1.
Limerick
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Limerick is a city in county Limerick, Ireland. It is located in the Mid-West Region and is part of the province of Munster. Limerick City and County Council is the authority for the city. The city lies on the River Shannon, with the core of the city located on Kings Island, which is bounded by the Shannon. Limerick is also located at the head of the Shannon Estuary where the river widens before it flows into the Atlantic Ocean. With a population of 95,854, Limerick is the third most populous area in the state. There are 102,161 people living in the Limerick City Metropolitan District, on 1 June 2014 following the merger of Limerick City and County Council a new Metropolitan District of Limerick was formed within the united council which extended the city area. The Metropolitan District includes the city area and extends outwards towards Patrickswell in the west. The City Metropolitan Area however excludes city suburbs located within County Clare, when included this increases the overall city and metropolitan area by a further 5,000 with a combined total population of 107,161. Limerick is one of the constituent cities of the Cork–Limerick–Galway corridor which has a population of 1 million people and it is located at a strategic position on the River Shannon with four main crossing points near the city centre. To the south of the city is the Golden Vale, an area of rich pastureland, historically, much of the citys industry was based on this rich agricultural hinterland and it is particularly noted for Limerick Ham. Luimneach originally referred to the area along the banks of the Shannon Estuary known as Loch Luimnigh. The earliest settlement in the city, Inis Sibhtonn, was the name for Kings Island during the pre-Viking and Viking eras. This island was also called Inis an Ghaill Duibh, The Dark- Foreigners Island, the name is recorded in Viking sources as Hlymrekr. Antiquitys map-maker, Ptolemy, produced in 150 the earliest map of Ireland, history also records an important battle involving Cormac mac Airt in 221 and a visit by St. Patrick in 434 to baptise an Eóganachta king, Carthann the Fair. Saint Munchin, the first bishop of Limerick died in 652, in 812 the Vikings sailed up the Shannon and pillaged the city, burned the monastery of Mungret but were forced to flee when the Irish attacked and killed many of their number. The Normans redesigned the city in the 12th century and added much of the most notable architecture, such as King Johns Castle, one of the kingdoms most notable kings was Brian Boru, ancestor of the OBrien Clan of Dalcassians. The word Thomond is synonymous with the region and is retained in place such as Thomondgate
2.
International Symposium on Graph Drawing
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The Graph Drawing symposia have been central to the growth and development of graph drawing as a research area, as Herman et al. write, the Graph Drawing community grew around the yearly Symposia. In a 2003 study the symposium was among the top 30% of computer science research publication venues, the first symposium was held in Marino, near Rome, Italy, in 1992, organized by Giuseppe Di Battista, Peter Eades, Pierre Rosenstiehl, and Roberto Tamassia. The first two symposia did not publish proceedings, but reports are available online, since 1994, the proceedings of the symposia have been published by Springer-Verlags Lecture Notes in Computer Science series. Countries in which the conference has been held include Australia, Austria, Canada, the Czech Republic, France, Germany, Greece, Ireland, Italy, the list of computer science conferences contains other academic conferences in computer science. Graphdrawing. org, the web site of the conference series
3.
England
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England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west, the Irish Sea lies northwest of England and the Celtic Sea lies to the southwest. England is separated from continental Europe by the North Sea to the east, the country covers five-eighths of the island of Great Britain in its centre and south, and includes over 100 smaller islands such as the Isles of Scilly, and the Isle of Wight. England became a state in the 10th century, and since the Age of Discovery. The Industrial Revolution began in 18th-century England, transforming its society into the worlds first industrialised nation, Englands terrain mostly comprises low hills and plains, especially in central and southern England. However, there are uplands in the north and in the southwest, the capital is London, which is the largest metropolitan area in both the United Kingdom and the European Union. In 1801, Great Britain was united with the Kingdom of Ireland through another Act of Union to become the United Kingdom of Great Britain and Ireland. In 1922 the Irish Free State seceded from the United Kingdom, leading to the latter being renamed the United Kingdom of Great Britain, the name England is derived from the Old English name Englaland, which means land of the Angles. The Angles were one of the Germanic tribes that settled in Great Britain during the Early Middle Ages, the Angles came from the Angeln peninsula in the Bay of Kiel area of the Baltic Sea. The earliest recorded use of the term, as Engla londe, is in the ninth century translation into Old English of Bedes Ecclesiastical History of the English People. According to the Oxford English Dictionary, its spelling was first used in 1538. The earliest attested reference to the Angles occurs in the 1st-century work by Tacitus, Germania, the etymology of the tribal name itself is disputed by scholars, it has been suggested that it derives from the shape of the Angeln peninsula, an angular shape. An alternative name for England is Albion, the name Albion originally referred to the entire island of Great Britain. The nominally earliest record of the name appears in the Aristotelian Corpus, specifically the 4th century BC De Mundo, in it are two very large islands called Britannia, these are Albion and Ierne. But modern scholarly consensus ascribes De Mundo not to Aristotle but to Pseudo-Aristotle, the word Albion or insula Albionum has two possible origins. Albion is now applied to England in a poetic capacity. Another romantic name for England is Loegria, related to the Welsh word for England, Lloegr, the earliest known evidence of human presence in the area now known as England was that of Homo antecessor, dating to approximately 780,000 years ago. The oldest proto-human bones discovered in England date from 500,000 years ago, Modern humans are known to have inhabited the area during the Upper Paleolithic period, though permanent settlements were only established within the last 6,000 years
4.
