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A side-by-side comparison of a standard flat driver’s side mirror with the mirror designed by Dr. R. Andrew Hicks, mathematics professor at Drexel University. With minimal distortion, Hicks’s mirror shows a much wider field of view (the wide area to the left of the silver car seen in the distance, behind the tree, in this image). Hicks’s mirror has a field of view of about 45 degrees, compared to 15 to 17 degrees of view in a flat mirror. Hicks’s mirror received a US patent in May 2012.

A side mirror that eliminates the dangerous “blind spot” for drivers has now received a U.S. patent. The subtly curved mirror, invented by Drexel University mathematics professor Dr. R. Andrew Hicks, dramatically increases the field of view with minimal distortion.

Traditional flat mirrors on the driver’s side of a vehicle give drivers an accurate sense of the distance of cars behind them but have a very narrow field of view. As a result, there is a region of space behind the car, known as the blind spot, that drivers can’t see via either the side or rear-view mirror. It’s not hard to make a curved mirror that gives a wider field of view; no blind spot; but at the cost of visual distortion and making objects appear smaller and farther away.

Hicks’s driver’s side mirror has a field of view of about 45 degrees, compared to 15 to 17 degrees of view in a flat driver’s side mirror. Unlike in simple curved mirrors that can squash the perceived shape of objects and make straight lines appear curved, in Hicks’s mirror the visual distortions of shapes and straight lines are barely detectable.

Hicks, a professor in Drexel’s College of Arts and Sciences, designed his mirror using a mathematical algorithm that precisely controls the angle of light bouncing off of the curving mirror.

“Imagine that the mirror’s surface is made of many smaller mirrors turned to different angles, like a disco ball,” Hicks said. “The algorithm is a set of calculations to manipulate the direction of each face of the metaphorical disco ball so that each ray of light bouncing off the mirror shows the driver a wide, but not-too-distorted, picture of the scene behind him.”

Hicks noted that, in reality, the mirror does not look like a disco ball up close. There are tens of thousands of such calculations to produce a mirror that has a smooth, nonuniform curve.

Hicks first described the method used to develop this mirror in Optics Letters in 2008

In the United States, regulations dictate that cars coming off of the assembly line must have a flat mirror on the driver’s side. Curved mirrors are allowed for cars’ passenger-side mirrors only if they include the phrase “Objects in mirror are closer than they appear.”

Because of these regulations, Hicks’s mirrors will not be installed on new cars sold in the U.S. any time soon. The mirror may be manufactured and sold as an aftermarket product that drivers and mechanics can install on cars after purchase. Some countries in Europe and Asia do allow slightly curved mirrors on new cars. Hicks has received interest from investors and manufacturers who may pursue opportunities to license and produce the mirror.

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Credit of the article given to Drexel University

EU researchers contributed important knowledge to the field of modular representation theory in the form of proofs and pioneering analyses.

Modular representation theory studies linear actions on finite groups, or groups of a countable (finite) number of elements.

A discussion of finite groups requires definition of several associated terms. The so-called representation of a given finite group can be reduced using a prime integer to get a modular representation of the group (sort of breaking down the whole into the sum of its parts).

Mathematically, an indecomposable or irreducible module of a finite group has only two submodules, the module itself and zero. Vertices and sources are mathematical entities associated with indecomposable modules.

While modular representation theory has evolved tremendously, many issues still remain to be addressed. In particular, modules of symmetric groups, a type of finite group whose elements allow only a certain number of structure-preserving transformations, are an active area of interest.

European researchers supported by funding of the ‘Vertices of simple modules for the symmetric and related finite groups’ (D07.SYMGPS.OX) project sought to develop fast algorithms for computation of vertices and sources of indecomposable modules as well as to study the Auslander-Reiten quiver considered to be part of a presentation of the category of all representations.

Investigators first analysed two-modular Specht modules and the position of Specht modules in the Auslander-Reiten quiver with important definitive results.

In addition, the team produced ground-breaking proofs regarding the Lie module of the symmetric group, shedding light on a topic of mathematics until now clouded in mystery.

Furthermore, the Fiet conjecture was proved and innovative results were obtained regarding vertices of simple modules of symmetric groups.

Overall, the project team provided pioneering work and definitive results and proofs regarding symmetric groups and related finite groups that promise to significantly advance the mathematical field of modular representation theory.

