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Math experts have developed new ways to provide further evidence for human-caused global heating and predict how close Earth is to reaching dangerous climate tipping points.

Tipping points occur when lots of small changes in climate build up to create a sudden, large change. Passing these thresholds leads to accelerated warming and extreme weather events.

For example, in years to come, the Atlantic Meridional Overturning Circulation (AMOC), is at risk of collapsing. The AMOC is an ocean current transport system that brings warm waterto the North Atlantic and helps to regulate temperatures in Europe and North America. If it collapses, the regional and global climate may become more erratic.

In July 2023, a study suggested the AMOC could collapse any time between 2025 and 2095. Another recent study, from October 2023, indicates that we are in dangerous proximity of the collapse of the Greenland ice sheet, yet with some hope of avoiding it if proper action is taken.

Now, a study published in the journal Nature Reviews Physics combines mathematics and physics to study climate change across time scales. It will help scientists refine their predictions for AMOC’s collapse as well as help them understand the proximity to various other climate tipping points.

Lead author Professor Valerio Lucarini, Professor of Statistical Mechanics at the University of Reading, said, “Our study provides academics and policymakers with rigorous mathematical tools needed to understand and predict climate change, and, specifically to detect and avoid climate tipping points resulting from human activities. It gives us a unified perspective linking climate variability and climate change. Our approach allows one to seamlessly study gradual climate changes and tipping points.

“We now have a robust framework for capturing the richness of climate dynamics across timescales. The findings provide tools for building up further evidence for human-caused global heating.”

Innovations and collaborations

The work will significantly advance the development of climate models and theories to generate more accurate predictions of climate change and evaluation of tipping point proximity, helping to inform mitigation policies and climate adaptation strategies.

The research critically investigated 2021 Nobel Prize in Physics winner Klaus Hasselmann’s stochastic modeling approach, which revolutionized climate change analysis. The new study refined Hasselmann’s techniques using recent tools developed within the mathematical and physical scientific literature.

The scientists noted how their methodology allows to better understand the nearing of the collapse of the AMOC. Observations show the AMOC is weakening. In addition to AMOC, the new method could be used to detect proximity to tipping points for:

• The collapse of ecosystems
• The melting of Greenland ice sheets
• The dieback of the Amazon rainforest

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to University of Reading

Chinese ice-ray lattice, or “binglie” as it is called in Chinese, is an intricate pattern that looks like cracked ice and is a common decorative element used in traditional Chinese window designs.

Originally inspired by fragmented patterns on ice or crackle-glazed ceramic surfaces, the design represents the melting of the ice and the beginning of a thriving spring.

When Dr. Iasef Md Rian, now an Associate Professor at Xi’an Jiaotong-Liverpool University’s Department of Architecture, arrived in China for the first time in 2019, he was immediately captivated by the latticed window designs in the classical gardens of Suzhou.

“Classical gardens in China strike me as very different from the Western ones, which are more symmetrical and organized,” he says. “Chinese gardens, however, have a more natural formation in their layout and design. The ice-ray window design is one of the manifestations.”

Having focused on fractal geometry in architectural design for many years, Dr. Rian felt an urge to explore the beauty in the patterns.

“My mind is always looking for this kind of inspiration source, so I was motivated right away to study the underlying geometric principles of the ice-ray patterns, he says.”

Revealing the underlying rule

Dr. Rian finds that the rule of creating ice-ray patterns is actually very simple.

He explains, “Take Type 1 as an example; a square is first divided into two quadrilaterals, and then each quadrilateral is further divided into two quadrilaterals. In each step, the proportions of the subdivided quadrilaterals are different, and this is how the random pattern is created using a simple rule.

“Through this configuration, Chinese craftsmen might have intended to increase its firmness so it can function as a window fence to provide protection. The random configuration of ice-ray lattices provides multi-angled connections, which transform the window into a collection of resultant forces and uniform stress distribution, in turn achieving a unique degree of stiffness.

“The microstructure of trabecular bone tissue in our own bodies serves as an excellent natural example of the potential of random lattices. It balances high stiffness, which contributes to strength, with a surprisingly lightweight structure.”