Irvine, California
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Irvine is an affluent city in Orange County, California, United States. It is a city, the Irvine Company started developing the area in the 1960s. Formally incorporated on December 28,1971, the 66-square-mile city had a population of 212,375 as of the 2010 census, a number of corporations, particularly in the technology and semiconductor sectors, have their national or international headquarters in Irvine. The Gabrieleño indigenous group inhabited Irvine about 2,000 years ago, gaspar de Portolà, a Spanish explorer, came to the area in 1769, which led to the establishment of forts, missions and cattle herds. The King of Spain parceled out land for missions and private use, after Mexicos independence from Spain in 1821, the Mexican government secularized the missions and assumed control of the lands. It began distributing the land to Mexican citizens who applied for grants, three large Spanish/Mexican grants made up the land that later became the Irvine Ranch, Rancho Santiago de Santa Ana, Rancho San Joaquin and Rancho Lomas de Santiago. In 1864, Jose Andres Sepulveda, owner of Rancho San Joaquin sold 50,000 acres to Benjamin and Thomas Flint, Llewellyn Bixby, in 1866, Irvine, Flint and Bixby acquired 47, 000-acre Rancho Lomas de Santiago for $7,000. After the Mexican-American war the land of Rancho Santiago de Santa Ana fell prey to tangled titles, in 1868, the ranch was divided among four claimants as part of a lawsuit, Flint, Bixby and Irvine. The ranches were devoted to sheep grazing, however, in 1870, tenant farming was permitted. In 1878, James Irvine acquired his partners interests for $150,000 and his 110,000 acres stretched 23 miles from the Pacific Ocean to the Santa Ana River. The ranch was inherited by his son, James Irvine, Jr. who incorporated it into The Irvine Company, James, Jr. shifted the ranch operations to field crops, olive and citrus crops. In 1888, the Santa Fe Railroad extended its line to Fallbrook Junction, north of San Diego, the town that formed around this station was named Myford, after Irvines son, because a post office in Calaveras County already bore the family name. The town was renamed Irvine in 1914, by 1918,60,000 acres of lima beans were grown on the Irvine Ranch. Two Marine Corps facilities, MCAS El Toro and MCAS Tustin, were built during World War II on ranch land sold to the government, James Irvine, Jr. died in 1947 at the age of 80. His son, Myford, assumed the presidency of The Irvine Company and he began opening small sections of the Irvine Ranch to urban development. The Irvine Ranch played host to the Boy Scouts of Americas 1953 National Scout Jamboree, Jamboree Road, a major street which now stretches from Newport Beach to the city of Orange, was named in honor of this event. David Sills, then a young Boy Scout from Peoria, Illinois, was among the attendees at the 1953 Jamboree, Sills came back to Irvine as an adult and went on to serve four terms as the citys mayor. The same year, the University of California asked The Irvine Company for 1,000 acres for a new university campus, the Irvine Company sold the requested land for $1 and later the state purchased an additional 500 acres
5.
Stanford University
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Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California, adjacent to Palo Alto and between San Jose and San Francisco. Its 8, 180-acre campus is one of the largest in the United States, Stanford also has land and facilities elsewhere. The university was founded in 1885 by Leland and Jane Stanford in memory of their only child, Stanford was a former Governor of California and U. S. Senator, he made his fortune as a railroad tycoon. The school admitted its first students 125 years ago on October 1,1891, Stanford University struggled financially after Leland Stanfords death in 1893 and again after much of the campus was damaged by the 1906 San Francisco earthquake. Following World War II, Provost Frederick Terman supported faculty and graduates entrepreneurialism to build self-sufficient local industry in what would later be known as Silicon Valley. The university is one of the top fundraising institutions in the country. There are three schools that have both undergraduate and graduate students and another four professional schools. Students compete in 36 varsity sports, and the university is one of two institutions in the Division I FBS Pac-12 Conference. Stanford faculty and alumni have founded a number of companies that produce more than $2.7 trillion in annual revenue. It is the alma mater of 30 living billionaires,17 astronauts and it is also one of the leading producers of members of the United States Congress. Sixty Nobel laureates and seven Fields Medalists have been affiliated with Stanford as students, alumni, Stanford University was founded in 1885 by Leland and Jane Stanford, dedicated to Leland Stanford Jr, their only child. The institution opened in 1891 on Stanfords previous Palo Alto farm, despite being impacted by earthquakes in both 1906 and 1989, the campus was rebuilt each time. In 1919, The Hoover Institution on War, Revolution and Peace was started by Herbert Hoover to preserve artifacts related to World War I, the Stanford Medical Center, completed in 1959, is a teaching hospital with over 800 beds. The SLAC National Accelerator Laboratory, which was established in 1962, in 2008, 60% of this land remained undeveloped. Besides the central campus described below, the university also operates at more remote locations, some elsewhere on the main campus. Stanfords main campus includes a place within unincorporated Santa Clara County. The campus also includes land in unincorporated San Mateo County, as well as in the city limits of Menlo Park, Woodside. The academic central campus is adjacent to Palo Alto, bounded by El Camino Real, Stanford Avenue, Junipero Serra Boulevard, the United States Postal Service has assigned it two ZIP codes,94305 for campus mail and 94309 for P. O. box mail
6.
Columbia University
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Columbia University is a private Ivy League research university in Upper Manhattan, New York City. It was established in 1754 as Kings College by royal charter of George II of Great Britain, after the American Revolutionary War, Kings College briefly became a state entity, and was renamed Columbia College in 1784. Columbia is one of the fourteen founding members of the Association of American Universities and was the first school in the United States to grant the M. D. degree. The university also has global research outposts in Amman, Beijing, Istanbul, Paris, Mumbai, Rio de Janeiro, Santiago, Asunción, Columbia administers annually the Pulitzer Prize. Additionally,100 Nobel laureates have been affiliated with Columbia as students, researchers, faculty, Columbia is second only to Harvard University in the number of Nobel Prize-winning affiliates, with over 100 recipients of the award as of 2016. In 1746 an act was passed by the assembly of New York to raise funds for the foundation of a new college. Classes were initially held in July 1754 and were presided over by the colleges first president, Dr. Johnson was the only instructor of the colleges first class, which consisted of a mere eight students. Instruction was held in a new schoolhouse adjoining Trinity Church, located on what is now lower Broadway in Manhattan, in 1763, Dr. Johnson was succeeded in the presidency by Myles Cooper, a graduate of The Queens College, Oxford, and an ardent Tory. In the charged political climate of the American Revolution, his opponent in discussions at the college was an undergraduate of the class of 1777. The suspension continued through the occupation of New York City by British troops until their departure in 1783. The colleges library was looted and its sole building requisitioned for use as a hospital first by American. Loyalists were forced to abandon their Kings College in New York, the Loyalists, led by Bishop Charles Inglis fled to Windsor, Nova Scotia, where they founded Kings Collegiate School. After the Revolution, the college turned to the State of New York in order to restore its vitality, the Legislature agreed to assist the college, and on May 1,1784, it passed an Act for granting certain privileges to the College heretofore called Kings College. The Regents finally became aware of the colleges defective constitution in February 1787 and appointed a revision committee, in April of that same year, a new charter was adopted for the college, still in use today, granting power to a private board of 24 Trustees. On May 21,1787, William Samuel Johnson, the son of Dr. Samuel Johnson, was unanimously elected President of Columbia College, prior to serving at the university, Johnson had participated in the First Continental Congress and been chosen as a delegate to the Constitutional Convention. The colleges enrollment, structure, and academics stagnated for the majority of the 19th century, with many of the college presidents doing little to change the way that the college functioned. In 1857, the college moved from the Kings College campus at Park Place to a primarily Gothic Revival campus on 49th Street and Madison Avenue, during the last half of the 19th century, under the leadership of President F. A. P. Barnard, the institution assumed the shape of a modern university
7.
