Article
Mathematics, Applied
Hanne Hardering, Benedikt Wirth
Summary: We prove quartic convergence of cubic spline interpolation for curves into Riemannian manifolds as the grid size tends to zero. In contrast to cubic spline interpolation in Euclidean space, where linearity is classical, the interpolation operator is no longer linear in the Riemannian case. Nevertheless, concepts from the linear setting can be generalized to the Riemannian case using intrinsic Riemannian formulations and avoiding charts as much as possible.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2022)
Article
Computer Science, Theory & Methods
Nicolas Guigui, Xavier Pennec
Summary: In this work, we show that Taylor approximations of elementary constructions of Schild's ladder and the pole ladder can converge with quadratic speed. Moreover, we establish a new connection between Schild's ladder and the Fanning scheme and explain their convergence properties.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2022)
Article
Mathematics, Applied
Boris Shustin, Haim Avron
Summary: Optimization problems on the generalized Stiefel manifold are widely encountered in various scientific and engineering fields. Applications include computational science, statistics, machine learning, and deep learning. The standard geometric components for the generalized Stiefel manifold may be inefficient, but this paper proposes a technique called Riemannian preconditioning to address the issue and develop new geometric components. The effectiveness of Riemannian preconditioning is demonstrated theoretically and numerically.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Operations Research & Management Science
Shimin Zhao, Tao Yan, Yuanguo Zhu
Summary: This paper studies the problem of minimizing the sum of a smooth function and nonsmooth function over a Riemannian manifold. A Riemannian proximal gradient algorithm with a trust region scheme is proposed. Global convergence is shown under natural assumptions. An O(1/epsilon(2)) iteration complexity bound is established, which matches the best-known complexity bound for smooth optimization on Riemannian manifolds. Additionally, a nonmonotone version and an accelerated version of the algorithm with a trust region scheme are provided, and their global convergence is proven. Numerical results validate the effectiveness of the proposed methods.
JOURNAL OF GLOBAL OPTIMIZATION
(2023)
Article
Mathematics
Marian Ioan Munteanu, Ana Irina Nistor
Summary: In this study, the magnetic Jacobi fields in cosymplectic manifolds of dimension 3 are classified and examples of Jacobi magnetic fields in the Euclidean space E-3 are provided. The description of magnetic Jacobi fields in the product spaces S(2)xR and H(2)xR is also given.
Article
Mathematics, Applied
Jun-ichi Inoguchi, Marian Ioan Munteanu
Summary: We investigate the magnetic curves in Killing submersions and find that the bundle curvature remains constant when the magnetic curves have constant mean curvature in the vertical tubes derived from them. We extend important results obtained for horizontal geodesics to horizontal magnetic curves in the total space of a Killing submersion. In addition, we study magnetic Jacobi fields along horizontal Killing magnetic trajectories in 3-dimensional Sasakian space forms.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics
Jun-ichi Inoguchi, Marian Ioan Munteanu
Summary: This article investigates all magnetic Jacobi fields along contact magnetic curves in 3-dimensional Sasakian space forms, distinguishing between uniform and non-uniform magnetic fields.
JOURNAL OF GEOMETRIC ANALYSIS
(2022)
Article
Automation & Control Systems
Xin Li, Yu Yang, Wang Ping, Wang Jian, Junsheng Cheng
Summary: A scheme for bearing fault diagnosis using statistical-enhanced covariance matrix (SECM) and Riemannian maximum margin flexible convex hull (RMMFCH) has been proposed, which enhances the accuracy and efficiency of the method by introducing statistical parameters and Riemannian kernel mapping functions.
Article
Mathematics, Applied
Jun-ichi Inoguchi, Ji-Eun Lee
Summary: In this paper, we study the parallelism of the characteristic Jacobi operator in almost Kenmotsu 3-manifolds. We first prove that there are no almost Kenmotsu 3-manifolds with vanishing characteristic Jacobi operator. Furthermore, we show that there are no almost Kenmotsu 3-manifolds with parallel characteristic Jacobi operator. However, we find the existence of almost Kenmotsu 3-manifolds with eta-parallel characteristic Jacobi operator and provide the necessary and sufficient conditions for them. Additionally, we classify almost Kenmotsu 3-manifolds with pseudo-parallel characteristic Jacobi operator into four classes and give a complete classification of all homogeneous almost Kenmotsu 3-manifolds with pseudo-parallel characteristic Jacobi operator.
