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36 results on '"Academy of Mathematics and Systems Science (AMSS)"'

1. Le louage tunisien : une alternative sociétale opérationnelle aux VTC et à la ubérisation à tout-va

Author

Hassine, Mohamed, Canalda, Philippe, Hassine, Idriss, Academy of Mathematics and Systems Science (AMSS) (Academy of Mathematics and Systems Science (AMSS)), Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174) (FEMTO-ST), Université de Technologie de Belfort-Montbeliard (UTBM)-Ecole Nationale Supérieure de Mécanique et des Microtechniques (ENSMM)-Université de Franche-Comté (UFC), and Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[INFO.INFO-IU]Computer Science [cs]/Ubiquitous Computing, [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], [INFO.INFO-MA]Computer Science [cs]/Multiagent Systems [cs.MA], [INFO.INFO-ET]Computer Science [cs]/Emerging Technologies [cs.ET], [INFO.INFO-SE]Computer Science [cs]/Software Engineering [cs.SE], [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; Le louage est un service de transport tunisien de taxi collectif pour les espaces intra et inter gouvernorats. Comme UBER, il complète opérationnellement l'offre globale de transport public et se déclenche suite à la demande des passagers. Dans cette étude, nous proposons une modélisation du problème d'optimisation sous-jacent au service de louage en Tunisie, et une implémentation de résolution exacte d'un algorithme glouton de ce problème. L'évaluation de la solution s'effectue à partir de cas réels du service de louage, mis en place sur le territoire tunisien.Les simulations effectuées ont permis de satisfaire à 20000 demandes et 4000 offres, et pour un temps de réponse de notre système réduit à quelques secondes. Ces résultats permettent d'informatiser ce système et de le rendre plus efficace.

Published
2017

2. Hydraulic traits are coupled with plant anatomical traits under drought–rewatering cycles in Ginkgo biloba L

Author

Shan Li, Xin Li, Jie Wang, Zhicheng Chen, Sen Lu, Xianchong Wan, Hongyan Sun, Li Wang, Sylvain Delzon, Herve Cochard, Xiaomei Jiang, Jianhua Shu, Jingming Zheng, Yafang Yin, Chinese Academy of Forestry, Institut de Physique de Nice (INPHYNI), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Shaanxi University of Science and Technology, Princeton University, Biologie Cellulaire et Cancer, Institut Curie [Paris]-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Biodiversité, Gènes & Communautés (BioGeCo), Université de Bordeaux (UB)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire de Physique et Physiologie Intégratives de l’Arbre en environnement Fluctuant (PIAF), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Université Clermont Auvergne (UCA), Beijing Inst Landscape Architecture, Beijing Forestry University, and Beijing Natural Science Foundation 6184048National Natural Science Foundation of China (NSFC) 32001291Talent Project of Shaanxi University of Science and Technology126022037

Subjects
lethal water potential under drought, Physiology, fungi, xylem vulnerability curves, Ginkgo biloba, Water, food and beverages, Plant Science, Droughts, Trees, cambium and phloem cell vitality, Xylem, xylem growth ring width, pit aspiration rate, tree mortality, [SDV.BV]Life Sciences [q-bio]/Vegetal Biology, pit membrane thickness
Abstract

Investigating the responses of plant anatomical traits of trees to drought–rewatering cycles helps us to understand their responses to climate change; however, such work has not been adequately reported. In this study, Ginkgo biloba L. saplings were subjected to moderate, severe, extreme and lethal drought conditions by withholding water according to the percentage loss of hydraulic conductivity (PLC) and rewatering on a regular basis. Samples of phloem, cambium and xylem were collected to quantify their cellular properties including cambium and phloem cell vitality, xylem growth ring width, pit aspiration rates and pit membrane thickness using light microscopy and transmission microscopy. The results showed that the mortality rate of G. biloba saplings reached 90% at approximately P88 (xylem water potential inducing 88% loss of hydraulic conductivity). The onset of cambium and phloem cell mortality might be in accordance with that of xylem embolism. Close negative correlations between xylem water potential and PLC and between xylem water potential and cambium and phloem mortality suggested that xylem hydraulic traits are coupled with anatomical traits under declining xylem water potential. Cambium and phloem cell vitality as well as xylem growth ring width decreased significantly with increasing drought conditions. However, xylem pit membrane thickness, cambial zone width and cambial cell geometry were not affected by the drought–rewatering cycles. The tracheid radial diameter, intertracheid cell wall thickness and tracheid density decreased significantly during both drought conditions and rewatering conditions. In addition to hydraulic traits, cambium and phloem cell vitality can be used as anatomical traits to evaluate the mortality of G. biloba under drought. Future work is proposed to observe the dynamics of pit aspiration rates under drought–rewatering cycles in situ to deepen our understanding of the essential role of bordered pits in the ‘air-seeding’ mechanism.

Published
2021
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3. State polynomials: positivity, optimization and nonlinear Bell inequalities

Author

Klep, Igor, Magron, Victor, Volčič, Jurij, Wang, Jie, Department of Mathematics (University of Ljubljana), University of Ljubljana, Equipe Polynomial OPtimization (LAAS-POP), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Drexel University, Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Slovenian Research Agency grants J1-2453, N1-0217, J1-3004 and P1-0222.Institut Quantique Occitan.PHC Proteus grant 46195TA.National Research Foundation, Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme.NSF grant DMS-1954709.NSFC grant 12201618., ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), and H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019)

Subjects
Mathematics - Functional Analysis, Quantum Physics, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Optimization and Control (math.OC), FOS: Mathematics, FOS: Physical sciences, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Quantum Physics (quant-ph), Mathematics - Optimization and Control, Functional Analysis (math.FA)
Abstract

This paper introduces state polynomials, i.e., polynomials in noncommuting variables and formal states of their products. A state analog of Artin's solution to Hilbert's 17th problem is proved showing that state polynomials, positive over all matrices and matricial states, are sums of squares with denominators. Somewhat surprisingly, it is also established that a Krivine-Stengle Positivstellensatz fails to hold in the state polynomial setting. Further, archimedean Positivstellens\"atze in the spirit of Putinar and Helton-McCullough are presented leading to a hierarchy of semidefinite relaxations converging monotonically to the optimum of a state polynomial subject to state constraints. This hierarchy can be seen as a state analog of the Lasserre hierarchy for optimization of polynomials, and the Navascu\'es-Pironio-Ac\'in scheme for optimization of noncommutative polynomials. The motivation behind this theory arises from the study of correlations in quantum networks. Determining the maximal quantum violation of a polynomial Bell inequality for an arbitrary network is reformulated as a state polynomial optimization problem. Several examples of quadratic Bell inequalities in the bipartite and the bilocal tripartite scenario are analyzed. To reduce the size of the constructed SDPs, sparsity, sign symmetry and conditional expectation of the observables' group structure are exploited. To obtain the above-mentioned results, techniques from noncommutative algebra, real algebraic geometry, operator theory, and convex optimization are employed.