Graph theory
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In mathematics graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices, nodes, or points which are connected by edges, arcs, Graphs are one of the prime objects of study in discrete mathematics. Refer to the glossary of graph theory for basic definitions in graph theory, the following are some of the more basic ways of defining graphs and related mathematical structures. To avoid ambiguity, this type of graph may be described precisely as undirected, other senses of graph stem from different conceptions of the edge set. In one more generalized notion, V is a set together with a relation of incidence that associates with each two vertices. In another generalized notion, E is a multiset of unordered pairs of vertices, Many authors call this type of object a multigraph or pseudograph. All of these variants and others are described more fully below, the vertices belonging to an edge are called the ends or end vertices of the edge. A vertex may exist in a graph and not belong to an edge, V and E are usually taken to be finite, and many of the well-known results are not true for infinite graphs because many of the arguments fail in the infinite case. The order of a graph is |V|, its number of vertices, the size of a graph is |E|, its number of edges. The degree or valency of a vertex is the number of edges that connect to it, for an edge, graph theorists usually use the somewhat shorter notation xy. Graphs can be used to model many types of relations and processes in physical, biological, social, Many practical problems can be represented by graphs. Emphasizing their application to real-world systems, the network is sometimes defined to mean a graph in which attributes are associated with the nodes and/or edges. In computer science, graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, etc. For instance, the structure of a website can be represented by a directed graph, in which the vertices represent web pages. A similar approach can be taken to problems in media, travel, biology, computer chip design. The development of algorithms to handle graphs is therefore of major interest in computer science, the transformation of graphs is often formalized and represented by graph rewrite systems. Graph-theoretic methods, in forms, have proven particularly useful in linguistics. Traditionally, syntax and compositional semantics follow tree-based structures, whose power lies in the principle of compositionality
8.
Computer science
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Computer science is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. An alternate, more succinct definition of science is the study of automating algorithmic processes that scale. A computer scientist specializes in the theory of computation and the design of computational systems and its fields can be divided into a variety of theoretical and practical disciplines. Some fields, such as computational complexity theory, are highly abstract, other fields still focus on challenges in implementing computation. Human–computer interaction considers the challenges in making computers and computations useful, usable, the earliest foundations of what would become computer science predate the invention of the modern digital computer. Machines for calculating fixed numerical tasks such as the abacus have existed since antiquity, further, algorithms for performing computations have existed since antiquity, even before the development of sophisticated computing equipment. Wilhelm Schickard designed and constructed the first working mechanical calculator in 1623, in 1673, Gottfried Leibniz demonstrated a digital mechanical calculator, called the Stepped Reckoner. He may be considered the first computer scientist and information theorist, for, among other reasons and he started developing this machine in 1834, and in less than two years, he had sketched out many of the salient features of the modern computer. A crucial step was the adoption of a card system derived from the Jacquard loom making it infinitely programmable. Around 1885, Herman Hollerith invented the tabulator, which used punched cards to process statistical information, when the machine was finished, some hailed it as Babbages dream come true. During the 1940s, as new and more powerful computing machines were developed, as it became clear that computers could be used for more than just mathematical calculations, the field of computer science broadened to study computation in general. Computer science began to be established as an academic discipline in the 1950s. The worlds first computer science program, the Cambridge Diploma in Computer Science. The first computer science program in the United States was formed at Purdue University in 1962. Since practical computers became available, many applications of computing have become distinct areas of study in their own rights and it is the now well-known IBM brand that formed part of the computer science revolution during this time. IBM released the IBM704 and later the IBM709 computers, still, working with the IBM was frustrating if you had misplaced as much as one letter in one instruction, the program would crash, and you would have to start the whole process over again. During the late 1950s, the science discipline was very much in its developmental stages. Time has seen significant improvements in the usability and effectiveness of computing technology, modern society has seen a significant shift in the users of computer technology, from usage only by experts and professionals, to a near-ubiquitous user base
9.
University of California, Irvine
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The University of California, Irvine, is a public research university located in Irvine, California, United States, and one of the 10 campuses in the University of California system. UC Irvine offers 80 undergraduate degrees and 98 graduate and professional degrees, UC Irvine became a member of the Association of American Universities in 1996, and is the youngest university to hold membership. UC Irvine set up the first Earth System Science Department in the United States, UCI was one of three new UC campuses established in the 1960s to accommodate growing enrollments across the UC system. A site in Orange County was identified in 1959, and in the year the Irvine Company sold the University of California 1,000 acres of land for one dollar to establish the new campus. President Lyndon B. Johnson dedicated the campus in 1964, the UC Irvine Anteaters compete in 18 mens and womens sports in the NCAA Division I as members of the Big West Conference and the Mountain Pacific Sports Federation. The Anteaters have won 28 national championships in nine different team sports,64 Anteaters have won national championships. One of the new campuses was to be in the Los Angeles area, the location selected was Irvine Ranch, an area of agricultural land bisecting Orange County from north to south. Unlike most other University of California campuses, UCI was not named for the city it was built in, at the time of the universitys founding, the name Irvine is a reference to James Irvine, a landowner who administered the 94, 000-acre Irvine Ranch. In 1960, The Irvine Company sold 1,000 acres of the Irvine Ranch to the University of California for one dollar, the University purchased an additional 510 acres in 1964 for housing and commercial developments. Much of the land that was not purchased by UCI is now held under The Irvine Company, during this time, the University also hired William Pereira and Associates as the Master Planner of the Irvine Ranch area. Pereira intended for the UC Irvine campus to complement the community. Soon after UC Irvine opened in 1965, the City of Irvine became incorporated and established in 1971 and 1975, respectively. The College of Arts, Letters, and Science was composed of twenty majors in five Divisions, Biological Sciences, Fine Arts, Humanities, Physical Sciences, and Social Sciences. However, many of UCIs buildings were still under construction and landscaping was still in progress, with the campus only at 75% completion. By June 25,1966, UCI held its first Commencement with fourteen students, in 1965 the California College of Medicine became part of UC Irvine. In 1976, plans to establish a hospital were set aside, with the university instead purchasing the Orange County Medical Center around 12 miles from UC Irvine. As the second largest employer in Orange County, UCI contributes an annual impact of $5 billion. There are 87 undergraduate degree programs,59 masters and 46 Ph. D. programs, in June 2014, President Barack Obama gave the commencement speech for UC Irvine’s graduating class
10.
