November 30, 2004
Evolutionary roots of altruism, moral outrageIf you've ever been tempted to drop a friend who tended to freeload, then you have experienced a key to one of the biggest mysteries facing social scientists, suggests a study by UCLA anthropologists. "If the help and support of a community significantly affects the well-being of its members, then the threat of withdrawing that support can keep people in line and maintain social order," said Karthik Panchanathan, a UCLA graduate student whose study appears in Nature. "Our study offers an explanation of why people tend to contribute to the public good, like keeping the streets clean. Those who play by the rules and contribute to the public good will be included and outcompete freeloaders." This finding -- at least in part -- may help explain the evolutionary roots of altruism and human anger in the face of uncooperative behavior, both of which have long puzzled economists and evolutionary biologists, he said. "If you put two dogs together, and one dog does something inappropriate, the other dog doesn't care, so long as it doesn't get hurt," Panchanathan said. "It certainly wouldn't react with moralistic outrage. Likewise, it wouldn't experience elation if it saw one dog help out another dog. But humans are very different; we're the only animals that display these traits." The study, which uses evolutionary game theory to model human behavior in small social groups, is the first to show that cooperation in the context of the public good can be sustained when freeloaders are punished through social exclusion, said co-author Robert Boyd, a UCLA professor of anthropology and fellow associate in UCLA's Center for Behavior, Evolution and Culture. "Up to this point, social scientists interested in the evolutionary roots of cooperative behavior have been hard-pressed to explain why any single individual would stick his neck out to punish those who fail to pull their weight in society," Boyd said. "But without individuals willing to mete out punishment, we have a hard time explaining how societies develop and sustain cooperative behavior. Our model shows that as long as it is socially permissible, withholding help from a deadbeat actually proves to be in an individual's self-interest." With funding from the National Science Foundation, Panchanathan set out to recreate mathematically a small community in which people participate in a public good, such as an annual clearing of a mosquito-infested swamp, which takes time from their day but which saves the entire community time down the line because the work prevents them from getting sick. He assumed that individuals in the close-knit community frequently swap favors, like helping neighbors repair their homes after a storm. He also assumed that no single individual or agency was being paid to keep individuals in line. Community members had to do it themselves, much as our evolutionary ancestors would have done. In his mathematical model, Panchanathan pitted three types of society members: -- "Cooperators," or people who always conntribute to the public good and who always assist individual community members in the group with the favors that are asked of them. -- "Defectors," who never contribute to thhe public good nor assist other community members who ask for help. -- "Shunners," or hard-nosed types who conntribute to the public good, but only lend aid to those individuals with a reputation for contributing to the public good and helping other good community members who ask for help. For members in bad standing, shunners withhold individual assistance. During the course of the game, both cooperators and shunners helped to clear the swamp. The benefits from the mosquito-free swamp, however, flowed to the whole community, including defectors. When the researcher took only this behavior into account, the defectors come out on top because they enjoyed the same benefits the other types, but they paid no costs for the benefits. But when it came to getting help in home repair, the defectors didn't always do so well. The cooperators helped anyone who asked, but the shunners were selective; they only help those with a reputation for clearing the swamp and helping good community members in home repair. By not helping defectors when they ask for help, shunners were able to save time and resources, thus improving their score. If the loss that defectors experienced from not being helped by shunners was greater than the cost they would have paid to clear the swamp, then defectors lost out. After these social interactions went on for a period of time that might approximate a generation, individuals were allowed to reproduce based on accumulated scores, so that those with more "fitness points" had more children. Those children were assumed to have adopted their parents' strategy. Eventually, Panchanathan found that communities end up with either all defectors or all shunners. "Both of those end points represent 'evolutionarily stable equilibriums'; no matter how much time passes, the make-up of the population does not change," Panchanathan said. In a community with just cooperators and defectors, defectors -- not surprisingly -- always won. Also when shunners were matched against cooperators, shunners won. "The cooperators were too nice; they died out," Panchanathan said. "In order to survive, they had to be discriminate about the help they gave." But when shunners were matched against defectors, the outcome was either shunners or defectors. The outcome depended on the initial frequency of shunners. If enough shunners were present at the beginning of the exercise, then shunners prevailed. Otherwise, defectors prevailed, potentially pointing to the precarious nature of cooperative society. "We know that people pay their taxes and engage in all kinds of other cooperative behaviors in modern society because they're afraid they'll get punished," Panchanathan said. "The problem for the social scientist becomes how did the propensity to punish get started? Why do I get angry if someone doesn't contribute? Isn't it just better to say, 'It's their business,' and let everybody else in the group get angry? After all, punishing someone else will take time and energy away from activities that are more directly important to me and I may get hurt." "By withdrawing my support from a freeloader, I benefit because every time I do something nice for someone, it costs me something," Panchanathan said. "By withdrawing that support, I'm spared the energy, time or whatever costs are entailed. I retain my contribution, but the deadbeat is punished." In practice, however, cooperative societies hold defectors in line through a series of measures, Panchanathan said. "The first level is disapproval: you say, 'That wasn't cool' or you give a funny look," he said. "Then you withdraw social support. Finally, you lower the boom and either physically hurt the defector or run him out of town." Ultimately, he admits, this model is "a very simple and crude approximation" of the real world. "For example, in my model, only defectors or shunners can persist. They cannot coexist," he said. "But we know that some people are generally cooperative, playing by society's rules, while others are not. This type of modeling doesn't explain everything. Instead, it boils down a complex social world and tries to understand one small piece. In this case, we found that cooperation can persist if people need to maintain a good reputation in their community." Evolutionary roots of altruism, moral outrage |
November 30, 2004
Computer program helps decode cancerResearchers at the University of Newcastle, Australia have developed a computer program that implements a novel algorithm, which will aid in the identification of specific cancer causing genes. Dr Pablo Moscato from the Faculty of Engineering and Built Environment, and Director of the Newcastle Bioinformatics Initiative, who led the team that developed the new algorithm, says that it is capable of "rapidly extracting hidden information from an otherwise uninformative jumble of biological data." "Humans have over 20,000 genes. Understanding their role in health and disease requires analysis of how the genes behave under different circumstances." "It is now possible to map the genes that are active in different parts of the body at different times or during development, and to determine how diseases, drugs or toxic chemicals can alter the pattern of gene behaviour." "The algorithm identifies specific genes and then groups together those with similar patterns of activity. The patterns of activity provide a molecular fingerprint which could potentially be used to identify specific cancer genes." "By using these techniques to identify gene profiles, biologists will have new mathematical methods to understand their roles and identify ways to control these genes. New methods are needed as a deluge of data is expected from new biotechnologies in the 21st century." "Analysis of individual variations in genetic profile could lead to personalised medicine, where treatments for diseases or strategies for health promotion can be specifically tailored to the genetic makeup of the individual," says Dr Moscato. Computer program helps decode cancer |
November 30, 2004
New physics proof bridges gap between two disciplines, opens doors for medicine(PRLEAP.COM) SACRAMENTO, CALIFORNIA – November 29, 2004. Advanced Electrical Engineer and physics theorist William T. Gray today released his “Wave-Particle Duality” proof. The mathematical proof, online at www.MQNF.com, provides the first ever predictability for quantum behaviors through an explanation of the experimentally observed but little understood wave-particle relationship. Once thought of to be one in the same. “The evidence has been there for decades, it just took someone willing to step back and put all the pieces together,” says William Gray. “We now know a particle’s wave nature is not a property of that particle, but rather an effect of its motion upon space. The particles are like a boat traveling across a lake. The waves it causes are not a part of the boat.” The significance of solving the cause of the wave nature is it allows predictability of quantum behavior, which translates to the predictability of other quantum behaviors through a recursive mathematical model. “Basically, if you know what causes the wave behavior and can predict it, then it is no longer random and establishes a pattern,” says Gray. Predicting atomic behavior facilitates technology. By bridging the gap between quantum physics and relativity, this answers previously unanswered questions between the two disciplines and will allow the first ever predictability in quantum physics. According to Gray, “The most obvious application is it represents a new opportunity in our ability to advance technology on an atomic level. This paves the way for quantum computers by allowing circuitry to be placed inside the nuclei of atoms, thereby reducing their size and increasing their speeds by a million fold,” says Gray. “Nanotechnology just received a mega booster shot.” Synthesizing neutrons is not new, but doing it without radioactivity and from non-isotopic elements sure is. “We also know this leap in understanding leads to technology which provides new energy sources, as well as treatment in diseases such as cancer. By controlling the decay of neutrons to cellular accuracy, it will allow tumors to be treated with non-radioactive high energy without destroying surrounding healthy human tissue. It could save 50,000 lives a year in this country alone,” says Gray. “Imagine being able to treat our terminally ill children who are unresponsive to traditional therapies, and curing them without any harmful side effects.” Mr. Gray has not applied this mathematical proof to gambling, yet. New physics proof bridges gap between two disciplines, opens doors for medicine |
November 30, 2004
How do Internet search engines work?A. Dharia Javed Mostafa, the Victor Yngve Associate Professor of information science and director of the Laboratory of Applied Informatics at Indiana University, Bloomington, explains. It has been estimated that the amount of textual information accessible via search engines is at least 40 times larger than the digitized content of all the books in the Library of Congress, the world's largest library. It is a challenge to provide access to such a large volume of information, yet current search engines do remarkably well in sifting through the content and identifying related links to queries. There is a multitude of information providers on the web. These include the commonly known and publicly available sources such as Google, InfoSeek, NorthernLight and AltaVista, to name a few. A second group of sources--sometimes referred to as the "hidden web"--is much larger than the public web in terms of the amount of information they provide. This latter group includes sources such as Lexis-Nexis, Dialog, Ingenta and LoC. They remain hidden for various reasons: they may not allow other information providers access to their content; they may require subscription; or they may demand payment for access. This article is concerned with the former group, the publicly available web search services, collectively referred to here as search engines. Search engines employ various techniques to speed up searches. Some of the common techniques are briefly described below. Preprocessed Data One way search engines save time is by preprocessing the content of the web. That is, when a user issues a query, it is not sent to millions of web sites. Instead, the matching takes place against preprocessed data stored in one site. The preprocessing is carried out with the aid of a software program called a crawler. The crawler is sent out periodically by the database maintainers to collect web pages. A specialized computer program parses the retrieved pages to extract words. These words are then stored along with the links to the corresponding pages in an index file. Users' queries are matched against this index file, not against other web sites. Smart Representation In this technique, the representation for the index is carefully selected with an eye toward minimizing search time. Information scientists have produced an efficient data structure called a tree that can guarantee significantly shorter overall search time compared with searches conducted against a sequential list (see sidebar). To accommodate searches conducted by many users simultaneously and eliminate "wait queues," the index is usually duplicated on multiple computers in the search site. Prioritizing Results The URLs or links produced as a result of searches are usually numerous. But due to ambiguities of language (for instance, "window blind" versus "blind ambition"), the resulting links would generally not be equally relevant to a user’s query. To provide quicker access to the most relevant records (and to place them at or near the top), the search algorithm applies various ranking strategies. A common ranking method known as term-frequency-inverse document-frequency (TFIDF) considers the distribution of words and their frequencies and generates numerical weights for words signifying their importance in individual documents. It produces word weights whereby words that are highly frequent (such as 'or,' 'to' or 'with') and that appear in many documents have substantially less weight than words that are semantically more relevant and appear in relatively few documents. In addition to term weighting, web pages can be weighted using other strategies. For example, link analysis considers the nature of each page in terms of its association with other pages—namely if it is an authority (number of other pages that point to it) or a hub (number of pages it points to). The highly successful Google search engine uses link-analysis to improve the ranking of its search results. Context and Distance In order to identify the most relevant links quickly, certain search engines compare query terms to contextual information such as recent queries the user submitted. This technique is sometimes referred to as query catching, and involves collecting the words from recent queries and using these words to disambiguate, refine or expand the current query. Another way certain information providers can speed up the delivery of search results is by using a distributed delivery model, whereby copies of the index and related content are duplicated and moved to multiple geographical locations so as to shorten the network distance between users and content. The content providers work with third-party services such as Akamai to implement distributed content delivery. Limitations There are costs associated with some of the speed-up techniques described above. The separation of the organizations conducting the indexing from the organizations that produce the actual content can lead to so-called rotting links, which point to pages that no longer exist. Alternatively, links to new web content could be missing. Both rotting and missing links may occur due to delays in crawling or re-indexing. Some crawlers retrieve pages blindly, without attention to either the reputation or the authority of information providers. This process encourages manipulation of indexing for malicious purposes. One common phenomenon is called index-spamming. Sites desiring to artificially increase their ranking in search results may place thousands of words in pages using font colors that match the background of the pages. This procedure hides the words from viewers but makes them available to indexes. Finally, by taking advantage of a feature of web server software, information providers can manipulate it to return different pages for the same request made by different hosts. This has lead to page-jacking, whereby a site can copy a competitor’s page, have it indexed by a search engine host as its own, and direct requests from other hosts for the original page to alternative content or sites. How do Internet search engines work? |
November 30 2004
Professor Wake elected Fellow to the Royal SocietyThe dedication of Professor Graeme Wake to advancing the problem solving power of mathematics in industry and in other challenging scenarios, has earned him a place in the who’s who of science in New Zealand. Professor Wake has been elected as a Fellow to the Royal Society of New Zealand, joining a prestigious academy with just 322 leading scientists on its list of Fellows. The selection process is rigorous, involving discipline-specific selection panels and independent international review. Only a small number of those nominated are ultimately selected. Professor Wake came to Albany campus from Canterbury University in 2003 with a strong history for taking mathematics out of the classroom and gaining new recognition for the importance of his subject to business and to society at large. Professor Wake is the Director of the Centre for Mathematics in Industry and is the driving figure behind the Mathematics in Industry Study Group. Each summer this group pulls together the country’s top mathematicians to brainstorm solutions and develop models for a wide range of industry groups. The success of this group is such that Professor Wake is helping to establish the concept in Korea and Thailand. Professor Wake was one of four mathematicians amongst the 12 Fellows elected this year. Royal Society Academy Council President, Professor Carolyn Burns noted the significance of the recognition of excellence in mathematics: “Concerns have been expressed over the past decade about declining mathematical skills among young New Zealanders,” she said. The Royal Society citation for Professor Wake acknowledges him as a talented and versatile applied mathematician who has been instrumental in focusing applied mathematics on issues of specific relevance to New Zealand, particularly in modeling biological systems in the agricultural, health and industrial sectors. The citation says he has applied ingenious mathematics to develop models for the spontaneous combustion of wool, hay and lignite, the growth of pasture for optimum production, population dynamics and control of unwanted animals and plants, and in minimizing the effects of epidemics and environmental damage by pests. In collaboration with biologists and clinical oncologists, he has developed innovative models of tumour cell growth with applications to cancer therapy. His world-class work is reported in more than 165 refereed publications. “He has significantly advanced the teaching and application of mathematics in New Zealand. His enthusiasm and energy have inspired numerous research students and collaborators.” Professor Wake elected Fellow to the Royal Society |
November 30, 2004
Math factorBy ANDREA ROGERS The state Board of Regents has a unique opportunity to unequivocally define the mathematics that all graduating high school students should know. The board is scheduled to vote in January on recommendations made by the Mathematics Standards Committee, a panel created to clarify and fortify the state's mathematics learning standards. The simple and correct course of action -- requiring all graduating seniors to know algebra, geometry and trigonometry -- unfortunately was not among the panel's proposals. Instead, the panel recommended changing the current 1 1/2 year Math A course to a one-year intense study of algebra, and splitting the current one-year Math B course of study into a one-year course focused solely on geometry and a second one-year focused on integrated algebra and trigonometry. To graduate, students now must complete Math A and the accompanying Regents exam. This course's current mix of mathematics includes a little geometry and a little trigonometry, as well as algebra. So students must demonstrate that they at least have skimmed the surface of these topics in order to graduate. If adopted by the Regents, the committee's proposal to refocus Math A on algebra would guarantee that this discipline is the only math topic specifically required for graduation. Focusing high school mathematics by discipline instead of the current "a little bit of everything" approach makes a lot of sense, but the panel's common-sense revisions to clarify and strengthen the math learning standards should be linked to common-sense expectations of achievement for all students. Excluding any requirement that students also learn and be tested on geometry and trigonometry seriously weakens graduation standards. Instead, the Regents should ensure that both the refined Math A and the reconstituted Math B are required of all high school students. Geometry and trigonometry are covered in detail on college entrance exams and, along with algebra, are becoming increasingly necessary for success in college and the workplace. Efforts by area leaders to market this region as Tech Valley and to lure technology companies to our area, for example, will be accentuated by providing a work force that knows math. The Regents can ensure students are mathematically well-versed by simply linking the proposed learning standards overhaul with a graduation requirement that all students take the Math A and Math B courses and pass the associated exams. Expecting proficiency in these three fundamental areas of mathematics over four years is a reasonable standard. While many school districts in the state already achieve very high passing rates on math Regents exams, other districts -- including both small cities such as Albany and the state's larger urban areas -- will find that meeting these standards is a significant challenge. But to simply exclude these disciplines from required study would be a dangerous mistake. Switching to research-based curricula that have a track record of success; ensuring that middle school math teachers, as well as high school math teachers, have subject mastery; dedicating larger blocks of class time to math from kindergarten on up; and replicating teaching methods that have been shown to work are all routes to success that should be employed to meet these challenges. Opponents of high academic standards will be among the first to oppose this idea, likely implying that New York's students just aren't smart enough or capable enough to handle three years of high school math. This notion insults the intelligence of our teachers and our kids, diminishes the value of a New York state diploma and jeopardizes the competence of our future work force. The sooner the Board of Regents and state Education Commissioner Richard Mills hold teachers and students to higher and more coherent math standards, the better. We don't need graduation standards that assume students aren't bright enough to learn; we need a world-class school system that recognizes the demands of today's technological era by both challenging and preparing its students to succeed. Maybe then we can start talking about requiring calculus. Math factor |
November 29, 2004
On your marksBy Simon Tsang They walk, tumble, crawl, writhe, roll and bounce around. It's a race and contestants can take any shape or form, from four-legged walkers to amoebas. The only thing is, this race doesn't exist in the real world. It's entirely online and competing "animals" are little more than wire-frame models that follow some basic physical principles such as mass and gravity. Welcome to Sodarace. Developed as a joint project between Soda - a British multimedia design company - and the University of London, Sodarace tackles the age-old question: which is better - man or machine? Human ingenuity or artificial intelligence? Indeed, its website promotes the venture as "the online Olympics pitting human creativity against machine learning". Users can build any creature they conjure up using the Sodaconstructor virtual construction kit - a Java application from the Sodarace website. Programmers and those in the field of AI can then apply their algorithms to the creature to come up with a faster model. The virtual creatures are then submitted to compete in races across all kinds of two-dimensional terrain in the Sodarace forums. Stefan Westen is a software developer for Wallingford Software in the UK and discovered Sodarace from a story in ZDNet. The idea of humans versus AI in a race intrigued him. "I had a look on the Sodarace website and saw that others had written AI programs to design models for the race," he says. "Then I decided to try and write a simple AI program to optimise these models." In doing this, programmers take an existing model and use their AI algorithms to improve it. One popular method is to use a genetic algorithm that - put simply - tests a large number of possible combinations and carries the best mix into the "next generation" of the model. It's a method likened to the theory of evolution and has its share of passionate proponents and detractors. "Humans can beat AI because we can think, we're not just a program that takes a model and randomly changes it millions of times. The only thing computers have that beats us is the processing speed at which they carry out tasks," wrote one website user in the forum's artificial intelligence thread. "Why do you feel the need to attack AI? Are you insecure?" responded another. It's as much about good old-fashioned one-upmanship as it is about serious scientific research. "In the race forum on the Sodarace website there was a very interesting competition going on where AI programmers would post a model and then model builders would post a faster [one]," Westen says. "I spent many evenings programming until late at night to optimise my program so it would beat the fastest model in the forum. As far as I can remember I still have the record for this race: 381 frames." Looking at the models, they appear remarkably complex - a two-dimensional line drawing that has the illusion of existing in three dimensions. However, the creatures are made up of surprisingly simple parts of "springs", "muscles" and "joints" defined by a small set of variable parameters such as gravity, friction and spring stiffness. That Sodarace is designed to be fun and work like a game is no accident. Soda - the co-developer - believes in breeding creativity through play. There are no age limits. Anyone can join in and build models. They don't even have to race them. Some have submitted simple drawings that animate, such as the creative entry called "London Bridge" that (of course) tumbles down as soon as you load it up. This doesn't mean it's easy though; just that it can be as simple or complex as you want. It took me at least 10 attempts before coming up with a design that didn't collapse like a marionette with its strings cut as soon as I turned the simulator on. A year on from when it was introduced, however, the Sodarace story has a twist. Westen b ecame frustrated with its limitations and decided to build his own race called Mins (Mins Is Not Soda). "I started to notice that somehow there was an 'upper limit' for the speed of models. They just wouldn't go any faster," he explains. "I found that there is a hard limit on the speed of Soda models. In theory, there is no maximum limit in Mins." Westen is even talking about adding other "events" such as high jump and tug-of-war to further challenge builders and AI programmers. Meanwhile, the debate about humans versus AI continues in the Sodarace forums. Perhaps if the two would just learn to work together. But then again, where's the fun in that? On your marks |
