Fermat’s algorithm was based on the fact that any odd number can be expressed as the difference between two squares. When the factors are near the root of the number, they can be calculated easily and quickly. The method isn’t feasible when factors are truly random and hence far apart.
Source: Researcher uses 379-year-old algorithm to crack crypto keys found in the wild | Ars Technica
But now even Ke, the reigning top-ranked Go player, has acknowledged that human beings are no match for robots in the complex board game, after he lost three games to an AI that mysteriously popped up online in recent days.
The AI turned out to be AlphaGo in disguise.
Source: The AI “Master” bested the world’s top Go players—and then revealed itself as Google’s AlphaGo in disguise — Quartz
An image kernel is a small matrix used to apply effects like the ones you might find in Photoshop or Gimp, such as blurring, sharpening, outlining or embossing. They’re also used in machine learning for ‘feature extraction’, a technique for determining the most important portions of an image. In this context the process is referred to more generally as “convolution” (see: convolutional neural networks.)
Source: Image Kernels explained visually
The puzzle that required the 200-terabyte proof, called the Boolean Pythagorean triples problem, has eluded mathematicians for decades. In the 1980s, Graham offered a prize of US$100 for anyone who could solve it. (He duly presented the cheque to one of the three computer scientists, Marijn Heule of the University of Texas at Austin, earlier this month.) The problem asks whether it is possible to colour each positive integer either red or blue, so that no trio of integers a, b and c that satisfy Pythagoras’ famous equation a2 + b2 = c2 are all the same colour. For example, for the Pythagorean triple 3, 4 and 5, if 3 and 5 were coloured blue, 4 would have to be red.
Source: Two-hundred-terabyte maths proof is largest ever
There are more than 102,300 ways to colour the integers up to 7,825, but the researchers took advantage of symmetries and several techniques from number theory to reduce the total number of possibilities that the computer had to check to just under 1 trillion. It took the team about 2 days running 800 processors in parallel on the University of Texas’s Stampede supercomputer to zip through all the possibilities. The researchers then verified the proof using another computer program.
I get a lot of questions from aspiring programmers on what’s the best tool or languages to learn. It’s almost always a premature question to ask. I used to come up with answers like “depending on what you’re building” or “pick a beginner friendly community” or “invest in a growing language”. I think all of these are good answers, but it doesn’t really matter that early on in a programmer’s learning journey. It’s all the same when you’re essentially learning how to compute. Furthermore, these sort of answers enable the culture of tooling obsession.
Source: Overcoming Intuition in Programming
According to the University of Chicago’s theory seminar calendar, on Tuesday of next week (November 10), the legendary Laszlo Babai will be giving a talk about a new algorithm that solves the graph isomorphism problem in quasipolynomial time.
Source: Shtetl-Optimized » Blog Archive » G. Phi. Fo. Fum.
Uptake’s model is to partner with well-known companies in various industries — from construction to mining to aviation — and create software and special algorithms that help these customers collect and understand huge amounts of data. The company is already producing positive cash flow, according to a person with knowledge of the financials who spoke on the condition of anonymity.
Source: Midwest Start-Up Achieves Rare $1 Billion Valuation – The New York Times
As far as computer scientists know, the only general-purpose method to find the correct answer to a SAT problem is to try all possible settings of the variables one by one. The amount of time that this exhaustive or “brute-force” approach takes depends on how many variables there are in the formula. As the number of variables increases, the time it takes to search through all the possibilities increases exponentially. To complexity theorists and algorithm designers, this is bad. (Or, technically speaking, hard.)
SETH takes this situation from bad to worse. It implies that finding a better general-purpose algorithm for SAT — even one that only improves on brute-force searching by a small amount — is impossible.
Source: Edit Distance Reveals Hard Computational Problems | Quanta Magazine
The Hacker Cup goes much the same way as other sport-coding contests: five puzzles to finish in any order over three hours. Keep the programming as efficient as possible. The cleanest, most accurate code in the fastest time takes first place. A common type of problem might ask for the shortest route between San Francisco and Los Angeles given a number of constraints. Or perhaps the problem is about how to tile a floor in a specific pattern. The questions typically revolve around a well-known algorithm or mathematical structure with a fresh twist. Elite sport coders must figure out the underlying logic quickly and then trust their abilities.
Source: The Jocks of Computer Code Do It for the Job Offers
Mr Hocking, who led the new work, commented: “The important thing about our algorithm is that we have not told the machine what to look for in the images, but instead taught it how to ‘see’.”
Source: Analysing galaxy images with artificial intelligence: astronomers teach a machine how to ‘see’
The new work appears in “Teaching a machine to see: unsupervised image segmentation and categorisation using growing neural gas and hierarchical clustering”, A. Hocking, J. E. Geach, N. Davey & Y. Sun. The paper has been submitted to Monthly Notices of the Royal Astronomical Society.