Humans are animals (in the sense that they are members of the biological kingdom “Animalia”), but in English, they can be animals in a different sense: “John’s a chicken, he won’t dare say something against me” is quite clear to a native speaker. In Hebrew, by the way, saying that someone is “a chicken” makes … More If you can be an animal, why can’t you be math?
Question: Alice decides to visit her good friend Bob. How much time will it take her to get there? Alas, in life, as in mathematics, we do not always know everything, and predicting exactly how much time it will take Alice to get to Bob can be a hard task. But we can try to … More Are we there yet?
Although I would never willingly be part of a club that would willingly accept me as a member, I have relatively recently entered (relative to the cosmic timescale, anyway) the fatherhood club. One perk of the job is that you get to completely indoctrinate and brainwash a child from a very early age. Literally no … More Stochastic Calculus for Babies
Over the past thousand years, I’ve been working on setting up a shared online wiki called the Boolean Zoo (https://booleanzoo.weizmann.ac.il/index.php/Main_Page). The point of the wiki is to collect lots of different examples of Boolean functions, together with pretty much all the properties that are known about them. Each function has a page containing a short … More The Boolean Zoo
Disclaimer: I first of all want to say that it’s perfectly, perfectly normal to think about these issues. Trust me, I have a dog. Garbage collection is no joke, and no amount of algorithms is too great when planning where to put the next bin. For several years now, I have proudly called myself the … More Garbage planning
At the beginning of the year, Israel’s “health-labelling” law came into effect. The law mandates that all food items be labelled with stickers depending on the healthiness of their ingredients. There are three bad red stickers: One for foods with high sodium value, one for high levels of saturated fats, and one for high sugar. … More Label me this
In case the previous post concerning concentration on the Boolean hypercube wasn’t enough for you, you can now watch a short, 20-minute animated video that I made for the STOC 2020 conference in theoretical computer science: STOC is a large (by theoretical computer science standards anyway) annual conference, which was supposed to take place in … More STOC 2020 lecture available online
I’m happy to say that the paper “A phase diagram for bacterial swarming” has been published in Communication Physics (https://www.nature.com/articles/s42005-020-0327-1). This paper is the result of ancient long-running research (started in 2015…) and is joint work with Avraham Be’er, Bella Ilkanaiv, Daniel Kearns, Sebastian Heidenreich, Markus Bär and Gil Ariel. In it, we analyze how … More New paper in Communication Physics: A phase diagram for bacterial swarming
I’m happy to say that my advisor Ronen Eldan and I somewhat recently uploaded a paper to the arXiv under the title “Concentration on the Boolean hypercube via pathwise stochastic analysis” (https://arxiv.org/abs/1909.12067), wherein we prove inequalities on the Boolean hypercube using a cool continuous-time random process. In the previous post, I pretended that I had … More New paper on arXiv: Concentration on the Boolean hypercube via pathwise stochastic analysis
I’m happy to say that my advisor Ronen Eldan and I somewhat recently uploaded a paper to the arXiv under the title “Concentration on the Boolean hypercube via pathwise stochastic analysis” (https://arxiv.org/abs/1909.12067), wherein we prove inequalities on the Boolean hypercube using a cool continuous-time random process. That’s quite a mouthful, I know, and quite unfortunately, … More Catastrophic cubic crash course
The Technion offers many of its mathematics courses, such as infinitesimal calculus and algebra, at several levels, with each course aimed at a different audience. At the lowest level are courses aimed at the “soft sciences”, such as biology, which usually need only elementary, practical calculations. In the middle sit the majority of the Technion’s … More Introduction to sandwich making
My wife has (repeatedly) brought to my attention the following two facts: Of the 135+ posts on this blog, none is about cats (I guess that this complex transformation post doesn’t really count). This blog is on the internet. A glaring omission if ever there was one, and not one easily forgiven. So today I’d … More Kot Theodore
This post is about the basics of the “gradient descent” method for finding the minimum of a function. I started writing it mainly to review the optimization material of lectures by Sébastien Bubeck given in Seattle. All of the material can be found elsewhere (for example, Sébastien’s book), but I can assure you that in … More Descent into madness
I just got back from Paris, where I participated in a summer school on high dimensional probability and algorithms. This was a cool school, with a course on mirror descent by Sébastien Bubeck and a course on applications of matrix sampling by Joel Tropp. I might even get to write about the mathematical content one … More People of Paris
I recently stumbled across a nice word game called “Doublets”, invented by Lewis Carroll. It goes like this. Player 1 writes two words with the same number of letters, say “cone” and “hoof”. Player 2 must then find a chain of words, each of them differing by one letter, which starts at the first word … More Doublets: From amok to updo in 14 easy steps
I’m happy to say that I recently uploaded a paper to the arXiv under the title “A conformal Skorokhod embedding” (https://arxiv.org/abs/1905.00852). In this post, I’d like to explain what the Skorokhod embedding problem is, how I came across it, some previously known solutions, and my own tiny contribution. But really, all of this is just … More New paper on arXiv: A conformal Skorokhod embedding