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Credit of the article given to CORDIS

This graphic shows a matter wave hitting a Schrodinger’s hat. The wave inside the container is magnified. Outside, the waves wrap as if they had never encountered any obstacle. Credit: G. Uhlmann, U. of Washington

Invisibility, once the subject of magic or legend, is slowly becoming reality. Over the past five years mathematicians and other scientists have been working on devices that enable invisibility cloaks – perhaps not yet concealing Harry Potter, but at least shielding small objects from detection by microwaves or sound waves.

A University of Washington mathematician is part of an international team working to understand invisibility and extend its possible applications. The group has now devised an amplifier that can boost light, sound or other waves while hiding them inside an invisible container.

“You can isolate and magnify what you want to see, and make the rest invisible,” said corresponding author Gunther Uhlmann, a UW mathematics professor. “You can amplify the waves tremendously. And although the wave has been magnified a lot, you still cannot see what is happening inside the container.”

The findings were published this week in the Proceedings of the National Academy of Sciences.

As a first application, the researchers propose manipulating matter waves, which are the mathematical description of particles in quantum mechanics. The researchers envision building a quantum microscope that could capture quantum waves, the waves of the nanoworld. A quantum microscope could, for example, be used to monitor electronic processes on computer chips.

The authors dubbed their system “Schrödinger’s hat,” referring to the famed Schrödinger’s cat in quantum mechanics. The name is also a nod to the ability to create something from what appears to be nothing.

“In some sense you are doing something magical, because it looks like a particle is being created. It’s like pulling something out of your hat,” Uhlmann said.

Matter waves inside the hat can also be shrunk, though Uhlmann notes that concealing very small objects “is not so interesting.”

Uhlmann, who is on leave at the University of California, Irvine, has been working on invisibility with fellow mathematicians Allan Greenleaf at the University of Rochester, Yaroslav Kurylev at University College London in the U.K., and Matti Lassas at the University of Helsinki in Finland, all of whom are co-authors on the new paper.

The team helped develop the original mathematics to formulate cloaks, which must be realized using a class of engineered materials, dubbed metamaterials, that bend waves so that it appears as if there was no object in their path. The international team in 2007 devised wormholes in which waves disappear in one place and pop up somewhere else.

For this paper, they teamed up with co-author Ulf Leonhardt, a physicist at the University of St. Andrews in Scotland and author on one of the first papers on invisibility.

Recent progress suggests that a Schrodinger’s hat could, in fact, be built for some types of waves.

“From the experimental point of view, I think the most exciting thing is how easy it seems to be to build materials for acoustic cloaking,” Uhlmann said. Wavelengths for microwave, sound and quantum matter waves are longer than light or electromagnetic waves, making it easier to build the materials to cloak objects from observation using these phenomena. “We hope that it’s feasible, but in science you don’t know until you do it,” Uhlmann said. Now that the paper is published, they hope to find collaborators to build a prototype.

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Credit of the article given to University of Washington

The same freezing which is responsible for transforming liquids into glasses can help to predict some patterns observed in prime numbers, according to a team of scientists from Queen Mary, University of London and Bristol University.

At a low enough temperature, water freezes into ice by arranging its molecules into a very regular pattern called crystal. However many other liquids freeze not into crystals, but in much less regular structures called glasses – window glass being the most familiar example. Physicists have developed theories explaining the freezing phenomena, and built models for understanding the properties of glasses.

Now, a researcher from Queen Mary’s School of Mathematical Sciences, together with his colleagues from Bristol have found that frozen glasses may have something common with prime numbers and the patterns behind them.

Dr Fyodorov explained: “The prime numbers are the elements, or building blocks, of arithmetic. Our work provides evidence for a surprising connection between the primes and freezing in certain complex materials in Physics.”

A prime number is a whole number greater than 1 which can only be divided by 1 or itself. Primes play fundamentally important role in pure mathematics and its applications; and many mathematicians have tried to predict the patterns observed in prime numbers. One theory, called the Riemann Zeta Function is believed to be the most successful in revealing and explaining properties of primes.

The Riemann Zeta Function detects patterns in prime numbers in the same way that you might spot harmonies in music. It can be thought of as a series of peaks and troughs – which may be legitimately called a ‘landscape’ – encoding the properties of primes.