Dr. Rian recently published a paper in Frontiers of Architectural Research that explores the geometric qualities of ice-ray patterns and expands the possibilities of integrating random patterns into structural designs, especially the lattice shell design, which is often used in spherical domes and curved structures.

“In my research, I developed an algorithm to model the ice-ray patterns for lattice shell designs and assessed their feasibility and effectiveness compared to conventional gridshells. These gridshells, made from regular grids, contrast with continuous shells.

“While regular gridshells perform well under uniform loads, the ice-ray lattice offers strength under asymmetric loads. Some ice-ray patterns, resulting from optimization, surprisingly provide better strength than regular gridshells under self-weight. There is also an additional aesthetic advantage when applying the ice-ray pattern to a lattice shell design.

“I extend the application of this pattern to curved surfaces, which helps to unlock its potential in the geometric, structural, and constructional aspects of lattice shell design,” he says.

Dr. Rian has also integrated ice-ray patterns and complex geometries into his teaching. In 2022, he organized a workshop for students to design ice-ray lattice roofs.

He explains that learning the concept of fractal geometry can really push the students’ ideas toward a unique design.

“This is very different from what they’ve learned in high school. In learning to create this geometry system, they will also learn computational modeling and simulations. In the end, they’ll get comprehensive knowledge of advanced architectural and digital design,” he says.

Rediscovering traditional designs

To extend the research in this field, Dr. Rian is investigating the effectiveness of complex geometry in various aspects like micro-scale material design and structural design.

He says, “For instance, in facade design, we usually use conventional or parametric geometry to design regular shapes. However, the random shapes designed with complex geometry can offer a more natural impression and daylight penetration.”

He encourages design students and researchers to learn from the past.

“Any traditional design has a hidden rule in it. We can now use digital technologies and advanced tools to extend and expand the knowledge of traditional craftsmanship for contemporary design.

“There are many inspirations behind the traditional designs, and those principles can really inspire us designers to make innovative designs for the future,” he says.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to Yi Qian, Xi’an jiaotong-Liverpool University

Homeschooled children don’t always get a well-rounded curriculum. miniseries via Getty Images

Homeschooling is the fastest-growing education setting in the United States. More than 3 million students were educated at home in the 2021-22 school year, up from 2.5 million in the spring of 2019. Current estimates from the U.S. Census Bureau indicate that there are 3.62 million students homeschooled in the United States. That’s a meteoric increase from about 1 million in 1997.

Some experts, including Harvard law professor Elizabeth Bartholet, find the increase a cause to call for greater regulation. University of Washington education policy professor David Knight agrees, citing a lack of accountability and measures of student progress. Knight also worries about an absence of certain disciplines such as social studies that public schools are required to teach.

For those of us who have researched the homeschool movement and studied its past, these are not new concerns. So, what do we know about homeschooling and preparedness for college?

Data shows homeschooled students fare well

In 2020, we reviewed the evidence about how well homeschooling prepares people for college, career and life and published what we learned in a book chapter titled: “Life after Homeschool.”

We found evidence that homeschooled students are just as prepared academically for higher education as traditionally schooled peers. In one study, researchers drew a sample of 825,672 students – including 732 students who had been homeschooled – and found the homeschooled group scored higher on several measures of college preparedness, including the SAT and first-year GPA in college.

Ave Maria University education professor Marc Snyder came to similar results in a 2013 study. Snyder compared homeschooled and traditional students at his Catholic university in Florida to find the average ACT scores for homeschooled students was 26. Public school students averaged 24.22, and students who attended Catholic schools averaged 24.53.

Snyder’s study reinforces data from the ACT itself. The testing outlet reported that from 2001-2019, the average ACT scores for homeschooled students trended up, while public school students’ scores declined slightly. In 2023, the national average on the ACT was 19.9; the average for homeschoolers was 22.8.

Areas of concern abound as homeschool growth accelerates

Still, calls for regulation persist because of a host of challenges homeschooled students present. The Coalition for Responsible Home Education wants states to require minimal qualifications of a high school diploma or GED for the parent providing primary instruction, instruction for students in the same subjects as in public schools, and annual standardized assessments. In some states, they note, parents don’t even have to tell their local school district of their intent to homeschool.

