Month: October 2018

Grand Slam tennis players in the US, Wimbledon and Australian Opens could improve their chances of winning sets, matches and even tournaments through more aggressive and strategic use of challenges, Swinburne research has found.

Analysis of the ‘nested’ scoring system used in tennis by esteemed Swinburne sports statistician, Professor Stephen Clarke and Sheffield University’s John Norman, found that players don’t have to increase their chances of winning a point very much, to significantly increase their chances of winning a match.

The two to four player challenges allowed on show courts in three of the Grand Slam tournaments are much more important than previously realised, and should be deployed later in games, later in sets and when players are behind, the new statistical modelling has shown.

“Optimal use of the three challenges available (in the Australian Open) can increase a player’s chance of winning a set to 55 per cent in an otherwise even contest,’’ Professor Clarke writes in a paper accepted for publication in the Journal of the Operational Research Society.

“This increases their chance of winning a best of three-set match to 58 per cent, and a best of five-set match to 59 per cent, which is nearly 60:40. That’s a lot of difference,” he said.

The ‘moneyball’-like analysis of the increased strategic advantage of a challenge acted much like compound interest, he said.

“If your chance of winning a match is 60 per cent, the chance of winning seven matches in a row to win the tournament is probably double what you had before, so it could have quite a drastic effect over the life of the tournament.

“There should be more aggressive challenging in more important points which tend to occur later in games, later in sets and when the player is behind rather than when ahead.”

To date, analysis of challenges from both Wimbledon and the Australian Open shows players are sparing in their deployment of challenges, and are successful only about 30 per cent of the time. It was unlikely players, coaches or commentators realised the strategic importance of challenges, he said.

Professor Clarke – himself a keen tennis, Australian Rules Football and cricket fan – said the Australian Open tennis crowd enjoyed the process of the challenge – which is replayed and dramatised using proprietary technology, as it added much to the tension and enjoyment of the tournament.

Similar challenge rules are expected to be introduced in other sports, prompting academics to consider the growing use of technology and how it will increasingly enable players to challenge umpires’ decisions.

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

Credit of the article given to Swinburne University of Technology

Dipak Dey, Board of Trustees Distinguished Professor of Statistics and associate dean in the College of Liberal Arts and Sciences.

Dipak Dey, Board of Trustees Distinguished Professor of Statistics and associate dean in the College of Liberal Arts and Sciences, has been called an ambassador for the field. A prolific researcher, he is best known for his contributions in the areas of statistical decision theory and Bayesian statistics.

A Fellow of both the American Statistical Association and the Institute of Mathematical Statistics, he is also recognized for developing and maintaining collaborative research programs with other departments and organizations. He recently sat down to answer questions about his field.

We’ve all heard the saying, “Statistics don’t lie.” Yet it’s not uncommon to see statistics misused to prove a point. As a statistics expert, does this frustrate you? And how do you respond?

Statistics do not lie, but sometimes researchers do by misusing and misunderstanding. Sometimes people try to misuse statistics to get across a particular agenda. As a discipline, statistics is a sound science and is being prominently used in all disciplines. Unfortunately statisticians and scientists can’t control how others with a specific agenda may or may not misuse the sound principles and paradigms for their personal benefit.

Data can often be manipulated or ignored to come to a specific conclusion, but that in and of itself is not a reflection on the theory and modeling used in the field. The situation is similar to misusing any kind of legitimate system for one’s personal agenda. People are warned against doing such things, but every year we hear about some powerful interests misusing statistical data to prove a specific point. This is unfortunate and indeed frustrating. In case of such cases, are the principles of statistics at fault? We need to think before we answer.

Personally, I feel happy and proud to know what statistics is about, and how it helps society and life as a whole. After, all knowledge is golden. So I keep learning through the knowledge that can be acquired through the regular use of statistics.

Why should we all know more about statistics?

