Publications related to Hermitian manifold

Geometric deep learning: going beyond Euclidean data

Many signal processing problems involve data whose underlying structure is non-Euclidean, but may be modeled as a manifold or (combinatorial) graph. For instance, in social networks, the characteristics of users can be modeled as signals on the vertices of ...

2017

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Tudor Ratiu

Bi-Jacobi fields are generalized Jacobi fields, and are used to efficiently compute approximations to Riemannian cubic splines in a Riemannian manifold M. Calculating bi-Jacobi fields is straightforward when M is a symmetric space such as bi-invariant SO(3 ...

Int Press Boston, Inc2016

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

Joachim Krieger, Roland Donninger, Willie Wai Yeung Wong

We study time-like hypersurfaces with vanishing mean curvature in the (3+1) dimensional Minkowski space, which are the hyperbolic counterparts to minimal embeddings of Riemannian manifolds. The catenoid is a stationary solution of the associated Cauchy pro ...

Duke Univ Press2015

Dynamics of particles with anisotropic mass depending on time and position

Tudor Ratiu

Representations of solutions of equations describing the diffusion and quantum dynamics of particles in a Riemannian manifold are discussed under the assumption that the mass of particles is anisotropic and depends on both time and position. These equation ...

Springer Verlag2015

Discrete variational Lie group formulation of geometrically exact beams dynamics

Yves Weinand, Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures

The goal of this paper is to derive a structure preserving integrator for geometrically exact beam dynamics, by using a Lie group variational integrator. Both spatial and temporal discretization are implemented in a geometry preserving manner. The resultin ...

Springer Verlag2015

Convergence Results For Projected Line-Search Methods On Varieties Of Low-Rank Matrices Via Lojasiewicz Inequality

André Uschmajew

The aim of this paper is to derive convergence results for projected line-search methods on the real-algebraic variety M-

Siam Publications2015

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Volkan Cevher, Jonathan Mark Scarlett, Yen-Huan Li

We consider the model selection consistency or sparsistency of a broad set of

\ell_1

-regularized

M

-estimators for linear and non-linear statistical models in a unified fashion. For this purpose, we propose the local structured smoothness condition (LSS ...

2015

Note on Solutions of the Strominger System from Unitary Representations of Cocompact Lattices of SL(2, C)

Mario Garcia Fernandez

This note is motivated by a recently published paper (Biswas and Mukherjee in Commun Math Phys 322(2):373-384, 2013). We prove a no-go result for the existence of suitable solutions of the Strominger system in a compact complex parallelizable manifold . Fo ...

Springer Verlag2014

Principal Flows

Victor Panaretos, Tung Huy Pham, Zhigang Yao

We revisit the problem of extending the notion of principal component analysis (PCA) to multivariate datasets that satisfy nonlinear constraints, therefore lying on Riemannian manifolds. Our aim is to determine curves on the manifold that retain their cano ...

American Statistical Association2014

Hermitian Categories, Extension Of Scalars And Systems Of Sesquilinear Forms

Eva Bayer Fluckiger, Daniel Arnold Moldovan

We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be unimodular or defined o ...

Pacific Journal Mathematics2014

Hermitian manifold

Graph Chatbot

Chat with Graph Search

Geometric deep learning: going beyond Euclidean data

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

Dynamics of particles with anisotropic mass depending on time and position

Discrete variational Lie group formulation of geometrically exact beams dynamics

Convergence Results For Projected Line-Search Methods On Varieties Of Low-Rank Matrices Via Lojasiewicz Inequality

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Note on Solutions of the Strominger System from Unitary Representations of Cocompact Lattices of SL(2, C)

Principal Flows

Hermitian Categories, Extension Of Scalars And Systems Of Sesquilinear Forms

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Note on Solutions of the Strominger System from Unitary Representations of Cocompact Lattices of SL(2, C)

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

Geometric deep learning: going beyond Euclidean data

Convergence Results For Projected Line-Search Methods On Varieties Of Low-Rank Matrices Via Lojasiewicz Inequality

Dynamics of particles with anisotropic mass depending on time and position

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Principal Flows

Hermitian Categories, Extension Of Scalars And Systems Of Sesquilinear Forms

Discrete variational Lie group formulation of geometrically exact beams dynamics