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Direct reciprocity facilitates cooperation in repeated social interactions. Traditional models suggest that individuals learn to adopt conditionally cooperative strategies if they have multiple encounters with their partner. However, most existing models make rather strong assumptions about how individuals decide to keep or change their strategies. They assume individuals make these decisions based on a strategy’s average performance. This in turn suggests that individuals would remember their exact payoffs against everyone else.

In a recent study, researchers from the Max Planck Institute for Evolutionary Biology, the School of Data Science and Society, and the Department of Mathematics at the University of North Carolina at Chapel Hill examine the effects of realistic memory constraints. They find that cooperation can evolve even with minimal memory capacities. The research is published in the journal Proceedings of the Royal Society B: Biological Sciences.

Direct reciprocity is based on repeated interactions between two individuals. This concept, often described as “you scratch my back, I’ll scratch yours,” has proven to be a pivotal mechanism in maintaining cooperation within groups or societies.

While models of direct reciprocity have deepened our understanding of cooperation, they frequently make strong assumptions about individuals’ memory and decision-making processes. For example, when strategies are updated through social learning, it is commonly assumed that individuals compare their average payoffs.

This would require them to compute (or remember) their payoffs against everyone else in the population. To understand how more realistic constraints influence direct reciprocity, the current study considers the evolution of conditional behaviours when individuals learn based on more recent experiences.

Two extreme scenarios

This study first compares the classical modeling approach with another extreme approach. In the classical approach, individuals update their strategies based on their expected payoffs, considering every single interaction with each member of the population (perfect memory). Conversely, the opposite extreme is considering only the very last interaction (limited memory).

Comparing these two scenarios shows that individuals with limited payoff memory tend to adopt less generous strategies. They are less forgiving when someone defects against them. Yet, moderate levels of cooperation can still evolve.

Intermediate cases

The study also considers intermediate cases, where individuals consider their last two or three or four recent experiences. The results show that cooperation rates quickly approach the levels observed under perfect payoff memory.

Overall, this study contributes to a wider literature that explores which kinds of cognitive capacities are required for reciprocal altruism to be feasible. While more memory is always favourable, reciprocal cooperation can already be sustained if individuals have a record of two or three past outcomes.

This work’s results have been derived entirely within a theoretical model. The authors feel that such studies are crucial for making model-informed deductions about reciprocity in natural systems.

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Credit of the article given to Michael Hesse, Max Planck Society

Bob Moses, who helped register Black residents to vote in Mississippi during the Civil Rights Movement, believed civil rights went beyond the ballot box. To Moses, who was a teacher as well as an activist, math literacy is a civil right: a requirement to earning a living wage in modern society. In 1982, he founded the Algebra Project to ensure that “students at the bottom get the math literacy they need.”

As a researcher who studies ways to improve the math experiences of students, WEbelieve a new approach that expands access to algebra may help more students get the math literacy Moses, who died in 2021, viewed as so important. It’s a goal districts have long been struggling to meet.

Efforts to improve student achievement in algebra have been taking place for decades. Unfortunately, the math pipeline in the United States is fraught with persistent opportunity gaps. According to the Nation’s Report Card – a congressionally mandated project administered by the Department of Education – in 2022 only 29% of U.S. fourth graders and 20% of U.S. eighth graders were proficient in math. Low-income students, students of color and multilingual learners, who tend to have lower scoreson math assessments, often do not have the same access as others to qualified teachers, high-quality curriculum and well-resourced classrooms.

A new approach

The Dallas Independent School District – or Dallas ISD – is gaining national attention for increasing opportunities to learn by raising expectations for all students. Following in the footsteps of more than 60 districts in the state of Washington, in 2019 the Dallas ISD implemented an innovative approach of having students be automatically enrolled rather than opt in to honours math in middle school.

Under an opt-in policy, students need a parent or teacher recommendation to take honours math in middle school and Algebra 1 in eighth grade. That policy led both to low enrollment and very little diversity in honours math. Some parents, especially those who are Black or Latino, were not aware how to enroll their students in advanced classes due to a lack of communication in many districts.

In addition, implicit bias, which exists in all demographic groups, may influence teachers’ perceptions of the behaviour and academic potential of students, and therefore their subsequent recommendations. Public school teachers in the U.S. are far less racially and ethnically diverse than the students they serve.

Dallas ISD’s policy overhaul aimed to foster inclusivity and bridge educational gaps among students. Through this initiative, every middle school student, regardless of background, was enrolled in honours math, the pathway that leads to taking Algebra 1 in eighth grade, unless they opted out.

Flipping the switch from opt-in to opt-out led to a dramatic increase in the number of Black and Latino learners, who constitute the majority of Dallas students. And the district’s overall math scores remained steady. About 60% of Dallas ISD eighth graders are now taking Algebra 1, triple the prior level. Moreover, more than 90% are passing the state exam.

