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Even if it were finite, you can't simulate it completely because the simulation would then be part of the universe, leading to an infinite recursion.
Wavelet transform is an invaluable tool in signal processing, which has applications in a variety of fields - from hydrodynamics to neuroscience. This revolutionary method allows us to uncover structures, which are present in the signal but are hidden behind the noise. The key feature of wavelet transform is that it performs function decomposition in both time and frequency domains. In this video we will see how to build a wavelet toolkit step by step and discuss important implications and prerequisites along the way.This is my entry for Summer of Math Exposition 2022 ( #SoME2 ).My name is Artem, I'm a computational neuroscience student and researcher at Moscow State University. Twitter: @artemkrsvOUTLINE:00:00 Introduction01:55 Time and frequency domains03:27 Fourier Transform05:08 Limitations of Fourier08:45 Wavelets - localized functions10:34 Mathematical requirements for wavelets12:17 Real Morlet wavelet 13:02 Wavelet transform overview14:08 Mother wavelet modifications15:46 Computing local similarity18:08 Dot product of functions?21:07 Convolution24:55 Complex numbers27:56 Wavelet scalogram 30:46 Uncertainty & Heisenberg boxes33:16 Recap and conclusion
DrEureka might signal the start of a transition, from humans training robots, to machines teaching machines. Nvidia have demonstrated how LLMs can have immense impacts, even with their flaws. This video is about one paper, one concept ... and it's a genius one.