Results 51 to 60 of about 12,561 (233)
Stochastic Gradient Descent in High Dimensions for Multi‐Spiked Tensor PCA
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We study the high‐dimensional dynamics of online stochastic gradient descent (SGD) for the multi‐spiked tensor model. This multi‐index model arises from the tensor principal component analysis (PCA) problem with multiple spikes, where the goal is to estimate the unknown signal vectors within the N$N$‐dimensional unit sphere through maximum ...
Gérard Ben Arous +2 more
wiley +1 more source
Low Dimensional Flat Manifolds with Some Elasses of Finsler Metric
پژوهشهای ریاضی, 2020 Introduction An -dimensional Riemannian manifold is said to be flat (or locally Euclidean) if locally isometric with the Euclidean space, that is, admits a covering of coordinates neighborhoods each of which is isometric with a Euclidean domain.
Sedigheh Alavi Endrajemi +1 more
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IEEE Open Journal of Signal Processing, 2021 This work exploits Riemannian manifolds to build a sequential-clustering framework able to address a wide variety of clustering tasks in dynamic multilayer (brain) networks via the information extracted from their nodal time-series.
Cong Ye +4 more
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Compact Manifolds With Unbounded Nilpotent Fundamental Groups and Positive Ricci Curvature
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT It follows from the work of Kapovitch and Wilking that a closed manifold with nonnegative Ricci curvature has a uniformly almost nilpotent fundamental group. Leftover questions and conjectures, have asked if in this context the fundamental group is actually uniformly almost abelian. The main goal of this work is to construct examples (Mk9,gk)$(
Elia Bruè, Aaron Naber, Daniele Semola
wiley +1 more source
Relational divergence based classification on Riemannian manifolds [PDF]
, 2013 A recent trend in computer vision is to represent images through covariance matrices, which can be treated as points on a special class of Riemannian manifolds.
Sanderson, Conrad +6 more
core +1 more source
Seiberg-Witten Equations on Pseudo-Riemannian Spinc Manifolds With Neutral Signature
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2012 Pseudo-Riemannian spinc manifolds were introduced by Ikemakhen in [7]. In the present work we consider pseudo-Riemannian 4-manifolds with neutral signature whose structure groups are SO+(2; 2).
Değirmenci Nedim, Karapazar Şenay
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On Jacobi-Type Vector Fields on Riemannian Manifolds
Mathematics, 2019 In this article, we study Jacobi-type vector fields on Riemannian manifolds. A Killing vector field is a Jacobi-type vector field while the converse is not true, leading to a natural question of finding conditions under which a Jacobi-type vector field ...
Bang-Yen Chen +2 more
doaj +1 more source
Weak Nearly Sasakian and Weak Nearly Cosymplectic Manifolds
Mathematics, 2023 Weak contact metric structures on a smooth manifold, introduced by V. Rovenski and R. Wolak in 2022, have provided new insight into the theory of classical structures.
Vladimir Rovenski
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Kuga–Satake Construction on Families of K3 Surfaces of Picard Rank 14
Mathematische Nachrichten, EarlyView.ABSTRACT The isometry between the type IV6 and the type II4 hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank 14 and of polarized abelian 8‐folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces
Flora Poon
wiley +1 more source
Kahler manifolds and their relatives [PDF]
, 2010 Let M1 and M2 be two K¨ahler manifolds. We call M1 and M2 relatives if they share a non-trivial K¨ahler submanifold S, namely, if there exist two holomorphic and isometric immersions (K¨ahler immersions) h1 : S → M1 and h2 : S → M2. Moreover, two K¨ahler
Loi, A., Di Scala, Antonio Jose'
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