Civil rights activist Bob Moses believed math literacy was critical for students to be able to make a living. Robert Elfstrom/Villon Films via Getty Images

Efforts spread

Other cities are taking notice of the effects of Dallas ISD’s shifting policy. The San Francisco Unified School District, for example, announced plans in February 2024 to implement Algebra 1 in eighth grade in all schools by the 2026-27 school year.

In fall 2024, the district will pilot three programs to offer Algebra 1 in eighth grade. The pilots range from an opt-out program for all eighth graders – with extra support for students who are not proficient – to a program that automatically enrolls proficient students in Algebra 1, offered as an extra math class during the school day. Students who are not proficient can choose to opt in.

Nationwide, however, districts that enroll all students in Algebra 1 and allow them to opt out are still in the minority. And some stopped offering eighth grade Algebra 1 entirely, leaving students with only pre-algebra classes. Cambridge, Massachusetts – the city in which Bob Moses founded the Algebra Project – is among them.

Equity concerns linger

Between 2017 and 2019, district leaders in the Cambridge Public Schools phased out the practice of placing middle school students into “accelerated” or “grade-level” math classes. Few middle schools in the district now offer Algebra 1 in eighth grade.

The policy shift, designed to improve overall educational outcomes, was driven by concerns over significant racial disparities in advanced math enrollment in high school. Completion of Algebra 1 in eighth grade allows students to climb the math ladder to more difficult classes, like calculus, in high school. In Cambridge, the students who took eighth grade Algebra 1 were primarily white and Asian; Black and Latino students enrolled, for the most part, in grade-level math.

Some families and educators contend that the district’s decision made access to advanced math classes even more inequitable. Now, advanced math in high school is more likely to be restricted to students whose parents can afford to help them prepare with private lessons, after-school programs or private schooling, they said.

While the district has tried to improve access to advanced math in high school by offering a free online summer program for incoming ninth graders, achievement gaps have remained persistently wide.

Perhaps striking a balance between top-down policy and bottom-up support will help schools across the U.S. realize the vision Moses dreamed of in 1982 when he founded the Algebra Project: “That in the 21st century every child has a civil right to secure math literacy – the ability to read, write and reason with the symbol systems of mathematics.”

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Credit of the article given to Liza Bondurant, The Conversation

The good news is that—statistically speaking—there is reason to believe Edmonton Oilers goalie Stuart Skinner will improve against the Florida Panthers in the Stanley Cup final.

The bad news is it may not be enough to make a difference.

That’s according to a new study, “Do NHL goalies get hot in the playoffs?” by Likang Ding, a doctoral student studying operations and information systems in the Alberta School of Business. The study is published on the arXivpreprint server.

Ding’s statistical analysis—in the final stage of review for publication—disproves the long-held and prevailing “hot hand” theory that if a goalie is performing well, he’ll continue to perform as well or better as pressure intensifies.

The term “hot hand” derives from basketball, where it is believed a shooter is more likely to score if their previous attempts were successful.

“Our main finding is the nonexistence of the hot-hand phenomenon (for hockey goaltenders),” says Ding. “That is, no positive influence of recent save performance on the save probability for the next shot.”

Instead, Ding and co-authors Ivor Cribben, Armann Ingolfsson and Monica Tran found that, by a small margin, “better past performance may result in a worse future performance.”

That could mean Panthers goaltender Sergei Bobrovsky is due for a slight slump, given his relatively hot streak of late. But according to Ding, that decline may amount to no more than about 1%—certainly nothing to count on.

The reverse is also true, says Ding. If a goalie is underperforming, as Skinner has on occasion during the playoffs, statistics would forecast a slight uptick in his save percentage.

The explanation in that case might be the “motivation effect”; when a goaltender’s recent save performance has been below his average, his effort and focus increase, “causing the next-shot save probability to be higher.”

Here Ding quotes Hall of Fame goaltender Ken Dryden, who once said, “If a shot beats you, make sure you stop the next one, even if it is harder to stop than the one before.”

Though it wasn’t part of his current study, Ding says he reviewed Skinner’s stats before the finals and found a worse-than-average performance, “so I’m hoping he will come back eventually.”

Ding wanted to take a closer look at the hot hand theory because it is crucial in understanding coaches’ decisions about which goaltender to start in a given game. It could mean the second goalie deserves a chance to enter the fray, get used to the pace and stay fresh, even if it might seem risky.

Ding’s data set includes information about all shots on goal in the NHL playoffs from 2008 to 2016, amounting to 48,431 shots faced by 93 goaltenders over 795 games and nine playoff seasons.

The hot hand theory has been around for at least as long as professional sports and is often applied to a range of human endeavour to support the notion that “success breeds success”—an appealing, almost intuitive assumption.