November 28, 2004
Devaney named Professor of the YearRobert Devaney, professor of mathematics and statistics at Boston University, has been named the 2004 Massachusetts Professor of the Year by the Carnegie Foundation for the Advancement of Teaching and the Council for the Advancement and Support of Education. Devaney was honored recently during ceremonies at the Willard InterContinental Hotel in Washington, D.C. A widely respected expert in complex dynamical systems, Devaney has also achieved acclaim for his pioneering use of technology in teaching. He has directed the National Science Foundation's Dynamical Systems and Technology Project since 1989, a project that helps high school and college educators use technology to more effectively teach modern mathematics such as chaos, fractals, and dynamics. He was the first mathematician to win the NSF Director's Award for Distinguished Teaching Scholars (2002), for contributions to enhancing undergraduate education, and has received the Mathematical Association of America's Teacher of the Year Award (1995). In 2003, Devaney received Boston University's Metcalf Award for Excellence in Teaching. The Professors of the Year program was established in 1981. It is co-sponsored by the Carnegie Foundation for the Advancement of Teaching and CASE. The Carnegie Foundation, the only advanced-study center for teachers in the world, is the third-oldest foundation in the United States. CASE is the largest international association of educational institutions, with more than 3,200 colleges, universities, and independent elementary and secondary schools in nearly 50 countries. Faculty in Boston University's Mathematics and Statistics Department conduct research in a number of areas including algebra, applied statistics, dynamical systems and their applications, mathematical physics, number theory, partial differential equations and probability. Boston University is the fourth largest independent university in the United States. Devaney named Professor of the Year |
November 28, 2004
Learning math will now be funAshima Bajpai When it comes to mathematics, many students find the subject torturous while others find it difficult to remember the formulae. To put it simply, ‘mathematics-phobia’ is what many school students suffer from. Taking the problem into perspective, the Mathematical Sciences’ Foundation (MSF) of St Stephens College, has set up its resource centres in a few schools in Delhi. The Indian School is one such school where the resource center has been running successfully for the past three months. Besides this, they have recently started another center at the Tagore International School in Vasant Vihar. MSF is the brainchild of Dinesh Singh, professor of mathematics at the University of Delhi. The society runs various other programmes and their school project for the Indian School called ‘sahyog’ has worked wonders for students. “Mathematics as a concept needs a strong foundation without which a student cannot move forward. Our main aim is to strengthen their basic concepts and make mathematics fun for them,” said Dr Manika Agarwal, associate professor at MSF. Their way of teaching is unique and fun-filled. Experimental games are conducted amongst the students where they are expected to derive a certain formula through a game. Other games on integers are also conducted where the students are made to stand in various combinations to understand the concepts of integers. “The whole idea is to make the subject fun so that the students enjoy studying it and not avoid it,” she said. The Indian School conducts the classes after school hours for classes VI to VIII. “We have had a very good response from the students. Their performance has really gone up,” said Poonam Chopra, principal, The Indian School. She further informed that the school might have a mathematics laboratory in the near future where the practical aspect of the subject will be taught. Interestingly, even parents have a role to play in the MSF programme. Regular interactive sessions are held between the MSF staff and the parents. The staff informs the parents how they can make mathematics fun at home. Learning math will now be fun |
November 28, 2004
GCU to arrange Maths OlympiadsLAHORE: The National Centre for Mathematics (NCM) at Government College University (GCU) is going to formulate policies to reform the mathematics curriculum and will hold countrywide competitions and mathematics Olympiads, said Dr Ghulam Murtaza of GCU, while addressing the inaugural session of a daylong symposium on mathematics. The symposium was arranged by the NCM. “The NCM’s objectives are to pursue excellence in mathematical sciences, to develop MPhil and PhD Programmes, to organise conferences, courses, workshops, symposia and seminars every year in various sub-disciplines, to lead Pakistan’s development of mathematics by organising workshops for curricula revision, to improve teaching methods, to hold refresher courses for both university and college teachers and to organise mathematics Olympiads in the country,” said Dr Murtaza. Dr Murtaza said that the centre would operate in a similar manner to the Max Planck Institute of Germany, Abdus Salam International Centre for Theoretical Physics and the Tata Institute of Fundamental Research of India. He said that the GCU’s School of Mathematics Sciences (SMS) had launched an ‘Associate Scheme’ under which a person could join SMS for mathematical guidance for three months or more. Under the scheme, all travel and subsistence allowances will be provided to the associate, he added. Dr Khalid Aftab, the GCU vice chancellor, said that the centre would be a model of excellence in South Asia. “All resources are being utilised to convert this dream into a reality. We will have to maintain pace with domestic and global changes to meet national expectations,” he said. Dr AD Raza Choudry, the SMS director general, introduced foreign faculty members and hoped they would do their best. Scholars and students from various Pakistani universities participated in the inaugural ceremony of the symposium. During the symposium technical sessions, Dr Sever Angel Popescu, Dr Amir Iqbal, Dr Nicolae Popescu, Dr Alexander Kondratyev, Dr Oleg I Reinov and Dr Sergei Borisenok talked about different aspects of the subject. GCU to arrange Maths Olympiads |
November 28, 2004
String swing a hitBy Geoff Mosher When students at Gibbons Middle School play musical chair, they're getting math and physics lessons, in addition to music instruction. For a couple months now, the school has been integrating a new invention called the "string swing" into the curriculum. Built out of scrap metal and wood, the popular musical device resembles a porch swing. The swing's seat is suspended on each side by steel piano wire, which is attached to a small sounding board at the top of the swing. When a volunteer sits on the seat, tension is placed on the wires. The strings, which are of unequal length, can then be plucked, and the resulting notes, or pitches, are measured with an electronic tuner. "The heavier you are, the higher the pitch (of the notes); the lighter you are, the lower it is, which is against what most students would think," said seventh-grader Ben Warshaw, one of many students who's learned the intricacies of the swing. Industrial arts teacher David Hagberg conceived of the idea for the swing while teaching a music class last year. A former piano technician, Hagberg wanted to build a device that would interest music students and also have cross-curriculum appeal. Hagberg recruited his son Andrew, now a seventh-grader, tech ed. teacher Bill Parsons, music teacher Sue Cooper and Ross Giovannucci, a high school Quest student intern, to help him design the swing. After months of hard tinkering, it was unveiled at a parent open house night in September. One of the first parents to see it was a patent attorney. He suggested to Hagberg that the device could be patented, that it might be marketable. But Hagberg said it would be "too sterile" and lose its appeal if it were manufactured. "When it looks like a pile of junk, the kids find it more interesting," he said. Gibbons students have grown fond of the invention. "I've never seen something tied in with so many different things," said seventh-grader Gillian Biggert "It shows us what we're learning," said Clarissa Savage, an eighth-grader. The string swing is a fixture in Cooper's classroom. To date, students have used it to learn about pitches, octaves, variable frequencies, forces on structures, ratios, proportional relationships and acoustics. "There's so much involved in this," Cooper said. "It's a real hands-on learning tool for the kids." Warshaw said he thinks the swing's many practical uses make it appealing to middle-schoolers. "Students are more geared toward hands-on (learning)," he said. The swing helped eighth-grader Tyler Smith understand the connection between math and music. "If you know math, you're probably good in music," Smith said. Students can even use the swing to compose music. All they need to do is record the varying pitches in standard musical notation. "If we could have a whole lot (of volunteers), we could get a song going," Cooper said. "We could do a fantasy on the theme of the weight of the subjects," Hagberg added. String swing a hit |
November 28, 2004
String Theory Gets Real--Sort OfAdrian Cho ASPEN, COLORADO--Twenty years ago, this chic playground for skiers and celebrities gave birth to a scientific revolution. An abstruse mathematical discovery made here sparked the explosion of "string theory," humanity's best attempt at the ultimate explanation of matter and energy, space and time. Now, 2 decades later, physicists have returned to a cloistered compound at the north end of town to mull over a nagging question: Can string theory account for what we already know about the universe? At a monthlong workshop, more than 50 researchers have gathered to discuss whether the theory can accommodate the data they already have and make predictions about future experiments--fundamental scientific tests that this vaunted "theory of everything" has yet to pass. The revolution began "right over there in Bethe," says John Schwarz, a physicist at the California Institute of Technology (Caltech) in Pasadena and one of the revolutionaries. Lounging on a bench, he motions toward one of three tiny single-story buildings that house the Aspen Center for Physics. In 1984, Schwarz and Michael Green, a physicist at the University of Cambridge in the U.K., found a way around key mathematical pitfalls in string theory, which assumes that every elementary particle is a tiny vibrating string and that space has more dimensions than we see. The esoteric advance suggested that the theory might be a viable explanation of all the forces of nature. "Almost overnight, hundreds of people started working on this stuff," Schwarz says. "People were almost too enthusiastic--naïve about the problems we had to overcome." String theory promises to reconcile Einstein's theory of gravity with the bizarre rules of quantum mechanics, answer the deepest conceptual questions in particle physics, and even explain how the universe sprang into existence. Hundreds of physicists and mathematicians work on one aspect of string theory or another. Now a small but growing number of them are trying to forge connections between string theory and detailed data-- a practice physicists call "phenomenology." Some say the effort is long overdue. Theorists in other sciences focus on explaining experimental data, but most string theorists study formal aspects of the theory itself, says Gordon Kane, a particle theorist at the University of Michigan, Ann Arbor. "Only in string theory is there a complete disconnect in which string theorists don't make any effort to make contact with experiment," Kane says. Stuart Raby, a particle theorist at Ohio State University in Columbus, says string theorists must find a way to account for experimental observations, especially in particle physics, in order to maintain the theory's credibility. "You're not going to believe string theory until you see the real world coming out of it," he says. Recent astronomical observations, the construction of a huge new particle collider in Europe, and advances in the theory itself have whetted researchers' appetites for analyzing hard data. But the task remains daunting, and some string theorists say the theory isn't ready for this kind of test. "There's a lot of stuff that we know, but I still feel that there's some missing idea or some very difficult mathematics that needs to be done before we can tie that [information] to string theory," says string theorist Jeffrey Harvey, in a phone interview from his office at the University of Chicago, Illinois. Moreover, most researchers believe that a huge number of distinct versions of the theory may jibe with what we know and can measure. If so, physicists may have to rethink what it means for a theory to explain experimental data. In summer, Aspen lends itself to contemplation. At the physics center, sunlight shimmers silver on fluttering aspen leaves as researchers chat in the shade or work at picnic tables. A brook babbles across the courtyard, branching once, then once again, like diverging lines of inquiry. Yet newcomers to the center often struggle to sleep. They rise in the morning with dry eyes and headaches. It's the effect of the thin mountain air. Or perhaps it's the strain of thinking that particles are tiny strings and that the universe has 10 dimensions. But that's precisely what string theory says. We observe only four dimensions--three spanning space and one ticking away time--because the other six curl up tight. In effect, spacetime is a bit like a tightrope, which appears essentially one dimensional to a large creature such as a human. But to an ant, the tightrope appears two dimensional, with the second dimension curled around the rope. In string theory, however, the six "compactified" dimensions of the universe curl together to form a kind of six-dimensional multiholed doughnut. The intricate shape determines how strings can vibrate and, hence, what kinds of particles exist. All this may seem far-fetched and needlessly complicated, but string theory possesses a virtue for which many physicists are willing to accept these seeming absurdities: It can reconcile quantum mechanics and Einstein's theory of gravity. According to Einstein's general theory of relativity, mass and energy warp spacetime, producing the effects we call gravity. However, the uncertainty principle of quantum mechanics implies that at very short length and time scales, spacetime cannot remain smooth but must burst into a chaotic froth in which notions such as before and after and ahead and behind can lose their meanings. This "quantum foam" overwhelms any conventional theory of pointlike particles, causing it to go mathematically haywire. String theory avoids this problem because the strings are long enough to stretch over ripples and bubbles in the quantum foam. They ignore the effects of the foam much as a large ocean liner plows through the buffeting of small, choppy waves. As a quantum theory of gravity, string theory remains mathematically reasonable, as physicists have known since the 1970s. But it wasn't until Green and Schwarz ignited the "first string revolution" that physicists realized string theory might realistically account for particle physics, too. Within months, others found that if the six extra dimensions wound into a shape called a Calabi-Yau manifold, the theory came very close to producing the particles we see in nature, says string theorist Andrew Strominger from his office at Harvard University. "It was like hitting a golf ball from 200 yards away and coming within a centimeter of the hole," he says. "There was a feeling that it was going to take only one more shot to get it in." Twenty years later physicists have yet to pick up that gimme. For a while researchers hoped there would be only one way to curl up the extra dimensions--and, perforce, only one logically consistent explanation of all the forces of nature. But fairly quickly researchers realized that there were a great number of Calabi-Yau manifolds, Strominger says. And directly observing the putative strings would require collisions more than a million billion times more energetic than any that have been produced in a particle collider. Meanwhile, other researchers are tackling an entirely different problem: They're trying to use string theory to explain the accelerating expansion of the universe. In 1998, astronomers detected the cosmic speedup by studying distant stellar explosions called supernovae. The observations suggested that something is stretching spacetime. And that's precisely what Einstein had in mind 80 years earlier when he dreamt up a space-stretching energy called the "cosmological constant." Although Einstein later abandoned the idea, the cosmological constant now appears to be real, and string theorists hope to calculate its value. But that's not going to be easy, says Shamit Kachru, a string theorist at Stanford University in California. Most theorists assume that the cosmological constant is the energy trapped in the vacuum of empty space, which isn't zero because, thanks to the uncertainty principle, particles keep flitting in and out of existence. Basic string theory calculations yield vacuum energies that are many, many orders of magnitude too big. Moreover, each way of winding the extra dimensions corresponds to a different version of the vacuum. Work on moduli stabilization suggests that there are a whopping 10300 different stable vacua, and theorists have no way to choose among them. String theorists now talk of a vast, cratered "landscape" in which each dimple corresponds to a possible vacuum. "If this picture is correct," Kachru says, "then it's unlikely that we'll explain the cosmological constant in a simple way." Facing that landscape, some researchers are questioning what it will mean to make calculations and predictions. "In string theory as we know it, we can give up on making unique predictions because there are just so many vacua," says Scott Thomas, a particle theorist at Stanford University. Some, such as Thomas, favor measuring the statistical properties of the landscape and making more probabilistic predictions. A few prefer analyses that rely on the "anthropic principle," which essentially says that the cosmological constant can only have a value consistent with our own existence. Many seem to hope that some new principle or idea will point the way out of the conceptual wilderness. Even if they don't pay off immediately, renewed efforts to connect string theory to data are beneficial, researchers say. Such work opens lines of communication, says Eva Silverstein, a string theorist at Stanford University and the Stanford Linear Accelerator Center in Menlo Park, California. "There was a period when there was an almost ethnic conflict between string theorists and phenomenologists," she says. "The situation is a lot healthier now." Nevertheless, tensions still exist. For example, many string theorists point to the discovery of the accelerating expansion of the universe as the observation that gives them the best chance for making a connection with data. However, Raby, the particle theorist from Ohio State, says that for decades particle physics has provided far more data of far greater detail. "Since 1975, we've had a huge amount of information that everybody has ignored," Raby says. Even as some researchers struggle to connect string theory to experimental data, the theory itself continues to grow more complicated and mysterious. Ten years ago, researchers knew of five distinct types of string theory, which differed in, for example, whether the strings had to be closed loops. But in 1995, Edward Witten of the Institute for Advanced Study in Princeton, New Jersey, argued that all of them were different approximations of a single underlying theory he dubbed M-theory. It possesses yet another dimension and is filled not just with strings but with two-dimensional membranes and "branes" of three or more dimensions as well. This "second string revolution" reassured string theorists that they were all working on the same thing. But in some ways it leaves them even farther from their goal of a single, definite theory of the physical world. No one knows what M-theory really is. And no one can say when theorists are likely to find out. "How many more string revolutions will we need?" Caltech's Schwarz wonders. "I don't know, but I think we'll need many more." But that's probably acceptable to most of the researchers at the workshop, who seem genuinely pleased just to participate in such a grand pursuit. In the evening, they gather in the courtyard to grill steaks and hamburgers and to share a beer or a glass of wine. After dinner, the younger crowd engages in a spirited game of volleyball. Night falls, and a black bear wanders into the parking lot. Some people rush into the nearest building to get away from it; others rush out to glimpse the ursine intruder fleeing into the nearby sage and scrub. Its inky form quickly dissolves into the darkness like a phantom--or the dream of the ultimate theory. String Theory Gets Real--Sort Of |
November 28, 2004
Do the math: They need helpBY BEV MCCARRON New Jersey kids have a problem with math. And whether you use old math, new math or everyday math, it comes down to this: Students here still score noticeably higher on language arts portions of their closely watched fourth- and eighth-grade proficiency tests than the math sections. State data released this month show a gap of 10 percentage points between language arts and math on both grade levels. In fourth grade, about 72 percent of students pass math (it's 82 percent for language arts) and the passing rate falls to just under 62 percent in eighth grade (versus 72 for language arts). The problem gets worse when kids hit high school. Scores for 2004 are not yet available, but in the previous year, 80 percent of high school test-takers sailed though language arts, while just 66 percent passed math. "It doesn't appear to be a secret math scores are disappointing," said Richard Ten Eyck, assistant commissioner with the Department of Education. Troubled by these gaps across age groups, education officials are about to a appoint a task force to address the problem. Officials hope it will be as successful as an earlier effort on reading and writing that was credited with boosting scores. The new task force can expect to be confronted by several issues and agendas from classrooms and kitchen tables alike when it plows into the so-called math wars. On one side are traditional basic skills advocates. On the other are those who favor conceptual understanding and problem-solving -- the experts who say student improvement lies in teacher re-education. "People hate the way (math) was taught. It was boring. It was about skill and drill," said Eric Milou, president of the Association of Math Teachers of New Jersey and a math professor at Rowan University who is working with a number of districts to improve math skills. "We have to talk about how math should be taught." At its annual meeting Wednesday, the state school board is expected to set parameters for the 15- to 18-member task force, and it may name panel members. The state has long been troubled by lagging math scores, particularly in middle and high schools. The results of a pilot program last summer to help juniors who failed the state graduation test led the Department of Education to conclude that by the time a student gets to high school, it is too late to fix math deficiencies. Even with intensive remediation, most students still couldn't get over the math hurdle. Fixing the math problem, officials concluded, has to start in elementary school. EVERYDAY MATH Many districts already are changing curriculums, lengthening math periods and retraining teachers, beginning in the earliest grades. One district already boosting fourth-grade scores is Washington Township, Gloucester County. Its schools adopted a curriculum called Everyday Math, expanded teacher training and lengthened math periods. The new curriculum introduces young kids to algebra and geometry concepts through series of activities and games rather than by rote memorization of times tables or formulas. This year, the 9,600-student district is introducing a similar curriculum in middle school called Connected Math. The program stresses teaching math concepts by giving students problems and letting them work formulas that lead to answers, an approach that encourages analyzing a problem before trying to solve it. Recently in Cathy Sherry's sixth-grade class at Bunker Hill Middle School, students were getting a dose of geometry as they plotted a graph. For coordinates, the class had measured each student's arm span and height. "It isn't lecture," Sherry said, expecting the kids also would pick up on a pattern that showed that the size of a person's arm gives a good estimate of their height. "It's hands-on." Sixth-grader Kira Parkin likes the class, not only because she is given a different problem every day to work on with a partner. "I like figuring things out, getting stumped and finding the right answer," she said. Everyday Math is controversial in other states. California legislators, for instance, refused to fund the program. Washington Township and many other districts in New Jersey, including Montclair and Newark, are convinced that the problem-solving approach is better. It gives students a better understanding of how math relates to their daily lives, and better prepares them for later courses that demand higher-level reasoning skills, advocates say. Parents can have difficulty understanding the method. Earlier this year in Washington Township, a meeting on Everyday Math for parents of students in grades 2 to 5 drew 700. When the sixth grade held a similar meeting, 75 parents attended. "My parents are like, 'What?' They're having to learn (math) all over again," said sixth-grader Sara Palmerchuck. Rose Dindino, whose daughter Sabrina is in the second grade at Birches School, acknowledged some concern, at first. "It was not the way I learned,' she said. "But it seems to be working with my daughter. She enjoys math." It's too soon to see results in middle school but at each of the district's six elementary schools, math scores went up across the board last year over the previous year, rising overall from 75.6 to 82.5 percent. "We wanted our students to achieve higher, and to like math and to be comfortable and confident with math," said Bobbie Marciano, director of elementary education in Washington Township. FUNDAMENTAL DIFFERENCE Problem-solving curricula like Everyday Math and its dozen or so variations, worry others who fear that without drills and repetition kids won't master fundamentals of multiplication and addition. They also question whether elementary teachers are prepared to teach more advanced math theories. Districts using the problem-solving approach point out the method is more in line with thinking and reasoning skills measured on New Jersey proficiency tests and research also shows improvement on standardized test scores in general. The Department of Education's Ten Eyck said the task force would be unlikely to press any specific curriculum on schools. But the panel will be expected to identify curricula with a proven track record and make recommendations. A NEW APPROACH At the high school level, Mississippi mathematician Robert P. Moses, the architect of the Algebra Project launched in urban districts to raise the scores of minorities, has found a formula for success. He created his own nontraditional curriculum. But, he said, beyond switching math programs, districts also have to pay attention to class size and teacher preparation. Teaching in one of the Mississippi's poorest districts, he got 45 of his 46 students who have been with him since ninth grade to pass the state's proficiency test. He did it, he said, with smaller classes, longer class periods and a demand that teachers get a planning period to work together every other day. "It's not just, 'How do we get some better test scores?' There has got to be a real shift in priorities," he said. Do the math: They need help |
