VLSI algorithms for finding a fundamental set of cycles and a fundamental set of cutsets of
高三现代科技前沿探索英语阅读理解20题
高三现代科技前沿探索英语阅读理解20题1<背景文章>Artificial intelligence (AI) is rapidly transforming the field of healthcare. In recent years, AI has made significant progress in various aspects of medical care, bringing new opportunities and challenges.One of the major applications of AI in healthcare is in disease diagnosis. AI-powered systems can analyze large amounts of medical data, such as medical images and patient records, to detect diseases at an early stage. For example, deep learning algorithms can accurately identify tumors in medical images, helping doctors make more accurate diagnoses.Another area where AI is making a big impact is in drug discovery. By analyzing vast amounts of biological data, AI can help researchers identify potential drug targets and design new drugs more efficiently. This can significantly shorten the time and cost of drug development.AI also has the potential to improve patient care by providing personalized treatment plans. Based on a patient's genetic information, medical history, and other factors, AI can recommend the most appropriate treatment options.However, the application of AI in healthcare also faces some challenges. One of the main concerns is data privacy and security. Medicaldata is highly sensitive, and ensuring its protection is crucial. Another challenge is the lack of transparency in AI algorithms. Doctors and patients need to understand how AI makes decisions in order to trust its recommendations.In conclusion, while AI holds great promise for improving healthcare, it also poses significant challenges that need to be addressed.1. What is one of the major applications of AI in healthcare?A. Disease prevention.B. Disease diagnosis.C. Health maintenance.D. Medical education.答案：B。
Algorithms for manifold learning
Lawrence Cayton lcayton@ June 15, 2005
Abstract
Dimensionality reduction has other, related uses in addition to simplifying data so that it can be effiManifold learning is a popular recent approach to ciently processed. Perhaps the most obvious is vinonlinear dimensionality reduction. Algorithms for sualization; if data lies in a 100-dimensional space, this task are based on the idea that the dimensional- one cannot get an intuitive feel for what the data ity of many data sets is only artificially high; though looks like. However, if a meaningful two- or threeeach data point consists of perhaps thousands of fea- dimensional representation of the data can be found, tures, it may be described as a function of only a then it is possible to “eyeball” it. Though this may few underlying parameters. That is, the data points seem like a trivial point, many statistical and machine are actually samples from a low-dimensional manifold learning algorithms have very poor optimality guarthat is embedded in a high-dimensional space. Man- antees, so the ability to actually see the data and the ifold learning algorithms attempt to uncover these output of an algorithm is of great practical interest. parameters in order to find a low-dimensional repreBeyond visualization, a dimensionality reduction sentation of the data. In this paper, we discuss the procedure may help reveal what the underlying forces motivation, background, and algorithms proposed for governing a data set are. For example, suppose we are manifold learning. Isomap, Locally Linear Embedto classify an email as spam or not spam. A typical ding, Laplacian Eigenmaps, Semidefinite Embedding, approach to this problem would be to represent an and a host of variants of these algorithms are examemail as a vector of counts of the words appearing in ined. the email. The dimensionality of this data can easily be in the hundreds, yet an effective dimensionality reduction technique may reveal that there are only a 1 Introduction few exceptionally telling features, such as the word Many recent applications of machine learning – in “Viagra.” data mining, computer vision, and elsewhere – require deriving a classifier or function estimate from an extremely large data set. Modern data sets often consist of a large number of examples, each of which is made up of many features. Though access to an abundance of examples is purely beneficial to an algorithm attempting to generalize from the data, managing a large number of features – some of which may be irrelevant or even misleading – is typically a burden to the algorithm. Overwhelmingly complex feature sets will slow the algorithm down and make finding global optima difficult. To lessen this burden on standard machine learning algorithms (e.g. classifiers, function estimators), a number of techniques have been developed to vastly reduce the quantity of features in a data set —i.e. to reduce the dimensionality of data. 1 There are many approaches to dimensionality reduction based on a variety of assumptions and used in a variety of contexts. We will focus on an approach initiated recently based on the observation that highdimensional data is often much simpler than the dimensionality would indicate. In particular, a given high-dimensional data set may contain many features that are all measurements of the same underlying cause, so are closely related. This type of phenomenon is common, for example, when taking video footage of a single object from multiple angles simultaneously. The features of such a data set contain much overlapping information; it would be helpful to somehow get a simplified, non-overlapping representation of the data whose features are identifiable with the underlying parameters that govern the data. This intuition is formalized using the notion of a manifold:
《小型微型计算机系统》征订启事
4期谢旭明等:搜索空间自适应量子搜索算法735Computing,1997,26(5):1484-1509.[3]Grover L K.A fast quantum mechanical algorithm for databasesearch[C]//Proceedings of the28th Annual ACM Symposium on the Theory of Computing,New York,1996：212-219.[4]Sun Guo-dong,Su Sheng-hui,Xu Mao-zhi.Quantum mechanicalalgorithms for solving root finding problem[J]-Journal of Beijing University of Technology,2015,41(3)：366-371.[5]Zhu Wan-ning,Liu er identifying algorithm based onquantum computing[J].Acta Electronica Sinica,2018,46(1)：24-30.[6]Indranil C,Shahzor K,Vanshdeep S.Dynamic grover search:applications in recommendation systems and optimization problemsf J].Quantum Information Processing,2017,16(6):1570-1573.[7]Yang Jie,Yuan Jia-bin,Sun Jing.Security research of BLAKE algorithm based on Grover quantum search algorithm and quantum counting[J].Journal of Chinese Computer Systems,2013,34(1)：159-162.[8]Ruan Yue,Chen Han-wu,Liu Zhi-hao.Quantum principal component analysis algorithm[J].Chinese Journal of Computers,2014, 37(3)：666-676.[9]Yu Chao-hua,Gao Fei,Wang Qing-le,et al.Quantum algorithm forassociation rules mining[J].Physical Review A,2016,94(4): 042311.[10]He Zhi-min,Li Lv-zhou,Huang Zhi-ming,et al.Quantum-enhanced feature selection with forward selection and backward elimi-nation[J].Quantum Information Processing,doi:10.1007/sl1128-018-1924-8.[11]Zhou Xiao-yan,An Xing-xing,Liu Wen寸ie,et al.Quantum k-means algorithm based on the minimum distance[J].Journal of Chinese Computer Systems,2017,38(5)：1059-1062.[12]Li Xin,Li Pan-chi.A fixed-phase quantum search algorithm withmore flexible behavior[J].Journal of Quantum Information Science,2012,2(2)：28-34.[13]Zhong Pu-cha,Bao Wan-su.Research on quantum searching algorithms based on phase shifts[J].Chinese Physics Letters,2008,25(8)：2774-2777.[14]Younes A.Towards more reliable fixed phase quantum search algo-rithmf J].Applied Mathematics and Information Sciences,2013,7(1):93-98.附中文参考文献：[4]孙国栋，苏胜辉,徐茂智.求根问题的量子计算算法[J].北京工业大学学报,2015,41(3):366-371.[5]朱皖宁，刘志昊.基于量子计算的用户识别算法[J].电子学报，2018,46(1)：24-30.[7]杨婕,袁家斌，孙静.基于Grover量子搜索算法和量子计数的BLAKE算法安全性分析[J].小型微型计算机系统,2013,34(1):159-162.[8]阮越，陈汉武,刘志昊，等.量子主成分分析算法[J].计算机学报,2014,37(3):666-676.[11]周晓彦，安星星,刘文杰，等.一种基于最小距离的量子k-means算法[J].小型微型计算机系统,2017,38(5):1059-1062.《小型微型计算机系统》征订启事《小型微型计算机系统》创刊于1980年，由中国科学院主管，中国科学院沈阳计算技术研究所主办，中国计算机学会会刊（月刊），国内外公开发行.《小型微型计算机系统》内容涵盖计算机学科各领域，包括:计算机科学理论、体系结构、数据库理论、计算机网络与信息安全、人工智能与算法、服务计算、计算机图形与图像等.收录情况冲文核心期刊冲国学术期刊文摘（中英文版）；中国科学引文数据库（CSCD）来源期刊;英国《科学文摘》（INSPEC）;美国《剑桥科学文摘（自然科学）》CSA（NS）；Cambridge Scientific Abstracts（Natural Science）等.《小型微型计算机系统》（月刊），国内外公开发行，大16开，224页，每期定价40元，全年定价480元，全国各地邮局均可订阅.国内邮发代号:8-108国外发行代号:M349国内统一连续出版物号:CN21-1106/TP国际标准连续出版物号：ISSN1000-1220编辑部地址:沈阳市浑南区南屏东路16号《小型微型计算机系统》编辑部邮政编码:110168电话：************E-mail:xwjxt@网±lt:http：//。
Insight Problem Solving A Critical Examination of the Possibility
The Journal of Problem Solving • volume 5, no. 1 (Fall 2012)56Insight Problem Solving: A Critical Examination of the Possibilityof Formal TheoryWilliam H. Batchelder 1 and Gregory E. Alexander 1AbstractThis paper provides a critical examination of the current state and future possibility of formal cognitive theory for insight problem solving and its associated “aha!” experience. Insight problems are contrasted with move problems, which have been formally defined and studied extensively by cognitive psychologists since the pioneering work of Alan Newell and Herbert Simon. To facilitate our discussion, a number of classical brainteasers are presented along with their solutions and some conclusions derived from observing the behavior of many students trying to solve them. Some of these problems are interesting in their own right, and many of them have not been discussed before in the psychologi-cal literature. The main purpose of presenting the brainteasers is to assist in discussing the status of formal cognitive theory for insight problem solving, which is argued to be considerably weaker than that found in other areas of higher cognition such as human memory, decision-making, categorization, and perception. We discuss theoretical barri-ers that have plagued the development of successful formal theory for insight problem solving. A few suggestions are made that might serve to advance the field.Keywords Insight problems, move problems, modularity, problem representation1 Department of Cognitive Sciences, University of California Irvine/10.7771/1932-6246.1143Insight Problem Solving: The Possibility of Formal Theory 57• volume 5, no. 1 (Fall 2012)1. IntroductionThis paper discusses the current state and a possible future of formal cognitive theory for insight problem solving and its associated “aha!” experience. Insight problems are con-trasted with so-called move problems defined and studied extensively by Alan Newell and Herbert Simon (1972). These authors provided a formal, computational theory for such problems called the General Problem Solver (GPS), and this theory was one of the first formal information processing theories to be developed in cognitive psychology. A move problem is posed to solvers in terms of a clearly defined representation consisting of a starting state, a description of the goal state(s), and operators that allow transitions from one problem state to another, as in Newell and Simon (1972) and Mayer (1992). A solu-tion to a move problem involves applying operators successively to generate a sequence of transitions (moves) from the starting state through intermediate problem states and finally to a goal state. Move problems will be discussed more extensively in Section 4.6.In solving move problems, insight may be required for selecting productive moves at various states in the problem space; however, for our purposes we are interested in the sorts of problems that are described often as insight problems. Unlike Newell and Simon’s formal definition of move problems, there has not been a generally agreed upon defini-tion of an insight problem (Ash, Jee, and Wiley, 2012; Chronicle, MacGregor, and Ormerod, 2004; Chu and MacGregor, 2011). It is our view that it is not productive to attempt a pre-cise logical definition of an insight problem, and instead we offer a set of shared defining characteristics in the spirit of Wittgenstein’s (1958) definition of ‘game’ in terms of family resemblances. Problems that we will treat as insight problems share many of the follow-ing defining characteristics: (1) They are posed in such a way as to admit several possible problem representations, each with an associated solution search space. (2) Likely initial representations are inadequate in that they fail to allow the possibility of discovering a problem solution. (3) In order to overcome such a failure, it is necessary to find an alternative productive representation of the problem. (4) Finding a productive problem representation may be facilitated by a period of non-solving activity called incubation, and also it may be potentiated by well-chosen hints. (5) Once obtained, a productive representation leads quite directly and quickly to a solution. (6) The solution involves the use of knowledge that is well known to the solver. (7) Once the solution is obtained, it is accompanied by a so-called “aha!” experience. (8) When a solution is revealed to a non-solver, it is grasped quickly, often with a feeling of surprise at its simplicity, akin to an “aha!” experience.It is our position that very little is known empirically or theoretically about the cogni-tive processes involved in solving insight problems. Furthermore, this lack of knowledge stands in stark contrast with other areas of cognition such as human memory, decision-making, categorization, and perception. These areas of cognition have a large number of replicable empirical facts, and many formal theories and computational models exist that attempt to explain these facts in terms of underlying cognitive processes. The main goal58W. H. Batchelder and G. E. Alexander of this paper is to explain the reasons why it has been so difficult to achieve a scientific understanding of the cognitive processes involved in insight problem solving.There have been many scientific books and papers on insight problem solving, start-ing with the seminal work of the Gestalt psychologists Köhler (1925), Duncker (1945), and Wertheimer (1954), as well as the English social psychologist, Wallas (1926). Since the contributions of the early Gestalt psychologists, there have been many journal articles, a few scientific books, such as those by Sternberg and Davidson (1996) and Chu (2009), and a large number of books on the subject by laypersons. Most recently, two excellent critical reviews of insight problem solving have appeared: Ash, Cushen, and Wiley (2009) and Chu and MacGregor (2011).The approach in this paper is to discuss, at a general level, the nature of several fun-damental barriers to the scientific study of insight problem solving. Rather than criticizing particular experimental studies or specific theories in detail, we try to step back and take a look at the area itself. In this effort, we attempt to identify principled reasons why the area of insight problem solving is so