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| | www.jeremykun.com
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| | In our last primer we saw the Fourier series, which flushed out the notion that a periodic function can be represented as an infinite series of sines and cosines. While this is fine and dandy, and quite a powerful tool, it does not suffice for the real world. In the real world, very little is truly periodic, especially since human measurements can only record a finite period of time. Even things we wish to explore on this blog are hardly periodic (for instance, image analysis).
| | almostsuremath.com
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| | In today's post, I investigate a simple recurrence relation and show how it is possible to describe its behaviour asymptotically at large times. The relation describing how the series evolves at a time n will depend both on its value at the earlier time n/2 and on whether n is even or odd, which, as...
| | fredrikj.net
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| | fa.bianp.net
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| The Langevin algorithm is a simple and powerful method to sample from a probability distribution. It's a key ingredient of some machine learning methods such as diffusion models and differentially private learning. In this post, I'll derive a simple convergence analysis of this method in the special case when the ...