Российская наука и мир (дайджест) - Июнь 2003 г. (часть 2)
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Look around at the world, and the objects in it-buildings, trees, people, birds, insects-appear to come in an endless variety of shapes. At first, cataloging these diverse shapes may seem impossible. But on closer inspection, relationships emerge. The bumpy surface of a starfish, for example, is simply a stretched and distorted version of a sphere. The same goes for the surface of a table or a telephone pole. In contrast, a coffee cup is not a sphere but instead a distorted version of a doughnut, and a pretzel can be considered a doughnut with three holes instead of one.
What about more complicated shapes like a fishnet or a bicycle wheel? Amazingly, more than a hundred years ago, mathematicians proved that every closed surface in space is simply some version of a sphere, a doughnut surface-which they call a torus-or a torus with extra holes.
Even though spheres and tori sit in three-dimensional space, mathematicians focus on their surfaces and so view them as two-dimensional, unlike solid balls and filled-in doughnuts, which are three-dimensional. A small patch of a sphere or torus surface looks almost like a piece of a flat plane and has area rather than volume.
Mathematicians also study an analogous collection of what they call closed three-dimensional shapes. Unlike ordinary three-dimensional objects, these shapes live in four-dimensional-or higher-space and curve in on themselves as the sphere and torus do in three-dimensional space. Although such shapes are difficult to visualize, some cosmologists speculate that our own universe may be of that form, rather than the infinitely extending space that most people envision.
For a century, mathematicians have wondered whether there's a classification of three-dimensional shapes like the simple breakdown of two-dimensional shapes into spheres and tori. Now, a Russian mathematician may finally have proved that the answer is yes (SN: 4/26/03, p. 259: Available to subscribers at www.sciencenews.org/20030426/fob1.asp Details are starting to emerge of his work, which gives a way to distort a three-dimensional object, little by little, to make its shape more uniform.
A few years ago, the Clay Mathematics Institute in Cambridge, Mass., offered a $1 million bounty to anyone who could settle the Poincarй conjecture, a 99-year-old question about three-dimensional shapes that's one of the most famous problems in mathematics. After working for years in near seclusion and supporting himself largely on personal savings, Grigory Perelman of the Steklov Institute of Mathematics in St. Petersburg, Russia, announced that he has proved the conjecture, which gives a way to identify whether a complicated shape is a distorted version of a sphere. He also claims to have proved the much broader Thurston geometrization conjecture, which considers all closed three-dimensional shapes.
Over the years, dozens of mathematicians have mistakenly claimed to have proved the Poincarй conjecture. For this reason, mathematicians-including Perelman himself-are not rushing to judgment. Perelman has declined to talk to the press until colleagues verify his proof.
It will take months, some mathematicians say, to dissect the details of Perelman's densely written papers. But Perelman's track record makes many optimistic that his work will stand up to scrutiny. "He's singularly brilliant," says Jeff Cheeger of the Courant Institute of Mathematical Sciences at New York University. What's more, Perelman's colleagues note, the portions of his work that have already been verified are full of groundbreaking ideas.
"Whether or not he has a complete proof, he has clearly made very important contributions to mathematics," says John Milnor, a mathematician at the State University of New York at Stony Brook who attended a series of lectures Perelman gave there in April and May.
Many past attempts to prove the Poincarй conjecture have involved intricate, hard-to-check arguments. "This one feels like a much more natural, very promising approach," Milnor says. "It seems like the right way to handle the problem."
Recognizing the hypersphere
Even though a sphere and a torus are two-dimensional to mathematicians, there's no way to fit them into a flat plane without squashing them. Similarly, some three-dimensional shapes can't fit comfortably into ordinary three-dimensional space.
For instance, just as the sphere is the two-dimensional boundary of the three-dimensional ball, mathematicians have defined the hypersphere as the three-dimensional boundary of the four-dimensional ball-a space that's hard to visualize but that can nevertheless be analyzed mathematically. Researchers have also discovered a three-dimensional analog of the torus, as well as an infinitely large family of more exotic three-dimensional spaces.