We all need to know more statistics because it is the science of using data in all fields and disciplines to determine and draw true conclusions about the world. The knowledge gained from statistics is used regularly in technology, business, economics, medicine, social science, and can be related as fact-based knowledge to help people’s daily lives.

What are statisticians doing to expand the public’s understanding of statistics and how they are used?

Besides teaching statistics at the educational level, statisticians have now joined various government agencies, nonprofit organizations, corporations, and other sectors in everything from technology to fashion. As I mentioned before, the discipline of statistics is used in virtually all fields. Whether it is for the analysis of polling data for politics or the analysis of air and water quality for the environment or the analysis of cancer data for smokers, statistics plays a key role in gaining fact-based knowledge. Specifically when it comes to the example of our government, where the decisions being made impact all citizens of the country, statisticians are playing determinative roles in the Food and Drug Administration, the National Institutes of Health, the Census Bureau, the Bureau of Labor Statistics, the United States Department of Agriculture, the National Center for Atmospheric Research, the National Institute for Environmental Research, the National Institute for Educational and Health Statistics, etc.

What role do statistics play in the public debate about an issue, such as what governments should do to deal with climate change?

Statistics play a major role in the public debate about various issues, often controversial issues. Fact-based data gathered through surveys and opinion polls often determine how much support the government has toward a specific point of view or agenda. Statistics can be used to model and track climate change through scientific data. Similarly, statistics can be used to determine how people feel about certain scientific conclusions. Statistics can be used to both refute and support specific claims. Many debates are resolved by using appropriately designed models to demonstrate a point. Many agencies, e.g. Gallup and Westat, are taking polls on major issues from the public. The Roper Center at UConn is a major archive that maintains a huge database of public opinion about science, economics, and government matters. The government constantly turns to statistics to gauge the way to make policy.

What the government should or wants to do in regards to climate change is based both on public opinion statistics as well as various fact-based expert opinions from scientists. Climatologists, for example, often extensively use statistics in risk analysis and extreme event modeling to factually measure climate change. They draw conclusions based on the detailed statistical analysis.

Why should students who are considering a major pick statistics?

The two primary reasons would be a love for science and, arguably more important, the need for a fruitful career. The job market in statistics is flourishing at a rapid pace. One North American job website recently published its 2011 job ratings where they ranked “statistician” as the fourth best job of 2011. Statistics as a field is extremely popular in all sectors, and its popularity and the need for statisticians will only grow. A statistician’s talent is needed virtually everywhere, and most students should have no problem finding a job post-college. A statistics major has the choice to join various sectors, as I mentioned before, ranging from sports to the government. With a BS or BA in statistics, students can also choose to pursue higher education in a specialty fields such as biostatistics, bioinformatics, computational statistics, actuarial science, financial statistics, etc.

What are some of the career paths for statisticians now that didn’t exist a few years ago? And what types of jobs do your graduates get?

There are many career paths for today’s statisticians. Many of them evolved due to the cutting-edge development of computers that didn’t exist in the past. These include but are certainly not limited to opportunities in pharmaceutical companies, market research firms, biotech companies, insurance industries, and the government. The job prospects are endless and yet to be fully determined.

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

Credit of the article given to Cindy Weiss, University of Connecticut

The Fourier transform is one of the most fundamental concepts in the information sciences. It’s a method for representing an irregular signal — such as the voltage fluctuations in the wire that connects an MP3 player to a loudspeaker — as a combination of pure frequencies. It’s universal in signal processing, but it can also be used to compress image and audio files, solve differential equations and price stock options, among other things.

The reason the Fourier transform is so prevalent is an algorithm called the fast Fourier transform (FFT), devised in the mid-1960s, which made it practical to calculate Fourier transforms on the fly. Ever since the FFT was proposed, however, people have wondered whether an even faster algorithm could be found.

At the Association for Computing Machinery’s Symposium on Discrete Algorithms (SODA) this week, a group of MIT researchers will present a new algorithm that, in a large range of practically important cases, improves on the fast Fourier transform. Under some circumstances, the improvement can be dramatic — a tenfold increase in speed. The new algorithm could be particularly useful for image compression, enabling, say, smartphones to wirelessly transmit large video files without draining their batteries or consuming their monthly bandwidth allotments.

