Psychiatric Genomics Consortium Most psychiatric disorders are moderately to highly heritable. The degree to which genetic variation is unique to individual disorders or shared across disorders is unclear. To examine shared genetic etiology, we use genome-wide genotype data from the Psychiatric Genomics Consortium (PGC) for cases and controls in schizophrenia, bipolar disorder, major depressive disorder, autism spectrum disorders (ASD) and attention-deficit/hyperactivity disorder (ADHD). We apply univariate and bivariate methods for the estimation of genetic variation within and covariation between disorders. SNPs explained 17-29% of the variance in liability. The genetic correlation calculated using common SNPs was high between schizophrenia and bipolar disorder (0.68 ± 0.04 s.e.), moderate between schizophrenia and major depressive disorder (0.43 ± 0.06 s.e.), bipolar disorder and major depressive disorder (0.47 ± 0.06 s.e.), and ADHD and major depressive disorder (0.32 ± 0.07 s.e.), low between schizophrenia and ASD (0.16 ± 0.06 s.e.) and non-significant for other pairs of disorders as well as between psychiatric disorders and the negative control of Crohn's disease. This empirical evidence of shared genetic etiology for psychiatric disorders can inform nosology and encourages the investigation of common pathophysiologies for related disorders.

Published
2013

36. Maximal bifix decoding

Author

Christophe Reutenauer, Julien Leroy, Clelia De Felice, Francesco Dolce, Dominique Perrin, Giuseppina Rindone, Valérie Berthé, Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Dipartimento Informatica ed Applicazioni 'Renato M. Capocelli' (DIA), Università degli Studi di Salerno = University of Salerno (UNISA), Laboratoire d'Informatique Gaspard-Monge (LIGM), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Université du Luxembourg (Uni.lu), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), ANR-13-BS02-0003,DynA3S,Dynamique des algorithmes du pgcd : une approche Algorithmique, Analytique, Arithmétique et Symbolique(2013), ANR-11-BS02-0004,EQINOCS,Entropie et quantité d'information dans les modèles des systèmes computationnels(2011), Università degli Studi di Salerno (UNISA), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)

Subjects
Class (set theory), Generalization, Symbolic dynamics, 0102 computer and information sciences, Interval (mathematics), 01 natural sciences, Theoretical Computer Science, Combinatorics, Tree (descriptive set theory), [INFO.INFO-FL]Computer Science [cs]/Formal Languages and Automata Theory [cs.FL], FOS: Mathematics, Combinatorics on words, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, 0101 mathematics, Mathematics, Discrete mathematics, 010102 general mathematics, 010201 computation theory & mathematics, Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], Combinatorics (math.CO), Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Decoding methods, Computer Science::Formal Languages and Automata Theory
Abstract

We introduce a class of sets of words which is a natural common generalization of Sturmian sets and of interval exchange sets. This class of sets consists of the uniformly recurrent tree sets, where the tree sets are defined by a condition on the possible extensions of bispecial factors. We prove that this class is closed under maximal bifix decoding. The proof uses the fact that the class is also closed under decoding with respect to return words., arXiv admin note: text overlap with arXiv:1305.0127

Published
2013

37. C9orf72 repeat expansions are a rare genetic cause of parkinsonism.: C9ORF72 repeat expansion in parkinsonism

Author

Lesage, Suzanne, Le Ber, Isabelle, Condroyer, Christel, Broussolle, Emmanuel, Gabelle, Audrey, Thobois, Stéphane, Pasquier, Florence, Mondon, Karl, Dion, Patrick, Rochefort, Daniel, Rouleau, Guy, Dürr, Alexandra, Brice, Alexis, INSERM UMR_S975, Centre de Recherche de l'Institut du Cerveau et de la Moelle épinière (CRICM), 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)-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), 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)-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)-Centre de référence sur les démences rares et maladie de Pick, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Sorbonne Université (SU), Institut des sciences cognitives Marc Jeannerod - Centre de neuroscience cognitive - UMR5229 (CNC), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Département de neurologie, Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)-Hôpital Gui de Chauliac [Montpellier], Service de Neurologie [Lille], Hôpital Roger Salengro [Lille]-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Centre Mémoire de Ressources et de Recherche (CMRR), Centre Hospitalier Régional Universitaire de Tours (CHRU Tours), Department of Pathology and Cell Biology, Centre de Recherche du Centre Hospitalier de l’Université de Montréal (CR CHUM), Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Department of Medicine, Service de Génétique Cytogénétique et Embryologie [CHU Pitié-Salpêtrière], CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Centre de Recherche de l'Institut du Cerveau et de la Moelle épinière (CRICM), 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), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU), PSP-France Association (R12116DD), France Parkinson (R12010DD), French Agency for Research (ANR) program (R08200DS/ANR-08-NEUR-004-01, R08109DS/ANR-08-MNP-012-02)., for the French Parkinson's Disease Genetics (PDG) Study Group, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU), Institut des sciences cognitives Marc Jeannerod - Centre de neuroscience cognitive - UMR5229 (ISC-MJ), Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)-Hôpital Gui de Chauliac [CHU Montpellier], Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier), Département de neurologie [Lille], Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-CHU Pitié-Salpêtrière [AP-HP], Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU), Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Centre de Recherche de l'Institut du Cerveau et de la Moelle épinière (CRICM), and Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)

