I would like to bring attention to the lack of videos accompanying published research despite the widespread availibility of cameras and many conference talks being slide talks and what we could possibly do about this. Even online conferences like SODA have not made their videos public as far as I know.
Very cool. The x * e^x part reminds me strongly of the Gamma Probability Distribution (which involves an integral containing x^a * e^(-x); note the negative exponentiation) -- which is something I've been wrestling to fully understand for a long while now, so it's interesting to find this kind of 'sideways' perspective on it, involving the Lambert W function. I would imagine that there's probably a much deeper connection between the two, but I'm not at the point I can guess what it might be. They do both involve probability, though! So there's that! Congrats on proving this conjecture! I can kinda imagine how it might be used in practice, even. Though I guess a lot probably depends on the constant factor. It would be easy to undershoot the number of tests needed to achieve some maximum 'error' rate (randomly generated CA not actually a CA), if you're not careful with the constant factor. Somewhere between 1 and v^t is quite a margin! And that's just for the log k term. I wonder what it's like for the lambda term. I guess I'll go check out your preprint. 😅 BTW: If you have any experience or background knowledge on the Gamma distribution, I'd be very interested to hear about it. (I don't need the basics, though. More like how to work with it practically. E.g. how might one numerically evaluate it if one didn't have access to a pre-existing software implementation?)
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Great Video and congrats on the result.
Also, I like the fact that you're wearing Tool merch when talking about the proof.
I would like to bring attention to the lack of videos accompanying published research despite the widespread availibility of cameras and many conference talks being slide talks and what we could possibly do about this.
Even online conferences like SODA have not made their videos public as far as I know.
Very cool.
The x * e^x part reminds me strongly of the Gamma Probability Distribution (which involves an integral containing x^a * e^(-x); note the negative exponentiation) -- which is something I've been wrestling to fully understand for a long while now, so it's interesting to find this kind of 'sideways' perspective on it, involving the Lambert W function. I would imagine that there's probably a much deeper connection between the two, but I'm not at the point I can guess what it might be. They do both involve probability, though! So there's that!
Congrats on proving this conjecture! I can kinda imagine how it might be used in practice, even. Though I guess a lot probably depends on the constant factor. It would be easy to undershoot the number of tests needed to achieve some maximum 'error' rate (randomly generated CA not actually a CA), if you're not careful with the constant factor. Somewhere between 1 and v^t is quite a margin! And that's just for the log k term. I wonder what it's like for the lambda term. I guess I'll go check out your preprint. 😅
BTW: If you have any experience or background knowledge on the Gamma distribution, I'd be very interested to hear about it. (I don't need the basics, though. More like how to work with it practically. E.g. how might one numerically evaluate it if one didn't have access to a pre-existing software implementation?)
Wuju!!🎉👏🏽👏🏽congrats, man🎊
You are a handsome guy with a brilliant mind!
I can make conjecture law fail . I know its weakness.