Around 1900, French mathematician Henri Poincarй wondered whether there's an easy way to tell when a given closed three-dimensional space is a distorted version of the hypersphere. Poincarй made a daring conjecture. To recognize a hypersphere, he guessed, all that's needed is information about one-dimensional curves in the space. If every closed loop of thread in the space can be drawn in to a single point, then the space is a hypersphere in disguise, he hypothesized. On a torus, by contrast, a loop that goes around the hole can't be pulled tight to a single point.
Poincarй's conjecture is one of the simplest possible questions to ask about three-dimensional spaces, yet it has stumped mathematicians from Poincarй's time to the present. Surprisingly, higher-dimensional spheres turn out to be more amenable to analysis. Decades ago, mathematicians proved the corresponding conjectures for spheres of four dimensions and higher.
Geometric building blocks
In the late 1970s, mathematician William Thurston, now at the University of California, Davis, envisioned a way to tame the menagerie of three-dimensional spaces-an idea that gave mathematicians a roadmap for proving the Poincarй conjecture. The key, Thurston suspected, was in an analogy between the geometry of three-dimensional spaces and that of two-dimensional surfaces.
Every closed surface can be distorted into a particular shape with an especially uniform geometry. For starfish, tables, and telephone poles, that most uniform shape is simply the sphere, which looks the same at every point.
Among tori, the doughnut surface is more homogeneous than the coffee cup, but it is not perfectly uniform. Points on the outer ring are positively curved, like a sphere, while points on the inner ring are negatively curved, like a saddle's central point. However, mathematicians have found a way to conceptualize a completely uniform torus, in which each small patch of the torus has the same geometric structure as a flat piece of paper.
All other two-dimensional surfaces-the tori with multiple holes-can be given what's called hyperbolic geometry, which makes the surfaces negatively curved at all points.
Among closed surfaces, spherical, flat, and hyperbolic geometry are mutually exclusive. Breaking down these surfaces into geometric types thus gives a way to distinguish two-dimensional spheres, for example, from other surfaces. A similar breakdown for three-dimensional spaces, Thurston realized, would give mathematicians a useful tool for distinguishing hyperspheres from other shapes, the goal of the Poincarй conjecture.
Mathematicians have known for decades that three-dimensional spaces can't be categorized as neatly as two-dimensional surfaces can. Some spaces, for instance, consist of a hyperbolic chunk and a flat chunk sewn together. Other spaces have geometric structures that don't match any of spherical, flat, or hyperbolic geometry.
In pioneering work, Thurston proposed that there is nevertheless a precise way to classify the geometry of three-dimensional spaces. Each closed space, he conjectured, can be given a special geometric structure built from components selected from eight geometric types. Three of the eight are spherical, flat, and hyperbolic geometry; the other five are slightly more complicated but still uniform geometries. Thurston, who proved large portions of his conjecture, was awarded a Fields Medal-mathematics' version of a Nobel prize-in large part for this body of work.
"What Thurston proposed was a revolutionary idea that went well beyond the Poincarй conjecture," Cheeger says.
Erasing the bar
If Thurston's conjecture can be proved, the Poincarй conjecture will follow automatically. The logic goes more or less like this: In a closed three-dimensional space, if all loops of thread can be pulled tight to a point, mathematicians know that the only one of the eight geometries that can fit the space is spherical geometry. That means that no matter how convoluted the space appears, it must simply be a distorted version of the hypersphere.
After Thurston's work, mathematicians who wanted to prove the Poincarй conjecture could focus on demonstrating that Thurston's vision of three-dimensional spaces is correct. By the early 1990s, Richard Hamilton of Columbia University had proposed a technique that he hoped would do just that-show that each three-dimensional space can be smoothed out into Thurston's special pieces. He defined a method, called the Ricci flow, for changing the shape gradually at each point to make the space more uniform. His equation resembles the physics equation that describes how heat spreads through a material.