Subjects
C9ORF72, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], parkinsonism, nervous system diseases, dementia
Abstract

International audience; The recently identified C9orf72 gene accounts for a large proportion of amyotrophic lateral sclerosis and frontotemporal lobar degenerations. As several forms of these disorders are associated with parkinsonism, we hypothesized that some patients with Parkinson's disease or other forms of parkinsonism might carry pathogenic C9orf72 expansions. Therefore, we looked for C9orf72 repeat expansions in 1446 unrelated parkinsonian patients consisting of 1225 patients clinically diagnosed with Parkinson's disease, 123 with progressive supranuclear palsy, 21 with corticobasal degeneration syndrome, 43 with Lewy body dementia and 25 with multiple system atrophy-parkinsonism. Of the 1446 parkinsonian patients, five carried C9orf72 expansions: three patients with typical Parkinson's disease, one with corticobasal degeneration syndrome and another with progressive supranuclear palsy. This study shows that (i) although rare, C9orf72 repeat expansions may be associated with clinically typical Parkinson's disease and also with other parkinsonism; (ii) in several patients, parkinsonism was levodopa-responsive and remained pure, without associated dementia, for >10 years and (iii) interestingly, all C9orf72 repeat expansion carriers had positive family histories of parkinsonism, degenerative dementias or amyotrophic lateral sclerosis. This study also provides the tools for identifying parkinsonian patients with C9orf72 expansions, with important consequences for genetic counselling.

Published
2013

38. Assessment of Response to Lithium Maintenance Treatment in Bipolar Disorder: A Consortium on Lithium Genetics (ConLiGen) Report

