A Bristol academic has achieved a milestone in statistical/mathematical physics by solving a 100-year-old physics problem—the discrete diffusion equation in finite space.
Just as a literature buff might explore a novel for recurring themes, physicists and mathematicians search for repeating structures present throughout nature.
For example, a certain geometrical structure of knots, which scientists call a Hopfion, manifests itself in unexpected corners of the universe, ranging from particle physics, to biology, to cosmology. Like the Fibonacci spiral and the golden ratio, the Hopfion pattern unites different scientific fields, and deeper understanding of its structure and influence will help scientists to develop transformative technologies.
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Mathematicians were shocked when a graduate student worked through a decades-old problem in just a few days. University of Texas at Austin mathematician Lisa Piccirillo learned about the Conway knot—a knot with 11 crossings, so named for the late mathematician John Horton Conway—from a colleague’s talk during a conference. Within a week, she’d solved the longstanding problem of whether or not the special knot was slice. (It’s not.)
Zhou Yi was terrible at math. He risked never getting into college. Then a company called Squirrel AI came to his middle school in Hangzhou, China, promising personalized tutoring. He had tried tutoring services before, but this one was different: instead of a human teacher, an AI algorithm would curate his lessons. The 13-year-old decided to give it a try. By the end of the semester, his test scores had risen from 50% to 62.5%. Two years later, he scored an 85% on his final middle school exam.
“I used to think math was terrifying,” he says. “But through tutoring, I realized it really isn’t that hard. It helped me take the first step down a different path.”
In the summer of 2018, at a conference on low-dimensional topology and geometry, Lisa Piccirillo heard about a nice little math problem. It seemed like a good testing ground for some techniques she had been developing as a graduate student at the University of Texas, Austin.
“I didn’t allow myself to work on it during the day,” she said, “because I didn’t consider it to be real math. I thought it was, like, my homework.”
The question asked whether the Conway knot — a snarl discovered more than half a century ago by the legendary mathematician John Horton Conway — is a slice of a higher-dimensional knot. “Sliceness” is one of the first natural questions knot theorists ask about knots in higher-dimensional spaces, and mathematicians had been able to answer it for all of the thousands of knots with 12 or fewer crossings — except one. The Conway knot, which has 11 crossings, had thumbed its nose at mathematicians for decades.
After translating some of math’s complicated equations, researchers have created an AI system that they hope will answer even bigger questions.
As expected, they discovered large fluctuations in the composition and daily changes of the human and mouse gut microbiomes. But strikingly, these apparently chaotic fluctuations followed several elegant ecological laws.
“Similar to many animal ecologies and complex financial markets, a healthy gut microbiome is never truly at equilibrium,” Vitkup says. “For example, the number of a particular bacterial species on day one is never the same on day two, and so on. It constantly fluctuates, like stocks in a financial market or number of animals in a valley, but these fluctuations are not arbitrary. In fact, they follow predictable patterns described by Taylor’s power law, a well-established principle in animal ecology that describe how fluctuations are related to the relative number of bacteria for different species.”
Other discovered laws of the gut microbiome also followed principles frequently observed in animal ecologies and economic systems, including the tendency of gut bacteria abundances to slowly but predictably drift over time and the tendency of species to appear and disappear from the gut microbiome at predictable times.
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For fun, Apple software developer, Forrest Heller, pits a USB-C charger chip against the computer that landed astronauts on the moon. Here’s what he found.
Plant scientists have long known that crop yield is proportional to the dose of nitrogen fertilizer, but the increased use of fertilizers is costly and harmful to the environment. Until now, the underlying mechanisms by which plants adjust their growth according to the nitrogen dose has been unknown—a key finding that could help enhance plant growth and limit fertilizer use.
In a new study published in the Proceedings of the National Academy of Sciences (PNAS), plant genomic scientists at New York University’s Center for Genomics & Systems Biology discovered the missing piece in the molecular link between a plant’s perception of the nitrogen dose in its environment and the dose-responsive changes in its biomass.
Taking a novel approach, the NYU researchers examined how increasing doses of nitrogen created changes in plants’ genome-wide expression as a function of time. They then used mathematical models to investigate the rate of change of messenger RNA (mRNA) for thousands of genes within the genome to this experimental set up.
Zeno’s paradox stumped philosophers, mathematicians, and intellectuals for millennia. It took physics to finally solve it.
