The Covariant Picard Groupoid in Differential Geometry
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Plant and Animal Life of the Pacific IslandsOCEANIAThere are both great similarities and considerable diversity in the ecosystems that evolved on the islands of Oceania in and around the Pacific Ocean. The islands, such as New Zealand, that were originally parts of continents still carry some small plant and animal remnants of their earlier biota (animal and plant life), and they also have been extensively modified by evolution. adaptation, and the arrival of new species. By contrast, the other islands, which emerged via geological processes such as volcanism, possessed no terrestrial life, but over long periods, winds, ocean currents, and the feet, feathers, and digestive tracts of birds brought the seeds of plants and a few species of animals. Only those species with ways of spreading to these islands were able to undertake the long journeys, and the various factors at play resulted in diverse ombinations of new colonists on the islands. One estimate is that the distribution of plants was 75 percent by birds, 23 percent by floating, and only 2 percent by windThe migration of Oceanic biota was generally from west to east, with four major factors influencing their distribution and establishment. The first was the size and fertility of the islands on which they landed, with larger islands able to provide hospitality for a wider range of species. Second, the further east the islands, generally the less the species diversity, largely because of the distance that had to be crossed and because the eastern islands tended to be smaller, more scattered, and remote. This easterly decline in species diversity is well demonstrated by birds and coral fish. It is estimated that there were over 550 species of birds in New Guinea, 127 in the15慢跑的石头:Solomon Islands, 54 in Fiji, and 17 in the Society Islands. From the west across the Pacific, the Bismarck Archipelago and the Solomon Islands have more than 90 families of shore fish (witl any species within the families), Fiji has 50 families, and the Society Islands have 30. Third latitude of the islands also influenced the biotic mix, as those islands in relatively cooler latitude notably New Zealand, were unsuited to supporting some of the tropical plants with which Pacific islands are generally associatedFinally, a fourth major factor in species distribution, and indeed in the shaping of Pacific ecosystems, was wind. It takes little experience on Pacific islands to be aware that there prevailing winds To the north of the equator these are called north- easterlies, while to the south hey are called south-easterlies. Further south, from about 30" south, the winds are generally from the west. As a result on nearly every island of significant size there is an ecological difference between its windward and leeward (away from the wind) sides. Apart from the wind action itself on plants and soils, wind has a major effect on rain distribution. The Big Island of Hawaii offers a prime example: one can leave Kona on the leeward side in brilliant sunshine and drive across to the windward side where the city of Hilo is blanketed in mist andWhile such localized plant life and climatic conditions are very noticeable, over Oceania as a whole there is relatively little biodiversity, and the smaller the island and the further east it lies the less there is likely to be. When humans moved beyond the islands of Near Oceania(Australia, New Guinea, and the Solomon Islands), they encountered no indigenous mammals except for flying foxes, fruit bats, and seals on some islands. Other vertebrate species were restricted to flying animals and a few small reptiles. However, local adaptations and evolution over long periods of isolation promoted fascinating species adaptations to local conditions. Perhaps most notable. in the absence of mammals and other predators, are the many species of flightless and ground-nesting birds. Another consequence of evolution was that many small environments boasted their own endemic(native)species, often small in number, unused to serious predation.limited in range, and therefore vulnerable to disruption. In Hawaii, for example, the highly adapted 39 species and subspecies of honeycreepers, several hundred species of fruit flies, and more than 750 species of tree snails are often cited to epitomize the extent of localized Oceanic endemism(species being native to the areParagraph 1There are both great similarities and considerable diversity in the ecosystems that evolved on the islands of Oceania in and around the Pacific Ocean. The islands, such as New Zealand, that were originally parts of continents still carry some small plant and animal remnants of their earlier iota (animal and plant life), and they also have been extensively modified by evolution adaptation, and the arrival of new species. By contrast, the other islands, which emerged via geological processes such as volcanism, possessed no terrestrial life, but over long periods, win ocean currents, and the feet, feathers, and digestive tracts of birds brought the seeds of plants and a few species of animals. Only those species with ways of spreading to these islands were able to undertake the long journeys, and the various factors at play resulted in diverse combinations of new colonists on the islands. One estimate is that the distribution of plants was 75 percent by birds, 23 percent by floating, and only 2 percent by wind慢跑的石头:29. The word"remnants" in the passage is closet in meaning to○remainders○remindereproductions○resemblances30. The passage supports which of the following statements about species on volcanic islands? o Volcanic island species are unlike the species found in other Pacific Ocean locationso Volcanic islands lack the diversity of species found elsewhere in the Pacific.o Volcanic island species are all transplants from distant locations and exist in combinationsnot found elsewhereo Volcanic island species differ from those on other islands in that animal species show greater diversity than plant species do.31. According to paragraph 1, how did the majorityof plant species arrive on islands created by geological processes such as volcanismo They were transported by ocean currentso They were carried to the islands by birdso They were brought to the islands by humanso They were transported by windsThe migration of Oceanic biota was generally from west to east, with four major factors influencing their distribution and establishment. The first was the size and fertility of the islands on which they landed, with larger islands able to provide hospitality for a wider range of species Second, the further east the islands, generally the less the species diversity, largely because of the distance that had to be crossed and because the eastern islands tended to be smaller, more scattered, and remote. This easterly decline in species diversity is well demonstrated by birds and coral fish. It is estimated that there were over 550 species of birds in New Guinea, 127 in the Solomon Islands, 54 in Fiji, and 17 in the Society Islands. From the west across the Pacific, theBismarck Archipelago and the Solomon Islands have more than 90 families of shore fish(with many species within the families), Fiji has 50 families, and the Society Islands have 30. Third, the latitude of the islands also influenced the biotic mix, as those islands in relatively cooler latitudes notably New Zealand, were unsuited to supporting some of the tropical plants with which Pacitic islands are generally associated32. The word "remote" in the passage is closet in meaning toO unknownO isolate33. In paragraph 2, what is the authors purpose in mentioning the estimated numbers of birds17慢跑的石头:nd coral fish species on various Oco To give examples of the wide range of species that can be found on Oceanic islandso To illustrate the decline in species diversity from west to east on Oceanic islandso To identify the influence of latitude upon Oceanic plants and animals34.Which of the sentences below best expresses the essential information in the highlighted sentence in the passage? Incorrect choices change the meaning in important ways or leaveout essential informationo Because of its latitude, New Zealand had a relatively cooler climate than other PacificO New Zealand, like other Pacific islands, showed the effects of latitudes on its rich tropical plants.o Because the latitudinal position of an island also affected its biotic mix, islands in cooler latitudes did not support some tropical species typical of the Pacifo Pacific islands were notable for their impressive biotic mix and association with tropicaplants35. According to paragraph 2, all of the following types of islands are associated with higher species diversity EXCEPTO islands that are large in sizeO islands located in cool latitudesO islands located in the western part of OceaniaO islands located near other landmassesParagraph 3Finally, a fourth major factor in species distribution, and indeed in the shaping of Pacific ecosystems, was wind. It takes little experience on Pacific islands to be aware that there are prevailing winds. To the north of the equator these are called north-easterlies, while to the south they are called south-easterlies. Further south, from about 30 south, the winds are generafrom the west. As a result on nearly every island of significant size there is an ecological difference between its windward and leeward (away from the wind) sides. Apart from the wind action itself on plants and soils, wind has a major effect on rain distribution, The Big Island of Hawaii offers a prime example: one can leave Kona on the leeward side in brilliant sunshine and drive across to the windward side where the city of Hilo is blanketed in mist and rain36. The Big Island of Hawaiis discussed in the passage as an example ofo the relationship between latitude and windo how prevailing winds influence rainfall patternso the relationship between rainfall and species distributiono the effects of wind action upon plants and soils37. What can be inferred from paragraph 3 about Kona and Hiloo The ecosystems of Kona and Hilo differ from each other慢跑的石头:Kona and Hilo have approximately the same rainfall in a given yearta receives northeasterly winds while Hilo receives southeasterly windso Both Aona and Hilo have plants and soils that are often damaged by windsParagraph 4While such localized plant life and climatic conditions are very noticeable, over Oceania as a whole there is relatively little biodiversity, and the smaller the island and the further east it lies the less there is likely to be. When humans moved beyond the islands of Near Oceania (Australia New Guinea, ande Solomon Islandds), they encountered no indigenous mammals except forflying foxes, fruit bats, and seals on some islands. Other vertebrate species were restricted to flying animals and a few small reptiles. However, local adaptations and evolution over long periods of isolation promoted fascinating species adaptations to local conditions. Perhaps most notable, in the absence of mammals and other predators, are the many species of flightless and ground-nesting birds. Another consequence of evolution was that many small environments boasted their own endemic (native) species, often small in number, unused to serious predation, limited in range, and therefore vulnerable to disruption. In Hawaii, for example, the highly adapted 39 species and subspecies of honeycreepers, several hundred species of fruit fiies,and more than 750 species of tree snails are often cited to epitomize the extent of localized Oceanic endemism (species being native to the area8. The word "cited" in the passage is closet in meaning toO expectedO believedO compared39. According to paragraph 4, why have species of flightless and ground-nesting birds become sonumerous on Oceanic islands?o They have no predators on the islandso They were some of the strongest species to arrive on the islandsThey live closer to their food sources than other species doo They are affected less by climatic changes than other animals are40, Which of the following is NOT mentioned in paragraph 4 about the species that live on Oceanic islands?o Certain species are native only to particular islandso Species that are native to Oceanic islands include relatively few mammalsO Populations of most species are small in number.O Some species have evolved over time to become predatorsThere are both great similarities and considerable diversity in the ecosystems that evolved on the Paragraph 1islands of Oceania in and around the Pacific Ocean. The islands, such as New Zealand, thatwere originally parts of continents still carry some small plant and animal remnants of their19慢跑的石头:earlier biota (animal and plant life), and they also have been extensively modified by evolution adaptation, and the arrival of new species. aBy contrast, the other islands, which emerged via geological processes such as volcanism, possessed no terrestrial life, but over long periods, winds. ocean currents, and the feet, feathers, and digestive tracts of birds brought the seeds of plants and a few species of animals. BOnly those species with ways of spreading to these islandsable to undertake the long journeys, and the various factors at play resulted in diverse ombinations of new colonists on the islands. One estimate is that the distribution of plantswas 75 percent by birds, 23 percent by floating, and only 2 percent by wind41. Look at the four squares [] that indicate where the following sentence can be added to the passage.When varied ecosystems are present, they can be explained as resulting in part from the process that formed the islands.Where would the sentence best fit Click on a square [] to add the sentence to the passage.42. Directions: An introductory sentence for a brief summary of the passage is provided below Complete the summary by selecting the THREE answer choices that express the mosmportant ideas in the passage. Some answer choices do not belong in the summary becauseley express ideas that are not presented in the passage or are minor ideas in the passagThis question is worth 2 pointDrag your choices to the spaces where they belong. To review the passag, click view Text. Biodiversity on Oceanic islands is dependent on a number of factors.Answer ChoicesUnlike Oceanic islands that were once part ofcontinental landmasses, islands formed by Species distribution in Oceania is determinedsuch geological processes as volcanism by the location of islands, their size, and thecontain only plants and animals that could be direction of the windtransported thereMost Oceanic islands are similar to oneislands size is less important than its another in latitude and contain plants and latitude in determining species diversityanimals typical of tropical islands.Though biodiversity is low on many Oceanic The absence of natural predators on the islands, many native species have evolved eastern Oceanic islands allowed many species nat are uniquely adapted to their local of large mammals to evolve that we environmentsof inhibiting a wide range of territory。