Dr Fyodorov continues: “One of important questions about the Riemann Zeta function relates to determining how large the highest of the peaks in the landscape are. In our paper we have argued that, unexpectedly, answering that question is related to the problem of characterizing the nature of the freezing transition in certain complex materials in Physics, such as glasses.

The team hope that understanding freezing could help mathematicians make progress in attacking some of the grand challenges of number theory.

Dr Fyodorov concludes: “Looking for connections between the statistical mechanics of random energy landscapes, random matrix theory, and the theory of the Riemann zeta function appeared to be a fruitful and promising approach.”

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Credit of the article given to Queen Mary, University of London

Professor Graeme Pettet is using mathematical equations to better understand how to heal wounds and bone fractures.

Understanding the way our bodies heal is not as easy as 1, 2, 3. But a Queensland University of Technology (QUT) researcher believes mathematics holds the answers to complex biological problems.

Professor Graeme Pettet, a mathematician from QUT’s Institute of Health Biomedical Innovation (IHBI), said maths could be used to better understand the structure of skin and bones and their response to healing techniques, which will eventually lead to better therapeutic innovations.

“Mathematics is the language of any science so if there are spatial or temporal variations of any kind then you can describe it mathematically,” he said.

Professor Pettet is a member of the Tissue Repair and Regeneration group, which in part focuses on growing skin in a laboratory and analysing its growth and repair process.

His team concentrates on the theoretical material, using data to build and solve mathematical equations.

“Skin is very difficult to describe. It’s very messy and very complicated. In fact most of the descriptions that engineers and biologists use are schematic stories (diagrams),” he said.

“Once we understand the structure (of the skin) and how it develops we can begin to analyse how that development impacts upon healing in the skin and maybe also diseases of the skin.”

Professor Pettet said his research would, for the first time, formalise the theories about the way cells interact when healing.

“It is clear that by improving our understanding of how the multiple cellular processes work together in a complex but orchestrated way has great potential in leading to therapeutic innovations,” he said.

Despite skin being our most accessible organ, Professor Pettet said there was a lot more to learn about how and what made it function.

“There’s a lot of structure just in the upper layer of the skin despite the fact it’s only a few cells thick,” he said.

“This can be characterised by how the cells function and change appearance, but what drives them to be that way is not completely known.

“My job is to try and understand and develop ways to describe how the bits and pieces everybody knows about are somehow connected.”

Professor Pettet is also working on applying similar techniques to figure out how to show how small, localised damage at the site of bone fractures can impact on healing.

While the long-term goal of understanding and being able to predict how our bodies heal is still a way off, Professor Pettet’s research is opening up a realm of biological problems where mathematical equations and techniques that have not previously been applied, are providing insights into the biology as well as the maths.

“We’ve discovered essentially new sets of solutions in these contexts and that’s led onto other projects looking at new mathematical tools to describe these new solutions that we’ve never seen before,” he said.

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Credit of the article given to Alita Pashley, Queensland University of Technology

There’s been plenty of commentary recently on the “numeracy crisis” threatening the economies of many developed nations, including Australia.

A 2009 report by the National Academies in the US was not the first to highlight the desperate need to improve mathematical education, particularly at the K-12 level, where so many otherwise talented students either fall behind or lose interest. The report’s summary concluded:

“The new demands of international competition in the 21st century require a workforce that is competent in and comfortable with mathematics.

“There is particular concern about the chronically low mathematics and science performance of economically disadvantaged students and the lack of diversity in the science and technical workforce. Particularly alarming is that such disparities exist in the earliest years of schooling and even before school entry …”

The committee found that, although virtually all young children have the capability to learn and become competent in mathematics, the potential to learn mathematics in the early years of school is not currently realised for most.

This stems from a lack of opportunities to learn mathematics either in early childhood settings or through everyday experiences at home and in communities. And this is especially the case for the economically disadvantaged.

A UK report released last month found that millions of British adults have numerical skills at a level more commonly expected of an 11-year-old. The report also found that young people with poor numeracy skills were twice as likely to drop out of school and twice as likely to be unemployed.

The report’s authors called for a change in society’s attitude to mathematics, so that being bad at maths should no longer be seen as a “badge of honour”.

According to the same UK report, one in five of business members questioned last year said they had to teach remedial mathematics to their employees. As James Fothergill, head of education and skills at the employers’ group CSI, explained:

“It’s really important that [employees] are helped to apply maths skills and concepts in practical situations, such as being able to work out what a 30% discount is without doing it on the till.”

