April 30, 2006
Teaching Math
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April 30, 2006
The curious side of big mathMathematics works best when it's fun. Welcome to the Gathering for Gardner Apr. 30, 2006. 01:00 AM SIOBHAN ROBERTS SPECIAL TO THE STAR
At a packed house party of 250-plus mathematicians, Robert Barrington Leigh, a decidedly unscathed-looking 19-year-old and third-year, prize-winning mathematics student at the University of Toronto, is hanging tentatively back from the crowd.
The G4G7 conference proper, held in the ballroom at Atlanta's Ritz-Carlton hotel downtown, is a four-day curiosity cabinet of similar brainteasers.
`(Playful math) helps keep you sharp. But right now my work is more about remembering than being creative' Robert Barrington Leigh Math whiz
"I used to be more [into playful math] when I was younger," said Barrington Leigh. "It helps keep you sharp. But right now my work is more about remembering than being creative."
Siobhan Roberts is a Toronto freelancer writer. Her book "King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry" is being published by Anansi this fall.
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April 30, 2006
Clever proof that math has its charmsA winsome series of letters to a fictitious mentee hints at the mysterious beauty of mathematics. By Paul A. Robinson Jr.
Is it possible to trisect an angle using only a straight edge and a compass? This is not the central point of Ian Stewart's Letters to a Young Mathematician, but it is one of the curious threads woven into these delightful letters written to "Meg," a fictitious mentee, as she advances through a career in mathematics.
• Paul A. Robinson Jr. is a professor of physics at Principia College.
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April 24, 2006
Professor receives top physics prizejanice hamilton  Mathematics Professor John Harnad finds that mathematics serves as both a language to express problems and a tool to find solutions. His career led him across North America before he settled in Montreal. Photo by kate hutchinson
At its annual meeting this June, the Canadian Association of Physicists (CAP) will present Concordia Mathematics Professor John Harnad with the CAP-CRM prize in theoretical and mathematical physics in recognition of his "deep and lasting contributions to the theory of integrable systems with connections to gauge theory, inverse scattering and random matrices." |
April 24, 2006
Can you solve Franklin's puzzle?By Jack Malvern IN BETWEEN performing his role as a founding father of the United States, inventing the lightning rod and coming up with bifocal spectacles, Benjamin Franklin found time to create a frustrating new type of number puzzle. Some 240 years before Britain was seized by the craze for Su Doku, Franklin set a teaser for Britain's mathematicians in the form of a "magic square". One of his number grids, which has been recovered from the archives of the British Library to celebrate the 300th anniversary of his birth, has been reconstructed as a puzzle in today's Times for readers to solve. Franklin's conundrum was so fiendish that he wrote to his friend John Winthrop, a professor of mathematics at Harvard, to rejoice at having foxed the British Empire's finest minds. "The magic square . . . has occasioned a good deal of puzzling among the mathematicians here," he wrote. "But no one has desired me to show him my method of disposing the numbers. It seems they wish rather to investigate it themselves." Magic squares — grids of numbers in which the rows, columns and both diagonals add up to the same number — date back to Chinese documents written more than 3,000 years ago. Franklin took the traditional grid and rearranged it so that bent diagonal lines, in the shape of chevrons, also added up to the same number. In his magic square all rows, columns and bent diagonals add up to 2,056. (Unlike traditional magic squares, the diagonals do not add up to the same number.) For the sake of simplicity we have marked only the bent diagonals that point upwards, but solvers will find that bent diagonals in all directions add up to 2,056. Su Doku addicts will be familiar with magic squares: every row and column of a Su Doku adds up to 45. Solving Franklin's magic square will be tougher, however, since it involves arithmetic as well as recognising patterns. Franklin is believed to have printed his magic square on leaflets and handed them out to friends and fellow academics at the Royal Society. Rupert Baker, library manager at the Royal Society, said that Franklin was a regular at the institution when he lived in London in the 1760s. He did not hand out grids with blanks, but challenged mathematicians to work out how he had constructed them. Franklin was inspired to experiment with number grids after he was shown a French book of magic squares. He was "not willing to be outdone" by the Frenchman, he wrote in his autobiography, and went home that evening to compile a superior square. But he was not proud of his grids, lamenting in a letter to a friends that he was "rather ashamed to have it known I spent any part of my time in an employment that cannot possibly be of any use to myself or others". The first known magic square is mentioned in the Lo Shu, or "book of the river Lo", an ancient Chinese document that is also the basis for some of the principles of feng shui. Su Doku was first published in 1979 in an American puzzle book under the name "number place". In 1984 it was introduced to Japan, where it gained mass appeal. The Times first carried the puzzle in November 2004, leading to a national obsession. Wayne Gould, who compiles Su Doku puzzles for The Times, said that Franklin's magic square called for different skills from Su Doku because it required arithmetic. "But the kind of person whose mindset makes them want to do Su Doku would want to do this," he said. MANY TALENTS Apart from creating number grids, Benjamin Franklin is also famous for:
Can you solve Franklin's puzzle? |
April 24, 2006
Delft mathematician enhances protectiveness of military uniformUntil now, little was known about the physiochemical processes that determine the protective qualities of military uniforms (for example, for protection against poisonous gases). Delft University of Technology researcher Michal Sobera has changed all this, however, through the use of computer modeling. He believes that within a few years it will be possible to calculate a realistic model of the human body with protective clothing. On April 25, Sobera will receive his PhD based on this research subject. During his PhD research, Michal Sobera studied clothing that protects people against so-called NBC-weapons (Nuclear, Biological and Chemical). This clothing is for example worn by soldiers and fire department personnel, protecting them (as far as possible) against for instance poisonous gases. Sobera conducted his research for, and in close cooperation with, research institute TNO Defense & Safety, and he also worked together with the United States military – to be precise, the US Army Soldier Systems Center, a US Department of Defense research institute that specializes in issues that are directly related to military personnel. Until now, there was relatively little fundamental knowledge available about how the functioning of this type of clothing is effected by flows and transfers of heat and mass. Sobera's research findings have taken this knowledge to a higher level. Sobera's research was entirely conducted using a computer. No test subjects were used. Sobera arrived at his conclusions via computer modeling of the relevant body parts, the protective clothing and the physical laws that dangerous gasses (and the like) must adhere to. A key focal point of the research is determining at which point in time the clothing loses its effectiveness. At a certain point, the absorbent carbon layers in the clothing become saturated, whereby the protective function of the clothing rapidly diminishes. Sobera used his computer models to calculate this moment in time for various situations. This was done using relatively simple models, but Sobera believes that calculations for a completely realistic model of the human body, including protective clothing, will be possible in a few years. Delft mathematician enhances protectiveness of military uniform |
April 24, 2006
Mathematical Model May Provide Insight into How We SenseThe individual cells responsible for responding to sensory inputs--the strong scent of a flower, the light touch of a spring breeze--can cope with only a small amount of input. Yet the human ear can hear and process sounds ranging from a pin drop to the roar of a jet engine. Scientists have struggled to account for how this individually narrow range combines in a network to produce the wide range of sensed experience. Now physicists have shown how the mathematical models that describe phase transitions in physical systems might also explain our capacity to hear, see, smell, taste and touch. Mauro Copelli and Osame Kinouchi of the University of Sao Paulo in Brazil used a mathematical formula to show how a random network of "excitable elements," such as neurons or axons, have a collective response that is both exquisitely sensitive and broad in scope. When subtle stimuli hit the network, sensitivity is improved because of the ability of one neuron to excite its neighbor. When strong stimuli hit the network, the response is similarly strong, following what are known as power laws--mathematical relationships that do not vary with scale. But although a mathematical model seems to fit a natural phenomenon it does not necessarily follow that the two are actually related, according to some scientists. In a paper published last September in BioEssays, Evelyn Fox Keller of the Massachusetts Institute of Technology explained that just because mathematical models help explain physical systems, like the density of a gas, it does not mean that they also apply to biological systems, even if they seem to fit. "Fitting available data to such distributions is suspiciously easy," she wrote. "Even when the fit is robust, it adds little if anything to our knowledge of the actual architecture of the network." Time--and experiments--will tell. Copelli and Kinouchi point to one experiment that might prove or disprove their hypothesis. Tests of mice genetically engineered to lack a protein that facilitates electrical connections between cells have shown that they do not see as well. The Brazilian physicists predict that they will not hear as well either. The paper was published yesterday in Nature Physics. --David Biello Mathematical Model May Provide Insight into How We Sense |
April 24, 2006
Study predicts water pollution degradationUTRECHT, Netherlands: Dutch researcher Phil Ham announced the development of mathematical models to calculate the natural degradation capacity of polluted groundwater. As a result, the hydro geologist at the University of Utrecht says it can be predicted whether a polluted area will become larger or smaller. In the latter case, expensive remediation methods can be avoided. Groundwater under contaminated sites, such as waste disposal sites and industrial areas, is often polluted. Such a polluted groundwater plume can grow, shrink or remain stable due to interplay between physical, chemical and biological processes. Ham devised mathematical expressions to determine the size of a plume and to assess the natural degradation capacity of contaminated sites. His analytical models calculate the reactive transport of dissolved matter in water through porous soil and the characteristics of the mixing processes. Such a scientifically supported method has not previously been available. He said his research enables predictions about the effectiveness of natural degradation as a responsible alternative to aquifer remediation. Study predicts water pollution degradation |
April 24, 2006
How long can Tamiflu hold out against bird flu?A Swiss study predicts that the deadly bird flu virus will develop resistance to new anti-viral drugs, if a pandemic breaks out. The mathematical model used by researchers at Zurich's Federal Institute of Technology (ETH) to plot the likely course of an outbreak showed that resistance is more likely if drugs are used as prophylactics. The study, commissioned by the respected journal, Science, used data from previous influenza outbreaks combined with recent information about bird flu and the results of clinical trials on resistance to so-called neuraminidase inhibitor drugs such as Tamiflu, made by Switzerland's Roche. The model then calculated the likely consequences of a hypothetical bird flu outbreak in a school containing 500 people. The programme was repeated to theorise how the virus would spread if the victims were only treated once they showed symptoms compared to people who had also taken drugs as a prophylactic. Resistance "If you are going to use neuraminidase inhibitors such as Tamiflu as a prophylactic then, in my view, the inevitable consequence will be the likelihood of a faster emergence of resistance," he said. "Reviewing the [medical] literature we had the feeling that a considerable fraction of the medical community hoped that with neuraminidase inhibitors the situation would be different." But Bonhoeffer warned against using the results of the study to draw too many conclusions. "This should not be interpreted that they should not be used as a prophylactic because they are the only first line of defence in the absence of a vaccine," he said. "By using neuraminidase inhibitors as a first line of defence, hopefully resistance will not happen too fast, buying enough time to develop a vaccine." Mutated Bonhoeffer also conceded that it is so far unknown how effective mutated forms of the virus could be at transmitting from one person to another. The World Health Organization played down the report, saying more research needs to be done to obtain a clear picture. "This is a mathematical model that is not based on real life experience," said spokeswoman Maria Cheng. "We have never said Tamiflu is a silver bullet. We do not recommend its widespread use as past evidence shows that the general distribution of medicaments among populations increases the chance of resistance." swissinfo, Matthew Allen in Zurich How long can Tamiflu hold out against bird flu? |
April 24, 2006