雅思ogtest8阅读答案passage3原文题目及答案解析内容本文为大家带来雅思OGtest8阅读passage3原文题目及答案解析内容。
Left or right?An overview of some research into liberalization: the dominance of one side of the body over the otherACreatures across the animal kingdom have a preference for one foot, eye or even antenna. The cause of this trait, called liberalization, is fairly simple: one side of the brain, which generally controls the opposite side of the body, is more dominant than the other when processing certain tasks. This does, on some occasions, let the animal down: such as when a toad fails to escape from a snake approaching from the right, just because its right eye is worse at spotting danger than its left. So why would animals evolve a characteristic that seems to endanger them?BFor many years it was assumed that liberalization was a uniquely human trait, but this notion rapidly fell apart as researchers started uncovering evidence of liberalization in all sorts of animals. For example, in the 1970s, Lesley Rogers, now at the University of New England in Australia, was studying memory and learning in chicks. She had been injecting a chemical into chicks brains to stop them learning how to spot grains of food among distracting pebbles, and was surprised to observe that the chemical only worked when applied to the left hemisphere of the brain. That strongly suggested that the right side of the chicks brain played little or no role in the learning of such behaviours. Similar evidence appeared in songbirds and rats around the same time, and since then, researchers have built up an impressive catalogue of animal liberalization.CIn some animals, liberalization is simply a preference for a single paw or foot, while in others it appears in more general patterns of behaviour. The left side of most vertebrate brains, for example, seems to process and control feeding. Since the left hemisphere processes input from the right side of the body, that means animals as diverse as fish, toads and birds are more likely to attack prey or food items viewed with their right eye. Even humpback whales prefer to use the right side of their jaws to scrape sand eels from the ocean floor.DGenetics plays a part in determining liberalization, but environmental factors have an impact too. Rogers found that a chick's liberalization depends on whether it is exposed to light before hatching from its egg - if it is kept in the dark during this period, neither hemisphere becomes dominant. In 2004, Rogers used this observation to test the advantages of brain bias in chicks faced with the challenge of multitasking. She hatched chicks with either strong or weak liberalization, then presented the two groups with food hidden among small pebbles and the threatening shape of a fake predator flying overhead. As predicted, the birds incubated in the light looked for foodmainly with their right eye, while using the other to check out the predator. The weakly-lateralized chicks, meanwhile, had difficulty performing these two activities simultaneously.ESimilar results probably hold true for many other animals. In 2006, Angelo Bisazza at the University of Padua set out to observe the differences in feeding behaviour between strongly-lateralized and weakly-lateralized fish. He found that strongly-lateralized individuals were able to feed twice as fast as weakly-lateralized ones when there was a threat of a predator looming above them. Assigning different jobs to different brain halves may be especially advantageous for animals such as birds or fish, whose eyes are placed on the sides of their heads. This enables them to process input from each side separately, with different tasks in mind.FAnd what of those animals who favour a specific side for almost all tasks? In 2009, Maria Magat and Culum Brown at Macquarie University in Australia wanted to see if there was general cognitive advantage in liberalization. To investigate, they turned to parrots, which can be either strongly right- or left-footed, or ambidextrous (without dominance). The parrots were given the intellectually demanding task of pulling a snack on a string up to their beaks, using a co-ordinated combination of claws and beak. The results showed that the parrots with the strongest foot preferences worked out the puzzle far more quickly than their ambidextrous peers.GA further puzzle is why are there always a few exceptions, like left-handed humans, who are wired differently from the majority of the population? Giorgio Vallortigara and Stefano Ghirlanda of Stockholm University seem to have found the answer via mathematical models. These have shown that a group of fish is likely to survive a shark attack with the fewest casualties if the majority turn together in one direction while a very small proportion of the group escape in the direction that the predator is not expecting.HThis imbalance of liberalization within populations may also have advantages for individuals. Whereas most co-operative interactions require participants to react similarly, there are some situations - such as aggressive interactions - where it can benefit an individual to launch an attack from an unexpected quarter. Perhaps this can partly explain the existence of left-handers in human societies. It has been suggested that when it comes tohand-to-hand fighting, left-handers may have the advantage over the right-handed majority. Where survival depends on the element of surprise, it may indeed pay to be different.Questions 27-30Complete each sentence with the correct ending, A-F, below.Write the correct letter, A-F, in boxes 27-30 on your answer sheet.27 In the 1970s, Lesley Rogers discovered that28 Angelo Bisazza’s experiments revealed that29 Magat and Brown’s studies show that30 Vallortigara and Ghirlanda’s research findings suggest thatA liberalization is more common in some species than in others.B it benefits a population if some members have a different liberalization than the majority.C liberalization helps animals do two things at the same time.D liberalization is not confined to human beings.E the greater an animal’s liberalization, the better it is at problem-solving.F strong liberalization may sometimes put groups of animals in danger.Questions 31-35 Complete the summary below.Choose ONE WORD ONLY from the passage for each answer.Write your answers in boxes 31-35 on your answer sheet.Lesley Rogers’ 2004 Experimentliberalization is determined by both genetic and 31__________ influences. Rogers found that chicks whose eggs are given 32__________ during the incubation period tend to have a stronger liberalization. Her 2004 experiment set out to prove that these chicks were better at 33__________ than weakly lateralized chicks. As expected, the strongly lateralized birds in the experiment were more able to locate 34__________ using their right eye, while using their left eye to monitor an imitation 35__________ located above them.Questions 36-40Reading Passage 3 has eight paragraphs, A-H.Which paragraph contains the following information?Write the correct letter, A-H, in boxes 36-40 on your answer sheet.NB You may use any letter more than once.36 description of a study which supports another scientist’s findings37 the suggestion that a person could gain from having an opposing liberalization to most of the population38 reference to the large amount of knowledge of animal liberalization that has accumulated39 research findings that were among the first to contradict a previous belief40 a suggestion that liberalization would seem to disadvantage animalsQuestion 27答案:D关键词:Lesley Rogers定位原文:B段最后两句“That strongly suggested that the right side … animal liberalization.”解题思路:利用人名Lesley Rogers作为关键词,定位到B段,关于Lesley Rogers所做的实验发现,需要具体定位到B段最后2句话,“这有力地表明,在这些行为的学习中,小鸡的大脑右侧发挥了很少或没有作用。
colocalization analysisColocalization analysis is a powerful technique used in various fields such as cell biology, immunology, neuroscience, and ecology. It involves the quantification and analysis of the spatial overlap or association between two or more molecules or structures within a biological sample. This can provide insights into the functional relationships and interactions between these molecules, as well as their subcellular localization and distribution patterns.There are several methods and approaches that can be used for colocalization analysis, depending on the nature of the data and the specific research question. One commonly used approach is the calculation of colocalization coefficients, such as the Pearson's correlation coefficient or the Manders' overlap coefficient. These coefficients provide a measure of the degree of colocalization between two molecules, ranging from -1 to 1, where values close to 1 indicate high colocalization and values close to 0 indicate no colocalization.In addition to colocalization coefficients, other statistical methods can be employed to assess the significance of colocalization. These include permutation tests, Monte Carlo simulations, and statistical hypothesis testing using appropriate thresholds. These approaches help determine whether the observed colocalization is statistically significant or if it could occur by chance.There are various software tools available for colocalization analysis, such as ImageJ, Fiji, CellProfiler, and Imaris. These tools provide a range of image processing and analysis functions,including algorithms for colocalization analysis. They allow researchers to analyze and quantify colocalization patterns in their images, and often include visualization options to display colocalization as scatter plots, heatmaps, or intensity overlays.It is important to note that colocalization does not necessarily imply direct interaction or functional association between the molecules being analyzed. It merely indicates that the two molecules are present in the same spatial location within the sample. To determine functional interactions, additional experiments or techniques such as co-immunoprecipitation, co-localization microscopy, or proximity ligation assays may be needed.Some recent studies have utilized colocalization analysis to investigate the localization and interaction of specific molecules within cells or tissues. For example, a study published in the journal Nature Communications used colocalization analysis to examine the spatial relationship between mitochondria and lipid droplets in liver cells. The researchers found that these organelles were closely associated and proposed that this colocalization is essential for lipid metabolism.Another study published in the journal PLOS Genetics used colocalization analysis to study the relationship between gene expression and DNA methylation in human blood cells. The researchers found that certain genomic regions showed high colocalization between these two molecular markers, suggesting a functional association between gene regulation and DNA methylation.In conclusion, colocalization analysis is a valuable technique for studying the spatial relationships and functional associations between molecules in biological samples. By quantifying and analyzing colocalization patterns, researchers can gain insights into the subcellular localization, interactions, and functional relationships of molecules within cells or tissues. These analyses can be performed using various software tools and statistical methods, enabling researchers to extract meaningful information from their imaging data.。
2025届广东省两校联考高三上学期(10月)一模考试英语试题一、阅读理解Career Development in Florence: A Journey Through Craftsmanship and LearningThe art of leather craftsmanship in Florence has a rich history, dating back to the 13th century. This exploration into the city’s leather artisans offers insights into the essence of Italian leather craftsmanship.The Leather Career Development Center — PIEROTUCCIEnroll in a complimentary workshop at the PIEROTUCCI Career Development Center and immerse yourself in the intricate process of crafting a leather handbag. Witnessing the meticulous handiwork involved will demystify the premium pricing of PIEROTUCCI products, assuring you that an investment in their bags is an investment in longevity.The Footwear Training Institute — STEFANO BEMERSTEFANO BEMER is renowned for its bespoke footwear, crafted with precision and elegance. The store, which sells luxury shoes ranging from hundreds to thousands of dollars, also serves as a training ground for aspiring shoemakers, with the workshop visible to customers in the front section.The Leather Artisan School — Scuola del CuoioStep into the Scuola del Cuoio, and you’ll feel as though you’ve entered a small college campus. This historic building houses a school dedicated to creating unique leather goods and educating paying students in the art of high-quality leatherworking.The Bookbinding Atelier — Il TorchioRun by Erin Ciulla, Il Torchio is a charming bookbinding workshop. Ciulla might give you a tour of the “guillotine,” an antique-looking machine used for cutting large volumes of paper. In addition to binding books with leather covers, Ciulla also offers services to cover books, journals, and photo albums with hand-made papers.1.What is the primary benefit of attending a workshop at PIEROTUCCI?A.Learning about the history of leather-making.B.Understanding the high cost of luxury shoes.C.Gaining hands-on experience in handbag crafting.D.Observing the antique machinery used in bookbinding.2.Which institution offers a comprehensive education in leather craftsmanship?A.Il Torchio.B.Scuola del Cuoio.C.STEFANO BEMER.D.PIEROTUCCI. 