The asymptotic dependence structure of the linear fractional Lévy motion

the managerial discretion theoryThe Managerial Discretion TheoryIntroduction:The managerial discretion theory is a popular theory in the field of management that explains how managers have the ability to exercise discretion in decision-making and shape the direction of their organization. This theory suggests that managers have a significant impact on organizational outcomes and that their discretion in decision-making plays a crucial role in determining the success or failure of an organization. In this essay, we will explore the various aspects of the managerial discretion theory, including its origins, key concepts, applications, and criticisms. Origins of the Managerial Discretion Theory:The managerial discretion theory emerged during the late 1960s and early 1970s, in response to the dominance of the bureaucratic management approach. This approach emphasized the importance of rules, procedures, and hierarchy in decision-making, leaving little room for managerial discretion. Theorists such as Richard Cyert and James March challenged this approach by arguing that managers should be allowed to exercise discretion and use their judgment in decision-making, as they possess unique knowledge and expertise about the organization and its environment.Key Concepts of the Managerial Discretion Theory:The managerial discretion theory is based on several key concepts that help to explain how managers exercise discretion and shape organizational outcomes. These concepts include bounded rationality, goal ambiguity, resource dependence, and institutionalpressures.Bounded rationality refers to the limitation of human rationality in decision-making. According to Cyert and March, managers are not capable of making fully rational decisions due to cognitive limitations, time constraints, and incomplete information. Instead, managers rely on heuristics and biases to make decisions, which may not always result in the optimal outcome.Goal ambiguity refers to the lack of clarity and consensus among organizational members about organizational goals. This ambiguity provides managers with room for discretion in interpreting and pursuing organizational goals. Managers can prioritize certain goals over others and allocate resources accordingly, based on their own judgment and interpretation of the situation.Resource dependence theory suggests that managers exercise discretion to manage their organization's resource dependencies. Organizations rely on external resources, such as capital, labor, and technology, to function effectively. Managers must negotiate and make decisions to acquire and allocate these resources, which gives them significant discretion in shaping the organization's strategy and direction.Institutional pressures refer to the external social, cultural, and political forces that influence managerial discretion. Managers face pressures from various stakeholders, such as employees, customers, suppliers, government agencies, and the broader society. These pressures shape the decision-making process and can limit orexpand the manager's discretion.Applications of the Managerial Discretion Theory:The managerial discretion theory has been extensively applied in organizational research to understand managerial decision-making and its impact on organizational outcomes. Researchers have examined how managers exercise discretion in various contexts, including strategic decision-making, organizational change, innovation, and corporate governance.Strategic decision-making is a key area where managers exercise discretion. They make choices about the organization's competitive positioning, resource allocation, product development, and diversification. The managerial discretion theory suggests that managers' cognitive biases, heuristics, and interpretation of organizational goals will influence these decisions and their subsequent impact on organizational performance.Organizational change is another area where managerial discretion plays a crucial role. Managers have discretion in initiating and implementing change initiatives, such as restructuring, mergers, acquisitions, and downsizing. The success of these change efforts depends on the manager's ability to exercise discretion effectively, navigate internal and external pressures, and align the organization's goals with the change initiative.Innovation is an important driver of organizational success and competitiveness. Managers play a critical role in fostering innovation within their organizations by creating a supportive culture, allocating resources, and providing necessary autonomyfor employees. The managerial discretion theory suggests that managers with high levels of discretion are more likely to support and promote innovation within their organizations.Corporate governance is the system of rules, practices, and processes by which a company is directed and controlled. The managerial discretion theory has been applied to understand how managers exercise discretion in corporate governance decisions, such as executive compensation, board composition, and shareholder relationships. Managers can shape the governance structure to align their interests with those of shareholders or other stakeholders, depending on their level of discretion.Criticisms of the Managerial Discretion Theory:While the managerial discretion theory has made significant contributions to the field of management, it is not without its criticisms. Some scholars argue that the theory overemphasizes the role of individual managers and neglects the importance of structural and contextual factors. They contend that managers' discretion is constrained by organizational structures, external pressures, and industry dynamics, which limit their ability to shape organizational outcomes.Another criticism of the theory is that it assumes managers always act in the best interest of the organization. However, managers may have their biases, self-interests, and personal agendas that can influence their decision-making and compromise organizational outcomes. This criticism raises questions about the ethical implications of managerial discretion and the need for accountability mechanisms to ensure that managers exercisediscretion responsibly.Conclusion:The managerial discretion theory provides valuable insights into how managers exercise discretion in decision-making and shape organizational outcomes. It emphasizes the importance of managers' knowledge, judgment, and interpretation of organizational goals in driving success. While the theory has been widely applied and has contributed to our understanding of managerial behavior, it is not without its limitations and criticisms. Future research should address these criticisms and further refine the theory to enhance its applicability and validity.。

OG13 SC正确句子汇总1. In a review of 2,000 studies of human behavior that date back to the 1940s, two Swiss psychologists declared that since most of the studies had failed to control for variables such as social class and family size, none could be taken seriously2. Manufacturers rate batteries in watt-hours; if the higher the watt-hour rating, the longer the battery can be excepted to last.3. Although a surge in retail sales has raised hopes that a recovery is finally under way, many economists say that without a large amount of spending the recovery might not last.4. At the end of 1930s, Duke Ellington was looking for a composer to assisthim-——someone who could not only arrange music for his successful big band, but also mirror his eccentric writing style in order to finish the many pieces he had started but never completed.5. Of all the vast tides of migration that have swept through history, perhaps none was more concentrated than the wave that brought 12 million immigrants onto American shores in little more than three decades.6. Diabetes, together with its serious complications, ranks as the nation's third leading cause of death, surpassed only by heart disease and cancer.7. The intricate structure of the compound insect eye, with its hundreds of miniature eyes called ommatidia, helps explain why scientists have assumed that it evolved independently of the vertebrate eye.8. In late 1997, the chambers inside the pyramid of the Pharaoh Menkaure at Giza were closed to visitors for cleaning and repair because moisture exhaled by tourists had raised the humidity within them to such levels that salt from the stone was crystallizing and fungus was growing on the walls.9. In 1979 lack of rain reduced India's rice production to about 41 million tons, nearly 25 percent less than the 1978 harvest.10. The widely accepted big bang theory holds that the universe began in an explosive instant ten to twenty billion years ago and has been expanding ever since.11. Like the Brontes and Brownings, James Joyce and Virginia Woolf areoften subjected to kind of veneration that blurs the distinction between the artist and human being.12. Carnivorous mammals can endure what would otherwise be lethal levels of body heat because they have a heat-exchange network that keeps the brain from getting too hot.13. There are several ways to build solid walls using just mud or clay, but the most extensively used method has been to form the mud or clay into bricks, and, after some preliminary air drying or sun drying, to lay them in the wall in mud mortar.14. Rising inventories, if not accompanied by corresponding increases in sales, can lead to production cutbacks that would hamper economic growth.15. Many experts regarded the large increase in credit card borrowing in March not as a sign that households were pressed for cash and forced to borrow, but as a sign that households were confident they could safely handle new debt.16. A surge in new home sales and a drop in weekly unemployment claims suggest that the economy might not be as weak as some analysts previously thought.17. Sunspots, vortices of gas associated with strange electromagnetic activity, are visible as dark spots on the surface of the Sun but have never been sighted on the Sun's poles or equator.18. Warning that computers in the United States are not secure, the National Academy of Sciences has urged the nation to revamp computer security procedures, institute new emergency response teams, and create a special nongovernment organization to take charge of computer security planning.19. The exploits of Nellie Bly, a pioneer journalist, included circling the globe faster than Jules Verne's fictional Phileas Fogg.20. Retail sales rose 0.8 of 1 percent in August, intensifying expectations that personal spending in the July-September quarter would more than double the 1.4 percent growth rate in personal spending foe the previous quarter.21. The commission has directed advertisers to restrict the use of the word "natural" to foods that do not contain colour or flavor additives, chemical preservatives, or anything that has been synthesized.22. Plants are more efficient than fungi at acquiring carbon, in the form of carbon dioxide, and converting it to energy-rich sugars.23. The Iroquois were primarily planters, although they supplemented their cultivation of maize, squash, and beans with fishing and hunting.24. Unlike the honeybee, the yellow jacket can sting repeatedly without dying and carries a potent venom that cause intense pain.25. Neuroscientists, having amassed a wealth of knowledge over the past twenty years about the brain and its development from birth to adulthood, are now drawing solid conclusions about how the human brain grows and how babies acquire language.26. Tropical bats play important roles in the rain forest ecosystem, aiding in the dispersal of cashew, date, and fig seeds; pollinating banana, breadfruit, and mango trees; and indirectly helping to produce tequila by pollinating agave plants.27. None of the attempts to specify the causes of crime explains why most of the people exposed to the alleged causes do not commit crimes and, conversely, why so many of those not so exposed do.28. In virtually all types of tissue in every animal species, dioxin induces the production of enzymes that are the organism's attempt to metabolize, or render harmless, the chemical irritant.29. Emily Dickinson's letters to Susan Huntington Dickinson, which were written over a period beginning a few years before Susan's marriage to Emily's brother and ending shortly before Emily's death in 1886, outnumber her letters to anyone else.30. Paleontologists believe that fragments of a primate jawbone unearthed in Burma and estimated to be 40 to 44 million years old provide evidence of a crucial step along the evolutionary path that led to human beings.31. Even though many of her colleagues were convinced that genes were relatively simple and static, Barbara McClintock adhered to her own more complicated ideas about how genes might operate, and in 1983, at age of 81, was awarded a Nobel Prize for her discovery that the genes in corn are capable of moving from one chromosomal site to another.32. Galileo was convinced that natural phenomena, as manifestations of the laws of physics, would appear the same to someone on the deck of a ship moving smoothly and uniformly through the water as to a person standing on land.33. Because an oversupply of computer chips has sent prices plunging, the manufacturer has announced that it will cut production by closing its factories for two days a month.34. Beyond the immediate cash flow crisis that the museum faces, its survival depends on whether it can broaden its membership and leave its cramped quarters for a site where it can store and exhibit its more than 12,000 artifacts.35. By 1940, the pilot Jacqueline Cochran held seventeen official national and international speed records, earned at a time when aviation was still so new that many of the planes she flew were dangerously experimental design.36. Along with the drop in producer prices announced yesterday, the strong retail sales figures released today seem to indicate that the economy, although growing slowly, is not nearing a recession.37. Dressed as a man and using the name Robert Shurtleff, Deborah Sampson, the first woman to draw a soldier's pension, joined the Continental Army in 1782 at the age of 22, was injured three times, and was discharged in 1783 because she had become too ill to serve.38. Bengal-born writer, philosopher, and educated Rabindranath T agore had the greatest admiration for Mohandas K. Gandhi as a person and as a politician, butT agore was also skeptical of Gandhi's form of nationalism and his conservative opinions about India's cultural traditions.39. Although schistosomiasis is not often fatal, it is so debilitating that it has become an economic drain on many developing countries.40. The organization of Petroleum Exporting Countries (OPEC) had long been expected to announce a reduction in output to bolster sagging oil prices, but officials of the organization just recently announced that the group will pare daily production by 1.5 million barrels by the beginning of next year only if non-OPEC nations, including Norway, Mexico, and Russia, trim output by a total of 500,000 barrels a day.41. In 1850, Lucretia Mott published her discourse on Women, a treatise that argued for equal political and legal rights for women and for changes in the married women's property laws.42. T o develop more accurate population forecasts, demographers would have to know a great deal more than they do now about the social and economic determinants of fertility.43. Laos has a land area comparable to that of Great Britain but a population of only four million people, many of whom are members of hill tribes ensconced in the virtually inaccessible mountain valleys of the north.44. The plot of the Bostonians centres on the rivalry that develops between Olive Chancellor, an active feminist, and Basil Ransom, her charming and cynical cousin, when they find themselves drawn to the same radiant young woman whose talent for public speaking has won her ardent following.45. Quasars, at billions of light-years from Earth the most distant observable objects in the universe, are believed to be the cores of galaxies in an early stage of development.46. In ancient Thailand, much of the local artisan's creative energy was expended on the creation of Buddha images and on construction and decoration of the temples in which they were enshrined.47. In 1713, Alexander Pope began his translation of the Iliad, a work that took him seven years to complete and that literacy critic Samuel Johnson, Pope's contemporary, pronounced the greatest translation in any language.48. Though called a sea, the landlocked Caspian is actually the largest lake on Earth, covering more than four times the surface area of its closest rival in size, North America's Lake Superior.49. The automotive conveyor-belt system, which Henry Ford modeled after an seemly-line technique introduced by Ransom Olds, reduced the time required to assemble a Model T from a day and a half to 93 minutes.50. According to some analysts, the gains in the stock market reflect growing confidence that the economy will avoid the recession that many had feared earlier in the year and instead come in for a "soft landing," followed by a gradual increase in business activity.51. A new study suggests that the conversational pace of everyday life may be so brisk that it hampers the ability of some children to distinguish discrete sounds and words and, as a result, to make sense if speech.52. Long before it was fashionable to be an expatriate, Josephine Baker made Paris her home, and she remained in France during the Second World War as a performer and an intelligence agent for the Resistance.53. The nineteenth-century chemist Humphry Davy presented the results of his early experiments in his "Essay on heat and Light," a critique of all chemistry since Robert Boyle as well as a vision of a new chemistry that DAvy hoped to found. 54. The report recommended that the hospital eliminate unneeded beds, consolidate expensive services, and use space in other hospitals.55. Many house builders offer rent-to-buy programs that enable a family with insufficient savings for a conventional down payment to move into new housing and to apply part of the rent to a purchase later.56. Elizabeth Barber, the author of both Prehistoric T extiles, a comprehensive work on cloth in the early cultures of the Mediterranean, and Women's Work, a more general account of early cloth manufacture, is an authority on textiles in ancient societies.57. Many of the earliest known images of Hindu deities in India date from the time of the Kushan Empire and were fashioned either from the spotted sandstone of Mathura or from Gandharan grey schist.58. It can hardly be said that educators are at fault for not anticipating the impact of microcomputer technology: Alvin T offler, one of the most prominent students of the future, did not even mention microcomputers in Future Shock, published in 1970.59. A leading figure in the Scottish Enlightenment, Adam Smith wrote two major books that are to democratic capitalism what Marx's Das Kapital is to socialism.60. The Olympic Games helped to keep pace among the pugnacious states of the Greek world, for a sacred true was proclaimed during the month of the festival.61. While all states face similar industrial waste problems, the predominant industries and the regulatory environment of each state obviously determine the types and amounts of waste produced, as well as the cost of disposal.62. Rivaling the pyramids of Egypt or even the ancient cities if the Maya as an achievement, the army of terra-cotta warriors created to protect Qin Shi Huang, China's first emperor, in his afterlife is more than 2,000 years old and took 700,000 artisans more than 36 years to complete.63. When Congress reconvenes, some newly elected members from rural states will try to establish tighter restrictions on the amount of grain farmers will be allowed to grow and to encourage more aggressive sales of United States farm products overseas.64. Doctors generally agree that such factors as cigarette smoking, eating rich foods high in fats, and alcohol consumption not only do damage by themselves but also aggravate genetic predispositions toward certain diseases.65. Digging in sediments in northern China, scientists have gathered evidence suggesting that complex life-forms emerged much earlier than previous thought.66. In a plan to stop the erosion of East Coast Beaches, the Army Corps of Engineers proposed building parallel to shore a breakwater of rock that would rise six feet above the waterline and act as a buffer, absorbing the energy of crashing waves and protecting the beaches.67. The 32 species that make up dolphin family are closely related to whales and in fact include the animal known as the killer whale which can grow to be 30 feet long and is famous for its aggressive hunting pods.68. Outlining his strategy for nursing the troubled conglomerate back to health, the chief executive announced plans Wednesday to cut the company's huge debt by selling nearly $12 billion in assets over the next 18 months.69. Affording strategic proximity to the Strait of Gibraltar Morocco was also of interest to the French throughout the first half of the twentieth century because they assumed that without it their grip on Algeria would never be secure.70. The first trenches cut into a 500-acre site at T ell Hamoukar, Syria, have yielded strong evidence that centrally administered complex societies in northern regions of Middle East arose simultaneously with but independently of the more celebrated city-states of southern Mesopotamia, in what is now southern Iraq.71. Along the major rivers that traverse the deserts of northeast Africa, the Middle East, and northwest India, the combination of a reliable supply of water and good growing conditions encouraged farming traditions that have, in places, endured for at least 6,000 years.72. His studies of ice-polished rocks in his Alpine homeland, far outside the range of present-day glaciers, led Louis Agassiz in 1837 to propose the concept of an age in which great ice sheets existed in what are temperature areas.73. Unlike the original National Museum of Science and T echnology in Italy, where the models are encased in glass or operated only by staff member, the Virtual Leonardo Project, an online version of the museum, encourages visitors to "touch" each exhibit and thereby active the animated functions of the piece.74. Although it covers the entire planet, Earth's crust is neither seamless nor stationary, but rather fragmented into mobile semirigid plates.75. More and more in recent years, cities are stressing the arts as a means to greater economic development and investing millions of dollars in cultural activities, despite strained municipal budgets and fading federal support.76. Combining enormous physical strength with higher intelligence, the Neanderthals appear to have been equipped to face any obstacle the environment could put in their path, but their relatively sudden disappearance during the Paleolithic era indicates that an inability to adapt to some environmental change led to their extinction.77. A 1972 agreement between Canada and the United States reduced the amount of phosphates that municipalities are allowed to dump into the Great Lakes.78. A proposal has been made to trim the horns from rhinoceroses to discourage poachers; the question is whether tourists will continue to visit game parks to see rhinoceroses once the animals' horn have been trimmed.79. Ryunosuke Akutagawa's knowledge of the literatures of Europe, China, and Japan was instrumental in his development as a writer, informing both his literary style and the content of his fiction.80. The only way for growers to salvage frozen citrus is to have it quickly processed into juice concentrate before warmer weather returns and rots the fruit.81. Fossils of the arm of a sloth, found in Puerto Rico in 1991, have been dated at 34 million years old, making the sloth the earliest known mammal on the Greater Antilles Islands.82.Defense attorneys have occasionally argued that their clients' misconduct stemmed from a reaction to something ingested, but if criminal or delinquent behaviour is attributed to an allergy to some food, the perpetrators are in effect told that they are not responsible for their actions.83. A report by the American Academy for the Advancement of Science has concluded that many of the currently uncontrolled dioxins to which North Americans are exposed come from the incineration of wastes.84. Recently physicians have determined that stomach ulcers are caused not by stress, alcohol, or rich foods, but by a bacterium that dwells in the mucous lining of the stomach.85. According to a recent poll, owning and living in a freestanding house on its own land is still a goal of a majority of young adults, as it was of earlier generations. 86. In 2000, a mere two dozen products accounted for half the increase in spending on prescription drugs, a phenomenon that is explained not just by the fact that drugsare becoming more expensive but also by the fact that doctors are writing many more prescriptions for higher-cost drugs.87. According to scientists who monitored its path, an expanding cloud of energized particles ejected from the Sun recently triggered a large storm in the magnetic field that surrounds EArth, brightening the Northern Lights and possibly knocking out a communications satellite.88. Often visible as smog, ozone is formed in the atmosphere when hydrocarbons and nitrogen oxides, two major pollutants emitted by automobiles, react with sunlight.89. Salt deposits and moisture threaten to destroy the Mohenjo-Daro excavation in Pakistan, the site of an ancient civilization that flourished at the same time as the civilizations in the Nile Delta and the river valleys of the Tigris and Euphrates.90. The result of the company's cost-cutting measures are evident in its profits, which have increase 5 percent during the first 3 months of this year after failing over the last two years.91. In an effort to reduce their inventories, Italian vintners have cut prices; their wines are priced to sell, and they do.92.Jazz pianist and composer Thelonious Monk produced a body of work that was rooted in the stride-piano tradition of Willie (The Lion) Smith and Duke Ellington, yet in many ways he stood apart from the mainstream jazz repertory.93. Nobody knows exactly how many languages there are in the world, partly because of the difficulty of distinguishing between a language and the sublanguages or dialects within it, but those who have tried to count typically have found about five thousand.94. Heating-oil price are expected to be higher this year than last because refiners are paying about $5 a barrel more for crude oil than they were last year.95. One of the primary distinctions between our intelligence and that of other pirates may lie not so much in any specific skill as in our ability to extend knowledge gained in one context to new and different ones.96. Even though Clovis points, spear points with longitudinal grooves chipped onto their faces, have been found all over North America, they are named for the New Mexico site where they were fist discovered in 1932.97. Some anthropologists believe that the genetic homogeneity evident in theworld's people is the result of a "population bottleneck"——that at some time in the past our ancestors suffered an event that greatly reduced their numbers and thus our genetic variation.98. Ranked as one of the most important of Europe's young playwrights, Franz Xaver Kroetz has written 40 plays; his works——translated into more than 30 languages——as produced more often than those of any contemporary German dramatist.99. Like the planets, the stars are in motion, some of them at tremendous speed, but they are so faraway from Earth that their apparent positions in the sky do not change enough for their movement to be observed during a single human lifetime.100. Being heavily committed to a course of action, especially one that has worked well in the past, is likely to make an executive miss signs of incipient trouble or misinterpret them when they do appear.101. As rainfall began to decrease in the Southwest about the middle of the twelfth century, most of the the Monument Valley Anasazi abandoned their homes to join other clans whose access to water was less limited.102. Y ellow jackets number among the 900 or so species of the world's social wasps, wasps that live in a highly cooperative and organized society consisting almost entirely of females——the queen and her sterile female workers.103. El Nino, the periodic abnormal warming of the sea surface off Peru, is a phenomenon in which changes in the ocean and atmosphere combine to allow the warm water that has accumulated in the western Pacific to flow back to the east. 104. In her book illustration, which she carefully coordinated with her narratives, Beatrix Potter capitalized on her keen observation and love of the natural world.105. Marconi conceived of the radio as a tool for private conversation that could substitute for the telephone; instead, it has become precisely the opposite, atoll for communicating with a large, public audience.106. Originally developed for detecting air pollutants, a technique calledproton-induced X-ray emission, which can quickly analyze the chemical elects in almost any substance without destroying it, is finding uses in medicine, archaeology, and criminology.107. While the costs of running nuclear plants is about the same as for other types of power plants, the fixed costs that stem from building nuclear plants make the electricity they generate more expensive.108. Authoritative parents are more likely than permissive parents to have children who as adolescents are self-confident,high in self-esteem, and responsibly independent.109. Among the objects found in the excavated temple were small terra-cotta effigies left by supplicants who were either asking the goddess Bona Dea's aid in heating physical and mental ills or thanking her for such help.110. Published in Harlem, The Messenger was owned and edited by two young journalists, A. Philip Randolph, who would later make his reputation as a labor leader, and Chandler Owen.111. A mutual fund having billions of dollars in assets will typically invest that money in hundreds of companies, rarely holding more than one percent of the shares of any particular corporation.112. Construction of the Roman Colosseum, which was officially known as the Flavian Amphitheater, began in A.D. 69, during the reign of Vespasian, and was completed a decade later, during the reign of Titus, who opened the Colosseum with a one-hundred-day cycle of religious pageants, gladiatorial games and spectacles.113. A baby emerges from the darkness of the womb with a rudimentary sense of vision that would be rated about 20/500; an adult with such vision would be deemed legally blind.114. Starfish, with anywhere from five to eight arms, have a strong regenerative ability, and if one arm is lost it is quickly replaced, with the animal sometimes overcompensating and growing an extra one or two.115. Because the new maritime code provides that even tiny islets can be the basis for claims to the fisheries and oil fields of large sea areas, it has already stimulated international disputes over uninhabited islands.116. The original building and loan associations were organized as limited life funds, whose members made monthly payments on their share subscriptions and then took turns drawing on the funds for home mortgages.117. Gall's hypothesis that different mental functions are localized in different parts of the brain is widely accepted today.118.Mauritius was a British colony for almost 200 years, but except in the domains of administration and teaching, the English language was never really spoken on the island.119. George Sand (Aurore Lucile Dupin) was one of the first European writers to consider the rural poor legitimate subjects for literature and to portray them with sympathy and respect in her novels.120. The World Wildlife Fund has declared that global warming, a phenomenon that most scientists agree is caused by human beings' burning of fossil fuels, will create havoc among migratory birds by altering the environment in ways harmful to their habitats.121. New theories propose that catastrophic impacts of asteroids and comets may have caused reversals in the Earth's magnetic field, the onset of ice ages, the splitting apart continents 80 million years ago, and great volcanic eruptions.122. A firm that specializes in the analysis of handwriting claims to be able, from a one-page writing sample, to assess more than 300 personality traits, including enthusiasm, imagination, and ambition.123. Sales of wines declined in the late 1980s, but they began to grow again after the 1991 report that linked moderate consumption of alcohol, and particularly of red wine, with a reduced risk of heart disease.124. Less successful after she emigrated to New Y ork than she had been in her native Germany, photographer Lotte Jacobi nevertheless earned a small group of discerning admirers, and her photographs were eventually exhibited in prestigious galleries across the United States.125. T oday, because of improvements in agricultural technology, the same amount of acreage produces twice as many apples as it did in 1910.126. The use of lie detectors is based on the assumption that lying produces emotional reactions in an individual that, in turn, create unconscious physiological responses.127. Joan of Arc, a young Frenchwoman who claimed to be divinely inspired, turned the tide of English victories in her country by liberating the city of Orleans and persuaded Charles VII of France to claim his throne.128. Australian embryologists have found evidence to suggest that the elephant is descended from an aquatic animal and that its trunk originally evolved as a kind of snorkel.129. Cajuns speak a dialect brought to southern Louisiana by the 4,000 Acadians who migrated there in 1755; their language is basically seventieth-century French to which English, Spanish, and Italian words have been added.130. Over 75 percent of the energy produced in France derives from nuclear power, whereas nuclear power accounts for just over 33 percent of the energy produced in Germany.131. Although the term "psychopath" is popularly applied to an especially brutal criminal, in psychology it refers to someone who is apparently incapable of feeling compassion or the pangs of conscience.132. Although heirloom tomatoes, grown from seeds saved during the previous year, appear less appetizing than most of their round and red supermarket cousins——they are often green and striped, or have plenty of bumps and viruses——heirlooms are more flavourful and thus in increasing demand.133. Last week local shrimpers held a new conference to take some credit for the resurgence of the rare Kemp's ridley turtle, saying that their compliance with laws requiring turtle-excluder devices on shrimp nets is protecting adult sea turtles.134. Recently implemented "shift-work equations" based on studies of the human sleep cycle have reduced sickness, sleeping on the job, and fatigue among shift workers while raising production efficiency in various industries.135. Spanning more than 50 years, Friedrich Muller's career began in an unpromising apprenticeship as a Sanskrit scholar and culminated in virtually every honour that European governments and learned societies could bestow.136. Whereas in mammals the tiny tubes that convey nutrients to bone cells are arrayed in parallel lines, in birds the tubes form a random pattern.137. Joachim Raff and Giacomo Meyerbeer are examples of the kind of composer who receives popular acclaim while living, but whose reputation declines after death and never regains its former status.138. Most efforts to combat such mosquito-borne diseases as malaria and dengue have focused on either vaccinating humans or exterminating.。

