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In a recent development at Fudan University, a team of applied mathematicians and AI scientists has unveiled a cutting-edge machine learning framework designed to revolutionize the understanding and prediction of Hamiltonian systems. The paper is published in the journal Physical Review Research.

Named the Hamiltonian Neural Koopman Operator (HNKO), this innovative framework integrates principles of mathematical physics to reconstruct and predict Hamiltonian systems of extremely-high dimension using noisy or partially-observed data.

The HNKO framework, equipped with a unitary Koopman structure, has the remarkable ability to discover new conservation laws solely from observational data. This capability addresses a significant challenge in accurately predicting dynamics in the presence of noise perturbations, marking a major breakthrough in the field of Hamiltonian mechanics.

A mathematical historian at Trinity Wester University in Canada, has found use of a decimal point by a Venetian merchant 150 years before its first known use by German mathematician Christopher Clavius. In his paper published in the journal Historia Mathematica, Glen Van Brummelen describes how he found the evidence of decimal use in a volume called “Tabulae,” and its significance to the history of mathematics.

The invention of the decimal point led to the development of the decimal system, and that in turn made it easier for people working in multiple fields to calculate non-whole numbers (fractions) as easily as whole numbers. Prior to this new discovery, the earliest known use of the decimal point was by Christopher Clavius as he was creating astronomical tables—the resulting work was published in 1593.

The new discovery was made in a part of a manuscript written by Giovanni Bianchini in the 1440s—Van Brummelen was discussing a section of trigonometric tables with a colleague when he noticed some of the numbers included a dot in the middle. One example was 10.4, which Bianchini then multiplied by 8 in the same way as is done with modern mathematics. The finding shows that a decimal point to represent non-whole numbers occurred approximately 150 years earlier than previously thought by math historians.

A team of economists from Switzerland and Germany has found, via model testing, that two leading theories created to explain why humans engage in cooperation with one another tend to fail under scrutiny. In their paper published in the journal Nature the group describes how further model and field testing showed that it was only when the two theories were combined that they proved able to describe scenarios where humans cooperated.

Humans cooperate with one another on a variety of levels and in different kinds of situations. Research suggests that the reason humans have evolved in a way that promotes cooperation is that it leads to an eventual payoff for both parties. Such research has also shown that it is much easier to explain how and why reciprocity works when it is clear that the person performing the first act is reasonably sure they will see the other person again, likely leading them to reciprocate.

Much more difficult to explain is why humans sometimes engage in behaviors that would normally be seen as a first move in cooperation, when there is no assurance they will see the recipient again, and thus may not reap a reward. In this new study, the research team tested theories that have attempted to explain such behavior.

Understanding cloud patterns in our changing climate is essential to making accurate predictions about their impact on society and nature. Scientists at the Institute of Science and Technology Austria (ISTA) and the Max-Planck-Institute for Meteorology published a study in the journal Science Advances that uses a high-resolution global climate model to understand how the clustering of clouds and storms impacts rainfall extremes in the tropics. They show that with rising temperatures, the severity of extreme precipitation events increases.

Extreme rainfall is one of the most damaging natural disasters costing human lives and causing billions in damage. Their frequency has been increasing over the last years due to the warming climate.

For several decades, scientists have been using computer models of the Earth’s climate to better understand the mechanisms behind these events and to predict future trends.

A new technique for electrospinning sponges has allowed scientists from the University of Surrey to directly produce 3D scaffolds—on which skin grafts could be grown from the patient’s own skin.

Electrospinning is a technique that electrifies droplets of liquid to form fibers from plastics. Previously, scientists had only been able to make 2D films. This is the first time anybody has electro-spun a 3D structure directly and on-demand so that it can be produced to scale. The research is published in the journal Nanomaterials.

Chloe Howard, from Surrey’s School of Computer Science and Electronic Engineering, said, After spinning these scaffolds, we grew skin cells on them. Seven days later, they were twice as viable as cells grown on 2D films or mats. They even did better than cells grown on plasma-treated polystyrene—previously, the gold standard. They were very happy cells on our 3D scaffolds.

A material coating, whose light refraction properties can be precisely switched between different states, has been developed by an interdisciplinary research team from the Chemistry and Physics departments at the University of Jena. The team, led by Felix Schacher, Sarah Walden, Purushottam Poudel, and Isabelle Staude, combined polymers that react to light with so-called metasurfaces.

This innovation has led to the creation of new optical components that could potentially be used in signal processing. Their findings have now been published in the journal ACS Nano.

Networks can represent changing systems, like the spread of an epidemic or the growth of groups in a population of people. But the structure of these networks can change, too, as links appear or vanish over time. To better understand these changes, researchers often study a series of static “snapshots” that capture the structure of the network during a short duration.

Network theorists have sought ways to combine these snapshots. In a new paper in Physical Review Letters, a trio of SFI-affiliated researchers describe a novel way to aggregate static snapshots into smaller clusters of networks while still preserving the dynamic nature of the system. Their method, inspired by an idea from quantum mechanics, involves testing successive pairs of network snapshots to find those for which a combination would result in the smallest effect on the dynamics of the system—and then combining them.

Importantly, it can determine how to simplify the history of the network’s structure as much as possible while maintaining accuracy. The math behind the method is fairly simple, says lead author Andrea Allen, now a data scientist at Children’s Hospital of Philadelphia.

If the fractional quantum Hall regime were a series of highways, these highways would have either two or four lanes. The flow of the two-flux or four-flux composite fermions, like automobiles in this two-to four-flux composite fermion traffic scenario, naturally explains the more than 90 fractional quantum Hall states that form in a large variety of host materials. Physicists at Purdue University have recently discovered, though, that fractional quantum Hall regimes are not limited to two-flux or four-flux and have discovered the existence of a new type of emergent particle, which they are calling six-flux composite fermion.

They have recently published their groundbreaking findings in Nature Communications.

Gabor Csathy, professor and head of the Department of Physics and Astronomy at the Purdue University College of Science, along with Ph.D. students Haoyun Huang, Waseem Hussain, and recent Ph.D. graduate Sean Myers, led this discovery from the West Lafayette campus of Purdue. Csathy credits lead author Huang as having conceived and led the measurements, and having written a large part of the manuscript. All the ultra-low-temperature measurements were completed in Csathy’s Physics Building lab. His lab conducts research on strongly correlated electron physics, sometimes referred to as topological electron physics.

Researchers report in the journal Cell that ancient viruses may be to thank for myelin—and, by extension, our large, complex brains.

The team found that a retrovirus-derived genetic element or “retrotransposon” is essential for myelin production in mammals, amphibians, and fish. The gene sequence, which they dubbed “RetroMyelin,” is likely a result of ancient viral infection, and comparisons of RetroMyelin in mammals, amphibians, and fish suggest that retroviral infection and genome-invasion events occurred separately in each of these groups.

“Retroviruses were required for vertebrate evolution to take off,” says senior author and neuroscientist Robin Franklin of Altos Labs-Cambridge Institute of Science. “If we didn’t have retroviruses sticking their sequences into the vertebrate genome, then myelination wouldn’t have happened, and without myelination, the whole diversity of vertebrates as we know it would never have happened.”