Information theory | Inequalities
In information theory, Fano's inequality (also known as the Fano converse and the Fano lemma) relates the average information lost in a noisy channel to the probability of the categorization error. It was derived by Robert Fano in the early 1950s while teaching a Ph.D. seminar in information theory at MIT, and later recorded in his 1961 textbook. It is used to find a lower bound on the error probability of any decoder as well as the lower bounds for in density estimation. Let the random variables and represent input and output messages with a joint probability . Let represent an occurrence of error; i.e., that , with being an approximate version of . Fano's inequality is where denotes the support of , is the conditional entropy, is the probability of the communication error, and is the corresponding binary entropy. (Wikipedia).
Nexus Trimester - Suresh Venkatasubramanian (University of Utah) 3/3
From Pigeons to Fano, and beyond Suresh Venkatasubramanian (University of Utah) February 17, 2016 Abstract: Fano's inequality can be viewed as capturing a deep interplay between information and computation. It links storage, reconstruction and transmission in one inequality, generalizing
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Viviani's Theorem | Visualization and Proof
A visual proof of Viviani's theorem. For any point inside an equilateral triangle, the sum of its perpendicular distances from the three sides is constant. And, this sum is equal to the length of the triangle's altitude. Follow: https://instagram.com/doubleroot.in Music by CeeaDidIt from
From playlist Summer of Math Exposition Youtube Videos
Nexus Trimester - Suresh Venkatasubramanian (University of Utah) 1/3
From Pigeons to Fano, and beyond Suresh Venkatasubramanian (University of Utah) February 17, 2016 Abstract: Fano's inequality can be viewed as capturing a deep interplay between information and computation. It links storage, reconstruction and transmission in one inequality, generalizing
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
The golden angle | Lecture 18 | Fibonacci Numbers and the Golden Ratio
Definition of the golden angle from the golden ratio. Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1
From playlist Fibonacci Numbers and the Golden Ratio
The golden ratio | Lecture 3 | Fibonacci Numbers and the Golden Ratio
The classical definition of the golden ratio. Two positive numbers are said to be in the golden ratio if the ratio between the larger number and the smaller number is the same as the ratio between their sum and the larger number. Phi=(1+sqrt(5))/2 approx 1.618. Join me on Coursera: http
From playlist Fibonacci Numbers and the Golden Ratio
Nexus Trimester - Suresh Venkatasubramanian (University of Utah) 2/3
From Pigeons to Fano, and beyond Suresh Venkatasubramanian (University of Utah) February 17, 2016 Abstract: Fano's inequality can be viewed as capturing a deep interplay between information and computation. It links storage, reconstruction and transmission in one inequality, generalizing
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
This is a short, animated visual proof of Viviani's theorem, which states that the sum of the distances from any interior point to the sides of an equilateral triangle is equal to the length of the triangle's altitude. #math #geometry #mtbos #manim #animation #theorem #pww #proofwith
From playlist MathShorts
Understanding Wealth Inequality
We've talked about public goods and externalities, and one negative externality associated with economic decisions is wealth inequality. A certain measure of wealth inequality is expected and desirable for any economy. But when this becomes extreme, as it is in the United States and many o
From playlist Economics
Marta Pieropan, The split torsor method for Manin’s conjecture
See https://tinyurl.com/y98dn349 for an updated version of the slides with minor corrections. VaNTAGe seminar 20 April 2021
From playlist Manin conjectures and rational points
Introduction to Differential Inequalities
What is a differential inequality and how are they useful? Inequalities are a very practical part of mathematics: They give us an idea of the size of things -- an estimate. They can give us a location for things. It is usually far easier to satisfy assumptions involving inequalities t
From playlist Advanced Studies in Ordinary Differential Equations
Nexus Trimester - Randall Dougherty (Center for Communications Research)
Entropy inequalities and linear rank inequalities Randall Dougherty (Center for Communications Research) February 16, 2016 Abstract: Entropy inequalities (Shannon and non-Shannon) have been used to obtain bounds on the solutions to a number of problems. When the problems are restricted t
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Thibaut Delcroix : Kähler-Einstein metrics on group compactifications
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Complex Brunn–Minkowski theory and positivity of vector bundles – Bo Berndtsson – ICM2018
Geometry | Analysis and Operator Algebras Invited Lecture 5.2 | 8.2 Complex Brunn–Minkowski theory and positivity of vector bundles Bo Berndtsson Abstract: This is a survey of results on positivity of vector bundles, inspired by the Brunn–Minkowski and Prékopa theorems. Applications to c
From playlist Geometry
La théorie l’information sans peine - Bourbaphy - 17/11/18
Olivier Rioul (Telecom Paris Tech) / 17.11.2018 La théorie l’information sans peine ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter : https://twitter.com
From playlist Bourbaphy - 17/11/18 - L'information
Uniformly valuative stability of polarized varieties and applications
Speaker: Yaxiong Liu (Tsinghua University) Abstract: In the study of K-stability, Fujita and Li proposed the valuative criterion of K-stability on Fano varieties, which has played an essential role of the algebraic theory of K-stability. Recently, Dervan-Legendre considered the valuative
From playlist Informal Geometric Analysis Seminar
Viviani's Theorem: "Proof" Without Words
Link: https://www.geogebra.org/m/BXUrfwxj
From playlist Geometry: Challenge Problems