Understanding behavioural patterns: why bird flocks move in unison

Animal flocks, be it honeybees, fish, ants or birds, often move in surprising synchronicity and seemingly make unanimous decisions at a moment’s notice, a phenomenon which has remained puzzling to many researchers.

New research published today in the New Journal of Physics ( co-owned by the Institute of Physics and German Physical Society ), uses a particle model to explain the collective decision making process of flocks of birds landing on foraging flights.

Using a simple self-propelled particle (SPP) system, which sees the birds represented by particles with such parameters as position and velocity, the researchers from Budapest, Hungary, find that the collective switching from the flying to the landing state overrides the individual landing intentions of each bird.

Math behind Internet encryption wins top award: Abel prize awarded to number theorist John Tate

The Abel prize--considered the "Nobel" prize of mathematics--has been awarded to John Tate, recently retired from the University of Texas at Austin, for his work on algebraic number theory, the mathematical discipline that deals with connections between whole numbers and lies at the heart of Internet security.
Established in 2002, the Abel Prize is presented annually by the King of Norway and carries a cash award of $1 million.

Ian Stewart:  Try to find the prime factors of a 200-digit number with pencil and paper--or even with a computer program--and it would take longer than the age of the Universe .

John Tate Biography in Wikipedia

Global classical solutions of the Boltzmann equation with long-range interactions

Ludwig Boltzmann
1844-1906

This is a brief announcement of our recent proof of global existence and rapid decay to equilibrium of classical solutions to the Boltzmann equation without any angular cutoff, that is, for long-range interactions. We consider perturbations of the Maxwellian equilibrium states and include the physical cross-sections arising from an inverse-power intermolecular potential r ^-(p-1) with p > 2, and more generally. We present here a mathematical framework for unique global in time solutions for all of these potentials.  We consider it remarkable that this equation, derived by Boltzmann in 1872 and Maxwell in 1867, grants a basic example where a range of geometric fractional derivatives occur in a physical model of the natural world . Our methods provide a new understanding of the effects due to grazing collisions.

http://www.pnas.org/content/107/13/5744.abstract?sid=9d675b61-b4d1-4bc0-88d1-b450d0b4b5ca
 
Philip T. Gressman and Robert M. Strain
University of Pennsylvania, Department of Mathematics, Philadelphia, PA 19104-6395

Perelman wins Millenium Prize for proving Poincaré conjecture

The American Clay Mathematics Institute has awarded the Russian maths genius Grigori Perelman a million dollars for proving what is known as the Poincare Conjecture, a milestone theorem which opens up a whole new field in geometry. The Institute says such breakthroughs happen once in a millennium and cannot be allowed to pass unrewarded. Forty-six-year-old Mr. Perelman meantime is a known recluse who has already rejected a gold medal and cash from the latest World Mathematical Congress for his remarkable discovery. He has spent the period since 2006 in a remote suburban location without contact with colleagues. His former superior at the Steklov Mathematical Institute Professor Sergei Kislyakov warns the Clay Institute that Dr. Perelman is likely to ignore his latest international honour.

Preserving the past for the future; Grant aids archival work at Institute. (Old Einstein pictures)

Princeton Township --The archivist lifted the pearl-gray cover off of an oversized folio of photographs recently found at the The National Medal of Science, Awarded by the President of the United States to Kurt Gödel in 1974, part of the Institute for Advanced Study archive collection, photographed on Friday, October 23, 2009. here. From beneath the protective tissue paper emerged a black and white photograph of the great, leonine face of Albert Einstein.

Mark Gimein -> Swan Song: Why Nassim Taleb is Still Wrong

While for just about everyone involved in the markets the last two years of financial history have been a massacre, they have been a long victory lap for Nassim Nicholas Taleb. Taleb is the author of The Black Swan, the book about, as the subtitle puts it, "The Impact of the Highly Improbable." It came out in 2007, just before everything that seemed highly improbable became painfully actual. As everyone else's fortunes have shrunk, Taleb's have risen. Not only have his books made him the public face of the New Catastrophism, but his insights have turned out to be extremely profitable: The Wall Street Journal reports that Universa, a hedge fund for which Taleb serves as guru and adviser, gained more than 100 percent last year and now holds $6 billion.

Examples of Mathematical Physics

One challenge in a course like this is to maintain the connection with actual applications of the techniques one is covering. Since I was originally taught this material in a set of courses as a mathematics undergraduate, my own take on the material can be rather formal, and I have worked over the years to balance this out. However, as you might guess, my own examples are predominantly drawn from those areas of physics with which I am most familiar - for example, supersymmetry, and the restrictions that holomorphy places on superpotentials, is a nice illustration of the power of complex analysis.

See this useful link.

Fuzzy Math

Have the votes for president been properly counted in Florida ?. On the surface, that's a question of simple math. But beneath the number crunching, Republicans and Democrats are waging a war of disguised biases. When data don't turn out the way your theory predicts, should you question the theory or the data ?. When a new vote tally contradicts an old one, should you distrust the first count or the second ?. When one kind of recount is more evenhanded but another is more comprehensive, which is better ?. These dilemmas form the hidden crux of the debate over whether to recount Florida's ballots by hand, as Democrats prefer, or to rely on a machine recount, as Republicans prefer. The two parties aren't being candid about these questions. And math won't answer them.

Guilt by Calculation

This kind of statistical gumshoeing has a long history. In 1936, for example, English biologist and statistician R. A. Fisher went gunning for Gregor Mendel, whose experimental results Fisher believed had been tweaked to be more favorable to Mendel's ideas. "Fictitious data can seldom survive a careful scrutiny," Fisher wrote, "and, since most men underestimate the frequency of large deviations arising by chance, such data may be expected generally to agree more closely with expectation than genuine data would." In other words, it was precisely the beautiful agreement of experiment with theory that exposed Mendel's thumb on the scale. Only once in 15,000 times, Fisher computed, could one expect such strong conformity. ( The controversy over Mendel's research practices continues to this day, with notable scientists lining up on both men's sides ).

The human brain is on the edge of chaos

Cambridge-based researchers provide new evidence that the human brain lives "on the edge of chaos", at a critical transition point between randomness and order. The study, published March 20 in the open-access journal PLoS Computational Biology, provides experimental data on an idea previously fraught with theoretical speculation.

Self-organized criticality (where systems spontaneously organize themselves to operate at a critical point between order and randomness), can emerge from complex interactions in many different physical systems, including avalanches, forest fires, earthquakes, and heartbeat rhythms.

According to this study, conducted by a team from the University of Cambridge, the Medical Research Council Cognition & Brain Sciences Unit, and the GlaxoSmithKline Clinical Unit Cambridge, the dynamics of human brain networks have something important in common with some superficially very different systems in nature. Computational networks showing these characteristics have also been shown to have optimal memory (data storage) and information-processing capacity. In particular, critical systems are able to respond very rapidly and extensively to minor changes in their inputs.

Centro Virtual de la Divulgación de las Matemáticas

A New Puzzle Challenges Math Skills

KenKen shares some properties with sudoku. Each is a pure logic challenge in which numbers are filled in the squares of a grid. Unlike sudoku, though, in which the numbers act solely as symbols (letters or pictures would work as well), KenKen requires arithmetic. The rules are simple: Fill the grid with digits so as not to repeat a digit within any row or column, and so the digits within each heavily outlined box (called a cage) go together using the arithmetic operation shown to make the target number indicated.