Published
2023
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4. Exploiting Term Sparsity in Moment-SOS hierarchy for Dynamical Systems

Author

Magron, Victor, Wang, Jie, Schlosser, Corbinian, Korda, Milan, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Equipe Polynomial OPtimization (LAAS-POP), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011), ANR-18-ERC2-0004,COPS,Optimisation garantie pour la vérification des systèmes cyber-physiques(2018), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019), Magron, Victor, Artificial and Natural Intelligence Toulouse Institute - - ANITI2019 - ANR-19-P3IA-0004 - P3IA - VALID, Centre International de Mathématiques et d'Informatique (de Toulouse) - - CIMI2011 - ANR-11-LABX-0040 - LABX - VALID, TREMPLIN-ERC - Optimisation garantie pour la vérification des systèmes cyber-physiques - - COPS2018 - ANR-18-ERC2-0004 - TERC - VALID, Polynomial Optimization, Efficiency through Moments and Algebra - POEMA - - H20202019-01-01 - 2022-12-31 - 813211 - VALID, Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, and European Project: 813211,H2020,POEMA(2019)

Subjects
Optimization and Control (math.OC), FOS: Mathematics, 93C10, 93C15, 93C20, 90C22, 90C23, 34C11, 37C10, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control
Abstract

In this paper we present term sparsity sum-of-squares (TSSOS) methods applied to several problems from dynamical systems, such as region of attraction, maximum positively invariant sets and global attractors. We combine the TSSOS algorithm of Wang, Magron and Lasserre [SIAM J. Optim., 31(1):30-58, 2021] with existing infinite dimensional linear program representations of those sets. This leads to iterative schemes in the moment-sum-of-squares hierarchy which allows less expensive computations while keeping convergence guarantees. Finally this procedure is closely related to sign symmetries of the dynamical system as was already revealed for polynomial optimization. Numerical examples demonstrate the efficiency of the approach in the presence of appropriate sparsity., 16 pages

Published
2021

5. Anthracycline-free or short-term regimen as adjuvant chemotherapy for operable breast cancer: A phase III randomized non-inferiority trial

Author

Claire F. Verschraegen, Zhi-Ming Shao, Genhong Di, Daniel G. Stover, Mohammed A. Osman, Li Chen, Armando Orlandi, Giuseppe Lippi, Miao Mo, Lei Fan, François Bertucci, Jiong Wu, Jie Wang, Guangyu Liu, Ke-Jin Wu, Zhigang Zhuang, Ke-Da Yu, Xi-Yu Liu, Fudan University Shanghai Cancer Center [China], Centre de Recherche en Cancérologie de Marseille (CRCM), Aix Marseille Université (AMU)-Institut Paoli-Calmettes, Fédération nationale des Centres de lutte contre le Cancer (FNCLCC)-Fédération nationale des Centres de lutte contre le Cancer (FNCLCC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), University Hospital of Verona, Cooperative Institute for Mesoscale Meteorological Studies (CIMMS), and Southwest University [Chongqing]

Subjects
Oncology, medicine.medical_specialty, Anthracycline, Lymphovascular invasion, Population, [SDV.CAN]Life Sciences [q-bio]/Cancer, breast cancer, Breast cancer, Internal medicine, Internal Medicine, medicine, education, ComputingMilieux_MISCELLANEOUS, education.field_of_study, business.industry, Health Policy, Public Health, Environmental and Occupational Health, Obstetrics and Gynecology, Cancer, Anthracycline, breast cancer, phase III, trial, trial, medicine.disease, phase III, Psychiatry and Mental health, Regimen, Infectious Diseases, Docetaxel, Pediatrics, Perinatology and Child Health, Public aspects of medicine, RA1-1270, Geriatrics and Gerontology, business, medicine.drug, Epirubicin, Research Paper
Abstract

Background De-escalating anthracycline is gaining popularity for breast cancer patients. We aim to evaluate the non-inferiority of an anthracycline-free or short-term regimen to the standard anthracycline-based regimen for operable patients with human epidermal growth factor receptor 2 (HER2)-negative breast cancer. Methods It is a prospective, open-label, phase 3, randomized non-inferiority trial from June 1, 2010 to June 1, 2017. Follow-up had been kept until July 2019. This trial was conducted at Fudan University Shanghai Cancer Center. Patients with pT1–3N+ or pT2–3N0 but high-risk (grade II/III, lymphovascular invasion, ≤35 years of age or hormone-receptor negative) HER2-negative operable breast cancer were eligible and stratified by age, pathological tumour stage, pathological node status and hormone-receptor status. Patients were randomized to 6 cycles of docetaxel and cyclophosphamide (TC, n = 524), 3 cycles of cyclophosphamide/epirubicin/fluorouracil followed by 3 cycles of docetaxel (CEF-T, n = 523) or epirubicin and cyclophosphamide for 4 cycles followed by paclitaxel for 12 weeks (EC-P, n = 524) as the intention-to-treat population. Of these patients, 94% completed allocated therapy. Difference in disease-free survival (DFS) compared to EC-P. The prespecified non-inferiority margin was 4.5%, corresponding to the hazard ratio (HR) of 1.44 (one-sided α = 0.05), with an assumed 5-year DFS of 89% for EC-P. Findings Included in the intention-to-treat population were 1571 patients (median [IQR] age, 50 [45–57] years; 92% estrogen receptor [ER]-positive; 59% pN+). Through a median follow-up of 5.5 years, HR for TC versus EC-P was 1.05 (5-year DFS: 85.0% vs. 85.9%; 90% confidence interval [CI]: 0.79–1.39, non-inferior P = 0.048) and for CEF-T versus EC-P, 0.99 (5-year DFS: 85.1% vs. 85.9%; 90% CI: 0.75–1.30, non-inferior P = 0.045). Grade 3 or 4 adverse events for TC included rash (3.9%) and peripheral neuropathy (2.8%) and for CEF-T and EC-P diarrhea and nausea/vomiting were predominant. Results of per-protocol analyses were similar. Interpretation Both TC and CEF-T are non-inferior adjuvant regimen to EC-P mainly in patients with ER+HER2- breast cancer. TC is a safe regimen that avoids anthracycline-related side effects. Funding This work was supported by grants from the National Natural Science Foundation of China (Grants 81672600, 81722032, 82072916, and 91959207), the 2018 Shanghai Youth Excellent Academic Leader, the Fudan ZHUOSHI Project, the Municipal Project for Developing Emerging and Frontier Technology in Shanghai Hospitals (grant SHDC12010116), the Cooperation Project of Conquering Major Diseases in the Shanghai Municipality Health System (grant 2013ZYJB0302), the Innovation Team of the Ministry of Education (grant IRT1223), and the Shanghai Key Laboratory of Breast Cancer (grant 12DZ2260100) and the National Cancer Institute (grant P30 CA16058).

Published
2021
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6. Geometric Particle-in-Cell methods for the Vlasov-Maxwell equations with spin effects

Author

Yajuan Sun, Yingzhe Li, Giovanni Manfredi, Paul-Antoine Hervieux, Nicolas Crouseilles, Crouseilles, Nicolas, Multi-scale numerical geometric schemes (MINGUS), 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 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 (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), 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)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), 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 (UR), Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et Nanosciences Grand-Est (MNGE), Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Université de Strasbourg (UNISTRA), Max-Planck-Institut für Plasmaphysik [Garching] (IPP), Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-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)-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)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)-Inria Rennes – Bretagne Atlantique, Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UNIV-RENNES), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et nanosciences d'Alsace, Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Université de Strasbourg (UNISTRA)-Réseau nanophotonique et optique, Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Université de Strasbourg (UNISTRA), 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)-AGROCAMPUS OUEST, Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Inria Rennes – Bretagne Atlantique, Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Université de Strasbourg (UNISTRA)-Matériaux et nanosciences d'Alsace (FMNGE), Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, and Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)

Subjects
Physics, [PHYS.PHYS.PHYS-COMP-PH] Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], Semiclassical physics, Electron, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Condensed Matter Physics, 01 natural sciences, 7. Clean energy, Electromagnetic radiation, 010305 fluids & plasmas, [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], symbols.namesake, Distribution function, Maxwell's equations, Physics::Plasma Physics, Phase space, Quantum mechanics, 0103 physical sciences, symbols, Particle-in-cell, 010306 general physics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Spin-½
Abstract

We propose a numerical scheme to solve the semiclassical Vlasov–Maxwell equations for electrons with spin. The electron gas is described by a distribution function $f(t,{\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ that evolves in an extended 9-dimensional phase space $({\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ , where $\boldsymbol s$ represents the spin vector. Using suitable approximations and symmetries, the extended phase space can be reduced to five dimensions: $(x,{{p_x}}, {\boldsymbol s})$ . It can be shown that the spin Vlasov–Maxwell equations enjoy a Hamiltonian structure that motivates the use of the recently developed geometric particle-in-cell (PIC) methods. Here, the geometric PIC approach is generalized to the case of electrons with spin. Total energy conservation is very well satisfied, with a relative error below $0.05\,\%$ . As a relevant example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, where the electrons are partially or fully spin polarized. It is shown that the Raman instability is very effective in destroying the electron polarization.