The pro-regulation side points to studies showing homeschooled students feel less prepared for college and are four times less likely to go to college after high school. Homeschool students also take an average of one fewer math and science course than traditional peers.

Homeschooled students also often lack resources and guidance provided in traditional high schools for college prep. And social challenges abound when these students transition; a study of seven homeschooled graduates in Pennsylvania found students struggling to maintain their existing moral beliefs related to drinking, drug use and sexual norms, with the majority admitting they changed some beliefs and practices.

There’s also data that shows homeschooled students find the more structured academic environment on university campuses to be difficult to adjust to after a more lax experience learning at home.

Still, efforts to regulate homeschooling face opposition from parents as well as advocacy groups such as the Home School Legal Defense Association. In March 2024, for example, these forces defeated an attempt in New Hampshire to require homeschool students to take a statewide exam.

3 ways to improve homeschooling

To help homeschooled students transition to college, we recommend parents take three steps to better prepare their kids.

• Prioritize math and scienceto help address the math and science gap. Parents can use online courses offered through virtual high schools or employ tutors.
• Enroll in dual-credit or community college coursesto provide a taste of the structure of college life and to interact with peers from diverse backgrounds.
• Talk to children about the diversity of perspectivesthey will encounter at college. This can help prepare them for how to negotiate and respect the opinions of others.

Homeschooled students can successfully transition to college and compete with their peers. The challenges they face are entirely foreseeable, which means they can be addressed easily.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to The Conversation

Australian teenagers have more disruptive maths classrooms and experience bullying at greater levels than the OECD average, a new report shows.

But in better news, Australian students report high levels of curiosity, which is important for both enjoyment and achievement at school.

The report, by the Australian Council for Educational Research (ACER) analysed questionnaire responses from more than 13,430 Australian students and 743 principals, to understand how their school experiences impact on maths performance.

What is the research?

This is the second report exploring Australian data from the 2022 Programme for International Student Assessment (PISA).

Australian teenagers have more disruptive maths classrooms and experience bullying at greater levels than the OECD average, a new report shows.

But in better news, Australian students report high levels of curiosity, which is important for both enjoyment and achievement at school.

The report, by the Australian Council for Educational Research (ACER) analysed questionnaire responses from more than 13,430 Australian students and 743 principals, to understand how their school experiences impact on maths performance.

What is the research?

This is the second report exploring Australian data from the 2022 Programme for International Student Assessment (PISA).

Author provided (no reuse)

The advantage gap

ACER’s first PISA 2022 report showed students from disadvantaged socioeconomic backgrounds were six times more likely to be low performers in maths than advantaged students.

It also showed the achievement gap between these two groups had grown by 19 points (or about one year of learning) since 2018.

This second report provides more insight into the challenges faced by disadvantaged students.

It shows a greater proportion of this group report learning in a less favourable disciplinary climate, experience lower levels of teacher support and feel less safe at school than their more advantaged peers.

Girls are more worried than boys

In last year’s report, the mean score for maths performance across OECD countries was nine points lower for girls than it was for boys. In Australia, the difference was 12 points.

The new report also showed differences in wellbeing. In 2022, a greater number of girls reported they panicked easily (58% compared to 23% of boys), got nervous easily (71% compared to 39%) and felt nervous about approaching exams (75% compared 49%).

Almost double the percentage of girls reported feeling anxious when they didn’t have their “digital device” near them (20% compared to 11%). Whether this was a phone, tablet or computer was not specified.

Overall, students who reported feeling anxious when they did not have their device near them scored 37 points lower on the maths test than those who reported never feeling this way or feeling it “half the time”.

Author provided (no reuse)

Curiosity a strong marker for performance

Curiosity was measured for the first time in PISA 2022. This included student behaviours such as asking questions, developing hypotheses, knowing how things work, learning new things and boredom.

Students in Singapore, the highest performing country in PISA 2022, showed the greatest levels of curiosity, followed by Korea and Canada. These were the only comparison countries to have a significantly higher curiosity score than Australia, with the Netherlands showing the lowest curiosity score overall.