Origami has math-savvy thinking creativelyA Telegraph Column By Dave Brooks All of the greatest accomplishments of the human race have interesting math underlying them: the pyramids, the moon launch, the ability to fold a dollar bill into a little swan. You name it. But it's not so easy to get an idea of what that math might be, which is why the Thursday lunchtime demonstration and lecture on origami at Rivier College is so welcome. "I won't be assuming any particular mathematical background . . . but I think people can get a feel for where the deep mathematics in origami comes from," said Amanda Serenevy of Boston University, a math Ph.D. candidate who will be giving the unusual presentation. Deep, indeed. Things like combinatorial geometry, Euclidean constructible numbers and the classification of tessellations can crop up in the study of origami these days. Fortunately for the math-phobic, Serenevy has your number (so to speak), even if you don't care two hoots about that stuff, because modern origami has blossomed in eye-popping directions thanks to computer modeling and mathematical insight. You've got to see it to believe it – and, if Serenevy has her way, to construct it. "People have a lot of fun. . . . I talk about the nuts and bolts of how you can explore and play, how to make lots of different shapes, just from knowing how to make one building block," she said. Different shapes, indeed, including the delightfully named PHiZZ, which stands for pentagon-hexagon zig-zag. It can be used to create, say, a soccer ball from Bizarro World or a bagel just returned from an inadvertent trip through the fifth dimension. Serenevy, 31, has made a sidelight of public math-based demonstrations about a host of cool stuff, including origami. She's making her first trip to Nashua because she's a friend of Rivier professor Teresa Magnus. Serenevy's Ph.D., by the way, shows the interesting directions that math can go. It concerns ways to create accurate numerical simulations of neurons as a way to help medical research. One of her thesis advisers, in fact, is a biomedical engineer. She likes origami because it's a fast way to get people to appreciate that dry old math can lead to interesting, as well as beautiful, places. "I'll be walking down the street with my origami polyhedron in my bag, and kids have stopped me and wanted to know how to do it," she said. If such an introduction can draw more kids into mathematics – and particularly more girls, who are still under-represented in the field – then so much the better. As for origami research, there's a chance you might have heard of it, or at least of Erik Demaine of MIT, whose insight into origami has made him the closest thing to a math superstar today, with appearances in The New York Times and elsewhere. Admittedly, most of this attention comes because origami is a rare serious-math field that has an appealing visual element. Fractals share that appeal. But origami is also interesting because it's a visible case in which experiment-driven mathematics, fueled by computing power that allows "what-if" scenarios too complex for paper and pencil, is producing deep insight that was long reserved for abstract thinkers. While it may not be true that mathematicians are pondering "the death of proof," to quote the title of a 1993 Scientific American article that still has some academics muttering in annoyance, it is true that computers have altered even the purest of pure math in very interesting ways. But it's also true that you don't have to worry about that a bit if you don't want to. Show up Thursday, learn to play with paper in very cool ways, and who knows – maybe the mathematician in you will bloom. Origami has math-savvy thinking creatively |
April 24, 2006
The myth of the selfish geneBy Carolyn Meinel Is life a zero-sum game? For one person to win, must another person always lose? Is there really no such thing as a true "win-win" situation? Colin F. Camerer is one of the world's leading experts in behavioral economics, a growing field of study that seeks connections between human psychology and human choices, economic or otherwise. Supporters of behavioral economics argue that human beings can and do act more altruistically than many economists have assumed. Given the proper environment, human beings can move beyond self-interest to become individuals who see benefits to others as central to their own decision making, said Camerer, the Rea A. and Lela G. Axline Professor of Business Economics at the California Institute of Technology in Pasadena, Calif. In one sense, this isn't a new idea. Camerer recently has argued that 18th-century economist Adam Smith, considered to be the father of freemarket capitalism, articulated many of the principles of behavioral economics in his book The Theory of Moral Sentiments. The difference is that Smith never linked his psychological insights into human nature with the moral pessimism set forth in his more famous book The Wealth of Nations. Camerer recently spoke with Science & Theology News correspondent Carolyn Meinel about how economists are slowly coming to take a rosier view of how humans act in the marketplace — and why the hard scientific data is pushing them in that direction. Q: What would you say is the most significant aspect of your research? A: Economists uniquely have a very cynical attitude toward human nature — that people are basically selfish, which makes mathematical modeling easy. My goal has been to restore common sense over the wishful thinking that this simple model is adequate. The model of human nature used by classical economists is a shortcut. Their default thinking is that people care only about themselves. As George Stigler, the Nobel Prize-winning economist, has argued, most of the time when self-interest conflicts with altruism, self-interest will win. It is no longer so true that economists take this viewpoint, but it used to be that you had to give this as the correct answer to get your Ph.D. Q: Why has it taken so long for economists to change their views? A: The first experiment that cast doubt on the "economic man" model was conducted at a Rand Corp. workshop in the summer of 1952. [Leading game theorist] John Nash was there. He recruited some secretaries and staff to play some games. However, they didn't follow his theory. Thinking like a mathematician, Nash and others thought of games as mathematical puzzles to solve. There isn't really a solution to these games, for human nature is not a puzzle to solve. It is a scientific problem to be measured and understood, but he didn't realize this. Nash's limitation was that he was not a psychologist. Consequently, he remained caught up in the math nuances of game theory and couldn't make sense of natural human behavior. After those early experiments, game theorists got caught up in important mathematical projects expanding the scope of the theory and postponed the project of creating a psychological theory. In the 1960s, game theorists began considering how information impacts the outcomes. What if one player knows something the other doesn't? What if both have this knowledge? These new ideas kept researchers busy figuring out the math. Not until the 80s and 90s did they become interested in psychology .... Now research on what we call "limited rationality" is booming among graduate students and even established leaders in economics looking for new challenges. Q: How do reciprocity games work? A: The ultimatum game measures numerically how likely people are to punish selfish behavior, meaning negative reciprocity. It's a one-shot game. The first player makes an offer to the second. Let's say it's $20, and the first player gets a portion of the $20 if he accepts the offer of the second player for how they will share the money. The purely self-interested player will accept any offer, even if it is unfair. The altruistic player will punish an unfair offer by refusing to accept it, even though both will get nothing. The trust game measures positive reciprocity. It's like investment but with no enforcement mechanism. One person has some money, say $10, which they can invest part of, keeping the rest. The amount they invest is tripled. But that tripled amount rests in the hands of a second person — a trustee — who is free to repay as much as she likes and keep the rest. To make the game challenging and scientifically interesting, if the trustee keeps all the money there is nothing the first person can do about it. The amount the first person invests shows how much she expects the trustee to repay her. The amount the trustee repays is a measure of trustworthiness, moral obligation or reciprocity. How people score in this game is also influenced by their culture. Kenya and Vietnam are relatively corrupt — compared to most Western countries — and their people show low trust. Richard Thaler [professor of behavioral science and economics at the Graduate School of Business] at the University of Chicago has an example of how trust affects economic systems. In upstate New York, farmers set up tables to sell their sweet corn. Each table is unattended. It has a sign saying when the sweet corn was picked, the price, and on each table is a box to accept payment. The box has a narrow slit for the money, so people can't take money back out, and the box is nailed to the table so they can't steal the entire box. Most people pay for the sweet corn. Those who are dishonest can only take the corn, but it's too hard to steal the money. Trust and verify. It's a good system because it relies upon good faith, but does not tempt the few who are dishonest too far. The myth of the selfish gene |
April 19, 2006
A new and much simpler proofThere has been sensational recent progress in the study of universal quadratic forms, a subject which originated in 1910 when Ramanujan wrote down 54 examples of such quadratic forms. These recent developments were related by Professor Manjul Bhargava of Princeton University while delivering the Third Ramanujan Commemoration Lecture at SASTRA University , Kumbakonam, on December 22. One of the most important results in number theory is a 1770 theorem of Lagrange which states that every positive integer is a sum of four squares. This motivated Ramanujan to investigate those quadratic forms which would represent all positive integers. In his notebooks Ramanujan wrote 54 examples of such quadratic forms. Ramanujan's discovery resulted in a flood of activity in the ensuing decades in the study of universal quadratic forms, namely, quadratic forms representing all positive integers. A startling result In 1993 Conway and Schneebeger announced a startling result that in order to decide whether certain special quadratic forms defined via matrices are universal, one need only check whether these represent the integers from 1 to 15. Their proof of this result, which was very intricate, was never published. Prof. Bhargava has found a new and much simpler proof of this result using geometric notion, which he presented in this lecture. Conway had conjectured that in the general case of integer valued quadratic forms, in order to decide which of those are universal, it suffices to check whether a certain special set of 29 integers up to 290 can be represented. This is a very difficult problem and Conway said he did not expect to see a proof in his lifetime! Quite surprisingly, during the summer of 2005, Prof. Bhargava and Jonathan Hanke proved Conway 's conjecture, and following this, were able to determine the complete list of all 6,436 integer valued quadratic forms that are universal. In establishing this results, they used a variety of techniques and results due to Ramanujan such as the circle method that Hardy and Ramanujan introduced in the asymptotic study of partitions, and Ramanujan's bounds for the coefficients of certain modular forms of integral weight that were proved by Fields Meadalist Pierre Deligne. Prof. Bhargava said that Ramanujan would have been quite pleased not only at the complete resolution of the problem of universal quadratic forms, but also at the methods employed in the proofs. "I am pleased to present these results in Ramanujan's home town on Ramanujan's birthday," he said. The Ramanujan Commemoration Lecture by Prof.Bhargava was the concluding event for the International Conference on Number Theory and Mathematical Physics held at SASTRA University in Kumbakonam, On the opening day of the conference, he and Kannan Soundararajan (University of Michigan) were each awarded the First SASTRA Ramanujan Prizes of US$10,000 for outstanding contribution in areas of mathematical influenced by Ramanujan. Prof. Bhargava announced that he would be donating a portion of the prize to SASTRA to support mathematically gifted students. (Krishnaswami Alladi is with the University of Florida , Gainesville , U.S. ) - The Hindu dated on 23 - December - 2005 A new and much simpler proof See also: The mathematician and musician, October 11, 2005 |
April 19, 2006
Young 'mathematics poet' receives prestigious US awardHCM CITY — The Mathematics department of the Courant Institute at New York University has awarded the Harold Grad Memorial Prize to Le Quang Nam and one other student out of the institute's 120 other doctorate students. The Courant Institute is a leader in pure and applied mathematics, especially in ordinary and partial differential equations. Every year, the Institute only accepts 15 students for its doctorate course. Le Quang Nam received a scholarship from Viet Nam Education Foundation to study at the Courant Institute in 2004 and became the first Vietnamese student there. At schools in Viet Nam, Nam was well known for his mathematics talent. In 1997, he won the Golden Prize in the Asia-Pacific's Mathematics Olympic competition. And as a third year student at HCM City National University, he was known as a mathematics poet, publishing the book To Search and to Study Math. Nam is an example for people because he overcame many difficulties to study. He was born into a poor family in the central province of Quang Ngai and his father moved to HCM City just to earn money for his son's studies. — VNS. Young 'mathematics poet' receives prestigious US award |
April 19, 2006
Fibonacci Poems Multiply on the Web After Blog's InvitationBy MOTOKO RICH Published: April 14, 2006  Gregory K. Pincus, with an example of his poetry, said that more than 1,000 "Fibs" have been written so far. - Stephanie Diani for The New York Times
Blogs spread gossip and rumor But how about a Rare, geeky form of poetry?THAT'S exactly what happened after Gregory K. Pincus, a screenwriter and aspiring children's book author in Los Angeles, wrote a post on his GottaBook blog (gottabook.blogspot.com) two weeks ago inviting readers to write "Fibs," six-line poems that used a mathematical progression known as the Fibonacci sequence to dictate the number of syllables in each line. Within a few days, Mr. Pincus, 41, had received about 30 responses, a large portion of them Fibonacci poems. Most of them were from friends or relatives or people who regularly read his blog, which focuses on children's literature. Then, last Friday, a subscriber to the popular Web site slashdot.org — which runs over a tagline that reads "News for nerds. Stuff that matters" — linked to Mr. Pincus's original post, and suddenly, it seemed, Fibs were sprouting all over the Internet. Mr. Pincus, who wrote in his original post that he conceived of the Fibonacci poems in part as a writing exercise, said in an interview that he figures more than 100 other Web sites have linked to his post and more than 1,000 Fibs have been written since the beginning of April, which just happens to be both National Poetry Month and Mathematics Awareness Month. "It tickles me that it can spread like that," said Mr. Pincus. "It's such a wonderful thing." Readers of the blockbuster best-selling "Da Vinci Code," of course, may recognize the Fibonacci sequence as the key to one of the first clues left for the novel's hero and heroine. It is also a staple of middle-school math classes. Though relatively rare in poetry, it shows up in the musical compositions of the early 20th-century composer Bartok and the progressive metal band Tool, the spiraling shape of the Nautilus shell and in knitting patterns. By and large, most of the people who have written Fibonacci poems over the past couple of weeks are not professional poets, but actors, comedians, video role-play enthusiasts, musicians, computer scientists, lawyers and schoolchildren. Casey Kelly Barton, a stay-at-home mother and home-schooler in Austin, Tex., who started a blog called Redneck Mother to chronicle her "dissatisfaction after Bush got re-elected," used the Fib form to write a rant against the president. Chat rooms linked to Web sites ranging from Actuarial Outpost, a forum for actuaries, to em411.com, a site for electronic musicians, have taken up Mr. Pincus's challenge and generated strings of the whimsical poems. Even a Hungarian technology site has linked to the Fibonacci post. The allure of the form is that it is simple, yet restricted. The number of syllables in each line must equal the sum of the syllables in the two previous lines. So, start with 0 and 1, add them together to get your next number, which is also 1, 2 comes next, then add 2 and 1 to get 3, and so on. Mr. Pincus structured the Fibs to top out at line six, with eight syllables. For many people, writing one of the poems is a little like solving a puzzle. Suresh Venkatasubramanian, a 32-year-old computer science researcher at AT&T Labs-Research in Florham Park, N.J., said he was attracted to the Fibonacci poetry because it reminded him of "what a computer scientist would call the 'resource constraints.' " On his blog, Geomblog, Mr. Venkatasubramanian added two more lines to Mr. Pincus's original prescription, while still keeping to the Fibonacci sequence: I like to blog. Frequently. Theory matters. Computer science (theory) is my home and geometric algorithms are sublime. Let P be a set of points in general position in the plane. Amen.The last line, said Mr. Venkatasubramanian, is an inside joke in geometry. Emily Galvin, a screenwriter and film production assistant who is writing a collection of poems and short plays in verse for Tupelo Press, has written one of her plays using the Fibonacci sequence. Instead of using the progression to dictate the number of syllables in a line, she let it regulate the number of words. Ms. Galvin, who said an ex-boyfriend once sent her love notes composed in the Fibonacci sequence, was delighted to learn of Mr. Pincus's success in spreading Fibs around the Internet. "How great that something mathematical could be bringing together all sorts of people who don't write professionally and giving them a form," she said. More professional poets may be attracted to the form, said Annie Finch, a poet who teaches at the University of Southern Maine. "Poets are very, very hungry for constraint right now," said Ms. Finch, who has written about formal poetry. "Poets are often poets because they love to play with words and love constraints that allow the self to step out of the picture a little bit. The form gives you something to dance with so it's not just you alone on the page." Even those who were not compelled by the idea of Fibonacci poetry could not resist the challenge. When asked for her insights, Judith Roitman, a poet and math professor at the University of Kansas, wrote in an e-mail message that she "found the phenomenon pretty uninteresting." But she then went on to write: So you no doubt will not find it interesting to talk to me about this stuff.Fibonacci Poems Multiply on the Web After Blog's Invitation |
