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Comparing Wavelets for Image Compression
For something to be considered a ‘signal’, as opposed to just noise, there has to be some redundancy in the data, some relationship between samples which makes one predictable from another. This is the principle behind compression: Find the smallest number of data points that capture as much of the signal variation as possible. The […]
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Duality for the Uninitiated
Duality is one of the most – if not the most – fundamental principles in our universe. It’s a principle that, once in your gut, transforms the way you approach equations and algebraic concepts; putting a perimeter around each problem rather than letting the edges disappear into the obscure distance. However, unless you’ve taken specific […]
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Using SVD to simplify quantum dynamics
There are many hard things to grasp in quantum mechanics: the algebra of commutators Hamiltonians & Lagrangians Hilbert-Space Sturm-Liouville theory the inexplicable profusion of complex numbers, etc. One of these things is the ‘quantum mode’. We’re told that such modes live in an infinite-dimensional space, and that in order to identify them analytically we need […]
