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The Total Variation-Wasserstein Problem: A New Derivation of the Euler-Lagrange Equations 全变分-瓦瑟斯坦问题:欧拉-拉格朗日方程的一种新推导
International Conference on Geometric Science of Information Pub Date : 2023-08-21 DOI: 10.1007/978-3-031-38271-0_61
A. Chambolle, V. Duval, J. Machado
{"title":"The Total Variation-Wasserstein Problem: A New Derivation of the Euler-Lagrange Equations","authors":"A. Chambolle, V. Duval, J. Machado","doi":"10.1007/978-3-031-38271-0_61","DOIUrl":"https://doi.org/10.1007/978-3-031-38271-0_61","url":null,"abstract":"","PeriodicalId":379504,"journal":{"name":"International Conference on Geometric Science of Information","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116509401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Casimir-dissipation stabilized stochastic rotating shallow water equations on the sphere 球上卡西米尔耗散稳定的随机旋转浅水方程
International Conference on Geometric Science of Information Pub Date : 2023-07-18 DOI: 10.48550/arXiv.2307.09194
W. Bauer, Rudiger Brecht
{"title":"Casimir-dissipation stabilized stochastic rotating shallow water equations on the sphere","authors":"W. Bauer, Rudiger Brecht","doi":"10.48550/arXiv.2307.09194","DOIUrl":"https://doi.org/10.48550/arXiv.2307.09194","url":null,"abstract":"We introduce a structure preserving discretization of stochastic rotating shallow water equations, stabilized with an energy conserving Casimir (i.e. potential enstrophy) dissipation. A stabilization of a stochastic scheme is usually required as, by modeling subgrid effects via stochastic processes, small scale features are injected which often lead to noise on the grid scale and numerical instability. Such noise is usually dissipated with a standard diffusion via a Laplacian which necessarily also dissipates energy. In this contribution we study the effects of using an energy preserving selective Casimir dissipation method compared to diffusion via a Laplacian. For both, we analyze stability and accuracy of the stochastic scheme. The results for a test case of a barotropically unstable jet show that Casimir dissipation allows for stable simulations that preserve energy and exhibit more dynamics than comparable runs that use a Laplacian.","PeriodicalId":379504,"journal":{"name":"International Conference on Geometric Science of Information","volume":"abs/2212.10234 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115373314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Chan-Vese Attention U-Net: An attention mechanism for robust segmentation Chan-Vese Attention U-Net:一种稳健分割的注意机制
International Conference on Geometric Science of Information Pub Date : 2023-06-28 DOI: 10.48550/arXiv.2306.16098
Nicolas Makaroff, L. Cohen
{"title":"Chan-Vese Attention U-Net: An attention mechanism for robust segmentation","authors":"Nicolas Makaroff, L. Cohen","doi":"10.48550/arXiv.2306.16098","DOIUrl":"https://doi.org/10.48550/arXiv.2306.16098","url":null,"abstract":"When studying the results of a segmentation algorithm using convolutional neural networks, one wonders about the reliability and consistency of the results. This leads to questioning the possibility of using such an algorithm in applications where there is little room for doubt. We propose in this paper a new attention gate based on the use of Chan-Vese energy minimization to control more precisely the segmentation masks given by a standard CNN architecture such as the U-Net model. This mechanism allows to obtain a constraint on the segmentation based on the resolution of a PDE. The study of the results allows us to observe the spatial information retained by the neural network on the region of interest and obtains competitive results on the binary segmentation. We illustrate the efficiency of this approach for medical image segmentation on a database of MRI brain images.","PeriodicalId":379504,"journal":{"name":"International Conference on Geometric Science of Information","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116630953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometry of Saccades and Saccadic Cycles 跳变和跳变循环的几何
International Conference on Geometric Science of Information Pub Date : 2023-06-26 DOI: 10.1007/978-3-031-38299-4_51
D. Alekseevsky, I. Shirokov
{"title":"Geometry of Saccades and Saccadic Cycles","authors":"D. Alekseevsky, I. Shirokov","doi":"10.1007/978-3-031-38299-4_51","DOIUrl":"https://doi.org/10.1007/978-3-031-38299-4_51","url":null,"abstract":"","PeriodicalId":379504,"journal":{"name":"International Conference on Geometric Science of Information","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132601385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Approximate Projection onto the Tangent Cone to the Variety of Third-Order Tensors of Bounded Tensor-Train Rank 有界张量列秩的三阶张量变化在切锥上的近似投影
International Conference on Geometric Science of Information Pub Date : 2023-06-23 DOI: 10.48550/arXiv.2306.13360
Charlotte Vermeylen, Guillaume Olikier, M. Barel