resistant to scientific progress. To assist in this approach we discuss and informally analyze eighteen classical brainteasers in the main sections of the paper. These problems are among many that have been posed to hundreds of upper divisional undergraduate students in a course titled “Human Problem Solving” taught for many years by the senior author. Only the first two of these problems can be regarded strictly as move problems in the sense of Newell and Simon, and most of the rest share many of the characteristics of insight problems as described earlier.The paper is divided into five main sections. After the Introduction, Section 2 describes the nature of the problem solving class. Section 3 poses the eighteen brainteasers that will be discussed in later sections of the paper. The reader is invited to try to solve these problems before checking out the solutions in the Appendix. Section 4 lays out six major barriers to developing a deep scientific theory of insight problem solving that we believe are endemic to the field. We argue that these barriers are not present in other, more theo-retically advanced areas of higher cognition such as human memory, decision-making, categorization, and perception. These barriers include the lack of many experimental paradigms (4.1), the lack of a large, well-classified set of stimulus material (4.2), and the lack of many informative behavioral measures (4.3). In addition, it is argued that insight problem solving is difficult to study because it is non-modular, both in the sense of Fodor (1983) but more importantly in several weaker senses of modularity that admit other areas of higher cognition (4.4), the lack of theoretical generalizations about insight problem solv-ing from experiments with particular insight problems (4.5), and the lack of computational theories of human insight (4.6). Finally, in Section 5, we suggest several avenues that may help overcome some of the barriers described in Section 4. These include suggestions for useful classes of insight problems (5.1), suggestions for experimental work with expert problem solvers (5.2), and some possibilities for a computational theory of insight.The Journal of Problem Solving •Insight Problem Solving: The Possibility of Formal Theory 592. Batchelder’s Human Problem Solving ClassThe senior author, William Batchelder, has taught an Upper Divisional Undergraduate course called ‘Human Problem Solving” for over twenty-five years to classes ranging in size from 75 to 100 students. By way of background, his active research is in other areas of the cognitive sciences; however, he maintains a long-term hobby of studying classical brainteasers. In the area of complex games, he achieved the title of Senior Master from the United States Chess Federation, he was an active duplicate bridge player throughout undergraduate and graduate school, and he also achieved a reasonable level of skill in the game of Go.The content of the problem-solving course is split into two main topics. The first topic involves encouraging students to try their hand at solving a number of famous brainteasers drawn from the sizeable folklore of insight problems, especially the work of Martin Gardner (1978, 1982), Sam Loyd (1914), and Raymond Smullyan (1978). In addition, games like chess, bridge, and Go are discussed. The second topic involves presenting the psychological theory of thinking and problem solving, and in most cases the material is organized around developments in topics that are covered in the first eight chapters of Mayer (1992). These topics include work of the Gestalt psychologists on problem solving, discussion of experiments and theories concerning induction and deduction, present-ing the work on move problems, including the General Problem Solver (Newell & Simon, 1972), showing how response time studies can reveal mental architectures, and describing theories of memory representation and question answering.Despite efforts, the structure of the course does not reflect a close overlap between its two main topics. The principal reason for this is that in our view the level of theoreti-cal and empirical work on insight problem solving is at a substantially lower level than is the work in almost any other area of cognition dealing with higher processes. The main goal of this paper is to explain our reasons for this pessimistic view. To assist in this goal, it is helpful to get some classical brainteasers on the table. While most of these problems have not been used in experimental studies, the senior author has experienced the solu-tion efforts and post solution discussions of over 2,000 students who have grappled with these problems in class.3. Some Classic BrainteasersIn this section we present eighteen classical brainteasers from the folklore of problem solving that will be discussed in the remainder of the paper. These problems have de-lighted brainteaser connoisseurs for years, and most are capable of giving the solver a large dose of the “aha!” experience. There are numerous collections of these problems in books, and many collections of them are accessible through the Internet. We have selected these problems because they, and others like them, pose a real challenge to any effort to • volume 5, no. 1 (Fall 2012)60W. H. Batchelder and G. E. Alexander develop a deep and general formal theory of human or machine insight problem solving. With the exception of Problems 3.1 and 3.2, and arguably 3.6, the problems are different in important respects from so-called move problems of Newell and Simon (1972) described earlier and in Section 4.6.Most of the problems posed in this section share many of the defining characteristics of insight problems described in Section 1. In particular, they do not involve multiple steps, they require at most a very minimal amount of technical knowledge, and most of them can be solved by one or two fairly simple insights, albeit insights that are rarely achieved in real time by problem solvers. What makes these problems interesting is that they are posed in such a way as to induce solvers to represent the problem information in an unproductive way. Then the main barrier to finding a solution to one of these problems is to overcome a poor initial problem representation. This may involve such things as a re-representation of the problem, the dropping of an implicit constraint on the solution space, or seeing a parallel to some other similar problem. If the solver finds a productive way of viewing the problem, the solution generally follows rapidly and comes with burst of insight, namely the “aha!” experience. In addition, when non-solvers are given the solu-tion they too may experience a burst of insight.What follows next are statements of the eighteen brainteasers. The solutions are presented in the Appendix, and we recommend that after whatever problem solving activity a reader wishes to engage in, that the Appendix is studied before reading the remaining two sections of the paper. As we discuss each problem in the paper, we provide authorship information where authorship is known. In addition, we rephrased some of the problems from their original sources.Problem 3.1. Imagine you have an 8-inch by 8-inch array of 1-inch by 1-inch little squares. You also have a large box of 2-inch by 1-inch rectangular shaped dominoes. Of course it is easy to tile the 64 little squares with dominoes in the sense that every square is covered exactly once by a domino and no domino is hanging off the array. Now sup-pose the upper right and lower left corner squares are cut off the array. Is it possible to tile the new configuration of 62 little squares with dominoes allowing no overlaps and no overhangs?Problem 3.2. A 3-inch by 3-inch by 3-inch cheese cube is made of 27 little 1-inch cheese cubes of different flavors so that it is configured like a Rubik’s cube. A cheese-eating worm devours one of the top corner cubes. After eating any little cube, the worm can go on to eat any adjacent little cube (one that shares a wall). The middlemost little cube is by far the tastiest, so our worm wants to eat through all the little cubes finishing last with the middlemost cube. Is it possible for the worm to accomplish this goal? Could he start with eating any other little cube and finish last with the middlemost cube as the 27th?The Journal of Problem Solving •Insight Problem Solving: The Possibility of Formal Theory 61 Figure 1. The cheese eating worm problem.Problem 3.3. You have ten volumes of an encyclopedia numbered 1, . . . ,10 and shelved in a bookcase in sequence in the ordinary way. Each volume has 100 pages, and to simplify suppose the front cover of each volume is page 1 and numbering is consecutive through page 100, which is the back cover. You go to sleep and in the middle of the night a bookworm crawls onto the bookcase. It eats through the first page of the first volume and eats continuously onwards, stopping after eating the last page of the tenth volume. How many pieces of paper did the bookworm eat through?Figure 2.Bookcase setup for the Bookworm Problem.Problem 3.4. Suppose the earth is a perfect sphere, and an angel fits a tight gold belt around the equator so there is no room to slip anything under the belt. The angel has second thoughts and adds an inch to the belt, and fits it evenly around the equator. Could you slip a dime under the belt?• volume 5, no. 1 (Fall 2012)62W. H. Batchelder and G. E. Alexander Problem 3.5. Consider the cube in Figure 1 and suppose the top and bottom surfaces are painted red and the other four sides are painted blue. How many little cubes have at least one red and at least one blue side?Problem 3.6. Look at the nine dots in Figure 3. Your job is to take a pencil and con-nect them using only three straight lines. Retracing a line is not allowed and removing your pencil from the paper as you draw is not allowed. Note the usual nine-dot problem requires you to do it with four lines; you may want to try that stipulation as well. Figure 3.The setup for the Nine-Dot Problem.Problem 3.7. You are standing outside a light-tight, well-insulated closet with one door, which is closed. The closet contains three light sockets each containing a working light bulb. Outside the closet, there are three on/off light switches, each of which controls a different one of the sockets in the closet. All switches are off. Your task is to identify which switch operates which light bulb. You can turn the switches off and on and leave them in any position, but once you open the closet door you cannot change the setting of any switch. Your task is to figure out which switch controls which light bulb while you are only allowed to open the door once.Figure 4.The setup of the Light Bulb Problem.The Journal of Problem Solving •Insight Problem Solving: The Possibility of Formal Theory 63• volume 5, no . 1 (Fall 2012)Problem 3.8. We know that any finite string of symbols can be extended in infinitely many ways depending on the inductive (recursive) rule; however, many of these ways are not ‘reasonable’ from a human perspective. With this in mind, find a reasonable rule to continue the following series:Problem 3.9. You have two quart-size beakers labeled A and B. Beaker A has a pint of coffee in it and beaker B has a pint of cream in it. First you take a tablespoon of coffee from A and pour it in B. After mixing the contents of B thoroughly you take a tablespoon of the mixture in B and pour it back into A, again mixing thoroughly. After the two transfers, which beaker, if either, has a less diluted (more pure) content of its original substance - coffee in A or cream in B? (Forget any issues of chemistry such as miscibility).Figure 5. The setup of the Coffee and Cream Problem.Problem 3.10. There are two large jars, A and B. Jar A is filled with a large number of blue beads, and Jar B is filled with the same number of red beads. Five beads from Jar A are scooped out and transferred to Jar B. Someone then puts a hand in Jar B and randomly grabs five beads from it and places them in Jar A. Under what conditions after the second transfer would there be the same number of red beads in Jar A as there are blue beads in Jar B.Problem 3.11. Two trains A and B leave their train stations at exactly the same time, and, unaware of each other, head toward each other on a straight 100-mile track between the two stations. Each is going exactly 50 mph, and they are destined to crash. At the time the trains leave their stations, a SUPERFLY takes off from the engine of train A and flies directly toward train B at 100 mph. When he reaches train B, he turns around instantly, A BCD EF G HI JKLM.............64W. H. Batchelder and G. E. Alexander continuing at 100 mph toward train A. The SUPERFLY continues in this way until the trains crash head-on, and on the very last moment he slips out to live another day. How many miles does the SUPERFLY travel on his zigzag route by the time the trains collide?Problem 3.12. George lives at the foot of a mountain, and there is a single narrow trail from his house to a campsite on the top of the mountain. At exactly 6 a.m. on Satur-day he starts up the trail, and without stopping or backtracking arrives at the top before6 p.m. He pitches his tent, stays the night, and the next morning, on Sunday, at exactly 6a.m., he starts down the trail, hiking continuously without backtracking, and reaches his house before 6 p.m. Must there be a time of day on Sunday where he was exactly at the same place on the trail as he was at that time on Saturday? Could there be more than one such place?Problem 3.13. You are driving up and down a mountain that is 20 miles up and 20 miles down. You average 30 mph going up; how fast would you have to go coming down the mountain to average 60 mph for the entire trip?Problem 3.14. During a recent census, a man told the census taker that he had three children. The census taker said that he needed to know their ages, and the man replied that the product of their ages was 36. The census taker, slightly miffed, said he needed to know each of their ages. The man said, “Well the sum of their ages is the same as my house number.” The census taker looked at the house number and complained, “I still can’t tell their ages.” The man said, “Oh, that’s right, the oldest one taught the younger ones to play chess.” The census taker promptly wrote down the ages of the three children. How did he know, and what were the ages?Problem 3.15. A closet has two red hats and three white hats. Three participants and a Gamesmaster know that these are the only hats in play. Man A has two good eyes, man B only one good eye, and man C is blind. The three men sit on chairs facing each other, and the Gamesmaster places a hat on each man’s head, in such a way that no man can see the color of his own hat. The Gamesmaster