Lifeboat Foundation

Universal law always works perfectly well.

Wherever there is sand and an atmosphere, prevailing winds may whip the grains into undulating shapes, pleasing to the eye with their calming repetition.

Certain sand waves, with wavelengths between 30 centimeters (almost 12 inches) and several meters (around 30 feet), are known as megaripples: they’re between ordinary beach ripples and full dunes in size, and we’ve seen them not just on Earth, but even on other planets such as Mars, well known for its all-encompassing dust storms.

Continue reading “There’s a Hidden Mathematical ‘Law’ in The Sand Megaripples Found All Over Earth” »

Paul Nelson has solved the subconvexity problem, bringing mathematicians one step closer to understanding the Riemann hypothesis and the distribution of prime numbers.

The notion that some computational problems in math and computer science can be hard should come as no surprise. There is, in fact, an entire class of problems deemed impossible to solve algorithmically. Just below this class lie slightly “easier” problems that are less well-understood—and may be impossible, too.

David Gamarnik, professor of operations research at the MIT Sloan School of Management and the Institute for Data, Systems, and Society, is focusing his attention on the latter, less-studied category of problems, which are more relevant to the everyday world because they involve randomness —an integral feature of natural systems. He and his colleagues have developed a potent tool for analyzing these problems called the overlap gap property (or OGP). Gamarnik described the new methodology in a recent paper in the Proceedings of the National Academy of Sciences.

More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective.

From the cosmic microwave background to Feynman diagrams — what are the underlying rules that work to create patterns of action, force and consequence that make up our universe?
Brian’s new book “Ten Patterns That Explain the Universe” is available now: https://geni.us/clegg.
Watch the Q&A: https://youtu.be/RZB95znAGRE

Brian Clegg will explore the phenomena that make up the very fabric of our world by examining ten essential sequenced systems. From diagrams that show the deep relationships between space and time to the quantum behaviours that rule the way that matter and light interact, Brian will show how these patterns provide a unique view of the physical world and its fundamental workings.

Continue reading “The Fundamental Patterns that Explain the Universe — with Brian Clegg” »

Many of these systems are kept out of equilibrium because individual constituents have their own power source — ATP for cells, gas for cars. But all these extra energy sources and mismatched reactions make for a complex dynamical system beyond the reach of statistical mechanics. How can we analyze phases in such ever-changing systems?

Vitelli and his colleagues see an answer in mathematical objects called exceptional points. Generally, an exceptional point in a system is a singularity, a spot where two or more characteristic properties become indistinguishable and mathematically collapse into one. At an exceptional point, the mathematical behavior of a system differs dramatically from its behavior at nearby points, and exceptional points often describe curious phenomena in systems — like lasers — in which energy is gained and lost continuously.

Now the team has found that these exceptional points also control phase transitions in nonreciprocal systems. Exceptional points aren’t new; physicists and mathematicians have studied them for decades in a variety of settings. But they’ve never been associated so generally with this type of phase transition. “That’s what no one has thought about before, using these in the context of nonequilibrium systems,” said the physicist Cynthia Reichhardt of Los Alamos National Laboratory in New Mexico. “So you can bring all the machinery that we already have about exceptional points to study these systems.”

A research team from MIT, Columbia University, Harvard University and University of Waterloo proposes a neural network that can solve university-level mathematics problems via program synthesis.

The sun can power many things, but it takes a lot of math to realize it’s not ideal for powering cars.

AutoML-Zero is unique because it uses simple mathematical concepts to generate algorithms “from scratch,” as the paper states. Then, it selects the best ones, and mutates them through a process that’s similar to Darwinian evolution.

AutoML-Zero first randomly generates 100 candidate algorithms, each of which then performs a task, like recognizing an image. The performance of these algorithms is compared to hand-designed algorithms.-Zero then selects the top-performing algorithm to be the “parent.”

“This parent is then copied and mutated to produce a child algorithm that is added to the population, while the oldest algorithm in the population is removed,” the paper states.