Computers Math

For millennia, humanity has observed the changing phases of the Moon. The rise and fall of sunlight reflected off the Moon, as it presents its different faces to us, is known as a “phase curve.” Measuring phase curves of the Moon and Solar System planets is an ancient branch of astronomy that goes back at least a century. The shapes of these phase curves encode information on the surfaces and atmospheres of these celestial bodies. In modern times, astronomers have measured the phase curves of exoplanets using space telescopes such as Hubble, Spitzer, TESS and CHEOPS. These observations are compared with theoretical predictions. In order to do so, one needs a way of calculating these phase curves. It involves seeking a solution to a difficult mathematical problem concerning the physics of radiation.
Approaches for the calculation of phase curves have existed since the 18th century. The oldest of these solutions goes back to the Swiss mathematician, physicist and astronomer, Johann Heinrich Lambert, who lived in the 18th century. “Lambert’s law of reflection” is attributed to him. The problem of calculating reflected light from Solar System planets was posed by the American astronomer Henry Norris Russell in an influential 1916 paper. Another well-known 1981 solution is attributed to the American lunar scientist Bruce Hapke, who built on the classic work of the Indian-American Nobel laureate Subrahmanyan Chandrasekhar in 1960. Hapke pioneered the study of the Moon using mathematical solutions of phase curves. The Soviet physicist Viktor Sobolev also made important contributions to the study of reflected light from celestial bodies in his influential 1975 textbook. Inspired by the work of these scientists, theoretical astrophysicist Kevin Heng of the Center for Space and Habitability CSH at the University of Bern has discovered an entire family of new mathematical solutions for calculating phase curves. The paper, authored by Kevin Heng in collaboration with Brett Morris from the National Center of Competence in Research NCCR PlanetS — which the University of Bern manages together with the University of Geneva — and Daniel Kitzmann from the CSH, has just been published in Nature Astronomy.
Generally applicable solutions
“I was fortunate that this rich body of work had already been done by these great scientists. Hapke had discovered a simpler way to write down the classic solution of Chandrasekhar, who famously solved the radiative transfer equation for isotropic scattering. Sobolev had realised that one can study the problem in at least two mathematical coordinate systems.” Sara Seager brought the problem to Heng’s attention by her summary of it in her 2010 textbook.
By combining these insights, Heng was able to write down mathematical solutions for the strength of reflection (the albedo) and the shape of the phase curve, both completely on paper and without resorting to a computer. “The ground-breaking aspect of these solutions is that they are valid for any law of reflection, which means they can be used in very general ways. The defining moment came for me when I compared these pen-and-paper calculations to what other researchers had done using computer calculations. I was blown away by how well they matched,” said Heng.
Successful analysis of the phase curve of Jupiter
“What excites me is not just the discovery of new theory, but also its major implications for interpreting data,” says Heng. For example, the Cassini spacecraft measured phase curves of Jupiter in the early 2000s, but an in-depth analysis of the data had not previously been done, probably because the calculations were too computationally expensive. With this new family of solutions, Heng was able to analyze the Cassini phase curves and infer that the atmosphere of Jupiter is filled with clouds made up of large, irregular particles of different sizes. This parallel study has just been published by the Astrophysical Journal Letters, in collaboration with Cassini data expert and planetary scientist Liming Li of Houston University in Texas, U.S.A.
New possibilities for the analysis of data from space telescopes
“The ability to write down mathematical solutions for phase curves of reflected light on paper means that one can use them to analyze data in seconds,” said Heng. It opens up new ways of interpreting data that were previously infeasible. Heng is collaborating with Pierre Auclair-Desrotour (formerly CSH, currently at Paris Observatory) to further generalize these mathematical solutions. “Pierre Auclair-Desrotour is a more talented applied mathematician than I am, and we promise exciting results in the near future,” said Heng.
In the Nature Astronomy paper, Heng and his co-authors demonstrated a novel way of analyzing the phase curve of the exoplanet Kepler-7b from the Kepler space telescope. Brett Morris led the data analysis part of the paper. “Brett Morris leads the data analysis for the CHEOPS mission in my research group, and his modern data science approach was critical for successfully applying the mathematical solutions to real data,” explained Heng. They are currently collaborating with scientists from the American-led TESS space telescope to analyze TESS phase curve data. Heng envisions that these new solutions will lead to novel ways of analyzing phase curve data from the upcoming, 10-billion-dollar James Webb Space Telescope, which is due to launch later in 2021. “What excites me most of all is that these mathematical solutions will remain valid long after I am gone, and will probably make their way into standard textbooks,” said Heng.
