MIT News - Mathematics
http://newsoffice.mit.edu/rss/topic/mathematics
MIT News is dedicated to communicating to the media and the public the news and achievements of the students, faculty, staff and the greater MIT community.enTue, 08 Apr 2014 16:35:31 -0400MIT students dominate Putnam Mathematical Competition, winning team event
http://newsoffice.mit.edu/2014/mit-students-dominate-putnam-mathematical-competition-winning-team-event
Four of five top individual finishers, known as “Putnam Fellows,” also hail from MIT.Tue, 08 Apr 2014 16:35:31 -0400Chuck Leddy, MIT News correspondenthttp://newsoffice.mit.edu/2014/mit-students-dominate-putnam-mathematical-competition-winning-team-event<p>The recently announced results of the annual <a href="http://math.scu.edu/putnam/index.html">William Lowell Putnam Mathematical Competition</a>, the prestigious undergraduate mathematics contest that this year included more than 4,100 students from 557 colleges and universities across the U.S. and Canada, represented a sweeping victory for MIT.</p>
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<p>The Institute not only won the team competition — placing ahead of runners-up Carnegie Mellon University and Stanford University — but also placed four students in the top five individual spots, an achievement that earns those contestants designation as “Putnam Fellows”: sophomore Mitchell Lee, junior Zipei Nie, freshman Bobby Shen, and freshman David Yang.</p>
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<p>A large number of other MIT students also delivered <a href="http://math.mit.edu/news/spotlight/documents/2014_04_02_Putnam.pdf">strong performances</a> on the famously challenging six-hour, 12-question exam.</p>
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<p>“The Putnam exam is brutally graded,” explains Henry Cohn, an adjunct professor of applied mathematics who helped students prepare for the Putnam by teaching — along with Abhinav Kumar, an associate professor of applied mathematics — 18.A34 (Problem Solving Seminar). “There’s almost no partial credit given, so, for example, on question B6 this year, <a href="http://tech.mit.edu/V134/N16/graphics/putnam.html">exactly zero students received full credit</a>. This year’s median score was around one point out of 120 points available, so even students who scored zero were in good company.”</p>
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<p>“There were 87 MIT students in the top 442 this year, which is amazing,” Cohn adds. “No other school had even half that many.”</p>
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<p>Cohn and members of MIT’s team first learned of the Putnam triumph via Wikipedia.</p>
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<p>“We noticed a day or two before we received the ‘official’ results in the mail that somebody had altered the Wikipedia entry for the Putnam Competition to reflect that MIT had won, but we didn’t know if it was a prank,” he says. “When the ‘official’ results finally came, I was thrilled.”</p>
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<p><strong>Winning MIT team of Lee, Nie, and Gunby</strong></p>
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<p>The three members of MIT’s winning team — Lee, Nie, and junior Benjamin Gunby, also a mathematics major — competed in Putnam for a variety of reasons.</p>
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<p>“I find the Putnam Competition to be a fun experience,” explains Lee, a mathematics major and two-time Putnam Fellow. “Besides that, I hope that my performance will help me if I apply for graduate school. I also appreciate the prize money.” (Lee won $3,500 for his efforts.)</p>
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<p>Lee also enjoys the team camaraderie. He attributes MIT’s performance this year to “the overall strength of the math community here at MIT.”</p>
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<p>“We enjoy talking about math,” he says. “We all support each other and congratulate each other. The things I have learned from other competitors undoubtedly played a role in my own performance.”</p>
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<p>Nie, also a mathematics major and two-time Putnam Fellow, says that math contests provide a sense of belonging. As a high school student in China, Nie says, he felt “pessimistic day after day, so I decided to let math be the meaning of my life. Math and the support of my high school teachers cured me. Math Olympiad training became my main work during those years. Fortunately, I made great progress.”</p>
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<p>Gunby, a Putnam Fellow last year and a member of the winning MIT trio this year, says math contests represent an intellectual challenge. “Math competitions have played a big part of my life,” he says, “especially during high school. Before college, math classes didn’t do much to improve my problem-solving skills. But everyone in college can find a math class that’s interesting and challenging.”</p>
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<p>Michael Sipser, the Barton L. Weller Professor of Mathematics, head of the Department of Mathematics, and interim dean of the School of Science, says: “I’m proud that our department has attracted such a high caliber of student. We had an extraordinary number of top performers on the Putnam: 80 percent of the top five and 60 percent of the top 25.”</p>
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<p>“Word has gotten out that MIT is the place to be for competitive math,” Sipser says, “and success breeds even more success. Winning helps us attract even more strong students, and not just math competitors, but smart kids in general.”</p>
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<p>Sipser hopes that attention on events like the Putnam Competition can trigger larger public conversations about math. “It helps us celebrate math in a playful way,” he says.</p>
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<p><strong>Contest math vs. research math</strong></p>
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<p>How well does success at “contest math,” like the Putnam Competition, correlate with later achievement in math? As Sipser puts it, comparing time-limited contest math to research math “is like comparing regular chess to blitz chess.”</p>
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<p>Bjorn Poonen, the Claude E. Shannon Professor of Mathematics and one of just eight students ever to be a four-time Putnam Fellow (as an undergraduate at Harvard University), agrees: “The Putnam differs from math research in that it rewards speed more than the ability to develop deep insights over time. There is some overlap in the skills, but there are many excellent mathematicians who didn’t do well on the Putnam. Also, as far as content goes, math majors at MIT learn much more than what is covered on the Putnam.”</p>
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<p>Cohn, who received his SB in mathematics from MIT in 1995 and who participated in the Putnam Competition as an undergraduate, says: “While we rightfully celebrate these clever and quick problem-solvers who did so well on the Putnam, there are amazing MIT students who don’t even take the exam, as well as wonderful students who are going to accomplish fantastic things in mathematics even though they scored one point on the Putnam. The mathematics department doesn’t value students who win contests any more than we value the rest of our great students.”</p>
In the cloud: How coughs and sneezes float farther than you think
http://newsoffice.mit.edu/2014/coughs-and-sneezes-float-farther-you-think
Novel study uncovers the way coughs and sneezes stay airborne for long distances.Tue, 08 Apr 2014 00:00:02 -0400Peter Dizikes | MIT News Officehttp://newsoffice.mit.edu/2014/coughs-and-sneezes-float-farther-you-think<p>The next time you feel a sneeze coming on, raise your elbow to cover up that multiphase turbulent buoyant cloud you’re about to expel.</p>
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<p>That’s right: A novel study by MIT researchers shows that coughs and sneezes have associated gas clouds that keep their potentially infectious droplets aloft over much greater distances than previously realized.</p>
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<p>“When you cough or sneeze, you see the droplets, or feel them if someone sneezes on you,” says John Bush, a professor of applied mathematics at MIT, and co-author of a new paper on the subject. “But you don’t see the cloud, the invisible gas phase. The influence of this gas cloud is to extend the range of the individual droplets, particularly the small ones.”</p>
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<p>Indeed, the study finds, the smaller droplets that emerge in a cough or sneeze may travel five to 200 times further than they would if those droplets simply moved as groups of unconnected particles — which is what previous estimates had assumed. The tendency of these droplets to stay airborne, resuspended by gas clouds, means that ventilation systems may be more prone to transmitting potentially infectious particles than had been suspected.</p>
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<p>With this in mind, architects and engineers may want to re-examine the design of workplaces and hospitals, or air circulation on airplanes, to reduce the chances of airborne pathogens being transmitted among people.</p>
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<p>“You can have ventilation contamination in a much more direct way than we would have expected originally,” says Lydia Bourouiba, an assistant professor in MIT’s Department of Civil and Environmental Engineering, and another co-author of the study.</p>
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<p>The paper, “Violent expiratory events: on coughing and sneezing,” was published in the <em>Journal of Fluid Mechanics</em>. It is co-written by Bourouiba, Bush, and Eline Dehandschoewercker, a graduate student at ESPCI ParisTech, a French technical university, who previously was a visiting summer student at MIT, supported by the MIT-France program.</p>
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<p><strong>Smaller drops, longer distances</strong></p>
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<p>The researchers used high-speed imaging of coughs and sneezes, as well as laboratory simulations and mathematical modeling, to produce a new analysis of coughs and sneezes from a fluid-mechanics perspective. Their conclusions upend some prior thinking on the subject. For instance: Researchers had previously assumed that larger mucus droplets fly farther than smaller ones, because they have more momentum, classically defined as mass times velocity.</p>
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<p>That would be true if the trajectory of each droplet were unconnected to those around it. But close observations show this is not the case; the interactions of the droplets with the gas cloud make all the difference in their trajectories. Indeed, the cough or sneeze resembles, say, a puff emerging from a smokestack.</p>
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<p>“If you ignored the presence of the gas cloud, your first guess would be that larger drops go farther than the smaller ones, and travel at most a couple of meters,” Bush says. “But by elucidating the dynamics of the gas cloud, we have shown that there’s a circulation within the cloud — the smaller drops can be swept around and resuspended by the eddies within a cloud, and so settle more slowly. Basically, small drops can be carried a great distance by this gas cloud while the larger drops fall out. So you have a reversal in the dependence of range on size.”</p>
<p>Specifically, the study finds that droplets 100 micrometers — or millionths of a meter — in diameter travel five times farther than previously estimated, while droplets 10 micrometers in diameter travel 200 times farther. Droplets less than 50 micrometers in size can frequently remain airborne long enough to reach ceiling ventilation units.</p>
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<p>A cough or sneeze is a “multiphase turbulent buoyant cloud,” as the researchers term it in the paper, because the cloud mixes with surrounding air before its payload of liquid droplets falls out, evaporates into solid residues, or both.</p>
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<p>“The cloud entrains ambient air into it and continues to grow and mix,” Bourouiba says. “But as the cloud grows, it slows down, and so is less able to suspend the droplets within it. You thus cannot model this as isolated droplets moving ballistically.”</p>
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<p><strong>Ready for a close-up</strong></p>
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<p>Other scholars say the findings are promising. Lidia Morawska, a professor at Queensland University of Technology in Brisbane, Australia, who has read the study, calls it “potentially a very important paper” that suggests people “might have to rethink how we define the airborne respiratory aerosol size range.” However, Morawska also notes that she would still like to see follow-up studies on the topic.</p>
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<p>The MIT researchers are now developing additional tools and studies to extend our knowledge of the subject. For instance, given air conditions in any setting, researchers can better estimate the reach of a given expelled pathogen. </p>
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<p>“An important feature to characterize is the pathogen footprint,” Bush says. “Where does the pathogen actually go? The answer has changed dramatically as a result of our revised physical picture.”</p>
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<p>Bourouiba’s continuing research focuses on the fluid dynamics of fragmentation, or fluid breakup, which governs the formation of the pathogen-bearing droplets responsible for indoor transmission of respiratory and other infectious diseases. Her aim is to better understand the mechanisms underlying the epidemic patterns that occur in populations. </p>
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<p>“We’re trying to rationalize the droplet size distribution resulting from the fluid breakup in the respiratory tract and exit of the mouth,” she says. “That requires zooming in close to see precisely how these droplets are formed and ejected.”</p>
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<p>Funding for the study was provided by the National Science Foundation.</p>
How to beat others to the mathematical punch
http://newsoffice.mit.edu/2014/how-to-beat-others-to-the-mathematical-punch
New MITx MOOC brings the street fighting approach to solving math problems.Fri, 28 Mar 2014 11:00:01 -0400Sara Sezun and Steve Carson | Office of Digital Learninghttp://newsoffice.mit.edu/2014/how-to-beat-others-to-the-mathematical-punch<p>In a street fight, there are no rules of engagement. To win, you need to think quickly and do the unconventional. Sanjoy Mahajan, visiting associate professor in the Department of Electrical Engineering, brings this no-holds-barred spirit to his upcoming <i>MITx</i> course, <a href="https://www.edx.org/course/mitx/mitx-6-sfmx-street-fighting-math-1501#.UzR3615w1BI" target="_blank">6.SFMx Street-Fighting Math</a>, which starts April 8 and is open for registration on the edX platform. Mahajan will teach students how to calculate approximations in real-life situations, to arrive at an educated guess when exact answers are not easy to obtain.</p>
<p>Mahajan begins the first class of his residential course by writing on the board, “Rigor leads to rigor mortis.” He believes math should be fun, and criticizes methods that rely on rote memorization to teach math. He says, “Because of rigor mortis, people think I do it right, or I don’t do it," an attitude that intimidates many students. Mahajan likens math to physics experiments. “You investigate it, just like you investigate the world, as a giant laboratory with objects, devices, and patterns.”</p>
<p>One of Mahajan’s major research interests is improving the teaching of math and science by doing away with rote memorization, which he calls “brittle knowledge that doesn’t transfer to any new problem. For instance, in quadratic equations, students have a hard time using ‘y’ as a variable, because they’re always so used to using ‘x’.” He explains that while learning algebra, “[Students] didn’t understand what they were doing. They saw the pattern of using ‘x’ as a pin mark, but didn’t understand its meaning. They only remembered the order of symbols in a formula; they didn’t understand the meaning of what they were doing.”</p>
<p>Applying rigid formulas without considering their consequences can lead to serious mistakes. For example, when asked the answer to "6 x 3", most children give it correctly as 18, because they have memorized multiplication tables. When asked to write a story problem for this equation, the most common example deals with ducks in a pond. Children will typically write a problem that describes six ducks in a pond, joined by three more ducks. When the children ask how many ducks there are in total, they expect the answer to be 18, because they are following a pattern set by the equation. They do not stop to examine the facts, and consider the difference between addition and multiplication. Unfortunately, many children continue this habit of applying formulas without critical thinking throughout their school years.</p>
<p>To disseminate his innovative approach, Mahajan began teaching Street-Fighting Math in 2007 during the Independent Activities Period, a time in January before regular classes begin when MIT students can take enrichment courses. The residential course will be taught this semester during the last seven weeks. The curriculum will be exactly the same in terms of rigor and materials for both residential and <i>MITx</i> students. The only difference is that the residential students will be learning the curriculum a week before the <i>MITx</i> students, to test the materials before they go online.</p>
<p>Street-fighting math will have no lectures, just short videos of Mahajan explaining problem sets, which students will have to work on. The problems will be graded immediately by the computer. Mahajan explains, “The advantage is that students see the answer right away, while they’re still thinking about the problem . . . Lots of research shows that for feedback to be effective, it’s best for it to be immediate.” If the answer is wrong, “Students will have links to help them understand each problem, which will lead them to pieces in the reading (assignments), that will help them understand the problem.”</p>
<p>Along with teaching 6.SFMx, Mahajan will be conducting research on how students learn online, but he is still working on the details. “I’m learning too,” he says. “It’s my first online course.”</p>
<p>Mahajan is looking forward to the edX course, to reaching “people who have a math background, but it’s been wasted.” He wants to “teach if for the whole world”, to generate more enthusiasm for learning math, because it “can help you understand things. It can show you how the pieces of the world are put together.”</p>
<p>To give an actual example of street-fighting math in action, Mahajan tells a story from his teaching days at Cambridge, many years ago. Borders had just opened a new store in Cambridge and was holding a contest. They had a gigantic jar filled with beans, and were offering a prize for guessing the correct number. A group of Mahajan’s students entered the contest and won. They applied Mahajan’s method of breaking down difficult problems into easier ones, by counting the beans in each dimension: height, width, and depth. Then they multiplied these numbers to arrive at an approximate answer. “I call it divide-and-conquer reasoning,” says Mahajan. “It worked for the British to rule India, and it works for problem-solving.”</p>
U.S. News ranks MIT’s graduate program in Engineering No. 1; Sloan is No. 5 business school
http://newsoffice.mit.edu/2014/us-news-ranks-mits-graduate-program-in-engineering-no-1-sloan-is-no-5-business-school-0311
Institute’s programs rank first in 7 engineering, 5 science, and 3 business fields.Tue, 11 Mar 2014 00:01:00 -0400News Officehttp://newsoffice.mit.edu/2014/us-news-ranks-mits-graduate-program-in-engineering-no-1-sloan-is-no-5-business-school-0311<p>MIT’s graduate program in engineering has been ranked No. 1 in the country in <i>U.S. News & World Report</i>’s annual rankings — a spot the Institute has held since 1990, when the magazine first ranked graduate programs in engineering.</p>
<p><i>U.S. News</i> awarded MIT a score of 100 among <a href="http://grad-schools.usnews.rankingsandreviews.com/best-graduate-schools/top-engineering-schools" target="_blank">graduate programs in engineering,</a> followed by No. 2 Stanford University (93), No. 3 University of California at Berkeley (87), and No. 4 California Institute of Technology (80).</p>
<p>As was the case last year, MIT’s graduate programs led <i>U.S. News </i>lists in seven engineering disciplines. Top-ranked at MIT this year are programs in aerospace engineering; chemical engineering; materials engineering; computer engineering; electrical engineering (tied with Stanford and Berkeley); mechanical engineering (tied with Stanford); and nuclear engineering (tied with the University of Michigan). MIT’s graduate program in biomedical engineering was also a top-five finisher, tying for third with the University of California at San Diego.</p>
<p>In <i>U.S. News</i>’ first evaluation of <a href="http://grad-schools.usnews.rankingsandreviews.com/best-graduate-schools/top-science-schools" target="_blank">PhD programs in the sciences</a> since 2010, five MIT programs earned a No. 1 ranking: biological sciences (tied with Harvard University and Stanford); chemistry (tied with Caltech and Berkeley, and with a No. 1 ranking in the specialty of inorganic chemistry); computer science (tied with Carnegie Mellon University, Stanford, and Berkeley); mathematics (tied with Princeton University, and with a No. 1 ranking in the specialty of discrete mathematics and combinations); and physics. MIT’s graduate program in earth sciences was ranked No. 2.</p>
<p>The MIT Sloan School of Management ranked fifth this year among the nation’s <a href="http://grad-schools.usnews.rankingsandreviews.com/best-graduate-schools/top-business-schools" target="_blank">top business schools</a>, behind Harvard Business School, Stanford’s Graduate School of Business, the Wharton School at the University of Pennsylvania, and the Booth School of Business at the University of Chicago.</p>
<p>Sloan’s graduate programs in information systems, production/operations, and supply chain/logistics were again ranked first this year; the Institute’s graduate offerings in entrepreneurship (No. 3) and finance (No. 5) also ranked among top-five programs.</p>
<p><i>U.S. News</i> does not issue annual rankings for all doctoral programs, but revisits many every few years. In the magazine’s 2013 evaluation of graduate programs in economics, MIT tied for first place with Harvard, Princeton, and Chicago.</p>
<p><i>U.S. News</i> bases its rankings of graduate schools of engineering and business on two types of data: reputational surveys of deans and other academic officials, and statistical indicators that measure the quality of a school’s faculty, research, and students. The magazine’s less-frequent rankings of programs in the sciences, social sciences, and humanities are based solely on reputational surveys.</p>
New algorithm can dramatically streamline solutions to the ‘max flow’ problem
http://newsoffice.mit.edu/2014/new-algorithm-can-dramatically-streamline-solutions-to-max-flow-problem-0107
Research could boost the efficiency even of huge networks like the Internet.Tue, 07 Jan 2014 05:00:04 -0500Helen Knight, MIT News correspondenthttp://newsoffice.mit.edu/2014/new-algorithm-can-dramatically-streamline-solutions-to-max-flow-problem-0107<p>Finding the most efficient way to transport items across a network like the U.S. highway system or the Internet is a problem that has taxed mathematicians and computer scientists for decades.<br />
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To tackle the problem, researchers have traditionally used a maximum-flow algorithm, also known as “max flow,” in which a network is represented as a graph with a series of nodes, known as vertices, and connecting lines between them, called edges.<br />
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Given that each edge has a maximum capacity — just like the roads or the fiber-optic cables used to transmit information around the Internet — such algorithms attempt to find the most efficient way to send goods from one node in the graph to another, without exceeding these constraints.<br />
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But as the size of networks like the Internet has grown exponentially, it is often prohibitively time-consuming to solve these problems using traditional computing techniques, according to Jonathan Kelner, an associate professor of applied mathematics at MIT and a member of MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL).<br />
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So in a paper to be presented at the ACM-SIAM Symposium on Discrete Algorithms in Portland, Ore., this week, Kelner and his colleague Lorenzo Orecchia, an applied mathematics instructor, alongside graduate students Yin Tat Lee and Aaron Sidford, will describe a new theoretical algorithm that can dramatically reduce the number of operations needed to solve the max-flow problem, making it possible to tackle even huge networks like the Internet or the human genome.<br />
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“There has recently been an explosion in the sizes of graphs being studied,” Kelner says. “For example, if you wanted to route traffic on the Internet, study all the connections on Facebook, or analyze genomic data, you could easily end up with graphs with millions, billions or even trillions of edges.”<br />
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Previous max-flow algorithms have come at the problem one edge, or path, at a time, Kelner says. So for example, when sending items from node A to node B, the algorithms would transmit some of the goods down one path, until they reached its maximum capacity, and then begin sending some down the next path.<br />
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“Many previous algorithms,” Kelner says, “would find a path from point A to point B, send some flow along it, and then say, ‘Given what I’ve already done, can I find another path along which I can send more?’ When one needs to send flow simultaneously along many different paths, this leads to an intrinsic limitation on the speed of the algorithm.”<br />
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But in 2011 Kelner, CSAIL graduate student Aleksander Madry, mathematics undergraduate Paul Christiano, and colleagues at Yale University and the University of Southern California developed a technique to analyze all of the paths simultaneously.<br />
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The researchers viewed the graph as a collection of electrical resistors, and then imagined connecting a battery to node A and a ground to node B, and allowing the current to flow through the network. “Electrical current doesn’t pick just one path, it will send a little bit of current over every resistor on the network,” Kelner says. “So it probes the whole graph globally, studying many paths at the same time.”<br />
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This allowed the new algorithm to solve the max-flow problem substantially faster than previous attempts.<br />
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Now the MIT team has developed a technique to reduce the running time even further, making it possible to analyze even gigantic networks, Kelner says.<br />
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Unlike previous algorithms, which have viewed all the paths within a graph as equals, the new technique identifies those routes that create a bottleneck within the network. The team’s algorithm divides each graph into clusters of well-connected nodes, and the paths between them that create bottlenecks, Kelner says.<br />
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“Our algorithm figures out which parts of the graph can easily route what they need to, and which parts are the bottlenecks. This allows you to focus on the problem areas and the high-level structure, instead of spending a lot of time making unimportant decisions, which means you can use your time a lot more efficiently,” he says.<br />
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The result is an almost linear algorithm, Kelner says, meaning the amount of time it takes to solve a problem is very close to being directly proportional to the number of nodes on the network. So if the number of nodes on the graph is multiplied by 10, the amount of time would be multiplied by something very close to 10, as opposed to being multiplied by 100 or 1,000, he says. “This means that it scales essentially as well as you could hope for with the size of the input,” he says.<br />
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Shanghua Teng, a professor of computer science at the University of Southern California who was not involved in the latest paper, says it represents a major breakthrough in graph algorithms and optimization software.<br />
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“This paper, which is the winner of the best paper award at the [ACM-SIAM] conference, is a result of sustained efforts by Kelner and his colleagues in applying electrical flows to design efficient graph algorithms,” Teng says. “The paper contains an amazing array of technical contributions.”<br />
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The paper was posted alongside work by Jonah Sherman of the University of California at Berkeley, who has also developed an almost linear algorithm for solving the max-flow problem, using an alternative technique.</p>
Getting a move on in math
http://newsoffice.mit.edu/2013/getting-a-move-on-in-math-1223
Marshall Scholar Kirin Sinha is motivating young women to pursue math through dance.Mon, 23 Dec 2013 05:00:00 -0500Jennifer Chu, MIT News Officehttp://newsoffice.mit.edu/2013/getting-a-move-on-in-math-1223<p>MIT senior Kirin Sinha was just 3 years old when she took her first dance class. Unlike other girls who sign up for tap dancing or ballet to channel a gregarious personality, Sinha, by her own account, was painfully shy, and dance was a way for her to come out of her shell.<br />
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She soon found that she didn’t mind the spotlight. That first dance class led to many more; in grade school, Sinha started performing competitively, and later professionally, in classical Indian dance. Around the same time, she also discovered another interest: math. In high school, she competed in state and national mathematics competitions — often as the only female in the top ranks.<br />
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“I was constantly asked the question, ‘Why doesn’t it ever bother you that you’re the only girl, or that guys don’t think it’s cool if you’re good at math?’” Sinha recalls. “And I never had a good answer.”<br />
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It wasn’t until she was at MIT that Sinha realized that her confidence in math came from an unlikely source: dance.<br />
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“[Dance] teaches you discipline, attention to detail, and creativity,” she says. “It gives you the confidence to stand up there and not apologize for anything you’re doing. And that’s something I thought was missing with girls in mathematics.”<br />
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Compelled by this connection, in 2012 Sinha founded SHINE, a program whose mission is Supporting, Harnessing, Inspiring, Nurturing, and Empowering middle school girls to learn math by building their confidence through dance. This past year, Sinha recruited 37 girls from middle schools in Boston and Cambridge, as well as mentors from MIT, to participate in eight-week sessions of dance routines and math puzzles. Reluctant at first, the girls soon showed tangible improvement, pulling their grades up from C’s to A’s. And, Sinha adds, they liked the challenge.<br />
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Now she plans to take the program abroad: Sinha was one of 34 students nationwide — and four at MIT — awarded Marshall Scholarships last month to pursue two years of graduate studies in the United Kingdom. Starting next fall, she will undertake two master’s degrees, in mathematics and in advanced computer science, at Cambridge University, and hopes to explore ways to integrate SHINE into the British educational system. <br />
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<strong>Ahead of the curve</strong><br />
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Sinha was born in Baltimore and spent most of her childhood in Bethesda, Md. She remembers coming home from school each day, eager to tackle the math problems her mother gave her for fun. By third grade, she was working out equations in algebra — a subject typically taught in eighth or ninth grade. Because of her accelerated learning, Sinha says she was able to appreciate what others often don’t see in mathematics.<br />
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“I believe the reason people fall out of math is because it takes a long time to realize how beautiful it is,” Sinha says. “It’s when you get into number theory and abstract algebra and group theory — that’s when things get deconstructed at such a fundamental level that people get really excited, that they’re discovering a truth or structure to the universe. And people often lose interest before that level because it’s not taught like that.”<br />
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In high school, Sinha placed in the top 10 in national mathematics competitions, and was the highest scoring female in her state’s American Mathematics Competition and the American Invitational Mathematics Examination. She also applied this drive to other subjects, graduating from high school in three years.<br />
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While she was in high school, teachers from various local schools approached Sinha with the same question: Could she come tutor girls in math? Particularly in middle school, the educators noticed, girls’ performance and interest in the subject waned. So Sinha tutored young women and gave motivational talks about pursuing careers in science.<br />
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“I don’t think girls have less ability in math — that’s absurd,” Sinha says. “I think the only reason girls do poorly is that in their head, they don’t want to be the one girl who’s doing well — they don’t want to stand out.”<br />
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<strong>Building perspectives</strong><br />
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After graduation, Sinha headed to MIT to pursue majors in theoretical mathematics and in electrical engineering and computer science and a minor in music. She was particularly drawn to the elegant architecture of pure math, a subject that required “moving piece by piece to string together something that works.”<br />
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But Sinha also made an effort to seek out different perspectives, particularly in applied math. During her time at MIT, she took on several internships at companies that looked for mathematical solutions to practical problems. At the investment firm Blackstone Group, Sinha was part of a team that developed mathematical models to analyze hedge fund portfolios and perform risk analysis. And at the New York startup ADAPTLY, she helped create models that analyze advertising for ways to increase visibility on social networking sites like Facebook and Twitter.<br />
