Differential structures | 4-manifolds
In mathematics, an exotic is a differentiable manifold that is homeomorphic (i.e. shape preserving) but not diffeomorphic (i.e. non smooth) to the Euclidean space The first examples were found in 1982 by Michael Freedman and others, by using the contrast between Freedman's theorems about topological 4-manifolds, and Simon Donaldson's theorems about smooth 4-manifolds. There is a continuum of non-diffeomorphic differentiable structures of as was shown first by Clifford Taubes. Prior to this construction, non-diffeomorphic smooth structures on spheres – exotic spheres – were already known to exist, although the question of the existence of such structures for the particular case of the 4-sphere remained open (and still remains open as of 2022). For any positive integer n other than 4, there are no exotic smooth structures on in other words, if n ≠ 4 then any smooth manifold homeomorphic to is diffeomorphic to (Wikipedia).
R Programming Introduction: Matrices (R intro-05)
[script is here https://github.com/bionicturtle/youtube/tree/master/r-intro] In R a matrix is an atomic vector with the dimension attribute. In this example, the correlation matrix is entered as a vector with sixteen elements: rho_v <-c(1.000, ...). Then the vector is translated into a mat
From playlist R Programming: Intro
1.6 Arrays and matrices in R | statistical analysis and data science course Rstudio | Dimensional
In this chapter of the video series in the crash course in statistics and data science with R / Rstudio we will see the definition, utilization, and importance of arrays with R. Also, we discuss their extension from vectors to matrices. Part 1: Definition - What is an array? - Array or
From playlist R Tutorial | Rstudio
Discover how Easystats in R can improve your linear and regression model analysis | Tutorial Data
Revolutionize your data analysis game with Easystats - the library that makes linear and regression model analysis a breeze!!! #R #rstudio #datascience #regression Comprehensive visualization of model checks checking model assumptions comparing models with plots model performances and co
From playlist Regression with R
Mark Hughes: Branched Coverings Over Surface Braids and (Broken) Lefschetz Fibrations
Mark Hughes, Brigham Young University Title: Branched Coverings Over Surface Braids and (Broken) Lefschetz Fibrations on Non- compact 4-Manifold In this talk I will discuss a construction of Lefschetz type fibrations on 4–manifolds via coverings branched over braided surfaces. When applied
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
C07 Homogeneous linear differential equations with constant coefficients
An explanation of the method that will be used to solve for higher-order, linear, homogeneous ODE's with constant coefficients. Using the auxiliary equation and its roots.
From playlist Differential Equations
R Programming: Introduction: Factors (R Intro-04)
[my R script is here https://github.com/bionicturtle/youtube/tree/master/r-intro] Factors are categorical vectors. Specifically, they are (integer) vectors that store categorical values, or ordinal values. Ordinal values are *ranked* categories (but they are not intervals).Factors can only
From playlist R Programming: Intro
In this lesson we learn about the most basic compound data type in R: the vector. Vectors in R are essentially lists of values of the same basic data type. R vectors are great for data analytics and data science because many common functions are built to operate on entire vectors all at on
From playlist Introduction to R
Daniel Friedan - Where does quantum field theory come from?
Daniel Friedan (Rutgers Univ.) Where does quantum field theory come from? This will be an interim report on a long-running project to construct a mechanism that produces spacetime quantum field theory; to indentify possible exotic, non-canonical low- energy phenomena in SU(2) and SU(3) gau
From playlist Conférence à la mémoire de Vadim Knizhnik
Symplectically knotted cubes - Felix Schlenk
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Symplectically knotted cubes Speaker: Felix Schlenk Affiliation: Université de Neuchâtel Date: July 02, 2021 While by a result of McDuff the space of symplectic embeddings of a closed 4-ball into an open 4-ball is con
From playlist Mathematics
Jack Calcut: Mazur and Jester 4-manifolds
Jack Calcut, Oberlin College Title: Mazur and Jester 4-manifolds Mazur and Po{\'e}naru constructed the first compact, contractible manifolds distinct from disks. More recently, Sparks modified Mazur's construction and defined Jester manifolds. Sparks used Jester manifolds to produce compac
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Using Factors - Introduction to R Programming - Part 8
When working with categorical data or categories, it is useful to treat these as factor levels. Learn how to cast character strings or numbers as factors so that they are treated as categories. -- Learn more about Data Science Dojo here: https://datasciencedojo.com/data-science-bootcamp/
From playlist Introduction to R Programming
Quaternions as 4x4 Matrices - Connections to Linear Algebra
In math, it's usually possible to view an object or concept from many different (but equivalent) angles. In this video, we will see that the quaternions may be viewed as 4x4 real-valued matrices of a special form. What is interesting here is that if you know how to multiply matrices, you a
From playlist Quaternions
Jialong Deng - Enlargeable Length-structures and Scalar Curvatures
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Jialong Deng, University of Goettingen Title: Enlargeable Length-structures and Scalar Curvatures Abstract: We define enlargeable length-structures on closed topological manifolds and then show that the connected sum of a
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
An introduction to Regression Analysis
Regression Analysis, R squared, statistics class, GCSE Like us on: http://www.facebook.com/PartyMoreStudyLess Related Videos Playlist on Linear Regression http://www.youtube.com/playlist?list=PLF596A4043DBEAE9C Using SPSS for Multiple Linear Regression http://www.youtube.com/playlist?li
From playlist Linear Regression.
Étienne Ghys: A guided tour of the seventh dimension
Abstract: One of the most amazing discoveries of John Milnor is an exotic sphere in dimension 7. For the layman, a sphere of dimension 7 may not only look exotic but even esoteric... It took a long time for mathematicians to gradually accept the existence of geometries in dimensions higher
From playlist Abel Lectures
You Could Have Invented Homology, Part 2: Some Simple Spaces | Boarbarktree
If it looks like this video increases dramatically in production quality over its runtime that's because this thing took hundreds of hours so I genuinely just got better at animating this kind of thing P.S., I make a slight mistake in the voice-over. First person to find it gets a special
From playlist You Could Have Invented Homology | Boarbarktree
Counting Cars: Danny's Quick Flip on Chevy Blazer (Season 6) | History
Watch all new episodes of Counting Cars returning soon, and stay up to date on all of your favorite History Channel shows at https://history.com/schedule. Danny goes nuts, revamping a classic 1972 Chevy Blazer into a bad car with some real road power, in this clip from Season 6, "Blinged
From playlist Counting Cars: Season 6 | History
Counting Cars: Danny's 1962 Cadillac Quick Flip Fiasco (Part 2) | History
Watch all new episodes of Counting Cars, returning soon, and stay up to date on all of your favorite History Channel shows at http://history.com/schedule. Now that Danny's 1962 Cadillac restoration is back on track mechanically, he's able to focus on making it BEAUTIFUL, in this scene fro
From playlist Counting Cars: Official Series Playlist | History
Data Types in R - Introduction to R Programming - Part 2
It’s really important to know your main data types so you can check what kind of values you’re working with when modeling data, or when casting it as a certain data type. Learn how to check numeric data types from integers, to floating-point numbers, to negative and positive numbers, as we
From playlist Introduction to R Programming