Bergli J.,University of Oslo |
Galperin Y.M.,University of Oslo |
Galperin Y.M.,Norwegian Academy of Science and Letters
Physical Review B - Condensed Matter and Materials Physics | Year: 2012
Slow relaxation and aging of the conductance are experimental features of a range of materials, which are collectively known as electron glasses. We report dynamic Monte Carlo simulations of the standard electron glass lattice model. In a nonequilibrium state, the electrons will often form a Fermi distribution with an effective electron temperature higher than the phonon bath temperature. We study the effective temperature as a function of time in three different situations: relaxation after a quench from an initial random state, during driving by an external electric field, and during relaxation after such driving. We observe logarithmic relaxation of the effective temperature after a quench from a random initial state as well as after driving the system for some time t w with a strong electric field. For not too strong electric field and not too long t w we observe that data for the effective temperature at different waiting times collapse when plotted as functions of t/t w-the so-called simple aging. During the driving period we study how the effective temperature is established, separating the contributions from the sites involved in jumps from those that were not involved. It is found that the heating mainly affects the sites involved in jumps, but at strong driving, also the remaining sites are heated. © 2012 American Physical Society.
Cocks L.R.M.,Natural History Museum in London |
Torsvik T.H.,University of Oslo |
Torsvik T.H.,Norwegian Academy of Science and Letters |
Torsvik T.H.,Geological Survey of Norway |
Torsvik T.H.,University of Witwatersrand
Earth-Science Reviews | Year: 2013
New palaeogeographical reconstructions are presented for eleven time intervals through the Palaeozoic of the eastern Asia region from the Middle Cambrian at 510. Ma to the end of the Permian at 250. Ma. They centre on the continental blocks of North China, South China, and Annamia (Indochina) and their relationships with northeastern Gondwana (which was united to form part of Pangea from the Late Carboniferous onwards). Also shown is the continent of Tarim during the Lower Palaeozoic, as well as the Hutag Uul-Songliao and Khanka-Jiamasu-Bureya terranes, both of which straddle the Russian, Mongolian and Chinese borders today, from Silurian times onwards. We conclude that Annamia and South China were united as a single continent throughout the Lower Palaeozoic and Early Devonian and were translocated by major strike-slip faulting along the northeastern Gondwana margin during that period from off Afghanistan to outboard of the Sibumasu and Australian sectors of the superterrane. They left the Gondwana marginal area together during the Lower Devonian opening of the Palaeotethys Ocean, but very shortly afterwards they themselves divided into the two separate continental blocks that we recognise today, not to reunite until the Triassic. The various Cambrian to Permian rocks found in Japan largely represent active volcanic arcs which originally lay to the southeast of South China, although the Carboniferous was more quiescent there. The Neotethys Ocean opened during the Permian, dividing Sibumasu and the Tibetan terranes from Gondwana, and the Palaeotethys Ocean started to close progressively in the Upper Palaeozoic as most of the East Asian continents and smaller terranes moved towards Siberia. The positions of the various continents and terranes have been deduced from a mixture of palaeomagnetic and faunal data, the positions of Large Igneous Provinces and kimberlites, and the need to provide kinematic continuity between maps of successive ages. However, many uncertainties remain. © 2012 Elsevier B.V.
The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2016 to Sir Andrew J. Wiles (62), University of Oxford, “for his stunning proof of Fermat’s Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era in number theory.” The President of the Norwegian Academy of Science and Letters, Ole M. Sejersted, announced the winner of the 2016 Abel Prize at the Academy in Oslo on March 15. Andrew J. Wiles will receive the Abel Prize from H.R.H. Crown Prince Haakon at an award ceremony in Oslo on May 24. The Abel Prize recognizes contributions of extraordinary depth and influence to the mathematical sciences and has been awarded annually since 2003. It carries a cash award of NOK 6,000,000 (about EUR 600,000 or USD 700,000). Andrew J. Wiles is one of very few mathematicians — if not the only one — whose proof of a theorem has made international headline news. In 1994 he cracked Fermat’s Last Theorem, which at the time was the most famous, and long-running, unsolved problem in the subject’s history. Wiles’ proof was not only the high point of his career — and an epochal moment for mathematics — but also the culmination of a remarkable personal journey that began three decades earlier. In 1963, when he was a 10-year-old boy growing up in Cambridge, England, Wiles found a copy of a book on Fermat’s Last Theorem in his local library. Wiles recalls that he was intrigued by the problem that he as a young boy could understand, and yet it had remained unsolved for three hundred years. “I knew from that moment that I would never let it go,” he said. “I had to solve it.” The Abel Committee says: “Few results have as rich a