3.What service does Erin Ciulla provide at Il Torchio?A.Selling high-quality leather bags.B.Customizing book covers with leather.C.Teaching courses on leatherworking.D.Manufacturing antique-looking machines.Nicole Latham, a youthful 21-year-old scholar at the University of Leeds, dedicates her time not solely to the pursuit of legal academia, but also to the rigorous domain of weightlifting contests. In parallel, she exhibits proficiency in the martial art of karate. Beyond these physical pursuits, Latham’s health journey is marked by frequent visits to medical practitioners, a consequence of her recent acquisition of a rare affliction: multiple sclerosis (MS). This condition made its insidious debut during her preparation for the A-Level examinations, a period fraught with tension for numerous scholars. Initially, she attributed her symptoms to stress, but it soon became apparent that she was experiencing the onset of MS, specifically vertigo.Despite the onset of this debilitating disease, Nicole persisted in her academic endeavors, even resorting to ocular occlusion in a bid to ameliorate her impaired vision. It was at this juncture that she resolved to revisit her physician, embarking on a regimen of numerous medications, yet to no avail. Sensing a potential misdiagnosis, she promptly sought further diagnostic scrutiny at a hospital.Subsequent to an MRI examination, her condition was confirmed as MS. Following this inaugural episode and her subsequent diagnosis, Latham remained MS-free for several years. However, in August of the year 2021, she encountered another exacerbation, this time manifesting as a persistent tremor in her left hand for a duration of two months. Undeterred by the palpable impediments imposed by her condition in her day-to-day existence, she remained undaunted and resolute in her pursuit. Her aspiration was to inspire her contemporaries with disabilities, demonstrating that a life of vibrancy and fulfillment is attainable despite the adversities posed byMS.In the present day, Nicole leverages her digital platform not only to disseminate awareness regarding MS but also to exhort individuals to heed potential symptoms, a lesson she herself learned the hard way. Moreover, she endeavors to showcase that a life replete with richness and gratification is within reach for those afflicted with MS. Her narrative seeks to illuminate both the exultant peaks and the somber troughs of living with this condition.4.How did Nicole react when the first attack happened?A.She went to the hospital immediately.B.She turned to taking more exercise.C.She took a break from studying.D.She paid no attention to it.5.How did Nicole most probably feel after taking a lot of medicines?A.Relieved.B.Worried.C.Curious.D.Inspired. 6.Which of the following statements shows Nicole’s view on overcoming difficulties?A.Rome was not built in a day.B.Prevention is better than cure.C.Strength comes from a strong will.D.All things are difficult before they are easy.7.What would be the best title for the text?A.Nicole Latham:Always be Ready to HelpB.Meet N icole Latham — a T alented AthleteC.Nicole Latham:Never Let Anyone DownD.Meet Nicole Latham — a Fighter Suffering from MSA radiant grin is a reflection of inner joy. Have you ever been in a public space and received a smile from a stranger? Perhaps you were feeling low, yet their warm and amicable expression could lift your spirits. That person’s smile had the power to shift your gloomy mood. It’s astonishing how such a minor action can influence your emotions so profoundly, and I can attest to this, as I’m sure many of you can.This phenomenon isn’t just a feeling; it’s backed by science. What causes these positive emotions? When you smile at someone, you might feel a fleeting sense of joy. This is because your brain releases endorphins, which are like natural painkillers and can boost your self-esteem.Smiling is a straightforward act of kindness that can also enhance your self-regard.To illustrate, consider someone attending a job interview with their head held high and a smile on their face. They are more likely to be successful. Employers often note that a candidate who avoids eye contact and hides their smile may seem untrustworthy. In contrast, a person with a genuine smile exudes confidence. Regardless of your appearance, a smile can speak volumes and convey sincerity.I find great satisfaction in helping individuals of all ages build their self-esteem. Witnessing the joy and newfound confidence in my clients after our sessions is immensely rewarding. I firmly believe that a genuine, heartfelt smile can bridge gaps between people, even without words. 8.What does the underlined word “low” mean in Paragraph 1?A.Depressed.B.Strengthened.C.Multiplied.D.Returned. 9.What is the role of endorphins? ______A.They induce a sense of happiness.B.They inspire acts of kindness.C.They accelerate brain function.D.They cure certain illnesses.10.Why might someone who doesn’t smile have difficulty getting a job?A.They hold their head too high.B.They look down on others.C.They appear somewhat dishonest.D.They are overly confident.11.What kind of profession might the author have?A.An educator.B.A philanthropist.C.A researcher.D.A counselor.The Renaissance of Creative Thought is burgeoning, perhaps even burgeoning. If you attempted to absorb all the wisdom available today, you would need more than 180 million years to do so. But you are mistaken to assume that all this wisdom would stimulate a surge of innovation to match the abundance of knowledge. Indeed, the last time we found ourselves in a period of significant innovation, pursuing the ideas with the most profound impact, was more than 120 years ago, in a period called the Renaissance of Insight.Innovations, both grand and modest, originate from a new idea. Often, these ideas emerge as a moment of insight — the outcome of a novel connection in our minds made between existing and new knowledge. Studies reveal insights involve quiet signals deep in the brain, just under the surface of awareness. Anything that aids us in noticing quiet signals, such as taking breaksbetween engagements, adopting essential learning approaches, or steering clear of distractions like social media, can enhance the likelihood of insights. However, it is becoming increasingly challenging to find those quiet signals with the escalating use of technology, filling every moment with emergencies and an endless supply of content.Moreover, we also aspire to elevate the quality of them — to be able to sift through grand new ideas and identify the ones that hold genuine value, which can be difficult to measure. Launched in 2015, the Insight Meter (洞察力计量器) permits us to evaluate the potency of our insight experiences on a five-point scale, which is marked by intense emotions, motivation, memory advantage, aftershocks, and subsequent ideas. The Meter consolidates these five variables into a solitary value and enables us to define the significance of a new idea. The level-5 insight, involving the richest emotion, motivation, and lasting impact, holds the utmost significance.Since insights are one of the most effective ways to stimulate engagement, innovation, and behavioral change, the Insight Meter has extensive applications for gauging and enhancing individual and organizational performance. More importantly, it can be employed to measure the impact of different types of work environments and learning approaches on participants’ development — both in the moment or afterward.For organizations to reap the benefits of another age of insight, it is not sufficient to attempt to access more data or augment the number of insights we generate. Instead, it is about creating space for the most significant ideas to emerge from all the knowledge. Utilizing the shared language of the Insight Meter as a means to measure how important ideas are, relative to each other, will enable superior decision-making toward practical and competitive outcomes. And if we are to enter a new age of insight, we must design our environments to allow for the most exceptional insight possible to surface.12.What does the underlined word “burgeoning” in Paragraph 1 probably mean?A.Stabilizing.B.Exploding.C.Shifting.D.Collapsing. 13.According to the passage, how can the likelihood of insights be increased?A.By engaging in ongoing social media interactions.B.By relying on technology to receive regular notifications.C.By stepping away from computers between engagements.D.By participating in additional training and coaching sessions.14.What can be inferred from the passage?A.The Insight Meter dictates the influence of our insights.B.Possessing minimal emotional responses is a level-5 insight.C.Both the quantity and quality of insights are essential to innovation.D.A breakthrough has been made in innovation due to a wealth of information.15.What is the author’s attitude towards the current environment for innovations?A.Uncertain.B.Optimistic.C.Unconcerned.D.Dissatisfied.How to Teach ConfidenceWhile it might seem like some people are just born confident, confidence is largely an acquired skill. 16 Start by building up their self-esteem, independent thought, and positive self—talk. Show them how to achieve goals, and how to deal with failure when it happens. With lessons like these, you can teach the people around you to become more confident.Model confident behavior far people.If you’re trying to improve someone’s confidence, be a model for how they should behave in a confident way. 17 Show them confident interpersonal relations like eye contact, handshakes, and making small talk. This lets them practice in a safe environment.Praise small accomplishments to raise a person’s self-worth.If you’re trying to build someone’s confidence, start small. Each accomplishment they complete is a cause for celebration, even if it seems small. Be happy for your friends, kids, or students. 18Give specific praise so people know what they did well.A specific praise is better than a simple “You did well”. 19 . This makes your praise more genuine and boosts the person self-esteem more by showing them their strengths.Start with a positive statement before correcting something.20 This is especially important if you’re a parent, teacher, or coach. If you do have to make criticisms or corrections, always start by saying something positive first. This raises the person’s spirits and makes it easier for them to take the critical feedback that’s coming up. A.Instead, tell the person exactly what they did well.B.It’s something you can model and teach other people.C.You may have to point out where someone needs to improve.D.Instead of feeling criticized, the person will know you’re sincere.E.Act confident around them and in your interpersonal interactions.F.Your positive energy will teach them to celebrate their achievements.G.You might show someone’s strengths to help them see the bright side.二、完形填空Boo is a 5-year -old rooster. He loves going on road trips, watching TV, and 21 with other house pets: chickens and cats. Boo enjoys many things in his life, but most of all, he 22 to hug with his human mother Mary Bowman.Before he was 23 , Boo’s life wasn’t always that beautiful. He spent the first six months of his life on a farm with many other chickens, where he was treated more like a 24 than a unique being. He was given constant feeding, which is 25 unhealthy because he can not 26 his feed consumption.His now mother adopted him after learning about him from a friend; she was 27 when knowing his unfortunate fate. She decided to help this little guy 28 the meat factory and finally live 29 .In the house, Boo stays close to his humans. When the family goes for a walk in the wild, he wanders free. He, even like a dog, 30 the family when they come home. He likes to spend time with his dad reading comics. Even though Boo can’t read, he likes to look at pictures in the 31 . They play games together as well. Boo spends time with his grandma, too. When she’s playing the piano, he is looking, learning little by little what those 32 do.Boo is an 33 pet. He knows his family and where he lives. He is the soul of the house, the brightest star in the air. Today, Boo is an active part of the local 34 and has a personal account on which he 35 his everyday life with 35K fans.21.A.working out B.hanging out C.figuring out D.carrying out 22.A.benefits B.inspires C.loves D.advocates 23.A.protected B.replaced C.selected D.adopted 24.A.performer B.chief C.product D.species25.A.occasionally B.illegally C.gradually D.extremely 26.A.control B.obey C.predict D.permit 27.A.heartbroken B.patient C.grateful D.disappointed 28.A.complain B.detect C.escape D.resist 29.A.flexibly B.safely C.gently D.regularly 30.A.proves B.assists C.welcomes D.admits 31.A.books B.riddles C.puzzles D.applications 32.A.heels B.legs C.hands D.fingers 33.A.intelligent B.abnormal C.odd D.energetic 34.A.department B.community C.authority D.charity 35.A.drafts B.illustrates C.chats D.shares三、语法填空阅读下面短文,在空白处填入1个适当的单词或括号内单词的正确形式。
s Data mining and knowledge discovery in databases have been attracting a significant amount of research, industry, and media atten-tion of late. What is all the excitement about?This article provides an overview of this emerging field, clarifying how data mining and knowledge discovery in databases are related both to each other and to related fields, such as machine learning, statistics, and databases. The article mentions particular real-world applications, specific data-mining techniques, challenges in-volved in real-world applications of knowledge discovery, and current and future research direc-tions in the field.A cross a wide variety of fields, data arebeing collected and accumulated at adramatic pace. There is an urgent need for a new generation of computational theo-ries and tools to assist humans in extracting useful information (knowledge) from the rapidly growing volumes of digital data. These theories and tools are the subject of the emerging field of knowledge discovery in databases (KDD).At an abstract level, the KDD field is con-cerned with the development of methods and techniques for making sense of data. The basic problem addressed by the KDD process is one of mapping low-level data (which are typically too voluminous to understand and digest easi-ly) into other forms that might be more com-pact (for example, a short report), more ab-stract (for example, a descriptive approximation or model of the process that generated the data), or more useful (for exam-ple, a predictive model for estimating the val-ue of future cases). At the core of the process is the application of specific data-mining meth-ods for pattern discovery and extraction.1This article begins by discussing the histori-cal context of KDD and data mining and theirintersection with other related fields. A briefsummary of recent KDD real-world applica-tions is provided. Definitions of KDD and da-ta mining are provided, and the general mul-tistep KDD process is outlined. This multistepprocess has the application of data-mining al-gorithms as one particular step in the process.The data-mining step is discussed in more de-tail in the context of specific data-mining al-gorithms and their application. Real-worldpractical application issues are also outlined.Finally, the article enumerates challenges forfuture research and development and in par-ticular discusses potential opportunities for AItechnology in KDD systems.Why Do We Need KDD?The traditional method of turning data intoknowledge relies on manual analysis and in-terpretation. For example, in the health-careindustry, it is common for specialists to peri-odically analyze current trends and changesin health-care data, say, on a quarterly basis.The specialists then provide a report detailingthe analysis to the sponsoring health-care or-ganization; this report becomes the basis forfuture decision making and planning forhealth-care management. In a totally differ-ent type of application, planetary geologistssift through remotely sensed images of plan-ets and asteroids, carefully locating and cata-loging such geologic objects of interest as im-pact craters. Be it science, marketing, finance,health care, retail, or any other field, the clas-sical approach to data analysis relies funda-mentally on one or more analysts becomingArticlesFALL 1996 37From Data Mining to Knowledge Discovery inDatabasesUsama Fayyad, Gregory Piatetsky-Shapiro, and Padhraic Smyth Copyright © 1996, American Association for Artificial Intelligence. All rights reserved. 