Author

J. Raymond DePaulo, Martin Alda, Alfonso Tortorella, Susan G. Leckband, Jean-Michel Aubry, James B. Potash, Clara Brichant-Petitjean, Layla Kassem, Joanna Hauser, Tomas Novak, David Zilles, Claire O'Donovan, Rebecca Hoban, Sarah Kittel-Schneider, Claire Slaney, Lena Backlund, Peter Falkai, Andrew T. A. Cheng, John R. Kelsoe, Andrea Pfennig, Janice M. Fullerton, Marcella Rietschel, Caterina Chillotti, Stéphane Jamain, Elise Bui, Po-Hsiu Kuo, Alessio Squassina, Claudio E. M. Banzato, Joanna M. Biernacka, Lisa R. Seymour, Naomi R. Wray, Ichiro Kusumi, Thomas Stamm, Fernando S. Goes, Audrey Nallet, Sarah K. Tighe, Giovanni Severino, Jean-Pierre Kahn, Maria Neuner, Nirmala Akula, Norio Ozaki, Francis J. McMahon, Frank Bellivier, Andreas Reif, Ryota Hashimoto, Barbara W. Schweizer, Palmiero Monteleone, Florian Seemüller, Urs Heilbronner, Sevilla D. Detera-Wadleigh, Pavla Stopkova, Martin Schalling, Julie Garnham, Sébastien Gard, Mark A. Frye, Eva Z. Reininghaus, Lina Martinsson, Urban Ösby, Maria Grigoroiu-Serbanescu, Sara Richardson, Tadafumi Kato, Marion Leboyer, Catharina Lavebratt, Piotr M. Czerski, Scott R. Clark, Daniela Reich-Erkelenz, Sebastian Kliwicki, Guy A. Rouleau, Oliver Gruber, Gonzalo Laje, Adam Wright, Gustavo Turecki, Roy H. Perlis, Takuya Masui, Mirko Manchia, Bernhard T. Baune, Mazda Adli, Michael Bauer, Sven Cichon, Frank Mondimore, Bruno Etain, Philip B. Mitchell, Thomas G. Schulze, Peter P. Zandi, Raffaella Ardau, Peter R. Schofield, Susanne Bengesser, Liping Hou, Janusz K. Rybakowski, Mario Maj, Clarissa de Rosalmeida Dantas, Louise Frisén, O. Schubert, Carlos Jaramillo, Maria Del Zompo, Paul Grof, Cynthia V. Calkin, Jo Steele, Jordan W. Smoller, Alain Malafosse, Manchia, M, Adli, M, Akula, N, Ardau, R, Aubry, Jm, Backlund, L, Banzato, Ce, Baune, Bt, Bellivier, F, Bengesser, S, Biernacka, Jm, Brichant Petitjean, C, Bui, E, Calkin, Cv, Cheng, At, Chillotti, C, Cichon, S, Clark, S, Czerski, Pm, Dantas, C, Zompo, Md, Depaulo, Jr, Detera Wadleigh, Sd, Etain, B, Falkai, P, Frisén, L, Frye, Ma, Fullerton, J, Gard, S, Garnham, J, Goes, F, Grof, P, Gruber, O, Hashimoto, R, Hauser, J, Heilbronner, U, Hoban, R, Hou, L, Jamain, S, Kahn, Jp, Kassem, L, Kato, T, Kelsoe, Jr, Kittel Schneider, S, Kliwicki, S, Kuo, Ph, Kusumi, I, Laje, G, Lavebratt, C, Leboyer, M, Leckband, Sg, López Jaramillo, Ca, Maj, Mario, Malafosse, A, Martinsson, L, Masui, T, Mitchell, Pb, Mondimore, F, Monteleone, P, Nallet, A, Neuner, M, Novák, T, O'Donovan, C, Osby, U, Ozaki, N, Perlis, Rh, Pfennig, A, Potash, Jb, Reich Erkelenz, D, Reif, A, Reininghaus, E, Richardson, S, Rouleau, Ga, Rybakowski, Jk, Schalling, M, Schofield, Pr, Schubert, Ok, Schweizer, B, Seemüller, F, Grigoroiu Serbanescu, M, Severino, G, Seymour, Lr, Slaney, C, Smoller, Jw, Squassina, A, Stamm, T, Steele, J, Stopkova, P, Tighe, Sk, Tortorella, Alfonso Antonio Vincenzo, Turecki, G, Wray, Nr, Wright, A, Zandi, Pp, Zilles, D, Bauer, M, Rietschel, M, Mcmahon, Fj, Schulze, Tg, Alda, M., Department of Psychiatry, Dalhousie University [Halifax], Department of Psychiatry and Psychotherapy, Charité - UniversitätsMedizin = Charité - University Hospital [Berlin], Human Genetics Branch, National Institutes of Health [Bethesda] (NIH)-National Institute of Mental Health (NIMH), Unit of Clinical Pharmacology, University-Hospital of Cagliari, Department of Mental Health and Psychiatry, University Hospital of Geneva, Trinity College Dublin-St. James's Hospital, University of Campinas [Campinas] (UNICAMP), University of Adelaide, Pôle de Psychiatrie, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Groupe Hospitalier Saint Louis - Lariboisière - Fernand Widal [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), Medical University Graz, Mayo Clinic, Division of Epidemiology and Genetics, Academia Sinica-Institute of Biomedical Sciences (ICB/USP), Universidade de São Paulo (USP)-Universidade de São Paulo (USP), Department of Genomics, Life and Brain Center, University of Bonn, Psychiatric Genetic Unit, Poznan University of Medical Sciences, Section of Neuroscience and Clinical Pharmacology, University of Cagliari, Department of Psychiatry and Behavioral Sciences, Johns Hopkins University School of Medicine, Institut Mondor de Recherche Biomédicale (IMRB), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-IFR10, University of Homburg, Genetics of Mental Illness and Brain Function, Neuroscience Research Australia, Service de psychiatrie adulte, Université Bordeaux Segalen - Bordeaux 2-Hôpital Charles Perrens-Centre Expert Trouble Bipolaire, Mood Disorders Center of Ottawa (MDCO), University of Ottawa [Ottawa], University of Toronto, Georg-August-University [Göttingen], Osaka University Graduate School of Medicine, University of California [San Diego] (UC San Diego), University of California-University of California, Service de Psychiatrie et Psychologie Clinique, Centre Hospitalier Régional Universitaire de Nancy (CHRU Nancy)-Hôpital Jeanne-d'Arc, Laboratory for Molecular Dynamics of Mental Disorders, RIKEN Center for Brain Science [Wako] (RIKEN CBS), RIKEN - Institute of Physical and Chemical Research [Japon] (RIKEN)-RIKEN - Institute of Physical and Chemical Research [Japon] (RIKEN), Mental Health Sciences Unit, University College of London [London] (UCL), Department of Adult Psychiatry, Institute of Epidemiology and Preventive Medicine, National Taiwan University [Taiwan] (NTU), Hokkaido University Graduate School of Medicine, Molecular Medicine and Surgery department, Karolinska Institutet [Stockholm], Center for Molecular Medicine, Karolinska University Hospital [Stockholm], Department of Pharmacy, Veterans Affairs San Diego Healthcare System, Skaggs School of Pharmacy and Pharmaceutical Sciences [San Diego], University of Antioquia, University of Napoli, School of Psychiatry, University of New South Wales [Sydney] (UNSW)-Black Dog Institute, Prague Psychiatric Center, University of Prague, Fujita Health University School of Medicine, Nagoya University Graduate School of Medicine, Harvard Medical School [Boston] (HMS)-Massachusetts General Hospital [Boston], Technische Universität Dresden = Dresden University of Technology (TU Dresden), University of Iowa [Iowa City], Center of Excellence in Neuroscience, CHU de Montréal, Department of Medicine, Centre de Recherche du Centre Hospitalier de l’Université de Montréal (CR CHUM), Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Biometric Psychiatric Genetics Research Unit, Alexandru Obregia Psychiatric Hospital, McGill Group for Suicide Studies, Douglas Mental Health University Institute, Queensland Brain Institute, University of Queensland [Brisbane], Department of Mental Health, Johns Hopkins Bloomberg School of Public Health [Baltimore], Johns Hopkins University (JHU)-Johns Hopkins University (JHU), Department of Genetic Epidemiology in Psychiatry [Mannhein], Universität Heidelberg [Heidelberg]-Central Institute of Mental Health Mannheim, The work on assessment of lithium response has been supported by a grant from Canadian Institutes of Health Research #64410 to MA. MG-S was supported by Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii (UEFISCDI), Bucharest, Romania (grant no. 89/2012). JMA and AN were supported by a grant from the Swiss National Foundation (#32003B_125469/1 to JM Aubry). ConLiGen is in part supported by funds from the Intramural Research Program of the National Institute of Mental Health (NIMH) at the National Institutes of Health (NIH), Department of Health and Human Services, United States Government, Aubry, Jean-Michel, Universidade Estadual de Campinas = University of Campinas (UNICAMP), Universidade de São Paulo = University of São Paulo (USP)-Universidade de São Paulo = University of São Paulo (USP), Institut National de la Santé et de la Recherche Médicale (INSERM)-IFR10-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), Georg-August-University = Georg-August-Universität Göttingen, University of California (UC)-University of California (UC), Guellaen, Georges, Université Bordeaux Segalen - Bordeaux 2-Centre hospitalier Charles Perrens [Bordeaux]-Centre Expert Trouble Bipolaire, and Ikeda, Kazutaka