金融幂律：实证，模型以及原理Thomas Lux1Department of EconomicsUniversity of Kiellux@bwl.uni-kiel.de为社会科学中的幂律而准备：发现社会科学的复杂性和非均衡动态，Claudio Cioffi,编者.概述：金融市场（股票市场，外汇市场以及其他市场）均以一系列普遍使用的幂律为特征，最突出的例子是以强健的，近似三次幂律（cubic power law）来描述大量回报（large returns）的分布这一独特发现。

一个几乎同样强健特征是对波动性的长期依赖（例如：其自相关函数的双曲线递减）。

最近的文献加入了交易量的时间标度（temporal scaling）和higher moments of returns的multi-scaling. 最近，对于这些特征的关注引起了人们对市场过程中这些关键特征之所以出现的原因进行理论解释的尝试。

理论上来讲，不用种类的动态过程可能造成了这些幂律。

在经济学文献中找到的例子包括乘法随机过程（multiplicative stochastic processes）和多均衡的动态过程。

尽管这两种过程dynamics均以间歇产生大规模活动爆发的间断行为为特征，而事实上它们则可能是基于对交易过程上根本性地不同的理解。

前面的章节既回顾了在经济学文献中提出的相关模型，又复习了出现在以上数据到产生机制中的幂律的分析背景。

一简介尽管关于收入和资产中的幂律研究可以追溯到19世纪（Pareto）, 但对于在金融数据中幂律的关注还是最近的事情。

幂律在金融中第一次体现可能是在Mandelbrot 的Journal of Business 中1963卷的具有开启意义的Variation of Certain Speculative Prices"一文中，随后紧接着Eugene Fama在随后的一篇名为“Mandelbrot and the Stable Paretian Hy-pothesis"的一文中，进一步阐述了同一个问题。