offers a deal, namely if any man correctly states the color of his hat, he will get $50,000; however, if he is in error, then he has to serve the rest of his life as an indentured servant to the Gamesmaster. Man A looks around and says, “I am not going to guess.” Then Man B looks around and says, “I am not going to guess.” Finally Man C says, “ From what my friends with eyes have said, I can clearly see that my hat is _____”. He wins the $50,000, and your task is to fill in the blank and explain how the blind man knew the color of his hat.Problem 3.16. A king dies and leaves an estate, including 17 horses, to his three daughters. According to his will, everything is to be divided among his daughters as fol-lows: 1/2 to the oldest daughter, 1/3 to the middle daughter, and 1/9 to the youngest daughter. The three heirs are puzzled as to how to divide the horses among themselves, when a probate lawyer rides up on his horse and offers to assist. He adds his horse to the kings’ horses, so there will be 18 horses. Then he proceeds to divide the horses amongThe Journal of Problem Solving •Insight Problem Solving: The Possibility of Formal Theory 65 the daughters. The oldest gets ½ of the horses, which is 9; the middle daughter gets 6 horses which is 1/3rd of the horses, and the youngest gets 2 horses, 1/9th of the lot. That’s 17 horses, so the lawyer gets on his own horse and rides off with a nice commission. How was it possible for the lawyer to solve the heirs’ problem and still retain his own horse?Problem 3.17. A logical wizard offers you the opportunity to make one statement: if it is false, he will give you exactly ten dollars, and if it is true, he will give you an amount of money other than ten dollars. Give an example of a statement that would be sure to make you rich.Problem 3.18. Discover an interesting sense of the claim that it is in principle impos-sible to draw a perfect map of England while standing in a London flat; however, it is not in principle impossible to do so while living in a New York City Pad.4. Barriers to a Theory of Insight Problem SolvingAs mentioned earlier, our view is that there are a number of theoretical barriers that make it difficult to develop a satisfactory formal theory of the cognitive processes in play when humans solve classical brainteasers of the sort posed in Section 3. Further these barriers seem almost unique to insight problem solving in comparison with the more fully developed higher process areas of the cognitive sciences such as human memory, decision-making, categorization, and perception. Indeed it seems uncontroversial to us that neither human nor machine insight problem solving is well understood, and com-pared to other higher process areas in psychology, it is the least developed area both empirically and theoretically.There are two recent comprehensive critical reviews concerning insight problem solving by Ash, Cushen, and Wiley (2009) and Chu and MacGregor (2011). These articles describe the current state of empirical and theoretical work on insight problem solving, with a focus on experimental studies and theories of problem restructuring. In our view, both reviews are consistent with our belief that there has been very little sustainable progress in achieving a general scientific understanding of insight. Particularly striking is that are no established general, formal theories or models of insight problem solving. By a general formal model of insight problem solving we mean a set of clearly formulated assumptions that lead formally or logically to precise behavioral predictions over a wide range of insight problems. Such a formal model could be posed in terms of a number of formal languages including information processing assumptions, neural networks, computer simulation, stochastic assumptions, or Bayesian assumptions.Since the groundbreaking work by the Gestalt psychologists on insight problem solving, there have been theoretical ideas that have been helpful in explaining the cog-nitive processes at play in solving certain selected insight problems. Among the earlier ideas are Luchins’ concept of einstellung (blind spot) and Duncker’s functional fixedness, • volume 5, no. 1 (Fall 2012)as in Maher (1992). More recently, there have been two developed theoretical ideas: (1) Criterion for Satisfactory Progress theory (Chu, Dewald, & Chronicle, 2007; MacGregor, Ormerod, & Chronicle, 2001), and (2) Representational Change Theory (Knoblich, Ohls-son, Haider, & Rhenius, 1999). We will discuss these theories in more detail in Section 4. While it is arguable that these theoretical ideas have done good work in understanding in detail a few selected insight problems, we argue that it is not at all clear how these ideas can be generalized to constitute a formal theory of insight problem solving at anywhere near the level of generality that has been achieved by formal theories in other areas of higher process cognition.The dearth of formal theories of insight problem solving is in stark contrast with other areas of problem solving discussed in Section 4.6, for example move problems discussed earlier and the more recent work on combinatorial optimization problems such as the two dimensional traveling salesman problem (MacGregor and Chu, 2011). In addition, most other higher process areas of cognition are replete with a variety of formal theories and models. For example, in the area of human memory there are currently a very large number of formal, information processing models, many of which have evolved from earlier mathematical models, as in Norman (1970). In the area of categorization, there are currently several major formal theories along with many variations that stem from earlier theories discussed in Ashby (1992) and Estes (1996). In areas ranging from psycholinguistics to perception, there are a number of formal models based on brain-style computation stemming from Rumelhart, McClelland, and PDP Research Group’s (1987) classic two-volume book on parallel distributed processing. Since Daniel Kahneman’s 2002 Nobel Memorial Prize in the Economic Sciences for work jointly with Amos Tversky developing prospect theory, as in Kahneman and Tversky (1979), psychologically based formal models of human decision-making is a major theoretical area in cognitive psychology today. In our view, there is nothing in the area of insight problem solving that approaches the depth and breadth of formal models seen in the areas mentioned above.In the following subsections, we will discuss some of the barriers that have prevented the development of a satisfactory theory of insight problem solving. Some of the bar-riers will be illustrated with references to the problems in Section 3. Then, in Section 5 we will assuage our pessimism a bit by suggesting how some of these barriers might be removed in future work to facilitate the development of an adequate theory of insight problem solving.4.1 Lack of Many Experimental ParadigmsThere are not many distinct experimental paradigms to study insight problem solving. The standard paradigm is to pick a particular problem, such as one of the ones in Section 3, and present it to several groups of subjects, perhaps in different ways. For example, groups may differ in the way a hint is presented, a diagram is provided, or an instruction。
Text Deblurring Using OCR Word Confidence(IJIGSP-V9-N1-5)
I.J. Image, Graphics and Signal Processing, 2017, 1, 33-40Published Online January 2017 in MECS (/)DOI: 10.5815/ijigsp.2017.01.05Text Deblurring Using OCR Word ConfidenceAvinash VermaResearch Scholar, BBD University Lucknow, IndiaEmail: avinash.verma93@Dr. Deepak Kumar SinghAssociate Professor, Integral University Lucknow, IndiaEmail: deepak.iiita@Abstract—Objective of this paper is to propose a new Deblurring method for motion blurred textual images. This technique is based on estimating the blur kernel or the Point Spread Function of the motion blur using Blind Deconvolution method. Motion blur is either due to the movement of the camera or the object at the time of image capture. The point spread function of the motion blur is governed by two parameters length of the motion and the angle of the motion. In this approach we have estimated point spread function for the motion blur iteratively for different values of the length and angle of motion. For every estimated PSF we perform the Deconvolution operation with the blurred image to get the non- blurred or the latent image. Latent image obtained is then feed to an Optical character recognition so that the text in that image can be recognized. Then we calculate the Average Word Confidence for the recognized text. Thus for every estimated Point Spread Function and the obtained latent image we get the value of Average Word Confidence. The Point Spread Function with the highest Average Word Confidence value is the optimal Point Spread Function which can be used to deblur the given textual image. In this method we do not have any prior information about the PSF and only single image is used as an input to the system. This method has been tested with the naturally blurred image taken manually and through the internet as well as artificially blurred image for the evaluation of the results. The implementation of the proposed algorithm has been done in MATLAB.Index Terms—Deblurring, Point Spread Function, Optical Character Recognition, Motion blur and Blind deconvolution.I.I NTRODUCTIONA lot of text information can be extracted from the images of the text documents. Images of the text document can be taken either with the help of a scanner or with the help of a portable camera or smart phone camera. A lot of research is done on the image acquired by portable camera for efficient optical character recognition. But the image acquired using a camera is affected with problem of blur, skew and variation in the lighting conditions. In this paper we are dealing with the problem of blurred textual image that too affected with a uniform motion blur.Text Deblurring is image restoration problem in which the image of the text document taken form a camera is blurred or degraded due to motion of the camera or the object at the time of image capture then to estimate the Blur kernel and convert the blurred image to a Deblurred image or restored Image using Deconvolution operation. Blur is caused by camera sensor motion which is represented by a blur kernel. Theoretically, the motion blur process is modeled as the convolution of the Image and a blur kernel with additive noise.()()()() (1) Where () is the Observed blurred Image ( ) is the Non-blurred Original image and () is the blur kernel also known as Point Spread Function and () is the additive noise is the convolution operator in equation (1). Therefore, motion Deblurring tries to estimate the blur kernel and then it performs the Deconvolution operation to recovers Original image also known as latent Image from the blurred image. The Deconvolution operation is the inverse of convolution operation used in the Blurring process.A.Model of Image Degradation and RestorationThe degraded image is () is obtained by applying the degradation operation over the input image ( ) along with the additive noise().()[()] ( ) (2) The objective of Deblurring [25] is to recover ( ) form the degraded observed image () using the estimated value of. Here can be linear or non-linear. Mostly it is assumed to be linear and satisfies the linear property of homogeneity and superposition. The degradation operator H is also considered to be space invariant or position invariant that is its response at any point depends on the value at that point but not on the position of the point and is defined mathematically as [()] ( ) (3)For all ( ) and any and. The overall model ofdegradation and restoration operations is shown in Fig. 1. Here Latent image ()in the figure is the restored image after the Deconvolution operation which is the inverse of the Convolution operation which has degraded the Input Image. Deblurring is almost irreversible due to additional noise which gets amplified at the time of Deconvolution operation. So Latent Image () cannot be the exact same as Input Image ( ) it is the restored version of the Input Image.Fig.1. Overall degradation and restoration Model Impulse function ( ) is expressed as,()∫∫()() (4)Substituting (4) in (2) we get the blurred image ( ) as()[∫∫()()]() (5)As () is independent of x and y, using Linearity, the () can be expressed as,()[∫∫()()]() (6)Where ()[()] is called point spread function (PSF) in the optics Since H is spatial invariantSo the expression of H can be rewritten as,[()]() (7) And the blurred image is given as,()[∫∫()()]( ) (8) This expression is called the convolution integral in the continuous variable.B.Discrete Convolution model for Degraded Image Generally Image can be constructed in two ways either discrete or continuous. The continuous image can be converted to a discrete image by sampling, quantization and coding. The discrete model of the degraded image caused by the blur and the additive noise added can be expressed as,()∑∑()()() (9) Where () represents the original image of size and ()represents the PSF of size. In the above equation () is taken as additive noise introduced by the system and is assumed to be zero mean white Gaussian noise.Using spatial invariant property of PSF, the ( ) can be described as,()∑∑()()()(10) ( )()() ( ) (11) Where * denote the two dimensional linear convolution.C.Motion Blur ModelMotion blur in the image is caused due to either the motion of the image capturing device or the object to be captured. Image capturing device can be a scanner or portable camera. Motion Blur is governed by two parameter that is the length of motion () and the angle of motion (). When the text document to be captured translates with a relative velocity V in respect to the camera, the blur length in pixels is VT exposure where, T exposure is the time duration of the exposure. The expression for motion blur is given as,(){||When the angle of blur = 0, it is called horizontal motion blur. Point spread function can be represented indiscrete as,(){|||()| { ()||}||⌈ ⌉D.Noise Model for Gaussian NoiseImage capture and transmission is also affected with the additive noise which is induced to the image. Basically the most common types of noise are impulsive and Gaussian noise, which affect the image at the time of capturing due to the noisy sensors which induce the noise in the image. As the image has to be transmitted through different channel it gets affected by the noise due to channel error. There are many noise models in our study we will be dealing with the Gaussian noise which is the most common in practical applications. Gaussian noise is a random variable and is expressed as,( )( ) (12) It is characterized by its variance. The noisy image ( ) is the addition of the original image () with the noise term. It is given as,()()( ) (13)E.Deblurring using Blind Deconvolution operation The problem of Image restoration after the blur is known as Deblurring. In Deblurring the original image() requires the deconvolution of the PSF () with the observed image ( ). In most of the cases the PSF is known prior to the deblurring this type of deblurring is done using the classical well known techniques such as inverse filtering, wiener filtering , least square filtering, recursive Kalman filtering is available. PSF is unknown in various applications and very little information is available about the original image. To recover the original image () from the observed image ( ) using partial or no information about the blurring process this phenomenon is known as Blind Deconvolution.Blind Deconvolution algorithm can be broadly classified in two types. In first type PSF is identified first and then utilized to deblur the image using any of the classical Deblurring techniques. In second type algorithm we estimate the PSF and restore the image simultaneously.A number of methods exist to remove the blur from the observed image ( ) using a linear filter. The restored image ( ) from a given blurred image is given by()() ( ) (14) Where *denotes the Deconvolution which represents the inverse of the convolution. In the frequency domain, this can be expressed as()() ( ) (15) Where ()denotes the estimated image in spectral domain. ( ) And ()are the blurred image and PSF in frequency domain respectively.Motion Deblurring with single-input image is more complicated than that with two-or-more-input images because multiple blurred images always provide more information in solving the problem. In this paper, we mainly focus on Blind image Deconvolution in which we try to estimate the PSF ( ) and then we perform the Deconvolution operation of this PSF with the blurred Image ( ) to get the Original Image ( ). As deblurring is ill poised problem is difficult to recover the original image due to additive noise. In the process of motion blur, the Deblurred image loses much high-frequency information. The traditional methods always give undesirable Deblurring results because of the effect of the additive noise on the single image based motion Deblurring.II.R ELATED W ORKDeblurring Text image is a problem which is being researched due to its wide application in optical character recognition. We know that the recognition of a blurred text is still a big problem for the most efficient optical character Recognition (OCR) engine. Text Deblurring can increase the efficiency of OCR. Hence various Deblurring techniques have been proposed so far are either based on blur kernel estimation also known as blind Deconvolution method and non-blind Deconvolution method. In blind convolution method no information about the blur kernel is known. In non-blind Deconvolution method we have some knowledge about the blur kernel.Blur can be estimated by the estimation of the blur kernel or the PSF ( ). PSF for the motion blur depends on the pixel length of the blur ( ) and the angle of the blur( ). Based on these two parameters we can estimate the blur kernel and use this kernel for deblurring process. Blur Kernel estimation is iterative process in which we have to find the blur kernel which can help us to restore the original image ( ). But as we know that after deblurring we cannot get the exact Deblurred image as the original image due to the additive noise ( ) which is induced due to the deconvolution process. So we try to get the image that much deblurred so that we can extract the desired information in our case the text information. Various kernel estimation technique have been proposed for the estimation of the motion blur kernel for Deblurring in which Taeg Sang Cho and Sylvain Paris [1] proposed a method to estimate blur caused by the camera shakes using edge analysis and byconstructing Randon Transform of the blur Kernel. Shamik Tiwari [2] in his paper compared the entire blind Deconvolution algorithm to estimate the PSF and then estimated motion blur parameter can be used in a standard non blind Deconvolution algorithm. Lu Fang [4] proposed method by decomposing a blur kernel into three individual descriptors trajectory, intensity and point spread function. So that it can be optimized separately. Nimali RajaKaruna [5] proposed a method for Deblurring for visually impaired people it used a 3-axis accelerometers and gyroscopes of the smart phone camera used for image capture to get the motion vector and the heuristics method is developed to determine the optimal motion vector to Deblur. Jing Wang [6] proposed a blind motion Deblurring approach that works by kernel optimization using edge mask is used. An alternative iterative method is introduced to perform kernel optimization under a multiscale scheme. Total-variation based algorithm is proposed to recover the latent image via non-blind Deconvolution. Long Mai [7] addressed the problems of fussing multiple kernels estimated using different methods into a more accurate one that give better Deblurring result. Jinshan Pan [8] proposed Lo-regularized prior based on intensity and gradient for Deblurring using distinct property of the text image. Deblurring can also be performed using non-blind Deconvolution technique in which we have more than one blurred image of the input. We also have some knowledge about the PSF. So it helps us in the estimation of the blur Kernel which can then be used to get the latent Image. Another solution to Deblurring is through the neural networks in this approach we train a neural network using a back propagation algorithm [13] in which we require both the ideal image as well as the blurred image of the ideal image. We train the neural network with blur image and ideal image pairs to find the relationship between the blur Image to the ideal Image. Convolution Neural Network (CNN) [20] is also one of the solutions for Deblurring using blind Deconvolution method. CNN is based on the concept of deep learning and is powerful machine learning technique [21]. CNN is trained using large collections of diverse images. From diverse image it can learn rich features representations. We can also use a pre-trained CNN. It is a multi layered structure which can help in extracting different features in each layer. In Deblurring the blurred images are used to input and they are mapped into its corresponding ideal image to learn various features relationship between blurred and ideal image in the training phase. Thus after training lots of diverse blurred image into its ideal image. The CNN can then deblur an input image based on the learning from the trained samples.III.P ROPOSED A PPROACHIn our proposed approach we have followed the blind Deconvolution method for the estimation of the blur kernel or the PSF. As we know that Motion blur is caused by motion of the camera at the time of the image acquisition. So the PSF of motion blur is a function of the length ()and angle of blur ( ).So we tried an iterative method to estimate the length ()and angle of blur ( ). For each PSF estimated with a length and the angle iteratively, we check its Optical character Recognition [23] result simultaneously by finding the cumulative sum of the confidence of each word recognized and then calculating the Average Word Confidence (AWC) metric by dividing the cumulative sum of word confidence by number of words.[∑( )]Where n is the total number of words in the text obtained after OCR result. We keep the value of the length ( ) and angle( ) of the blur kernel along with the corresponding deblurred image OCR Average Word Confidence AWC in a two dimensional array. Then we find the value of the length ()and angle of blur ( ) corresponding to the maximum Average Word Confidence( ) result of the OCR. Hence this value of the blur length and angle is the value at which the Deblurring or Deconvolution method gives the optimal text recognition result using Average Word Confidence metrics of OCR. Thus blur kernel or PSF is estimated using the OCR Average Word Confidence metrics iteratively which gives us a criteria on which we can say that this PSF is the optimal for Deconvolution using any filter. Thus Average Word Confidence for the best recognition will be the highest and the length and the angle corresponding to it will be optimized PSF to get the latent or original image with higher text recognition rate than other PSF.A.Estimating Point Stread Function (PSF) for motionblurMotion blur is caused by the motion of the camera at the time of image capture. Point spread function of the motion blur depends on the length ()and angle of blur( ). Estimation of PSF is blind Deconvolution problem. In our approach we have tried to find out the length of blur ( ) for various images and we have estimated the length of the blur to be between 0 to 25 pixels based on our practical requirements. This value can be increased or decreased based on the requirement. We have taken the value of the angle for a blur ()in between 0 to 180 degree counter clockwise. As the value of is taken in the broad range it can easily estimate the angle in the textual input image.This means if length of blur and angle is 0 degree then the blurred Observed image ( ) will a translated image of Original image ( ) by 9 pixels. We have iteratively created the blur kernel or PSF for the different value of length ()and angle of blur ( ).For each estimated PSF we apply Deconvolution operation which is the inverse of convolution operation with the blurred image ( ) to obtain a latent image ( ). From the latent image obtained weperform the OCR operation to find the value of word confidence of each word.B.OCR Evalution of the latent ImageOCR is the image processing technology which helps to recognize the text in the image. OCR operation requires to converts true color or grayscale input images to a binary image which contains only two values that is 0 which represents black pixel or 1 which represent white pixel, before the recognition process. It uses the Otsu's thresholding technique [22] for the conversion. Then segmentation of text and non-text is the next step for the OCR. Obtained text is segmented into line and then individual words. Words are recognized and a text file containing the recognized word is the output of OCR.In OCR evaluation of the latent Image obtained after the Deconvolution operation of the Blurred Input Image and the estimated PSF. We apply the OCR on the Latent Image and the from the OCR result we find the value of Word Confidence of the recognized words that indicates the confidence level with which the word is recognized. Word Confidence is normalized value between 0 and 1. The Word Confidence of Individual word is calculated and then the Average Word Confidence ( ) is calculated which the mathematical average of the all the Word Confidence obtained. Then this value will be used as a metrics for the estimation of the Optimal PSF for the Deblurring Process.C.OCR Word Confidence MetricsWe have used Word Confidence attribute of the OCR result. Word Confidence is determined based on character level confidence. Character Confidence gives the normalized value of how effectively the character is recognized. Better the Character Confidence of recognition better is the Word Confidence of Recognition. In addition the Word Confidence is affected by the dictionary based verification. If a word is found in the dictionary, it increases the Word Confidence value of that word. The longer the word, the higher will be the confidence value if it is found in the dictionary. For example if a long word of around 15 characters is found in dictionary it is pretty sure that the word is correct and will yield a higher word confidence, while on wrongly detected character a match against the dictionary by mistake is unlikely to occur. Short words like 'add' or 'odd' will both be found in dictionary. Therefore for smaller words there is a probability that we can get the dictionary match. Hence to overcome this problem words with 2 or less characters are not checked against the dictionary. The word confidence is normalized to an interval of 0.00 to 1.00 where 1.00 is the best and 0.00 is the worst word confidence. This OCR word Confidence metrics is used for the evaluation of the Deblurring result for the estimation of the Blur Kernel or the PSF. Algorithm of the proposed approachStep 1: Input a blurred image ( ).Step 2: Repeat step 3 to 8 for length ( ) =1 to 25 pixels Step 3: Repeat step 4 to 8 for angle ( )=0 to 180 degreeStep 4: Create a blur kernel of motion blur using length and angle as ( ).Step 5: Apply Deconvolution operation between ( ) and ( ) to get the latent image ( ).Step 6: Apply OCR on latent image ( ) obtained in step 5.Step 7: Find the sum of word confidence of every word in the latent image ( ) then find Average word confidence by dividing sum of word confidence by number of words n.[∑( )] Step 8: Store the value of length( ), angle( ) and obtained in a 2D-array R or a table.