Many business leaders also pointed to the fact few of their employees were able to spot “rogue figures” – data that is likely to be in error.

In February this year, speaking at a forum of national educators in Canberra, Australia’s Nobel Prize-winning astronomer Brian Schmidt went so far as to warn that Australia’s resource boom was threatened by a lack of highly-trained engineers, saying:

“Too many kids who are willing and able to excel at maths are taught by teachers without the competency required to teach the subjects they are teaching.”

At the same forum, Australia’s Chief Scientist Ian Chubb said part of the problem was that mathematics and science courses were considered “boring”.

“We need to think about how to deliver the science and mathematics to a generation of students that have many more options available to them,” he said.

The situation is better elsewhere. Finland and Canada, for example, rated an “A” in an international ranking of 17 developed nations in education and skills. Finland has ranked at (or near) the top of the OECD nations in educational performance for more than ten straight years.

Canada’s strength derives in part from the system’s primary focus on K-12 education. On the other hand, Canada faces the challenge of educating and training the three million adults, in a country of under 35m people, who have only “Level 1” literacy. This would seem to show that you do get what you pay for.

Of course, other countries, such as Japan, Taiwan, China, Korea and Singapore are not standing still, with impressive gains in educational performance.

So, what can be done, for the good of everyone? Perhaps all nations can examine the educational programs of highly successful nations such as Finland.

The Finnish educational system eschews standards tests, preferring instead custom tests devised by highly qualified teachers. (Several decades ago, the government required all teachers to have master’s degrees).

Another is Finland’s focus on basic education from age seven until 16, at which point 95% of the population continues in either vocational or academic high schools. According to Pasi Sahlberg, a Finnish educator and author:

“The primary aim of education is to serve as an equalising instrument for society.”

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Credit of the article given to Jonathan Borwein and David H. Bailey

This is a simulation of a network of people playing Prisoner’s Dilemma. Red are cooperators; blue are defectors.

For the past twenty years, there has been a great controversy regarding whether the structure of interactions among individuals (that is, if the existence of a certain contact network or social network) helps to foment cooperation among them in situations in which not cooperating brings benefits without generating the costs of helping. Many theoretical studies have analysed this subject, but the conclusions have been contradictory since the way in which people make decisions is almost always based on a hypothesis of the models with very little basis to justify it.

The study carried out by these university researchers adopts a pioneering perspective on the theoretical study of the emergence of cooperation: rather than postulating that people make decisions according to one procedure or another, it incorporates the results obtained in experiments designed precisely to analyse how people decide whether to cooperate or not. The authors of the study are professors from the Interdisciplinary Complex Systems Group (Grupo Interdisciplinar de Sistemas Complejos – GISC) of the Mathematics Department of Carlos III University of Madrid, José Cuesta and Ángel Sánchez, together with Carlos Gracia and Yamir Moreno, from the Complex Systems and Networks Group (Grupo de Redes y Sistemas Complejos – COSNET Lab) of the Institute for Biocomputation and Physics of Complex Systems (Instituto de Biocomputación y Física de Sistemas Complejos – BIFI) of the University of Zaragoza. Their study was recently published in Scientific Reports, Nature’s new open access magazine.

This work is based on the results of an experiment carried out by the researchers and on information from other previous studies, as well as on the results (as yet unpublished) obtained from their own new experiments. The observations from these studies coincide in indicating that people do not consider what those they interact with gain; rather they think about whether or not they cooperate. In addition, their decisions usually depend on their own mood. That is, the authors noticed that the probability of cooperation occurring was considerably higher if there had been cooperation in the previous interaction. They also observed a certain heterogeneity in behaviour, finding a certain percentage of individuals who cooperated very little, regardless of what those around them did, and other individuals who almost always cooperated, again, no matter what others did.

These researchers have mathematically examined what occurs when groups of people who behave as the experiments say have to decide whether or not to cooperate, and how the existence of cooperation, globally or in the group, depends on the structure of the interactions. Specifically, the study analyses what happens if each person interacts with all of the others, if the people are placed in a square reticule and they interact with their four closest neighbours, or if they are arranged in a network that is more similar to a social network, in which the number of neighbours is highly variable and is dependent on each person. In the first case (each individual interacts with all of the others), the problem can be solved mathematically, so the level of resulting cooperation can be predicted. What the researchers observed is that this depends on the makeup of the population; that is, what proportion of the individuals use the previously described strategy, and what proportion almost always cooperates or almost never does, regardless of what the others do. Afterwards, this prediction can be compared with the results of numeric simulations obtains for the populations placed in each of the two networks, and it can be shown that the result is exactly the same, unlike what had been concluded in previous studies.

