Computers Math

Community structure, including relationships between and within groups, is foundational to our understanding of the world around us. New research by mathematics and statistics professor Kenneth Berenhaut, along with former postdoctoral fellow Katherine Moore and graduate student Ryan Melvin, sheds new light on some fundamental statistical questions.
“When we encounter complex data in areas such as public health, economics or elsewhere, it can be valuable to address questions regarding the presence of discernable groups, and the inherent “cohesion” or glue that holds these groups together. In considering such concepts, socially, the terms “communities,” “networks” and “relationships” may come to mind,” said Berenhaut.
The research leverages abstracted social ideas of conflict, alignment, prominence and support, to tap into the mathematical interplay between distance and cohesiveness — the sort evident when, say, comparing urban and rural settings. This enables adaptations to varied local perspectives.
“For example, we considered psychological survey-based data reflecting differences and similarities in cultural values between regions around the world — in the U.S., China, India and the EU,” Berenhaut said. “We observed distinct cultural groups, with rich internal network structure, despite the analytical challenges caused by the fact that some cohesive groups (such as India and the EU) are far more culturally diverse than others. Mark Twain once referred to India as ‘the country of a hundred nations and a hundred tongues, of a thousand religions and two million gods.’ Regions (such as the Southeast and California in the U.S.) can be perceived as locally distinct, despite their relative similarity in a global context. It is these sorts of characteristics that we are attempting to detect and understand.”
The paper, “A social perspective on perceived distances reveals deep community structure,” published by PNAS (Proceedings of the National Academy of Sciences of the United States) can be found here.
“I am excited by the manner in which a social perspective, along with a probabilistic approach, can illuminate aspects of communities inherent in data from a variety of fields,” said Berenhaut. “The concept of data communities proposed in the paper is derived from and aligns with a shared human social perspective. The work crosses areas with connections to ideas in sociology, psychology, mathematics, physics, statistics and elsewhere.”
Leveraging our experiences and perspectives can lead to valuable mathematical and statistical insights.
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Asymptomatic COVID-19 cases are the bane of computer modelers’ existences — they throw off the modeling data to an unknown degree. You can’t measure what you can’t detect, right? A new approach from Los Alamos National Laboratory’s Theoretical Division, however, explores using historic epidemic data from eight different countries to estimate the transmission rate and fraction of under-reported cases.
“Asymptomatic cases are the ‘dark matter’ of epidemics,” said Nick Hengartner, one of the authors on the report published today in the journal PLOS ONE. “We see only the indirect evidence that more people are sick than reported, and if we don’t account for them, we may wrongly conclude that the epidemic is under control. So we changed the model to focus on the observed counts instead of trying to model the ‘perfect’ world. By looking back through the time series of historical data, we can see from their dynamics what’s missing.”
The importance of capturing the undocumented cases is significant, especially in a disease such as COVID-19, where asymptomatic individuals have accounted for 20-70 percent of all infections.
Co-author Imelda Trejo, a postdoctoral fellow at Los Alamos noted, “This is a new extension of the standard SIR (susceptible-infected-recovered) epidemiological models to study the underreported incidence of infectious disease. The new model reveals that trying to fit an SIR model type directly to raw incidence data will underestimate the true infectious rate. This could actually lead decisionmakers to declare the epidemic under control prematurely.” Instead, the team presented a Bayesian method (a statistical model using probability to represent all uncertainty within the model) to estimate the transmission rate and fraction of underreported cases.
As tested against the data of eight countries (Argentina, Brazil, Chile, Colombia, Mexico, Panama, Peru and the U.S.), the new approach directly describes the dynamics of the observed, under-reported cases. “We use the local dynamics of the observed cases to propose a model that gives us a conditional expectation of new cases, based on the observed history,” Trejo said.
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Mathematicians at the University of Leicester have developed a new mathematical model which could greatly increase the efficiency of pest control and hence significantly reduce the impact of pests on crops whilst minimising the damage to environment.
A new study, published in Scientific Reports, builds upon individual-based model (IBM) techniques to explain and predict the formation of high slug density patches in arable fields.
While existing models built around the Turing theory of pattern formation (named for AI pioneer Alan Turing) and its generalisations are shown to work well for patterns in plant distribution, these are rarely able to accurately predict the distribution of animals due to the complexity of behavioural responses.
Drawing on field data collected in a three-year project, computational modelling experts in the University of Leicester’s School of Computing and Mathematical Sciences, alongside colleagues from The University of Birmingham and Harper Adams University, applied mathematical concepts to build a new model which shows trends of distribution, accounting for the movements of individual creatures.
Their model could be used in creating more efficient methods of pest control — by targeting the use of pesticides and other techniques to protect crops — and could be adapted to better understand the collective behaviour in other species, such as fish schools, bird flocks, and insect swarms.
Sergei Petrovskii is a Professor in Applied Mathematics at the University of Leicester and lead author for the study. Professor Petrovskii said:
“This study is an example of how a fundamental ecological concept, when applied to a real-world problem, can lead to breakthrough findings and ultimately helps to make agriculture more sustainable”
Keith Walters, Professor in Agriculture and Pest Control at Harper Adams University, said:
“Understanding factors determining slug distribution in agricultural fields have been a long-standing problem. Using unique field techniques specifically developed to support modelling and simulations allowed progress that would hardly be possible with empirical tools alone.”