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“Having different perspectives is almost like having different tools,” Sinha says. “It makes you a better problem-solver.”<br />
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In the summer before her sophomore year, Sinha lived in an Italian monastery for six weeks. She slept under a bell tower, waking to its clanging early each morning. Not knowing the language, she spent most days in silence, washing clothes by hand, without electricity or hot water. The spare lifestyle left plenty of room for reflection.<br />
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“Being able to spend meaningful time with yourself is a very difficult thing,” Sinha says. “It very much helped clarify what I wanted to do and why.”<br />
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<strong>Dancing through the pipeline</strong><br />
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Upon returning to MIT, Sinha quickly drew up a proposal that ultimately became SHINE. She obtained funding with help from MIT’s Public Service Center, and started reaching out to area schools for willing participants. Thinking back to her tutoring experiences, Sinha decided to target girls in sixth and seventh grade — a time when girls’ interest and performance in math severely drops off.<br />
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“I’m worried about the girls who think they can’t do math, honestly believe that, and don’t care,” Sinha says. “If you say to these girls, ‘Hey, do you want to do math after school,’ they’re going to roll their eyes at you and not say anything. It’s a challenging pool, but I think it’s the key demographic.”<br />
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As Sinha found, dance is an enticing hook to get these girls interested and receptive to challenges in math. This past year, she led two sessions of SHINE, with a total of 37 middle school girls. Each day, the girls learned dance routines and worked on math problems; Sinha sometimes found ways to combine the two in exercises of “kinesthetic learning.” For example, she would integrate a lesson on the Cartesian plane into a dance routine, asking girls to rotate on the dance floor by a given number of degrees — an illustration of the coordinate system.<br />
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“It may not feel like work or learning, but it’s actually being embedded in your brain much deeper than just doing millions of practice exercises,” Sinha says.<br />
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Sinha hopes to pursue an academic path, and one day become a professor. She recently worked with professor of mathematics Scott Sheffield on problems in decision theory, and is currently working with professor of applied mathematics John Bush on the wave behavior of water droplets.<br />
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She says that while her mentors have been supportive and encouraging, she has never had a female math professor.<br />
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“I think there need to be more women in that role to encourage more women to move that way,” Sinha says. “We’re losing many of them around middle school, and if you consider in college you might lose more, by the time we get to PhDs, we’re talking about a very small pool. By increasing that pipeline, I think we’re doing a huge service.”</p>
Kirin SinhaIt’s a negative on negative absolute temperatures
http://newsoffice.mit.edu/2013/its-a-negative-on-negative-absolute-temperatures-1220
New research shows negative absolute temperatures — and perpetual motion machines — are still out of reach.Fri, 20 Dec 2013 05:00:01 -0500Jennifer Chu, MIT News Officehttp://newsoffice.mit.edu/2013/its-a-negative-on-negative-absolute-temperatures-1220The concept of a perpetual motion machine is an enticing one: Imagine a machine that runs continuously without requiring any external energy — a feat that could make refueling vehicles a thing of the past. <br /><br />While a perpetual motion machine inspires appealing possibilities, most scientists agree that such a machine is impossible, as the very concept — doing work without any energy input — defies the laws of thermodynamics. Nevertheless, some researchers have forged ahead with efforts to create systems resembling perpetual motion at microscopic scales, including spin systems and ultracold quantum gas, which have suggested that perpetual motion machines may be more than pie-in-the-sky notions. <br /><br />But now, mathematicians at MIT and the Max Planck Institute for Astrophysics have challenged these ideas with equations showing that such systems, while innovative, do not illustrate the dynamics of perpetual motion. The main claim of such experiments is that they are able to produce systems with negative absolute temperatures, or temperatures below 0 degrees Kelvin. If true, such systems could be used to build machines that produce more work than the heat energy put into them — a key characteristic of perpetual motion.<br /><br />In a paper published this month in the journal <i>Nature Physics</i>, the researchers analyzed past claims of negative absolute temperature and found that in all cases, scientists were interpreting experiments based on a flawed — though universally accepted — definition of entropy, or heat. This definition, called the Boltzmann entropy, appears in modern physics textbooks, and is widely used to calculate the absolute temperature of a wide range of physical systems. <br /><br />But as the MIT team found, the definition only works when atomic or molecular energy states exhibit a normal distribution, where higher energy levels are less frequently populated than lower ones. In more exotic systems, such as certain quantum gases, the definition breaks down. Accounting for this error, the team performed mathematical consistency checks using an earlier definition of entropy, and found that such systems actually exhibited positive absolute temperatures — a result suggesting that previous studies were using the wrong definition, or essentially an inaccurate theoretical “thermometer,” to measure the absolute temperature of exotic systems. <br /><br />“It’s sad in a sense, because you want something to be spectacular, and you want to find something new,” says Jörn Dunkel, an assistant professor of mathematics at MIT. “But it’s good, in a way, because the implications of negative absolute temperatures would have shaken up the foundations of physics.”<br /><br /><strong>The case for going below absolute zero</strong><br /><br />We typically think of temperature as measured in degrees Celsius or Fahrenheit, which can reach subzero temperatures. In contrast, absolute temperature, measured along the Kelvin scale, represents the motion of molecules within a system. At absolute zero, molecules stop moving, and the system cannot get any colder. <br /><br />Interestingly, the concept of negative absolute temperature doesn’t imply that a system is colder than absolute zero, but in fact, much, much hotter. Systems above absolute zero typically exhibit a normal energy distribution in which there are more atoms or molecules in lower than higher energy states. <br /><br />Under very special conditions, it is possible to flip-flop, or invert, such energy distributions. A well-known example is the laser, which relies on the fact that the majority of its electrons occupy high-energy states. Applying Boltzmann’s definition of entropy in these situations yields a negative temperature. If one inserts such negative temperatures into an equation for the efficiency of a heat engine, known as Carnot’s formula, then one can obtain efficiency values larger than 1 — predicting, in effect, perpetual motion.<br /><br /><strong>Rewriting the textbooks</strong><br /><br />To check whether past claims of negative absolute temperatures were indeed correct, Dunkel and Stefan Hilbert, a postdoc at the Max Planck Institute, methodically examined the equations used in earlier studies to calculate absolute temperature. They found that, while the Boltzmann definition of entropy works well in calculating positive absolute temperature, it quickly falls apart when used to find the temperature of systems with an inverted distribution of molecules. <br /><br />Going further back in the literature of thermodynamics, the researchers reviewed another definition of entropy described by physicist J. Willard Gibbs in the early 20th century. As it turns out, the absolute temperatures derived using both the Gibbs and Boltzmann definitions for entropy are nearly identical for classical systems with a normal molecular distribution. But for more exotic systems with an inverted distribution, results from the two equations diverge greatly. <br /><br />Dunkel and Hilbert performed mathematical checks and found that, using the Gibbs equation, they calculated positive absolute temperatures in inverted systems that scientists had thought were negative. The group’s new calculations are consistent with the laws of thermodynamics and agree with standard measurement conventions for pressure and other thermodynamic variables, showing that while a system may exhibit an inverted distribution of atomic or molecular energies, this abnormal spread doesn’t necessarily signal negative absolute temperatures. <br /><br />Dunkel suggests that going forward, any researchers seeking to accurately measure the absolute temperature of exotic systems such as quantum gases should use Gibbs’ formula over Boltzmann’s. <br /><br />“There are only a small number of textbooks that teach [Gibbs’] formula,” Dunkel says. “They don’t discuss negative temperatures, because at the time, it wasn’t really relevant. But then [the formula] got lost at some point, and now all the modern textbooks publish the other formula. To correct that will be difficult.”<br /><br />Peter Hanggi, a professor of physics at the University of Augsburg, says the paper’s findings will help scientists make much more accurate interpretations of rare, exotic systems. <br /><br />“There were a lot of things being claimed and repeated in the general literature over 50 years, and this group has done an excellent job in sorting out the incorrect from the correct,” says Hanggi, who was not involved in the research. “The main significance is to point out to everybody, ‘Hey, wait a minute, if you calculate temperature, what does it mean for thermodynamics and for the experiment?’ One cannot be too quick in their calculations.” <br /><br />As for creating a perpetual motion machine, Dunkel says the possibility is slim at best, and will require very careful calculations to verify.<br /><br />“If you create a new class of systems, that’s a huge experimental feat,” Dunkel says. “But if you go on and interpret the things you measure on these systems, you need to be really careful. If you make just a small mistake in your assumptions, it can amplify hugely.”A 1660 wood engraving of Robert Fludd's 1618 "water screw" perpetual motion machine, widely credited as the first recorded attempt to describe such a device for useful work. Crossing disciplines, and international borders
http://newsoffice.mit.edu/2013/crossing-disciplines-and-international-borders-1217
Rhodes Scholar John Mikhael, who calls both the U.S. and Lebanon home, is also comfortable in many scientific fields.Tue, 17 Dec 2013 05:00:02 -0500Anne Trafton, MIT News Officehttp://newsoffice.mit.edu/2013/crossing-disciplines-and-international-borders-1217<p>John Mikhael sees three fields as key to understanding the brain: math, neuroscience, and medicine. “If you want to understand how the brain works, combining those three is a great way to get there,” he says.<br />
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Mikhael, who graduated from MIT in June with a bachelor’s degree in mathematics, plans to pursue his study of neuroscience next fall when he enters an MD/PhD program at Oxford University with a Rhodes Scholarship.<br />
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“Neuroscience is a very exciting field,” he says. “In many ways, the brain is the most sophisticated computer out there. Our brains can do things effortlessly that we couldn’t even dream of teaching computers how to do, like producing language, understanding social cues, or recognizing faces with our level of proficiency.”<br />
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“We can identify clouds that look like ponies — computers can barely even identify ponies that look like ponies,” Mikhael adds. “Neuroscience can inform medicine, computer science, and machine learning. From there, it’s hard to think of a field it can’t benefit.”<br />
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<strong>Between two worlds</strong><br />
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Born in Dallas to a family of Lebanese and Syrian descent, Mikhael grew up as a typical American kid until third grade, when his parents decided to move back to Lebanon. Arriving in his new home outside Beirut, Mikhael felt some culture shock, but it was mitigated by the fact that so many Lebanese were familiar with American culture, which at the time was all he knew.<br />
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“Everybody knows how to talk to an American, a lot of people speak English there, and everybody watches ‘Friends,’” Mikhael says. “But there were small elements here and there that struck me as very different,” he recalls.<br />
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From large differences such as focus on family values versus focus on individuality, to smaller things like older men and women constantly giving him wet triple-kisses on the cheek, it took Mikhael a while to get used to his new environment, but eventually Lebanon started to feel like home.<br />
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In April, Mikhael won MIT’s Isabelle de Courtivron Prize for an essay about his experiences growing up in two different cultures and trying to figure out where he fit in. After he won the Rhodes, many more people read his essay and he started hearing from people around the world. “I was getting emails from people in Indonesia who said, ‘I completely identify with what you wrote, and here are my reasons why.’ It’s very nice,” Mikhael says.<br />
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<strong>Pursuing research, advancing humanity</strong><br />
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As a high-school student, Mikhael was already determined to pursue a career in scientific research. To do that, he believed that he needed to return to the United States, and he singled out MIT as his top choice.<br />
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“I wanted to go to a place that really cares about research and cares about advancing humanity. Once you say those two words, MIT comes to mind. That’s why I applied here.”<br />
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Mikhael ended up majoring in mathematics with a minor in chemistry. What drew him to math is the elegance of sitting down with a piece of paper and a pen and coming up with a new way to tackle a problem.<br />
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“At the end of the day you can forget formulas, and you can forget the theorem that you learned last year, but in learning the theorem, you learned how to sharpen the way you think, and that’s one of the big attractions of math,” he says.<br />
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His courses in chemistry also taught him a great deal about analytical thinking, but with physical materials instead of numbers. “It’s nice to know how science works, and that’s something that you don’t really get as a mathematician,” he says.<br />
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When not in the lab or working on math proofs, Mikhael spent his undergraduate years volunteering for Habitat for Humanity; working with MedLinks, an MIT student group that supports undergraduate health and well-being; and participating in interfaith discussions as an Addir Interfaith Fellow. He also likes to relax by playing table tennis, a sport he played competitively in high school.<br />
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<strong>Probing the brain</strong><br />
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In his future career, Mikhael hopes to use his mathematical and analytical skills to probe the inner workings of the human brain — a subject that has fascinated him since high school.<br />
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This year he is working at MIT’s McGovern Institute for Brain Research in the lab of Nancy Kanwisher, the Walter A. Rosenblith Professor of Brain and Cognitive Sciences, studying how the brain makes judgments and predictions concerning physical phenomena. The brain can easily predict in which direction a leaning tower will fall, or the path of a ball flying in a parabola, or how two colliding objects will interact, but neuroscientists don’t know how the brain does this.<br />
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Mikhael plans to continue studying this problem in graduate school at Oxford, taking a computational approach. “It’s starting to look like a big math problem, and that’s how I want to tackle it,” he says.</p>
John MikhaelMichael Sipser named interim dean of the School of Science
http://newsoffice.mit.edu/2013/michael-sipser-named-interim-dean-of-the-school-of-science-1206
Mathematician has been a member of the faculty since 1980 and department head since 2004.Fri, 06 Dec 2013 21:04:22 -0500News Officehttp://newsoffice.mit.edu/2013/michael-sipser-named-interim-dean-of-the-school-of-science-1206Michael Sipser, the Barton L. Weller Professor of Mathematics and head of the Department of Mathematics since 2004, has been named interim dean of the School of Science, effective Dec. 16. <br /><br />Sipser succeeds Marc Kastner, the Donner Professor of Physics, who was recently nominated by President Barack Obama to lead the Department of Energy’s Office of Science. A faculty search committee will work to identify a permanent dean. <br /><br />“We are grateful to Mike Sipser for his willingness to accept this role and responsibility, and deeply appreciative of Marc’s tremendous leadership as Dean of Science,” Acting Provost Martin Schmidt wrote today in an email to the faculty and to staff within the School of Science. <br /><br />A member of the MIT faculty since 1980, Sipser is a leading theoretical computer scientist and a member of the Computer Science and Artificial Intelligence Laboratory. <br /><br />Under his leadership, the Department of Mathematics has launched several successful fundraising efforts, securing funds for the renovation of Building 2, for endowed chairs, and for fellowships: Thanks to these efforts, the department now provides fellowships to all first-year graduate students. During the same period, the department has seen a 54 percent increase in the number of undergraduate majors, from 186 in 2004 to 287 this year. Sipser has also appointed more than half of the department’s 50 current faculty members.<br /><br />Sipser is a fellow of the American Academy of Arts and Sciences. He authored the widely used textbook “Introduction to the Theory of Computation,” first published in 1996 and now in its third edition. Sipser received the MIT Graduate Student Council Teaching Award in 1984, 1989, and 1991, and the School of Science Student Advising Award in 2003. <br /><br />A native of Brooklyn, N.Y., Sipser earned his BA in mathematics from Cornell University in 1974 and his PhD in engineering from the University of California at Berkeley in 1980. He joined MIT’s Laboratory for Computer Science as a research associate in 1979, becoming an assistant professor of applied mathematics in 1980; associate professor of applied mathematics in 1983; and professor of applied mathematics in 1989.<br />Michael SipserJohn Mikhael ’13 wins Rhodes Scholarship
http://newsoffice.mit.edu/2013/john-mikhael-rhodes-scholarship-1123
Recent MIT graduate in mathematics, who has also conducted research in neuroscience, will study at Oxford next year.Sun, 24 Nov 2013 03:30:07 -0500Nora Delaney | Global Education and Career Developmenthttp://newsoffice.mit.edu/2013/john-mikhael-rhodes-scholarship-1123<p>John Mikhael, who received his bachelor’s degree in mathematics with a minor in chemistry from MIT in June, has received a Rhodes Scholarship to study next year at Oxford University. He is one of 32 American recipients selected this weekend by the Rhodes Trust.<br />
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A native of Dallas, Mikhael joins 45 previous MIT recipients who have won the prestigious international scholarships since they were first awarded to Americans in 1904, according to the Institute’s Distinguished Fellowships office.<br />
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At MIT, Mikhael completed his undergraduate degree requirements in three years. With his Rhodes Scholarship, Mikhael will undertake graduate studies in neuroscience at Oxford, with the goal of pursuing an MD/PhD. Mikhael’s ultimate goal is a career researching neurological disorders.<br />
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Mikhael’s work in mathematics has been supplemented by neuroscience research in the laboratory of Nancy Kanwisher, the Walter A. Rosenblith Professor of Cognitive Neuroscience at MIT. He began this research in early 2011, continued it through graduation, and is now working as a full-time scientist in Kanwisher’s lab. Mikhael has studied cortical plasticity and how functional regions in the brain allow us to understand physical interactions. Mikhael’s drive to help others has also led him to volunteer with Habitat for Humanity; <a href="http://medlinks.mit.edu " target="_blank">MedLinks</a>, an MIT student group that supports undergraduate health and well-being; and as an <a href="http://studentlife.mit.edu/content/addir-interfaith-program" target="_blank">Addir Interfaith Fellow</a>. He has also taught mathematics as a teaching assistant for MIT lecturer Jeremy Orloff.<br />
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Before coming to MIT, Mikhael lived for a number of years in Lebanon. At MIT, Mikhael was awarded this year’s <a href="http://shass.mit.edu/news/news-2013-john-g-mikhael-13-wins-isabelle-de-courtivron-prize" target="_blank">Isabelle de Courtivron Prize</a> for an essay on <a href="http://web.mit.edu/cbbs/images/LostInTranslation.pdf" target="_blank">cross-cultural fluency</a>.<br />
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“John is an exceptional talent,” says John Ochsendorf, the Class of 1942 Professor of Building Technology and Civil and Environmental Engineering and co-chair of MIT’s Presidential Committee on Distinguished Scholarships. “Clearly brilliant and a phenomenal researcher, he is driven to a career in science because of his humanitarian compassion.”<br />
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Jason Fischer, a postdoc who works with Mikhael in the Kanwisher lab, notes, “John has an exceptional mind for science — a rare combination of creativity and fierce technical skill. He has exactly what it takes to show the world something new and extraordinary.”<br />
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“MIT has once again supported the applications of remarkable Rhodes candidates this year,” says Kimberly Benard, assistant director of distinguished fellowships in MIT Global Education & Career Development. “They represent the very best of MIT and are all worthy of celebration.”</p>
John MikhaelDoing the math
http://newsoffice.mit.edu/2013/doing-math
MIT management professor Vivek Farias crunches the numbers to see how complex systems can be optimized.Mon, 18 Nov 2013 17:00:00 -0500Peter Dizikes, MIT News Officehttp://newsoffice.mit.edu/2013/doing-math<p>When consumers look at cars at an auto dealership, they have speed on their minds — and not necessarily the sort measured by 0-to-60 acceleration. Rather, they want to buy cars quickly: Evidence shows that people tend to purchase something that’s available on the lot, rather than waiting for an order to arrive from another site, even though an auto is a major purchase.<br />
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This presents an interesting problem for dealers and manufacturers: Considering factors such as popularity and profit margin, what’s the optimal mix of models to showcase on the lot, given that buyers can be steered toward what’s available?<br />
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Vivek Farias builds mathematical tools that can answer this for automakers and dealers — as well as tools that can help businesses in online searches and recommendations: If a customer enjoyed one purchase, what are the best recommendations for future products? </p>
<p>Skill in addressing these questions is valuable. But according to the self-effacing Farias, an associate professor at the MIT Sloan School of Management, his ability to tackle tough business issues is mostly a byproduct of his pursuit of interesting questions. <img alt="" src="" /></p>
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<p>Vivek Farias<br /><span class="credits">Photo: Bryce Vickmark</span></p>
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<p>“I don’t think there is a deep plan connecting my research efforts,” Farias says. “There is just a class of applied mathematics problems that I know how to think about, at the interface of optimization, probability and stochastic control.”</p>
<p>These optimization questions apply in many fields. Let’s say an airport has a lot of planes ready to roll out to the taxiway: In what order should they take off? Or suppose you want to match organs for transplantation with potential recipients more effectively: How would you do that?<br />
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Potential solutions are tucked into Farias’ burgeoning body of work: He has published 15 research papers in peer-reviewed journals since joining MIT in 2007, along with several other refereed papers presented at conferences, and more in the pipeline.<br />
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That commitment to research and teaching helped Farias, at age 31, earn tenure from MIT earlier this year. Beyond his publications, former students whose PhD theses he co-supervised have landed jobs at Harvard University and New York University.<br />
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“You work with these amazing students,” Farias says of his experience at MIT. “Life would be different without them. That’s the reason I come in to work every day.”<br />
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<strong>‘Random’ route to MIT</strong><br />
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By Farias’ own account, he had a “fairly random” path to academia. He was born and raised in Mumbai. His father is a contractor who runs a construction firm, and his mother is a teacher. Farias did well in school, although he says he was not obsessed with it.<br />
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Casting around for college opportunities in the United States — which he had never visited before — Farias attended the University of Arizona, where a scholarship helped pay his way. Today, he happily recounts his undergraduate experience: Professors took an interest in him, helping spur his studies, and a nearby family hosted him at times, giving him meals, presents and moral support.<br />
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“It was a really great experience,” Farias says. “It was an amazing place to be. People were incredibly kind to me. All of these things made a huge difference.”<br />
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Following a freshman course in crystallography with a professor named Brian Zelinski, Farias spent the following summer in the labs of two other professors in the same field, Dunbar Birnie and Michael Weinberg. “I started working with them and discovered research, and it was just phenomenal,” Farias says. “My ability to get into graduate school was very much a function of their helping me along. I owe a huge debt of gratitude to these people.”<br />
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Farias majored in computer engineering at Arizona, then received his PhD in electrical engineering at Stanford University in 2007, working with Benjamin Van Roy. That year, he received a job offer from MIT, which he was delighted to accept.<br />
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“It was a big surprise,” Farias says. “I hardly expected it to happen.” Indeed, he adds, being at MIT was “a little intimidating” at first, except that his colleagues soon started reaching out to him, in some cases by mentoring graduate students with him.<br />
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<strong>The price of fairness</strong><br />
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One of those colleagues, Dimitri Bertsimas of MIT Sloan, agreed to co-advise, with Farias, a graduate student named Nikos Trickhakis. Together, the three of them began working on a way to make the holding of aircraft on the ground, at airports, more equitable for a larger number of passengers. That research question was motivated by prior work of Bertsimas and MIT aeronautics and astronautics professor Amadeo Odoni on optimizing those ground holding patterns.<br />
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Suppose, again, that you want to select the best process for a backlog of airplanes to take off. The easiest way, perhaps, would be for planes to depart according to how long they have been waiting. But the issue is not so simple: Suppose the first planes in such a queue are small regional jets with few passengers, while waiting behind those planes are several bigger aircraft with hundreds of passengers who have connections to make at other airports. To make the whole system function better, you might want to boost the priority of the bigger planes. Otherwise, Farias observes, “You’re affecting more people and potentially creating network delays.”<br />
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That might not seem perfectly fair to the passengers in the regional jets, but it is a factor, Farias contends, that should enter into the decision-making process.<br />
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“How should we think about this tradeoff between efficiency and equity?” Farias asks. “What is the price of fairness, so to speak? And can we think about this in a rigorous way that informs policymaking?”<br />
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A similar analytical framework informs Farias’ research on organ transplants — work that asks if there is a way to increase the years of use from donated organs while staying within medicine’s ethical guidelines. His analysis shows that when it comes to kidneys, for instance, it may be possible to increase the years of use for transplanted organs by 7 to 8 percent. Farias is now serving on the Technical Advisory Committee of the Scientific Registry of Transplant Recipients, a national group that studies organ transplant policy.<br />
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It’s a long way, in a sense, from the car dealership to the airport to the operating room. But building the mathematical framework for examining the issues found in such diverse places, Farias says, keeps him motivated and energized: “It’s why I’m in academia.”</p>
Vivek FariasMIT economist's 'hard math' books inspire young students
http://newsoffice.mit.edu/2013/mit-economists-hard-math-books-inspire-young-students
Tue, 12 Nov 2013 14:30:00 -0500School of Humanities, Arts, and Social Scienceshttp://newsoffice.mit.edu/2013/mit-economists-hard-math-books-inspire-young-studentsSix years ago when Glenn Ellison volunteered to coach his daughter Caroline's middle-school math team, he hardly realized he would soon become a leading authority in the niche market of advanced mathematics textbooks for elementary- and middle-school students.<br /><br />After coaching Caroline's team for two years, Ellison, Gregory K. Palm (1970) Professor of Economics, decided to compile the notes, worksheets, and packets he had created into <i>Hard Math for Middle School: IMLEM Edition</i> (CreateSpace Independent Publishing Platform, 2008) to make the information more easily accessible to kids not on his team.<br /><br />Although Ellison had intended the book for a small local audience — the middle-school students who participated in the Intermediate Math League of Eastern Massachusetts (IMLEM) — the book took off nationally, selling thousands of copies across the country. <br /><br />The enthusiastic response to <i>Hard Math for Middle School</i> made apparent the absence of excellent textbooks for above-average math students. This revelation — in addition to the frequent requests from his youngest daughter, Kate — spurred Ellison to create a follow-up textbook designed for an even younger audience. <br /><br /><br /><strong>Raising the bar</strong><br /><br />Earlier this year, Ellison released his second book, <i>Hard Math for Elementary School</i> (CreateSpace Independent Publishing Platform, 2013), geared to challenge third- to sixth-grade students who are capable of working above grade-level math. Ellison hopes his latest book will arm elementary school kids with solid fundamental math skills, as well as curiosity, and an enduring passion for mathematics.<br /><br />He explains that young, high-achieving students can become complacent or even apathetic in their math classes because the material isn't difficult enough to sustain their interest. To keep such students occupied during class, teachers will often give them the next grade-level textbook; but in many cases even the next-level material is not challenging enough, and these most advanced students simply lose interest in math. <br /><br />That's where <i>Hard Math for Elementary School</i> comes in. Presenting above-average students math problems that are more difficult and more widely ranging than standard texts, the book has proven exciting to gifted young students. <br /><br />"Math is really intriguing," says Ellison, "and it's critical for kids to learn math well while they're still young. High school students are harder to reach than third graders, but you can make an impact on elementary school kids by showing them that math is not only interesting, but also pretty cool."<br /><br /><strong>Challenging with a side of fun</strong><br /> <br />Ellison composed <i>Hard Math for Elementary School</i> to be used as an enrichment textbook to supplement classroom lessons. The problems covered in the text are broad and deep in scope, and introduce topics now commonly omitted from elementary school curricula, such as prime numbers, counting, and probability.<br /><br />The chapters are structured so the first few pages are relatively easy, followed by pages that gradually increase in difficulty, an approach enables kids to gain confidence. <br /><br />Although Ellison alerts his readers in the introduction that some of the problems are extremely difficult to answer (even for adults), he finds that does not deter high achievers from using the book. Rather, the challenges enthrall such students, who often equate "difficult" with "fun," and feel a great sense of accomplishment when they can solve an especially complex math problem.<br /><br />Parents who use the book with their children substantiate Ellison's theory. "I love that Glenn does not talk down to students," said Lakshmi Iyer, who uses the book with her second-grade daughter. "He makes it clear early on that this book will be challenging — but most importantly, he presents math as something powerful, beautiful, and fun. I love that he is encouraging kids to reach high. My daughter feels a strong sense of achievement when she manages to get a problem right in his 'hard math' book."<br /><br /><strong>A great resource for students of all ages</strong><br /><br />Others who have used Ellison's textbook laud him for creating unparalleled supplemental math textbooks.<br /><br />"I loved the way the book was written — Glenn knows very well how to make difficult material engaging and interesting," said Dina Mayzlin SB '97, PhD '02, who used a pre-publication copy of <i>Hard Math for Elementary School</i> to teach her son's Math Challenge club. "It's an excellent resource with few (if any) alternatives. I am so grateful that Glenn has devoted the time and effort to write this book. His books will have a lot of impact on young kids."<br /><br />Ying Gao, a senior at Newton North High School, used Ellison's book <i>Hard Math for Middle School</i>throughout middle school to prepare for the IMLEM and MATHCOUNTS. However, she still references the book and its more advanced topics for her current coursework. And now her nine-year-old brother Steven has begun using Ellison's newest book. He describes the book as "fun" and especially enjoys the jokes Ellison interspersed throughout the lessons.<br /><br /> <strong>Inspiring the next generation</strong><br /><br />Ellison hopes his books ignite more interest in math among younger students. For now, he can appreciate the impact his books are making whenever he attends his daughter's math competitions, where he has attained quasi-celebrity status. Here Ellison encounters numerous kids carrying his middle school math book—an occurrence he describes as "very cool."<br /><br />"I do get kids who come up to me to tell me how much they like the book, or ask if I can autograph their book," said Ellison. "What would be great is if in 10 to 12 years my MIT students come up to me and say I used your book when I was in fifth grade. That would be really awesome." <br /><br />
