Computers Math

Difficulty sleeping, sleep apnea and narcolepsy are among a range of sleep disorders that thousands of Danes suffer from. Furthermore, it is estimated that sleep apnea is undiagnosed in as many as 200,000 Danes.
In a new study, researchers from the University of Copenhagen’s Department of Computer Science have collaborated with the Danish Center for Sleep Medicine at the danish hospital Rigshospitalet to develop an artificial intelligence algorithm that can improve diagnoses, treatments, and our overall understanding of sleep disorders.
“The algorithm is extraordinarily precise. We completed various tests in which its performance rivaled that of the best doctors in the field, worldwide,” states Mathias Perslev, a PhD at the Department of Computer Science and lead author of the study, recently published in the journal npj Digital Medicine (link).
Can support doctors in their treatments
Today’s sleep disorder examinations typically begin with admittance to a sleep clinic. Here, a person’s night sleep is monitored using various measuring instruments. A specialist in sleep disorders then reviews the 7-8 hours of measurements from the patient’s overnight sleep.
The doctor manually divides these 7-8 hours of sleep into 30-second intervals, all of which must be categorized into different sleep phases, such as REM (rapid eye movement) sleep, light sleep, deep sleep, etc. It is a time-consuming job that the algorithm can perform in seconds. More

Anyone who collects mushrooms knows that it is better to keep the poisonous and the non-poisonous ones apart. Not to mention what would happen if someone ate the poisonous ones. In such “classification problems,” which require us to distinguish certain objects from one another and to assign the objects we are looking for to certain classes by means of characteristics, computers can already provide useful support to humans.
Intelligent machine learning methods can recognise patterns or objects and automatically pick them out of data sets. For example, they could pick out those pictures from a photo database that show non-toxic mushrooms. Particularly with very large and complex data sets, machine learning can deliver valuable results that humans would not be able to find out, or only with much more time. However, for certain computational tasks, even the fastest computers available today reach their limits. This is where the great promise of quantum computers comes into play: that one day they will also perform super-fast calculations that classical computers cannot solve in a useful period of time.
The reason for this “quantum supremacy” lies in physics: quantum computers calculate and process information by exploiting certain states and interactions that occur within atoms or molecules or between elementary particles.
The fact that quantum states can superpose and entangle creates a basis that allows quantum computers the access to a fundamentally richer set of processing logic. For instance, unlike classical computers, quantum computers do not calculate with binary codes or bits, which process information only as 0 or 1, but with quantum bits or qubits, which correspond to the quantum states of particles. The crucial difference is that qubits can realise not only one state — 0 or 1 — per computational step, but also a state in which both superpose. These more general manners of information processing in turn allow for a drastic computational speed-up in certain problems.
Translating classical wisdom into the quantum realm
These speed advantages of quantum computing are also an opportunity for machine learning applications — after all, quantum computers could compute the huge amounts of data that machine learning methods need to improve the accuracy of their results much faster than classical computers. More

Adolescents who stopped studying maths exhibited greater disadvantage — compared with peers who continued studying maths — in terms of brain and cognitive development, according to a new study published in the Proceedings of the National Academy of Sciences.
133 students between the ages of 14-18 took part in an experiment run by researchers from the Department of Experimental Psychology at the University of Oxford. Unlike the majority of countries worldwide, in the UK 16-year-old students can decide to stop their maths education. This situation allowed the team to examine whether this specific lack of maths education in students coming from a similar environment could impact brain development and cognition.
The study found that students who didn’t study maths had a lower amount of a crucial chemical for brain plasticity (gamma-Aminobutyric acid) in a key brain region involved in many important cognitive functions, including reasoning, problem solving, maths, memory and learning. Based on the amount of brain chemical found in each student, researchers were able to discriminate between adolescents who studied or did not study maths, independent of their cognitive abilities. Moreover, the amount of this brain chemical successfully predicted changes in mathematical attainment score around 19 months later. Notably, the researchers did not find differences in the brain chemical before the adolescents stopped studying maths.