Thesis
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A thesis or dissertation is a document submitted in support of candidature for an academic degree or professional qualification presenting the authors research and findings. In some contexts, the thesis or a cognate is used for part of a bachelors or masters course, while dissertation is normally applied to a doctorate, while in other contexts. The term graduate thesis is used to refer to both masters theses and doctoral dissertations. The required complexity or quality of research of a thesis or dissertation can vary by country, university, or program, the word dissertation can at times be used to describe a treatise without relation to obtaining an academic degree. The term thesis is used to refer to the general claim of an essay or similar work. The term thesis comes from the Greek θέσις, meaning something put forth, Dissertation comes from the Latin dissertātiō, meaning path. A thesis may be arranged as a thesis by publication or a monograph, with or without appended papers, an ordinary monograph has a title page, an abstract, a table of contents, comprising the various chapters, and a bibliography or a references section. They differ in their structure in accordance with the different areas of study. In a thesis by publication, the chapters constitute an introductory, Dissertations normally report on a research project or study, or an extended analysis of a topic. The structure of the thesis or dissertation explains the purpose, the research literature which impinges on the topic of the study, the methods used. Degree-awarding institutions often define their own style that candidates have to follow when preparing a thesis document. Other applicable international standards include ISO2145 on section numbers, ISO690 on bibliographic references, some older house styles specify that front matter uses a separate page-number sequence from the main text, using Roman numerals. They therefore avoid the traditional separate number sequence for front matter, however, strict standards are not always required. Most Italian universities, for example, have only general requirements on the size and the page formatting. A thesis or dissertation committee is a committee that supervises a students dissertation, the committee members are doctors in their field and have the task of reading the dissertation, making suggestions for changes and improvements, and sitting in on the defense. Sometimes, at least one member of the committee must be a professor in a department that is different from that of the student, all the dissertation referees must already have achieved at least the academic degree that the candidate is trying to reach. At English-speaking Canadian universities, writings presented in fulfillment of undergraduate coursework requirements are normally called papers, a longer paper or essay presented for completion of a 4-year bachelors degree is sometimes called a major paper. High-quality research papers presented as the study of a postgraduate consecutive bachelor with Honours or Baccalaureatus Cum Honore degree are called thesis
11.
Zvi Galil
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Zvi Galil is an Israeli computer scientist and mathematician. He is the dean of the Georgia Institute of Technology College of Computing and his research interests include the design and analysis of algorithms, computational complexity and cryptography. He has been credited with coining the terms stringology and sparsification and he has published over 170 scientific papers and is listed as an ISI highly cited researcher. Zvi Galil was born in Tel Aviv in 1947 and he completed both his B. Sc. and his M. Sc. in Applied Mathematics at Tel Aviv University before earning his Ph. D. in Computer Science at Cornell in 1975 under the supervision of John Hopcroft. He then spent a working as a post-doctorate researcher at IBMs Thomas J. Watson Research Center in Yorktown Heights. From 1976 until 1995 he worked in the science department of Tel Aviv University. In 1982 he joined the faculty of Columbia University, serving as the chair of the Computer Science Department from 1989-1994, from 1995-2007, he served as the dean of the Fu Foundation School of Engineering & Applied Science. In this position he oversaw the renaming of the school in honor of Chinese businessman Z. Y, Fu after a large donation was given in his name. At Columbia, he was appointed the Julian Clarence Levi Professor of Mathematical Methods and Computer Science in 1987, from 1983 to 1987, Galil served as the chairman of ACM SIGACT, an organization that promotes research in theoretical computer science. Galil served as the President of Tel Aviv University starting in 2007 and he was named as the dean of Georgia Techs College of Computing on April 9,2010. Galils research is in the areas of algorithms, particularly string and graph algorithms, complexity, cryptography, among his most highly cited work are the following, Gabber, O. Galil, Z. Journal of Computer and System Sciences, gabow, H. N. Galil, Z. Spencer, T. Tarjan, R. E. Efficient algorithms for finding minimum spanning trees in undirected and directed graphs. Efficient algorithms for finding maximum matching in graphs, an improved algorithm for approximate string matching. Proceedings of 16th International Colloquium on Automata, Languages and Programming, in 2005 he was selected as a Fellow of the American Academy of Arts and Sciences. In 2009 the Columbia Society of Graduates awarded him the Great Teacher Award, in 2012, The University of Waterloo awarded Galil with an honorary Doctor of Mathematics degree for his fundamental contributions in the areas of graph algorithms and string matching
12.
Mathematician
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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, the number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was All is number. It was the Pythagoreans who coined the term mathematics, and with whom the study of mathematics for its own sake begins, the first woman mathematician recorded by history was Hypatia of Alexandria. She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems
13.
ACM Fellow
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ACM Fellowship is an award and fellowship that recognises outstanding members of the Association for Computing Machinery. New fellows are elected annually since 1993, as of 2016 examples of ACM Fellows include Vint Cerf, Anne Condon and Serge Abiteboul. See also the List of Fellows of the Association for Computing Machinery and Category, some fellows use the post-nominal letters FACM
14.
Santa Barbara, California
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Santa Barbara is the county seat of Santa Barbara County in the U. S. state of California. Situated on a section of coastline, the longest such section on the West Coast of the United States. Santa Barbaras climate is described as Mediterranean, and the city has been promoted as the American Riviera. The population of the county in 2010 was 423,895. In 2004, the sector accounted for fully 35% of local employment. Education in particular is well represented, with four institutions of learning on the south coast. The Santa Barbara Airport serves the city, as does Amtrak, U. S. Highway 101 connects the Santa Barbara area with Los Angeles to the southeast and San Francisco to the northwest. Behind the city, in and beyond the Santa Ynez Mountains, is the Los Padres National Forest, Channel Islands National Park and Channel Islands National Marine Sanctuary are located approximately 20 miles offshore. Evidence of human habitation of the area begins at least 13,000 years ago, an estimated 8,000 to 10,000 Chumash lived on the south coast of Santa Barbara County at the time of the first European explorations. Five Chumash villages flourished in the area, portuguese explorer João Cabrilho, sailing for the Kingdom of Spain, sailed through what is now called the Santa Barbara Channel in 1542, anchoring briefly in the area. In 1602, Spanish maritime explorer Sebastián Vizcaíno gave the name Santa Barbara to the channel, a land expedition led by Gaspar de Portolà visited in 1769, and Franciscan missionary Juan Crespi, who accompanied the expedition, named a large native town Laguna de la Concepcion. Cabrillos earlier name, however, is the one that has survived, the first permanent European residents were Spanish missionaries and soldiers under Felipe de Neve, who came in 1782 to build the Presidio. They were sent both to fortify the region against expansion by other such as England and Russia. Many of the Spaniards brought their families with them, and those formed the nucleus of the small town – at first just a cluster of adobes – that surrounded the Presidio, the Santa Barbara Mission was established on the Feast of Saint Barbara, December 4,1786. It was the tenth of the California Missions to be founded by the Spanish Franciscans and it was dedicated by Padre Fermín Lasuén, who succeeded Padre Junipero Serra as the second president and founder of the California Franciscan Mission Chain. The Mission fathers began the work of converting the native Chumash to Christianity. The Chumash laborers built a connection between the creek and the Santa Barbara Mission water system through the use of a dam. During the following decades, many of the natives died of such as smallpox
15.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
16.
