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lucatrevisan.wordpress.com | ||
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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). | |
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terrytao.wordpress.com
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| | | | | A key theme in real analysis is that of studying general functions $latex {f: X \rightarrow {\bf R}}&fg=000000$ or $latex {f: X \rightarrow {\bf C}}&fg=000000$ by first approximating them b | |
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thenumb.at
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| | | | | [AI summary] The text discusses the representation of functions as vectors and their applications in various domains such as signal processing, geometry, and physics. It explains how functions can be treated as vectors in a vector space, leading to the concept of eigenfunctions and eigenvalues, which are crucial for understanding and manipulating signals and geometries. The text also covers different types of Laplacians, including the standard Laplacian, higher-dimensional Laplacians, and the Laplace-Beltrami operator, and their applications in fields like image compression, computer graphics, and quantum mechanics. The discussion includes spherical harmonics, which are used in representing functions on spheres, and their applications in game engines and glo... | |
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www.jeremykun.com
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| | | When addressing the question of what it means for an algorithm to learn, one can imagine many different models, and there are quite a few. This invariably raises the question of which models are "the same" and which are "different," along with a precise description of how we're comparing models. We've seen one learning model so far, called Probably Approximately Correct (PAC), which espouses the following answer to the learning question: | ||
