The minimax optimization over Riemannian manifolds (possibly nonconvex constraints) has been actively applied to solve many problems, such as robust dimensionality reduction and deep neural networks with orthogonal weights (Stiefel manifold). Although algorithms for problems have developed in the Euclidean setting, it is difficult convert them into cases, constraints are even rare. On other han...

Svctan, D., New plethysm operation, Checn characters of exterior and symmetric powers with applications to Stiefel-Whitney classes of gcassmannians, Theoretical Computer Science 117 (1993) 289-301. In this paper a new plethysm operation is proposed and a technique for coefficient extraction for a fairly general class of symmetric power series (e.g. multiplicative sequences of the theory of ?cha...

Howard Hughes Medical Institute, Computational Neurobiology Lab, The Salk Institute for Biological Studies, 10010 N. Torrey Pines Road, La Jolla, CA 92037, USA Department of Biology, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92037, USA # Present address: Theoretical and Experimental Neurobiology Unit, Okinawa Institute of Science and Technology, 12-22, Suzaki, Uruma, ...

The present research work proposes a new fast fixed-point averaging algorithm on the compact Stiefel manifold based on a mixed retraction/lifting pair. Numerical comparisons between fixed-point algorithms based on the proposed non-associated retraction/lifting map pair and two associated retraction/lifting pairs confirm that the averaging algorithm based on a combination of mixed maps is remark...

Biological rhythms such as circadian rhythms, biochemical rhythms and neural oscillators are based on the mathematical model of the theory of harmonic oscillators. These are solutions of certain second-order differential equations. They can also be viewed as spherical harmonics on the circle in the two-dimensional Euclidean space. The spherical harmonics on (n-1)-spheres and, more generally, th...

This paper presents an overview of various matrix manifolds that are commonly used in computer vision applications. It covers the following manifoldsLie groups, Stiefel manifolds, Grassmann manifolds and Riemannian manifolds. A manifold of dimension n is a topological space that near each point resembles n-dimensional Euclidean space. More precisely, each point of an n-dimensional manifold has ...

Estimating and modeling functional connectivity in the brain is a challenging problem with potential applications in the understanding of brain organization and various neurological and neuropsychological conditions. An important objective in connectivity analysis is to determine the connections between regions of interest in the brain. However, traditional functional connectivity analyses have...

In this paper, we compute the $BP$ -cohomology of complex projective Stiefel manifolds. The method involves homotopy fixed point spectral sequence, and works for oriented cohomology theories. We also use these calculations -operations to prove new results about equivariant maps between