Latin
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Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets, Latin was originally spoken in Latium, in the Italian Peninsula. Through the power of the Roman Republic, it became the dominant language, Vulgar Latin developed into the Romance languages, such as Italian, Portuguese, Spanish, French, and Romanian. Latin, Italian and French have contributed many words to the English language, Latin and Ancient Greek roots are used in theology, biology, and medicine. By the late Roman Republic, Old Latin had been standardised into Classical Latin, Vulgar Latin was the colloquial form spoken during the same time and attested in inscriptions and the works of comic playwrights like Plautus and Terence. Late Latin is the language from the 3rd century. Later, Early Modern Latin and Modern Latin evolved, Latin was used as the language of international communication, scholarship, and science until well into the 18th century, when it began to be supplanted by vernaculars. Ecclesiastical Latin remains the language of the Holy See and the Roman Rite of the Catholic Church. Today, many students, scholars and members of the Catholic clergy speak Latin fluently and it is taught in primary, secondary and postsecondary educational institutions around the world. The language has been passed down through various forms, some inscriptions have been published in an internationally agreed, monumental, multivolume series, the Corpus Inscriptionum Latinarum. Authors and publishers vary, but the format is about the same, volumes detailing inscriptions with a critical apparatus stating the provenance, the reading and interpretation of these inscriptions is the subject matter of the field of epigraphy. The works of several hundred ancient authors who wrote in Latin have survived in whole or in part and they are in part the subject matter of the field of classics. The Cat in the Hat, and a book of fairy tales, additional resources include phrasebooks and resources for rendering everyday phrases and concepts into Latin, such as Meissners Latin Phrasebook. The Latin influence in English has been significant at all stages of its insular development. From the 16th to the 18th centuries, English writers cobbled together huge numbers of new words from Latin and Greek words, dubbed inkhorn terms, as if they had spilled from a pot of ink. Many of these words were used once by the author and then forgotten, many of the most common polysyllabic English words are of Latin origin through the medium of Old French. Romance words make respectively 59%, 20% and 14% of English, German and those figures can rise dramatically when only non-compound and non-derived words are included. Accordingly, Romance words make roughly 35% of the vocabulary of Dutch, Roman engineering had the same effect on scientific terminology as a whole
17.
Bachelor of Science
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A Bachelor of Science is an undergraduate academic degree awarded for completed courses that generally last three to five years. Whether a student of a subject is awarded a Bachelor of Science degree or a Bachelor of Arts degree can vary between universities. For one example, a degree may be given as a Bachelor of Arts by one university but as a B. Sc. by another. Some liberal arts colleges in the United States offer only the BA, even in the natural sciences, in both instances, there are historical and traditional reasons. Northwestern Universitys School of Communication grants B. Sc. degrees in all of its programs of study, including theater, dance, the first university to admit a student to the degree of Bachelor of Science was the University of London in 1860. Prior to this, science subjects were included in the B. A. bracket, notably in the cases of mathematics, physics, physiology, in Argentina and Chile, most university degrees are given as a license in a field or discipline. For instance, besides the courses, biochemistry and biology require 1–2 years hands-on training either in a clinical laboratory plus a final exam or in a research laboratory plus a thesis defense. The degrees are term licenses in the field of study or profession i. e. biology, nutrition, physical therapy or kinesiology, etc. However, a masters degree requires 2-3 more years of specific training, engineering and medical degrees are also different and are six-year programs of specific classes and training starting immediately after high school. No intermediate degrees count towards the admission examination or even exist, medical degrees are complemented with a 3–4 years of hospital residence plus 1–2 years of specialization training. In Australia, the B. Sc. is generally a three-four year degree, an honours year or a Master of Science is required to progress on to the Doctor of Philosophy. In New Zealand, in cases, the honours degree comprises an additional postgraduate qualification. In South Africa, the B. Sc. is taken three years, while the postgraduate B. Sc. Entails an additional year of study, admission to the honours degree is on the basis of a sufficiently high average in the B. Sc. major, an honours degree is required for M. Sc. Level study, and admission to a doctorate is via the M. Sc, commonly in British Commonwealth countries and Ireland graduands are admitted to the degree of Bachelor of Science after having completed a programme in one or more of the sciences. These programmes may take different lengths of time to complete, note that in British English, no full stops are used in the title, hence BSc, not B. Sc. A Bachelor of Science receives the designation BSc or BS for a major/pass degree, in England, Wales and Northern Ireland an honours degree is typically completed over a three-year period, though there are a few intensified two-year courses. Bachelors degrees were typically completed in two years for most of the twentieth century, in Scotland, where access to university is possible after one less year of secondary education, degree courses have a foundation year making the total course length four years
18.
