Computers Math

Imagine you have a group of 30 children who want to play soccer. You would like to divide them into two teams, so they can practice their skills and learn from their coaches to become better players.
But what is the most effective way for them to improve: Should you group the children according to skill level, with all of the most skilled players in one group and the rest of the players in the other group? Or, should you divide them into two equal teams by talent and skill?
For a fresh approach to this age-old question in grouping theory, a researcher from the University of Rochester, along with his childhood friend, an education professor at the University of Nevada, Las Vegas, turned to math.
“The selection and grouping of individuals for training purposes is extremely common in our society,” says Chad Heatwole, a professor of neurology at the University of Rochester Medical Center and the director of Rochester’s Center for Health + Technology (CHeT). “There is a historic and ongoing rigorous debate regarding the best way to group students for the purpose of instruction.”
In a paper published in the journal Education Practice and Theory, the research team — which also includes Peter Wiens, an associate professor of teaching and learning at the University of Nevada, Las Vegas, and Christine Zizzi, a director at CHeT — developed, for the first time, a mathematical approach to grouping. The approach compares different grouping methods, selecting the optimal way to group individuals for teacher-led instruction. The research has broad implications in education, as well as in economics, music, medicine, and sports.
“Our solution was to look at this through a purely mathematical lens, evaluating for the greatest good of the entire sample,” Heatwole says. “To our knowledge, this novel mathematical approach has never been described or utilized in this way.”
Two approaches in grouping theory More

This encouraging response may actually do more harm than good to children’s math performance, according to a new study by the University of Georgia.
Co-conducted by Michael Barger, an assistant professor in the Mary Frances Early College of Education’s Department of Educational Psychology, the study found that encouraging children with responses related to their personal traits or innate abilities may dampen their math motivation and achievement over time.
Parents who make comments linking their children’s performance to personal attributes like intelligence (e.g., “You’re so smart” or “Math just isn’t your thing”) are using what’s referred to as person responses. In contrast, parents who link their children’s actions, such as effort or strategy use, to their performance (e.g., “You worked hard” or “What might be useful next time you have a math test?”) are using process responses.
“Person-focused praise sounds good on its face, but ultimately, it might undermine students’ motivation if they run into challenges,” said Barger. “Because if you run into challenges after being told you’re so smart, you might think, ‘Maybe they were wrong.’ We also know that people tend to think about math as something that some people can do and others can’t, and that language is pretty common, whether it’s among parents or teachers, even with young kids.”
Praising strategy and effort
For the study, researchers asked more than 500 parents to report on how they respond to their children’s math performance and their math beliefs and goals. Students were assessed in two waves across a year to measure their math motivation and achievement. More

A groundbreaking mathematical equation has been discovered, which could transform medical procedures, natural gas extraction, and plastic packaging production in the future.
The new equation, developed by scientists at the University of Bristol, indicates that diffusive movement through permeable material can be modelled exactly for the very first time. It comes a century after world-leading physicists Albert Einstein and Marian von Smoluchowski derived the first diffusion equation and marks important progress in representing motion for a wide range of entities from microscopic particles and natural organisms to human-made devices.
Until now, scientists looking at particle motion through porous materials such as biological tissues, polymers, various rocks and sponges, have had to rely on approximations or incomplete perspectives.
The findings, published today in the journal Physical Review Research, provide a novel technique presenting exciting opportunities in a diverse range of settings including health, energy, and the food industry.
Lead author Toby Kay, who is completing a PhD in Engineering Mathematics, said: “This marks a fundamental step forward since Einstein and Smoluchowski’s studies on diffusion. It revolutionises the modelling of diffusing entities through complex media of all scales, from cellular components and geological compounds to environmental habitats.
“Previously, mathematical attempts to represent movement through environments scattered with objects that hinder motion, known as permeable barriers, have been limited. By solving this problem, we are paving the way for exciting advances in many different sectors because permeable barriers are routinely encountered by animals, cellular organisms and humans.”
Creativity in mathematics takes different forms and one of these is the connection between different levels of description of a phenomenon. In this instance, by representing random motion in a microscopic fashion and then subsequently zooming out to describe the process macroscopically, it was possible to find the new equation.
Further research is needed to apply this mathematical tool to experimental applications, which could improve products and services. For example, being able to model accurately the diffusion of water molecules through biological tissue will advance the interpretation of diffusion-weighted MRI (Magnetic Resonance Imaging) readings. It could also offer more accurate representation of air spreading through food packaging materials, helping to determine shelf life and contamination risk. In addition, quantifying the behaviour of foraging animals interacting with macroscopic barriers, such as fences and roads, could provide better predictions on the consequence of climate change for conservation purposes.
The use of geolocators, mobile phones, and other sensors has seen the tracking revolution generate movement data of ever-increasing quantity and quality over the past 20 years. This has highlighted the need for more sophisticated modelling tools to represent the movement of wide-ranging entities in their environment, from natural organisms to human-made devices.
Senior author Dr Luca Giuggioli, Associate Professor in Complexity Sciences at the University of Bristol, said: “This new fundamental equation is another example of the importance of constructing tools and techniques to represent diffusion when space is heterogeneous, that is when the underlying environment changes from location to location.
“It builds on another long-awaited resolution in 2020 of a mathematical conundrum to describe random movement in confined space. This latest discovery is a further significant step forward in improving our understanding of motion in all its shapes and forms — collectively termed the mathematics of movement — which has many exciting potential applications.”
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Key studies in the last decade have shown that the gut microbiome, the collection of hundreds of bacterial species that live in the human digestive system, influences neural development, response to cancer immunotherapies, and other aspects of health. But these communities are complex and without systematic ways to study the constituents, the exact cells and molecules linked with certain diseases remain a mystery.
Stanford University researchers have built the most complex and well-defined synthetic microbiome, creating a community of over 100 bacterial species that was successfully transplanted into mice. The ability to add, remove, and edit individual species will allow scientists to better understand the links between the microbiome and health, and eventually develop first-in-class microbiome therapies.
Many key microbiome studies have been done using fecal transplants, which introduce the entire, natural microbiome from one organism to another. While scientists routinely silence a gene or remove a protein from a specific cell or even an entire mouse, there is no such set of tools to remove or modify one species among the hundreds in a given fecal sample.
“So much of what we know about biology, we wouldn’t know if it weren’t for the ability to manipulate complex biological systems piecewise,” said Michael Fischbach, Institute Scholar at Sarafan ChEM-H and corresponding author on the study, published in Cell on Sept. 6.
Fischbach, who is an associate professor of bioengineering and of microbiology and immunology, and others saw one solution: Build a microbiome from scratch by growing individually and then mixing its constituent bacteria.
Building the ark
Each cell in the microbiome occupies a specific functional niche, performing reactions that break down and build up molecules. To build a microbiome, the team had to ensure that the final mixture was not only stable, maintaining a balance without any single species overpowering the rest, but also functional, performing all the actions of a complete, natural microbiome. Selecting species to include in their synthetic community was also difficult given the natural variation across individuals; two people selected at random share less than half of their microbial genes. More