<hr />
<p class="shass">Story prepared by MIT SHASS Communications<br />Editorial and Design Director: Emily Hiestand<br />Writer, Communications Assistant: Kierstin Wesolowski<br />Images, details from <i>Hard Math</i> covers</p>Cocktail novelties inspired by nature’s designs
http://newsoffice.mit.edu/2013/cocktail-novelties-inspired-nature%E2%80%99s-designs
Mechanisms behind water bugs and lilies applied to culinary devices.Wed, 06 Nov 2013 05:00:02 -0500Jennifer Chu, MIT News Officehttp://newsoffice.mit.edu/2013/cocktail-novelties-inspired-nature%E2%80%99s-designsAn MIT mathematician and a celebrity chef have combined talents to create two culinary novelties inspired by nature. <br /><br />John Bush, a professor of applied mathematics, and renowned Spanish chef José Andrés have designed a cocktail accessory and a palate cleanser based on the mechanics of water bugs and water lilies, respectively. <br /><br />The cocktail accessory — an edible “boat” produced by 3-D printing — motors around on the surface of an alcoholic drink, propelled by the same fluid mechanics as certain water bugs. About the size of a raisin, the boat is filled with alcohol of a higher proof than the drink in which it floats. The boat steadily releases alcohol through a notch at one end, creating a difference in surface tension that propels it forward. This approach mimics one used by some insects, which release a chemical that drives them toward shore after an accidental fall into water. <br /><br />The team also designed a “floral pipette” resembling an upside-down flower. When dipped into a drink, the pipette captures and closes around a drop or two of liquid, which a diner can sip as a palate-cleanser. The device is the opposite of a water lily, which closes its petals when submerged, keeping liquid out. Both mechanisms work via surface tension and hydrostatic forces. <br /><br />Bush, who has published the details of both designs in the journal <i>Bioinspiration & Biomimetics</i>, says the culinary novelties stem from his group’s attempts to rationalize nature’s designs. <br /><br />“Nature tends to come up with ingenious mechanisms that are optimized over evolutionary time,” Bush says. “Engineers often take it to the next step by asking, ‘How can we apply this?’ In this collaboration, scientists and engineers have combined with chefs, allowing us to follow the entire route from nature to the kitchen.” <br /><br />
<div class="video_captions"><iframe frameborder="0" height="360" src="http://video.mit.edu/embed/26270/" width="560"></iframe><br /> <span class="image_caption">MIT scientists design two culinary novelties, inspired by nature. The first is a small, raisin-sized cocktail boat propelled by a higher proof liquor that leaks out one side of the boat, creating a difference in surface tension that pushes the boat forward. The design mimics the mechanics of certain water bugs, which skim across water by releasing a chemical as fuel. The second design is a floral pipette which, when dipped in liquid, closes around a few drops, which diners can then use as a palate cleanser between meals. The mechanism is opposite that of some water lilies, which act via surface tension and hydrostatic forces to close in times of rising waters, keeping water out. </span> <span class="image_credit">Video courtesy of the researchers</span></div>
<br /><strong> Is that a boat in my drink?</strong><br /><br />This particular collaboration began when Bush attended a science and cooking lecture at Harvard University, where Andrés was invited to speak. After the talk, Bush approached the chef with ideas from his work in fluid mechanics. The concept attracted Andrés, and the two began to brainstorm ways to apply Bush’s designs to the culinary arts. <br /><br />The cocktail boat, their first project together, is propelled by a phenomenon called the Marangoni effect, which arises when two liquids with different surface tensions come into contact: When a floating object is in contact with two such fluids, it is pulled towards the fluid with the higher surface tension. <br /><br />When certain bugs accidentally fall into water, they release a chemical that reduces the surface tension behind them, pushing them forward, toward the shore. Bush’s cocktail boat works via this same principle, taking advantage of the difference in surface tension between higher- and lower-proof alcohol to make the boat move.<br /><br />To make the cocktail boats, Lisa Burton and Nadia Cheng — at the time, graduate students in mechanical engineering — fabricated silicone molds using a 3-D printer. They filled the molds with various edible materials, such as gelatin and melted candies, and cast them in the shape of small boats. The boats were filled with alcohol, which leaked onto the surface through a notch at the rear of the boat, reducing the surface tension and propelling the boat forward.<br /><br />The researchers then experimented with various liquors and boat designs to optimize both the speed and duration of the boat’s motion. The team found that the boats could motor around for up to two minutes before running out of fuel. <br /><br /><strong>Printing petals for your palate</strong><br /><br />The team’s floral pipette is based on the behavior of certain water lilies, which float at the surface of ponds or lakes while anchored to the floor. As water rises, hydrostatic forces act to close a lily’s petals, preventing water from flooding in. Taking the water lily as inspiration, Pedro Reis, the Esther and Harold E. Edgerton Assistant Professor of Mechanical Engineering and Civil and Environmental Engineering, designed an upside-down flower that does the opposite, grabbing water as it’s pulled up, thereby reversing the role of gravity. <br /><br />Reis and Bush calculated the optimal petal size for capturing a small sip of liquid, then used a 3-D printer to form molds of the flower, each of which is about 35 millimeters wide — about the size of a small dandelion. <br /><br />“By pulling this out of liquid, you get something that seals shut and looks like a cherry. Touch it to your lips, and it releases its fluid,” Bush says. “It turns out to be an elegant way to serve a small volume of palate-cleansing liquor between courses.”<br /><br />The group has handed off the molds for both the cocktail boat and the floral pipette to Andrés’ management company, ThinkFoodGroup, where chefs are experimenting with the molds, filling them with various edible materials. <br /><br />Bush says that in many ways, scientists and chefs are like-minded in their approach to innovation. <br /><br />“Both should be familiar with a rich culture of all that has come before them,” Bush says. “The challenge, then, is not to create something from nothing, but rather to combine things in novel, interesting ways.”A new cocktail novelty is inspired by certain water bugs that release chemicals to propel them across water.MIT students help middle-school girls SHINE in dance and math
http://newsoffice.mit.edu/2013/mit-students-help-middle-school-girls-shine-dance-and-math
Senior Kirin Sinha has founded an after-school program to connect seventh-grade girls with MIT female student-mentors.Fri, 01 Nov 2013 14:03:14 -0400Sarah Coe | Public Service Centerhttp://newsoffice.mit.edu/2013/mit-students-help-middle-school-girls-shine-dance-and-mathWhen Kirin Sinha ’14 was growing up, she often found herself as the only girl taking advanced math classes and placing in the top 10 in national math competitions. She was regularly asked why being the only girl did not bother her, and she never had a good answer.<br /><br />During her junior year in the mathematics and electrical engineering and computer science departments at MIT, Sinha had the realization that her background as a dancer was one of the reasons she always has been comfortable standing out in math. Dancing since the age of three, and professionally since the age of 17, Sinha had learned growing up that “the harder you work and the better you get, the more you stand out and the better your life will be.”<br /><br />Realizing that this willingness to strive for the spotlight could be cultivated to spark a passion for mathematics, Sinha sought to create an after-school program for middle-school girls that would combine training in dance with enrichment in mathematics. After seeking support from the Public Service Center and the Department of Mathematics, Sinha founded SHINE (an acronym for Supporting, Harnessing, Inspiring, Nurturing, Empowering) in November 2012.<br /><br /><strong>An afternoon at SHINEs</strong><br /><br />During its first term, 14 middle-school girls enrolled in SHINE to work with 10 female MIT student-mentors. A typical session of SHINE starts with the girls tackling a challenging mathematics problem with their mentors nearby to coach them.<br /><br />After a word problem game gets the group thinking analytically, the girls transition to a warm up and practice individual dance moves. In the second half of the dance lesson, the students work on choreography. Each SHINE session culminates in a final performance where each girl performs a solo for family and friends to emphasize and celebrate each girl’s ability to stand out in her excellence.<br /><br />To transition to the mathematics portion of the program, mentors call out rapid-fire questions and movement combinations. These might include directions to turn to different angles (such as 45 or 90 degrees) or to spin while reciting multiplication tables.<br /><br />Sinha says that such kinesthetic learning reinforces a concept by tying it to a concrete physical action.<br /><br />“I got the idea by combining concepts that had worked well when I had tutored girls in math and taught dance classes in the past,” Sinha says. “Dance was a natural pairing with mathematics for girls since, aside from providing physical activity, it requires dedication, attention to detail, and confidence to succeed. These same tools enable the girls to excel in mathematics.”<br /><br />After the exercise, the girls catch up with their mentors over a snack while going over homework from the previous week. At the end of each session the group moves on to discussing new curriculum topics.<br /><br />Prior to beginning the program, the girls take an entrance survey to gauge their math abilities and self-confidence. According to Sinha, 80 percent initially say they do not want to stand out even when they are good at something.<br /><br />“At the beginning of the program, many of the girls would refuse to do the mathematics problems, but now they’re totally willing,” Sinha says. “When we began the program, only one person would even attempt to solve the challenge problem, but now, they all try and more and more of them are able to complete it. It’s the attitude shift that was really significant. We saw every girl improve in both math and confidence and a 40 percent improvement in their overall math scores from the beginning to end of the program.”<br /><br /><strong>The future of SHINE</strong><br /><br />The response from the girls have been so enthusiastic that Sinha increased the size of the summer program and opened it to outgoing and incoming seventh graders to accommodate the girls who would like to come back for another session. During the summer term, there were 20 students and eight MIT mentors engaged in the program. Sinha says her ambition is to see SHINE spread all over the country.<br /><br />“It’s a very reproducible program,” she says. “People can start branches everywhere… it has franchise potential.”<br /><br />But, she also knows there are many questions left to answer about the feasibility of scaling the SHINE model.<br /><br />“Does this only work in cities or in the U.S., or can it be a solution globally?” she asks. “We want to test it internationally. We’re hoping to see if it can be successful abroad, a larger solution.”<br /><br />The one thing Sinha says she wants people to take away from hearing SHINE’s origin story is that there is no such thing as “it’s too late” or “it’s too much” at MIT if someone has the passion to do something. Just over a year ago, SHINE was nothing more than an idea in her mind, and now it is a huge part of her life.<br /><br />“Even if SHINE died tomorrow, we would have affected the lives of 34 girls in a tangible way,” she says. “That alone would have made it worth the work so far. If you put your entire self behind what you do, and don’t apologize about it, then you will be able to stand out in a positive way and really give something back.”MIT student-mentors help SHINE students through a tailored math curriculum.When fluid dynamics mimic quantum mechanics
http://newsoffice.mit.edu/2013/when-fluid-dynamics-mimic-quantum-mechanics-0729
MIT researchers expand the range of quantum behaviors that can be replicated in fluidic systems, offering a new perspective on wave-particle duality.Mon, 29 Jul 2013 04:00:00 -0400Larry Hardesty, MIT News Officehttp://newsoffice.mit.edu/2013/when-fluid-dynamics-mimic-quantum-mechanics-0729In the early days of quantum physics, in an attempt to explain the wavelike behavior of quantum particles, the French physicist Louis de Broglie proposed what he called a “pilot wave” theory. According to de Broglie, moving particles — such as electrons, or the photons in a beam of light — are borne along on waves of some type, like driftwood on a tide. <br /><br />Physicists’ inability to detect de Broglie’s posited waves led them, for the most part, to abandon pilot-wave theory. Recently, however, a real pilot-wave system has been discovered, in which a drop of fluid bounces across a vibrating fluid bath, propelled by waves produced by its own collisions.<br /> <br />In 2006, Yves Couder and Emmanuel Fort, physicists at Université Paris Diderot, used this system to reproduce one of the most famous experiments in quantum physics: the so-called “double-slit” experiment, in which particles are fired at a screen through a barrier with two holes in it.<br /><br />In the latest issue of the journal <i>Physical Review E</i> (PRE), a team of MIT researchers, in collaboration with Couder and his colleagues, report that they have produced the fluidic analogue of another classic quantum experiment, in which electrons are confined to a circular “corral” by a ring of ions. In the new experiments, bouncing drops of fluid mimicked the electrons’ statistical behavior with remarkable accuracy.<br /><br />“This hydrodynamic system is subtle, and extraordinarily rich in terms of mathematical modeling,” says John Bush, a professor of applied mathematics at MIT and corresponding author on the new paper. “It’s the first pilot-wave system discovered and gives insight into how rational quantum dynamics might work, were such a thing to exist.”<br /><br />Joining Bush on the PRE paper are lead author Daniel Harris, a graduate student in mathematics at MIT; Couder and Fort; and Julien Moukhtar, also of Université Paris Diderot. In a separate pair of papers, appearing this month in the Journal of Fluid Mechanics, Bush and Jan Molacek, another MIT graduate student in mathematics, explain the fluid mechanics that underlie the system’s behavior.<br /><br /><strong>Interference inference</strong><br /><br />The double-slit experiment is seminal because it offers the clearest demonstration of wave-particle duality: As the theoretical physicist Richard Feynman once put it, “Any other situation in quantum mechanics, it turns out, can always be explained by saying, ‘You remember the case of the experiment with the two holes? It’s the same thing.’”<br /><br /><iframe frameborder="0" height="435" src="http://www.youtube.com/embed/nmC0ygr08tE?rel=0" width="580"></iframe> <br /><br /> If a wave traveling on the surface of water strikes a barrier with two slits in it, two waves will emerge on the other side. Where the crests of those waves intersect, they form a larger wave; where a crest intersects with a trough, the fluid is still. A bank of pressure sensors struck by the waves would register an “interference pattern” — a series of alternating light and dark bands indicating where the waves reinforced or canceled each other.<br /><br />Photons fired through a screen with two holes in it produce a similar interference pattern — even when they’re fired one at a time. That’s wave-particle duality: the mathematics of wave mechanics explains the statistical behavior of moving particles.<br /><br />In the experiments reported in PRE, the researchers mounted a shallow tray with a circular depression in it on a vibrating stand. They filled the tray with a silicone oil and began vibrating it at a rate just below that required to produce surface waves.<br /><br />They then dropped a single droplet of the same oil into the bath. The droplet bounced up and down, producing waves that pushed it along the surface.<br /><br />The waves generated by the bouncing droplet reflected off the corral walls, confining the droplet within the circle and interfering with each other to create complicated patterns. As the droplet bounced off the waves, its motion appeared to be entirely random, but over time, it proved to favor certain regions of the bath over others. It was found most frequently near the center of the circle, then, with slowly diminishing frequency, in concentric rings whose distance from each other was determined by the wavelength of the pilot wave. <br /><br />The statistical description of the droplet’s location is analogous to that of an electron confined to a circular quantum corral and has a similar, wavelike form. <br /><br />“It’s a great result,” says Paul Milewski, a math professor at the University of Bath, in England, who specializes in fluid mechanics. “Given the number of quantum-mechanical analogues of this mechanical system already shown, it’s not an enormous surprise that the corral experiment also behaves like quantum mechanics. But they’ve done an amazingly careful job, because it takes very accurate measurements over a very long time of this droplet bouncing to get this probability distribution.”<br /><br />“If you have a system that is deterministic and is what we call in the business ‘chaotic,’ or sensitive to initial conditions, sensitive to perturbations, then it can behave probabilistically,” Milewski continues. “Experiments like this weren’t available to the giants of quantum mechanics. They also didn’t know anything about chaos. Suppose these guys — who were puzzled by why the world behaves in this strange probabilistic way — actually had access to experiments like this and had the knowledge of chaos, would they have come up with an equivalent, deterministic theory of quantum mechanics, which is not the current one? That’s what I find exciting from the quantum perspective.”<br />When the waves are confined to a circular corral, they reflect back on themselves, producing complex patterns (grey ripples) that steer the droplet in an apparently random trajectory (white line). But in fact, the droplet’s motion follows statistical patterns determined by the wavelength of the waves.A new way to trap light
http://newsoffice.mit.edu/2013/a-new-way-to-trap-light-0710
MIT researchers discover a new phenomenon that could lead to new types of lasers and sensors.Wed, 10 Jul 2013 17:00:00 -0400David L. Chandler, MIT News Officehttp://newsoffice.mit.edu/2013/a-new-way-to-trap-light-0710There are several ways to “trap” a beam of light — usually with mirrors, other reflective surfaces, or high-tech materials such as photonic crystals. But now researchers at MIT have discovered a new method to trap light that could find a wide variety of applications.<br /><br />The new system, devised through computer modeling and then demonstrated experimentally, pits light waves against light waves: It sets up two waves that have the same wavelength, but exactly opposite phases — where one wave has a peak, the other has a trough — so that the waves cancel each other out. Meanwhile, light of other wavelengths (or colors) can pass through freely.<br /><br />The researchers say that this phenomenon could apply to any type of wave: sound waves, radio waves, electrons (whose behavior can be described by wave equations), and even waves in water.<br /><br />The discovery <a href="http://www.nature.com/nature/journal/v499/n7457/full/nature12289.html" target="_blank">is reported this week</a> in the journal <i>Nature</i> by professors of physics Marin Soljačić and John Joannopoulos, associate professor of applied mathematics Steven Johnson, and graduate students Chia Wei Hsu, Bo Zhen, Jeongwon Lee and Song-Liang Chua.<br /><br />“For many optical devices you want to build,” Soljačić says — including lasers, solar cells and fiber optics — “you need a way to confine light.” This has most often been accomplished using mirrors of various kinds, including both traditional mirrors and more advanced dielectric mirrors, as well as exotic photonic crystals and devices that rely on a phenomenon called Anderson localization. In all of these cases, light’s passage is blocked: In physics terminology, there are no “permitted” states for the light to continue on its path, so it is forced into a reflection.<br /><br />In the new system, however, that is not the case. Instead, light of a particular wavelength is blocked by destructive interference from other waves that are precisely out of phase. “It’s a very different way of confining light,” Soljačić says.<br /><br />While there may ultimately be practical applications, at this point the team is focused on its discovery of a new, unexpected phenomenon. “New physical phenomena often enable new applications,” Hsu says. Possible applications, he suggests, could include large-area lasers and chemical or biological sensors.<br /><br />The researchers first saw the possibility of this phenomenon through numerical simulations; the prediction was then verified experimentally. <br /><br />In mathematical terms, the new phenomenon — where one frequency of light is trapped while other nearby frequencies are not — is an example of an “embedded eigenvalue.” This had been described as a theoretical possibility by the mathematician and computational pioneer John von Neumann in 1929. While physicists have since been interested in the possibility of such an effect, nobody had previously seen this phenomenon in practice, except for special cases involving symmetry.<br /><br />This work is “very significant, because it represents a new kind of mirror which, in principle, has perfect reflectivity,” says A. Douglas Stone, a professor of physics at Yale University who was not involved in this research. The finding, he says, “is surprising because it was believed that photonic crystal surfaces still obeyed the usual laws of refraction and reflection,” but in this case they do not.<br /><br />Stone adds, “This is in fact a realization of the famous ‘bound state in the continuum’ proposed by von Neumann and [theoretical physicist and mathematician Eugene] Wigner at the dawn of quantum theory, but in a practical, realizable form. The potential applications the authors mention, to high-power single-mode lasers and to large-area chemical [and] biological sensing, are very intriguing and exciting if they pan out.”Light is found to be confined within a planar slab with periodic array of holes, although the light is theoretically "allowed" to escape. Blue and red colors indicate surfaces of equal electric field.Before the wreckage comes ashore
http://newsoffice.mit.edu/2013/before-the-wreckage-comes-ashore
MIT paves the way towards smarter environmental disaster responseThu, 30 May 2013 16:37:51 -0400Genevieve Wanucha | Oceans at MIThttp://newsoffice.mit.edu/2013/before-the-wreckage-comes-ashoreFrom the Fukushima tsunami disaster to the Deep Water Horizon oil spill, environmental disasters exact all-too-memorable damage to coastal communities. Imagine if it was possible to predict the exact place a blob of spilled oil or dangerous tsunami debris would hit a coastline two days ahead of time. Imagine if we could pinpoint where the pollution would never make landfall. Early detection, rapid-response actions and efficient use of limited resources only hint at the potentials of smarter disaster response.<br /><br /> That dream is more of a reality now, thanks to a culminating decade of work in an environmental application of dynamic systems theory, a branch of mathematics used to understand complex phenomena that change over time. Oceanographers around the world, with MIT mechanical engineering associate professor Thomas Peacock at the helm, have found the invisible organizing structures that govern how pollutants move along an ocean's chaotically swirling surface.<br /><br /> These structures, called Lagrangian coherent structures (LCS), are the dividing lines between parts of a flow that are moving at varying speeds and in different directions, often called the "hidden skeleton of fluid flow." These curvy lines of water particles act to attract or repel the other fluid elements around them. "For example, if something is dropped in the Gulf stream," Peacock says, "it would hit the coast of the United Kingdom, but dropped just outside of the Gulf stream, it would go off somewhere else, maybe down to the South Atlantic or up off to the North Pole." The key, he says, is to find the LCS and identify them, which is a challenge for an ocean surface with flows that are constantly changing shape and form.<br /><br /> Peacock and his collaborators at MIT's Experimental and Nonlinear Dynamics Lab are now applying the LCS approach to predict the path of debris swept out into the Pacific Ocean's Kuroshio Current when the Tohoku tsunami hit the coast of Fukushima, Japan back in May 2011. Detritus has been washing ashore along the west coast of the United States and Canada and will continue to for at least five more years. The debris is not radioactive, but the rouge Japanese fishing boats and docks deliver dozens of potentially invasive organisms to the coastal ecosystems of the Pacific Northwest.<br /><br /> To locate and study the LCS guiding the debris to the U.S., Peacock's group relies on data from high-frequency (HF) radar systems, buoys and satellites. They are increasingly benefiting from a strengthening infrastructure of high frequency radar installations, built along the West Coast by researchers at<a href="http://cordc.ucsd.edu/projects/mapping/" target="_blank"> </a>Scripps Oceanographic Institution. These monitoring stations provide a wealth of readily available, up-to-the minute data on ocean surface currents in real time. In tandem, the National Oceanic and Atmospheric Administration (NOAA) keeps close track of tsunami debris sightings and provides an<a href="https://www.erma.unh.edu/arctic/erma.html#x=-139.14383&y=58.19371&z=5&layers=12959+355+13494" target="_blank"> online interactive map </a>of the debris.<br /><br /> In the lab, computers capable of rapid information processing apply the Lagrangian rules to these data, supporting Peacock's goal to create a "nowcast," which is an accurate map of the key transport barriers organizing the debris at the present time. The idea is that at any particular time of year, he can make a big picture statement about the particular regions of the West Coast that are likely to attract the debris. "So far, we have identified time windows when there is a switch between where the stuff is going to be pushed up to the Gulf of Alaska and where its going to be pushed south towards Oregon and Washington," he says. "These insights are substantial advances and nicely complement traditional modeling efforts."<br /><br /> The common approach to tracking the fate of ocean contaminants involves running computer models that estimate the likelihood a pollutant will travel a certain path. "While certainly a powerful tool," says Peacock, "direct trajectory analysis doesn't really give you an understanding of why things went off to one location as opposed to another." These traditional models produce what are unfavorably referred to as "spaghetti plots" because of their hard-to-decipher tangled lines of possible pollutant pathways. "The LCS analysis helps us process the trajectory information in a different way and identify key transport barriers to pollutant transport."<br /><br /> The goal for the tsunami debris is to extend "now-casting" to forecasting, and this feat depends on the quality of data Peacock can get his hands on. "The holy grail in a few years time, say, will be to have the entire West Coast peppered with the monitoring stations that can measure 100 kilometers or more out to sea," he says. "With that information, we could then fairly accurately find all the attracting and repelling LCS and decide which regions we might expect something to come ashore or not."<br />
<p style="text-align: center;"><strong>***</strong></p>
In April 2010, a blowout caused an explosion on the Deepwater Horizon (DWH) offshore oil rig in the Gulf of Mexico, resulting in a three-month spill of about four million barrels of oil. In the Lagrangian world, disaster is opportunity. In the years that followed, the enormous amount of satellite data from the unprecedented disaster became the single best way to hone LCS methods.<br /><br /> To validate the LCS results, researchers confirm their transport barrier predictions with a blob of tracer in water, capturing its motions, speed and trajectory with high-resolution digital cameras. "Normally, you don't have such a huge tracer blob in the ocean that's so visible from the surface," says <a href="http://georgehaller.com/index.htm/Welcome.html" target="_blank">George Haller</a>, professor of nonlinear dynamics at ETH Zurich, who forged this dynamical systems theory approach to questions about ocean surface transport. "So, the Gulf Oil Spill was almost the ideal tracer experiment." In 2012, Haller and <a href="http://www.rsmas.miami.edu/users/jolascoaga/" target="_blank">María J. Olascoaga</a> of the University of Miami<a href="http://www.pnas.org/content/early/2012/03/05/1118574109.abstract" target="_blank"> identified</a> a single, key LCS that had pushed the oil spill toward the northeast coast of Florida for about two weeks in June — information that would have been key for hard decisions during the spill.<br /><br /> CJ Beegle-Krause has seen 250 oil spills. She is an oceanographer currently at the independent research organization SINTEF and serves as an oil spill trajectory forecaster for NOAA — which is why she got calls from high school friends asking if the Gulf Oil spill would reach their vacation homes. From her experience, she predicts that core-structure analysis will have huge social value.<br /><br /> For example, during the oil spill, the city of Tampa, Fla., repeatedly requested resources from the Unified Command Center. "That was a very difficult situation," Beegle-Krause says, "because the oil was close enough to make residents and responders worried, but all the three-day forecasts did not show the oil reaching that coast." People didn't believe the government, and mass cancellations devastated the tourism industry. She thinks that LCS analysis could buffer a spill's psychological impact. "My hope," she says, "is that having transport barrier predictions as an independent source of information will reassure people and help them understand why they aren't getting resources." Just as with the weather report, maps, animations and pictures bring the message home more than tables of numbers and probabilities.<br /><br /> The big environmental potential for the LCS approach is optimized deployment of oil spill equipment, such as skimmers, dispersants and absorbent booms. "We can also develop a monitoring program based on transport barriers," Beegle-Krause says, "so we can monitor less in areas that are outside of transport barriers that contain the spill." Plus, she suggests, if responders had a heads up as to where the spill would break up into sheens, or very thin layers of oil, they could quickly decide not send skimmers out to those areas of unrecoverable oil.<br /><br /> Looking ahead to a time when the melting Arctic is <a href="http://www.nytimes.com/2012/09/19/science/earth/arctic-resources-exposed-by-warming-set-off-competition.html?pagewanted=all" target="_blank">home to increased oil exploration</a>, Beegle-Krause can't help but think of the insurmountable obstacles an oil spill in the region would pose without the next generation of response tools. "For example, in the Deepwater Horizon disaster, the entire spill was surveyed with data from satellites and helicopters within 24 to 48 hours," she says. "But if there is a well blowout in the Arctic and oil gets under ice, it's much harder to locate the spill and send appropriate resources. You can't just fly over and see oil under pack ice." Getting a handle on the spill would involve sending instruments through the ice in remote, frigid locations. Deep Water Horizon would look easy.<br />
<p style="text-align: center;"><strong>***</strong></p>
Back at the MIT Experimental and Non Linear Dynamics Lab, their LCS approach is going global, from Brazil to Taiwan, all the way off the northwest coast of Australia to the Ningaloo Reef, a <a href="http://www.australiangeographic.com.au/journal/ningaloo-given-world-heritage-status.htm" target="_blank">World Heritage ecosystem</a> facing oil spill threats from close proximity offshore facilities in operation, as well as planned exploratory drilling. But the reef has guardians. Peacock and collaborator Greg Ivey, professor of geophysical fluid dynamics at the University of Western Australia, are analyzing the complex flow fields that prevail in the waters off Ningaloo. They hope to determine when the reef is at high risk and how long those danger periods last.<br /><br /> So, what if another spill the size of Deep Water Horizon happened today? "We would be in a better position than we were at the time," Beegle-Krause says. "We have the analysis method. But we don't have a product ready yet that responders can use to make decisions in a spill. That's what needs to happen — the transition from peer-reviewed science to a decision support product." Beegle-Krause and Peacock are now collaborating on such an industry product. She estimates that with all necessary funding, the product could be ready in two years.<br /><br /> If there ever was at time to push this application forward, this is it. In the last three years, we experienced the largest accidental marine oil spill in the history of the petroleum industry and the largest accidental release of radioactive material into the ocean, along with five million tons of debris. "That has certainly made funding agencies sit up and take notice," notes Peacock, who has recently received new funding from the National Science Foundation and the Office of Naval Research to advance these methods. These familiar disasters are, inevitably, not the last marine "accidents." If we can't prevent the disasters, we might as well beat the wreckage to the shore.This barnacle-covered Japanese fishing boat washed up on the coast of the state of Washington in the summer of 2012. Local fifth graders explore mathematics with MIT graduate students
