Hilbert R-tree, an R-tree variant, is an index for multidimensional objects such as lines, regions, 3-D objects, or high-dimensional feature-based parametric objects. It can be thought of as an extension to B+-tree for multidimensional objects. The performance of R-trees depends on the quality of the algorithm that clusters the data rectangles on a node. Hilbert R-trees use space-filling curves, and specifically the Hilbert curve, to impose a linear ordering on the data rectangles. There are two types of Hilbert R-trees: one for static databases, and one for dynamic databases. In both cases Hilbert space-filling curves are used to achieve better ordering of multidimensional objects in the node. This ordering has to be "good", in the sense that it should group "similar" data rectangles together, to minimize the area and perimeter of the resulting minimum bounding rectangles (MBRs). Packed Hilbert R-trees are suitable for static databases in which updates are very rare or in which there are no updates at all. The dynamic Hilbert R-tree is suitable for dynamic databases where insertions, deletions, or updates may occur in real time. Moreover, dynamic Hilbert R-trees employ flexible deferred splitting mechanism to increase the space utilization. Every node has a well defined set of sibling nodes. This is done by proposing an ordering on the R-tree nodes. The Hilbert R-tree sorts rectangles according to the of the center of the rectangles (i.e., MBR). (The Hilbert value of a point is the length of the Hilbert curve from the origin to the point.) Given the ordering, every node has a well-defined set of sibling nodes; thus, deferred splitting can be used. By adjusting the split policy, the Hilbert R-tree can achieve a degree of space utilization as high as desired. To the contrary, other R-tree variants have no control over the space utilization. (Wikipedia).
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/2toQ.
From playlist 3D printing
Algebraic geometry 49: Hilbert polynomials
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives a review of the Hilbert polynomial of a graded module over a graded ring, and classifies integer-valued polynomials.
From playlist Algebraic geometry I: Varieties
This shows a 3d printed mobile produced using shapeways.com. This is joint work with Marco Mahler. This is available at http://shpws.me/nPh7.
From playlist 3D printing
Anthony Licata: Hilbert Schemes Lecture 7
SMRI Seminar Series: 'Hilbert Schemes' Lecture 7 Kleinian singularities 2 Anthony Licata (Australian National University) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students inter
From playlist SMRI Course: Hilbert Schemes
Lecture 24. Hilbert basis theorem
From playlist Abstract Algebra 2
Noah Arbesfeld: A geometric R-matrix for the Hilbert scheme of points on a general surface
Abstract: We explain how to use a Virasoro algebra to construct a solution to the Yang-Baxter equation acting in the tensor square of the cohomology of the Hilbert scheme of points on a generalsurface S. In the special case where the surface S is C2, the construction appears in work of Mau
From playlist Algebraic and Complex Geometry
Finding the Tallest Tree: comparing tree-based models
Tree-based models such as decision trees, random forests, and boosted trees provide powerful predictions and are fast to compute. There are many different ways to fit these models in R, including the rpart, randomForest, and xgboost packages. During this talk, we'll examine numerous ways t
From playlist Introduction to Machine Learning
R programming for Beginners | R programming for data Science
R is a programming language and free software environment for statistical computing and graphics supported by the R Foundation for Statistical Computing. The R language is widely used among statisticians and data miners for developing statistical software and data analysis. This video is a
From playlist Programming
Amine Marrakchi: Ergodic theory of affine isometric actions on Hilbert spaces
The Gaussian functor associates to every orthogonal representation of a group G on a Hilbert space, a probability measure preserving action of G called a Gaussian action. This construction is a fundamental tool in ergodic theory and is the source of a large and interesting class of probabi
From playlist Probability and Statistics
Joshua Ciappara: Hilbert Schemes Lecture 10
SMRI Seminar Series: 'Hilbert Schemes' Lecture 10 Representations of Heisenberg algebras on homology of Hilbert schemes Joshua Ciappara (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way tha
From playlist SMRI Course: Hilbert Schemes
Anthony Nouy: Approximation and learning with tree tensor networks - Lecture 1
Recorded during the meeting "Data Assimilation and Model Reduction in High Dimensional Problems" the July 21, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Récanzone A kinetic description of a plasma in external and self-consistent fiel
From playlist Numerical Analysis and Scientific Computing
Actions on Delta-Median Spaces by Indira Chatterji
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
Nonlinear Dvoretzky Theory - Assaf Naor
Assaf Naor Institute for Advanced Study December 6, 2010 The classical Dvoretzky theorem asserts that for every integer k greater than 1 and every target distortion D greater than 1 there exists an integer n=n(k,D) such that any n-dimensional normed space contains a subspace of dimension
From playlist Mathematics
Minerva Lectures 2013 - Assaf Naor Talk 1: An introduction to the Ribe program
For more information, please see: http://www.math.princeton.edu/events/seminars/minerva-lectures/minerva-lecture-i-introduction-ribe-program
From playlist Minerva Lectures - Assaf Naor
Geometry of the Hilbert cuspidal eigenvariety at weight one Eisenstein by Mladen Dimitrov
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
Clément Dell’aiera - Paires de Hecke et K-théorie
Introduites par Shimura en théorie des nombres dans les années 50, les paires de Hecke sont des inclusions de sous-groupes qui sont presque normales : leurs conjugués sont tous commensurables. À une paire de Hecke est associée un groupe localement compact totalement discontinu : sa complét
From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”
Graph comparison - Anton Petrunin
Analysis Seminar Topic: Graph comparison Speaker: Anton Petrunin Affiliation: Pennsylvania State University Date: March 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Tutorial for Yang-Hui He lectures by Ed Hirst & Jiakang Bao
PROGRAM KAVLI ASIAN WINTER SCHOOL (KAWS) ON STRINGS, PARTICLES AND COSMOLOGY (ONLINE) ORGANIZERS Francesco Benini (SISSA, Italy), Bartek Czech (Tsinghua University, China), Dongmin Gang (Seoul National University, South Korea), Sungjay Lee (Korea Institute for Advanced Study, South Korea
From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology (ONLINE) - 2022
IGA: Luca di Cerbo - The Singer conjecture in dimension three revisited and its extensions
Abstract: In this talk, I will show how Price inequalities for harmonic forms combined with some standard topology and geometry of 3-manifolds imply the Singer conjecture in dimension three. This provides an alternative proof of a result of Lott and Lueck (Invent. Math., 1995). Finally, I
From playlist Informal Geometric Analysis Seminar
This video introduces rooted trees and how to define the relationships among vertices in a rooted tree. mathispower4u.com
From playlist Graph Theory (Discrete Math)