Published
2021
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7. Image reconstruction through metamorphosis

Author

Ozan Öktem, Chong Chen, Barbara Gris, Department of Mathematics [Sweden] (KTH), Stockholm University, Centre National de la Recherche Scientifique (CNRS), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), and Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)

Subjects
FOS: Computer and information sciences, Computer Vision and Pattern Recognition (cs.CV), Computer Science - Computer Vision and Pattern Recognition, Structure (category theory), Stability (learning theory), 010103 numerical & computational mathematics, Iterative reconstruction, 01 natural sciences, Regularization (mathematics), Theoretical Computer Science, Image (mathematics), Convergence (routing), 0101 mathematics, [MATH]Mathematics [math], Mathematical Physics, Mathematics, Indirect registration, Metamorphosis, Applied Mathematics, 65F22, 65R32, 65R30, 65D18, 94A12, 94A08, 92C55, 54C56, 57N25, 47A52, Resolution (logic), Inverse problem, Computer Science Applications, 010101 applied mathematics, Signal Processing, Algorithm
Abstract

This article adapts the framework of metamorphosis to solve inverse problems in imaging that includes joint reconstruction and image registration. The deformations in question have two components, one that is a geometric deformation moving intensities and the other a deformation of intensity values itself, which, e.g., allows for appearance of a new structure. The idea developed here is to reconstruct an image from noisy and indirect observations by registering, via metamorphosis, a template to the observed data. Unlike a registration with only geometrical changes, this framework gives good results when intensities of the template are poorly chosen. We show that this method is a well-defined regularisation method (proving existence, stability and convergence) and present several numerical examples.

Published
2020
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8. Normal Forms for Rigid $\mathfrak{C}_{2,1}$ Hypersurfaces $M^5 \subset \mathbb{C}^3$

Author

Zhangchi Chen, Wei Guo Foo, Joël Merker, The Anh Ta, Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)

Subjects
Mathematics - Differential Geometry, Mathematics - Complex Variables, General Mathematics, Mathematics::Number Theory, 010102 general mathematics, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], Automorphism, 01 natural sciences, 010101 applied mathematics, Combinatorics, Formalism (philosophy of mathematics), Mathematics - Algebraic Geometry, Hypersurface, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Light cone, FOS: Mathematics, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], 0101 mathematics, [MATH]Mathematics [math], Complex Variables (math.CV), Algebraic Geometry (math.AG), Mathematics
Abstract

Consider a $2$-nondegenerate constant Levi rank $1$ rigid $\mathcal{C}^\omega$ hypersurface $M^5 \subset \mathbb{C}^3$ in coordinates $(z, \zeta, w = u + iv)$: \[ u = F\big(z,\zeta,\bar{z},\bar{\zeta}\big). \] The Gaussier-Merker model $u=\frac{z\bar{z}+ \frac{1}{2}z^2\bar{\zeta}+\frac{1}{2} \bar{z}^2 \zeta}{1-\zeta \bar{\zeta}}$ was shown by Fels-Kaup 2007 to be locally CR-equivalent to the light cone $\{x_1^2+x_2^2-x_3^2=0\}$. Another representation is the tube $u=\frac{x^2}{1-y}$. Inspired by Alexander Isaev, we study rigid biholomorphisms: \[ (z,\zeta,w) \longmapsto \big( f(z,\zeta), g(z,\zeta), \rho\,w+h(z,\zeta) \big) =: (z',\zeta',w'). \] The G-M model has 7-dimensional rigid automorphisms group. A Cartan-type reduction to an e-structure was done by Foo-Merker-Ta in 1904.02562. Three relative invariants appeared: $V_0$, $I_0$ (primary) and $Q_0$ (derived). In Pocchiola's formalism, Section 8 provides a finalized expression for $Q_0$. The goal is to establish the Poincar\'e-Moser complete normal form: \[ u = \frac{z\bar{z}+\frac{1}{2}\,z^2\bar{\zeta} +\frac{1}{2}\,\bar{z}^2\zeta}{ 1-\zeta\bar{\zeta}} + \sum_{a,b,c,d \atop a+c\geqslant 3}\, G_{a,b,c,d}\, z^a\zeta^b\bar{z}^c\bar{\zeta}^d, \] with $0 = G_{a,b,0,0} = G_{a,b,1,0} = G_{a,b,2,0}$ and $0 = G_{3,0,0,1} = {\rm Im}\, G_{3,0,1,1}$. We apply the method of Chen-Merker 1908.07867 to catch (relative) invariants at every point, not only at the central point, as the coefficients $G_{0,1,4,0}$, $G_{0, 2, 3, 0}$, ${\rm Re} G_{3,0,1,1}$. With this, a brige Poincar\'e $\longleftrightarrow$ Cartan is constructed. In terms of $F$, the numerators of $V_0$, $I_0$, $Q_0$ incorporate 11, 52, 824 differential monomials., Comment: This work was supported in part by the Polish National Science Centre (NCN) via the grant number 2018/29/B/ST1/02583

Published
2019

9. Enumerating the morphologies of non-degenerate Darboux cyclides

Author

Bernard Mourrain, Xiaohong Jia, Mingyang Zhao, Wenping Wang, Changhe Tu, Key Laboratory of Mathematics Mechanization (KLMM), Chinese Academy of Sciences [Changchun Branch] (CAS)-Institute of Systems Science (ISS), China-Academy of Mathematics and Systems Science [Beijing], National Center for Mathematics and Interdisciplinary Sciences [Beijing] (NCMIS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS)-Chinese Academy of Sciences [Beijing] (CAS), Computer Graphics Group [Hong Kong], Department of Computer Science [Hong Kong], City University of Hong Kong [Hong Kong] (CUHK)-City University of Hong Kong [Hong Kong] (CUHK), Shandong University, AlgebRe, geOmetrie, Modelisation et AlgoriTHmes (AROMATH), Inria Sophia Antipolis - Méditerranée (CRISAM), and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-National and Kapodistrian University of Athens (NKUA)

Subjects
Surface (mathematics), Pure mathematics, Quadric, Degenerate energy levels, Aerospace Engineering, Stereographic projection, 020207 software engineering, Darboux cyclides, morphologies, 02 engineering and technology, 01 natural sciences, Computer Graphics and Computer-Aided Design, 0104 chemical sciences, Segre characteristic, 010404 medicinal & biomolecular chemistry, stereographic projection, Intersection, Modeling and Simulation, Automotive Engineering, 0202 electrical engineering, electronic engineering, information engineering, Enumeration, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Algebraic number, index sequences, Mathematics
Abstract

We provide an enumeration of all possible morphologies of non-degenerate Darboux cyclides. Based on the fact that every Darboux cyclide in R 3 is the stereographic projection of the intersection surface of a sphere and a quadric in R 4 , we transform the enumeration problem of morphologies of Darboux cyclides to the enumeration of the algebraic sequences that characterize the intersection of a sphere and a quadric in R 4 .

