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I won with 1. e4 e5 2. Qh5 a6 3.Bc4 a5 4. Qxf7#. I wonder if you could implement a stronger engine in regex (stockfish classic at O(1) nodes is plenty strong already)

The momentum analogue for Langevin is known as underdamped Langevin, which if you optimize the discretization scheme hard enough, converges faster than ordinary Langevin. As for your question, your guess is as good as mine, but I would guess that the nonconvexity of AI applications causes problems. Sampling is a hard enough problem already in the log-concave setting…

Does this really require stochastic calculus to prove? This should just be a standard integration, based on the fact that the expected number of samples required for fixed A being 1/(1-A).

To be fair, CS theory is basically just mathematics :)

2 to the billion is still constant....

Yep, Whink brand rust remover is 4% HF. It's a somewhat useful source of hydrofluoric acid in a pinch. I recall a procedure for making uranium tetrafluoride from uranium trioxide (which in turn was extracted from uranium ore) using that brand of rust remover as the acidic fluoride source.

For a specific example of something like this being important, remember the (very impressive) Watch for Rolling Rocks in 0.5 A presses video from a couple years ago? https://www.youtube.com/watch?v=kpk2tdsPh0A (For the uninitiated, this video presents a TAS of Super Mario 64 which beats the level Watch for Rolling Rocks without pressing the A button outside of keeping it held from entering the level.) It turns out that the route presented in the video actually fails console verification, since the crazy things he does trigger some annoying FPU crashes on console, but not on emulator. There is a happy end, though: a fixed route was published after this was discovered, and it passes console verification just fine (assuming the inputs dont desync over the 13 hour run)

We had plenty of evidence that a deterministic primality testing algorithm exists, though. The Miller-Rabin test was known to be randomized polynomial time since the 70s, and assuming the generalized Riemann hypothesis it can be made deterministic polynomial.

And while there was some nuemerical evidence that the Polya conjecture was false, there really wasnt all that much evidence that the conjecture was false. The first counterexample is around 9 billion-- you could find it yourself if you wanted.

Magnesium will only burn when heated to near its melting point of ~400 C, and thermite can only be set off at temperatures that would melt aluminum. Shipping them together is not an issue, unless the aluminum and iron oxide are freely dispersed in air.

From a practical point of view, the only semi-common thermites that can actually explode are copper and silver. However, these thermites do not "detonate" as in the definition. They merely deflagrate extremely quickly, quickly enough to fool an observer but not in the true physical sense.

Alternatively, the three components for gunpowder can be bought very cheaply and nigh-untraceably from hardware stores: potassium nitrate is stump remover, sulfur is used to reduce the pH of soils for gardening, and charcoal can be made from pyrolyzing wood in your backyard.

Guns aren't a major industrial commodity chemical with hundreds if not thousands of valid non-violent civil uses, however...

Potentially, but the neutralization of sulfuric acid releases a ton of heat (sometimes enough to crack glassware). By neutralizing the sulfuric acid without giving the heat anywhere to dissipate, you might just end up making things worse.

Also, as a small unrelated note, I doubt calcium carbonate would work well for neutralizing sulfuric acid-- the calcium sulfate formed is for the most part insoluble and stops the reaction.

Yep, that server is indeed still at Stanford. It is now in the basement of the Huang building in the engineering quad.

Well, pH refers to the concentration of protons in water solvent. Since pure sulfuric acid has no water (excluding that which is in equilibrium with sulfur trioxide), pH isn't really well defined for it. A better definition of acidity which does not have this problem is the Hammett acidity function. Sulfuric acid on this scale has an acidity of -12. (Note that this acidity score is not fully comparable to pH. However, with a difference so massive (a factor of one trillion times more acidic), this subtle difference ceases to be relevant.)

If you're asking about corrosivity, sulfuric acid gets its reputation because its also strongly dehydrating. Thus, it does wonderful things like rip the water out of your skin or char paper. I would hazard a guess that the water they've found in the paper does neither of those things.

Conway showed that the generalized Collatz conjecture (recurrences with arbitrary cases dependent on the modulus) is computationally undecidable (halting problem reduces to it). The choice of modulus doesn't even need to be that big to get this result, only ~6500 or so. As far as I know, this is the only substantial result in either direction for this problem.

Then again, both have something to do with bugs on some level...

The thing with these substances is that although these substances are best known for their psychological effects, they may also have some medically useful effects for somatic disorders. For example, some of the psychedelic phenethylamines and tryptamines are extremely effective agonists of 5-HT2A, which is a seretonin receptor found in the brain which modulates certain aspects of cognition. However, this receptor is also expressed throughout the body, and it seems to have something to do with rheumatoid arthritis. (This is why SSRIs are occasionally prescribed off-label for RA.) The phenethylamine DOI is actually such a strong agonist for this receptor that it is used in biology labs to study the receptor in vitro, and it has actually been studied and found to at least partially alleviate rheumatoid pain. [1]

[1] http://journals.plos.org/plosone/article/file?id=10.1371/jou...