Research led by the University of Exeter and Kent and Medway NHS and Social Care Partnership Trust, published in Age and Ageing, assessed a new tool designed to calculate which medicines are more likely to experience adverse anticholinergic effects on the body and brain. These complications can occur from many -prescription and over-the-counter drugs which affects the brain by blocking a key neurotransmitter called acetylcholine. Many medicines, including some bladder medications, anti-depressants, medications for stomach and Parkinson’s disease have some degree of anticholinergic effect. They are commonly taken by older people.
Anticholinergic side effects include confusion, blurred vision, dizziness, falls and a decline in brain function. Anticholinergic effects may also increase risks of falls and may be associated with an increase in mortality. They have also been linked to a higher risk of dementia when used long term.
Now, researchers have developed a tool to calculate harmful effects of medicines using artificial intelligence. The team created a new online tool, International Anticholinergic Cognitive Burden Tool (IACT), is uses natural language processing which is an artificial intelligence methdolody and chemical structure analysis to identify medications that have anticholinergic effect.
The tool is the first to incorporate a machine learning technique, to develop an automatically updated tool available on a website portal. The anticholinergic burden is assessed by assigning a score based on reported adverse events and aligning closely with the chemical structure of the drug being considered for prescription, resulting in a more accurate and up-to-date scoring system than any previous system. Ultimately, after further research and modelling with real world patient data the tool developed could help to support prescribing reducing risks form common medicines.
Professor Chris Fox, at the University of Exeter, is one of the study authors. He said:: “Use of medicines with anticholinergic effects can have significant harmful effects for example falls and confusion which are avoidable, we urgently need to reduce the harmful side effects as this can leads to hospitalisation and death. This new tool provides a promising avenue towards a more tailored personalised medicine approach, of ensuring the right person gets a safe and effective treatment whilst avoiding unwanted anticholinergic effects.”
The team surveyed 110 health professionals, including pharmacists and prescribing nurses. Of this group, 85 per cent said they would use a tool to assess risk of anticholinergic side effects, if available. The team also gathered usability feedback to help improve the tool further.
Dr Saber Sami, at the University of East Anglia, said: “Our tool is the first to use innovative artificial intelligence technology in measures of anticholinergic burden — ultimately, once further research has been conducted the tool should support pharmacists and prescribing health professionals in finding the best treatment for patients.”
Professor Ian Maidment, from Aston University, said: “I have been working in this area for over 20 years. Anti-cholinergic side-effects can be very debilitating for patients. We need better ways to assess these side-effects.”
The research team includes collaboration with AKFA University Medical School, Uzbekistan, and the Universities of East Anglia, Aston, Kent and Aberdeen. They aim to continue development of the tool with the aim that it can be deployed in day-to-day practice which this study supports.
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Abrahamic texts treat slithering as a special indignity visited on the wicked serpent, but evolution may draw a more continuous line through the motion of swimming microbes, wriggling worms, skittering spiders and walking horses.
A new study found that all of these kinds of motion are well represented by a single mathematical model.
“This didn’t come out of nowhere — this is from our real robot data,” said Dan Zhao, first author of the study in the Proceedings of the National Academy of Sciences and a recent Ph.D. graduate in mechanical engineering at the University of Michigan.
“Even when the robot looks like it’s sliding, like its feet are slipping, its velocity is still proportional to how quickly it’s moving its body.”
Unlike the dynamic motion of gliding birds and sharks and galloping horses — where speed is driven, at least in part, by momentum — every bit of speed for ants, centipedes, snakes and swimming microbes is driven by changing the shape of the body. This is known as kinematic motion.
The expanded understanding of kinematic motion could change the way roboticists think about programming many-limbed robots, opening new possibilities for walking planetary rovers, for instance. More

