Computers Math

America was unprepared for the magnitude of the pandemic, which overwhelmed many counties and filled some hospitals to capacity. A new paper in PNAS suggests there may have been a mathematical method, of sorts, to the madness of those early COVID days.
The study tests a model that closely matches the patterns of case counts and deaths reported, county by county, across the United States between April 2020 and June 2021. The model suggests that unprecedented COVID spikes could, even now, overwhelm local jurisdictions.
“Our best estimate, based on the data, is that the numbers of cases and deaths per county have infinite variance, which means that a county could get hit with a tremendous number of cases or deaths,” says Rockefeller’s Joel Cohen. “We cannot reasonably anticipate that any county will have the resources to cope with extremely large, rare events, so it is crucial that counties — as well as states and even countries — develop plans, ahead of time, to share resources.”
Predicting 99 percent of a pandemic
Ecologists might have guessed that the spread of COVID cases and deaths would at least roughly conform to Taylor’s Law, a formula that relates a population’s mean to its variance (a measure of the scatter around the average). From how crop yields fluctuate, to the frequency of tornado outbreaks, to how cancer cells multiply, Taylor’s Law forms the backbone of many statistical models that experts use to describe thousands of species, including humans.
But when Cohen began looking into whether Taylor’s Law could also describe the grim COVID statistics provided by The New York Times, he ran into a surprise. More

A new way to combine two materials with special electrical properties — a monolayer superconductor and a topological insulator — provides the best platform to date to explore an unusual form of superconductivity called topological superconductivity. The combination could provide the basis for topological quantum computers that are more stable than their traditional counterparts.
Superconductors — used in powerful magnets, digital circuits, and imaging devices — allow the electric current to pass without resistance, while topological insulators are thin films only a few atoms thick that restrict the movement of electrons to their edges, which can result in unique properties. A team led by researchers at Penn State describe how they have paired the two materials in a paper appearing Oct. 27 in the journal Nature Materials.
“The future of quantum computing depends on a kind of material that we call a topological superconductor, which can be formed by combining a topological insulator with a superconductor, but the actual process of combining these two materials is challenging,” said Cui-Zu Chang, Henry W. Knerr Early Career Professor and Associate Professor of Physics at Penn State and leader of the research team. “In this study, we used a technique called molecular beam epitaxy to synthesize both topological insulator and superconductor films and create a two-dimensional heterostructure that is an excellent platform to explore the phenomenon of topological superconductivity.”
In previous experiments to combine the two materials, the superconductivity in thin films usually disappears once a topological insulator layer is grown on top. Physicists have been able to add a topological insulator film onto a three-dimensional “bulk” superconductor and retain the properties of both materials. However, applications for topological superconductors, such as chips with low power consumption inside quantum computers or smartphones, would need to be two-dimensional.
In this paper, the research team stacked a topological insulator film made of bismuth selenide (Bi2Se3) with different thicknesses on a superconductor film made of monolayer niobium diselenide (NbSe2), resulting in a two-dimensional end-product. By synthesizing the heterostructures at very lower temperature, the team was able to retain both the topological and superconducting properties.
“In superconductors, electrons form ‘Cooper pairs’ and can flow with zero resistance, but a strong magnetic field can break those pairs,” said Hemian Yi, a postdoctoral scholar in the Chang Research Group at Penn State and the first author of the paper. “The monolayer superconductor film we used is known for its ‘Ising-type superconductivity,’ which means that the Cooper pairs are very robust against the in-plane magnetic fields. We would also expect the topological superconducting phase formed in our heterostructures to be robust in this way.”
By subtly adjusting the thickness of the topological insulator, the researchers found that the heterostructure shifted from Ising-type superconductivity — where the electron spin is perpendicular to the film — to another kind of superconductivity called “Rashba-type superconductivity” — where the electron spin is parallel to the film. This phenomenon is also observed in the researchers’ theoretical calculations and simulations.
This heterostructure could also be a good platform for the exploration of Majorana fermions, an elusive particle that would be a major contributor to making a topological quantum computer more stable than its predecessors.
“This is an excellent platform for the exploration of topological superconductors, and we are hopeful that we will find evidence of topological superconductivity in our continuing work,” said Chang. “Once we have solid evidence of topological superconductivity and demonstrate Majorana physics, then this type of system could be adapted for quantum computing and other applications.”
In addition to Chang and Yi, the research team at Penn State includes Lun-Hui Hu, Yuanxi Wang, Run Xiao, Danielle Reifsnyder Hickey, Chengye Dong, Yi-Fan Zhao, Ling-Jie Zhou, Ruoxi Zhang, Antony Richardella, Nasim Alem, Joshua Robinson, Moses Chan, Nitin Samarth, and Chao-Xing Liu. The team also includes Jiaqi Cai and Xiaodong Xu at the University of Washington.
This work was primarily supported by the Penn State MRSEC for Nanoscale Science and also partially supported by the National Science Foundation, the Department of Energy, the University of North Texas, and the Gordon and Betty Moore Foundation.
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Materials provided by Penn State. Original written by Gail McCormick. Note: Content may be edited for style and length. More

