Linear systems are the workhorse of modern computation

Quanta Magazine  March 8, 2021 For solving linear systems researchers at the Georgia Institute of Technology have developed a technique that employs an enhanced version of the iterated guessing strategy: Instead of making just a single guess, their algorithm makes many guesses in parallel. This approach speeds up the search. The key feature to the algorithm’s ultimate success is that it makes the three initial guesses at random. Randomness ensures you do not accidentally end up biasing your search toward one part of the problem, potentially neglecting the space where the actual solution lies. They showed that the different strands […]

The mystique of mathematics: 5 beautiful math phenomena

Phys.org  May 20, 2020 According to a researcher in Australia mathematics is visible everywhere in nature, even where we are not expecting it. It can help explain the way galaxies spiral, a seashell curves, patterns replicate, and rivers bend. Some of his favorite connections between maths and beauty are Symmetry—but with a touch of surprise, Fractals: infinite and ghostly, Pi: an unknowable truth, A golden and ancient ratio, and A paradox closer to magic…read more. 2018 TEDx talk on The emotions of mathematics 

Novel math could bring machine learning to the next level

EurekAlert  September 2, 2019 Before the neural network can begin to perform facial recognition, it is typically necessary to present it with thousands of faces. Much of these machines have been increasingly successful at pattern recognition but what goes on inside them as they learn their task is unknown. An international team of researchers (Portugal, Italy) has shown that artificial vision machines can learn to recognize complex images faster by using topological data analysis which was developed 25 years ago. Current neural networks are not good at topology. The team mathematically describe how to enforce certain symmetries, and this provides […]