0738-4602-1996 / $2.00areas is astronomy. Here, a notable success was achieved by SKICAT ,a system used by as-tronomers to perform image analysis,classification, and cataloging of sky objects from sky-survey images (Fayyad, Djorgovski,and Weir 1996). In its first application, the system was used to process the 3 terabytes (1012bytes) of image data resulting from the Second Palomar Observatory Sky Survey,where it is estimated that on the order of 109sky objects are detectable. SKICAT can outper-form humans and traditional computational techniques in classifying faint sky objects. See Fayyad, Haussler, and Stolorz (1996) for a sur-vey of scientific applications.In business, main KDD application areas includes marketing, finance (especially in-vestment), fraud detection, manufacturing,telecommunications, and Internet agents.Marketing:In marketing, the primary ap-plication is database marketing systems,which analyze customer databases to identify different customer groups and forecast their behavior. Business Week (Berry 1994) estimat-ed that over half of all retailers are using or planning to use database marketing, and those who do use it have good results; for ex-ample, American Express reports a 10- to 15-percent increase in credit-card use. Another notable marketing application is market-bas-ket analysis (Agrawal et al. 1996) systems,which find patterns such as, “If customer bought X, he/she is also likely to buy Y and Z.” Such patterns are valuable to retailers.Investment: Numerous companies use da-ta mining for investment, but most do not describe their systems. One exception is LBS Capital Management. Its system uses expert systems, neural nets, and genetic algorithms to manage portfolios totaling $600 million;since its start in 1993, the system has outper-formed the broad stock market (Hall, Mani,and Barr 1996).Fraud detection: HNC Falcon and Nestor PRISM systems are used for monitoring credit-card fraud, watching over millions of ac-counts. The FAIS system (Senator et al. 1995),from the U.S. Treasury Financial Crimes En-forcement Network, is used to identify finan-cial transactions that might indicate money-laundering activity.Manufacturing: The CASSIOPEE trou-bleshooting system, developed as part of a joint venture between General Electric and SNECMA, was applied by three major Euro-pean airlines to diagnose and predict prob-lems for the Boeing 737. To derive families of faults, clustering methods are used. CASSIOPEE received the European first prize for innova-intimately familiar with the data and serving as an interface between the data and the users and products.For these (and many other) applications,this form of manual probing of a data set is slow, expensive, and highly subjective. In fact, as data volumes grow dramatically, this type of manual data analysis is becoming completely impractical in many domains.Databases are increasing in size in two ways:(1) the number N of records or objects in the database and (2) the number d of fields or at-tributes to an object. Databases containing on the order of N = 109objects are becoming in-creasingly common, for example, in the as-tronomical sciences. Similarly, the number of fields d can easily be on the order of 102or even 103, for example, in medical diagnostic applications. Who could be expected to di-gest millions of records, each having tens or hundreds of fields? We believe that this job is certainly not one for humans; hence, analysis work needs to be automated, at least partially.The need to scale up human analysis capa-bilities to handling the large number of bytes that we can collect is both economic and sci-entific. Businesses use data to gain competi-tive advantage, increase efficiency, and pro-vide more valuable services to customers.Data we capture about our environment are the basic evidence we use to build theories and models of the universe we live in. Be-cause computers have enabled humans to gather more data than we can digest, it is on-ly natural to turn to computational tech-niques to help us unearth meaningful pat-terns and structures from the massive volumes of data. Hence, KDD is an attempt to address a problem that the digital informa-tion era made a fact of life for all of us: data overload.Data Mining and Knowledge Discovery in the Real WorldA large degree of the current interest in KDD is the result of the media interest surrounding successful KDD applications, for example, the focus articles within the last two years in Business Week , Newsweek , Byte , PC Week , and other large-circulation periodicals. Unfortu-nately, it is not always easy to separate fact from media hype. Nonetheless, several well-documented examples of successful systems can rightly be referred to as KDD applications and have been deployed in operational use on large-scale real-world problems in science and in business.In science, one of the primary applicationThere is an urgent need for a new generation of computation-al theories and tools toassist humans in extractinguseful information (knowledge)from the rapidly growing volumes ofdigital data.Articles38AI MAGAZINEtive applications (Manago and Auriol 1996).Telecommunications: The telecommuni-cations alarm-sequence analyzer (TASA) wasbuilt in cooperation with a manufacturer oftelecommunications equipment and threetelephone networks (Mannila, Toivonen, andVerkamo 1995). The system uses a novelframework for locating frequently occurringalarm episodes from the alarm stream andpresenting them as rules. Large sets of discov-ered rules can be explored with flexible infor-mation-retrieval tools supporting interactivityand iteration. In this way, TASA offers pruning,grouping, and ordering tools to refine the re-sults of a basic brute-force search for rules.Data cleaning: The MERGE-PURGE systemwas applied to the identification of duplicatewelfare claims (Hernandez and Stolfo 1995).It was used successfully on data from the Wel-fare Department of the State of Washington.In other areas, a well-publicized system isIBM’s ADVANCED SCOUT,a specialized data-min-ing system that helps National Basketball As-sociation (NBA) coaches organize and inter-pret data from NBA games (U.S. News 1995). ADVANCED SCOUT was used by several of the NBA teams in 1996, including the Seattle Su-personics, which reached the NBA finals.Finally, a novel and increasingly importanttype of discovery is one based on the use of in-telligent agents to navigate through an infor-mation-rich environment. Although the ideaof active triggers has long been analyzed in thedatabase field, really successful applications ofthis idea appeared only with the advent of theInternet. These systems ask the user to specifya profile of interest and search for related in-formation among a wide variety of public-do-main and proprietary sources. For example, FIREFLY is a personal music-recommendation agent: It asks a user his/her opinion of several music pieces and then suggests other music that the user might like (<http:// www.ffl/>). CRAYON(/>) allows users to create their own free newspaper (supported by ads); NEWSHOUND(<http://www. /hound/>) from the San Jose Mercury News and FARCAST(</> automatically search information from a wide variety of sources, including newspapers and wire services, and e-mail rele-vant documents directly to the user.These are just a few of the numerous suchsystems that use KDD techniques to automat-ically produce useful information from largemasses of raw data. See Piatetsky-Shapiro etal. (1996) for an overview of issues in devel-oping industrial KDD applications.Data Mining and KDDHistorically, the notion of finding useful pat-terns in data has been given a variety ofnames, including data mining, knowledge ex-traction, information discovery, informationharvesting, data archaeology, and data patternprocessing. The term data mining has mostlybeen used by statisticians, data analysts, andthe management information systems (MIS)communities. It has also gained popularity inthe database field. The phrase knowledge dis-covery in databases was coined at the first KDDworkshop in 1989 (Piatetsky-Shapiro 1991) toemphasize that knowledge is the end productof a data-driven discovery. It has been popular-ized in the AI and machine-learning fields.In our view, KDD refers to the overall pro-cess of discovering useful knowledge from da-ta, and data mining refers to a particular stepin this process. Data mining is the applicationof specific algorithms for extracting patternsfrom data. The distinction between the KDDprocess and the data-mining step (within theprocess) is a central point of this article. Theadditional steps in the KDD process, such asdata preparation, data selection, data cleaning,incorporation of appropriate prior knowledge,and proper interpretation of the results ofmining, are essential to ensure that usefulknowledge is derived from the data. Blind ap-plication of data-mining methods (rightly crit-icized as data dredging in the statistical litera-ture) can be a dangerous activity, easilyleading to the discovery of meaningless andinvalid patterns.The Interdisciplinary Nature of KDDKDD has evolved, and continues to evolve,from the intersection of research fields such asmachine learning, pattern recognition,databases, statistics, AI, knowledge acquisitionfor expert systems, data visualization, andhigh-performance computing. The unifyinggoal is extracting high-level knowledge fromlow-level data in the context of large data sets.The data-mining component of KDD cur-rently relies heavily on known techniquesfrom machine learning, pattern recognition,and statistics to find patterns from data in thedata-mining step of the KDD process. A natu-ral question is, How is KDD different from pat-tern recognition or machine learning (and re-lated fields)? The answer is that these fieldsprovide some of the data-mining methodsthat are used in the data-mining step of theKDD process. KDD focuses on the overall pro-cess of knowledge discovery from data, includ-ing how the data are stored and accessed, howalgorithms can be scaled to massive data setsThe basicproblemaddressed bythe KDDprocess isone ofmappinglow-leveldata intoother formsthat might bemorecompact,moreabstract,or moreuseful.ArticlesFALL 1996 39A driving force behind KDD is the database field (the second D in KDD). Indeed, the problem of effective data manipulation when data cannot fit in the main memory is of fun-damental importance to KDD. Database tech-niques for gaining efficient data access,grouping and ordering operations when ac-cessing data, and optimizing queries consti-tute the basics for scaling algorithms to larger data sets. Most data-mining algorithms from statistics, pattern recognition, and machine learning assume data are in the main memo-ry and pay no attention to how the algorithm breaks down if only limited views of the data are possible.A related field evolving from databases is data warehousing,which refers to the popular business trend of collecting and cleaning transactional data to make them available for online analysis and decision support. Data warehousing helps set the stage for KDD in two important ways: (1) data cleaning and (2)data access.Data cleaning: As organizations are forced to think about a unified logical view of the wide variety of data and databases they pos-sess, they have to address the issues of map-ping data to a single naming convention,uniformly representing and handling missing data, and handling noise and errors when possible.Data access: Uniform and well-defined methods must be created for accessing the da-ta and providing access paths to data that were historically difficult to get to (for exam-ple, stored offline).Once organizations and individuals have solved the problem of how to store and ac-cess their data, the natural next step is the question, What else do we do with all the da-ta? This is where opportunities for KDD natu-rally arise.A popular approach for analysis of data warehouses is called online analytical processing (OLAP), named for a set of principles pro-posed by Codd (1993). OLAP tools focus on providing multidimensional data analysis,which is superior to SQL in computing sum-maries and breakdowns along many dimen-sions. OLAP tools are targeted toward simpli-fying and supporting interactive data analysis,but the goal of KDD tools is to automate as much of the process as possible. Thus, KDD is a step beyond what is currently supported by most standard database systems.Basic DefinitionsKDD is the nontrivial process of identifying valid, novel, potentially useful, and ultimate-and still run efficiently, how results can be in-terpreted and visualized, and how the overall man-machine interaction can usefully be modeled and supported. The KDD process can be viewed as a multidisciplinary activity that encompasses techniques beyond the scope of any one particular discipline such as machine learning. In this context, there are clear opportunities for other fields of AI (be-sides machine learning) to contribute to KDD. KDD places a special emphasis on find-ing understandable patterns that can be inter-preted as useful or interesting knowledge.Thus, for example, neural networks, although a powerful modeling tool, are relatively difficult to understand compared to decision trees. KDD also emphasizes scaling and ro-bustness properties of modeling algorithms for large noisy data sets.Related AI research fields include machine discovery, which targets the discovery of em-pirical laws from observation and experimen-tation (Shrager and Langley 1990) (see Kloes-gen and Zytkow [1996] for a glossary of terms common to KDD and machine discovery),and causal modeling for the inference of causal models from data (Spirtes, Glymour,and Scheines 1993). Statistics in particular has much in common with KDD (see Elder and Pregibon [1996] and Glymour et al.