The consequences of this prediction are very important, according to the authors of the study, because if they are true, it would rule out the existence of one of the five mechanisms that have been proposed to explain the emergence of cooperation, the so-called “network reciprocity” mechanism. In order to prove the prediction, it will be necessary to carry out a large-scale experiment, something that this group of researchers in currently very involved in. These experiments are very difficult to carry out, given that studying heterogeneous networks in such a way as to obtain significant results, the team must work with hundred of volunteers simultaneously. If, as the team hopes, the experiments confirm what this study predicts, we would be witnessing a paradigm shift in the interpretation of decision-making in cooperative dilemmas: instead of considering what is to be gained, individuals would base their decisions on the cooperation they have received, and this would mean that the way that they interact (the underlying social network) would cease to be important.

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Credit of the article given to Carlos III University of Madrid

This is a sample from a Spacemath@NASA problem. This diagram shows disks representing the planets discovered in orbit around eight different stars all drawn to the same scale. Earth and Jupiter are also shown for size comparison. This lesson asks the viewer to solve problems using fraction arithmetic to find out how big these new planets are compared to Earth and Jupiter.

NASA today announced that Houghton Mifflin Harcourt (HMH), Boston, has incorporated math problems developed by the SpaceMath@NASA program into some of its latest curriculum and educational products. SpaceMath uses the latest discoveries from NASA’s space science missions to develop grade-appropriate math problems spanning all of the contemporary mathematics topics areas in formal education.

“We are proud of the partnership with HMH, especially at a time when a vibrant, national science, engineering, technology, and math (STEM) education program is a major priority,” said astronomer Sten Odenwald of ADNET Systems, Inc., Lanham, Md. “SpaceMath@NASA has partnered with a major STEM education solutions provider to help students see the deep connections between math and science using NASA and space exploration as a theme.” Odenwald, who is stationed at NASA’s Goddard Space Flight Center in Greenbelt, Md., leads a team of education and public outreach (E&PO) professionals who develop the SpaceMath materials.

“Other education companies are welcome to work with SpaceMath and follow HMH’s example,” says Odenwald. “The informal partnership entails periodic consultation with the company to understand its interests and what types of content best suits its goals. We then build modules on the SpaceMath@NASA website that contain as many content requests as we can accommodate. In turn, we can offer our NASA-version of these modules for open access by all visiting teachers, while HMH is free to download those module elements to populate their own Web pages and books.”

SpaceMath products, simple one-page problems featuring a NASA discovery or engineering issue, are designed for direct classroom use by students in grades 3 through 12 using authentic, on-grade-level math topics rooted in real-world science and engineering data. It was developed in 2003 to help NASA missions upgrade their E&PO offerings by explicitly integrating mathematics problems into the science content. It was also specifically designed to meet the needs of the No Child Left Behind classroom environment where short, targeted math problems in a one-page format were now becoming the preferred method for presenting a variety of math experiences.

Problems are commonly extracted from NASA press releases and written to feature some surprising but quantifiable aspect of an image or discovery that can be paraphrased as simple mathematical problems. “These can be as diverse as a problem on fractions and percentages using Kepler exoplanet data, or as involved as determining the volume of Comet Hartley-2 using integral calculus,” said Odenwald.

“We are very excited to partner with NASA,” said Jim O’Neill, Senior Vice President, Portfolio Strategy and Marketing Management for HMH. “By incorporating the resources provided by SpaceMath@NASA into our programs, HMH can help develop students’ critical thinking skills through real-world applications that are taken from the headlines. These STEM activities also highlight the pedagogy of the Common Core for Mathematics by strengthening students’ abilities to apply concepts and integrate the Standards for Mathematical Practice.”

“Our partnership with HMH has grown out of a 10-year collaboration with them, so we consider them a major partner for future resource development,” adds Odenwald.

SpaceMath was originally funded by NASA’s E&PO programs for the IMAGE and Hinode missions. Since 2008, the program has been funded by two grants from the NASA Science Mission Directorate at NASA Headquarters, Washington – through the Research Opportunities in Space and Earth Sciences/Education and Public Outreach for Earth and Space Science (ROSES/EPOESS) program.