{"title":"An Approximate Projection onto the Tangent Cone to the Variety of Third-Order Tensors of Bounded Tensor-Train Rank","authors":"Charlotte Vermeylen, Guillaume Olikier, M. Barel","doi":"10.48550/arXiv.2306.13360","DOIUrl":"https://doi.org/10.48550/arXiv.2306.13360","url":null,"abstract":"An approximate projection onto the tangent cone to the variety of third-order tensors of bounded tensor-train rank is proposed and proven to satisfy a better angle condition than the one proposed by Kutschan (2019). Such an approximate projection enables, e.g., to compute gradient-related directions in the tangent cone, as required by algorithms aiming at minimizing a continuously differentiable function on the variety, a problem appearing notably in tensor completion. A numerical experiment is presented which indicates that, in practice, the angle condition satisfied by the proposed approximate projection is better than both the one satisfied by the approximate projection introduced by Kutschan and the proven theoretical bound.","PeriodicalId":379504,"journal":{"name":"International Conference on Geometric Science of Information","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115368857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Determinantal Expressions of Certain Integrals on Symmetric Spaces 对称空间上某些积分的行列式
International Conference on Geometric Science of Information Pub Date : 2023-06-17 DOI: 10.1007/978-3-031-38271-0_43
S. Said, Cyrus Mostajeran
{"title":"Determinantal Expressions of Certain Integrals on Symmetric Spaces","authors":"S. Said, Cyrus Mostajeran","doi":"10.1007/978-3-031-38271-0_43","DOIUrl":"https://doi.org/10.1007/978-3-031-38271-0_43","url":null,"abstract":"","PeriodicalId":379504,"journal":{"name":"International Conference on Geometric Science of Information","volume":"54 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124872040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Sub-Riemannian Model of the Functional Architecture of M1 for Arm Movement Direction 臂运动方向M1功能体系的亚黎曼模型
International Conference on Geometric Science of Information Pub Date : 2023-06-13 DOI: 10.1007/978-3-031-38299-4_50
Caterina Mazzetti, A. Sarti, G. Citti
{"title":"A Sub-Riemannian Model of the Functional Architecture of M1 for Arm Movement Direction","authors":"Caterina Mazzetti, A. Sarti, G. Citti","doi":"10.1007/978-3-031-38299-4_50","DOIUrl":"https://doi.org/10.1007/978-3-031-38299-4_50","url":null,"abstract":"","PeriodicalId":379504,"journal":{"name":"International Conference on Geometric Science of Information","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126900285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Perturbation of Fiedler vector: interest for graph measures and shape analysis 菲尔德勒矢量的摄动:对图形测度和形状分析的兴趣
International Conference on Geometric Science of Information Pub Date : 2023-06-07 DOI: 10.48550/arXiv.2306.04327
J. Lefévre, Justine Fraize, D. Germanaud
{"title":"Perturbation of Fiedler vector: interest for graph measures and shape analysis","authors":"J. Lefévre, Justine Fraize, D. Germanaud","doi":"10.48550/arXiv.2306.04327","DOIUrl":"https://doi.org/10.48550/arXiv.2306.04327","url":null,"abstract":"In this paper we investigate some properties of the Fiedler vector, the so-called first non-trivial eigenvector of the Laplacian matrix of a graph. There are important results about the Fiedler vector to identify spectral cuts in graphs but far less is known about its extreme values and points. We propose a few results and conjectures in this direction. We also bring two concrete contributions, i) by defining a new measure for graphs that can be interpreted in terms of extremality (inverse of centrality), ii) by applying a small perturbation to the Fiedler vector of cerebral shapes such as the corpus callosum to robustify their parameterization.","PeriodicalId":379504,"journal":{"name":"International Conference on Geometric Science of Information","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127349025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Madelung Transform and Variational Asymptotics in Born-Oppenheimer Molecular Dynamics Born-Oppenheimer分子动力学中的Madelung变换和变分渐近
International Conference on Geometric Science of Information Pub Date : 2023-05-30 DOI: 10.1007/978-3-031-38299-4_25
P. Bergold, C. Tronci
{"title":"Madelung Transform and Variational Asymptotics in Born-Oppenheimer Molecular Dynamics","authors":"P. Bergold, C. Tronci","doi":"10.1007/978-3-031-38299-4_25","DOIUrl":"https://doi.org/10.1007/978-3-031-38299-4_25","url":null,"abstract":"","PeriodicalId":379504,"journal":{"name":"International Conference on Geometric Science of Information","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133442151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Forward and Inverse Approximation Theory for Linear Temporal Convolutional Networks 线性时间卷积网络的正反逼近理论
International Conference on Geometric Science of Information Pub Date : 2023-05-29 DOI: 10.48550/arXiv.2305.18478
Hao Jiang, Qianxiao Li
{"title":"Forward and Inverse Approximation Theory for Linear Temporal Convolutional Networks","authors":"Hao Jiang, Qianxiao Li","doi":"10.48550/arXiv.2305.18478","DOIUrl":"https://doi.org/10.48550/arXiv.2305.18478","url":null,"abstract":"We present a theoretical analysis of the approximation properties of convolutional architectures when applied to the modeling of temporal sequences. Specifically, we prove an approximation rate estimate (Jackson-type result) and an inverse approximation theorem (Bernstein-type result), which together provide a comprehensive characterization of the types of sequential relationships that can be efficiently captured by a temporal convolutional architecture. The rate estimate improves upon a previous result via the introduction of a refined complexity measure, whereas the inverse approximation theorem is new.","PeriodicalId":379504,"journal":{"name":"International Conference on Geometric Science of Information","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114530629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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