SEMIPARAMETRIC DENSITY ESTIMATION FOR TIME SERIESWITH MULTIPLICATIVE ADJUSTMENT1Kaiping Wang1,2and Lu Lin11School of Mathematics and System Sciences,Shandong UniversityJinan250100,P.R.China2School of Management,Shandong University,Jinan250100,P.R.Chinawkp@AbstractIn this paper,we extend a class of semiparametric density estimators to time series context.The asymptotic theory and simulation study are discussed.Theoretical results and numerical comparison show that,in the time series case,the estimators in this class are better than,or at least competitive with,the traditional kernel density estimator in a broad class of densities.Keywords:semiparametric density estimation,time series,multiplicative adjustment.1.INTRODUCTIONDensity estimation is one of the most fundamental areas in statistical analysis.Tradition-ally,there are two approaches for density estimation.One is called the parametric approach, the other,nonparametric.The parametric approach is attractive for a number of reasons.1This paper is supported by RFDP project(20070422034)of China.1One reason is its statistical simplicity,i.e.,estimation of the entire function boils down to inferring a few parameter values.Another reason is that,if the parametric assumption is justified,the density function can be estimated more efficiently than it can be by a nonpara-metric approach.However,the nonparametric approach has attractiveflexibility which can be used without the structural assumption that the underlying structure is controlled by a finite-dimensional parameter.A representative method for nonparametric density estimation is the traditional kernel density estimation.Most of the work focuses on independent random samples.For time series data,the kernel method has also been studied,see,e.g.the book by Bosq(1996).Let{X t}Tt=1be a realization from a stationary process with marginal density f.The kernel density estimator of f is defined by˜f(x)=T−1Tt=1K h(X t−x),(1.1)where K h(z)=h−1K(h−1z),K(·)is usually a nonnegative,symmetric and unimodal prob-ability density function withfinite values ofσ2K =z2K(z)dz and R(K)=K(z)2dz,andh is the bandwidth.Under certain mixing and smoothness conditions,the basic statistical properties are thatE[ˆf(x)]=f(x)+σ2K2f (x)h2+O(h4),V ar{ˆf(x)}=f(x)T h R(K)+o(1T h).(1.2)(Fan and Yao,2003).In recent years,there have been increasing interests and activities in the general area of semiparametric approaches.Let X1,X2,···,X n be independently and identically distributed2with density f,to estimate the density f from the data,Naito(2004)provided a class of semiparametric density estimators that have multiplicative adjustment,including estimators proposed by several authors(Hjort and Glad,1995,Hjort and Jones,1996)as special cases. In the proposed approach,a parametric density estimator g(x,ˆθ)is utilized,but it is seen as a crude guess of the true density f.This initial parametric approximation is adjusted via multiplication by an adjustment factorξ=ξ(x).ξis determined by minimization of the empirical version of the functionQ(x,ξ|α)=K h(t−x)[f(t)−g(t,ˆθ)ξ]2g(t,ˆθ)αdt,(1.3)for afixed target point x,whereαis a real number called the index.This method is called the local L2-fitting criterion.After omitting the irrelevant term,the empirical version of (1.3)can be expressed asQ n(x,ξ|α)=ξ2K h(t−x)g(t,ˆθ)2−αdt−2ξnni=1K h(X i−x)g(X i,ˆθ)1−α.The minimizer can be easily determined asˆξ=ˆξ(x)=arg minξQ n(x,ξ|α)=n−1ni=1K h(X i−x)g(X i,ˆθ)1−αK h(t−x)g(t,ˆθ)2−αdt.Using thisˆξ,a class of semiparametric density estimators is obtained byˆf α(x)=g(x,ˆθ)ˆξ=g(x,ˆθ)n−1ni=1K h(X i−x)g(X i,ˆθ)1−αK h(t−x)g(t,ˆθ)2−αdt.(1.4)Theoretical comparison reveals that the estimators in this class are better than,or at least competitive with,the traditional kernel estimator in a broad class of densities.3In this paper,we extend this semiparametric multiplicative approach to time series con-text.In Section2,we study the asymptotic behavior ofˆfα,forα-mixing time series.This approach is shown to be effective and yields a class of theoretically good estimators in the sense of mean integrated squared error(MISE).Finite sample performance of the proposed estimators,and comparison to the kernel density estimator(1.1)are investigated by Monte Carlo simulation in section3.Proofs of the theoretical results are presented in section4. 2.ASYMPTOTIC THEORYLet{X t}Tt=1be a realization from a stationary process with marginal density f.Sup-pose g(x,θ)be a given parametric family of densities,where the possibly multidimensional parameterθ=(θ1,...,θp) belongs to some open and connected region in p-space.Let the parametric-start estimate be g(x,ˆθ),whereˆθis an estimator of the least false valueθ0ac-cording to a certain distance measure between f and g(·,θ).For concreteness we here choseˆθas the maximum likelihood estimator and defineθas the minimizer of the kullback-Leibler distance onθ.From(1.4),the class of semiparametric multiplicative estimators of f isˆf α(x)=g(x,ˆθ)ˆξ=g(x,ˆθ)T−1Tt=1K h(X t−x)g(X t,ˆθ)1−αK h(t−x)g(t,ˆθ)2−αdt,(2.1)where K(·)is the kernel function as in(1.1).In this section,we investigate various statistically important quantities about(2.1),such as bias and variance.We will use the following assumptions:(a)Let{X t}be anα-mixing process with the mixing coefficient| (l)|≤cl−βfor some4c>0andβ>2.(b)Let g l(x,y)be the joint density of X1and X l+1and assume that g l(x,y) =sup(x,y)g l(x,y)is bounded.Remark2.1According to Collomb(1985),theα-mixing condition is the most suitable one when working with time series since the ARMA processes with continuous white noise satisfy it,among others(see Doukhan(1994)for a more complete discussion of theα-mixing condition).Theorem 1.Assume that conditions(a)and(b)hold,h→0in such a way thatT h→∞.If f has the continuous second derivative at an interior point x of the support of f,then,Biasˆfα(x)=h22σ2K[(g0(x)1−αf(x))g0(x)1−α−f(x)(g0(x)2−α)g0(x)2−α]+O(h2T+h4+T−2),V arˆfα(x)=1T h R(K)f(x)+o(1T h).(2.2)Remark2.2Whenα=0,1and2,we have the following relationships:ˆf(x)=ˆf HJ(x),ˆf1(x)=ˆf LL(x),ˆf2(x)=ˆf HG(x),whereˆf HJ(x)andˆf LL(x)are two estimators proposed by Hjort and Jones(1996),andˆf HG(x) is the density estimator proposed by Hjort and Glad(1995).In Section3,we will compareˆfαwith˜f,ˆf HJ(x),ˆf LL(x)andˆf HG(x)in time series settings by Monte Carlo simulation and get some insights about the practically good choice ofα.Remark2.3From above theorem,we can see that,the results are very much like those for independent samples.The bias is unaffected by dependence and the asymptotic variance5is the same as in the i.i.d.case.However,the result for the asymptotic variance heavily depends on the strength of the dependence among the X t’s.Let z t=K h(X t−x)g0(X t)1−α, thenV ar(T−1Tt=1z t)=1TV ar(z1)+2TT−1l=1(1−lT)Cov(z1,z l+1)(2.3)Thefirst term on the right hand side of(2.3)is equal to the variance based on independent data.The second term reflects the extra variability due to the dependence of the X t’s.Thestrength of the dependence can be measured through the size of T−1l=1Cov(z1,z l+1).For anα-mixing process,a standard result is T−1l=1|Cov(z1,z l+1)|=o(h−1)(see Lemma1).SoV arˆfα(x)=1T hR(K)f(x)+o(1T h).However,if without condition(a),the size of the second term on the right side of(2.3)can be significantly larger and can dominate the usual leading variance term,leading to a worse rate of convergence ofˆfα(x).Remark2.4From(2.2)and(1.2),the AMISE ofˆfα(x)and˜f are,respectively,given byAMISE(ˆfα)=h44(σ2k)2 (ˆfα)+R(K)T handAMISE(˜f)=h44(σ2k)2 (˜f)+R(K)T h,where(ˆfα)=[(g0(x)1−αf(x))1−α−f(x)(g0(x)2−α)2−α]2dx,(˜f)=[f (x)]2dx.6So this class of new estimators is better than the traditional kernel density estimator in all cases where (ˆfα)is smaller in size than (˜f).Furthermore,if f is in the model{g(x,θ):θ∈Θ},that is,g0(x)=f(x),then the O(h2)term of the bias vanishes.Naito(2004) compared (ˆfα)with (˜f)for the case in which f belongs to a class of normal mixture densities used in Marron and Wand(1992).The class of normal mixture densities is a very broad one because any density can be approximated arbitrarily closely in various senses by a normal mixture(Marron and Wand,1992).Naito confirmed thatˆfαis better than,or at least competitive with,˜f for all cases in that comparison.3.A SIMULATION STUDYFinite sample performance of the class of proposed density estimators was investigated by Monte Carlo simulation.The process{X t}we considered was a stationary moving average process of order1,X t=εt−pεt−1,where p=0.2and{εt}is a sequence of independent and continuous random variables with common density function g.As a direct consequence,the marginal density of the process isf(x)=g(y)g(x+py)dy.(3.1)The Gaussian,skewed unimodal and separated bimodal distributions were considered as the density function g of the noiseε(see Marron and Wand(1992)for the definitions about the last two densities)because they typify some different challenges to curve estimation.7By(3.1),f is Gaussian,skewed unimodal and bimodal,respectively.In each case200 samples of size T=500were generated.The MISE(α,h)value for a given combination of(α,h)was estimated by the average of these200realizations of ISE(α,h).To obtain a precise approximation to the minimum MISE,a grid search of the combination(α,h)was implemented.The Gaussian kernel was used throughout.Letα0be the optimalαwhich we obtained by the grid search,the estimators compared in this study were˜f andˆfαforα=0, 1,2andα0.We utilized g(x,ˆθ)=φˆσ−1(x−ˆµ)for all cases,i.e.,we started with a Gaussian MA(1) approximation,where(ˆµ,ˆσ2)is the MLE of(µ,σ2)(see,e.g.,Brockwell and Davis(2002) for computing the MLE of an ARMA model).Values of105×minMISE are tabulated in Table1,where the minimum is taken over h. Also tabulated in parentheses are105times the standard error(SE)for each case.Table1:The value of estimated min h MISE(h)×105for samples of size T=500from three densities over.The standard error×105is given in parentheses for each case. 200simulations for˜f,ˆf0,ˆf1,ˆf2andˆfαValues of the optimal indexα0are listed in theα0column for each case.α0f˜fˆf0ˆf1ˆf2ˆfα#1Gaussian16.53 3.94 3.74 5.01 3.73 1.31(11)(4)(4)(4)(4)#2skewed unimodal25.5626.1621.6519.5719.55 1.91(15)(14)(13)(12)(12)#3bimodal28.4331.5828.4427.4127.36 1.83(15)(16)(15)(15)(15)First we see#1.This case is that f is in the parametric model so that the O(h2)term8of the bias ofˆfαvanishes,as mentioned in Remark(2.4).For#1all ofˆfαare significantly better than˜f and the optimalαis around1.For cases#2and#3,the estimatorˆfαis the best.Furthermore,it is worth noting that α0is around2.This reveals that the Hjort and Glad estimatorˆf HG=ˆf2is also good for these cases.4.PROOFSIn this section the proofs of theoretical results are presented.First we prepare the fol-lowing lemma.Lemma4.1.Assume that conditions(a)and(b)in section2hold.Suppose g(x,θ0)is afixed density.Let g0(x)=g(x,θ0)andf∗α(x)=g0(x)T−1Tt=1K h(X t−x)g0(X t)1−αK h(t−x)g0(t)2−αdt.Suppose that h→0in such a way that T h→∞.If f has the continuous second derivative at an interior point x of the support of f,thenBiasf∗α(x)=h22σ2K[(g0(x)1−αf(x))g0(x)1−α−f(x)(g0(x)2−α)g0(x)2−α]+O(h4),V arf∗α(x)=1R(K)f(x)+o(1). Proof.By Taylor expansion,we haveBiasf∗α(x)=Ef∗α(x)−f(x)=g0(x)E[T−1Tt=1K h(X t−x)g0(X t)1−α]−f(x)K h(t−x)g0(t)2−αdtK h(t−x)g0(t)2−αdt,in which the denominator can be expressed asK(u)g0(x+hu)2−αdu=g0(x)2−α+O(h2),9and the numerator can be expressed asg0(x)[g0(x)1−αf(x)+12σ2kh2g0(x)1−αf (x)+σ2k h2(g0(x)1−α) f (x)+12σ2kh2(g0(x)1−α) f(x)+O(h4)]−[f(x)g0(x)2−α+f(x)σ2kh2(g0(x)2−α) +O(h4)]=1σ2kh2g0(x)[g0(x)1−αf (x)+2(g0(x)1−α) f (x)+(g0(x)1−α) f(x)]−σ2kh2(g0(x)2−α) f(x)+O(h4).ThenBiasf∗α(x)=h22σ2K[(g0(x)1−αf(x))g0(x)1−α−f(x)(g0(x)2−α)g0(x)2−α]+O(h4).The varianceV arf∗α(x)=V ar[g0(x)T−1Tt=1K h(X t−x)g0(X t)1−αK h(t−x)g0(t)2−αdt]=g2(x)[K h(t−x)g0(t)2−αdt]2V ar[T−1Ti=1K h(X t−x)g0(X t)1−α].Let z t=K h(X t−x)g0(X t)1−α,thenV ar(T−1Tt=1z t)=1TV ar(z1)+2TT−1l=1(1−lT)Cov(z1,z l+1).Note that Ez1=E[K h(X t−x)g0(X t)1−α]=f(x)g0(x)1−α+O(h2)=O(1),by a change of variables and Taylor expansion,we haveV ar(z1)=E[K h(X t−x)g0(X t)1−α]2−(Ez1)2=1hK2(u)g0(x+hu)2(1−α)f(x+hu)du−(Ez1)2=1hR(K)g0(x)2(1−α)f(x)+o(h−1).10Thus,we need only to show thatT−1l=1|Cov(z1,z l+1)|=o(h−1).By using Billingsley’s inequality,we have|Cov(z1,z l+1)|≤4 (l) z1 ∞ z l+1 ∞≤4 (l)D/h2(4.1) for some constant D.On the other hand,|Cov(z1,z l+1)|=|Ez1z l+1−(Ez1)2|≤ ∞−∞∞−∞K h(u−x)K h(v−x)g0(u)g0(v)g l(u,v)dudv+(Ez1)2(4.2)Hence,the covariance is bounded by a constant C.Let d T→∞be a sequence of integers.Then,by(4.2), dT−1l=1|Cov(z1,z l+1)|≤Cd T.Using(4.1)and the assumption on the mixing coefficient,we haveT−1l=d T |Cov(z1,z l+1)|≤D∞l=d Tl−β/h2.By taking d T=h−2/β,we haveT−1l=1|Cov(z1,z l+1)|=O(h−2/β)=o(h−1),for someβ>2.Hence,wefinish the proof.Proof of Theorem1.Let x n=(x1,...,x n)be a sequence of real-valued and dependent random variables,with joint probability density function(p.d.f.)given byg(x1,...,x n,θ)=g(x n,θ).11The conditional p.d.f.of x i given x i−1isg i,θ=g(x i,θ|x i−1)=g(x i,θ)/g(x i−1,θ).Letθ0be the true but unknown value ofθ,and let I(X i)=J−1(∂/∂θ)log g i,θ,whereJ=−E f[(∂2/∂θ∂θT)log g i,θ].Under certain conditions(e.g.Bhat,1974),we haveˆθ=θ0+1nni=1I(X i)+dn+εn(4.3)whereεn=O p(1/n)with mean O(1/n2).Define u0(x)=∂log g(x,θ0)/∂θ,v0(x)=∂2log g(x,θ0)/∂θ∂θT.Using Taylor expansions,we can expandˆfαasˆf α(x)=f∗α(x)+V T(x)+12W T(x)+o p(T−1).We write V T(x)=¯BT(ˆθ−θ0),and W T(x)=(ˆθ−θ0) ¯C T(ˆθ−θ0),whereB t=K h(X t−x)g0(X t)1−αg0(x)η0(x)[(1−α)u0(X t)−2−αη0(x)η1(x)+u0(x)],C t=K h(X t−x)g0(X t)1−αg0(x)η0(x){−2(1−α)(2−α)η0(x)η1(x)u0(X t)T+2(1−α)u0(x)u0(X t)T+(1−α)[v0(X t)+(1−α)u0(X t)u0(X t)T]−2(2−α)η0(x)u0(x)η1(x)T+[v0(x)+u0(x)u0(x)T]+2(2−α)η0(x)2[(2−α)η1(x)η1(x)T−12η0(x)η2(x)]},whereη0(x)=K h(t−x)g0(t)2−αdt,η1(x)=K h(t−x)u0(t)g0(t)2−αdt,η2(x)=K h(t−x)[v0(t)+(2−α)u0(t)u0(t)T]g0(t)2−αdt.12From Lemma4.1,we already know that,Biasf∗α(x)=h22σ2K[(g0(x)1−αf(x))g0(x)1−α−f(x)(g0(x)2−α)g0(x)2−α]+O(h4).Through(4.3),wefindEV T(x)=E[1TTt=1Bt(ˆθ−θ0)]=1T2E[nt=1BtTt=1I t]+1TE(Tt=1Bt)d+O(T−2),1 T2E(Tt=1BtTt=1I t)=1TE(BtI t)+2TT−1l=1(1−lT)E(B1I l+1).It is not difficult to see that EB t,EBtI t,EC t is of size O(h2).WhileT−1l=1(1−l/T)E(B1I l+1)≤T−1l=1|E(B1I l+1)|=T−1l=1|Cov(B1,I l+1)|≤T−1l=14α(l)C≤4CT−1l=1l−β,forβ>2, T−1l=1l−βconverges,we have2/TT−1l=1(1−l/T)E(B1I l+1)=O(1/T).Thus,EV T(x)=O(h2T+T−2).Similarly,EW T(x)=E[(ˆθ−θ0) ¯C T(ˆθ−θ0)]=O(h2T+T−2).We haveBiasˆfα(x)=h22σ2K[(g0(x)1−αf(x))g0(x)1−α−f(x)(g0(x)2−α)g0(x)2−α]+O(h2T+h4+T−2).13Next we turn to the variance.The variance of f∗α(x)is known from Lemma4.1.V ar(V T(x))=V ar[¯BT(ˆθ−θ0)]=V ar[¯BT ¯In]+O(T−2)=O(h4T+T−2).Similarly,W T(x)can be seen to have uninfluential variance O(h4T2).Finally,Cov[f∗(x),V T(x)]=O(h2T).This combines to giveV arˆfα(x)=1T hR(K)f(x)+o(1T h).ReferencesBhat,B.R.(1974).On the method of maximum-likelihood for dependent observations.J. Roy.Statist.Soc.Ser.B,36,48-53.Bosq,D.(1996).Nonparametric statistics for stochastic processes.New York:Springer-Verlag.Brockwell,P.J.and Davis,R.A.(2002).Introduction to Time Series and Forecasting.New York:Springer-Verlag.Collomb,G.(1985).Nonparametric time series analysis and prediction:uniform almost sure convergence.Statist.,2,297-307.Doukhan,P.(1994).Mixing:properties and examples.Berlin:Springer.Fan,J.Q.and Yao,Q.W.(2003).Nonlinear Time Series:Nonparametric and Parametric14Methods.New York:Springer-Verlag.Hjort,N.L.and Glad,I.K.(1995).Nonparametric density estimation with a parametric start.Ann.Statist.,23,882-904.Marron,J.S.and Wand,M.P.(1992).Exact mean integrated squared error.Ann.Statist., 20,712-736.Hjort,N.L.and Jones,M.C.(1996).Locally parametric nonparametric density estimation. Ann.Statist.,24,1619-1647.Naito,K.(2004).Semiparametric density estimation by local L2-fitting.Ann.Statist.,32, 1162-1191.15。