As ACER researchers note: “curiosity is associated with greater psychological wellbeing” and “leads to more enjoyment and participation in school and higher academic achievement”.

They found Australia’s foreign-born students reported being more curious than Australian-born students, with 74% compared to 66% reporting that they liked learning new things.

What next?

Their findings highlight concerns for Australian education, such as persistently poor outcomes for disadvantaged students and higher stress levels experienced by girls. We need to better understand why this is happening.

But they also identify behaviours and conditions – such as high levels of curiosity – that contribute to a good maths performance and can be used by schools and policymakers to plan for better outcomes.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to The Conversation

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.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to The Conversation

In the 18th century, the philosopher David Hume observed that induction—inferring the future based on what’s happened in the past—can never be reliable. In 1997, SFI Professor David Wolpert with his colleague Bill Macready made Hume’s observation mathematically precise, showing that it’s impossible for any inference algorithm (such as machine learning or genetic algorithms) to be consistently better than any other for every possible real-world situation.

Over the next decade, the pair proved a series of theorems about this that were dubbed the “no-free-lunch” theorems. These proved that one algorithm could, in fact, be a bit better than another in most circumstances—but only at the cost of being far worse in the remaining circumstances.

These theorems have been extremely controversial since their inception, since they punctured the claims of many researchers that the algorithms they had developed were superior to other algorithms. As part of the controversy, in 2019, the philosopher Gerhard Schulz wrote a book wrestling with the implications of Hume’s and Wolpert’s work.

A special issue of the Journal for General Philosophy of Science published in March 2023 is devoted to Schulz’s book, and includes an article by Wolpert himself, in which he reviews the “no-free-lunch” theorems, pointing out that there are also many “free-lunch” theorems.

He states that the meta-induction algorithms that Schurz advocates as a “solution to Hume’s problem” are simply examples of such a free lunch based on correlations among the generalization errors of induction algorithms. Wolpert concludes that the prior algorithms that Schurz advocates, which is uniform over bit frequencies rather than bit patterns, is contradicted by thousands of experiments in statistical physics and by the great success of the maximum entropy procedure in inductive inference.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to Santa Fe Institute

Finding bats is hard. They are small, fast and they primarily fly at night.  But our new research could improve the way conservationists find bat roosts. We’ve developed a new algorithm that significantly reduces the area that needs to be searched, which could save time and cut labour cost.

Of course, you may wonder why we would want to find bats in the first place. But these flying mammals are natural pest controllers and pollinators, and they help disperse seeds. So they are extremely useful in contributing to the health of our environment.

Despite their importance though, bat habitats are threatened by human activities such as increased lighting, noise and land use. To ensure that we can study and enhance the health of our bat population, we need to locate their roosts. But finding bat roosts is a bit like finding a needle in a haystack.

Our previous work measured and modelled the motion of greater horseshoe bats in flight. Having such a model means we can predict where bats will be, depending on their roost position. But the position of the roost is something we often don’t know.

Our new research combines our previous mathematical model of bat motion with data gathered from acoustic recorders known as “bat detectors”. These bat detectors are placed around the environment and left there for several nights.

Seeing with sound

Bats use echolocation, which allows them to “see with sound” when they’re flying. If these ultrasonic calls are made within ten to 15 metres of a bat detector, the device is triggered to make a recording, providing an accurate record of where and when a bat was present.

The sound recordings also provide clues about the identity of the species. Greater horseshoe bats make a very distinctive “warbling” call at almost exactly 82kHz in frequency, so we can easily tell whether the species is present or not.

Assuming that a bat detector’s batteries last for a few nights, its memory card is not full, and the units are not stolen or vandalised, then we can use the bat call data to generate a map that shows the proportion of bat calls at each detector location.

Our model can also be used to predict the proportion of bat calls based on a given roost location. So, we split the environment up into a grid and simulate bats flying from each grid square. The grid square, or squares, whose simulations best reproduce the bat detector data will then be the most likely locations of the roost.