Published
2019
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10. Joint Image Reconstruction and Motion Estimation for Spatiotemporal Imaging

Author

Chen, Chong, Gris, Barbara, Öktem, Ozan, Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics (KTH Royal Institute of Technology), Royal Institute of Technology [Stockholm] (KTH ), and Gris, Barbara

Subjects
Large diffeomorphic deformations, Image reconstruction, AMS subject classifications.65F22, 65R32, 65R30, 65D18, 65J22, 65J20, 65L09, 68U10, 94A12, 94A08, 92C55, 54C56, 57N25, 47A52, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Joint variational model, [MATH] Mathematics [math], [MATH]Mathematics [math], Motion estimation, Shape theory, Spatiotemporal imaging
Abstract

International audience; We propose a variational model for joint image reconstruction and motion estimation applicable to spatiotemporal imaging. This model consists of two parts, one that conducts image reconstruction in a static setting and another that estimates the motion by solving a sequence of coupled indirect image registration problems, each formulated within the large deformation diffeomorphic metric mapping framework. The proposed model is compared against alternative approaches (optical flow based model and diffeomorphic motion models). Next, we derive efficient algorithms for a time-discretized setting and show that the optimal solution of the time-discretized formulation is consistent with that of the time-continuous one. The complexity of the algorithm is characterized and we conclude by giving some numerical examples in 2D space + time tomography with very sparse and/or highly noisy data

Published
2019

11. ON LOWER BOUNDS AT BLOW UP OF SCALE INVARIANT NORMS FOR THE NAVIER-STOKES EQUATIONS

Author

Chemin, Jean-Yves, Gallagher, Isabelle, Zhang, Ping, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Département de Mathématiques et Applications - ENS Paris (DMA), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Université Paris Diderot - Paris 7 (UPD7), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics::Fluid Dynamics, Incompressible Navier-Stokes Equations, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Mathematics::Analysis of PDEs, Anisotropic, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], AMS Subject Classification (2000): 35Q30, 76D03, Littlewood-Paley Theory, Blow-up criteria
Abstract

In this work we investigate the problem of preventing the incompressible 3D Navier-Stokes from developing singularities with the control of one component of the velocity field only in L ∞ norm in times with values in a scaling invariant space. We introduce a space " almost " invariant under the action of the scaling such that if one component measured in this space remains small enough, then there is no blow up.

Published
2018

12. Sur la contrôlabilité de l'équation de Navier-Stokes dans un rectangle avec l'aide d'une force fantôme distribuée

Author

Coron, Jean-Michel, Marbach, Fr��d��ric, Sueur, Franck, Zhang, Ping, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UNIV-RENNES), Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Hua Loo-Keng Key Laboratory of Mathematic [Beijing], Université de Rennes (UR), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mathematics - Analysis of PDEs, 35Q30, 93B05, 93C20, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Computer Science - Systems and Control, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Systems and Control (eess.SY), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Analysis of PDEs (math.AP)
Abstract

This note echoes the talk given by the second author during the Journ\'ees EDP 2018 in Obernai. Its aim is to provide an overview and a sketch of proof of the result obtained by the authors, concerning the controllability of the Navier-Stokes equation. We refer the interested readers to the original paper for the full technical details of the proof, which will be omitted here, to focus on the main underlying ideas., Comment: Notes on arxiv:1801.01860

Published
2018

13. On the controllability of the Navier-Stokes equation in a rectangle, with a little help of a distributed phantom force

Author

Coron, Jean-Michel, Marbach, Frédéric, Sueur, Franck, Zhang, Ping, Marbach, Frédéric, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UNIV-RENNES), Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), and Hua Loo-Keng Key Laboratory of Mathematic [Beijing]

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

International audience; This note echoes the talk given by the second author during the Journées EDP 2018 in Obernai. Its aim is to provide an overview and a sketch of proof of the result obtained by the authors, concerning the controllability of the Navier-Stokes equation. We refer the interested readers to the original paper for the full technical details of the proof, which will be omitted here, to focus on the main underlying ideas.

Published
2018

14. MINIMALITY OF p-ADIC RATIONAL MAPS WITH GOOD REDUCTION

Author

Fan, Ai-Hua, Fan, Shilei, Liao, Lingmin, Wang, Yuefei, Laboratoire Amiénois de Mathématique Fondamentale et Appliquée (LAMFA), Université de Picardie Jules Verne (UPJV)-Centre National de la Recherche Scientifique (CNRS), Central China Normal University (CCNU), Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), ANR-11-JS01-0009,MUTADIS,Multifractales et Théorie Métrique de l'Approximation Diophantienne(2011), Central China Normal University [Wuhan, China], and Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM)

Subjects
good reduction, projective line, rational map, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], FOS: Mathematics, minimal decomposition, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, p-adic dynamical system, 37P05, 11S82, 37B05
Abstract

A rational map with good reduction in the field $\mathbb{Q}\_p$ of $p$-adic numbers defines a $1$-Lipschitz dynamical system on the projective line $\mathbb{P}^1(\mathbb{Q}\_p)$ over $\mathbb{Q}\_p$. The dynamical structure of such a system is completely described by a minimal decomposition. That is to say, $\mathbb{P}^1(\mathbb{Q}\_p)$ is decomposed into three parts: finitely many periodic orbits; finite or countably many minimal subsystems each consisting of a finite union of balls; and the attracting basins of periodic orbits and minimal subsystems. For any prime $p$, a criterion of minimality for rational maps with good reduction is obtained. When $p=2$, a condition in terms of the coefficients of the rational map is proved to be necessary for the map being minimal and having good reduction, and sufficient for the map being minimal and $1$-Lipschitz. It is also proved that a rational map having good reduction of degree $2$, $3$ and $4$ can never be minimal on the whole space $\mathbb{P}^1(\mathbb{Q}\_2)$., 21 pages

Published
2017

15. Hasse principle and weak approximation for multinorm equations

Author

Cyril Demarche, Dasheng Wei, Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), and Chinese Academy of Sciences [Beijing] (CAS)

Subjects
Conjecture, Mathematics - Number Theory, General Mathematics, Mathematical analysis, Separable space, Combinatorics, Mathematics - Algebraic Geometry, Hasse principle, Field extension, Norm (mathematics), FOS: Mathematics, Number Theory (math.NT), [MATH]Mathematics [math], Algebra over a field, Algebraic Geometry (math.AG), Global field, Mathematics, Counterexample
Abstract

In this note, we are interested in local-global principles for multinorm equations of the form $\prod_{i=1}^n N_{L_i /k}(z_i) = a$ where $k$ is a global field, $L_i/k$ are finite separable field extensions and $a \in k^*$. In particular, we prove a result relating weak approximation for this equation to weak approximation for some classical norm equation $N_{F/k}(w) = a$ where $F := \bigcap_{i=1}^n L_i$. It provides a proof of a "weak approximation" analogue of a recent conjecture by Pollio and Rapinchuk about multinorm principle. We also provide a counterexample to the original conjecture concerning Hasse principle., Comment: 14 pages, Final version

Published
2014
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16. Global Unique Solvability of Inhomogeneous Navier-Stokes Equations with Bounded Density

Author

Ping Zhang, Zhifei Zhang, Marius Paicu, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), School of Mathematical Sciences, Peking University, 100871, P. R. China, and School of Mathematical Sciences, Peking University, China

Subjects
Applied Mathematics, 010102 general mathematics, Mathematical analysis, 35Q30, 76D05, Mathematics::Analysis of PDEs, 01 natural sciences, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Physics::Fluid Dynamics, 010101 applied mathematics, Lagrangian and Eulerian specification of the flow field, Mathematics - Analysis of PDEs, Bounded function, FOS: Mathematics, Compressibility, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Uniqueness, 0101 mathematics, Navier–Stokes equations, Analysis, Well posedness, Analysis of PDEs (math.AP), Mathematics
Abstract

International audience; In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for $d=2,3$) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from above and below by some positive constants, and with initial velocity $u_0\in H^s(\R^2)$ for $s>0$ in 2-D, or $u_0\in H^1(\R^3)$ satisfying $\|u_0\|_{L^2}\|\nabla u_0\|_{L^2}$ being sufficiently small in 3-D. This in particular improves the most recent well-posedness result in [10], which requires the initial velocity $u_0\in H^2(\R^d)$ for the local well-posedness result, and a smallness condition on the fluctuation of the initial density for the global well-posedness result.

