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djalil.chafai.net | ||
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mycqstate.wordpress.com
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| | | | | Today I'd like to sketch a question that's been pushing me in a lot of different directions over the past few years --- some sane, others less so; few fruitful, but all instructive. The question is motivated by the problem of placing upper bounds on the amount of entanglement needed to play a two-player non-local... | |
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nickhar.wordpress.com
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| | | | | 1. Low-rank approximation of matrices Let $latex {A}&fg=000000$ be an arbitrary $latex {n \times m}&fg=000000$ matrix. We assume $latex {n \leq m}&fg=000000$. We consider the problem of approximating $latex {A}&fg=000000$ by a low-rank matrix. For example, we could seek to find a rank $latex {s}&fg=000000$ matrix $latex {B}&fg=000000$ minimizing $latex { \lVert A - B... | |
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fabricebaudoin.blog
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| | | | | In this section, we consider a diffusion operator $latex L=\sum_{i,j=1}^n \sigma_{ij} (x) \frac{\partial^2}{ \partial x_i \partial x_j} +\sum_{i=1}^n b_i (x)\frac{\partial}{\partial x_i}, $ where $latex b_i$ and $latex \sigma_{ij}$ are continuous functions on $latex \mathbb{R}^n$ and for every $latex x \in \mathbb{R}^n$, the matrix $latex (\sigma_{ij}(x))_{1\le i,j\le n}$ is a symmetric and non negative matrix. Our... | |
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www.jeremykun.com
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| | | For fixed integers $ r > 0$, and odd $ g$, a Moore graph is an $ r$-regular graph of girth $ g$ which has the minimum number of vertices $ n$ among all such graphs with the same regularity and girth. (Recall, A the girth of a graph is the length of its shortest cycle, and it's regular if all its vertices have the same degree) Problem (Hoffman-Singleton): Find a useful constraint on the relationship between $ n$ and $ r$ for Moore graphs of girth $ 5$ and degree $ r$. | ||