Doctor of Philosophy
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A Doctor of Philosophy is a type of doctoral degree awarded by universities in many countries. Ph. D. s are awarded for a range of programs in the sciences, engineering. The Ph. D. is a degree in many fields. The completion of a Ph. D. is often a requirement for employment as a university professor, researcher, individuals with an earned doctorate can use the title of Doctor with their name and use the post-nominal letters Ph. D. The requirements to earn a Ph. D. degree vary considerably according to the country, institution, a person who attains a doctorate of philosophy is automatically awarded the academic title of doctor. A student attaining this level may be granted a Candidate of Philosophy degree at some institutions. A Ph. D. candidate must submit a project, thesis or dissertation often consisting of a body of academic research. In many countries, a candidate must defend this work before a panel of examiners appointed by the university. Universities award other types of doctorates besides the Ph. D. such as the Doctor of Musical Arts, a degree for music performers and the Doctor of Education, in 2016, ELIA launched The Florence Principles on the Doctorate in the Arts. The Florence Principles have been endorsed are supported also by AEC, CILECT, CUMULUS, the degree is abbreviated PhD, from the Latin Philosophiae Doctor, pronounced as three separate letters. In the universities of Medieval Europe, study was organized in four faculties, the faculty of arts. All of these faculties awarded intermediate degrees and final degrees, the doctorates in the higher faculties were quite different from the current Ph. D. degree in that they were awarded for advanced scholarship, not original research. No dissertation or original work was required, only lengthy residency requirements, besides these degrees, there was the licentiate. According to Keith Allan Noble, the first doctoral degree was awarded in medieval Paris around 1150, the doctorate of philosophy developed in Germany as the terminal Teachers credential in the 17th century. Typically, upon completion, the candidate undergoes an oral examination, always public, starting in 2016, in Ukraine Doctor of Philosophy is the highest education level and the first science degree. PhD is awarded in recognition of a contribution to scientific knowledge. A PhD degree is a prerequisite for heading a university department in Ukraine, upon completion of a PhD, a PhD holder can elect to continue his studies and get a post-doctoral degree called Doctor of Sciences, which is the second and the highest science degree in Ukraine. Scandinavian countries were among the early adopters of a known as a doctorate of philosophy
19.
Xerox
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Xerox Corporation /ˈzɪərɒks/ is an American global corporation that sells document solutions and services, and document technology products in more than 160 countries. Xerox is headquartered in Norwalk, Connecticut, though its largest population of employees is based around Rochester, New York, the company purchased Affiliated Computer Services for $6.4 billion in early 2010. As a large developed company, it is placed in the list of Fortune 500 companies. Xerox completed the separation of Conduent Incorporated effective on Dec.31,2016, creating two market-leading, publicly- traded companies. In connection with the spin-off, Xerox received a transfer from Conduent of $1.8 billion. Xerox continues to trade on the NYSE under the ticker symbol “XRX”, researchers at Xerox and its Palo Alto Research Center invented several important elements of personal computing, such as the desktop metaphor GUI, the computer mouse and desktop computing. These concepts were frowned upon by the board of directors. The concepts were adopted by Apple and, later, Microsoft, with the help of these innovations, Apple and Microsoft came to dominate the personal computing revolution of the 1980s, whereas Xerox was not a major player. Xerox was founded in 1906 in Rochester as The Haloid Photographic Company, in 1938 Chester Carlson, a physicist working independently, invented a process for printing images using an electrically charged photoconductor-coated metal plate and dry powder toner. However, it would more than 20 years of refinement before the first automated machine to make copies was commercialized, using a document feeder, scanning light. Wilson, credited as the founder of Xerox, took over Haloid from his father and he saw the promise of Carlsons invention and, in 1946, signed an agreement to develop it as a commercial product. Wilson remained as President/CEO of Xerox until 1967 and served as Chairman until his death in 1971, looking for a term to differentiate its new system, Haloid coined the term Xerography from two Greek roots meaning dry writing. Haloid subsequently changed its name to Haloid Xerox in 1958 and then Xerox Corporation in 1961, before releasing the 914, Xerox tested the market by introducing a developed version of the prototype hand-operated equipment known as the Flat-plate 1385. The 1385 was not actually a viable copier because of its speed of operation and it was little more than a high quality, commercially available plate camera mounted as a horizontal rostrum camera, complete with photo-flood lighting and timer. The glass film/plate had been replaced with an aluminum plate. Clever electrics turned this into a developing and reusable substitute for film. A skilled user could produce fast, paper and metal printing plates of a higher quality than almost any other method, having started as a supplier to the offset lithography duplicating industry, Xerox now set its sights on capturing some of offsets market share. The 1385 was followed by the first automatic xerographic printer, the Copyflo, the Copyflo was a large microfilm printer which could produce positive prints on roll paper from any type of microfilm negative
20.
PARC (company)
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PARC, formerly Xerox PARC, is a research and development company in Palo Alto, California, with a distinguished reputation for its contributions to information technology and hardware systems. Xerox formed Palo Alto Research Center Incorporated as an owned subsidiary in 2002. Pake selected Palo Alto, California, as the site of what was to become known as PARC. S, the integration of Ethernet prompted the development of the PARC Universal Packet architecture, much like todays Internet. Xerox has been criticized for failing to properly commercialize and profitably exploit PARCs innovations. A favorite example is the user interface, initially developed at PARC for the Alto. Although very significant in terms of its influence on future system design, a small group from PARC led by David Liddle and Charles Irby formed Metaphor Computer Systems. They extended the Star desktop concept into a graphic and communicating office-automation model. Among PARCs distinguished researchers were three Turing Award winners, Butler W. Lampson, Alan Kay, and Charles P. Thacker. The Association for Computing Machinery Software System Award recognized the Alto system in 1984, Smalltalk in 1987, InterLisp in 1992, and the remote procedure call in 1994. Lampson, Kay, Bob Taylor, and Charles P. Thacker received the National Academy of Engineerings prestigious Charles Stark Draper Prize in 2004 for their work on the Alto, PARCs developments in information technology served for a long time as standards for much of the computing industry. Many advances were not equalled or surpassed for two decades, enormous timespans in the fast-paced high-tech world, a number of GUI engineers left to join Apple Computer. Work at PARC since the early 1980s includes advances in computing, aspect-oriented programming. Xerox Daybreak GlobalView Michael A. Hiltzik, Dealers of Lightning, Xerox PARC, alexander, Fumbling the Future, How Xerox Invented, Then Ignored, the First Personal Computer ISBN 1-58348-266-0 M. Mitchell Waldrop, The Dream Machine, J. C. R. Strassmann Charles Babbage Institute, University of Minnesota, Minneapolis Oral history interview with William Crowther Charles Babbage Institute, University of Minnesota, Minneapolis
21.