"If you take a body where parts are hot and parts are cold and you let it stand, heat tends to flow by itself until the temperature is even," Milnor says. "In Hamilton's process, you have a manifold that is very curved in some places, maybe flat or negatively curved in other places, and you just let the curvature flow and try to even itself out."
For instance, the Ricci flow would make an egg-shaped surface gradually flatten out on the ends and bulge even more in the middle, getting closer and closer to a perfect sphere.
Hamilton was aware, however, that the flow would not always produce a uniform geometry. At any point in the space, the flow is determined mainly by the local geometry, not by the overall shape of the space. So, sometimes the geometry of one part of the space might change much faster than that of another part, producing a highly uneven geometry overall.
For example, picture a dumbbell-two weights connected by a thin bar-each portion of which is flowing with a mind of its own. The bar wants to even out its geometry with the weights to turn the whole thing into a nicely rounded sphere. Each weight, on the other hand, wants to make itself as spherical as possible. In the three-dimensional version of the dumbbell, depending on the initial geometry, the weights may predominate, growing rounder and rounder while the bar stretches into a long, thin neck.
Hamilton's idea for dealing with this difficulty was simply to snip out the neck at some appropriate point, continue the Ricci flow on the pieces, and glue the neck back in at the end. The resulting shape would have the right kinds of building blocks for Thurston's conjecture. But for more complicated shapes than the dumbbell, he couldn't show that these necks were the only extreme geometric forms the flow would produce. Other extremities, such as awkward protrusions he called cigars, might result.
What's more, perhaps every time the flow evened out one portion of the space, that portion's extreme shape would have moved somewhere else, like bulges in a rug that is being fit into a room too small for it. Extreme geometric features might cycle around and around, without the whole space ever growing uniform.
These questions dogged Hamilton and his followers for more than a decade. Then last November, Perelman sent several mathematicians an e-mail, saying only that he had posted a paper on the Internet that might be of interest to them. In the paper, he writes that his work "removes the major stumbling block in Hamilton's approach to geometrization." Although the posted paper makes no reference to the Poincarй conjecture, experts in the field immediately realized what he was driving at.
Music of the spheres
In the early 1990s, working in the United States, Perelman had emerged as a major player in Riemannian geometry, which studies subjects such as curvature. "In that domain he was considered a phenomenon at that time, incredibly brilliant," recalls Cheeger.
Then abruptly, Perelman all but vanished from the mathematical scene. In 1995, he turned down job offers from several top universities and returned to Russia. When U.S. mathematicians asked Perelman's colleagues at the Steklov Institute what he was working on, they generally replied that they had no clue.
Some mathematicians speculated that Perelman had quit mathematics. Every now and then, however, one or another mathematician would receive an e-mail from Perelman with probing, insightful questions. "All of a sudden, there would be concrete evidence that he was following certain developments," Cheeger says.
Once Perelman's first paper on the Ricci flow appeared on the Internet in November 2002, rumors started flying that he had proven the Poincarй conjecture and Thurston's geometrization conjecture. On March 10, Perelman posted a second paper that developed the ideas in his first paper and explicitly claimed a proof of the two conjectures. He has promised a third paper with a few remaining details.
This spring, Perelman visited the United States to present lectures on his work in Cambridge, Mass., and Stony Brook. So far, he has answered all the questions raised about his work, several mathematicians told Science News.
To understand the behavior of the Ricci flow, Perelman devised a way to capture a specific characteristic of any three-dimensional space. Roughly, he described what the pitch of a space would be if someone could ring the space like a bell. Perelman then proved that as the space slowly morphs under the Ricci flow, its pitch gets higher and higher.
Perelman's result immediately shows that the geometry of a space can't cycle around under the Ricci flow-if it did, its pitch would be unchanged after each cycle. Perelman claims that the result about pitch, together with other ideas that he develops in his papers, also does away with the possibility of cigars and other potential obstacles to carrying out Hamilton's program.
"Perelman's results are as spectacular as the Poincarй conjecture," says Dennis Sullivan, a mathematician at Stony Brook. "In just a few pages of work, he puts a hand grenade in the brick wall Hamilton had run into and blows a hole through it. Whether that has enabled him to crawl through to the meadow on the other side remains to be seen."