Music and arts classes are often first on the chopping block when schools face tight budgets and pressure to achieve high scores on standardized tests. But it’s precisely those classes that can increase student interest in school and even benefit their math achievement, according to a new study.
Daniel Mackin Freeman, a doctoral candidate in sociology, and Dara Shifrer, an associate professor of sociology, used a large nationally representative dataset to see which types of arts classes impact math achievement and how it varies based on the socio-economic composition of the school. Schools with lower socio-economic status (SES) have a higher percentage of students eligible for free or reduced lunch.
The researchers found that taking music courses at higher- or mid-SES schools relates to higher math scores. Mackin Freeman said that’s not a surprise given the ways in which music and math overlap.
“If you think about it at an intuitive level, reading music is just doing math,” he said. “Of course, it’s a different type of math but it might be a more engaging form of math for students than learning calculus.”
However, the positive relationship between music course-taking and math achievement is primarily isolated to schools that serve more socially privileged students. The study suggests this could be because arts courses in low-SES schools are of lower quality and/or under-resourced. Students in low-SES schools also take fewer music and arts classes on average compared to their peers, also suggesting low-SES schools are under-resourced when it comes to arts courses.
“It’d be reasonable to expect that at under-resourced schools, the quality of the music program would differentiate any potential connection to other subjects,” Mackin Freeman said. “For programs as resource-intensive as something like band, under-resourced schools are less likely to even have working instruments, let alone an instructor who can teach students to read music in a way that they can make connections to arithmetic.”
Mackin Freeman said the findings suggest that learning shouldn’t happen in subject silos and the ways some schools have attempted to increase math achievement — by doubling down on math and cutting the arts — is shortsighted and counterproductive.
“Creating an environment where students have access to a well-rounded curriculum might indirectly affect math achievement,” he said. “That could be something as simple as, they’re willing to go to class because they have band or painting class to look forward to.”
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Materials provided by Portland State University. Original written by Cristina Rojas. Note: Content may be edited for style and length. More

Researchers at MIT have developed a technique for precisely controlling the arrangement and placement of nanoparticles on a material, like the silicon used for computer chips, in a way that does not damage or contaminate the surface of the material.
The technique, which combines chemistry and directed assembly processes with conventional fabrication techniques, enables the efficient formation of high-resolution, nanoscale features integrated with nanoparticles for devices like sensors, lasers, and LEDs, which could boost their performance.
Transistors and other nanoscale devices are typically fabricated from the top down — materials are etched away to reach the desired arrangement of nanostructures. But creating the smallest nanostructures, which can enable the highest performance and new functionalities, requires expensive equipment and remains difficult to do at scale and with the desired resolution.
A more precise way to assemble nanoscale devices is from the bottom up. In one scheme, engineers have used chemistry to “grow” nanoparticles in solution, drop that solution onto a template, arrange the nanoparticles, and then transfer them to a surface. However, this technique also involves steep challenges. First, thousands of nanoparticles must be arranged on the template efficiently. And transferring them to a surface typically requires a chemical glue, large pressure, or high temperatures, which could damage the surfaces and the resulting device.
The MIT researchers developed a new approach to overcome these limitations. They used the powerful forces that exist at the nanoscale to efficiently arrange particles in a desired pattern and then transfer them to a surface without any chemicals or high pressures, and at lower temperatures. Because the surface material remains pristine, these nanoscale structures can be incorporated into components for electronic and optical devices, where even minuscule imperfections can hamper performance.
“This approach allows you, through engineering of forces, to place the nanoparticles, despite their very small size, in deterministic arrangements with single-particle resolution and on diverse surfaces, to create libraries of nanoscale building blocks that can have very unique properties, whether it is their light-matter interactions, electronic properties, mechanical performance, etc.,” says Farnaz Niroui, the EE Landsman Career Development Assistant Professor of Electrical Engineering and Computer Science (EECS) at MIT, a member of the MIT Research Laboratory of Electronics, and senior author on a new paper describing the work. “By integrating these building blocks with other nanostructures and materials we can then achieve devices with unique functionalities that would not be readily feasible to make if we were to use the conventional top-down fabrication strategies alone.”
The research is published in Science Advances. Niroui’s co-authors are lead author Weikun “Spencer” Zhu, a graduate student in the Department of Chemical Engineering, as well as EECS graduate students Peter F. Satterthwaite, Patricia Jastrzebska-Perfect, and Roberto Brenes. More