April 19, 2006
Mathematician wins statewide distinguished teaching award Dan Maki (Courtesy of Indiana University) "Dan Maki has had a long and truly distinguished career in classroom teaching, curriculum development, educational outreach, and service to his department and the mathematical community," said John Lorch, chair of the Indiana Section of the Mathematical Association of America. "He has displayed excellence in teaching at all levels from freshman service courses through mainstream graduate-level mathematics courses. He has developed, organized or participated in numerous curriculum-development and outreach programs, activities which have had an enormous impact on the quality of the educational experience for students at his home institution as well as on the quality of mathematics teaching at the elementary and high school levels throughout the state of Indiana." When students in a large mathematics course were asked what they liked most about the class, they spoke about Maki. He "is the most effective math teacher I've ever had," "has a sense of humor and knows everything about this course," "related math to everyday life very well," and "was very excited to teach and wanted everyone to understand," the students said. In the words of one of his colleagues, Maki "has developed a cadre of very effective, high-quality faculty in secondary schools around the state that are having a significant real impact on strengthening secondary teaching, curriculum and standards." Another colleague said he has "encountered no faculty member more concerned with undergraduate teaching or who has done more to improve the undergraduate experience" than Maki. A third described Maki's role in designing and implementing an engaging cablecast television program directed at students in the finite mathematics course. "This year's award recipient has had the positive impact upon students that all teachers hope to achieve," Lorch said at the presentation ceremony. Mathematician wins statewide distinguished teaching award |
April 19, 2006
U of M researchers help uncover mystery evolutionary cycle of zeolite crystalsMINNEAPOLIS / ST. PAUL (4/18/2006) -- The porous, sieve-like minerals known as zeolites have been used for decades in purifiers, filters and other devices. Yet creating and refining a new type of zeolite is still a matter of sophisticated trial and error: No one has been able to figure out exactly how the crystals form, even in the laboratory. Now, however, a team of chemists, engineers and mathematicians, using some of the most advanced microscopes in the research arsenal, has uncovered new details for the step-by-step evolution from molecular soup to carefully engineered zeolite crystal. With this knowledge, laboratories may be able to use targeted methods to create zeolites with precisely the crystal sizes and shapes demanded by molecule-specific applications such as chemical sensing. University of Minnesota chemical engineer Michael Tsapatsis, graduate student and lead author Tracy Davis, and their colleagues report their findings Apr. 17 online in Nature Materials. The research was supported by several National Science Foundation (NSF) grants. Zeolites are familiar to consumers as, for example, the white crystals in aquarium filters or the ion-exchanging workhorses in advanced detergents. But their real economic impact is behind the scenes, where they are critical for extracting various chemical components out of petroleum and its byproducts on an industrial scale. Zeolites accomplish this feat by trapping and removing specific target chemicals, which makes it easier for companies to purify the chemicals they want. So the challenge for researchers is to tailor a zeolite for each application that traps just the right set of chemicals. Ultimately, their goal is to control the structure, size and shape of the crystals well enough for zeolites to serve as sponges for hydrogen in fuel tanks, channels in next-generation sensors and separation membranes for chemical manufacturing. "Controlling the growth of a certain crystal structure is difficult because it is done by trial and error, or what some critics may call a 'mix, wait and see' approach," said Tsapatsis. "Researchers have lacked a clear understanding of nucleation and growth processes that control formation of those zeolites and related organic-inorganic nanostructures." In an effort to improve that understanding, Tsapatisis and his colleagues have spent more than a year monitoring the growth of zeolites in a laboratory setting, where they could watch the crystal growth process in exquisite detail. "These are complex structures containing hundreds of atoms per unit cell, and their formation is determined largely by kinetics," said Tsapatsis. "Our approach is to slow down the kinetics and exhaustively study the evolution by all techniques available to us." The study showed that the zeolites form in a step-by-step, "hierarchical" fashion, with silicon-oxygen nanoparticles forming first. Those particles then aggregate into larger, more complex structures, incorporating other atoms and molecules while still leaving substantial pores and tunnels. Based on their findings, the researchers developed a set of mathematical equations that describe the nucleation and growth process. "There are essentially unlimited opportunities for these crystals if we can control their pore structure and crystal shape, tailoring designs to specific applications ranging from catalysts to bio-implants," Tsapatsis added. While laboratory zeolites tend to exist as microcrystal powders, the researchers hope the new insight may help yield larger structures--even layers and thin films--that are perfect for optoelectronics, sensors and micro-reactors. Funding for this work was provided by the NSF Directorate for Engineering Division for Chemical and Transport Systems, the Directorate for Mathematical and Physical Sciences Division for Materials Research and Division for Mathematical Sciences, and support through the NSF National Nanotechnology Infrastructure Network. U of M researchers help uncover mystery evolutionary cycle of zeolite crystals |
April 19, 2006
UCLA study may explain pitfalls of drug holidaysResearchers have been puzzled over why HIV-positive patients who have periodic interruptions in their drug therapy reach a point where the therapy no longer reduces their HIV viral loads, even in the absence of any evidence of acquired drug resistance. Now two researchers at the University of California, Los Angeles's AIDS Institute have devised a novel hypothesis based upon mathematical modeling linked to the physical phenomenon known as "resonance." Based on the assumption that viral dynamics have a cycle that varies from patient to patient, the researchers suggest that these forces interact with treatment interruptions in a way that causes high fluctuations in the patient's viral load and, ultimately, virologic failure. At that point, the drugs can no longer reduce the levels of virus in the patient's blood. Therefore, the UCLA researchers feel there may not be a single, structured treatment-interruption therapy that will be effective for all HIV patients. "This is important to keep in mind when developing therapies for HIV-patients," Sally Blower, professor of biomathematics and coauthor of the study with postdoctoral researcher Romulus Breban, says in a press statement, "Our research shows that mathematical models can be extremely useful as tools for generating hypotheses." Resonance is the oscillation that results when a system with natural cycles is affected by an external force that is itself moving at an appropriate frequency, resulting in a strong fluctuation. A swing pushed in the same direction in which it is already moving, for instance, will swing higher as a result of that force placed upon it at a frequency that corresponds to the natural periodicity of the swing. In the same way, the periodic interruptions in HIV antiretroviral therapy might contribute toward pushing the viral load higher when those interruptions occur at a specific time during the viral load's cycle, the researchers suggest. Resonance is observed when the antiretroviral drugs cannot reduce the viral load. "Resonance is a very general phenomenon that has been long known in physics and engineering," Breban says in a press statement. "We are the first to apply it to virology." "At the beginning of treatment, the patient's viral load is quickly suppressed," Breban continues. "But the therapy interruptions combined with the viral dynamics, which can vary widely from person to person, can lead to treatment failure." While small initial pilot studies into treatment interruptions showed no virologic failure in the test subjects, a large-scale clinical trial in 2003 was prematurely terminated due to a 53% virologic failure rate. And the disappointing findings have continued, prompting authorities to cancel another treatment-interruption study. On January 18, the National Institute of Allergy and Infectious Diseases halted enrollment into an international HIV/AIDS trial known as Strategies for Management of Anti-Retroviral Therapy, which compared continuous antiretroviral therapy with episodic drug treatments, after researchers determined that patients on episodic treatment faced more than double the risk of disease progression than the other patients. If the resonance hypothesis to treatment interruptions is correct, then the results of the Blower-Breban study have important implications for the treatment of patients, clinical trial design, and public health. The National Institutes of Health/National Institute of Allergy and Infectious Disease funded the study, which appears in the April 15 issue of the medical journal The Lancet. (The Advocate) UCLA study may explain pitfalls of drug holidays |
April 19, 2006
President Establishes National Mathematics Advisory PanelPresident Bush today issued an executive order creating a National Mathematics Advisory Panel to advise him and Secretary of Education Margaret Spellings on the best use of scientifically based research on the teaching and learning of math. Based on the influential National Reading Panel, the math advisory board will convene experts to evaluate the effectiveness of various approaches to teaching math and in so doing, create a research base to improve instructional methods for teachers. The group's interim report will be submitted to the president and secretary by Jan. 31 with specific recommendations on a range of topics related to math education, based on the best available scientific evidence. "We look forward to receiving the panel's recommendations, and we hope it will form a blueprint on how to promote excellence in mathematics education," Secretary Spellings said. "As I've said before, it is more important than ever that our students receive solid math instruction in the early grades to prepare them to take and pass algebra and other challenging courses in middle and high school." Among the topics to be addressed in the panel's report: The skills needed for students to learn algebra and be ready for higher levels of mathematics. The appropriate design of systems for delivering math instruction that combine elements of learning, curricula, instruction, teacher training, and standards, assessments and accountability. And, Research needs in support of mathematics education. The National Mathematics Advisory Panel is part of the president's plan to strengthen math education so that America's students receive the tools and skills necessary for success in the 21st century. Included in his fiscal year 2007 budget request is $10 million to carry out the group's recommendations. The spending plan also includes $250 million for the newly proposed Math Now programs. Modeled after the successful and popular Reading First program, the Math Now for Elementary School Students project would use the recommendations of the National Math Panel to promote scientifically based research and promising practices in mathematics instruction to prepare students for more rigorous coursework in middle and high school. The program is similar to the current Striving Readers Initiative and would diagnose students' deficiencies in math, providing intensive and systematic instruction to enable them to pass algebra courses. Secretary Spellings stressed the need for today's high school graduates to have solid math skills -- whether they are proceeding to college or going straight into the workforce. She and others have pointed out that U.S. students are currently performing below their international peers on math and science assessments. For example, only seven percent of fourth- and eighth-graders achieved the "advanced" level on the 2003 Trends in International Mathematics and Science Study (TIMSS) test. By contrast, in Singapore, 38 percent of fourth-graders and 44 percent of eighth-graders reached that level. On the most recent Program for International Student Assessment (PISA), American 15-year-olds performed below the international average in mathematics literacy and problem-solving. And, almost half of American 17-year-olds do not have the basic understanding of math needed to qualify for a production associate's job at a modern auto plant. In addition, studies have found that students from low-income families who acquire strong math skills by the eighth-grade are 10 times more likely to finish college than peers of the same socioeconomic background who do not. For a fact sheet on The American Competitiveness Initiative: Encouraging Innovation and for more information on the President's National Mathematics Advisory Panel, please visit: http://www.ed.gov/news/opeds/factsheets/index.html?src=gu President Establishes National Mathematics Advisory Panel |
April 19, 2006
Higson, Irwin named Evan Pugh professors Mary Jane Irwin, left, and Nigel Higson have been named Evan Pugh professors.