This simple algorithm can then be applied to whole terrains, meaning that we can create a map of likely roost locations. Cutting out the regions that are least likely to contain the roost can mean we shrink the search space to less than 1% of the initially surveyed area. Simplifying the process of finding bat roosts allows more of an ecologist’s time to be spent on conservation projects, rather than laborious searching.

In 2022, we developed an app that uses publicly available data to predict bat flight lines. At the moment the app can help ecologists, developers or local authority planners, know how the environment is used by bats. However, it needs a roost location to be specified first, and this information is not always known. Our new research removes this barrier, making the app easier to use.

Our work offers a way of identifying likely roost locations. These estimates can then be verified either by directly observing particular features, or by capturing bats at a nearby location and following them back home, using radiotracking.

Over the past two decades, bat detectors have gone from simple hand-held machines to high-performance devices that can collect data for days at a time. Yet they are usually deployed only to identify bat species. We have shown they can be used to identify the areas most likely to contain bat roosts, uncovering critical information about these most secretive of animals.

We hope that this will provide further tools for ecologists to optimise the initial microphone detector locations, thereby providing a holistic way of detecting bat roosts.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to Thomas Woolley and Fiona Mathews, The Conversation

“We wanted to investigate how second pillar pension funds react to financial crises and how to protect them from the crises,” says Kaunas University of Technology (KTU) professor Dr. Audrius Kabašinskas, who, together with his team, discovered a way to achieve this goal. The discovery in question is the development of stress tests for pension funds. Lithuanian researchers were the first in the world to come up with such an adaptation of the stress tests.

Stress tests are usually carried out on banks or other financial institutions to allow market regulators to determine and assess their ability to withstand adverse economic conditions.

According to the professor at KTU Faculty of Mathematics and Natural Sciences, this innovative pension fund stress testing approach will benefit both regulators and pension fund managers.

“Making sure your pension fund is resilient to harsh financial market conditions will help you sleep better, save more, and have increased trust in your funds and the pension system itself,” Kabašinskas adds.

Results based on two major crises

First, the study needed to collect data from previous periods. “Two major events that shocked the whole world—COVID-19 and the first year of Russian invasion of Ukraine—just happened to occur during the project. This allowed us to gather a lot of relevant information and data on changes in the performance of pension funds,” says Kabašinskas.

The Hidden Markov Model (HMM), which, according to a professor at KTU Department of Mathematical Modelling, is quite simple in its principle of operation, helped to forecast future market conditions in this study.

The paper is published in the journal Annals of Operations Research.

“The observation of air temperature could be an analogy for it. All year round, without looking at the calendar, we observe the temperature outside and, based on the temperature level, we decide what time of the year it is. Of course, 15 degrees can occur in winter and sometimes it snows in May but these are random events. The state of the next day depends only on today,” he explains vividly.

According to the KTU researcher, this describes the idea of the Hidden Markov Model: by observing the changes in value, one can judge the state of global markets and try to forecast the future.

“In our study, we observed two well-known investment funds from 2019 to 2022. Collected information helped us identify that global markets at any given moment are in one of four states: no shock regime, a state of shock in stock markets, a state of shock in bond markets, and a state of global financial shock—a global crisis,” says Kabašinskas.

Using certain methods, the research team led by a professor Miloš Kopa representing KTU and Charles University in Prague found that these periods were aligned with the global events in question. Once the transition probabilities between the states were identified, it was possible to link the data of pension funds to these periods and simulate the future evolution of the pension funds’ value.

That’s where the innovation of stress testing came in. The purpose of this test is to determine whether a particular pension fund can deliver positive growth in the future when faced with a shock in the financial markets.

“In our study, we applied several scenarios, extending financial crises and modeling the evolution of fund values over the next 5 years,” says a KTU researcher.

This methodology can be applied not only to pension funds but also to other investments.

Example of Lithuanian pension funds

The research and the new stress tests were carried out on Lithuanian pension funds.

Kabašinskas says that the study revealed several interesting things. Firstly, on average, Lithuanian second pillar pension funds can withstand crises that are twice as long.

“However, the results show that some Lithuanian funds struggle to cope with inflation, while others, the most conservative funds for citizens who are likely to retire within next few years or who have already retired, are very slow in recovering after negative shocks,” adds the KTU expert.