Roi Cohen Kadosh, Professor of Cognitive Neuroscience at the University of Oxford, led the study. He said: “Maths skills are associated with a range of benefits, including employment, socioeconomic status, and mental and physical health. Adolescence is an important period in life that is associated with important brain and cognitive changes. Sadly, the opportunity to stop studying maths at this age seems to lead to a gap between adolescents who stop their maths education compared to those who continue it. Our study provides a new level of biological understanding of the impact of education on the developing brain and the mutual effect between biology and education.
“It is not yet known how this disparity, or its long-term implications, can be prevented. Not every adolescent enjoys maths so we need to investigate possible alternatives, such as training in logic and reasoning that engage the same brain area as maths.”
Professor Cohen Kadosh added, “While we started this line of research before COVID-19, I also wonder how the reduced access to education in general, and maths in particular (or lack of it due to the pandemic) impacts the brain and cognitive development of children and adolescents. While we are still unaware of the long-term influence of this interruption, our study provides an important understanding of how a lack of a single component in education, maths, can impact brain and behaviour.”
The study has been undertaken by University of Oxford researchers George Zacharopolous, Roi Cohen Kadosh, and Francesco Sella (now at the Centre for Mathematical Cognition, Loughborough University).
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Researchers have discovered a new electronic property at the frontier between the thermal and quantum sciences in a specially engineered metal alloy — and in the process identified a promising material for future devices that could turn heat on and off with the application of a magnetic “switch.”
In this material, electrons, which have a mass in vacuum and in most other materials, move like massless photons or light — an unexpected behavior, but a phenomenon theoretically predicted to exist here. The alloy was engineered with the elements bismuth and antimony at precise ranges based on foundational theory.
Under the influence of an external magnetic field, the researchers found, these oddly behaving electrons manipulate heat in ways not seen under normal conditions. On both the hot and cold sides of the material, some of the electrons generate heat, or energy, while others absorb energy, effectively turning the material into an energy pump. The result: a 300% increase in its thermal conductivity.
Take the magnet away, and the mechanism is turned off.
“The generation and absorption form the anomaly,” said study senior author Joseph Heremans, professor of mechanical and aerospace engineering and Ohio Eminent Scholar in Nanotechnology at The Ohio State University. “The heat disappears and reappears elsewhere — it is like teleportation. It only happens under very specific circumstances predicted by quantum theory.”
This property, and the simplicity of controlling it with a magnet, makes the material a desirable candidate as a heat switch with no moving parts, similar to a transistor that switches electrical currents or a faucet that switches water, that could cool computers or increase the efficiency of solar-thermal power plants. More

The friendship paradox is the observation that the degrees of the neighbors of a node within any network will, on average, be greater than the degree of the node itself. In other words: your friends probably have more friends than you do.
While the standard framing of the friendship paradox is essentially about averages, significant variations occur too.
In the Journal of Complex Networks, Santa Fe Institute and University of Michigan researchers George Cantwell, Alec Kirkley, and Mark Newman address this by developing the mathematical theory of the friendship paradox.
Some people have lots of friends, while others have only a few. Unless you have good reason to believe otherwise, it’s reasonable to assume you have roughly an average number of friends.
But if you compare yourself to your friends, you may see a different picture. In fact, a simple calculation — provided by Scott L. Field’s 1991 paper entitled “Why your friends have more friends than you do” — shows it’s likely many of your friends are more popular than you.
Almost by definition, your friends are likely to be the sorts of people that have lots of friends. Perhaps worse, this effect means your friends might not only be more popular than you but also more wealthy and more attractive.
These kinds of friendship paradoxes have been explored by network scientists for 30 years.
“Standard analyses are concerned with average behavior, but there’s a lot of heterogeneity among people,” says Cantwell. “Could the average results, for example, be skewed by a few outliers? To get a fuller picture, we studied the full distribution describing how people compare to their friends — not simply the average.”
