Plus Blog

July 5, 2006
Wednesday, July 05, 2006

Eliminating the photographer

Photographing artwork is a subjective business. The photographer has to make aesthetic decisions on lighting and the angle from which the picture is taken, based on his or her aesthetic instincts. But accurate representations of paintings and sculptures are important for scholars, collectors and other art lovers who view them in books, museum archives and on websites.

To get around the problem of subjective photography, the Andrew W. Mellon Foundation has awarded a grant of $855,000 to the Rochester Institute of Technology and the colour scientist Roy Berns. The scientists will use maths to build a system that photographers can use in situ to eliminate subjective decisions.

The main part of the project will be to build an instrument that can capture information about an object's geometry and colour and measure how these depend on lighting. This involves reducing the painting or sculpture to its most basic optical blueprint, and stripping it of any attributes that are down to subjective perception. Additional instruments that can gather information on the gallery's shape will also be developed later on in the project. Using mathematical models from computer graphics software, the piece of art can then be rendered as it is when viewed in real life, bypassing any input of the photographer.

You can find out more in the RIT press release.

posted by Plus @ 1:29 PM

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May 31, 2006
Wednesday, May 31, 2006

Taking a leaf out of Nature's book

Computer networks, connecting people, organisations and places, are becoming increasingly complex. So complex, in fact, that many are starting to buckle under their load. The huge amount of information sent through networks and the increasing complexity of this information can overwhelm particular nodes in the network, and before you know it your files have disappeared or your printer connection has failed.

Nature, on the other hand, has no such problems: ant colonies and bee hives are networks of thousands of individuals engaged in complicated communal tasks, and evolution has made sure that these networks function perfectly. The BISON project, funded under the European Commission's FET (Future and Emerging Technologies) initiative of the IST programme, has been set up to learn from these little animals.

The project takes its inspiration from the techniques used by ants to find their way to and from food sources, and by fireflies' ability to synchronise their flashing. Using computer models of these animals' behaviour, the project scientists developed algorithms that can optimally route information through a constantly changing network, and synchronise important network functions.

Although most of the project's work is not yet ready for commercial use, initial tests seem very promising. Maybe a bug in the system isn't that bad after all. To find out more read the IST's news release.

posted by Plus @ 1:26 PM

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May 31, 2006
Wednesday, May 31, 2006

Nano fractals

Fractals are abundant in Nature and even molecules can have a fractal structure. Now, scientists from the University of Akron in Ohio and Clemson University have created the largest man-made fractal molecule at the nanoscale. And they even captured an image of it. The molecule is made up of six rings, each composed of six smaller rings, each of which is in turn each made up of six smaller rings, and so on, giving rise to the self-similarity and incredibly intricate structure that makes a fractal.

These new man-made molecules are extremely precise and could be used to engineer new kinds of photoelectric cells, molecular batteries and energy storage. The molecules are about twelve nanometres wide, a nanometre being a billionth of a metre. This is pretty small to you and me but, apparently, it's big on the nanoscale. One of the scientists involved even called it huge. To see an image of the molecule — enlarged a million times — and to find out more, read the University of Ohio's news release. The scientists' work was published in the journal Science.

posted by Plus @ 1:27 PM

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May 17, 2006
Wednesday, May 17, 2006

The million Dollar questions

If you'd like to have a go at solving one of the most tricky and important open questions in maths and get rich in the process, then the QEDen web site is worth a look. The site has been set up with the ambitious goal to solve the Millennium Prize Problems, seven of the most difficult unsolved problems in maths. The Clay Mathematics Institute has promised a million Dollars to anyone who solves one of the problems, but so far solutions remain elusive.

QEDen is designed to be "an online playground for the mathematically and scientifically minded people on the internet to converge and wrap their minds around the toughest problems yet to face the planet". As yet, its "progress thermometer" is firmly stuck at zero. But, who knows, maybe you could deliver a vital clue. And, don't worry, if you solve the problem, all the money is yours alone.

You can find out more about these problems in the Plus articles How maths can make you rich and famous and How maths can make you rich and famous: part II.

posted by Plus @ 1:23 PM

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May 17, 2006
Wednesday, May 17, 2006

Maths maps musical emotion

Music makes emotion and maths underpins music. But can the emotional part of music be captured by maths? To find the answer to this question Elaine Chew, assistant professor of industrial and systems engineering at the USC Viterbi School of Engineering, set up a graduate course called "Computational Modelling of Expressive Performance" to look for answers. The aim of the course is to teach students how to use tools from engineering and computation to understand our emotional responses to music.

Chew pursues a successful career as a pianist along side her research, and so is perfectly qualified. But as she admits, teaching the course is a challenge, as students need expertise from a huge range of different disciplines. They need to use tools from music theory, cognitive science, artificial intelligence, experimental psychology, signal processing and neuroscience, to name but a few. Not many students have the necessary pre-requisites, but some of those that do have now put an exhibition of their projects online.

One pair of students have created "emotiongrams" that map musical characteristics to colour patterns to capture their emotional impact. Another project involves analysing scores of silent movies that have been specifically created to evoke certain emotions, and yet another one involves a system that allows you to add extra rules to a musical score and observe whether this changes the impact on your feelings.

You can read about all the projects on the course website. Plus has a number of articles on the mathematics of music, which you can find in our archive under keyword or topic "maths and music".

posted by Plus @ 1:19 PM

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April 26, 2006
Wednesday, April 26, 2006

29 steps to universal (26/04/2006)

Think of a number, any number, and see if you can write it as the sum of square numbers: 13 = 22 + 32, 271 = 12 + 12 + 102 + 132, 4897582 = 62 + 952 + 22112...

In 1770, Lagrange proved that every positive integer, no matter how large, can be written as a sum of at most four squares, x2 + y2 + z2 + t2. In the centuries since, mathematicians searched for other universal quadratic forms which could represent all the positive integers. Another 53 expressions, including 1x2 + 2y2 + 3z2 + 5t2, were found by Ramanujan in 1916. So many such universal forms exist, but how can you predict if a particular quadratic form is universal?

Now the brilliant young mathematician Manjul Bhargava and his colleague Jonathan Hanke have found a surprisingly simple result that completely solves the problem of finding and understanding universal quadratic forms. They found a shortcut to deciding if a quadratic form is universal — to check if the form represents every single positive integer, you only have to check it represents a mere 29 particular integers, the largest of which is 290. Bharghava and Hanke then went on to find every universal quadratic form (with four variables), all 6,436 of them. You can read about this surprising result in Ivars Peterson's excellent article in Science News.

Apart from Bhargava's brilliance as a mathematician (he was one of the youngest people to be made a full professor at just 28), he is also an accomplished musician. Both number theory and tabla playing may be viewed as the study of patterns, Bhargava told Peterson. "The goal of every number theorist and every tabla player," he explains in the article, "is to combine these patterns, carefully and creatively, so that they flow as a sequence of ideas, tell a story, and form a complete and beautiful piece."

If you're struggling with a sum of squares, try out this useful applet by Dario Alpern.

posted by Plus @ 2:15 PM

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