Published
2013
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17. Prediction of human population responses to toxic compounds by a collaborative competition

Author

Eduati, F, Mangravite, L, Wang, T, Tang, Hongxiang, Bare, J, Huang, R, Norman, T, Kellen, M, Menden, M, Yang, J, Zhan, X, Zhong, R, Xiao, G, Xia, M, Abdo, N, Kosyk, O, Friend, S, Stolovitzky, G, Dearry, A, Tice, R, Simeonov, S, Rusyn, I, Wright, F, Xie, Y, Alaimo, S, Amadoz, A, Ammad-ud-din, M, Chloé-Azencott, A, Bacardit, J, Barron, P, Bernard, E, Beyer, A, Bin, S, van Bömmel, A, Borgwardt, K, Brys, A, Caffrey, B, Chang, J, Christodoulou, E, Clément-Ziza, M, Cohen, T, Cowherd, M, Demeyer, S, Dopazo, J, Elhard, J, Falcao, A, Ferro, A, Friedenberg, D, Giugno, R, Gong, Y, Gorospe, J, Granville, C, Grimm, D, Heinig, M, Hernansaiz, R, Hochreiter, S, Liang-Huang, C, Huska, M, Jiao, Y, Klambauer, G, Kuhn, M, Kursa, M, Kutum, R, Lazzarini, N, Lee, I, Leung, M, K W, Lim, Liu, C, F L, López, Mammana, A, Mayr, A, Michoel, T, Mongiovì, M, Moore, J, Narasimhan, R, Opiyo, S, Pandey, G, Peabody, A, Perner, J, Pulvirenti, A, Rawlik, K, Reinhardt, S, Riffle, C, Ruderfer, D, Sander, A, Savage, R, Scornet, E, Sebastian-Leon, P, Sharan, R, Simon-Gabriel, C, Stoven, V, Sun, J, Tang, H, Teixeira, A, Tenesa, A, Jean-Vert, P, Vingron, M, Walter, T, Whalen, S, Wiśniewska, Z, Wu, Y, Xu, H, Zhang, S, Zhao, J, W Zheng J, Ziwei, D, Simeonov, A, Raymond, R Tice, Saez-Rodriguez, J., NIEHS-NCATS-UNC DREAM Toxicogenetics Collaboration, Institut de Recherche pour le Développement (IRD), National Center for Advancing Translational Sciences (NCATS), National Institutes of Health [Bethesda] (NIH), Data Storage Institute - A*STAR, Capital Normal University [Beijing], Southwest University of China, sans affiliation, Shanghai Ocean University, Centre de Bioinformatique (CBIO), MINES ParisTech - École nationale supérieure des mines de Paris-PSL Research University (PSL), Cancer et génôme: Bioinformatique, biostatistiques et épidémiologie d'un système complexe, MINES ParisTech - École nationale supérieure des mines de Paris-Institut Curie-Institut National de la Santé et de la Recherche Médicale (INSERM), Institut National de l'Information Géographique et Forestière [IGN] (IGN), Systèmes Productifs, Logistique, Organisation des Transports et Travail (IFSTTAR/AME/SPLOTT), Communauté Université Paris-Est-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR), Biotechnology Center [Dresden] (BIOTEC), Technische Universität Dresden (TUD), Laboratoire National de Métrologie et d'Essais [Trappes] (LNE ), Centre for Biomedical Network Research on Rare Diseases (CIBERER), Department of Computational Genomics, Centro de Investigación Príncipe Felipe (CIPF), Functional Genomics Node (INB), CIPF, Computational Intelligence Research Group (CA3), Centre of Technology and Systems (CTS), Faculty of Sciences and Technology (FCT NOVA), Universidade Nova de Lisboa (NOVA)-Universidade Nova de Lisboa (NOVA)-Faculty of Sciences and Technology (FCT NOVA), Universidade Nova de Lisboa (NOVA)-Universidade Nova de Lisboa (NOVA)-Faculdade de Ciências e Tecnologia (FCT NOVA), Universidade Nova de Lisboa (NOVA), ACEEE, The Institute of Doctors Engineers and Scientists - IDES, Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Laboratory of Information, Network and Communication Sciences (LINCS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Mines-Télécom [Paris] (IMT), Institute of Computational Biology, Helmholtz-Zentrum München (HZM), Stony Brook University [SUNY] (SBU), State University of New York (SUNY), University of Pensylvania, Institute for Infocomm Research - I²R [Singapore], Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, Department of Mechanical and Aerospace Engineering [Davis], University of California [Davis] (UC Davis), University of California-University of California, Commonwealth Scientific and Industrial Research Organisation [Canberra] (CSIRO), Ludwig-Maximilians-Universität München (LMU), Laboratoire Architecture, Ville, Urbanisme, Environnement (LAVUE), École nationale supérieure d'architecture de Paris-La Villette (ENSAPLV)-École nationale supérieure d'architecture de Paris Val-de-Seine (ENSA PVDS)-Université Paris 8 Vincennes-Saint-Denis (UP8)-Ministère de la Culture (MC)-Université Paris Nanterre (UPN)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Statistique Théorique et Appliquée (LSTA), Université Pierre et Marie Curie - Paris 6 (UPMC), Agricultural Technological Extensive Station of Luntai County in Xinjiang, Medstar Research Institute, Huawei Technologies [Shanghaï], School of Economics and Business Administration (School of Economics and Business Administration), Beijing Normal University, National Center for Mathematics and Interdisciplinary Sciences [Beijing] (NCMIS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS)-Chinese Academy of Sciences [Beijing] (CAS), Division of Biostatistics, Helmholtz-Institute for Biomedical Engineering [RWTH Aachen University], European Bioinformatics Institute [Hinxton] (EMBL-EBI), EMBL Heidelberg, Agricultural Information Institute (AII), Chinese Academy of Agricultural Sciences (CAAS), Department of Computer Science - Lafayette College, Lafayette College [Easton], MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Cancer et génome: Bioinformatique, biostatistiques et épidémiologie d'un système complexe, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut Curie [Paris]-Institut National de la Santé et de la Recherche Médicale (INSERM), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Communauté Université Paris-Est, Technische Universität Dresden = Dresden University of Technology (TU Dresden), Faculdade de Ciências e Tecnologia = School of Science & Technology (FCT NOVA), Universidade Nova de Lisboa = NOVA University Lisbon (NOVA)-Universidade Nova de Lisboa = NOVA University Lisbon (NOVA)-Faculdade de Ciências e Tecnologia = School of Science & Technology (FCT NOVA), Universidade Nova de Lisboa = NOVA University Lisbon (NOVA)-Universidade Nova de Lisboa = NOVA University Lisbon (NOVA), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Paris 8 Vincennes-Saint-Denis (UP8)-École nationale supérieure d'architecture de Paris-La Villette (ENSAPLV)-Université Paris Nanterre (UPN)-École nationale supérieure d'architecture de Paris Val-de-Seine (ENSA PVDS)-Centre National de la Recherche Scientifique (CNRS)-Ministère de la Culture (MC), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Beijing Normal University (BNU), Sans affiliation, Mines Paris - PSL (École nationale supérieure des mines de Paris), Helmholtz Zentrum München = German Research Center for Environmental Health, Université Fédérale Toulouse Midi-Pyrénées-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse III - Paul Sabatier (UT3), Department of Mechanical and Aerospace Engineering [Univ California Davis] (MAE - UC Davis), University of California (UC)-University of California (UC), Université Paris 8 Vincennes-Saint-Denis (UP8)-École nationale supérieure d'architecture de Paris-La Villette (ENSAPLV), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Université Paris Nanterre (UPN)-École nationale supérieure d'architecture de Paris Val-de-Seine (ENSA PVDS)-Centre National de la Recherche Scientifique (CNRS)-Ministère de la Culture (MC), Centre National de la Recherche Scientifique (CNRS)-Université Paris Nanterre (UPN)-Ministère de la Culture (MC)-Université Paris 8 Vincennes-Saint-Denis (UP8)-École nationale supérieure d'architecture de Paris Val-de-Seine (ENSA PVDS)-École nationale supérieure d'architecture de Paris-La Villette (ENSAPLV), Institut Mines-Télécom [Paris] (IMT)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Pierre et Marie Curie - Paris 6 (UPMC), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT), and MINES ParisTech - École nationale supérieure des mines de Paris-Institut Curie [Paris]-Institut National de la Santé et de la Recherche Médicale (INSERM)

