Time series | Entropy and information
In statistics, an approximate entropy (ApEn) is a technique used to quantify the amount of regularity and the unpredictability of fluctuations over time-series data. For example, consider two series of data: Series A: (0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, ...), which alternates 0 and 1.Series B: (0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, ...), which has either a value of 0 or 1, chosen randomly, each with probability 1/2. Moment statistics, such as mean and variance, will not distinguish between these two series. Nor will rank order statistics distinguish between these series. Yet series A is perfectly regular: knowing a term has the value of 1 enables one to predict with certainty that the next term will have the value of 0. In contrast, series B is randomly valued: knowing a term has the value of 1 gives no insight into what value the next term will have. Regularity was originally measured by exact regularity statistics, which has mainly centered on various entropy measures.However, accurate entropy calculation requires vast amounts of data, and the results will be greatly influenced by system noise, therefore it is not practical to apply these methods to experimental data. ApEn was developed by to handle these limitations by modifying an exact regularity statistic, Kolmogorov–Sinai entropy. ApEn was initially developed to analyze medical data, such as heart rate, and later spread its applications in finance, physiology, human factors engineering, and climate sciences. (Wikipedia).
Physics - Thermodynamics 2: Ch 32.7 Thermo Potential (10 of 25) What is Entropy?
Visit http://ilectureonline.com for more math and science lectures! In this video explain and give examples of what is entropy. 1) entropy is a measure of the amount of disorder (randomness) of a system. 2) entropy is a measure of thermodynamic equilibrium. Low entropy implies heat flow t
From playlist PHYSICS 32.7 THERMODYNAMIC POTENTIALS
Topics in Combinatorics lecture 10.0 --- The formula for entropy
In this video I present the formula for the entropy of a random variable that takes values in a finite set, prove that it satisfies the entropy axioms, and prove that it is the only formula that satisfies the entropy axioms. 0:00 The formula for entropy and proof that it satisfies the ax
From playlist Topics in Combinatorics (Cambridge Part III course)
The ENTROPY EQUATION and its Applications | Thermodynamics and Microstates EXPLAINED
Entropy is a hotly discussed topic... but how can we actually CALCULATE the entropy of a system? (Note: The written document discussed here can be found in the pinned comment below!) Hey everyone, I'm back with a new video, and this time it's a bit different to my usual ones! In this vid
From playlist Thermodynamics by Parth G
Entropy is often taught as a measure of how disordered or how mixed up a system is, but this definition never really sat right with me. How is "disorder" defined and why is one way of arranging things any more disordered than another? It wasn't until much later in my physics career that I
From playlist Thermal Physics/Statistical Physics
Teach Astronomy - Entropy of the Universe
http://www.teachastronomy.com/ The entropy of the universe is a measure of its disorder or chaos. If the laws of thermodynamics apply to the universe as a whole as they do to individual objects or systems within the universe, then the fate of the universe must be to increase in entropy.