Until recently, it was widely believed among physicists that it was impossible to compress light below the so-called diffraction limit, except when using metal nanoparticles, which unfortunately also absorb light. It therefore seemed impossible to compress light strongly in dielectric materials such as silicon, which are key materials in information technologies and come with the important advantage that they do not absorb light. Interestingly, it was shown theoretically already in 2006 that the diffraction limit also does not apply to dielectrics. Still, no one has succeeded in showing this in the real world, simply because it requires such advanced nanotechnology that no one has been able to build the necessary dielectric nanostructures until now.
A research team from DTU has successfully designed and built a structure, a so-called dielectric nanocavity, which concentrates light in a volume 12 times below the diffraction limit. The result is ground-breaking in optical research and has just been published in Nature Communications.
“Although computer calculations show that you can concentrate light at an infinitely small point, this only applies in theory. The actual results are limited by how small details can be made, for example, on a microchip,” says Marcus Albrechtsen, PhD-student at DTU Electro and first author of the new article.
“We programmed our knowledge of real photonic nanotechnology and its current limitations into a computer. Then we asked the computer to find a pattern that collects the photons in an unprecedentedly small area — in an optical nanocavity — which we were also able to build in the laboratory.”
Optical nanocavities are structures specially designed to retain light so that it does not propagate as we are used to but is thrown back and forth as if you put two mirrors facing each other. The closer you place the mirrors to each other, the more intense the light between the mirrors becomes. For this experiment, the researchers have designed a so-called bowtie structure, which is particularly effective at squeezing the photons together due to its special shape.
Interdisciplinary efforts and excellent methods
The nanocavity is made of silicon, the dielectric material on which most advanced modern technology is based. The material for the nanocavity was developed in cleanroom laboratories at DTU, and the patterns on which the cavity is based are optimized and designed using a unique method for topology optimization developed at DTU. Initially developed to design bridges and aircraft wings, it is now also used for nanophotonic structures. More

The LiDAR sensor, which recognizes objects by projecting light onto them, functions as eyes for autonomous vehicles by helping to identify the distance to surrounding objects and speed or direction of the vehicle. To detect unpredictable conditions on the road and nimbly respond, the sensor must perceive the sides and rear as well as the front of the vehicle. However, it has been impossible to observe the front and rear of the vehicle simultaneously because a rotating LiDAR sensor was used.
To overcome this issue, a research team led by Professor Junsuk Rho (Department of Mechanical Engineering and Department of Chemical Engineering) and Ph.D. candidates Gyeongtae Kim, Yeseul Kim, and Jooyeong Yun (Department of Mechanical Engineering) from POSTECH has developed a fixed LiDAR sensor that has 360° view, in collaboration with Professor Inki Kim (Department of Biophysics) from Sungkyunkwan University.
This new sensor is drawing attention as an original technology that can enable an ultra-small LiDAR sensor since it is made from the metasurface, which is an ultra-thin flat optical device that is only one-thousandth the thickness of a human hair strand.
Using the metasurface can greatly expand the viewing angle of the LiDAR to recognize objects three-dimensionally. The research team succeeded in extending the viewing angle of the LiDAR sensor to 360° by modifying the design and periodically arranging the nanostructures that make up the metasurface.
It is possible to extract three-dimensional information of objects in 360° regions by scattering more than 10,000 dot array (light) from the metasurface to objects and photographing the irradiated point pattern with a camera.
This type of LiDAR sensor is used for the iPhone face recognition function (Face ID). The iPhone uses a dot projector device to create the point sets but has several limitations; the uniformity and viewing angle of the point pattern are limited, and the size of the device is large.
The study is significant in that the technology that allows cell phones, augmented and virtual reality (AR/VR) glasses, and unmanned robots to recognize the 3D information of the surrounding environment is fabricated with nano-optical elements. By utilizing nanoimprint technology, it is easy to print the new device on various curved surfaces, such as glasses or flexible substrates, which enables applications to AR glasses, known as the core technology of future displays.
Professor Junsuk Rho explained, “We have proved that we can control the propagation of light in all angles by developing a technology more advanced than the conventional metasurface devices.” He added, “This will be an original technology that will enable an ultra-small and full-space 3D imaging sensor platform.”
Recently published in Nature Communications, this study was conducted with the support from the Samsung Research Funding & Incubation Center.
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Materials provided by Pohang University of Science & Technology (POSTECH). Note: Content may be edited for style and length. More