Like the FFT, the new algorithm works on digital signals. A digital signal is just a series of numbers — discrete samples of an analog signal, such as the sound of a musical instrument. The FFT takes a digital signal containing a certain number of samples and expresses it as the weighted sum of an equivalent number of frequencies.

“Weighted” means that some of those frequencies count more toward the total than others. Indeed, many of the frequencies may have such low weights that they can be safely disregarded. That’s why the Fourier transform is useful for compression. An eight-by-eight block of pixels can be thought of as a 64-sample signal, and thus as the sum of 64 different frequencies. But as the researchers point out in their new paper, empirical studies show that on average, 57 of those frequencies can be discarded with minimal loss of image quality.

Heavyweight division

Signals whose Fourier transforms include a relatively small number of heavily weighted frequencies are called “sparse.” The new algorithm determines the weights of a signal’s most heavily weighted frequencies; the sparser the signal, the greater the speedup the algorithm provides. Indeed, if the signal is sparse enough, the algorithm can simply sample it randomly rather than reading it in its entirety.

“In nature, most of the normal signals are sparse,” says Dina Katabi, one of the developers of the new algorithm. Consider, for instance, a recording of a piece of chamber music: The composite signal consists of only a few instruments each playing only one note at a time. A recording, on the other hand, of all possible instruments each playing all possible notes at once wouldn’t be sparse — but neither would it be a signal that anyone cares about.

The new algorithm — which associate professor Katabi and professor Piotr Indyk, both of MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL), developed together with their students Eric Price and Haitham Hassanieh — relies on two key ideas. The first is to divide a signal into narrower slices of bandwidth, sized so that a slice will generally contain only one frequency with a heavy weight.

In signal processing, the basic tool for isolating particular frequencies is a filter. But filters tend to have blurry boundaries: One range of frequencies will pass through the filter more or less intact; frequencies just outside that range will be somewhat attenuated; frequencies outside that range will be attenuated still more; and so on, until you reach the frequencies that are filtered out almost perfectly.

If it so happens that the one frequency with a heavy weight is at the edge of the filter, however, it could end up so attenuated that it can’t be identified. So the researchers’ first contribution was to find a computationally efficient way to combine filters so that they overlap, ensuring that no frequencies inside the target range will be unduly attenuated, but that the boundaries between slices of spectrum are still fairly sharp.

Zeroing in

Once they’ve isolated a slice of spectrum, however, the researchers still have to identify the most heavily weighted frequency in that slice. In the SODA paper, they do this by repeatedly cutting the slice of spectrum into smaller pieces and keeping only those in which most of the signal power is concentrated. But in an as-yet-unpublished paper, they describe a much more efficient technique, which borrows a signal-processing strategy from 4G cellular networks. Frequencies are generally represented as up-and-down squiggles, but they can also be though of as oscillations; by sampling the same slice of bandwidth at different times, the researchers can determine where the dominant frequency is in its oscillatory cycle.

Two University of Michigan researchers — Anna Gilbert, a professor of mathematics, and Martin Strauss, an associate professor of mathematics and of electrical engineering and computer science — had previously proposed an algorithm that improved on the FFT for very sparse signals. “Some of the previous work, including my own with Anna Gilbert and so on, would improve upon the fast Fourier transform algorithm, but only if the sparsity k” — the number of heavily weighted frequencies — “was considerably smaller than the input size n,” Strauss says. The MIT researchers’ algorithm, however, “greatly expands the number of circumstances where one can beat the traditional FFT,” Strauss says. “Even if that number k is starting to get close to n — to all of them being important — this algorithm still gives some improvement over FFT.”

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Credit of the article given to Larry Hardesty, Massachusetts Institute of Technology

The humble pigeon mightn’t look smart, but it’s no bird-brain.