University Park, Pa. -- Nigel Higson, distinguished professor of mathematics and head of the Department of Mathematics, and Mary Jane Irwin, who holds the A. Robert Noll chair in engineering and is co-director of the Embedded and Mobile Computing Center, have been named Evan Pugh professors, the highest distinction that Penn State can bestow upon a faculty member. |
April 13, 2006
Campbell awarded for teaching expertiseBY ROB MATTHEWS  According to the MAA Web site, the award honors beginning college or university faculty whose teaching has been successful in influencing students beyond the classroom. Each year, at most three college or university teachers receive the $1,000 prize and certificate of recognition from the MAA. In order to be eligible for this highly prestigious award, potential candidates must be nominated by a member or section of the MAA, in this case the Swarthmore Mathematics department. "I'm delighted but not surprised," Mathematics Department Chair Stephen Maurer said in response to Campbell's award. "We nominated him because when we looked at everything that he did, I thought that it was impressive for someone so early in his career to have done so many things. He had letters from students who worked with him, students in his classes who visited him during office hours, students at the various summer programs in which he taught and also from faculty who worked with him at these programs. Teaching is not just in the classroom and the institution." Former students Sally Hall '06 and Jaky Joseph '06 had nothing but praise for Campbell's teaching methods. "He [Campbell] really deserves it. I have never seen someone so dedicated to students. He is always there and always willing to help," Hall said. Joseph, for whom Campbell is his thesis advisor, agreed. "He's very deserving. He's an excellent professor. He helped me in and out of class," he said. "He is the kind of professor who will hold himself up to make sure that the whole class is on the same page." Campbell said he was pleasantly surprised that his colleagues and advisers thought to nominate him for the Alder Award. "I am honored not only that my department and my colleague Cheryl Grood in particular thought to nominate me, but I am also honored to be chosen to receive such a distinguished award," Campbell said. "I have been surrounded by so many fantastic teachers, both in the department here and in several of the programs I've had the pleasure of being involved with, that winning the award is also oddly humbling. I view this award as a real testament to the support and encouragement I have received from the students, from the department, from the college and from my family and friends for all the things I have valued and put energies into as part of being a professor." Even though he was recognized for his exemplary teaching methods, Campbell said there are still areas that he can improve. "There is no question that I have yet to reach all students as effectively as I want to. It is in my nature to try new things — not all of which work for all students," Campbell said. "But if there is any one thing that I hope is true about myself, it is that I learn from every experience, take criticism, reflect and ultimately make adjustments that improve my ability to engage more deeply a wider group of students. So, will I make changes to my teaching? Absolutely." When asked about what he wanted students to take away from his classes, Campbell outlined three main aims. "Probably least interesting, there is always some core material that I hope students learn. Second, I hope to convey the beauty in some of the mathematical ideas we cover. Finally, I try to pay special attention to developing mathematical maturity. I may not always actually articulate this as a goal to students, but I think it's always there," he said. "I really want students to understand how a mathematician might approach a problem, to recognize some of the common threads that appear in mathematics and to be okay with the patience and diligence it sometimes requires to get through some mathematical ideas. Each step up that I took in my own mathematical development was a challenge and part of what I'm hoping to do is to make the next mathematical step my students may take a little easier." As far as plans for the future, Campbell said he intends to take a sabbatical next year. "I will be spending that time looking at new techniques and new problems related to mathematical objects called elliptic curves, reflecting on and making the kinds of changes to my teaching I was alluding to earlier and developing some tools that I hope will help some of the students who find themselves struggling with mathematics. Thinking more long term, I do hope to make significant contributions to areas of the college that effect more than my own courses," he said. "For example, there has been some discussion in The Phoenix recently on the issue of retention, and to a lesser extent achievement, of underrepresented groups in the sciences. This is a complicated issue that the college has been investigating for some time now and is an issue being examined at a great many undergraduate institutions," Campbell said. "One of the things I hope to do is to contribute to the college's efforts in developing tools and strategies that help minimize any gaps that might exist in retention and achievement among various groups." Campbell awarded for teaching expertise |
April 13, 2006
How a wave led to a prizeDevlin's Angle This year's Mathematics Awareness Month - this month in fact - sees the MAM celebrate its 20th birthday, the annual festival having been first launched in 1986. With this years theme being Mathematics and Internet Security, it is perhaps fitting that it is also the 30th anniversary of the introduction by Whitfield Diffie and Martin Hellman of the idea of Public Key Cryptography. To find out more about MAM and what Diffie and Hellman did, click over to the Mathematics Awareness Month Website at www.mathaware.org, where you will find various articles describing the different ways that mathematics plays important roles in Internet Security. The remainder of this month's column has nothing to do with either Mathematics Awareness Month or Internet security - at least as far as I know. But having found myself organizing the MAM national campaign this year, I couldn't resist giving it one final plug. What I really want to talk about is the recent awarding of the Abel Prize to Swedish mathematician Lennart Carleson. The idea for the prize, awarded annually by the Norwegian Academy of Science and Letters for work in mathematics, goes back to the start of the twentieth century. Observing that when Swedish scientist, industrialist, and philanthropist Alfred Nobel established the Nobel Prizes in 1895, he did not stipulate a prize for mathematics, the Norwegian government at the time decided to fill what they saw as an unfortunate gap and create an equivalent prize for mathematicians. They further decided that the prize should be named after the man who was arguably Norway's most famous mathematician of all time, Niels Henrik Abel, who had lived in the early part of the 19th century. Unfortunately, the breakup of the Swedish-Norwegian union in 1905 prevented the completion of the prize creation process, and it was not until 2003 that the Norwegian government finally made good on the century-old intention of their predecessors. With this years award, the prize goes to a Scandinavian for the first time. Announcing the 2006 award on 23 March, Norwegian Academy President Ole Didrik Laerum cited Lennart "for his profound and seminal contribution to harmonic analysis and the theory of smooth dynamical systems." Lennart will receive his prize from Queen Sonja of Norway at a ceremony in Oslo on 23 May. The result for which Lennart is most widely known is his completion of the work on wave analysis begun by Jean Baptiste Joseph Fourier (1768-1830) Fourier analysis, the basis of today's music synthesizers, iPod music players, and so forth. Fourier showed how to take the graph of a wave, such as a sound wave or heat radiation, and decompose it into an infinite sum of sine waves. Fourier's approach worked for all of the naturally occurring waves that people looked at, but would it work for all waves? Or were there some strange pathological waves that could not be expressed as an infinite sum of sine waves? That question remained open for many years until Carleson answered it in 1966, showing that the Fourier decomposition process does indeed work for all waves. For most mathematicians, one result of that magnitude in a lifetime would be more than enough, but Carleson scored big a second time in 1991, when, together with his colleague Michael Benedicks, he gave a rigorous proof of an "order out of chaos" result that had been suggested by computer work but had long resisted definite proof - namely the existence of a so-called strange attractor for a certain widely studied dynamical system known as the Henon system. For more details about Carleson's work and on the Abel Prize, see the Abel Prize website at www.abelprisen.no/en/ Oh, and one final thing. Please do not write to tell me that you once heard that the reason there is no Nobel Prize in Mathematics is that Nobel feared that the great Swedish mathematician Gosta Mittag-Leffler might win such a prize, and Nobel hated him for having an affair with his wife. This story is not true. It could not possibly be, since Nobel never married. bla How a wave led to a prize |
April 13, 2006
A Helix with a HandleMathematicians prove the existence of a new class of minimal surfaces Fenella Saunders Dip a loop of wire into a soapy solution, and the film that covers the loop will be what mathematicians call a minimal surface. The soap forms such a shape because it minimizes surface tension. At any point, a minimal surface is maximally curved in one direction and minimally curved in the opposite direction, but the amount of curvature in each direction is exactly the same. As a result, each point on the surface is either a flat plane or a saddle shape, never a sharp peak or valley. But a minimal surface doesn't have to be flat or simple overall: A plane can be twisted into a parking-ramp shape called a helicoid, which mathematicians proved over two centuries ago is also a minimal surface. Mathematicians have proved the existence of a class of minimal surfaces that cannot be embodied by soap bubbles but can be visualized by computer simulation. This surface, called a genus-one helicoid, is a variation on a standard helicoid, but there is a tunnel through the deck of the parking-ramp spiral. When untwisted, this surface looks like a flat sheet with a coffee-mug-handle shape grafted onto it. "Think of a torus, like an inner tube," says Matthias Weber of Indiana University. "Now imagine that you puncture the torus. This results in a surface that can be stretched and deformed into the genus-one helicoid. I think that's a real mind bender." As they reported in the November 15, 2005, issue of the Proceedings of the National Academy of Sciences, Weber, David Hoffman of Stanford University and Michael Wolf of Rice University have proven that such shapes, whether they have one or an infinite number of handles, are indeed minimal surfaces that can go on forever in all directions and never fold back to intersect themselves. Over a decade ago, Hoffman, with Fusheng Wei, then of the University of Massachusetts at Amherst, and Hermann Karcher of the University of Bonn in Germany, had created computer simulations of such handled helicoids, but an airtight demonstration of minimal surfacehood eluded them. "Computer graphics programs enabled us to visualize these surfaces, but we couldn't bring them back into the mathematical fold," says Hoffman. "I think the information about how to solve this problem was lurking in the pictures all the time, but we just had to think about it for a long time and have the theory catch up with the evidence we had." Catching up can be hard to do: The mathematical proof takes up more than 100 pages. An advanced understanding of minimal surfaces could be relevant to materials science; for instance, some compound polymers, such as Kevlar, have interfaces between molecules that are approximately minimal surfaces, the shape of which can influence the chemical properties of the material. As mathematicians, Weber and his colleagues are most excited about a potentially large, new class of minimal surfaces that have not been found in nature and which no investigators had imagined could exist until recently. "It's easy to come up with one new example of a minimal surface, but this one is of a very different nature than others that have been found before," Weber said. "So it's opened a new field within the theory of minimal surfaces." A Helix with a Handle |
April 13, 2006
Geometry + algebra = good time at math meetWednesday, April 12, 2006 - Bangor Daily News ORONO - Nearly 900 high school students filled Alfond Arena Tuesday without making a sound. Sitting at long tables, hunched over clipboards, they chewed furiously on gum and nervously played with locks of hair as they mulled over math questions. "These are killers," said Madawaska High School junior Melissa Nadeau, one of the participants in the 30th annual Maine State Math Meet. "We're just trying to do our personal best and have a good time." The daylong event called on students from 86 communities to demonstrate their ability in almost all types of high school math including geometry, algebra, trigonometry, logarithms, linear equations and number theory, as they competed individually and in teams. Students said they enjoyed the challenge and that they liked competing. Participating in math teams is good preparation for the SATs as well as for college and provides a welcome chance to meet other students who also love math, they agreed. "It's like going to a sporting game, but it's something I'm really good at it," said Alex Patten, a senior at Berwick Academy. Teachers, meanwhile, said math teams create stellar students who are skilled at problem solving. They enter the nation's top colleges and universities and become leaders in science, math, engineering and technology. Steve Godsoe, one of Bangor High School's math coaches, said students take the competition seriously. "They give it everything they can. They work hard and want to do really well." Math team students practice regularly and compete in meets throughout the year, so "they're constantly reviewing and renewing," said Mary Wilbur, a retired math teacher from Mattanawcook Academy in Lincoln. "They don't just learn for a test and forget everything," said Wilbur, who coached math teams for 20 years. They're an outlet for "students who are academically talented and want to go beyond what they get in regular school," said Pete Pederson, math teacher at the Maine School of Science and Math in Limestone, and one of the coordinators of the event. "It's lots of fun," said senior Paul Wilson of Hampden Academy as his team dug into a Pat's Pizza. "You get free food and you get to do math. We're kind of nerdy - we love math." At John Bapst Memorial High School in Bangor almost 50 students out of a total enrollment of 450 are on the math team, said math coach Kim Jones. Each school was only allowed to send 10 students per team for Tuesday's event, however. Students see that "math is cool now," she said. During the competitions, students sometimes even point out errors or new ways of looking at problems, said organizers. "They're very bright kids and sometimes they see things that we overlooked," said Oxford High School math teacher Allen Gerry. The top performing school for the meet was the Maine School of Science and Mathematics, followed by Brunswick High School, Portland High School, and Bangor High School. Hampden Academy came in 13th and Brewer High School was ranked 17th. Shortly after the award ceremony, MSSM student Justin Haines said the team was excited about its third win in four years. "We went into the event expecting to do well, but not necessarily to win," said Haines, the meet's highest scoring senior. Math meets can be nerve wracking, admitted senior Melanie Craig of Bangor High School. "But then the adrenaline kicks in," she said. Hampden Academy junior Corey Cole said some of the math she was called on to use during the event was familiar. "But sometimes it's like, "Wow, I've never seen this before," she said. Amanda Greenfield, a senior who's been on the Caribou High School team for three years, said, "It's nice to go from year to year to see how you've improved." Watching her students relax during an afternoon break, Vanda Madore, math teacher and coach in Caribou said she just wanted everyone to enjoy the experience and connect with other math lovers. "They've got the math skills, now I want them to focus on having a good time," she said. "We need to make this fun for them." For Mattanawcook senior Josh Tilton, the afternoon team rounds were the toughest part of the meet. During each round, each team was given eight problems to solve, with team members discussing possible equations and formulas and working out solutions as quickly as possible within the overall 12-minute time limit. With everyone on his team calling out answers, Tilton had to decide which ones to submit to the judges. But he had a strategy. "If someone comes up with an answer and someone else says the same thing, you know it's right," he said. During one break, Lee Academy students were going over problems to figure out where they went wrong. "Once the pressure's off you can go back and look through it," said senior Crystal McLaine. Josh Pietras, a math teacher at Central High School in Corinth, recalled that he had been a member of the math team at Mattanawcook. Math team students are the ones who are always asking "prodding" questions, who don't get discouraged when they don't understand something and who look at a difficult problem as a challenge, he said. MSSM Coach Heather Van Ligten said when she tells people about her job as a math teacher they often wrinkle their nose and confide that they weren't particularly good in math. "All of these kids like to do this," she said. "That's what makes it fun." According to organizers, photos and results of the math meet will be posted within the next two days at www.maml.net. Geometry + algebra = good time at math meet |
April 13, 2006
Google wins rights to Aussie algorithmBy Stephen Hutcheon April 10, 2006 Google has snapped up the rights to an advanced text search algorithm invented by a University of NSW student. The algorithm, or search engine tool, is called Orion and was developed by UNSW PhD student Ori Allon at the university's School of Computer Science. Orion works as an add-on to existing search engines to improve the relevance of searches and won praise from Microsoft founder Bill Gates last year. The algorithm is a problem-solving computational procedure and is the building block for all search engines such as those operated by Google and Yahoo! Orion finds pages where the content is about a topic strongly related to the key word. It then returns a section of the page, and lists other topics related to the key word so the user can pick the most relevant. The results of the query are displayed immediately in the form of expanded text extracts, giving the searcher the relevant information without having to go to the website - although there is still that option. Mr Allon, a 26-year-old computer scientist, was born in Israel but came to study at Melbourne's Monash University in the '90s. After completing his bachelor and masters degrees, he moved to UNSW to further his studies and research. The Israeli newspaper Ha'aretz reported on Sunday that Google had acquired Mr Allon's advanced text search algorithm. Mr Andrew Stead, the business development manager at UNSW's NewSouth Innovations agency confirmed that Mr Allon left Australia six weeks ago and was now working at Google's headquarters at Mountain View, California. Mr Stead said the move was not a secondment; Mr Allon's move was permanent. Some work on the project, however, would continue to be undertaken by Mr Allon's supervisor in Sydney, Dr Eric Martin. Mr Stead confirmed that the university had held talks with the big three internet search operations: Google, Yahoo! and MSN. Beyond confirming that Mr Allon was now working for Google, Mr Stead was not able to confirm any other of the reported details. However, given Google's desire to continue dominating the search business and the fact that there were other interested parties, the deal could potentially be worth millions. While Mr Allon is the key person behind Orion, the university retains ownership of the intellectual property as it was developed within the university's research facilities. Mr Stead said Mr Allon, who is an Australian citizen, hoped to complete his PhD with the university and one day hoped to return to Australia. Google wins rights to Aussie algorithm |
April 13, 2006
Specific Mechanisms May Not Exist For Facial Recognition"We found that faces aren't special in the way many scientists once thought. Rather, they are particular group of objects which the brain has learned to distinguish very well, much as it would for any other similar objects that are critical to human survival and communication." By Georgetown University Medical Center, Although the human brain is skilled at facial recognition and discrimination, new research from Georgetown University Medical Center suggests that the brain may not have developed a specific ability for "understanding faces" but instead uses the same kind of pattern recognition techniques to distinguish between people as it uses to search for differences between other groups of objects, such as plants, animals and cars. The study, published in the April 6 edition of the journal Neuron, adds new evidence to the debate over how the brain understands and interprets faces, an area of neuroscience that has been somewhat controversial. Because the process of facial perception is complicated and involves different and widespread areas of the brain, there is much that remains unknown about how humans perform this task. "We found that faces aren't special in the way many scientists once thought," says Maximilian Riesenhuber, PhD, assistant professor of neuroscience and senior author of the study. "Rather, they are particular group of objects which the brain has learned to distinguish very well, much as it would for any other similar objects that are critical to human survival and communication." Riesenhuber hopes that integrative research of this kind will help scientists better understand the neural bases of object recognition deficits in mental disorders, such as autism, dyslexia or schizophrenia. People with autism, for example, experience difficulty with recognizing faces, which might be caused by a defect on the neural level. Breakthroughs in this kind of research could someday lead to targeted therapies for the millions of people who suffer from these disorders. "The findings are exciting because we are now going to apply this technique to probe the neural bases of face perception deficits in autism," Riesenhuber said. Because humans are so talented in recognizing faces, many in the scientific community have argued that the brain has developed unique mechanisms for understanding and distinguishing them. However, Riesenhuber and his team thought that a different model could help explain some of the existing knowledge about facial recognition, including a behavioral phenomenon known as the "inversion effect," which has shown that turning a picture upside down has a strong effect on people's ability to recognize faces whereas the ability to recognize other objects, such as houses, is affected only slightly. "We think that this is because we are face 'experts,' having learned over many years to spot fine differences in upright faces, but not in inverted faces. That experience makes faces unique, but there's nothing scientifically special about faces," Riesenhuber says. The Georgetown scientists hypothesized that facial recognition does not rely on face-specific mechanisms but instead uses the same neural mechanisms for faces that are used to discriminate other objects. Over the years, because of the importance of facial identity and expression for social communication, humans have simply developed a strong talent for recognizing and distinguishing faces. This experience with faces then leads to the learning of a population of neurons finely tuned to different faces, Riesenhuber says. The researchers tested their theories using a computational model previously developed by Riesenhuber and his team to predict how different neurons would react during the recognition of non-face objects. They then showed that this simple model, even though not developed for face recognition, could quantitatively account for the inversion effect and make predictions about how selective the group of "face neurons" should be to explain human performance, which provided further evidence that it was unnecessary to postulate any kind of special processing in the brain for faces. The researchers then tested these predictions against experimental data measured in a functional Magnetic Resonance Imaging (fMRI) machine, a high-powered imaging technology that can measure the brain activity of test subjects, and by other behavioral techniques. Subjects were shown pairs of images of similar human faces that had been morphed using computer graphics software, while the researchers observed how brain activation changed for more or less similar pairs of faces. They found that a small group of neurons in the "fusiform face area," an area of the brain generally thought to be responsible for face recognition, was highly selective for different faces, just as the model predicted they would behave. "We knew that the fusiform face area is highly involved and necessary for us to understand faces, but we did not know what kind of processing was going on inside that 'black box'," he said. "By using a computational model to quantitatively link neuronal processing, brain imaging and behavior, we now have a mechanistic model describing which neurons are involved and how they are behaving when we look at faces." - April 6 edition of the journal Neuron gumc.georgetown.edu Specific Mechanisms May Not Exist For Facial Recognition |
April 06, 2006
Math matters in many livesWednesday, April 05, 2006 - Bangor Daily News By Jerry Farlow Recently, someone asked me how many of the following names I recognized: Barry Bonds, Johann Radon, Britney Spears, Yves Meyer, Ben Stiller, Sergey Brin, Tom Brady and Isaac Schoenberg, and I'd like to pose the question to you. My guess is you will recognize four of the eight. Actually, my quiz is a fraud. It's just my awkward way of announcing that April is National Mathematics Awareness Month, and to make the point that although mathematics and mathematical discoveries never make the headlines of the Bangor Daily News, like winning a Super Bowl, they might be more important in our daily lives, and that's where the four unrecognizable names come in. First, let me tell you about Johann Radon. Johann Radon was an Austrian mathematician who in 1917 worked out a mathematical theory for reconstructing the shape of an object by looking at its shadow from different directions. It's a little bit like finding out where all the nuts and fruit are inside a fruitcake by looking at slices of the cake. Radon's ideas went unnoticed until the 1970s when an English engineer and a physician from Tufts University used Radon's theory in the invention of the CAT Scan. To them the fruitcake was the human body, the nuts and fruit were our internal organs (or maybe a tumor), and the slices of the cake were X-ray images. The problem with X-rays in determining where things are located inside our body is that they only give a shadow of the thing. To produce a picture that shows the exact location of things, the CAT scan takes X-rays from different angles, then use Radon's formulas (called the inverse Radon transform) to reconstruct the picture. We are in a golden age of mathematics. If you want to see just a few ways mathematics is affecting our lives, go to http://www.ams.org/mathmoments , a site run by the American Mathematical Society. Let's move on to person no. 2 on your don't-know-who list. Thirty years ago a French mathematician, Yves Meyes, created the Wavelet Transform, a mathematical theory with applications in all areas of science and technology, one of which is the compression of television pictures, digital camera pictures, jpg pictures in your computer, mp3 digital music, and so on. If these files can be compressed without losing any resolution, then they can be transmitted faster, either by television transmitters or over the Internet. The basic idea behind wavelets is that if a picture consists of only one color, there is no reason to send every pixel or dot; just sending the color is sufficient. It's never that simple of course since pictures are always a complex mixture of colors, but in Meyes theory, the different colors and hues are collected by a complex process into "wavelets" and these wavelets are transmitted rather than transmitting every pixel. Most TV stations are not set up for wavelet technology yet, but many researchers say they will be in the future. Wavelets are used by the FBI today to compress the 200,000,000,000,000,000 bits of data required to store the fingerprints of convicted felons. You can learn more about this technology at http://www.ams.org/ams/mm8s-fingerprints.pdf. Why it is so many people are turned off by mathematics? Someone said it's a result of the "piano syndrome." Learning to play the piano and learning elementary mathematics are a lot alike. In both cases the beginner must pass through a rigid orientation. The beginning pianist spends months developing finger dexterity by playing scale after scale. Only after the basics are mastered can a student of the piano interpret a Chopin concerto or the student of mathematics use one's imagination to build mathematical worlds. The point is most beginning students of mathematics do not have a good idea of