Subjects
Bioinformatics, MESH: Risk Assessment, Applied Microbiology and Biotechnology, MESH: Dose-Response Relationship, Drug, Genotype, MESH: Incidence, MESH: Models, Genetic, Cytotoxicity, ComputingMilieux_MISCELLANEOUS, media_common, education.field_of_study, High-throughput screening, MESH: Genetic Predisposition to Disease, drug, [SDV.BIBS]Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Trait, Molecular Medicine, Health occupations, Predictive medicine, Risk factors, Risk assessment, Biotechnology, data mining, expression, MESH: High-Throughput Screening Assays, media_common.quotation_subject, Population, Biomedical Engineering, MESH: Genetics, Population, Bioengineering, Computational biology, Biology, Competition (biology), Article, MESH: Computer Simulation, ddc:570, 1000 Genomes Project, education, MESH: Toxicity Tests, ta113, MESH: Humans, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], MESH: Hazardous Substances, MESH: Lymphocytes, [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM], RA
Abstract

The ability to computationally predict the effects of toxic compounds on humans could help address the deficiencies of current chemical safety testing. Here, we report the results from a community-based DREAM challenge to predict toxicities of environmental compounds with potential adverse health effects for human populations. We measured the cytotoxicity of 156 compounds in 884 lymphoblastoid cell lines for which genotype and transcriptional data are available as part of the Tox21 1000 Genomes Project. The challenge participants developed algorithms to predict interindividual variability of toxic response from genomic profiles and population-level cytotoxicity data from structural attributes of the compounds. 179 submitted predictions were evaluated against an experimental data set to which participants were blinded. Individual cytotoxicity predictions were better than random, with modest correlations (Pearson's r < 0.28), consistent with complex trait genomic prediction. In contrast, predictions of population-level response to different compounds were higher (r < 0.66). The results highlight the possibility of predicting health risks associated with unknown compounds, although risk estimation accuracy remains suboptimal., Nature Biotechnology, 33 (9), ISSN:1546-1696, ISSN:1087-0156

Published
2015
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18. Minimal rational curves on wonderful group compactifications

Author

Brion, Michel, Fu, Baohua, Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Rolland, Ariane, Institut Fourier (IF), and Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)

Subjects
Mathematics - Algebraic Geometry, FOS: Mathematics, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Algebraic Geometry (math.AG)
Abstract

Consider a simple algebraic group G of adjoint type, and its wonderful compactification X. We show that X admits a unique family of minimal rational curves, and we explicitly describe the subfamily consisting of curves through a general point. As an application, we show that X has the target rigidity property when G is not of type A_1 or C., 16p

Published
2015

19. Inhomogeneous Navier-Stokes equations in the half-space, with only bounded density

Author

Danchin, Raphael, Zhang, Ping, Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), and Danchin, Raphaël

Subjects
Mathematics - Analysis of PDEs, 35Q30, 76D03, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Analysis of PDEs (math.AP)
Abstract

43 pages, submitted paper; International audience; In this paper, we establish the global existence of small solutions to the inhomo- geneous Navier-Stokes system in the half-space. The initial density only has to be bounded and close enough to a positive constant, and the initial velocity belongs to some critical Besov space. With a little bit more regularity for the initial velocity, those solutions are proved to be unique. In the last section of the paper, our results are partially extended to the bounded domain case.

Published
2014

20. Global large solutions to 3-D inhomogeneous Navier-Stokes system with one slow variable

Author

Marius Paicu, Jean-Yves Chemin, Ping Zhang, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Littlewood–Paley theory, Applied Mathematics, 35Q30, 76D03, Isotropy, Mathematical analysis, Mathematics::Analysis of PDEs, Probability density function, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Nonlinear system, Mathematics - Analysis of PDEs, Norm (mathematics), Compressibility, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Vector field, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Anisotropy, Analysis, Mathematics, Analysis of PDEs (math.AP)
Abstract

In this paper, we are concerned with the global wellposedness of 3-D inhomogeneous incompressible Navier-Stokes equations \eqref{1.3} in the critical Besov spaces with the norm of which are invariant by the scaling of the equations and under a nonlinear smallness condition on the isentropic critical Besov norm to the fluctuation of the initial density and the critical anisotropic Besov norm of the horizontal components of the initial velocity which have to be exponentially small compared with the critical anisotropic Besov norm to the third component of the initial velocity. The novelty of this results is that the isentropic space structure to the homogeneity of the initial density function is consistent with the propagation of anisotropic regularity for the velocity field. In the second part, we apply the same idea to prove the global wellposedness of \eqref{1.3} with some large data which are slowly varying in one direction.

Published
2013
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21. Symplectic resolutions for conical symplectic varieties

Author

Baohua Fu, Michel Brion, Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Institut Fourier (IF), and Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)

Subjects
Symplectic group, General Mathematics, 010102 general mathematics, Mathematics::Rings and Algebras, 14L30, 14E15, 17B08, Symplectic representation, 01 natural sciences, Symplectic matrix, Algebra, Mathematics - Algebraic Geometry, Symplectic vector space, 0103 physical sciences, FOS: Mathematics, 010307 mathematical physics, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], 0101 mathematics, Symplectomorphism, Mathematics::Representation Theory, Moment map, Mathematics::Symplectic Geometry, Algebraic Geometry (math.AG), Symplectic manifold, Symplectic geometry, Mathematics
Abstract

We introduce the notion of a conical symplectic variety, and show that any symplectic resolution of such a variety is isomorphic to the Springer resolution of a nilpotent orbit in a semisimple Lie algebra, composed with a linear projection., Comment: Final version to appear in IMRN

Published
2013
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22. Decay estimates of global solutions to 2D incompressible inhomogeneous Navier-Stokes equations with variable viscosity

Author

Huang, Jingchi, Paicu, Marius, Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Institut de Mathématiques de Bordeaux (IMB), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
35Q30, 76D03, Mathematics::Analysis of PDEs, Classical Physics (physics.class-ph), FOS: Physical sciences, Physics - Classical Physics, Decay estimates, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Physics::Fluid Dynamics, Inhomogeneous Navier-Stokes equations, Mathematics - Analysis of PDEs, FOS: Mathematics, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Analysis of PDEs (math.AP)
Abstract

In this paper, we investigate the time decay behavior to Lions weak solution of 2D incompressible density-dependent Navier-Stokes equations with variable viscosity., arXiv admin note: text overlap with arXiv:1301.2371 by other authors

Published
2012

23. Global wellposedness to incompressible inhomogeneous fluid system with bounded density and non-Lipschitz velocity

Author

Jingchi Huang, Ping Zhang, Marius Paicu, Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Institut de Mathématiques de Bordeaux (IMB), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mathematics::Analysis of PDEs, Context (language use), 01 natural sciences, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Littlewood-Paley theory, Mathematics (miscellaneous), Inhomogeneous Navier-Stokes equations, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics, Scaling, Heat kernel, Mathematics, maximal regularity for heat kernel, Mathematics::Operator Algebras, Mechanical Engineering, 010102 general mathematics, Mathematical analysis, Lipschitz continuity, 010101 applied mathematics, Bounded function, Compressibility, Vector field, Analysis, Analysis of PDEs (math.AP)
Abstract

In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier-Stokes equations with initial data in critical Besov spaces, which satisfies a non-linear smallness condition. The regularity of the initial velocity is critical to the scaling of this system and is general enough to generate non-Lipschitz velocity field. Furthermore, with additional regularity assumption on the initial velocity or on the initial density, we can also prove the uniqueness of such solution. We should mention that the classical maximal regularity theorem for the heat kernel plays an essential role in this context.

