Numerical analysis | Partial differential equations
The mathematical term well-posed problem stems from a definition given by 20th-century French mathematician Jacques Hadamard. He believed that mathematical models of physical phenomena should have the properties that: 1. * a solution exists, 2. * the solution is unique, 3. * the solution's behaviour changes continuously with the initial conditions. Examples of archetypal well-posed problems include the Dirichlet problem for Laplace's equation, and the heat equation with specified initial conditions. These might be regarded as 'natural' problems in that there are physical processes modelled by these problems. Problems that are not well-posed in the sense of Hadamard are termed ill-posed. Inverse problems are often ill-posed. For example, the inverse heat equation, deducing a previous distribution of temperature from final data, is not well-posed in that the solution is highly sensitive to changes in the final data. Continuum models must often be discretized in order to obtain a numerical solution. While solutions may be continuous with respect to the initial conditions, they may suffer from numerical instability when solved with finite precision, or with errors in the data. Even if a problem is well-posed, it may still be ill-conditioned, meaning that a small error in the initial data can result in much larger errors in the answers. Problems in nonlinear complex systems (so-called chaotic systems) provide well-known examples of instability. An ill-conditioned problem is indicated by a large condition number. If the problem is well-posed, then it stands a good chance of solution on a computer using a stable algorithm. If it is not well-posed, it needs to be re-formulated for numerical treatment. Typically this involves including additional assumptions, such as smoothness of solution. This process is known as regularization. Tikhonov regularization is one of the most commonly used for regularization of linear ill-posed problems. (Wikipedia).
The Problems of Being Very Beautiful
We often have time for the challenges of not looking great in a looks-obsessed world. But spare a thought for that more unusual problem: that of being too beautiful... If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/HbGH1a FURTHER READING “It sounds pa
From playlist SELF
How to Cope If the Worst Came to the Worst..
Many of us suffer enormous anxieties about what might happen if the worst came to the worst. Well-meaning friends often reassure us that things might go really well, but there is often great relief to be found in imagining the darkest scenarios and being able to see that we could, ultimate
From playlist SELF
When you FINALLY get the courage to perform a Magic Trick!
*Awkward silence
From playlist Magician Problems.
The Mind-Body problem is one of the greatest conundrums of philosophy and of our everyday lives too. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/BxHqGF Join our exclusive mailing list: http://bit.ly/2e0TQNJ Or visit us in person at our London HQ
From playlist SELF
Hint to Solve the Difficult Problem of the Day
Hint to Solve the Difficult Problem of the Day
From playlist Short Videos
Is It Better to Be Polite or Frank?
We live in an age that thinks highly of frankness and directness. But there are – nevertheless – a few reasons why politeness remains a hugely important quality. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/hMBQQs FURTHER READING “For most of hu
From playlist RELATIONSHIPS
How to Be Charming When Talking About Yourself
It’s sometimes assumed that talking too much about ourselves is rude; and asking questions of others is polite and charming. But the distinction is not quite so simple. There are far better and worse ways of speaking about ourselves. We end up charming when we dare to reveal our vulnerabil
From playlist SELF
If you are interested in learning more about this topic, please visit http://www.gcflearnfree.org/ to view the entire tutorial on our website. It includes instructional text, informational graphics, examples, and even interactives for you to practice and apply what you've learned.
From playlist Career Challenges
Frederick Poitevin - Inference Poses for Reconstruction of 3D Molecular Volumes from Cryo-EM Images
Recorded 16 November 2022. Frederick Poitevin of SLAC National Accelerator Laboratory presents "Amortized Inference of Poses for Ab Initio Reconstruction of 3D Molecular Volumes from Experimental Cryo-EM Images" at IPAM's Cryo-Electron Microscopy and Beyond Workshop. Abstract: Cryo-electro
From playlist 2022 Cryo-Electron Microscopy and Beyond
Tommi Jaakola - Diffusion based distributional modeling of conformers, blind docking and proteins
Recorded 24 January 2023. Tommi Jaakkola of the Massachusetts Institute of Technology presents "Diffusion based distributional modeling of conformers, blind docking and proteins" at IPAM's Learning and Emergence in Molecular Systems Workshop. Learn more online at: http://www.ipam.ucla.edu/
From playlist 2023 Learning and Emergence in Molecular Systems
Understanding SLAM Using Pose Graph Optimization | Autonomous Navigation, Part 3
This video provides some intuition around Pose Graph Optimization—a popular framework for solving the simultaneous localization and mapping (SLAM) problem in autonomous navigation. We’ll cover why uncertainty in a vehicle’s sensors and state estimation makes building a map of the environm
From playlist Autonomous Navigation
Geoffrey Hinton talk "What is wrong with convolutional neural nets ?"
Brain & Cognitive Sciences - Fall Colloquium Series Recorded December 4, 2014 Talk given at MIT. Geoffrey Hinton talks about his capsules project. Talks about the papers found here: https://arxiv.org/abs/1710.09829 and here: https://openreview.net/pdf?id=HJWLfGWRb
From playlist AI talks
Lec 29 | MIT 18.086 Mathematical Methods for Engineers II
Duality Puzzle / Inverse Problem / Integral Equations View the complete course at: http://ocw.mit.edu/18-086S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.086 Mathematical Methods for Engineers II, Spring '06
Geoffrey Hinton: "Does the Brain do Inverse Graphics?"
Graduate Summer School 2012: Deep Learning, Feature Learning "Does the Brain do Inverse Graphics?" Geoffrey Hinton, University of Toronto Institute for Pure and Applied Mathematics, UCLA July 12, 2012 For more information: https://www.ipam.ucla.edu/programs/summer-schools/graduate-summe
From playlist GSS2012: Deep Learning, Feature Learning
Yoga Pose - Andy Ruestow & Bryan Donovan - JSConf US 2019
Let's have some fun with TensorFlow and React. Not familiar with TensorFlow? No problem, you will get a fast crash course and learn how to track faces and add silly adornments (I bet you would look good with a new set of reading frames) entirely in the browser with TensorFlow and React. Wi
From playlist JSConf US 2019
ml5.js: Pose Regression with PoseNet and ml5.neuralNetwork()
This tutorial builds on the previous video combining PoseNet and ml5.neuralNetwork(). Once again, the output of the pre-trained model (the "pose" itself) is the input to an ml5.js neural network. However, this time the final output is a regression (3 continuous values) instead of classific
From playlist Beginners Guide to Machine Learning in JavaScript
Graham Taylor: "Feature Learning for Comparing Examples"
Graduate Summer School 2012: Deep Learning, Feature Learning "Feature Learning for Comparing Examples" Graham Taylor, University of Guelph Institute for Pure and Applied Mathematics, UCLA July 13, 2012 For more information: https://www.ipam.ucla.edu/programs/summer-schools/graduate-summ
From playlist GSS2012: Deep Learning, Feature Learning
Ellen Zhoung - Machine learning for determining protein structure and dynamics from cryo-EM images
Recorded 14 November 2022. Ellen Zhong of Princeton University presents "Machine learning for determining protein structure and dynamics from cryo-EM images" at IPAM's Cryo-Electron Microscopy and Beyond Workshop. Abstract: Major technological advances in cryo-electron microscopy (cryo-EM)
From playlist 2022 Cryo-Electron Microscopy and Beyond
Very Dangerous Incident ....By Kaushal
Please don't try this at railway track...
From playlist Interesting Videos