Last time I introduced a neat little question: Is it true that every infinite path in contains arbitrarily long arithmetic progressions? For example, in the following path, the squares colored in red have coordinates , which form an arithmetic progression of length 3, where every two consecutive points differ by . As it turns out, … More Arithmetic progressions in space!
Here is a neat question that I stumbled upon during my academic random walk. A sequence of vectors is called an arithmetic progression of length k if there exists a vector such that . In other words, an arithmetic progression in is exactly the generalization you would expect of your good ol’ high-school arithmetic progression … More Arithmetic progressions in space?
In recent years, there has been an increasing interest in academic papers whose opening paragraphs describe the increasing interest in the (increasingly common) field of network theory. From mathematicians to sociologists, many a great scientist have written introductory paragraphs on this interesting explosion. For example: Chatterjee and Diaconis (2013): Bhamidi, Bresler and Sly (2011): Yan, … More New paper on arXiv: Exponential random graphs behave like mixtures of stochastic block models
I’m happy to say that fellow student Uri Grupel and I uploaded a paper to the arXiv recently under the title “Indistinguishable sceneries on the Boolean hypercube” (https://arxiv.org/abs/1701.07667). We had great fun working on it, and most of the theorems are actually pretty simple and do not use heavy mathematical machinery, so I’d like to … More New paper on arXiv: Indistinguishable sceneries on the Boolean hypercube
Valentine’s day is upon us, a cheerful reminder that the main purpose of every living creature is to copulate as much as possible and spray the world with its offspring; the more, the merrier. This is certainly easy enough for all those twice blessed prokaryotes; twice blessed, first, for their asexual reproduction via mitosis, obliviating … More The Perfect Match