Mathematical modeling | Differential equations | Numerical analysis | Partial differential equations
The forward problem of electrocardiology is a computational and mathematical approach to study the electrical activity of the heart through the body surface. The principal aim of this study is to computationally reproduce an electrocardiogram (ECG), which has important clinical relevance to define such as ischemia and infarction, or to test . Given their important functionalities and the relative small invasiveness, the electrocardiography techniques are used quite often as clinical diagnostic tests. Thus, it is natural to proceed to computationally reproduce an ECG, which means to mathematically model the cardiac behaviour inside the body. The three main parts of a forward model for the ECG are: * a model for the cardiac electrical activity; * a model for the diffusion of the electrical potential inside the torso, which represents the extracardiac region; * some specific heart-torso coupling conditions. Thus, to obtain an ECG, a mathematical electrical cardiac model must be considered, coupled with a diffusive model in a passive conductor that describes the electrical propagation inside the torso. The coupled model is usually a three-dimensional model expressed in terms of partial differential equations. Such model is typically solved by means of finite element method for the solution's space evolution and involving finite differences for the solution's time evolution. However, the computational costs of such techniques, especially with three dimensional simulations, are quite high. Thus, simplified models are often considered, solving for example the heart electrical activity independently from the problem on the torso. To provide realistic results, three dimensional anatomically-realistic models of the heart and the torso must be used. Another possible simplification is a made of three ordinary differential equations. (Wikipedia).
Example: Optical Path Length (with phase shifts)
In this video, we calculate the optical path length that light takes from one point to another, incorporating phase shifts due to reflection. I also briefly discuss when phase shifts happen and the equations that underlie them (the Fresnel Equations). To support the creation of videos lik
From playlist Introductory Electromagnetism
FEM@LLNL | Computing Meets Cardiology: Making Heart Simulations Fast and Accurate
Sponsored by the MFEM project, the FEM@LLNL Seminar Series focuses on finite element research and applications talks of interest to the MFEM community. On September 13, 2022, Dennis Ogiermann of the University of Bochum presented "Computing Meets Cardiology: Making Heart Simulations Fast
From playlist FEM@LLNL Seminar Series
How to solve a sample DC motor problem with solution
This is a sample worked solution of a problem involving torque in a DC motor See www.physicshigh.com for all my videos and other resources. If you like this video, please press the LIKE and SHARE with your peers. And please add a COMMENT to let me know I have helped you. Follow me faceboo
From playlist Electromagnetism
force between wires problem with solution
A worked solution to a force between wires problem. Part of a series of worked solutions for my website - www.physicshigh.com check out www.physicshigh.com and follow me on facebook and twitter @physicshighSupport me on www.patreon.com/highschoolphysicsexplained
From playlist Electromagnetism
DDPS | Industrial Grade Scientific Machine Learning: Challenges and Opportunities by Santi Adavani
Description: There has been increasing interest in Scientific Machine Learning (SciML), which leverages advances in modern deep learning approaches to model complex engineered systems represented by partial differential equations (PDEs). This rapidly evolving research topic is of interest
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
Workshop on Mathematics for the Health Sciences - Day II
- Nader El Khatib (Lebanese American University, Lebanon) “Mathematical Modeling of Atherosclerosis” - Vitaly Volpert(National Center for Scientific Research – France, RUDN – Russia) “Mathematical Modelling of Respiratory Viral Infections” - Mostafa Adimy (INRIA, France) “Modelling the Rel
From playlist Mathematical Biology
Example: E-field from 3 Linear Polarizers
In this video, I go over how to find the electric field at each stage of a set of 3 linear polarizers, both in terms of the intensity of the light and the electric field. We use vector projections to find that the output intensity is 1/4 of the intensity after the first polarizer, or 1/8 o
From playlist Introductory Electromagnetism
In this video, I describe what optical path length is, in terms of how far light "thinks" it has traveled. I give an expression for the optical path length in terms of the refractive index, and a more general expression if the refractive index varies over space. To support the creation of
From playlist Introductory Electromagnetism
The Long Story of How Neural Nets Got to Where They Are: A Conversation with Terry Sejnowski
Stephen Wolfram plays the role of Salonnière in this on-going series of intellectual explorations with special guests. Watch all of the conversations here: https://wolfr.am/youtube-sw-conversations Originally livestreamed at: https://twitch.tv/stephen_wolfram 00:00 Start stream 5:26 SW st
From playlist Conversations with Special Guests
A sample charge in magnetic field problem with solution
A sample problem with working on charge behaviour in a magnetic field. Part of a series of worked solutions for my website - www.physicshigh.com. Follow me on www.facebook.com/highschoolphysicsexplained Twitter @physicshigh Support me on www.patreon.com/highschoolphysicsexplained
From playlist Electromagnetism
Physics - E&M: Maxwell's Equations (1 of 30) What are the Maxwell equations? Introduction
Visit http://ilectureonline.com for more math and science lectures! In this video I will introduction to Maxwell's equations.