[1996] for a more detailed discussion of this synergy). Knowledge discovery from data is fundamentally a statistical endeavor. Statistics provides a language and framework for quan-tifying the uncertainty that results when one tries to infer general patterns from a particu-lar sample of an overall population. As men-tioned earlier, the term data mining has had negative connotations in statistics since the 1960s when computer-based data analysis techniques were first introduced. The concern arose because if one searches long enough in any data set (even randomly generated data),one can find patterns that appear to be statis-tically significant but, in fact, are not. Clearly,this issue is of fundamental importance to KDD. Substantial progress has been made in recent years in understanding such issues in statistics. Much of this work is of direct rele-vance to KDD. Thus, data mining is a legiti-mate activity as long as one understands how to do it correctly; data mining carried out poorly (without regard to the statistical as-pects of the problem) is to be avoided. KDD can also be viewed as encompassing a broader view of modeling than statistics. KDD aims to provide tools to automate (to the degree pos-sible) the entire process of data analysis and the statistician’s “art” of hypothesis selection.Data mining is a step in the KDD process that consists of ap-plying data analysis and discovery al-gorithms that produce a par-ticular enu-meration ofpatterns (or models)over the data.Articles40AI MAGAZINEly understandable patterns in data (Fayyad, Piatetsky-Shapiro, and Smyth 1996).Here, data are a set of facts (for example, cases in a database), and pattern is an expres-sion in some language describing a subset of the data or a model applicable to the subset. Hence, in our usage here, extracting a pattern also designates fitting a model to data; find-ing structure from data; or, in general, mak-ing any high-level description of a set of data. The term process implies that KDD comprises many steps, which involve data preparation, search for patterns, knowledge evaluation, and refinement, all repeated in multiple itera-tions. By nontrivial, we mean that some search or inference is involved; that is, it is not a straightforward computation of predefined quantities like computing the av-erage value of a set of numbers.The discovered patterns should be valid on new data with some degree of certainty. We also want patterns to be novel (at least to the system and preferably to the user) and poten-tially useful, that is, lead to some benefit to the user or task. Finally, the patterns should be understandable, if not immediately then after some postprocessing.The previous discussion implies that we can define quantitative measures for evaluating extracted patterns. In many cases, it is possi-ble to define measures of certainty (for exam-ple, estimated prediction accuracy on new data) or utility (for example, gain, perhaps indollars saved because of better predictions orspeedup in response time of a system). No-tions such as novelty and understandabilityare much more subjective. In certain contexts,understandability can be estimated by sim-plicity (for example, the number of bits to de-scribe a pattern). An important notion, calledinterestingness(for example, see Silberschatzand Tuzhilin [1995] and Piatetsky-Shapiro andMatheus [1994]), is usually taken as an overallmeasure of pattern value, combining validity,novelty, usefulness, and simplicity. Interest-ingness functions can be defined explicitly orcan be manifested implicitly through an or-dering placed by the KDD system on the dis-covered patterns or models.Given these notions, we can consider apattern to be knowledge if it exceeds some in-terestingness threshold, which is by nomeans an attempt to define knowledge in thephilosophical or even the popular view. As amatter of fact, knowledge in this definition ispurely user oriented and domain specific andis determined by whatever functions andthresholds the user chooses.Data mining is a step in the KDD processthat consists of applying data analysis anddiscovery algorithms that, under acceptablecomputational efficiency limitations, pro-duce a particular enumeration of patterns (ormodels) over the data. Note that the space ofArticlesFALL 1996 41Figure 1. An Overview of the Steps That Compose the KDD Process.methods, the effective number of variables under consideration can be reduced, or in-variant representations for the data can be found.Fifth is matching the goals of the KDD pro-cess (step 1) to a particular data-mining method. For example, summarization, clas-sification, regression, clustering, and so on,are described later as well as in Fayyad, Piatet-sky-Shapiro, and Smyth (1996).Sixth is exploratory analysis and model and hypothesis selection: choosing the data-mining algorithm(s) and selecting method(s)to be used for searching for data patterns.This process includes deciding which models and parameters might be appropriate (for ex-ample, models of categorical data are differ-ent than models of vectors over the reals) and matching a particular data-mining method with the overall criteria of the KDD process (for example, the end user might be more in-terested in understanding the model than its predictive capabilities).Seventh is data mining: searching for pat-terns of interest in a particular representa-tional form or a set of such representations,including classification rules or trees, regres-sion, and clustering. The user can significant-ly aid the data-mining method by correctly performing the preceding steps.Eighth is interpreting mined patterns, pos-sibly returning to any of steps 1 through 7 for further iteration. This step can also involve visualization of the extracted patterns and models or visualization of the data given the extracted models.Ninth is acting on the discovered knowl-edge: using the knowledge directly, incorpo-rating the knowledge into another system for further action, or simply documenting it and reporting it to interested parties. This process also includes checking for and resolving po-tential conflicts with previously believed (or extracted) knowledge.The KDD process can involve significant iteration and can contain loops between any two steps. The basic flow of steps (al-though not the potential multitude of itera-tions and loops) is illustrated in figure 1.Most previous work on KDD has focused on step 7, the data mining. However, the other steps are as important (and probably more so) for the successful application of KDD in practice. Having defined the basic notions and introduced the KDD process, we now focus on the data-mining component,which has, by far, received the most atten-tion in the literature.patterns is often infinite, and the enumera-tion of patterns involves some form of search in this space. Practical computational constraints place severe limits on the sub-space that can be explored by a data-mining algorithm.The KDD process involves using the database along with any required selection,preprocessing, subsampling, and transforma-tions of it; applying data-mining methods (algorithms) to enumerate patterns from it;and evaluating the products of data mining to identify the subset of the enumerated pat-terns deemed knowledge. The data-mining component of the KDD process is concerned with the algorithmic means by which pat-terns are extracted and enumerated from da-ta. The overall KDD process (figure 1) in-cludes the evaluation and possible interpretation of the mined patterns to de-termine which patterns can be considered new knowledge. The KDD process also in-cludes all the additional steps described in the next section.The notion of an overall user-driven pro-cess is not unique to KDD: analogous propos-als have been put forward both in statistics (Hand 1994) and in machine learning (Brod-ley and Smyth 1996).The KDD ProcessThe KDD process is interactive and iterative,involving numerous steps with many deci-sions made by the user. Brachman and Anand (1996) give a practical view of the KDD pro-cess, emphasizing the interactive nature of the process. Here, we broadly outline some of its basic steps:First is developing an understanding of the application domain and the relevant prior knowledge and identifying the goal of the KDD process from the customer’s viewpoint.Second is creating a target data set: select-ing a data set, or focusing on a subset of vari-ables or data samples, on which discovery is to be performed.Third is data cleaning and preprocessing.Basic operations include removing noise if appropriate, collecting the necessary informa-tion to model or account for noise, deciding on strategies for handling missing data fields,and accounting for time-sequence informa-tion and known changes.Fourth is data reduction and projection:finding useful features to represent the data depending on the goal of the task. With di-mensionality reduction or transformationArticles42AI MAGAZINEThe Data-Mining Stepof the KDD ProcessThe data-mining component of the KDD pro-cess often involves repeated iterative applica-tion of particular data-mining methods. This section presents an overview of the primary goals of data mining, a description of the methods used to address these goals, and a brief description of the data-mining algo-rithms that incorporate these methods.The knowledge discovery goals are defined by the intended use of the system. We can distinguish two types of goals: (1) verification and (2) discovery. With verification,the sys-tem is limited to verifying the user’s hypothe-sis. With discovery,the system autonomously finds new patterns. We further subdivide the discovery goal into prediction,where the sys-tem finds patterns for predicting the future behavior of some entities, and description, where the system finds patterns for presenta-tion to a user in a human-understandableform. In this article, we are primarily con-cerned with discovery-oriented data mining.Data mining involves fitting models to, or determining patterns from, observed data. The fitted models play the role of inferred knowledge: Whether the models reflect useful or interesting knowledge is part of the over-all, interactive KDD process where subjective human judgment is typically required. Two primary mathematical formalisms are used in model fitting: (1) statistical and (2) logical. The statistical approach allows for nondeter-ministic effects in the model, whereas a logi-cal model is purely deterministic. We focus primarily on the statistical approach to data mining, which tends to be the most widely used basis for practical data-mining applica-tions given the typical presence of uncertain-ty in real-world data-generating processes.Most data-mining methods are based on tried and tested techniques from machine learning, pattern recognition, and statistics: classification, clustering, regression, and so on. The array of different algorithms under each of these headings can often be bewilder-ing to both the novice and the experienced data analyst. It should be emphasized that of the many data-mining methods advertised in the literature, there are really only a few fun-damental techniques. The actual underlying model representation being used by a particu-lar method typically comes from a composi-tion of a small number of well-known op-tions: polynomials, splines, kernel and basis functions, threshold-Boolean functions, and so on. Thus, algorithms tend to differ primar-ily in the goodness-of-fit criterion used toevaluate model fit or in the search methodused to find a good fit.In our brief overview of data-mining meth-ods, we try in particular to convey the notionthat most (if not all) methods can be viewedas extensions or hybrids of a few basic tech-niques and principles. We first discuss the pri-mary methods of data mining and then showthat the data- mining methods can be viewedas consisting of three primary algorithmiccomponents: (1) model representation, (2)model evaluation, and (3) search. In the dis-cussion of KDD and data-mining methods,we use a simple example to make some of thenotions more concrete. Figure 2 shows a sim-ple two-dimensional artificial data set consist-ing of 23 cases. Each point on the graph rep-resents a person who has been given a loanby a particular bank at some time in the past.The horizontal axis represents the income ofthe person; the vertical axis represents the to-tal personal debt of the person (mortgage, carpayments, and so on). The data have beenclassified into two classes: (1) the x’s repre-sent persons who have defaulted on theirloans and (2) the o’s represent persons whoseloans are in good status with the bank. Thus,this simple artificial data set could represent ahistorical data set that can contain usefulknowledge from the point of view of thebank making the loans. Note that in actualKDD applications, there are typically manymore dimensions (as many as several hun-dreds) and many more data points (manythousands or even millions).ArticlesFALL 1996 43Figure 2. A Simple Data Set with Two Classes Used for Illustrative Purposes.。
Parrots are known for their vibrant colors and remarkable ability to mimic human speech.Here are some points to consider when writing an essay about parrots:1.Introduction to Parrots:Begin your essay by introducing parrots as a group of birds known for their intelligence and social nature.Mention their wide variety of species, ranging from the small lovebirds to the large macaws.2.Physical Characteristics:Describe the physical features of parrots,such as their beaks, which are adapted for cracking seeds and nuts,and their strong feet for perching and climbing.3.Coloration and Species:Discuss the diversity in coloration among parrots,from the green of the budgerigar to the vibrant hues of the scarlet macaw.Mention the different species and their unique characteristics.4.Habitat and Distribution:Explain where parrots are typically found,such as tropical and subtropical regions,and how their distribution is affected by factors like climate and habitat loss.5.Diet and Feeding Habits:Describe the diet of parrots,which includes seeds,nuts,fruits, and sometimes insects.Highlight their feeding habits,such as their use of their beaks to manipulate food.6.Social Behavior:Parrots are known for their social behavior.Discuss how they live in flocks and communicate with each other using a variety of calls and sounds.7.Mimicry and Communication:One of the most fascinating aspects of parrots is their ability to mimic sounds,including human speech.Explain how this ability is used for communication within their social groups and how it has made them popular pets.8.Conservation Status:Discuss the conservation status of parrots,highlighting the threats they face such as habitat destruction,poaching for the pet trade,and climate change.9.Captive Care and Ethical Considerations:If youre writing about parrots as pets,its important to address the ethical considerations of keeping such intelligent and social creatures in captivity.Discuss the importance of providing them with a suitable environment,social interaction,and mental stimulation.10.Conclusion:Conclude your essay by summarizing the key points and emphasizing the importance of protecting parrots in the wild and providing proper care for those kept aspets.Remember to use descriptive language and,if possible,include anecdotes or personal experiences to make your essay more engaging.Additionally,ensure that your essay is wellstructured,with a clear introduction,body,and conclusion.。
基于网络药理学探讨丹参-葛根药对治疗心肌纤维化的作用机制张力立1,马瑞松1,张曦1,陈娇2,秦贞苗21.海南省人民医院&海南医学院附属海南医院心血管内科,海南海口570311;2.海南医学院药学院,海南海口571199【摘要】目的采用网络药理学探讨丹参-葛根药对治疗心肌纤维化的活性成分及作用机制。
方法从中药系统药理学分析平台获取丹参-葛根药对活性成分和作用靶点,通过GeneCards 数据库获取心肌纤维化的相关靶点,使用Venny 2.1软件获取两者共同靶点;运用STRING 数据库和Cytoscape 3.7.1软件构建共同靶点的蛋白-蛋白互作(PPI)网络并进行拓扑学分析;采用ClusterProfiler R 功能包对共同靶点进行基因本体(GO)功能和KEGG 通路富集分析;最后使用Cytoscape 3.7.1软件构建“活性成分-靶点-通路”网络并分析。
结果筛选得到丹参-葛根药对候选活性成分30个,活性成分和心肌纤维化共同靶点41个。
共同靶点PPI 网络的平均点度值为19.7,平均介数为19.1,度值和介数均超过平均值的靶点共有14个。
KEGG 显著富集到73条通路,其中与心肌纤维化相关的通路有6条。
“活性成分-靶点-通路”网络显示,丹参中的木犀草素、丹参酮IIA 和葛根中的葛根素、β-谷甾醇等活性成分通过共同调控脂质与动脉粥样硬化、糖尿病并发症中的AGE-RAGE 、血流剪切力与动脉粥样硬化、缺氧诱导因子-1(HIF -1)、肿瘤坏死因子(TNF)、白细胞介数-17(IL -17)等信号通路起到抗心肌纤维化的功效。