http://newsoffice.mit.edu/2013/local-fifth-graders-explore-mathematics-with-mit-graduate-students
MITxplore, a free after-school math program, transforms math into an adventure.Tue, 28 May 2013 14:04:26 -0400Sarah Coe | Public Service Centerhttp://newsoffice.mit.edu/2013/local-fifth-graders-explore-mathematics-with-mit-graduate-students“We’re going to explore math.”<br /><br />That’s the adventure MITxplore co-founders Leon Dimas, Narges Kaynia and Debbie Nguyen say they are trying to bring to the lives of local fifth graders through a weekly after-school program focused on participatory mathematics. Every week, about 10 students at both the Fletcher Maynard Academy in Cambridge and the Hurley School in Boston meet with three MITxplore mentors to discuss mathematical concepts, engage in fun activities and learn from each other.<br /><br />MITxplore’s founders saw a need for more math-focused after-school enrichment programs, specifically those which convey the beauty and creativity inherent in the art of mathematics. They noticed that such programs are more prevalent for science, where exciting hands-on projects draw students, and they wanted to show that math is captivating as well.<br /><br />As a result, the founders chose to approach mathematics from a different angle than the “dry box of equations” they say many students are familiar with.<br /><br />“We wanted to make sure children were aware of how creative mathematics can be,” says Dimas, a graduate student in civil and environmental engineering. “Students think it’s cool to explore, to talk about rockets — we wanted to incorporate that into mathematics.”<br /><br />In MITxplore lessons, students are not expected to understand concepts right away. Confusion is not an unpleasant failure but an opportunity for adventure and learning.<br /><br />“MITxplore is a group process,” says Kaynia, a graduate student in mechanical engineering. “We tell the kids in the beginning, ‘We’re all explorers on a ship. How do you steer a ship?’ Everyone works together, and that’s how you get from one island to another. A student who struggles with the concepts in class might still have good, outside-the-box ideas. We encourage everyone to discuss and come to a solution together.”<br /><br /><strong>A typical mathematical adventure</strong><br /><br />MITxplore sessions feature repeating cycles of discussion, activities and reflection. A typical day might start with the mentors asking the students in a Socratic fashion how they would set up a number line. (“Where would you put number one? Where would you put number 50?”) Together, the students build on this, constructing a number line on a whiteboard by asking each other questions and suggesting examples.<br /><br />“They see for themselves and understand why it is the way it is: why it’s infinite, why there are negative numbers, why it’s mirrored around zero,” says Kaynia. “We only facilitate their own learning; we do not necessarily teach them new math. We believe students have a born intuition and logic, and we’re connecting that with the tools they learn in school.”<br /><br /><strong>From idea to realization</strong><br /><br />As graduate students at MIT, Dimas, Kaynia and Nguyen say they are in a great position to take advantage of MIT’s unique support structure for innovation and humanitarianism. They reached out to the Public Service Center, faculty and local businesses for funding and advice.<br /><br />Dimas says he meets a new person with great insights every day. “MIT is a wonderful place to start something,” he says. “All the resources are there; everyone wants to help you.”<br /><br />“We’re so lucky to be at MIT, with all the knowledge, the resources, the facilities, the inspiration,” Kaynia says. “At some point you ask, ‘What am I doing to give back to society?’”<br /><br />Ultimately, the mentors of MITxplore hope to answer that question by creating a model for mathematics outreach that can be adopted by anyone. The team is working to create a framework that distills their philosophy and hard work into a clear guide.<br /><br />“There are many people out there who have the same desire to work with local students,” Kaynia says. “They don’t necessarily have to be a PhD student at MIT — a lot of the magic happens just by creating that discussion. Once this framework exists, parents could use it for their own neighborhood kids.”<br /><br /><strong>The power of mathematical service</strong><br /><br />All three co-founders derive satisfaction from their work on a deeply personal level. “It’s so wonderfully rewarding seeing that little spark in a kid’s eye when they understand something,” Dimas says. “It’s like you open the door to an entirely new space.”<br /><br />Nguyen, a graduate student in mechanical engineering, also sees that spark, but to her it represents something different. Growing up as the daughter of Vietnamese refugees, Nguyen says she never would have been able to achieve her dream of studying engineering without the support of inspiring people who told her that her background and her gender did not have to hold her back.<br /><br />“I think that spark is when they notice their potential to do anything that they want,” Nguyen says.<br /><br />To help create that spark, MITxplore welcomed grade 4-6 students and parents from around Massachusetts to the MIT Media Lab on May 12 for its Spring Math Treasure Hunt. The day featured talks by Larry Guth, professor of mathematics, and Rodolfo Rosales, professor of applied mathematics, and more than 30 MIT students were on hand to guide the participants through educational activities about probability, geometry and topology, and numbers and limits. MITxplore aims to host a series of similar Math Days in the future.<br />MITxplorers build skyscrapers with spaghetti and marshmallows under the encouragement of co-president and mentor Debbie Nguyen (right).MIT students, alumni awarded 2013 Fulbright grants
http://newsoffice.mit.edu/2013/mit-students-awarded-2013-fulbright-grants
Selected on the basis of academic or professional achievement, as well as demonstrated leadership potential in their fieldsMon, 20 May 2013 17:50:33 -0400News Officehttp://newsoffice.mit.edu/2013/mit-students-awarded-2013-fulbright-grantsSeveral MIT undergraduate and graduate students and alumni — Noam Angrist, Marvin Arnold, Dorothy Brown, Hyunjii (Justina) Cho, Deborah Hanus and Marisa Lau — have been awarded Fulbright study/research grants for the upcoming academic year. <br /><br />The Fulbright Program is the flagship international educational exchange program sponsored by the United States government and is designed to increase mutual understanding between the peoples of the U.S. and other countries. Recipients of Fulbright grants are selected on the basis of academic or professional achievement, as well as demonstrated leadership potential in their fields. The grant allows students to undertake projects or academic programs in 155 countries around the world.<br /><br />The MIT students awarded Fulbright study/research grants for this year have proposed a range of projects or courses of study. <br /><br />Angrist, from Brookline, Mass., will be graduating this spring from MIT with a bachelor’s degree in mathematics and economics. He will travel to Botswana to work on educational reform, conducting research on how the structure of the school term affects educational outcomes and determining alternative models. This project builds on previous work Noam has done with the World Bank Education Sector. <br /><br />Arnold, from Silver Spring, Md., graduated with a bachelor’s degree in electrical engineering and computer science from MIT in 2010. The Fulbright grant will allow Arnold to complete an MBA at the IE Business School in Madrid, Spain. Marvin plans to be involved with IE’s Venture Labs, where he can work closely with Spanish businesses and develop cross-cultural collaborations.<br /><br />Brown '10, SM '10 — a first-generation American from New York City — graduated from MIT with a master’s degree in civil and environmental engineering. Her project will take her to Brazil, where she will study the use of rice husk ash in concrete as a low-cost and environmentally friendly construction material. This project builds on research Brown conducted for her master’s thesis. <br /><br />Cho, from Orland Park, Ill., will graduate this spring with a bachelor’s degree in biology. She will travel to Berlin, Germany to conduct microbiology and immunology research in Professor Arturo Zychlinsky's laboratory at the Max Planck Institute for Infection Biology. She will be studying how white blood cells respond to infection by investigating the mechanism of neutrophil extracellular trap (NET) formation. Her interest in blood cells stems from work she has done in Professor Harvey Lodish's lab at MIT.<br /><br />Hanus, a resident of Cambridge, Mass., graduated this year with a bachelor’s degree in electrical engineering and computer science. With the Fulbright grant, Hanus plans to travel to Cambodia to research education and employment, focusing on the social factors that contribute to underemployment. She is particularly interested in the potential of experiential learning and plans to build on work she had already done in Cambodia in 2011 with the Harpswell Foundation and Small World.<br /><br />Lau, from Plainfield, N.J., acquired a master’s degree in city planning from MIT in 2012, following a master’s in cultural heritage management from Koc University in Turkey, in 2010, and a bachelor’s degree in political science and art history from Williams College in 2006. She will create a heritage conservation plan for the water system of Nicosia, Cyprus. This work will involve mapping the city’s historic water system and creating recommendations for conservation.Four MIT professors elected to the National Academy of Sciences
http://newsoffice.mit.edu/2013/four-mit-professors-elected-to-the-national-academy-of-sciences
Field, Kac, Vogan and Walker bring to 76 the number of Institute faculty who are NAS members.Mon, 13 May 2013 19:12:04 -0400News Officehttp://newsoffice.mit.edu/2013/four-mit-professors-elected-to-the-national-academy-of-sciencesFour MIT professors have been named to the prestigious National Academy of Sciences (NAS), an honor recognizing distinguished and continuing achievements in original research.<br /> <br />This year’s new NAS members are <a href="http://www.mit.edu/~chemistry/faculty/field.html" target="_blank">Robert Field</a>, the Haslam and Dewey Professor of Chemistry; <a href="http://www-math.mit.edu/~kac/" target="_blank">Victor Kac</a>, professor of mathematics; <a href="http://www-math.mit.edu/people/profile.php?pid=286" target="_blank">David Vogan</a>, professor of mathematics; and <a href="http://biology.mit.edu/people/graham_walker" target="_blank">Graham Walker</a>, professor of biology. <br /><br />Including these four, 76 MIT faculty members now hold NAS membership. A total of 158 MIT affiliates — including emeritus and former faculty, current and former staff, and alumni — are members of the NAS.<br /><br />The MIT professors were among 84 members and 21 foreign associates from 14 countries elected to the NAS this year. <br /><br />NAS membership is one of the highest honors afforded to scientists and engineers. Past members have included Albert Einstein, Thomas Edison and Alexander Graham Bell, and nearly 200 living NAS members have earned Nobel Prizes.<br /><br />The new members will be inducted next April during the NAS’s annual meeting, held in Washington.<br /><br />The NAS, when founded in 1863, called upon a group of scholars to “investigate, examine, experiment, and report upon any subject of science or art” whenever requested by the government. There are currently 2,179 NAS members and 437 foreign associates.MIT senior Holden Lee wins Gates Scholarship
http://newsoffice.mit.edu/2013/mit-senior-holden-lee-wins-gates-scholarship
Lee will pursue graduate studies in mathematics at the University of Cambridge.Mon, 08 Apr 2013 18:22:59 -0400News Officehttp://newsoffice.mit.edu/2013/mit-senior-holden-lee-wins-gates-scholarshipMIT senior Holden Lee has been awarded a 2013 Gates Cambridge Scholarship to pursue graduate studies in mathematics at the University of Cambridge. <br /><br />The prestigious Gates Cambridge Scholarships were established in 2000 through a donation from the Bill and Melinda Gates Foundation to cover the costs of graduate education at Cambridge for 90 students from around the world — 40 of them from the United States — each year. Lee will start a master’s program in pure mathematics at Cambridge this fall.<br /><br />Lee’s primary interest is in number theory. After completing his master’s at Cambridge, he plans to acquire a PhD so that he can teach and conduct further research in this field. <br /><br />At MIT, Lee has served as vice president of the Undergraduate Math Association, worked as a teaching assistant in a mathematics summer program for high school students, and developed mathematical curricula and online-learning resources. <br /><br />Ken Ono, the Asa Griggs Candler Professor of Mathematics at Emory University, praised Lee’s undergraduate research experience contributions at Emory in summer 2011, highlighting in particular a paper Lee co-authored on p-adic modular forms. <br /><br />Sug Woo Shin, an assistant professor of mathematics at MIT, and Lee’s advisor in the mathematics department, observed, “Holden grasps new mathematical notions quickly and has insatiable thirst for discovering beautiful symmetries hidden in number theory.” Shin also commended Lee’s work teaching high school students and writing lessons on math that are free and available to the public. <br /><br />“Holden is greatly concerned with math education,” Shin wrote, and has a great desire “to share his knowledge.”<br /><br />Lee is the second MIT student to have won a Gates Scholarship this year, joining <a href="/newsoffice/2013/daniel-jimenez-named-gates-cambridge-scholar-2013.html" target="_self">Daniel D. Jimenez</a> BSc ’10, MEng ’11, who will enroll in an MPhil in engineering for sustainable development at Cambridge in October. <br /><br />Students interested in the Gates Scholarship should speak with <a href="mailto:benard@mit.edu">Kimberly Benard</a> in MIT Global Education and Career Development.Holden LeeOCW provides challenges for talented young student
http://newsoffice.mit.edu/2013/ocw-provides-challenges-for-a-talented-young-student
Indian teen Tuhin Bagi uses MIT OpenCourseWare to enhance his studies and set his sights on future endeavors.Tue, 26 Mar 2013 20:30:32 -0400Mark Brown | MIT OpenCourseWarehttp://newsoffice.mit.edu/2013/ocw-provides-challenges-for-a-talented-young-student<div class="video_captions" style="float: right; padding: 10px 0px 10px 10px; width: 200px;"><img src="/newsoffice/sites/mit.edu.newsoffice/files/images/ocw-1.jpg" border="0" alt="Tuhin Bagi" /><br /> <span class="image_caption">Tuhin Bagi's dream is to attend MIT and work as an automobile engineer.</span> <span class="image_credit">Photo courtesy of Tuhin Bagi</span></div>
The city of Nasik has long been known as the wine capital of India for its plentiful supply of grapes. But more recently it has become a high-tech and engineering hub — one of the fastest growing cities in the country. Born and raised there, 15-year-old Tuhin Bagi shares his native city’s fascination with science and technology, and maintains an equally breathless pace. He's captain of his school’s badminton team (the reigning champs), plays classical Indian music, frequently competes in regional science fairs, and follows a full curriculum of advanced courses in physics, chemistry and biology.<br /><br />His parents are strong supporters of Tuhin's academic interests, but found themselves challenged by his curiosity. "Tuhin is an eager learner," explains his father, an industrial automation engineer, "and his interests took him far beyond his school syllabus. I tried to answer his questions and have regular sessions with him, but I could not always be home." One day, while looking for online resources to help Tuhin answer a question in physics, his mother came across MIT OpenCourseWare. At first she worried that its material might be too advanced for a high school freshman, and wrote to OCW for advice. To her surprise, she received a personal response from MIT professor Walter Lewin, who suggested that Tuhin give his lectures a try.<br /><br />Tuhin loved the lectures immediately, and every day after school his mother would find him watching them on the computer (both <a href="http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/" target="_blank">8.01 Physics I</a>: Classical Mechanics and <a href="http://ocw.mit.edu/courses/physics/8-02sc-physics-ii-electricity-and-magnetism-fall-2010/" target="_blank">8.02SC Physics II</a>: Electricity and Magnetism). He sometimes needed to watch a single lecture several times to really capture everything, but acknowledges that it's a big achievement for someone his age to follow a university-level science course. "It is a bit unusual," he admits with a smile. "I don't know anyone else at my school who is doing this."<br /><br />Since then, it's been a steady progression of additional OCW courses for Tuhin, including Professor Donald Sadoway's Introduction to Solid State Chemistry (<a href="http://ocw.mit.edu/courses/materials-science-and-engineering/3-091sc-introduction-to-solid-state-chemistry-fall-2010/" target="_blank">3.091SC</a>) and Single Variable Calculus (<a href="http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/" target="_blank">18.01SC</a>). Explaining Tuhin's attraction to OCW, his father notes that he appreciates how the lectures offer clear and practical illustrations to demonstrate how various theories actually work. But Tuhin views it in simpler terms: "I just feel <i>at home</i> learning," he says.<br /><br />On close examination, it’s clear that OCW serves Tuhin in two ways. He sees it as a tool for improving his grasp of key concepts in his current studies. "In school there are times when I don't completely understand a topic that my teacher is lecturing. After I go to OCW, I understand it properly." At the same time, he sees OCW as a means to help him realize his future ambitions. "I want to pursue my future studies in the U.S. and OCW helps prepare me. My dream is to go to MIT and become an automobile engineer. The fossil fuels are depleting and new fuels have to be developed—I would like to design new engines to do that."<br /><br />Tuhin's parents are thrilled at how much OCW has helped him in school, and the drive and confidence it’s inspired in him. "It has certainly expanded his horizons," says his father proudly, while his mother is even more enthusiastic: "My son's life has totally changed since he is using OCW, and being his mother, I am totally satisfied that I am giving him what is required. OCW is fantastic."Fifteen-year-old Tuhin Bagi's dream is to attend MIT and work as an automobile engineer.Research update: A new model accurately predicts three-dimensional sand flow
http://newsoffice.mit.edu/2013/research-update-sand-modeling-0325
Model may be useful in improving the flow of grain in silos, and drug capsules in pharmaceutical manufacturing.Mon, 25 Mar 2013 19:00:00 -0400Jennifer Chu, MIT News Officehttp://newsoffice.mit.edu/2013/research-update-sand-modeling-0325A typical storage silo can hold several thousand tons of corn, seed, sawdust and other granular material. These particles funnel down through a hopper, or chute, into freight cars, which haul the material away for processing. But it’s not uncommon for a chute to clog, and the only fix in many cases is for a worker to stand by the opening and break up the jam with a mallet. At other times, a worker may need to climb into the silo to loosen material from the walls — a dangerous task that can trigger a deadly avalanche. <br /><br />Such accidents might be prevented if silos were designed to accommodate granular flow. The problem is, it’s extremely difficult to predict how grains behave collectively: While kernels of corn are solid, they behave more like a liquid when flowing through a silo. Simulating the flow of grains in silos, and in other geometries, has proven a tricky, centuries-old problem for scientists. <br /><br />Now researchers at MIT have devised a model of granular flow in three dimensions. The team found the model accurately predicts the results of granular flow experiments, including a flow configuration that has long puzzled scientists. The results of the team’s research are published this week in the Proceedings of the <i>National Academy of Sciences</i>.<br /><br />Ken Kamrin, the Class of 1956 Career Development Assistant Professor of Mechanical Engineering at MIT, says the model may also be useful for improving the flow of drug powders, tablets and capsules in pharmaceutical manufacturing. <br /><br />“There are a lot of big questions in granular materials,” says Kamrin, who co-authored the paper with MIT postdoc David Henann. “One of the biggest is, ‘If I draw a silo and tell you about the grains I fill it with, can you predict how rapidly it will flow?’ Now we can try this with demonstrable accuracy … that’s much easier than trying to track every single grain of sand.”<br /><br /><strong>A neighborly effect</strong><br /><br />The new three-dimensional granular flow model builds upon a two-dimensional prototype that Kamrin <a href="/newsoffice/2012/sand-modeling-0406.html" target="_self">developed last year</a>. In that model, he made a key adjustment to an existing set of equations that are normally used to describe the way liquids flow. To predict, for example, how water flows through a funnel, these equations essentially divide the volume of water into a fine grid, predicting how the whole volume will flow based on how water molecules behave in a single box of the grid. <br /><br />Kamrin says such “local” equations do a good job of accurately predicting water flow because water molecules are so much smaller than most vessels they flow through. But the same is not true of granular materials. Kamrin realized that, in granular flow, size matters: Because grains are not vanishingly small compared to their environment — they are much larger than water molecules — their size affects how neighboring grains move, making it impossible to generalize the flow of one tiny box of grains to an entire silo. Recognizing this, Kamrin added a new “nonlocal” term to the equations to account for grain size, and found that the resulting predictions matched simple, two-dimensional, particle-by-particle simulations of granular flow. <br /><br /><strong>A new dimension</strong><br /><br />In the current paper, Kamrin and Henann propose a general, three-dimensional model for granular flow. It adopts a similar nonlocal term, taking into account the size of individual grains and the effect of neighboring grains. The researchers then tested the model against experimental flows of glass beads in various geometries, including the split-bottom cell — a geometry that has long confounded scientists, as its flow of grains has been difficult to describe mathematically.<br /><br />A split-bottom cell resembles the bowl of a food processor, with an inner and outer cylinder mounted on a cylindrical floor; the inner cylinder remains stationary as the outer ring rotates. In experiments, scientists have observed that grains in this geometry flow in a cooperative fashion: Those in the very bottom layer move with either the inner or outer ring, while the next layer up begins to flow more smoothly. With each higher layer, Kamrin says the movement of grains “smears,” since the speed of one layer affects layers further up in the cylinder. In this way, the sharp motion of the grains at the bottom of the cell induces a spread-out, wide flow in the grains at the top.<br /><br />Kamrin and Henann applied their model to this geometry, and found that their equations accurately predicted the flow of grains throughout the rotating cylinder — a first in granular modeling. They then dug through the granular literature and tested the same model against other three-dimensional geometries examined in more than 150 published experiments, finding quantitative agreement between their predictions and actual observations. <br /><br />This model may work well in predicting the flow of glass beads, sand and agricultural grains, says Martin van Hecke, a professor of condensed matter physics at Leiden University in the Netherlands. <br /><br />“By tuning a few physical parameters [such as] friction [and] length-scale, a host of other materials can be described,” says van Hecke, who did not contribute to the study. “Granular media are the most abundant materials in industrial processes … a proper understanding of slow granular flows therefore has the potential for very wide impact.”<br /><br />Going forward, Kamrin and Henann hope to test the model against experiments, and plan to build various structures to observe the way grains of different sizes flow. The goal, Henann says, is to provide manufacturers with a tool to design more efficient silos and other grain-handling equipment.Two earn School of Science teaching awards
http://newsoffice.mit.edu/2013/two-earn-school-of-science-teaching-awards
Kelner, Mavalvala honored for undergraduate educationThu, 07 Mar 2013 11:39:10 -0500School of Sciencehttp://newsoffice.mit.edu/2013/two-earn-school-of-science-teaching-awardsJonathan Kelner, the Kokusai Denshin Denwa Assistant Professor of Applied Mathematics, and Nergis Mavalvala, the Curtis (1963) and Kathleen Marble Professor of Astrophysics, were honored in late February with School of Science teaching awards.<br /><br />The annual awards are given for faculty members’ work as undergraduate instructors: Kelner teaches 18.440, Probability and Random Variables; Mavalvala teaches 8.13, Experimental Physics. <br /><br />Kelner’s research focuses on the application of techniques from pure mathematics to the solution of fundamental problems in algorithms and complexity theory. He received a BA from Harvard and a PhD from MIT in 2006. In 2011, Kelner also received the Harold E. Edgerton Faculty Achievement Award.<br /><br />Mavalvala's research focuses on interferometric gravitational waves and quantum measurement, through the Laser Interferometer Gravitational Wave Observatory. She received a BA from Wellesley College, and a PhD from MIT in 1997. Mavalvala was named a MacArthur Fellow in 2010.<br />Short algorithm, long-range consequences
http://newsoffice.mit.edu/2013/short-algorithm-long-range-consequences-0301
A new technique for solving ‘graph Laplacians’ is drastically simpler than its predecessors, with implications for a huge range of practical problems.Fri, 01 Mar 2013 15:00:03 -0500Larry Hardesty, MIT News Officehttp://newsoffice.mit.edu/2013/short-algorithm-long-range-consequences-0301In the last decade, theoretical computer science has seen remarkable progress on the problem of solving graph Laplacians — the esoteric name for a calculation with hordes of familiar applications in scheduling, image processing, online product recommendation, network analysis, and scientific computing, to name just a few. Only in 2004 did researchers first propose an algorithm that solved graph Laplacians in “nearly linear time,” meaning that the algorithm’s running time didn’t increase exponentially with the size of the problem.<br /><br />
<div class="video_captions" style="width: 368px; float: right; margin: 0 0 10px 10px;"><img src="/newsoffice/sites/mit.edu.newsoffice/files/images/animations/laplacians.gif" border="0" width="368" /> <span class="image_caption">This animation shows two different "spanning trees" for a simple graph, a grid like those used in much scientific computing. The speedups promised by a new MIT algorithm require "low-stretch" spanning trees (green), in which the paths between neighboring nodes don't become excessively long (red).</span> <span class="image_credit">Images courtesy of the researchers</span></div>
At this year’s ACM Symposium on the Theory of Computing, MIT researchers will present <a href="http://arxiv.org/pdf/1301.6628" target="_blank">a new algorithm</a> for solving graph Laplacians that is not only faster than its predecessors, but also drastically simpler. “The 2004 paper required fundamental innovations in multiple branches of mathematics and computer science, but it ended up being split into three papers that I think were 130 pages in aggregate,” says Jonathan Kelner, an associate professor of applied mathematics at MIT who led the new research. “We were able to replace it with something that would fit on a blackboard.”<br /><br />The MIT researchers — Kelner; Lorenzo Orecchia, an instructor in applied mathematics; and Kelner’s students Aaron Sidford and Zeyuan Zhu — believe that the simplicity of their algorithm should make it both faster and easier to implement in software than its predecessors. But just as important is the simplicity of their conceptual analysis, which, they argue, should make their result much easier to generalize to other contexts.<br /><br /><strong>Overcoming resistance</strong><br /><br />A graph Laplacian is a matrix — a big grid of numbers — that describes a <a href="/newsoffice/2012/explained-graphs-computer-science-1217.html" target="_blank">graph</a>, a mathematical abstraction common in computer science. A graph is any collection of nodes, usually depicted as circles, and edges, depicted as lines that connect the nodes. In a logistics problem, the nodes might represent tasks to be performed, while in an online recommendation engine, they might represent titles of movies. <br /><br />In many graphs, the edges are “weighted,” meaning that they have different numbers associated with them. Those numbers could represent the cost — in time, money or energy — of moving from one step to another in a complex logistical operation, or they could represent the strength of the correlations between the movie preferences of customers of an online video service.<br /><br />The Laplacian of a graph describes the weights between all the edges, but it can also be interpreted as a series of linear equations. Solving those equations is crucial to many techniques for analyzing graphs.<br /><br />One intuitive way to think about graph Laplacians is to imagine the graph as a big electrical circuit and the edges as resistors. The weights of the edges describe the resistance of the resistors; solving the Laplacian tells you how much current would flow between any two points in the graph.<br /><br />Earlier approaches to solving graph Laplacians considered a series of ever-simpler approximations of the graph of interest. Solving the simplest provided a good approximation of the next simplest, which provided a good approximation of the next simplest, and so on. But the rules for constructing the sequence of graphs could get very complex, and proving that the solution of the simplest was a good approximation of the most complex required considerable mathematical ingenuity.<br /><br /><strong>Looping back</strong><br /><br />The MIT researchers’ approach is much more straightforward. The first thing they do is find a “spanning tree” for the graph. A tree is a particular kind of graph that has no closed loops. A family tree is a familiar example; there, a loop might mean that someone was both parent and sibling to the same person. A spanning tree of a graph is a tree that touches all of the graph’s nodes but dispenses with the edges that create loops. Efficient algorithms for constructing spanning trees are well established.<br /><br />The spanning tree in hand, the MIT algorithm then adds back just one of the missing edges, creating a loop. A loop means that two nodes are connected by two different paths; on the circuit analogy, the voltage would have to be the same across both paths. So the algorithm sticks in values for current flow that balance the loop. Then it adds back another missing edge and rebalances.<br /><br />In even a simple graph, values that balance one loop could imbalance another one. But the MIT researchers showed that, remarkably, this simple, repetitive process of adding edges and rebalancing will converge on the solution of the graph Laplacian. Nor did the demonstration of that convergence require sophisticated mathematics: “Once you find the right way of thinking about the problem, everything just falls into place,” Kelner explains.<br /><br /><strong>Paradigm shift</strong><br /><br />Daniel Spielman, a professor of applied mathematics and computer science at Yale University, was Kelner’s thesis advisor and one of two co-authors of the 2004 paper. According to Spielman, his algorithm solved Laplacians in nearly linear time “on problems of astronomical size that you will never ever encounter unless it’s a much bigger universe than we know. Jon and colleagues’ algorithm is actually a practical one.”<br /><br />Spielman points out that in 2010, researchers at Carnegie Mellon University also presented a practical algorithm for solving Laplacians. Theoretical analysis shows that the MIT algorithm should be somewhat faster, but “the strange reality of all these things is, you do a lot of analysis to make sure that everything works, but you sometimes get unusually lucky, or unusually unlucky, when you implement them. So we’ll have to wait to see which really is the case.”<br /><br />The real value of the MIT paper, Spielman says, is in its innovative theoretical approach. “My work and the work of the folks at Carnegie Mellon, we’re solving a problem in numeric linear algebra using techniques from the field of numerical linear algebra,” he says. “Jon’s paper is completely ignoring all of those techniques and really solving this problem using ideas from data structures and algorithm design. It’s substituting one whole set of ideas for another set of ideas, and I think that’s going to be a bit of a game-changer for the field. Because people will see there’s this set of ideas out there that might have application no one had ever imagined.”<br />A great attitude is an excellent thing
http://newsoffice.mit.edu/2013/excellence-awards-preview
