Hyperbolic geometry | Kleinian groups

Kleinian model

In mathematics, a Kleinian model is a model of a three-dimensional hyperbolic manifold N by the quotient space where is a discrete subgroup of PSL(2,C). Here, the subgroup , a Kleinian group, is defined so that it is isomorphic to the fundamental group of the surface N. Many authors use the terms Kleinian group and Kleinian model interchangeably, letting one stand for the other. The concept is named after Felix Klein. Many properties of Kleinian models are in direct analogy to those of Fuchsian models; however, overall, the theory is less well developed. A number of unsolved conjectures on Kleinian models are the analogs to theorems on Fuchsian models. (Wikipedia).

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generative model vs discriminative model

understanding difference between generative model and discriminative model with simple example. all machine learning youtube videos from me, https://www.youtube.com/playlist?list=PLVNY1HnUlO26x597OgAN8TCgGTiE-38D6

From playlist Machine Learning

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(ML 16.7) EM for the Gaussian mixture model (part 1)

Applying EM (Expectation-Maximization) to estimate the parameters of a Gaussian mixture model. Here we use the alternate formulation presented for (unconstrained) exponential families.

From playlist Machine Learning

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Definition of a hidden Markov model (HMM). Description of the parameters of an HMM (transition matrix, emission probability distributions, and initial distribution). Illustration of a simple example of a HMM.

From playlist Machine Learning

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Ian Agol, Lecture 3: Applications of Kleinian Groups to 3-Manifold Topology

24th Workshop in Geometric Topology, Calvin College, June 30, 2007

From playlist Ian Agol: 24th Workshop in Geometric Topology

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(PP 6.1) Multivariate Gaussian - definition

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From playlist Probability Theory

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(PP 6.3) Gaussian coordinates does not imply (multivariate) Gaussian

An example illustrating the fact that a vector of Gaussian random variables is not necessarily (multivariate) Gaussian.

From playlist Probability Theory

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Cannon–Thurston maps – Mahan Mj – ICM2018

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From playlist Geometry

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G. Walsh - Boundaries of Kleinian groups

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From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie

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Hausdorff dimension of Kleinian group uniformization of Riemann surface... - Yong Hou

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From playlist Mathematics

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Profinite rigidity – Alan Reid – ICM2018

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From playlist Topology

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Hyperbolic groups, Cannon-Thurston maps, and hydra - Timothy Riley

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From playlist Mathematics

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(ML 7.7) Dirichlet-Categorical model (part 1)

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From playlist Machine Learning

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From playlist Workshop on Geometric Structures on 3-Manifolds

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JosLeys-Kleinian Adventures

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From playlist AI Animations

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Ahlfors-Bers 2014 "Quasi-isometric rigidity of the class of convex-cocompact Kleinian groups"

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From playlist The Ahlfors-Bers Colloquium 2014 at Yale

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(ML 7.7.A1) Dirichlet distribution

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From playlist Machine Learning

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(ML 16.6) Gaussian mixture model (Mixture of Gaussians)

Introduction to the mixture of Gaussians, a.k.a. Gaussian mixture model (GMM). This is often used for density estimation and clustering.

From playlist Machine Learning

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(ML 13.3) Directed graphical models - formalism (part 1)

Definition of a directed graphical model, or more precisely, what it means for a distribution to respect a directed acyclic graph.

From playlist Machine Learning

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Algebraic Ending Laminations and Quasiconvexity by Mahan Mj

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From playlist Surface Group Representations and Geometric Structures

Related pages

Fundamental group | Quotient space (topology) | Discrete group | Kleinian group | Mathematics | Felix Klein | Hyperbolic 3-manifold | Hyperbolic manifold | Fuchsian model