The researchers found that applying mathematics to real-world data reveals a slightly more nuanced picture. For example, popular people are more likely to be friends with one another, whereas less popular people are more likely to be friends with less popular people.
Conversely, some people have just one or two friends, while others have hundreds. “This has a tendency to magnify the effect,” says Cantwell. “While there are surely other effects at play, around 95% of the variation within social networks can be explained by just these two.”
We should all “simply be wary of impressions we get about our success and social status from looking at the people around us because we get a distorted view,” Cantwell adds. “In the offline social world, the bias is partially mitigated by the fact we tend to end up around similar others. On online social media, however, the effect can be exacerbated — there’s virtually no limit on the number of people who can follow someone online and no reason to only look at ‘similar’ people.”
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Many modern fitness trackers and smartwatches feature integrated LEDs. The green light emitted, whether continuous or pulsed, penetrates the skin and can be used to measure the wearer’s heart rate during physical activity or while at rest.
These watches have become extremely popular. A team of ETH researchers now wants to capitalise on that popularity by using the LEDs to control genes and change the behaviour of cells through the skin. The team is led by Martin Fussenegger from the Department of Biosystems Science and Engineering in Basel. He explains the challenge to this undertaking: “No naturally occurring molecular system in human cells responds to green light, so we had to build something new.”
Green light from the smartwatch activates the gene
The ETH professor and his colleagues ultimately developed a molecular switch that, once implanted, can be activated by the green light of a smartwatch.
The switch is linked to a gene network that the researchers introduced into human cells. As is customary, they used HEK 293 cells for the prototype. Depending on the configuration of this network — in other words, the genes it contains — it can produce insulin or other substances as soon as the cells are exposed to green light. Turning the light off inactivates the switch and halts the process.
Standard software
As they used the standard smartwatch software, there was no need for the researchers to develop dedicated programs. During their tests, they turned the green light on by starting the running app. “Off-the-shelf watches offer a universal solution to flip the molecular switch,” Fussenegger says. New models emit light pulses, which are even better suited to keeping the gene network running.
The molecular switch is more complicated, however. A molecule complex was integrated into the membrane of the cells and linked to a connecting piece, similar to the coupling of a railway carriage. As soon as green light is emitted, the component that projects into the cell becomes detached and is transported to the cell nucleus where it triggers an insulin-producing gene. When the green light is extinguished, the detached piece reconnects with its counterpart embedded in the membrane.
Controlling implants with wearables
The researchers tested their system on both pork rind and live mice by implanting the appropriate cells into them and strapping a smartwatch on like a rucksack. Opening the watch’s running program, the researchers turned on the green light to activate the cascade.
“It’s the first time that an implant of this kind has been operated using commercially available, smart electronic devices — known as wearables because they are worn directly on the skin,” the ETH professor says. Most watches emit green light, a practical basis for a potential application as there is no need for users to purchase a special device.
According to Fussenegger, however, it seems unlikely that this technology will enter clinical practice for at least another ten years. The cells used in this prototype would have to be replaced by the user’s own cells. Moreover, the system has to go through the clinical phases before it can be approved, meaning major regulatory hurdles. “To date, only very few cell therapies have been approved,” Fussenegger says.
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Like all metals, silver, copper, and gold are conductors. Electrons flow across them, carrying heat and electricity. While gold is a good conductor under any conditions, some materials have the property of behaving like metal conductors only if temperatures are high enough; at low temperatures, they act like insulators and do not do a good job of carrying electricity. In other words, these unusual materials go from acting like a chunk of gold to acting like a piece of wood as temperatures are lowered. Physicists have developed theories to explain this so-called metal-insulator transition, but the mechanisms behind the transitions are not always clear.
“In some cases, it is not easy to predict whether a material is a metal or an insulator,” explains Caltech visiting associate Yejun Feng of the Okinawa Institute for Science and Technology Graduate University. “Metals are always good conductors no matter what, but some other so-called apparent metals are insulators for reasons that are not well understood.” Feng has puzzled over this question for at least five years; others on his team, such as collaborator David Mandrus at the University of Tennessee, have thought about the problem for more than two decades.
