Hyperbolic geometry | Kleinian groups
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).
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
(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
(ML 14.4) Hidden Markov models (HMMs) (part 1)
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
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
(PP 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
(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
Cannon–Thurston maps – Mahan Mj – ICM2018
Geometry Invited Lecture 5.9 Cannon–Thurston maps Mahan Mj Abstract: We give an overview of the theory of Cannon–Thurston maps which forms one of the links between the complex analytic and hyperbolic geometric study of Kleinian groups. We also briefly sketch connections to hyperbolic sub
From playlist Geometry
G. Walsh - Boundaries of Kleinian groups
We study the problem of classifying Kleinian groups via the topology of their limit sets. In particular, we are interested in one-ended convex-cocompact Kleinian groups where each piece in the JSJ decomposition is a free group, and we describe interesting examples in this situation. In ce
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
Hausdorff dimension of Kleinian group uniformization of Riemann surface... - Yong Hou
Topic: Hausdorff dimension of Kleinian group uniformization of Riemann surface and conformal rigidity Speaker: Yong Hou Date:Tuesday, November 24 For this talk I'll discuss uniformization of Riemann surfaces via Kleinian groups. In particular question of conformability by Hasudorff dimens
From playlist Mathematics
Profinite rigidity – Alan Reid – ICM2018
Topology Invited Lecture 6.7 Profinite rigidity Alan Reid Abstract: We survey recent work on profinite rigidity of residually finite groups. © International Congress of Mathematicians – ICM www.icm2018.org Os direitos sobre todo o material deste canal pertencem ao Instituto de Mat
From playlist Topology
Hyperbolic groups, Cannon-Thurston maps, and hydra - Timothy Riley
Timothy Riley Cornell University; Member, School of Mathematics November 17, 2014 Groups are Gromov-hyperbolic when all geodesic triangles in their Cayley graphs are close to being tripods. Despite being tree-like in this manner, they can harbour extreme wildness in their subgroups. I wil
From playlist Mathematics
(ML 7.7) Dirichlet-Categorical model (part 1)
The Dirichlet distribution is a conjugate prior for the Categorical distribution (i.e. a PMF a finite set). We derive the posterior distribution and the (posterior) predictive distribution under this model.
From playlist Machine Learning
Boundaries of Kleinian groups - Genevieve Walsh
Genevieve Walsh, Tufts October 7, 2015 http://www.math.ias.edu/wgso3m/agenda Monday, October 5, 2015 - 08:00 to Friday, October 9, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 academic year at t
From playlist Workshop on Geometric Structures on 3-Manifolds
I was meant to be going to Canadia, but the boat sank and I really needed a boat for some reason. So instead I took my spaceship to JosLeys-Kleinianland. It's weird there... Fractal rendered in Mandelbulber2 3d model created in Oculus Medium Composited in HitFilm 12 "Flying Free" audio
From playlist AI Animations
Ahlfors-Bers 2014 "Quasi-isometric rigidity of the class of convex-cocompact Kleinian groups"
Peter Haïssinsky (Toulouse): The talk will be devoted to discussing background and ingredients for the proof of the following theorem: a finitely generated group quasi-isometric to a convex-cocompact Kleinian group contains a finite index subgroup isomorphic to a convex-cocompact Kleinian
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
(ML 7.7.A1) Dirichlet distribution
Definition of the Dirichlet distribution, what it looks like, intuition for what the parameters control, and some statistics: mean, mode, and variance.
From playlist Machine Learning
(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
(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
Algebraic Ending Laminations and Quasiconvexity by Mahan Mj
Surface Group Representations and Geometric Structures DATE: 27 November 2017 to 30 November 2017 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classi
From playlist Surface Group Representations and Geometric Structures