[End of angle for loop][End of length for loop]Step 9: Find the value of length and angle corresponding to largest value of Average word confidence .Step 10: Return length and angle obtained in step 9.Step 11: END.Fig.2 Blurred Input Image ( )Fig.3. Latent Image () with = 0.508564115 for PSF with =17and = 10.Fig.4. Latent Image () with = 0.756988287 for PSF with =20and = 14.Fig.5. Latent Image () with = 0.621142268 for PSF with =25and = 13.Table 1. Results of the Average Word Confidence MetricsIV.R ESULT A NALYSISIn the proposed work we have estimated the PSF for the blurred image ( ) using blind deconvolutionmethod iteratively by calculating the Average Word Confidence metrics that help us to estimate theoptimal PSF. For every Estimated PSF value we applythe Deconvolution operation between the Blurred Image() and the PSF to get the latent image ()then result of OCR Average Word Confidence is calculated. For latent Image highest WordConfidence means that its word recognition rate is higherthan the others. Hence it can be the optimal PSF for recovering the text information using the OCR efficiently. Based on the Proposed Algorithm we have calculated for different values of Blur Length and Blur Angle. In Fig.2 the Blurred Input Image () containing the text is shown this is the Input to our Algorithm. The next Fig.3 shows the Output latent Image ( ) after the Deconvolution operation of () and the estimated PSF with Blur LengthAnd Angle degree. The individual Word Confidences are 0.39378 and 0.62334 respectively. Hence the AWC evaluates to 0.508564115 this value represents the Confidence for the recognition of text in the image. The individual Word Confidence value is shown in the figures with the help of Yellow boxes. Similarly Fig.4 shows the Latent image () obtained for the PSF with Blur Length and Angle degree with AWC = 0.756999287. Fig.5 also shows the Latent image () obtained for the PSF with Blur Length and Angle degree with AWC = 0.621142268.It is quite evident from the figures that the based on the value of AWC we can estimate the value of Blur Length and Angle for which the text recognition efficiency will be the highest. The highest value of Average Word Confidence = 0.756988287 for the length of blur = 20 pixels and angle of blur= 14 degree. This is the value for the PSF or the blur kernel estimated using our method which will get the best OCR output for the input blurred image ( ) using Blind Deconvolution method. The highest value of the Average Word Confidence means that the text document is best recognized with that PSF.We have represented the top 20 values of Average Word Confidence for different values of Blur Length and Blur Angle of blur in the Table I. The Table shows that the Blur Length varies from 19 to 25 pixels and Blur Angle varies in the range 8 to 14 degree. The value of Average Word Confidence () varies in the range 0.756988287 to 0.632594824. These values of are acceptable but the highest value will give the best Text Recognition result so the value Blur Length and Blur Angle corresponding to it gives the optimal PSF to apply Deconvolution operation with the Blurred Input Image to get the Latent Image which can be feed to an Optical Character Recognition Engine. Then the Optical Character Recognition engine will give better text recognition for a Blurred Input image with text, which was one of the biggest problems with the existing system.V.C ONCLUSION AND F UTURE W ORKThis method is applied successful on the Blurred image taken manually and through the internet. We have also tested this method on artificially blurred images to validate our result. This method works successfully for the image having text and it cannot be used for deblurring any type of image it is only meant for the image having text in it. As OCR word confidence is used. If the image does not have any text then this method cannot be used. This method was proposed to overcome a problem that was to deblur a text document image So as to increase the accuracy of Recognition. The existing system was heavily dependent on OCR for text segmentation and recognition. But when the acquired image was blurred Image then most of the Efficient OCR engines performance was not satisfactory. In this paper we have worked on the issue of Motion blur which is the most common type of blur. The Blur kernels or the PSF were estimated and evaluated with the Average Word Confidence value. Based on we have estimated the optimal PSF for the Input Image with text.The method used is based on the estimation of PSF which is an iterative process and another solution to the Deblurring text is through Artificial Neural Network. Training a Neural Network is a time taking process and requires a lot of computation. As a part of future work we would like combine our approach and a Neural Networkbased approach together to get more optimized solution to Deblurring textual images.A CKNOWLEDGMENTI would like to express my gratitude towards almighty God the mother father of this universe for giving me strength and positive thinking to work on this research topic. I would like extend my gratitude towards my PhD guide Dr. Deepak Kumar Singh for encouraging me to write this paper. He has motivated me whenever I was down and has helped me in writing this paper. With his deep knowledge of the subject he has time and again helped and given his valuable suggestion which have helped to improve my work. I would also like to thank my parents and family for being my strength.R EFERENCES[1]Taeg Sang Cho,Sylvain Paris,Berthold K. P. Horn,WilliamT. Freeman “Blur Kernel Estimatio n using the Radon Transform” Computer Vision and Pattern Recognition (CVPR), 2011 IEEE Conference on June 2011.[2]Shamik Tiwari, V. P. 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Bhagat,Puran Gour "Novel Approach toEstimate Motion Blur Kernel Parameters and Comparative Study of Restoration Techniques"International Journal of Computer Applications (0975 – 8887) Volume 72– No.17, June 2013.[4]Lu Fang, Haifeng Liu, Feng Wu, Xiaoyan Sun, HouqiangLi "Separable Kernel for Image Deblurring" 2014 IEEE Conference on Computer Vision and Pattern Recognition Pages: 2885 - 2892, DOI: 10.1109/CVPR.2014.369.[5]Nimali Rajakaruna,Chamila Rathnayake,Kit Yan Chan,IainMurray "Image deblurring for navigation systems of vision impaired people using sensor fusion data" Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), 2014 IEEE Ninth International Conference on Year: 2014.[6]Jing Wang, Ke Lu, Qian Wang, and Jie Jia "KernelOptimization for Blind Motion Deblurring with Image Edge Prior" Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2012, Article ID 639824,10 pages doi:10.1155/2012/639824.[7]Long Mai,Feng Liu "Kernel fusion for better imagedeblurring" 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Pages: 371 - 380, DOI:10.1109/CVPR.2015.7298634.[8]Jinshan Pan, Zhe Hu,Zhixun Su,Ming-Hsuan Yang"Deblurring Text Images via L0-Regularized Intensity and Gradient Prior" 2014 IEEE Conference on Computer Vision and Pattern Recognition Pages: 2901 - 2908, DOI:10.1109/CVPR.2014.371.[9]Nam-Yong Lee “Block-iterative Richardson-Lucy methodsfor image deblurring" Lee EURASIP Journal on Image and Video Processing (2015) Springer 2015:14 DOI10.1186/s13640-015-0069-2.[10]Linyang He, Gang Li,and Jinghong Liu "Joint MotionDeblurring and Superresolution from Single Blurry Image"Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 965690.[11]Tae Hyun Kim and Kyoung Mu Lee "Generalized VideoDeblurring for Dynamic Scenes" 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Year:2015 Pages: 5426 - 5434, DOI:10.1109/CVPR.2015.7299181.[12]Wei-Sheng Lai; Jian-Jiun Ding; Yen-Yu Lin; Yung-YuChuang "Blur kernel estimation using normalized color-line priors" 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Year: 2015 Pages: 64 - 72, DOI: 10.1109/CVPR.2015.7298601.[13]Neeraj Kumar, Rahul Nallamothu, Amit Sethi "NeuralNetwork Based Image Deblurring" Neural Network Applications in Electrical Engineering (NEUREL), 2012 11th Symposium on Year: 2012 IEEE Pages: 219 - 222, DOI: 10.1109/NEUREL.2012.6420015.[14]J.Amudha, N.Pradeepa, R.Sudhakar "A Survey on DigitalImage Restoration" ELSEVIER Procedia Engineering, Volume 38, 2012, Pages 2378-2382.[15]Haichao Zhang,David Wipf,Yanning Zhang "Multi-imageBlind Deblurring Using a Coupled Adaptive Sparse Prior"Computer Vision and Pattern Recognition (CVPR), 2013 IEEE Conference on Year: 2013 Pages: 1051 - 1058, DOI:10.1109/CVPR.2013.140.[16]Neeraj Kumar, Rahul Nallamothu, Amit Sethi "NeuralNetwork Based Image Deblurring" Neural Network Applications in Electrical Engineering (NEUREL), 2012 IEEE 11th Symposium onYear: 2012 Pages: 219 - 222, DOI: 10.1109/NEUREL.2012.6420015.[17]Amudha.J,Pradeepa.N,Sudhakar.R " A Survey on DigitalImage Restoration" ELSEVIER Procedia Engineering 38 (2012) 2378 – 2382.[18]Alex Krizhevsky , Ilya Sutskever , Geoffrey E. Hinton"Imagenet classification with deep convolutional neural networks" CiteSeer Document Advances in Neural Information Processing Systems 2012.[19]Jian Sun; Wenfei Cao; Zongben Xu; Jean Ponce "Learninga convolutional neural network for non-uniform motionblur removal" 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Year: 2015 Pages: 769 - 777, DOI: 10.1109/CVPR.2015.729867.[20]Michal Hradis, Jan Kotera, Pavel Zemˇcík, Filip Šroubek"Convolutional Neural Networks for Direct Text Deblurring" British Machine Vision Conference 2015 September.[21]Li Xu, Jimmy SJ. Ren, Ce Liu, Jiaya Jia "DeepConvolutional Neural Network for Image Deconvolution"conference on Advances in Neural Information Processing Systems 27 (NIPS 2014).[22]C. Gonzalez Richard E. Woods “Digital Image Processing”Book Third Edition Rafael Interactive Pearson International Edition prepared by Pearson Education PEARSON Prentice Hall.[23]Ray Smith Google Inc. theraysmith@ “AnOverview of the Tesseract OCR Engine” Google Inc OSCON 2007.[24]Marion A.Hersh, Michael A.Johnson “Assistivetechnology for Visually Impaired and Blind people” Book by Springer ISBN 978-1-84628-866.[25]Ratnakar Dash “Parameter Estimation for ImageRestoration” PhD thsis NIT Rourkela, Orrisa,India March 2012.[26]Zohair Al-Ameen,Ghazali Bin Sulong,Md. Gapar Md.Johar “Computer Forensics and Image Deblurring: An Inclusive Investigation”IJMECS Vol.5, No. 11, November 2013 PP.42-48, DOI: 10.5815/ijmecs.2013.11.06.。
Research Findings Methods
Research Findings MethodsResearch findings methods are crucial for the advancement of knowledge in various fields. These methods provide a systematic approach to gathering, analyzing, and interpreting data in order to answer research questions and test hypotheses. There are several research findings methods that researchers can employ, each with its own strengths and limitations. In this response, we will explore some of the most common research findings methods, including experimental research, survey research, qualitative research, and mixed methods research.Experimental research is a method in which the researcher manipulates one or more variables and measures the effect of the manipulation on other variables. This method allows researchers to establish cause-and-effect relationships between variables, making it a powerful tool for testing hypotheses. However, experimental research is often conducted in artificial laboratory settings, which may limit the generalizability of the findings to real-world situations. Additionally, ethical considerations may restrict the types of experiments that can be conducted on human subjects.Survey research involves the collection of data from a sample of individuals through the use of questionnaires or interviews. This method is commonly used to gather information about people's attitudes, beliefs, and behaviors. Survey research is relatively quick and cost-effective, making it a popular choice for researchers studying large populations. However, survey research is susceptible to response bias, as participants may provide inaccurate or socially desirable responses. Additionally, the quality of the data collected is highly dependent on the wording and structure of the survey questions.Qualitative research is a method that focuses on understanding the meaning and experiences of individuals within their social context. This method often involves the collection and analysis of textual data, such as interviews, observations, and documents. Qualitative research allows researchers to explore complex phenomena in depth and from multiple perspectives. However, qualitative research is often criticized for its subjectivity and lack of generalizability. Additionally, the process of analyzing qualitative data can be time-consuming and challenging.Mixed methods research is an approach that combines qualitative and quantitative research methods in a single study. This method allows researchers to gain a more comprehensive understanding of a research problem by triangulating different sources of data. Mixed methods research is particularly useful for addressing complex research questions that cannot be adequately answered by either qualitative or quantitative methods alone. However, conducting mixed methods research requires expertise in both qualitative and quantitative data collection and analysis, which can be challenging for researchers with limited experience in one or both methods.In conclusion, research findings methods play a critical role in generating new knowledge and advancing our understanding of the world. Each research findings method has its own strengths and limitations, and researchers must carefully consider which method is most appropriate for their research questions and objectives. By employing a variety of research findings methods, researchers can triangulate their findings and strengthen the validity and reliability of their conclusions. Ultimately, the choice of research findings method should be guided by the specific research question and the nature of the phenomenon being studied.。
Fast monte-carlo algorithms for finding low-rank approximations
Fast Monte-Carlo Algorithms forfinding low-rank approximationsAlan Frieze Department of Mathematical Sciences, Carnegie Mellon University,Pittsburgh,PA15213. Email:af1p@.Ravi Kannan Computer Science Department,Yale University,New Haven,CT06511. Email:kannan@.Santosh V empalaDepartment of Mathematics andLaboratory for Computer Science,M.I.T.,Cambridge,MA02139.Email:vempala@October22,1998AbstractIn several applications,the data consists of an matrix and it is of interest tofind an approximation of a specified rank to where,is much smaller than and.Traditionalmethods like the Singular V alue Decomposition(SVD)help usfind the“best”such approxima-tion.However,these methods take time polynomial in which is often too prohibitive.In this paper,we develop an algorithm which is qualitatively faster provided we may sample the entries of the matrix according to a natural probability distribution.Indeed,in the applica-tions such sampling is possible.Our main result is that we canfind the description of a matrix of rank at most so thatrankholds with probability at least.(For any matrix,denotes the sum of the squaresof all the entries of.)The algorithm takes time polynomial in only,indepen-dent of.1IntroductionIn many applications,the data consists of an matrix and it is of interest tofind an approx-imation of a specified rank to where,is much smaller than and.Traditional methods like the Singular Value Decomposition(SVD)help usfind the“best”such approximation.However, these methods take time polynomial in.In this paper,we essentially reduce the problem to a singular value problem in dimensions where depends only upon.The traditional“random projection”method(where one projects the problem into a randomly chosen subspace of small dimension)would also accomplish a similar reduction in dimension;but carrying out the random projection amounts to premultiplying the given matrix by a matrix which itself takes time dependent upon(and in fact,it can be argued that this is not competitive with known Numerical Analysis techniques like the Lanczos method,in the case where the top few singular values dominate.)In this paper,we describe an algorithm which is qualitatively faster provided we may sample the entries of the matrix according to a natural probability distribution which we describe presently. For a matrix,denotes,where denotes the th entry of..Our main result is expressed as the following:Theorem1Given an matrix,and,there is a randomized algorithm whichfinds the description of a matrix of rank at most so thatrankholds with probability at least.The algorithm takes time polynomial in only, independent of.The most complex computational task is tofind thefirst singular values of a randomly chosen submatrix where.The matrix can be explicitly constructed from its description in time.This depends on the following existence theorem.Let(2)This theorem asserts the existence of“good”vectors in the row space of.It follows from Linear Algebra that we may take to be the largest generalized eigenvectors of with respect to.Note that both of these matrices are,where we should take.They can both be exactly computed(by direct multiplication)in time ;so it follows that in time,we canfind the vectors of the Theorem.This time bound may be good enough for several applications.The paper is organized as follows.After recalling the SVD and related definitions,we prove Theo-rem2.As already remarked this immediately leads to an poly time algorithm.We develop a theoretically better(“constant time”)algorithm in Section5,which relies heavily on sampling and in the last two sections we analyse its quality and efficiency.Assumptions on samplingWe now state in detail the assumptions we make on the ability to sample.We discuss in the next section some prominent applications where these assumptions are naturally satisfied.Also,in the important“dense”case,uniformly sampling the entries satisfies the assumptions.