November 26, 2004
Einstein and businessRecently, I read a brilliant essay (Scientific American, September, 2004) comparing the genius of Isaac Newton and Albert Einstein that provided me a very interesting perspective on the challenges businesses (and societies) face and some direction on how at least some of us can handle the same. Without going into too much detail, the essay highlighted the contribution of Newton through his very "precise, mathematical survey of all phenomenon of the physical world -- from pendulums to springs to comets to grand trajectories of planets" and in the process "invented calculus, formulated the laws of mechanics and motion and proposed a universal theory of gravitation." However, Einstein "with his extraordinary and seemingly absurd postulates of special relativity and quantum mechanics, demonstrated that the great truths of nature cannot be arrived at merely [by] close observation of the external world. Rather, scientists must sometimes begin within their own minds, inventing hypotheses and logical systems that can only later be tested against experiment." The world we are living in seems to be undergoing very fundamental changes. These changes are manifesting demographically, politically, technologically, and sociologically. On account of these changes, new winners (and losers) are coming to the fore--whether in terms of countries, or companies, or even societies. Technologically, some incredible new developments (e.g. nano technology, fuel cells, bio-technology, to name a few) are now on the horizon of making a way out of hypotheses and laboratories to commercial applications within the next 15-20 years, perhaps fundamentally changing the way we live. As far as India is concerned, the changes are even more pronounced, be it in our demographics, education level, urbanisation, access to information, economic and social aspirations, or a desire to compete and integrate with the rest of the world. However, it is becoming increasingly complicated to predict the impact of such changes on specific businesses (or even countries, for that matter, if we take China as one example). Each time any effort is made using "classical" tools of observation and then applying "mathematical" models, something can change, and the result is like that of a kaleidoscope: the situation looks very different once again. With this rather long introduction, what is the point that I am trying to make? Essentially, it is to suggest that today's businesses need more Einsteins than Newtons. Classical management theory and marketing principles are likely to prove inadequate in the coming years for providing a direction to existing and new businesses. The most basic challenge would be to predict consumer behaviour, and consumers' perception of value. For instance, in the US, over 80 per cent of the population now periodically shop at one of the Wal-Mart stores / formats. At the same time, there are many in this group who splurge heavily on cosmetic surgery, personal care and stress relief therapy, luxury vacations, and gourmet dining. In India, consumers who otherwise own and drive the so-called C and D segment automobiles do not mind flying the deep discounted, no-frills Air Deccan or taking Apex fares while splurging thousands the same evening in lounge bars or replacing their mobile phones every six months even though their current models are perfectly usable. The same SEC A consumer households will bargain to the last 500 rupees while buying a new high-end TV or a Home Theater system, and at the same time, do not think twice when going out to watch the latest movie in an overpriced Multiplex and in the process spending many thousand rupees on a single evening out. Likewise, the impact of advances in communication, in computing power, in bio-technology, and in applications of nano technology in our day to day life will fundamentally alter the way we would buy and consume goods and services. Advances in computing / communication power are already creating new (and complex) product design, manufacturing, and marketing networks truly spanning the globe--for the first time in human history. Nano-technology promises to create radically different paradigms about creating products atom by atom, potentially ushering in a new "industrial revolution". Developments in biotechnology can literally impact the human race as we have known it through evolution. Modern-day business needs many Einsteins who can develop new postulates and invent new hypotheses and logic systems on how the consumers and the business environment would behave under these changes. Of course, this is easier said than done. At the very least, however, companies can create an internal environment that allows challenging conventional wisdom, and encourages highly lateral thinking for hypotheses generation. Iconoclasts have to be hired and given positions of importance. Boards have to be strengthened not with more accountants and "management" experts but with out-of-the-box thinkers and visionaries who can challenge current paradigms and prevailing management dogma. The CEO and her/ his strategists have to redefine their existing understanding of what businesses they are currently in, and would like to be in the future, which (global) market they should focus on, which (global) competitor (country or company) would challenge them, and what kind of (global) supply chain they should develop. Marketing professionals have to think beyond conventional market research and focus group studies. Alas, the very subject of market segments and segmentation has to be approached from a very different perspective wherein the classical determinants such as age, income, education, and profession may no longer be relevant or significant. New determinants could well come from behavioral sciences. Can this all be done? After all, in the last millennium, we have just seen two true geniuses as per this Scientific American essay! Probably it can--since for the very first time in human existence, it is becoming increasingly feasible to create global networks of human brains that can work in tandem and thereby possibly match or exceed the genius of an Einstein! Einstein and business |
November 26, 2004
Are we living in a virtual reality?Christophe Schmidt Is it all just a dream? Speculation that reality is nothing but an illusion, or simulation, or controlled environment, has been with us for thousands of years, most recently doled out as pop culture brain candy with the likes of the US film 'The Matrix'. But now two respected British scientists, physicist Martin Rees and mathematician John Barrow, are questioning whether all matter and mind we know is not the creation of some mega-supercomputer somewhere. "A few decades ago, computers were only able to simulate very simple patterns. They can now create virtual worlds with a lot of detail," Rees said. "In the future, we could imagine computers able to simulate worlds perhaps even as complicated as the one we think we're living in." Martin, an astronomer at the prestigious Cambridge University, dares a thought that could have been deemed far-fetched among serious scientists only a while back: "The question is: Could we be in such a simulation?" Mr Mega is watching you In this case, the universe would not be all-encompassing but only part of an ensemble Rees and Barrow call the "multiverse". Barrow, who also teaches as Cambridge, described in an academic article that it was long known that a civilisation slightly more advanced than our own could simulate "universes in which self-conscious entities can emerge and communicate with one another". In a much more computer-savvy society with vastly more advanced technology, "instead of merely simulating their weather or the formation of galaxies, like we do, they would be able to go further and watch the appearance of stars and planetary systems," he added. "Then, having coupled the rules of biochemistry into their astronomical simulations, they would be able to watch the evolution of life and consciousness." With the same ease that we humans watch the "life cycle of fruit flies", Barrow said, the machine masters of the universe could "watch the civilisations grow and communicate with each other, argue about whether there existed a Great Programmer in the Sky who could intervene at will in defiance of the laws of Nature they habitually observed". Theory meets approval The theory of the Cambridge pair of scientists has not met with widespread approval among peers, however. Seth Lloyd, professor of quantum mechanical engineering at the Massachusetts Institute of Technology (MIT), pointed out such a simulation would require an "unimaginably large" computer. Lloyd, in comments published last week in The Sunday Times, gave a jab to the duo, comparing them to a science fiction book with a cult following — Douglas Adams' 'The Hitchhiker's Guide to the Galaxy', which stars a supercomputer named Deep Thought. "The Hitchhiker's Guide is a great book but it remains fiction," Lloyd said. Are we living in a virtual reality? |
November 26, 2004
Peter TwinnTHE mathematician Peter Twinn became the first British cryptographer to decipher a message encoded by a German Enigma coding machine while he was working at the Government Code and Cipher School (GC&CS) at Bletchley Park during the Second World War. Fifty miles north of London, Bletchley was the wartime headquarters of Britain’s codebreakers. The Enigma decryption project there, conducted in secrecy and known as Operation Ultra, was instrumental in some of the greatest Allied coups of the war — from steering convoys through the U-Boat blockade of Britain to arranging the successful Overlord landings in Normandy on D-Day. Peter Frank George Twinn was born in Streatham, South London, the son of a senior Post Office official. He began his education at Manchester Grammar School and then went to Dulwich College. He went on to Brasenose College, Oxford, to take a degree in mathematics. He was then awarded a scholarship to study physics. In early 1939, he was well into his postgraduate studies when he saw a notice advertising unspecified jobs with the Government for mathematicians. At the time, Twinn was unsure what career would be of interest to him. Also, in that unsettled period after the Munich Agreement, international relations between the major European powers were tense and getting tenser. Twinn decided to reply to one of the cryptic advertisements, and upon doing so he was offered a job. He began as an assistant to Alfred Dilwyn (“Dilly”) Knox, who headed a team of codebreakers at GC&CS. An eccentric but brilliant character, Dilly Knox was the first British codebreaker to work on the Enigma cipher. Like most GC&CS experts, he was a classicist. But, as war loomed, GC&CS began employing mathematicians, as well as chess players and crossword experts. Twinn was in fact the first mathematician to join the team. Knox believed in throwing his new recruits in at the deep end. He gave Twinn a mere five minutes’ training before telling him to go and get on with it. The Enigma machine dated back to 1919, when Hugo Alexander Koch, a Dutchman, patented an invention that he called a secret writing machine. A little later, Arthur Scherbius, an engineer, was experimenting with this and similar machines and became enthusiastic about encryption machines that used rotors. He recommended them to Siegfried Turkel, the director of the Institute of Criminology in Vienna, who also became interested in them. In the meantime, Koch had set up a company with the hope of selling his encryption machine for commercial use. But industry was not interested. However, in 1926 the German Navy looked at the Koch machine. Senior officers were impressed with it and ordered a large number. The purchase of the device — called Enigma — was kept strictly secret. The Enigma machine was a very complicated instrument. It had a keyboard, like the ones used on a typewriter, containing all the letters of the alphabet. Each of the 26 letters was connected electrically to one of three rotors, each provided with a ring. Each ring also held the 26 letters of the alphabet. Further electrical connections led from the rotors to 26 illuminated letters. When an operator, enciphering a message, pressed a key, an electric current passed through the machine and the rotors turned mechanically, but not in unison. Every time a key was pushed, the first rotor would rotate one letter. This happened 26 times until the first rotor had made a complete revolution. Then the second rotor would start to rotate. And so on. When a key was pressed, a light came on behind the cipher text letter, always different from the original letter in the plain text. The illuminated letters made up the coded message. The system worked in reverse. The person decoding a cipher message would use an Enigma with identical settings. When he pressed the cipher text letter, the letter in the original plain text message lit up. The illuminated letters made up the original message. To make the codes more difficult to break, each of the rotors could be taken out and replaced in a different order. Also, the rings on the rotors could be put in a different order each day — for example, on one day the first rotor could be set at B, the next day at F, and so on. The military version of Enigma was provided with a plug board, like an old telephone switchboard. This allowed an extra switching of the letters, both before they entered the rotors and after leaving them. The plug board had 26 holes. Connections were made with wires and plugs. With three rotors and, say, six pairs of letters connected with the plug board, there would be 105,456 different combinations of the alphabet. In December 1938 the Germans added additional rotors (up to six) and the number of combinations increased dramatically. The Germans believed that messages sent on their most sophisticated Enigma machines were so well coded that they could not be decoded. But Twinn and his colleagues proved them wrong. In July 1939 GC&CS moved from London to Bletchley Park. The mansion in the park was used by the staff, but many other buildings had to be constructed to accommodate the large number of people who worked for GC&CS during the war. These temporary buildings were known as the “huts”. About 10,000 people worked at Bletchley. The core group was the small number of cryptanalysts trying to crack the Enigma machine; at the beginning, this group consisted of no more than ten people, with Knox and Twinn in charge. The British codebreakers had been working on the commercial version of Enigma, the easier of the two to break, during the 1920s and 1930s, and they had made much progress in breaking the military version. But Twinn and his colleagues were stymied because they could not work out the order in which the Enigma keys were wired up. In July 1939, a month or so before the war started, Knox and some others travelled to Poland. Polish cryptologists, some of whom were brilliant, handed over to their British colleagues key information about Enigma, including replica machines. The British discovered that Enigma machines were wired alphabetically: A to the first contact, B to the second, and so on. This was the order given in the diagram attached to the patent application. But Twinn and his colleagues thought it such an obvious thing to do that nobody considered it worth trying. In early 1940 Twinn made the first break into Enigma. This could have been done much earlier if only they had tried the alphabetical system detailed in the patent application. The ability to read German encoded military messages was of inestimable help to the Allies in winning the war. It was achieved largely because of the efforts of Twinn, Knox, Alan Turing (who later became the father of artificial intelligence) and others at Bletchley Park. Turing, a brilliant mathematician, developed a machine called the “bombe”, which speeded up the deciphering process by trial and error — a crucial development for the codebreakers. Twinn worked with Turing on breaking the German Naval Enigma. Their success helped allied convoys to avoid German U-boats. Knox worked on the German Army (Abwehr) codes, a task that Twinn took over when Knox became ill. This operation was crucial in the Allied campaign to deceive the Germans about their plans to invade Normandy in June 1944. The work of GC&CS, however, remained one of Britain’s best-kept secrets until 1974, nearly 30 years after the end of the war. After the war ended, Twinn worked for the Ministry of Technology, becoming director of hovercraft. He served in other government departments before being appointed Secretary of the Royal Aircraft Establishment (RAE), Farnborough. While at Farnborough, he became seriously interested in insects, using RAE’s sophisticated cameras to photograph them. He took a doctorate in entomology at London University, researching the jumping mechanism of the click beetle. In 1999 he co-wrote A Provisional Atlas of the Longhorn Beetle of Britain, which is still a standard reference book on the subject. He was also an accomplished musician on the clarinet and the viola. Twinn had a rare gift for painstaking and meticulous work, the most important ability for a first-class codebreaker. He was a very modest man who continually played down his crucial contributions to Britain’s war effort. His wife, three daughters and a son survive him. Peter Twinn, codebreaker, mathematician and entomologist, was born on January 9, 1916. He died on October 29, 2004, aged 88. Peter Twinn |
November 26, 2004
Q. What is the 13th root of a hundred-digit number? |
November 26, 2004
Determined to Fight AidsLillian Ikulumet Our hearts beat so fast as we walk up to the eighth floor of Bugolobi Flats for the long awaited interview with one of Uganda's Aid's activists Dr. Dickson Opul. We knock at the door and a tall, giant gentle man wearing black shorts, and a brown T-shirt ushers me and the photographer in. It's a Sunday and the atmosphere is homely, with some visitors in the house. We take to the black leather sofas, probably the only black item in the living room that is painted white with the floor tiled white. "I am Dr Dickson Opul," he says and introduces the other two male visitors in the house as colleagues. "I am sorry I am dressed lousily, but this is how I want my Sunday's to be, just a home man," he says cheekily. Prior to the interview I had heard about Opul as one of the many Ugandans who is an HIV/Aids activist but above all one of the few Ugandans who has addressed a US senate congress. Opul comes from a very big family, the Opul sons and probably from one of the largest clans in Lango called Okabo. He was born to catholic parents Solomon Opul (deceased) and Dorothy Agnes Arach in 1970. He is the first born with four sisters and four brothers. During Idi Amin's regime, Opul's family was exiled in Kenya where he spent the first 18 years of his life. He then took his elementary education in Kisoko Primary School, Kiswa were he was head of debating club in P7, St Mary's College Kisubi and then Makerere University medical school where he was the chairman of Livingstone hall. "Me I was born a leader and I always want to be a leader," he says. Opul says he grew up as a fighter but a quiet fighter. He always wanted to be the winner. Once a sports man, he played javelin and broke his arm, played football and lost his tooth, was a good chess player but got a problem with his eyes, so basically Dr Opul has resigned from active sports. "But I love chess very much except that my eyes can't stick to that chess board for long." At 34 Dr Opul is the managing director of Uganda Business Coalition on HIV/Aids (UBC), an organisation he set up in 2002 because of his interest in fighting against Aids. "My turning point was in HSC, I was a great mathematician, but had an interest in space engineering, but I later did medicine out of curiosity. "While a third year student in medical school, after getting to know what I wanted to know about the human body I got bored of doing medicine." He then felt like the challenge of medicine had diminished. "Probably I thought I knew it more than I had to and there was not much challenge but, I think the advent of preventing Aids created a new challenge to better understand life. So HIV/Aids renewed my interest in medicine." Opul says that at UBC they manage programmes and develop designs that need to get the impact of HIV/Aids in our society. They also try to reduce the mortalities associated with Aids. As a director he does both the technical and managerial roles. What inspired Dr. Opul to get into the field of prevention of Aids was in 1998 when he heard of people flocking to Masaka to swallow mouthfuls of sand with the hope of being cured. The loss of close family members inspired him even more to look into the problem in a much more detailed way. Being a fighter of the unknown motivates him. "This is a new disease, which sparked my curiosity. What I know does not stimulate me than the unknown. To know it and to overcome it is a unique challenge for me to look into." The doctor gave his very first talk on HIV/Aids when he was 19 when he was in Kyankwazi for military training in 1990-1991. "Afande Walusimbi and Afande Orita, I forget their second names, asked us in a gathering who knew about the disease of Aids. Amidst hundreds of people I put up my hand and started explaining about HIV. The comment I made was how HIV can be transmitted. "I then started to focus more on HIV/Aids while at university fourth year and that's the same year when I lost two brothers and an uncle to AIDS." Opul has since then addressed many congresses on HIV/Aids. He addressed the US senate congress in 2003, the partisan congress in America, Business School of Harvard and other gatherings in so many other countries. He is a widely travelled man who finds Barcelona, Spain an interesting place to stay. From that time Dr Opul got involved in organising various Aids conferences. He organised the first ever African Aids conference in 1995-1996 when he was the chairman of the medical Brain TRUST, a medical school programme at Makerere University. One of the most memorable moments in his life is when he travelled to Rwanda to look for a job in 1998 in a place called Kyangungu. On returning, the place was attacked by rebels and everyone died. He had survived. It's then that he got a job with Mark a big international Pharmaceutical to introduce antiretrovirals to people. He says there is a significant gap in addressing Aids in the private sector and a lot of focus is put on communities. His goal at UBC is to provide adequate services to all the people. He now cares for more than 3,000 people in his UBC treatment centres since the year 2000 and wants to reach to 20,000 more people in 3-4 years. "We are blessed because the government of Uganda through the leadership of Museveni has created a good working environment." As the interview is carried on Opul cuddles his five months baby girl Devine Dorothy Opul. Opul who is happily married to a beautiful lady, Caroline Asio Opul says that he wants to have as many as 12 children God willing. "I love children and I want to be a good father," he says. He admires President Gorge W. Bush. "He is a world leader who is ruling at the time the world is at cross roads and also his decisive strong character and personal values on family life makes me admire him." Besides his busy schedule, Opul is a family man, he spends all his Sundays at home after church. His daily schedules are always the same. He wakes up at 6 a.m. to go jogging. He then does computer work from 7-9 a.m. He then drives to the office and is there till 5 p.m. After that, its back home where he watches movies, his favourites being adventure, from 7 to 8 p.m. He is also a man who likes to read. He normally reads from 10-12 a.m. then does office work from 12-3 a.m. The doctor's advice to all is that there is a risk of Africans especially sub-Saharan Africa being depopulated or even completely wiped out due to HIV/Aids. "The signs are there but prevention is in our society, we should adopt to change. Nations should set up a standard moral code of behaviour. People should also turn back to God. I am a Christian and Christianity is the centre of all good moral codes." Determined to Fight Aids |
November 24, 2004
Want to be able to tell a real work of art from a forgery? Do the mathsBy Steve Connor Science Editor Scientists have created a computer that can tell the mathematical difference between a genuine work of art and a forgery by analysing features invisible to the human eye, paving the way to a new method of art fraud detection. The computer can also distinguish between the different contributions of apprentices who collaborated on a well-known masterpiece officially attributed to a single artist. Scientists said the technique meant academics could have a better understanding of the hidden contributions made by lesser-known artists. The researchers used a mathematical approach, analysing the statistical likelihood that a particular brush or pen stroke was performed by the artist. A similar mathematical approach powered by computer has been used to analyse the words in famous texts to see whether they were the sole creation of a well-known author. Henry Farid, associate professor of computer science at Dartmouth College in Hanover, New Hampshire, said the technique could be applied to fine art thanks to the widespread use of high-resolution digital imagery that collects up to 2,400 points of light in a single square inch of canvas. "We have been able to mathematically capture subtle characteristics of an artist that are not necessarily visible to the human eye," he said. "We expect this technique, in collaboration with existing physical authentication, to play an important role in the field of art authentication. Similar methods have been used to analyse works of literature. "We can find things in art work that are unique to the artist, such as the subtle choice of words or phrasing and cadence that are characteristic of a certain writer." Scientists had to program the computer with an artist's personal style of painting or drawing using digital images of masterpieces known to be the work of the same painter. The machine was then able to decide whether a new work it subsequently analysed was likely to be a forgery. Professor Farid and his colleagues analysed 13 drawings that had been attributed - at least at some time - to the Flemish artist Pieter Bruegel the Elder. The computer successfully distinguished between eight of the paintings known to be by the artist and five famous imitations by contemporary artists, including some by artists who intended to commit a forgery. A second part of the research, in the journal Proceedings of the National Academy of Sciences, analysed digital images of the Madonna with Child by the great Italian renaissance artist Perugino who became famous for his altar pieces. The way the faces of the six figures in the work were painted were analysed mathematically for similarities. That found the three on the left of the painting appear to have been the work of one artist, and the three on the right were different enough from all other faces to have been the work of different artists, probably Perugino's apprentices, a common practice in Renaissance art. Analysing brush and pen strokes mathematically will be used with other techniques, such as X-rays to see underneath a coat of paint, in determining a painting's authenticity, the researchers say. Want to be able to tell a real work of art from a forgery? Do the maths |
November 23, 2004
PURE SCIENCE, EXPO |
November 23, 2004