Many mathematicians have accepted the correctness of Perelman's result about the pitch of a space, but they have not finished studying the portions of Perelman's papers that explore the ramifications of the result. Once Perelman's papers have been published, if no one exposes a hole in his work within 2 years, he will be eligible for the Clay Institute's prize.
For many mathematicians, however, the appeal of the Poincarй conjecture lies beyond the million-dollar prize and accompanying fame. "It's important for the same reason Beethoven's Ninth Symphony is important," Sullivan says. "It's great."

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    Daily Times, Pakistan 1 Jun 2003
    Scientists use DNA to trace the migration of modern humans Ученые используют ДНК, чтобы проследить миграцию современных людей

Human beings may have made their first journey out of Africa as recently as 70,000 years ago, according to a new study by geneticists from Stanford University and the Russian Academy of Sciences. Writing in the American Journal of Human Genetics, the researchers estimate that the entire population of ancestral humans at the time of the African expansion consisted of only about 2,000 individuals.
"This estimate does not preclude the presence of other populations of Homo sapiens [modern humans] in Africa, although it suggests that they were probably isolated from one another genetically, and that contemporary worldwide populations descend from one or very few of those populations," said Marcus W. Feldman, the Burnet C. and Mildred Finley Wohlford Professor at Stanford and co-author of the study.
The small size of our ancestral population may explain why there is so little genetic variability in human DNA compared with that of chimpanzees and other closely related species, Feldman added.
The study, published in the May edition of the journal, is based on research conducted in Feldman`s Stanford laboratory in collaboration with co-authors Lev A. Zhivotovsky of the Russian Academy and former Stanford graduate student Noah A. Rosenberg, now at the University of Southern California.
"Our results are consistent with the `out-of-Africa` theory, according to which a sub-Saharan African ancestral population gave rise to all populations of anatomically modern humans through a chain of migrations to the Middle East, Europe, Asia, Oceania and America," Feldman noted.
Ancient roots: Since all human beings have virtually identical DNA, geneticists have to look for slight chemical variations that distinguish one population from another. One technique involves the use of "microsatellites" - short repetitive fragments of DNA whose patterns of variation differ among populations. Because microsatellites are passed from generation to generation and have a high mutation rate, they are a useful tool for estimating when two populations diverged.
In their study, the research team compared 377 microsatellite markers in DNA collected from 1,056 individuals representing 52 geographic sites in Africa, Eurasia (the Middle East, Europe, Central and South Asia), East Asia, Oceania and the Americas.
Statistical analysis of the microsatellite data revealed a close genetic relationship between two hunter-gatherer populations in sub-Saharan Africa - the Mbuti pygmies of the Congo Basin and the Khoisan (or "bushmen") of Botswana and Namibia. These two populations "may represent the oldest branch of modern humans studied here," the authors concluded.
The data revealed a genetic split between the ancestors of these hunter-gatherer populations and the ancestors of contemporary African farming people - Bantu speakers who inhabit many countries in southern Africa. "This division occurred between 70,000 and 140,000 years ago and was followed by the expansion out of Africa into Eurasia, Oceania, East Asia and the Americas - in that order," Feldman said.
This result is consistent with an earlier study in which Feldman and others analyzed the Y chromosomes of more than 1,000 men from 21 different populations. In that study, the researchers concluded that the first human migration from Africa may have occurred roughly 66,000 years ago.
Population bottlenecks: The research team also found that indigenous hunter-gatherer populations in Africa, the Americas and Oceania have experienced very little growth over time. "Hunting and gathering could not support a significant increase in population size," Feldman explained. "These populations probably underwent severe bottlenecks during which their numbers crashed - possibly because of limited resources, diseases and, in some cases, the effects of long-distance migrations."
The ancestors of sub-Saharan African farming populations appear to have experienced a population expansion that started around 35,000 years ago: "This increase in population sizes might have been preceded by technological innovations that led to an increase in survival and then an increase in the overall birth rate," the authors wrote.