what the discipline is all about and do not survive the orientation to see the beauty of the subject and the rewards that await its practice. So, who is Sergey Brin? Well, he along with Larry Page were graduates students at Stanford in the 1990s when they decided to create a better search engine for the World Wide Web. To determine how this might be accomplished they imagined a person picking a Web page at random and then going from Web page to Web page, choosing an outgoing link at a given page to get the next page. This can lead to dead ends at Web pages that have no outgoing links or around endless cliques of interconnected Web pages. This kind of random walk is called a Markov Chain in mathematics and was invented in 1887 by the Russian mathematician, Andrei Markov. Now, suppose a given individual surfs the web an infinite number of times. Of course, no real human can but we can imagine it mathematically. The probability this imaginary mathematical web surfer will ever reach a given Web page is called the PageRank of the Web page. A Web page will have a high PageRank if it has links to and from other pages of high ranks. The computation of the PageRank of a webpage requires finding what are called the eigenvalues and eigenvectors of the transition matrix of the Markov Chain, and this PageRank system of assigning ranks Web pages is the trademark of Google, of which Brin and Page are its founders. Google is the main search engine of the Internet and has made both its founders, Sergey Brin and Larry Page, multi-billionaires. Today there are many great math Web sites for persons of all interests and expertise. A great Web site to get information on almost any math topic is http://mathworld.wolfram.com/. So, who is no. 4? In the 1940s while a professor of mathematics at the University of Pennsylvania, Professor Schoenberg developed the theory of what is called "spline curves." Splines are special kinds of curves and surfaces that have a nice appearance, are flexible, and most importantly, can be manipulated in a computer. His early work in splines is one of the cornerstones in the broader area of computer graphics. Automobile draftsmen for Ford and General Motors create new car designs by means of spline surfaces drawn by a computer. Figures drawn in animated movies, such as Shrek or the Lion King, also owe a lot to the invention of splines. The next time you go to an animated movie you may think you're watching Shrek, but you may be watching one of Schoenberg's splines generated by a computer. Jerry Farlow is a professor of mathematics at the University of Maine. Math matters in many lives |
April 06, 2006
Puzzles, Origami and Other Mind-TwistersBy EDWARD ROTHSTEIN Published: April 3, 2006  Erik S. Lesser for The New York Times Kate Jones with one of her puzzle designs at the Gardner gamesfest. Simple, right? The scoop removes only a very small proportion of green marbles, so more green remain in the red jar. Except that's wrong: both jars begin and end with 200 marbles, so any green marble missing from the green jar had to have been replaced by a red one, and vice versa. The two jars end up with exactly the same number of wrongly colored marbles. That's an old puzzle. I had heard it posed about glasses of water and wine, with a teaspoon of wine being added to the water, and another teaspoon of the mixture spooned back. But even well-known puzzles retain their power, as was made clear again and again last month at the seventh "Gathering for Gardner." These conferences of mathematicians, puzzlers, game-players and magicians at the Ritz-Carlton here began as personal tributes to Martin Gardner, Scientific American's legendary Mathematical Games columnist, and now take place without the master's presence (he is 91). During four days of talks and tricks, the oldest puzzles mixed freely with the newest. Puzzles are a strong lure. So when the mathematician Solomon W. Golomb discussed the marble problem as one of his "favorite quickies," or when the mathematician Peter Winkler posed puzzles about people with blue and red dots on their foreheads, or about prisoners doomed to die if they don't find their names inside boxes, or when the Google software engineer and puzzle master Wei-Hwa Huang explained how he should have solved the puzzle that cost him the championship in a sudoku competition in Italy last month, one willingly put aside concerns of daily life. It hardly mattered that there is no such thing as a tribe of truth tellers, or a man with a pet monkey and a pile of coconuts, or any other of those strange inhabitants of puzzle universes. There are no sudoku number-puzzle grids in nature, either. We imagine them, along with marbles in jars, or magic squares, or eggs covered with flexible tiles. We stage esoteric treasure hunts and construct three-dimensional models of four-dimensional objects. The only requirement is that everything be clearly defined with a limited number of laws governing behavior. Puzzles can seem magical because they really are from a made-up universe that is bounded and simplified. Within that universe, though, free play is allowed. That is why these conferences, organized with almost theatrical dash by the mathematician Elwyn Berlekamp, the puzzle enthusiast (and generous sponsor) Tom Rodgers and the magician Mark Setteducati also include demonstrations of sleight of hand, feats of memory and exotic juggling. They are also attracting more and more invited attendees (over 270 this time, about 100 more than the last conference). The mixture becomes surprisingly provocative. When the Swedish physician turned card virtuoso Lennart Green seems to clumsily drop a shuffled deck of cards and then shows how it magically organized itself by suit from high to low, or causes any card a viewer names to fly out from the center of a deck, order is created out of chaos, logic out of confusion. Sleight of hand or sleight of mind? It hardly matters. When Robert J. Lang, a laser physicist, talks with passion about origami — the Japanese art of paper folding — the line between play and discovery also completely dissolves. Mr. Lang is what might be called an origamist (see www.langorigami.com). He wrote the book "Origami Design Secrets: Mathematical Methods for an Ancient Art" (AK Peters, 2003) and has created tarantulas, delicate herons, 12-spined shells and big-horned elk out of single, uncut, folded sheets of paper. This is maximal effect with maximal constraints and minimal materials. In that respect, origami is like the puzzle about marbles or a riddle about truth tellers or a game like Go involving black and white stones on a square board: artifice with the ability to amaze. How much can you understand or create when there is so little provided, so many restrictions, and so much possibility? Mr. Lang points out that while in 1950 there only about 100 standard origami designs, in recent years a "mathematics of origami," studying the theory of folds and constructions, has evolved. As a result, he says, more than 30,000 origami designs now exist, and in September a fourth international conference on origami will be held at the California Institute of Technology. Once restricted to domestic decoration, origami has also become useful for designing everything from foldable tourist maps to expandable heart stents. Mr. Lang has worked on the folding of air bags in a car, and on a design for a collapsible telescope-mirror more than 300 feet wide that might unfold in space. This is also a legacy that Mr. Gardner leaves to generations of researchers, teachers and entertainers: don't try to understand the whole world at once. Take only a small part of it. Or better yet: invent your own universe in which there are very few elements and very few rules — a game, a puzzle, a theory. These circumscribed and artificial worlds are like sheets of paper subject to the rules of folding, yet they can yield remarkable results having almost uncanny power. The science fiction writer Arthur C. Clarke once said that any sufficiently advanced technology is indistinguishable from magic, but maybe it's also true that any sufficiently powerful "magic" eventually evolves into essential technology. That magic is produced when one begins to see a baffling puzzle from a different perspective: what once seemed impenetrable suddenly becomes transparent. The effect resembles the images involving optical illusions or Escher-like transformations of foreground and background that are often displayed at these gatherings. The eye and mind look at one thing and start to see another. Instead of seeing fish in the sea, as in one famous Escher image, one gradually begins to see birds in the sky. Instead of thinking about how many green marbles are in the scoop, one thinks about the unchanging numbers of marbles in the jars. Solving puzzles often means seeing double — an experience singularly magical. And afterwards, one returns to daily life — absurdly confident that some day it too will begin to make sense. Puzzles, Origami and Other Mind-Twisters |
April 06, 2006
Robert Aumann to Deliver Lectures on Game Theory at Sy Syms School of Business Robert J. Aumann, winner of the 2005 Nobel Prize in Economic Sciences
Apr 6, 2006 -- Robert J. Aumann, winner of the 2005 Nobel Prize in Economic Sciences will spend Tuesday, April 25 at Yeshiva University's (YU) Sy Syms School of Business (SSSB) lecturing on different aspects of game theory and interacting with students and faculty. |
April 06, 2006
Math Team Repeats High Rating in COMAP
Three talented mathematicians have continued Bethel University's strong performance in an annual problem-solving competition among colleges and universities worldwide. Phil Kaasa, Matt Seaberg, and Matt Knutson earned "meritorious" mention - the second-highest rating possible - in the Mathematical Contest in Modeling, organized by the Consortium for Mathematics and Its Applications (COMAP). The team from Bethel ranked in the top 18% out of 748 schools internationally for their solution to a complex, open-ended math problem. |
April 06, 2006
Four juniors named Goldwater scholarsBy Angela Cai Princetonian Staff Writer Juniors Tamara Broderick, Jonathan Charlesworth, Lester Mackey and Julie Wu were selected as winners of the 2006 Goldwater Scholarship on the basis of their academic merit in math, science or engineering. This is the fourth straight year that all four nominees from Princeton — the maximum any University can nominate — were named winners. Harvard had two winners, while Yale and MIT each had three. The $7,500 award is designed to "provide a continuing source of highly qualified scientists, mathematicians and engineers by awarding scholarships to college students who intend to pursue careers in those fields," according to the scholarship's website. The prize money will go towards tuition and fees in the 2006-07 academic year. Though all four winners this year were juniors, the prize is available to sophomores as well. Sophomore winners receive the stipend for two years. Broderick, a math major from Cleveland, Ohio, said that she heard about the award opportunity from friends and approached Associate Dean of the College Claire Fowler about being nominated. "I guess that showed that I was expressing interest, and I guess that put me in the pool," she said. Generally, Fowler nominates a group of sophomores and juniors and then narrows the pack to four before submitting the applications to the Goldwater Foundation. Broderick has been conducting research since her senior year in high school, when she studied the physics of dark energy. In the summer after her freshman year, she worked with the Gravity Group in the physics department on a project about gravitational lensing. Broderick also worked for the Department of Defense in her sophomore summer. Her junior paper revolves around "a machine-learning project for tracking animals in Panama," for which statistics are used to maximize the expected likelihood of the animals' paths. She plans to pursue a Ph.D. in applied mathematics. Charlesworth, a molecular biology major from Richmond, Va., plans to pursue a Ph.D. in neuroscience and aims to conduct cellular and molecular research to study cognitive processes. He is also a mile runner on the Princeton track team. Mackey, a computer science major from Long Island, N.Y., also plans to pursue a Ph.D. and research efficient dispersal of digital information. Wu, a molecular biology major, is from Marlboro, N.J. She plans to pursue a M.D./Ph.D. in molecular biology and wants to combine physics, chemistry, computer science and biology to study critical biomedical issues. The Goldwater Foundation, established by Congress in 1986, is a federally-endowed program to honor the late Arizona senator and presidential candidate Barry Goldwater. To date, the Foundation has awarded approximately 4,885 awards, totaling around $48 million. Out of a total of 1,081 nominees, 323 scholars were ultimately selected, of which 182 are men and 141 are women. About two-thirds of the winners are science majors, while the rest are mathematics, engineering or computer science majors. Almost all scholars indicated that they plan to pursue Ph.D.'s in their fields. Many Goldwater Scholars go on to receive Rhodes Scholarships and Marshall awards, as well as other honors. Four juniors named Goldwater scholars |
April 06, 2006
NSF MATHEMATICS EXPERIENCE OPENS NEW HORIZONS FOR CMU, |
April 06, 2006
