Computers Math

Mathematical constructions of the action of SARS-CoV-2 and its multiple spikes, which enable its success at infecting cells, can give vaccine developers and pharmaceutical companies alike a more precise picture of what the virus is doing inside us and help fine tune prevention and treatment, mathematical modelers say.
Mathematical construction enables examination of the activity of individual virus particles including the emergence of new spikes — and more severe infection potential — that can result when a single virus particle infects a human cell, says Dr. Arni S.R. Rao, director of the Laboratory for Theory and Mathematical Modeling in the Section of Infectious Diseases at the Medical College of Georgia.
The number of spikes and the way they are distributed on a virus particle are believed to be key in the spread of the virus, Rao and his colleague Dr. Steven G. Krantz, professor of mathematics at Washington University in St. Louis, Missouri, write in the Journal of Mathematical Analysis and Applications.
Laboratory experiments on virus particles and their bonding, or infection, of cells more typically are done on a group of viruses, they write.
“Right now, we don’t know when a spike bonds with a cell, what happens with that virus particle’s other spikes,” says Rao, the study’s corresponding author. “How many new infected cells are being produced has never been studied for the coronavirus. We need quantification because ultimately the vaccine or pharmaceutical industry needs to target those infected cells,” he says of the additional insight their mathematical methodology, which also enables the study of the growth of the virus’ spikes over time, provides.
Viral load is considered one of the strong predictors of the severity of sickness and risk of death and the number of spikes successfully bonding with cells is an indicator of the viral load, Rao says. PCR, or polymerase chain reaction, which is used for COVID testing, for example, provides viral load by assessing the amount of the virus’ RNA present in a test sample. More

A prescriptive computer program developed by the USC Marshall School of Business and Wharton School of Business of the University of Pennsylvania for Greece to identify asymptomatic, infected travelers may have slowed tCOVID-19’s spread through its borders, a new study in the journal Nature indicates.
“It was a very high-impact artificial intelligence project, and I believe we saved lives by developing a cutting edge, novel system for targeted testing during the pandemic,” said Kimon Drakopoulos, a USC Marshall assistant professor of Data Sciences and Operations and one of the study’s authors.
In July 2020, Greece largely reopened its borders to spare its tourism-dependent economy from the devastating impact of long-term shutdowns amid COVID-19.
Greece collaborated with USC Marshall and Wharton to create “Eva,” an artificial intelligence algorithm that uses real-time data to identify high-risk visitors for testing. Evidence shows the algorithm caught nearly twice as many asymptomatic infected travelers as would have been caught if Greece had relied on only travel restrictions and randomized COVID testing.
“Our work with Eva proves that carefully integrating real-time data, artificial intelligence and lean operations offers huge benefits over conventional, widely used approaches to managing the pandemic,” said Vishal Gupta, a USC Marshall associate professor of data science another of the study’s authors.
The joint study was published Wednesday in the journal Nature. More

We can learn a lot by studying microscopic and macroscopic changes in a material as it crosses from one phase to another, for example from ice to water to steam. A new Australian study examines systems transitioning from ‘normal’ fluid to a quantum state known as a superfluid, which can flow with zero friction, with a view to future, superfluid-based, quantum technologies, such as ultra-low energy electronics.We can learn a lot by studying microscopic and macroscopic changes in a material as it crosses from one phase to another, for example from ice to water to steam.
But while these phase transitions are well understood in the case of water, much less is known about the dynamics when a system goes from being a normal fluid to a superfluid, which can flow with zero friction, ie without losing any energy.
A new Swinburne study observing transition of an atomic gas from normal fluid to superfluid provides new insights into the formation of these remarkable states, with a view to future, superfluid-based, quantum technologies, such as ultra-low energy electronics.
Superfluid formation was seen to involve a number of different timescales, associated with different dynamical processes that take place upon crossing the phase boundary.
UNDERSTANDING DYNAMIC TRANSITIONS, TOWARDS FUTURE TECHNOLOGIES
As a nonequilibrium, dynamic process, phase transitions are challenging to understand from a theoretical perspective, inside these fascinating and potentially useful states of matter. More

