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Archive for the ‘mathematics’ category: Page 8

Mar 8, 2022

In New Math Proofs, Artificial Intelligence Plays to Win

Posted by in categories: mathematics, robotics/AI

A new computer program fashioned after artificial intelligence systems like AlphaGo has solved several open problems in combinatorics and graph theory.

Mar 7, 2022

Progress and prospects in magnetic topological materials

Posted by in categories: energy, mathematics, quantum physics

A new review paper on magnetic topological materials introduces a theoretical concept that interweaves magnetism and topology. It identifies and surveys potential new magnetic topological materials and suggests possible future applications in spin and quantum electronics and as materials for efficient energy conversion.

Magnetic topological materials represent a class of compounds whose properties are strongly influenced by the of the electronic wavefunctions coupled with their spin configuration. Topology is a simple concept dealing with the surfaces of objects. The topology of a mathematical structure is identical if it is preserved under continuous deformation. A pancake has the same topology as a cube, a donut as a coffee cup, and a pretzel as a board with three holes. Adding spin offers additional structure—a new degree of freedom—for the realization of new states of matter that are not known in non-magnetic materials. Magnetic topological materials can support chiral channels of electrons and spins, and can be used for an array of applications including information storage, control of dissipationless spin and charge transport, and giant responses under such as temperature and light.

The review summarizes the theoretical and experimental progress achieved in the field of magnetic topological materials beginning with the theoretical prediction of the quantum anomalous Hall effect without Landau levels, leading to recent discoveries of magnetic Weyl semimetals and antiferromagnetic topological insulators. It also outlines recent tabulations of all magnetic symmetry group representations and topology. As a result, all known magnetic materials—including future discoveries—can be fully characterized by their topological properties. The identification of materials for a specific technological application (e.g., quantum anomalous Hall) is straightforward.

Mar 3, 2022

Physics: Speed of Light Could Be Dropped to Zero Using Crystals

Posted by in categories: mathematics, particle physics

In a vacuum like space, the speed of light is just over 186,280 miles per second. Scientists have now shown it’s possible to slow it down to zero miles per second without sacrificing its brightness, regardless of its frequency or bandwidth.

A team of researchers from the Israel Institute of Technology and the Institute of Pure and Applied Mathematics in Brazil discovered a method of theoretically bringing the speed of light to a halt by capitalizing on “exceptional points”—coordinates at which two separate light emissions reach each other and merge into a single one, according to Phys.org. A paper describing the research was published in the scientific journal Physical Review Letters.

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Mar 3, 2022

Dark energy: Neutron stars will tell us if it’s only an illusion

Posted by in categories: computing, cosmology, mathematics

A huge amount of mysterious dark energy is necessary to explain cosmological phenomena, such as the accelerated expansion of the Universe, using Einstein’s theory. But what if dark energy was just an illusion and general relativity itself had to be modified? A new SISSA study, published in Physical Review Letters, offers a new approach to answer this question. Thanks to huge computational and mathematical effort, scientists produced the first simulation ever of merging binary neutron stars in theories beyond general relativity that reproduce a dark-energy like behavior on cosmological scales. This allows the comparison of Einstein’s theory and modified versions of it, and, with sufficiently accurate data, may solve the dark energy mystery.

For about 100 years now, general relativity has been very successful at describing gravity on a variety of regimes, passing all experimental tests on Earth and the solar system. However, to explain cosmological observations such as the observed accelerated expansion of the Universe, we need to introduce dark components, such as and , which still remain a mystery.

Enrico Barausse, astrophysicist at SISSA (Scuola Internazionale Superiore di Studi Avanzati) and principal investigator of the ERC grant GRAMS (GRavity from Astrophysical to Microscopic Scales) questions whether dark is real or, instead, it may be interpreted as a breakdown of our understanding of gravity. “The existence of dark energy could be just an illusion,” he says, “the accelerated expansion of the Universe might be caused by some yet unknown modifications of general relativity, a sort of ‘dark gravity’.”

Mar 3, 2022

AI-generated faces have crossed the uncanny valley and are now more trustworthy than real ones

Posted by in categories: mathematics, robotics/AI

“We were really surprised by this result because our motivation was to find an indirect route to improve performance, and we thought trust would be that—with real faces eliciting that more trustworthy feeling,” Nightingale says.