Biomedical and electrical engineers at UNSW Sydney have developed a new way to measure neural activity using light — rather than electricity — which could lead to a complete reimagining of medical technologies like nerve-operated prosthetics and brain-machine interfaces.
Professor François Ladouceur, with UNSW’s School of Electrical Engineering and Telecommunications, says the multi-disciplinary team has just demonstrated in the lab what it proved theoretically shortly before the pandemic: that sensors built using liquid crystal and integrated optics technologies — dubbed ‘optrodes’ — can register nerve impulses in a living animal body.
Not only do these optrodes perform just as well as conventional electrodes — that use electricity to detect a nerve impulse — but they also address “very thorny issues that competing technologies cannot address,” says Prof. Ladouceur.
“Firstly, it’s very difficult to shrink the size of the interface using conventional electrodes so that thousands of them can connect to thousands of nerves within a very small area.
“One of the problems as you shrink thousands of electrodes and put them ever closer together to connect to the biological tissues is that their individual resistance increases, which degrades the signal-to-noise ratio so we have a problem reading the signal. We call this ‘impedance mismatch’.
“Another problem is what we call ‘crosstalk’ — when you shrink these electrodes and bring them closer together, they start to talk to, or affect each other because of their proximity.”
But because optrodes use light and not electricity to detect neural signals, the problems of impedance mismatch is redundant and crosstalk minimised. More

Remember iron-on decals? All you had to do was print something out on special paper with a home printer, then transfer it onto a T-shirt using an iron. Now, scientists have developed a very similar scheme, but instead of family photos or logos, it prints circuitry. The method, reported in ACS Applied Materials & Interfaces, can print functional circuits onto items ranging from ukuleles to teacups.
As electronics continue to evolve, so too do the circuit boards that control them. Most boards used today are rigid, built on solid fiberglass backings. As electronic systems are integrated into floppy and pliable items, such as clothing and soft robots, electronics need to be flexible too. This has led to increased interest in liquid metal circuits, which often include a special alloy of gallium metal that is a liquid at room temperature. One way to make these devices is to print them out with a modified inkjet or 3D printer. But these methods require complicated steps and sophisticated equipment, making the resulting devices expensive and unsuitable for large-scale manufacturing. To make the fabrication process quicker, easier and cheaper, Xian Huang and colleagues wanted to develop a method of creating liquid metal circuitry using a desktop laser printer that could place the electronics onto many types of surfaces.
To create the circuits, the researchers printed out a connected design onto heat-transferrable thermal paper with an ordinary laser printer. The printer laid down a carbon-based toner, which was transferred to a pane of glass by heating it. These toner patterns roughened the surface and created a hydrophobic gap of air between the carbon and the liquid metal. This prevented the metal from sticking when brushed on top, so the electronic ink-based pattern only adhered on the exposed parts of the surface.
This circuit could then be stuck directly to a smooth surface, such as a plastic soda bottle. If the surface was too uneven, like the bumpy skin of an orange, the device was first placed on a piece of flexible plastic, then onto the rougher surface. Regardless of how they were attached, however, the simple electronics all functioned as intended on their various substrates — from displaying images, to RFID tagging, to sensing temperature and sound. The researchers say that this protocol should greatly expand the applications of liquid metal circuits.
The authors acknowledge funding from the Key Research and Development Program of Zhejiang Province and the National Natural Science Foundation of China.
Video: https://youtu.be/HQattovte08
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Materials provided by American Chemical Society. Note: Content may be edited for style and length. More