We humans have long been interested in defining the abilities that set us apart from other species. Along with capabilities such as language, the ability to recognise and manipulate numbers (“numerical competence”) has long been seen as a hallmark of human cognition.

In reality, a number of animal species are numerically competent and according to new research from psychologists at the University of Otago in New Zealand, the humble pigeon could be one such species.

Damian Scarf, Harlene Hayne and Michael Colombo found that pigeons possess far greater numerical abilities than was previously thought, actually putting them on par with primates.

More on pigeons in a moment, but first: why would non-human animals even need to be numerically competent? Would they encounter numerical problems in day-to-day life?

In fact, there are many reports indicating that number is an important factor in the way many species behave.

Brown cowbirds are nest parasites – they lay their eggs in the nests of “host” species; species that are then landed with the job of raising a young cowbird.

Cowbirds are sensitive to the number of eggs in the host nest, preferring to lay in nests with three host eggs rather than one. This presumably ensures the host parent is close to the end of laying a complete clutch and will begin incubating shortly after the parasite egg has been added.

Crows identify individuals by the number of caw sounds in their vocalisations, while lionesses appear to evaluate the risk of approaching intruder lions based on how many individuals they hear roaring.

But numerical competence is about more than an ability to count. In fact, it’s three distinct abilities:

• the “cardinal” aspect: the ability to evaluate quantity (eg. counting the number of eggs already in a nest)
• the “ordinal” aspect: the ability to put an arbitrary collection of items in their correct order or rank (eg. ordering a list of animals based on the number of legs they have, or ordering the letters of the alphabet)
• the “symbolic” aspect: the ability to symbolically represent a given numerical quantity (eg. the number “3” or the word “three” are symbols that represent the quantity 3).

We know that humans are capable of all three aspects of numerical competence, but what about other animals?

For a start, we already know that the cowbird, lion and crow possess the cardinal aspect of numerical competency – they are all able to count. Pigeons possess the cardinal aspect too (as was reported as early as 1941) as do several other vertebrate and invertebrate species.

And in 1998, Elizabeth Brannon and Herbert Terrace showed that rhesus monkeys have the ability to order arrays of objects according to the number of items contained within these arrays. After learning to order sets of one, two and three items, the monkeys were able to order any three sets containing from one to nine items.

This discovery represented a clear progression in complexity, since ranking according to numerical quantity is an abstract ability – the ordinal aspect.

The new research by Scarf, Hayne and Colombo – which was published in Science in late December – has pushed, even further, our understanding of numerical abilities in the animal kingdom.

So what did they do?

Well, first they trained pigeons to peck three “stimulus arrays” – collections of objects on a touch screen. These arrays contained one, two or three objects and to receive a reward, the pigeon had to peck the arrays in order – the array with one object first, the array with two objects second, the array with three objects third.

Once this basic requirement was learned, the pigeons were presented with different object sets – one set containing arrays with one to three objects, and sets containing up to nine objects.

Having been presented with these novel object sets, the pigeons were once again required to peck the sets in ascending order. Pigeons solved the task successfully, even though they had never been trained with arrays containing more than three items.

A pigeon taking part in the University of Otago experiment.

In fact, they performed on par with rhesus monkeys, demonstrating that both pigeons and monkeys are able to identify and order the numbers from one to nine. This is significant because it shows these complex numerical abilities are not confined to the primates (and that pigeons are smarter than many people think!)

So if non-human animals possess the cardinal and ordinal aspects of numerical competency, that means it’s the symbolic representation of numbers that makes humans unique, right?

As it turns out, no.

It’s been shown that red wood ants (Formica polyctena) can not only count up to several tens (20, 30 etc.), but can also communicate this numerical information to their brethren.

It would seem, therefore, that not even the symbolic representation of numerical information is specific to humans.

Of course, we still have much more to discover and understand within this fascinating field of research. In the meantime, you might want to think twice before dismissing pigeons as “stupid birds”.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to David Guez and Andrea S. Griffin*