Researchers are developing artificial intelligence that could assess climate change tipping points. The deep learning algorithm could act as an early warning system against runaway climate change.
Chris Bauch, a professor of applied mathematics at the University of Waterloo, is co-author of a recent research paper reporting results on the new deep-learning algorithm. The research looks at thresholds beyond which rapid or irreversible change happens in a system, Bauch said.
“We found that the new algorithm was able to not only predict the tipping points more accurately than existing approaches but also provide information about what type of state lies beyond the tipping point,” Bauch said. “Many of these tipping points are undesirable, and we’d like to prevent them if we can.”
Some tipping points that are often associated with run-away climate change include melting Arctic permafrost, which could release mass amounts of methane and spur further rapid heating; breakdown of oceanic current systems, which could lead to almost immediate changes in weather patterns; or ice sheet disintegration, which could lead to rapid sea-level change.
The innovative approach with this AI, according to the researchers, is that it was programmed to learn not just about one type of tipping point but the characteristics of tipping points generally.
The approach gains its strength from hybridizing AI and mathematical theories of tipping points, accomplishing more than either method could on its own. After training the AI on what they characterize as a “universe of possible tipping points” that included some 500,000 models, the researchers tested it on specific real-world tipping points in various systems, including historical climate core samples.
“Our improved method could raise red flags when we’re close to a dangerous tipping point,” said Timothy Lenton, director of the Global Systems Institute at the University of Exeter and one of the study’s co-authors. “Providing improved early warning of climate tipping points could help societies adapt and reduce their vulnerability to what is coming, even if they cannot avoid it.”
Deep learning is making huge strides in pattern recognition and classification, with the researchers having, for the first time, converted tipping-point detection into a pattern-recognition problem. This is done to try and detect the patterns that occur before a tipping point and get a machine-learning algorithm to say whether a tipping point is coming.
“People are familiar with tipping points in climate systems, but there are tipping points in ecology and epidemiology and even in the stock markets,” said Thomas Bury, a postdoctoral researcher at McGill University and another of the co-authors on the paper. “What we’ve learned is that AI is very good at detecting features of tipping points that are common to a wide variety of complex systems.”
The new deep learning algorithm is a “game-changer for the ability to anticipate big shifts, including those associated with climate change,” said Madhur Anand, another of the researchers on the project and director of the Guelph Institute for Environmental Research.
Now that their AI has learned how tipping points function, the team is working on the next stage, which is to give it the data for contemporary trends in climate change. But Anand issued a word of caution of what may happen with such knowledge.
“It definitely gives us a leg up,” she said. “But of course, it’s up to humanity in terms of what we do with this knowledge. I just hope that these new findings will lead to equitable, positive change.”
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Mathematical modeling of disease spread suggests that herd immunity could be achieved with fewer vaccine doses by using Bluetooth-based contact-tracing apps to identify people who have more exposure to others — and targeting them for vaccination. Mark Penney, Yigit Yargic and their colleagues from the Perimeter Institute for Theoretical Physics in Ontario, Canada, present this approach in the open-access journal PLOS ONE on September 22, 2021.
The COVID-19 pandemic has raised questions about how to best allocate limited supplies of vaccines for the greatest benefit against a disease. Mathematical models suggest that vaccines like those available for COVID-19 are most effective at reducing transmission when they are targeted to people who have more exposure to others. However, it can be challenging to identify such individuals.
Penney and colleagues hypothesized that this challenge could be addressed by harnessing existing apps that anonymously alert users to potential COVID-19 exposure. These apps use Bluetooth technology to determine the duration of contact between any pair of individuals who both have the same app downloaded on their smart phones. The researchers wondered whether this technology could also be used to help identify and target vaccines to those with greater exposure — a strategy analogous to a wildfire-fighting practice called “hot-spotting,” which targets sites with intense fires.
To explore the effectiveness of a hot-spotting approach to vaccination, Penney and colleagues used mathematical modeling to simulate how a disease would spread among a population with such a strategy in place. Specifically, they applied an analytical technique borrowed from statistical physics known as percolation theory.
The findings suggest that a Bluetooth-based hot-spotting approach to vaccination could reduce the number of vaccine doses needed to achieve herd immunity by up to one half. The researchers found improvements even for simulations in which relatively few people use contact-tracing apps — a situation mirroring reality for COVID-19 in many regions.
In the future, the modeling approach used for this study could be refined, such as by incorporating the effects of strains on the healthcare system. Nonetheless, the researchers note, the new findings highlight a technically feasible way to implement a strategy that previous research already supports.
The authors add: “The technology underlying digital contact tracing apps has made it possible to implement novel decentralized and efficient vaccine strategies.”
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Quantum cryptography is one of the most promising quantum technologies of our time: Exactly the same information is generated at two different locations, and the laws of quantum physics guarantee that no third party can intercept this information. This creates a code with which information can be perfectly encrypted.
The team of Prof. Marcus Huber from the Atomic Institute of TU Wien developed a new type of quantum cryptography protocol, which has now been tested in practice in cooperation with Chinese research groups: While up to now one normally used photons that can be in two different states, the situation here is more complicated: Eight different paths can be taken by each of the photons. As the team has now been able to show, this makes the generation of the quantum cryptographic key faster and also significantly more robust against interference. The results have now been published in the scientific journal Physical Review Letters.
Two states, two dimensions
“There are many different ways of using photons to transmit information,” says Marcus Huber. “Often, experiments focus on their photons’ polarisation. For example, whether they oscillate horizontally or vertically — or whether they are in a quantum-mechanical superposition state in which, in a sense, they assume both states simultaneously. Similar to how you can describe a point on a two-dimensional plane with two coordinates, the state of the photon can be represented as a point in a two-dimensional space.”
But a photon can also carry information independently of the direction of polarization. One can, for example, use the information about which path the photon is currently travelling on. This is exactly what has now been exploited: “A laser beam generates photon pairs in a special kind of crystal. There are eight different points in the crystal where this can happen,” explains Marcus Huber. Depending on the point at which the photon pair was created, each of the two photons can move along eight different paths — or along several paths at the same time, which is also permitted according to the laws of quantum theory.
These two photons can be directed to completely different places and analysed there. One of the eight possibilities is measured, completely at random — but as the two photons are quantum-physically entangled, the same result is always obtained at both places. Whoever is standing at the first measuring device knows what another person is currently detecting at the second measuring device — and no one else in the universe can get hold of this information. More