This can be explained by regulatory aspects and the related investment strategy, as stock markets recover several times faster than bond markets, and the above-mentioned funds invest more than 90% in bonds and other less risky instruments.

A complementary study has also been carried out to show how pension funds should change their investment strategy to avoid the drastic negative consequences of various financial crises and shocks.

“Funds that invest heavily in stocks and other risky instruments should increase the number of risk-free instruments slightly, up to 10%, before or after the financial crisis hits. Meanwhile, funds investing mainly in bonds should increase the number of stocks in their holdings. In both cases, the end of the crisis should be followed by a slow return to the typical strategy,” advises a mathematician.

Although the survey did not aim to increase people’s confidence in pension funds, the results showed that Lithuania’s second pillar pension funds are resilient to crisis and are worth trust. Historically they have delivered long-term growth, some have even outperformed inflation and price increases.

“Although short-term changes can be drastic, long-term growth is clearly visible,” says KTU professor Dr. Kabašinskas. “Lithuania, by the way, has a better system than many European countries,” he adds.

For more insights like this, visit our website at www.international-maths-challenge.com.

April 2023 marks the 100th anniversary of the death of mathematician and philosopher John Venn. You may well be familiar with Venn diagrams—the ubiquitous pictures of typically two or three intersecting circles, illustrating the relationships between two or three collections of things.

For example, during the pandemic, Venn diagrams helped to illustrate symptoms of COVID-19 that are distinct from seasonal allergies. They are also often taught to school children and are typically part of the early curriculum for logic and databases in higher education.

Venn was born in Hull, UK, in 1834. His early life in Hull was influenced by his father, an Anglican priest—it was expected John would follow in his footstep. He did initially begin a career in the Anglican church, but later moved into academia at the University of Cambridge.

One of Venn’s major achievements was to find a way to visualize a mathematical area called set theory. Set theory is an area of mathematics which can help to formally describe properties of collections of objects.

For example, we could have a set of cars, C. Within this set, there could be subsets such as the set of electric cars, E, the set of petrol based cars, say P, and the set of diesel powered cars, D. Given these, we can operate on them, for example, to apply car charges to the sets P and D, and a discount to the set E.

These sorts of operations form the basis of databases, as well as being used in many fundamental areas of science. Other major works of Venn’s include probability theory and symbolic logic. Venn had initially used diagrams developed by the Swiss mathematician Leonard Euler to show some relationships between sets, which he then developed into his famous Venn diagrams.

Venn used the diagrams to prove a form of logical statement known as a categorical syllogism. This can be used to model reasoning. Here’s an example: “All computers need power. All AI systems are computers.” We can chain these together to the conclusion that “all AI systems need power.”

Today, we are familiar with such reasoning to illustrate how different collections relate to each other. For example, the SmartArt tool in Microsoft products lets you create a Venn diagram to illustrate the relationships between different sets. In our earlier car example, we could have a diagram showing electric cars, E, and petrol powered cars, P. The set of hybrid cars that have a petrol engine would be in the intersection of P and E.

Logic and computing

The visualization of sets (and databases) is helpful, but the importance of Venn’s work then—and now—is the way they allowed proof of George Boole’s ideas of logic as a formal science.

Venn used his diagrams to illustrate and explore such “symbolic logic”—defending and extending it. Symbolic logic underpins modern computing, and Boolean logic is a key part of the design of modern computer systems—making his work relevant today.

Venn’s work was also crucial to the work of philosopher Bertrand Russell, showing that there are problems that are unsolvable. We can express such problems with sets, in which each is an unsolvable problem. One such unsolvable problem can be expressed with the “Barber paradox.” Suppose we had an article in Wikipedia containing all the articles that don’t contain themselves—a set. Is this new article itself in that set?

Luckily we can visualize that with a Venn diagram with two circles, where one circle is the set of entries that don’t include themselves, A, and the other circle is the set of entries that do include themselves, B.

We can then ask the question: where do we put the article that contains all the articles that don’t contain themselves? Have a think about it, then see where you would put it.