God or science?By Mark Sappenfield and Mary Beth McCauley DOVER, PA. – In the boldest strike against the teaching of evolution in more than a decade, the school board of this one-stoplight farming town has tilted its textbooks against virtually the entire scientific establishment - and brought home a lesson from this month's presidential election. By mandating that ninth-grade biology teachers include "intelligent design" in their instruction, board members set a precedent last month. Never before has a school district decided to offer intelligent design, which suggests that only the action of a higher intelligence can explain the complexities of evolution. Moreover, say observers, it is a sign of what's to come. Religious conservatives have battled against evolution theory in classrooms since the Scopes trial of 1925. Now, they are finding fresh purpose in the conservative resurgence so evident on Election Day, as well as in a new strategy of attacking evolution without mentioning God. The result is a handful of high-profile cases nationwide that challenge Darwin's place in the curriculum and presage a new offensive in America's culture war. "We're seeing a growing number of these cases," says Eugenie Scott, director of the National Center for Science Education in Oakland, Calif., a group that seeks to protect evolution education. "Certainly, with the greater confidence given to the religious right in the last election, we see no end in sight." Near Atlanta, in suburban Cobb County, the local school board demanded that teachers put stickers inside the front cover of middle and high school science books. They read, in part: "Evolution is a theory, not a fact." In rural Wisconsin, the Grantsburg school board voted last month to allow teachers to discuss various theories of creation in their classrooms, opening the door to intelligent design. Together with the decision by the Dover school board, the flare-ups point to an emerging trend - an escalating batttle against the teaching of evolution which has been building slowly for nearly two decades. Since the United States Supreme Court in 1987 outlawed the teaching of creationism in public schools on the grounds of separation of church and state, anti-evolution activists have all but dropped divine creation and instead focused solely on discrediting Darwin. That they are finding traction - especially in places like Dover - is not surprising. In Pennsylvania, a state where Red and Blue teeter in an almost perfect equilibrium, Dover is clearly on the Red end of the seesaw. While Sen. John Kerry scratched out a narrow victory in Pennsylvania in the Nov. 2 election, York County - which includes Dover - gave President Bush 65 percent of its votes. Traditionally agrarian, traditionally Republican, this is a town of small brick and clapboard houses, framed by autumnal arrangements of pumpkins and hay bales, and set amid rolling hills. It is a slice of the Midwest in the mid-Atlantic - the image of wheat-waving countryside perched on the edge of York's suburban sprawl. And today, a text known around here simply as the "panda book" has made Dover the local stage for a national drama. The book's full name is "Of Pandas and People," and it is the newest addition to the Dover science curriculum. It is not mandatory reading, says district superintendent Richard Nilsen, adding: "The teachers have a [different] biology book, and when they get to the origins of life, they state that if anyone wants to look at another book, they give them the 'panda' book." Those who take it will learn about intelligent design. Intelligent design steers clear of the claims made by creationists: that the world is roughly 6,000 years old and that life was created in its present form by God. Intelligent design accepts an ancient Earth and even embraces evolution. But where most scientists see a series of fits and starts - evolutionary trials and failures - eventually leading to life as we know it, proponents of intelligent design see the guiding hand of some greater wisdom. For example, natural selection is not enough to explain the "eerie perfection" of the genetic code, says John Calvert of the Intelligent Design Network, an advocacy group in Shawnee Mission, Kan. Something so flawlessly "designed" could not be the product of random actions, he says. Proponents of intelligent design make no claim to knowing the source of this order. No scientist "can use science to get to what that intelligence is," says John West of the Discovery Institute in Seattle, which backs intelligent-design research. But for much of middle America, it's easy enough to fill in the blank. "The book's going to be a good resource for children and parents who try to believe in God and be religious," says John Workman, whose daughter is a sophomore at Dover High. "God should always be in the country, and in the schools." To critics, his words provoke a collective "I told you so." Intelligent design, they say, is merely creationism in a lab coat. Dr. Scott calls it the evolution of creationism: "They're trying to find a strategy that will stand up in court, and they only have a chance if it is something as far away from religion as possible." Yet even Scott acknowledges that Mr. Workman has hit upon something deeper - a desire among many Americans that the cold facts of science not quench the spark of faith. It is the tendency of science to say, "God had nothing to do with it," she says, and for students therefore to think, "I can't listen to what the teacher is saying or I'm sinning." Intelligent design, it seems, would at least have science and spirit shake hands. Barbara Tubbs, for one, supports the curriculum, but only because it is optional. "[I believe] we came from God," says Ms. Tubbs, the mother of a freshman whose class is due to study evolution - and to be offered the panda book - in January. "But I wouldn't want to push it on anybody." Yet a fair amount of pushing might be required. Even here, intelligent design has rankled school board members. At one tumultuous meeting, a supporter of the change reportedly asked an opposing member whether she was "born again." After the plan passed, two board members resigned. In Cobb County, meanwhile, several parents have sued to make the district remove the "evolution is a theory" stickers. For their part, scientists don't feel that they can budge. Evolution is a theory only in the scientific sense of the word - like the theory of a sun-centered solar system, they say. The fact is, in contrast to the uncertainty about evolution among average Americans, scientists are nearly unanimous in their acceptance of it. To them, teaching anything else in classrooms as "science" is an adulteration of the word. Moved in large part by cases like those in Pennsylvania and Georgia, National Geographic recently ran a cover story headlined: "Was Darwin Wrong?" The first page of the article answered: "No." "Science has to be based on facts," says William Allen, editor of the magazine. "When you are talking about creationism and intelligent design, there is no scientific basis." Like many others, he agrees that a discussion of different creation theories could be suitable for social studies or comparative religion - just not science class. And to Dover parent Holly Martz, that sounds about right. Intelligent design, she says, is "intertwined with religion," and says if it is taught, the variety of religions should be taught. " If they present all the views, that's fine." God or science? |
November 22, 2004
Back to the Drawing BoardMIKE MESTERTON-GIBBONS Back to the Drawing Board Genetic and Cultural Evolution of Cooperation. Peter Hammerstein, ed. MIT Press, Cambridge, MA, 2003. 450 pp., illus. $45.00 (ISBN 0262083264 cloth). The question of how cooperation evolves is fundamentally a question of mathematical biology or sociology. Recent theory about cooperation has been overwhelmingly mathematical, and virtually all of the 40 contributors to the 90th Dahlem Workshop report, Genetic and Cultural Evolution of Cooperation, are in some sense mathematicians. Yet arguably the most striking feature of this four- part book is a virtual absence of mathematics. What could be the reason for that? Could it simply reflect that publishers like to sell books, and equations reduce sales dramatically? Could it just mean that brainstorming at a workshop is more conducive to talking than to doing? Or is it perhaps a sober reflection of how little we truly understand about the evolution of cooperation, despite decades of concerted effort? In a timely article, Michael Reed (2004) has reminded us that evolution makes mathematical biology hard for many reasons, including that a priori reasoning is frequently misleading, and that different species may accomplish the same task by different mechanisms, astounding in their variety. For example, that reciprocity can sustain cooperation has been demonstrated ad nauseam in theory; but there is surprisingly little evidence of such "reciprocal altruism" in nature, as editor Peter Hammerstein- lamenting the amount of energy invested "in the publishing of toy models with limited applicability"-protests in his personal contribution to part 1 of the volume. Indeed, as Joan Silk stresses, keeping score-and how can there be reciprocity without scorekeeping?- is a proven detriment to friendships. To be sure, reciprocity is not the only mechanism for cooperation that theoreticians have considered. There is first of all relatedness, but this book addresses only cooperation among unrelated individuals. Can such cooperation be sustained in humans, if not by reciprocal altruism, then by "costly signaling,""indirect reciprocity,'" or "genetic group selection"? The usual suspects are trotted out by Ernst Fehr and Joseph Henrich, but soon dismissed as unlikely perpetrators of "strong reciprocity"-defined to arise when one is willing to incur long-term net costs from helping another in response to a kindness. Of the known suspects, only "cultural group selection" survives pretrial scrutiny, to be revisited in part 4 by Peter Richerson, Robert Boyd, and Henrich. The evidence for such strong reciprocity, now seemingly overwhelming, is effectively evidence that animals-especially humans- are much more cooperative than game theory has predicted. So what have the models been neglecting? One good answer is psychological mechanisms. Daniel Fessier and Kevin Haley argue that "our emotions, long disparaged as both a reflection of our animality and the source of our irrationality, are... exactly the opposite, namely, the keys to our complexity, efficacy, and remarkable ability to cooperate," and they discuss the "thirteen emotions that seem to have the greatest impact": anger, contempt, envy, guilt, gratitude, righteousness, romantic love, pride, shame, moral approbation or outrage, admiration, elevation, and mirth. Their view is echoed by Edward Hagen, who argues that depression, far from being a mental illness, may be an adaptive emotional strategy. These and other themes (e.g., reputation) coalesce in the final chapter of part 1, a group report by Richard McElreath and 10 others on cognitive and emotional mechanisms that may sustain cooperation. Part 4 of the book, on cooperation in human societies, picks up a thread left dangling at the end of part 1. Richerson, Boyd, and Henrich propose that group selection on cultural variation is at the heart of human cooperation (though they acknowledge a role for other mechanisms); Peyton Young describes how social norms can coalesce from the decentralized, uncoordinated choices of many interacting individuals; Eric Smith emphasizes the importance of language's role in human cooperation; Bowles and Herbert Gintis discuss a special mechanism for human cooperation that stresses the role of gene- culture coevolution in group dynamics; and Henrich and eight others conclude with a group report. The book is a refreshingly candid portrait of what we know and- more important-don't yet know about the evolution of cooperation. Honest disagreements abound (e.g., between Smith and Boyd and Richerson over the importance of group selection in the evolution of human cooperation), yet there is at least a universal consensus that, as Silk puts it, "As always, more data and better models are needed." The group reports are splendid state-of-the-art summaries emphasizing open questions, unsolved problems, and directions for future research; and all agree that the challenges are considerable. Which brings us full circle to Reed, who has warned against doing mathematical biology to satisfy a desire to find universal structural relationships, because "you'll be disappoi\nted" (Reed 2004, p. 339). Is it therefore a strategic error even to seek a general theory of cooperation? That remains an open question, but if you want insightful perspectives on most of the relevant issues, I heartily recommend that you read this book. And even if now is not the time for a general theory, we mustn't forget that now is not forever. After all, when all is said and done, who will disagree with W. G. Runciman's categorical assertion that "our social behaviour is as reliably patterned as our individual behaviour is unmanageably diverse" (Runciman 2000, p. 88)?
References cited |
November 22, 2004
Computer grid to help the worldLaunched this week, the World Community Grid will use idle computer time to test solutions to these problems. The donated processor cycles will help the WCG create virtual supercomputers via the net. The idea follows the success of other similar projects that have used the untapped processing power of millions of desktop PCs. One of the most successful collaboration projects was Seti@home, run by the Search for Extra Terrestrial Life project, which sorted through radio signals looking for signs of alien communication. Anyone can volunteer to donate the spare time of their computers by downloading a special screensaver from the WGC website. Once installed, the virtual terminal gets a chunk of the computational task to process, and reports back after completing that task. The first WCG problem being tackled will be the Human Proteome Folding Project, which hopes to identify the ways that the proteins in our body fold. The subjects of study are being selected by an international advisory board of experts specializing in health sciences, and technology. The body will evaluate proposals from leading research, public and not-for-profit organizations, and is expected to oversee up to six projects a year. Organisations also represented on the board include the United Nations Development Programme and the World Health Organisation. "The World Community Grid will enable researchers around the globe to gather and analyze unprecedented quantities of data to help address important global issues," said Elain Gallin, program director for medical research at the Doris Duke Charitable Foundation. "[It] will inspire us to look beyond the technological limitations that have historically restricted us from addressing some of our most intractable problems", she added. IBM has donated the hardware, software, technical services and expertise to build the basic infrastructure for the grid. The computer company, working with United Devices, previously developed the Smallpox Research Grid, which linked together more than two million volunteers from 226 countries to speed the analysis of some 35 million drug molecules in the search for a treatment for Smallpox. Computer grid to help the world |
November 20, 2004
Flu season remains a mathematical mysteryA Hamilton mathematician predicts doctors will never know why the flu hits every winter. It’s a question that has long baffled scientists who have come up with theories ranging from people spending more time in close contact inside during the winter months to the virus living longer in cold temperatures to kids being in school. But so far, researchers have not been able to prove why roughly 90 per cent of influenza occurs from November to April. “There’s a lot of speculation about it,” said Dr. Mark Loeb, an infectious disease physician at Hamilton Health Sciences and associate professor at McMaster University. “But we’ve never seen a good explanation.” A good explanation may be impossible to find, said mathematician David Earn. His study published Monday in the U.S. journal Proceedings of the National Academy of Sciences uses a mathematical model to show that it would take a “hardly noticeable” change in conditions to cause the yearly spike that starts in Southeast Asia and makes its way to Canada each November. “The cause of the seasonal change could be so small that we’re never able to detect it,” he said. “That would not be the case for other diseases.” Earn, associate professor of mathematics at McMaster, found it would take a change of five per cent or less in the variables affecting flu to bring about large fluctuations in the number of people infected. Influenza is a common respiratory illness that infects 10 to 25 per cent of the population from November to April. It’s spread by droplets coughed or sneezed into the air by someone with the virus. Contrary to popular belief, it’s not characterized by vomiting. Instead, symptoms start with a headache, chills and cough and rapidly escalate to fever, loss of appetite, muscle aches, runny nose, sneezing, watery eyes, sore throat and fatigue. It usually lasts a week to 10 days, but some people, particularly the elderly and small children, can become severely ill and develop complications such as pneumonia. About 500 to 1,500 Canadians—mostly seniors—die every year from the flu. Flu season remains a mathematical mystery |
November 20, 2004
Unusual material that contracts when heated is giving up its secrets to physicistsSANTA CRUZ, CA--Most solids expand when heated, a familiar phenomenon with many practical implications. Among the rare exceptions to this rule, the compound zirconium tungstate stands out by virtue of the enormous temperature range over which it exhibits so-called "negative thermal expansion," contracting as it heats up and expanding as it cools, and because it does so uniformly in all directions. While engineers are already pursuing practical applications in areas ranging from electronics to dentistry, physicists have had a hard time explaining exactly what causes zirconium tungstate to behave in such a bizarre manner. Now, a team of researchers at the University of California, Santa Cruz, and other institutions has reported new insights into the atomic interactions underlying this phenomenon. A paper describing their findings will be posted online on November 22 and will appear in the November 26 issue of the journal Physical Review Letters. "We have shown that a combination of geometrical frustration and unusual atomic motions are likely to be important to the negative thermal expansion in zirconium tungstate," said Zack Schlesinger, a professor of physics at UCSC. Geometrical frustration sounds like something a high-school math student might feel, but is actually a rich area of research in physics and material science. In simple terms, geometrical frustration is like trying to tile a floor with pentagons--the shapes just won't fit together. In the case of zirconium tungstate, geometrical frustration comes into play during certain temperature-related vibrations of the compound's crystal lattice structure, the configuration of atomic bonds that holds the atoms together in a crystal. The normal thermal expansion of solids results from changes in the atomic motions that make up these lattice vibrations. As heating adds more kinetic energy to the system, the lattice structure expands (in most solids) to accommodate the increasingly energetic atomic motions. To study the atomic motions involved in lattice vibrations, physicists separate the vibrations into discrete "modes" or types of vibrations. In their investigation of zirconium tungstate, Schlesinger and his collaborators found evidence for a rotational ("twisting") mode that, due to geometrical frustration, occurs together with a translational ("back-and-forth") mode. This mixing of rotational and translational motion has the effect of pulling the overall structure together as heating puts more energy into the vibrations. In other materials that show negative thermal expansion, the vibrational modes that pull the solid together create instabilities that eventually lead to rearrangements in the atomic structure. As a result, the negative thermal expansion only occurs over a narrow temperature range. In zirconium tungstate, however, geometrical frustration appears to block any such instability. Schlesinger said he initially gave the project to an undergraduate working in his lab, Chandra Turpen. When she began finding anomalous results, graduate student Jason Hancock used mathematical modeling to help figure out what the results meant. "It started out as a senior thesis project that just became a lot more interesting as we went along," Schlesinger said. In addition to Schlesinger, Turpen, and Hancock, who is the first author of the paper, the other coauthors are Glen Kowach of the City College of New York and Arthur Ramirez of Bell Laboratories, Lucent Technologies, in New Jersey. Schlesinger said the findings are interesting with respect to both pure physics and practical applications. On the pure physics side, they seem to provide a new and unusual example of geometrical frustration, which is most often studied in the realm of magnetism and disordered systems such as spin glasses. "This material is not disordered--it is a perfect stoichiometric crystal--so we are seeing geometrical frustration manifested in a whole new system," Schlesinger said. On the practical side, thermal expansion is a big problem in many different areas. In dentistry, most cracked fillings are the result of uneven expansion and contraction--the so-called "tea-to-ice-cream problem." And engineers working on everything from electronics to high-performance engines must cope with the effects of thermal expansion. A material that did not expand or contract with changing temperatures would have broad applications. "If you could create the right mix of materials to neutralize thermal expansion, that would be quite a significant technological advance," Schlesinger said. Unusual material that contracts when heated is giving up its secrets to physicists |
November 20, 2004
New Sampling Method to Track HIV-Risk BehaviorNewswise — What's the best way to get a statistically reliable sample of people who are hard to identify, such as illegal-drug users in large cities, itinerant jazz musicians, aging Manhattan artists and semi-professional storytellers? Answer: Use a new "pyramid" sampling method developed by a Cornell University sociologist. The Centers for Disease Control and Prevention (CDC) will use the method to recruit injection drug users (IDUs) and measure their HIV-risk behavior in the 25 U.S. cities with the largest number of AIDS cases. The sampling method, called respondent-driven sampling (RDS), combines "snowball sampling" (identifying a set of initial respondents, who recruit their peers into the study, and each new set of respondents then recruit their own peers) with a mathematical model that weights the sample to compensate for the fact that it was obtained in a non-random way. "The statistical method enables researchers to provide both unbiased population estimates and measures of the precision of those estimates," explains Douglas Heckathorn, professor of sociology at Cornell. He developed RDS in 1997 for a National Institute on Drug Abuse HIV-prevention research project targeting drug users in several Connecticut cities. "When applied in a way that fits the mathematical model on which RDS is based, its results have proven to be unbiased for samples of meaningful size," he says. RDS is already used by the CDC's Global AIDS Program to survey IDUs in Bangkok and IDUs and commercial sex workers in Vietnam. It is also being used by Family Health International, the largest non-profit agency in international public health, in more than a dozen countries and provinces, including Bangladesh, Myanmar (Burma), Cambodia, Egypt, Honduras, India, Kosovo, Mexico, Nepal, Vietnam, Pakistan, Papua New Guinea and Russia to study gay men, IDUs and prostitutes. The National Institute on Drug Abuse also uses RDS to survey IDUs in several cities in Russia. RDS is now getting its first broad national use to survey IDUs as part of CDC's National HIV Behavioral Surveillance System. (The CDC is part of the U.S. Department of Health and Human Services.) Heckathorn notes that drug injection was related to about 15 percent of new HIV cases reported in the United States in 2002 and accounted for nearly 20 percent of new cases among women. "This new system will provide the first nationally comprehensive estimates of HIV risk behaviors among IDUs, thereby providing the detailed information needed to determine where new interventions will be most effective and where current interventions are working best," Heckathorn says. Heckathorn notes that RDS improves upon standard probability sampling methods because it reaches members of the target population that would otherwise be overlooked. "For example, while drug injectors could be sampled from needle exchanges and from the streets on which drugs are sold, this approach misses many women, youths and those who only recently started injecting," says Heckathorn, who has published a study using RDS to sample jazz musicians in four cities, is now preparing to apply RDS to aging artists and to storytellers. He is completing a book on RDS while serving as a visiting scholar at the Russell Sage Foundation. A similar problem faced pollsters during the recent presidential election. "Phone-based polls were not able to access voters who had abandoned land-based phones in favor of cell and Internet phones or voters who merely refused to be interviewed," Heckathorn notes. "What little was known about these inaccessible voters showed that they were not the same as other voters; for example, they tended to be younger." Pollsters, he says, had no way of knowing how to adjust their estimates to compensate for voters they had missed. "Similarly, public health researchers had no reliable way before RDS to determine how those they could access through location-based sampling differed from those who were inaccessible." New Sampling Method to Track HIV-Risk Behavior |
November 18, 2004
X = not a whole lotJohn Allen Paulos George Bush's election has generated far too many ill-founded conclusions about the US electorate. Despite Bush's assertions to the contrary, the voters certainly did not give him a mandate to further "traditional moral values" (or, indeed, to do anything else). No deep theorem in arithmetic is needed to see that the 51% of the electorate who voted for him constitute a bare majority. The outcome looks even more questionable in the electoral college. Bush received approximately 130,000 more votes than John Kerry in Ohio, so if 65,000 Bush voters in the state had switched, we'd now be talking about president-elect Kerry. Looking back over recent elections strengthens the view that no seismic realignment of the electorate has occurred. Of the last four presidential elections, the Democratic candidate has received a greater popular vote in three and a greater electoral vote in two. Excuse my mathematician's obsession with coin flips, but consider this. There is a large bloc of people who will vote for the Republican candidate no matter what, and a similarly reliable Democratic bloc of roughly the same size. There is also a smaller group of voters who either do not have fixed opinions or are otherwise open to changing their vote. To an extent, these latter people's votes (and thus elections themselves) are determined by chance (external events, campaign gaffes, etc). So what conclusion would we draw about a coin that landed heads two or three times out of four flips (or about a sequence of two or three Democratic victories in the last four elections)? The answer, of course, is that we would draw no conclusions at all. One reason we tend to draw far-reaching conclusions about elections is the charming superstition that significant events must be the consequence of significant events. This psychological foible is illustrated by an experiment in which a group of subjects is told that a man parked his car on a hill. It then rolled into a fire hydrant. A second group is told that the car rolled into a pedestrian. The members of the first group generally view the event as an accident; the members of the second generally hold the driver responsible. People are more likely to attribute an event to an agent than to chance if it has momentous or emotional implications. Likewise with elections. Another argument against the claim that the electorate has undergone a drastic change derives from so-called statistical regression models. One of the most cited models of this type was constructed by Yale economist Ray Fair and is based on six factors. The first is incumbency, which has been a distinct advantage historically. The second is party (Republicans have a slight historical edge), and the third is "party fatigue" (two or more terms out of power offers some benefit). The remaining three factors concern the economy: GDP's per capita growth rate (higher is better for the incumbent), the number of quarters during the preceding four years in which the growth rate exceeded 3.2% (the more, the better), and the inflation rate (lower is better). On the basis of these six factors, Fair's model has generated quite accurate vote percentages in presidential elections dating back to 1916. (It should be noted, however, that a degree of after-the-fact torturing of the data to reveal meaningless correlations can make a model appear more impressive than it is. Predicting the past isn't too difficult). In 2004, Fair's regression model (and several others) predicted that the election wouldn't even be close, that the incumbent Bush would win somewhere around 58 per cent of the vote. If we give more credence to Fair's model than it perhaps deserves, the fact that Bush won only 51% of the vote can be interpreted optimistically, at least by Kerry supporters. Fully 7% of the electorate - 8 million voters - resisted the compulsions of incumbency and the economy to vote for Kerry. Moderately impressive, if true. In any case, my meta-conclusion is that there are no very compelling conclusions to be drawn about the electorate. Bush received more votes than Kerry. Period. I don't think this simple fact means the country supports the Bush agenda. X = not a whole lot |