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In a move that could one day free the world’s countertops from their snarl of charging cords, researchers at the University of Michigan and University of Tokyo have developed a system to safely deliver electricity over the air, potentially turning entire buildings into wireless charging zones.
Detailed in a new study published in Nature Electronics, the technology can deliver 50 watts of power using magnetic fields.
Study author Alanson Sample, U-M professor of computer science and engineering, says that in addition to untethering phones and laptops, the technology could also power implanted medical devices and open new possibilities for mobile robotics in homes and manufacturing facilities. The team is also working on implementing the system in spaces that are smaller than room-size, for example a toolbox that charges tools placed inside it.
“This really ups the power of the ubiquitous computing world — you could put a computer in anything without ever having to worry about charging or plugging in,” Sample said. “There are a lot of clinical applications as well; today’s heart implants, for example, require a wire that runs from the pump through the body to an external power supply. This could eliminate that, reducing the risk of infection and improving patients’ quality of life.”
The team, led by researchers at the University of Tokyo, demonstrated the technology in a purpose-built aluminum test room measuring approximately 10 feet by 10 feet. They wirelessly powered lamps, fans and cell phones that could draw current from anywhere in the room regardless of the placement of people and furniture.
The system is a major improvement over previous attempts at wireless charging systems, which used potentially harmful microwave radiation or required devices to be placed on dedicated charging pads, the researchers say. Instead, it uses a conductive surface on room walls and a conductive pole to generate magnetic fields. More

The Human Cell Atlas is the world’s largest, growing single-cell reference atlas. It contains references of millions of cells across tissues, organs and developmental stages. These references help physicians to understand the influences of aging, environment and disease on a cell — and ultimately diagnose and treat patients better. Yet, reference atlases do not come without challenges. Single-cell datasets may contain measurement errors (batch effect), the global availability of computational resources is limited and the sharing of raw data is often legally restricted.
Researchers from Helmholtz Zentrum München and the Technical University of Munich (TUM) developed a novel algorithm called “scArches,” short for single-cell architecture surgery. The biggest advantage: “Instead of sharing raw data between clinics or research centers, the algorithm uses transfer learning to compare new datasets from single-cell genomics with existing references and thus preserves privacy and anonymity. This also makes annotating and interpreting of new data sets very easy and democratizes the usage of single-cell reference atlases dramatically,” says Mohammad Lotfollahi, the leading scientist of the algorithm.
Example COVID-19
The researchers applied scArches to study COVID-19 in several lung bronchial samples. They compared the cells of COVID-19 patients to healthy references using single-cell transcriptomics. The algorithm was able to separate diseased cells from the references and thus enabled the user to pinpoint the cells in need for treatment, for both mild and severe COVID-19 cases. Biological variation between patients did not affect the quality of the mapping process.
Fabian Theis: “Our vision is that in the future we will use cell references as easily as we nowadays do for genome references. In other word, if you want to bake a cake, you usually do not want to try coming up with your own recipe — instead you just look one up in a cookbook. With scArches, we formalize and simplify this lookup process.”
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Increasingly, movies featuring humanoid robots, like Terminator or Ex Machina, are showing the titular “robot” akin to humans not only in intelligence but also appearance. What if Terminator-esque robots became the norm, making it difficult for us to tell them apart from actual human beings?
This is the premise of a new study published in PLOS ONE, which evaluated how human beings respond to images of people with the same face. It is not too far-fetched to imagine a future where human-like androids are mass-produced and are indistinguishable from flesh-and-blood human beings. Robotics and artificial intelligence are advancing at an unprecedented rate, with very closely human-like robots and CG characters, such as Geminoid, Saya, and Sophia already having been produced. Developers are optimistic they will one day create robots that surpass the uncanny valley — a well-known phenomenon where humanoids elicit unpleasant and negative emotions in viewers when their appearance becomes similar to that of humans.
In such a future, how would we react?
A team of researchers from Kyushu University, Ritsumeikan University, and Kansai University, collaboratively conducted a series of six experiments involving different batches of hundreds of people to try and find that answer.
