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
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 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
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!
Dedicated to Harold Cohen, who died last year, and to his son AARON. I Grunting softly, the father slipped out of bed. The mother stirred the faintest amount, her shoulders sliding a sliver of a hair, noticing the sudden emptiness besides her. But her breathing kept its pace, and she remained in gentle slumber. No … More Three scenes from childhood
At the end of the semester, in order to see their grades, students at the Weizmann Institute must complete an online survey about each course they participated in. The survey asks questions about both the course and the teachers, and the results are then shown in a “previously, on ‘Topics in Holomorphy’ ”-styled section in … More Few courses are better
My piano is mentally ill. Now, you might be wondering how it is that a piano can be sick, but it’s an electronic piano (Korg SP250), and thus has a specialized electronic brain in charge of imitating the sound of tiny hammers hitting strings when I press its plastic keyboard. And like any brain, it … More Electric Insanity
My wife and I have a problem. Well, I mean, not a problem, per se. We are “of divided opinions”. She wants to have a baby. I want to program. The two are obviously incompatible. And it’s not that she doesn’t like to program, she loves it very much, coding away her will and command; … More Skin and bits
Or: fooling around with image processing kernels. Original greyscale: Edge fit + bw cutoff: Partition into multiple bw images and taking Laplacians: Plain Laplacian + bw cutoff: High frequency removal by partitioning into multiple bw images: Sexy dark high frequency removal: Subtracting low frequencies from original image: Overshooting Laplace central element (does this filter make … More The many faces of Mona Lisa
Facebook should change their “It’s complicated” status to “It’s complex”. That way, real people with imaginary girlfriends could spread the news to all their friends! – Ancient proverb We were learning about conformal maps in complex function theory. While we did plenty of “circles are sent to circles” and “connected components are sent to connected … More Programming complex transformations
My O(1) readers are probably restlessly wondering where I’ve been, how I survived Israel’s freakishly sweaty summer, and what’s up in general. Well, the truth is, I did manage to sweat under the Mediterranean sun, but most of the summer I spent in the United States. The official reason, given to the consulate and on … More They should have sent a complexity theorist
“Home is where the wifi connects automatically”. The question remains to be asked, how does it know to connect automatically? Well, of course, the computer saves a list of network names (or other identifiers) and their passwords, and tries to connect when it sees one it recognizes. I bet the passwords are saved in plaintext, … More Do not track
[Written under the influence of QCSD] Not so long ago, I happened to watch the totally-accurate-in-every-possible-way film, “Travelling Salesman”. tl;dw: a squad of government-hired mathematicians are finally able to prove that P = NP, giving the state the power to answer every important computational question they can imagine (aka rob banks and fight terrorism). But … More Zero knowledge in the real world?