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Yet another proof that primes are infinite
In CS131, we see the “Proof from the Book” due to Euclide that the number of prime numbers is infinite. Here is another favorite proof that is based on elementary facts. Suppose that is a list of all the primes. From what we have learnt about the sum of geometric progressions we know that for […]
The densest subgraph problem with negative weights
Few days ago I uploaded on Arxiv our preprint “Novel Dense Subgraph Discovery Primitives: Risk Aversion and Exclusion Queries”. This is joint work with Tianyi, Nao, and Jakub. In this paper we study the following extension of the densest subgraph problem (DSP) that is known to be solvable exactly in polynomial time on graphs with […]
Denoising binary images
Let’s start by writing the letter T using numpy in Python, encoded in a 0/1 array. Let’s visualize this. This is what we get, indeed the array represents the letter “T”. Now, let’s generate a corrupted version of this image by flipping each bit with some probability p. We can also do it a bit faster […]
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