Subjects
Male, Bipolar Disorder, Lithium (medication), Psychometrics, Psychopharmacology, Epidemiology, International Cooperation, lcsh:Medicine, Lithium, Maintenance Treatment, ConLiGen, ddc:616.89, 0302 clinical medicine, Antimanic Agents, Psychology, lcsh:Science, Reliability (statistics), Psychiatry, Genetics, 0303 health sciences, Multidisciplinary, ASSOCIATION, Genomics, Pharmacoepidemiology, 3. Good health, Mental Health, Phenotype, Treatment Outcome, MAPPING SUSCEPTIBILITY GENES, Behavioral Pharmacology, RELIABILITY, Lithium Compounds, Medicine, Female, Research Article, medicine.drug, Drugs and Devices, MAPPING SUSCEPTIBILITY GENES, PROPHYLACTIC LITHIUM, OBSERVER AGREEMENT, MOOD DISORDERS, ONSET, ASSOCIATION, RELIABILITY, MORTALITY, ILLNESS, AGE, ILLNESS, PROPHYLACTIC LITHIUM, 03 medical and health sciences, AGE, Neuropharmacology, Genomic Medicine, [SDV.BBM] Life Sciences [q-bio]/Biochemistry, Molecular Biology, Genome-Wide Association Studies, medicine, Humans, [SDV.BBM]Life Sciences [q-bio]/Biochemistry, Molecular Biology, Bipolar disorder, ddc:610, Biology, 030304 developmental biology, Mood Disorders, business.industry, MORTALITY, lcsh:R, Computational Biology, Reproducibility of Results, Models, Theoretical, medicine.disease, OBSERVER AGREEMENT, Mood disorders, Pharmacogenetics, Therapies, ONSET, lcsh:Q, Pharmacogenomics, business, 030217 neurology & neurosurgery, Kappa
Abstract

Objective: The assessment of response to lithium maintenance treatment in bipolar disorder (BD) is complicated by variable length of treatment, unpredictable clinical course, and often inconsistent compliance. Prospective and retrospective methods of assessment of lithium response have been proposed in the literature. In this study we report the key phenotypic measures of the "Retrospective Criteria of Long-Term Treatment Response in Research Subjects with Bipolar Disorder" scale currently used in the Consortium on Lithium Genetics (ConLiGen) study. Materials and Methods: Twenty-nine ConLiGen sites took part in a two-stage case-vignette rating procedure to examine inter-rater agreement [Kappa (\(\kappa\))] and reliability [intra-class correlation coefficient (ICC)] of lithium response. Annotated first-round vignettes and rating guidelines were circulated to expert research clinicians for training purposes between the two stages. Further, we analyzed the distributional properties of the treatment response scores available for 1,308 patients using mixture modeling. Results: Substantial and moderate agreement was shown across sites in the first and second sets of vignettes (\(\kappa\) = 0.66 and \(\kappa\) = 0.54, respectively), without significant improvement from training. However, definition of response using the A score as a quantitative trait and selecting cases with B criteria of 4 or less showed an improvement between the two stages (\(ICC_1 = 0.71\) and \(ICC_2 = 0.75\), respectively). Mixture modeling of score distribution indicated three subpopulations (full responders, partial responders, non responders). Conclusions: We identified two definitions of lithium response, one dichotomous and the other continuous, with moderate to substantial inter-rater agreement and reliability. Accurate phenotypic measurement of lithium response is crucial for the ongoing ConLiGen pharmacogenomic study.

Published
2013

39. C9orf72 repeat expansions are a rare genetic cause of parkinsonism.: C9ORF72 repeat expansion in parkinsonism

Author

Lesage, Suzanne, Le Ber, Isabelle, Condroyer, Christel, Broussolle, Emmanuel, Gabelle, Audrey, Thobois, Stéphane, Pasquier, Florence, Mondon, Karl, Dion, Patrick, Rochefort, Daniel, Rouleau, Guy, Dürr, Alexandra, Brice, Alexis, Lesage, Suzanne, INSERM UMR_S975, Centre de Recherche de l'Institut du Cerveau et de la Moelle épinière (CRICM), 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)-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), 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)-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)-Centre de référence sur les démences rares et maladie de Pick, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Sorbonne Université (SU), Institut des sciences cognitives Marc Jeannerod - Centre de neuroscience cognitive - UMR5229 (CNC), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Département de neurologie, Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)-Hôpital Gui de Chauliac [Montpellier], Département de neurologie [Lille], Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Centre Mémoire de Ressources et de Recherche (CMRR), Centre Hospitalier Régional Universitaire de Tours (CHRU Tours), Department of Pathology and Cell Biology, Centre de Recherche du Centre Hospitalier de l’Université de Montréal (CR CHUM), Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Department of Medicine, Service de Génétique Cytogénétique et Embryologie [CHU Pitié-Salpêtrière], CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Centre de Recherche de l'Institut du Cerveau et de la Moelle épinière (CRICM), 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), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU), PSP-France Association (R12116DD), France Parkinson (R12010DD), French Agency for Research (ANR) program (R08200DS/ANR-08-NEUR-004-01, R08109DS/ANR-08-MNP-012-02)., and for the French Parkinson's Disease Genetics (PDG) Study Group

