A meromorphic quadratic differential on a punctured Riemann surface induces horizontal and vertical measured foliations with pole singularities. In neighborhood of pole, such foliation comprises foliated strips half-planes, its leaf space determines metric graph. We introduce the notion an asymptotic direction at each show that for equipped choice data, any compatible pair uniquely complex stru...

Wavefront sensorless adaptive optics methodologies are widely considered in scanning fluorescence microscopy where direct wavefront sensing is challenging. In these methodologies, aberration correction is performed by sequentially changing the settings of the adaptive element until a predetermined image quality metric is optimized. An efficient aberration correction can be achieved by modeling ...

quadratic equation is eigen-decomposed to build a linear This paper proposes a linear algorithm for metric equation to compute the projective-to-Euclidean trans-reconstruction from projective reconstruction. Metric formation matrix. reconstruction problem is equivalent to estimating the projective transformation matrix that converts projective reconstruction to Euclidean reconstruction. We buil...

By attaching basis vectors to the components of matter fields, one may render free action densities fully covariant. Both the connection and the tetrads are quadratic forms in these basis vectors. The metric of spacetime, which is quadratic in the tetrads, is then quartic in the basis vectors. ∗Submitted to the 1993 competition of the Gravity Research Foundation.

A criterion in terms of differential invariants for a metric on a surface to be Liouville is established. Moreover, in this paper we completely solve in invariant terms the local mobility problem of a 2D metric, considered by Darboux: How many quadratic in momenta integrals does the geodesic flow of a given metric possess? The method is also applied to recognition of other polynomial integrals ...

New forms of Born-Infeld, D-brane and M theory five-brane actions are found which are quadratic in the abelian field strength. The gauge fields couple both to a background or induced metric and a new auxiliary metric, whose elimination reproduces the non-polynomial Born-Infeld action. This is similar to the introduction of an auxiliary metric to simplify the Nambu-Goto string action. This simpl...

We systematically study the question of identification and consistent inclusion of the radion, within the Lagrangian approach, in a two brane Randall-Sundrum model. Exploiting the symmetry properties of the theory, we show how the radion can be identified unambiguously and give the action to all orders in the radion field and the metric. Using the background field method, we expand the theory t...

Distance metric learning is of fundamental interest in machine learning because the distance metric employed can significantly affect the performance of many learning methods. Quadratic Mahalanobis metric learning is a popular approach to the problem, but typically requires solving a semidefinite programming (SDP) problem, which is computationally expensive. Standard interior-point SDP solvers ...

In recent years, quadratic weighted kappa has been growing in popularity in the machine learning community as an evaluation metric in domains where the target labels to be predicted are drawn from integer ratings, usually obtained from human experts. For example, it was the metric of choice in several recent, high profile machine learning contests hosted on Kaggle : www.kaggle.com/c/asap-aes , ...