Dirichlet kernel

(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

NOT AS TRIVIAL AS IT MIGHT SEEM! Integrating the Dirichlet Kernel

Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy Let us make use of the Dirichlet Kernel today! We are going to integrate this one using its definition as a sum/approximate Fourier Series. Enjoy! My Website: http

From playlist Integrals

The Dirichlet Kernel - An Alternative Expression

Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy Moving on with the Dirichlet Kernel stuff! =) Today we are going to show, that said Kernel is not only a quotient of sine waves but also a superposition of cosine w

From playlist Fourier Series

The Dirichlet Kernel - Deriving a Quotient of Sine Waves

Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy Good morning flammers :vvv Let us introduce the Dirichlet Kernel today and then derive an alternative formulation of said expression using the geometric series. Enj

From playlist Fourier Series

Math 139 Fourier Analysis Lecture 06: Convolutions and Approximations of the Identity, ct'd.

Convolutions and Good Kernels, continued. Interaction of convolution with Fourier transform (for integrable functions). Approximations of the Identity (family of good kernels). Recovery of the value of a function at a point of continuity using approximations of the identity. Uniform co

From playlist Course 8: Fourier Analysis

(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

(ML 7.8) Dirichlet-Categorical model (part 2)

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

Dirichlet Eta Function - Integral Representation

Today, we use an integral to derive one of the integral representations for the Dirichlet eta function. This representation is very similar to the Riemann zeta function, which explains why their respective infinite series definition is quite similar (with the eta function being an alte rna

From playlist Integrals

Using Fourier Series to Derive the Dirichlet Kernel

Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://shop.spreadshirt.de/papaflammy Let's continue the Kernel Extravaganza! TOday we are going to approximate the fourier series of a random f

From playlist Fourier Series

Lecture 16: Fejer’s Theorem and Convergence of Fourier Series

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=8IxHMVf3jcA&list=PLUl4u3cNGP63micsJp_

From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021

Spectral Analysis of a Diffusion Operator with Random Jumps from theBoundary-Konstantin Pankrashkin

From playlist Mathematics of Condensed Matter and Beyond (February 22-25, 2021)

Radek Adamczak: Functional inequalities and concentration of measure III

Concentration inequalities are one of the basic tools of probability and asymptotic geo- metric analysis, underlying the proofs of limit theorems and existential results in high dimensions. Original arguments leading to concentration estimates were based on isoperimetric inequalities, whic

From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability

The Ground State of the Pauli Operator - Mikael Persson Sundqvist

From playlist Mathematics of Condensed Matter and Beyond (February 22-25, 2021)

Hamza Fawzi: "Sum-of-squares proofs of logarithmic Sobolev inequalities on finite Markov chains"

Entropy Inequalities, Quantum Information and Quantum Physics 2021 "Sum-of-squares proofs of logarithmic Sobolev inequalities on finite Markov chains" Hamza Fawzi - University of Cambridge Abstract: Logarithmic Sobolev inequalities play an important role in understanding the mixing times

From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021

Calderon problem (Lecture 1) by Venkateswaran P Krishnan

DISCUSSION MEETING WORKSHOP ON INVERSE PROBLEMS AND RELATED TOPICS (ONLINE) ORGANIZERS: Rakesh (University of Delaware, USA) and Venkateswaran P Krishnan (TIFR-CAM, India) DATE: 25 October 2021 to 29 October 2021 VENUE: Online This week-long program will consist of several lectures by

From playlist Workshop on Inverse Problems and Related Topics (Online)

Roland Bauerschmidt: Lecture #2

This is a second lecture on "Log-Sobolev inequality and the renormalisation group" by Dr. Roland Bauerschmidt. For more materials and slides visit: https://sites.google.com/view/oneworld-pderandom/home

From playlist Summer School on PDE & Randomness

Math 131 Spring 2022 050422 Riemann-Lebesgue lemma; Classical Fourier Series.

Recall definition of orthonormal systems. Results about General Fourier Series: Proof of "Best Mean Square Approximation" (that the partial sum of the Fourier series of a (Riemann integrable) function is the best linear combination approximating the function in the L2 sense). Consequence

From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)

Math 131 Fall 2018 121218 Advertising the Fourier Analysis course

Advertising Math 139: Fourier Analysis. Ubiquitous. Applications. Fourier Series: application (isoperimetric inequality). Fourier transform; application (Radon transform). Fourier series on finite abelian groups; application (Dirichlet's theorem). Brief introduction to Fourier series

From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)

On the Spectrum of Spiral Quantum Waveguides - Pavel Exner

From playlist Mathematics of Condensed Matter and Beyond (February 22-25, 2021)