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Superconcentrators From Expanders
Today I will be blogging about the construction of superconcentrators from expanders. This is directly from the expanders survey. I am just reviewing it here for my own learning. First some...
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Tensor Calculus – Part 1
Firstly, I am sorry for the outage in posts. Could not find time to write up anything worth a really good post. I have received some verbal requests for a new post. I appreciate all such requests! So...
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Tensor Calculus II
In the last post I described a contravariant tensor of rank 1 and a covariant tensor of rank 1. In this post we will consider generalizations of these. We will introduce tensors of arbitrary rank where...
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Jung’s Theorem
Given a set of points of diameter in dimensional Euclidean space it is trivial to see that it can be covered by a ball of radius . But the following theorem by Jung improves the result by a factor of...
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Bounding the Volume of Hamming Balls
In this post I will derive an oft used inequality in Theoretical computer science, using the Chernoff technique. The following function turns up in a few places in combinatorial geometry and other...
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Projections onto a Convex Body
Given a point and an affine subspace , the projection of onto is the point such that, One can obviously define other notions of projection but the above is probably the most commonly used in geometry....
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