RESULTS IN MATHEMATICS
(2023)
Article
Mathematics, Applied
Alessandro Goffi, Francesco Pediconi
Summary: In this paper, the Sobolev regularity of solutions to nonlinear second order elliptic equations with super-linear first-order terms on Riemannian manifolds, complemented with Neumann boundary conditions, is studied. The source term of the equation belongs to a Lebesgue space under various integrability regimes. The method used is based on an integral refinement of the Bochner identity and leads to semilinear Calderon-Zygmund type results. It also discusses the applications to the smoothness problem of solutions to Mean Field Games systems with Neumann boundary conditions posed on convex domains of the Euclidean space.
FORUM MATHEMATICUM
(2023)
Article
Mathematics, Applied
Diego Alonso-Oran, Angel David Martinez
Summary: This note demonstrates the finite time blow-up phenomenon of a class of non-local active scalar equations on compact Riemannian manifolds. The strategy used in this study was introduced by Silvestre and Vicol in Trans. Amer. Math. Soc. (368 (2016), pp. 6159-6188) to deal with the one-dimensional C ' ordoba-C ' ordoba-Fontelos equation and can be considered as an instance of De Giorgi's method.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Computer Science, Software Engineering
Wen Huang, Ke Wei
Summary: The paper presents a Riemannian proximal gradient method and its accelerated variant for optimization problems constrained on a manifold. Global convergence and a convergence rate of O(1/k) for the RPG algorithm are established, with the sequence generated converging to a single stationary point under the assumption of a Riemannian KL property. Additionally, the flexibility of RPG on the Stiefel manifold covers a variety of problems, including sparse PCA.
MATHEMATICAL PROGRAMMING
(2022)
Article
Mathematics, Applied
Jun-ichi Inoguchi, Marian Ioan Munteanu
Summary: In this paper, the magnetic Jacobi fields on Sasakian space forms of dimension greater or equal to 5 are completely determined.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Hiroyuki Sato
Summary: This paper proposes a general framework that unifies Riemannian conjugate gradient methods and develops new methods. It also clarifies the convergence conditions of the algorithms and analyzes the global convergence properties. Numerical experiments are conducted to validate the theoretical results.
SIAM JOURNAL ON OPTIMIZATION
(2022)
Article
Mathematics
Xuefeng Zhao, Yong Li
Summary: We study the iso-manifold persistence in formulism and show that unperturbed tori can give rise to invariant tori in the perturbed system while maintaining the ratio of certain frequency components. We also consider the iso-manifold Melnikov persistence.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Computer Science, Interdisciplinary Applications
Junhao Wen, Jorge Samper-Gonzalez, Simona Bottani, Alexandre Routier, Ninon Burgos, Thomas Jacquemont, Sabrina Fontanella, Stanley Durrleman, Stephane Epelbaum, Anne Bertrand, Olivier Colliot
Summary: Diffusion MRI is commonly used to study white matter alterations and automatically classify Alzheimer's disease. However, comparing classification performance is challenging due to variations in components, while reproducibility is hindered by the lack of readily available components. By extending an open-source framework to diffusion MRI data, it was found that feature selection has a positive impact on classification results, voxel-wise features generally outperform regional features, and adjustments in smoothing and registration methods do not significantly affect classification results.
Article
Anatomy & Morphology
Jean Dumoncel, Gerard Subsol, Stanley Durrleman, Anne Bertrand, Edwin de Jager, Anna C. Oettle, Zarina Lockhat, Farhana E. Suleman, Amelie Beaudet
Summary: The study collected morphological and structural information on endocasts and brains of extant human individuals through imaging techniques and 3D modeling methods. It found a close correspondence in terms of morphology and organization between the brain and the corresponding endocast, except in the superior region. This work serves as an important reference for paleoneurological studies by quantifying the shape and organization of the brain and endocast.