Unless my understanding of things is wrong, I'm pretty sure that unless the strong exponential time hypothesis (essentially, n variable CNF-SAT takes O(2^n) time in the worst case) is false, no diff algorithm can run in subquadratic time. If you could, then you would be able to solve longest common subsequence in subquadatic time, and that in turn implies SETH being false by https://arxiv.org/abs/1501.07053 .

I'm pretty sure exact diff in subquadratic time is therefore impossible. It's still a nice heuristic though.

When mixed with sulfuric acid, it forms manganese heptoxide, which does lovely things like ignite paper on contact and detonate if heated above 50 C!

A lot of the posts here seem to be missing something important: permanganate is an EXTREMELY vividly colored ion in solution. The bright colors of the water in the pictures is about in line with what a 20 ppm permanganate solution looks like. Considering manganese is an essential trace mineral (although it is neurotoxic above a certain point, the amounts in the water are minimal), I doubt there is any real toxic effect caused by drinking the water. Permanganate is a very strong oxidizer, but it is not much stronger than the commonly used chlorine and chlorine dioxide to be of concern (and it's weaker than ozone anyways).

The whole reason permanganate is added in the first place is twofold: it oxidizes simple organics all the way to carbon dioxide (think nail polish remover, denatured alcohol), and it oxidizes soluble ferrous iron to insoluble ferric iron. The byproduct of the oxidation, manganese dioxide, is insoluble and if balanced correctly the treatment does not increase manganese levels in the water.

For what it's worth, permanganate is an extremely strong oxidizer (probably the second strongest stable solid oxidant known, after persulfate), but at neutral pH it is unable to oxidize chloride to hypochlorite and beyond. (The electrode potentials are too close, and anyways the maganese dioxide byproduct turns hypochlorite to chloride and oxygen.) Instead of reacting with a reducing agent in water, (the main possibilities are simple organics and ferrous iron, and these turn to carbon dioxide or insoluble ferric oxide [sidenote: this is why permanganate is added to water in the first place]) permanganate tends to break down to oxygen and manganese dioxide, which settles out.

A good game to test this on is http://www.chessgames.com/perl/chessgame?gid=1139126 .

Tal played the move 19. Rf6!!, which instantly wins the game. However, (at least when I tested this a few months ago), Stockfish takes a fairly long time to recognize this-- it prefers the more conservative 19. c4 instead.

There's a pretty easy proof to show why compression of truly random data is impossible. Let C be a compression algorithm. Assume that for all bit strings S, C(S) is not longer than S, and assume that there exists strings S' such that C(S') is shorter than S'. Also, assume that for any two distinct bit strings S1 and S2, C(S1) != C(S2). Let S'' be the shortest such string: the shortest string that C shortens. Let the length of S'' be M, and the length of C(S'') be N < M. Note N >= 1, and by assumption every string of length N does not have its length changed by C. There are 2^N strings of length N, and by assumption it is easy to see that since the images of any pair of N bit strings under C are distinct, every string of N bits is the image of some other N bit string. But now, S'' has length M but has an image of length N. This necessarily collides with the image of some string of length N, a contradiction. Thus, for any compression algorithm which is injective (in effect, reversible) and successfully shortens some strings, the algorithm must lengthen some others.

What this short proof shows is that even though random data may have patterns, no compression algorithm can successfully leverage this for every random string.

Yeah, as of a month ago he works at Google.

Source: current Stanford PhD student

If you're still curious, Firefox for android has full support for all of the desktop extensions, including uBlock.

Overall abundance of an element in the earth's crust doesn't mean as much as you'd think -- for example the element scandium is even more common than lead in the crust (20 ppm) and is a dream metal both in bulk and as a strengthening additive to aluminum, but due to a lack of readily extractable ores very little of it is produced a year. Lead is only as common and cheap as it is because it forms a variety of easy to get at ores.

There's a more fundamental issue here-- when talking about approximation algorithms reductions don't necessarily preserve approximation ratios. If you take a standard TSP instance with optimal tour length C and add the largest distance between two points M to every edge, you get a new (metric) TSP with optimal tour length C + nM, where n is the number of nodes of the graph. Applying the Christofides algorithm to this new metric TSP instance can only guarantee a tour of length 1.5C + 1.5nM, and when you subtract M from every edge again to get a tour in the original TSP instance, this scheme will return a tour of length at most 1.5C + .5nM, a bound which is provably tight. This is a terrible approximate solution, since if the largest two-node distance is O(C) (for example), the approximation obtained has value O(n)C-- a monstrously bad O(n) approximation!

Sure thing. Mind if we start with you?

/s

or Cargill, or Mars....