Farid noted that in order to create more controlled experiments, he and Nightingale had worked to make provenance the only substantial difference between the real and fake faces. For every synthetic image, they used a mathematical model to find a similar one, in terms of expression and ethnicity, from databases of real faces. For every synthetic photo of a young Black woman, for example, there was a real counterpart.

Mar 3, 2022

For new insights into aerodynamics, scientists turn to paper airplanes

Posted by in categories: drones, mathematics, robotics/AI

A series of experiments using paper airplanes reveals new aerodynamic effects, a team of scientists has discovered. Its findings enhance our understanding of flight stability and could inspire new types of flying robots and small drones.

“The study started with simple curiosity about what makes a good airplane and specifically what is needed for smooth gliding,” explains Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and an author of the study, which appears in the Journal of Fluid Mechanics. “Answering such basic questions ended up being far from child’s play. We discovered that the aerodynamics of how paper airplanes keep level flight is really very different from the stability of conventional airplanes.”

“Birds glide and soar in an effortless way, and paper airplanes, when tuned properly, can also glide for long distances,” adds author Jane Wang, a professor of engineering and physics at Cornell University. “Surprisingly, there has been no good mathematical model for predicting this seemingly simple but subtle gliding flight.”

Mar 3, 2022

Researchers show they can steal data during homomorphic encryption

Posted by in categories: computing, encryption, mathematics, security

Homomorphic encryption is considered a next generation data security technology, but researchers have identified a vulnerability that allows them to steal data even as it is being encrypted.

“We weren’t able to crack using mathematical tools,” says Aydin Aysu, senior author of a paper on the work and an assistant professor of computer engineering at North Carolina State University. “Instead, we used . Basically, by monitoring in a device that is encoding data for homomorphic encryption, we are able to read the data as it is being encrypted. This demonstrates that even next generation encryption technologies need protection against side-channel attacks.”

Homomorphic encryption is a way of encrypting data so that third parties cannot read it. However, homomorphic encryption still allows third parties and third-party technologies to conduct operations using the data. For example, a user could use homomorphic encryption to upload sensitive data to a cloud computing system in order to perform analyses of the data. Programs in the cloud could perform the analyses and send the resulting information back to the user, but those programs would never actually be able to read the .

Feb 23, 2022

New project creates digital clones of human brains to help treat neurological disorders

Posted by in categories: biotech/medical, computing, mathematics, neuroscience

More recently, digital twins have been the focus of a European Union-funded project that seeks to clone a patient’s entire brain. Dubbed Neurotwin, the research project aims to create virtual models that can be used to predict the effects of stimulation for the treatment of neurological disorders—including epilepsy and Alzheimer’s disease. When it comes to epilepsy, non-invasive stimulations (where electrical currents are painlessly delivered to the brain) have proven effective in tackling seizures. Given how drugs don’t help a third of epilepsy patients, the technology is coveted yet needs refinement. This is where virtual clones come in.

“The digital avatar is essentially a mathematical model running on a computer,” Giulio Ruffini, coordinator of the Neurotwin project, told WIRED. Including a network of embedded “neural mass models,” the technology hopes to create a map of the neural connections in the brain—a concept termed as the ‘connectome’. “In the case of epilepsy, some areas of the connectome could become overexcited,” the outlet mentioned. “In the case of, say, stroke, the connectome might be altered.” Once the digital clone has been created by the team, with about half an hour-worth of magnetic resonance imaging (MRI) data and ten minutes of electroencephalography (EEG) readings to capture electrical activities and realistically simulate the brain’s main tissues (including the scalp, skull, cerebrospinal fluid, and grey and white matter), it can then be used to optimise stimulation of the real patient’s brain.

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Feb 16, 2022

Your brain might be a quantum computer that hallucinates math

Posted by in categories: computing, mathematics, neuroscience, quantum physics

You’re not bad at math. Like pearls before swine, your beautiful brain is just far too complex for such basic things. property= description.

Feb 15, 2022

Machine Learning Becomes a Mathematical Collaborator

Posted by in categories: mathematics, robotics/AI

Two recent collaborations between mathematicians and DeepMind demonstrate the potential of machine learning to help researchers generate new mathematical conjectures.

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