FINITE DIMENSIONAL REDUCTION OF NONAUTONOMOUS DISSIPATIVESYSTEMSAlain MiranvilleUniversit´e de Poitiers Collaborators:Long time behavior of equations of the formy′=F(t,y)For autonomous systems:y′=F(y)In many situations,the evolution of the sys-tem is described by a system of ODEs:y=(y1,...,y N)∈R N,F=(F1,...,F N)Assuming that the Cauchy problemy′=F(y),y(0)=y0,is well-posed,we can define the family of solv-ing operators S(t),t≥0,acting on a subset φ⊂R N:S(t):φ→φy0→y(t)This family of operators satisfiesS(0)=Id,S(t+s)=S(t)◦S(s),t,s≥0We say that it forms a semigroup onφQualitative study of such systems:goes back to Poincar´eMuch is known nowadays,at least in low di-mensionsEven relatively simple systems can generate very complicated chaotic behaviorsThese systems are sensitive to perturbations: trajectories with close initial data may diverge exponentially→Temporal evolution unpredictable on ti-me scales larger than some critical value→Show typical stochastic behaviorsExample:Lorenz systemx′=σ(y−x)y′=−xy+rx−yz′=xy−bzObtained by truncature of the Navier-Stokes equationsGives an approximate description of a layer of fluid heated from belowSimilar to what is observed in the atmosphereFor a sufficiently intense heating:sensitive dependence on the initial conditions,repre-sents a very irregular convection→Butterfly effectVery often,the trajectories are localized in some subset of the phase space having a very complicated geometric structure(e.g.,locally homeomorphic to the product of R m and a Cantor set)→Strange attractor(Ruelle and Takens)Main feature of a strange attractor:dimen-sionSensitivity to initial conditions:>2(dimen-sion of the phase space≥3,say,3)Contraction of volumes:its volume is equal to0→noninteger,strictly between2and3→Fractal dimensionExample:Lorenz system:dim F A=2.05...Distributed systems:systems of PDEsφis a subset of an infinite dimensional func-tion space(e.g.,L2(Ω)or L∞(Ω))Solution:y:R+→φt→y(t)x→y(t,x)If the problem is well-posed,we can define the semigroup S(t):S(t):φ→φy0→y(t)The analytic structure of a PDE is much more complicated than that of an ODE:the global well-posedness can be a very difficult problemSuch results are known for a large class of PDEs→it is natural to investigate whether the notion of a strange attractor extends to PDEsSuch chaotic behaviors can be observed in dissipative PDEsChaotic behaviors arise from the interaction of•Energy dissipation in the higher part of the Fourier spectrum•External energy income in the lower part•Energyflux from the lower to the higher modesThe trajectories are localized in a”thin”in-variant region of the phase space having a very complicated geometric structure→the global attractor1.The global attractor.S(t)semigroup acting on E:S(t):E→E,t≥0S(0)=Id,S(t+s)=S(t)◦S(s),t,s≥0 Continuity:x→S(t)x is continuous on E,∀t≥0A set A⊂E is the global attractor for S(t)if(i)it is compact(ii)it is invariant:S(t)A=A,t≥0(iii)∀B⊂A,lim t→+∞dist(S(t)B,A)=0dist(A,B)=supa∈A infb∈Ba−b EEquivalently:∀B⊂φbounded,∀ǫ>0,∃t0= t0(B,ǫ)s.t.t≥t0implies S(t)B⊂UǫThe global attractor is uniqueIt is the smallest closed set enjoying(iii)It is the maximal bounded invariant setTheorem:(Babin-Vishik)We assume that S(t)possesses a compact attracting set K, i.e.,∀B⊂E bounded,lim t→+∞dist(S(t)B,K)=0Then S(t)possesses the global attractor A.The global attractor is oftenfinite dimen-sional:the dynamics,restricted to A isfinite dimensionalFractal dimension:Let X be a compact setdim F X=lim supǫ→0+ln Nǫ(X)ǫNǫ(X):minimum number of balls of radius ǫnecessary to cover XIf Nǫ(X)≤c(1Theorem:(H¨o lder-Ma˜n´e theorem)Let X⊂E compact satisfy dim F X=d and N>2d be an integer.Then almost every bounded linear projector P:E→R N is one-to-one on X and has a H¨o lder continuous inverse.This result is not valid for other dimensions (e.g.,the Hausdorffdimension)If A hasfinite fractal dimension,then,fixing a projector P satisfying the assumptions of the theorem,we obtain a reduced dynamical system(S),S= P(A),which isfinite dimensional(in R N)and H¨o lder continuousDrawbacks:(S)cannot be realized as a system of ODEs which is well-posedReasonable assumptions on A which would ensure that the Ma˜n´e projectors are Lipschitz are not knownComplicated geometric structure of A and AThe lower semicontinuitydist(A0,Aǫ)→0asǫ→0is more difficult to prove and may not hold It may be unobservable:∂y∂x2+y3−y=0,x∈[0,1],ν>0y(0,t)=y(1,t)=−1,t≥0A={−1}There are many metastable”almost station-ary”equilibria which live up to t⋆≡eν−12.Inertial manifolds.A Lipschitzfinite dimensional manifold M⊂E is an inertial manifold for S(t)if(i)S(t)M⊂M,∀t≥0(ii)∀u0∈E,∃v0∈M s.t.S(t)u0−S(t)v0 E≤Q( u0 E)e−αt,α>0,Q monotonicM contains A and attracts the trajectories exponentiallyConfirms in a perfect way thefinite dimen-sional reduction principle:The dynamics reduced to M can be realized as a Lipschitz system of ODEs(inertial form)Perfect equivalence between the initial sys-tem and the inertial formDrawback:all the known constructions are based on a restrictive condition,the spectral gap condition→The existence of an inertial manifold is not known for several important equations, nonexistence results for damped Sine-Gordon equations3.Exponential attractors.A compact set M⊂E is an exponential at-tractor for S(t)if(i)It hasfinite fractal dimension(ii)S(t)M⊂M,∀t≥0(iii)∀B⊂E bounded,dist(S(t)B,M)≤Q( B E)e−αt,α>0,Q monotonicM contains AIt is stillfinite dimensional and one has a uni-form exponential control on the rate of at-traction of trajectoriesIt is no longer smoothDrawback:it is not unique→One looks for a simple algorithm S→M(S)Initial construction:non-constructible and valid in Hilbert spaces onlyConstruction in Banach spaces:Efendiev, Miranville,Zelik→Exponential attractors are as general as global attractorsMain tool:Compact smoothing property on the difference of2solutionsLet S:E→E.We consider the discrete dynamical system generated by the iterations of S:S n=S◦...◦S(n times)Theorem:(Efendiev,Miranville,Zelik)We consider2Banach spaces E and E1s.t.E1⊂E is compact.We assume that•S maps theδ-neighborhood Oδ(B)of a bounded subset B of E into B•∀x1,x2∈Oδ(B),≤K x1−x2 ESx1−Sx2 E1Then the discrete dynamical system gener-ated by the iterations of S possesses an ex-ponential attractor M(S)s.t.(i)M(S)⊂B,is compact in E anddim F M(S)≤c1(ii)S M(S)⊂M(S)(iii)dist(S k B,M(S))≤c2e−c3k,k∈N,c3>0 (iv)The map S→M(S)is H¨o lder continu-ous:∀S1,S2,dist sym(M(S1),M(S2))≤c4 S1−S2 c5,c5>0, wheredist sym(A,B)=max(dist(A,B),dist(B,A))S =supSh Eh∈Oδ(B)Furthermore all the constants only depend on B,E,E1,δand K and can be computed explicitly.Remarks:1)We have a mapping S→M(S)and,due to the H¨o lder continuity,we can construct continuous families of exponential attractors2)Exponential attractors for a continuous semigroup S(t):Prove that∃t⋆>0s.t.S⋆=S(t⋆)satisfies the assumptions of the theorem→M⋆for S⋆If(x,t)→S(t)x is Lipschitz(or H¨o lder)on B×[0,t⋆],setS(t)M⋆M=∪t∈[0,t⋆]We again have a mapping S(t)→M(S)which is H¨o lder continuous3)For damped hyperbolic equations:asymp-totically smoothing property4.Finite dimensional reduction of nonau-tonomous systems.Systems of the form∂yDrawback:the uniform attractor has infinite dimension in general.Example:∂yThe family{A(t),t∈R}is a pullback attrac-tor for U(t,τ)if(i)A(t)is compact in E,∀t∈R(ii)U(t,τ)A(τ)=A(t),∀t≥τ(iii)∀B⊂E bounded,dist(U(t,t−s)B,A(t))=0lims→+∞Remarks:1)The pullback attractor is unique2)If the system is autonomous,we recover the global attractor3)In general,A(t)hasfinite fractal dimen-sion,∀t∈RDrawback:The forward convergence does not hold in generalExample:y′=f(t,y),where f(t,y)=−y if y≤0,(−1+2t)y−ty2 if t∈[0,1],and y−y2if t≥1Then A(t)={0},∀t∈R,but every trajectory starting from a neighborhood of0leaves this neighborhood never to enter it againThe forward convergence does not hold be-cause the rate of attraction is not uniform in t→This can be solved by constructing ex-ponential attractorsWe can construct a family{M(t),t∈R}, called nonautonomous exponential attractor, s.t.(i)dim F M(t)≤c1,∀t∈R,c1independent of t(ii)U(t,τ)M(τ)⊂M(t),∀t≥τ,(iii)∀B⊂E bounded,dist(U(t,τ)B,M(t+τ))≤Q( B E)e−αt,t∈R,t≥τ,α>0,Q monotonic(iii)implies the pullback attraction,but also the forward attraction→(i)and(iii)yield a satisfactoryfinite di-mensional reduction principle for nonautono-mous systemsRemarks:1)The time dependence is arbitrary2)The map U(t,τ)→{M(t),t∈R}is also H¨o lder continuous。

a r X i v :c o n d -m a t /0604296v 1 [c o n d -m a t .s o f t ] 12 A p r 2006Dependence of self-assembled amphiphile structure on interaction betweenhydrophilic groupsHIROAKI NAKAMURA ∗and YUICHI TAMURANational Institute for Fusion Science,Oroshi-cho 322-6,Toki 509-5292,JAPAN(Dated:23August 2005and accepted 12April 2006)In a previous study (.(2005)169,139–143),we clarified the dependence of the phase structure on the hydrophilicity of an amphiphilic molecule by varying the interaction potential between the hydrophilic molecule and water (a AW )in a dissipative particle dynamics (DPD)simulation using the Jury model.In the present paper,we perform another DPD simulation using the previous model to investigate the dependence of the interaction potential between adjacent hydrophilic groups on the phase structure.By varying the coefficient of the interaction potential between adjacent hydrophilic groups a AA (a AA =15,25,40,and 250)at a dimensionless temperature of T =0.5and a concentration of amphiphilic molecules in water of φ=50%,hexagonal (a AA =14,25,40)and micellar (a AA =250)phases were observed.In comparison with the previous results,the dependence of the A-B dimer’s shape on a AA was determined to be weaker than that on a AW .Therefore,it is concluded that the solvent water W plays an important role in aggregation of the A-B dimers.I.INTRODUCTION Amphiphilic molecules have many degrees of freedom in the structures they adopt.However,when the temperature and concentration of an aqueous solution of the amphiphilic molecules are fixed,the molecules are restricted to a certain molecular shape and aggregate to form a variety of mesoscopic structures,for example,micellar,lamellar and hexagonal phases.In previous papers[1,2],we have investigated the amphiphilic molecule hexaethylene glycol dodecyl ether (C 12E 6),a popular surfactant in water that forms a variety of self-assembled structures.The phase structure of C 12E 6was investigated by Mitchell[3]in 1983.In our work,we clarified[2]the dependence of the phase structure on hydrophilicity by varying the interaction potential (a A W )between the hydrophilic molecules and water in a dissipative particle dynamics (DPD)simulation using the Jury model[4].In the present paper,to determine the relative dominance of different microscopic interaction potentials in de-termining the mesoscopic phase structure,we investigated the dependence of the phase structure on the interaction potential between adjacent hydrophilic groups a AA .The details of the DPD simulation algorithm and models can not be included due to lack of space but are the same as reported previously[2]with the exception of the interaction potentials a A W and a AA .The differences with the previous simulation are described in Section 2.II.SIMULATION METHOD We used the same DPD model and algorithm[4,5]as described previously[1,2],with a modification of the conser-vative force F C ij between particles i and j ,given in the present paper by F C ij ≡ a ij (1−r ij )n ij if r ij <1,0if r ij ≥1,(1)where n ij ≡(r i −r j )/|r i −r j |,and r i is a position vector for particle i .Coefficients a ij in Eq.(1)denote thecoupling constants between particles i and j .The numerical values of a ij are given by Table I.III.SIMULATION RESULTS AND DISCUSSIONTo demonstrate the dependence of the mesoscopic phase structure on the interaction potential between adjacent hydrophilic groups,we varied the A-A interaction potential coefficient such that a AA =15,25,40,and 250.FIG.1:Structures formed for each potential coefficient,a AA=15(a),25(b),40(c),and250(d).We set T=0.5andφ=50% during simulation.The aggregation structure for each value of a AA is shown in Fig.1.To quantitatively classify the phase structure, we also plot the radial distribution function of the solute particles for each a AA in Fig. 2.Thefigures show that hexagonal phases(a AA=15,25,40)and micellar(a AA=250)phases are formed depending on the coefficient a AA of the A-A interaction potential.The distance R between a hydrophilic group in an A-B dimer and another group in the nearest A-B dimer(Fig.3) is shown as thefirst peak R(a AA)of g AA(r)in Fig.2(a).On the other hand,the intramolecular distance between A and B,that is l in Fig.3,is shown as thefirst peak in Fig.2(b).We plotted the dependence of the distance R and the length l on the interaction potential a AA in Fig.4(a).Figure4(a)indicates that the dependence of the length l(a AA)on a AA is weaker than that for R.We also plotted the dependence of1/(R2l)on the interaction potential a AA in Fig.4(b).Here we consider the packing parameter introduced by Israelachvili[2,6,7].According to this description,the hexagonal and micellar phases correspond to1/2≤p≤1/3and p≤1/3,respectively.The packing parameter p is considered to be proportional to1/(R2l).From Fig.4(b),p∝1/(R2l)decreases as a AA increases.Therefore,it is found that A-B dimers form cylinders for small a AA values,and that AB dimers modify their shape from cylinders to cones by increasing the distance between the neighboring head groups as a AA increases.Lastly,we compare the present results with our previous work[2],which investigated the dependence of the phase structure on a A W.In that previous work,we showed that the A-B dimer modifies its shape with changing hydrophilicity a A W.It is intuitively expected that the shape of the A-B dimer would depend more strongly on the parameter a AA than the parameter a A W,because a AA affects the distance between the hydrophilic groups more directly than a A W. However,contrary to our expectation,the present simulation results show that the dependence of the A-B dimer’s shape on a AA is weaker than that on a A W.Based on this result,we conclude that the solvent water W plays an important role in determining the phase structure of the A-B dimers in aggregation.FIG.2:Radial distribution functions for the solute particles vs.distance between the two particles r for a AA=15,25,40 and250.(a)The A-A radial distribution function g AA(r).Thefirst peak R(a AA)of each curve corresponds to the A-A distance between two adjacent AB dimers.R(15)=0.889,R(25)=0.889,R(40)=0.904,R(250)=0.963.(b)The A-B radial distribution function g AB(r).Thefirst peaks correspond to the length of the A-B dimer l in Fig.3.l(15)=0.326,l(25)= 0.326,l(40)=0.326,l(250)=0.296.W A B25050A503025IV.CONCLUSIONWe demonstrated the dependence of the A-B dimer’s aggregated structure in solvent water W by varying the A-A interaction potential a AA in a dissipative particle dynamics simulation.The present simulation and the previous results[2]show that the a AA-dependence of the A-B dimer’s shape is weaker than the a A W-dependence.Therefore,it is concluded that the solvent water W plays an important role in forming the phase structure of the A-B dimers in aggregation.AcknowledgmentsThis research was supported by the Ministry of Education,Culture,Sports,Science and Technology of Japan, Grant-in-Aid for Scientific Research(C),2005,No.17540384.[1]Nakamura,H.2004,Molecular Simulation30,941–945.[2]Nakamura,H.&Tamura,Y.2005,.169,139–143.[3]Mitchell,D.J.,Tiddy,G.J.T.,Waring,L.,Bostock,T.&MacDonald,M.P.1983,J.Chem.Soc.,Faraday Trans.179,975–1000.[4]Jury,S.,Bladon,P.,Cates,M.,Krishna,S.,Hagen,M.,Ruddock,N.&Warren P.1999,Phys.Chem.Chem.Phys.1,2051–2056.[5]Groot,R.D.&Warren,P.B.1997,J.Chem.Phys.107,4423–4435.[6]Israelachvili,J.N.,Mitchell,D.J.&Ninham,B.W.1976,J.Chem.Soc.Faraday Trans.II72,1525–1568.[7]Israelachvili,J.N.1992Intermolecular and Surface Forces(Academic Press,London)2nd ed.。