And yet, a series of studies in the 1980s focused on basketball shooting percentages showed there was no statistical evidence to support the theory, says Ding, attributing it instead to a psychological tendency to see patterns in random data.

The hot hand theory remained controversial after the statistical methods used in those studies were later shown to be biased, says Ding. But even once the bias was corrected, the theory has since been largely disproven.

Nobel Prize-winning cognitive scientist Daniel Kahneman once called the phenomenon “a massive and widespread cognitive illusion.” Ding’s study is one more confirming the consensus that the hot hand is no more than wishful thinking.

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Credit of the article given to Geoff McMaster, University of Alberta

Ever wondered how your friends shape your music taste? In a recent study, researchers at the Complexity Science Hub (CSH) demonstrated that social networks are a powerful predictor of a song’s future popularity. By analysing friendships and listening habits, they’ve boosted machine learning prediction precision by 50%.

“Our findings suggest that the social element is as crucial in music spread as the artist’s fame or genre influence,” says Niklas Reisz from CSH. By using information about listener social networks, along with common measures used in hit song prediction, such as how well-known the artist is and how popular the genre is, the researchers improved the precision of predicting hit songs from 14% to 21%. The study, published in Scientific Reports, underscores the power of social connections in music trends.

A deep dive into data

The CSH team analysed data from the music platform last.fm, analysing 2.7 million users, 10 million songs, and 300 million plays. With users able to friend each other and share music preferences, the researchers gained anonymized insights into who listens to what and who influences whom, according to Reisz.

For their model, the researchers worked with two networks: one mapping friendships and another capturing influence dynamics—who listens to a song and who follows suit. “Here, the nodes of the network are also people, but the connections arise when one person listens to a song and shortly afterwards another person listens to the same song for the first time,” explains Stefan Thurner from CSH.

Examining the first 200 plays of a new song, they predicted its chances of becoming a hit—defined as being in the top 1% most played songs on last.fm.

User influence

The study found that a song’s spread hinges on user influence within their social network. Individuals with a strong influence and large, interconnected friend circles accelerate a song’s popularity. According to the study, information about social networks and the dynamics of social influence enable much more precise predictions as to whether a song will be a hit or not.

“Our results also show how influence flows both ways—people who influence their friends are also influenced by them” explains CSH researcher Vito Servedio. “In this way, multi-level cascades can develop within a very short time, in which a song can quickly reach many other people, starting with just a few people.”

Social power in the music industry

Predicting hit songs is crucial for the music industry, offering a competitive edge. Existing models often focus on artist fame and listening metrics, but the CSH study highlights the overlooked social aspect—musical homophily, which is the tendency for friends to listen to similar music. “It was particularly interesting for us to see that the social aspect, musical homophily, has so far received very little attention—even though music has always had a strong social aspect,” says Reisz.

The study quantifies this social influence, providing insights that extend beyond music to areas like political opinion and climate change attitudes, according to Thurner.

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Credit of the article given to Complexity Science Hub Vienna

 

A research article published June 10 in the Proceedings of the National Academy of Sciences highlights the importance of careful application of high-tech forensic science to avoid wrongful convictions.

In a study with implications for an array of forensic examinations that rely on “vast databases and efficient algorithms,” researchers found the odds of a false match significantly increase when examiners make millions of comparisons in a quest to match wires found at a crime scene with the tools allegedly used to cut them.

The rate of mistaken identifications could be as high as one in 10 or more, concluded the researchers, who are affiliated with the Center for Statistics and Applications in Forensic Evidence (CSAFE), based in Ames, Iowa.

“It is somewhat of a counterintuition,” said co-author Susan VanderPlas, an assistant professor of statistics at the University of Nebraska-Lincoln. “You are more likely to find the right match—but you’re also more likely to find the wrong match.”

VanderPlas worked as a research professor at CSAFE before moving to Nebraska in 2020. Co-authors of the study, “Hidden Multiple Comparisons Increase Forensic Error Rates,” were Heike Hoffmann and Alicia Carriquiry, both affiliated with CSAFE and Iowa State University’s Department of Statistics.

Wire cuts and tool marks are used frequently as evidence in robberies, bombings, and other crimes. In the case of wire cuts, tiny striations on the cut ends of a wire may be matched to one of many available tools in a toolbox or garage. Comparing the evidence to more tools increases the chances that similar striations may be found on unrelated tools, resulting in a false accusation and conviction.

Wire-cutting evidence has been at issue in at least two cases that garnered national attention, including one where the accused was linked to a bombing based on a small piece of wire, a tiny fraction of an inch in diameter, that was matched to a tool found among the suspect’s belongings.

“Wire-cutting evidence is used in court and, based on our findings, it shouldn’t be—at least not without presenting additional information about how many comparisons were made,” VanderPlas said.