From playlist PHYSICS - ELECTRICITY AND MAGNETISM 3
Example: Computing Optical Path Length
In this video, I go over how to compute optical path length (OPL) in several examples of increasing complexity, without dealing with phase shifts. To support the creation of videos like these, get early access, access to a community, behind-the scenes and more, join me on patreon: https
From playlist Introductory Electromagnetism
Electromagnetism - Part 1 - A Level Physics
Continuing the A Level Physics revision series, this video looks at Electromagnetism covering the magnetic field, the force when a current moves along a wire in a magnetic field and electromagnetic induction. The full playlist of A Level Physics revision videos is at http://www.youtube.com
From playlist Electricity & Magnetism
Stanford Seminar - Deep Learning for Symbolic Mathematics - Guillaume Lample & Francois Charton
Guillaume Lample & Francois Charton Facebook AI Research April 16, 2020 View the full playlist: https://www.youtube.com/playlist?list=PLoROMvodv4rMWw6rRoeSpkiseTHzWj6vu 0:00 Introduction 1:06 Deep learning for symbolic mathematics 2:27 Starting point 4:22 Basic intuition 6:44 The plan
From playlist Stanford EE380-Colloquium on Computer Systems - Seminar Series
Accelerating Deep Learning by Focusing on the Biggest Losers
What if you could reduce the time your network trains by only training on the hard examples? This paper proposes to select samples with high loss and only train on those in order to speed up training. Abstract: This paper introduces Selective-Backprop, a technique that accelerates the tra
From playlist General Machine Learning
DDPS | Model-constrained deep learning approaches for inference, control and UQ
In this talk from July 1, 2021, University of Texas at Austin associate professor Tan Bui-Thanh discusses model-constrained deep learning approaches for inference, control and uncertainty quantification (UQ). The fast growth in practical applications of machine learning in a range of con
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 View the complete course: http://ocw.mit.edu/6-041SCF13 Instructor: Kuang Xu License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
New Wikipedia sized proof explained with a puzzle
A new mathematical proof was in the news this week, which partially solves the Erdos Discrepancy Problem. The proof was described as "bigger than Wikipedia". I attempt to explain the problem using a puzzle which you can try at home. The puzzle was my idea to explain it to you - that's not
From playlist My Maths Videos
Lars Ruthotto: "Deep Neural Networks Motivated By Differential Equations (Part 1/2)"
Watch part 2/2 here: https://youtu.be/1mVycBKb1TE Machine Learning for Physics and the Physics of Learning Tutorials 2019 "Deep Neural Networks Motivated By Differential Equations (Part 1/2)" Lars Ruthotto, Emory University Abstract: In this short course, we establish the connection bet
From playlist Machine Learning for Physics and the Physics of Learning 2019
Schrodinger equation | Derivation and how to use it
In this video we see how the Schrodinger equation comes out very simply from the conservation of energy. This is the second video. Click here for the first: https://youtu.be/ZfKq3g3MHqE My twitter: twitter.com/Looking_glass_u First. Throughout these 2 videos, I kept talking about predi
From playlist Quantum Mechanics (all the videos)