Wow. I worked on Millwheel as a summer intern the summer before last. At the time it was a team of about 11 people. I'm honestly pretty surprised to see this comment as I thought it was just a small internal research project.
Have you seen any references to it in the wild other than the Google Research paper?
Feature request: Could you strip the dots from user input if the email address is @gmail.com, and similarly strip the dots from the records of pwned email addresses? Gmail usernames are dot agnostic, and I sometimes use [email protected], [email protected], etc. This makes it hard to use the tool to check of my Gmail has been pwned. (Also, I assume you don't do this already).
I wrote a simple neural network about a year ago for doing optical character recognition as a class project. I think looking over the code could be good for learning, as it has a pretty simple OOP structure: https://github.com/bcuccioli/neural-ocr
There are two good correct equivalent ways to think of the determinant of varying generality. One is as the function from a ring of square matrices to the underlying field (e.g. from R^(n^2) -> R) that sends identity to identity, is alternating (swapping two rows or columns negates the function) and is multilinear (is a linear function in each of the columns independently). These properties are all useful and important on their own, so there is motivation to study a function which has all of them. It's not obvious that such a function exists, but you can prove that. As it turns out, these three properties uniquely determine such a function, which makes it seem like that function might be really important!
There's a more general definition too, which is based around the wedge product, a quintessential object in algebra and calculus. There's a good exposition here: http://codeblank.com/~int/det.pdf .
The difference is calc 1 is not higher level math and the derivative of a real function is not an abstract concept. Professional mathematicians/grad students/high level undergrads don't think of the determinant via some weird geometric intuition, as that won't really provide enough information or rigor to do anything useful.
A worse system (read: hack) is to put variable amounts of dots in your email address when you sign up for something, because Gmail strips dots from your account name when delivering your mail. It requires you to remember or write down who got what amount of dots though.
A worse system (read: hack) is to put variable amounts of dots in your email address when you sign up for something, because Gmail strips dots from your account name when delivering your mail. It requires you to remember or write down who got what amount of dots though.
The irony of this article is that the author is trying to sneer at someone for making a mathematical mistake, which is not technically wrong, but himself falsely asserts that "The use of the phrase 'even number, or the number zero' implies that zero is not even", which is not true in the usual first order logic.
I don't get why people don't do this. It's not that hard. The modification would be about 2 lines of code. If you're unhappy about storing 128 bits for everyone's password you could even just take an 8 character substring of the hash or something. It would be a lot better than nothing.
https://linux.ime.usp.br/~renatolg/lights_out.pdf