The first experiment involved rating the subjective eeriness, emotional valence, and realism of a photoshopped photograph of six human subjects with the exact same face (clone image), six people with different faces (non-clone image), and one person (single image). The second experiment comprised rating another set of clone images and non-clone images, while the third experiment consisted of rating clone and non-clone images of dogs. The fourth experiment had two parts: rating clone images of two sets of twins and then rating clone faces of twins, triplets, quadruplets, and quintuplets. The fifth experiment involved clone images of Japanese animation and cartoon characters. And the sixth and final experiment involved evaluating the subjective eeriness and realism of a different set of clone and non-clone images while also answering the Disgust Scale Revised to analyze disgust sensitivity.
The results were striking. Participants from the first study rated individuals with clone faces as eerier and more improbable than those with different faces and a single person’s face.
The researchers termed this negative emotional response as the clone devaluation effect.
“The clone devaluation effect was stronger when the number of clone faces increased from two to four,” says lead author Dr. Fumiya Yonemitsu from Graduate School of Human-Environment Studies at Kyushu University, who is also a Research Fellow of Japan Society for the Promotion of Science. “This effect did not occur when each clone face was indistinguishable, like animal faces in experiment three involving dogs.”
According to him, “We also noticed that the duplication of identity, that is the personality and mind unique to a person, rather than their facial features, has an important role in this effect. Clone faces with the duplication of identity were eerier, as the fourth experiment showed. The clone devaluation effect became weaker when clone faces existed in the lower reality of the context, such as in the fifth experiment. Furthermore, the eeriness of clone faces stemming from improbability could be positively predicted by disgust, in particular animal-reminder disgust, as noticed in the sixth experiment. Taken together, these results suggest that clone faces induce eeriness and that the clone devaluation effect is related to realism and disgust reaction.”
These results show that human faces provide important information for identifying individuals because human beings have a one-to-one correspondence between face and identity. Clone faces violate this principle, which may make humans misjudge the identity of people with clone faces as being the same.
So, what does this mean for a future in which humanoids are inevitable? According to the researchers, we need to think critically about introducing new technology in robotics or human cloning because of the potential for unpleasant psychological reactions other than the uncanny valley phenomenon.
“Our study clearly shows that uncomfortable situations could occur due to the rapid development of technology. But we believe our findings can play an important role in the smooth acceptance of new technologies and enhance people’s enjoyment of their benefits”, observes co-author Dr. Akihiko Gobara, Senior Researcher from BKC Research Organization of Social Science at Ritsumeikan University.
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Researchers from the University of Kent, the Research Institute for Environment Treatment and Vita-Market Ltd have discovered a universal mathematical formula that can describe any bird’s egg existing in nature, a feat which has been unsuccessful until now.
Egg-shape has long attracted the attention of mathematicians, engineers, and biologists from an analytical point of view. The shape has been highly regarded for its evolution as large enough to incubate an embryo, small enough to exit the body in the most efficient way, not roll away once laid, is structurally sound enough to bear weight and be the beginning of life for so many species. The egg has been called the “perfect shape.”
Analysis of all egg shapes used four geometric figures: sphere, ellipsoid, ovoid, and pyriform (conical or pear-shaped), with a mathematical formula for the pyriform yet to be derived.
To rectify this, researchers introduced an additional function into the ovoid formula, developing a mathematical model to fit a completely novel geometric shape characterized as the last stage in the evolution of the sphere-ellipsoid, which it is applicable to any egg geometry.
This new universal mathematical formula for egg shape is based on four parameters: egg length, maximum breadth, shift of the vertical axis, and the diameter at one quarter of the egg length.
This long sought-for universal formula is a significant step in understanding not only the egg shape itself, but also how and why it evolved, thus making widespread biological and technological applications possible.
Mathematical descriptions of all basic egg shapes have already found applications in food research, mechanical engineering, agriculture, biosciences, architecture and aeronautics. As an example, this formula can be applied to engineering construction of thin walled vessels of an egg shape, which should be stronger than typical spherical ones.