Dr Natalia Petrovskaya, Senior Lecturer in Applied Mathematics at the University of Birmingham and corresponding author for the study, added:
“Computer simulations helped us to reveal a hidden link between biological processes going on very different spatial scales, which was crucial for the success of this project.”
‘A predictive model and a field study on heterogeneous slug distribution in arable fields arising from density dependent movement’ is published in Scientific Reports.
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Spatial training with blocks and puzzles could unlock mathematical potential. A sustained focus on spatial reasoning training could help children learn science, technology, engineering and mathematics, according to new research from the University of Surrey.
The Surrey study found that teaching spatial skills — particularly with the use of blocks, puzzles and other physical manipulatives — is highly effective at improving mathematics performance. The team also found that physical spatial reasoning training was far more effective than digital sessions.
Dr Katie Lee-Gilligan, co-author of the study and Lecturer in Developmental Psychology at the University of Surrey, said:
“Our research confirms that when children learn the relationship between space and shapes through tangible physical tools such as puzzles, their mathematics performance improves. This is critical information for us all, particularly parents, teachers and decision-makers, at a time when the UK is lagging behind its international competitors when it comes to STEM skills.”
Spatial reasoning is defined as a person’s ability to think about shapes and space in two and three dimensions, and previous research has shown that spatial reasoning is crucial for daily living, for example, navigating to work, filling the dishwasher, and putting on your shoes.
The research, which was conducted in partnership with the University of Toronto and the University of Maryland, also highlights the importance of not restricting the teaching of spatial reasoning to young children as they found evidence of mathematical gains in older groups past the age of seven.
Dr Zack Hawes, co-author of the study and Assistant Professor at the University of Toronto, commented:
“Despite these and other findings that demonstrate the fundamental importance of spatial thinking for STEM learning and performance, spatial thinking remains a neglected aspect of educational practice and policy. We hope the current findings inspire new research, professional practice, and insights into the ways in which spatial thinking may be used to make learning more engaging, accessible, and equitable.”
The research has been published by the American Psychological Association and details a meta-analysis on how spatial reasoning training impacted the mathematical abilities of 3,700 participants aged between three to 20 years old.
In a 2021 open letter to the UK Government, the Institute of Engineering and Technology estimated a shortfall of over 173,000 workers in the science, technology, engineering and mathematics sectors, with an average of 10 unfilled roles per business in the UK. The letter, signed by 150 of the UK’s top firms, warned that if the country did not plug this skills gap, it would cost the economy £1.5bn per year. This research suggests that spatial skill training could be a novel, untapped avenue for improving STEM skills.
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Many sufferers of rare diseases endure an odyssey until the correct diagnosis is made. “The goal is to detect such diseases at an early stage and initiate appropriate therapy as soon as possible,” says Prof. Dr. Peter Krawitz from the Institute for Genomic Statistics and Bioinformatics (IGSB) at the University Hospital Bonn (Germany). The researcher is a member of the Cluster of Excellence ImmunoSensation2 and the Transdisciplinary Research Area “Modelling” at the University of Bonn.
The majority of rare diseases are genetic. The underlying hereditary mutations often cause varying degrees of impairment in different areas of the body. In most cases, these hereditary changes are also expressed by characteristic facial features: for example, because eyebrows, the base of the nose or the cheeks are shaped in a distinctive way. However, this varies from disease to disease. Artificial intelligence (AI) uses these facial characteristics, calculates the similarities, and automatically links them to clinical symptoms and genetic data of patients. “The face provides us with a starting point for diagnosis,” says Tzung-Chien Hsieh of Krawitz’s team. “It is possible to calculate what the disease is with a high degree of accuracy.”
“GestaltMatcher” requires only a few patients
The AI system “GestaltMatcher” described in the current publication is a continued development of “DeepGestalt,” which the IGSB team trained with other institutions a few years ago. While DeepGestalt still required about ten non-related affected persons as a reference for training, its successor “GestaltMatcher” requires significantly fewer patients for feature matching. This is a great advantage in the group of very rare diseases, where only a few patients are reported worldwide. Furthermore, the new AI system also considers similarities with patients who have also not yet been diagnosed, and thus combinations of characteristics that have not yet been described. GestaltMatcher therefore also “recognizes” diseases that were previously unknown to it and suggests diagnoses based on this. “This means we can now classify previously unknown diseases, search for other cases and provide clues as to the molecular basis,” says Krawitz.
The team used 17,560 patient photos, most of which came from digital health company FDNA, which the research team worked with developing the web service through which the AI can be used. Around 5,000 of the photos and patient data were contributed by the research team at the Institute of Human Genetics at the University of Bonn, along with nine other university sites in Germany and abroad. The researchers focused on disease patterns that were as diverse as possible. They were able to consider a total of 1,115 different rare diseases. “This wide variation in appearance trained the AI so well that we can now diagnose with relative confidence even with only two patients as our baseline at best, if that’s possible,” Krawitz says.