Published
2012

24. k-Chordal Graphs: from Cops and Robber to Compact Routing via Treewidth

Author

Bi Li, Adrian Kosowski, Nicolas Nisse, Karol Suchan, Algorithmics for computationally intensive applications over wide scale distributed platforms (CEPAGE), Université Sciences et Technologies - Bordeaux 1 (UB)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), 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), Algorithms, simulation, combinatorics and optimization for telecommunications (MASCOTTE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-COMmunications, Réseaux, systèmes Embarqués et Distribués (Laboratoire I3S - COMRED), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Facultad de Ingeniería y Ciencias [Santiago], Universidad Adolfo Ibáñez [Santiago], Partially supported by programs Fondap and Basal-CMM, Anillo ACT88 and Fondecyt 11090390 (K.S.), FP7 STREP EULER (B.L.,N.N.), INRIA, ANR-09-BLAN-0159,AGAPE,Algorithmes de graphes parametres et exacts(2009), European Project: 258307,EC:FP7:ICT,FP7-ICT-2009-5,EULER(2010), Université Sciences et Technologies - Bordeaux 1-Inria Bordeaux - Sud-Ouest, Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Networks, Graphs and Algorithms (GANG), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institute of Applied Mathematics, AAMS, CAS, Combinatorics, Optimization and Algorithms for Telecommunications (COATI), Faculty of Applied Mathematics [Krakow], AGH University of Science and Technology [Krakow, PL] (AGH UST), ANR-11-BS02-0014,DISPLEXITY,Calculabilité et complexité en distribué(2011), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Mathieu, Fabien et Hanusse, and Nicolas

Subjects
hyperbolicity, General Computer Science, Routing table, Treewidth, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], 0102 computer and information sciences, 02 engineering and technology, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], Tree-depth, 01 natural sciences, Combinatorics, Indifference graph, Pathwidth, Chordal graph, Computer Science::Discrete Mathematics, Partial k-tree, chordality, 0202 electrical engineering, electronic engineering, information engineering, Mathematics, Distance-hereditary graph, Discrete mathematics, cops and robber games, compact routing, Applied Mathematics, 1-planar graph, Computer Science Applications, 010201 computation theory & mathematics, Theory of computation, 020201 artificial intelligence & image processing
Abstract

Cops and robber games, introduced by Winkler and Nowakowski (in Discrete Math. 43(2---3), 235---239, 1983) and independently defined by Quilliot (in J. Comb. Theory, Ser. B 38(1), 89---92, 1985), concern a team of cops that must capture a robber moving in a graph. We consider the class of k-chordal graphs, i.e., graphs with no induced (chordless) cycle of length greater than k, k?3. We prove that k?1 cops are always sufficient to capture a robber in k-chordal graphs. This leads us to our main result, a new structural decomposition for a graph class including k-chordal graphs. We present a polynomial-time algorithm that, given a graph G and k?3, either returns an induced cycle larger than k in G, or computes a tree-decomposition of G, each bag of which contains a dominating path with at most k?1 vertices. This allows us to prove that any k-chordal graph with maximum degree Δ has treewidth at most (k?1)(Δ?1)+2, improving the O(Δ(Δ?1)k?3) bound of Bodlaender and Thilikos (Discrete Appl. Math. 79(1---3), 45---61, 1997. Moreover, any graph admitting such a tree-decomposition has small hyperbolicity). As an application, for any n-vertex graph admitting such a tree-decomposition, we propose a compact routing scheme using routing tables, addresses and headers of size O(klogΔ+logn) bits and achieving an additive stretch of O(klogΔ). As far as we know, this is the first routing scheme with O(klogΔ+logn)-routing tables and small additive stretch for k-chordal graphs.

Published
2012

25. Fast Computation of Common Left Multiples of Linear Ordinary Differential Operators

Author

Bruno Salvy, Éric Schost, Romain Lebreton, Muhammad F. I. Chowdhury, Alin Bostan, Algorithms (ALGORITHMS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Symbolic Special Functions : Fast and Certified (SPECFUN), Inria Saclay - Ile de France, Key Laboratory of Mathematics Mechanization (KLMM), Chinese Academy of Sciences [Changchun Branch] (CAS)-Institute of Systems Science (ISS), China-Academy of Mathematics and Systems Science [Beijing], Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Arithmetic and Computing (ARIC), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), van Hoeij, Mark and van der Hoeven, Joris, École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL)

Subjects
Power series, Large class, Computer Science - Symbolic Computation, FOS: Computer and information sciences, Polynomial, Logarithm, Differential equation, Computation, G.1.7, ACM: I.: Computing Methodologies/I.1: SYMBOLIC AND ALGEBRAIC MANIPULATION/I.1.2: Algorithms/I.1.2.0: Algebraic algorithms, 0102 computer and information sciences, 010103 numerical & computational mathematics, Symbolic Computation (cs.SC), 01 natural sciences, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Applied mathematics, 0101 mathematics, Multiple, Mathematics, Discrete mathematics, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], 68Q25, 34A30, 68W30, 010102 general mathematics, General Medicine, Operator theory, Differential operator, Polynomial matrix, I.1.2, 010201 computation theory & mathematics, Linear algebra, F.2.1, Order of magnitude, Differential (mathematics)
Abstract

We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We propose a new algorithm that recasts the LCLM computation in a linear algebra problem on a polynomial matrix. This algorithm yields sharp bounds on the coefficient degrees of the LCLM, improving by one order of magnitude the best bounds obtained using previous algorithms. The complexity of the new algorithm is almost optimal, in the sense that it nearly matches the arithmetic size of the output., Comment: The final version will appear in Proceedings of ISSAC 2012

Published
2012
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26. Lectures on the analysis of nonlinear partial differential equations. Part 2

Author

Lin, Fanghua, Wang, Xue Ping, Zhang, Ping, Courant Institute of Mathematical Sciences [New York] (CIMS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), Equations aux dérivées partielles, Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), Academy of Mathematics and Systems Science (AMSS), and Chinese Academy of Sciences [Beijing] (CAS)

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Published
2012

27. Lectures on the analysis of nonlinear partial differential equations. Part 1

Author

Lin, Fanghua, Wang, Xue Ping, Zhang, Ping, Courant Institute of Mathematical Sciences [New York] (CIMS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), Equations aux dérivées partielles, Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), Academy of Mathematics and Systems Science (AMSS), and Chinese Academy of Sciences [Beijing] (CAS)

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2012

28. Global solutions to 2-d inhomogeneous navier-stokes system with general velocity

Author

Huang, Jingchi, Paicu, Marius, Zhang, Ping, Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Institut de Mathématiques de Bordeaux (IMB), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics::Fluid Dynamics, Mathematics - Analysis of PDEs, Wellposedness, 35Q30, 76D03, Mathematics::Analysis of PDEs, FOS: Mathematics, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Littlewood-Paley Theory, Inhomogeneous Navier-Stokes Equations, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Analysis of PDEs (math.AP)
Abstract

International audience; In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations and under a non-linear smallness condition on fluctuation of the initial density which has to be doubly exponential small compared with the size of the initial velocity. In the second part of the paper, we apply our methods combined with the techniques of R. Danchin and P. B. Mucha to prove the global existence of solutions to inhomogeneous Navier-Stokes system with piecewise constant initial density which has small jump at the interface and is away from vacuum. In particular, this latter result removes the smallness condition for the initial velocity in a corresponding theorem of R. Danchin and P. B. Mucha.