Now, a new study from Feng and colleagues, published in Nature Communications, offers the cleanest experimental proof yet of a metal-insulator transition theory proposed 70 years ago by physicist John Slater. According to that theory, magnetism, which results when the so-called “spins” of electrons in a material are organized in an orderly fashion, can solely drive the metal-insulator transition; in other previous experiments, changes in the lattice structure of a material or electron interactions based on their charges have been deemed responsible.
“This is a problem that goes back to a theory introduced in 1951, but until now it has been very hard to find an experimental system that actually demonstrates the spin-spin interactions as the driving force because of confounding factors,” explains co-author Thomas Rosenbaum, a professor of physics at Caltech who is also the Institute’s president and the Sonja and William Davidow Presidential Chair.
“Slater proposed that, as the temperature is lowered, an ordered magnetic state would prevent electrons from flowing through the material,” Rosenbaum explains. “Although his idea is theoretically sound, it turns out that for the vast majority of materials, the way that electrons interact with each other electronically has a much stronger effect than the magnetic interactions, which made the task of proving the Slater mechanism challenging.”
The research will help answer fundamental questions about how different materials behave, and may also have applications in technology, for example in the field of spintronics, in which the spins of electrons would form the basis of electrical devices instead of the electron charges as is routine now. “Fundamental questions about metal and insulators will be relevant in the upcoming technological revolution,” says Feng. More

A team led by Carnegie’s Thomas Shiell and Timothy Strobel developed a new method for synthesizing a novel crystalline form of silicon with a hexagonal structure that could potentially be used to create next-generation electronic and energy devices with enhanced properties that exceed those of the “normal” cubic form of silicon used today.
Their work is published in Physical Review Letters.
Silicon plays an outsized role in human life. It is the second most abundant element in the Earth’s crust. When mixed with other elements, it is essential for many construction and infrastructure projects. And in pure elemental form, it is crucial enough to computing that the longstanding technological hub of the U.S. — California’s Silicon Valley — was nicknamed in honor of it.
Like all elements, silicon can take different crystalline forms, called allotropes, in the same way that soft graphite and super-hard diamond are both forms of carbon. The form of silicon most commonly used in electronic devices, including computers and solar panels, has the same structure as diamond. Despite its ubiquity, this form of silicon is not actually fully optimized for next-generation applications, including high-performance transistors and some photovoltaic devices.
While many different silicon allotropes with enhanced physical properties are theoretically possible, only a handful exist in practice given the lack of known synthetic pathways that are currently accessible.
Strobel’s lab had previously developed a revolutionary new form of silicon, called Si24, which has an open framework composed of a series of one-dimensional channels. In this new work, Shiell and Strobel led a team that used Si24 as the starting point in a multi-stage synthesis pathway that resulted in highly oriented crystals in a form called 4H-silicon, named for its four repeating layers in a hexagonal structure.
“Interest in hexagonal silicon dates back to the 1960s, because of the possibility of tunable electronic properties, which could enhance performance beyond the cubic form” Strobel explained.
Hexagonal forms of silicon have been synthesized previously, but only through the deposition of thin films or as nanocrystals that coexist with disordered material. The newly demonstrated Si24 pathway produces the first high-quality, bulk crystals that serve as the basis for future research activities.
Using the advanced computing tool called PALLAS, which was previously developed by members of the team to predict structural transition pathways — like how water becomes steam when heated or ice when frozen — the group was able to understand the transition mechanism from Si24 to 4H-Si, and the structural relationship that allows the preservation of highly oriented product crystals.
“In addition to expanding our fundamental control over the synthesis of novel structures, the discovery of bulk 4H-silicon crystals opens the door to exciting future research prospects for tuning the optical and electronic properties through strain engineering and elemental substitution,” Shiell said. “We could potentially use this method to create seed crystals to grow large volumes of the 4H structure with properties that potentially exceed those of diamond silicon.”
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