mathematical history and as dramatic a proof as Fermat’s Last Theorem.” Andrew J. Wiles, born on April 11, 1953 in Cambridge, earned his bachelor’s degree in mathematics in 1974 at Merton College, Oxford, and a Ph.D. in 1980 at Clare College, Cambridge. After a period at the Institute for Advanced Study in New Jersey in 1981, Wiles became a professor at Princeton University. In 1985-86, Wiles was a Guggenheim Fellow at the Institut des Hautes Études Scientifiques near Paris and at the École Normale Supérieure. From 1988 to 1990, Wiles was a Royal Society Research Professor at the University of Oxford, before returning to Princeton. He rejoined Oxford in 2011 as Royal Society Research Professor. Andrew J. Wiles has been awarded a number of major prizes in mathematics and science. They include the Rolf Schock Prize, the Ostrowski Prize, the Wolf Prize, the Royal Medal of the Royal Society, the U.S. National Academy of Science’s Award in Mathematics, and the Shaw Prize. The International Mathematical Union presented him with a silver plaque, the only time they have ever done so. He was awarded the inaugural Clay Research Award. In 2000, he was given a knighthood. Andrew J. Wiles is a Fellow of the Royal Society. He is a foreign member of the US National Academy of Sciences and of the French Academy of Sciences. He has honorary degrees from Oxford, Cambridge, Columbia, Yale, Warwick and Nottingham. The Abel Prize is awarded by the Norwegian Academy of Science and Letters. The choice of the Abel Laureate is based on the recommendation of the Abel Committee, which is composed of five internationally recognized mathematicians. The members of the current committee are: John Rognes (chair), Rahul Pandharipande, Éva Tardos, Luigi Ambrosio and Marta Sanz-Solé.
Fermat proof prize Andrew Wiles has received the 2016 Abel Prize for mathematics for his solution to Fermat’s last theorem, the Norwegian Academy of Science and Letters announced on 15 March. The problem had stumped some of the world’s greatest minds for three and a half centuries. Wiles, a number theorist now at the University of Oxford, UK, will receive 6 million kroner (US$700,000) for his 1994 proof showing that there cannot be any positive whole numbers x, y and z such that xn + yn = zn, if n is greater than 2. See go.nature.com/yf1nxj for more. Famous killer whale nears end of life Tilikum, a killer whale (Orcinus orca) at SeaWorld in Orlando, Florida, has an incurable lung infection, the theme park’s veterinary team has announced. In February 2010, Tilikum dragged his trainer Dawn Brancheau into the pool and killed her. The whale was also involved in two deaths in the 1990s, and the story of his life in captivity was told in the controversial 2013 documentary film Blackfish. SeaWorld bought Tilikum in 1983; he is thought to be 35 years old. The species’ life expectancy in captivity versus that in the wild is still debated by scientists. AlphaGo victorious The world’s leading Go player, South Korea’s Lee Sedol, lost his final match in Seoul against Google DeepMind’s AlphaGo machine on 15 March. The tightly fought game brought the best-of-five competition to an end with four wins for the computer versus one for the human player. Sedol came back from three consecutive losses to beat the artificial-intelligence system in the fourth match, but ultimately missed out on the US$1-million prize. Go originated more than 2,500 years ago in China and involves placing black and white counters on a board. See page 284 for more. Brexit warning Physicist Stephen Hawking is one of more than 150 scientists, mathematicians, economists and engineers at the University of Cambridge, UK, who warn of a disaster for the nation’s science if Britain exits the European Union (known as Brexit). A referendum to be held on 23 June will ask whether the country should leave the EU. In a 10 March letter to The Times, organized by protein scientist Alan Fersht, the group argues that the free movement of workers between EU countries helps in the recruitment of high-quality researchers to the United Kingdom. The letter’s signatories are all fellows of the Royal Society in London. Zika meeting With the Zika virus still spreading rapidly across the Americas, the World Health Organization (WHO) in Geneva held an emergency meeting on mosquito control on 14–15 March. The WHO’s Vector Control Advisory Group intends to review evidence to support new and innovative techniques for combating the Aedes aegypti mosquitoes that transmit Zika virus, along with dengue and Chikungunya viruses. These techniques include deploying mosquitoes that have been made infertile through genetic modification or irradiation. Infrastructure map The European Commission has published its latest wish list of the research-infrastructure projects that it considers most deserving of continent-wide support. The European Strategy Forum on Research Infrastructures road map, released on 10 March, details 21 facilities across all scientific areas to help national governments to prioritize how they spend infrastructure money, and to encourage them to share costs and responsibilities. New facilities listed in the 2016 road map include two in environmental sciences and one in health and food sciences, as well as solar and neutrino telescopes and an infrastructure for scientific research into cultural heritage. Minister keeps title German defence minister Ursula von der Leyen, who was accused in September 2015 of