A mathematician whose research generates a sequence of numbers can turn to the OEIS to discover other contexts in which the sequence arises and any papers that discuss it. The repository has spawned countless mathematical discoveries and has been cited more than 4,000 times.
Source: Neil Sloane, Connoisseur of Number Sequences | Quanta Magazine
the Online Encyclopedia of Integer Sequences (OEIS), often simply called “Sloane” by its users.
The updated document, Recommendation for Random Number Generation Using Deterministic Random Bit Generators, describes algorithms that can be used to reliably generate random numbers, a key step in data encryption.
Source: NIST revises key computer security publication on random number generation
The computation uses dynamic programming to count the number of paths through a graph consisting of 18^2=324 layers with up to 81 billion nodes each. Each node corresponds to a set of partial board (e.g. the top 7 rows plus 6 points on the 8th row) positions that are equivalent in their set of valid completions. Our paper explains the algorithm in detail, and also explains how the resulting exact counts allow derivation of the approximation formula
L(m,n) ~ 0.850639925845714538 * 0.96553505933837387^{m+n} * 2.97573419204335724938^{m*n}
which gives us the approximate number of legal positions on a standard board size
L(19,19) ~ 2.08168199381982*10^170
via Counting Legal Positions in Go.
Thanks to the Chinese Remainder Theorem, the work of computing L(19,19) can be split up into 9 jobs that each compute 64 bits of the 566-bit result. Allowing for some redundancy, we need from 10 to 13 servers, each with at least 8 cores, 512GB RAM, and ample disk space (10-15TB), running for about 5-9 months.
As an example, the researchers wrote about looking at data from September 23 and 24 and who went to a bakery one day and a restaurant the other. Searching through the data set, they found there could be only person who fits the bill – they called him Scott. The study said, “and we now know all of his other transactions, such as the fact that he went shopping for shoes and groceries on 23 September, and how much he spent.”
Poker being what it is, the robot, named Cepheus after a constellation in the northern hemisphere, will lose if it’s dealt an inferior hand, but it will minimize its losses as best as is mathematically possible and will slowly but surely take your money by making the “perfect” decision in any given scenario. Heads-up limit Hold’Em, it can be said, has been “solved.”
via This Robot Is the Best Limit Texas Hold’Em Player in the World | Motherboard.
And it was solved by computer scientists at the University of Alberta who don’t actually play the game. That’s because solving the game is more of a math problem than anything else.
This development is like when they discovered Basic Strategy for blackjack.
Predictions are made for the number of chapters told from the point of view of each character in the next two novels in George R. R. Martin’s \emph{A Song of Ice and Fire} series by fitting a random effects model to a matrix of point-of-view chapters in the earlier novels using Bayesian methods. {\textbf{SPOILER WARNING: readers who have not read all five existing novels in the series should not read further, as major plot points will be spoiled.}}
via [1409.5830] Bayesian Prediction for The Winds of Winter.
It seems that someone would have come up with such a metric by now. But, says Weissman, “there are two communities: the practitioners, who care about running time, and the theoreticians, who care about how succinctly you can represent the data and don’t worry about the complexity of the implementation.” As a result of this split, he says, no one had yet combined, in a single number, a means of rating both how fast and how tightly an algorithm compresses.
Misra came up with a formula (photo above), incorporating both. Along with existing benchmarks the formula creates a metric that the show writers tagged the “Weissman Score.” It’s not a fictional metric: although it didn’t exist before Misra created it for the show, it works and may soon find use in the real world.
via A Fictional Compression Metric Moves Into the Real World – IEEE Spectrum.
The take-home message from Yuan-Jia and Bih-Yaw’ work is that the Brazuca ball does have a fullerene that is its molecular analogue, just like its predecessors at all the world cups dating back to 1970
Estimating causal impacts is fraught with difficulty. Even randomized trials are imperfect, in part because we can seldom, if ever, conduct true experiments (though experimental design is still the gold standard of statistical research). IV is one of the more compelling quasi-experimental methods of estimating impacts, largely because the assumptions needed to justify the IV method are often more plausible than those needed to justify other methods, such as regression.
via The Urban Institute | Toolkit | Data Methods | Instrumental Variables Methods.
So let’s look at the probability that none of the 23 people in the room share the same birthday. For two people, the probability that the second person doesn’t have the same birthday as the first is 364/365. Then the probability that those two are different and that a third doesn’t share the same birthday as either of them is 364/365 × 363/365. Likewise, the probability that those three have different birthdays and that the fourth does not share the same birthday as any of those first three is 364/365 × 363/365 × 362/365. Continuing like this, the probability that none of the 23 people share the same birthday is 364/365 × 363/365 × 362/365 × 361/365 … × 343/365.
This equals 0.49
via Math Explains Likely Long Shots, Miracles and Winning the Lottery – Scientific American.