15 individuals and four teams to be honored at the 2013 Excellence Awards ceremonyWed, 20 Feb 2013 18:59:00 -0500Michelle Choate | Human Resourceshttp://newsoffice.mit.edu/2013/excellence-awards-previewOpen minds. Great attitudes. Heartfelt appreciation for MIT and its contributions to the world. These are the qualities of the 19 recipients of this year’s Excellence Awards. While they represent a broad range of backgrounds, expertise and experience, they all focus on advancing the mission of MIT, and are proud to call themselves MIT employees. <br /><br />Among these deserving honorees are two long-time employees, Angela Mickunas and Oliver Thomas, and one who has just completed his first full year of employment, Cesar Duarte. <br /><br /><strong>Advancing inclusion through an open mind</strong><br /><br />Mickunas will receive the Advancing Inclusion and Global Perspectives Award. As assistant director of finance and administration for the Center for Clean Water and Clean Energy (CCWCE) at MIT and King Fahd University of Petroleum and Minerals (KFUPM), Mickunas supports the center’s research and educational projects, as well as a women’s outreach program and a postdoctoral fellowship for Saudi women.<br /><br />For Mickunas, her responsibilities extend far beyond policies and balance sheets — she is an open-minded ambassador dedicated to promoting understanding and ideas. In her travels to Saudi Arabia and her study of Muslim culture, Mickunas’ has gained precious insights into a region and religion that are often misunderstood — insights that she feels compelled to share with colleagues and students. “Because of my experiences in Saudi Arabia and my relationships with the people, I can cut through the stereotypes and tell people the real story,” Mickunas says. <br /><br />Mickunas is honored to be recognized for reflecting the Institute’s global perspective. “MIT’s tolerant environment is one of the beautiful things about being here. It teaches us not to be judgmental, to learn a little bit more before we speak about something,” <br /><br />As her nominator, Kate Anderson states, “Angela has been an instrumental player in bringing diverse individuals together through her work as a cultural interpreter and her tireless efforts to promote cultural sensitivity and awareness within the community. Without her, the center’s mission to ‘open venues of broad collaboration and cultural understanding’ would be in jeopardy.”<br /><strong><br />Unsung hero values relationships and teamwork</strong><br /><br />Thomas, the manager of faculty and student experience in IS&T, will receive the Unsung Hero Award. While the technical knowledge and support he provides are invaluable to clients and colleagues, Thomas believes the most critical part of his job is to build relationships. “Technology will change,” explains Thomas, “but what’s going to stay around are the relationships between departments and people.”<br /><br />Throughout his long career at MIT — starting from when he was an Institute undergraduate — Thomas has had a deep understanding and appreciation for how his works supports the Institute’s mission.<br /><br />“One of the big rewards of being at MIT is that I feel I’m contributing to something that’s much larger than IT," Thomas says. "Our work in IT is supporting the work of people who are contributing to huge changes in the world.”<br /><br />It’s clear from his nominator that Thomas’ contributions are understood and appreciated: “Oliver is one-of-a-kind — in his thinking, his approach, his outstanding customer service, and all around as a colleague. He is a role model — the type of person who exemplifies ‘excellence at MIT,’ supporting the Institute’s mission of teaching and learning in everything he does.”<br /><br />“The award is a great honor and very flattering,” Thomas says. “I’m not sure about the name of the award though, because I feel pretty validated. MIT is a great place and people tend to recognize contributions. It’s very rewarding.”<br /><br /><strong>A fresh perspective leads to innovative solutions</strong><br /><br />The Innovative Solutions Award will be presented to Duarte, administrative assistant in the Department of Mathematics. As a relatively new employee (he’s been with the Institute just over a year), Duarte had been unaware of the Excellence Awards until he was contacted about being a winner.<br /><br />“To have that recognition is pretty great,” Duarte says. “But the most satisfying part is knowing that you’re helping out and making a difference in how a department works.”<br /><br />With his background in design and architecture, Duarte has been a critical contributor in the space planning for the math department’s move to a new area. Duarte used his knowledge of the day-to-day workings of the department to set up a space that best suits the way people work and encourages efficiency and collaboration.<br /><br />As his nominator Anthony Pelletier states, “Cesar demonstrates true excellence, not simply by his efforts for the headquarters office, but by improving the day-to-day life of the entire department, faculty, students and staff as well as his colleagues in math HQ.”<br /><br /><strong>Join in the celebration</strong><br /><br />The ceremony — which will take place on March 6 at 3 p.m. in Kresge Auditorium — will also honor award winners in the categories of Greening MIT, Bringing out the Best and Serving the Client; a total of 19 awards in 2013. A reception in the Kresge lobby will follow and all members of the MIT community are encouraged to attend.<br /><br />For a complete list of the 2013 award winners and a schedule of ceremony events, visit <a href="http://hrweb.mit.edu/rewards/excellence" target="_blank">http://hrweb.mit.edu/rewards/excellence</a>.Mathematical philanthropy
http://newsoffice.mit.edu/2013/mathematical-philanthropy
MIT PhD candidate donates one ton of books to library half a world away.Tue, 19 Feb 2013 20:02:55 -0500Sarah Coe | Public Service Centerhttp://newsoffice.mit.edu/2013/mathematical-philanthropy<i>Derya Akkaynak Yellin SM '05, a PhD candidate in the MIT/WHOI (</i><i><i>Woods Hole Oceanographic Institution)</i> Joint Program in Oceanography, has donated more than 2,000 pounds of mathematics books and journals to the new library of the <a href="http://matematikkoyu.org/eng/" target="_blank">Nesin Mathematics Village</a> near Şirince, Turkey. The village is a remote campus dedicated to the communal study of mathematics at all levels.</i><br /><br /> <i>In May, Yellin, who is originally from Turkey, read in the Nesin Foundation's newsletter that a new mathematics library was to be built, and she thought that it would be a great idea if its first books came from MIT. Not quite knowing what she was getting herself into, Derya embarked on this ambitious project. Ultimately, 41 boxes of mathematics texts were loaded onto two pallets and shipped from Cambridge to the remote Turkish village.</i><br /><br /> <strong>Q.</strong> How did you get the word out to people to donate their books?<br /><br /> <strong>A.</strong> As I was collecting mathematics books and journals, I naturally started to spread the word with the mathematics department. I made an appointment with department head Professor [Michael] Sipser, and he told me that over the summer the entire department was going to move out of their building so renovations could begin. This meant that many people would be packing up their libraries as part of the moving process. I found a great contact, Michael Collver, who would email me every time there was a box of books left for donation, and I would go pick it up. This worked very well.<br /><br /> <strong>Q.</strong> What was the biggest challenge of the project?<br /><br /> <strong>A.</strong> If Sally Susnowitz at the Public Service Center had not stepped in and offered her office for a place to store the books, finding a place to store 2,000 pounds of books for six months would have been a big challenge. Thankfully, this was a non-issue from the start. Finding a good, reliable estimate of how much each leg of the shipping process would cost was not easy and it took me a long time to figure that out. We had a budget of $2,500 from the PSC, and for a couple of months, I had no idea how many pounds of books we had, how much space they would take and whether it'd be below or above budget to ship them all. In the end, I found a Turkish logistics company who not only handled the initial expensive Cambridge to New Jersey shipment, but also gave me an $800 discount on the overall shipping cost. (You could say I used my Turkish bargaining skills.) A customs agent helped me use the correct language and include the required terms on the customs documents. Once I had a ballpark estimate of domestic shipping, ocean shipping, customs fees, customs agent fees and local delivery, it was much easier to make decisions and move on. In the end, the whole campaign cost under $2,000.<br /><br /> <strong>Q.</strong> Has the village appreciated your efforts?<br /><br /> <strong>A.</strong> Yes, very much. They put my name on their website for book donors before they even received the shipment (it says: MIT students via Derya Akkaynak Yellin). The books cleared customs in just a couple of days and were delivered to the village in late December. Professor Ali Nesin, the founder of the Mathematics Village, opened up one of the boxes as a New Year's present, but the rest of the boxes will stay sealed until the library construction is finished.<br /><br /> <strong>Q.</strong> Do you think other departments might consider a similar book drive?<br /><br /> <strong>A.</strong> I hope they will. The variety and level of books I collected for the Nesin Mathematics Village in Turkey cannot be matched by any local campaign. I am sure there are books that are sitting idle in many departments at MIT, perhaps outdated by their online versions, which would find great use at similar specialized schools and camps throughout the world.<br /><br /> <strong>Q.</strong> Would you have any advice for other book drives?<br /><br /> <strong>A.</strong> It is important to start an inventory as soon as the first book arrives. I had a database of every book title, a photo of the book and how much each book weighed individually. This saved me a lot of time later. Also I would suggest that they get in touch with the PSC, of course.<br /><br /> <strong>Q.</strong> What drew you, as an engineer, to support the field of mathematics?<br /><br /> <strong>A.</strong> I find many things about mathematics inspiring; proofs are elegant, fractals are beautiful! Mathematical thinking makes a big difference in my life as an engineer and I think that if more people in Turkey embraced math, as a society our quality of life would improve. I hope that world-class mathematicians will emerge from the Nesin Mathematics Village, and one day, mathematics will be the common denominator in our highly polarized country. Professor Ali Nesin, the founder of the Nesin Mathematics Village, has a saying I like very much: "In a modern sense, the difference between the master and a slave is that the master understands the mathematical proof behind a concept and the slave does not."<br /><br /> <strong>Q.</strong> Is there anything else you would like to share about your story?<br /><br /> <strong>A.</strong> I learned a lot during the course of the six months this campaign was active for. I learned that even if you are one person, it is possible that you can make a valuable contribution to a cause you believe in. Having gone through this personally, I gained a lot of respect for the MIT Public Service Center and its mission. It would not have been possible for me to make a contribution of this magnitude if it had not been for the experience, the help and the funds the PSC provided.<br /><br /> My next project is already underway, and it does not involve collecting, packing or shipping anything. I want to raise awareness about the planned construction of an irrigation dam on the Aras River in eastern Turkey. The dam would destroy the rich wetland habitat that is home to 240 species of Turkish birds and a crucial stopover location for migratory birds. There are alternatives to the dam — such as drip irrigation — and I am working as a volunteer with the environmental non-governmental organization KuzeyDoga to not only stop the planned dam construction, but also obtain protection status for the wetlands.From left, Derya Akkaynak Yellin, PhD student in the Department of Mechanical Engineering and WHOI; her friend Krista Ehinger, PhD student in the Department of Brain and Cognitive Sciences; and Michael Fahie of the Department of Facilities pack and load the books onto pallets for shipping.A physicist and her neutrinos
http://newsoffice.mit.edu/2013/christie-chiu-profile-0128
MIT senior Christie Chiu has found her focus: the study of tiny particles.Mon, 28 Jan 2013 05:00:00 -0500Jessica Fujimori, MIT News correspondenthttp://newsoffice.mit.edu/2013/christie-chiu-profile-0128Quarks, bosons, muons, electrons, neutrinos: This is the stuff the universe is made of, and these particles fascinate MIT senior Christie Chiu.<br /><br />A physics and math major from Bedford, Mass., Chiu excelled in math and science from an early age and dreamed of attending MIT, her father’s alma mater. She and her best friend throughout grade school “would tell all our teachers — any adults, literally anyone who would listen — that when we grew up, we were going to become engineers, go to MIT, and be roommates,” Chiu recounts.<br /><br />In middle school and high school, Chiu’s interest in MIT grew when she attended Splash, an annual, weekend-long program at the Institute packed with classes taught by MIT students. “I really liked the atmosphere, the energy that was here,” Chiu says.<br /><br />As a freshman at the Institute, she found herself drawn to the physics department. “The professors were just so engaged in what they were teaching,” Chiu says. “I felt a lot of energy in the classrooms.”<br /><br />Now, Chiu channels that same energy as a teaching assistant for Junior Lab, the notoriously challenging lab class for physics majors. “I absolutely fell in love with it, while other people were maybe not liking it so much,” Chiu says. “That’s one of the reasons I became a TA — so that I could get people more excited about this and make them want to go into experimental physics.”<br /><br />Her efforts as a fervent ambassador for the Department of Physics have also included work as a counselor for PhysPOP, the department’s pre-orientation program for incoming freshmen. “It’s like summer camp for a week,” she says, smiling. “You get to play with all the cool things in the physics department at MIT!”<br /><br />When she’s not busy with physics-related activities, Chiu spends time with her sorority sisters in Kappa Alpha Theta and captains the MIT sport pistol team, which she describes as a surprisingly meditative activity. “There’s a lot of mental focus and composure that’s required to excel in the sport,” she says. <br /><br /><strong>Neutrinos in the spotlight</strong><br /><br />Chiu is currently working with physics professor Janet Conrad on research related to neutrinos: tiny particles, primarily produced in the sun, that constantly shower down upon the Earth.<br /><br />Physicists have learned that these particles continually oscillate, or transform, among three types: electron, muon and tau neutrinos. To better understand this neutrino oscillation, researchers at the <a href="http://www.fnal.gov/" target="_blank">Fermi National Accelerator Laboratory</a>, in Illinois, are conducting an experiment called <a href="http://www-microboone.fnal.gov/" target="_blank">MicroBooNE</a> (Micro-scale Booster Neutrino Experiment). They use accelerators to generate a beam of neutrinos that then pass through very cold liquid argon, exciting some of the argon atoms. When the atoms return to a lower-energy state, they emit photons called “scintillation light” — which can give researchers valuable information about those neutrinos and their oscillations, helping to resolve discrepancies among the results from various neutrino experiments.<br /><br />But that scintillation light has a wavelength of around 128 nanometers — which might as well be invisible. “It’s in the vacuum UV; it can’t even pass through glass,” Chiu says. “So that makes it very difficult for us to detect it.”<br /><br />A chemical called tetraphenyl butadine, or TPB, provides a solution to the problem. When the scintillation light hits TPB, it is absorbed and re-emitted as blue light, at a longer wavelength of 425 nanometers — which can easily be detected. The only problem was that TPB seemed to stop working well after a while: For some reason, it degraded over time. <br /><br />Chiu’s lab bench is surrounded by piles of acrylic plates, some clear and some with a milky coating of TPB. “We found that if we just left these laying out, then over time, the amount of light that it would be able to wavelength-shift went down,” Chiu explains. “We thought there might be effects from humidity, light or heat.”<br /><br />Chiu’s research during her junior year finally identified the culprit: It was indeed light — specifically, the ultraviolet rays from sunlight streaming in through the large windows along one wall of the lab and from the overhead lights. Both are now covered with shielding material, allowing the TPB — and the researchers — to work uninhibited.<br /><br />Last summer, Chiu presented the results of her TPB study at Fermilab alongside graduate students and postdocs from all over the country — and received first-place recognition for her research and poster.<br /><br /><strong>New challenges</strong><br /><br />Now that Chiu has finished her work with TPB, she’s working on computer-generated simulations of neutrinos in liquid argon for MicroBooNE. The scintillation light that researchers detect is actually produced through two different microscopic processes, she explains. “Knowing the breakdown of how the light is produced between these two processes actually helps us identify the particle,” Chiu says. “We want to simulate the processes to verify that we fully understand the system.”<br /><br />After graduating this spring, Chiu plans to pursue a PhD in particle physics and hopes to one day combine her love of research and teaching as a professor.<br /><br />“There are still a lot of unanswered questions in particle physics,” Chiu says. “Believe it or not, the particles most people are familiar with — that is, protons, neutrons and electrons — compose very little of all the matter in the universe. There are so many things we don’t understand, like dark matter and dark energy, not to mention much about the elementary particles themselves. To learn more about these things — that’s what these experiments are here for.”Christie Chiu is currently working with physics professor Janet Conrad on research related to neutrinosPioneering applied mathematician Chia-Chiao Lin dies at 96
http://newsoffice.mit.edu/2013/obit-chia-chiao-lin
An Institute Professor since 1966, he was an active member of the MIT faculty for 40 years.Mon, 14 Jan 2013 15:20:00 -0500News Officehttp://newsoffice.mit.edu/2013/obit-chia-chiao-linChia-Chiao Lin, an Institute Professor Emeritus at MIT who played a pivotal role in the development of applied mathematics both in the United States and in China, died Sunday in Beijing. <br /><br />He was 96. The cause of death was heart failure, Lin’s family said. <br /><br />Lin’s broad and seminal research, together with his service to the community, were instrumental in the growth of applied mathematics at MIT and elsewhere in the United States. More recently, he had helped build the field in China as a Distinguished Professor at Tsinghua University since 2002. <br /><br />Lin joined MIT as an associate professor of applied mathematics in 1947, becoming a full professor in 1953. In 1966, he was named an Institute Professor — MIT’s most prestigious faculty appointment. He retired from MIT in 1987. <br /><br /><strong>Real-world applications</strong><br /><br />Lin was an applied mathematician whose research initially concentrated on fluid mechanics, focusing on hydrodynamics stability and turbulence, and addressing the aerodynamics of gas turbines, oscillating airfoils and shock waves. His doctoral dissertation solved an outstanding problem, stemming from Werner Heisenberg’s work, concerning the stability of parallel flows. He also resolved a long-standing problem concerning the theory of asymptotic solutions of ordinary differential equations (of higher order than 2), which are uniformly valid around turning points. <br /><br />With Theodore von Kármán, his thesis advisor, Lin proposed a spectral theory for homogeneous turbulence, further developing von Kármán’s similarity theory and the statistical theory of turbulence. These investigations in hydrodynamic stability and turbulence greatly impacted engineering and science fields dealing with fluid flow, including geophysical fluid dynamics. In 1955, Lin published a monograph titled “The Theory of Hydrodynamic Stability,” the first such publication in this developing field. <br /><br />Lin’s research interests then turned to problems in the hydrodynamics of superfluid helium and astrophysics. In 1964, in collaboration with Frank Shu of the University of California at Berkeley, Lin advanced the density-wave theory of galaxy formation (based on the earlier work of Bertil Lindblad) to account for sustained spiral structures. He also contributed to related problems in gravitational collapse and star formation. <br /><br />In 1974 Lin co-authored, with his former student L. A. Segel, the now-classic treatise, “Mathematics Applied to Deterministic Problems in the Natural Sciences.” More recently, in 1996, with Giuseppe Bertin, he published another monograph, “Spiral Structure in Galaxies: A Density Wave Theory.”<br /><br /><strong>Contributions in China</strong><br /><br />For many years, Lin was interested in the development of science and education in China. In 1972, as the deputy leader of a delegation of Chinese-born American scientists, Lin returned to his homeland, receiving a warm welcome from Premier Zhou Enlai and other leaders. He visited China regularly in the ensuing years, inviting many well-known experts to give lectures there. He also facilitated study and research by Chinese scholars at MIT — many of whom have since become leaders in various fields in China. <br /><br />In 2002, Lin returned to his alma mater, Tsinghua University, as Distinguished Professor. He founded the Zhou Pei-Yuan Center for Applied Mathematics — now an active hub of research in quantitative biology, applied partial differential equations, scientific computation, and other interdisciplinary subjects linking mathematics, natural sciences and engineering — and served as its honorary director, undertaking research on protein folding. He worked tirelessly at Tsinghua University to set an example for young researchers, overseeing the research of more than 10 PhD students. <br /><br />Lin was also a visiting professor of mathematics at Florida State University from 1994 to 2011.<br /><br /><strong>A celebrated scholar</strong><br /><br />Lin was born July 7, 1916, in Beijing. He received a BSc in physics from Tsinghua University in 1937 and an MSc in applied mathematics from the University of Toronto in 1941. He then earned his PhD, in aeronautics, from the California Institute of Technology in 1944; Caltech honored Lin with its Distinguished Alumni Award in 1992.<br /><br />Lin did postdoctoral work at the Jet Propulsion Lab before joining the faculty of Brown University in 1945 as an assistant professor of applied mathematics, becoming an associate professor in 1946. He joined MIT’s mathematics faculty the following year.<br /><br />Twice named a Guggenheim Fellow, in 1954 and 1960, Lin received major recognitions from a variety of professional societies, including the Otto Laporte Award of the American Physical Society. In 1975, he received the Timoshenko Medal of the American Society of Mechanical Engineering “for outstanding contributions to fluid mechanics, especially to hydrodynamic stability and turbulence, superfluid helium, aerodynamics and galactic structures.” He received the Award in Applied Mathematics and Numerical Analysis from the National Academy of Sciences in 1977 and the first Fluid Dynamic Prize of the American Physical Society in 1979. <br /><br />In 1981, the MIT faculty selected Lin for the James R. Killian Jr. Faculty Achievement Award; he delivered the Killian Lecture to the MIT community in the spring of 1982. Lin’s Killian Award citation noted that he was highly influential in “developing a more comprehensive approach to applied mathematics.” <br /><br />Within MIT’s Department of Mathematics, Lin served as the first faculty chair of the applied mathematics group, from 1961 to 1966. He was president of the Society for Industrial and Applied Mathematics from 1973 to 1974, and a member of its board of trustees from 1978 to 1980. <br /><br />Lin held honorary doctorates from the Chinese University of Hong Kong (1973), Tsinghua University (1987) and Taiwan’s National Tsing Hua University (2005). He was also, his family said, an honorary professor at the Chinese Academy of Sciences and at Nankai University. His professional honors included selection as a fellow of the American Academy of Arts and Sciences (1951), as academician of Academia Sinica (1958), as a member of the National Academy of Sciences (1962), and as a foreign member of the Chinese Academy of Sciences (1994).<br /><br />Lin was twice a member of the Institute for Advanced Study, in 1959 to 1960 and 1965 to 1966. He was also a member or fellow of the American Astronomical Society, the American Mathematical Society, the American Physical Society, the Society for Industrial and Applied Mathematics, and the Institute of Aerospace Sciences.<br /><br />Lin is survived by his wife of 66 years, Shouying Liang Lin, of Beijing and Cambridge, Mass.; daughter Lillian Shengjung Lin and her husband, Alan Stephen Crawford, of Decatur, Ga.; sister Xiaoyuan Lin and her husband, Shukai Li; sister Xiaoying Lin and her husband, Junjie Gu; and brother-in-law Hongmo Dong. He is also survived by stepgrandson Scott Crawford and his wife, Shay, and their children; stepgrandson Joshua Taylor and his wife, Sarah, and their children; stepgranddaughter Yolanda Jones and her husband, Darius, and their children; and numerous cousins, nephews, nieces, great-nephews, and great-nieces.<br /><br />Lin was preceded in death by his son Edward; brother Jiaxin Lin and his wife, Shunzu Huang; brother Jiatian Lin; brother Jiakeng Lin and his wife, Kanghuai Cheng; sister Xiaohua Lin; brother-in-law Shoupan Liang and his wife, He Fu; brother-in-law Shouchu Liang; and sister-in-law Shoubin Liang and her husband, Xiaoshen Chen.Chia-Chiao Lin, an Institute Professor Emeritus, has died at 96.Two MIT professors win prestigious Wolf Prize
http://newsoffice.mit.edu/2013/artin-langer-win-wolf-prizes
Michael Artin and Robert Langer honored for groundbreaking work in mathematics and chemistry.Fri, 04 Jan 2013 15:44:02 -0500News Officehttp://newsoffice.mit.edu/2013/artin-langer-win-wolf-prizesMIT professors Michael Artin and Robert Langer are among eight recipients worldwide of the 2013 Wolf Prize, the Israel-based Wolf Foundation announced this week.<br /><br />The prestigious international prizes are awarded annually in five categories, each worth $100,000; Artin and Langer were cited for their contributions in mathematics and chemistry, respectively. More than 30 Wolf Prize recipients have gone on to win the Nobel Prize.<br /><br />Israeli President Shimon Peres will present the prizes in May at a special session hosted by the Knesset, the Israeli parliament. <br /><br />Artin, a professor emeritus of mathematics at MIT, helped introduce and define a number of tools and theories in modern algebraic geometry, including the Artin Stack, which is a generalized version of an algebraic stack. His contributions to the theory of surface singularities introduced several concepts — such as rational singularity and fundamental cycle — that became seminal to the field. <br /><br />“Artin is one of the main architects of modern algebraic geometry,” the Wolf Foundation said in announcing him as a winner of the Wolf Prize. “His fundamental contributions encompass a bewildering number of areas in this field. … He is one of the great geometers of the 20th century.”<br /><br />In 2002, Artin won the American Mathematical Society’s annual Steele Prize for Lifetime Achievement; in 2005, he was awarded the Harvard Centennial Medal. Artin is also a member of the National Academy of Sciences, as well as a fellow of the American Academy of Arts and Sciences, the American Association for the Advancement of Science, the Society for Industrial and Applied Mathematics, and the American Mathematical Society. <br /><br />Langer, the David H. Koch Institute Professor at MIT, focuses on developing new ways to administer drugs to patients. A biomedical engineer, he developed a variety of novel drug-delivery systems based on polymers, including materials that can release drugs continuously over a prolonged period of time. In the 1970s, Langer developed polymers that allowed the large molecules of a protein to pass through membranes in a controlled manner to inhibit angiogenesis, the process by which tumors recruit blood vessels.<br /><br />“Robert Langer is primarily responsible for innovations in polymer chemistry that have had profound impact on medicine, particularly in the areas of drug delivery and tissue engineering,” the Wolf Foundation said in its announcement. <br /><br />Last month, Langer was among 23 eminent researchers nationwide to be awarded the United States’ highest honors for scientists, engineers and inventors. He will receive the National Medal of Technology and Innovation from President Barack Obama at a ceremony this year. <br /><br />Langer is a member of the Institute of Medicine, the National Academy of Engineering, and the National Academy of Sciences, making him one of only a few people to hold membership in three national academies. Over the years, he has earned more than 200 major awards in science, including the 2006 National Medal of Science, presented by the president of the United States to scientists and engineers who have made important contributions in their fields. <br /><br />Wolf Prizes have been awarded since 1978 to outstanding scientists and artists “for achievements in the interest of mankind and friendly relations among peoples, irrespective of nationality, race, color, religion, sex or political view.” The prizes are presented annually in agriculture, chemistry, mathematics, medicine, and/or physics, as well as in the arts.Michael Artin, left, and Robert LangerA new ‘branch’ of math
http://newsoffice.mit.edu/2012/river-networks-mathematics-1205
Researchers find a common angle and tipping point of branching valley networks.Wed, 05 Dec 2012 18:04:13 -0500Jennifer Chu, MIT News Officehttp://newsoffice.mit.edu/2012/river-networks-mathematics-1205Over the course of decades or even centuries, Earth’s landscape can appear relatively static, with mountains and valleys seemingly anchored firmly in place. Viewed over a longer timescale, however — on the order of hundreds of thousands of years — the Earth’s topography becomes a rippling, shifting, changing tableau. <br /><br />Rivers and valleys, in particular, form intricately branching patterns, the shapes of which have inspired a field of mathematical study in which scientists have developed a theoretical understanding of river-network geometry, and how that geometry might change over time. Now two research groups from MIT, in separate efforts, have come up with mathematical explanations for different characteristics of river and valley networks. <br /><br />In a <a href="http://www.pnas.org/content/early/2012/12/05/1215218109" target="_blank">paper published this week</a> in the <i>Proceedings of the National Academy of Sciences</i>, Dan Rothman and his colleagues formulate a mathematical theory to discover a common angle at which valleys branch. In environments where erosion is driven by the seepage of water out of the ground, the group’s theory predicts that rivers branch at an angle of 72 degrees. <br /><br />Putting the theory to the test, Rothman and his group measured 5,000 branching angles in the Florida Panhandle, a region of soft, sandy soils — finding that the average valley branching was indeed 72 degrees. Rothman, a professor of geophysics in MIT’s Department of Earth, Atmospheric and Planetary Sciences (EAPS), says such a mathematical analysis may also be applicable to other systems, such as neuron dendrites and fungal filaments.<br /><br />Similarly, a team led by Taylor Perron has <a href="http://www.nature.com/nature/journal/v492/n7427/full/nature11672.html" target="_blank">published a paper this week</a> in <i>Nature</i> in which another mathematical model of river networks has identified a tipping point at which rivers branch. Depending on a river’s capacity to erode a landscape — and how quickly creeping soil may fill its valley — the river may give rise to a dense network of tributaries, or remain as a single rivulet. <br /><br />“We use mathematics to speed up time and help us understand how these systems evolve,” says Perron, the Cecil and Ida Green Assistant Professor of Geology in EAPS. “If you could speed up the clock, you would see that the landscape is a lot more dynamic.”<br /><br /><strong>Angling for a theory</strong><br /><br />Near the town of Bristol, along the eastern stretch of the Florida Panhandle, a network of valleys cuts into the landscape, resembling a tree with ever-smaller branches spreading from a main trunk. From an aerial view, one can see midsized branches, or valleys, running with water, and feeding into a wider river. Over time, the very tips of the smallest valleys themselves branch to create an even denser valley network. <br /><br />To understand how these valleys branch, Rothman and his team — former postdoc Olivier Devauchelle, former graduate student Alexander Petroff and postdoc Hansjoerg Seybold — looked to the mechanics of groundwater flow. Unlike river water that flows over land, groundwater flows under the surface, through material such as porous sand. In an environment such as the Florida Panhandle, groundwater may act to incise, or cut into, a network of valleys: Essentially, groundwater stored in the hills surrounding a valley slowly seeps out, carrying with it some sand. Over time, the process slowly erodes the surrounding hills, extending a valley and eventually splitting it in two. <br /><br />To find the angle at which this split occurs, Rothman’s group derived a mathematical expression for the paths taken by groundwater as it flows toward a newly split stream. Such paths generally curve either away from each other, when the angle between the streams is small, or toward each other, when the angle is large. However, Rothman’s group found that there is a special angle — 72 degrees — for which the paths are straight, reasoning that this is the angle at which streams branch. They subsequently confirmed their prediction by examining nearly 5,000 stream junctions in the Florida Panhandle. <br /><br />“What we show is that because of the properties of groundwater flow, one can understand something about the organization of this pattern,” Rothman says. “It opens a world into a really interesting geometry.” <br /><br /><strong>A geologic tug-of-war</strong><br /><br />In contrast to Rothman’s work, which focused on the effects of groundwater on valley formation, Perron and his colleagues examined the formation of river networks over land. His group sought to answer one main question: What governs the branching pattern that emerges over time? <br /><br />To answer that question, the researchers developed a simple mathematical model representing the erosional mechanisms that act on a river network. Through their model, Perron found that the shape a river network takes is governed by a tug of war between two forces: the strength of river incision, or how quickly a river erodes its banks and the underlying material; and the strength of soil creep, or how quickly soil from surrounding hills fills in a river valley. <br /><br />Running the model on a simulated landscape, the researchers found that as they turned up river incision — or turned down soil creep — a river basin with a single river channel morphs into a network of branching channels at a very specific tipping point. Because river incision is stronger in larger river basins that collect more water, this tipping point explains why larger rivers develop a network of tributaries, whereas small rivers may have no tributaries at all. <br /><br />Moreover, relating the tipping point to specific erosional mechanisms allowed the group to understand why river basins in landscapes with different bedrock or climates grow tributaries at different scales. They predicted that river basins should branch at a smaller size in environments where river incision is strong — for example, areas with heavy rainfall, or soft bedrock — or where soil creep is weak. <br /><br />Perron tested this prediction in two locations with similar river networks, but at different scales: the Allegheny Plateau, in southwest Pennsylvania, and Gabilan Mesa, in California’s Salinas Valley — a region with similarly-patterned river networks, but at one-quarter the size. The group found that the pattern of river networks in both locations matched predictions from its models, despite their difference in scale and environment. <br /><br />While Gabilan Mesa has a drier climate than the Allegheny Plateau, its rock is softer and its soil less permeable. On the rare occasions when it does rain hard, the water accumulates faster and cuts more easily into the surface, leading to strong river incision that encourages river branching. <br /><br />“We tested the model in these two places so we could compare the predicted instability, the breaking point at which rivers should start to branch,” Perron says. “That’s interesting, because it means we can do that for landscapes where we can’t do fieldwork — possibly landscapes on another planet.” <br /><br />Mikael Attal, a lecturer in landscape dynamics at the University of Edinburgh, says the results from both Perron’s and Rothman’s work shed light on what may cause such intricate patterns in rivers and other natural landscapes.<br /><br />“Understanding how river networks originate and evolve is key to understanding how landscapes have evolved in the past, and how they will evolve in the future,” says Attal, who did not participate in the research. “What is fascinating about these two papers is that they provide a physical explanation for the geometry of river networks using some very simple concepts. Studies such as these will help better parameterize models and help make more accurate predictions of what may happen in the future.”<br />A topographic map of a section of the central Amazon River Basin near in Manaus, Brazil.The music of the silks
