Uploaded November 2024 | Updated September 2026, 2 weeks ago
Here we introduce the binomial distribution, which is one of the most important distributions in all of probability. It will be the basis of the Normal distribution and the Poisson distribution. The binomial distribution quantifies the probability of getting "r" successes in "n" Bernoulli trials. For example, the probability of getting 5 heads in 10 coin flips is Binomially distributed. We also introduce the more general multinomial distribution.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:25 Binomial Coefficients
07:34 Defining the Multinomial Distribution
10:39 Proving the Formula
14:33 Outro
Here we introduce the binomial distribution, which is one of the most important distributions in all of probability. It will be the basis of the Normal distribution and the Poisson distribution. The binomial distribution quantifies the probability of getting "r" successes in "n" Bernoulli trials. For example, the probability of getting 5 heads in 10 coin flips is Binomially distributed. We also introduce the more general multinomial distribution.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:25 Binomial Coefficients
07:34 Defining the Multinomial Distribution
10:39 Proving the Formula
14:33 Outro
![[6/8] Control for Societal-Scale Challenges: Road Map 2030 [Education]](https://i.ytimg.com/vi/VuAFZPwygyE/mqdefault.jpg "[6/8] Control for Societal-Scale Challenges: Road Map 2030 [Education]
This video explores the importance of education in realizing the ambitious goals of this road map document. This follows Chapter 6 of the Control for Societal-Scale Challenges: Road Map 2030 document.
https://www.ieeecss.org/control-societal-scale-challenges-road-map-2030
The production of this video was supported by the IFAC.
Roadmap Abstract: The world faces some of its greatest challenges of modern time and how we address them will have a dramatic impact on the life for generations to come. Simultaneously, control systems, consisting of information enriched by various degrees of analytics followed by decision-making, are pervading a variety of sectors, not only in engineering but beyond, into financial services, socio-economic analysis, entertainment and sports, and political and social sciences. Increased levels of automation are sought after in various sectors and being introduced into new domains. All of these advances and transformations urge a shift in the conversation toward how control systems can meet grand societal- scale challenges. The document seeks to chart a roadmap for the evolution of control systems, identifying several areas where our discipline can have an impact over the next decade.
Edited by: Anuradha M. Annaswamy, Karl H. Johansson, and George J. Pappas
Authors: Andrew Alleyne, Frank Allgöwer, Aaron D. Ames, Saurabh Amin, James Anderson, Anuradha M. Annaswamy, Panos J. Antsaklis, Neda Bagheri, Hamsa Balakrishnan, Bassam Bamieh, John Baras, Margret Bauer, Alexandre Bayen, Paul Bogdan, Steven L. Brunton, Francesco Bullo, Etienne Burdet, Joel Burdick, Laurent Burlion, Carlos Canudas de Wit, Ming Cao, Christos G. Cassandras, Aranya Chakrabortty, Giacomo Como, Marie Csete, Fabrizio Dabbene, Munther Dahleh, Amritam Das, Eyal Dassau, Claudio De Persis, Mario di Bernardo, Stefano Di Cairano, Dimos V. Dimarogonas, Florian Dörfler, John C. Doyle, Francis J. Doyle III, Anca Dragan, Magnus Egerstedt, Johan Eker, Sarah Fay, Dimitar Filev, Angela Fontan, Elisa Franco, Masayuki Fujita, Mario Garcia-Sanz, Dennice Gayme, Wilhelmus P.M.H. Heemels, João P. Hespanha, Sandra Hirche, Anette Hosoi, Jonathan P. How, Gabriela Hug, Marija Ilić, Hideaki Ishii, Ali Jadbabaie, Matin Jafarian, Samuel Qing-Shan Jia, Tor Arne Johansen, Karl H. Johansson, Dalton Jones, Mustafa Khammash, Pramod Khargonekar, Mykel J. Kochenderfer, Andreas Krause, Anthony Kuh, Dana Kulić, Françoise Lamnabhi-Lagarrigue, Naomi E. Leonard, Frederick Leve, Na Li, Steven Low, John Lygeros, Iven Mareels, Sonia Martinez, Nikolai Matni, Tommaso Menara, Katja Mombaur, Kevin Moore, Richard Murray, Toru Namerikawa, Angelia Nedich, Sandeep Neema, Mariana Netto, Timothy O’Leary, Marcia K. O’Malley, Lucy Y. Pao, Antonis Papachristodoulou, George J. Pappas, Philip E. Paré, Thomas Parisini, Fabio Pasqualetti, Marco Pavone, Akshay Rajhans, Gireeja Ranade, Anders Rantzer, Lillian Ratliff, J. Anthony Rossiter, Dorsa Sadigh, Tariq Samad, Henrik Sandberg, Sri Sarma, Luca Schenato, Jacquelien Scherpen, Angela Schoellig, Rodolphe Sepulchre, Jeff Shamma, Robert Shorten, Bruno Sinopoli, Koushil Sreenath, Jakob Stoustrup, Jing Sun, Paulo Tabuada, Emma Tegling, Dawn Tilbury, Claire J. Tomlin, Jana Tumova, Kevin Wise, Dan Work, Junaid Zafar, Melanie Zeilinger
This video was produced at the University of Washington")
![Fourier Neural Operator (FNO) [Physics Informed Machine Learning]](https://i.ytimg.com/vi/W8PybqAk6Ik/mqdefault.jpg "Fourier Neural Operator (FNO) [Physics Informed Machine Learning]
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:54 Operators as Images, Fourier as Convolution
04:43 Zero-Shot Super Resolution
07:33 Generalizing Neural Operators
09:47 Conditions and Operator Kernels
10:53 Mesh Invariance
12:31 Why Neural Operators // Or Neural operators vs other methods
13:47 Result: Greens Function
15:14 Laplace Neural Operators
17:14 Outro")