(See Remark1). In any case,after a one-pass preprocessing of the matrix,the assumptions can be satisfied.(See Remark2).For a matrix,denotes the th row,denotes the th column.Assumption1We can choose row of the matrix with probability satisfying for some constant independent of.The are known to us.Assumption2For any given,we can pick a with probabilities satisfying where.The are known to us. Remark1:Note that if the matrix is dense,i.e.,for some constant,then we may take.Then of course we can take and we may takefor all and.Remark2:For any matrix at all,we claim that after making one pass through the entire matrix,we can set up data structures so that after that we can sample the entries fast-time per sample,so as to satisfy Assumptions(1)and(2).During the one pass,we do several things.Suppose is such that for allORour algorithm and thus obtain the SVD approximation more efficiently.Applications that we do not discuss include face recognition and picture compression.2.1Low-Rank Approximations and the Regularity LemmaThe fundamental Regularity Lemma of Szemer´e di’s in Graph Theory gives a partition of the vertex set of any graph so that“most”pairs of parts are“nearly regular”.(We do not give details here.)This lemma has a host of applications(see[10])in Graph Theory.The Lemma was non-constructive in that it only asserted the existence of the partition(but did not give an algorithm tofind it.)Alon, Duke,Lefmann,R¨o dl aand Yuster werefinally able to give an algorithm tofind such a partition in polynomial time[1].In earlier papers[6,7],we related low-rank approximations of the adjacency matrix of the graph to regular partitions and from that were able to derive both Szemer´e di’s Lemma and a“more user friendly version”and in fact showed that the partition could be constructed in con-stant time for any graph.While this connection is not directly relevant to this paper,we point this out here as one more case where low-rank approximations come in handy.2.2Latent Semantic IndexingThis is a general technique for analysing a collection of“documents”which are assumed to be related (for example,they are all documents dealing with a particular subject,or a portion of the web;see [2,3,4,5]for details and empirical results).We give a very cursory description of this broad area here and discuss its relation to our main problem.Suppose there are documents and“terms”which occur in the documents.(Terms may be all the words that occur in the documents or key words that occur in them.)The model hypothesizes that(because there are relationships among the documents),there are a small number of main (unknown)“topics”which the documents are about.Thefirst aim of the technique is tofind a set of topics which best describe the documents.(This is the only part which concerns us here.)A topic is modelled as an vector of non-negative reals summing to1,where the interpretation is that the th component of a topic vector gives the frequency with which the th term occurs in(a discussion of)the topic.With this model on hand,it is easy to argue(using Linear Algebra and a line of reasoning similar to thefield of“Factor Analysis”in Statistics)that the best topics are the top singular vectors of the so-called“document-term”matrix,which is an matrix with being the frequency of the th term in the th document.Alternatively,one can define as0 or1depending upon whether the th term occurs in the th document.Here we argue that in practice,we can implement the assumptions of our algorithm.It is easy to see that if we are allowed one pass through each document,we can set up data structures for sampling (in a pragmatic situation one could have the creator of a document supply a vector of squared term frequencies).Otherwise,if no frequency is too large(this is typical since words that occur too often, so-called“buzz words”,are removed from the analysis),all we need to precompute is the length (),of each document.This is typically available(as say“file size”).In this case, assumption(1)is easily implemented—we pick a document with probability proportional to its length.This is easily seen to satisfy Assumption1,but without the squares(i.e.we sample the th entry with probability(because the frequencies are all in some small range).Assumption2is similarly implemented—given a document,we pick a word uniformly at random from it,i.e.,for any.For a positive integer,we let.For a matrix and vectors we defineUsing the fact that Tr for any matrix,we see that equalsTrTr(3) 4Proof of Theorem24.1Singular Value DecompositionEvery real matrix can be expressedwhere and the form an orthonormal set of vectors and so do the. Also and for.This is called the singular value decomposition of.So if in(3)the vectors are singular vectors of M then(4)From Linear Algebra,[8]we know that the matrix producing the minimum of among all matrices of rank or less is given byThis implies(see(1)for the definition of)thatWe now show that we canfind a good approximation to by looking in a subspace generated by a small number of rows of.This will be done by independently choosing rows of A(sufficiently large)from a distribution where the probability that we choose row satisfiesfor and let.Let be an orthonormal basis of with.LetandThen(7) NowTaking expectations and using(6)we getProof Let.Suppose that has a unit eigenvector with eigenvalue such that(9) But the rank of is at most,and we know that this cannot be better than the best rank approximation to,i.e.,5Sampling AlgorithmThe aim of this section is to develop a“constant time”algorithm to produce the approximation.What we do below is tofirst pick a set of rows of.We form a matrix from these rows after scaling them.We then pick again columns of from a probability distribution satisfying a condition of the type stated in Assumtion(1)and scale the columns to get a matrix.Wefind the singular vectors of this matrix and argue that from those,we may get a good low-rank approxmation to. Wefirst present the algorithm.Algorithmis given andLet be the matrix with rowsfor.pute the maximum of over all sets of unit vectors in the columnspace of.(We may assume at this point that are thefirst singular vectors of .)4.Letwhere5.Output for.(I.e.,output as the approximation to).Note that5.1Implementation IssuesImplementation Issues We explore some issues related to the implementation of the above algo-rithm.First of all,how do we carry out Step2?Wefirst pick a row of,each row with probability; suppose the chosen row is the th row of.Then pick with probabilities.This defines the probabilities.We then have(with is a row of),LetPrThenfrom which it follows thatwe have,(13) So let us assume from now on that5.2Basic LemmaLemma1Let be an matrix and let be a probability distribution on such thatThen for all,PrThe result follows from the Markov inequality.It follows from the above lemma and the definition of–(10)–that with probability at least9/10 both of the following events hold:and(14) whereAssume from now on that they do.So if are unit vectors in the row space of thenand if are unit vectors in the column space of(15) It follows after a little calculation that if are unit vectors in the row space of then(16) Similarly,are unit vectors in the column space of then(17) 5.3Analysis of the AlgorithmIt follows from Theorem2that with probability at least9/10there are unit vectors in the row space of such thatApplying(16)we see thatApplying Theorem2with A replaced by and S replaced by we see that with probability at least9/10there are unit vectors in the column space of such thatApplying(17)we see thatTherefore the vectors computed by the algorithm satisfyIt follows from(17)that(18) and thatFurthermore,Similarly,using(20),Hence,(21) For any vector and any matrixSo forObserve that(15)impliesSo,[3]S.Deerwester,S.T.Dumais,ndauer,G.W.Furnas,and R.A.Harshman.“Indexingby latent semantic analysis,”Journal of the Society for Information Science,41(6),391-407, 1990.[4]S.T.Dumais,G.W.Furnas,ndauer,and S.Deerwester,“Using latent semantic analysisto improve information retrieval,”In Proceedings of CHI’88:Conference on Human Factors in Computing,New York:ACM,281-285,1988.[5]S.T.Dumais,“Improving the retrieval of information from external sources”,Behavior Re-search Methods,Instruments and Computers,23(2),229-236,1991.[6]A.M.Frieze and R.Kannan,“The Regularity Lemma and approximation schemes for denseproblems”,Proceedings of the37th Annual IEEE Symposium on Foundations of Computing, (1996)12-20.[7]A.M.Frieze and R.Kannan,“Quick approximations to matrices and applications,”to appear inCombinatorica./af1p/papers.html.[8]G.H.Golub and C.F.Van Loan,Matrix Computations,Johns Hopkins University Press,Lon-don,1989.[9]J.Kleinberg,“Authoritative sources in a hyperlinked environment,”Proc.9th ACM-SIAMSymposium on Discrete Algorithms,1998.[10]J.Koml´o s and M.Simonovits,“Szemer´e di’s Regularity Lemma and its applications in graphtheory”,to appear.。
启发式算法（HeuristicAlgorithm）
启发式算法（HeuristicAlgorithm）启发式算法（Heuristic Algorithm）有不同的定义：⼀种定义为，⼀个基于直观或经验的构造的算法，对优化问题的实例能给出可接受的计算成本（计算时间、占⽤空间等）内，给出⼀个近似最优解，该近似解于真实最优解的偏离程度不⼀定可以事先预计；另⼀种是，启发式算法是⼀种技术，这种技术使得在可接受的计算成本内去搜寻最好的解，但不⼀定能保证所得的可⾏解和最优解，甚⾄在多数情况下，⽆法阐述所得解同最优解的近似程度。
我⽐较赞同第⼆种定义，因为启发式算法现在还没有完备的理论体系，只能视作⼀种技术。
_______________________________________名词解释Heuristics，我喜欢的翻译是“探索法” ，⽽不是“启发式”，因为前者更亲民⼀些，容易被理解。
另外，导致理解困难的⼀个原因是该词经常出现在⼀些本来就让⼈迷糊的专业领域语境中，例如，经常看到某某杀毒软件⽤启发式⽅法查毒，普通民众本来就对杀毒软件很敬畏，看到“启发式”就更摸不着北了。
实际上，这个词的解释⼗分简单，例如，查朗⽂词典，可以看到：The use of experience and practical efforts to find answers to questions or to improve performance维基百科词条heuristic，将其定义为基于经验的技巧（technique），⽤于解决问题、学习和探索。
并对该词进⾏了更详尽的解释并罗列了多个相关领域：A heuristic method is used to rapidly come to a solution that is hoped to be close to the best possible answer, or 'optimal solution'. A heuristic is a "rule of thumb", an educatedguess, an intuitive judgment or simply common sense.A heuristic is a general way of solving a problem. Heuristics as a noun is another name for heuristic methods.Heuristic可以等同于：实际经验估计（rule of thumb）、有依据的猜测（educated guess, a guess beased on a certain amount of information, and therefore likely to be right）和常识（由经验得来的判断⼒）。
A Tutorial on Support Vector Machines for Pattern Recognition
burges@
Bell Laboratories, Lucent Technologies Editor: Usama Fayyad Abstract. The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and non-separable data, working through a non-trivial example in detail. We describe a mechanical analogy, and discuss when SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very large (even infinite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization performance is guaranteed for SVMs, there are several arguments which support the observed high accuracy of SVMs, which we review. Results of some experiments which were inspired by these arguments are also presented. We give numerous examples and proofs of most of the key theorems. There is new material, and I hope that the reader will find that even old material is cast in a fresh light. Keywords: support vector machines, statistical learning theory, VC dimension, pattern recognition
(MIT经典)算法设计与分析教学课件ch05
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Example – directed graph
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Breadth-first traversal:
Design and Analysis of Algorithms - Chapter 5
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Breadth-first search: Notes
BFS has same efficiency as DFS and can be implemented with graphs represented as:
Design and Analysis of Algorithms - Chapter 5 9
Breadth-first search
Explore graph moving across to all the neighbors of last visited vertex Similar to level-by-level tree traversals Instead of a stack, breadth-first uses queue
• • Insertion sort Graph search algorithms:
– DFS – BFS – Topological sorting
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Algorithms for generating permutations, subsets
Decrease by a constant factor
Applications: same as DFS, but can also find paths from a vertex to all other vertices with the smallest number of edges
正确对待算法的作文题目
正确对待算法的作文题目英文回答：When it comes to dealing with algorithms, it is important to approach them with a balanced perspective. On one hand, algorithms have greatly improved our lives by providing efficient solutions to complex problems. For example, search engines like Google use algorithms toquickly deliver relevant search results, saving us time and effort. Algorithms also play a crucial role in various industries, such as finance, healthcare, and transportation, where they help optimize processes and make informed decisions.However, it is equally important to acknowledge the potential drawbacks and ethical concerns associated with algorithms. One major concern is the issue of bias. Algorithms are created by humans and can inadvertentlyreflect the biases and prejudices of their creators. For instance, facial recognition algorithms have been found tohave higher error rates for people with darker skin tones, leading to potential discrimination. Another concern is the lack of transparency and accountability in algorithmic decision-making. When algorithms are used to make important decisions, such as in hiring or loan approvals, it iscrucial to ensure that they are fair, unbiased, and explainable.To address these concerns, it is necessary to have regulations and guidelines in place to govern the development and use of algorithms. Governments and organizations should promote transparency andaccountability by requiring algorithmic systems to be auditable and explainable. Additionally, there should be diversity and inclusivity in the teams developingalgorithms to minimize biases. Regular audits and evaluations of algorithms should be conducted to identify and rectify any biases or errors.Moreover, it is essential to educate the public about algorithms and their impact. Many people are unaware of how algorithms work and the potential consequences of their use.By promoting digital literacy and providing accessible resources, individuals can make informed decisions and actively engage in discussions about algorithmic fairness and ethics.In conclusion, algorithms have become an integral partof our lives, bringing numerous benefits and conveniences. However, we must approach them with caution and address the potential biases and ethical concerns they may pose. By implementing regulations, promoting transparency, and educating the public, we can ensure that algorithms are developed and used in a responsible and fair manner.中文回答：谈到处理算法时，我们需要以平衡的态度来对待它们。