Minimum spanning tree
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That is, it is a spanning tree whose sum of edge weights is as small as possible. More generally, any undirected graph has a spanning forest. There are quite a few use cases for minimum spanning trees, one example would be a telecommunications company which is trying to lay out cables in new neighborhood. If it is constrained to bury the cable only along certain paths, some of those paths might be more expensive, because they are longer, or require the cable to be buried deeper, these paths would be represented by edges with larger weights. Currency is a unit for edge weight – there is no requirement for edge lengths to obey normal rules of geometry such as the triangle inequality. A spanning tree for that graph would be a subset of paths that has no cycles but still connects to every house. A minimum spanning tree would be one with the lowest total cost, if there are n vertices in the graph, then each spanning tree has n −1 edges. There may be several spanning trees of the same weight, in particular, if all the edge weights of a given graph are the same. If each edge has a distinct weight then there will be only one and this is true in many realistic situations, such as the telecommunications company example above, where its unlikely any two paths have exactly the same cost. This generalizes to spanning forests as well, proof, Assume the contrary, that there are two different MSTs A and B. Since A and B differ despite containing the same nodes, there is at least one edge that belongs to one, among such edges, let e1 be the one with least weight, this choice is unique because the edge weights are all distinct. Without loss of generality, assume e1 is in A, as B is a MST, ∪ B must contain a cycle C. As a tree, A contains no cycles, therefore C must have an edge e2 that is not in A. Since e1 was chosen as the unique lowest-weight edge among those belonging to one of A and B. Replacing e2 with e1 in B therefore yields a spanning tree with a smaller weight and this contradicts the assumption that B is a MST. More generally, if the weights are not all distinct then only the set of weights in minimum spanning trees is certain to be unique. If the weights are positive, then a minimum spanning tree is in fact a minimum-cost subgraph connecting all vertices, since subgraphs containing cycles necessarily have more total weight. For any cycle C in the graph, if the weight of an edge e of C is larger than the weights of all other edges of C
22.
Shortest path problem
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In graph theory, the shortest path problem is the problem of finding a path between two vertices in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a map may be modeled by a special case of the shortest path problem in graphs. The shortest path problem can be defined for graphs whether undirected, directed and it is defined here for undirected graphs, for directed graphs the definition of path requires that consecutive vertices be connected by an appropriate directed edge. Two vertices are adjacent when they are incident to a common edge. A path in a graph is a sequence of vertices P = ∈ V × V × ⋯ × V such that v i is adjacent to v i +1 for 1 ≤ i < n. Such a path P is called a path of length n −1 from v 1 to v n, let e i, j be the edge incident to both v i and v j. When each edge in the graph has unit weight or f, E →, the single-destination shortest path problem, in which we have to find shortest paths from all vertices in the directed graph to a single destination vertex v. This can be reduced to the single-source shortest path problem by reversing the arcs in the directed graph, the all-pairs shortest path problem, in which we have to find shortest paths between every pair of vertices v, v in the graph. These generalizations have significantly more efficient algorithms than the approach of running a single-pair shortest path algorithm on all relevant pairs of vertices. The most important algorithms for solving this problem are, Dijkstras algorithm solves the single-source shortest path problem, bellman–Ford algorithm solves the single-source problem if edge weights may be negative. A* search algorithm solves for single pair shortest path using heuristics to try to speed up the search, Floyd–Warshall algorithm solves all pairs shortest paths. Johnsons algorithm solves all pairs shortest paths, and may be faster than Floyd–Warshall on sparse graphs, viterbi algorithm solves the shortest stochastic path problem with an additional probabilistic weight on each node. Additional algorithms and associated evaluations may be found in Cherkassky, Goldberg & Radzik, an algorithm using topological sorting can solve the single-source shortest path problem in linear time, Θ, in weighted DAGs. The following table is taken from Schrijver, a green background indicates an asymptotically best bound in the table. The all-pairs shortest path problem finds the shortest paths between every pair of v, v in the graph. Shortest path algorithms are applied to find directions between physical locations, such as driving directions on web mapping websites like MapQuest or Google Maps. For this application fast specialized algorithms are available, in a networking or telecommunications mindset, this shortest path problem is sometimes called the min-delay path problem and usually tied with a widest path problem. For example, the algorithm may seek the shortest widest path, a more lighthearted application is the games of six degrees of separation that try to find the shortest path in graphs like movie stars appearing in the same film
23.
Graph (abstract data type)
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In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from mathematics. These pairs are known as edges, arcs, or lines for a graph and as arrows, directed edges, directed arcs. The vertices may be part of the structure, or may be external entities represented by integer indices or references. A graph data structure may also associate to each edge some edge value and this data structure allows the storage of additional data on the vertices. Additional data can be stored if edges are stored as objects, in which case each vertex stores its incident edges. Adjacency matrix A two-dimensional matrix, in which the rows represent source vertices, data on edges and vertices must be stored externally. Only the cost for one edge can be stored between each pair of vertices, incidence matrix A two-dimensional Boolean matrix, in which the rows represent the vertices and columns represent the edges. The entries indicate whether the vertex at a row is incident to the edge at a column. The following table gives the time complexity cost of performing operations on graphs, for each of these representations, with |V | the number of vertices. In the matrix representations, the entries encode the cost of following an edge, the cost of edges that are not present are assumed to be ∞. Adjacency lists are generally preferred because they efficiently represent sparse graphs. a, boost Networkx, a Python graph library Graphs Tutorial by Jebril FILALI
24.
Graph coloring
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In graph theory, graph coloring is a special case of graph labeling, it is an assignment of labels traditionally called colors to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a such that no two adjacent vertices share the same color, this is called a vertex coloring. Vertex coloring is the point of the subject, and other coloring problems can be transformed into a vertex version. For example, a coloring of a graph is just a vertex coloring of its line graph. However, non-vertex coloring problems are often stated and studied as is and that is partly for perspective, and partly because some problems are best studied in non-vertex form, as for instance is edge coloring. The convention of using colors originates from coloring the countries of a map and this was generalized to coloring the faces of a graph embedded in the plane. By planar duality it became coloring the vertices, and in form it generalizes to all graphs. In mathematical and computer representations, it is typical to use the first few positive or nonnegative integers as the colors, in general, one can use any finite set as the color set. The nature of the coloring problem depends on the number of colors, graph coloring enjoys many practical applications as well as theoretical challenges. Beside the classical types of problems, different limitations can also be set on the graph, or on the way a color is assigned and it has even reached popularity with the general public in the form of the popular number puzzle Sudoku. Graph coloring is still an active field of research. Note, Many terms used in this article are defined in Glossary of graph theory, the first results about graph coloring deal almost exclusively with planar graphs in the form of the coloring of maps. Guthrie’s brother passed on the question to his mathematics teacher Augustus de Morgan at University College, arthur Cayley raised the problem at a meeting of the London Mathematical Society in 1879. The same year, Alfred Kempe published a paper that claimed to establish the result, for his accomplishment Kempe was elected a Fellow of the Royal Society and later President of the London Mathematical Society. In 1890, Heawood pointed out that Kempe’s argument was wrong, however, in that paper he proved the five color theorem, saying that every planar map can be colored with no more than five colors, using ideas of Kempe. The proof went back to the ideas of Heawood and Kempe, the proof of the four color theorem is also noteworthy for being the first major computer-aided proof. Kempe had already drawn attention to the general, non-planar case in 1879, the conjecture remained unresolved for 40 years, until it was established as the celebrated strong perfect graph theorem by Chudnovsky, Robertson, Seymour, and Thomas in 2002. One of the applications of graph coloring, register allocation in compilers, was introduced in 1981
25.