纵向数据半参数建模研究计划一、研究回顾纵向数据是指对一组个体按时间顺序或空间顺序追踪重复测得的数据，对每一个体在不同时间或不同实验条件下多次测量，所得的数据兼有时间序列和截面数据的特点。

这种数据的特点是所研究的反应变量的观测值随时间变化，相关的协变量也随时间变化有一系列的观察，具有上述特点的数据在医学、生物学、社会学、经济学、心理学等领域极为常见。

由于在纵向数据中对同一个个体的多次重复观察之间往往具有相关性，如何处理这种个体内的相关性便成为纵向分析中不可回避的问题。

此外，在纵向数据分析中还要较好地研究协变量对反应变量的影响，同一个体重复测量值内部的相关结构的信息在统计分析中应得到充分的利用。

作为对重复测量数据的相关性的刻画，早期主要采用参数的方法。

比如误差项为时间序列的多元线性模型、生长曲线模型等，由于随机误差项的结构很复杂，经常会不可避免的遇到维数灾祸。

以后又发展到非线性形式、离散的泛函形式的纵向数据模型，形成了比较成熟的非参数模型和半参数模型。

由于在纵向数据中经常遇到缺失或测量误差，这些都会增加统计分析的难度。

纵向数据的参数回归分析方法是早期研究的主要方法。

一般线性模型往往假定误差项为多元正态分布，零均值向量，协方差阵为分块对角阵。

进一步按协方差阵可细分均匀相关，指数相关，一步相关等。

可用极大似然法或加权最小二乘法以及广义估计方程的方法进行估计或统计推断。

广义线性模型可将连续型反应变量的研究推广至离散型，如Logistic边缘模型、泊松回归模型等，还可解决反应变量是分类数据的情形。

混合效应模型是研究纵向数据的强有力的工具。

对于具有不同类的个体（heterogeneous individuals)的研究，引入随机效应来反映个体的异质性，从而反映同一个体的观测的内相关性，这是纵向数据研究的十分重要的方法。

参数模型直观且易于进行统计分析,当假设的模型成立时,其推断的精度也较高。

然而如果假设的模型与实际不符,参数模型就会带来很大偏差。

Test 1: Development of MicrobiologyMultiple-choice:1.The fundamental(基本的) unit of all living organisms is the:所有生物体的基本单位是A. membraneB. cellC. nucleusD. cell wallanisms that do not contain a true nucleus are referred to as:（不具有真正细胞核的生物叫做：）A. Fungi（真菌）B. Eukaryotic（真核生物）C. prokaryotic （原核生物）D. nankaryotic3.The three kingdom classification system of organisms was proposed by:谁提出···A. PasteurB. BaconC. Winogradsky4.Fungi真菌differ from bacteria细菌in a number of characteristics特征. The cell walls infungi are composed of 由…组成, while the cell walls of bacteria are composed ofB. Phospholipids（磷脂）C. proteinD. Glucosamine（氨基葡糖）5.The first microscopes were developed by:A.EhrlichB. Metchnikoff D. Lister6.Control of microbial can be accomplished by chemical orimmune mechanisms免疫机制. The first report on the production of an antibiotic抗生素is credited to:A. ListerB. FlemingC. EhrlichD. Koch7.The term "antibiotic（抗菌的；抗生素）" means:A. a substance produced by the laboratory（化工厂，药厂）that kills or inhibits other microorganismsD. a substance produced by microorganisms that kills or inhibits cancer cells8. The first documented use of a vaccine疫苗for smallpox天花was reported by the English physician:A. ListerB. FloreyC. FlemingD. Jenner9.The genetic material遗传物质of a bacteria is located in the molecule（分子）:A．RNA B. DNA C. protein D. lipidFILL IN BLANKS:anisms that contain a true nucleus are called_eukaryotic__（真核生物）____2.3.菌）_.4._anaerobes（厌氧菌）_ are organisms that can grow without using molecular oxygen（氧分子）.5. Microorganisms that can synthesize（合成）complex organic compounds （有机复合物）from CO2 are called _autotroph（自养生物）_.6. _phototrophs（光养生物）are microorganisms that obtain（获得）their energy to synthesize organic compounds from light.7. Heterotroph（异养生物）require organic compounds有机物for growth.8. Organisms that survive only at very high temperatures are referred to as_thermophile（极端嗜热生物）_.9. _methanogen（产烷菌）_ are organisms that produce methane（甲烷）from CO2.10. _halophile_（嗜盐微生物）____organisms grow under conditions of high salinity（盐分）.11. Eubacteria真细菌can exhibit（显现，展示）a number of morphological shapes（形态）. Identify four: a._spherical（球状）or cocci_____ b._cylindrical（圆柱状）or rod（杆状）_____c._spirality（螺旋状）_____d._irregular（无规则）or filamen（丝状体）12.Fungi真菌, algae藻类and protozoa can be differentiated（区别，鉴别）from bacteria by the following characteristic:_eukaryotic_真核细胞_____ .13. Fungi have cell wall consisting of _chitin（几丁质）______.14.Viruses consist of _nucleic acid_核酸____surrounded by a protein coat.15. The theory spontaneous generation 自然发生说of held that living organisms couldarise from nonliving matter来自非生命物质.16.The process used to reduce the number of viable organisms by moderate heating is called用适度加热来减少活生物体的过程叫：_pasteurization（巴斯德消毒法、巴氏消毒法）_ . 17.The process of tyndallization间歇性灭菌过程uses repeated heating重复加热toeliminate消除or_ _sterilize_消毒____ microorganisms from solutions.18.18 .An _antibiotic（抗生素）______is a substance produced by microorganisms that inhibits orkills other microorganisms.19. The process of stimulating（刺激）the immune（免疫）defenses （防御）of the body is referred to as__immunization（免疫）_____.20. A substance in serum（血清）that can neutralize（使无效，抵消）foreign material is referred to as _antitoxin_（抗毒素）____or __antibody（抗体）____.21.Avery, Colin and MacLeod first demonstrated that transformation of nonpathogenic to pathogenic strains of bacteria could be carried out by the transfer of _DNA_.22. Exchange of genetic information by direct contact直接接触is referred to as__conjugation （结合，组合）.23. _transformation__(转移)___ is the process in which DNA is transferred from one bacteria to another.Test 2: Organization and Structure of Microorganisms1.Eukaryotic membranes真核细胞膜can be differentiated from prokaryotic membranes 原核细胞膜because eukaryotic membranes contain as part of the lipid component脂质成分of the membrane.A.phosphates磷酸盐类B. fatty acids脂肪酸类C, proteins蛋白类 D. sterols甾醇类2.A. C. trilayer model D. permeable （可渗透的）model3.The movement运动of water molecules水分子across the membrane in response to aconcentration（浓度）gradient（坡度）is referred to as:A. Diffusion（扩散作用）B. Osmosis（渗透作用）C. TranslocationD. transport4.The membrane of a cell is able to differentiate区分molecules that enter or exit the cell andact as a ____ barrier屏障.A. semipermanent （非永久性的）B. Semitransparent（磨砂）C. Semipermeable（半透性）D. semidiffuse5. Movement of molecules at an enhanced（增大）rate across the membrane is called:A. facilitated diffusion（促进扩散）B. passive diffusion（被动扩散）C. Osmosis（渗透作用）D. Permeation（渗透作用）6. Which of the following mechanisms transports molecules分子运输机制with chemicalalteration?A. active transport C. facilitated diffusion易化扩散D. binding protein transport蛋白质转运7. Which of the following transport mechanisms occurs only in prokaryotes原核?A. active transportC. facilitated diffusionD. binding protein transport8. Lysozyme溶菌酶and penicillin青霉素have activity against the cell wall. Lysozyme breaksthis component; penicillin prevents its formation .A.Lipopolysaccharide(脂多糖类)B.Phospholipid磷脂Peptidoglycan肽聚糖D. teichoic acid（胞壁酸）9. Partial（胞壁酸）destruction of the cell wall with lysozyme（胞壁酸酶，溶菌酶）leavesa cell called a:A. protoplast原生质体 C. periplast （周质体） D. Capsule（荚膜）10. DNA transfers（转录）information to make proteins in molecules referred to as:A. iRNA C. rRNA D. tRNA11. The endoplasmic reticulum (ER) 内质网is a membranous （膜的）structure within eukaryotic cells. It is the site for protein synthesis and for storage（贮存）and transportation of molecules out of the cell. Which part of the ER is used for protein synthesis?A. golgi apparatus（高尔基体） C. smooth ER D. Microbody （微体）12. Gram-positive（革兰氏阳性菌）bacteria can be differentiated from Gram-negative bacteriasince the peptidoglycan（肽聚糖）layer comprises包括____% of the cell wall.A. 90B. 50C. 30D.1013. Which of the following is not found in all bacterial cell?A. cell membraneB. a nucleoidC. Ribosomes（核糖体）D. Capsule（荚膜）14. Pili菌毛are tubular（管状的）shafts in bacteria that serve as a means of .A. gram-positive, genetic exchangeB. gram-positive, attachmentC. gram-negative, genetic exchangeD. gram-negative, protection15. Which of the following is a primary bacterial cell wall function细菌细胞壁的主要功能?A. transportB. motilityC. supportD. Adhension（附着）16. Which of the following is present in both gram-positive and gram-negative cell wall?A. an outer membrane（外包膜）B. peptidoglycan （肽聚糖）C. teichoic acid （胞壁酸）D. Lipopolysaccharides（多脂糖类）17. Mesosomes（间体，中膜体）are internal extensions（延伸）of theA. cell wallB. cell membraneC. Chromosome（染色体）D. capsule18. Bacterial endospores内生孢子function inA. reproductionB. survivalC. Protein synthesisD. storage19. A bacterial arrangement in packets of eight cells is described as a .A. Micrococcus（球球状菌）B. Tetrad（四分体）C. Diplococcus（双球菌）D. sacina20. In general, if two haploid （单倍体）cells fuse, will result.A. a germ cellB. Mitosis（细胞有丝分裂）C. a diploid zygote（二倍体合子）D. Meiosis（减数分裂）21. The cell wall is found in which eukaryotes:A. fungiB. algaeC. ProtozoaD. A and B22. Yeasts酵母菌are fungi, and molds霉菌are fungi.A. macroscopic, microscopicB. Unicellular（单细胞的）, filamentous（丝状的）C. Motile（能动的）, nonmotileD. water, terrestrial（陆生的）23. In general, fungi derive nutrients throughA. Photosynthesis（光合作用）B. engulfing bacteria （吞噬细菌）C. digesting organic substrates分解有机物D. Parasitism（寄生）24. A hypha（菌丝）divided into compartments（划分）by cross walls is called .A. nonseptateB. imperfectC. Septate（有隔膜的）D. perfect25. A conidium（分生孢子）is a/an spore, and a zygospore（接合孢子）is a/an spore.A. Sexual（有性的）, asexualB. free, endo（内部的）C. Ascomycete（子囊菌类）,basidiomycete（担子菌类）D. asexual, sexual26.Algae generally contain some types ofA. sporeB. Chlorophyll（叶绿素）C. locomotor organelle（可移动的细胞器）D. Toxin（毒素）27. Mitochondria（线粒体）likely originated fromA. archaeaB. Invaginations（套入部分）of the cell membraneC. purple bacteria（紫细菌）D. cyanobacteria （蓝细菌）28. A virus is a tiny infectious感染A. cellB. living thingC. Particle（颗粒）D. nucleic acid29. Virus are known to infectA. plantsB. bacteriaC. fungiD. all organisms30. The capsid （衣壳）is composed of protein subunits calledA. spikesB. Virions（病毒粒子）C. Protomers（原聚体）D. Capsomers（衣壳粒）31. The envelope外壳of an animal virus is derived from来自the of its host cell.A. cell wallB. cell membraneC. Glycolyx（糖被）D. Receptors（受体）32. The nucleic acid of a virus isA. DNA onlyB. RNA onlyC. both DNA and RNAD. either DNA or RNA33. The general steps in a viral multiplication增殖cycle areA. Adsorption（吸附）, penetration（侵入）, replication（复制）, maturation（成熟）, and release（释放）B. endocytosis, uncoating, replication, assembly, and buddingC. adsorption, uncoating, duplication, assembly, and lysisD. endocytosis, penetration, replication, maturation, and exocytosis34. A prophage（原噬菌体）is an early stage in the development of a/anA. bacterial virusB. Poxvirus（痘病毒）C. Lytic（细胞溶解酶的）virusD. enveloped virus35. Enveloped viruses carry surface receptors called包膜病毒进行表面受体称为A. Buds（芽体）B. Spikes（刺突）C. fibersD. Sheaths（芽鞘）36. Viruses cannot be cultivated inA. tissue culture组织培养B. live mammals哺乳动物C. bird embryos鸟胚D. blood agar（血琼脂）37. The protein coat structure of the virus is called a:A. coatB. envelopC. receptorD.capsid衣壳38. The composition组成of the envelop包围of some viruses is:A. phospholipids and proteins coded by the viral genomeB. phospholipids磷脂and proteins coded编码by the host genome宿主基因组C. phospholipids coded by the host genome and proteins coded by the viral genomeD. phospholipids coded by the viral genome and proteins coded by the host genome39. In some cases intact（完整的）viruses are not needed to infect感染a cell. Infectious传染性protein molecules that can cause disease are given the term:A.Prions（朊病毒）B. Viroids（类病毒）C. Capsomers（衣壳粒）D.Virions（病毒粒子）FILL IN BLANKS:1.Most cells use energy in the form of_ ATP__ to run the cell.2. The region区域between the outer membrane外膜in Gram-negative bacteria and the cell wallis called the _periplasmic space（周质间隙）___.2.Extrachromosomal （染色体外的）DNA elements found in bacteria are called_plasmids（质粒）_______.3.The fluid inside a cell is referred to as the _cytoplasm_（细胞质）______.4.The hereditary（遗传的，世代的）organelle（细胞器）of eukaryotic真核cells is calledthe _nucleus细胞核_____.5.Bacteria stained by the gram method fall into two groups: Gram positive bacteria (G+), appeardeep violet（紫色）in color; Gram negative bacteria (G-) appear red红in color.6.Staphylococcus aureus金黄色葡萄球菌stained by the gram method appear deep violet incolor7.Escherichia coli 大肠杆菌stained by the gram method appear red in color.8.The cell walls of most Gram-positive eubacteria have peptidoglycan肽聚糖and teichoicacids磷壁酸.9.The outer membrane of the Gram-negative cell wall contains phospholipid磷脂on its innersurface and lipopolysaccharide（脂多糖类）(LPS) on its outer surface.10.Among the more prominent（凸起的）PHB and glycogen碳存储聚合物–PHB及糖原、Granules硫磺颗粒、Gas V acuoles气泡。