Rutgers researchers and their collaborators have found that learning — a universal feature of intelligence in living beings — can be mimicked in synthetic matter, a discovery that in turn could inspire new algorithms for artificial intelligence (AI).
The study appears in the journal PNAS.
One of the fundamental characteristics of humans is the ability to continuously learn from and adapt to changing environments. But until recently, AI has been narrowly focused on emulating human logic. Now, researchers are looking to mimic human cognition in devices that can learn, remember and make decisions the way a human brain does.
Emulating such features in the solid state could inspire new algorithms in AI and neuromorphic computing that would have the flexibility to address uncertainties, contradictions and other aspects of everyday life. Neuromorphic computing mimics the neural structure and operation of the human brain, in part, by building artificial nerve systems to transfer electrical signals that mimic brain signals.
Researchers from Rutgers, Purdue and other institutions studied how the electrical conductivity of nickel oxide, a special type of insulating material, responded when its environment was changed repeatedly over various time intervals.
“The goal was to find a material whose electrical conductivity can be tuned by modulating the concentration of atomic defects with external stimuli such as oxygen, ozone and light,” said Subhasish Mandal, a postdoctoral associate in the Department of Physics and Astronomy at Rutgers-New Brunswick. “We studied how this material behaves when we dope the system with oxygen or hydrogen, and most importantly, how the external stimulation changes the material’s electronic properties.”
The researchers found that when the gas stimulus changed rapidly, the material couldn’t respond in full. It stayed in an unstable state in either environment and its response began to decrease. When the researchers introduced a noxious stimulus such as ozone, the material began to respond more strongly only to decrease again.
“The most interesting part of our results is that it demonstrates universal learning characteristics such as habituation and sensitization that we generally find in living species,” Mandal said. “These material characteristics in turn can inspire new algorithms for artificial intelligence. Much as collective motion of birds or fish have inspired AI, we believe collective behavior of electrons in a quantum solid can do the same in the future.
“The growing field of AI requires hardware that can host adaptive memory properties beyond what is used in today’s computers,” he added. “We find that nickel oxide insulators, which historically have been restricted to academic pursuits, might be interesting candidates to be tested in future for brain-inspired computers and robotics.”
The study included Distinguished Professor Karin Rabe from Rutgers and researchers from Purdue University, the University of Georgia and Argonne National Laboratory.
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Researchers have designed a 4D-printed soft robot that self-assembles when heated and can take on challenging tasks like rolling uphill and navigating a bumpy and unpredictable landscape. The prototype, which is tube-shaped, appears September 22nd in the journal Matter.
“Like an insect with antennae, the robot can surmount a small obstacle. But when the obstacle is too high, it will turn back,” says senior author Wei Feng, a materials scientist at Tianjin University in China. “The whole process is spontaneous without human interference or control.”
The robot starts off as a flat, rectangular sheet of a 3D-printed liquid crystal elastomer, a type of stretchy plastic material. When the surface beneath it is heated, the robot spontaneously twists up to form a tubule resembling a spring. The change in shape under external stimulation adds time as a fourth dimension to the printing process, making it 4D.
Once the robot forms a tubule, the contact from the hot surface induces a strain in the material, which causes it to roll in one direction. The driving force behind this motion is so strong that the robot can climb up a 20° incline or even carry a load 40 times its own weight. The length of the robot affects its velocity, with longer robots rolling faster than their shorter counterparts.
The researchers captured videos showing off the robot’s skills, including a race between differently sized robots and another robot carrying a cart. The videos also show how its behavior changes based on its surroundings, with the robot either climbing up a step or changing directions when encountering an insurmountable obstacle.
For Feng, the behavior of the robot came as a surprise. “We processed the liquid crystal elastomers into samples of various shapes through 4D printing and stimulated these samples with light, heat, and electricity to observe their response,” he says. “We found many interesting driving phenomena besides deformation.”
In the future, these soft robots may be used to perform work in small, confined places like in a pipe or under extreme conditions like a 200? surface. “We hope that soft robots will no longer be limited to simple actuators, which can only change shape in a fixed position,” says Feng.
This work was supported by the State Key Program of National Natural Science Foundation of China, National Key R&D Program of China, and National Natural Science Foundation of China.
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