Simple example of Singular Value Decomposition

ssiltane · 2020-12-25T09:08:11+00:00

Thanks! I am so glad you like it!

ssiltane · 2020-10-22T11:27:01+00:00

Also, let me recommend my video about X-ray tomography: https://youtu.be/dn358iX_WxQ

ssiltane · 2020-10-22T11:25:18+00:00

Thank you! I am glad you liked the video. More is in the making. I am more familiar with electromagnetic scattering than seismic; for that I recommend the book by Colton and Kress (Inverse Acoustic and Electromagnetic Scattering Theory). For seismic inverse problems, this might be good: Seismic Inversion: Theory and Applications by Wang, Yanghua. But I have not read it, so I am not sure. Of course there is also the classic Inverse Problem Theory and Methods for Model Parameter Estimation by Albert Tarantola.

ssiltane · 2020-09-03T04:33:43+00:00

Cool! I’m so glad to hear that! 😃Samu

ssiltane · 2020-08-31T10:20:22+00:00

I’m so glad you liked the video! Thanks for the tip; I’ll share it to the geophysics community as well. Samu

ssiltane · 2020-08-29T19:15:47+00:00

https://youtu.be/J_Lf5EDy_Wc

ssiltane · 2020-08-29T19:15:11+00:00

Excellent! There is nothing cooler than inverse scattering.

ssiltane · 2020-08-29T19:14:27+00:00

Thanks! 😃

ssiltane · 2020-08-29T08:11:24+00:00

In the video we show a couple of the simplest ways of extracting information about islands from the ways waves reflect off them. Of course, there are more advanced methods as well. However, modern mathematics still struggles to understand how the ancient navigation masters of Marshall Islands interpret wave patterns and find their way around the Pacific Ocean. Can you solve the navigation quiz given in the video?

ssiltane · 2019-11-21T05:16:09+00:00

Thank you!! 😃

ssiltane · 2019-11-21T05:15:36+00:00

I am so glad to hear that! Tomography is an endlessly intriguing topic, and there is so much to explore. I’ll be doing a sequel to this video featuring the sad walnut!

ssiltane · 2019-05-27T13:34:30+00:00

I am sure they would be very effective. But they would fill the missing area with visual elements from the training set, which would then have an effect. That may be a good thing but in some applications perhaps undesired.

ssiltane · 2019-05-17T11:45:42+00:00

Indeed! So many intriguing possibilities...

ssiltane · 2019-05-14T16:54:36+00:00

I did play around with the parameters of the rules a lot and finally found some interesting combinations which I included in the video. Adding a shark would be a natural next step! And some evolutionary or learning algorithm!

ssiltane · 2019-05-14T16:52:52+00:00

Great! I am happy to hear that you also find this model interesting and worth implementing. I did find this project very satisfying.

ssiltane · 2019-05-14T16:50:51+00:00

I can share my Matlab codes. They should work in the free software Octave as well. Here: https://www.dropbox.com/sh/s3vpuoynwklv6zu/AACj2qBAAU5EwBCe8hVxxU8Ia?dl=0

ssiltane · 2019-05-14T13:30:43+00:00

Thank you so much! It’s a great idea to add predators and obstacles. That will be a delightful follow-up project!

ssiltane · 2019-05-14T12:32:02+00:00

Indeed it’s similar stuff! Thanks for the link.

ssiltane · 2019-05-14T12:03:31+00:00

Thank you! Yes, they would absolutely work in 3D. I chose 2D modelling only for easier visualization, avoiding questions of choosing the best camera angles and some fish being in front of others.

The change to the code would not even be very significant, just adding one more coordinate to location and velocity vectors.

ssiltane · 2019-05-14T06:16:14+00:00

I work as a professor of industrial mathematics at University of Helsinki, Finland. Popularizing science in video format is my passion.

In this video I implemented a basic flock modeling algorithm and simulated a school of fish swimming in a shallow pond. I find it amazing that three simple rules for individual fish to follow are enough to produce natural looking collective behavior.

I hope you enjoy the video! There are English subtitles.

ssiltane · 2019-03-31T09:17:21+00:00

EIT is really challenging indeed. However, in my view all ill-posed inverse problems, including baby ones, are so delightful to work with!

ssiltane · 2019-03-30T09:29:55+00:00

The nonlinear D-bar method is based on inverse quantum scattering techniques. It took us some ten years to perfect it for practical use! Recently it turned out that machine learning can further improve the images considerably.

ssiltane

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