plagiarism in her medical dissertation in obstetrics, will not lose the title of doctor or her job. The senate of Hanover Medical School, which awarded the title in 1990, announced on 9 March that its formal investigation revealed that some passages in von der Leyen’s dissertation were copied from original sources. But these were mostly in the introduction, it said, and the main body of research was original and valid. Since 2011, two German federal ministers have lost their titles and government posts to plagiarism charges. Call to save bees The US Government Accountability Office (GAO) says that US regulatory bodies need to do more to protect bee populations. In a report made public on 11 March, the GAO called on the US Department of Agriculture (USDA) to work more closely with other agencies to protect bee health. The report says that although the USDA has upped efforts to monitor honeybee colonies managed by beekeepers, it does not coordinate the monitoring of wild, native bees. The report also recommends that the Environmental Protection Agency identifies the mixtures of pesticides most commonly used by farmers. Gene data shared Researchers and the public can now access a database of anonymized genetic information from 10,000 people with hereditary breast or ovarian cancer. The database, called AmbryShare, was launched on 8 March by Ambry Genetics, a genetic-testing company in Aliso Viejo, California — making Ambry the first private company to release its customers’ information for free. The Broad Institute of MIT and Harvard in Cambridge, Massachusetts, has an open-access database of more than 60,000 genomes collected from the public, but AmbryShare’s data currently focus on specific diseases. Ambry hopes to release up to 200,000 aggregated genomes per year from people with various conditions. India vaccine fight The medical charity Médecins Sans Frontières (MSF) is challenging pharmaceutical company Pfizer’s application for a patent in India on pneumonia vaccine PCV13, marketed as Prevenar 13 in India. MSF says that it wants to allow other manufacturers to make the vaccine, and lower its cost. The 11 March challenge asserts that the method that Pfizer is trying to patent is too obvious to deserve a patent under Indian law. Pfizer is reported as saying that the complexity of the vaccine justifies the price. In partnership with the vaccine alliance GAVI, Pfizer has reduced the price of Prevenar since 2013. Mosquito trial A proposed field trial of genetically modified mosquitoes in the Florida Keys poses no threat to human health or the environment, the US Food and Drug Administration has determined. Members of the public have 30 days to submit comments on the draft assessment, which was released on 11 March. The Aedes aegypti mosquitoes developed by Oxitec of Oxford, UK, are engineered to produce short-lived young to temporarily reduce mosquito populations and combat diseases that they carry. The project has received increased attention from the media and politicians amid concerns about the spread of Zika virus. The level of atmospheric carbon dioxide at the Mauna Loa Observatory in Hawaii rose by 3.05 parts per million (p.p.m.) in 2015 — the largest annual increase since records began 56 years ago, says the US National Oceanic and Atmospheric Administration. After correcting for seasonal swings from plant-growth cycles in the Northern Hemisphere, the average CO concentration in 2015 was 400.83 p.p.m. — a 43% rise compared to the CO level of around 280 p.p.m. that existed during the pre-industrial era. 10 Consecutive months in which the global monthly temperature record has been broken. February’s temperature was 1.35 °C above average for the month. A strong El Niño weather system has contributed to the record-breaking run. Source: NOAA 17–18 March Commercializing 3D printing for biological applications is discussed at the second Tissue Engineering, Biofabrication & 3D-Bioprinting in Life Sciences conference in Boston, Massachusetts. go.nature.com/rggrat 21–23 March NASA holds a meeting in Washington DC to develop its technology road maps. go.nature.com/dhmq2e 21–25 March The annual Lunar and Planetary Science Conference convenes in The Woodlands, Texas. go.nature.com/qpnoxd
British number theorist Andrew Wiles has received the 2016 Abel Prize for his solution to Fermat’s last theorem — a problem that stumped some of the world’s greatest minds for three and a half centuries. The Norwegian Academy of Science and Letters announced the award — considered by some to be the 'Nobel of mathematics' — on 15 March. Wiles, who is 62 and now at the University of Oxford, UK, will receive 6 million kroner (US$700,000) for his 1994 proof of the theorem, which states that there cannot be any positive whole numbers x, y and z such that xn + yn = zn, if n is greater than 2. Soon after receiving the news on the morning of 15 March, Wiles told Nature that the award came to him as a “total surprise”. That he solved a problem considered too hard by so many — and yet a problem relatively simple to state — has made Wiles arguably “the most celebrated mathematician of the twentieth century”, says Martin Bridson, director of Oxford's Mathematical Institute — which is housed in a building named after Wiles. Although his achievement is now two decades old, he continues to inspire young minds, something that is apparent when school children show up at his public lectures. “They treat him like a rock