In type theory, a type system has the property of subject reduction (also subject evaluation, type preservation or simply preservation) if evaluation of expressions does not cause their type to change. Formally, if Γ ⊢ e1 : τ and e1 → e2 then Γ ⊢ e2 : τ. Intuitively, this means one would not like to write a expression, in say Haskell, of type Int, and have it evaluate to a value v, only to find out that v is a string. Together with , it is an important meta-theoretical property for establishing type soundness of a type system. The opposite property, if Γ ⊢ e2 : τ and e1 → e2 then Γ ⊢ e1 : τ, is called subject expansion. It often does not hold as evaluation can erase ill-typed sub-terms of an expression, resulting in a well-typed one. (Wikipedia).
Data-Driven Control: The Goal of Balanced Model Reduction
In this lecture, we discuss the overarching goal of balanced model reduction: Identifying key states that are most jointly controllable and observable, to capture the most input—output energy. https://www.eigensteve.com/
From playlist Data-Driven Control with Machine Learning
The concept of “dimension” in measured signals
This is part of an online course on covariance-based dimension-reduction and source-separation methods for multivariate data. The course is appropriate as an intermediate applied linear algebra course, or as a practical tutorial on multivariate neuroscience data analysis. More info here:
From playlist Dimension reduction and source separation
6A Matrix Reduction with Gauss Elimination-YouTube sharing.mov
The complicated issue of row reduction using elementary row operations (Gauss elimination).
From playlist Linear Algebra
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
At times, it might be useful to express a single column in a table as a single value, such as adding all the values in that column or calculating the mean or variance of the values in that column. This can be achieved using the reduce() function. For a full course in Julia, have a look a
From playlist Julia on Coursera
Computing Limits from a Graph with Infinities
In this video I do an example of computing limits from a graph with infinities.
From playlist Limits
Sensors: Direct sensing - A Level Physics
Part 1 of 2: What a direct sensor is, how to incorporate it in a circuit such that it can cause action to happen when external circumstances (light levels, temperature, pressure) change.
From playlist A Level Physics Revision
Sensitivity (Electrical Engineering)
https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. In this video
From playlist Advanced Circuit Design
Electrical Engineering: Ch 12 AC Power (48 of 58) What is the Power Factor Correction? 1
Visit http://ilectureonline.com for more math and science lectures! In this video I will reduce the phase angle in a way that we can provide the same amount to the load with less current to the load. We can accomplish that putting in a capacitor parallel to the load. (From the last video
From playlist ELECTRICAL ENGINEERING 12 AC POWER
2008 AP Statistics Form B FRQ #4: Test Design and Type I and II Errors
This video helps students work through problem 4 from the 2008 AP Statistics exam, Form B, that deals with test design and errors. The free-response section of the AP Stats exam tests your ability to apply your knowledge of a variety of areas in statistics, including hypothesis testing, re
From playlist AP® Statistics Exam: Free Response Questions
Synthesis Workshop: Synthesis of Cardiotonic Steroids with Dr. Zachary Fejedelem (Episode 78)
In this Research Spotlight episode, we're joined by Dr. Zachary Fejedelem (Nagorny lab doctoral alumnus, University of Michigan), who shares with us his work on the synthesis of the cardiotonic steroids oleandrigenin and rhodexin B. Key reference: J. Org. Chem. 2021, 86, 10249−10262. http
From playlist Research Spotlights
Synthesis Workshop: Syntheses of Macfarlandin C + Dendrillolide A with Dr. Tyler Allred (Episode 40)
In this Research Spotlight episode, we're joined by Dr. Tyler Allred (postdoc in Overman group, UC Irvine), who shares with us his work on the synthesis of Macfarlandin C and Dendrillolide A. Parent references: Angew. Chem. Int. Ed. 2020, 59, 6268-6272. J. Org. Chem. 2020, 85, 15532-15551
From playlist Research Spotlights
Simultaneous equidistribution of supersingular reductions of CM-curves by Manuel Luethi
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
Can Human Action Be Explained? (Charles Taylor)
Charles Taylor (Professor Emeritus of Philosophy at McGill University) considers and discusses the issue of explanation in the sphere of human action in a lecture given at Columbia University in 2009. It was co-sponsored with the Committee on Global Thought; Heyman Center for Humanities; C
From playlist Free Will, Determinism, & Action
Synthesis Workshop: Total Synthesis of (-)-Strempeliopine with Xianhuang Zeng (Episode 65)
In this Research Spotlight Episode, we're joined by Xianhuang Zeng, who takes us through his work on the total synthesis of (-)-strempeliopine (Boger Lab, Scripps). Key reference: J. Am. Chem. Soc. 2021, 143, 12412-12417. https://doi.org/10.1021/jacs.1c06913 Other references (in order of
From playlist Research Spotlights
Representations of finite groups of Lie type (Lecture 2) by Dipendra Prasad
PROGRAM : GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fun
From playlist Group Algebras, Representations And Computation
Representations of finite groups of Lie type (Lecture 1) by Dipendra Prasad
PROGRAM : GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fun
From playlist Group Algebras, Representations And Computation
Machine Learning from First Principles, with PyTorch AutoDiff — Topic 66 of ML Foundations
#MLFoundations #Calculus #MachineLearning In preceding videos in this series, we learned all the most essential differential calculus theory needed for machine learning. In this epic video, it all comes together to enable us to perform machine learning from first principles and fit a line
From playlist Calculus for Machine Learning
Atroposelective Total Synthesis of Darobactin A
An organic chemistry minilecture on the Atroposelective Total Synthesis of Darobactin A by You-Chen Lin, Fabian Schneider, Kelly J. Eberle, Debora Chiodi, Hugh Nakamura, Solomon H. Reisberg, Jason Chen, Masato Saito, and Phil S. Baran*. Highlights include a Decarboxylative Alkynylation, a
From playlist Total Synthesis
There are two different types of reductionism. One is called methodological reductionism, the other one theory reductionism. Methodological reductionism is about the properties of the real world. It’s about taking things apart into smaller things and finding that the smaller things determ
From playlist Philosophy of Science