http://newsoffice.mit.edu/2012/the-music-of-the-silks-1128
Researchers synthesize a new kind of silk fiber — and find that music can help fine-tune the material’s properties.Wed, 28 Nov 2012 05:00:00 -0500David L. Chandler, MIT News Officehttp://newsoffice.mit.edu/2012/the-music-of-the-silks-1128Pound for pound, spider silk is one of the strongest materials known: Research by MIT’s Markus Buehler has helped explain that this strength arises from silk’s unusual hierarchical arrangement of protein building blocks. <br /><br />Now Buehler — together with David Kaplan of Tufts University and Joyce Wong of Boston University — has synthesized new variants on silk’s natural structure, and found a method for making further improvements in the synthetic material.<br /><br />And an ear for music, it turns out, might be a key to making those structural improvements.<br /><br />The work stems from a collaboration of civil and environmental engineers, mathematicians, biomedical engineers and musical composers. The <a href="http://www.sciencedirect.com/science/article/pii/S1748013212001041" target="_blank">results are reported</a> in a paper published in the journal <i>Nano Today</i>.<br /><br />“We’re trying to approach making materials in a different way,” Buehler explains, “starting from the building blocks” — in this case, the protein molecules that form the structure of silk. “It’s very hard to do this; proteins are very complex.”<br /><br />Other groups have tried to construct such protein-based fibers using a trial-and-error approach, Buehler says. But this team has approached the problem systematically, starting with computer modeling of the underlying structures that give the natural silk its unusual combination of strength, flexibility and stretchiness. <br /><br />Buehler’s previous research has determined that fibers with a particular structure — highly ordered, layered protein structures alternating with densely packed, tangled clumps of proteins (ABABAB) — help to give silk its exceptional properties. For this initial attempt at synthesizing a new material, the team chose to look instead at patterns in which one of the structures occurred in triplets (AAAB and BBBA).<br /><br />Making such structures is no simple task. Kaplan, a chemical and biomedical engineer, modified silk-producing genes to produce these new sequences of proteins. Then Wong, a bioengineer and materials scientist, created a microfluidic device that mimicked the spider’s silk-spinning organ, which is called a spinneret.<br /><br />Even after the detailed computer modeling that went into it, the outcome came as a bit of a surprise, Buehler says. One of the new materials produced very strong protein molecules — but these did not stick together as a thread. The other produced weaker protein molecules that adhered well and formed a good thread. “This taught us that it’s not sufficient to consider the properties of the protein molecules alone,” he says. “Rather, [one must] think about how they can combine to form a well-connected network at a larger scale.”<br /><br />The team is now producing several more variants of the material to further improve and test its properties. But one wrinkle in their process may provide a significant advantage in figuring out which materials will be useful and which ones won’t — and perhaps even which might be more advantageous for specific uses. That new and highly unusual wrinkle is music.<br /><br />
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The different levels of silk’s structure, Buehler says, are analogous to the hierarchical elements that make up a musical composition — including pitch, range, dynamics and tempo. The team enlisted the help of composer John McDonald, a professor of music at Tufts, and MIT postdoc David Spivak, a mathematician who specializes in a field called category theory. Together, using analytical tools derived from category theory to describe the protein structures, the team figured out how to translate the details of the artificial silk’s structure into musical compositions.<br /><br />The differences were quite distinct: The strong but useless protein molecules translated into music that was aggressive and harsh, Buehler says, while the ones that formed usable fibers sound much softer and more fluid.<br /><br />Buehler hopes this can be taken a step further, using the musical compositions to predict how well new variations of the material might perform. “We’re looking for radically new ways of designing materials,” he says.<br /><br />Combining materials modeling with mathematical and musical tools, Buehler says, could provide a much faster way of designing new biosynthesized materials, replacing the trial-and-error approach that prevails today. Genetically engineering organisms to produce materials is a long, painstaking process, he says, but this work “has taught us a new approach, a fundamental lesson” in combining experiment, theory and simulation to speed up the discovery process.<br /><br />Materials produced this way — which can be done under environmentally benign, room-temperature conditions — could lead to new building blocks for tissue engineering or other uses, Buehler says: scaffolds for replacement organs, skin, blood vessels, or even new materials for use in civil engineering.<br /><br />Elliott Schwartz, professor emeritus of music at Bowdoin College, says: “For centuries, mathematics, logic and science have provided important models for musical structures, processes, and our understanding of sonic materials. The present research may well lead to one more important chapter in this ongoing story of mutual interaction.”<br /><br />Jessica Garb, an assistant professor of biological sciences at the University of Massachusetts at Lowell, says, "The approach these authors take to designing new biomaterials is completely novel [and] represents a bold approach to unite bioengineering and music." She says that the researchers' suggestion of attempting to reverse the process — starting with the music to design new versions of the protein structure — "could result in some exciting new materials. The practical impacts could be enormous."<br /><br />It may be that the complex structures of music can reveal the underlying complex structures of biomaterials found in nature, Buehler says. “There might be an underlying structural expression in music that tells us more about the proteins that make up our bodies. After all, our organs — including the brain — are made from these building blocks, and humans’ expression of music may inadvertently include more information that we are aware of.”<br /><br />“Nobody has tapped into this,” he says, adding that with the breadth of his multidisciplinary team, “We could do this — making better bio-inspired materials by using music, and using music to better understand biology.”This diagram of the molecular structure of one of the artificially produced versions of spider silk depicts one that turned out to form strong, well-linked fibers. A different structure, made using a variation of the same methods, was not able to form into the long fibers needed to make it useful. Musical compositions based on the two structures helped to show how they differed.Proving quantum computers feasible
http://newsoffice.mit.edu/2012/proving-quantum-computers-feasible-1127
With a new contribution to probability theory, researchers show that relatively simple physical systems could yield powerful quantum computers.Tue, 27 Nov 2012 05:00:02 -0500Larry Hardesty, MIT News Officehttp://newsoffice.mit.edu/2012/proving-quantum-computers-feasible-1127Quantum computers are devices — still largely theoretical — that could perform certain types of computations much faster than classical computers; one way they might do that is by exploiting “spin,” a property of tiny particles of matter. A “spin chain,” in turn, is a standard model that physicists use to describe systems of quantum particles, including some that could be the basis for quantum computers.<br /><br />Many quantum algorithms require that particles’ spins be “entangled,” meaning that they’re all dependent on each other. The more entanglement a physical system offers, the greater its computational power. Until now, theoreticians have demonstrated the possibility of high entanglement only in a very complex spin chain, which would be difficult to realize experimentally. In simpler systems, the degree of entanglement appeared to be capped: Beyond a certain point, adding more particles to the chain didn’t seem to increase the entanglement.<br /><br />This month, however, in the journal <i>Physical Review Letters</i>, a group of researchers at MIT, IBM, Masaryk University in the Czech Republic, the Slovak Academy of Sciences and Northeastern University proved that even in simple spin chains, <a href="http://prl.aps.org/abstract/PRL/v109/i20/e207202" target="_blank">the degree of entanglement scales with the length of the chain</a>. The research thus offers strong evidence that relatively simple quantum systems could offer considerable computational resources.<br /><br />In quantum physics, the term “spin” describes the way that tiny particles of matter align in a magnetic field: A particle with spin up aligns in one direction, a particle with spin down in the opposite direction. But subjecting a particle to multiple fields at once can cause it to align in other directions, somewhere between up and down. In a complex enough system, a particle might have dozens of possible spin states.<br /><br />A spin chain is just what it sounds like: a bunch of particles in a row, analyzed according to their spin. A spin chain whose particles have only two spin states exhibits no entanglement. But in the new paper, MIT professor of mathematics Peter Shor, his former student Ramis Movassagh, who is now an instructor at Northeastern, and their colleagues showed that unbounded entanglement is possible in chains of particles with only three spin states — up, down and none. Systems of such particles should, in principle, be much easier to build than those whose particles have more spin states.<br /><br /><strong>Tangled up</strong><br /><br />The phenomenon of entanglement is related to the central mystery of quantum physics: the ability of a single particle to be in multiple mutually exclusive states at once. Electrons, photons and other fundamental particles can, in some sense, be in more than one place at the same time. Similarly, they can have more than one spin at once. If you try to measure the location, spin or some other quantum property of a particle, however, you’ll get a definite answer: The particle will snap into just one of its possible states.<br /><br />If two particles are entangled, then performing a measurement on one tells you something about the other. For instance, if you measure the spin of an electron orbiting a helium atom, and its spin is up, the spin of the other electron in the same orbit must be down, and vice versa. For a chain of particles to be useful for quantum computing, all of their spins need to be entangled. If, at some point, adding more particles to the chain ceases to increase entanglement, then it also ceases to increase computational capacity.<br /><br />To show that entanglement increases without bound in chains of three-spin particles, the researchers proved that any such chain with a net energy of zero could be converted into any other through a small number of energy-preserving substitutions. The proof is kind of like one of those puzzles where you have to convert one word into another of the same length, changing only one letter at a time.<br /><br />“Energy preserving” just means that changing the spins of two adjacent particles doesn’t change their total energy. For instance, if two adjacent particles have spin up and spin down, they have the same energy as two adjacent particles with no spin. Similarly, swapping the spins of two adjacent particles leaves their energy the same. Here, the “puzzle” is to convert one spin chain into another using only these and a couple of other substitutions.<br /><br /><strong>No bottlenecks</strong><br /><br />If you envision every set of definite spins for a chain of three-spin particles as a point in space, and draw lines only between those that that are interchangeable using energy-preserving substitutions, then you end up with a well-connected network. <br /><br />“If you want to go from any state to another state, it has high conductivity,” Movassagh says. “It’s like, if you have a town with a bunch of alleys, and you want to go from any neighborhood to any other, you can only go rapidly if there’s no one road that’s necessary to use and congested.” To prove that, in systems of three-spin particles, transitions between sets of spin were possible through these “back alleys,” Movassagh says, “we proved something that we think is new in probability theory.”<br /><br />“It’s been known that if the particles can have constant but rather high dimension” — that is, number of possible spin states — “the entanglement can be pretty high,” says Sandy Irani, a professor of computer science at the University of California at Irvine who specializes in quantum computation. “But the requirement is that these little particles have something like dimension 14, 15, 16. In terms of what people are actually looking at experimentally, they’re looking at very low-dimensional things. Having particles of dimension of 15, 16, is much more difficult to bring about in the lab.” <br /><br />Shor, Movassagh and their colleagues, Irani says, “have shown that if you just step up from two to three, the entanglement can actually grow with the number of particles.”<br /><br />Irani cautions, however, that the new paper shows only that entanglement scales logarithmically with the length of the spin chain. “If you go up to these larger-dimension particles, in the teens, you get entanglement that can scale with the number of particles instead of the log of the number of particles,” she says, “and that may be required for quantum computing.”The possible quantum states of a chain of particles can be represented as points in space, with lines connecting states that can be swapped with no change in the chain's total energy. MIT researchers and their colleagues
showed that such networks are densely interconnected, with heavily trafficked pathways between points.From the water to Washington
http://newsoffice.mit.edu/2012/student-profile-noam-angrist-1115
MIT senior Noam Angrist works to reform education and health care through youth mentorship and economics.Thu, 15 Nov 2012 05:00:00 -0500Jessica Fujimori, MIT News correspondenthttp://newsoffice.mit.edu/2012/student-profile-noam-angrist-1115When he got his first-ever C on a history essay in high school, Noam Angrist stayed after school every day for the rest of the year, honing his writing with a teacher. When an unexpected injury cut short his rowing career, he started coaching. When a middle-school student he was tutoring refused to learn the standard material, Angrist introduced him to <i>The Economist</i>.<br /><br />Passionate about education, economics, crew and making the world a better place, Angrist’s drive and work ethic are matched by his creativity and unconventional methods. The MIT senior believes anyone can learn to do anything.<br /><br />“I don’t believe in natural talent,” he says — inspirational words, coming from a double major in math and economics who has contributed to several published research papers, a stellar rower turned coach, and the co-founder of a successful youth mentorship program. <br /><br />Eight years ago, Angrist says, he was a solid student but had “no ambition athletically.” Then, when he was in eighth grade, his family moved to Israel for a year when his father — Joshua Angrist, the Ford Professor of Economics at MIT — took a fellowship at Hebrew University. “Everything was different,” Angrist remembers. “The school doesn’t emphasize academics; they’re huge on athletics.”<br /><br />When he walked into gym class on the first day, Angrist was instructed to show how many pull-ups he could do. “I couldn’t do a single one,” Angrist says. “You can’t even do one pull-up, you sausage!” his gym teacher growled. “I walked out mortified,” Angrist remembers.<br /><br />From that moment on, Angrist had a goal: He stayed up late researching nutrition and athletics, making schedules of when he would eat, when he would exercise. He devoured fat-free cottage cheese, and he jumped rope every morning. “That’s just the way I am, when I have a focus,” Angrist says.<br /><br />Angrist became a star performer in his gym class — and the student who could do the most pull-ups.<br /><br />When he returned to the United States for high school, Angrist took up crew, a sport that he says “gives you a chance to be the person you want to be.”<br /><br />“It rewards hard work,” he says. “And I worked really freakin’ hard.” Despite being the shortest team member in a sport where height can make a big difference, Angrist says, he emerged as one of the best rowers and a team captain. <br /><br />When a blood clot forced the removal of one of his ribs — ending his rowing career — Angrist switched to coaching the Brookline High School novice boys’ team. He was decades younger than his fellow coaches, but still led his boats to gold medals in the state championships.<br /><br />To Angrist, coaching crew was a chance to make a measurable difference. “As a coach, I’m the independent variable, and the success of the students is the dependent variable,” he says. “I wouldn’t do anything if I didn’t feel like it had a direct and tangible impact.” Though Angrist is a tough coach, he says, his rowers are grateful. They may never see him smile, but he says, “Kids know when you invest your heart and soul in something.” <br /><br />Crew has helped him succeed as well: Despite the intense time commitment, Angrist says, it helped him focus and excel in his studies. Now, he helps others do the same. <br /><br />At the end of their sophomore year at the Institute, Angrist and fellow MIT senior Ron Rosenberg founded <a href="http://amphibious.mit.edu/" target="_blank">Amphibious Achievement</a>, an athletic and academic mentorship program for low-income high school students in Boston. Amphibious Achievement has been featured in local and national publications, and students in the program have shown marked progress in school and on the water. Angrist knows because he’s been keeping careful track.<br /><br />As a student of economics and math, Angrist values data-based evidence and advocates its use in the creation of policies and programs. In Amphibious Achievement as well as in TechLit — a project he recently started to evaluate the use of Kindle e-readers in schools — Angrist makes sure to keep a careful record of students’ progress.<br /><br />“We need to revolutionize the way we run and create programs, because right now it’s not based on evidence,” Angrist says. “It’s shocking how much policy is made on the basis of politics and opinions.”<br /><br />Angrist is working to collect that evidence and to bridge the gap between science and policy. He has spent the last three years working with MIT Professor of Economics Jon Gruber to research the impact of the 2010 Affordable Care Act. <br /><br />In summer 2011, Angrist worked in Washington at the Council of Economic Advisors, a group that advises the president on economic policy. His work included the design of “randomized trials to analyze the effectiveness of educational software” — something he is currently putting into practice with TechLit. This past summer, Angrist returned to Washington to work for the World Bank’s education sector. “I am super-passionate about the power of economics to do good,” Angrist says.<br /><br />Though he knows change ultimately must come from high-level policy decisions, Angrist has spent a lot of time on the ground, working personally with the students he is trying to help. In that time, he has seen kids who were slack-jawed in the face of standardized test problems become engaged and excited in discussions of articles from <i>The Economist</i> and history books. He insists that it is important for learning to be fun. <br /><br />“Even though I am a data-driven guy with a heavy math background, what really inspires me — and the reason I think my programs are effective — are the first-hand connections and experiences I’ve had,” Angrist says. “Kids won’t care how much you know until they know how much you care.”Amphibious Achievers' coaches Noam Angrist, Alice Huang, middle, and Sixing Zhao, right, cheer on Achiever Chalayna Smart as she nears the end of the team relays, a key part of every practice, where teams of four compete to row 400 meters in the fastest time.MIT sailing receives trio of ICSA All-Academic Team honors
http://newsoffice.mit.edu/2012/mit-sailing-receives-trio-of-icsa-all-academic-team-honors
Wed, 31 Oct 2012 11:08:15 -0400Mindy Brauer | DAPERhttp://newsoffice.mit.edu/2012/mit-sailing-receives-trio-of-icsa-all-academic-team-honorsSenior skipper Andrew Sommer along with former teammates Eamon Glackin ’12 and Steph Tong ’12 were named to the Inter-Collegiate Sailing Association (ICSA) All-Academic Team. Sommer and Tong earned spots on the first team while Glackin received his second straight second-team nod, increasing MIT’s total to 13 accolades in the five-year history of the award.<br /><br />The Engineers’ three selections led the way as 19 sailors were voted to the All-Academic Team while 16 more landed on the All-Conference Team. In addition, only five student-athletes came from the Division III ranks.<br /><br />Sommer, a mechanical engineering major, competed in 16 regattas last season as a skipper and was named to the All-NEISA Coed Skipper second team. He was the runner-up in the B Division of the Hatch Brown Trophy and the A Division of the New England Dinghy Championship, finished tied for second in the A Division of the Eckerd Intersectional, and captured third place in the B Division of the Danmark Trophy and the A Division of the Thompson Trophy.<br /><br />Tong competed in 16 regattas as the crew last year and was voted to the ICSA Crew All-America Team and the All-NEISA Coed Crew first team while majoring in brain and cognitive sciences with a minor in management and a concentration in neuroscience. She was the runner-up in the B Division of the Hatch Brown Trophy and the A Division of the New England Dinghy Championship, finished tied for second in the A Division of the Eckerd Intersectional, was third in the B Division of the Danmark Trophy, ranked fourth in the B Division of the Moody Trophy, and claimed fifth place in the A Division of the Hood Trophy and the B Division of the Navy Fall Intersectional.<br /><br />In his final season with the team, Glackin competed in 16 regattas as a skipper and majored in mathematics and management science with a concentration in Spanish. He claimed third place in the B Division of the Thompson Trophy, secured fourth place in the B Division of the Atlantic Coast Championship and the Eckerd Intersectional, finished sixth in the A Division of the Harry Anderson Trophy and the Hatch Brown Trophy, and captured sixth place in the B Division of the Erwin Schell Trophy.<br /><br />The 2012 ICSA All-Academic Sailing Team recognizes collegiate sailors who have achieved excellence in national and inter-conference competition as well as excelling at the highest academic level for the 2011-12 academic year. A nominated sailor must have a minimum of a 3.5 cumulative GPA (on a 4.0 scale), junior or senior academic standing and they must be a key starter or reserve on a school’s sailing team. Each school is allowed three nominations.<br />From left: Eamon Glackin, Steph Tong and Andrew SommerThe mathematics of leaf decay
http://newsoffice.mit.edu/2012/leaf-decay-1004
A mathematical model reveals commonality within the diversity of leaf decay.Thu, 04 Oct 2012 04:00:00 -0400Jennifer Chu, MIT News Officehttp://newsoffice.mit.edu/2012/leaf-decay-1004The colorful leaves piling up in your backyard this fall can be thought of as natural stores of carbon. In the springtime, leaves soak up carbon dioxide from the atmosphere, converting the gas into organic carbon compounds. Come autumn, trees shed their leaves, leaving them to decompose in the soil as they are eaten by microbes. Over time, decaying leaves release carbon back into the atmosphere as carbon dioxide.<br /><br />In fact, the natural decay of organic carbon contributes more than 90 percent of the yearly carbon dioxide released into Earth’s atmosphere and oceans. Understanding the rate at which leaves decay can help scientists predict this global flux of carbon dioxide, and develop better models for climate change. But this is a thorny problem: A single leaf may undergo different rates of decay depending on a number of variables: local climate, soil, microbes and a leaf’s composition. Differentiating the decay rates among various species, let alone forests, is a monumental task.<br /><br />Instead, MIT researchers have analyzed data from a variety of forests and ecosystems across North America, and discovered general trends in decay rates among all leaves. The scientists devised a mathematical procedure to transform observations of decay into distributions of rates. They found that the shape of the resulting curve is independent of climate, location and leaf composition. However, the details of that shape — the range of rates that it spans, and the mean rate — vary with climatic conditions and plant composition. In general, the scientists found that plant composition determines the range of rates, and that as temperatures increase, all plant matter decays faster.<br /><br />“There is a debate in the literature: If the climate warms, do all rates become faster by the same factor, or will some become much faster while some are not affected?” says Daniel Rothman, a co-founder of MIT’s <a href="http://web.mit.edu/lorenzcenter/" target="_blank">Lorenz Center</a>, and professor of geophysics in the Department of Earth, Atmospheric and Planetary Sciences. “The conclusion is that all rates scale uniformly as the temperature increases.”<br /><br />Rothman and co-author David Forney, a PhD graduate in the Department of Mechanical Engineering, have published <a href="http://rsif.royalsocietypublishing.org/content/9/74/2255" target="_blank">the results of their study</a>, based largely on Forney’s PhD thesis, in the <i>Journal of the Royal Society Interface</i>.<br /><br /><strong>Litter delivery</strong><br /><br />The team obtained data from an independent 10-year analysis of North American forests called the Long-term Intersite Decomposition Experiment Team (LIDET) study. For this study, researchers collected leaf litter — including grass, roots, leaves and needles — from 27 locations throughout North and Central America, ranging from Alaskan tundra to Panamanian rainforests.<br /><br />The LIDET researchers separated and weighed each litter type, and identified litter composition and nutrient content. They then stored the samples in porous bags and buried the bags, each filled with a different litter type, in each of the 27 geographic locations; the samples were then dug up annually and reweighed. The data collected represented the mass of litter, of different composition, remaining over time in different environments.<br /><br />Forney and Rothman accessed the LIDET study’s publicly available data online, and analyzed each dataset: the litter originating at one location, subsequently divided and distributed at 27 different locations, and weighed over 10 years.<br /><br />The team developed a mathematical model to convert each dataset’s hundreds of mass measurements into rates of decay — a “numerically delicate” task, Rothman says. They then plotted the converted data points on a graph, yielding a surprising result: The distribution of decay rates for each dataset looked roughly the same, forming a bell curve when plotted as a function of the order of magnitude of the rates — a surprisingly tidy pattern, given the complexity of parameters affecting decay rates.<br /><br />“Not only are there different environments like grasslands and tundra and rainforest, there are different environments at the microscale too,” Forney says. “Each plant is made up of different tissues … and these all have different degradation pathways. So there’s heterogeneity at many different scales … and we’re trying to figure out if there’s some sort of commonality.”<br /><br /><strong>Common curves</strong><br /><br />Going a step further, Forney and Rothman looked for parameters that affect leaf decay rates. While each dataset resembled a bell curve, there were slight variations among them. For example, some curves had higher peaks, while others were flatter; some curves shifted to the left of a graph, while others lay more to the right. The team looked for explanations for these slight variations, and discovered the two parameters that most affected the details of a dataset’s curve: climate and leaf composition.<br /><br />In general, the researchers observed, warmer climates tended to speed the decay of all plants, whereas colder climates slowed plant decay uniformly. The implication is that as temperatures increase, all plant matter, regardless of composition, will decay more quickly, with the same relative speedup in rate.<br /><br />The team also found that plant matter such as needles that contain more lignin — a sturdy building block — have a smaller range of decay rates than leafier plants that contain less lignin and more nutrients that attract microbes. “This is an interesting ecological finding,” Forney says. “Lignin tends to shield organic compounds, which may otherwise degrade at a faster rate.”<br /><br />Mark Harmon, principal investigator for the LIDET study and a professor of forest science at Oregon State University, says the team’s results add evidence to a long-held debate over rising temperature’s effect on organic decay: As temperatures rise, decomposition will likely speed up, releasing more carbon dioxide into the atmosphere, which in turn creates warmer temperatures, further speeding decay in a positive feedback loop. <br /><br />“There is a wide range of results on temperature response,” says Harmon, who was not involved in the study. “Some have proposed that materials that are hard to decompose will respond more to temperature increases, and others have proposed the opposite. The current study indicates they may be the same,” meaning the positive feedback from rising temperatures may not be as strong as others have predicted.<br /><br />Rothman adds that in the future, the team may use the model to predict the turnover times of various ecosystems — a finding that may improve climate change models, and help scientists understand the flux of carbon dioxide around the globe.<br /><br />“It’s a really messy problem,” Rothman says. “It’s as messy as the pile of leaves in your backyard. You would think that each pile of leaves is different, depending on which tree it’s from, where the pile is in your backyard and what the climate is like. What we’re showing is that there’s a mathematical sense in which all of these piles of leaves behave in the same way.”Three MIT faculty named Simons Investigators
http://newsoffice.mit.edu/2012/three-affiliates-named-simons-investigators-0724
Goldwasser, Guionnet and Seidel are among 21 researchers selected.Tue, 24 Jul 2012 13:00:00 -0400News Officehttp://newsoffice.mit.edu/2012/three-affiliates-named-simons-investigators-0724Three MIT faculty are among 21 mathematicians, theoretical physicists and theoretical computer scientists who have been selected by the Simons Foundation as Simons Investigators.<br /><br />The MIT recipients are Shafi Goldwasser, professor of computer science and engineering; Alice Guionnet, who will join MIT in September as a professor of mathematics; and Paul Seidel, professor of mathematics.<br /><br />Simons Investigators receive $100,000 annually to support their research. The support is for an initial period of five years, with the possibility of renewal for an additional five years. The goal of the program is to provide a stable base of support for outstanding scientists in their most productive years, enabling them to undertake long-term study of fundamental questions.<br /><br />Goldwasser has had tremendous impact on the development of cryptography and complexity theory. She has created rigorous definitions and constructions of well-known primitives such as encryption schemes (both public- and private-key versions) and digital signatures, as well as brand-new ones that she invented: zero-knowledge interactive proof systems. Goldwasser suggested efficient probabilistic primality testers as a means of recognizing (and generating) prime numbers, addressing an algorithmic problem of great significance; these output short proofs of primality, based on the theory of elliptic curves. Continuing her work on interactive proofs, she suggested the notion of two-prover systems, which have turned out to be important in complexity theory. In recent work, Goldwasser has adapted ideas from interactive proofs to show how a client can delegate computation to a not-so-trusted server and verify that the computation of the server is correct. She showed that this technique is applicable to a rich class of computational problems.<br /><br />Guionnet’s work on large deviations for spectra of random matrices has extended the large deviation principle to the context of Dan-Virgil Voiculescu’s free probability theory. In a series of works with Thierry Cabanal-Duvillard, Mireille Capitaine and Philippe Biane, she proved various large-deviation bounds in this more general setting. These bounds enabled her to prove an inequality between the two notions of free entropy given by Voiculescu, settling half of the most important question in the field. With her former students Mylène Maïda and Édouard Maurel-Segala, and more recently with Vaughan Jones and Dimitri Shlyakhtenko, Guionnet has studied statistical mechanics on random graphs through multi-matrix models. This work on the general Potts models on random graphs branches out in promising directions of operator algebra theory. Guionnet has also done work on statistical mechanics of disordered systems (and in particular the dynamics and aging of spin glasses), random matrices (with an emphasis on the combinatorics of maps) and operator algebra.<br /><br />Seidel has done major work on the border of symplectic and algebraic geometry. His work is distinguished by an understanding of very abstract algebraic constructs (such as derived twisted categories) in sufficiently concrete terms to derive results about the analytic/geometric objects at the basis of symplectic geometry. In this way Seidel has made substantial advances towards proving Maxim Kontsevich’s homological mirror symmetry conjecture, actually proving the conjecture in several special cases. Jointly with Ivan Smith, Seidel constructed the first deformationally non-standard examples of Stein complex structures on a Euclidean space. With his former student Mohammed Abouzaid, he has developed this into a powerful technique to construct infinitely many examples of non-symplectomorphic Stein structures on a any smooth manifold of dimension greater than four.Berger named ISCB fellow
http://newsoffice.mit.edu/2012/berger-named-iscb-fellow