The problem is that it cannot be on the left, as it would contain itself, and would therefore be inconsistent. And it cannot be on the right, as then it would be missing, or incomplete. And it can’t be in both. It must be in one or the other. This paradox illustrates how unsolvable statements can arise—they are valid in terms of expressing them within the logical system, but ultimately unanswerable. We could possibly extend our system to solve this, but then we would end up with another unanswerable question.

Venn’s diagrams were crucial in understanding this. And this area of science is still important, for example when considering the limitations of machine learning and AI, where we may ask questions that cannot be answered.

Venn also had an interest in building mechanical machines—including a bowling machinewhich proved so effective it was able to bowl out some top Australian batsmen of the day.

Following his abstract work on logic, he developed the concept of a logical-diagram machine with a lot of processing power: though this brilliant idea from 1881 would take many decades to appear as modern computers.

We remember Venn here in Hull, with a bridge close to his birthplace decorated with Venn circle inspired artwork. At the University of Hull’s main administration building, there’s an intersection of management and academia which is called the Venn building.

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Credit of the article given to Neil Gordon, The Conversation

With mass shootings happening randomly every year in the United States, it may seem that there is no way to predict where the next horrific event is most likely to occur. In a new study published by the journal Risk Analysis, scientists at Iowa State University calculate the annual probability of a mass shooting in every state and at public places such as shopping malls and schools.

Their new method for quantifying the risk of a mass shooting in specific places could help security officials make informed decisions when planning for emergency events.

For their analysis, Iowa State associate professor Cameron MacKenzie and his doctoral student Xue Lei applied statistical methods and computer simulations to a database of mass shootings recorded from 1966 to 2020 by the Violence Project. The Violence Project defines a mass shooting as an incident with four or more victims killed by a firearm in a public place.

According to the Violence Project, the U.S. has experienced 173 public mass shootings from 1966 to 2020—with at least one mass shooting every year since 1966.

After they generated a probability distribution of annual mass shootings in the U.S., the scientists used two different models to simulate the annual number of mass shootings in each state. The results were used to calculate the expected number of mass shootings and the probability that at least one mass shooting would occur in each state in one year.

The Violence Project also provides the percentage of mass shootings in different types of locations. MacKenzie and Lei used that data to calculate the probability of a mass shooting in nine different types of public locations (including a restaurant, school, workplace, or house of worship) in the states of California and Iowa and also at the two largest high schools in each of those states.

Their findings include the following:

• The states with the greatest risk of a mass shooting are the most populous states: California, Texas, Florida, New York, and Pennsylvania. Together they account for almost 50% of all mass shootings.
• Some states, such as Iowa and Delaware, have never experienced a mass shooting.
• The annual risk of a mass shooting at the largest California high school is about 10 times greater than the risk at the largest Iowa high school.
• The number of mass shootings in the U.S. has increased by about one shooting every 10 years since the 1970s.

Importantly, MacKenzie points out that the probability of a mass shooting at a specific location depends on the definition of a mass shooting. In contrast to the Violence Project, the Gun Violence Archive defines a mass shooting as four or more individuals shot, injured or killed, in any location, not necessarily a public location. As a result, The Gun Violence Archive has collected data on shootings that occur in both public and private locations as well as targeted shootings (i.e., a gang shooting).

When the researchers applied data from The Gun Violence Archive to their models, the predicted number of annual mass shootings was nearly 100 times greater than the forecast based on The Violence Project’s data. The models predicted 639 mass shootings in 2022 with a 95% chance that the U.S. would experience between 567 and 722 mass shootings in that same year.

MacKenzie points out that “most media appear to use this broader definition of mass shootings.” Because of this, he urges that journalists explain how they are defining a mass shooting when reporting the statistical data.

With regard to the danger posed to children at school, MacKenzie explains, that “our results show that it is very, very unlikely that a specific student will attend a K-12 school and experience a mass shooting. But to parents of a child at a school that has experienced a mass shooting, explaining that the school was extremely unlucky provides no comfort.”

While it is important to take precautions, he adds that “we should not live in fear that our children will experience such a horrific event. Mass shootings are very low probability but very high consequence events.”

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Credit of the article given to Society for Risk Analysis