Wire cutting evidence is evaluated by comparing the striations found on the cut end of a piece of wire against the cutting blades of tools suspected to have been used in the crime. In a manual test, the examiner slides the end of the wire along the path created along another piece of material cut by the same tool to see where the pattern of striations match.

An automated process uses a comparison microscope and pattern-matching algorithms, to find possible matches pixel by pixel.

This can result in thousands upon thousands of individual comparisons, depending upon the length of the cutting blade, diameter of the wire, and even the number of tools checked.

For example, VanderPlas said she and her husband tallied the various tin snips, wire cutters, pliers and similar tools stored in their garage and came up with a total of 7 meters in blade length.

Examiners may not even be aware of the number of comparisons they are making as they search for a matching pattern, because those comparisons are hidden in the algorithms.

“This often-ignored issue increases the false discovery rate, and can contribute to the erosion of public trust in the justice system through conviction of innocent individuals,” the study authors wrote.

Forensic examiners typically testify based upon subjective rules about how much similarity is required to make an identification, the study explained. The researchers could not obtain error rate studies for wire-cut examinations and used published error rates for ballistics examinations to estimate possible false discovery rates for wire-cut examinations.

Before wire-cut examinations are used as evidence in court, the researchers recommended that:

• Examiners report the overall length or area of materials used in the examination process, including blade length and wirediameter. This would enable examination-wide error rates to be calculated.
• Studies be conducted to assess both false discovery and false elimination error rates when examiners are making difficult comparisons. Studies should link the length and area of comparison to error rates.
• The number of items searched, comparisons made and results returned should be reported when a database is used at any stage of the forensic evidence evaluation process.

The VanderPlas article joins other reports calling for improvements in forensic science in America. The National Academies Press, publisher of the PNAS journal and other publications of the National Academies of Sciences, Engineering and Medicine, also published the landmark 2009 report “Strengthening Forensic Science in the United States: A Path Forward.”

 

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Credit of the article given to University of Nebraska-Lincoln

How can we explain and predict human behaviour? Are mathematics and probability up to the task, or are humans too complex and irrational?

Often, people’s actions take us by surprise, particularly when they seem irrational. Take the COVID pandemic: one thing nobody saw coming was a rush on toilet paper that left supermarket shelves bare in many countries.

But by combining ideas from mathematics, economics and behavioural science, researchers were eventually able to make mathematical models of how panic spreads between people, which made sense of the toilet paper panic.

In new research published in the Journal of the Royal Society Interface, we have taken a similar approach to the spread of disease – and showed that human reactions to the spread of disease can be as important as the behaviour of the disease itself when it comes to determining how an outbreak develops.

The power of context

One thing we know is that context can shape people’s behaviour in surprising ways. A nightly example of this is the popular TV game show Deal or No Deal, in which contestants regularly turn down offers of free money because they hope they will get a larger sum later.

If you carry out a rational calculation of the probabilities, most of the time the contestant’s “best” move is to accept the offer. But in practice, people often turn down a reasonable offer and hold out for a tiny chance at the big bucks.

Would a person refuse $5,000 if they were offered it in any other context? In this situation, straightforward maths can’t predict how people will behave.

 

The science of irrationality

What if we go beyond maths? Behavioural science has much to say about what drives people to take specific actions.

In this case, it might suggest people behave more reasonably if they set a realistic goal (such as getting $5,000) and position the goal in a powerful motivational context (such as planning to use the money to pay for a holiday).

Yet time and again even people with clear, achievable goals are swept up by emotion and context. At the right time and place, they will believe that luck is with them and refuse a $5,000 offer in the hope of something bigger.

Nevertheless, researchers have found ways to understand the behaviour of Deal or No Deal contestants by combining ideas from mathematics, economics and the study of behaviour around risky choices.

In essence, the researchers found contestants’ decisions are “path-dependent”. This means their choice to accept a bank offer depends not only on their goal and the odds, but also the choices they have already made.

Group behaviours

Deal or No Deal, of course, is largely about individuals making decisions in a certain context. But when we’re trying to understand the spread of disease, we’re interested in how whole groups of people behave.

This is the realm of social psychology, where group behaviours and attitudes can influence individual actions. In some ways this makes groups easier to predict, and it’s where combining mathematics and behavioural science really starts to produce results.

Although some mass behaviours at the start of the COVID pandemic were highly visible – like panic-buying toilet paper – others were not. Mobility data from Google showed people were choosing to limit their own movement, for example, before any mandated restrictions were in place.

Feedback loops

Fear and perceived risk can promote self-preservation through positive mass behaviours. For example, as more sickness appears in the community, people are more likely to act to prevent themselves getting sick.

These actions in turn have a direct impact on the spread of the disease, which further affects human behaviour, and so on. Many mathematical models of how diseases spread have failed to take this feedback loop into account.

Our new study is a step toward combining population disease spread modelling with mass behaviour modelling, aimed at understanding the links between behaviour and infection.