Explaining how the brain recognizes facesThe mechanism by which the brain recognizes faces has long fascinated neurobiologists, many of whom believe that the brain perceives faces as "special" and very different from other visual objects. For example, classic studies found that turning the image of a face upside down compromises recognition much more than does similarly inverting other objects. More recent studies have suggested that there may even be particular neurons tuned to the identity of one particular person. These neurons, according to that theory, lie in the "fusiform face area," FFA, known to be particularly active when a person encounters a face. However, in the April 6, 2006 issue of Neuron, Maximilian Riesenhuber of Georgetown University Medical Center and his colleagues (Jiang et al.) report evidence for a theory that the FFA, instead, contains tightly integrated circuitry that recognizes faces based on selective processing of shapes of facial features. In their studies, the researchers first constructed a computational model that represented how their hypothesized neuronal circuitry would work. This model aimed at predicting how the circuitry could give rise to the perception of faces. Such perception includes the shape of specific features--eyes, noses, and mouths--as well as the "configuration" of those features--their position on the face. The researchers found that their model captured such aspects of face perception, even though the circuitry in their model had not explicitly coded them. To demonstrate that their model could also account for how other neuronal circuitry could be similarly tuned to other objects, they also tested how it might behave when it encountered images of cars. They found that model worked just as well to produce the same recognition characteristics as in faces. Riesenhuber and his colleagues tested their "shape-based" model experimentally by exposing volunteers to images of faces that could be precisely "morphed" with a computer program to subtly alter the facial features. And at the same time, the subjects' brains were scanned by using functional magnetic resonance imaging (fMRI) to detect patterns of activity in the FFA. The technique of fMRI involves using harmless magnetic fields and radio waves to measure blood flow in brain regions, which reflects their activity. The researchers found that the results from the fMRI studies agreed with those of the computational model. The researchers concluded that "we have shown that a computational implementation of a physiologically plausible neural model of face processing can quantitatively account for key data, leading to the prediction that human face discrimination is based on a sparse population code of sharply tuned face neurons. "In particular, we have shown that a shape-based model can account for the face inversion effect, can produce 'configural' effects without explicit configural coding, and can quantitatively account for the experimental data. The model thus constitutes a computational counterexample to theories that posit that human face discrimination necessarily relies on face-specific processes." In a preview of the paper in the same issue of Neuron, Tzvi Ganel wrote that Riesenhuber and colleagues "provide a compelling array of evidence supporting the idea that the processing of faces and objects do not rely on qualitatively different mechanisms. In a series of experiments, Jiang et al. present and integrate findings from neural modeling, behavior, and fMRI, showing that face classification, similarly to object classification, can be achieved by a simple-to-complex architecture based on hierarchical shape detectors. "Jiang et al.'s modeling and behavioral findings have strong implications for understanding how faces and objects are processed in the human brain," wrote Ganel. The researchers include Xiong Jiang, Ezra Rosen, Maximilian Riesenhuber, Thomas Zeffiro, and John VanMeter of Georgetown University Medical Center in Washington, D.C.; Volker Blanz of Max-Planck-Institut für Informatik in Saarbrücken, Germany. This research was supported in part by NIMH grants 1P20MH66239-01A1, 1R01MH076281-01, and an NSF CAREER Award (#0449743). Jiang et al.: "Evaluation of a Shape-Based Model of Human Face Discrimination Using fMRI and Behavioral Techniques." Publishing in Neuron 50, 159–172, April 6, 2006. DOI 10.1016/j.neuron.2006.03.012 www.neuron.org. Explaining how the brain recognizes faces |
April 06, 2006
Applying A Mathematical Method That Refines The Contour Of Tumors To Image Analysis To Improve TreatmentMain Category: Cancer/Oncology News Article Date: 05 Apr 2006 - 0:00am (UK) Cancer treatment needs refinement. Any method aimed at treating a tumor, from extirpation to radiotherapy, requires a precise knowledge of the cancerous tumor margins so that the intervention on it may be performed in such a way that the possibilities of healing are maximised and the effects on surrounding healthy tissues are minimised. A group of researchers from the Department of Mathematics at the Universitat Jaume I in Castelló have implemented a mathematical method that is applied to medical imaging analysis, which enables to determine the margins of a tumor in the prostate, lung or bladder. In most cases, the task of delimitating the contour of a tumor is carried out manually by a specialist. According to his or her experience, the doctor draws the perimeter within which he or she locates the cancerous tissue on an image obtained by computerised axial tomography (CAT) or magnetic resonance (MR) images. This perimeter may vary slightly depending on the professional who traces it. The method developed by the mathematicians at the UJI does away with such a great subjective variability, and enables a single, more objective and standardised confidence interval to be obtained for each tumor type and patient depending on his or her characteristics. "What we have done is to define an average and most adjusted confidence interval possible from a series of contours delineated by various professionals on one same tumor, in such a way that it only surrounds the tissue that is considered cancerous and leaves any surrounding tissue which is not to be submitted to treatment unharmed", as Ximo Gual, the person in charge of the research, explains. By combining concepts of geometry, statistics and probability, the scientists at the UJI in cooperation with the radiotherapist oncology service at the Hospital Universitari La Fe in Valencia have developed a standard method for prostate cancer cases in patients aged 40-60 years. "All that remains now is to incorporate these mathematical formulae into the software used by medical teams", Gual points out. The idea is that the machine can automatically write the confidence interval on the contour of the tumor previously drawn by the specialist. However, the subjectivity of the health professionals is not the only variable that affects the task of determining the margins of a tumor. Indeed, this internal organ motion itself hinders the identification and subsequent monitoring of cancerous tissue. This is particularly obvious in the case of lungs. The problem is that the CAT or MR images corresponding to the same patient but taken on different days do not fit owing to internal organ motion, even though the external cut-off at which the images are taken is the same on each occasion. "Our aim is to make progress in our research in order to achieve a 3D contouring of the tumor. The idea is to rebuild the tumor in 3D from crosscut images, and to define the three-dimensional confidence interval that accounts for the variability due to internal organ motion", Ximo Gual explains. This study has been carried out by researchers Ximo Gual and María Victoria Ibáñez, both of them from the Universitat Jaume I, and Françoise Lliso and Susana Roldán, from the Hospital Universitari La Fe. It has recently been published in the journal Computerized Medical Imaging and Graphics. Applying A Mathematical Method That Refines The Contour Of Tumors To Image Analysis To Improve Treatment |
April 06, 2006
'Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos'Seth Lloyd Alfred A. Knopf: 226 pp., $25.95 Review by Margaret Wertheim It is a truism of the 21st century that we swim in a sea of information. It gushes forth from the morning paper, it croons from the racks of magazine stands and the million-plus volumes on Amazon.com. It floods down the pipelines of the Internet into our laptops, iPods, PDAs and cellphones. Life is increasingly structured around the delivery and reception of information — ever more, ever faster and ever timelier data. Of course information has always been a valuable commodity, but until recently it largely served as a means to other ends, say, as a tool to gain military advantage or a competitive edge in the marketplace. In "Programming the Universe," Seth Lloyd sets out to convince us that information is the foundation of reality itself and that the cosmos may be seen as a vast computer for processing and transforming data. Lloyd is a professor of quantum mechanical engineering at MIT and a pioneer in the field of quantum computing. He was the first person to propose how a quantum computer could be built, a task that is now proceeding apace in research labs around the world. Along with a growing number of physicists, he believes that computation and information theory offer a new paradigm for understanding the physical world. His aim in this dense but utterly charming book is to trace the history of computational manipulation of information along with the rise of "information science," and simultaneously to tell the story of our universe as an unfolding sequence of "information revolutions." Humans have been computing almost since we became human. "Like the first tools, the first computers were rocks," Lloyd writes. "Calculus" is the Latin word for pebble, and the first calculations were made by rearranging pebbles. "Rock computers didn't have to be small," Lloyd tells us. "Stonehenge may well have been a big rock computer for calculating the relations between the calendar and the arrangement of the planets." Rocks eventually led to the abacus, which remains one of the most successful computing devices of all time. Later revolutions were made possible by the slide rule in the 17th century; geared cogs in the 19th century (these formed the basis of mechanical calculators); vacuum tubes in the 1940s; and transistors in the 1960s. Over the last half-century, the computational power available to us has roughly doubled every 18 months, a fact first articulated by Intel co-founder Gordon E. Moore and formally known as Moore's Law. But we are approaching the limits of what silicon can do, and it is clear that if we are to keep up the blinding pace of computational enhancement a new technology is needed. Many scientists are hoping that quantum mechanics holds the key and that quantum computers will take us as far past semiconductors as semiconductors took us from pebbles. Lloyd and his colleagues are leading that charge. As humans have learned to process information on ever grander scales, so too Lloyd sees the history of the universe as a series of information-processing revolutions. The first was the Big Bang, which brought into being from nothingness the cosmic seed of space and time. In the beginning, he tells us, there was very little information in the universe, but as the nascent bubble of spacetime fluoresced into being, its data content exploded. "The Big Bang was also a Bit Bang," he cutely surmises. Soon the primal bits were coalescing into the structures we know as particles (protons, electrons and so on), which later congregated to form atoms, which in turn clumped together to make stars and galaxies. "Every time a new ingredient of the soup condensed out … new information was written in the cosmic cookbook." Planetary systems formed and more complicated molecules came into being, including eventually the life-encoding information structure known as DNA. The evolution of higher organisms required a revolution in intracellular communication or information processing between cells, as did the development of immune systems. Living things in the form of hairless apes soon began to orchestrate their own informatics revolutions. "Life, language, human beings, society, culture — all owe their existence to the intrinsic ability of matter and energy to process information," Lloyd writes. This view of reality has been gaining ground in scientific circles for several decades. But though it has come to the fore in the age of computers, its roots lie in the attempts of 19th century physicists to understand steam engines. That effort led to the laws of thermodynamics and the articulation of the concept of "entropy," a mysterious quality that always increases when any action is carried out. It turns out that entropy is a measure of the information content of a system and as time goes on, both entropy and information in the universe increase. Though the thermodynamicists of the 19th century did not understand it at the time, they were casting information as a fundamental quality of nature, along with that other great pillar known as energy. In the informatics' view of reality, energy and information are the two complementary forces acting upon matter. As Lloyd puts it: "Energy makes physical systems do things. Information tells them what to do." The idea that the entire universe may be an information-processing system — some sort of giant computer — was first put forward in the 1960s by Edward Fredkin (then at MIT) and Konrad Zuse, who constructed the first electronic computers in Germany in the 1940s. Both Fredkin and Zuse proposed that our world might be a digital computer, but since the universe is built on a quantum mechanical foundation, Lloyd tells us that a digital computer could never capture its immensity. Only a quantum computer would be sufficiently complex to do that. In theory, Lloyd says, we could make a quantum computer that would model the complexity of the entire universe, a simulation that would be effectively indistinguishable from the actual universe. Since the universe itself is built on quantum systems such as atoms, and since all quantum systems are continually exchanging information, Lloyd concludes that the universe must be a giant quantum computer. And what does this machine compute? "It computes itself. The universe computes its own behavior." In his final chapters, Lloyd argues that understanding quantum computation will lead us to an understanding of how the universe truly works and what it is truly doing. Specifically, he believes this line of research will resolve one of the major questions in science today — how increasingly complex systems, such as molecules and people, have emerged from simple ones, such as electrons and protons. That is no small claim. But can quantum computing shoulder such a heavy epistemological burden? Throughout history, humans have interpreted the world in terms of things they know. The ancient creator gods behaved like super-humans, coupling and breeding and giving birth to the cosmos, or fashioning its elements from familiar technologies such as weaving or molding clay. Modern scientific accounts also have drawn heavily on familiar contemporary tropes: In the 17th century, the universe was seen as a vast clockwork system. By the 19th, when the study of magnetic and electrical phenomena was hot, it was reconceived as a network of invisible force fields. At the dawn of the age of digital computers, scientists speculated that it was one of these machines. Inevitably, we see the whole through the lens of the particular. Though I do not doubt that the quantum computational view will yield new insights, history would suggest that a final metaphor is illusory. To reify that metaphor and insist the universe is a quantum computer seems almost as philosophically quaint as the Norse myth Lloyd describes in which "the universe begins when a giant cow licks the gods out of the salty lip of a primordial pit." Although I question his conclusion, the journey Lloyd takes in this rich and complex book is genuinely thrilling. For those willing to work through some difficult examples, it is a clear account of quantum computing and an insightful rumination on both the physical and computational sciences. • Margaret Wertheim, author of "The Pearly Gates of Cyberspace: A History of Space From Dante to the Internet," is at work on a book about the role of imagination in theoretical physics. 'Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos' |
April 06, 2006