This new formula is an important breakthrough with multiple applications including: Competent scientific description of a biological object. Now that an egg can be described via mathematical formula, work in fields of biological systematics, optimization of technological parameters, egg incubation and selection of poultry will be greatly simplified. Accurate and simple determination of the physical characteristics of a biological object. The external properties of an egg are vital for researchers and engineers who develop technologies for incubating, processing, storing and sorting eggs. There is a need for a simple identification process using egg volume, surface area, radius of curvature and other indicators for describing the contours of the egg, which this formula provides. Future biology-inspired engineering. The egg is a natural biological system studied to design engineering systems and state-of-the-art technologies. The egg-shaped geometric figure is adopted in architecture, such as London City Hall’s roof and the Gherkin, and construction as it can withstand maximum loads with a minimum consumption of materials, to which this formula can now be easily applied.Darren Griffin, Professor of Genetics in the University of Kent and PI on the research, said: “Biological evolutionary processes such as egg formation must be investigated for mathematical description as a basis for research in evolutionary biology, as demonstrated with this formula. This universal formula can be applied across fundamental disciplines, especially the food and poultry industry, and will serve as an impetus for further investigations inspired by the egg as a research object.”
Dr Michael Romanov, Visiting Researcher at the University of Kent, said: “This mathematical equation underlines our understanding and appreciation of a certain philosophical harmony between mathematics and biology, and from those two a way towards further comprehension of our universe, understood neatly in the shape of an egg.”
Dr Valeriy Narushin, former visiting researcher at the University of Kent, said: “We look forward to seeing the application of this formula across industries, from art to technology, architecture to agriculture. This breakthrough reveals why such collaborative research from separate disciplines is essential.”
The paper “Egg and math: introducing a universal formula for egg shape” is published in Annals of the New York Academy of Sciences (Valeriy G. Narushin, Research Institute for Environment Treatment and Vita-Market Ltd, Ukraine; Dr Michael N. Romanov, University of Kent; Professor Darren K. Griffin, University of Kent).
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From small committees to national elections, group decision-making can be complicated — and it may not always settle on the best choice. That’s partly because some members of the group do research on their own, and others take their cues from the people around them.
That distinction is readily observed around election time. “Many voters couldn’t tell you the policy platforms for the candidates they’re voting for,” says applied mathematician Vicky Chuqiao Yang at the Santa Fe Institute. “Many individuals are uninformed, and they’re most likely to rely on information they get from others.”
Social scientists have long sought ways to study the phenomenon of group decision-making, but that’s a tricky undertaking. Researchers in a range of disciplines have tried to tackle the problem, with parallel efforts often leading to conflicting conclusions. Most existing models examine the effect of a single variable, which means they don’t capture the whole picture.
“The outcome of collective decision making is the result of complex interactions of many variables,” says Yang, “and those interactions are rarely taken into account” in previous work.
To overcome that challenge, Yang recently led the development of a mathematical framework that captures the influence of multiple interactions among members of a group. “You can plug in multiple effects and see their behavior and how they manifest in the group at the same time,” she explains.
Those effects include the influence of social learners. The model predicted, for example, that decision-making groups have a critical threshold of people who get their information from others. Below that threshold, the group chooses the high-quality outcome. Above it, the group can end up choosing the better or worse option.
The model also predicted a significant role for “committed minorities,” or people who refuse to change their minds, no matter the evidence. These committed minorities can be bolstered, Yang says, by social learners, though every group is different.
The mathematical model is both simple and general, and can accurately reflect the multitude of moving parts within a system. Yang’s collaborators include psychologist and SFI Professor Mirta Galesic, economist Ani Harutyunyan at the Sunwater Institute, and Harvey McGuinness, an undergraduate at Johns Hopkins University and former student researcher at SFI. (The whole project began, said Yang, with a question from McGuinness.) The group reported on the framework in a paper published in Proceedings of the National Academy of Sciences.
Yang says she hopes the model will help bring together parallel work from different disciplines. These disciplines have found separate effects at work in collective decision-making, “but we don’t yet have a holistic understanding that gives a recipe for good collective decision making,” she said. “Our work brings us one step closer to it.”
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Ultrafast electron microscope opens up new avenues for the development of sensors and quantum devices.
Everyone who has ever been to the Grand Canyon can relate to having strong feelings from being close to one of nature’s edges. Similarly, scientists at the U.S. Department of Energy’s (DOE) Argonne National Laboratory have discovered that nanoparticles of gold act unusually when close to the edge of a one-atom thick sheet of carbon, called graphene. This could have big implications for the development of new sensors and quantum devices.