JOURNAL OF ANATOMY
(2021)
Review
Computer Science, Artificial Intelligence
Manon Ansart, Stephane Epelbaum, Giulia Bassignana, Alexandre Bone, Simona Bottani, Tiziana Cattai, Raphael Couronne, Johann Faouzi, Igor Koval, Maxime Louis, Elina Thibeau-Sutre, Junhao Wen, Adam Wild, Ninon Burgos, Didier Dormont, Olivier Colliot, Stanley Durrleman
Summary: This systematic review focused on automatic prediction of mild cognitive impairment to Alzheimer's disease dementia and analyzed the impact of methodological choices on performance. It found that using certain variables significantly improves predictive performance, while cognitive assessments question the wide use of imaging for prediction. Methodological issues, such as the absence of a test set, were also identified.
MEDICAL IMAGE ANALYSIS
(2021)
Article
Engineering, Biomedical
Alexis Guyot, Ana B. Graciano Fouquier, Emilie Gerardin, Marie Chupin, Joan A. Glaunes, Linda Marrakchi-Kacem, Johanne Germain, Claire Boutet, Claire Cury, Lucie Hertz-Pannier, Alexandre Vignaud, Stanley Durrleman, Thomas R. Henry, Pierre-Francois van de Moortele, Alain Trouve, Olivier Colliot
Summary: This study introduces a method to analyze the thickness of the hippocampus from 7-Tesla MRI and detected local thinning patterns predominantly ipsilaterally to the seizure focus in patients with temporal lobe epilepsy. The method shows good robustness and potential for detecting local atrophy in patients.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING
(2021)
Article
Mathematical & Computational Biology
Alexandre Routier, Ninon Burgos, Mauricio Diaz, Michael Bacci, Simona Bottani, Omar El-Rifai, Sabrina Fontanella, Pietro Gori, Jeremy Guillon, Alexis Guyot, Ravi Hassanaly, Thomas Jacquemont, Pascal Lu, Arnaud Marcoux, Tristan Moreau, Jorge Samper-Gonzalez, Marc Teichmann, Elina Thibeau-Sutre, Ghislain Vaillant, Junhao Wen, Adam Wild, Marie-Odile Habert, Stanley Durrleman, Olivier Colliot
Summary: Clinica is an open-source software platform designed to simplify and enhance the reproducibility of clinical neuroscience studies. Researchers can efficiently manage data, evaluate methods, and share research findings through automatic pipelines and tools for processing multimodal neuroimaging data.
FRONTIERS IN NEUROINFORMATICS
(2021)
Article
Computer Science, Artificial Intelligence
Anupama Goparaju, Krithika Iyer, Alexandre Bone, Nan Hu, Heath B. Henninger, Andrew E. Anderson, Stanley Durrleman, Matthijs Jacxsens, Alan Morris, Ibolya Csecs, Nassir Marrouche, Shireen Y. Elhabian
Summary: Statistical shape modeling (SSM) is widely used in biology and medicine for quantitative analysis of anatomical shapes. Different SSM tools show varying levels of consistencies in capturing clinically relevant population-level variability. Validation frameworks and lesion screening methods are proposed for assessing shape models.
MEDICAL IMAGE ANALYSIS
(2022)
Article
Computer Science, Artificial Intelligence
Thomas Lartigue, Stanley Durrleman, Stephanie Allassonniere
Summary: This paper introduces a theoretical framework with state-of-the-art convergence guarantees for any deterministic approximation of the E step in the Expectation Maximisation algorithm. The authors analyze several approximations that fit into this framework and validate their effectiveness through theoretical and empirical results.
Article
Multidisciplinary Sciences
Igor Koval, Thomas Dighiero-Brecht, Allan J. Tobin, Sarah J. Tabrizi, Rachael Scahill, Sophie Tezenas du Montcel, Stanley Durrleman, Alexandra Durr
Summary: This study utilizes disease course mapping to forecast biomarker progression for individual carriers of the pathological CAG repeat expansions responsible for Huntington disease, in order to select participants at risk for progression and compute the power of trials for such an enriched population, ultimately reducing sample sizes and ensuring a more homogeneous group of participants.
