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polymathprojects.org | ||
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francisbach.com
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| | | | | [AI summary] The blog post discusses the spectral properties of kernel matrices, focusing on the analysis of eigenvalues and their estimation using tools like the matrix Bernstein inequality. It also covers the estimation of the number of integer vectors with a given L1 norm and the relationship between these counts and combinatorial structures. The post includes a detailed derivation of bounds for the difference between true and estimated eigenvalues, highlighting the role of the degrees of freedom and the impact of regularization in kernel methods. Additionally, it touches on the importance of spectral analysis in machine learning and its applications in various domains. | |
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raphlinus.github.io
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| | | | | Finding the optimal Bézier path to fit some source curve is, surprisingly, not yet a completely solved problem. Previous posts have given good solutions for specific instances: Fitting cubic Bézier curves primarily addressed Euler spirals (which are very smooth), while Parallel curves of cubic Béziers rendered parallel curves. In this post, I describe refinements of the ideas to solve the much more general problem of simplifying arbitrary paths. Along with the theoretical ideas, a reasonably solid implementation is landing in kurbo, a Rust library for 2D shapes. | |
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terrytao.wordpress.com
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| | | | | Building on the interest expressed in the comments to this previous post, I am now formally proposing to initiate a Polymath project on the topic of obtaining new upper bounds on the | |
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rhubbarb.wordpress.com
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| | | My previous post was written with the help of a few very useful tools: LaTeX mathematical typesetting Gummi LaTeX editor Python programming language PyX Python / LaTeX graphics package my own PyPyX wrapper around PyX LaTeX2WP script for easy conversion from LaTeX to WordPress HTML | ||