Subjects
C9ORF72, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [SDV.NEU] Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], parkinsonism, nervous system diseases, dementia
Abstract

International audience; The recently identified C9orf72 gene accounts for a large proportion of amyotrophic lateral sclerosis and frontotemporal lobar degenerations. As several forms of these disorders are associated with parkinsonism, we hypothesized that some patients with Parkinson's disease or other forms of parkinsonism might carry pathogenic C9orf72 expansions. Therefore, we looked for C9orf72 repeat expansions in 1446 unrelated parkinsonian patients consisting of 1225 patients clinically diagnosed with Parkinson's disease, 123 with progressive supranuclear palsy, 21 with corticobasal degeneration syndrome, 43 with Lewy body dementia and 25 with multiple system atrophy-parkinsonism. Of the 1446 parkinsonian patients, five carried C9orf72 expansions: three patients with typical Parkinson's disease, one with corticobasal degeneration syndrome and another with progressive supranuclear palsy. This study shows that (i) although rare, C9orf72 repeat expansions may be associated with clinically typical Parkinson's disease and also with other parkinsonism; (ii) in several patients, parkinsonism was levodopa-responsive and remained pure, without associated dementia, for >10 years and (iii) interestingly, all C9orf72 repeat expansion carriers had positive family histories of parkinsonism, degenerative dementias or amyotrophic lateral sclerosis. This study also provides the tools for identifying parkinsonian patients with C9orf72 expansions, with important consequences for genetic counselling.

Published
2013

40. Immaculate basis of the non-commutative symmetric functions

Author

Berg, Chris, Bergeron, Nantel, Saliola, Franco, Serrano, Luis, Zabrocki, Mike, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Department of Mathematics and Statistics [Toronto], York University [Toronto], Fields Institute for Research In Mathematical Sciences, Alain Goupil and Gilles Schaeffer, Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), and Monteil, Alain

Subjects
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Mathematics::Complex Variables, Mathematics::Number Theory, Mathematics::History and Overview, quasi-symmetric functions, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], non-commutative symmetric functions, tableaux, Schur functions
Abstract

We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions and decompose Schur functions according to a signed combinatorial formula., Nous introduisons une nouvelle base des fonctions syméetriques non commutatives dont les images commutatives sont des fonctions de Schur. Nous construisons la base duale des fonctions quasi-symétriques qui s’expriment de façon positive en fonction de la base fondamentale et décomposent les fonctions de Schur.

Published
2013

41. Acyclic, connected and tree sets

Author

Christophe Reutenauer, Dominique Perrin, Valérie Berthé, Clelia De Felice, Julien Leroy, Francesco Dolce, Giuseppina Rindone, Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Dipartimento Informatica ed Applicazioni 'Renato M. Capocelli' (DIA), Università degli Studi di Salerno (UNISA), Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Université du Luxembourg (Uni.lu), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Università degli Studi di Salerno = University of Salerno (UNISA), and Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS)

Subjects
FOS: Computer and information sciences, Formal Languages and Automata Theory (cs.FL), General Mathematics, Computer Science - Formal Languages and Automata Theory, 0102 computer and information sciences, 01 natural sciences, Combinatorics, combinatorial group theory, [INFO.INFO-FL]Computer Science [cs]/Formal Languages and Automata Theory [cs.FL], symbolic dynamics, FOS: Mathematics, Mathematics - Combinatorics, Family of sets, combinatorics on words, 0101 mathematics, Undirected graph, Mathematics, Combinatorics on words, Combinatorial group theory, Symbolic dynamics, 010102 general mathematics, 16. Peace & justice, 010201 computation theory & mathematics, If and only if, Free group, Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], Graph (abstract data type), Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Combinatorics (math.CO), Alphabet, Computer Science::Formal Languages and Automata Theory, MathematicsofComputing_DISCRETEMATHEMATICS
Abstract

Given a set $F$ of words, one associates to each word $w$ in $F$ an undirected graph, called its extension graph, and which describes the possible extensions of $w$ on the left and on the right. We investigate the family of sets of words defined by the property of the extension graph of each word in the set to be acyclic or connected or a tree. We prove that in a uniformly recurrent tree set, the sets of first return words are bases of the free group on the alphabet. Concerning acyclic sets, we prove as a main result that a set $F$ is acyclic if and only if any bifix code included in $F$ is a basis of the subgroup that it generates., Comment: arXiv admin note: substantial text overlap with arXiv:1305.0127, arXiv:1011.5369, Monatsh. Math. (2015)

Published
2013
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42. On Generalized Pseudostandard Words Over Binary Alphabets

Author

Blondin Masse, Alexandre, Paquin, Geneviève, Tremblay, Jérome, Vuillon, Laurent, Laboratoire de Mathématiques, Département d'Informatique et de Mathématiques (DIM), Université du Québec à Chicoutimi (UQAC)-Université du Québec à Chicoutimi (UQAC), Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Vuillon, Laurent, Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)