© Daily Times - All Rights Reserved
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After DNA collected from more than 1,000 people around the world, researchers report humans first ventured out of Africa just 70,000 years ago. Geneticists from Stanford University and the Russian Academy of Sciences also speculate the entire population of ancestral humans numbered only about 2,000 at the time of the Africa expansion. The small size of the ancestral population could explain why there is so little genetic variation in human DNA today. Since all humans have virtually identical DNA, scientists look for slight chemical variations that distinguish one population from another. One technique involves the use of micro-satellites, short repetitive fragments of DNA whose patterns of variation differ among populations. In this study, the researchers compared 377 micro-satellite markers in DNA collected from 1,056 individuals representing 52 geographic sites in Africa, Eurasia, East Asia, Oceania and the Americas. "Our results are consistent with the 'out-of-Africa' theory, according to which a sub-Saharan African ancestral population gave rise to all populations of anatomically modern humans through a chain of migrations to the Middle East, Europe, Asia, Oceania and America," the researchers conclude. The study appeared in the May issue of the American Journal of Human Genetics.

© 2003 News World Communications, Inc.
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    Технология распознавания почерка, разработанная группой российских ученых, привлекает внимание ряда больших компаний. Одна из компаний по производству программ создает всеобщую технологию распознавания, которая конвертирует информацию на бумаге, например, почерка на чеках и конвертах в данные, пригодные для использования на компьютере. Это выполняется через комбинацию алгоритмов, которая распознает образцы в напечатанном материале

Handwriting-recognition technology developed by a team of Russian scientists is drawing attention from a string of big companies - allowing Parascript LLC to chisel a niche in its industry.
The Niwot-based software company makes Total Recognition technology that converts paper-based information, such as handwriting on checks and envelopes, into computer-usable data. This is accomplished through a combination of algorithms that recognizes patterns in the printed material.
Parascript, whose products recognize more than 100 million documents daily in organizations such as the U.S. Postal Service, Chase Manhattan Bank and TIAA-CREF, just signed a deal with Unisys, a Blue Bell, Penn., IT-solutions company that provides check recognition services for more than 80 percent of the world's largest banks.
Under the deal, Unisys is implementing Parascript's CheckPlus 3.0 recognition software to increase its banking customers' recognition of information on checks, speed processing, improve accuracy rates and lower manual labor costs, said Mike Fenton, director of banking and financial services for Parascript.
Though Unisys already had its own check processing center and recognition technology (called SoftCAR+) in place, its recognition rate was only about 70 percent, Fenton said. The other 30 percent were labeled "rejects," or checks that the technology couldn't read.
He said Parascript's technology increases that rate to 80 percent by reading 30 percent of those rejects.
"Basically, we gave them a boost in their existing technology," Fenton said. "Parascript's CheckPlus was selected for its proven ability to read even the hardest-to-read payment forms, reducing the time, effort and expense associated with manual processing," said Barbara Seguin, Unisys payment systems program manager for SoftCAR+. "It is in the best interest of our company and our clients for Parascript to continue to make advances in its technology, which has already led to significant processing improvements and higher read rates."
According to industry analyst Arthur Gingrande, Parascript's technology is special because it can recognize cursive handwriting, as well as the hand-printed and machine-printed information that can be read by many intelligent character recognition software engines in the industry. "They've got a little niche. Nobody else is really competing with them" in the recognition of the "legal amount" on checks, said Gingrande, a partner with Imerge Consulting, a business-process consulting firm based in Boston. The legal amount is the handwritten part of the check that spells out how much the check is worth. However, a French company called A2iA recently entered the American market in Parascript's niche area. Gingrande said Parascript, which owns about 75 percent of its market, should be able to hold its own against this burgeoning competition, though.
"As long as they continue to be smart and move with the market and listen to their customer base, they'll do well," he said. "They've already got a good position and they've got a good handle on it."
Gingrande said the market potential in this area is "enormous," given the prevalence of paper.