结论揭示了丹参-葛根药对多成分、多靶点、多通路治疗心肌纤维化的作用特点,为进一步研究丹参-葛根药对治疗心肌纤维化的作用机制提供理论依据和新的思路。
【关键词】网络药理学;丹参;葛根;心肌纤维化;作用机制【中图分类号】R542.2+3【文献标识码】A【文章编号】1003—6350(2024)06—0862—08Mechanisms of the herbal pair of Salvia miltiorrhiza and Pueraria lobata in treating myocardial fibrosis based on network pharmacology.ZHANG Li-li 1,MA Rui-song 1,ZHANG Xi 1,CHEN Jiao 2,QIN Zhen-miao 2.1.Department of Cardiovasology,Hainan General Hospital,Hainan Hospital Affiliated to Hainan Medical University,Haikou 570311,Hainan,CHINA;2.School of Pharmacy,Hainan Medical University,Haikou 571199,Hainan,CHINA【Abstract 】ObjectiveTo investigate the active ingredients and mechanism of Salvia miltiorrhiza and Puerarialobata in treating myocardial fibrosis by network pharmacology.MethodsThe pharmacologic analysis platform of tra-ditional Chinese medicine system was used to search the active ingredients and the action targets of herbal pair of Salvia miltiorrhiza and Pueraria lobata.The related target of myocardial fibrosis was obtained by GeneCards database.The com-mon targets of the above two were obtained by Venny 2.1software.The protein-protein interaction (PPI)network of common targets was constructed and topological analysis was carried out by using STRING database and Cytoscape 3.7.1software.Gene ontology (GO)function and KEGG pathway enrichment of common targets were analyzed using ClusterProfiler R function package.Finally,Cytoscape 3.7.1was used to construct and analyze the network diagram of “active ingredients-targets-pathways ”.ResultsThirty candidate active ingredients and 41common targets of active in-gredients and myocardial fibrosis were obtained.The average point degree value and median number of common target PPI network were 19.7and 19.1,and there were 14targets with both degree value and median number exceeding the av-erage.KEGG was significantly enriched to 73pathways,of which 6pathways were associated with myocardial fibrosis.The active ingredient-target-pathway network showed that luteolin and tanshinone IIA in salvia miltiorrhiza,puerarin and β-sitosterol in Pueraria lobata jointly regulated the signaling pathways of lipid and atherosclerosis,AGE-RAGE in diabetic complications,atherosclerosis,hypoxia inducible factor (HIF -1),tumor necrosis factor (TNF),interleukin (IL -17)to play an anti-myocardial fibrosis effect.ConclusionSalvia miltiorrhiza and Pueraria lobata treated myocardi-al fibrosis through multi-ingredient,multi-target,and multi-path ways,which provides theoretical basis and new thought for further research on the anti-myocardial fibrosis mechanism of Salvia miltiorrhiza and Pueraria lobata.【Key words 】Network pharmacology;Salvia miltiorrhiza Bge.;Pueraria lobata (Willd.)Ohwi;Myocardial fibro-sis;Mechanism ·论著·doi:10.3969/j.issn.1003-6350.2024.06.020基金项目:2021年海南省自然科学基金(编号:821RC679、821RC581)。
Vol.3, No.1, 65-68 (2011)doi:10.4236/ns.2011.31009Natural ScienceEntropy changes in the clustering of galaxies in an expanding universeNaseer Iqbal1,2*, Mohammad Shafi Khan1, Tabasum Masood11Department of Physics, University of Kashmir, Srinagar, India; *Corresponding Author:2Interuniversity Centre for Astronomy and Astrophysics, Pune, India.Received 19 October 2010; revised 23 November 2010; accepted 26 November 2010.ABSTRACTIn the present work the approach-thermody- namics and statistical mechanics of gravitating systems is applied to study the entropy change in gravitational clustering of galaxies in an ex-panding universe. We derive analytically the expressions for gravitational entropy in terms of temperature T and average density n of the par-ticles (galaxies) in the given phase space cell. It is found that during the initial stage of cluster-ing of galaxies, the entropy decreases and fi-nally seems to be increasing when the system attains virial equilibrium. The entropy changes are studied for different range of measuring correlation parameter b. We attempt to provide a clearer account of this phenomena. The entropy results for a system consisting of extended mass (non-point mass) particles show a similar behaviour with that of point mass particles clustering gravitationally in an expanding uni-verse.Keywords:Gravitational Clustering; Thermodynamics; Entropy; Cosmology1. INTRODUCTIONGalaxy groups and clusters are the largest known gravitationally bound objects to have arisen thus far in the process of cosmic structure formation [1]. They form the densest part of the large scale structure of the uni-verse. In models for the gravitational formation of struc-ture with cold dark matter, the smallest structures col-lapse first and eventually build the largest structures; clusters of galaxies are then formed relatively. The clus-ters themselves are often associated with larger groups called super-clusters. Clusters of galaxies are the most recent and most massive objects to have arisen in the hiearchical structure formation of the universe and the study of clusters tells one about the way galaxies form and evolve. The average density n and the temperature T of a gravitating system discuss some thermal history of cluster formation. For a better larger understanding of this thermal history it is important to study the entropy change resulting during the clustering phenomena be-cause the entropy is the quantity most directly changed by increasing or decreasing thermal energy of intraclus-ter gas. The purpose of the present paper is to show how entropy of the universe changes with time in a system of galaxies clustering under the influence of gravitational interaction.Entropy is a measure of how disorganised a system is. It forms an important part of second law of thermody-namics [2,3]. The concept of entropy is generally not well understood. For erupting stars, colloiding galaxies, collapsing black holes - the cosmos is a surprisingly or-derly place. Supermassive black holes, dark matter and stars are some of the contributors to the overall entropy of the universe. The microscopic explanation of entropy has been challenged both from the experimental and theoretical point of view [11,12]. Entropy is a mathe-matical formula. Standard calculations have shown that the entropy of our universe is dominated by black holes, whose entropy is of the order of their area in planck units [13]. An analysis by Chas Egan of the Australian National University in Canberra indicates that the col-lective entropy of all the supermassive black holes at the centers of galaxies is about 100 times higher than previ-ously calculated. Statistical entropy is logrithmic of the number of microstates consistent with the observed macroscopic properties of a system hence a measure of uncertainty about its precise state. Statistical mechanics explains entropy as the amount of uncertainty which remains about a system after its observable macroscopic properties have been taken into account. For a given set of macroscopic quantities like temperature and volume, the entropy is a function of the probability that the sys-tem is in various quantumn states. The more states avail-able to the system with higher probability, the greater theAll Rights Reserved.N. Iqbal et al. / Natural Science 3 (2011) 65-6866 disorder and thus greater the entropy [2]. In real experi-ments, it is quite difficult to measure the entropy of a system. The technique for doing so is based on the thermodynamic definition of entropy. We discuss the applicability of statistical mechanics and thermodynam-ics for gravitating systems and explain in what sense the entropy change S – S 0 shows a changing behaviour with respect to the measuring correlation parameter b = 0 – 1.2. THERMODYNAMIC DESCRIPTION OF GALAXY CLUSTERSA system of many point particles which interacts by Newtonian gravity is always unstable. The basic insta-bilities which may occur involve the overall contraction (or expansion) of the system, and the formation of clus-ters within the system. The rates and forms of these in-stabilities are governed by the distribution of kinetic and potential energy and the momentum among the particles. For example, a finite spherical system which approxi-mately satisfies the viral theorem, contracts slowlycompared to the crossing time ~ ()12G ρ- due to the evaporation of high energy particles [3] and the lack of equipartition among particles of different masses [4]. We consider here a thermodynamic description for the sys-tem (universe). The universe is considered to be an infi-nite gas in which each gas molecule is treated to be agalaxy. The gravitational force is a binary interaction and as a result a number of particles cluster together. We use the same approximation of binary interaction for our universe (system) consisting of large number of galaxies clustering together under the influence of gravitational force. It is important to mention here that the characteri-zation of this clustering is a problem of current interest. The physical validity of the application of thermody-namics in the clustering of galaxies and galaxy clusters has been discussed on the basis of N-body computer simulation results [5]. Equations of state for internal energy U and pressure P are of the form [6]:(3122NTU =-)b (1) (1NTP V=-)b (2) b defines the measuring correlation parameter and is dimensionless, given by [8]()202,23W nb Gm n T r K Tτξ∞=-=⎰,rdr (3)W is the potential energy and K the kinetic energy ofthe particles in a system. n N V = is the average num-ber density of the system of particles each of mass m, T is the temperature, V the volume, G is the universalgravitational constant. (),,n T r ξ is the two particle correlation function and r is the inter-particle distance. An overall study of (),n T r ξ has already been dis-cussed by [7]. For an ideal gas behaviour b = 0 and for non-ideal gas system b varies between 0 and 1. Previ-ously some workers [7,8] have derived b in the form of:331nT b nT ββ--=+ (4) Eq.4 indicates that b has a specific dependence on the combination 3nT -.3. ENTROPY CALCULATIONSThermodynamics and statistical mechanics have been found to be equal tools in describing entropy of a system. Thermodynamic entropy is a non-conserved state func-tion that is of great importance in science. Historically the concept of entropy evolved in order to explain why some processes are spontaneous and others are not; sys-tems tend to progress in the direction of increasing en-tropy [9]. Following statistical mechanics and the work carried out by [10], the grand canonical partition func-tion is given by()3213212,1!N N N N mkT Z T V V nT N πβ--⎛⎫⎡=+ ⎪⎣Λ⎝⎭⎤⎦(5)where N! is due to the distinguishability of particles. Λrepresents the volume of a phase space cell. N is the number of paricles (galaxies) with point mass approxi-mation. The Helmholtz free energy is given by:ln N A T Z =- (6)Thermodynamic description of entropy can be calcu-lated as:,N VA S T ∂⎛⎫=- ⎪∂⎝⎭ (7)The use of Eq.5 and Eq.6 in Eq.7 gives()3120ln ln 13S S n T b b -⎛⎫-=-- ⎪ ⎪⎝⎭- (8) where S 0 is an arbitary constant. From Eq.4 we write()31bn b T β-=- (9)Using Eq.9, Eq.8 becomes as3203ln S S b bT ⎡⎤-=-+⎢⎣⎦⎥ (10)Again from Eq.4All Rights Reserved.N. Iqbal et al. / Natural Science 3 (2011) 65-68 6767()13221n b T b β-⎡⎤=⎢⎣⎦⎥ (11)with the help of Eq.11, Eq.10 becomes as()011ln ln 1322S S n b b b ⎡-=-+-+⎡⎤⎣⎦⎢⎥⎣⎦⎤ (12) This is the expression for entropy of a system consist-ing of point mass particles, but actually galaxies have extended structures, therefore the point mass concept is only an approximation. For extended mass structures we make use of softening parameter ε whose value is taken between 0.01 and 0.05 (in the units of total radius). Following the same procedure, Eq.8 becomes as()320ln ln 13N S S N T N b Nb V εε⎡⎤-=---⎢⎥⎣⎦(13)For extended structures of galaxies, Eq.4 gets modi-fied to()()331nT R b nT R εβαεβαε--=+ (14)where α is a constant, R is the radius of a cell in a phase space in which number of particles (galaxies) is N and volume is V . The relation between b and b ε is given by: ()11b b b εαα=+- (15) b ε represents the correlation energy for extended mass particles clustering gravitationally in an expanding uni-verse. The above Eq.10 and Eq.12 take the form respec-tively as;()()3203ln 111bT b S S b b ααα⎡⎤⎢⎥-=-+⎢⎥+-+-⎢⎥⎣⎦1 (16) ()()()120113ln ln 2111b b b S S n b b ααα⎡⎤-⎡⎤⎢⎥⎣⎦-=-++⎢⎥+-+-⎢⎥⎣⎦1 (17)where2R R εεεα⎛⎫⎛⎫=⎪ ⎪⎝⎭⎝⎭(18)If ε = 0, α = 1 the entropy equations for extended mass galaxies are exactly same with that of a system of point mass galaxies approximation. Eq.10, Eq.12, Eq.16and Eq.17 are used here to study the entropy changes inthe cosmological many body problem. Various entropy change results S – S 0 for both the point mass approxima-tion and of extended mass approximation of particles (galaxies) are shown in (Figures 1and2). The resultshave been calculated analytically for different values ofFigure 1. (Color online) Comparison of isothermal entropy changes for non-point and point mass particles (galaxies) for an infinite gravitating system as a function of average relative temperature T and the parameter b . For non-point mass ε = 0.03 and R = 0.06 (left panel), ε = 0.04 and R = 0.04 (right panel).All Rights Reserved.N. Iqbal et al. / Natural Science 3 (2011) 65-68 68Figure 2. (Color online) Comparison of equi-density entropy changes for non-point and point mass particles (galaxies) for an infinite gravitating system as a function of average relative density n and the parameter b. For non-point mass ε= 0.03 and R = 0.04.R (cell size) corresponding to different values of soften-ing parameter ε. We study the variations of entropy changes S – S0with the changing parameter b for differ-ent values of n and T. Some graphical variations for S – S0with b for different values of n = 0, 1, 100 and aver-age temperature T = 1, 10 and 100 and by fixing value of cell size R = 0.04 and 0.06 are shown. The graphical analysis can be repeated for different values of R and by fixing values of εfor different sets like 0.04 and 0.05. From both the figures shown in 1 and 2, the dashed line represents variation for point mass particles and the solid line represents variation for extended (non-point mass) particles (galaxies) clustering together. It has been ob-served that the nature of the variation remains more or less same except with some minor difference.4. RESULTSThe formula for entropy calculated in this paper has provided a convenient way to study the entropy changes in gravitational galaxy clusters in an expanding universe. Gravity changes things that we have witnessed in this research. Clustering of galaxies in an expanding universe, which is like that of a self gravitating gas increases the gases volume which increases the entropy, but it also increases the potential energy and thus decreases the kinetic energy as particles must work against the attrac-tive gravitational field. So we expect expanding gases to cool down, and therefore there is a probability that the entropy has to decrease which gets confirmed from our theoretical calculations as shown in Figures 1 and 2. Entropy has remained an important contributor to our understanding in cosmology. Everything from gravita-tional clustering to supernova are contributors to entropy budget of the universe. A new calculation and study of entropy results given by Eqs.10, 12, 16 and 17 shows that the entropy of the universe decreases first with the clustering rate of the particles and then gradually in-creases as the system attains viral equilibrium. The gravitational entropy in this paper furthermore suggests that the universe is different than scientists had thought.5. ACKNOWLEDGEMENTSWe are thankful to Interuniversity centre for Astronomy and Astro-physics Pune India for providing a warm hospitality and facilities during the course of this work.REFERENCES[1]Voit, G.M. (2005) Tracing cosmic evolution with clus-ters of galaxies. Reviews of Modern Physics, 77, 207- 248.