Lifeboat Foundation

A research team is studying how light moves through special circuits called optical waveguides, using a concept called topology. They’ve made an important discovery that combines stable light paths with light particle interactions, which could make quantum computers more reliable and lead to new technological advancements.

Scientific innovation often arises as synthesis from seemingly unrelated concepts. For instance, the reciprocity of electricity and magnetism paved the way for Maxwell’s theory of light, which, up until now, is continually being refined and extended with ideas from quantum mechanics.

Similarly, the research group of Professor Alexander Szameit at the Institute of Physics at the University of Rostock explores light evolution in optical waveguide circuits in the presence of topology. This abstract mathematical concept was initially developed to classify solid geometries according to their global properties. Szameit explains: “In topological systems, light only follows the global characteristics of the waveguide system. Local perturbations to the waveguides such as defects, vacancies, and disorder cannot divert its path.”

Our favorite mathematical constant, pi (π), describing the ratio between a circle’s circumference and its diameter, has taken on new meaning.

The new representation was borne out of the twists and turns of string theory, and two mathematicians’ attempts to better describe particle collisions.

“Our efforts, initially, were never to find a way to look at pi,” says Aninda Sinha of the Indian Institute of Science (IISc) who co-authored the new work with fellow IISc mathematician Arnab Priya Saha.

Lakes and seas of liquid methane exist on Saturn’s largest moon, Titan, due to the moon’s bone-chilling cold temperatures at-290 degrees Fahrenheit (−179 degrees Celsius), whereas it can only exist as a gas on Earth. But do these lakes and seas of liquid methane strewn across Titan’s surface remain static, or do they exhibit wave activity like the lakes and seas of liquid water on Earth? This is what a recent study published in Science Advances hopes to address as a team of researchers have investigated coastal shoreline erosion on Titan’s surface resulting from wave activity. This study holds the potential to help researchers better understand the formation and evolution of planetary surfaces throughout the solar system and how well they relate to Earth.

For the study, the researchers used a combination of shoreline analogs on Earth, orbital images obtained by NASA’s now-retired Cassini spacecraft, coastal evolution models, and several mathematical equations to ascertain the processes responsible for shoreline morphology across Titan’s surface. Through this, the researchers were able to construct coastal erosion models depicting how wave activity could be responsible for changes in shoreline morphology at numerous locations across Titan’s surface.

“We can say, based on our results, that if the coastlines of Titan’s seas have eroded, waves are the most likely culprit,” said Dr. Taylor Perron, who is a Cecil and Ida Green Professor of Earth, Atmospheric and Planetary Sciences at the Massachusetts Institute of Technology and a co-author on the study. “If we could stand at the edge of one of Titan’s seas, we might see waves of liquid methane and ethane lapping on the shore and crashing on the coasts during storms. And they would be capable of eroding the material that the coast is made of.”

Not content with shapes in two or three dimensions, mathematicians like to explore objects in any number of spatial dimensions. Now they have discovered shapes of constant width in any dimension, which roll like a wheel despite not being round.

By Alex Wilkins

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The universe creates complexity out of simplicity, but despite many attempts at understanding how, scientists still have not figured it out. We do know that complexity relies on the emergence of new features and laws, but then again we don’t understand emergence either. The first step must be to clearly define what we are talking about and to measure it. A group of scientists now put forward a way to do exactly this. Let’s have a look.

Continue reading “This New Idea Could Explain Complexity” »

👉 Researchers at the Shanghai Artificial Intelligence Laboratory are combining the Monte Carlo Tree Search (MCTS) algorithm with large language models to improve its ability to solve complex mathematical problems.

Integrating the Monte Carlo Tree Search (MCTS) algorithm into large language models could significantly enhance their ability to solve complex mathematical problems. Initial experiments show promising results.

While large language models like GPT-4 have made remarkable progress in language processing, they still struggle with tasks requiring strategic and logical thinking. Particularly in mathematics, the models tend to produce plausible-sounding but factually incorrect answers.

Continue reading “AI that defeated humans at Go could now help language models master mathematics” »

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Be sure to check out the Infinite Series episode Singularities Explained • Singularities Explained | Infinite Se… or How I Learned to Stop Worrying and Divide by Zero.

Continue reading “PBS Space Time” »

Data assimilation is a mathematical discipline that integrates observed data and numerical models to improve the interpretation and prediction of dynamical systems. It is a crucial component of Earth sciences, particularly in numerical weather prediction (NWP).

Officials of the U.S. Defense Advanced Research Projects Agency (DARPA) in Arlington, Va., issued a broad agency announcement (HR001124S0029) for the Artificial Intelligence Quantified (AIQ) project.

AIQ seeks to find ways of assessing and understanding the capabilities of AI to enable mathematical guarantees on performance. Successful use of military AI requires ensuring safe and responsible operation of autonomous and semi-autonomous technologies.