“We are very happy to finally have a phenotype analysis solution for the ultra-rare cases, which can help clinicians solve challenging cases, and researchers to progress rare disease understanding,” says Aviram Bar-Haim of FDNA Inc. in Boston, USA. In Germany, too, the application in doctors’ offices, for example, is not far off, adds Krawitz. Doctors can already use their smartphones to take a portrait photo of a patient and use AI to make differential diagnoses, he says. “GestaltMatcher helps the physician make an assessment and complements expert opinion.”
Peter Krawitz and his team turned over the data they collected themselves to the non-profit Association for Genome Diagnostics (AGD), to provide researchers with access. “The GestaltMatcher Database (GMDB) will improve the comparability of algorithms and provide the basis for further development of artificial intelligence for rare diseases, including other medical image data such as X-rays or retinal images from ophthalmology,” Krawitz says.
Participating institutions and funding:
In addition to the Institute for Genomic Statistics and Bioinformatics and the Institute of Human Genetics of the University Hospital Bonn, the Charité-Universitätsmedizin Berlin, the universities of Greifswald, Tübingen, Düsseldorf, Lübeck, Heidelberg, the Technical University of Munich as well as universities from South Africa, France, the USA and Norway were involved. The study was mainly funded by the German Research Foundation (DFG).
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Rare earth elements are hard to get and hard to recycle, but a flash of intuition led Rice University scientists toward a possible solution.
The Rice lab of chemist James Tour reports it has successfully extracted valuable rare earth elements (REE) from waste at yields high enough to resolve issues for manufacturers while boosting their profits.
The lab’s flash Joule heating process, introduced several years ago to produce graphene from any solid carbon source, has now been applied to three sources of rare earth elements — coal fly ash, bauxite residue and electronic waste — to recover rare earth metals, which have magnetic and electronic properties critical to modern electronics and green technologies.
The researchers say their process is kinder to the environment by using far less energy and turning the stream of acid often used to recover the elements into a trickle.
The study appears in Science Advances.
Rare earth elements aren’t actually rare. One of them, cerium, is more abundant than copper, and all are more abundant than gold. But these 15 lanthanide elements, along with yttrium and scandium, are widely distributed and difficult to extract from mined materials. More

A person who is generous and caring at home may be cutthroat at work, striving to bring in the most sales or advance up a corporate management chain. In a similar vein, a self-centered neighbor may be a model of altruism on Twitter.
It’s a widespread feature of human society: People can adopt different behaviors depending on the social context they’re in. Yet according to a new study by Penn biologists out today in Science Advances, that context-dependent behavior tends to promote the spread of cooperative behavior across a whole society.
Using models rooted in game theory, the researchers show that cooperation is particularly favored when there is room for “spillover” between domains. In other words, a worker can observe how their colleague behaves with her friends when deciding how to interact with that person and others in the workplace.
“We studied groups both small and large,” says Joshua Plotkin, a professor in Penn’s Department of Biology and senior author on the new paper, “and we find that the simple idea of conditioning behavior on the social context, while allowing imitation of behaviors across different contexts — that alone facilitates cooperation in all domains simultaneously.”
That work, along with a related study in Nature Human Behaviour, suggests that the greater the number of domains of social life, the higher the likelihood that cooperative interactions will eventually dominate.
“This shows that the structure of interactions in different aspects of our social lives can galvanize each other — for the benefit of mutual cooperation,” Plotkin says. More

Imagine a small autonomous vehicle that could drive over land, stop, and flatten itself into a quadcopter. The rotors start spinning, and the vehicle flies away. Looking at it more closely, what do you think you would see? What mechanisms have caused it to morph from a land vehicle into a flying quadcopter? You might imagine gears and belts, perhaps a series of tiny servo motors that pulled all its pieces into place.
If this mechanism was designed by a team at Virginia Tech led by Michael Bartlett, assistant professor in mechanical engineering, you would see a new approach for shape changing at the material level. These researchers use rubber, metal, and temperature to morph materials and fix them into place with no motors or pulleys. The team’s work has been published in Science Robotics. Co-authors of the paper include graduate students Dohgyu Hwang and Edward J. Barron III and postdoctoral researcher A. B. M. Tahidul Haque.
Getting into shape
Nature is rich with organisms that change shape to perform different functions. The octopus dramatically reshapes to move, eat, and interact with its environment; humans flex muscles to support loads and hold shape; and plants move to capture sunlight throughout the day. How do you create a material that achieves these functions to enable new types of multifunctional, morphing robots?
“When we started the project, we wanted a material that could do three things: change shape, hold that shape, and then return to the original configuration, and to do this over many cycles,” said Bartlett. “One of the challenges was to create a material that was soft enough to dramatically change shape, yet rigid enough to create adaptable machines that can perform different functions.”
To create a structure that could be morphed, the team turned to kirigami, the Japanese art of making shapes out of paper by cutting. (This method differs from origami, which uses folding.) By observing the strength of those kirigami patterns in rubbers and composites, the team was able to create a material architecture of a repeating geometric pattern. More