[2]Rief, F. (1965)Fundamentals of statistical and thermalphysics. McGraw-Hill, Tokyo.[3]Spitzer, L. and Saslaw, W.C. (1966) On the evolution ofgalactic nuclei. Astrophysical Journal, 143, 400-420.doi:10.1086/148523[4]Saslaw, W.C. and De Youngs, D.S. (1971) On the equi-partition in galactic nuclei and gravitating systems. As-trophysical Journal, 170, 423-429.doi:10.1086/151229[5]Itoh, M., Inagaki, S. and Saslaw, W.C. (1993) Gravita-tional clustering of galaxies. Astrophysical Journal, 403,476-496.doi:10.1086/172219[6]Hill, T.L. (1956) Statistical mechanics: Principles andstatistical applications. McGraw-Hill, New York.[7]Iqbal, N., Ahmad, F. and Khan, M.S. (2006) Gravita-tional clustering of galaxies in an expanding universe.Journal of Astronomy and Astrophysics, 27, 373-379.doi:10.1007/BF02709363[8]Saslaw, W.C. and Hamilton, A.J.S. (1984) Thermody-namics and galaxy clustering. Astrophysical Journal, 276, 13-25.doi:10.1086/161589[9]Mcquarrie, D.A. and Simon, J.D. (1997) Physical chem-istry: A molecular approach. University Science Books,Sausalito.[10]Ahmad, F, Saslaw, W.C. and Bhat, N.I. (2002) Statisticalmechanics of cosmological many body problem. Astro-physical Journal, 571, 576-584.doi:10.1086/340095[11]Freud, P.G. (1970) Physics: A Contemporary Perspective.Taylor and Francis Group.[12]Khinchin, A.I. (1949) Mathamatical Foundation of statis-tical mechanics. Dover Publications, New York.[13]Frampton, P., Stephen, D.H., Kephar, T.W. and Reeb, D.(2009) Classical Quantum Gravity. 26, 145005.doi:10.1088/0264-9381/26/14/145005All Rights Reserved.。
a rXiv:mat h-ph/05954v123Sep25The Covariant Picard Groupoid in Differential Geometry ∗Stefan Waldmann ∗∗Fakult¨a t f¨u r Mathematik und Physik Albert-Ludwigs-Universit¨a t Freiburg Physikalisches Institut Hermann Herder Straße 3D 79104Freiburg Germany September 2005FR-THEP 2005/10Abstract In this article we discuss some general results on the covariant Picard groupoid in the context of differential geometry and interpret the problem of lifting Lie algebra actions to line bundles in the Picard groupoid approach.Keywords:Morita equivalence,∗-Algebras,Picard groupoid,Hopf algebra actions.MSC (2000):16D90,16W30,16W10,53D55Contents 1Introduction 12From Geometry to Algebra 23Morita Equivalence in Different Flavours 44The Covariant Situation 75The case of a Lie algebra 81IntroductionIn this work we would like to illustrate and exemplify some general results from [16]where the general framework of a Morita theory which is covariant under a given Hopf algebra was studied.One main motivation to do so is coming from (deformation)quantization theory [3],see e.g [12,14]for recent reviews.Here Morita equivalence provides an important notion of equivalence ofobservable algebras[6,31].In particular,on cotangent bundles the condition for star products to be Morita equivalent is shown to coincide with Dirac’s integrality condition for magnetic charges of a background magneticfield[6]leading to a natural interpretation of Morita equivalence also in more general situations.From the differential geometric point of view,it is a natural question whether all these techniques as developed in[5,7–9,31]can be made compatible with a certain given symmetry of the underlying manifold.On the purely algebraic level,a fairly general notion of‘symmetry’is that of a Hopf algebra action of a given Hopf algebra.In[16]we studied this type of symmetry in the general situation.From this general framework we shall specialize now into two directions:on one hand,the algebras on which the symmetry acts and whose Morita theory shall be studied will now be com-mutative:we are interested in the algebra of functions C∞(M)on a manifold.On the other hand, the symmetry in question will either be coming from a Lie group action on M or from a Lie algebra action as its infinitesimal counterpart.It is well-known that two commutative algebras are Morita equivalent if and only if they are isomorphic,see e.g.the textbook[19],whence for commutative algebras Morita equivalence seems to be a useless notion.However,this is not true as things become interesting if one asks in addition in how many ways two algebras can be Morita equivalent compared to the ways in which they can be isomorphic.It turns out that in general there are new possibilities which makes Morita theory interesting even in the commutative framework.This phenomenon is precisely encoded in the so-called Picard groupoid which we shall compute for the case of function algebras.This way,wefind an interesting and non-trivial class of examples illustrating the general ideas of[16].Moreover,it will also be of independent interest as we are now able to re-interpret several well-known problems and results in differential geometry from a Morita theoretic point of view.Finally,the commutative situation with the algebras being function algebras C∞(M)is expected to be the starting point for a discussion of Morita equivalence of star products as in[6]but now being compatible with a symmetry of the classical phase space[15].The article is organized as follows:In Section2we recall some well-known arguments why one should and how one can pass from a geometric to a more algebraic description of differential geometry.The next section is devoted to a general discussion on Morita theory in differentflavours, taking into account specific structures of the algebras in question.Here we are mainly interested in∗-involutions and notions of positivity.In Section4we add one more structure to be preserved by Morita theory,namely a symmetry which we model by a Hopf algebra action.This can be specialized to group actions and Lie algebra actions.The last section contains some new material, namely the explicit computation of a certain part of the Lie algebra covariant Picard group. Acknowledgments:It is a pleasure for me to thank the organizers and in particular Michel Cahen and Willy Sarlet for their kind invitation to the20th International Workshop on Differential Geo-metric Methods in Theoretical Mechanics in Ghent where the content of this work was presented. Moreover,I would like to thank Stefan Jansen and Nikolai Neumaier for valuable discussions and comments on the manuscript.2From Geometry to AlgebraIn some sense,differential geometric methods in mathematical physics correspond mainly to clas-sical theories:Hamiltonian mechanics on a symplectic or Poisson manifold M is one prominent example.On the other hand,quantum theories require a more algebraic approach:here the un-certainty relations in physics are modelled mathematically by non-trivial commutation relationsbetween observables in some noncommutative algebra,the observable algebra.Thus quantization in a very broad sense can be understood as the passage from geometric to noncommutative algebraic structures.An intermediate step is of course to encode the geometric structures on M in algebraic terms based on the commutative algebra of functions C∞(M)where,in view of applications to quantization,it is convenient to consider complex-valued functions.Then it is a folklore statement(Milnor’s exercise)that one can recover the smooth manifold M from the∗-algebra C∞(M).More specifically:every∗-homomorphismΦ:C∞(M)−→C∞(N) between function algebras is actually of the formΦ=φ∗with some smooth mapφ:N−→M between the underlying manifolds,see e.g.[13,24]for a recent discussion.Thus the category of ∗-algebras with∗-homomorphisms as morphisms becomes relevant to differential geometry.The‘dictionary’to translate geometric to algebraic terms,which is also one of the cornerstones of Connes’noncommutative geometry[11],can be extended in various directions.We mention just one further example also relevant to Morita theory:by the well-known Serre-Swan theorem, see e.g.[29],the(complex)vector bundles E−→M correspond tofinitely generated projective modules over the algebra C∞(M)via E↔Γ∞(E).In more geometric terms this means that for any vector bundle there exists another vector bundle F−→M such that E⊕F is a trivial vector bundle.This is of course the key to relate the algebraic K0-theory of C∞(M)to the topological K0-theory of M.Let us now turn to Morita theory.Itsfirst motivation came from the question what one can say about two algebras A and B provided one knows that their categories of(left)modules are equivalent,see[19,23].Clearly,in view of applications to quantum mechanics a good understanding of the more specific modules given by∗-representations of the observable algebras on(pre)Hilbert spaces is crucial for any physical interpretation.As we shall not start to define what a reasonable category of modules over the∗-algebra C∞(M)should be—though this can perfectly be done,see e.g.[7,27,31]and references therein—we take a different motivation which will lead essentially to the same structures.The idea is to take the category of∗-algebras,keep the objects and enhance the notion of morphisms.This can be expected to be interesting as for function algebras we already know what the‘ordinary’morphisms are:pull-backs by smooth maps.Thus a generalization would lead to a generalization of smooth maps between manifolds,when we translate things back using our‘dictionary’.In particular,it might happen that algebras become isomorphic in this new, enhanced category(which will turn out to be not the case for function algebras)and one might have more‘automorphisms’of a given algebra(which will indeed be the case for function algebras). In general,the invertible morphisms in a category form a(large)groupoid in the obvious sense which is called the Picard groupoid of the category.Thus a major step in understanding the whole category is to consider its Picard groupoid of invertible arrowsfirst.In principle,the whole idea should be familiar from geometric mechanics as one example of en-hancing a category by allowing more general morphisms is given by the symplectic‘category’:first one considers symplectic manifolds as objects and symplectomorphisms as morphisms.Though this is a reasonable choice to look at,it turns out to be rather boring as the choice for the morphisms is too restrictive.More interesting is the‘category’where one considers morphisms to be canonical relations,see e.g.[2].However,this is no longer an honest category since the composition of mor-phisms is only defined when certain technical requirements like clean intesections of the canonical relations are fulfilled.Nevertheless this‘symplectic category’is by far more interesting now.Other examples are the Morita theory for(integrable)Poisson manifolds by Xu[32]as well as the Morita theory of Lie groupoids,see e.g.[22].3Morita Equivalence in Different FlavoursAfter having outlined the general ideas in the previous section we should start being more concrete now.As warming up we discuss the‘enhancing of the category’for the category of unital algebras with usual algebra morphismsfirst,see e.g.[4,19]for this classical approach.Here the generalized morphisms are the bimodules:For two algebras A and B a(B,A)-bimoduleE,which we shall frequently denote byB EAto indicate that B acts from the left while A acts fromthe right,is considered as an arrow A−→B.Why does this give a reasonable notion of morphisms?In particular,we have to define the com-position of morphisms.Thus letB EAandCFBbe bimodules then their tensor productCFB⊗BBEAover B is a(C,A)-bimodule and hence an arrow A−→C.However,this is not yet an associativecomposition law as for three bimodulesD GC,CFB,BEAwe have a canonical isomorphismD GC⊗C(CFB⊗BBEA)∼=(DGC⊗CCFB)⊗BBEA(3.1)as(D,A)-bimodules but not equality.The way out is to use isomorphism classes of bimodules as arrows instead of bimodules themselves.Then the tensor product becomes indeed associative andthe isomorphism class of the canonical bimoduleA AAserves as the identity morphism of the objectA since we use unital algebras for simplicity.Thefinal restriction we have to impose is that in a category the morphism space between two objects has to be a set,which is a priori not clear in our enhanced category.Therefor one should pose additional constraints on the bimodules likefinitely generatedness.However,we shall ignore these subtleties in the following as the new notion of isomorphisms in this category will be unaffected anyway.However,we still have to show that we really get an extension of our previous notion of mor-phisms.Thus letΦ:A−→B be an algebra homomorphism.Then on B we define a right A-modulestructure by b·Φa=bΦ(a)and obtain a bimoduleB BΦA.Its isomorphism class is denoted byℓ(Φ).It is easy to see thatℓ(Φ◦Ψ)=ℓ(Φ)◦ℓ(Ψ)andℓ(id A)is the class ofA AAwhence our previousnotion of morphisms is indeed contained in the new one.If we denote this new category by ALG then two unital algebras A and B are called Morita equivalent iffthey are isomorphic in ALG.Without going into the details this is equivalent to the existence of a certain bimodule which is‘invertible’with respect to the composition⊗.In fact, such bimodules can be characterized rather explicitly,see e.g.[19].The isomorphism classes of these invertible bimodules constitute now the Picard groupoid of this category ALG which we shall denote by Pic.The invertible arrows from A to B are denoted by Pic(B,A)while the isotropy group of this groupoid at the local unit A is denoted by Pic(A),the Picard group of A.The mapℓinduces now a group homomorphism such that1−→InnAut(A)−→Aut(A)ℓ−→Pic(A)(3.2) is exact,whence in the commutative case,the automorphism group of A is a subgroup of the Picard group Pic(A).Finally,it can be shown that for commutative A,the exact sequence(3.2)is split whencePic(A)=Aut(A)⋉Pic A(A),(3.3) where the subgroup Pic A(A)consists of the symmetric invertible bimodules,i.e.those where a·x=x·a for all x∈E and a∈A.Then Pic A(A)is called the commutative or static Picard group, see e.g.