Subjects
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Abstract

International audience; In this paper, we study generalized pseudostandard words over a two-letter alpha- bet, which extend the classes of standard Sturmian, standard episturmian and pseu- dostandard words, allowing different involutory antimorphisms instead of the usual palindromic closure or a fixed involutory antimorphism. We first discuss about pseu- doperiods, a useful tool for describing words obtained by iterated pseudopalindromic closure. Then, we introduce the concept of normalized directive bi-sequence (Θ,w) of a generalized pseudostandard word, that is the one that exactly describes all the pseudopalindromic prefixes of it. We show that a directive bi-sequence is normalized if and only if its set of factors does not intersect a finite set of forbidden ones. Moreover, we provide a construction to normalize any directive bi-sequence. Next, we present an explicit formula, generalizing the one for the standard episturmian words introduced by Justin, that computes recursively the next prefix of a generalized pseudostandard word in term of the previous one. Finally, we focus on generalized pseudostandard words having complexity 2n, also called Rote words. More precisely, we prove that the normalized bi-sequences describing Rote words are completely characterized by their factors of length 2.

Published
2013

43. Over-MAP: Structural Attention Mechanism and Automated Semantic Segmentation Ensembled for Uncertainty Prediction

Author

Kantor, Charles A., Léonard Boussioux, Brice Rauby, Hugues Talbot, OPtimisation Imagerie et Santé (OPIS), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de vision numérique (CVN), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-CentraleSupélec-Université Paris-Saclay, Montreal Institute for Learning Algorithms [Montréal] (MILA), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), CentraleSupélec, Université Paris-Saclay, Massachusetts Institute of Technology (MIT), and École Polytechnique de Montréal (EPM)

Subjects
[INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], General Medicine, [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM]
Abstract

International audience; Both theoretical and practical problems in deep learning classification require solutions for assessing uncertainty prediction but current state-of-the-art methods in this area are computationally expensive. In this paper, we propose a new confidence measure dubbed Over-MAP that utilizes a measure of overlap between structural attention mechanisms and segmentation methods, that is of particular interest in accurate fine-grained contexts. We show that this classification confidence increases with the degree of overlap. The associated confidence and identification tools are conceptually simple, efficient, and of high practical interest as they allow for weeding out misleading examples in training data. Our measure is currently deployed in the real-world on widely used platforms to annotate large-scale data efficiently.

Published
2021

44. Impact of emerging pollutants on pulmonary inflammation in asthmatic rats: ethanol vapors and agglomerated TiO2 nanoparticles

Author

Alexandra Noël, A. Scarino, Michel Charbonneau, Yves Cloutier, Ginette Truchon, Robert Tardif, P. M. Renzi, Renaud Vincent, Institut Armand Frappier (INRS-IAF), Institut National de la Recherche Scientifique [Québec] (INRS)-Réseau International des Instituts Pasteur (RIIP), Département de santé environnementale et santé au travail, Université de Montréal (UdeM), Notre-Dame Hospital, Centre de Recherche du Centre Hospitalier de l’Université de Montréal (CR CHUM), Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre Hospitalier de l'Université de Montréal (CHUM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Institut de recherche Robert-Sauvé en santé et en sécurité du travail (IRSST), Inhalation Toxicology Laboratory, and Healthy Environments and Consumer Safety Branch, Health Canada

Subjects
Male, MESH: Asthma, MESH: Air Pollutants, Health, Toxicology and Mutagenesis, Toxicology, MESH: Dose-Response Relationship, Drug, MESH: Aerosols, chemistry.chemical_compound, Rats, Inbred BN, MESH: Animals, Lung, Titanium, MESH: Cytokines, Air Pollutants, Inhalation Exposure, biology, Inhalation, Chemistry, respiratory system, MESH: Rats, Inbred BN, medicine.anatomical_structure, MESH: Titanium, [SDV.TOX]Life Sciences [q-bio]/Toxicology, Cytokines, Female, MESH: Inhalation Exposure, medicine.symptom, Bronchoalveolar Lavage Fluid, MESH: Pneumonia, MESH: Ethanol, MESH: Rats, Ovalbumin, Inflammation, Context (language use), medicine, Animals, MESH: Lung, Asthma, Pollutant, Aerosols, MESH: Ovalbumin, Ethanol, Dose-Response Relationship, Drug, MESH: Bronchoalveolar Lavage Fluid, technology, industry, and agriculture, Pneumonia, medicine.disease, MESH: Male, Rats, Disease Models, Animal, Immunology, biology.protein, MESH: Volatilization, Nanoparticles, MESH: Disease Models, Animal, Volatilization, MESH: Female, MESH: Nanoparticles
Abstract