Applied mathematics, computer science professor honored for contributions in computational biology and bioinformatics.Mon, 16 Jul 2012 17:07:50 -0400CSAILhttp://newsoffice.mit.edu/2012/berger-named-iscb-fellowBonnie Berger, a professor of applied mathematics and computer science at MIT and a principal investigator at the Computer Science and Artificial Intelligence Lab (CSAIL), has been named a 2012 fellow of the International Society for Computational Biology (ISCB). The ISCB fellows program honors members that have distinguished themselves through outstanding contributions to the fields of computational biology and bioinformatics.<br /><br />"ISCB fellows represent the absolute pillars of our community,” said Burkhard Rost, president of the ISCB. "I can imagine that the ISCB fellows will become an active group of the society, serving as a pool of experts that can help drive the scientific excellence of our field.”<br /><br />At CSAIL, Berger leads the <a href="http://theory.csail.mit.edu/groups/biology.html" target="_blank">Computation and Biology Group</a> and is a member of the <a href="http://theory.csail.mit.edu/" target="_blank">Theory of Computation Group</a>. Berger’s recent work focuses on designing algorithms to gain biological insights from advances in automated data collection and the subsequent large data sets drawn from them. She works on a diverse set of problems, including network inference, protein folding, compressive genomics and medical genomics. Additionally, she collaborates closely with biologists in order to design experiments to maximally leverage the power of computation for biological explorations.<br /><br />After beginning her career working in algorithms at MIT, Berger was one of the pioneer researchers in the area of computational molecular biology. Berger has won numerous awards including a National Science Foundation Career Award, a Radcliffe Bunting Institute Science Scholarship and the Biophysical Society's Dayhoff Award for research.<br /><br />Berger and the six other individuals named to the ISCB fellows class of 2012 were recognized for their contributions to computational biology and bioinformatics at the ISCB members meeting on July 15. The ISCB is a not-for-profit scholarly society dedicated to advancing the scientific understanding of living systems through computation.<br />Bonnie Berger, a professor of applied mathematics and computer science.Civil engineers find savings where the rubber meets the road
http://newsoffice.mit.edu/2012/pavement-savings-tires-0523
Study shows that pavement deflection under vehicle tires makes for a continuous uphill drive that increases fuel consumption.Wed, 23 May 2012 04:00:00 -0400Denise Brehm, Civil and Environmental Engineeringhttp://newsoffice.mit.edu/2012/pavement-savings-tires-0523A new study by civil engineers at MIT shows that using stiffer pavements on the nation’s roads could reduce vehicle fuel consumption by as much as 3 percent — a savings that could add up to 273 million barrels of crude oil per year, or $15.6 billion at today’s oil prices. This would result in an accompanying annual decrease in CO<sub>2</sub> emissions of 46.5 million metric tons. <br /><br />The study, released in a recent peer-reviewed report, is the first to use mathematical modeling rather than roadway experiments to look at the effect of pavement deflection on vehicle fuel consumption across the entire U.S. road network. A paper on this work has also been accepted for publication later this year in the <i>Transportation Research Record</i>.<br /><br />By modeling the physical forces at work when a rubber tire rolls over pavement, the study’s authors, Professor Franz-Josef Ulm and PhD student Mehdi Akbarian, conclude that because of the way energy is dissipated, the maximum deflection of the load is behind the path of travel. This has the effect of making the tires on the vehicle drive continuously up a slight slope, which increases fuel use.<br /><br />The deflection under the tires is similar to that of beach sand underfoot: With each step, the foot tamps down the sand from heel to toe, requiring the pedestrian to expend more energy than when walking on a hard surface. On the roadways, even a 1 percent increase in aggregate fuel consumption leaves a substantial environmental footprint. Stiffer pavements — which can be achieved by improving the material properties or increasing the thickness of the asphalt layers, switching to a concrete layer or asphalt-concrete composite structures, or changing the thickness or composition of the sublayers of the road — would decrease deflection and reduce that footprint.<br /><br />“This work is literally where the rubber meets the road,” says Ulm, the George Macomber Professor in the Department of Civil and Environmental Engineering. “We’ve got to find ways to improve the environmental footprint of our roadway infrastructure, but previous empirical studies to determine fuel savings all looked at the impact of roughness and pavement type for a few non-conclusive scenarios, and the findings sometimes differed by an order of magnitude. Where do you find identical roadways on the same soils under the same conditions? You can’t. You get side effects. The empirical approach doesn’t work. So we used statistical analysis to avoid those side effects.”<br /><br />The new study defines the key parameters involved in analyzing the structural (thickness) and material (stiffness and type of subgrade) properties of pavements. The mathematical model is therefore based on the actual mechanical behavior of pavements under load. To obtain their results, Ulm and Akbarian fed their model data on 5,643 representative sections of the nation’s roadways taken from Federal Highway Administration data sets. These data include information on the surface and subsurface materials of pavements and the soils beneath, as well as the number, type and weight of vehicles using the roads. The researchers also calculated and incorporated the contact area of vehicle tires with the pavement. <br /><br />Ulm and Akbarian estimate that the combined effects of road roughness and deflection are responsible for an annual average extra fuel consumption of 7,000 to 9,000 gallons per lane-mile on high-volume roads (not including the most heavily traveled roads) in the 8.5 million lane-miles making up the U.S. roadway network. They say that up to 80 percent of that extra fuel consumption, in excess of the vehicles’ normal fuel use, could be reduced through improvements in the basic properties of the asphalt, concrete and other materials used to build the roads. <br /><br />“We’re wasting fuel unnecessarily because pavement design has been based solely on minimizing initial costs more than performance — how well the pavement holds up — when it should also take into account the environmental footprint of pavements based on variations in external conditions,” Akbarian says. “We can now include environmental impacts, pavement performance and — eventually — a cost model to optimize pavement design and obtain the lowest cost and lowest environmental impact with the best structural performance.” <br /><br />The researchers say the initial cost outlay for better pavements would quickly pay for itself not just in fuel efficiency and decreased CO<sub>2</sub> emissions, but also in reduced maintenance costs.<br /><br />“There’s a misconception that if you want to go green you have to spend more money, but that’s not necessarily true,” Akbarian says. “Better pavement design over a lifetime would save much more money in fuel costs than the initial cost of improvements. And the state departments of transportation would save money while reducing their environmental footprint over time, because the roads won’t deteriorate as quickly.”<br /><br />This research was conducted as part of the <a href="http://web.mit.edu/cshub/" target="_blank">Concrete Sustainability Hub</a> at MIT, which is sponsored by the Portland Cement Association and the Ready Mixed Concrete Research & Education Foundation with the goal of improving the environmental footprint of that industry.<br /><br />“This work is not about asphalt versus concrete,” Ulm says. “The ultimate goal is to make our nation’s infrastructure more sustainable. Our model will help make this possible by giving pavement engineers a tool for including sustainability as a design parameter, just like safety, cost and ride quality.”<br /><br />“This MIT research pioneered a rigorous mathematical framework relating fuel consumption with mathematically predicted pavement deflection. This framework lays a foundation for continued development and future improvement of advanced pavement-vehicle interaction models,” says Lev Khazanovich, a professor of civil engineering at the University of Minnesota who was not involved in this research. “Integration of the results of this study with the Mechanistic-Empirical Pavement Design Guide recently adopted by the American Association of State Highway Transportation Officials will enable transportation agencies to account for traffic fuel consumption in pavement design decisions. This makes Akbarian and Ulm’s research especially important today in light of the efforts of transportation agencies to reduce the environmental footprint of the transportation system.” <br />When the tires of a car or truck roll over a roadway, the maximum pavement deflection is just behind the path of travel. This has the effect of making the vehicle’s tires roll continuously up a slight slope (exaggerated in this illustration), increasing the vehicle's fuel consumption.Algorithmic incentives
http://newsoffice.mit.edu/2012/algorithmic-incentives-0425
A new twist on pioneering work done by MIT cryptographers almost 30 years ago could lead to better ways of structuring contracts.Wed, 25 Apr 2012 04:00:00 -0400Larry Hardesty, MIT News Officehttp://newsoffice.mit.edu/2012/algorithmic-incentives-0425<div class="video_captions"><img src="/newsoffice/sites/mit.edu.newsoffice/files/images/algoincent.jpg" border="0" /><br /><strong>Interactive proofs are a type of mathematical game, pioneered at MIT, in which one player — often called Arthur — tries to extract reliable information from an unreliable interlocutor — Merlin. In a new variation known as a rational proof, Merlin is still untrustworthy, but he's a rational actor, in the economic sense.</strong><br /> <i>Image: Howard Pyle</i><br /><br /></div>
In 1993, MIT cryptography researchers Shafi Goldwasser and Silvio Micali shared in the first <a href="http://www.sigact.org/Prizes/Godel/" target="_blank">Gödel Prize</a> for theoretical computer science for their work on interactive proofs — a type of mathematical game in which a player attempts to extract reliable information from an unreliable interlocutor. <br /><br />In their groundbreaking 1985 paper on the topic, Goldwasser, Micali and the University of Toronto’s Charles Rackoff ’72, SM ’72, PhD ’74 proposed a particular kind of interactive proof, called a zero-knowledge proof, in which a player can establish that he or she knows some secret information without actually revealing it. Today, zero-knowledge proofs are used to secure transactions between financial institutions, and several startups have been founded to commercialize them.<br /><br />At the Association for Computing Machinery’s Symposium on Theory of Computing in May, Micali, the Ford Professor of Engineering at MIT, and graduate student Pablo Azar will present a new type of mathematical game that they’re calling a rational proof; it varies interactive proofs by giving them an economic component. Like interactive proofs, rational proofs may have implications for cryptography, but they could also suggest new ways to structure incentives in contracts.<br /><br />“What this work is about is asymmetry of information,” Micali says. “In computer science, we think that valuable information is the output of a long computation, a computation I cannot do myself.” But economists, Micali says, model knowledge as a probability distribution that accurately describes a state of nature. “It was very clear to me that both things had to converge,” he says.<br /><br />A classical interactive proof involves two players, sometimes designated Arthur and Merlin. Arthur has a complex problem he needs to solve, but his computational resources are limited; Merlin, on the other hand, has unlimited computational resources but is not trustworthy. An interactive proof is a procedure whereby Arthur asks Merlin a series of questions. At the end, even though Arthur can’t solve his problem himself, he can tell whether the solution Merlin has given him is valid.<br /><br />In a rational proof, Merlin is still untrustworthy, but he’s a rational actor in the economic sense: When faced with a decision, he will always choose the option that maximizes his economic reward. “In the classical interactive proof, if you cheat, you get caught,” Azar explains. “In this model, if you cheat, you get less money.”<br /><br /><strong>Complexity connection</strong><br /><br />Research on both interactive proofs and rational proofs falls under the rubric of computational-complexity theory, which classifies computational problems according to how hard they are to solve. The two best-known complexity classes are <a href="/newsoffice/2009/explainer-pnp.html" target="_blank">P and NP</a>. Roughly speaking, P is a set of relatively easy problems, while NP contains some problems that, as far as anyone can tell, are very, very hard. <br /><br />Problems in NP include the factoring of large numbers, the selection of an optimal route for a traveling salesman, and so-called satisfiability problems, in which one must find conditions that satisfy sets of logical restrictions. For instance, is it possible to contrive an attendance list for a party that satisfies the logical expression (Alice OR Bob AND Carol) AND (David AND Ernie AND NOT Alice)? (Yes: Bob, Carol, David and Ernie go to the party, but Alice doesn’t.) In fact, the vast majority of the hard problems in NP can be recast as satisfiability problems. <br /><br />To get a sense of how rational proofs work, consider the question of how many solutions a satisfiability problem has — an even harder problem than finding a single solution. Suppose that the satisfiability problem is a more complicated version of the party-list problem, one involving 20 invitees. With 20 invitees, there are 1,048,576 possibilities for the final composition of the party. How many of those satisfy the logical expression? Arthur doesn’t have nearly enough time to test them all.<br /><br />But what if Arthur instead auctions off a ticket in a lottery? He’ll write down one perfectly random list of party attendees — Alice yes, Bob no, Carol yes and so on — and if it satisfies the expression, he’ll give the ticketholder $1,048,576. How much will Merlin bid for the ticket?<br /><br />Suppose that Merlin knows that there are exactly 300 solutions to the satisfiability problem. The chances that Arthur’s party list is one of them are thus 300 in 1,048,576. According to standard econometric analysis, a 300-in-1,048,576 shot at $1,048,576 is worth exactly $300. So if Merlin is a rational actor, he’ll bid $300 for the ticket. From that information, Arthur can deduce the number of solutions.<br /><br /><strong>First-round knockout</strong><br /><br />The details are more complicated than that, and of course, with <a href="http://www.claymath.org/millennium/" target="_blank">very few exceptions</a>, no one in the real world wants to be on the hook for a million dollars in order to learn the answer to a math problem. But the upshot of the researchers’ paper is that with rational proofs, they can establish in one round of questioning — “What do you bid?” — what might require millions of rounds using classical interactive proofs. “Interaction, in practice, is costly,” Azar says. “It’s costly to send messages over a network. Reducing the interaction from a million rounds to one provides a significant savings in time.”<strong></strong><br /><br />“I think it’s yet another case where we think we understand what’s a proof, and there is a twist, and we get some unexpected results,” says <a href="http://www.wisdom.weizmann.ac.il/~naor/" target="_blank">Moni Naor</a>, the Judith Kleeman Professorial Chair in the Department of Computer Science and Applied Mathematics at Israel’s Weizmann Institute of Science. “We’ve seen it in the past with interactive proofs, which turned out to be pretty powerful, much more powerful than you normally think of proofs that you write down and verify as being.” With rational proofs, Naor says, “we have yet another twist, where, if you assign some game-theoretical rationality to the prover, then the proof is yet another thing that we didn’t think of in the past.”<br /><br />Naor cautions that the work is “just at the beginning,” and that it’s hard to say when it will yield practical results, and what they might be. But “clearly, it’s worth looking into,” he says. “In general, the merging of the research in complexity, cryptography and game theory is a promising one.”<br /><br />Micali agrees. “I think of this as a good basis for further explorations,” he says. “Right now, we’ve developed it for problems that are very, very hard. But how about problems that are very, very simple?” Rational-proof systems that describe simple interactions could have an application in crowdsourcing, a technique whereby computational tasks that are easy for humans but hard for computers are farmed out over the Internet to armies of volunteers who receive small financial rewards for each task they complete. Micali imagines that they might even be used to characterize biological systems, in which individual organisms — or even cells — can be thought of as producers and consumers.<br />13 faculty members elected to the American Academy of Arts and Sciences
http://newsoffice.mit.edu/2012/faculty-elected-to-academy
Tue, 17 Apr 2012 17:58:27 -0400News Officehttp://newsoffice.mit.edu/2012/faculty-elected-to-academyThirteen MIT faculty members are among 220 leaders from academia, business, public affairs, the humanities and the arts elected as new members of the American Academy of Arts and Sciences, the Academy <a href="http://www.amacad.org/news/pressReleaseContent.aspx?i=167" target="_blank">announced today</a>.<br /><br />One of the nation’s most prestigious honorary societies, the Academy is also a leading center for independent policy research. Members contribute to Academy publications and studies of science and technology policy, energy and global security, social policy and American institutions, the humanities and culture, and education.<br /><br />Those elected from MIT this year are:<br />
<ul>
<li>Robert Guy Griffin, professor of chemistry and director of the Francis Bitter National Magnet Laboratory;</li>
<li>Angela M. Belcher, the Germeshausen Professor of Materials Science and Engineering and Biological Engineering;</li>
<li>Emery N. Brown, professor of computational neuroscience and of health sciences and technology at MIT, and Warren M. Zapol Professor of Anaesthesia, Harvard Medical School and Massachusetts General Hospital;</li>
<li>Arvind, the Charles W. and Jennifer C. Johnson Professor of Computer Science and Engineering;</li>
<li>Matthew A. Wilson, Sherman Fairchild Professor of Neuroscience and associate head for education in the Department of Brain and Cognitive Sciences;</li>
<li>M. Frans Kaashoek, Charles Piper Professor in the Department of Electrical Engineering and Computer Science; associate director of the Computer Science and Artificial Intelligence Laboratory (CSAIL);</li>
<li>David Autor, professor of economics;</li>
<li>Bonnie Berger, professor of applied math and computer science;</li>
<li>Bjorn Mikhail Poonen, Claude E. Shannon (1940) Professor in Mathematics;</li>
<li>George Stephanopoulos, Arthur D. Little Professor of Chemical Engineering;</li>
<li><a href="http://shass.mit.edu/news/news-2012-yablo-elected-academy-arts-and-sciences-also-receives-guggenheim" target="_blank">Stephen Yablo</a>, professor of philosophy;</li>
<li>Amy Finkelstein, professor of economics; and</li>
<li>Tyler E. Jacks, director of the David H. Koch Institute for Integrative Cancer Research and David H. Koch Professor of Biology.</li>
</ul>
“Election to the Academy is both an honor for extraordinary accomplishment and a call to serve,” Academy President Leslie C. Berlowitz said in a statement. “We look forward to drawing on the knowledge and expertise of these distinguished men and women to advance solutions to the pressing policy challenges of the day.”<br /><br />The new class will be inducted at a ceremony on Oct. 6 at the Academy’s headquarters in Cambridge, Mass.<br /><br />Since its founding in 1780, the Academy has elected leading “thinkers and doers” from each generation, including George Washington and Benjamin Franklin in the 18th century, Daniel Webster and Ralph Waldo Emerson in the 19th century, and Albert Einstein and Winston Churchill in the 20th century. The current membership includes more than 250 Nobel laureates and more than 60 Pulitzer Prize winners.On the hunt for mathematical beauty
http://newsoffice.mit.edu/2012/profile-borodin-0323
Alexei Borodin uses sophisticated tools to extract information from large groups.Fri, 23 Mar 2012 04:00:00 -0400Helen Knight, MIT News correspondenthttp://newsoffice.mit.edu/2012/profile-borodin-0323For anyone who has ever taken a commercial flight, it’s an all-too-familiar scene: Hundreds of passengers sit around waiting for boarding to begin, then rush to be at the front of the line as soon as it does. <br /><br />Boarding an aircraft can be a frustrating experience, with passengers often wondering if they will ever make it to their seats. But Alexei Borodin, a professor of mathematics at MIT, can predict how long it will take for you to board an airplane, no matter how long the line. That’s because Borodin studies difficult probability problems, using sophisticated mathematical tools to extract precise information from seemingly random groups. <br /><br />
<div class="video_captions"><img src="/newsoffice/sites/mit.edu.newsoffice/files/images/borodin.jpg" border="0" alt="Alexei Borodin" /><br /> <strong>Alexei Borodin</strong><br /> <i>Photo: M. Scott Brauer</i><br /><br /></div>
“Imagine an airplane in which each row has one seat, and there are 100 seats,” Borodin says. “People line up in random order to fill the plane, and each person has a carry-on suitcase in their hand, which it takes them one minute to put into the overhead compartment.”<br /><br />If the passengers all board the plane in an orderly fashion, starting from the rear seats and working their way forwards, it would be a very quick process, Borodin says. But in reality, people queue up in a random order, significantly slowing things down.<br /><br />So how long would it take to board the aircraft? “It’s not an easy problem to solve, but it is possible,” Borodin says. “It turns out that it is approximately equal to twice the square root of the number of people in the queue.” So with a 100-seat airplane, boarding would take 20 minutes, he says.<br /><br />Borodin says he has enjoyed solving these kinds of tricky problems since he was a child growing up in the former Soviet Union. Born in the industrial city of Donetsk in eastern Ukraine, Borodin regularly took part in mathematical Olympiads in his home state. Held all over the world, these Olympiads set unusual problems for children to solve, requiring them to come up with imaginative solutions while working against the clock. <br /><br />It is perhaps no surprise that Borodin had an interest in math from an early age: His father, Mikhail Borodin, is a professor of mathematics at Donetsk State University. “He was heavily involved in research while I was growing up,” Borodin says. “I guess children always look up to their parents, and it gave me an understanding that mathematics could be an occupation.”<br /><br />In 1992, Borodin moved to Russia to study at Moscow State University. The dissolution of the USSR meant that, arriving in Moscow, Borodin found himself faced with a choice of whether to take Ukrainian citizenship, like his parents back in Donetsk, or Russian. It was a difficult decision, but for practical reasons Borodin opted for Russian citizenship.<br /><br />Times were tough while Borodin was studying in Moscow. Politically there was a great deal of unrest in the city, including a coup attempt in 1993. Many scientists began leaving Russia, in search of a more stable life elsewhere.<br /><br />Financially things were not easy for Borodin either, as he had just $15 each month to spend on food and accommodation. “But I still remember the times fondly,” he says. “I didn’t pay much attention to politics at the time, I was working too hard. And I had my friends, and my $15 per month to live on.”<br /><br />After Borodin graduated from Moscow State University in 1997, a former adviser who had moved to the United States invited Borodin over to join him. So he began splitting his time between Moscow and Philadelphia, where he studied for his PhD at the University of Pennsylvania. <br /><br />He then spent seven years at the California Institute of Technology before moving to MIT in 2010, where he has continued his research into probabilities in large random objects.<br /><br />Borodin says there are no big mathematical problems he is desperate to solve. Instead, his greatest motivation is the pursuit of what he calls the beauty of the subject. While it may seem strange to talk about finding beauty in abstract mathematical constructions, many mathematicians view their work as an artistic endeavor.<br /><br />“If one asks 100 mathematicians to describe this beauty, one is likely to get 100 different answers,” he says.<br /><br />And yet all mathematicians tend to agree that something is beautiful when they see it, he adds, saying, “It is this search for new instances of mathematical beauty that largely drives my research.”Alexei BorodinMoving past trial and error
http://newsoffice.mit.edu/2012/profile-braatz-0215
Richard Braatz applies math to design new materials and processes for drug manufacturing.Wed, 15 Feb 2012 05:00:00 -0500Jennifer Chu, MIT News Officehttp://newsoffice.mit.edu/2012/profile-braatz-0215<div class="video_captions"><img src="/newsoffice/sites/mit.edu.newsoffice/files/images/braatz.jpg" border="0" alt="Richard Braatz" /><br /> <strong>Richard Braatz</strong><br /> <i>Photo: Dominick Reuter</i><br /><br /></div>
Trial-and-error experimentation underlies many biomedical innovations. This classic method — define a problem, test a proposed solution, learn from failure and try again — is the main route by which scientists discover new biomaterials and drugs today. This approach is also used to design ways of manufacturing these new materials, but the process is immensely time-consuming, producing a successful therapeutic product and its manufacturing process only after years of experiments, at considerable expense.<br /> <br />Richard Braatz, the Edwin R. Gilliland Professor of Chemical Engineering at MIT, applies mathematics to streamline the development of pharmaceuticals. Trained as an applied mathematician, Braatz is developing mathematical models to help scientists quickly and accurately design processes for manufacturing drug compounds with desired characteristics. Through mathematical simulations, Braatz has designed a system that significantly speeds the design of drug-manufacturing processes; he is now looking to apply the same mathematical approach to designing new biomaterials and nanoscale devices. <br /> <br />“Nanotechnology is very heavily experimental,” Braatz says. “There are researchers who do computations to gain insights into the physics or chemistry of nanoscale systems, but do not apply these computations for their design or manufacture. I want to push systematic design methods to the nanoscale, and to other areas where such methods aren’t really developed yet, such as biomaterials.”<br /> <br /><strong>From farm to formulas</strong><br /> <br />Braatz’s own academic path was anything but systematic. He spent most of his childhood on an Oregon farm owned by his grandfather. Braatz says he absorbed an engineer’s way of thinking early on from his father, an electrician, by examining his father’s handiwork on the farm and reading his electrical manuals.<br /> <br />Braatz also developed a serious work ethic. From the age of 10, he awoke early every morning — even on school days — to work on the farm. In high school, he picked up a night job at the local newspaper, processing and delivering thousands of newspapers to stores and the post office, sometimes until just before dawn. <br /> <br />After graduating from high school in 1984, Braatz headed to Alaska for the summer. A neighbor had told him that work paid well up north, and Braatz took a job at a fish-processing facility, driving forklifts and hauling 100-pound bags of fishmeal 16 hours a day. He returned each summer for four years, eventually working his way up to plant operator, saving enough money each summer to pay for the next year’s tuition at Oregon State University.<br /> <br />As an undergraduate, Braatz first planned to major in electrical engineering. But finding the introductory coursework unstimulating — given the knowledge he’d absorbed from his father — he cast about for another major. <br /> <br />“There was no Internet back then, so you couldn’t Google; web searches didn’t exist,” Braatz says. “So I went to the library and opened an encyclopedia, and said, 'OK, what other engineering [is] there?'”<br /> <br />Chemical engineering caught his eye; he had always liked and excelled at chemistry in high school. While pursuing a degree in chemical engineering, Braatz filled the rest of his schedule with courses in mathematics.<br /> <br />
<div class="video_captions" style="float: right; width: 368px; margin: 0pt 0pt 10px 10px;"><img src="/newsoffice/sites/mit.edu.newsoffice/files/images/braatz-small.jpg" border="0" alt="Richard Braatz" /><br /><i>Photo: Dominick Reuter<br /></i></div>
After graduation, Braatz went on to the California Institute of Technology, where he earned both a master’s and a PhD in chemical engineering. In addition to his research, Braatz took numerous math and math-heavy courses in electrical engineering, applied mechanics, chemical engineering and chemistry. The combination of real applications and mathematical theory revealed a field of study Braatz had not previously considered: applied mathematics.<br /> <br />“This training was a very good background for learning how to derive mathematical solutions to research problems,” Braatz says.<br /> <br /><strong>A systems approach</strong><br /> <br />Soon after receiving his PhD, Braatz accepted an assistant professorship at the University of Illinois at Urbana-Champaign (UIUC). There, as an applied mathematician, he worked with researchers to tackle problems in a variety of fields: computer science, materials science, and electrical, chemical and mechanical engineering. <br /> <br />He spent eight years on a project spurred by a talk he attended at UIUC. In that talk, a representative of Merck described a major challenge in the pharmaceutical industry: controlling the size of crystals in the manufacture of any given drug. (The size and consistency of crystals determine, in part, a drug’s properties and overall efficacy.) <br /> <br />Braatz learned that while drug-manufacturing machinery was often monitored by sensors, much of the resulting data went unanalyzed. He pored over the sensors’ data, and developed mathematical models to gain an understanding of what the sensors reveal about each aspect of the drug-crystallization process. Over the years, his team devised an integrated series of algorithms that combined efficiently designed experiments with mathematical models to yield a desired crystal size from a given drug solution. They worked the algorithms into a system that automatically adjusts settings at each phase of the manufacturing process to produce an optimal crystal size, based on a “recipe” given by the algorithms.<br /> <br />“Sometimes the recipes are very weird,” Braatz says. “It might be a strange path you have to follow to manufacture the right crystals.” <br /> <br />The automated system, which has since been adopted by Merck and other pharmaceutical companies, provides a big improvement in efficiency, Braatz says, avoiding the time-consuming trial-and-error approach many drug manufacturers had relied on to design a crystallization process for a new drug. <br /> <br />In 2010, Braatz moved to MIT, where he is exploring mathematical applications in nanotechnology and tissue engineering — in particular, models to help design new drug-releasing materials. Such materials have the potential to deliver controlled, continuous therapies, but designing them currently takes years of trial-and-error experiments. <br /> <br />Braatz’s group is designing mathematical models to give researchers instructions, for example, on how to design materials that locally release drugs into a body’s cells at a desired rate. Braatz says approaching such a problem from a systematic perspective could potentially save years of time in the development of a biomedical material of high efficacy. <br /> <br />“Anything is a win if you could reduce those experiments from 10 years to several years,” Braatz says. “We’re talking hundreds of millions, billions of dollars. And the effect on people’s lives, you can’t put a price tag on that.” <br /><br /> <iframe frameborder="0" height="315" src="http://www.youtube.com/embed/xG0NU97EO8k?rel=0" width="560"></iframe><br /> Video: Melanie GonickRichard BraatzDifferential Equations now available in MIT OpenCourseWare's innovative OCW Scholar format
http://newsoffice.mit.edu/2012/differential-equations-now-available-mit-opencoursewares-innovative-ocw-scholar-format
18.03SC is the second of seven courses OCW will publish this spring specifically to meet the needs of independent learners.Mon, 13 Feb 2012 11:35:12 -0500Steve Carson | MIT OpenCourseWarehttp://newsoffice.mit.edu/2012/differential-equations-now-available-mit-opencoursewares-innovative-ocw-scholar-formatMIT OpenCourseWare has released a new version of Differential Equations in the innovative OCW Scholar format designed for independent learners. Organized by Professor Haynes Miller and Dr. Jeremy Orloff, <a href="http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011" target="_blank">18.03SC Differential Equations</a> includes lecture videos, exams and solutions, and interactive Java® demonstrations. Differential equations are important to scientists and engineers who need to model natural systems and solve engineering problems.<br /><br />The original version of 18.03 Differential Equations was first published on OCW in 2004 and has regularly been among the most visited courses on the site, attracting more than 30,000 users each month. Both the original version and the new Scholar version include video recorded in the MIT classroom by renowned math professor Arthur Mattuck. In 1992, Mattuck was among the first group of faculty to be designated Margaret MacVicar Fellows, which recognizes faculty who have made exemplary and sustained contributions to the teaching and education of undergraduates at MIT.<br /><br />"It's a real thrill to integrate these outstanding lectures into a format specifically designed to support online learning," Miller says. "It brings the best of the classroom together with new learning approaches enabled by the Internet." Miller is also a MacVicar Fellow.<br /><br />OCW Scholar courses represent a new approach to OCW publication. MIT faculty, staff and students work closely with the OCW team to structure the course materials for independent learners. These courses offer more materials than typical OCW courses and include new custom-created content. In addition to the lecture videos, exams and demonstrations, the OCW Scholar version of Differential Equations includes course notes, problem sets and solutions, and a unique series of video problem-solving sessions recorded specifically for this publication.<br /><br />The first five of a planned 15 OCW Scholar courses were launched by MIT OpenCourseWare in January 2011, and have collectively received more than 800,000 visits in less than a year. The initial OCW Scholar courses included Classical Mechanics, Electricity and Magnetism, Solid State Chemistry, Single Variable Calculus, and Multivariable Calculus.<br /><br />Linear Algebra was published earlier this year, and Differential Equations is the second of seven OCW Scholar courses that will be published in 2012. Other upcoming OCW Scholar courses include Principles of Microeconomics, Introduction to Psychology, Fundamentals of Biology, Introduction to Electrical Engineering and Computer Science I, and Introduction to Computer Science and Programming. OCW Scholar courses are published on the OCW site with the support of the Stanton Foundation.<br />Phase portrait of a damped harmonic oscillator.MIT OpenCourseWare publishes Linear Algebra in innovative OCW Scholar format
http://newsoffice.mit.edu/2012/mit-opencourseware-publishes-linear-algebra-in-innovative-ocw-scholar-format