SCIENTIFIC REPORTS
(2022)
Article
Multidisciplinary Sciences
Etienne Maheux, Igor Koval, Juliette Ortholand, Colin Birkenbihl, Damiano Archetti, Vincent Bouteloup, Stephane Epelbaum, Carole Dufouil, Martin Hofmann-Apitius, Stanley Durrleman
Summary: This study developed a statistical model, AD Course Map, for predicting the progression of Alzheimer's disease (AD) based on current medical and radiological data. The model was tested on a large dataset of over 96,000 cases and showed high accuracy in predicting clinical endpoints. By enriching the population with predicted progressors, the required sample size for trials could be reduced by 38% to 50%.
NATURE COMMUNICATIONS
(2023)
Article
Clinical Neurology
Cecile Di Folco, Raphael Couronne, Isabelle Arnulf, Graziella Mangone, Smaranda Leu-Semenescu, Pauline Dodet, Marie Vidailhet, Jean-Christophe Corvol, Stephane Lehericy, Stanley Durrleman
Summary: This study proposes a disease course map for Parkinson's disease (PD) and investigates the progression profiles of patients with or without rapid eye movement sleep behavioral disorders (RBD). The findings reveal distinct patterns of progression between PD patients with and without RBD, emphasizing the importance of understanding heterogeneity in PD progression for precision medicine.
MOVEMENT DISORDERS
(2023)
Proceedings Paper
Computer Science, Interdisciplinary Applications
Benoit Sauty, Stanley Durrleman
Summary: Disease progression models are important for understanding degenerative diseases, but rarely used for entire medical images. This study combines a Variational Auto Encoder with a temporal linear mixed-effect model to learn a latent representation of the data and recover patterns of structural and metabolic alterations of the brain.
MEDICAL IMAGE COMPUTING AND COMPUTER ASSISTED INTERVENTION, MICCAI 2022, PT I
(2022)
Proceedings Paper
Computer Science, Information Systems
K. Manouskova, V Abadie, M. Ounissi, G. Jimenez, L. Stimmer, B. Delatour, S. Durrleman, D. Racoceanu
Summary: Tau proteins play a role in Alzheimer's disease, and detecting and segmenting the aggregates is crucial. This study presents a 5-step pipeline that improves state-of-the-art performances in detecting and segmenting tau protein aggregates, providing valuable insights in the field.
MEDICAL IMAGING 2022: DIGITAL AND COMPUTATIONAL PATHOLOGY
(2022)
Proceedings Paper
Engineering, Biomedical
Benoit Sauty, Stanley Durrleman
Summary: This study proposes a geometric framework for learning a manifold representation of longitudinal data to model disease progression of biomarkers. By learning the metric from the data, the method can fit longitudinal datasets well and provide a few interpretable parameters.
2022 IEEE INTERNATIONAL SYMPOSIUM ON BIOMEDICAL IMAGING (IEEE ISBI 2022)
(2022)
Article
Statistics & Probability
Clement Mantoux, Stanley Durrleman, Stephanie Allassonniere
Summary: This paper provides asymptotic convergence guarantees for a hierarchical statistical model for matrix data sets. The model captures the variability of matrices by modeling a truncation of their eigendecomposition and offers consistent MAP estimation.
ESAIM-PROBABILITY AND STATISTICS
(2022)
Article
Medical Informatics
Thomas Nedelec, Baptiste Couvy-Duchesne, Fleur Monnet, Timothy Daly, Manon Ansart, Laurene Gantzer, Beranger Lekens, Stephane Epelbaum, Carole Dufouil, Stanley Durrleman
Summary: This study analyzed health records from France and the UK and found significant associations between certain health conditions and the risk of developing Alzheimer's disease. These associations were particularly evident within a window of 2-10 years before the first diagnosis of Alzheimer's disease. These findings provide important insights for improving early prevention and intervention strategies for Alzheimer's disease.
LANCET DIGITAL HEALTH
(2022)