The Value of Einstein's MistakesLetters April 2006, page 10 Steven Weinberg's love for and knowledge of history inform his instructive sampling of Albert Einstein's mistakes (PHYSICS TODAY, November 2005, page 31). One mistake, or at least one tantalizing omission, seems worth adding to the collection. In a May 1905 letter to Conrad Habicht, Einstein wrote that he thought his revolutionary contribution was the hypothesis that light consists of particles.1 Consider his lifelong passion for unification, as in his resolution of the clash between Isaac Newton's mechanics and James Clerk Maxwell's electrodynamics (with the special theory of relativity modifying the former). It is hard to believe that Einstein did not worry about reconciling the well-established wave aspects of light with his new particle hypothesis. If he had pursued that connection, he could have developed one-photon quantum mechanics in 1905 or shortly afterward, by combining the Poynting-vector expression for the power intensity of light with his own relation between frequency and energy of a particle to obtain the photon-number intensity of a light beam. The wave equation is the Maxwell equations, and the probability interpretation pops up immediately. Many observers have said that general relativity was one advance that would have taken a very long time without Einstein, but we have no direct test for that statement. However, if you accept my argument that Einstein could have developed the first true quantum mechanics, then we can say exactly how long it took the physics community to catch up—20 years for Heisenberg's matrix mechanics and Schrödinger's mathematically equivalent wave mechanics. Reference 1.A. Einstein, The Collected Papers of Albert Einstein, vol. 5, English translation, Princeton U. Press, Princeton, NJ (1995), p. 20. Alfred Scharff Goldhaber (goldhab@insti.physics.sunysb.edu) C. N. Yang Institute for Theoretical Physics Stony Brook University Stony Brook, New York As Steven Weinberg points out, it's a good thing for people to understand that even the greatest scientists make mistakes. However, I think Weinberg grossly understates the issue. Maybe his article should have been titled "Einstein's Published Mistakes." The practice of science, as PHYSICS TODAY readers surely know, involves making mistakes, realizations, corrections, and more mistakes. Trial and error is a fundamental part of the process. I think that point deserves emphasizing. Too many of our schoolchildren learn to avoid invention and new thinking because they have been convinced that making mistakes is shameful. Tom Cornsweet (tomc@vispath.com) Prescott, Arizona In his thoughtful and timely article, Steven Weinberg analyzes some of Einstein's mistakes and notes some others. Another fundamental conceptual mistake is hidden in Einstein's celebrated 1905 paper on relativity. In a lengthy discussion in the first part of that paper, Einstein showed that the speed of light can be made constant by adopting a clock synchronization based on two-way light signals. With that synchronization, measurements of the one-way speed of light become logically circular, and Einstein later declared that the constancy of the speed of light was "neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make at my free discretion to arrive at a definition of simultaneity."1 However, Einstein overlooked that the validity of Newton's laws at low speeds in each reference frame permits the use of simple mechanical methods of synchronization, such as slow clock transport or sound signals. Einstein's synchronization procedure with light signals is thus superfluous—it plays no fundamental role and is merely the most convenient of several possible synchronization procedures. Furthermore, if clocks are synchronized by slow clock transport or by some other mechanical procedure, then measurements of the one-way speed of light are not logically circular, and those measurements provide an unambiguous experimental test of the constancy of this speed. In fact, clock transport has been used in such experimental tests.2,3 Einstein should have considered the implications of alternative synchronization procedures for the conceptual foundations of relativity, and he should have recognized that the constancy of the speed of light had to be established by experiment, not by stipulation. References 1.A. Einstein, The Collected Papers of Albert Einstein, vol. 6, English translation, Princeton U. Press, Princeton, NJ (1996), p. 439. 2.T. P. Krisher et al., Phys. Rev. D 42, 731 (1990) [MEDLINE]. 3.P. Wolf, G. Petit, Phys. Rev. A 56, 4405 (1997) [INSPEC]. Hans C. Ohanian (hansohanian@cs.com) University of Vermont Burlington Steven Weinberg writes, "Einstein rejected the notion that the laws of physics could deal with probabilities, famously decreeing that God does not play dice with the cosmos. But history gave its verdict against Einstein—quantum mechanics went on from success to success, leaving Einstein on the sidelines." Einstein did not reject quantum theory merely because it is probabilistic. He wrote: "There is no doubt that quantum mechanics has seized hold of a beautiful element of truth, and that it will be a test stone for any future theoretical basis."1 Nor was Einstein unilaterally opposed to God playing dice. He expected God to either play dice all the way or not at all. If individual events were totally undetermined, then the overall events should also be undetermined, and not display remarkable regularity. "In for the penny, in for the pound," he wrote. Thus, a more accurate quote from Einstein about God and dice playing is the following: "That the Lord should play with dice, all right; but that He should gamble according to definite rules, that is beyond me."1 Reference 1.A. Einstein, quoted in J. Wheeler, W. Zurek, Quantum Theory and Measurement, Princeton U. Press, Princeton, NJ (1983), p. 8. Ravi Gomatam (rgomatam@bvinst.edu) Bhaktivedanta Institute Mumbai, India I enjoyed Steven Weinberg's article except for the not-so-subtle knock on religion at the beginning, where he refers to "other supposed paths to truth," and the subhead, "Science sets itself apart from other paths to truth by recognizing that even its greatest practitioners sometimes err." If the point of the article is to show the superiority of science over other "supposed paths," Weinberg confuses the issue by ending with the claim that Einstein "made no mistakes" in his decisions about "great public issues," including his opposition to militarism, his refusal to support the Stalinist Soviet Union, and his enthusiastic Zionism. Since none of those public issues are ones in which science alone can provide answers, how did Einstein achieve such infallible knowledge about them without relying on paths to truth other than science? With all due respect for his undoubted genius in science, I think Weinberg's hostility to religion is blinding him to errors in elementary logic. Ron Larson (rlarson@umich.edu) University of Michigan Ann Arbor How unfortunate that Steven Weinberg chose to insert a criticism of religion—"other supposed paths to truth"—in his article. That Einstein was not infallible seems to have little relevance to the question of whether the prophets of various religions are infallible, and the latter question seems to have little place in a piece about Einstein. Brian C. Hall (bhall@nd.edu) University of Notre Dame Notre Dame, Indiana While I very much enjoyed Steven Weinberg's article "Einstein's Mistakes," I am puzzled by the author's statement about quantum mechanics: "The difficulty is not that quantum mechanics is probabilistic—that is something we apparently have to live with. The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics." Quantum mechanics is an acausal deterministic theory in the sense that a physical system's state (mathematically described by a state vector) at a given initial time determines its state at a specified later time, but its state is not in one-to-one correspondence with sharp values of all its dynamical variables; that correspondence is probabilistic. Therefore events, identified by sharp values of those variables at one spacetime point, are not causally connected with other events. That is something we have to live with. Why does the combination of these two attributes—acausality and determinism—constitute a special difficulty? Weinberg asks, "So where do the probabilistic rules of the Copenhagen interpretation come from?" Why do they have to come from anywhere other than from human brains? Nature exists out there, independent of human thought, but its mathematical description surely is a human construction rather than an immutable law given to us on a stone tablet. Roger G. Newton (newton@indiana.edu) Indiana University Bloomington Einstein should be allowed his mis- takes, like the rest of us, and Steven Weinberg understandably points out only the most newsworthy. I write to point out another misunderstanding—mistake, if you will—in Einstein's work only because it is often found in the literature today. Einstein described diffusion as the motion of neutral particles on atomic (Brownian) length and time scales. He used a stochastic differential equation—a Langevin equation—in the high-friction limit to describe diffusive trajectories. Einstein did not discuss how his treatment could accommodate macroscopic boundary conditions or produce macroscopic flow, which is, after all, what Fick's law of diffusion is all about. Langevin equations, in the spirit of Einstein's work, are widely used today to describe the motion and fluctuations of density of charged particles in, for example, aqueous solutions. The electric force in those equations is usually described by a steady function. Fluctuations in number density of charged particles are allowed in Einstein's treatment but fluctuations in net charge and electric potential are not. Traditional Langevin equations of Brownian motion seem inconsistent with the idea that charge creates electric force and so are unlikely to be helpful, at least in my view. It is hard to imagine systems in which the number density of ions can fluctuate while the number density of charge does not. I believe Einstein's description of Brownian motion must be coupled to equations describing the electric field when the diffusing particles have significant charge. An equation is needed to show how the charge on one particle creates force on another. The ink particles studied by Robert Brown were surely charged. The fluctuating electric field and stochastic flow can be computed from the density of ink particles, ions, and solvent molecules by solving Poisson's or Maxwell's equations together with flow equations. (Spatially inhomogeneous boundary conditions are needed to force the macroscopic flow described by Fick's law.) This so-called self-consistent treatment of diffusion and the electric field is used in computational electronics to design the transistors and integrated circuits of our electronic technology.1 Diffusion and the electric field have not been treated self-consistently in most of computational chemistry and biology—for example, in simulations of molecular dynamics of ions or proteins—although such treatments are found in analyses of ionic motion through protein channels.2–5 References 1.S. Selberherr, Analysis and Simulation of Semiconductor Devices, Springer-Verlag, New York (1984); C. Jacoboni, P. Lugli, The Monte Carlo Method for Semiconductor Device Simulation, Springer-Verlag, New York (1989); see also [LINK]. 2.M. G. Kurnikova, R. D. Coalson, P. Graf, A. Nitzan, Biophys. J. 76, 642 (1999) [INSPEC]; W. Im, B. Roux, Biophys. J. 115, 4850 (2001). 3.S. Aboud, D. Marreiro, M. Saraniti, R. Eisenberg, J. Comput. Electron. 3, 117 (2004) . 4.T. A. van der Straaten, G. Kathawala, R. S. Eisenberg, U. Ravaioli, Mol. Simul. 31, 151 (2004). 5.B. Corry, S.-H. Chung, Eur. Biophys. J. 34, 208 (2005) . Bob Eisenberg (beisenbe@rush.edu) Rush Medical Center Chicago, Illinois The fascinating article recounting Einstein's mistakes at different stages of his career goes beyond the usual focus on the cosmological constant and quantum mechanics. In particular, the discussion of Kaluza–Klein theory examines Einstein's later attempts at a unification theory. But in the course of developing general relativity, Einstein made another assumption, which he later tried to revisit—one that future generations may come to regard as Einstein's greatest "mistake." Curvature of spacetime is, of course, related by general relativity to the presence of mass-energy. This curvature, though it plays out in the arena of four-dimensional spacetime, corresponds to our intuitive understanding of geometric curvature in three dimensions. General relativity also makes a crucial assumption that another geometric object, called the torsion, vanishes. That is not the only assumption that could have been made, however, and as Einstein explored extensions of general relativity after 1915, he reevaluated his initial assumption. In the 1920s and 1930s, Einstein collaborated1 with the eminent French mathematician Elie Cartan, who was responsible for much of the foundation of 20th-century differential geometry. As early as 1922, Cartan tried to explain to Einstein that a different type of curvature, which could be called a total curvature and which contains the traditional curvature as a piece, vanishes. With this condition, called teleparallelism (TP), the torsion need not vanish. Einstein and Cartan explored the implications of TP for generalizing general relativity beyond the gravitational field, but ultimately abandoned that route. Unfortunately, the tools Cartan himself offered to differential geometry were insufficiently mature at that stage to be exploited by Einstein even if the physicist had been able to fully understand them.1 Teleparallelism does offer advantages, including a greater mathematical richness than general relativity and a potential resolution of mathematical issues related to the nature of conservation laws in general relativity.2,3 Wielding the methods of modern differential geometry that Cartan first introduced, physicists in the past couple of decades have elaborated unified theories with TP as an important component.3,4 For instance, TP and another geometric ingredient5 lead to the "natural" incorporation of electromagnetism in one such theory, fully within the tradition of the geometrical paradigm of Einstein.3 TP may ultimately prove to be a better assumption for a geometric theory. If so, it would still be an extreme excess of Whiggery, to use Weinberg's wonderful phrase, for those future generations to fault Einstein for his choice in general relativity. The very mathematical concepts, let alone the tools, behind TP did not even exist in 1915 when general relativity was unveiled to the world. References 1.J. G. Vargas, D. G. Torr, Found. Phys. 29, 145 (1999) [INSPEC]. 2.J. G. Vargas, D. G. Torr, Gen. Rel. Grav. 23, 713 (1991). 3.R. E. Becker, in High Frequency Gravitational Wave Conference, May 6–9, 2003, R. Baker Jr, P. Murad, eds., Mitre Corp, McLean, VA (2003), paper HFGW-03-123 and references therein. 4.For a unified theory based on teleparallelism, see [LINK]. 5.J. G. Vargas, D. G. Torr, J. Math. Phys. 34, 4898 (1993) [SPIN]. Robert E. Becker (roberte.becker@prodigy.net) York, Pennsylvania
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