The Journal of Geometric Mechanics: latest papers
http://www.aimsciences.org/test_aims/journals/rss.jsp?journalID=17
Latest articles for selected journalhttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14271
About simple variational splines from the Hamiltonian viewpoint
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14271
Paula Balseiro, Teresinha J. Stuchi, Alejandro Cabrera and Jair KoillerFri, 1 Sep 2017 20:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14272
Probability measures on infinite-dimensional Stiefel manifolds
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14272
Suppose that $H$ is an infinite-dimensional separable Hilbert space.
Let $S\subset H$ be the sphere, $p\in S$. Let $\mu$ be the
push forward of a Gaussian measure $\gamma$ from
$T_p S$ onto $S$ using the exponential map. Let $v\in T_p S$ be
a Cameron--Martin vector for $\gamma$; let $R$ be a rotation
of $S$ in the direction $v$, and $\nu=R_\# \mu$ be the
rotated measure. Then $\mu,\nu$ are mutually singular. This is
counterintuitive, since the translation of a Gaussian measure
in a Cameron--Martin direction produces equivalent measures.
Let $\gamma$ be a Gaussian measure on $H$; then there
exists a smooth closed manifold $M\subset H$ such that the
projection of $H$ to the nearest point on $M$ is not well defined
for points in a set of positive $\gamma$ measure.
Instead it is possible to project a Gaussian measure
to a Stiefel manifold to define a probability.
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Eleonora Bardelli and Andrea Carlo Giuseppe MennucciFri, 1 Sep 2017 20:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14273
Complete spelling rules for the Monster tower over three-space
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14273
Alex Castro, Wyatt Howard and Corey ShanbromFri, 1 Sep 2017 20:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14274
Geometry of matrix decompositions seen through optimal transport and information geometry
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14274
Here we give a systematic description of classical matrix decompositions (or factorizations) in terms of Riemannian geometry and compatible principal bundle structures.
Both Wasserstein and Fisher--Rao geometries are discussed.
The link to matrices is obtained by considering OMT and information geometry in the category of linear transformations and multivariate Gaussian distributions.
This way, OMT is directly related to the polar decomposition of matrices, whereas information geometry is directly related to the $QR$, Cholesky, spectral, and singular value decompositions.
We also give a coherent description of gradient flow equations for the various decompositions;
most flows are illustrated in numerical examples.
The paper is a combination of previously known and original results.
As a survey it covers
the Riemannian geometry of OMT and polar decompositions (smooth and linear category),
entropy gradient flows, and the Fisher--Rao metric and its geodesics on the statistical manifold of multivariate Gaussian distributions.
The original contributions include new gradient flows associated with various matrix decompositions, new geometric interpretations of previously studied isospectral flows, and a new proof of the polar decomposition of matrices based an entropy gradient flow.
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Klas ModinFri, 1 Sep 2017 20:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14275
Modelling anisotropic covariance using stochastic development and sub-Riemannian
frame bundle geometry
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14275
Stefan Sommer and Anne Marie SvaneFri, 1 Sep 2017 20:00:00 GMT