November 18, 2004
Knotty four-decade-old math problem solved by team including UGA professorIt's not as famous as Fermat's Last Theorem. In fact, the math problem, which has not had a correct solution since it was proposed in the 1960s, doesn't even have a name. But a new, elegant solution for the unnamed 40-year old problem has intrigued scientists enough to be published in a two-part paper in one of the world's top math journals. Dino Lorenzini of the University of Georgia and two French colleagues, Michel Raynaud and Qing Liu, recently published the mathematical foundations for the new proof in the journal Inventiones Mathematicae and will soon published the proof itself. "What makes this problem possibly unusual," said Lorenzini, "is that two mathematical mistakes in the literature had to be corrected before the problem could be correctly solved." Intractable problems in mathematics have long had an allure for the general public. Fermat's Last Theorem, a significant hypothesis in number theory, was first stated by Pierre de Fermat, a 17th-century lawyer and amateur mathematician. The proposition was discovered by his son Samuel while collecting and organizing the elder Fermat's papers and letters posthumously. It took more than 350 years for mathematicians to solve the riddle, and that solution made front-page news worldwide. The problem solved by Lorenzini and his colleagues is much more difficult to explain. In its simplest form, it is about understanding certain arithmetically interesting points (x,y) on a curve. To study such a problem, mathematicians have ascribed to any curve C two special groups, called A and B, and first defined in the 1960s. Mathematical groups come in all sorts of shapes, sizes and patterns. Some are infinite, some are finite, some are big and some are small. They lie at the heart of attempts to classify what is going on in pure mathematics and in applications to chemistry, physics, biology and just about any subject using modern mathematics. In modern number theory, one understands the solutions, in whole numbers or fractions, to equations by understanding, in part, the special groups that underlie them. The conjecture is that the groups A and B always contain a finite number of elements. Despite the fact that top mathematicians believe this statement, until now, no one has been able to prove it, and this statement remains a major open problem in the field. Lorenzini and his colleagues assumed that the number of elements in the group B is finite, and they were then able to demonstrate under this hypothesis that the number of elements in Group B can only be a perfect square. ("Square" here refers not to a geometric figure but to the product of whole numbers multiplied by themselves, as 1, 2, 3, 4 'squared' give 1, 4, 9 and 16, for instance.) "Since mathematicians assumed that the groups A and B are finite, they have tried to compute the number of elements that such a group could contain," explained Lorenzini. "They believed in the early sixties that the number of elements in group A could only be a perfect square and, at the same time, they believed that the number of elements in group B wasn't always a perfect square." This view held for some 30 years, but in 1996, the edifice started to crumble. The Japanese mathematician Toshuke Urabe revisited group B and found a mistake in previous work. Three years later, Bjorn Poonen of the University of California at Berkeley and Michael Stoll, a German scientist, found an example in which the number of elements in group A is not a perfect square. "This was quite a reversal of fortune for these groups after 30 years," said Lorenzini. Earlier this year, Lorenzini, Liu and Raynaud produced and published a precise formula relating the number of elements in groups A and B. Using this formula and the work of Poonen and Stoll, they were then able to show that the number of elements in group B is always a perfect square. That part of the proof will be published soon, also in Inventiones Mathematicae. While Lorenzini cheerfully admits that the new solution doesn't have the cachet of Fermat's Last Theorem and "isn't a Fields Medal winner" – the equivalent of a Nobel Prize in mathematics –the proof nonetheless is drawing delighted interest from mathematicians. "What makes it interesting is the twist in the story," said Lorenzini. "It is not often in mathematics that two major assumptions on the same subject are corrected only after 30 years. But the real issue is that the groups A and B are so important and so difficult to study that any advance in this area is of interest to mathematicians." Knotty four-decade-old math problem solved by team including UGA professor |
November 18, 2004
Why Students Dread Mathematics, Science - ExpertsBayo Adeleke The fear of Mathematics, for many, is not the beginning of wisdom or is it? Some experts meet in Lagos at the weekend to deliberate on this question and proffer answers to it. At all levels of education, the population of those who dread Mathematics and Science subjects outnumber those who love the subjects. To some, the fear of mathematics is the "beginning of wisdom." As dreadful as Mathemathics and Science subjects are to some people, few still derive pleasure from them. They can forefeit their time for merry-making to solve an equation or tackle a stubborn theorem. If Mathematics had not been made compulsory by the government, irrespective of the course of study in higher institutions, many would have avoided it like a plague. But what is wrong with the subject or even the students? Is it the scheme, the textbooks, methodology of teaching, the Nigerian environment or what? These were some of the questions for which answers were sought at the maiden edition of the Science Week of the Salvation International Nursery and Primary School (SIS), held in Lagos at the weekend. With the theme 'Making Mathematics and Science More Friendly to the Pupils,' the workshop was attended by experts in education administration from higher institutions, members of the Mathematics Teachers Association (MAN), Nigeria Dyslexia Association. Speaking on the theme, Dr. (Mrs) Temi Busari of the Faculty of Education, Department of Science Education, University of Lagos (UNILAG) advised that teaching of Mathematics and Science subjects must be from primary school. According to her, the reasons pupils dread Mathe-matics and Science include learning disability, poor learning strategies, inability to develop the pupils' inquiry skills by parents and ineffective teaching. Others, she said, include too much emphasis on curriculum content, examination and textbooks. Overburdened national curriculum and engendering of negative attitudes towards Mathematics and Science. Explaining further, Busari said poor science culture in schools, too much distance between the science teacher and the pupils, peer attitudes and perceived difficulties among others are reasons for lack of interest in the subjects. Since the burden cannot be borne by teachers alone, parents were advised to join in the efforts at making Mathematics and Science more friendly to the pupils. She enjoined publishers to provide reading materials based on general curriculum for all pupils irrespective of contexts, background and needs. To arouse pupils interest, she further stressed, they must be motivated and taught learning strategies and life skills. Emphasis should also be placed on action research, promotion of meta-cognitive environment and Information Communication Technology (ICT). While praising teachers for their efforts, she said they must be well remunerated for effective and better performance. Principal, Badagry Senior Grammar School, Lagos, Mr. Moronfolu Ojutiku described Mathematics as the accepted language of science and the means of communication in the technological world. According to him, the world is moving fast and we must catch up with the train, hence the need to correct the perception and apathy towards Mathematics and Science. "This will remove the jinx affecting our development and we shall be reckoned with in the comity of developed and industrialised nations of the world," he said. To make the subjects more interesting to the pupils, Ojutiku said teachers should be prepared to explain the content of the subject matter through experiments, demonstrations and models, adding that they must be creative, innovative and inspiring. When teachers are warm, flexible and gentle disciplinarians, Ojutiku observed, students respond with more expression of feeling, open participation in the classroom and independence. He added that they must provide answers to questions asked, while pointing out that Mathematics and Science should be taught with audio-visual aids, required apparatus for the pupils and exposure through excursion to industrial concerns to aid learning. While advising the pupils to be diligent, determined, dedicated and desire good results, Ojutiku enjoined parents to continue to provide for their children, as well as impact positive values on them. He also charged them to promote good health and cultivate cordial relationship among everybody in the school, saying it was a wise mother who asked her young son after schoo not "what did you learn today?", but "what questions did you ask today?" To ensure good performance, Ojutiku said school should create a good rewarding system that would encourage and motivate the teachers and pupils to greater heights, saying this will encourage merit and hard work. Dr (Mrs) Ngozi Okafor of the Department of Science Education, Federal College of Education Technical), Lagos said the theme of the seminar was a topical issue that should be of interest to those who believe in the future of children and who share in the faith that they can still be salvaged from their present dread of Science and Mathematics. Okafor said the changing trend in science globally and the need for Mathematics call for an aggressive encouragement of children not to dread the subjects but be friendly with it. Okafor said as emphatic as promotion of Mathematics and Science education at grass root is stated in the new National Policy on Education (1998) through the launching of "Catch Them Young", pupils still dread the subjects because to some of them, Science and Mathematics are unreal, vague, uninspiring and meaningless to the real life situation. For the aims and objectives of the policy to be realised, Mrs. Okafor said it was imperative to lay a firm foundation of Science and Mathematics at the primary school level. "Today we live in a world dominated by Science, Technology and Mathematics without which, development in other sectors of the economy is bound to be difficult positively or negatively.... It is very instructive that children should be more prepared for such a world which may even become more exciting, challenging and explosive in the near future," she said. For the Nigerian child not to dread Science and Mathematics, Okafor stressed, he or she should understand more about his or her environment. Science should be culturally based, while the teaching and learning should be on prior knowledge of children and their environment. "Since Science and Mathematics are integral part of man's daily activities, children should be given the opportunity to experience science and mathematics by doing, seeing, touching, tasting and smelling," she said. She added that parents, Headteachers and teachers must play specific roles in assisting pupils to develop a more favourable attitude towards the subjects. While lamenting that our education system contributes a lot to the fear of Science and Mathematics, as more emphasis is placed on certificate rather than acquisition of knowledge, Okafor also said it was sad to note that the curriculum which has been in place for over seven years is yet to be revised. To ensure that children develop much interest in science and mathematics and not otherwise, she said the curricula being taught must to be relevant to the needs and aspirations of the learners. Headteacher, Salvation International Nursery and Primary School, Mrs. Ifueko Thomas said in her welcome address that there was a desperate need for everyone to get involved in the development of pupils. She said having discovered that the interest in Mathematics and Science subjects is going down because of the way pupils are been taught, the school had to seek expert advice on the way forward. "My experience on the subjects when I was in secondary school prompted the decision to see how the fear of the subjects can be reduced. Why Students Dread Mathematics, Science - Experts |
November 17, 2004
When worlds collideMarcus Chown In astronomical circles, it is pretty much official. The Moon was created when a body about the size of Mars slammed into the newborn Earth. In the cataclysm, the molten iron core of the impacting body sank to the Earth's core while its molten mantle splashed out into space to form a ring of debris. This congealed into the Moon. The Moon, originally about 20 times closer to the Earth, gradually moved out to its current location. This "Big Splash" picture, proposed by William Hartmann, Al Cameron and their colleagues in 1975, is very well-received. For instance, it explains why the Moon contains essentially no iron. Unfortunately, it has a big problem. It concerns the body that collided with the Earth. "Where did it come from?" says Richard Gott of Princeton University in New Jersey. "The clues suggest a seemingly impossible location." One such clue comes from comparing the composition of the Earth and Moon. Cosmologists are pretty sure that the disc of swirling debris from which the planets congealed had a different composition at different distances from the newborn Sun. The Mars-mass body would, therefore, not have had the same make-up as the Earth. In the impact, the Earth and Moon would have been contaminated by different amounts of this material, which means, when we examine terrestrial and lunar rocks, we should see marked differences in composition. "The bizarre thing is, we don't," says Gott. Take oxygen. It comes in three types - oxygen-16 and two heavier and rarer types, oxygen-17 and oxygen-18. The relative proportions of these are like a chemical "fingerprint". The prediction of the Big Splash scenario is that the Earth's oxygen fingerprint will be quite different from the Moon's. But it isn't. It's pretty much identical. The oxygen evidence forces the conclusion that the body that hit the Earth and created the Moon formed at exactly the same distance from the Sun as the Earth. This is also indicated by computer simulations of the birth of the Moon, which show that the impactor came in at relatively low speed, characteristic of bodies in the Earth's vicinity. "But if the impactor formed at the same distance from the Sun as the Earth, there is a big problem understanding how it ever managed to grow as big as Mars," says Gott. The accepted theory of the birth of the planets is that they gradually "accreted" from debris pulled in by their gravity. The bigger they got, the stronger was their gravity and the more matter they pulled in. Since it is a process in which the rich get richer and the poor poorer, the impactor should have been gobbled up by the proto-Earth long before it reached the mass of Mars. So, why wasn't it? Gott set out to solve the puzzle with Princeton colleague Edward Belbruno. They began by asking: is there some special location at the Earth's distance from the Sun where a body could grow to the mass of Mars? Immediately, they realised there is. In fact, there are two places. These are the "Lagrange-4" and "Lagrange-5" points, whose existence was first suggested by the French mathematician Joseph Louis Lagrange in 1772. One lags 60 degrees behind the Earth as it orbits the Sun and the other precedes the Earth in its orbit by the same amount. At the Lagrange points, all the forces in the Sun-Earth system miraculously balance each other. What's more, any slow-moving debris that happens to find its way there becomes hopelessly trapped in a kind of interplanetary Sargasso Sea. Gott and Belbruno say the Lagrange points are places where matter would naturally have accumulated and where a body could have grown in peace without being affected by the fast-growing Earth. Eventually, when it had reached the mass of Mars, the gravity of other embryonic planets in the Solar System, such as Jupiter, would have tugged it repeatedly, perhaps over millions of years, until it was ejected from the Lagrange point. In computer simulations, Gott and Belbruno have followed the subsequent course of events. They find nothing can prevent the inevitable - a titanic collision with the Earth. Everything appears to fit. The impactor comes in on a low-velocity orbit, delivering a glancing blow on the Earth. Gott and Belbruno's simulations show that, in a quarter of encounters, the end result is a body exactly like the Moon. If Gott and Belbruno are right, the Earth had once had a planetary which shared its orbit round the Sun. "It's a clever idea which would solve some obvious problems," says Carl Murray of Queen Mary University in London. But he thinks work still needs to be done to prove it. The most interesting consequence of Gott and Belbruno's scenario is its implications for our prospects of finding extraterrestrial life. The Earth has the biggest moon compared to its size of any planet in the Solar System (Pluto also has a big moon but is rarely considered a full-blown planet nowadays). And a giant moon has been important for the evolution of life. The Earth, for instance, spins around its axis like a top. And, in common with all tops, it has a tendency to wobble wildly. Such wobbles would cause severe changes in the Earth's climate, with grave consequences for life. But every time the Earth tips too far over on its axis, the Moon's gravity rights it. The Moon has, therefore, ensured a relatively stable climate for the evolution of life over billions of years. And this is not the only way that the Moon has been important in the evolution of life. The tides created by the Moon, which are three times bigger than those created by the Sun, leave large areas of the ocean margins high and dry twice a day. Hundreds of millions of years ago, this enabled marine creatures to gradually adapt to arid conditions - the first step in the conquest of the land. But the Moon's key importance in the evolution of life has a depressing consequence for our prospects of finding ET life. The reason is that the kind of collision needed to create a big moon has always seemed an extremely unlikely event. Gott and Belbruno don't see it like that. They say that the formation of a large Mars-mass body at one of the Lagrange points of other planetary systems may not be that uncommon at all. And, since their simulations show a big moon created in a quarter of cases, the formation of a big moon may be more likely than anyone expected. They even speculate that there may exist planetary systems in the Galaxy, where two or more terrestrial planets have big moons. Is there any way of proving Gott and Belbruno's scenario? At first sight, it would appear to be difficult. After all, the Moon was formed in a tremendously violent manner and the impactor was utterly destroyed. It would be highly unlikely that any unprocessed material from that time could have survived to the present day. "But perhaps not impossible," says Gott. Gott and Belbruno point to an asteroid, or chunk of interplanetary rubble, discovered in 2002. "2002 AA29" is barely the size of a football pitch and is currently in a orbit which periodically brings it within a mere 5.8 million kilometres of the Earth. The peculiar orbit is very similar to the one the impactor that created the Moon would have been in 4.55 billion years ago. "You have to ask yourself, how did 2002 AA29 get in that orbit?" says Belbruno. An intriguing possibility is that it might have been associated with Lagrange-4 or Lagrange-5 in the distant past and at some point was kicked out. If so, 2002 AA29 may carry the imprint of the material from which the impactor and the Earth were formed. Bizarrely, 2002 AA29 has been picked out by planetary physicists as an asteroid that would be relatively easy for a space probe to visit. Gott and Belbruno suggest that a mission to return a sample would be most interesting. If it found iron and material with the same oxygen fingerprint as the Earth and Moon, it would support the Lagrange point scenario. If it contained no iron, it could be a bit of the splashed out material from the impact that formed the Moon. "Either way, we think 2002 AA29 could tell us about the origin of the Earth and Moon," says Gott. "It may be the most valuable chunk of rock in the Solar System." When worlds collide |
November 17, 2004
Do the MathBY DEANNA JENT Nearly insane females seem to intrigue Stray Dog Theatre's artistic director Gary Bell: past productions featured the Wingfield women of The Glass Menagerie, the religiously "touched" Agnes of God and the pill-popping Harper in Angels in America. Bell inaugurates his third season with David Auburn's Tony and Pulitzer Prize-winning Proof, whose central character is Catherine, a mathematician's daughter seemingly on the verge of a breakdown. (He will continue featuring almost-crazy women in his next production, A Streetcar Named Desire, with the most famous of Tennessee Williams' mentally fragile Southern belles, Blanche DuBois.) In both Agnes and Angels, Bell overemphasized the mental frailty of his female characters. Proof does not escape this tendency to push actresses into exaggerating their symptoms of mental instability, and as a result the play's crucial relationship is rendered more confusing than compelling. Having cared for her mentally ill father for more than four years, Catherine is understandably depressed and tired. His death frees her from stifling responsibility but forces her to face the future. Kelley Ryan plays Catherine initially as an unformed lump of exhaustion, slumping in shapeless clothes in an old rocking chair. She is credibly lost in her inner world, but her vocal inflections are oddly flat. When forced to face reality in the character of Hal, one of her father's former students now anxious to study the mathematician's final writings, she doesn't emerge enough to make any connections with him. Andrew Zaruba gives Hal enjoyable energy and passion; he's a complex character who is both intelligent and hip (and doesn't wear a pocket protector). The play's crucial mystery -- whether Catherine wrote a brilliant new mathematical "proof" or stole it from her father -- is thankfully short on actual math and strong in dramatic tension. But this vital element isn't introduced until the final moment of the first act, which means that the development of Catherine and Hal's relationship is what must intrigue the audience for the first half of the play. Ryan and Zaruba portray their characters realistically, but Bell's direction fails to create a believable romance between them. The math problem and the theater problem are the same: The real work in fleshing out a mathematical proof is in making clear and compelling connections between seemingly disparate elements. The trick in making this Proof successful lies in precisely the same thing. Do the Math |
November 17, 2004