CORRELATION AND DEPENDENCE IN RISK MANAGEMENT:PROPERTIES AND PITF ALLSPAUL EMBRECHTS,ALEXANDER MCNEIL,AND DANIEL STRAUMANNAbstract.Modern risk management calls for an understanding of stochastic de-pendence going beyond simple linear correlation.This paper deals with the static(non-time-dependent)case and emphasizes the copula representation ofdepen-dence for a random vector.Linear correlation is a natural dependence measurefor multivariate normally and,more generally,elliptically distributed risks butother dependence concepts like comonotonicity and rank correlation should alsobe understood by the risk management ing counterexamples thefalsity of some commonly held views on correlation is demonstrated;in general,these fallacies arise from the naive assumption that dependence properties of theelliptical world also hold in the non-elliptical world.In particular,the problem offinding multivariate models which are consistent with prespecified marginal dis-tributions and correlations is addressed.Pitfalls are highlighted and simulationalgorithms avoiding these problems are constructed.1.Introduction1.1.Correlation infinance and insurance.Infinancial theory the notion of correlation is central.The Capital Asset Pricing Model(CAPM)and the Arbitrage Pricing Theory(APT)(Campbell,Lo,and MacKinlay1997)use correlation as a measure of dependence between differentfinancial instruments and employ an ele-gant theory,which is essentially founded on an assumption of multivariate normally distributed returns,in order to arrive at an optimal portfolio selection.Although insurance has traditionally been built on the assumption of independence and the law of large numbers has governed the determination of premiums,the increasing complexity of insurance and reinsurance products has led recently to increased ac-tuarial interest in the modelling of dependent risks(Wang1997);an example is the emergence of more intricate multi-line products.The current quest for a sound methodological basis for integrated risk management also raises the issue of corre-lation and dependence.Although contemporaryfinancial risk management revolves around the use of correlation to describe dependence between risks,the inclusion of non-linear derivative products invalidates many of the distributional assump-tions underlying the use of correlation.In insurance these assumptions are even more problematic because of the typical skewness and heavy-tailedness of insurance claims data.Recently,within the actuarial world,dynamicfinancial analysis(DFA)and dy-namic solvency testing(DST)have been heralded as a way forward for integrated risk management of the investment and underwriting risks to which an insurer(or Date:9.August1999.Key words and phrases.Risk management;correlation;elliptic distributions;rank correlation; dependence;copula;comonotonicity;simulation;Value-at-Risk;coherent risk measures.The work ofthe third author was supported by RiskLab;the second author would like to thank Swiss Re forfinancial support.12PAUL EMBRECHTS,ALEXANDER MCNEIL,AND DANIEL STRAUMANNbank)is exposed.DFA,for instance,is essentially a Monte Carlo or simulation-based approach to the joint modelling of risks (see e.g.Cas (1997)or Lowe and Stanard (1997)).This necessitates model assumptions that combine information on marginal distributions together with ideas on interdependencies.The correct im-plementation of a DFA-based risk management system certainly requires a proper understanding of the concepts of dependence and correlation.1.2.Correlation as a source ofconf usion.But correlation,as well as being one of the most ubiquitous concepts in modern finance and insurance,is also one of the most misunderstood concepts.Some of the confusion may arise from the literary use of the word to cover any notion of dependence.To a mathematician correlation is only one particular measure of stochastic dependence among many.It is the canonical measure in the world of multivariate normal distributions,and more generally for spherical and elliptical distributions.However,empirical research in finance and insurance shows that the distributions of the real world are seldom in this class.•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••X1Y 1024681012024681012Gaussian ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••X2Y 2024681012024681012Gumbel Figure 1.1000random variates from two distributions with iden-tical Gamma(3,1)marginal distributions and identical correlation ρ=0.7,but different dependence structures.As motivation for the ideas of this paper we include Figure 1.This shows 1000bivariate realisations from two different probability models for (X,Y ).In both mod-els X and Y have identical gamma marginal distributions and the linear correlation between them is 0.7.However,it is clear that the dependence between X and Y in the two models is qualitatively quite different and,if we consider the random vari-ables to represent insurance losses,the second model is the more dangerous model from the point of view of an insurer,since extreme losses have a tendency to occur together.We will return to this example later in the paper,see Section 5;for theCORRELATION AND DEPENDENCE IN RISK MANAGEMENT3 time-being we note that the dependence in the two models cannot be distinguished on the grounds of correlation alone.The main aim of the paper is to collect and clarify the essential ideas of depen-dence,linear correlation and rank correlation that anyone wishing to model depen-dent phenomena should know.In particular,we highlight a number of important fallacies concerning correlation which arise when we work with models other than the multivariate normal.Some of the pitfalls which await the end-user are quite subtle and perhaps counter-intuitive.We are particularly interested in the problem of constructing multivariate dis-tributions which are consistent with given marginal distributions and correlations, since this is a question that anyone wanting to simulate dependent random vectors, perhaps with a view to DFA,is likely to encounter.We look at the existence and construction of solutions and the implementation of algorithms to generate random variates.Various other ideas recur throughout the paper.At several points we look at the effect of dependence structure on the Value-at-Risk or VaR under a partic-ular probability model,i.e.we measure and compare risks by looking at quantiles. We also relate these considerations to the idea of a coherent measure of risk as introduced by Artzner,Delbaen,Eber,and Heath(1999).We concentrate on the static problem of describing dependence between a pair or within a group of random variables.There are various other problems concerning the modelling and interpretation of serial correlation in stochastic processes and cross-correlation between processes;see Boyer,Gibson,and Loretan(1999)for problems related to this.We do not consider the statistical problem of estimating correlations and rank correlation,where a great deal could also be said about the available estimators,their properties and their robustness,or the lack of it.Another statistical aspect which we do not cover in this paper is the issue of fitting copulas to data.For this important practical question there are a number of references.Frees and Valdez(1998),and Klugman and Parsa(1999)take an actu-arial point of view,whereas Genest and Rivest(1993),Genest,Ghoudi,and Rivest (1995),and Cap´e ra`a,Foug`e res,and Genest(1997)develop the general statistical theory offitting copulas.anization ofpaper.In Section2we begin by discussing joint distribu-tions and the use of copulas as descriptions of dependence between random variables. Although copulas are a much more recent and less well known approach to describ-ing dependence than correlation,we introduce themfirst for two reasons.First, they are the principal tool we will use to illustrate the pitfalls of correlation and second,they are the approach which in our opinion affords the best understanding of the general concept of dependence.In Section3we examine linear correlation and define spherical and elliptical distributions,which constitute,in a sense,the natural environment of the linear correlation.We mention both some advantages and shortcomings of correlation. Section4is devoted to a brief discussion of some alternative dependence concepts and measures including comonotonicity and rank correlation.Three of the most common fallacies concerning linear correlation and dependence are presented in Section5.In Section6we explain how vectors of dependent random variables may be simulated using correct methods.4PAUL EMBRECHTS,ALEXANDER MCNEIL,AND DANIEL STRAUMANN2.CopulasProbability-integral and quantile transforms play a fundamental role when work-ing with copulas.In the following proposition we collect together some essentialfacts that we use repeatedly in this paper.The notation X∼F means that the random variable X has distribution function F.Proposition1.Let X be a random variable with distribution function F.Let F−1 be the quantile function of F,i.e.F−1(α)=inf{x|F(x)≥α},α∈(0,1).Then1.For any standard-uniformly distributed U∼U(0,1)we have F−1(U)∼F.This gives a simple method for simulating random variates with distribution function F.2.If F is continuous then the random variable F(X)is standard-uniformly dis-tributed,i.e.F(X)∼U(0,1).Proof.In most elementary texts on probability.2.1.What is a copula?The dependence between the real-valued random vari-ables X1,...,X n is completely described by their joint distribution functionF(x1,...,x n)=P[X1≤x1,...,X n≤x n].The idea of separating F into a part which describes the dependence structure andparts which describe the marginal behaviour only,has led to the concept of a copula.Suppose we transform the random vector X=(X1,...,X n)t component-wise tohave standard-uniform marginal distributions,U(0,1)1.For simplicity we assume tobegin with that X1,...,X n have continuous marginal distributions F1,...,F n,so that this can be achieved by using the probability-integral transformation T:R n→R n,(x1,...,x n)t→(F1(x1),...,F n(x n))t.The joint distribution function C of (F1(X1),...,F n(X n))t is then called the copula of the random vector(X1,...,X n)tor the multivariate distribution F.It follows thatF(x1,...,x n)=P[F1(X1)≤F1(x1),...,F n(X n)≤F n(x n)]=C(F1(x1),...,F n(x n)).(1) Definition1.A copula is the distribution function of a random vector in R n with uniform-(0,1)marginals.Alternatively a copula is any function C:[0,1]n→[0,1] which has the three properties:1.C(x1,...,x n)is increasing in each component x i.2.C(1,...,1,x i,1,...,1)=x i for all i∈{1,...,n},x i∈[0,1].3.For all(a1,...,a n),(b1,...,b n)∈[0,1]n with a i≤b i we have:2i1=1···2i n=1(−1)i1+···+i n C(x1i1,...,x nin)≥0,(2)where x j1=a j and x j2=b j for all j∈{1,...,n}.These two alternative definitions can be shown to be equivalent.It is a par-ticularly easy matter to verify that thefirst definition in terms of a multivariate distribution function with standard uniform marginals implies the three properties above:property1is clear;property2follows from the fact that the marginals 1Alternatively one could transform to any other distribution,but U(0,1)is particularly easy.CORRELATION AND DEPENDENCE IN RISK MANAGEMENT 5are uniform-(0,1);property 3is true because the sum (2)can be interpreted as P [a 1≤X 1≤b 1,...,a n ≤X n ≤b n ],which is non-negative.For any continuous multivariate distribution the representation (1)holds for a unique copula C .If F 1,...,F n are not all continuous it can still be shown (see Schweizer and Sklar (1983),Chapter 6)that the joint distribution function can always be expressed as in (1),although in this case C is no longer unique and we refer to it as a possible copula of F .The representation (1),and some invariance properties which we will show shortly,suggest that we interpret a copula associated with (X 1,...X n )t as being the depen-dence structure.This makes particular sense when all the F i are continuous and the copula is unique;in the discrete case there will be more than one way of writing the dependence structure.Pitfalls related to non-continuity of marginal distributions are presented in Marshall (1996).A recent,very readable introduction to copulas is Nelsen (1999).2.2.Examples ofcopulas.For independent random variables the copula trivially takes the formC ind (x 1,...,x n )=x 1·...·x n .(3)We now consider some particular copulas for non-independent pairs of random vari-ables (X,Y )having continuous distributions.The Gaussian or normal copula isC Ga ρ(x,y )= Φ−1(x )−∞ Φ−1(y )−∞12π(1−ρ2)1/2exp −(s 2−2ρst +t 2)2(1−ρ2) dsdt,(4)where −1<ρ<1and Φis the univariate standard normal distribution func-tion.Variables with standard normal marginal distributions and this dependencestructure,i.e.variables with d.f.C Ga ρ(Φ(x ),Φ(y )),are standard bivariate normal variables with correlation coefficient ρ.Another well-known copula is the Gumbelor logistic copula C Gu β(x,y )=exp − (−log x )1/β+(−log y )1/β β ,(5)where 0<β≤1is a parameter which controls the amount of dependence betweenX and Y ;β=1gives independence and the limit of C Gu βfor β→0+leads to perfect dependence,as will be discussed in Section 4.This copula,unlike the Gaussian,isa copula which is consistent with bivariate extreme value theory and could be used to model the limiting dependence structure of component-wise maxima of bivariate random samples (Joe (1997),Galambos (1987)).The following is a simple method for generating a variety of copulas which will be used later in the paper.Let f,g :[0,1]→R with 10f (x )dx = 10g (y )dy =0and f (x )g (y )≥−1for all x,y ∈[0,1].Then h (x,y )=1+f (x )g (y )is a bivariate density function on [0,1]2.Consequently,C (x,y )= x 0 y0h (u,v )dudv =xy + x 0f (u )du y 0g (v )dv (6)is a copula.If we choose f (x )=α(1−2x ),g (y )=(1−2y ),|α|≤1,we obtain,for example,the Farlie-Gumbel-Morgenstern copula C (x,y )=xy [1+α(1−x )(1−y ))].Many copulas and methods to construct them can be found in the literature;see for example Hutchinson and Lai (1990)or Joe (1997).6PAUL EMBRECHTS,ALEXANDER MCNEIL,AND DANIEL STRAUMANN2.3.Invariance.The following proposition shows one attractive feature of the cop-ula representation of dependence,namely that the dependence structure as summa-rized by a copula is invariant under increasing and continuous transformations of the marginals.Proposition2.If(X1,...,X n)t has copula C and T1,...,T n are increasing con-tinuous functions,then(T1(X1),...,T n(X n))t also has copula C.Proof.Let(U1,...,U n)t have distribution function C(in the case of continuousmarginals F Xi take U i=F Xi(X i)).We may writeC(F T1(X1)(x1),...,F Tn(X n)(x n))=P[U1≤F T1(X1)(x1),...,U n≤F T n(X n)(x n)]=P[F−1T1(X1)(U1)≤x1,...,F−1T n(X n)(U n)≤x n]=P[T1◦F−1X1(U1)≤x1,...,T n◦F−1Xn(U n)≤x n] =P[T1(X1)≤x1,...,T n(X n)≤x n].Remark1.The continuity of the transformations T i is necessary for general ran-dom variables(X1,...,X n)t since,in that case,F−1T i(X i)=T i◦F−1Xi.In the case whereall marginal distributions of X are continuous it suffices that the transformations are increasing(see also Chapter6of Schweizer and Sklar(1983)).As a simple illustration of the relevance of this result,suppose we have a prob-ability model(multivariate distribution)for dependent insurance losses of various kinds.If we decide that our interest now lies in modelling the logarithm of these losses,the copula will not change.Similarly if we change from a model of percentage returns on severalfinancial assets to a model of logarithmic returns,the copula will not change,only the marginal distributions.3.Linear Correlation3.1.What is correlation?We begin by considering pairs of real-valued,non-degenerate random variables X,Y withfinite variances.Definition2.The linear correlation coefficient between X and Y isρ(X,Y)=Cov[X,Y]σ2[X]σ2[Y],where Cov[X,Y]is the covariance between X and Y,Cov[X,Y]=E[XY]−E[X]E[Y] andσ2[X],σ2[Y]denote the variances of X and Y.The linear correlation is a measure of linear dependence.In the case of indepen-dent random variables,ρ(X,Y)=0since Cov[X,Y]=0.In the case of perfect linear dependence,i.e.Y=aX+b a.s.or P[Y=aX+b]=1for a∈R\{0}, b∈R,we haveρ(X,Y)=±1.This is shown by considering the representationρ(X,Y)2=σ2[Y]−mina,bE[(Y−(aX+b))2]σ2[Y].(7)In the case of imperfect linear dependence,−1<ρ(X,Y)<1,and this is the case when misinterpretations of correlation are possible,as will later be seen in Section5. Equation(7)shows the connection between correlation and simple linear regression. The right hand side can be interpreted as the relative reduction in the variance ofCORRELATION AND DEPENDENCE IN RISK MANAGEMENT7 Y by linear regression on X,The regression coefficients a R,b R,which minimise the squared distance E[(Y−(aX+b))2]are given bya R=Cov[X,Y]σ2[X],b R=E[Y]−a R E[X].Correlation fulfills the linearity propertyρ(αX+β,γY+δ)=sgn(α·γ)ρ(X,Y),whenα,γ∈R\{0},β,δ∈R.Correlation is thus invariant under positive affine transformations,i.e.strictly increasing linear transformations.The generalisation of correlation to more than two random variables is straight-forward.Consider vectors of random variables X=(X1,...,X n)t and Y= (Y1,...,Y n)t in R n.We can summarise all pairwise covariances and correlations in n×n matrices Cov[X,Y]andρ(X,Y).As long as the corresponding variances arefinite we defineCov[X,Y]ij:=Cov[X i,Y j],ρ(X,Y)ij:=ρ(X i,Y j)1≤i,j≤n.It is well known that these matrices are symmetric and positive semi-definite.Often one considers only pairwise correlations between components of a single random vec-tor;in this case we set Y=X and considerρ(X):=ρ(X,X)or Cov[X]:=Cov[X,X]. The popularity of linear correlation can be explained in several ways.Correla-tion is often straightforward to calculate.For many bivariate distributions it is a simple matter to calculate second moments(variances and covariances)and hence to derive the correlation coefficient.Alternative measures of dependence,which we will encounter in Section4may be more difficult to calculate.Moreover,correlation and covariance are easy to manipulate under linear op-erations.Under affine linear transformations A:R n→R m,x→Ax+a and B:R n→R m,x→Bx+b for A,B∈R m×n,a,b∈R m we haveCov[A X+a,B Y+b]=A Cov[X,Y]B t.A special case is the following elegant relationship between variance and covariance for a random vector.For every linear combination of the componentsαt X with α∈R n,σ2[αt X]=αt Cov[X]α.Thus,the variance of any linear combination is fully determined by the pairwise covariances between the components.This fact is commonly exploited in portfolio theory.A third reason for the popularity of correlation is its naturalness as a measure of dependence in multivariate normal distributions and,more generally,in multivariate spherical and elliptical distributions,as will shortly be discussed.First,we mentiona few disadvantages of correlation.3.2.Shortcomings ofcorrelation.We consider again the case of two real-valued random variables X and Y.•The variances of X and Y must befinite or the linear correlation is not defined.This is not ideal for a dependence measure and causes problems when we work with heavy-tailed distributions.For example,the covariance and the correlation between the two components of a bivariate tν-distributed random8PAUL EMBRECHTS,ALEXANDER MCNEIL,AND DANIEL STRAUMANNvector are not defined for ν≤2.Non-life actuaries who model losses in different business lines with infinite variance distributions must be aware of this.•Independence of two random variables implies they are uncorrelated (linear correlation equal to zero)but zero correlation does not in general imply inde-pendence.A simple example where the covariance disappears despite strong dependence between random variables is obtained by taking X ∼N (0,1),Y =X 2,since the third moment of the standard normal distribution is zero.Only in the case of the multivariate normal is it permissable to interpret un-correlatedness as implying independence.This implication is no longer valid when only the marginal distributions are normal and the joint distribution is non-normal,which will also be demonstrated in Example 1.The class of spher-ical distributions model uncorrelated random variables but are not,except in the case of the multivariate normal,the distributions of independent random variables.•Linear correlation has the serious deficiency that it is not invariant under non-linear strictly increasing transformations T :R →R .For two real-valued random variables we have in generalρ(T (X ),T (Y ))=ρ(X,Y ).If we take the bivariate standard normal distribution with correlation ρand the transformation T (x )=Φ(x )(the standard normal distribution function)we have ρ(T (X ),T (Y ))=6πarcsin ρ2,(8)see Joag-dev (1984).In general one can also show (see Kendall and Stu-art (1979),page 600)for bivariate normally-distributed vectors and arbitrary transformations T, T:R →R that |ρ(T (X ), T(Y ))|≤|ρ(X,Y )|,which is also true in (8).3.3.Spherical and elliptical distributions.The spherical distributions extend the standard multivariate normal distribution N n (0,I ),i.e.the distribution of in-dependent standard normal variables.They provide a family of symmetric distri-butions for uncorrelated random vectors with mean zero.Definition 3.A random vector X =(X 1,...,X n )t has a spherical distribution if for every orthog-onal map U ∈R n ×n (i.e.maps satisfying UU t =U t U =I n ×n )U X =d X .2The characteristic function ψ(t )=E [exp(i t t X )]of such distributions takes a particularly simple form.There exists a function φ:R ≥0→R such that ψ(t )=φ(t t t )=φ(t 21+...+t 2n ).This function is the characteristic generator of the spherical distribution and we writeX ∼S n (φ).If X has a density f (x )=f (x 1,...,x n )then this is equivalent to f (x )=g (x t x )=g (x 21+...+x 2n )for some function g :R ≥0→R ≥0,so that the spherical distributionsare best interpreted as those distributions whose density is constant on spheres.2We standardly use =d to denote equality in distribution.CORRELATION AND DEPENDENCE IN RISK MANAGEMENT 9Some other examples of densities in the spherical class are those of the multivariate t-distribution with νdegrees of freedom f (x )=c (1+x t x /ν)−(n +ν)/2and the logistic distribution f (x )=c exp(−x t x )/[1+exp(−x t x )]2,where c is a generic normalizing constant.Note that these are the distributions of uncorrelated random variables but,contrary to the normal case,not the distributions of independent random variables.In the class of spherical distributions the multivariate normal is the only distribution of independent random variables,see Fang,Kotz,and Ng (1987),page 106.The spherical distributions admit an alternative stochastic representation.X ∼S n (φ)if and only ifX =d R ·U ,(9)where the random vector U is uniformly distributed on the unit hypersphere S n −1={x ∈R n |x t x =1}in R n and R ≥0is a positive random variable,independent of U (Fang,Kotz,and Ng (1987),page 30).Spherical distributions can thus be interpreted as mixtures of uniform distributions on spheres of differing radius in R n .For example,in the case of the standard multivariate normal distribution the generating variate satisfies R ∼ χ2n ,and in the case of the multivariate t-distribution with νdegrees of freedom R 2/n ∼F (n,ν)holds,where F (n,ν)denotesan F-distribution with n and νdegrees of freedom.Elliptical distributions extend the multivariate normal N n (µ,Σ),i.e.the distri-bution with mean µand covariance matrix Σ.Mathematically they are the affine maps of spherical distributions in R n .Definition 4.Let T :R n →R n ,x →A x +µ,A ∈R n ×n ,µ∈R n be an affine map.X has an elliptical distribution if X =T (Y )and Y ∼S n (φ).Since the characteristic function can be written asψ(t )=E [exp(i t t X )]=E [exp(i t t (A Y +µ))]=exp(i t t µ)exp(i (A t t )t Y )=exp(i t t µ)φ(t t Σt ),where Σ:=AA t ,we denote the elliptical distributionsX ∼E n (µ,Σ,φ).For example,N n (µ,Σ)=E n (µ,Σ,φ)with φ(t )=exp(−t 2/2).If Y has a density f (y )=g (y t y )and if A is regular (det(A )=0so that Σis strictly positive-definite),then X =A Y +µhas densityh (x )=1 det(Σ)g ((x −µ)t Σ−1(x −µ)),and the contours of equal density are now ellipsoids.Knowledge of the distribution of X does not completely determine the elliptical representation E n (µ,Σ,φ);it uniquely determines µbut Σand φare only determined up to a positive constant 3.In particular Σcan be chosen so that it is directly interpretable as the covariance matrix of X ,although this is not always standard.Let X ∼E n (µ,Σ,φ),so that X =d µ+A Y where Σ=AA t and Y is a random vector satisfying Y ∼S n (φ).Equivalently Y =d R ·U ,where U is uniformly distributed on S n −1and R is a positive random variable independent of U .If E [R 2]<∞it follows3If X is elliptical and non-degenerate there exists µ,A and Y ∼S n (φ)so that X =d A Y +µ,but for any λ∈R \{0}we also have X =d (A/λ)λY +µwhere λY ∼S n ( φ)and φ(u ):=φ(λ2u ).In general,if X ∼E n (µ,Σ,φ)=E n ( µ, Σ, φ)then µ=˜µand there exists c >0so that Σ=c Σand φ(u )=φ(u/c )(see Fang,Kotz,and Ng (1987),page 43).10PAUL EMBRECHTS,ALEXANDER MCNEIL,AND DANIEL STRAUMANNthat E [X ]=µand Cov[X ]=AA t E [R 2]/n =ΣE [R 2]/n since Cov[U ]=I n ×n /n .By starting with the characteristic generator φ(u ):=φ(u/c )with c =n/E [R 2]we ensure that Cov[X ]=Σ.An elliptical distribution is thus fully described by its mean,its covariance matrix and its characteristic generator.We now consider some of the reasons why correlation and covariance are natu-ral measures of dependence in the world of elliptical distributions.First,many of the properties of the multivariate normal distribution are shared by the elliptical distributions.Linear combinations,marginal distributions and conditional distri-butions of elliptical random variables can largely be determined by linear algebra using knowledge of covariance matrix,mean and generator.This is summarized in the following properties.•Any linear combination of an elliptically distributed random vector is also elliptical with the same characteristic generator φ.If X ∼E n (µ,Σ,φ)and B ∈R m ×n ,b ∈R m ,thenB X +b ∼E m (Bµ+b,B ΣB t ,φ).It is immediately clear that the components X 1,...,X n are all symmetrically distributed random variables of the same type 4.•The marginal distributions of elliptical distributions are also elliptical with the same generator.Let X = X 1X 2 ∼E n (Σ,µ,φ)with X 1∈R p ,X 2∈R q ,p +q =n .Let E [X ]=µ= µ1µ2 ,µ1∈R p ,µ2∈R q and Σ= Σ11Σ12Σ21Σ22 ,accordingly.ThenX 1∼E p (µ1,Σ11,φ),X 2∼E q (µ2,Σ22,φ).•We assume that Σis strictly positive-definite.The conditional distribution of X 1given X 2is also elliptical,although in general with a different generator φ:X 1|X 2∼E p (µ1.2,Σ11.2, φ),(10)where µ1.2=µ1+Σ12Σ−122(X 2−µ2),Σ11.2=Σ11−Σ12Σ−122Σ21.The distribu-tion of the generating variable Rin (9)corresponding to φis the conditional distribution (X −µ)t Σ−1(X −µ)−(X 2−µ2)t Σ−122(X 2−µ2) X 2.Since in the case of multivariate normality uncorrelatedness is equivalent to independence we have R =d χ2p and φ=φ,so that the conditional distribu-tion is of the same type as the unconditional;for general elliptical distributions this is not true.From (10)we see thatE [X 1|X 2]=µ1.2=µ1+Σ12Σ−122(X 2−µ2),so that the best prediction of X 1given X 2is linear in X 2and is simply the linear regression of X 1on X 2.In the case of multivariate normality we have additionallyCov[X 1|X 2]=Σ11.2=Σ11−Σ12Σ−122Σ21,4Two random variables X und Y are ofthe same type ifwe can find a >0and b ∈R so that Y =d aX +b.。