科学发现需要怀疑和坚持 作文
科学发现需要怀疑和坚持作文英文回答：Scientific discovery is a process of ongoing questioning, exploration, and refinement. It requires adeep-seated skepticism and a relentless pursuit of evidence. The scientific method is built upon the foundation of doubt, as it is through challenging existing knowledge and assumptions that new insights can be gained.The ability to question and challenge is essential for scientific progress. It forces scientists to examine their own beliefs and biases, and to consider alternative explanations for their observations. This critical thinking is vital for avoiding confirmation bias, the tendency to seek out evidence that supports one's existing beliefswhile ignoring evidence that contradicts them.Skepticism, however, must be balanced with a strong commitment to empirical evidence. Scientists must bewilling to abandon their cherished theories if the evidence no longer supports them. This requires a degree of intellectual humility and a willingness to admit when one is wrong.The history of science is replete with examples of discoveries that were made as a result of questioning and persistence. The heliocentric model of the solar system,for example, was initially met with great resistance, but eventually prevailed due to the overwhelming evidence inits favor. Similarly, the germ theory of disease wasinitially ridiculed, but eventually became accepted as the basis for modern medicine.These examples demonstrate the transformative power of scientific inquiry. By embracing doubt and relentlessly pursuing evidence, scientists have made countless discoveries that have revolutionized our understanding of the world and improved our lives.中文回答：科学发现是一个持续不断的质疑、探索和完善的过程。
发现人才的方法英语作文
发现人才的方法英语作文Identifying Talent: Strategies and Methods.Talent identification is a crucial process that plays a pivotal role in the success of any organization, industry, or society. The ability to recognize and nurture talent among a diverse pool of individuals is what drives innovation, creativity, and sustained growth. However, the task of finding and nurturing talent is not always straightforward, as it requires a combination of skills, knowledge, and experience. In this article, we will explore various methods and strategies for discovering talent effectively.Firstly, it is essential to understand that talent identification is not a one-size-fits-all process.Different industries, roles, and organizations require different skills, abilities, and experiences. Therefore, the methods used to identify talent should be tailored to the specific needs of the organization. For instance, inthe arts sector, talent scouts might look for creativity, uniqueness, and technical proficiency. In the scientific community, they might prioritize analytical skills, problem-solving abilities, and research experience.One of the most effective methods for discoveringtalent is through competitive events and competitions. These platforms allow individuals to showcase their skills and abilities in a controlled environment, making it easier for recruiters and scouts to identify those with exceptional potential. Competitions also provide an incentive for participants to excel and improve their skills, further increasing the pool of talent available.Another strategy for finding talent is through networking and referrals. This involves creating a network of individuals and organizations that can provide leads and recommendations on potential talent. Referrals from trusted sources can often be more reliable than traditional job postings or resumes, as they provide a firsthand account of the candidate's abilities and qualities.Social media has also emerged as a powerful tool for talent identification. Platforms like LinkedIn, Instagram, and YouTube allow individuals to showcase their skills, experiences, and achievements to a wide audience. Recruiters can use these platforms to search forindividuals with specific skills or interests, and engage with them directly. However, it's important to rememberthat social media should be used as a supplementary tool rather than a sole source of talent identification.Moreover, organizations should also consider implementing talent management systems. These systems allow organizations to track, evaluate, and develop the skills of their employees effectively. By identifying and nurturing internal talent, organizations can build a strong talent pipeline that ensures sustainable growth and success.Additionally, organizations should create an inclusive and diverse work environment. This encourages individuals from different backgrounds, experiences, and perspectives to come forward and share their talents. A diverse team brings a breadth of ideas, perspectives, and solutions thatcan lead to innovation and creativity.In conclusion, talent identification is a multifaceted process that requires a combination of strategies and methods. By tailoring their approach to the specific needs of their organization, recruiters and scouts caneffectively discover and nurture talent. By utilizing competitive events, networking and referrals, social media, talent management systems, and fostering an inclusive work environment, organizations can build a strong talent pipeline that drives their success.。
试错法
试错法作者：［比利时］弗兰克·罗杰朱知非来源：《科幻世界·译文版》2019年第01期1.所有与外界的通讯都中断了。
自从斯旺博士出事之后，我就被彻底困在了这里。
手机和电脑都没法使用，出口也被封死了。
外面有没有人意识到这里发生的事情？他们对此作何反应？我完全无从知晓。
我所能做的，只不过是写下这些笔记，希望有一天能对那些偶然发现这里的人有所帮助。
2.我是中途加入这个项目的，因为我觉得它的基本理念很有吸引力，于是就投了简历，并很快得到了录用。
我还记得很早以前，斯旺博士在一个电视访谈上介绍他的项目：“最根本的問题是——当某种生物必须依靠智慧才能维持生存的时候，它们是否会因此进化为智慧生物？我们这个项目努力想要实现的目标，就是逐步引导一个蚂蚁种群，使之向智慧生物演进。
当然，这一理论在昆虫身上能否适用还有待观察。
”主持人询问这个实验是否旨在支持生物进化学说，反对神创论。
斯旺博士表示，他认为生物进化论早已得到充分证明。
“我相信就算实验取得了成功，那些神创论者以及不少宗教人士肯定还是会拒绝承认我们的结论。
无所谓，我们是搞科学的。
”一个观众说：“我不明白你们是如何做到把一只蚂蚁变得更聪明的。
”斯旺博士解释道：“关键不是要让某一只蚂蚁变得更聪明，而是要通过自然选择，提高整个种群的智力。
这是一个涉及若干代蚂蚁的长期繁殖计划。
”他没能对此做更详尽的说明，因为广告时间到了。
这就是电视节目的特色，即便是科学节目也不能免俗。
3.计划是这样的：这个蚂蚁种群将在各种日常活动中受到干扰，包括觅食、维护蚁巢以及保护蚁后等等。
这些问题只能依靠智力解决：蚂蚁们必须理解干扰的性质，并找出解决之道。
只有高效地处理问题、战胜了困难的蚂蚁才可以生存下去，而其他的，用斯旺博士委婉的话来说，就要“从实验中移除”：被剔除并被加工成食物，喂养给那些更聪明的同类们。
实验的最初阶段并没有多少成效，斯旺博士甚至对整个项目的前景都快失去信心了。
From Data Mining to Knowledge Discovery in Databases
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.。
整式的加减
整式的加减整式的加减概念总汇1.整式加减的相关概念1) 同类项：所含字母相同且相同字母的指数也相同的项，称为同类项。
几个常数项也是同类项。
例如，6x2y2和-4x2y2是同类项，-3和5也是同类项；但4ab和3ab不是同类项，因为相同字母的指数不相同。
2) 合并同类项：将多项式中的同类项合并成一项，即将同类项的系数相加，字母和字母的指数不变。
例如，6x2y2+(-4x2y2)=2x2y2.说明：①只有同类项可合并，不是同类项的不能合并；②合并同类项时，只合并系数，字母与字母的指数不变；③合并同类项后，若其系数是带分数，要将其化为假分数；④多项式中，如果两同类项的系数互为相反数，合并后这两项互相抵消，结果为0.3) 去括号法则：括号前面是正号，将括号和括号前的正号去掉后，括号里的各项不改变符号；括号前是负号，将括号和括号前的负号去掉，括号里的各项都要改变符号。
例如，A+(5A+3B)-(A-2B)=A+5A+3B-A+2B=5A+5B。
说明：去括号法则相当于乘法分配律的应用。
例如，A+(5A+3B)-(A-2B)=A+1×(5A+3B)+(-1)×(A-2B)=A+5A+3B+(-1)A+(-1)×(-2B)=A+5A+3B-A+2B=5A+5B。
如果括号前面有数字因数，就按乘法分配律去括号。
例如：3a2-2ab+4b2)-2(a2-ab-3b2)=a2-ab+2b2-a2+2ab+6b2=ab+8b24) 添括号法则：给括号前添正号，括在括号里的各项都不改变符号；给括号前添负号，括到括号里的各项都要改变符号。
说明：去括号与添括号是互逆的过程，它们的依据是乘法分配律的顺逆运用。
可以将+（a-b）看作（+1）（a-b），将-（a-b）看作（-1）（a-b），则有+（a-b）=a-b，-（a-b）=-a+b。
这样，乘法分配律的一个应用便是去括号；添括号可理解为乘法分配律的逆用。
搜索算法中英文对照外文翻译文献
(文档含英文原文和中文翻译)中英文对照翻译外文资料1-Wire Search AlgorithmAbstractDallas Semiconductor's 1-Wire® devices each have a 64-bit unique registration number in read-only-memory (ROM).That is used to address them individually by a 1-Wire master in a 1-Wire network. If the ROM numbers of the slave devices on the 1-Wire network are not known, then using a search algorithm can discover them. This document explains the search algorithm in detail and provides an example implementation for rapid integration. This algorithm is valid for all current and future devices that feature a 1-Wire interface.Table 1 Bit Unique ROM 'Registration' Number.Search AlgorithmThe search algorithm is a binary tree search where branches are followed until a device ROM number, or leaf, is found. Subsequent searches then take the other branch paths until all of the leaves present are discovered.The search algorithm begins with the devices on the 1-Wire being reset using the reset and presence pulse sequence. If this is successful then the 1-byte search command is sent. The search command readies the 1-Wire devices to begin the search.There are two types of search commands. The normal search command (0F0 hex) will perform a search with all devices participating. The alarm or conditional search command (0EC hex) will perform a search with only the devices that are in some sort of alarm state. This reduces the search pool to quickly respond to devices that need attention.Following the search command, the actual search begins with all of theparticipating devices simultaneously sending the first bit (least significant) in their ROM number (also called registration number). (See Figure 1.) As with all 1-Wire communication, the 1-Wire master starts every bit whether it is data to be read or written to the slave devices. Due to the characteristics of the 1-Wire, when all devices respond at the same time, the result will be a logical AND of the bits sent. After the devices send the first bit of their ROM number, the master initiates the next bit and the devices then send the complement of the first bit. From these two bits, information can be derived about the first bit in the ROM numbers of the participating devices. (See Table 1.)According to the search algorithm, the 1-Wire master must then send a bit back to the participating devices. If the participating device has that bit value, it continues participating. If it does not have the bit value, it goes into a wait state until the next 1-Wire reset is detected. This 'read two bits' and 'write one bit' pattern is then repeated for the remaining 63 bits of the ROM number (see Table 2). In this way the search algorithm forces all but one device to go into this wait state. At the end of one pass, the ROM number of this last device is known. On subsequent passes of the search, a different path (or branch) is taken to find the other device ROM numbers. Note that this document refers to the bit position in the ROM number as bit 1 (least significant) to bit 64 (most significant). This convention was used instead of bit 0 to bit 63 for convenience to allow initialization of discrepancy counters to 0 for later comparisons.On examination of Table 1, it is obvious that if all of the participating devices have the same value in a bit position then there is only one choice for the branch path to be taken. The condition where no devices are participating is an atypical situation that may arise if the device being discovered is removed from the 1- Wire during the search. If this situation arises then the search should be terminated and a new search could be done starting with a 1-Wire reset.The condition where there are both 0s and 1s in the bit position is called a discrepancy and is the key to finding devices in the subsequent searches. The search algorithm specifies that on the first pass, when there is a discrepancy (bit/complement = 0/0), the '0' path is taken. Note that this is arbitrary for this particular algorithm. Another algorithm could be devised to use the '1' path first. The bit position for the last discrepancy is recorded for use in the next search. Table 3 describes the paths that are taken on subsequent searches when a discrepancy occurs.The search algorithm also keeps track of the last discrepancy that occurs within the first eight bits of the algorithm. The first eight bits of the 64-bit registrationnumber is a family code. As a result, the devices discovered during the search are grouped into family types. The last discrepancy within that family code can be used to selectively skip whole groups of 1-Wire devices. See the description of ADVANCED SEARCH VARIATIONS for doing selective searches. The 64-bit ROM number also contains an 8-bit cyclic-redundancy-check (CRC). This CRC value is verified to ensure that only correct ROM numbers are discovered. See Figure 1 for the layout of the ROM number.Figure 2 shows a flow chart of the search sequence. Note the Reference that explains the terms used in the flow chart. These terms are also used in the source code appendix to this document.ReferenceId_bit—the first bit read in a bit search sequence. This bit is the AND of all of the id_bit_number bits of the devices that are still participating in the search.cmp_id_bit—the complement of the id_bit .This bit is the AND of the complement of all of the id_bit_number bits of the devices that are still participating in the search.Id_bit_number—the ROM bit number 1 to 64 currently being searched.LastDeviceFlag—flag to indicate previous search was the last device.LastDiscrepancy—bit index that identifies from which bit the (next) search discrepancy check should start.LastFamilyDiscrepancy—bit index that identifies the LastDiscrepancy within the first 8-bit family code of ROM number.last_zero—bit position of the last zero written where there was a discrepancy.ROM_NO—8-byte buffer that contains the current ROM registration number discovered.search_direction—bit value indicating the direction of the search. All devices with this bit stay in the search and the rest go into a wait state for a 1-Wire reset.There are two basic types of operations that can be performed by using the search algorithm by manipulating the LastDiscrepancy, LastFamilyDiscrepancy, LastDeviceFlag, and ROM_NO register values (see Table 4). These operations concern basic discovery of the ROM numbers of 1-Wire devices.FirstThe 'FIRST' operation is to search on the 1-Wire for the first device. This is performed by setting LastDiscrepancy, LastFamilyDiscrepancy, and LastDeviceFlag to zero and then doing the search. The resulting ROM number can then be read from the ROM_NO register. If no devices are present on the 1- Wire the reset sequence will not detect a presence and the search is aborted.NextThe 'NEXT' operation is to search on the 1-Wire for the next device. This search is usually