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yufeizhao.com | ||
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www.jeremykun.com
Graphs are among the most interesting and useful objects in mathematics. Any situation or idea that can be described by objects with connections is a graph, and one of the most prominent examples of a real-world graph that one can come up with is a social network. Recall, if you aren't already familiar with this blog's gentle introduction to graphs, that a graph $ G$ is defined by a set of vertices $ V$, and a set of edges $ E$, each of which connects two vertices. |
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gowers.wordpress.com
Here is a simple but important fact about bipartite graphs. Let $latex G$ be a bipartite graph with (finite) vertex sets $latex X$ and $latex Y$ and edge density $latex \alpha$ (meaning that the number of edges is $latex \alpha |X||Y|$). Now choose $latex (x_1,x_2)$ uniformly at random from $latex X^2$ and $latex (y_1,y_2)$ uniformly |
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ptreview.sublinear.info
[AI summary] This post summarizes five recent academic papers on property testing, sublinear time algorithms, and theoretical computer science, covering topics like tolerant independent set testing, private distribution testing, mass estimation in conditional sampling motifs, and streaming lower bounds for max-cut. |
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dennybritz.com
All the code is also available as an Jupyter notebook on Github. |
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