[8,10]for a discussion and further references.It is a well-known theorem in Morita theory that for unital algebras A,B the equivalencebimodulesB EAare certainfinitely generated projective right A-modules such that Hom A(EA)∼=B.Coming back to our example A=C∞(M)we see,using the Serre-Swan theorem,that the only candidates for the symmetric self-equivalence bimodules are the sectionsΓ∞(L)of a complex line bundle.In fact,it turns out thatΓ∞(L)is indeed invertible with inverse given by the class of Γ∞(L∗)sinceΓ∞(L)⊗C∞(M)Γ∞(L)∼=Γ∞(L∗⊗L)∼=C∞(M)as C∞(M)-bimodules.This shows that the static Picard group of C∞(M)is just the‘geometric’Picard group,i.e.the group of isomorphism classes of complex line bundles with the tensor product as ing the Chern class to classify complex line bundles then gives according to(3.3)Pic(C∞(M))=Diffeo(M)⋉ˇH2(M,),(3.4) where the semidirect product structure comes from the usual action of diffeomorphisms onˇH2(M,).In general,all Morita equivalence bimodulesB EAfor A=C∞(M)are isomorphic to someΓ∞(E)with a vector bundle E−→M of non-zerofibre dimension.Moreover,B has to be isomorphic toΓ∞(End(E)).Thus for function algebras C∞(M)we have a complete description of the Picard groupoid.We shall now specialize our notion of Morita equivalence:we have already argued that the ∗-involution of C∞(M)should be taken into account when having applications to quantization in mind.Moreover,one can include notions of positivity into Morita theory.One defines a linear functionalω:A−→to be positive ifω(a∗a)≥0for all a∈A.Then an element a∈A is called positive ifω(a)≥0for all positive linear functionalsωof A,see[7,27,30,31]for a detailed discussion.It is clear that for applications to quantum theories such notions of positive functionals are crucial as they encode expectation value functionals and hence the physical states for the observable algebra.In particular,for A=C∞(M)onefinds that positive linear functionals are precisely the inte-grations with respect to compactly supported positive Borel measures.This follows essentially from Riesz’representation theorem,see[5,App.B].From this it immediately follows that f∈C∞(M) is positive ifff(x)≥0for all x∈M,whence the above,purely algebraic definition reproduces the usual notion.We can now state the definition of∗-Morita equivalence[1]and strong Morita equivalence bimodules,see[26]as well as[20]for Rieffel’s original formulation in the context of C∗-algebras and[5,7]for the general case of∗-algebras.Instead of describing the‘enhanced category’way,we directly give the definition in terms of bimodules which is entirely equivalent,see[7].Definition3.1A∗-Morita equivalence bimoduleB EAis a(B,A)-bimodule together with innerproducts·,·A:E×E−→A(3.5) andB ·,· :E×E−→B(3.6) such that for all x,y,z∈E,a∈A and b∈B we have:1. ·,·A(resp.B ·,· )is linear in the right(resp.left)argument.2. x,y·aA = x,yAa and B b·x,y =b B x,y .3. x,yA = y,xA∗andB x,y =B y,x∗.4. ·,·Aand B ·,· are non-degenerate.5. ·,· A and B ·,· are full.6. x,b ·y A = b ∗·x,y A andB x,y ·a =B x ·a ∗,y .7.B x,y ·z =x · y,z A .If in addition the inner products are completely positive thenB E A is called a strong Morita equiv-alence bimodule.Here ·,· A is called full if the -span of all elements x,y A is the whole algebra A ;in generalthese elements constitute a ∗-ideal.Moreover, ·,· A is called completely positive if for all n ∈and all x 1,...,x n ∈E the matrix ( x i ,x j A )∈M n (A )is positive in the ∗-algebra M n (A ).The composition of bimodules is again the tensor product where on C F B ⊗B B E A the A -valuedinner product is now defined by Rieffel’s formulax ⊗φ,y ⊗ψ F ⊗E A = φ, x,y F B ·ψ E A,(3.7)and analogously for the C -valued inner product.It is then a non-trivial theorem that this is indeed completely positive again,if the inner products on E and F have been completely positive [7].Passing to isometric isomorphism classes one can show that this gives a groupoid:the ∗-Picard groupoid Pic ∗and the strong Picard groupoid Pic str ,respectively.In particular,the local unit at A is given by the isometric isomorphism class of A A A equipped with the inner productsa,b A =a ∗b and A a,b =ab ∗.(3.8)More generally,A n ,viewed as (M n (A ),A )-bimodule equipped with the canonical inner productsM n (A ) x,y =ni =1x · y,· A and x,y A =ni =1x ∗i y i (3.9)implements the strong Morita equivalence between A and M n (A ).Since we simply can forget the additional structures we obtain canonical groupoid morphismsPic strPic ∗Pic ,(3.10)which have been studied in [7]:in general,none of them is surjective nor injective,even on the level of the Picard groups.The geometric interpretation of the inner products is that they correspond to Hermitian fiber metrics on the corresponding line bundles or vector bundles,respectively:Indeed,this can be seen easily from the very definitions.Since up to isometry there is only one positive Hermitian fiber metric on a given line bundle we have in the case of A =C ∞(M )Pic str (C ∞(M ))=Diffeo(M )⋉ˇH 2(M,)=Pic (C ∞(M )).(3.11)Remark 3.2In the approach of [5,7–9]one main point was to replace the real numbers by an arbitrary ordered ring R and by the ring extension C =R (i)with i 2=−1.This allows to include also the formal star product algebras from deformation quantization into the game.They are defined as algebras over the formal power series [[λ]].Surprisingly,essentially all of the constructions involving positivity go through without problems.4The Covariant SituationLet us now pass to the covariant situation:we want to incorporate some given symmetry of the∗-algebras in question.Here we have two main motivations and examples from differential geometry: First,a smooth actionΦ:M×G−→M of a Lie group G on M,where by convention we choose a right action in order to have a left action g→Φ∗g on C∞(M)by∗-automorphisms.Second,as infinitesimal version ofΦ,a Lie algebra action,i.e.a Lie algebra homomorphismϕ:g−→X(M) from a realfinite dimensional Lie algebra g into the Lie algebra of real vectorfields,which correspond to the∗-derivations of C∞(M).In order to formalize and unify both situations it is advantageous to consider Hopf∗-algebras and their actions on algebras.Thus let H be a Hopf∗-algebra,i.e.a unital∗-algebra with a coassociative coproduct∆,a counitǫand an antipode S such that∆:H−→H⊗H as well as ǫ:H−→are∗-homomorphisms and S(S(g∗)∗)=g for all g∈H,see e.g.[17,Sect.IV.8].For the coproduct we shall use Sweedler’s notation∆(g)=g(1)⊗g(2).The two geometric examples we want to discuss are now encoded in the following Hopf∗-algebras:First,recall that any group G defines its group algebra[G]which becomes a Hopf∗-algebra by setting∆(g)=g⊗g,ǫ(g)=1and S(g)=g−1=g∗for g∈G⊆[G].In this case H=[G]is even cocommutative,i.e.∆=∆opp where the opposite coproduct is defined by∆opp(g)=g(2)⊗g(1).Second,for any real Lie algebra the complexified universal enveloping algebra U(g)⊗= U(g)becomes a Hopf∗-algebra by setting∆(ξ)=ξ⊗+⊗ξ,ǫ(ξ)=0and S(ξ)=−ξ=ξ∗together with the resulting extensions to all of U(g).Again,U(g)is cocommutative.The situation that a group G acts by∗-automorphisms on a∗-algebra as well as a Lie algebra representation by∗-derivations can be unified in terms of Hopf∗-algebras as follows:A∗-action⊲of H on A is a bilinear map⊲:H×A−→A such that g⊲(h⊲a)=(gh)⊲a and H⊲a=a,i.e.A is a left H-module,and g⊲(ab)=(g(1)⊲a)(g(2)⊲b),g⊲A=ǫ(g)A,and(g⊲a)∗=S(g)∗⊲a∗for all g,h∈H and a,b∈A.Then it is well-known and easy to see that for our two examples[G] and U(g)this indeed generalizes and unifies the action by∗-automorphisms and∗-derivations, respectively.The interesting relations are all encoded in the different coproducts.In principle and probably even more naturally,one should consider coactions instead of actions of H,see e.g.[17,Sect.III.6].Nevertheless,we stick to the more intuitive point of view where H ‘acts’.Now suppose we have∗-algebras A,B with a∗-action of H.Let furthermoreB EAbe a strongor∗-Morita equivalence bimodule.Then we call the bimodule H-covariant if there is an H-module structure on E denoted by⊲,too,such that we have the following compatibilitiesg⊲(b·x)=(g(1)⊲b)·(g(2)⊲x)(4.1)g⊲(x·a)=(g(1)⊲x)·(g(2)⊲a)(4.2)g⊲B x,y =B g(1)⊲x,S(g(2))∗⊲y (4.3)g⊲ x,yA = S(g(1))∗⊲x,g(2)⊲yA(4.4)for all x,y∈E,a∈A,b∈B and g,h∈H.Of course,in the case of ring-theoretic Morita theory one only requires(4.1)and(4.2).Taking isometric isomorphism classes also respecting the action of H gives the H-covariantflavours of the Picard groupoids,denoted by Pic H,Pic∗H,andPic str H ,respectively.Since we can successively forget the additional structures we get the following commuting diagram of canonical groupoid morphisms:Pic str HPic ∗HPic HPic Pic strPic ∗,(4.5)Now let us interpret the diagram on the level of Picard groups and in our geometric situation:Let e.g.H =U (g )and A =C ∞(M )be as before,equipped with an action of g by ∗-derivations.Then the kernel and the image of the group morphismPic H (A )−→Pic (A )(4.6)encodes on which line bundles we can lift the g -action and if so,in how many different ways up to isomorphism.Analogously,in the strong situation one requires in addition compatibility with the Hermitian fiber metric.The case of H =[G ]leads to the question of existence and uniqueness of liftings of the group action on M to a group action on L by vector bundle automorphisms.In the strong case one requires the lift in addition to be unitary with respect to the fiber metric.All this can easily be seen from the compatibility requirements (4.1),(4.2),(4.3),and (4.4)applied to our situation.Clearly,all these lifting problems are very natural questions in differential geometry and have been discussed by various authors,see in particular [18,21,25,28],whence one can rely on the tech-niques developed there.Even though our approach does not give essential new techniques to attack the (in general quite difficult)lifting problem,it shines some new light on it and unreveals some additional structure of the problem,namely the groupoid structures together with the canonical groupoid morphisms (4.5).Moreover,this point of view embeds the lifting problem in some larger and completely algebraic context since neither the ∗-algebras have to be commutative nor has the Hopf ∗-algebra to be cocommutative.As remarked already,we can even replace and by R and C ,respectively,and incorporate in particular the formal star product algebras from deformation quantization as well.5The case of a Lie algebraIn this last section we consider the case of H =U (g )more closely and develop some general results from [16]slightly further.Assume that B E A is a ∗-Morita equivalence bimodule which allows for a lift of the actions ofH on A and B .Then it was shown in [16,Thm 4.14]in full generality that the possible lifts are parametrized by the following group U (H,A ):We consider linear maps Hom (H,A )with the usual convolution product given by (a ∗b )(g )=a (g (1))b (g (2)).This makes Hom (H,A )an associative algebra with unit e (g )=ǫ(g )A ,see e.g.[17,Sect.III.3].Then we consider the following conditions for a ∈Hom (H,A )a (H )=A ,(5.1)a (gh )=a (g (1))(g (2)⊲a (h ))for all g,h ∈H,(5.2)(g(1)⊲b)a(g(2))=a(g(1))(g(2)⊲b)for all b∈A,g∈H,(5.3))a S(g∗(2)) ∗=ǫ(g)A for all g∈H.(5.4)a(g(1)Then U(H,A)is defined to be the subset of those a∈Hom(H,A)which satisfy(5.1)–(5.4)and it turns out that U(H,A)is a group with respect to the convolution product[16,App.A].Moreover, for unitary central elements c∈U(Z(A))one definesˆc∈U(H,A)byˆc(g)=c(g⊲c−1).Then one obtains the exact sequence1−→U(Z(A))H−→U(Z(A)) −→U(H,A)(5.5) U(Z(A))⊆U(H,A)is a central and hence normal subgroup.Thus we can define and the imageU(Z(A)).the group U0(H,A)=U(H,A)The parametrization of all possible lifts is obtained by a free and transitive group action⊲→⊲b of U(H,B)on the set of lifts given by)·(g(2)⊲x),(5.6)g⊲b x=b(g(1)where b∈U(H,B),g∈H and x∈E.In fact,for H-covariantly∗-Morita equivalent algebras A and B we have U(H,A)∼=U(H,B).Moreover,⊲b and⊲give isomorphic actions iffb=ˆc for some c∈U(Z(B))whence the isomorphism classes of lifts are parametrized by the group U0(H,B)∼=U0(H,A)which acts freely and transitively via(5.6)on the isomorphism classes of lifts.While the above characterization works in full generality we want to specialize now to Lie algebra actions where H=U(g).First,it follows from[16,Prop.A.7]that U(U(g),A)= U(U(g),Z(A))and hence U0(U(g),A)=U0(U(g),Z(A))since U(g)is cocommutative.Thus the values of a∈U(U(g),A)are automatically central,essentially by(5.3).Moreover,the groups U(U(g),A)and U0(U(g),A)are abelian.Since the center Z(A)is invariant under the g-action (by derivations!)we can restrict a∈U(U(g),A)to g⊆U(g)and obtain a Chevalley-Eilenberg cochainα=a g∈C1CE(g,Z(A)).Evaluating the conditions(5.2),(5.3)and(5.4)on elements ξ,η∈g wefind by a simple computation the following lemma:Lemma5.1The restriction gives an injective group homomorphismU(U(g),A)∋a→α=a g∈Z1CE(g,Z(A)antiHermitian)(5.7) into the Chevalley-Eilenberg one-cocycles with values in the anti Hermitian central elements of A. The injectivity easily follows from successively applying(5.2).Conversely,givenα∈Z1CE(g,Z(A)antiHermitian)we can construct an element a∈U(U(g),A) with a g=α:Let T k(g)denote the k-th complexified tensor power of g and define a(k):T k(g)−→A inductively bya(0)=A and a(k)(ξ⊗Y)=α(ξ)a(k−1)(Y)+ξ⊲a(k−1)(Y)for k≥1,(5.8) where Y∈T k−1(g).Then a lenghty but straightforward computation usingδCEα=0shows that a= ∞k=0a(k)passes to the universal enveloping algebra U(g),viewed as a quotient of T•(g)in the usual way,and fulfills(5.1)to(5.4).Thus we have:Theorem5.2The map(5.7)is an isomorphism of abelian groups.Note that this is in some sense surprising as the condition for αto be a cocycle is linear while the condition (5.2)for a is highly non-linear .It only becomes linear when evaluated on ξ,η∈g ⊆U (g )thanks to the fact that these elements are primitive,i.e.satisfy ∆(ξ)=ξ⊗+⊗ξ.Thus a simplification like in Theorem 5.2cannot be expected for more non-trivial Hopf ∗-algebras.Moreover,under the identification (5.7)the elements ˆc give just the cocycles ˆc (ξ)=c (ξ⊲c −1)asusual.Note that in general U (Z (A ))⊆Z 1CE (g ,Z (A )antiHermitian )are not CE-coboundaries.Thus,if we want to relate U 0(U (g ),A )to Lie algebra cohomology we have to assume an additional structure for A :Definition 5.3Let A be a unital ∗-algebra.Then an exponential function exp is a map exp :Z (A )−→Z (A )such that1.exp(a +b )=exp(a )exp(b ),2.exp(0)=A ,3.D exp(a )=exp(a )Da ,4.exp(a ∗)=exp(a )∗,for all a,b ∈Z (A )and D ∈Der (A ).Note that D ∈Der (A )induces an outer derivation D Z (A )of the center.We shall now assume that A has an exponential function where our motivating example is of course A =C ∞(M )with the usual exponential.The first trivial observation is that for a ∈Z (A )we haveexp(a )(ξ)=−(δCE a )(ξ),(5.9)and for a =−a ∗∈Z (A )antiHermitian we clearly have exp(a )∈U (Z (A )).Thus in this case U (Z (A ))contains all anti Hermitian CE-coboundaries in Z 1CE (g ,Z (A )antiHermitian ).Note however,that ingeneral, U (Z (A ))is strictly larger.To measure this we consider those elements in U (Z (A ))which are not in the image of exp:we define the abelian groupH 1dR (Z (A ),2πi )=U (Z (A ))H 1dR (Z (A ),2πi ).(5.12)In particular,this applies to A =C ∞(M )whence we obtain the full classification of the in-equivalent lifts of the Lie algebra action to line bundles.Note that in general,U 0(U (g ),A )does not depend on the line bundle itself but is universal for all line bundles.。