Our framework accounts for dynamic and self-driven protective health behaviours in the presence of an infectious disease. This puts us in a better position to make informed choices and policy recommendations for future epidemics.

Notably, our approach allows us to understand how mass behaviours influence how great a burden the disease will impose on the population in the long term. There is still much work to develop in this area.

To better understand human behaviour from a mathematical perspective, we will need better data around human choices in the presence of an infectious disease. This lets us pick out patterns that can be used for prediction.

Predicting behaviour

So, to come back to the question: can we predict human behaviour? Well, it depends. Many factors contribute to our choices: emotion, context, risk perception, social observation, fear, excitement.

Understanding which of these factors to explore with mathematics is no easy feat. However, when society faces so many challenges related to changes in mass behaviour – from infectious diseases to climate change – using mathematics to describe and predict patterns is a powerful tool.

But no single discipline can provide the answer to global challenges which need changes in human behaviour at scale. We will need more interdisciplinary teams to achieve meaningful impacts.

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Credit of the article given to The Conversation

 

How can disaster response teams benefit from understanding how people most efficiently pick strawberries together, or how they choose the perfect ice cream shop with friends?

All these scenarios are based on the very fundamental question of how and when human groups manage to adapt collectively to different circumstances. Two recent studies on collective dynamics by the Cluster of Excellence Science of Intelligence (SCIoI) in Berlin, Germany, lay the groundwork to promote better coordinated operations while showcasing the potential of the Cluster’s analytic-synthetic loop approach: an interconnection of a human-focused (analytic) study with a novel computer simulation (synthetic).

By understanding how individual decisions impact group performance, we can possibly enhance emergency services and everyday teamwork, and further develop effective decentralized robotic systems that could benefit society in multiple ways (think robots that explore potentially dangerous places such as a crumbling building).

How groups of people move and make collective decisions (analytic side)

Through a naturalistic immersive-reality experiment, Science of Intelligence researchers have presented new findings on the dynamics of human collective behaviour. The study “Collective incentives reduce over-exploitation of social information in unconstrained human groups,” published in Nature Communications, explores how individual decisions shape collective outcomes in realistic group settings.

In the experiment, groups of participants freely moved through a 3D virtual environment similar to a video game, searching for hidden treasures. This resembled scenario of hunting and gathering, extinguishing wildfires, or searching for survivors together.

The researchers varied how resources were distributed and how participants were incentivized. Individuals often benefited from staying close to others and taking advantage of their discoveries. However, on the group level, this caused poor group performance.

“It’s a bit like copying homework: You are benefitting yourself but not contributing to group performance in the long run,” said Dominik Deffner. “But it also turned out that rewards on the group level, similar to bonuses for team achievements, reduced this copying behaviour and thereby improved group performance.”

To extract individual decisions from naturalistic societal interactions, the researchers developed a computational modelhelping them to understand key decision-making processes. This model inferred sequences of decisions from visual and movement data and showed that group rewards made people less likely to follow social information, encouraging them to become more selective over time.

The study also looked at how groups moved and acted over time and space, finding a balance between exploring new areas and using known resources at different times. These findings are important for improving group strategies in many areas, like solving problems in businesses or improving search and rescue operations.

How visual perception and embodiment shapes collective decisions (synthetic side)

In a complementary study, called “Visual social information use in collective foraging” and published in PLOS Computational Biology, researchers introduced a new computational model that explores how individual decisions shape collective behaviour.

The model applies to any realistic situation where groups of people, animals, or robots are searching for rewards together. This computational model addresses two main questions: how do individuals make decisions according to visible information around them? And how do they move in a physical space at the same time?

In this study, a simulated swarm of robots searches for resources in a virtual playground very similar to the one by Deffner described above. The resources are in patches and when depleted, they reappear in new spots. The virtual robots can choose between exploring the environment to find new resource patches, following other robots consuming resources, or staying and consuming resources until they’re gone.

The findings show how simple decisions, for example where to go next, can lead to complex group behaviour.

“The environment plays an important role in how groups work efficiently together” said David Mezey. “When resources are concentrated, working closely together and relying on shared information is the most efficient solution. However, when the resources are spread out it’s better for individuals or smaller subgroups to work independently. This explains some everyday group behaviours that many of us may be familiar with.

“Imagine a group of firefighters tasked with putting out a large fire in the forest. If the flames are concentrated in one well-defined area, the best strategy would be for all of them to work together in that specific location. But, if the fire has already spread across patches, it is more effective for the firefighters to split into smaller subgroups to find and tackle the distributed patches independently.”

The study also highlights how physical and visual limitations affect group performance. The authors included real-world limitations in their computer simulations, for example, individuals bumping into each other when too close, or blocking each other’s views.

