(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
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
Math 139 Fourier Analysis Lecture 35: Dirichlet's theorem pt. 2
Dirichlet's theorem: reduction of the problem. Dirichlet L-function. Product formula for L-functions. Extension of the logarithm to complex numbers. Convergence of infinite products.
From playlist Course 8: Fourier Analysis
Math 139 Fourier Analysis Lecture 38: Finishing proof of Dirichlet's theorem
Showing the non-vanishing of the L-function for real Dirichlet characters. Approximation of L(1,X) with hyperbolic sums to finish the theorem.
From playlist Course 8: Fourier Analysis
Representation theory: Dirichlet's theorem
In this talk we see how to use characters of finite abelian groups to prove Dirichlet's theorem that there are infinitely many primes in certain arithmetic progressions. We first recall Euler's proof that there are infinitely many primes, which is the simplest case of Dirichlet's proof. T
From playlist Representation theory
(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
Math 139 Fourier Analysis Lecture 37: Dirichlet's theorem pt.4
Defining the logarithm of an L-function. Second reduction of the problem: proving non-vanishing of the L-function. Case of complex Dirichlet characters.
From playlist Course 8: Fourier Analysis
Math 139 Fourier Analysis Lecture 08: Dirichlet Problem on the Unit Disc
Dirichlet problem on the Unit Disc: the problem; the Poisson integral solves the heat equation. L^2 convergence of Fourier Series: definition of L^2 norm; quick review of relevant ideas from linear algebra (vector space, inner product, norm, orthogonal, Pythagorean Theorem, Cauchy-Schwarz
From playlist Course 8: Fourier Analysis
Due to the COVID-19 pandemic, Carnegie Mellon University is protecting the health and safety of its community by holding all large classes online. People from outside Carnegie Mellon University are welcome to tune in to see how the class is taught, but unfortunately Prof. Loh will not be o
From playlist CMU 21-228 Discrete Mathematics
Index theorems for nodal count and a lateral variation principle - Gregory Berkolaiko
Analysis Seminar Topic: Index theorems for nodal count and a lateral variation principle Speaker: Gregory Berkolaiko Affiliation: Texas A&M University Date: February 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
CTNT 2022 - 100 Years of Chebotarev Density (Lecture 1) - by Keith Conrad
This video is part of a mini-course on "100 Years of Chebotarev Density" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)
A Taste of Calculus of Variations
Dirichlet's Principle In this video, I give you a taste of calculus of variations by illustrating Dirichlet's principle, which says that a function u is a minimizer of a certain Dirichlet energy (kinetic + potential energy) if and only if u solves Poisson's equation. This is a neat way of
From playlist Partial Differential Equations
James Maynard: Half-isolated zeros and zero-density estimates
We introduce a new zero-detecting method which is sensitive to the vertical distribution of zeros of the zeta function. This allows us to show that there are few 'half-isolated' zeros, and allows us to improve the classical zero density result to N(σ,T)≪T24(1−σ)/11+o(1) if we assume that t
From playlist Seminar Series "Harmonic Analysis from the Edge"
Adam Skalski: Translation invariant noncommutative Dirichlet forms
Talk by Adam Skalski in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on April 28, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
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
Low moments of character sums - Adam Harper
Joint IAS/Princeton University Number Theory Seminar Topic: Low moments of character sums Speaker: Adam Harper Affiliation: University of Warwick Date: April 08, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Math 139 Fourier Analysis Lecture 05: Convolutions and Approximation of the Identity
Convolutions and Good Kernels. Definition of convolution. Convolution with the n-th Dirichlet kernel yields the n-th partial sum of the Fourier series. Basic properties of convolution; continuity of the convolution of integrable functions.
From playlist Course 8: Fourier Analysis