“Funding at the Directorate level has been crucial in allowing SpaceMath to utilize all of NASA’s press releases and extensive resources as subject matter for mathematics problems, rather than focusing exclusively on only a few NASA missions and science themes,” said Odenwald.

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Credit of the article given to NASA’s Goddard Space Flight Center

Could different jury sizes improve the quality of justice? The answers are not clear, but mathematicians are analysing juries to identify potential improvements.

The U.S. Constitution does not say that juries in criminal cases must include 12 people or that their decisions must be unanimous. In fact, some states use juries of different sizes.

One primary reason why today’s juries tend to have 12 people is that the Welsh king Morgan of Gla-Morgan, who established jury trials in 725 A.D., decided upon the number, linking the judge and jury to Jesus and his Twelve Apostles.

The Supreme Court has ruled that smaller juries can be permitted. States such as Florida, Connecticut and others have used — or considered — smaller juries of six or nine people. In Louisiana, super-majority verdicts of nine jurors out of 12 are allowed.

However, in 1978, the Supreme Court ruled that a five-person jury is not allowed after Georgia attempted to assign five-person juries to certain criminal trials.

To mathematicians and statisticians, this offers a clear division between acceptable and not acceptable, and therefore an opportunity for analysis.

“What seems to be apparent reading the literature on this is that the Supreme Court is making these decisions basically on an intuitive basis,” said Jeff Suzuki, a mathematician at Brooklyn College in New York. “It’s their sense of how big a jury should be to ensure proper deliberation.”

At a mathematics conference earlier this year, Suzuki presented research comparing the likelihood of conviction of a hypothetical defendant with the same likelihood of guilt but different jury conditions.

Building on a well-established line of research, which began with 18th-century French philosopher and mathematician Nicolas de Condorcet, mathematical analysis of juries has continued over the years, beginning from Condorcet’s idea that each juror has some probability of coming to the correct conclusion about the defendant’s guilt or innocence.

Suzuki used three different probabilities to calculate the likely decision of a jury, including the probability that the defendant is actually guilty, the probability that a juror will make the correct decision if the defendant is guilty, and the probability that a juror will make the correct decision if the defendant is not guilty

Suzuki’s model suggests that smaller juries are more likely than larger juries to convict when the defendant appears less certain to be guilty. All the juries he modeled are very likely to convict when the evidence suggests that a defendant is almost certainly guilty. But for slightly less certain cases, differences become clear.

If it appears that there’s an 80 percent likelihood that the defendant is guilty, then Suzuki’s model suggests that less than 10 percent of the time a 12-person jury would unanimously vote to convict, but a 6-person jury would unanimously vote to convict over 25 percent of the time — and a Louisiana-style jury that can convict with nine out of 12 votes would convict in roughly 60 percent of such trials.

Suzuki admits that the models may not be capturing the complete picture. Even if states that use fewer than 12 jurors had higher conviction rates than other states, that wouldn’t mean smaller juries convict greater numbers of innocent defendants, he said.

One potential problem with translating this research to real world trials is that it leaves out the interaction between jurors, which Suzuki admitted is a problem.

“We don’t have a good model for how jurors interact with each other,” he said. “The real challenge is that the data doesn’t really exist.”

In addition to the issue of juror interaction, the [Suzuki’s] models leave out other factors important to finding the correct verdict, such as the possibility that testimony or evidence could deceive the jury, said Bruce Spencer, a professor of statistics at Northwestern University in Evanston, Ill., who did not work with Suzuki.

“If the evidence is very misleading, it’s going to tend to mislead all of [the jurors],” said Spencer.

In a separate study, Spencer analysed surveys completed by judges just before juries delivered their verdict and compared what the judges thought to the juries’ decisions, finding that the verdicts agreed about 80 percent of the time. He found that in about one in every five trials in his study sample, the judge and the jury came to different conclusions.

Real data on the true guilt or innocence of a defendant on trial is simply not available. The jury’s decision is only half the story of a verdict’s accuracy. Many factors in jury decisions cannot be captured quantitatively.

“If you’re coming up with a measure of the speed of light or a standard kilogram, you like to have some assessment of uncertainty,” said Spencer. “I think it is difficult to assess the uncertainty of our estimates.”