star,” Bridson says. “They line up to have their photos taken with him.” Wiles's story has become a classic tale of tenacity and resilience. While a faculty member at Princeton University in New Jersey in the 1980s, he embarked on a solitary, seven-year quest to solve the problem, working in his attic without telling anyone except for his wife. He went on to make a historic announcement at a conference in his hometown of Cambridge, UK, in June 1993, only to hear from a colleague two months later that his proof contained a serious mistake. But after another frantic year of work — and with the help of one of his former students, Richard Taylor, who is now at the Institute for Advanced Study in Princeton — he was able to patch up the proof. When the resulting two papers were published in 1995, they made up an entire issue of the Annals of Mathematics1, 2. But after Wiles's original claim had already made front-page news around the world, the pressure on the shy mathematician to save his work almost crippled him. “Doing mathematics in that kind of overexposed way is certainly not my style, and I have no wish to repeat it,” he said in a BBC documentary in 1996, still visibly shaken by the experience. “It’s almost unbelievable that he was able to get something done” at that point, says John Rognes, a mathematician at the University of Oslo and chair of the Abel Committee. “It was very, very intense,” says Wiles. “Unfortunately as human beings we succeed by trial and error. It’s the people who overcome the setbacks who succeed.” Wiles first learnt about French mathematician Pierre de Fermat as a child growing up in Cambridge. As he was told, Fermat formulated his eponymous theorem in a handwritten note in the margins of a book in 1637: “I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain,” he wrote (in Latin). “I think it has a very romantic story,” Wiles says of Fermat's idea. “The kind of story that catches people’s imagination when they’re young and thinking of entering mathematics.” But although he may have thought he had a proof at the time, only a proof for one special case has survived him, for exponent n = 4. A century later, Leonhard Euler proved it for n = 3, and Sophie Germain's work led to a proof for infinitely many exponents, but still not for all. Experts now tend to concur that the most general form of the statement would have been impossible to crack without mathematical tools that became available only in the twentieth century. In 1983, German mathematician Gerd Faltings, now at the Max Planck Institute for Mathematics in Bonn, took a huge leap forward by proving that Fermat's statement had, at most, a finite number of solutions, although he could not show that the number should be zero. (In fact, he proved a result viewed by specialists as deeper and more interesting than Fermat's last theorem itself; it demonstrated that a broader class of equations has, at most, a finite number of solutions.) To narrow it to zero, Wiles took a different approach: he proved the Shimura-Taniyama conjecture, a 1950s proposal that describes how two very different branches of mathematics, called elliptic curves and modular forms, are conceptually equivalent. Others had shown that proof of this equivalence would imply proof of Fermat — and, like Faltings' result, most mathematicians regard this as much more profound than Fermat’s last theorem itself. (The full citation for the Abel Prize states that it was awarded to Wiles “for his stunning proof of Fermat’s Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era in number theory.”) The link between the Shimura–Taniyama conjecture and Fermat's theorum was first proposed in 1984 by number theorist Gerhard Frey, now at the University of Duisburg-Essen in Germany. He claimed that any counterexample to Fermat's last theorem would also lead to a counterexample to the Shimura–Taniyama conjecture. Kenneth Ribet, a mathematician at the University of California, Berkeley, soon proved that Frey was right, and therefore that anyone who proved the more recent conjecture would also bag Fermat's. Still, that did not seem to make the task any easier. “Andrew Wiles is probably one of the few people on Earth who had the audacity to dream that he can actually go and prove this conjecture,” Ribet told the BBC in the 1996 documentary. Fermat's last theorem is also connected to another deep question in number theory called the abc conjecture, Rognes points out. Mathematician Shinichi Mochizuki of Kyoto University's Research Institute for Mathematical Sciences in Japan claimed to have proved that conjecture in 2012, although his roughly 500-page proof is still being vetted by his peers. Some mathematicians say that Mochizuki's work could provide, as an extra perk, an alternative way of proving Fermat, although Wiles says that sees those hopes with scepticism. Wiles helped to arrange an Oxford workshop on Mochizuki's work last December, although his research interests are somewhat different. Lately, he has focused his efforts on another major, unsolved conjecture in number theory, which has been listed as one of seven Millennium Prize problems posed by the Clay Mathematics Institute in Oxford, UK. He still works very hard and thinks about mathematics for most of his waking hours, including as he walks to the office in the morning. “He doesn’t want to cycle,” Bridson says. “He thinks it would be a bit dangerous for him to do it while thinking about mathematics.”