"Everyone thought that eventually computer technology would eliminate paper. But the phrase 'paperless office' is about as reasonable as the phrase 'paperless bathroom," he said, noting that the output of paper has doubled over the last 20 years. People write more than 70 billion checks a year, he said - a number that is only increasing.
Fenton sees lots of potential for Parascript, as well, given that the company's technology can be applied well beyond the banking and finance sphere. Other key areas include mail and package processing, insurance and health care and circulation management and publishing. Founded in 1996, Parascript was an off-shoot of ParaGraph International, a joint venture between American and Russian scientists. A team of Russian scientists at ParaGraph spent 10 years developing a single technology that could turn all character types into electronic data - an idea that originated with Russian scientist, Shelya Guberman, in 1976. ParaGraph is perhaps best known for developing the handwriting recognition capabilities of the Apple Newton. About 30 of Parascript's 120 employees still are based in Moscow, Fenton said. Another 20 employees are located in the company's Pen&Internet division in Sunnyvale, Calif., which makes electronic ink and handwriting recognition technologies. And 70 of Parascript's employees are based in Niwot. Though Fenton would not disclose the private company's revenues, he would share that Parascript has been profitable since its inception and has experienced about 5 percent compounded growth each year - with the exception of 2001, when the Sept. 11 terrorist attacks slowed down the company's projects.
This year, the company expects 15 percent growth over 2002, Fenton said. The same is predicted for 2004.

© 2003 American City Business Journals Inc
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MOSCOW, (AP) -- Alexander Krasovsky, a prominent Russian aerospace engineer, died Saturday of a heart attack after burglars locked him up in his bathroom and stole his Soviet-era medals. He was 82.
Krasovsky, a member of the prestigious Russian Academy of Sciences, had worked at the Zhukovsky Air Force Academy since 1954 and won numerous state decorations for his research in automatic control systems for the aerospace sector.
Krasovsky received one of the highest Soviet-era medals, the Hero of Socialist Labor, and several other awards for his work, which aided the development of Soviet air defense weapons and cruise missiles, the daily Izvestia reported.
Russian media said Krasovsky was the latest veteran to fall victim to burglars searching for Soviet-era medals for sale on the black market. The Hero of Socialist Labor medal fetches up to $1,000, Izvestia reported.

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    Российские ученые помогают медицинскому центру в Канзасе в разработке элемента, который можно вживить в мозг для обнаружения и контролирования эпилептического припадка

(KRT) - A Russian nuclear weapons scientist was finishing a weeklong trip to Kansas City, Kan., on Friday, part of a project intended to foster peace and treat epilepsy.
Gennady Kochemasov is working with Ivan Osorio, director of the Comprehensive Epilepsy Center at the University of Kansas Medical Center, to develop a device that can be implanted in the brain to detect and control epileptic seizures.
Creating the device means mastering technology that can detect minute temperature changes in the brain and rapidly cool brain tissue to prevent seizures. Researchers are also working on mechanisms that allow the cooling device and the temperature sensor to communicate through a wireless connection.
Officials at the U.S. Department of Energy weapons facility in Kansas City brought Osorio and Kochemasov together two years ago through a program aimed at preventing the spread of weapons of mass destruction from the former Soviet Union to nations such as Iraq and North Korea.
The Initiatives for Proliferation Prevention program funds nonmilitary research for weapons scientists in the former Soviet Union to lessen the likelihood that they will sell weapons' secrets abroad.
Kochemasov said most of his country's scientists were law-abiding citizens, but he acknowledged that the tough economic times back home had tempted some of his colleagues "to use our knowledge for bad aims."
The 59-year-old physicist, however, preferred to focus on the fact that his collaboration with Osorio fosters better relations between the United States and the former Soviet Union and helps treat the roughly 60 million epileptics around the world.
"We have the possibility to develop new technology for medical applications," he said. "It's interesting."
This is Kochemasov's third trip to the United States as part of the epilepsy project, but it was his first visit to Kansas City. He is scheduled to leave Sunday for Lawrence Livermore National Laboratory, an energy department lab operated by the University of California.

© 2003, The Kansas City Star
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