International audience; CONTEXT: Titanium dioxide nanoparticles (nano-TiO(2)) and ethanol vapors are air contaminants with increasing importance. The presence of a pathological pulmonary condition, such as asthma, may increase lung susceptibility to such contaminants. OBJECTIVE: This study aimed to investigate if exposure to inhaled ethanol vapors or nano-TiO(2) can modulate the rat pulmonary inflammatory response resulting from an allergic asthmatic reaction. MATERIALS AND METHODS: Brown Norway rats were sensitized (sc) and challenged (15 min inhalation, 14 days later) with chicken egg ovalbumin (OVA). Leukocytes were counted in bronchoalveolar lavages (BAL) performed at 6, 24, 36, 48 and 72 h following the challenge and either after ethanol exposures (3000 ppm, 6 h/day, daily) or at 48 h (peak inflammation) for nano-TiO(2) exposures (9.35 mg/m(3) aerosol for 6 and 42 h after the OVA challenge). For the nano-TiO(2) exposures, plasma and BAL cytokines were measured and lung histological analyzes were performed. RESULTS: Exposure to ethanol did not significantly affect BAL leukocytes after OVA challenge. Exposure to nano-TiO(2) significantly decreased BAL leukocytes compared to OVA-challenged controls. Plasma and BAL IL-4, IL-6, and INF-γ levels were also decreased in the nano-TiO(2) group. DISCUSSION: While ethanol vapors do not modify the pulmonary inflammation in rats during an asthmatic response, a surprising protective effect for agglomerated nano-TiO(2) was observed. A putative mechanistic basis involving a decrease in the Th2 response caused by OVA is proposed. CONCLUSION: Allergic pulmonary inflammation is not up-regulated by inhalation of the pollutants ethanol and nano-TiO(2). On the contrary, nano-TiO(2) decreases lung inflammation in asthmatic rats.

Published
2012

45. Bifix codes and Sturmian words

Author

Clelia De Felice, Christophe Reutenauer, Jean Berstel, Giuseppina Rindone, Dominique Perrin, Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Dipartimento Informatica ed Applicazioni 'Renato M. Capocelli' (DIA), Università degli Studi di Salerno (UNISA), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Università degli Studi di Salerno = University of Salerno (UNISA), Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM)

Subjects
FOS: Computer and information sciences, Factorial, Code (set theory), Formal Languages and Automata Theory (cs.FL), Computer Science - Formal Languages and Automata Theory, 0102 computer and information sciences, Combinatorial group theory, 01 natural sciences, Combinatorics, Set (abstract data type), [INFO.INFO-FL]Computer Science [cs]/Formal Languages and Automata Theory [cs.FL], FOS: Mathematics, Mathematics - Combinatorics, 0101 mathematics, Mathematics, Algebra and Number Theory, Degree (graph theory), 010102 general mathematics, Sturmian words, Basis (universal algebra), Bifix codes, 010201 computation theory & mathematics, Free group, Combinatorics (math.CO), Stallings automata, Word (group theory)
Abstract

We prove new results concerning the relation between bifix codes, episturmian words and subgroups offree groups. We study bifix codes in factorial sets of words. We generalize most properties of ordinary maximal bifix codes to bifix codes maximal in a recurrent set $F$ of words ($F$-maximal bifix codes). In the case of bifix codes contained in Sturmian sets of words, we obtain several new results. Let $F$ be a Sturmian set of words, defined as the set of factors of a strict episturmian word. Our results express the fact that an $F$-maximal bifix code of degree $d$ behaves just as the set of words of $F$ of length $d$. An $F$-maximal bifix code of degree $d$ in a Sturmian set of words on an alphabet with $k$ letters has $(k-1)d+1$ elements. This generalizes the fact that a Sturmian set contains $(k-1)d+1$ words of length $d$. Moreover, given an infinite word $x$, if there is a finite maximal bifix code $X$ of degree $d$ such that $x$ has at most $d$ factors of length $d$ in $X$, then $x$ is ultimately periodic. Our main result states that any $F$-maximal bifix code of degree $d$ on the alphabet $A$ is the basis of a subgroup of index $d$ of the free group on~$A$., 70 pages + index

Published
2012

46. Symmetries of the k-bounded partition lattice

Author

Chris Berg, Mike Zabrocki, Fields Institute for Research In Mathematical Sciences, York University [Toronto], Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Hiro-Fumi Yamada and Nantel Bergeron, Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM)

Subjects
Pure mathematics, Mathematics::Combinatorics, core partitions, General Computer Science, High Energy Physics::Lattice, Partition lattice, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], k-Schur functions, Theoretical Computer Science, Cyclic symmetry, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Bounded function, Lattice (order), Mathematics::Quantum Algebra, Homogeneous space, Discrete Mathematics and Combinatorics, Mathematics::Representation Theory, cyclic symmetry, Mathematics
Abstract

We generalize the symmetry on Young's lattice, found by Suter, to a symmetry on the $k$-bounded partition lattice of Lapointe, Lascoux and Morse., Nous généralisons la symétrie sur le treillis de Young, découvert par Suter, à une symétrie sur le treillis des partages bornés par $k$ et étudié par Lapointe, Lascoux and Morse.

Published
2012

47. A linear time and space algorithm for detecting path intersection in Zd

Author

Sreko Brlek, Xavier Provençal, Michel Koskas, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal (UQAM), Mathématiques et Informatique Appliquées (MIA-Paris), AgroParisTech-Institut National de la Recherche Agronomique (INRA), Laboratoire de Mathématiques (LAMA), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)

Subjects
Chain code, General Computer Science, Spacetime, Efficient algorithm, Radix tree, Self-intersection, Initialization, 0102 computer and information sciences, 02 engineering and technology, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], Data structure, 01 natural sciences, Theoretical Computer Science, Lattice paths, Freeman code, 010201 computation theory & mathematics, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Algorithm, Time complexity, Mathematics, Coding (social sciences)
Abstract

International audience; The Freeman chain code is a common and useful way for representing discrete paths by means of words such that each letter encodes a step in a given direction. In the discrete plane Z2Z2 such a coding is widely used for representing connected discrete sets by their contour which forms a closed and intersection free path. In this paper, we use a multidimensional radix tree like data structure for storing paths in the discretedd-dimensional space ZdZd. It allows to design a simple and efficient algorithm for detecting path intersection. Even though an extra initialization is required, the time and space complexities remain linear for any fixed dimension dd. Several problems that are solved by adapting our algorithm are also discussed.