This discovery was made possible with a newly established ultrafast electron microscope (UEM) at Argonne’s Center for Nanoscale Materials (CNM), a DOE Office of Science User Facility. The UEM enables the visualization and investigation of phenomena at the nanoscale and on time frames of less than a trillionth of a second. This discovery could make a splash in the growing field of plasmonics, which involves light striking a material surface and triggering waves of electrons, known as plasmonic fields.
“With ultrafast capabilities, there’s no telling what we might see as we tweak different materials and their properties.” — Haihua Liu, Argonne nanoscientist
For years, scientists have been pursuing development of plasmonic devices with a wide range of applications — from quantum information processing to optoelectronics (which combine light-based and electronic components) to sensors for biological and medical purposes. To do so, they couple two-dimensional materials with atomic-level thickness, such as graphene, with nanosized metal particles. Understanding the combined plasmonic behavior of these two different types of materials requires understanding exactly how they are coupled.
In a recent study from Argonne, researchers used ultrafast electron microscopy to look directly at the coupling between gold nanoparticles and graphene. More

“Skin electronics” are thin flexible electronics that could be mounted onto the skin. While it may sound like something out of science fiction, it is anticipated that soon such devices can serve as next-generation devices with a wide range of applications such as health monitoring, health diagnosis, virtual reality, and human-machine interface.
As it is expected, creating such devices requires components that are soft and stretchable to be mechanically compatible with the human skin. One of the vital components of skin electronics is an intrinsically stretchable conductor that transmits electrical signals between devices. For reliable operation and high-quality performance, a stretchable conductor which features ultrathin thickness, metal-like conductivity, high stretchability, and ease of patternability is required. Despite extensive research, it was not yet possible to develop a material that possesses all of these properties simultaneously, due to the fact that they often have trade-offs between one another.
Led by professor HYEON Taeghwan and KIM Dae-Hyeong, researchers at the Center for Nanoparticle Research within the Institute for Basic Science (IBS) in Seoul, South Korea unveiled a new method to fabricate a composite material in a form of nanomembrane, which comes with all of the above-mentioned properties. The new composite material consists of metal nanowires that are tightly packed in a monolayer within ultrathin rubber film.
This novel material was made using a process that the team developed called a “float assembly method.” The float assembly takes advantage of the Marangoni effect, which occurs in two liquid phases with different surface tensions. When there is a gradient in surface tension, a Marangoni flow is generated away from the region with lower surface tension towards the region with higher surface tension. This means that dropping a liquid with lower surface tension on the water surface lowers the surface tension locally, and the resulting Marangoni flow causes the dropped liquid to spread thinly across the surface of the water.
The nanomembrane is created using a float assembly method which consists of a three-step process. The first step involves dropping a composite solution, which is a mixture of metal nanowires, rubber dissolved in toluene, and ethanol, on the surface of the water. The toluene-rubber phase remains above the water due to its hydrophobic property, while the nanowires end up on the interface between the water and toluene phases. The ethanol within the solution mixes with the water to lower the local surface tension, which generates Marangoni flow that propagates outward and prevents the aggregation of the nanowires. This assembles the nanomaterials into a monolayer at the interface between water and a very thin rubber/solvent film. In the second step, the surfactant is dropped to generate a second wave of Marangoni flow which tightly compacts the nanowires. Finally, in the third step, the toluene is evaporated and a nanomembrane with a unique structure in which a highly compacted monolayer of nanowires is partially embedded in an ultrathin rubber film is obtained.
Its unique structure allows efficient strain distribution in ultrathin rubber film, leading to excellent physical properties, such as a stretchability of over 1,000%, and a thickness of only 250 nm. The structure also allows cold welding and bi-layer stacking of the nanomembrane onto each other, which leads to a metal-like conductivity over 100,000 S/cm. Furthermore, the researchers demonstrated that the nanomembrane can be patterned using photolithography, which is a key technology that is widely used for manufacturing commercial semiconductor devices and advanced electronics. Therefore, it is expected that the nanomembrane can serve as a new platform material for skin electronics.
The implications of this study may go well beyond the development of skin electronics. While this study showcased a composite material consisting of silver nanowires within styrene-ethylene-butylene-styrene (SEBS) rubber, it is also possible to use the float assembly method on various nanomaterials such as magnetic nanomaterials and semiconducting nanomaterials, as well as other types of elastomers such as TPU and SIS. Therefore, it is expected that the float assembly can open new research fields involving various types of nanomembranes with different functions.
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