No place to hideA high-tech arms race is heating up between spies and their targets. As the West monitors millions of phone calls and emails, terrorists find new ways of hiding information. Deborah Snow reports. The TV image of the laughing Bali bomber, Amrozi, might have tempted some to think of him as a simple son of the Indonesian soil, and Osama bin Laden strikes the pose of an old-time patriarch in his cave. But despite their medieval take on theology, there's nothing unsophisticated about the grasp which terrorism networks have on today's communications revolution. This year, Singapore's Home Affairs Minister, Wong Kan Seng, revealed his agents had found encrypted documents on computers seized from members of Jemaah Islamiah. Encryption, or cryptography, uses mathematical algorithms to "scramble" communications so they are meaningless to anyone who doesn't have a numerical "key" to decode them. Once the preserve of intelligence agencies and the rarefied world of applied mathematics, high-grade cryptography started to become widely commercially available a decade ago. Peter Coroneos, the chief executive of the Internet Industry Association, says the US tried at one stage to stop encryption technologies from leaving the country, "but once this stuff became commonly available on the net, the genie was out of the bottle". These days intelligence experts talk of a new kind of cyber arms race under way between the spy agencies and those who want to elude the eavesdropping net. Dr Alan Dupont, a former intelligence analyst now with the Lowy Institute for International Policy in Sydney, confirms "there is no doubt that the intelligence agencies would be very happy if a lot of this off-the-shelf, high-grade cryptography was not available. Unfortunately it is, and terrorists are availing themselves of it." A senior intelligence insider states grimly that "it was a problem 10 years ago, it's a problem today, it will be a problem in another 10 years. It's a game of chase, catch up, run ahead, and chase all over again." The difficulty for government is that the art of encryption also serves legitimate purposes. The world of e-commerce would collapse if companies couldn't encrypt customers' financial data. Protecting this while ensuring law enforcement and intelligence agencies have a window into the exchanges of those plotting terrorism or other crimes in cyberspace remains an unresolved dilemma. In Australia, a glimpse of the agencies' concerns came in a report prepared by a former deputy head of ASIO, Gerard Walsh, in 1997. The report, first suppressed then censored by the Federal Government, turned up later in an uncut version in a university library. It revealed the warning that "strong encryption, which cannot be defeated by law enforcement and national security agencies, is already ... in the public domain". More recently, this year's report on the intelligence agencies hints at ongoing frustration by government eavesdroppers. "Individual access to communications that are instantaneous, diverse and robustly encrypted" could impose "great difficulties and costs on intelligence collection", the author, Philip Flood, wrote. He warned that the Defence Signals Directorate (DSD), Australia's top code-cracking agency, was encountering limits to its ability to "exploit collected communications". This carries echoes of the complaint by the head of America's National Security Agency (NSA), Michael Hayden, three years ago that "we're behind the curve in keeping up with the global telecommunications revolution ... [It is] literally moving at the speed of light". However, Professor Des Ball, of the Australian National University and Australia's foremost expert on signals intelligence, believes the NSA has made dramatic progress in some areas since then, particularly in monitoring previously impenetrable fibre-optics traffic. Australia's DSD works closely with the NSA. Together with the Defence Imagery and Geospatial Organisation it forms part of a global eavesdropping and intelligence-sharing club run by the US, Britain, Australia, Canada and New Zealand under the decades-old "UKUSA" agreement. These five countries - but especially what some intelligence hands refer to as the most closely interconnected "three eyes" (the US, Australia and Britain) - run a matrix of spy satellites, satellite and radio listening facilities, undersea listening devices and eavesdropping spy planes to monitor the world's phone, radio, telex, fax and internet traffic. Australia's contribution is a ring of powerful satellite and radio intercept ground stations. The main ones are at Pine Gap in Central Australia, Cabarlah in Queensland, Kojarena near Geraldton in Western Australia, Shoal Bay in the Northern Territory, and the newest, the little-known DSD Riverina station near Wagga Wagga in NSW. There are also regular forays by RAAF Orion reconnaissance aircraft equipped with the latest surveillance equipment. To this the Federal Government wants to add a fleet of US-supplied aircraft, the Global Hawk unmanned aerial vehicles, which can be packed with listening and imaging equipment. Worldwide, the sheer scale of the information siphoning operation threatens at times to overwhelm the agencies. The NSA chief, Michael Hayden, admitted to a US intelligence committee that "the volume, variety and velocity of human communications makes our mission more difficult each day...". While DSD monitors communications traffic outside Australia, inside the country the task of intercepting communications is left to ASIO and the police, who may only do so under judicial warrant. Their job was made easier in 1997 when the Federal Government began compelling telecommunications carriers to build an intercept capability into networks. Yet there's not much point in eavesdropping on something if you can't crack the code it's in. Cryptography is not the only challenge. Some experts worry that al-Qaeda has mastered another of the black arts of the computing world - steganography, which involves hiding messages inside picture or music files sent over the internet. Intelligence and computer security experts vary widely in their assessments of how much an organisation like DSD can or can't crack. Ball says DSD computers are capable of crunching trillions of calculations a second. "If you want to apply all that computing power there's nothing they can't crack." However a senior intelligence insider disagreed with this assessment. Nick Ellsmore, a computer security expert who lectures to federal and state governments, is also convinced its virtually impossible to crack some of the newest algorithmic codes. He and other security experts say the easier alternative is to surreptitiously gain the "keys" to encrypted data. One way to do this is to secretly monitor the keystrokes someone makes when they enter passwords into a computer. This can be done by planting "keyboard sniffers" on a target computer, or using the more cumbersome method of remotely sensing the computer's electromagnetic emanations from a nearby eavesdropping site. A New York group of computer geeks claimed a few years ago that by using components bought easily from electronics stores, they were able to secretly extract data from an array of printers, cables and computer monitors in offices around the city, including the police department, a stockbroker's office and the World Trade Centre. A Cambridge PhD student, Marcus Kuhn, recently documented an optical eavesdropping technique which used a photo sensor to monitor light emissions from a computer terminal, using that to reconstruct the text remotely on another machine. But paradoxically these kinds of technical opportunities could be making the work of spies more dangerous. Ball says it is difficult to read microwave transmissions and computer emanations from satellites. "Some of this stuff can't be done remotely; you still need the ground element," he told the Herald. "The whole radio spectrum, which is how information flows, has changed to shorter and shorter wavelengths, which means you have to get in closer and closer. And that means the nature of covert operations is going back much more to what it was in the 1960s." No place to hide |
November 16, 2004
MIT: Folding, folding, folded: Origami creates beauty from repetitionDenise Brehm True, they rattled paper throughout the 90-minute lecture, but the audience--rapt, eager, enthusiastic--hung on every word from the lips of origami master Robert Lang as he demonstrated the basics of the art and described, in a very rudimentary way, the mathematics behind it. Lang had placed four sheets of 8.5 x 11 inch paper on all 318 seats in Kirsch Auditorium; each page had lines and dotted lines denoting crease-marks to come. Most members of the audience folded at least one of those forms while Lang talked about "From Flapping Birds to Space Telescopes: Origami, Mathematics and Art." Lang, a former laser physicist who now does origami full-time, was at MIT to work on an algorithm for computational geometry with Erik Demaine, an assistant professor of computer science. While on campus, he gave the public lecture on Thursday, Nov. 11 and taught a beginners and an advanced origami workshop. He also taught one class in Demaine's origami course--the first one MIT has ever offered--through the Department of Electrical Engineering and Computer Science. Although the public talk was an evening event on a mid-week holiday, the auditorium was packed, overflowing even, thanks to an article about Lang that appeared in the Boston Globe that day. Jon Madison of Newton, a neurobiologist at Massachusetts General Hospital, saw the article in the Globe and made his way across the river for Lang's talk. A novice, Madison had been working at the craft for three weeks, trying to teach his three-year-old daughter to fold farm animals. "Turned out she's not that interested, but I got hooked," said Madison, who came to hear Lang talk because he was intrigued "by the idea that you can apply mathematics to something I always thought was a game." At least a dozen youngsters age 10 or under were present, as well as many septuagenarians and all ages in between. Neat, conservatively dressed, middle-aged couples sat beside 20-something men wearing long hair and barrettes. They leaned forward in their seats, shouted questions to Lang well before the Q-and-A period, and exclaimed "Oh my God!" and "That is so cool!" when he demonstrated the "One Cut" property. That property, proved by Demaine and others in 1997, says that any shape or combination of shapes can be created using a single sheet of folded paper with a single, straight cut through it. Lang folded a sheet several times, cut once and unfolded it to reveal a star-shaped cutout in the center. He folded another sheet, made the cut, and unfolded it to reveal a triangle, a square and a pentagon lined up in a row. His final demonstration revealed the MIT letterform. A second property, "Two-colorability," describes origami's property of keeping the colors in a double-sided sheet of paper separate; once folded, no two adjacent facets will have the same color. Another, the "Maekawa-Justin Condition," says that the difference in the number of mountain folds (creased downwards) and valley folds (creased upwards) in an origami sculpture will always be two. The relationship between math and origami is symbiotic, Lang said, allowing mathematicians to use origami to prove mathematical theorems and vice versa. For instance, the "Delian Problems" had puzzled even the ancient Greeks, who couldn't trisect an angle, square the circle or double the cube using a compass and unmarked straight edge. The first two problems were solved by scientists using origami in the 1980s. When mathematicians and computer scientists started getting involved in origami in the 1990s, the art form of creating sculpture by simple folds became more dynamic. The basic valley and mountain folds were joined by linkages, flaps, circles, rivers and molecules. For instance, Lang's model for a deer requires 16 circles, 9 rivers and solving 200 equations to create. Lang's own models, many of which are made using the computer program he created called Treemaker, come in many shapes and sizes. His Black Forest Cuckoo Clock (folded from a single sheet of paper, unbelievably) has 216 steps, not counting repeated steps. He built a set of life-sized musicians using flaps and linkages. When the guitarist's head is pulled up, his arm moves, strumming his guitar. Similarly, the cellist moves his bow across his instrument, and the organist's arms move. Lang's forms also include sculptures with textured surfaces, such as the fish with 400 scales and the rattlesnake with 1,000 scales, each made with a single sheet of paper. "There'll never be a second one," Lang said of both of those. The true love for many origami masters, Lang said, is the creation of extremely detailed insects, many-legged creatures whose body, antennae and legs are all folded (and folded and folded) from a single sheet of paper. "Origami seems to be peculiarly well-suited to folding insects." said Lang. Theoretically, any shape can also be created by folding a single sheet of paper with no cuts, no tears. But, says Lang, the finished product could be microscopic, or it could be as tall as a building. The computer program lives in the realm of possibilities, not practicalities. Still, it all comes back to a love for the art. The algorithm Demaine and Lang are perfecting for Treemaker is one that would allow the computer to show a 3-D model of a form, rather than a stick figure, based on an image of, say, a raccoon or a car. Using that stick figure or 3-D model and the fold instructions given by the computer, a master like Lang can fold just about any figure. For now, the more robust computer program would still be used for artistic origami, rather than industrial applications. Airbags are a prime example of the use of origami, or computational geometry, in industry, Lang said. Later, near the end of the Q-and-A, one very young man asked if Lang thought there was the possibility of earning a living doing origami. "I sure hope so," said Lang, "since that's what I'm trying to do." MIT: Folding, folding, folded: Origami creates beauty from repetition |
November 16, 2004
Intelligence Agencies Take Steps to Recruit the Next Generation of SpiesBY CHUCK McCUTCHEON WASHINGTON -- The CIA and other spy agencies are trying to interest a critical new audience in their plans to expand their work force -- high school students. The intelligence community's 15 agencies are stepping up efforts to get teenagers to think seriously about spying. Though the CIA and FBI have long had high school outreach programs, the new push is aimed at giving students exposure to lesser-known outfits such as the National Security Agency (NSA), the spy world's electronic eavesdropping arm. "A lot of students who may want to get a math or hard science degree, or become a lawyer, might not know there are intelligence community agencies that use those skills," CIA spokesman Tom Crispell said. "They may think they have to go to America Online or IBM. But if you're a mathematician, you can go to NSA. Or there are ample opportunities for people with a foreign language background." Crispell and other officials emphasized that high school students are not recruited for jobs. They said no files are being kept on anyone considering a spying career. "The general message is really to encourage them," said FBI spokeswoman Megan Baroska. "It's more of a conversation -- we just want to get them interested." Intelligence agencies are in the midst of a hiring boom that began after the Sept. 11, 2001 attacks. The NSA, for example, is seeking to hire 7,500 employees within five years in its largest recruiting drive since the Cold War, focusing on Arabic and Chinese speakers as well as mathematicians and engineers. The agencies' combined youth outreach efforts began in July with a two-week summer camp for high school seniors at Livingstone College in Salisbury, N.C. Thirty students took part in mock intelligence-gathering missions and went on field trips to CIA and NSA headquarters. The agencies also held their first joint "information expo" last weekend in Washington, drawing more than 200 high school students from around the region. Officials hope to hold similar events elsewhere. Students and parents at the expo chatted with representatives of each agency, who handed out color brochures, pins and Hershey's Kisses. The messages from the officials were largely the same: Study hard, stay out of trouble and consider applying for summer internships and scholarships during college to make yourself an attractive hire. "I heard the FBI was going to be here, so I was going to get some information on the best colleges so I can get right into my career," said Tiffany Jordan, 17, of Hagerstown, Md. "I'm trying to keep my grades up and see what's offered as far as criminology and criminal practices." Jordan said she has long been fascinated with working at the bureau. "Maybe it's because I'm nosy," she said, smiling. Dozens of students waited in line to take part in a demonstration of a polygraph, which spy agencies require of prospective employees. After hooking them up to the machine, the examiner asked participants their ages and a few other innocuous questions, then provided them with a printout charting their responses. "It was very nerve-wracking," said Sammi Plourde, 14, of Fredericksburg, Va., after sitting for her polygraph. The examiner "told me ahead of time what he was going to ask, but I still got nervous." Sammi is a member of the Naval Sea Cadet Corps, a nonprofit organization educating students about maritime matters. She said she joined because of her interest in the Navy, but after talking with several spy agencies, she became interested in an intelligence career. "It's pretty cool -- just the fact that there are spies out there and you can go after them without getting caught and help your country," she said. "We liked what they did with satellites and stuff. It's really awesome they can take pictures in places where no one would expect it." Down the hall, Josh Houston, 16, of Frederick, Md., said he was interested in using his extensive knowledge of computers to help protect against terrorist attacks, preferably with the CIA. "It's always been a dream of mine to work and serve my country," Houston said. "I've wanted to use my abilities to do that ever since I was a little kid, but 9/11 helped. You always hear about the CIA in the news, but I haven't heard a lot about these other branches. So this is broadening my horizons." His mother, Hilary, interjected: "The NSA was hot on you when they found out about your computer background." Nov. 16, 2004 Intelligence Agencies Take Steps to Recruit the Next Generation of Spies |
November 15, 2004
Certicom First to Earn FIPS 186-2 Validation for Elliptic Curve Digital Signature AlgorithmMISSISSAUGA, ON, Nov. 15 /PRNewswire-FirstCall/ - Certicom Corp. (TSX: CIC), the authority for strong, efficient cryptography, today announced that its implementation for the Elliptic Curve Digital Signature Algorithm (ECDSA) has earned the Federal Information Processing Standards (FIPS) 186-2 validation certification No. 1 - making it the first company to receive the designation for an elliptic curve cryptography (ECC) -based algorithm. This validation is particularly valuable for original equipment manufacturers (OEMs) and software vendors who sell to government organizations. By using Certicom's ECDSA implementation in their products, they meet FIPS requirements without undergoing the time-consuming and costly testing process. ECDSA is used to build in digital signature functionality and is a faster alternative to legacy algorithms. For the cryptography community, and in particular proponents of ECC, the testing of ECC as part of the FIPS validation process is a significant step in the adoption of this public key cryptosystem. Considered a benchmark for security in government, a FIPS validation assures users that a given technology has passed rigorous testing by an accredited third party lab as set out by the National Institute of Standards for Technology (NIST) and can be used to secure sensitive information. Typically, it drives wide-scale adoption in government and in commercial sectors, particularly in the financial and healthcare sectors that recognize the significance of FIPS validation. This milestone in ECC's evolution follows last year's announcement from the National Security Agency (NSA) that ECC is a 'crucial technology'. Both events are part of the U.S. Government's crypto modernization program. "A major hurdle to widespread adoption of any security technology is standardization. We witnessed that 25 years ago with the Data Encryption Standard (DES) and now are seeing it play out with Advanced Encryption Standards (AES), the successor to DES," said Scott Vanstone, founder and executive vice-president, strategic technology at Certicom. "As a complementary cryptosystem to AES, we can expect the same for ECC. By testing ECC-based algorithms in the FIPS certification process, NIST added a level of assurance that says they've done the due diligence on it and now organizations can be very comfortable adopting it." ECC is a computationally efficient form of cryptography that offers equivalent security to other competing technologies but with much smaller key sizes. This results in faster computations, lower power consumption, as well as memory and bandwidth savings, thereby making it ideal for today's resource-constrained environments. Certicom is considered a pioneer in ECC research and implementations, backed by 20 years of experience. The company developed the industry's first toolkit to include ECC, which has since been adopted by over 300 organizations. Tomorrow it will host the Certicom ECC Conference 2004, the first-ever conference that brings together Elliptic Curve Cryptography researchers, industry experts and users. During the two-day conference, participants from North America, Europe and Asia will discuss the evolution of ECC and share best implementation practices and insights for future applications. Certicom First to Earn FIPS 186-2 Validation for Elliptic Curve Digital Signature Algorithm |
November 15, 2004
New algorithm ups accuracy of cancer detectionby Barbara Leonard The Courant Institute of Mathematical Sciences recently developed a math-based procedure that will allow for better detection of cancer genes and analysis of cancer patients' genomes. NYU professor Bud Mishra lead the research team, known as the Bioinfomatics Group, in developing the algorithm that can reveal genetic aberrations between normal and cancer-stricken cells. The process, carried out on a computer system, detects excessive or insufficient replicas of DNA segments, a phenomenon associated with various forms of cancer. After uncovering these cancer cells, the procedure locates cancer-suppressing genes. This process differs from previous attempts in that it can distinguish between the cancerous and non-cancerous genes in a single framework. • New algorithm ups accuracy of cancer detection |
November 15, 2004
The robot infiltrator that will lure pests to their doomBy Adam Sage IT BEHAVES like a cockroach. It smells like a cockroach. It is accepted by other cockroaches. But it is not a cockroach. It is a robot and scientists say that its invention is a breakthrough in mankind’s struggle to control the animal kingdom. The robot, InsBot, developed by researchers in France, Belgium and Switzerland, is capable of infiltrating a group of cockroaches, influencing them and altering their behaviour. Within a decade, its inventors believe, it will be leading the unwanted pests out of dark kitchen corners, to where they can be eliminated. But this is only the first of the applications for a pioneering programme that has got scientists dreaming out loud. They say that they will soon be using robots to stop sheep jumping off cliffs, to prevent outbreaks of panic among guinea fowl and to encourage chickens to take exercise. “The idea of using decoys to control animals is very old,” Jean-Louis Deneubourg, of the Belgian National Fund for Scientific Research, who is co-ordinating the programme, said. “Hunters and fishermen have used them for many years. The aim of this project is to develop a robot, or a robot-like artefact, capable of integrating and communicating with animals.” The cockroach research was the first step, Professor Deneubourg said. “Cockroaches are not an objective in their own right. But this shows what it is possible to do.” The initial task, carried out by the Centre for Research on the Cognition of Animals (CRCA) in Toulouse, France, was to analyse cockroach behaviour. A student spent three years filming the insects and making a computer programme that reproduced their movements. The study showed that cockroaches, like ants, are egalitarian creatures, without a group leader. They congregate as a result of a “collective intelligence” that depends upon interaction within the group. “Cockroaches like contact with each other. When they meet, they stay still. They are happy to be with a friend for a few moments. The more friends around them, the longer they stay,” the professor said. The second stage of the €2 million (£1.4 million) programme, called Leurre, was to build a robot capable of detecting cockroaches, of distinguishing them from other objects, of moving like them, and of becoming inactive in the dark. InsBot, which is green, the size of a matchbox, and equipped with lasers and a light sensor, was developed by Switzerland’s Federal Polytechnic School in Lausanne. When it bumps into a cockroach, it does what they do: it stops moving. The more cockroaches that approach it, the longer it remains stationary. The third stage, undertaken by the French Centre for Scientific Research’s laboratory in Rennes, Brittany, was to isolate the molecules that give cockroaches their smell — to create a cockroach perfume — and to spray it on to the robot. “Without the perfume, cockroaches consider InsBot a stranger and run away from it,” Professor Deneubourg said. Early next year he hopes to publish findings that demonstrate InsBot’s capacity to modify its friends’ behaviour. He is carrying out an experiment that involves placing cockroaches in a space that contains two shelters, one dark, one light. Naturally, they gather in the dark shelter, where they feel comfortable. But if the robots go to the light shelter, cockroaches follow — the desire for companionship proving stronger than the need for dark. “It is plausible and realistic to imagine that, in five or ten years’ time, people with a cockroach infestation will be buying robots to get rid of them,” Professor Deneubourg said. Other applications are also envisaged for the computer programmes developed under the Leurre project. Guy Theraulaz, the director of research at the CRCA, says that it may be possible to build chicken-like robots that will be used to stimulate poultry. “A lot of chickens don’t move at all and die as a result. They need to be encouraged to run around. Robots could do that.” He is also studying collective panic attacks among guinea fowl. “The idea is to analyse the reasons for the panic and develop sensors to detect when birds start moving abnormally. These sensors would be linked to a computer that would turn the lights on to calm them or something like that,” he said. Another area of research involves sheep. In mountainous regions when one sheep jumps off a cliff to escape a predator, the others tend to follow — with the result that the whole flock dies. M Theraulaz believes that his team will soon be able to identify flock leaders and give them collars equipped with receivers. They will then train these sheep to stand still — or move — when the receivers emit a signal such as a sound or an electric shock. The robot infiltrator that will lure pests to their doom |
November 15, 2004
New software to demolish the Tower of Babel on mobilesM RAJENDRAN The digital world is working on a solution to break the Tower of Babel — the biblical problem created by speakers of myriad tongues that ensured that no one understood the other. Soon, mobile users will be able to speak in their mother tongues — and find the people at the other end are able to comprehend them because technology translates the spoken word into another language. The solution, which is being cobbled by the Centre for Development of Advance Computing (C-DAC), is expected to be commercially available three years from now. After the huge business opportunities that was thrown up by the Y2K problem (which arose because computers then had not been configured back to recognise the new millennium) and business process outsourcing, India is all set to emerge as the leading supplier of speech and language systems software. Here’s how it works: the spoken word in Bengali or any other language is transformed into audio signals. This is then digitized and analysed to extract important features of the spoken word (which is done through a complex audio signal processing technique). This is then analysed with artificial intelligence techniques to decipher the spoken word. This process is known as speech-to-text translation. It entails the knowledge of linguistic structure of both language, the syntax, semantic, pragmatic knowledge along with lexical, dictionary and databases form an important part. The translated text in Tamil or another language is then converted into audio signals. This process is called text-to-speech conversion. In the scientific argot, this technique is called concatanative synthesis. Its use is based on extraction of knowledge from databases from computer servers and web pages. The speech-to-speech translation technology is being jointly developed by C-DAC in association with a few professors from Indian Institute of Technology (IIT) Kanpur, Indian Institute of Information Technology (IIIT) and Mysore. Shyam S. Agrawal, who has spent more than 35 years in the research of speech and language communication, says there is one problem with the software — the time lag, or latency, between speech at one end and its translation at the other. “Latency of a second or two will be experienced when the conversation begins since the knowledge has to be extracted from databases. But once the conversation moves ahead, it will become real time. In future there will be no need for computers and servers since the embedded chips in the mobile phones will have this capability,” Agrawal said. There is a big future for the new technology. Agrawal reckons that “technology of speech and language translation will have a major impact on the economy and the world market. Like the telephone, everyone will like to have the voice synthesizer or voice recognition at home.” “It will also help voice-based commands for physically challenged persons to undertake their daily activities. It will also have an easy consumer application like switching on a television with a voice command,” Agrawal said. New software to demolish the Tower of Babel on mobiles |
November 12, 2004