1．Most of Emily Dickinson‟s poems were published __________.A. when she was youngB. after her failed love affairC. in her old ageD. after her death2. __________is a kind of drama that expounds an existential ideology and views its task as essentially metaphysical. It represents a view of the absurdity of the human condition by the abandoning of rational devices and the nonrealistic form.A. black humorB. non-fictionC. anti-heroD. theater of the absurd3. The Importance of Being Earnest is a comedy by__________.A. George Bernard ShawB. Oscar WildeC. Richard Brinsley SheridandD. William Shakespeare4. The Gothic style started in _________and quickly spread through all parts of western Europe.A. FrenchB. EnglishC. HebrewD. Germanic5. Ireland is called the Emerald Isle because of __________.A. its connection with BritainB. its green countrysideC. its unique shapeD. its abundant natural resources6. __________is the oldest newspaper in Australia.A. The Sydney Morning HeraldB. he AustraliaC. Daily MirrorD. Sun7. __________ was once the president of the Royal Society for twenty-three years.A. William HarveyB. Francis BaconC. Isaac NewtonD. John Dalton8. What is the relationship between the two words “flower/rose”?A. HomonymyB. AntonymyC. HyponymyD. Polysemy9. The function of the sentence “How are you?”A. directiveB. informativeC. performativeD. phatic10. Homonyms __________.A. are words that share the same phonetic features and the same semantic featuresB. are words that share the same semantic features but have different sets of phonetic featuresC. are words that share the same phonetic features but have different sets of semantic featuresD. are two words that all but one of semantic feature in common1-10. D D B A B A C C D C11. The Ring and the Book is a masterpiece of ____.A. Alfred TennysonB. Robert BrowningC. Thomas HardyD. Ralph Waldo Emerson12. “Studies serve for delight, for ornament, and for ability” is one of the epigramsfound in _____A. Bacon‟s of StudiesB. Bunyan‟s The Pilgrim’s ProgressC. Fielding‟s Tom Jone sD. Johnson‟s A Dictionary of the English Language13. Who is Afraid of Virginia Woolf is written by ____.A. Samuel BeckettB. Virginia WolfC. Edward AlbeeD. John Barth14. The world‟s largest freshwater lake is Lake ____.A. SuperiorB. OntarioC. HuronD. Michigan15. The state _____is rich in fishing and trapping.A. HawaiiB. CaliforniaC. AlaskaD. New York16. The Australian National Day is set on January 26 to commemorate ____.A. the first European settlement of the continentB. the founding of the Commonwealth of AustraliaC. the discovery of the great southern “unknown land”D. Iacques Cartier‟s first voyage around Australia17. In 1788 Australia was settled by the British as a colony founded ____.A. to receive convicts from BritainB. to receive free settlersC. to supply Britain with wool and foodD. to expand Britain‟s imperial power18. The distinction between langue and parole is proposed by ____.A. HallidayB. SaussureC. ChomskyD. Firth19. In the following dialogue, the maxim of ____ is not observed.A. qualityB. quantityC. relevanceD. manner20. ____ are linguistic units larger than sentences.A. MovesB. DiscoursesC. TopicsD. Tendencies11-20. B A C A C A A B C B21. ____ is a classification of fiction in which a historical event is described in a way that exploits some of the devices of fiction, including a nonlineal time sequence and access to inner states of mind and feeling not commonly present in historical wirting.A. New fictionB. Nouveau RomanC. Historical storyD. Nonfiction Novel22. Ralph Waldo Emerson, the American Transcendentalist, argued for the following ideas except ____.A. man‟s dependence on himself for spiritual perfectionB. Faith in ChristianityC. direct intuition of a spiritual God in natureD. the importance of an independent American culture23. In the line “So ling lives this, and this gives life to thee”of Sonnet 18,Shakespeare ___A. meditates on man‟s mortalityB. eulogizes the power of artistic creationC. satirizes human vanityD. presents a dream vision24. Australia is the world‟s largest exporter of ____.A. wheatB. meatC. daily productsD. wool25. ____ is the most important work by Marx about Marxist economics.A. Thesis on FeuerbackB. The German IdeologyC. CapitalD. The capital26. Harvard University was founded in ____.A. 1366B. 1633C. 1636D. 136327. The state to which the Mayflower sailed is ____.A. FloridaB. MaineC. VirginiaD. Massachusetts28. Which of the following two-term sets shows the feature of complementarity?A. single/marriedB. big/smallC. hot/coldD. old/young29. Usually ____refers to the use of linguistic research in language teaching, but linguistics is used in other areas, as well.A. applied linguisticsB. theoretical linguisticsC. contextual linguisticsD. general linguistics30. Two words that are differentiated by one phoneme, such as “cat” and “rat”, are known as a ___A. distinctive featureB. argumentC. codeD. minimal pair21-30. D B B D C C D A A D31. “Utopia” was written by __________.A. Thomas MoreB. Francis BaconC. Daniel DefoeD. Jonathan Swift32. The Preface to Shakespeare and Lives of the Poets are the works of critic __________.A. G..B. Shaw B. Samuel JohnsonC. Ben JohnsonD. F. M. Foster33. In 1837, Ralph Waldo Emerson made a speech entitled __________ at Harvard, which was hailed by Oliver Wendell Holmes as “Our intellectual Declaration of Independence”.A. NatureB. Self-RelianceC. Divinity School AddressD. The American Scholar34. The U.S.A is known as a “Melting Pot” for its __________.A. mixture of nationalitiesB. mixture of climatesC. mixture of habitsD. mixture of religions35. __________ is regarded as the cradle of the Renaissance?A. GreeceB. ItalyC. GermanyD. England36. Who was “The father of psychoanalysis” and the author of The Interpretations ofDreams?A. MonetB. Sigmund FreudC. YeatsD. James Joyce37. As far as Australian culture is concerned, the history of Australia can be divided into the following phases with the exception of __________.A. the period of the original culture of Aboriginal peopleB. the period of the dominant British cultureC. the period of Asian cultureD. the period of a multicultural society38. __________ is often regarded as the founder of the study of sociolinguistics.A. SaussaureB. HallidayC. ChomskyD. Labov39. __________ is the academic discipline concerned with the study of the processes by which people learn languages in addition to their native tongue.A. IPAB. IC AnalysisC. SLAD. TG40. The __________ is the primary lexical units of a word, which carries the most significant aspects of semantic content and cannot be reduced into smaller constituents.A. bound morphemesB. affixC. rootD. prefix31-40. A B D A B B C D C C41. ____ is Mark Twain‟s master work, the one book from which as Ernest Hemingway noted, “all modern American literature comes.”A. The Gilded AgeB. The Celebrated Jumping Frog of Calaveras CountyC. The Adventures of Tom SawyerD. The Adventures of Huckleberry Finn42. Apart from the dislocation of time and the modern stream-of-consciousness, the other narrative techniques Faulkner used to construct his stories include ____, symbolism and mythological and biblical allusions.A. impressionismB. expressionismC. multiple points of viewD. first person point of view43. Murder on the Orient Express is written by ____ a novelist of detective fiction.A. Arthur Conan DoyleB. Edgar Allan PoeC. Agatha ChristieD. John Fowels44. Who was the first woman Prime Minister in British history?A. Elizabeth IB. Elizabeth IIC. Margaret ThatcherD. Diana Princess of Wales45. The important thing done in the Second Continental Congress was that ____.A. “the Declaration of the Independence” was signedB. the Revolutionary Was endedC. a new government was discussedD. Washington was appointed commander of the army46. Whose book Evolution and Ethics was translated into Chinese in 1897 by Yan Fu?A. DarwinB. Thomas HuxleyC. MalthusD. Herbert Spencer47. Who is the author of On the Principle of Population?A. DarwinB. Thomas HulxleyC. MalthusD. Herbert Spencer48. In terms of Searle‟s classification system of illocutionary acts, the sentence …Ten bucks say that The Yankee will win the game‟ used to bet belongs to _____.A. representativeB. commissiveC. directiveD. declaration49. Three factors involved in describing vowels are ____.A. place of articulation/part of the tongue raised/voicingB. tongue height/ part of the tongue raised/lip roundingC. articulators/extreme vowel positions/voicingD. teeth position alveolar ridge position/voicing50. In ____ the structure of words is studied.A. phoneticsB. phonologyC. morphologyD. syntax41-50. D C C C D B C A B C51．“The Three Unities”, formulated by Renaissance dramatists, are the unities of the following elements but ____.A. timeB. placeC. actionD. character52. “The founder of English materialist philosophy” is ____.A. Geoffrey ChaucerB. Edmund SpenserC. Francis BaconD. John Donne53. Babbitt is written by ____ who is also the writer of Main Street.A. William FaulknerB. Sinclair LewisC. John SteinbeckD. Jack London54. Under the Whitlam government “God Save the Queen” was replaced by ____ as Australian national anthem.A. “Waltzing Matilda”B. “Click Go the Shears”C. “Advance Australia FairD. “My Country”55. Australia is the world‟s largest exporter of ____.A. wheatB. meatC. daily productsD. wool56. The United States is ____ populous country in the world.A. the third mostB. the second mostC. the mostD. the fourth most57. Which of the following is the father of the modern mode of painting?A. RaphaelB. TitianC. da VinciD. Michelangelo58. If we begin interpretation of a sentence spontaneously and automatically on the basis of whatever information is available to us, that is called ___.A. top-down processingB. hotttom-up processingC. inductive analysisD. Comparative analysis59. ____ is a personal dialect of an individual speaker that combines elements regarding regional, social, gender, and age variations.A. DialectB. IdiolectC. Ethnic dialectD. Linguistics repertoire60. Of the following words, ____ is an initialism.A. UNB. NATOC. BASICD. UNESCO51-60: D C B C D A B A B A61. Which of the following writer was not the representative of Harlem Renaissance?A. Claude MckayB. Countee CullenC. Langston HughesD. J.D. Salinger62. Yoknapatawpha saga refers to a series of fictions written by _____.A. Thomas HardyB. Mark TwainC. William FaulknerD. Allan Poe63. Why is Samuel Johnson called “Dictionary Johnson”?A. Because he knows a lot more than other writers in words.B. Because he often consults an encyclopedia while writing.C. Because he is a master of English language.D. Because he is author of the first English dictionary by an Englishman.64. In Australia, under _____ the legislation to provide equal pay for men and women doing the same work was passed.A. the Whitlam governmentB. the Hawke governmentC. the keating governmentD. the Fraser government65．When did the third wave of migration begin in Australia?A. After the First World WarB. After the Second World WarC. During the Second World WarD. After the Vietnam War66. The “Big Stick” Policy was advanced by President _____.A. Franklin D. RooseveltB. William MekinleyC. Thomas Woodrow WilsonD. Theodore Roosevelt67. What is the largest river in America?A. The Ohio RiverB. The ColumbiaC. The Mississippi RiverD. The Colorado68. “Autumn” and “fall” are used respectively in Britain in and America, but refer to the same thing. The words are _____ synonyms.A. collocationalB. dialectalC. completeD. stylistic69. _____ is the abstract syntactic representation of a sentence, namely, the underlying level of structural organization which specifies all the factors governing the way the sentence should be interpreted.A. surface structureB. syntactic ambiguityC. syntactic componentD. deep structure70. London speech that was illustrated by Shakespear e‟s writing was generally termed _____.A. Old EnglishB. Middle EnglishC. Early Modern EnglishD. Late Modern61-70: D C D A B D C B D C71. Percy Bysshe Shelly is famous for ________.A. Ode to a Skylark and Ode to a NightingaleB. Ode on a Grecian Urn and Ode to the West WindC. Ode to a Nightingale and Ode on a Grecian UrnD. Ode to the West Wind and Ode to a Skylark72. “Tom Jones” was written by ________.A. Henry FieldingB. Daniel DefoeC. Jonathan SwiftD. Samuel Richardson73. Love Story is written by ________.A. Margaret MillarB. Mario PuzoC. Erich SegalD. Helen Eustis74. New Zealanders have adopted their name from the Kiwi, ________.A. which is an introduced flightless birdB. which was the only mammal in New ZealandC. which is a native flightless birdD. which was introduced to New Zealand 1000 years ago75. The two main land masses in New Zealand are ________.A. the White Island and the thermal regionB. the North Island and the South IslandC. Auckland and the South IslandD. the Southern Apls and the North Island76. Which of the following was best known for his Madona (Virgin Mary)?A. RaphaelB. MichelangeloC. Da VinciD. Titian77. The first American President who inaugurated in Washington City was ________.A. George WashingtonB. Thomas JeffersonC. John AdamsD. Andrew Jackson78. The study of the linguistic meaning of words, phrases, and sentences is called _____.A. semanticsB. pragmaticsC. syntaxD. language change79. In making conversation, the general principle that all participants are expected to observe is called the ________ principle proposed by J.Grice.A. comprehensiveB. generativeC. discourseD. cooperative80. ________ is concerned with the inherent meaning of the linguistic form.A. referenceB. lexical meaningC. senseD. word71-80: D A C C B A B A D C81. The Hairy Ape by Eugene O‟Neill is a drama in the styles of ____.A. realism and romanticismB. romanticism and symbolismC. romanticism and expressionismD. realism and expressionism82. Literary criticism written from the perspective of women, reflecting female attitudes, conerns and values is regarded as ____.A. New CriticismB. PsychoanalysisC. StructuralismD. Feminist Criticism83. “Three or four families in a country village is something to work.” This statement was presented by ___.A. Emily BronteB. Jane AustenC. Mrs. GaskellD. George Eliot84. ____ had the title “the Wizard of Menlo Park”.A. John StevensB. Charlie ChaplinC. Thomas A EdisonD. Robert Fulton85. ____ major works Last Supper is the most famous of religious pictures.A. Loenardo da Vinci‟sB. Titian‟sC. Raphael‟sD. Michelangelo‟s86. What is the other official language besides English in New Zealand?A. GermanB. JapaneseC. FrenchD. Maori87. Who produced the first complete map of New Zealand in 1769?A. Abel TasmanB. a DutchmanC. HobsonD. James Cook88. Of the following linguists, ____ should be grouped into London school.A. FirthB. BloomfieldC. BoasD. Trubetzkoy89. ____ refers to a marginal language of few lexical items and straightforward grammatical rules, used as a medium of communication.A. Lingua francaB. CreoleC. PidginD. Standard language90. The basic essentials of the first language are acquired in the short period from about age two to puberty, which is called the ____ period for first language acquisition.A. initialB. one-word stageC. pubertyD. critical81-90: D D B C A D D A C D91. John Milton created Satan the real hero in his poem ___.A. “Paradise Lost”B. “Paradise Regained”C. “A gonists”D. Lycidas92. Erehwon is a satiric novel written by ____.A. Samuel ButlerB. Henry FieldingC. Thomas MoreD. Mark Twin93. “ In a station of the Metro” by ____ has been regarded as a classic specimen of Imagist poetry.A. Ezra PoundB. T.S. EliotC. William Carlos WilliamsD. Amy Lowell94. The Head of State of New Zealand is ____.A. the Prime MinisterB. the British monarchC. the Governor-GeneralD. the President95. The first settlers of New Zealand were ____.A. European navigatorsB. sealers and whalersC. voyagers from East PolynesiaD. Christian missionaries96. ____ is the oldest of all the parties in Ireland.A. Finn GaelB. The Progressive DemocratsC. Finna FailD. The Irish Labour Party97. The largest state of all the states of America is ____.A. TexasB. AlaskaC. CaliforniaD. Hawaii98. The feature that distinguishes “hotdog” and “hot dog” is ____.A. toneB. stressC. intonationD. aspiration99. ____deals with how language is acquired, understood and produced.A. PsycholinguisticsB. SociolinguisticsC. NeurolinguisticsD. Anthropological linguistics100. The study of language at some point of time is generally termed as ____ linguistics.A. appliedB. diachronicC. comparativeD. synchronic91-100: A A A B C D B B A D101. Which of the following is not written by the author of The Scarlet Letter?A. The House of the Seven GablesB. Young Good man BrownC. The Fall of the House of UsherD. The Minister‟s Black Veil102. I Have a Dream is famous speech addressed by _____.A. Abraham LincolnB. Martin Luther KingC. Winston ChurchillD. Mark Twain103. All the following writers are the great masters of “stream of consciousness” but _____.A. James JoyceB. Virginia woolfC. William FaulknerD. Henry James104. The largest city in Canada is _____.A. OttawaB. TorontoC. VancouverD. Montreal105. About _____ of the people of Quebec are French descents.A. 80%B. 30%C. 90%D. 50%106. Today, the City of London is the business centre of London where you can find _____.A. big supermarketsB. theatres and cinemasC. large financial organizationsD. restaurants and cafes107. In the United Kingdom, the party which wins the _____ number of seats in the House of Commons becomes the official Opposition.A. largestB. third largestC. fourth largestD. second largest 108. “Speech Act Theory” was proposed by ____ in 1962.A. SaussureB. ChomskyC. Jane AustinD. John Austin109. The major new development in linguistics in 20th century was _____ grammar.A. speculativeB. traditionalC. structuralD. Interference110. _____ refers to the tendency of many learners to stop developing their interlanguage grammar in the direction of the target language.A. FossilizationB. Error analysisC. OvergeneralizationD. Interference101-110: C B D B A C D D D A111. Aspect of the Novel was originally a series of lectures delivered at Cambridge by ____. It was one of the most important books on the theory of novel.A. E.M. ForsterB. Mark TwainC. William FaulknerD. Henry James112. Daniel Defoe is a famous ____.A. poetB. novelistC. playwrightD. essayist113. The famous representative drama of “theatre of the absurd” is ____ by Samuel Beckett.A. Waiting for LeftyB. Who is Afraid of Virginia WoolfC. Waiting for GodotD. The Zoo Story114. When printing was invented in the 1500‟s, the ____ Bible was the first complete work printed.A. LatinB. EnglishC. AramaicD. Hebrew115. Which of the following is NOT a characteristic of the Open University?A. It‟s open to everybody.B. No university degree is awarded.C. It requires no formal educational qualification.D. University course are followed through TV, radio, correspondence, etc. 116. The backbone of Canada‟s economy is ____.A. crude oilB. cereal exportC. manufacturingD. timber117. The longest river in Canada is ____.A. the St. LawrenceB. the MackenzieC. the SevernD. the Yukon118. The most recognizable difference between American English and British English are in ____ and vocabulary.A. structureB. grammarC. usageD. pronunciation119. The study of how we do things with utterance is the study of ____, the nature of which is determined by context.A. contextB. pragmaticsC. speech actD. semantics120. A(n) ____ is a mild, indirect or less offensive word or expression that replaces a taboo word or serves to avoid more direct wording that might he harsh, unpleasantly direct, or offensive, e.g. “pass away” for “die”.A. euphemismB. deleteC. coinageD. taboo111-120: A B C A B C B D C A121. The first novel of stream of consciousness written by a black writer _____ was CranA. Claude MckayB. Countee CullenC. Langston HughesD. Jean Toomer122. The Tenth Muse Lately Sprung up in America was written by _____.A. John SmithB. John EllisC. Anne BradstreetD. Nathaniel Morton123. In reading Shakespeare, you must have come across the line “To be or not to be---that is the question” by ____.A. Iago in OthelloB. Lear in King LearC. Shylock in The Merchant of VeniceD. Hamlet in Hamlet124. The name “Canada”is thought to be derived from kanata, an Indian word meaning _____.A. a settlementB. a guitarC. a meeting placeD. a piece of land125. Canada has become the world‟s _____ exporter of fish.A. secondB. largestC. forthD. fifth126. The most important and influential of English Bible is the Authorized or King James version, first published in _____.A. 1382B. 1901C. 1611D. 1979127. In Britain, ministers are appointed by the Queen on the recommendation of _____.A. the lord ChancellorB. the Prime MinisterC. the SpeakerD. the Parliamentary Commissioner 128. In many societies of the world, we find a large number of people who speak more than one language. As a characteristic of societies, _____ inevitably results from the coming into contact of people with different cultures and different languages.A. transferB. bilingualismC. diglossiaD. interlanguage129. Pragmatics differs from traditional semantics in that it studies meaning not in isolation, but in _____.A. relationshipB. dependenceC. sentenceD. context130. _____ is a design feature of human language that enables speakers to talk about a wide range of things, free from barriers caused by separation in time and space.A. Cultural transmissionB. DualityC. DisplacementD. Productivity121-130: D C D A B C B B D C131. Robert Browning‟s “May Last Duchess” is composed in the form of a(n)____.A. dramatic monologueB. extended metaphorC. syllogistic argumentD. dialogue132. The novel starts with “It is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife.” This novel is Jane Austen‟s ____.A. EmmaB. PersuasionC. Sense and SensibilityD. Pride and Prejudice133. I‟m Nobody is a poem by ____ in the form of “dramatic monologue”.A. Ralph Waldo EmersonB. Emily DickinsonC. Edgar Allan PoeD. Robert Browning134. The Middle Ages is also called the ____.A. “Age of Faith”B. “Age of Christianity”C. “Age of Holy Spirit”D. “Age of Literature”135. In the latter part of the 4th century, which of the following tribes swept into Europe from central Asia, robbing and killing large numbers of the half civilized Germanic tribes?A. the MongoliansB. the TurkishC. the SyriansD. the Huns136. Who is the most influential person in the Canadian government?A. the QueenB. the Prime MinisterC. the ParliamentD. the Govbernor-General137. The Queen is represented by ____ in Canada.A. The leader of the majority partyB. the Prime MinisterC. the ParliamentD. the Governor-General138. Traditional grammarians begin with ____ definition of the sentence and its components.A. structuralB. notionalC. descriptiveD. prescriptive 139. ____ is defined as any regionally or socially definable human group identified by shared linguistic system.A. A speech communityB. A raceC. A societyD. A country140. ____ invasions established three major groups in England: Saxons, Angles and Jutes.A. GermanicB. NormanC. FrenchD. Roman131-140: A D B A D B D B A A141. Moby Dick is a novel by ____.A. Edgar Allan PoeB. Nanthaniel HawthornC. Herman MelvilleD. Henry James142. The God Father is written by ____.A. Margaret MillarB. Mario PuzoC. Dashiell HammettD. Helen Eustis143. The major concern of _____fiction lies in the tracing of the psychological development of his characters and in his energetic criticism of the dehumanizing effect of the capitalist industrialization on human nature.A. Charles Dickens‟B. D.H. Lawrence‟sC. Thomas Hardy‟sD. John Galsworthy‟s144. In Canada the Head of State is ____.A. the Prime MinisterB. the leader of the majority partyC. the government-GeneralD. Queen Elizabeth II145. What is the other official language besides English in Canada?A. GermanB. JapaneseC. FrenchD. Finnish146. The president of the Lords in Britain is called _____A. Lord ChancellorB. SpeakerC. Prime MinisterD. President147. The Church was divided into the Roman Catholic Church and Eastern OrthodoxChurch after ____.A. 1066B. 1296C. 1054D. 476148. Japanese is the only major language that uses ____ writing system.A. a word writingB. a logographicC. an alphabeticD. a syllabic149. ____ is one whose distribution is functionally equivalent to that of one or more of its constituents, i.e. a word or a group of words, which serves as a definable “centre” or “head”.A. Exocentric constructionB. CoordinationC. Endocentric constructionD. Collocation150. Of the following linguists, ____ should not be grouped into American school.A. FirthB. SapirC. BloomfieldD. Boas141-150: C B B D C A C D C A。