Published
2012
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29. Global solutions to the 3-D incompressible inhomogeneous Navier-Stokes system

Author

Paicu, Marius, Zhang, Ping, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), and Chinese Academy of Sciences [Beijing] (CAS)

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], ComputingMilieux_MISCELLANEOUS, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]
Abstract

International audience

Published
2012

30. Global solutions to the 3-D incompressible anisotropic Navier-Stokes system in the critical spaces

Author

Marius Paicu, Ping Zhang, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), and Chinese Academy of Sciences [Beijing] (CAS)

Subjects
Mathematics::Functional Analysis, 010102 general mathematics, Mathematics::Analysis of PDEs, Statistical and Nonlinear Physics, Geometry, Mathematics::Spectral Theory, Type (model theory), 01 natural sciences, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], 010101 applied mathematics, Combinatorics, Critical space, Besov space, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Navier stokes, 0101 mathematics, Anisotropy, ComputingMilieux_MISCELLANEOUS, Mathematical Physics, Mathematics
Abstract

In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial data in the critical Besov-Sobolev type spaces \({\mathcal{B}}\) and \({\mathcal{B}^{-\frac12,\frac12}_4}\) (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANSν) has a unique global solution with initial data \({u_0 = (u_0^h, u_0^3)}\) which satisfies \({\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu}\) or \({\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu}\) for some c0 sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner type spaces, \({\widetilde{L^p_t}(\mathcal{B})}\), we introduced here sort of weighted Chemin-Lerner type spaces, \({\widetilde{L^2_{t, f}}(\mathcal{B})}\) for some apropriate L1 function f(t).

Published
2011

31. Complexity of Creative Telescoping for Bivariate Rational Functions

Author

Alin Bostan, Ziming Li, Frédéric Chyzak, Shaoshi Chen, Algorithms (ALGORITHMS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), and Stephen Watt

Subjects
Computer Science - Symbolic Computation, FOS: Computer and information sciences, Power series, Telescoping series, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], Hermite polynomials, 010102 general mathematics, Diagonal, 33F10, 010103 numerical & computational mathematics, Bivariate analysis, Rational function, Symbolic Computation (cs.SC), 01 natural sciences, creative telescoping, Reduction (complexity), Algebra, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Hermite reduction, 0101 mathematics, Differential (infinitesimal), complexity, Mathematics
Abstract

The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger's framework of (differential) creative telescoping. Our complexity-driven approach is to obtain tight degree bounds on the various expressions involved in the method. To make the problem more tractable, we restrict to bivariate rational functions. By considering this constrained class of inputs, we are able to blend the general method of creative telescoping with the well-known Hermite reduction. We then use our new method to compute diagonals of rational power series arising from combinatorics., Comment: 8 pages

Published
2010

32. Global Optimization of Polynomials Using Generalized Critical Values and Sums of Squares

Author

Lihong Zhi, Feng Guo, Mohab Safey El Din, Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Solvers for Algebraic Systems and Applications (SALSA), Laboratoire d'Informatique de Paris 6 (LIP6), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Discrete mathematics, Polynomial, Optimization problem, 010102 general mathematics, Explained sum of squares, Moment matrix, 010103 numerical & computational mathematics, 01 natural sciences, Infimum and supremum, Combinatorics, Bounded function, [INFO]Computer Science [cs], 0101 mathematics, Global optimization, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

Let X = [X1, ..., Xn] and f ∈ R[X]. We consider the problem of computing the global infimum of f when f is bounded below. For A ∈ GLn(C), we denote by fA the polynomial f(A X). Fix a number M ∈ R greater than infx∈Rnf(x). We prove that there exists a Zariski-closed subset A [equation] GLn(C) such that for all A ∈ GLn(Q) \ A, we have fA ≥ 0 on Rn if and only if for all e > 0, there exist sums of squares of polynomials s and t in R[X] and polynomials [Equation]. Hence we can formulate the original optimization problems as semidefinite programs which can be solved efficiently in Matlab. Some numerical experiments are given. We also discuss how to exploit the sparsity of SDP problems to overcome the ill-conditionedness of SDP problems when the infimum is not attained.

Published
2010
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33. Sums of large global solutions to the incompressible Navier-Stokes equations

Author

Chemin, Jean-Yves, Gallagher, Isabelle, Zhang, Ping, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Jussieu (IMJ), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), ANR-08-BLAN-0301-01,Math Ocean,Analyse mathématique en océanographie et applications(2008), and ANR-08-BLAN-0301,MathOcean,Analyse mathématique en océanographie et applications(2008)

Subjects
Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Analysis of PDEs (math.AP)
Abstract

Let G be the (open) set of~$\dot H^{\frac 1 2}$ divergence free vector fields generating a global smooth solution to the three dimensional incompressible Navier-Stokes equations. We prove that any element of G can be perturbed by an arbitrarily large, smooth divergence free vector field which varies slowly in one direction, and the resulting vector field (which remains arbitrarily large) is an element of G if the variation is slow enough. This result implies that through any point in G passes an uncountable number of arbitrarily long segments included in G., Accepted for publication in Journal f\"ur die reine und angewandte Mathematik

Published
2010

34. The Navier-Stokes-Vlasov-Fokker-Planck system near equilibrium

Author

Ayman Moussa, Thierry Goudon, Ping Zhang, Lingbing He, SImulations and Modeling for PArticles and Fluids (SIMPAF), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Mathematical Sciences, Tsinghua University [Beijing] (THU), Centre de Mathématiques et de Leurs Applications (CMLA), École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences [Beijing] (CAS), Laboratoire Paul Painlevé - UMR 8524 (LPP), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Numerical simulation of biological flows (REO), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, and Université de Lille-Centre National de la Recherche Scientifique (CNRS)

Subjects
Coupling, Physics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Vlasov equation, Phase (waves), Mathematics::Analysis of PDEs, 01 natural sciences, 010101 applied mathematics, Physics::Fluid Dynamics, Computational Mathematics, symbols.namesake, Classical mechanics, Stokes' law, Hypoelliptic operator, symbols, Compressibility, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Fokker–Planck equation, 0101 mathematics, Convection–diffusion equation, ComputingMilieux_MISCELLANEOUS, Analysis
Abstract

International audience; This paper is concerned with a system that couples the incompressible Navier-Stokes equations to the Vlasov-Fokker-Planck equation. Such a system arises in the modeling of sprays, where a dense phase interacts with a disperse phase. The coupling arises from the Stokes drag force exerted by a phase on the other. We study the global-in-time existence of classical solutions for data close to an equilibrium. We investigate further regularity properties of the solutions as well as their long time behavior. The proofs use energy estimates and the hypoelliptic structure of the system.

Published
2010
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35. General liquid-crystal theory for anisotropically shaped molecules: Symmetry, orientational order parameters, and system free energy.

Author

Xu J and Chen JZY

Abstract

A general theory of liquid crystals is presented, starting from the group-theory symmetry analysis of the constituting molecules. A particular attention is paid to the type of elastic free-energies and their relationships with the molecular symmetries. The orientational order-parameter tensors are identified for each molecular symmetry, in a consideration of consistently keeping the leading, characteristic elastic free energies in a model. The order parameters are expressed in terms of symmetric traceless tensors, some of high orders, for all major molecular symmetries, including seven groups of axial symmetries and seven groups of polyhedral symmetries. For spatially inhomogeneous liquid crystals, the couplings of these tensors in the elastic energies are derived by expanding the interaction energies between these molecules. The aim is to provide a general view of the molecular symmetries of individual molecules, orientational order parameters characterizing the orientational distribution functions, and the elastic free energies, all under one single group-theory approach.

Published
2020
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36. Lotka-Volterra system with Volterra multiplier.

Author

Gürlebeck K and Ji X

Subjects
Animals, Computational Biology, Food Chain, Mathematical Concepts, Models, Biological, Models, Statistical, Predatory Behavior, Ecology statistics & numerical data, Ecosystem
Abstract

With the aid of Volterra multiplier, we study ecological equations for both tree system and cycle system. We obtain a set of sufficient conditions for the ultimate boundedness to nonautonomous n-dimensional Lotka-Volterra tree systems with continuous time delay. The criteria are applicable to cooperative model, competition model, and predator-prey model. As to cycle system, we consider a three-dimensional predator-prey Lotka-Volterra system. In order to get a condition under which the system is globally asymptotic stable, we obtain a Volterra multiplier, so that in a parameter region the system is with the Volterra multiplier it is globally stable. We have also proved that in regions in which the condition is not satisfied, the system is unstable or at least it is not globally stable. Therefore, we say that the three-dimensional cycle system is with global bifurcation.

Published
2011
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