Numbing numbersSu Doku — a new puzzle to intrigue and torment Times readers What is the next number in the sequence 1, 1, 2, 3, 5, 8, 13, x? For the quick among you the answer will be obvious. For the historically aware the recitation of the list will be as resonant as the opening bars of the Marseillaise. For this sequence, like the Revolutionary Anthem, marked the opening of an era: x is 21. The sequence is formed by adding the last two numbers to come up with the next. And the puzzle was the work of Leonardo Fibonacci, the father of modern mathematics. The Fibonacci sequence has generated a wealth of mathematical study, but while mathematicians can give thanks to old Leonardo for his trailblazing work, we can simply be obliged to him for reinventing one of mankind’s oldest, and most uplifting, solitary diversions — the numerical brain-teaser. The ancients were addicted to puzzles. The Egyptian Rhind papyrus contains a conundrum as tough as any of the Sphinx’s riddles. Archimedes and the Chinese created puzzles such as tangrams. But all such playful inventiveness ceased in the Dark Ages and was only revived when learning itself was rescuscitated in medieval Italy. History teaches us that mathematics is the heartbeat of intellectual life. When it is absent, so is thinking. When mathematical innovation quickens, mankind’s progress is on an upward curve. And the past also shows us that the great mathematical leaps forward spring from parlour puzzles. In that spirit the new numerical brain-teaser highlighted in T2, the game of Su Doku, is not just a sign of the intellectual Times but a chance for all readers to play their part in the progressive sequence begun all those years ago by Signor Fibonacci. Numbing numbers |
November 12, 2004
Mathematician reaches 100k milestone for online integer archiveBy Alonso del Arte Mathematician Neil Sloane drives a 1987 Honda Prelude with more than 100,000 miles on it. He has something else that has crossed the 100,000 milestone: the Online Encyclopedia of Integer Sequences. Sloane added the 100,000th sequence Monday. The database catalogs sequences of integers for the benefit of mathematicians, scientists and anyone interested in mathematics. The 100,000th sequence is of interest to archeologists. It is: 3, 6, 4, 8, 10, 5, 5, 7, which are the numbers that were found on the middle column of a 22,000-year-old bone in the Congo. The left column read 11, 13, 17, 19, which is a prime quadruplet, and the right column read 11, 21, 19, 9. There are sequences in the OEIS that relate to physics — such as the centered cube numbers that relate to shells of atoms — biology and even music (such as 2, 2, 4, 4, 2, 6, 6, 2, 8, 8, 16, which is in the lyrics of an Argentine children’s song). The OEIS works like a search engine. In the search box, one can enter a few terms of the sequence separated by either commas or spaces, for example, “5, 7, 11, 23, 47,” and it answers with all sequences it finds with those numbers, such as safe primes for the Diffie-Hellman data encryption algorithm in the example above. If a sequence, “2, 101, 149, 163,” for example, does not match anything in the database, the OEIS gives a link to a form to send the sequence in to Neil Sloane to look at. One can also use word search to look up the numbers by name, such as “Motzkin numbers,” and it replies with the sequence 1, 1, 2, 4, 9, 21, 51, 127, etc. In addition to as much as four lines of numbers for each sequence found, the database also replies with information on the sequence, such as relevant research papers and interesting comments. For example, someone researching centered triangular numbers might learn that adding up the first n centered triangular numbers gives the answer to an n-tall magic square. Sloane started rounding up integer sequences in the 1960s, entering them on punch cards, when he was working on neural networks as a graduate student at Cornell University. Many University of Michigan professors tell their students about this resource, and putting in a word search at the OEIS for “umich.edu” yields about 80 results, while a word search for “wayne.edu” turns up none. Anyone who spots an interesting sequence that’s not already in the database can send it in and get credit for it. Although Sloane acknowledges that all the “core” sequences — such as the prime numbers, Catalan numbers, and the Fibonacci sequence — are already in the database, he believes the OEIS has an infinite potential for expansion. “The world of science is continually expanding, and new problems arise every day, and produce new sequences,” Sloane said. Professor Lawrence Brenton, who headed the WSU Undergraduate Research Group, hearing about the OEIS for the first time yesterday, looked up the sequence “2, 3, 7, 43, 1807.” These relate to Znám’s problem, on which Brenton worked on in 1999 with Ana Vasiliu, an undergraduate student at Wayne State University at the time. They published a paper together listing all the possible solutions to this problem when one of the variables is set to 8, for which there are 93 solutions. While the OEIS does not mention Brenton or Vasiliu, it does have a link to the Mathworld page on Znám’s problem, which credits them with their discovery of the 93 solutions for Z(k) = 8. “This is a neat idea,” said Brenton of the OEIS. “This is the sort of thing that used to be put in book form.” Brenton reminisced about the time he spotted a mistake in Paulo Ribemboim’s “Book of Prime Number Records.” He sent Ribemboim a letter with a correction, but Ribemboim had retired from the book writing business. Sloane has published a couple of books of integer sequences, but the OEIS has the advantage of being updated on a more frequent basis. And while the OEIS, which is accessed through a Web browser, like Internet Explorer, is much faster than the punch cards Sloane originally stored the sequences in, Brenton was disappointed by the speed of the OEIS search engine when he entered the sequence “2, 3, 5, 7.” It’s not as fast as Google, but Brenton said he was fascinated enough to look up a few more sequences on it. The Online Encyclopedia of Integer Sequences is available online at http://www.research.att.com/~njas/sequences/index.html Mathematician reaches 100k milestone for online integer archive |
November 12, 2004
A New Way Out of the Prisoner’s Dilemma: CheatBy Camberley Crick 10 November 2004—Within a certain obsessive breed of computer scientists, the geek equivalent of the World Series is a little known tournament called the Iterated Prisoner’s Dilemma Competition. Academics from around the globe struggle to devise the best strategy for tackling one of the fundamental problems in game theory, Prisoner’s Dilemma, and then build artificially intelligent software “robots” to play their strategies in a competitive round-robin tournament. As it turns out, real-world situations from live auctions to nuclear standoffs can bear striking resemblance to this very simple game, and so it was no small matter when this year the longstanding champion of Iterated Prisoner’s Dilemma had to settle for silver. A team of robots submitted by computer scientists from Southampton University, in England, used conspiracy and collusion to sweep this year’s competition stealing the crown from the 20-year reigning incumbent, a simple strategy called Tit for Tat. The Prisoner’s Dilemma is a game theory problem in which two competing players must decide between cooperation and betrayal. In its classic form, two accomplices in a crime are arrested and then interrogated separately by the police. Each accomplice must choose either to confess to the crime (defection) or remain silent (cooperation). Depending on his choice, and the choice of the other player, different payoffs will be given. If one player defects and the other cooperates, the defector walks free, while the cooperator gets five years in jail. If both defect and confess, both get four years. But if the players both cooperate and remain silent, they each get only two years. In the actual Prisoner’s Dilemma competition, held in June at a conference in Portland, Ore., the various outcomes are given different point values, so that a score may be tallied after a series of rounds are played. Each player is aware of how his opponent behaved in previous rounds, and may adapt his strategy accordingly. During the course of the tournament, each robot will play every other robot, even those submitted by the same research team. “The Prisoner’s Dilemma encapsulates the essence of how cooperation can emerge when you have self-interested behavior,” said Nick Jennings, a computer science professor at Southampton University and member of the winning team. “It’s very, very simple, and yet very powerful.” The winning strategy, Tit for Tat, worked like this: a player began by cooperating each round, until his opponent defected. After this point, the player echoed his opponent’s last move, defecting after the other player had betrayed him, and cooperating when his opponent began to cooperate again. The Southampton University researchers, who entered a team of 60 software robots, or agents, into the competition, found that an even better strategy was to submit a group of robots that behaved in the tournament either as masters or slaves. A robot’s particular role was encoded in its pattern of opening moves, allowing any other robot that knew what to listen for to recognize its opponent as another Southampton player. When a Southampton “master” was pitted against a Southampton “slave”, the slave would sacrifice itself, cooperating every round to allow the master to defect repeatedly and rack up a huge score. In the end, the individual master robots scored more points than the robots playing Tit for Tat. “It was almost like a cult,” said Graham Kendall, a professor at the University of Nottingham, in England, who organized the 20th-anniversary competition, referring to the culture the Southampton entries created. “There were superagents who exploited all their friends.” While technically this strategy violates the spirit of the Prisoner’s Dilemma, which assumes that the two prisoners cannot communicate with one another, the Southampton system is not without its uses. In reality, collusion between competitors is generally impossible to prevent, and a whole field of research has sprung up to study how intelligent agents can use what’s called coding theory to communicate covertly, and how such collusion can in turn be prevented. For example, the U.S. Federal Communications Commission’s radio spectrum auctions have historically been plagued by cases of bidders colluding by coding hidden signals in their bids, and so the FCC has brought in researchers to advise it on how to modify the rules of its auctions to try to mitigate collusion. “How agents can collude and how you can stop that collusion—now that’s an interesting area of research,” said Southampton’s Jennings, who likened the discipline to an arms race between bidders and auctioneers. A second round of the Iterated Prisoner’s Dilemma competition will be held in April of 2005 at the IEEE Symposium on Computational Intelligence and Games hosted by the University of Essex, in England. Armchair game theorists may submit an entry by visiting http://www.prisoners-dilemma.com/. A New Way Out of the Prisoner’s Dilemma: Cheat |
November 12, 2004
VN professor wins prestigious awardHA NOI — A Vietnamese professor from the University of Paris 11 in France’s Palaiseau, has won the 2004 Clay Research Award from the Clay Mathematics Institute in Massachusetts. Ha Noi-based Ngo Bao Chau, 32, a maths lecturer and researcher, competed with numerous others from universities around the country for the prize, and is the first Vietnamese contender to win it in six years. His research partner, professor Gerard Laumon, from the University of Paris 6, shared the prize. Their research into the basic lemma for unitary groups, "Le lemme fondamental pour les groupes unitaires", has provided new mathematical and geometrical methodologies to the academic community. Founded in 1998 in Cambridge City, Massachusetts, the Clay Mathematics Institute is devoted to the advancement of knowledge and technical proficiency of mathematics professionals. It also organises international seminars and forums on the subject. The institute’s annual research prize aims to honour the most talented mathematicians, who, with their year’s work, have made significant mathematical contributions. "My former lecture, professor Gerard Laumon, and I worked hard on our research," Chau said, adding that he was surprised when he received news of the award from the Clay Institute’s chairman James Carlson. "I’m very proud of the prize," he said. "All I have achieved, I dedicate to my country and my family." One of Ha Noi National University’s top students, Chau won two top prizes at the Olympic mathematics competitions in Australia and Germany in 1988 and in 1989. Later he was selected to study maths in the University of Paris 6 and received his doctorate degree last year. "Living in a foreign country, a Vietnamese scientist must work harder to achieve something," Chau said. He now works as a maths lecture for the University of Paris 6. Although living in France, Chau often returns home for holidays and continues to work closely with local universities. VN professor wins prestigious award |
November 12, 2004
Breakthrough in Coding Theory and PracticeThe Board of Governors of the IEEE Information Theory Society has selected an article by professors from the University of California, San Diego (UCSD) and the University of Illinois at Urbana-Champaign (UIUC) as the top publication in information theory during the past two years. The article developed an improved decoding algorithm for error-correcting codes that are used today in communication and storage devices ranging from computer hard drives to deep-space probes. UIUC's Ralf Koetter and UCSD's Alexander Vardy received the award for their work on "Algebraic Soft-Decision Decoding of Reed-Solomon Codes," published in the November 2003 issue of IEEE Transactions on Information Theory (vol. 49, no. 11, pp. 2809-2825). The article described the first truly efficient and effective soft-decision decoding algorithm for Reed-Solomon codes, thereby solving a long-standing open problem in coding theory and practice. "Decoding is always a matter of probability," Vardy said. "There had been a mismatch between the probabilistic domain of the channel and the algebraic domain of the decoder. In a sense, what we had to do was to achieve a happy marriage of probability and algebra." Although they pre-date turbo codes and other recent codes, Reed-Solomon codes remain in widespread use. About 75% of error-correction circuits in operation today decode Reed-Solomon codes. For example, every CD player and most computer hard drives use these codes. The cited paper adapted a new decoding technique, developed by Venkatesan Guruswami and Madhu Sudan at MIT, and used it to design a soft-decision decoding algorithm, i.e., an algorithm that fully utilizes the probabilistic information available at the receiver. The Koetter-Vardy soft-decision decoding algorithm results in substantial coding gains in practice [up to 1.5 decibels on additive white Gaussian noise channels, and much more on Rayleigh-fading channels]. Due to these gains and feasible complexity, the new algorithm has the potential to make today's standard decoding algorithms obsolete. The Koetter-Vardy algorithm has already passed one practical test with flying colors. Ham radio operators used it to decode 'moonbounce' messages bounced off the Moon and back to Earth using low-power amplifiers and receivers. "This is where I started being so favorably impressed," said Princeton's Joe Taylor, a ham radio operator and a Nobel Laureate. "The KV algorithm is fully 2 dB better than what I have been using, and the advantage holds up over a wide range of signal-to-noise ratios. The use of the KV Reed-Solomon decoder in my moonbounce program has been a spectacular success. Many dozens, perhaps hundreds, of Earth-Moon-Earth contacts are being made with it every day now, all over the world." Breakthrough in Coding Theory and Practice |
November 09, 2004
Fingerprints in the sky explained by “beautiful mathematics”Tuesday 9 November 2004 Today, a group of physicists published the most compact and elegant explanation of one of nature’s simplest phenomena: the way light behaves in the sky above us. This research appears today in the New Journal of Physics, published jointly by the Institute of Physics and Deutsche Physikalische Gesellschaft (German Physical Society). Michael Berry and Mark Dennis from the University of Bristol, in collaboration with Raymond Lee of the US Naval Academy, have successfully predicted the patterns of polarisation of skylight, explained in broad outline by Lord Rayleigh in 1871, using elliptic integrals – a type of mathematics with deep geometrical roots, often described as “beautiful”. The blue sky seen through polaroid sunglasses gets darker and brighter as the glasses are rotated. This reveals something almost invisible to our unaided eyes: daylight is polarized light. This means that the light waves vibrate differently in different directions. The effect is strongest at right angles to the sun, and weaker elsewhere. It creates patterns in the sky that look similar to the ridges in human fingerprints and are used by many species of birds and flying insects as an aid to navigation. A striking feature of the pattern is a pair of points near the sun where the light is not polarized at all (this point is a singularity and the pattern breaks down here). Although they have been studied for nearly two centuries, no one attempted to construct a model using the most obvious feature - the singularities - until now. Sir Michael Berry said: “We wondered: what if you start with the singularities and write the simplest description of polarisation that puts the singularities in the right places? We found that this gives a remarkably good fit to the observational data, and predicts the pattern across the whole sky.” “This is beautiful mathematics in the sky. Using elliptic integrals, we’ve been able to replace pages and pages of formulae with one very simple solution that predicts the pattern extremely well” “After almost 200 years there’s now a way of understanding this natural phenomenon which is very different from previous models, but utterly natural. It’s a modern theme of physics to study things by looking at their singularities – to think about them geometrically.” In order to test their theory, co-author Raymond Lee took four different polarized photographs of each of two clear-sky cases at the United States Naval Academy in Annapolis, Maryland, using a Nikon digital camera with a specially converted fisheye lens. When they compared these detailed observations to the pattern predicted by their model, they found that the fit was very good, indicating that the arrangement of the singularities could be vital in shaping the overall “fingerprint in the sky”. Many scientists and mathematicians believe that simple, concise explanations of natural phenomena are better or closer to some underlying truth than more complex ones. Professor Marcus du Sautoy, from the Mathematical Institute at the University of Oxford, said: “Having a sense of beauty and aesthetics is an important part of being a scientist. Nature seems to be a believer in Occam's Razor: given a choice between something messy or a beautiful solution, Nature invariably goes for beauty. This is why those scientists with an eye for aesthetics are often better equipped for discovering the way Nature works. We might find a complicated ugly solution but that is probably a sign that we haven't yet found the best explanation. The fact that there is so much beauty at the heart of Nature is what gives scientists a constant sense of wonder and excitement about their subject.” Fingerprints in the sky explained by "beautiful mathematics" |
November 09, 2004
Fibonacci Numbers Topic - Of HSU Math Lecture“The Fabulous Fibonacci Numbers” will be summed up in a free mathematics lecture geared for the general public when Jennifer J. Quinn, mathematics department chairwoman at Occidental College, presents this semester's Harry S. Kieval lecture at Humboldt State University on Thursday, at 8 p.m. in Natural Resources 101. The Fibonacci numbers – 0,1,1,2,3,5,8,13,21,34,55 and so on – are a sequence that has long fascinated scholars because of its frequent occurrence in art, architecture, music, magic and nature. The sequence continues as the next number is generated by adding the two preceding numbers. “You may have read about them in Dan Brown’s novel ‘The DaVinci Code,’” Quinn said. “This talk will exhibit many natural examples of Fibonacci numbers while exploring the unusual and aesthetically pleasing patterns of the sequence itself.” Earlier Thursday, at 4 p.m., in Science B 135, Quinn will deliver “Synchronicity: Alternating Sums, Exclusion, and Determinants,” a more technical talk in a special edition of HSU's weekly mathematics colloquium. “One of my goals is to understand identities involving sums of alternating terms by finding a correspondence between odd and even sets,” Quinn said. “Coincidentally, a colleague asked me about calculating a particular determinant combinatorially. When the answer ended up being related to the alternating identities, I was stunned.” Fibonacci Numbers Topic |
November 09, 2004
Iranian mathematician takes 7th place in world contestTehran, Nov 8, IRNA -- Iranian mathematician Ali Bayat Movahed ranked seventh in the world subjective calculations contest in Germany. According to a report released by Iran's Elite Association on Monday the contest was held from October 29-30 in the German city of Anaberg with participation of 40 experts on subjective calculations from all around the world. The participants were from Germany, USA, Poland, France, Britain, Spain, India, Lebanon, Algeria and Iran. Mr. Movahed have devised hundreds of formulas and subjective methods for calculating square root, logarithm, trigonometric functions and matrix multiplication. He is also a known person in the United Nations Educational, Scientific and Cultural Organization (UNESCO). In the field of symmetry and division, Movahed ranked first by setting a record of 26 seconds and in total he took the seventh place. He also participated in logarithm and upper root calculation competition but because of absence of any other competitor the contest was not held. Iranian mathematician takes 7th place in world contest |
November 09, 2004
NYU team develops enhanced algorithm for detecting changes in cancer genomesResearchers at New York University's Courant Institute of Mathematical Sciences have developed a new algorithm that can lead to more accurate detection of cancer genes than previous versions. The algorithm, published in the latest issue of the Proceedings of the National Academy of Sciences (PNAS), can also be applied to the multiple biomedical technologies (e.g., different kinds of micro-arrays) used to analyze cancer patients' genomes. Headed by NYU Professor Bud Mishra, the research team developed the algorithm to detect the genetic differences between normal cells and cancer cells. Its application reveals several excess as well as missing copies of DNA segments associated with various forms of cancer and ultimately, points to locations of both oncogenes and tumor suppressor genes. In addition, the algorithm can be used to account for the varied genomes present across human population. An earlier version of the algorithm as well as several other competing algorithms were capable of dealing with only cancer data or only polymorphism data and were unable to separate variations in cancerous and non-cancerous genes in a single framework. Mishra's team, which forms NYU's Bioinfomatics Group, has previously examined new genomic technology for mapping and sequencing with single molecules, models of genome evolution, and computational and systems biology models of biological processes like apoptosis, cell divisions, and others involved in cancer. Two senior research scientists from the Bioinformatics Group, Raoul-Sam Daruwala and Archisman Rudra, collaborated with Mishra to devise the algorithm and create its software implementation. Daruwala, Rudra, and Mishra were joined in the study by colleagues from Cold Spring Harbor Laboratory and NYU School of Medicine. The algorithm runs through Valis, a software environment developed by Mishra and Courant's Salvatore Paxia in 2001, with the help of a New York State Office of Science, Technology and Academic Research (NYSTAR) grant. The software will be made available on-line in mid-December. This research was also funded by the Army's Prostate Cancer Research Program (PCRP). titolo |
November 07, 2004
Complexity, Randomness, and Impossible TasksBy JOHN ALLEN PAULOS Some things are simple, some are complicated. What makes them so? In fields ranging from biology to physics to computer science, we're often faced with the question of how to measure complexity. There are many possible measures, but one of the most important is algorithmic complexity. First described by two mathematicians, the Russian Andrei Kolmogorov and the American Gregory Chaitin, it has been extensively developed by Chaitin in recent years. The flavor of the subject can perhaps be sampled by considering this question: Why is it that the first sequence of 0's and 1's below is termed orderly or patterned and the second sequence random or patternless? (Note that since almost everything from DNA to symphonies to this very column can be encoded into 0's and 1's, this is not as specialized a question as it may at first appear.) (A) 0010010010010010010010010010010010010010010 … (B) 1000101101101100010101100101111010010111010 … Answering this question leads not only to the definition of algorithmic complexity, but also to a better understanding of (a type of) randomness as well as a proof of the famous incompleteness theorem first proved by the Austrian mathematician Kurt Godel. Hang on. The ride's going to be bumpy, but the view will be bracing. With sequences like those above in mind, Chaitin defined the complexity of a sequence of 0's and 1's to be the length of the shortest computer program that will generate the sequence. Let's assume that both sequences continue on and have lengths of 1 billion bits (0's and 1's). A program that generates sequence A will be essentially the following succinct recipe: print two 0's, then a 1, and repeat this x times. If we write the program itself in the language of 0's and 1's, it will be quite short compared to the length of the sequence it generates. Thus sequence A, despite its billion-bit length, has a complexity of, let's say, only 10,000 bits. A program that generates sequence B will be essentially the following copying recipe: first print 1, then 0, then 0, then 0, then 1, then 0, then 1, then … there is no way any program can compress the sequence. If we write the program itself in the language of 0's and 1's, it will be at least as long the sequence it generates. Thus sequence B has a complexity of approximately 1 billion bits. We define a sequence to be random if and only if its complexity is (roughly) equal to its length; that is, if the shortest program capable of generating it has (roughly) the same length as the sequence itself. Thus sequence A is not random, but sequence B is. Chaitin has employed the notions of complexity and randomness to demonstrate a variety of deep mathematical results. Some involve his astonishing number Omega, which establishes that chance lies at the very heart of deductive mathematics. These results are explained in many of his books, including the forthcoming, "Meta Math" (available on his Web site at http://www.cs.auckland.ac.nz/CDMTCS/chaitin/). Let me here just mention his proof of Godel's theorem. He begins with a discussion of the Berry sentence, first published in 1908 by Bertrand Russell. This paradoxical sentence asks us to consider the following task: "Find the smallest whole number that requires, in order to be specified, more words than there are in this sentence." Examples such as "number of hairs on my head," " number of different states of a Rubik cube," and "speed of light in centimeters per decade," each specify, using fewer than the 20 words in the given sentence, some particular whole number. The paradoxical nature of the task becomes clear when we realize that the Berry sentence specifies a particular whole number that, by its very definition, the sentence contains too few words to specify. (Not quite identical, but suggestive is this directive: You're a short person on an elevator in a very tall building with a bank of buttons before you, and you must press the first floor that you can't reach.) What yields a paradox about numbers can be modified to yield mathematical statements about sequences that can be neither proved nor disproved. Consider a formal mathematical system of axioms, rules of inference, and so on. Like almost everything else these axioms and rules can be systematically translated into a sequence of 0's and 1's, and if we do so, we get a computer program P. We can then conceive of a computer running this program and over time generating from it the theorems of the mathematical system (also encoded into 0's and 1's). Stated a little differently, the program P generates sequences of 0's and 1's that we interpret as the translations of mathematical statements, statements that the formal system has proved. Now we ask whether the system is complete. Is it always the case that for a statement S, the system either proves S or it proves its negation, ~S? To see that the answer to this question is "No," Chaitin adapts the Berry sentence to deal with sequences and their complexity. Specifically, he shows that the following task is also impossible (though not paradox-inducing) for our program P: "Generate a sequence of bits that can be proved to be of complexity greater than the number of bits in this program." The program P cannot generate such a sequence, since any sequence that it generates must, by definition of complexity, be of complexity less than P itself is. Stated alternatively, there is a limit to the complexity of the sequences of 0's and 1's (translations of mathematical statements) generated (proved) by P. That limit is the complexity of P, considered as a sequence of 0's and 1's, and so statements of complexity greater than P's can be neither proved nor disproved by P This is a sketch of a sketch of Godel's incompleteness theorem. It can be interpreted to be a consequence of the limited complexity of any formal mathematical system, a limitation affecting human minds as well as computers. The above leaves out almost all the details and is, I realize, almost impenetrably dense if you have never seen this kind of argument. It may, however, give you a taste of Chaitin's profound work. Complexity, Randomness, and Impossible Tasks |
