The Teichmüller harmonic map flow, introduced in [9], evolves both a map from a closed Riemann surface to an arbitrary compact Riemannian manifold, and a constant curvature metric on the domain, in order to reduce its harmonic map energy as quickly as possible. In this paper, we develop the geometric analysis of holomorphic quadratic differentials in order to explain what happens in the case th...

Contents 1. Introduction 2 Organization of the paper 3 2. The characterization theorem 4 2.1. Definitions and statement of the main theorem 4 2.2. Classification of postsingularly finite exponential maps 4 3. Iteration in Teichmüler space 6 3.1. The Teichmüler space of a topological exponential map 7 3.2. The Teichmüler metric and its dual 8 3.3. Examples of quadratic differentials 9 3.4. Proof...

We consider the most general Quadratic Metric-Affine Gravity setup in presence of generic matter sources with non-vanishing hypermomentum. The gravitational action consists all $17$ quadratic invariants (both parity even and odd) torsion non-metricity as well their mixings, along terms that are linear curvature namely Ricci scalar totally antisymmetric Riemann piece. Adding also a sector to lat...

We consider a model of 2D gravity with the action quadratic in curvature and represent path integrals as over SL(2,R) invariant Gaussian functional measure. reduce these to products Wiener calculate correlation function metric first perturbative order.

A bstract We transform the metric of an isolated matter source in multipolar post-Minkowskian approximation from harmonic (de Donder) coordinates to radiative Newman-Unti (NU) coordinates. To linearized order, we obtain NU as a functional mass and current multipole moments source, valid all-over exterior region source. Imposing appropriate boundary conditions recover generalized Bondi-van der B...

We derive the exact gravitational wave solutions in a general class of quadratic metric-affine gauge gravity models. The Lagrangian includes all possible linear and invariants constructed from torsion, nonmetricity curvature. ansatz for configuration properties are patterned following corresponding plane-fronted electromagnetic wave.

Patient similarity assessment is an important task in the context of patient cohort identification for comparative effectiveness studies and clinical decision support applications. The goal is to derive clinically meaningful distance metric to measure the similarity between patients represented by their key clinical indicators. It is desirable to learn the distance metric based on experts’ know...

0

Support Vector Machines, SVMs, and the Large Margin Nearest Neighbor algorithm, LMNN, are two very popular learning algorithms with quite different learning biases. In this paper we bring them into a unified view and show that they have a much stronger relation than what is commonly thought. We analyze SVMs from a metric learning perspective and cast them as a metric learning problem, a view wh...