非负相依随机变量和的尾部概率一致渐近估计唐风琴【摘要】Suppose that {Xi}i≥1 is a sequence of nonnegative and non-identically distributed random var-iables which belong to the subclass of heavy-tailed distributions-class C .The multivariate distribution function of the random variables is governed by the FGMcopula function.The uniformly asymptotic esti-mate for the partial sums and random sums of the sequence {Xi}i≥1 are studied,respectively.The ob-tained results extend the corresponding asymptotic estimate of the tail probability of the dependent random variables.%假设｛Xi｝i≥1为一列非负不同分布的随机变量，其分布函数属于重尾子族－C 族且联合分布满足多元FGMcopula 函数。

探讨了序列｛Xi｝i≥1的部分和及随机和的一致渐近估计，推广了相依结构随机变量尾部渐近概率的相应结果。

【期刊名称】《中山大学学报（自然科学版）》【年(卷),期】2016(055)003【总页数】4页(P55-58)【关键词】精细大偏差;FGM;C族【作者】唐风琴【作者单位】兰州大学数学与统计学院，甘肃兰州 730000; 淮北师范大学数学科学学院，安徽淮北 235000【正文语种】中文【中图分类】O211.65;O211.66假设{Xi}i≥1为不同分布的的非负随机变量序列，分布函数为Fi(x)=P(Xi≤x)，尾部概率为i(x)=P(Xi>x)且0<μi=EXi<∞,i≥1。