November 06, 2004
Norseen: Mathematical NatureBy Nan Norseen In this changing world of time and space few things remain constant. But if we examine the process of change, we will find a geometric proportion that is constant and yet is involved in creating our evolving world. The Greeks were the first to discover this proportion, which is now called the "Golden Rectangle," the "Golden Section" or the "Golden Ratio." This ratio governed Greek art and architecture. The Parthenon in Athens is a prime example. The rectangle produces a square and another rectangle of the same proportion, but smaller. This smaller rectangle can be divided again in the same way, producing the same results to infinity. It is the ratio that is important. How much smaller is one square from the previous square? Toward the end of the Middle Ages, in the early 13th century, an Italian mathematician known as Fibonacci made a leap in the understanding of the golden rectangle. He was able to do this by learning to use the Hindu-Arabic number system that we use today. Instead of the cumbersome Roman numerals; I, II, III, IV, V, VI ..., this Arabic system, using place values by introducing the concept of zero, made adding, subtracting and other computations easy - by using base 10: 3 in the 1's place = 3, but 3 in the 10's place = 30, 3 in the 100's place = 300 and so on. With this numerical system, Fibonacci was able to give the golden ratio a precise numerical value, the value of 1.6180339 ..., which is a non-repeating irrational number. The closest whole number ratio is 5:8. This may seem all too mathematical, but this ratio underlies the growth patterns of plants, animals and crystals. This proportion governs the growth of shells, shown here in the classic example of the chambered nautilus. And if you look at the seed head of a large sunflower, you will see the same spiral arrangement of the seeds. These are examples that are easy to see, but the ratio is apparent in numerous subtle variations. Leonardo da Vinci was fascinated with this ratio and used it often in his work. Whole books have been written showing how this sequential ratio can be found not only in material objects, but in the wave motion of light and sound. Which I will not try to explain here. But think of a major chord on the piano, the repeating intervals 1-3-5-8. Our ears hear this sequence as musically pleasing. The proportion even governs the form of spiral galaxies. And in geometry, underlying the forms of the regular or Platonic solids, such as the tetrahedron, octahedron, the hexahedron or cube and other symmetrical forms, such as the Star of David or the five-pointed star are the dimensions of the golden rectangle. Although the forces of nature make objects in our reality appear varied and irregular, this ratio governs the growth of a tree, leaf arrangement and even the proportions of our own bodies. In this short column I can only mention a few aspects of the golden rectangle or Fibonacci ratio, but it controls the creation of everything. Leonardo da Vinci called it "the divine proportion." Norseen: Mathematical Nature |
November 05, 2004
Cryptography: Beginning with a Simple Communication GameBy Wenbo Mao. Here is a simple problem. Two friends, Alice and Bob, want to spend an evening out together, but they cannot decide whether to go to the cinema or the opera. Nevertheless, they reach an agreement to let a coin decide: playing a coin tossing game which is very familiar to all of us. Alice holds a coin and says to Bob, "You pick a side then I will toss the coin." Bob does so and then Alice tosses the coin in the air. Then they both look to see which side of the coin landed on top. If Bob's choice is on top, Bob may decide where they go; if the other side of the coin lands on top, Alice makes the decision. In the study of communication procedures, a multi-party-played game like this one can be given a "scientific sounding" name: protocol. A protocol is a well-defined procedure running among a plural number of participating entities. We should note the importance of the plurality of the game participants; if a procedure is executed entirely by one entity only then it is a procedure and cannot be called a protocol. Now imagine that the two friends are trying to run this protocol over the telephone. Alice offers Bob, "You pick a side. Then I will toss the coin and tell you whether or not you have won." Of course Bob will not agree, because he cannot verify the outcome of the coin toss. However we can add a little bit of cryptography to this protocol and turn it into a version workable over the phone. The result will become a cryptographic protocol, our first cryptographic protocol in this book! For the time being, let us just consider our "cryptography" as a mathematical function f(x) which maps over the integers and has the following magic properties: Property 1.1: Magic Function f For every integer x, it is easy to compute f(x) from x, while given any value f(x) it is impossible to find any information about a pre-image x, e.g., whether x is an odd or even number. Protocol 1.1: Coin Flipping Over Telephone PREMISE Alice and Bob have agreed: a "magic function" f with properties specified in Property 1.1 an even number x in f(x) represents HEADS and the other case represents TAILS (* Caution: due to (ii), this protocol has a weakness, see Exercise 1.2 *) Alice picks a large random integer x and computes f(x); she reads f(x) to Bob over the phone; Bob tells Alice his guess of x as even or odd; Alice reads x to Bob; Bob verifies f(x) and sees the correctness/incorrectness of his guess. It impossible to find a pair of integers (x, y) satisfying x ? y and f(x) = f(y). In Property 1.1, the adjectives "easy" and "impossible" have meanings which need further explanations. Also because these words are related to a degree of difficulty, we should be clear about their quantifications. However, since for now we view the function f as a magic one, it is safe for us to use these words in the way they are used in the common language. In Chapter 4 we will provide mathematical formulations for various uses of "easy" and "impossible" in this book. One important task for this book is to establish various quantitative meanings for "easy," "difficult" or even "impossible." In fact, as we will eventually see in the final technical chapter of this book (Chapter 19) that in our final realization of the coin-flipping protocol, the two uses of "impossible" for the "magic function" in Property 1.1 will have very different quantitative measures. Suppose that the two friends have agreed on the magic function f. Suppose also that they have agreed that, e.g., an even number represents HEADS and an odd number represents TAILS. Now they are ready to run our first cryptographic protocol, Prot 1.1, over the phone. It is not difficult to argue that Protocol "Coin Flipping Over Telephone" works quite well over the telephone. The following is a rudimentary "security analysis." (Warning: the reason for us to quote "security analysis" is because our analysis provided here is far from adequate.) 1.1.1.1 A Rudimentary "Security Analysis" First, from "Property II" of f, Alice is unable to find two different numbers x and y, one is odd and the other even (this can be expressed as x ? y (mod 2)) such that f(x) = f(y). Thus, once having read the value f(x) to Bob over the phone (Step 1), Alice has committed to her choice of x and cannot change her mind. That's when Alice has completed her coin flipping. Secondly, due to "Property I" of f, given the value f(x), Bob cannot determine whether the pre-image used by Alice is odd or even and so has to place his guess (in Step 2) as a real guess (i.e., an uneducated guess). At this point, Alice can convince Bob whether he has guessed right or wrong by revealing her pre-image x (Step 3). Indeed, Bob should be convinced if his own evaluation of f(x) (in Step 4) matches the value told by Alice in Step 1 and if he believes that the properties of the agreed function hold. Also, the coin-flipping is fair if x is taken from an adequately large space so Bob could not have a guessing advantage, that is, some strategy that gives him a greater than 50-50 chance of winning. We should notice that in our "security analysis" for Prot 1.1 we have made a number of simplifications and omissions. As a result, the current version of the protocol is far from a concrete realization. Some of these simplifications and omissions will be discussed in this chapter. However, necessary techniques for a proper and concrete realization of this protocol and methodologies for analyzing its security will be the main topics for the remainder of the whole book. We shall defer the proper and concrete realization of Prot 1.1 (more precisely, the "magic function" f) to the final technical chapter of this book (Chapter 19). There, we will be technically ready to provide a formal security analysis on the concrete realization. Cryptography: Beginning with a Simple Communication Game |
November 03, 2004
Numbers don't add up in the land of GalileoBy Claudine Renaud Rome - Galileo Galilei, the father of modern scientific thinking, might have felt right at home in modern Italy. In 1592, he was appointed to the chair of mathematics at the University of Padua, and found himself earning only a fraction of what a professor of theology was making. One of Galileo's distant descendants, Enrico Giusti, knows the feeling. Giusti, who teaches at the University of Florence, finds himself addressing only 30 or 35 students in a class, while his colleagues who teach modish subjects like media studies, psychology, communication and architecture attract thousands. Giusti has founded a small museum in Florence aimed at "reversing the trend" and educating people about the magic of curves, equations and theorems. He also wrote a book about mathematics in the kitchen, in which readers can learn the formula, for example, of why it is quicker to peel large potatoes than small ones. His campaign has received indirect support from education minister Letizia Moratti, who recently said she would free up $10-million over three years to help whet the appetite of high school students for a career in mathematics. "The study of math must be reinforced, absolutely, from elementary school onwards," she said. The government is also offering 150 scholarships to encourage school teachers to upgrade their science skills, and says it will create a data base of openings in companies and laboratories to help students obtain work experience. These are not the only efforts to improve the image of hard science among young people. The 12-day festival of science that has just opened in Genoa aims to show the public that math is indeed fun. In Turin, the renowned Polytechnic school gave two promising math students a trip to the United States - which regularly outscores the rest of the world in Nobel science prizes - to promote a "less cold" image of tough science. Fifty years ago, nearly half of university students pursued a scientific subject of one kind another. Today that figure has declined to a third, and the education ministry said the disciplines that have proportionately lost the most are the hard sciences such as chemistry, physics and math. Over the 15-year period ending in 2000, university enrollments in the hard sciences dropped by three quarters from more than 29 000 to just over 7 000. Last year there was some room for optimism in that this downward trend was slightly reversed. Although it is difficult to identify the cause of the decline, one reason is that young people do not see much of a future in math in terms of money or prestige. "The image of the professor in society has greatly declined, and since one of the principle outcomes of math studies is the teaching profession, students are quitting the subject," Giusti said. "Young people perceive math as a difficult subject that requires a lot of work with little reward at the end." Tristino Marinelli, 25, the co-ordinator of the Union of University Students, couldn't agree more. "It is a problem of job openings, but also of images," he said. "The competition among the faculties to enrol students has led to a proliferation of very fascinating degrees, such as the sciences of investigation or biotechnology, and that has penalised the classic courses." Giusti said that although Italy still has some good students who plan careers in research, the discipline receives inadequate cash support, despite Moratti's offer to the schools. To which, physicist Enrico Predazzi added: "Some think that one can live without maths and that Italy could become the garden of the world by encouraging tourism. But all studies show that it is scientific research that creates progress and wealth in a country." Numbers don't add up in the land of Galileo |
November 03, 2004
Game, set and mathsBy Zara Bishop UNSURPRISINGLY, the masters of strategy board game Othello have yet to be offered million-pound endorsements. But Balham's Graham Brightwell could-n't be more proud having learned he will represent Britain in the World Othello Championships. The mathematician said: "The glory of the title is the main thing I am playing for. "It is purely a hobby. We are all amateurs." The 42-year-old, of Glenfield Road, works at the London School of Economics and is one of three players representing Britain. He secured his place in the team after finishing second in the British championships last month. Now he will face the world's best at the Selfridge Hotel in central London on November 13. He said: "There are not many rules, it is all about strategy. "It is simple to play which is one of its biggest advantages. I'm really pleased to be in the British team." The aim of the two-player game is to flip the colour of your opponent's discs into your own by capturing both ends of a line with your pieces. Whoever has the most discs face up at the end of the game wins. Graham said: "It is easy to learn but takes longer to master." FACTS OTHELLO was invented by Japanesegames enthusiast Goro Hasegawa 33years ago. To date Othello, which is played with 64reversible discs, has sold 30 million setsaround the world. It is the only licensed board game to host 27 consecutive world championshiptournaments. Game, set and maths |
November 02, 2004
The golden ratioBy D.J. BATZER THERE are certain numbers that are found everywhere deeply imbedded in the nature of the universe. The best known of these is “pi”, the circumference of a circle divided by its diameter. Less well known but just as ubiquitous is “phi” the 21st letter of the Greek alphabet. The extraordinary fact that this number turns up often through nature was recognised in the ancient world and it was Euclid of Alexandria, the father of geometry, who stumbled on its significance. This was followed up from Greek-Egyptian astronomer Ptolemy to Johann Kepler, who elucidated the rules of planetary orbits, and 16th century mathematician Luca Pacioli to 19th century physicist Martin Ohm, of electrical resistance fame, to modern astrophysics. It is usually called the golden ratio. It is found by cutting a line so that the ratio of the whole line to the larger segment is the same as the ratio of the larger segment to the smaller segment. The numerical value of the ratio in decimal form is 1.68103... It goes on indefinitely without repetition like “pi” or the square root of 2. In two dimensions, a square is drawn on the long side of a rectangle so that the new rectangle has the same ratio of short side to long side as the smaller rectangle. Alternatively, a square may be drawn in one end of a golden rectangle so that the remaining rectangle has the golden ratio. From one corner of successive square it is possible to draw a quarter circle to form a continuous spiral called a logarithmic curve. Such spirals are found throughout nature for instance in a snail’s shell or the arms of spiral galaxy, a good example of the latter is M51 in the constellation of Canes Venatici. The spiral arms of a galaxy are not attached to the disk material; if they were, they could not survive for long because different rings of a galactic disk rotate at different speeds. The arms represent density waves of compression that sweep through the disk, squeezing gas clouds on their way and triggering star formation. Kepler’s solar system model considers the planetary orbits as defined by spheres and the five platonic solids. These are the tetragon made of four equilateral triangles, the cube made of six squares, the octagon made of eight equilateral triangles, the dodecahedron made of 12 regular pentagons and the icosahedrons made of 20 equilateral triangles. Kepler said that the Earth’s sphere is the measure of all the other planetary orbits. Circumscribe a dodecahedron around it and the sphere surrounding that will be the orbit of Mars. Circumscribe a tetrahedron round Mars’ sphere and that is Jupiter’s sphere, circumscribe a cube round Jupiter’s sphere and that defines the orbit of Saturn. Going inwards inscribe an icosahedron within Earth’s orbit and the sphere in it is Venus’ sphere. Inscribe an octahedron inside Venus sphere and the sphere round that is Mercury’s orbit. The golden ratio is embedded in all these figures. This pleased Kepler’s mystical turn of mind, but it cannot have any real meaning since we now know of two more major planets, Uranus and Neptune unknown in Kepler’s time. Yet from this apparently absurd starting point Kepler was able to arrive at the first accurate model of planetary motion! Following Kepler, who died in 1630, the story of the golden ratio would have to wait nearly 400 years for a new chapter to be written. This involved the work of British cosmologist Roger Penrose at Oxford University in Britainand Paul Steinhardt of Princetown University in the United States. Both men are accomplished mathematicians. Penrose, while investigating Einstein’s theories in the extreme case of black hole formation, was first to recognise the gulf between quantum mechanics and relativity. Steinhardt is a key figure in the development of the current inflationary model of the universe. Remarkably it was the study of five-fold symmetry of crystals, thought not to exist, but discovered by Israeli materials engineer Dany Schectman in an aluminium-manganese alloy that helped to revive interest in phi. Also Penrose’s study of floor covering tiles with a five-fold symmetry where the golden ratio is involved. It was these cosmologists who showed that the golden ratio is also hidden in the heavens. Most stars have the peculiar property of heating up as they lose energy. The Sun, for example, contracts and heats up as it converts hydrogen into helium, because four hydrogen nuclear (protons) change to one helium nucleus, compacting the core and heating the Sun’s surface. Physicist Paul Davies has shown that rotating black holes undergo a phase transition when the ratio of the square of its mass to the square of its angular momentum is equal to the golden ratio! The golden ratio |
November 02, 2004
Calif.'s quiet benefactorBy Kenneth R. Weiss Los Angeles Times Originally published October 31, 2004 He has given more money to conservation causes in California than anyone else. His gifts have helped protect 1,179 square miles of mountain and desert landscapes, an area the size of Yosemite National Park. His donations to wilderness education programs have made it possible for 437,000 inner-city schoolchildren to visit the mountains, the desert or the beach, many of them for the first time. Over a decade of steadily growing contributions - including more than $100 million to the Sierra Club - this mathematician turned financial angel has taken great pains to remain anonymous. In manner and appearance, David Gelbaum has maintained a low profile for someone who can afford to give away hundreds of millions of dollars. At age 55, retired from the rarefied world of Wall Street hedge funds, he lives in Newport Beach, Calif., with his wife and two of his four children in a large home where visitors on occasion have mistaken him for the gardener. Bespectacled, 5 feet, 5 inches tall and slightly built, he speaks softly, barely above a hoarse whisper. He drives a Honda Civic hybrid, wears jeans and T-shirts to business meetings, and helps the youths clean up at the wilderness campouts he sponsors. Gelbaum, a native of Minnesota who moved to California as a teenager, was a math prodigy who parlayed his talents into a highly lucrative three-decade career using mathematical formulas to pick stocks and bonds for wealthy investors in hedge funds. It isn't enough, he said, "to protect wilderness just for people who can afford to go to it. I think bringing kids out to the wild is unquestionably the right thing to do. These kids have pretty tough lives. It opens their eyes to the world outside of their neighborhood. Some of the kids will grow up to protect the land they learn to love. You could look at it as an investment into the environment." Born in Minneapolis, the second of four sons, Gelbaum moved to California when his father, Bernard Gelbaum, became founding chairman of the University of California, Irvine math department. David Gelbaum showed early prowess in math, taking calculus at the University of California, Irvine while in high school. Months before he graduated in 1972, he was hired by math professor Edward O. Thorp to help with a business that needed a math researcher. Thorp, who wrote the book Beat the Dealer, about how to count cards and win at blackjack, was applying mathematical wizardry to Wall Street. His formulas, which later appeared in his book Beat the Market, led him to start the nation's first market-neutral hedge fund, one intended to make money for investors whether the market went up or down. From 1970 to 1989, the fund never had a losing quarter and increased investors' money more than 13-fold. Gelbaum was one of his first math researchers hired to track and exploit the price discrepancies between a company's stocks and its options, warrants and convertible bonds. "He was smart. He was idiosyncratic. He was always looking for more," Thorp said. Calif.'s quiet benefactor |
November 02, 2004
'Machine-brained' Briton is world's best at numbers gameALLAN HALL IN BERLIN A BRITON’S devotion to numbers added up to glory at the weekend when he was judged the world’s best at mental arithmetic. Doctor Robert Fountain won the inaugural Mental Arithmetic World Championships held in the birthplace of medieval German mathematician Adam Ries at Annaberg-Buchholz. He beat off 17 other challengers from 11 countries. Dr Fountain, 35, from Northwich, Cheshire, earned first place because he was able to solve one of the surprise tasks - to multiply three three-digit numbers without writing down the equations as he went. "This was the decider," said a spokesman for the organisers. "His brain worked like a machine - and a very fast one at that." Divesh Ramanlan Shah from India came second, while Dutchman Jan van Koningsveld was third. Contestants had ten minutes to add ten ten-digit numbers, then multiply ten eight-digit numbers, and work out the square root of a six-digit number. Contestants also had to answer two surprise questions and work out on what day a specific date in the year 1600 fell. Dr Fountain correctly answered that 6 January that year was a Thursday. Adam Ries was famous for writing arithmetic textbooks. His most important, Rechenung nach der lenge, auff den Linihen und Feder, was published in 1550 and contained addition, subtraction, multiplication and, very surprisingly for the period, division. 'Machine-brained' Briton is world's best at numbers game |
November 02, 2004
Predicting Infection Risk Of Mosquito-borne DiseaseMalaria, which is transmitted by mosquitoes, remains one of the greatest threats to global health, infecting more people than ever before. Understanding how the risk of catching a mosquito-borne infection varies depending on the environment is an important step in planning and implementing effective control measures. The rate at which humans become infected is determined by how often they are bitten by mosquitoes and the proportion of mosquitoes that are infectious. It is often assumed that if the percentage of infectious mosquitoes increases, so will the rate at which humans get bitten. But in a new study published in the open access journal PLoS Biology, David Smith, Jonathan Dushoff, and F. Ellis McKenzie challenge this assumption. Using a mathematical model, the authors show that the rate at which humans are bitten and the proportion of infectious mosquitoes peak at different times and places, revealing that the standard metric of estimating the risk of infection -- the average number of times an infectious mosquito bites a person per day -- is flawed. The distribution of humans and suitable habitat for mosquito larvae varies across the landscape. And the density of mosquito populations varies seasonally, rising and falling with changes in rainfall, temperature, and humidity. Temporal and spatial variations in mosquito populations affect the rate humans get bitten, the number of infectious mosquitoes, and the risk of infection. The mathematical model that Smith and colleagues developed predicts that human biting rate is highest shortly after mosquito population density peaks, typically either near breeding sites or where human density is highest. The proportion of infectious mosquitoes, on the other hand, reflects the age of the mosquito population: it peaks where older mosquitoes are found--farther from breeding sites--and when populations are declining. The combination of these factors results in, for example, the surprising prediction that the risk of infection can be lowest just outside an edge of town. By mapping larval habitats against the local risk of mosquito-borne infections, Smith and colleagues conclude, epidemiological models can be developed to predict risk for local populations. Their results make the case that mathematical models can help public health officials calculate risk of infectious diseases in heterogeneous environments--that is, real world conditions--when vector ecology and the parameters of transmission are well characterized. Any plan to prevent and control the spread of mosquito-born infections would clearly benefit from paying attention to mosquito demography and behavior. Predicting Infection Risk Of Mosquito-borne Disease |
Novenber 01, 2004
Alain Glavieux, mathematician and information technologist, was born on July 4, l949. |
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