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Found 8 papers, 4 papers with code
Families of costs with zero and nonnegative MTW tensor in optimal transport
We compute explicitly the MTW tensor (or cross curvature) for the optimal transport problem on $\mathbb{R}^n$ with a cost function of form $\mathsf{c}(x, y) = \mathsf{u}(x^{\mathfrak{t}}y)$, where $\mathsf{u}$ is a scalar function with inverse $\mathsf{s}$, $x^{\ft}y$ is a nondegenerate bilinear pairing of vectors $x, y$ belonging to an open subset of $\mathbb{R}^n$.
Road Damages Detection and Classification with YOLOv7
The results show that the data collection from Google Street View is efficient, and the proposed deep learning approach results in F1 scores of 81. 7% on the road damage data collected from the United States using Google Street View and 74. 1% on all test images of this dataset.
Understanding Public Opinion on Using Hydroxychloroquine for COVID-19 Treatment via Social Media
This paper studies the reactions of social network users on the recommendation of using HCQ for COVID-19 treatment by analyzing the reaction patterns and sentiment of the tweets.
Curvatures of Stiefel manifolds with deformation metrics
The second approach leads to curvature formulas for Cheeger deformation metrics on normal homogeneous spaces.
Riemannian Geometry with differentiable ambient space and metric operator
For a Riemannian submersion $\mathfrak{q}:\mathcal{M}\to \mathcal{B}$ from an embedded manifold $\mathcal{M}\subset \mathcal{E}$, we define a submersed ambient structure and obtain similar formulas, with the O'Neil tensor expressed in terms of the projection to the horizontal bundle $\mathcal{H}\mathcal{M}$.
Closed-form geodesics and trust-region method to calculate Riemannian logarithms on Stiefel and its quotient manifolds
Combining with the use of Fr{\'e}chet derivatives to compute the gradient of the square Frobenius distance between a geodesic ending point to a given point on the manifold, we show the logarithm map and geodesic distance between two endpoints on the manifold could be computed by {\it minimizing} this square distance by a {\it trust-region} solver.
Riemannian gradient and Levi-Civita connection for fixed-rank matrices
We provide formulas for Riemannian gradient and Levi-Civita connection for a family of metrics on fixed-rank matrix manifolds, based on nonconstant metrics on Stiefel manifolds.
Optimization and Control 65K10, 58C05, 49Q12, 53C25, 57Z20, 57Z25
Operator-valued formulas for Riemannian Gradient and Hessian and families of tractable metrics
We provide an explicit formula for the Levi-Civita connection and Riemannian Hessian for a Riemannian manifold that is a quotient of a manifold embedded in an inner product space with a non-constant metric function.