They discovered that these limitations can fundamentally change collective behaviour and, interestingly, in some cases, even improve group performance. For example, virtual robots with restricted vision focus only on nearby individuals, improving their search strategy. Imagine strawberry picking with friends: even if a friend finds some fruits far away from you, you might want to stay in your area to avoid reaching an already empty patch.

These limitations had similar effects on virtual robots, and this study shows why it’s so important to think about such limitations when studying group behaviour.

Analysing, synthesizing and looping back again

We’ve understood certain animal collective behaviours especially in fish, birds and sheep through simple interaction rules often based on physical principles. However, to understand collective behaviour in humans, we need to understand all the individual decisions that people make and the cognitive processes that produce them.

In the two studies, the researchers link individual cognition to collective outcomes in realistic environments and thus explain complex group outcomes based on individual decisions. In other words, insights from the human-focused study (analytic side) are used to create computational models (synthetic side) that can be applied to better understand phenomena such as collective behaviour and social learning (loop).

This provides a fruitful path forward, hopefully making it possible to understand, predict, and guide collective outcomes in crucial areas.Together, these studies offer a comprehensive understanding of the mechanisms linking individual cognition to collective outcomes in collective foraging tasks, providing new perspectives on optimizing collective performance across various fields. The implications for decentralized robotic systems are particularly promising.

Understanding realistic constraints on group performance might reshape how we develop efficient swarm robotic applications in the future.

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Credit of the article given to Maria Ott, Technische Universität Berlin – Science of Intelligence

The classic “secretary problem” involves interviewing job candidates in a random order. Candidates are interviewed one by one, and the interviewer ranks them. After each interview, the interviewer must either accept or reject the candidate. If they accept a candidate, the process stops; otherwise, the next candidate is interviewed and so on.

Of course, if a candidate is accepted, then a subsequent candidate who may well be better suited to the job will never be interviewed and so is never selected. Nevertheless, the goal is to maximize the probability of selecting the best candidate.

Since its introduction in the 1950s, this problem has been researched extensively because it is a fundamental example of optimal stopping problems. Many variants of the problem, such as multiple choices, regret-permit, and weighted versions, have been studied.

Research published in the International Journal of Mathematics in Operational Research has looked at a variant of the secretary problem.

Yu Wu of Southwest Jiaotong University in Chengdu, Sichuan, China, explains that in this variant the interviewer has a “look-ahead privilege” and can see some of the details regarding subsequent candidates before making a decision about the current interviewee at each step. Wu defines the degree of look-ahead privilege as the number of candidates interviewed between the first interview and the final decision.

In one sense, this version of the problem is a more realistic sequential interviewing scenario wherein the interviewer may well have seen the resumes of all candidates or perhaps even have met them all before the interviewing process begins.

This contrasts with the blind sequential interviewing of the classic problem and allows a decision to be deferred until subsequent candidates have been interviewed.

It should therefore allow a better decision to be made regarding the choice of candidate who is offered the job. This is the first time this variant has been studied in detail in this way.

Wu has proposed a general optimal decision strategy framework to maximize the probability of selecting the best candidate. He focuses on a specific look-ahead privilege structure, applying the strategy framework to derive a closed-form probability of success.

This provides for an optimal strategy. Computational experiments have been carried out to explore the relationships between the various factors in the process and to show how this variant of the problem can be solved.

 

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Credit of the article given to David Bradley, Inderscience

 

In times of crisis, effective humanitarian aid depends largely on the fast and efficient allocation of resources and personnel. Accurate data about the locations and movements of affected people in these situations is essential for this.

Researchers from the University of Tokyo, working with the World Bank, have produced a framework to analyse and visualize population mobility data, which could help in such cases. The research is publishedin the journal Scientific Reports.

Wars, famines, outbreaks, natural disasters—there are unfortunately many reasons why populations might be forced or feel compelled to leave their homes in search of refuge elsewhere, and these cases continue to grow.

The United Nations estimated in 2023 that there were more than 100 million forcibly displaced people in the world. More than 62 million of these individuals are considered internally displaced people (IDPs), those in particularly vulnerable situations due to being stuck within the borders of their countries, from which they might be trying to flee.

The circumstances that displace populations are inevitably chaotic and certainly, but not exclusively, in cases of conflict, information infrastructure can be impeded. So, authorities and agencies trying to get a handle on crises are often operating with limited data on the people they are trying to help. But the lack of data alone is not the only problem; being able to easily interpret data, so that nonexperts can make effective decisions based on it, is also an issue, especially in rapidly evolving situations where the stakes, and tensions, are high.

“It’s practically impossible to provide aid agencies and others with accurate real time data on affected populations. The available data will often be too fragmented to be useful directly,” said Associate Professor Yuya Shibuya from the Interfaculty Initiative in Information Studies.

“There have been many efforts to use GPS data for such things, and in normal situations, it has been shown to be useful to model population behaviour. But in times of crisis, patterns of predictability break down and the quality of data decreases.