performed after a 'FIRST' operation or another 'NEXT' operation. It is performed by leaving the state unchanged from the previous search and performing another search. The resulting ROM number can then be read from the ROM_NO register. If the previous search was the last device on the 1-Wire then the result will be FALSE and the condition will be set to execute a 'FIRST' with the next call of the search algorithm.The following goes through a simple search example with three devices. For illustration, this example assumes devices with a 2-bit ROM number only.Search Example(for simplicity the family discrepancy register and tracking has been left out of this example)FIRSTLastDiscrepancy = LastDeviceFlag = 0Do 1-Wire reset and wait for presence pulse ,if no presence pulse then doneid_bit_number = 1, last_zero = 0Send search command ,0F0 hexRead first bit id_bit : 1 (Device A) AND 0 (Device B) AND 1 (Device C) = 0Read complement of first bit cmp_id_bit : 0 (Device A) AND 1 (Device B) AND 0 (Device C) = 0Since id_bit_number > LastDiscrepancy，then search_direction = 0, last_zero = 1 Send search_direction bit of 0 , both Device A and C go into wait stateIncrement id_bit_number to 2Read second bit id_bit : 0(Device B) = 0Read complement of second bit cmp_id_bit : 1 (Device B) = 1Since bit and complement are different then search_direction = id_bitSend search_direction bit of 0 ,Device B is discovered with ROM_NO of ‘00’ and is now selectedLastDiscrepancy = last_zeroNEXTDo 1-Wire reset and wait for presence pulse ,if no presence pulse then doneid_bit_number = 1, last_zero = 0Send search command ,0F0 hexRead first bit id_bit : 1 (Device A) AND 0 (Device B) AND 1 (Device C) = 0Read complement of first bit cmp_id_bit : 0 (Device A) AND 1 (Device B) AND 0 (Device C) = 0Since id_bit_number = LastDiscrepancy then search_direction = 1Send search_direction bit of 1 , Device B goes into wait stateIncrement id_bit_number to 2Read second bit id_bit : 0(Device A) AND 1(Device C) = 0Read complement of second bit cmp_id_bit : 1(Device A) AND 0(Device C) = 0 Since id_bit_number > LastDiscrepancy，then search_direction = 0, last_zero = 2 Send search_direction bit of 0 , Device C goes into wait stateDevice A is discovered with ROM_NO of ‘01’ and is now selectedLastDiscrepancy = last_zeroNEXTDo 1-Wire reset and wait for presence pulse ,if no presence pulse then doneid_bit_number = 1, last_zero = 0Send search command ,0F0 hexRead first bit id_bit : 1 (Device A) AND 0 (Device B) AND 1 (Device C) = 0Read complement of first bit cmp_id_bit : 0 (Device A) AND 1 (Device B) AND 0 (Device C) = 0Since id_bit_number < LastDiscrepancy then search_direction = ROM_NO (first bit) = 1Send search_direction bit of 1 , Device B goes into wait stateIncrement id_bit_number to 2Read second bit id_bit : 0(Device A) AND 1(Device C) = 0Read complement of second bit cmp_id_bit : 1(Device A) AND 0(Device C) = 0 Since id_bit_number = LastDiscrepancy，then search_direction = 1Send search_direction bit of 1 , Device A goes into wait stateDevice C is discovered with ROM_NO of ‘11’ a nd is now selectedLastDiscrepancy = last_zero which is 0 so LastDeviceFlag = TRUENEXTLastDeviceFlag is true so return FALSELastDiscrepancy = LastDeviceFlag = 0Advanced Search VariationsThere are three advanced search variations using the same state information, namely LastDiscrepancy, LastFamilyDiscrepancy, LastDeviceFlag, and ROM_NO.These variations allow specific family types to be targeted or skipped and device present verification (see Table 4).VerifyThe 'VERIFY' operation verifies if a device with a known ROM number is currently connected to the 1- Wire. It is accomplished by supplying the ROM number and doing a targeted search on that number to verify it is present. First, set the ROM_NO register to the known ROM number. Then set the LastDiscrepancy to 64 (40 hex) and the LastDeviceFlag to 0. Perform the search operation and then read the ROM_NO result. If the search was successful and the ROM_NO remains the ROM number that was being searched for, then the device is currently on the 1-Wire.Target SetupThe 'TARGET SETUP' operation is a way to preset the search state to first find a particular family type. Each 1-Wire device has a one byte family code embedded within the ROM number (see Figure 1). This family code allows the 1-Wire master to know what operations this device is capable of. If there are multiple devices on the 1-Wire it is common practice to target a search to only the family of devices that are of interest. To target a particular family, set the desired family code byte into the first byte of the ROM_NO register and fill the rest of the ROM_NO register with zeros. Then set the LastDiscrepancy to 64 (40 hex) and both LastDeviceFlag and LastFamilyDiscrepancy to 0. When the search algorithm is next performed the first device of the desired family type will be discovered and placed in the ROM_NO register. Note that if no devices of the desired family are currently on the 1-Wire, then another type will be found, so the family code in the resulting ROM_NO must be verified after the search.Family Skip SetupThe 'FAMILY SKIP SETUP' operation sets the search state to skip all of the devices that have the family code that was found in the previous search. This operation can only be performed after a search. It is accomplished by copying the LastFamilyDiscrepancy into the LastDiscrepancy and clearing out the LastDeviceFlag. The next search will then find devices that come after the current family code. If the current family code group was the last group in the search then the search will return with the LastDeviceFlag set.Table5 Search Variations State SetupConclusionThe supplied search algorithm allows the discovery of the individually unique ROM numbers from any given group of 1-Wire devices. This is essential to any multidrop 1-Wire application. With the ROM numbers in hand, each 1-Wire device can be selected individually for operations. This document also discussed search variations to find or skip particular 1-Wire device types. See Appendix for a 'C' code example implementation of the search and all of the search variations.中文译文1-Wire 搜索算法绪论Dallas Semiconductor的每片1-Wire®器件都有唯一的64位注册码它存储在只读存储器(ROM)中。
微积分书——精选推荐
微积分书1.《微积分》作者Michael Spivak：我简直不知道该如何赞美它。
对我来说，这就是微积分书。
它精选了好的题目，谨慎的而且及其严格的证明，而且它超出了微积分的广度那么多，一个更好的书名应该是"实分析魅力导论"，因为它确实在微积分与高等实分析之间架起了一座桥梁，展示出数学有多么美丽。
Spivak简直将你领入一种领悟的感受，揭开微积分的面纱，从数的属性开始，紧接着是它的结构。
所举的例子都非常有意义，解释都非常清晰，这门课被这样好的展现并且激发着你的好奇心。
我觉得，这是我读过的最鼓舞人心的数学书之一。
每章最后的练习题，考察出对课程不同层次的理解，并且对读者来说具有挑战性。
这些练习让你觉得实在对课程的再学习。
事实上要我说，练习环节是这本书尤其有价值的部分，并且建议你把它们全做了。
对那些认真学习数学并希望有坚实的基础去迎接接下来更具挑战性的课程的人来书，这本书实在是很好。
Spivak这本书给出了奇数题号的习题的精选解答，但是如果你是自学或者足够的自律，你可以考虑一下参考的《习题解答》(已经出版，尽管Amazon有)。
2.微积分和数学分析引论，第一卷作者Richard Courant与Fritz John：一本正统的、精妙构思的微积分和单变量分析的入门书，这本书解释清晰，知识覆盖很具启发性。
这本书比其他微积分书要更实用而且更易懂，同时在数学的直观和严格方面保持了绝妙的平衡。
这本书给出足够的习题，它们能够充实学生的知识。
充足的物理应用，让它成为物理学专业学生与工程师理想的读物。
这是Springer版的三部曲的第一卷，如果你对微积分很认真，你会考虑更高级的另外两卷：卷II/1和卷II/2。
绝对是一套非常美丽的书。
3.微积分.卷1：作者Tom M.Apostol：一本非常全面的书，定理/证明方面很有系统，被一些高端的大学采用，当作第一年微积分课程的课本。
他对课题的覆盖度是惊人的，而且他提供了一些精选的经典的习题。
爆裂鼓手读后感英语作文
Whiplash, a film that has resonated with me deeply, is a testament to the relentless pursuit of perfection and the sacrifices one must make to achieve it. The story revolves around a young and talented drummer, Andrew Neiman, and his demanding and abusive instructor, Terence Fletcher. Their relationship forms the crux of the narrative, exploring the depths of obsession, the price of greatness, and the fine line between mentorship and tyranny.From the outset, Andrews passion for drumming is palpable. He is driven by a desire to be the best, to leave a mark on the world of jazz, much like his idol, Buddy Rich. This ambition is both his strength and his weakness. It propels him forward, but it also makes him susceptible to the harsh methods of Fletcher, who believes that only through pain and suffering can one reach true artistic heights.Fletchers character is a complex one. He is portrayed as a conductor with an almost messianic zeal for music, yet his methods are brutal and dehumanizing. He pushes Andrew to the brink of physical and emotional collapse, using fear, humiliation, and psychological manipulation to extract the best performance from him. This raises the question of whether the end justifies the means, and whether the pursuit of excellence can ever justify such extreme measures.As the story unfolds, Andrews journey becomes increasingly fraught with tension and conflict. He alienates his friends, neglects his studies, and even risks his health in his singleminded pursuit of perfection. The film does an excellent job of depicting the psychological toll this takes on him, showinghow the line between obsession and madness can become blurred.One of the most powerful scenes in the film is the climactic performance, where Andrew is pushed to his limits and beyond. The camera work and sound design in this scene are masterful, creating a sense of intensity and claustrophobia that mirrors Andrews own mental state. As he plays, bloodied and exhausted, it becomes clear that he has reached a point of no return. He has given everything to his art, and in doing so, has lost a part of himself.This is where the films title, Whiplash, comes into play. It refers not only to the physical act of drumming but also to the emotional and psychological toll that the pursuit of perfection takes on Andrew. The film suggests that the price of greatness is a heavy one, and that the road to it is paved with broken dreams and shattered lives.However, the film also offers a more nuanced perspective on this issue. It suggests that the pursuit of excellence can be a transformative and redemptive force, pushing individuals to achieve things they never thought possible. Andrews final performance, in which he rises above his previous failures and plays with a level of skill and passion that is truly aweinspiring, is a testament to this.In conclusion, Whiplash is a film that explores the complex and often fraught relationship between art, ambition, and the human spirit. It raises difficult questions about the nature of greatness and the sacrifices that must be made to achieve it. While it offers no easy answers, it provides acompelling and thoughtprovoking exploration of these themes, making it a film that will stay with me for a long time to come.。
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2 Model of Computation
I/O 1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 Ports 1,4 2,4 3,4 4,4 5,4 6,4 1,5 2,5 3,5 4,5 5,5 6,5 1,6 2,6 3,6 4,6 5,6 6,6
Figure 1: A 6x6 mesh with 6 I/O ports. We consider a model similar to those developed in the literature 1, 5, 6, 8] and which conforms to basic VLSI restrictions in Mead and Conway 13]. An nxn mesh?connected processor array with n I/O ports (see Figure 1) is used. We assume these processors are the ones in the rst row of the mesh. Each processor is connected only to its four immediate neighbors and has O(1) storage; that is, each processor has a constant number of registers. Each processor executes the same command, so it is a SIMD computer. This model is used for both algorithms given in the next two sections.
Abstract
1 Introduction
In graph analysis, it is often desirable to examine the cyclic structure of the given graph (see 2, 7, 9, 16] for applications). The most commonly used method is to generate a fundamental set of cycles. Let T be a spanning tree of a connected undirected graph G. The fundamental cycle set of G corresponding to T is the set of cycles (u; v; :::; u) of G, each consisting of one edge e(u; v) of G ? T together with the unique path (v; :::; u) in T (see Figure 4 for an example). It is known that any cycle C of G may be expressed as symmetric?di erence of one or more fundamental cycles of G 15]. There has been extensive work done on sequential algorithms for this problem 4, 14]. For parallel architectures, Levitt and Kautz 11] give an O(n3 ) algorithm on a two?dimensional cellular array for which parallelism doesn't buy us any speed-up. Also, Das et al. 3] give an O(n(logp + m=p)) algorithm (where p is the number of processors and m is the number of edges of the input graph) on a hypercube?connected model. Their algorithm is optimal when an appropriate number of processors is used. However, it uses O(m) storage in each processor and this makes the algorithm not suitable for easy VLSI implementation. In this paper, we give an O(n2 ) algorithm for this problem on an nxn mesh?connected SIMD processor array and we assume O(1) storage per processor. The same idea yields an O(n2 ) algorithm for generating the shortest paths between all pairs of a graph on the same model. A cutset S of a connected graph G is a minimal set of edges of G such that its removal from G disconnects G; that is, the graph G ? S is disconnected 17]. A spanning tree can also be used for nding a fundamental set of cutsets. Let T be a spanning tree of connected graph G. Let b be a branch of T . Removal of branch b disconnects T into exactly two components, T1 and T2 . Let V1 and
A preliminary version of this paper was presented in 6th International Conference on Computing and Information inห้องสมุดไป่ตู้May 94.
V2 , respectively, denote the vertex sets of T1 and T2 . The cut < V1 ; V2 > (that is, the minimal set of edges of G whose removal disconnects G into two graphs, G1 and G2 , which are induced subgraphs of G on the vertex sets V1 and V2 ) is a cutset of G. This cutset is known as the fundamental cutset of G with respect to the branch b of the spanning tree T of G. The set of all the n ? 1 fundamental cutsets with respect to the n ? 1 branches of a spanning tree T of a connected graph G is known as the fundamental set of cutsets of G with respect to the spanning tree T (e.g. Figure 5). The removal of a cutset S from a connected graph G destroys all the spanning trees of G. Cycles and cutsets of a graph
We present VLSI algorithms that run in O(n2 ) steps for nding (and reporting) a fundamental set of cycles and a fundamental set of cutsets of an undirected graph on an nxn mesh of processors (SIMD). Both algorithms are decomposable and run in O(n4 =k2) steps for a graph with n vertices when the size of the mesh-connected computer is kxk and k < n. An idea similar to the one used in nding a fundamental set of cycles of an undirected graph yields an O(n2 ) algorithm for generating shortest paths between all pairs of vertices of a graph on the same model. Keywords: VLSI algorithms, mesh-connected computers, parallel graph algorithms, fundamental set of cycles/cutsets.
VLSI Algorithms for Finding a Fundamental Set of Cycles and a Fundamental Set of Cutsets of a Graph
U. Dogrusoz and M. S. Krishnamoorthy Department of Computer Science Rensselaer Polytechnic Institute, Troy, New York 12180, USA E-mail : dogrusoz@, moorthy@