Although Spencer knows either the judge or jury must have been wrong in the 20 percent of cases in his study when the two disagreed, there was not enough information to know which was correct in a given case. Using statistical modeling, he found that overall the judges and juries were about equally accurate, but cautioned about drawing conclusions based on the limited number of cases in his study.

Suzuki is trying to figure out more about verdict accuracy with his research. He said that he can build estimates of false conviction rates by counting how many verdicts are later overturned. The estimates are imperfect, he said, especially given that new technology such as DNA testing was not available when some of the original verdicts were given.

But Suzuki feels that his research can at least examine some of the important details of jury trials. Making better models helps to draw general conclusions, despite the uniqueness of each trial.

“You can use probabilistic methods to model human behaviour, provided that you understand what the statistics are and are not telling you, ”Said Suzuki.

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Credit of the article given to Chris Gorski, Inside Science News Service

Alexei Borodin

For anyone who has ever taken a commercial flight, it’s an all-too-familiar scene: Hundreds of passengers sit around waiting for boarding to begin, then rush to be at the front of the line as soon as it does.

Boarding an aircraft can be a frustrating experience, with passengers often wondering if they will ever make it to their seats. But Alexei Borodin, a professor of mathematics at MIT, can predict how long it will take for you to board an airplane, no matter how long the line. That’s because Borodin studies difficult probability problems, using sophisticated mathematical tools to extract precise information from seemingly random groups.

“Imagine an airplane in which each row has one seat, and there are 100 seats,” Borodin says. “People line up in random order to fill the plane, and each person has a carry-on suitcase in their hand, which it takes them one minute to put into the overhead compartment.”

If the passengers all board the plane in an orderly fashion, starting from the rear seats and working their way forwards, it would be a very quick process, Borodin says. But in reality, people queue up in a random order, significantly slowing things down.

So how long would it take to board the aircraft? “It’s not an easy problem to solve, but it is possible,” Borodin says. “It turns out that it is approximately equal to twice the square root of the number of people in the queue.” So with a 100-seat airplane, boarding would take 20 minutes, he says.

Borodin says he has enjoyed solving these kinds of tricky problems since he was a child growing up in the former Soviet Union. Born in the industrial city of Donetsk in eastern Ukraine, Borodin regularly took part in mathematical Olympiads in his home state. Held all over the world, these Olympiads set unusual problems for children to solve, requiring them to come up with imaginative solutions while working against the clock.

It is perhaps no surprise that Borodin had an interest in math from an early age: His father, Mikhail Borodin, is a professor of mathematics at Donetsk State University. “He was heavily involved in research while I was growing up,” Borodin says. “I guess children always look up to their parents, and it gave me an understanding that mathematics could be an occupation.”

In 1992, Borodin moved to Russia to study at Moscow State University. The dissolution of the USSR meant that, arriving in Moscow, Borodin found himself faced with a choice of whether to take Ukrainian citizenship, like his parents back in Donetsk, or Russian. It was a difficult decision, but for practical reasons Borodin opted for Russian citizenship.

Times were tough while Borodin was studying in Moscow. Politically there was a great deal of unrest in the city, including a coup attempt in 1993. Many scientists began leaving Russia, in search of a more stable life elsewhere.

Financially things were not easy for Borodin either, as he had just $15 each month to spend on food and accommodation. “But I still remember the times fondly,” he says. “I didn’t pay much attention to politics at the time, I was working too hard. And I had my friends, and my $15 per month to live on.”

After Borodin graduated from Moscow State University in 1997, a former adviser who had moved to the United States invited Borodin over to join him. So he began splitting his time between Moscow and Philadelphia, where he studied for his PhD at the University of Pennsylvania.

He then spent seven years at the California Institute of Technology before moving to MIT in 2010, where he has continued his research into probabilities in large random objects.

Borodin says there are no big mathematical problems he is desperate to solve. Instead, his greatest motivation is the pursuit of what he calls the beauty of the subject. While it may seem strange to talk about finding beauty in abstract mathematical constructions, many mathematicians view their work as an artistic endeavor.

“If one asks 100 mathematicians to describe this beauty, one is likely to get 100 different answers,” he says.

And yet all mathematicians tend to agree that something is beautiful when they see it, he adds, saying, “It is this search for new instances of mathematical beauty that largely drives my research.”

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Credit of the article given to Helen Knight, Massachusetts Institute of Technology