Zeno’s paradox stumped philosophers, mathematicians, and intellectuals for millennia. It took physics to finally solve it.
Category: mathematics – Page 126
Circa 2018
After 10 years, Prof. Raimar Wulkenhaar from the University of Münster’s Mathematical Institute and his colleague Dr. Erik Panzer from the University of Oxford have solved a mathematical equation which was considered to be unsolvable. The equation is to be used to find answers to questions posed by elementary particle physics. In this interview with Christina Heimken, Wulkenhaar looks back on the challenges encountered in looking for the formula for a solution and he explains why the work is not yet finished.
You worked on the solution to the equation for 10 years. What made this equation so difficult to solve?
It’s a non-linear integral equation with two variables. Such an equation is so complex that you do actually think there can’t possibly be any formula for a solution. Two variables alone are a challenge in themselves, and there are no established approaches for finding a solution for non-linear integral equations. Nevertheless, again and again during those 10 years there were glimmers of hope and as a result, and despite all the difficulties, I thought finding an explicit formula for a solution – expressed through known functions – was actually possible.
Rice University researchers have discovered a hidden symmetry in the chemical kinetic equations scientists have long used to model and study many of the chemical processes essential for life.
The find has implications for drug design, genetics and biomedical research and is described in a study published this month in the Proceedings of the National Academy of Sciences. To illustrate the biological ramifications, study co-authors Oleg Igoshin, Anatoly Kolomeisky and Joel Mallory of Rice’s Center for Theoretical Biological Physics (CTBP) used three wide-ranging examples: protein folding, enzyme catalysis and motor protein efficiency.
In each case, the researchers demonstrated that a simple mathematical ratio shows that the likelihood of errors is controlled by kinetics rather than thermodynamics.
Hundreds of books are now free to download.
Springer has released hundreds of free books on a wide range of topics to the general public. The list, which includes 408 books in total, covers a wide range of scientific and technological topics. In order to save you some time, I have created one list of all the books (65 in number) that are relevant to the data and Machine Learning field.
Among the books, you will find those dealing with the mathematical side of the domain (Algebra, Statistics, and more), along with more advanced books on Deep Learning and other advanced topics. You also could find some good books in various programming languages such as Python, R, and MATLAB, etc.
Conway, who passed away on April 11, was known for his rapid computation, his playful approach, and solving problems with “his own bare hands.”
Using machine learning three groups, including researchers at IBM and DeepMind, have simulated atoms and small molecules more accurately than existing quantum chemistry methods. In separate papers on the arXiv preprint server the teams each use neural networks to represent wave functions of electrons that surround the molecules’ atoms. This wave function is the mathematical solution of the Schrödinger equation, which describes the probabilities of where electrons can be found around molecules. It offers the tantalising hope of ‘solving chemistry’ altogether, simulating reactions with complete accuracy. Normally that goal would require impractically large amounts of computing power. The new studies now offer a compromise of relatively high accuracy at a reasonable amount of processing power.
Each group only simulates simple systems, with ethene among the most complex, and they all emphasise that the approaches are at their very earliest stages. ‘If we’re able to understand how materials work at the most fundamental, atomic level, we could better design everything from photovoltaics to drug molecules,’ says James Spencer from DeepMind in London, UK. ‘While this work doesn’t achieve that quite yet, we think it’s a step in that direction.’
Two approaches appeared on arXiv just a few days apart in September 2019, both combining deep machine learning and Quantum Monte Carlo (QMC) methods. Researchers at DeepMind, part of the Alphabet group of companies that owns Google, and Imperial College London call theirs Fermi Net. They posted an updated preprint paper describing it in early March 2020.1 Frank Noé’s team at the Free University of Berlin, Germany, calls its approach, which directly incorporates physical knowledge about wave functions, PauliNet.2
Computer scientists established a new boundary on computationally verifiable knowledge. In doing so, they solved major open problems in quantum mechanics and pure mathematics.
John Horton Conway, a legendary mathematician who stood out for his love of games and for bringing mathematics to the masses, died on Saturday, April 11, in New Brunswick, New Jersey, from complications related to COVID-19. He was 82.
Known for his unbounded curiosity and enthusiasm for subjects far beyond mathematics, Conway was a beloved figure in the hallways of Princeton’s mathematics building and at the Small World coffee shop on Nassau Street, where he engaged with students, faculty and mathematical hobbyists with equal interest.
Conway, who joined the faculty in 1987, was the John von Neumann Professor in Applied and Computational Mathematics and a professor of mathematics until 2013 when he transferred to emeritus status.
The devil staircase findings.
April 14 (UPI) — The timing of large, shallow earthquakes across the globe follows a mathematical pattern known as the devil’s staircase, according to a new study of seismic sequences.
Previously, scientists and their models have theorized that earthquake sequences happen periodically or quasi-periodically, following cycles of growing tension and release. Researchers call it the elastic rebound model. In reality, periodic earthquake sequences are surprisingly rare.
Instead, scientists found global earthquake sequences tend to occur in clusters — outbursts of seismic events separated by long but irregular intervals of silence.