“As data scientists, we explore ways to mitigate these problems and have developed a tracking framework for monitoring population movements by studying IDPs displaced in Russia’s invasion of Ukraine in 2022.”

Even though Ukraine has good enough network coverage throughout to acquire GPS data, the data generated is not representative of the entire population. There are also privacy concerns, and likely other significant gaps in data due to the nature of conflict itself. As such, it’s no trivial task to model the way populations move.

Shibuya and her team had access to a limited dataset which covered the period a few weeks before and a few weeks after the initial invasion on Feb. 24, 2022. This data contained more than 9 million location records from more than 100,000 anonymous IDPs who opted in to share their location data.

“From these records, we could estimate people’s home locations at the regional level based on regular patterns in advance of the invasion. To make sure this limited data could be used to represent the entire population, we compared our estimates to survey data from the International Organization for Migration of the U.N.,” said Shibuya.

“From there, we looked at when and where people moved just prior to and for some time after the invasion began. The majority of IDPs were from the capital, Kyiv, and some people left as early as five weeks before Feb. 24, perhaps in anticipation, though it was two weeks after that day that four times as many people left. However, a week later still, there was evidence some people started to return.”

That some people return to afflicted areas is just one factor that confounds population mobility models—in actual fact, people may move between locations, sometimes multiple times. Trying to represent this with a simple map with arrows to show populations could get cluttered fast. Shibuya’s team used color-coded charts to visualize its data, which allow you to see population movements in and out of regions at different times, or dynamic data, in a single image.

“WE want visualizations like these to help humanitarian agencies gauge how to allocate human resources and physical resources like food and medicine. As they tell you about dynamic changes in populations, not just A to B movements, WEthink it could mean aid gets to where it’s needed and when it’s needed more efficiently, reducing waste and overheads,” said Shibuya.

“Another thing we found that could be useful is that people’s migration patterns vary, and socioeconomic status seems to be a factor in this. People from more affluent areas tended to move farther from their homes than others. There is demographic diversity and good simulations ought to reflect this diversity and not make too many assumptions.”

The team worked with the World Bank on this study, as the international organization could provide the data necessary for the analyses. They hope to look into other kinds of situations too, such as natural disasters, political conflicts, environmental issues and more. Ultimately, by performing research like this, Shibuya hopes to produce better general models of human behaviour in crisis situations in order to alleviate some of the impacts those situations can create.

 

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Credit of the article given to University of Tokyo

 

 

One hundred years ago, in the 1924 Paris Olympics, American Johnny Weissmuller won the men’s 100m freestyle with a time of 59 seconds. Nearly 100 years later, in the most recent Olympics, the delayed 2020 Games in Tokyo, Caeleb Dressel took home the same event with a time that was 12 seconds faster than Weissmuller’s.

Swimming times across the board have become much faster over the past century, a result of several factors, including innovations in training, recovery strategy, nutrition, and some equipment advances.

One component in the improvement in swimming performances over the years is the role of biomechanics—that is, how swimmers optimize their stroke, whether it’s the backstroke, breaststroke, butterfly, or freestyle.

Swimmers for decades have experimented with different techniques to gain an edge over their competitors. But in more recent years, the application of mathematics and science principles as well as the use of wearable sensor technology in training regimens has allowed some athletes to elevate their performances to new heights, including members of the University of Virginia’s swim team.

 

In a new research paper, a UVA professor who introduced these concepts and methods to the team and some of the swimmers who have embraced this novel approach to training lay out how the use of data is helping to transform how competitive swimmers become elite. The paper is published in The Mathematical Intelligencer journal.

‘Swimming in data’

Ken Ono thought his time working with swim teams was over. Ono—a UVA mathematics professor, professor of data science by courtesy, and STEM advisor to the University provost—had spent years working with competitive swimmers, first during his time at Emory University in Atlanta and then with other college teams, including Olympians, over the years.

However, he didn’t plan to continue that aspect of his work when he arrived at UVA in 2019. But after a meeting with Todd DeSorbo, who took over the UVA swim program in 2017, Ono soon found himself once again working closely with athletes, beginning his work as a consultant for the team during the 2020-21 season. The UVA women’s swim team would win their first of four consecutive national championships that year.

“One of the things that WElike quite a bit about this work is that swimming is crazy hard,” Ono said. “We were never meant to be swimmers, and it is both an athletic challenge as well as a scientific challenge—it has it all.”

Last fall, following a suggestion from DeSorbo, Ono offered a class that outlined the science-focused approach to improving swimming performances that had proven so successful at UVA, but he wanted to make sure there were no misconceptions about the seriousness of the material.

“We don’t want people thinking that it’s a cupcake course that’s offered for the swimmers,” Ono said.