From playlist 23. The Big Bang, Inflation, and General Cosmology 2
What is Geometric Entropy, and Does it Really Increase? - Jozsef Beck
Jozsef Beck Rutgers, The State University of New Jersey April 9, 2013 We all know Shannon's entropy of a discrete probability distribution. Physicists define entropy in thermodynamics and in statistical mechanics (there are several competing schools), and want to prove the Second Law, but
From playlist Mathematics
A better description of entropy
I use this stirling engine to explain entropy. Entropy is normally described as a measure of disorder but I don't think that's helpful. Here's a better description. Visit my blog here: http://stevemould.com Follow me on twitter here: http://twitter.com/moulds Buy nerdy maths things here:
From playlist Best of
Entropy production during free expansion of an ideal gas by Subhadip Chakraborti
Abstract: According to the second law, the entropy of an isolated system increases during its evolution from one equilibrium state to another. The free expansion of a gas, on removal of a partition in a box, is an example where we expect to see such an increase of entropy. The constructi
From playlist Seminar Series
From playlist Decision Tree Learning
A brief introduction to sofic entropy theory – Lewis Bowen – ICM2018
Analysis and Operator Algebras | Dynamical Systems and Ordinary Differential Equations Invited Lecture 8.15 | 9.16 A brief introduction to sofic entropy theory Lewis Bowen Abstract: Sofic entropy theory is a generalization of the classical Kolmogorov–Sinai entropy theory to actions of a
From playlist Dynamical Systems and ODE
Complexity Coarse - Graining in the Black Hole Information Problem - Netta Engelhardt
IAS It from Qubit Workshop Workshop on Spacetime and Quantum Information Tuesday December 6, 2022 Wolfensohn Hall Engelhardt-2022-12-06
From playlist IAS It from Qubit Workshop - Workshop on Spacetime and Quantum December 6-7, 2022
A modern take on the information paradox.... (Lecture - 03) by Ahmed Almheiri
INFOSYS-ICTS STRING THEORY LECTURES A MODERN TAKE ON THE INFORMATION PARADOX AND PROGRESS TOWARDS ITS RESOLUTION SPEAKER: Ahmed Almheiri (Institute for Advanced Study, Princeton) DATE: 30 September 2019 to 03 October 2019 VENUE: Emmy Noether Seminar Room, ICTS Bangalore Lecture 1: Mond
From playlist Infosys-ICTS String Theory Lectures
Nexus Trimester - Ronitt Rubinfeld (MIT and Tel Aviv University) 2/2
Testing properties of distributions over big domains : information theoretic quantities Ronitt Rubinfeld (MIT and Tel Aviv University) march 10, 2016 Abstract: We survey several works regarding the complexity of testing global properties of discrete distributions, when given access to o
From playlist 2016-T1 - Nexus of Information and Computation Theory - CEB Trimester
Cory Hauck: Approximate entropy-based moment closures
Recorded during the meeting "Numerical Methods for Kinetic Equations 'NumKin21' " the June 17, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M
From playlist Virtual Conference
Verifying The Unseen: Interactive Proofs for Label-Invariant Distribution Properties - Guy Rothblum
Computer Science/Discrete Mathematics Seminar I Topic: Verifying The Unseen: Interactive Proofs for Label-Invariant Distribution Properties Speaker: Guy Rothblum Affiliation: Weizmann Institute Date: October 4, 2021 Given i.i.d. samples drawn from an unknown distribution over a large do
From playlist Mathematics
Statistical Mechanics Lecture 3
(April 15, 20123) Leonard Susskind begins the derivation of the distribution of energy states that represents maximum entropy in a system at equilibrium. Originally presented in the Stanford Continuing Studies Program. Stanford University: http://www.stanford.edu/ Continuing Studies P
From playlist Course | Statistical Mechanics
Bourbaki - 16/01/2016 - 1/4 - Damien GABORIAU
Damien GABORIAU — Entropie sofique [d'après L. Bowen, D. Kerr et H. Li] L’entropie fut introduite en systèmes dynamiques par A. Kolmogorov. Initialement focalisée sur les itérations d’une transformation préservant une mesure finie, la notion fut peu à peu généralisée, jusqu’à embrasser l
From playlist Bourbaki - 16 janvier 2016
Lecture 5 | Modern Physics: Statistical Mechanics
April 27, 2009 - Leonard Susskind discusses the basic physics of the diatomic molecule and why you don't have to worry about its structure at low temperature. Susskind later explores a black hole thermodynamics. Stanford University: http://www.stanford.edu/ Stanford Continuing Studi
From playlist Lecture Collection | Modern Physics: Statistical Mechanics
(IC 3.4) Remark - an alternate proof
The non-negativity of relative entropy can also be used to show that the expected codeword length of a symbol code is bounded below by the entropy of the source. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F
From playlist Information theory and Coding