Logarithmic Bergman Kernel and Conditional Expectation of Gaussian Holomorphic Fields

The Bergman Kernel Function and Proper Holomorphic Mappings

It is proved that a proper holomorphic mapping / between bounded complete Reinhardt domains extends holomorphically past the boundary and that if, in addition, /~'(0) = {0}, then / is a polynomial mapping. The proof is accomplished via a transformation rule for the Bergman kernel function under proper holomorphic mappings.

Logarithmic Opinion Pools for Conditional Random Fields

Since their recent introduction, conditional random fields (CRFs) have been successfully applied to a multitude of structured labelling tasks in many different domains. Examples include natural language processing (NLP), bioinformatics and computer vision. Within NLP itself we have seen many different application areas, like named entity recognition, shallow parsing, information extraction from...

Neural Gaussian Conditional Random Fields

We propose a Conditional Random Field (CRF) model for structured regression. By constraining the feature functions as quadratic functions of outputs, the model can be conveniently represented in a Gaussian canonical form. We improved the representational power of the resulting Gaussian CRF (GCRF) model by (1) introducing an adaptive feature function that can learn nonlinear relationships betwee...

Gaussian Curvature of the Bergman Metric with Weighted Bergman Kernel on the Unit Disc

In the paper Gaussian curvature of Bergman metric on the unit disc and the dependence of this curvature on the weight function has been studied.

Bergman Kernels and Local Holomorphic Morseinequalitiesrobert