Published
2011

48. The number of intervals in the m-Tamari lattices

Author

Louis-François Préville-Ratelle, Mireille Bousquet-Mélou, Éric Fusy, Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), European Project: 208471,EC:FP7:ERC,ERC-2007-StG,EXPLOREMAPS(2008), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM)

Subjects
Path (topology), Enumeration, Tamari lattices, 0102 computer and information sciences, 01 natural sciences, Bijective proof, Theoretical Computer Science, Combinatorics, Lattice (order), Functional equation, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, 0101 mathematics, Algebraic number, Connection (algebraic framework), Mathematics, Discrete mathematics, AMS 05A10, 05A15, Applied Mathematics, 010102 general mathematics, Generating function, Lattice paths, Computational Theory and Mathematics, 010201 computation theory & mathematics, Combinatorics (math.CO), Geometry and Topology, Tamari lattice
Abstract

An m-ballot path of size n is a path on the square grid consisting of north and east steps, starting at (0,0), ending at (mn,n), and never going below the line {x=my}. The set of these paths can be equipped with a lattice structure, called the m-Tamari lattice, which generalizes the usual Tamari lattice obtained when m=1. We prove that the number of intervals in this lattice is $$ \frac {m+1}{n(mn+1)} {(m+1)^2 n+m\choose n-1}. $$ This formula was recently conjectured by Bergeron in connection with the study of coinvariant spaces. The case m=1 was proved a few years ago by Chapoton. Our proof is based on a recursive description of intervals, which translates into a functional equation satisfied by the associated generating function. The solution of this equation is an algebraic series, obtained by a guess-and-check approach. Finding a bijective proof remains an open problem., 19 pages

Published
2011

49. Closed paths whose steps are roots of unity

Author

Gilbert Labelle, Annie Lacasse, Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel, Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM)

Subjects
General Computer Science, Root of unity, $P$-recursive, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], 16. Peace & justice, Theoretical Computer Science, Combinatorics, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], closed polygonal paths, Discrete Mathematics and Combinatorics, Roots of unity, Asymptotics, Mathematics
Abstract

We give explicit formulas for the number $U_n(N)$ of closed polygonal paths of length $N$ (starting from the origin) whose steps are $n^{\textrm{th}}$ roots of unity, as well as asymptotic expressions for these numbers when $N \rightarrow \infty$. We also prove that the sequences $(U_n(N))_{N \geq 0}$ are $P$-recursive for each fixed $n \geq 1$ and leave open the problem of determining the values of $N$ for which the $\textit{dual}$ sequences $(U_n(N))_{n \geq 1}$ are $P$-recursive., Nous donnons des formules explicites pour le nombre $U_n(N)$ de chemins polygonaux fermés de longueur $N$ (débutant à l'origine) dont les pas sont des racines $n$-ièmes de l'unité, ainsi que des expressions asymptotiques pour ces nombres lorsque $N \rightarrow \infty$. Nous démontrons aussi que les suites $(U_n(N))_{N \geq 0}$ sont $P$-récursives pour chaque $n \geq 1$ fixé et laissons ouvert le problème de déterminer les valeurs de $N$ pour lesquelles les suites $\textit{duales}$ $(U_n(N))_{n \geq 1}$ sont $P$-récursives.

Published
2011

50. Primitive orthogonal idempotents for R-trivial monoids

Author

Franco Saliola, Sandeep Bhargava, Chris Berg, Nantel Bergeron, Fields Institute for Research In Mathematical Sciences, York University [Toronto], Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Université du Québec à Montréal = University of Québec in Montréal (UQAM)-Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM), Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel, Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM)

Subjects
Monoid, Pure mathematics, General Computer Science, monoids, 0102 computer and information sciences, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], 01 natural sciences, Representation theory, Theoretical Computer Science, Combinatorics, Free monoid, Mathematics::Category Theory, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Discrete Mathematics and Combinatorics, Representation Theory (math.RT), 0101 mathematics, Equivalence (formal languages), Mathematics, Discrete mathematics, Algebra and Number Theory, 010102 general mathematics, Syntactic monoid, 0-Hecke algebras, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], primitive orthogonal idempotents, 010201 computation theory & mathematics, left regular bands, Mathematics - Representation Theory, Trace theory
Abstract

We construct a recursive formula for a complete system of primitive orthogonal idempotents for any R-trivial monoid. This uses the newly proved equivalence between the notions of R-trivial monoid and weakly ordered monoid., Nous construisons une formule récursive pour un système complet d'idempotents orthogonaux primitifs pour tout monoïde R-trivial. Nous employons une nouvelle équivalence entre les notions de monoïde R-trivial et de monoïde faiblement ordonné.

Published
2011

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