One of OCW's most popular courses, Linear Algebra, is now available in a version designed to support independent learning.Thu, 09 Feb 2012 13:33:53 -0500Steve Carson | MIT OpenCourseWarehttp://newsoffice.mit.edu/2012/mit-opencourseware-publishes-linear-algebra-in-innovative-ocw-scholar-formatMIT’s OpenCourseWare has released a new version of Linear Algebra, one of its most visited courses, in the innovative OCW Scholar format designed for independent learners. Taught by Professor Gilbert Strang, <a href="http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/" target="_blank">18.06SC Linear Algebra</a> addresses systems of linear equations and the properties of matrices. The concepts of linear algebra are used to solve problems in physics, economics, engineering and other disciplines. 18.06SC is the first of six OCW Scholar courses planned for release by the end of February.<br /><br />Linear Algebra was one of the original 50 courses published on the MIT OpenCourseWare proof-of-concept site launched in 2002. Over the past 10 years, this course has received a total of 3.1 million visits from educators and learners around the world. Strang, who is one of the most widely known mathematicians in the world, hopes that the new, robust version — with its problem-solving videos — will help students everywhere.<br /><br />“I'm very proud of this new version of 18.06,” Strang says. “OCW has reached out to millions of educators and learners around the globe. With this new approach, even more people can see the beauty and usefulness of Linear Algebra.” In September, Strang was named the first MathWorks Professor of Mathematics, assuming a professorship recently endowed by MathWorks, the maker of mathematical software.<br /><br />OCW Scholar courses represent a new approach to OCW publication. MIT professors and students work closely with the OCW team to restructure the learning experience for independent learners, who typically have few additional resources available to them. The courses offer more materials than typical OCW courses and include new custom-created content. The OCW Scholar version of Linear Algebra includes videos of all the course lectures supplemented by lecture summaries and by 36 short videos showing how to solve specific problems.<br /><br />The first five of a planned 15 <a href="http://ocw.mit.edu/courses/ocw-scholar/" target="_blank">OCW Scholar courses</a> were launched by MIT OpenCourseWare in January 2011, and have collectively received more than 800,000 visits in less than a year. The initial OCW Scholar courses included Classical Mechanics, Electricity and Magnetism, Solid State Chemistry, Single Variable Calculus and Multivariable Calculus. Linear Algebra is the first of seven OCW Scholar courses that will be published in 2012. Other upcoming OCW Scholar courses include Principles of Microeconomics, Differential Equations, Introduction to Psychology, Fundamentals of Biology, Introduction to Electrical Engineering and Computer Science I, and Introduction to Computer Science and Programming. OCW Scholar courses are published on the OCW site with the support of the Stanton Foundation.This optical illusion was seen on a restaurant floor in Paris, and coded in MATLAB® by Shev Macnamara. Each color can become the tops of the cubes if you look at them correctly.Explained: Sigma
http://newsoffice.mit.edu/2012/explained-sigma-0209
How do you know when a new finding is significant? The sigma value can tell you — but watch out for dead fish.Thu, 09 Feb 2012 05:00:01 -0500David L. Chandler, MIT News Officehttp://newsoffice.mit.edu/2012/explained-sigma-0209It’s a question that arises with virtually every major new finding in science or medicine: What makes a result reliable enough to be taken seriously? The answer has to do with statistical significance — but also with judgments about what standards make sense in a given situation.<br /><br />The unit of measurement usually given when talking about statistical significance is the standard deviation, expressed with the lowercase Greek letter sigma (σ). The term refers to the amount of variability in a given set of data: whether the data points are all clustered together, or very spread out.<br /><br />In many situations, the results of an experiment follow what is called a “normal distribution.” For example, if you flip a coin 100 times and count how many times it comes up heads, the average result will be 50. But if you do this test 100 times, most of the results will be close to 50, but not exactly. You’ll get almost as many cases with 49, or 51. You’ll get quite a few 45s or 55s, but almost no 20s or 80s. If you plot your 100 tests on a graph, you’ll get a well-known shape called a bell curve that’s highest in the middle and tapers off on either side. That is a normal distribution.<br /><br />The deviation is how far a given data point is from the average. In the coin example, a result of 47 has a deviation of three from the average (or “mean”) value of 50. The standard deviation is just the square root of the average of all the squared deviations. One standard deviation, or one sigma, plotted above or below the average value on that normal distribution curve, would define a region that includes 68 percent of all the data points. Two sigmas above or below would include about 95 percent of the data, and three sigmas would include 99.7 percent.<br /><br />So, when is a particular data point — or research result — considered significant? The standard deviation can provide a yardstick: If a data point is a few standard deviations away from the model being tested, this is strong evidence that the data point is not consistent with that model. However, how to use this yardstick depends on the situation. John Tsitsiklis, the Clarence J. Lebel Professor of Electrical Engineering at MIT, who teaches the course Fundamentals of Probability, says, “Statistics is an art, with a lot of room for creativity and mistakes.” Part of the art comes down to deciding what measures make sense for a given setting.<br /><br />For example, if you’re taking a poll on how people plan to vote in an election, the accepted convention is that two standard deviations above or below the average, which gives a 95 percent confidence level, is reasonable. That two-sigma interval is what pollsters mean when they state the “margin of sampling error,” such as 3 percent, in their findings. <br /><br />That means if you asked an entire population a survey question and got a certain answer, and then asked the same question to a random group of 1,000 people, there is a 95 percent chance that the second group’s results would fall within two-sigma from the first result. If a poll found that 55 percent of the entire population favors candidate A, then 95 percent of the time, a second poll’s result would be somewhere between 52 and 58 percent.<br /><br />Of course, that also means that 5 percent of the time, the result would be outside the two-sigma range. That much uncertainty is fine for an opinion poll, but maybe not for the result of a crucial experiment challenging scientists’ understanding of an important phenomenon — such as last fall’s announcement of a possible detection of neutrinos moving faster than the speed of light in an experiment at the European Center for Nuclear Research, known as CERN.<br /><br /><strong>Six sigmas can still be wrong</strong><br /><br />Technically, the results of that experiment had a very high level of confidence: six sigma. In most cases, a five-sigma result is considered the gold standard for significance, corresponding to about a one-in-a-million chance that the findings are just a result of random variations; six sigma translates to one chance in a half-billion that the result is a random fluke. (A popular business-management strategy called “Six Sigma” derives from this term, and is based on instituting rigorous quality-control procedures to reduce waste.)<br /><br />But in that CERN experiment, which had the potential to overturn a century’s worth of accepted physics that has been confirmed in thousands of different kinds of tests, that’s still not nearly good enough. For one thing, it assumes that the researchers have done the analysis correctly and haven’t overlooked some systematic source of error. And because the result was so unexpected and so revolutionary, that’s exactly what most physicists think happened — some undetected source of error.<br /><br />Interestingly, a different set of results from the same CERN particle accelerator were interpreted quite differently. <br /><br />A possible detection of something called a Higgs boson — a theorized subatomic particle that would help to explain why particles weigh something rather than nothing — was also announced last year. That result had only a 2.3sigma confidence level, corresponding to about one chance in 50 that the result was a random error (98 percent confidence level). Yet because it fits what is expected based on current physics, most physicists think the result is likely to be correct, despite its much lower statistical confidence level.<br /><br /><strong>Significant but spurious</strong><br /><br />But it gets more complicated in other areas. “Where this business gets really tricky is in social science and medical science,” Tsitsiklis says. For example, a widely cited 2005 paper in the journal <i>Public Library of Science</i> — titled “Why most published research findings are wrong” — gave a detailed analysis of a variety of factors that could lead to unjustified conclusions. However, these are not accounted for in the typical statistical measures used, including “statistical significance.”<br /><br />The paper points out that by looking at large datasets in enough different ways, it is easy to find examples that pass the usual criteria for statistical significance, even though they are really just random variations. Remember the example about a poll, where one time out of 20 a result will just randomly fall outside those “significance” boundaries? Well, even with a five-sigma significance level, if a computer scours through millions of possibilities, then some totally random patterns will be discovered that meet those criteria. When that happens, “you don’t publish the ones that don’t pass” the significance test, Tsitsiklis says, but some random correlations will give the appearance of being real findings — “so you end up just publishing the flukes.”<br /><br />One example of that: Many published papers in the last decade have claimed significant correlations between certain kinds of behaviors or thought processes and brain images captured by magnetic resonance imaging, or MRI. But sometimes these tests can find apparent correlations that are just the results of natural fluctuations, or “noise,” in the system. One researcher in 2009 duplicated one such experiment, on the recognition of facial expressions, only instead of human subjects he scanned a dead fish — and found “significant” results. <br /><br />“If you look in enough places, you can get a ‘dead fish’ result,” Tsitsiklis says. Conversely, in many cases a result with low statistical significance can nevertheless “tell you something is worth investigating,” he says.<br /><br />So bear in mind, just because something meets an accepted definition of “significance,” that doesn’t necessarily make it significant. It all depends on the context.<br />On this chart of a 'normal' distribution, showing the classic 'bell curve' shape, the mean (or average) is the vertical line at the center, and the vertical lines to either side represent intervals of one, two and three sigma. The percentage of data points that would lie within each segment of that distribution are shown.Revealing how a battery material works
http://newsoffice.mit.edu/2012/lithium-battery-decoded-0208
MIT team uncovers a reason why the hottest new material for rechargeable batteries works so well.Wed, 08 Feb 2012 05:00:00 -0500David L. Chandler, MIT News Officehttp://newsoffice.mit.edu/2012/lithium-battery-decoded-0208<p>Since its discovery 15 years ago, lithium iron phosphate (LiFePO<sub>4</sub>) has become one of the most promising materials for rechargeable batteries because of its stability, durability, safety and ability to deliver a lot of power at once. It has been the focus of major research projects around the world, and a leading technology used in everything from power tools to electric vehicles. But despite this widespread interest, the reasons for lithium iron phosphate’s unusual charging and discharging characteristics have remained unclear.<br />
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Now, research by MIT associate professor of chemical engineering and mathematics Martin Z. Bazant has provided surprising new results showing that the material behaves quite differently than had been thought, helping to explain its performance and possibly opening the door to the discovery of even more effective battery materials.<br />
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The new insights into lithium iron phosphate’s behavior are <a href="http://pubs.acs.org/doi/abs/10.1021/nn204177u" target="_blank">detailed in a paper</a> appearing this week in the journal <i>ACS Nano</i>, written by Bazant and postdoc Daniel Cogswell. The paper is an extension of <a href="http://pubs.acs.org/doi/pdf/10.1021/nl202764f" target="_blank">research they reported late last year</a> in the journal <i>Nano Letters</i>.<br />
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When it was first discovered, lithium iron phosphate was considered useful only for low-power applications. Then, later developments — by researchers including MIT’s Yet-Ming Chiang, the Kyocera Professor of Ceramics — showed that its power capacity could be improved dramatically by using it in nanoparticle form, an approach that made it one of the best materials known for high-power applications.<br />
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But the reasons why nanoparticles of LiFePO<sub>4</sub> worked so well remained elusive. It was widely believed that while being charged or discharged, the bulk material separated into different phases with very different concentrations of lithium; this phase separation, it was thought, limited the material’s power capacity. But the new research shows that, under many real-world conditions, this separation never happens.<br />
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Bazant’s theory predicts that above a critical current, the reaction is so fast that the material loses its tendency for the phase separation that happens at lower power levels. Just below the critical current, the material passes through a new “quasi-solid solution” state, where it “doesn’t have time to complete the phase separation,” he says. These characteristics help explain why this material is so good for rechargeable batteries, he says.<br />
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The findings resulted from a combination of theoretical analysis, computer modeling and laboratory experiments, Bazant explains — a cross-disciplinary approach that reflects his own joint appointments in MIT’s departments of chemical engineering and mathematics.</p>
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<p>Previous analyses of this material had examined its behavior at a single point in time, ignoring the dynamics of its behavior. But Bazant and Cogswell studied how the material changes while in use, either while charging or discharging a battery — and its changing properties over time turned out to be crucial to understanding its performance.<br />
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“This hasn’t been done before,” Bazant says. What they found, he adds, is a whole new phenomenon, and one that could be important for understanding the performance of many battery materials — meaning this work could be significant even if lithium iron phosphate ends up being abandoned in favor of other new materials.<br />
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Researchers had thought that lithium gradually soaks into the particles from the outside in, producing a shrinking core of lithium-poor material at the center. What the MIT team found was quite different: At low current, the lithium forms straight parallel bands of enriched material within each particle, and the bands travel across the particles as they are charged up. But at higher electric-current levels, there is no separation at all, either in bands or in layers; instead, each particle soaks up the lithium all at once, transforming almost instantaneously from lithium-poor to lithium-rich.<br />
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<p>The new finding helps explain lithium iron phosphate’s durability as well. When there are stripes of different phases present, the boundaries between those stripes are a source of strain that can cause cracking and a gradual degradation in performance. But when the whole material changes at once, there are no such boundaries and thus less degradation.<br />
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That’s an unusual finding, Bazant says: “Usually, if you’re doing something faster, you do more damage, but in this case it’s the opposite.” Similarly, he and Cogswell predict that operating at a slightly higher temperature would actually make the material last longer, which runs counter to typical material behavior.<br />
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In addition to seeing how the material changes over time, understanding how it works involved looking at the material at scales that others had not examined: While much analysis had been done at the level of atoms and molecules, it turned out that the key phenomena could only be seen at the scale of the nanoparticles themselves, Bazant says — many thousands of times larger. “It’s a size-dependent effect,” he says.<br />
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MIT materials science professor Gerbrand Ceder observed and wrote about lithium iron phosphate’s behavior at high current levels last year; now, Bazant’s theoretical analysis could lead to a broader understanding not only of this material, but also of others that may undergo similar changes. The work was supported by a grant from the National Science Foundation and a seed grant from the MIT Energy Initiative.<br />
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Troy Farrell, an associate professor of mathematics at Queensland University of Technology in Australia, who was not involved in this work, says these findings are of great significance for those doing research on lithium batteries. He adds that this new understanding “enables material scientists to develop new structures and compounds that ultimately lead to batteries that have longer life and higher energy density. This is what is required if battery technology is to be used in high-power applications like electric vehicles.”<br />
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Understanding why lithium iron phosphate works so well was “one of the most interesting scientific puzzles I’ve encountered,” Bazant says. “It took five years to figure this out.”</p>
Lithium-rich and lithium-poor regions tend to form bands inside particles of lithium iron phosphate.Speed limit for birds
http://newsoffice.mit.edu/2012/speed-limit-for-birds-0120
MIT researchers find critical speed above which birds — and drones — are sure to crash.Fri, 20 Jan 2012 05:00:00 -0500Jennifer Chu, MIT News Officehttp://newsoffice.mit.edu/2012/speed-limit-for-birds-0120The northern goshawk is one of nature’s diehard thrill-seekers. The formidable raptor preys on birds and small mammals, speeding through tree canopies and underbrush to catch its quarry. With reflexes that rival a fighter pilot’s, the goshawk zips through a forest at high speeds, constantly adjusting its flight path to keep from colliding with trees and other obstacles. <br /><br />While speed is a goshawk’s greatest asset, researchers at MIT say the bird must observe a theoretical speed limit if it wants to avoid a crash. The researchers found that, given a certain density of obstacles, there exists a speed below which a bird — and any other flying object — has a fair chance of flying collision-free. Any faster, and a bird or aircraft is sure to smack into something, no matter how much information it has about its environment. A paper detailing the results has been accepted to the IEEE Conference on Robotics and Automation.<br />
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<li>Video: <a href="http://sertac.scripts.mit.edu/web/?p=528" target="_blank">Watch a hawk fly through a dense forest</a></li>
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These findings may not be news to the avian world, but Emilio Frazzoli, an associate professor of aeronautics and astronautics at MIT, says knowing how fast to fly can help engineers program unmanned aerial vehicles (UAVs) to fly at high speeds through cluttered environments such as forests and urban canyons. <br /><br />Frazzoli is part of an interdisciplinary team that includes biologists at Harvard University, who are observing flying behaviors in goshawks and other birds, and roboticists at MIT, who are engineering birdlike UAVs. With Frazzoli’s mathematical contributions, the team hopes to build fast, agile UAVs that can move through cluttered environments — much like a goshawk streaking through the forest. <br /><br /><strong>Speedy intuition</strong><br /><br />Most UAVs today fly at relatively slow speeds, particularly if navigating around obstacles. That’s mainly by design: Engineers program a drone to fly just fast enough to be able to stop within the field of view of its sensors. <br /><br />“If I can only see up to five meters, I can only go up to a speed that allows me to stop within five meters,” Frazzoli says. “Which is not very fast.”<br /><br />If the northern goshawk flew at speeds purely based on what it could immediately see, Frazzoli conjectures that the bird would not fly as fast. Instead, the goshawk likely gauges the density of trees, and speeds past obstacles, knowing intuitively that, given a certain forest density, it can always find an opening through the trees. <br /><br />Frazzoli points out that a similar intuition exists in downhill skiing. <br /><br />“When you go skiing off the path, you don’t ski in a way that you can always stop before the first tree you see,” Frazzoli says. “You ski and you see an opening, and then you trust that once you go there, you’ll be able to see another opening and keep going.” <br /><br />Frazzoli says that in a way, robots may be programmed with this same speedy intuition. Given some general information about the density of obstacles in a given environment, a robot could conceivably determine the maximum speed below at it can safely fly. <br /><strong><br />Forever flying</strong><br /><br />Toward this end, Frazzoli and PhD student Sertac Karaman developed mathematical models of various forest densities, calculating the maximum speed possible in each obstacle-filled environment. <br /><br />The researchers first drew up a differential equation to represent the position of a bird in a given location at a given speed. They then worked out what’s called an ergodic model representing a statistical distribution of trees in the forest — similar to those commonly used by ecologists to characterize the density of a forest. In an ergodic forest, while the size, shape and spacing of individual trees may vary, their distribution in any given area is the same as any other area. Such models are thought to be a fair representation of most forests in the world. <br /><br />Frazzoli and Karaman adjusted the model to represent varying densities of trees, and calculated the probability that a bird would collide with a tree while flying at a certain speed. The team found that, for any given forest density, there exists a critical speed above which there is no “infinite collision-free trajectory.” In other words, the bird is sure to crash. Below this speed, a bird has a good chance of flying without incident.<br /><br />“If I fly slower than that critical speed, then there is a fair possibility that I will actually be able to fly forever, always avoiding the trees,” Frazzoli says.<br /><br />The team’s work establishes a theoretical speed limit for any given obstacle-filled environment. For UAVs, this means that no matter how good robots get at sensing and reacting to their environments, there will always be a maximum speed they will need to observe to ensure survival. <br /><br />Steven LaValle, professor of computer science at the University of Illinois at Urbana-Champaign, says knowing where to cap a UAV’s speed can help engineers like himself design more agile robots.<br /><br />“Rather than trying to optimize robot speed, we might be able to [design] the robot at 95 percent of that speed, and achieve must simpler strategies that are also much safer to execute,” says LaValle, who did not contribute to the research.<br /><br />The researchers are now seeing if the theory bears out in nature. Frazzoli is collaborating with scientists at Harvard, who are observing how birds fly through cluttered environments — in particular, whether a bird will choose not to fly through an environment that is too dense. The team is comparing the birds’ behavior with what Frazzoli’s model can predict. So far, Frazzoli says preliminary results in pigeons are “very encouraging.”<br /><br />In the coming months, Frazzoli also wants to see how close humans can come to such theoretical speed limits. He and his students are developing a first-person flying game to test how well people can navigate through a simulated forest at high speeds. <br /><br />“What we want to do is have people play, and we’ll just collect statistics,” Frazzoli says. “And the question is, how close to the theoretical limit can we get?”Researchers link patterns seen in spider silk, melodies
http://newsoffice.mit.edu/2011/silk-music-proteins-1208
Analogy could help engineers develop materials that make use of repeating patterns.Thu, 08 Dec 2011 05:00:01 -0500Denise Brehm, Civil and Environmental Engineeringhttp://newsoffice.mit.edu/2011/silk-music-proteins-1208Using a new mathematical methodology, researchers at MIT have created a scientifically rigorous analogy that shows the similarities between the physical structure of spider silk and the sonic structure of a melody, proving that the structure of each relates to its function in an equivalent way. <br /><br />The step-by-step comparison begins with the primary building blocks of each item — an amino acid and a sound wave — and moves up to the level of a beta sheet nanocomposite (the secondary structure of a protein consisting of repeated hierarchical patterns) and a musical riff (a repeated pattern of notes or chords). The study explains that structural patterns are directly related to the functional properties of lightweight strength in the spider silk and, in the riff, sonic tension that creates an emotional response in the listener. <br /><br />While likening spider silk to musical composition may appear to be more novelty than breakthrough, the methodology behind it represents a new approach to comparing research findings from disparate scientific fields. Such analogies could help engineers develop materials that make use of the repeating patterns of simple building blocks found in many biological materials that, like spider silk, are lightweight yet extremely failure-resistant. The work also suggests that engineers may be able to gain new insights into biological systems through the study of the structure-function relationships found in music and other art forms.<br /><br />The MIT researchers — David Spivak, a postdoc in the Department of Mathematics, Associate Professor Markus Buehler of the Department of Civil and Environmental Engineering (CEE) and CEE graduate student Tristan Giesa — published their findings in the December issue of <i>BioNanoScience</i>.<br /><br />They created the analogy using ontology logs, or “ologs,” a concept introduced about a year ago by Spivak, who specializes in a branch of mathematics called category theory. Ologs provide an abstract means for categorizing the general properties of a system — be it a material, mathematical concept or phenomenon — and showing inherent relationships between function and structure. <br /><br />To build the ologs, the researchers used information from Buehler’s previous studies of the nanostructure of spider silk and other biological materials. <br /><br />“There is mounting evidence that similar patterns of material features at the nanoscale, such as clusters of hydrogen bonds or hierarchical structures, govern the behavior of materials in the natural environment, yet we couldn’t mathematically show the analogy between different materials,” Buehler says. “The olog lets us compile information about how materials function in a mathematically rigorous way and identify those patterns that are universal to a very broad class of materials. Its potential for engineering the built environment — in the design of new materials, structures or infrastructure — is immense.”<br /><br />“This work is very exciting because it brings forth an approach founded on category theory to bridge music (and potentially other aspects of the fine arts) to a new field of materiomics,” says Associate Professor of Biomedical Engineering Joyce Wong of Boston University, a biomaterials scientist and engineer, as well as a musician. “This approach is particularly appropriate for the hierarchical design of proteins, as they show in the silk example. What is particularly exciting is the opportunity to reveal new relationships between seemingly disparate fields with the aim of improving materials engineering and design.”<br /><br />At first glance, an olog may look deceptively simple, much like a corporate organizational chart that shows reporting relationships using directional arrows. But ologs demand scientific rigor to break a system down into its most basic structural building blocks, define the functional properties of the building blocks with respect to one another, show how function emerges through the building blocks’ interactions, and do this in a self-consistent manner. With this structure, two or more systems can be formally compared. <br /><br />“The fact that a spider’s thread is robust enough to avoid catastrophic failure even when a defect is present can be explained by the very distinct material makeup of spider-silk fibers,” Giesa says. “It’s exciting to see that music theoreticians observed the same phenomenon in their field, probably without any knowledge of the concept of damage tolerance in materials. Deleting single chords from a harmonic sequence often has only a minor effect on the harmonic quality of the whole sequence.” <br /><br />“The seemingly incredible gap between spider silk and music is no wider than the gap between the two disparate mathematical fields of geometry — think of triangles and spheres — and algebra, which uses variables and equations,” Spivak says. “Yet category theory’s first success, in the 1940s, was to express a rigorous mathematical analogy between these two domains and use it to prove new theorems about complex geometric shapes by importing existing theorems from algebra. It remains to be seen whether our olog will yield such striking results; however, the foundation for such an inquiry is now in place.”<br /><br />The project was funded by the U.S. Air Force Office of Scientific Research, a Department of Defense Presidential Early Career Award for Scientists and Engineers, the U.S. Office of Naval Research, and the German National Academic Foundation.Sal Khan to deliver 2012 Commencement address
http://newsoffice.mit.edu/2011/khan-commencement-address-1206
Online-education pioneer, MIT alumnus to speak to the Class of 2012 on June 8.Tue, 06 Dec 2011 16:36:29 -0500News Officehttp://newsoffice.mit.edu/2011/khan-commencement-address-1206Sal Khan ’98, MEng ‘98, an online-education pioneer whose free YouTube lectures have been viewed more than 100 million times, will deliver the address at MIT’s 146th Commencement exercises on Friday, June 8, in Killian Court.<br /><br />The holder of three MIT degrees — a bachelor’s in electrical engineering and computer science, a bachelor’s in mathematics, and a master’s in electrical engineering and computer science — Khan left his job as a hedge fund analyst to found the <a href="http://www.khanacademy.org/" target="_blank">Khan Academy</a>, whose library of nearly 3,000 homemade videos offers viewers a wide variety of lessons in mathematics and the sciences. The Khan Academy’s YouTube channel has more than 227,000 followers.<br /><br />“Sal Khan has been a remarkable global ambassador for science and mathematics education,” MIT President Susan Hockfield says. “He has reached millions of people around the world with his lucid and engaging online lectures. I can think of few people better positioned to show our Class of 2012 how a young MIT alumnus can take a big idea and change the world with it. I am delighted that he will share his story, and his wisdom, with our graduates.”<br /><br />Khan was president of MIT’s Class of 1998. While at the Institute, he was the recipient of a Peter J. Eloranta Summer Undergraduate Research Fellowship, which he used to develop web-based math software for children with ADHD.<br /><br />“My years at MIT were some of the best of my life,” Khan says. “It is the magical place where I was inspired by and bonded with the most fun, creative and passionate people I know — including my wife. I consider it the highest of honors to be able to speak to such an amazing group of people on such an important day. I hope that I’ll be able to help the graduating students fully appreciate the magnitude of the potential that they will be bringing into the world.”<br /><br />“Sal Khan is a great match for MIT,” says Undergraduate Association President Allan Miramonti ’13. “His work has helped countless students of all ages learn in a new way. He has taken a simple concept, making YouTube videos, and turned it into a cutting-edge way to teach people. When I look at his ability to teach and share knowledge with the world, I find his values to be in line with our own.”<br /><br />“Sal’s story of leaving his lucrative job in finance behind in pursuit of a greater calling is also inspiring,” says Nate Fox, president of the Class of 2012. “Many of us often talk about that crazy dream of ours, that one thing we’d love to do if money didn't matter. Sal is a man who not only left money to pursue his dream, but has succeeded in creating something truly remarkable: a free world-class education to anyone with a basic Internet connection.”<br /><br />A Bangladeshi-American born and raised in New Orleans, Khan began tutoring his young cousin, Nadia, in mathematics over the Internet in 2004. As friends and relatives began clamoring for wider access to his lectures, Khan started posting them on YouTube in 2006.<br /><br />Khan’s online lectures have become overwhelmingly popular; each has been viewed, on average, tens of thousands of times. The demand for his online lectures, and testimonials in support of them from students around the world, led him to quit his job at a hedge fund in 2009 to focus full time on his YouTube channel, by then known as the Khan Academy. <br /><br />Khan has described his goal as “changing education for the better by providing a free world-class education to anyone anywhere.” The Khan Academy is now a nonprofit with significant backing from the Bill and Melinda Gates Foundation and Google. All of its materials, lectures and resources are available to users worldwide, free of charge.<br /><br />“Sal’s dedication to giving freely of his education holds special resonance at MIT,” says Chancellor Eric Grimson, who has long served on the Commencement Committee. “When the Institute launched OpenCourseWare 10 years ago, we knew that we weren’t alone in wanting to share our knowledge with the world. It is thrilling to see one of our own graduates give that impulse such a wonderful shape, and I’m excited to hear Sal speak to the next class poised to make its mark on the world.”<br /><br />Khan joins a notable list of guest speakers at recent MIT Commencements, including Xerox CEO Ursula Burns (2011), Raymond S. Stata ’57, chairman and co-founder of Analog Devices Inc. (2010), Massachusetts Gov. Deval Patrick (2009), Nobel Peace Prize winner Muhammad Yunus (2008), MIT President Emeritus Charles M. Vest (2007) and alumnus and Federal Reserve Bank Chairman Ben Bernanke (2006).Sal Khan speaks at TED 2011. Khan, an MIT alumnus, will deliver the 2012 Commencement address on June 8.