Distribution (differential geometry)

About: Distribution (differential geometry) is a research topic. Over the lifetime, 911 publications have been published within this topic receiving 10149 citations.

A Kobayashi pseudo-distance for holomorphic bracket generating distributions

Abstract: In this paper, we generalize the Kobayashi pseudo-distance to complex manifolds which admit holomorphic bracket generating distributions. The generalization is based on Chow's theorem in sub-Riemannian geometry. Let G be a linear semisimple Lie group. For a complex $G$-homogeneous manifold M with a G-invariant holomorphic bracket generating distribution D, we prove that (M,D) is Kobayashi hyperbolic if and only if the universal covering of M is a canonical flag domain and the induced distribution is the superhorizontal distribution.

A water distribution manifold module, system and method for forming a module and method for modularly expanding a manifold.

Abstract: Title: A water distribution manifold module, system and method for forming a module and method for modularly expanding a manifold. Abstract A water distribution manifold module comprising: -a first thermoplastic manifold body defining a first inner chamber, wherein the body comprises a first end, a second end, and a plurality of side ports; - a first thermoplastic support plate comprising a first face, and a second face, wherein a first through hole extends from the first face to the second face such that the first inner chamber is fluidly accessible through the first through hole; and - a first mirror weld uniting the first body at its first end and the first plate at its first face.

Movable Poles of Painlevé I Transcendents and Singularities of Monodromy Data Manifolds

Abstract: We consider a classification of solutions to the first Painleve equation with respect to distribution of their poles at infinity. A connection is found between singularities of two-dimensional monodromy data manifold and analytic properties of solutions parametrized by this manifold. It is proved that solutions of Painleve I equation have no poles at infinity at a given critical sector of the complex plane iff the related monodromy data belong to the singular submanifold. Such solutions coincide with the class of “truncated” solutions (integrales tronquee) by classification of P. Boutroux. We derive further classification based on decomposition of singularities of monodromy data manifold.

Manifold Reconstruction of Differences: A Model-Based Iterative Statistical Estimation Algorithm with a Data-Driven Prior

Abstract: Manifold learning using deep neural networks been shown to be an effective tool for building sophisticated prior image models that can be applied to noise reduction in low-dose CT. We propose a new iterative CT reconstruction algorithm, called Manifold Reconstruction of Differences (MRoD), which combines physical and statistical models with a data-driven prior based on manifold learning. The MRoD algorithm involves estimating a manifold component, approximating common features among all patients, and the difference component which has the freedom to fit the measured data. By applying a sparsity-promoting penalty to the difference image rather than a hard constraint to the manifold, the MRoD algorithm is able to reconstruct features which are not present in the training data. The difference component itself may be independently useful. While the manifold captures typical patient features (e.g. healthy anatomy), the difference image highlights patient-specific elements (e.g. pathology). In this work, we present a description of an optimization framework which combines trained manifold-based modules with physical modules. We present a simulation study using anthropomorphic lung data showing that the MRoD algorithm can both isolate differences between a particular patient and the typical distribution, but also provide significant noise reduction with less bias than a typical penalized likelihood estimator in composite manifold plus difference reconstructions.