So, Ono teamed up with UVA students Kate Douglass, August Lamb, and Will Tenpas, as well as MIT graduate student Jerry Lu, who had worked with Ono and the UVA swim team while an undergraduate at the University, to produce a paper that covered the key elements of the class and Ono’s work with swimmers.

Tenpas and Lamb both recently completed the residential master’s program at the School of Data Science as well as their careers as competitive collegiate swimmers. Douglass, who finished her UVA swim career in 2023 as one of the most decorated swimmers in NCAA history, is a graduate student in statistics at the University and is set to compete in the Paris Olympics after winning a bronze medal in the 2020 games.

The group drafted the paper, which they titled “Swimming in Data,” over the course of two months, and it was quickly accepted by The Mathematical Intelligencer. There, Ono said, it has become one of the most-read papers on a STEM subject since tracking began. In July, a version of the paper will also be published in Scientific American.

“It seems to have taken off,” Ono said.

The impact of digital twins

After outlining the evolution of swimming over the past 100 years, the paper explains how an understanding of math and physics, combined with the use of technology to acquire individual-level data, can help maximize performances.

Essential to understanding the scientific principles involved with the swimming stroke, the paper says, are Newton’s laws of motion. The laws—which cover inertia, the idea that acceleration depends on an object’s mass and the amount of force applied, and the principle that an action exerted by an object on another elicits an equal and opposite reaction—help simplify how one should think about the many biomechanical factors involved with swimming, according to Tenpas.

“There are all sorts of flexibility limitations. You have water moving at you, you have wakes, you have currents—it’s easy to kind of get paralyzed by the number of factors,” said Tenpas, who after four years at Duke, where he studied mechanical engineering, enrolled in UVA’s data science program and joined the swim team with a fifth year of eligibility.

“WEthink having Newton’s laws is nice as it gives you this baseline we can all agree on,” he added.

It’s a way to understand pool mechanics given the counterintuitive motion swimmers must use to propel themselves forward, according to Ono.

“The reason that we go to great extent to recall Newton’s laws of motion is so that we can break down the factors that matter when you test a swimmer,” he said.

To conduct these tests, Ono and his team use sensors that can be placed on swimmers’ wrists, ankles, or backs to gather acceleration data, measured as inertial measurement units. That information is then used to generate what are called digital twins, which precisely replicate a swimmer’s movements.

These twins reveal strengths and weaknesses, allowing Ono and the coaching staff to make recommendations on technique and strategy—such as how to reduce drag force, a swimmer’s true opponent—that will result in immediate improvement. In fact, through the analysis of data and the use of Newton’s laws, it is possible to make an accurate prediction about how much time a swimmer can save by making a given adjustment.

Lamb, who swam for UVA for five years while a computer science undergrad, then as a data science master’s student, likened digital twins to a feature in the popular Nintendo game Mario Kart where you can race against a ghost version of yourself.

“Being able to have this resource where you can test for one month and then spend a month or two making that adjustment and then test again and see what the difference is—it’s an incredibly valuable resource,” he said.

To understand the potential of digital twins, one need only look at the example of Douglass, one of the co-authors, who is cited in the paper.

A flaw was identified in her head position in the 200m breaststroke. Using her digital twin, Ono and the coaching staff were able to quantify how much time she could save per streamline glide by making a modification, given her obvious talent and aerobic capacity. She did, and the results were remarkable. In November 2020, when her technique was tested, the 200m breaststroke wasn’t even on her event list. Three years later, she held the American record.

‘Everyone’s doing it now’

Swimming will be front and center in the national consciousness this summer. First, the U.S. Olympic Team Trials will be held in Indianapolis in June, leading up to the Paris Olympics in July and August, where DeSorbo, UVA’s coach who embraced Ono’s data-driven strategic advice, will lead the women’s team.

Many aspiring swimmers will undoubtedly be watching over the coming weeks, wondering how they might realize their full athletic potential at whatever level that might be.

For those who have access to technology and data about their technique, Tenpas encourages young swimmers to take advantage.

He noted the significant amount of time a swimmer must put in to reach the highest levels of the sport, estimating that he had been swimming six times per week since he was 12 years old.

“If you’re going to put all of this work in, at least do it smart,” Tenpas said.

At the same time, Lamb urged young swimmers who may not yet have access to this technology to not lose faith in their potential to improve.

“While this is an incredibly useful tool to make improvements to your technique and to your stroke, it’s not the end all, be all,” he said.

“There are so many different ways to make improvements, and we’re hopeful that this will become more accessible as time goes on,” Lamb said of the data methods used at UVA.

As for where this is all going, with the rapidly expanding use and availability of data and wearable technology, Ono thinks his scientific approach to crafting swimming strategies will soon be the norm.

“We think five years from now, our story won’t be a story. It’ll be, “Oh, everyone’s doing it now,'” he said.

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Credit of the article given to Cooper Allen, University of Virginia