Microbial populations may be small but they are surprisingly complex, making interactions with their surrounding environment difficult to study. But now, researchers from Japan have discovered that machine learning can provide the tools to do just that. In a study published this month in eLife, researchers from the University of Tsukuba have revealed that machine learning can be applied to bacterial population growth to discover how it relates to variations in their environment.
The dynamics of microbe populations are usually represented by growth curves. Typically, three parameters taken from these curves are used to evaluate how microbial populations fit with their environment: lag time, growth rate, and saturated population size (or carrying capacity). These three parameters are probably linked; trade-offs have been observed between the growth rate and either the lag time or population size within species, and with related changes in the saturated population size and growth rate among genetically diverse strains.
“Two questions remained: are these three parameters affected by environmental diversity, and if so, how?” says senior author of the study, Professor Bei-Wen Ying. “To answer these, we used data-driven approaches to investigate the growth strategy of bacteria.”
The researchers built a large dataset that reflected the dynamics of Escherichia coli populations under a wide variety of environmental conditions, using almost a thousand combinations of growth media composed from 44 chemical compounds under controlled lab conditions. They then analyzed the big data for the relationships between the growth parameters and the combinations of media using machine learning (ML). ML algorithms built a model based on sample data to make predictions or decisions without being specifically programmed to do so.
The analysis revealed that for bacterial growth, the decision-making components were distinct among different growth phases, e.g., serine, sulfate, and glucose for growth delay (lag), growth rate, and maximum growth (saturation), respectively. The results of additional simulations and analyses showed that branched-chain amino acids likely act as ubiquitous coordinators for bacterial population growth conditions.
“Our results also revealed a common and simple strategy of risk diversification in conditions where the bacteria experienced excess resources or starvation, which makes sense in both an evolutionary and ecological context,” says Professor Ying.
The results of this study have revealed that exploring the world of microorganisms with data-driven approaches can provide new insights that were previously unattainable via traditional biological experiments. This research shows that the ML-assisted approach, although still an emerging technology that will need to be developed in terms of its biological reliability and accessibility, could open new avenues for applications in the life sciences, especially microbiology and ecology.
The study was funded by Japan Society for the Promotion of Science 21K19815 and 19H03215.
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Appropriately balancing a videogame’s difficulty is essential to provide players with a pleasant experience. In a recent study, Korean scientists developed a novel approach for dynamic difficulty adjustment where the players’ emotions are estimated using in-game data, and the difficulty level is tweaked accordingly to maximize player satisfaction. Their efforts could contribute to balancing the difficulty of games and making them more appealing to all types of players.
Difficulty is a tough aspect to balance in video games. Some people prefer videogames that present a challenge whereas others enjoy an easy experience. To make this process easier, most developers use ‘dynamic difficulty adjustment (DDA).’ The idea of DDA is to adjust the difficulty of a game in real time according to player performance. For example, if player performance exceeds the developer’s expectations for a given difficulty level, the game’s DDA agent can automatically raise the difficulty to increase the challenge presented to the player. Though useful, this strategy is limited in that only player performance is taken into account, not how much fun they are actually having.
In a recent study published in Expert Systems With Applications, a research team from the Gwangju Institute of Science and Technology in Korea decided to put a twist on the DDA approach. Instead of focusing on the player’s performance, they developed DDA agents that adjusted the game’s difficulty to maximize one of four different aspects related to a player’s satisfaction: challenge, competence, flow, and valence. The DDA agents were trained via machine learning using data gathered from actual human players, who played a fighting game against various artificial intelligences (AIs) and then answered a questionnaire about their experience.
Using an algorithm called Monte-Carlo tree search, each DDA agent employed actual game data and simulated data to tune the opposing AI’s fighting style in a way that maximized a specific emotion, or ‘affective state.’ “One advantage of our approach over other emotion-centered methods is that it does not rely on external sensors, such as electroencephalography,” comments Associate Professor Kyung-Joong Kim, who led the study. “Once trained, our model can estimate player states using in-game features only.”
The team verified — through an experiment with 20 volunteers — that the proposed DDA agents could produce AIs that improved the players’ overall experience, no matter their preference. This marks the first time that affective states are incorporated directly into DDA agents, which could be useful for commercial games. “Commercial game companies already have huge amounts of player data. They can exploit these data to model the players and solve various issues related to game balancing using our approach,” remarks Associate Professor Kim. Worth noting is that this technique also has potential for other fields that can be ‘gamified,’ such as healthcare, exercise, and education.
This paper was made available online on June 3, 2022, and will be published in Volume 205 of the journal on November 1, 2022.
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