Graph drawing
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A drawing of a graph or network diagram is a pictorial representation of the vertices and edges of a graph. This drawing should not be confused with the graph itself, very different layouts can correspond to the same graph, in the abstract, all that matters is which pairs of vertices are connected by edges. In the concrete, however, the arrangement of vertices and edges within a drawing affects its understandability, usability, fabrication cost. The problem gets worse, if the changes over time by adding and deleting edges. Upward planar drawing uses the convention that every edge is oriented from a vertex to a higher vertex. Many different quality measures have been defined for graph drawings, in an attempt to find means of evaluating their aesthetics. In addition to guiding the choice between different layout methods for the graph, some layout methods attempt to directly optimize these measures. The crossing number of a drawing is the number of pairs of edges cross each other. If the graph is planar, then it is convenient to draw it without any edge intersections, that is, in this case. However, nonplanar graphs frequently arise in applications, so graph drawing algorithms must generally allow for edge crossings, the area of a drawing is the size of its smallest bounding box, relative to the closest distance between any two vertices. Drawings with smaller area are generally preferable to those with area, because they allow the features of the drawing to be shown at greater size. The aspect ratio of the box may also be important. Symmetry display is the problem of finding symmetry groups within a given graph, some layout methods automatically lead to symmetric drawings, alternatively, some drawing methods start by finding symmetries in the input graph and using them to construct a drawing. It is important that edges have shapes that are as simple as possible, in polyline drawings, the complexity of an edge may be measured by its number of bends, and many methods aim to provide drawings with few total bends or few bends per edge. Similarly for spline curves the complexity of an edge may be measured by the number of points on the edge. Several commonly used quality measures concern lengths of edges, it is desirable to minimize the total length of the edges as well as the maximum length of any edge. Additionally, it may be preferable for the lengths of edges to be rather than highly varied. Angular resolution is a measure of the sharpest angles in a graph drawing, if a graph has vertices with high degree then it necessarily will have small angular resolution, but the angular resolution can be bounded below by a function of the degree
26.
Geometry
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Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer, Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into a form by Euclid, whose treatment, Euclids Elements. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC, islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid footing by mathematicians such as René Descartes. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, while geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, contemporary geometry has many subfields, Euclidean geometry is geometry in its classical sense. The mandatory educational curriculum of the majority of nations includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, Euclidean geometry also has applications in computer science, crystallography, and various branches of modern mathematics. Differential geometry uses techniques of calculus and linear algebra to problems in geometry. It has applications in physics, including in general relativity, topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this often means dealing with large-scale properties of spaces, convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues, often using techniques of real analysis. It has close connections to convex analysis, optimization and functional analysis, algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques. It has applications in areas, including cryptography and string theory. Discrete geometry is concerned mainly with questions of relative position of simple objects, such as points. It shares many methods and principles with combinatorics, Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics. The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia, the earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, later clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiters position and motion within time-velocity space
27.
Mathematical optimization
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In mathematics, computer science and operations research, mathematical optimization, also spelled mathematical optimisation, is the selection of a best element from some set of available alternatives. The generalization of optimization theory and techniques to other formulations comprises an area of applied mathematics. Such a formulation is called a problem or a mathematical programming problem. Many real-world and theoretical problems may be modeled in this general framework, typically, A is some subset of the Euclidean space Rn, often specified by a set of constraints, equalities or inequalities that the members of A have to satisfy. The domain A of f is called the space or the choice set. The function f is called, variously, a function, a loss function or cost function, a utility function or fitness function, or, in certain fields. A feasible solution that minimizes the objective function is called an optimal solution, in mathematics, conventional optimization problems are usually stated in terms of minimization. Generally, unless both the function and the feasible region are convex in a minimization problem, there may be several local minima. While a local minimum is at least as good as any nearby points, a global minimum is at least as good as every feasible point. In a convex problem, if there is a minimum that is interior, it is also the global minimum. Optimization problems are often expressed with special notation, consider the following notation, min x ∈ R This denotes the minimum value of the objective function x 2 +1, when choosing x from the set of real numbers R. The minimum value in case is 1, occurring at x =0. Similarly, the notation max x ∈ R2 x asks for the value of the objective function 2x. In this case, there is no such maximum as the function is unbounded. This represents the value of the argument x in the interval, John Wiley & Sons, Ltd. pp. xxviii+489. (2008 Second ed. in French, Programmation mathématique, Théorie et algorithmes, Editions Tec & Doc, Paris,2008. Nemhauser, G. L. Rinnooy Kan, A. H. G. Todd, handbooks in Operations Research and Management Science. Amsterdam, North-Holland Publishing Co. pp. xiv+709, J. E. Dennis, Jr. and Robert B
28.
Finite element meshing
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The finite element method is a numerical method for solving problems of engineering and mathematical physics. It is also referred to as finite element analysis, typical problem areas of interest include structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The analytical solution of these problems generally require the solution to boundary value problems for partial differential equations, the finite element method formulation of the problem results in a system of algebraic equations. The method yields approximate values of the unknowns at discrete number of points over the domain, to solve the problem, it subdivides a large problem into smaller, simpler parts that are called finite elements. The simple equations that model these finite elements are assembled into a larger system of equations that models the entire problem. FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function, the global system of equations has known solution techniques, and can be calculated from the initial values of the original problem to obtain a numerical answer. To explain the approximation in this process, FEM is commonly introduced as a case of Galerkin method. The process, in language, is to construct an integral of the inner product of the residual. In simple terms, it is a procedure that minimizes the error of approximation by fitting trial functions into the PDE, the residual is the error caused by the trial functions, and the weight functions are polynomial approximation functions that project the residual. These equation sets are the element equations and they are linear if the underlying PDE is linear, and vice versa. In step above, a system of equations is generated from the element equations through a transformation of coordinates from the subdomains local nodes to the domains global nodes. This spatial transformation includes appropriate orientation adjustments as applied in relation to the coordinate system. The process is carried out by FEM software using coordinate data generated from the subdomains. FEM is best understood from its application, known as finite element analysis. FEA as applied in engineering is a tool for performing engineering analysis. It includes the use of mesh generation techniques for dividing a complex problem into small elements, FEA is a good choice for analyzing problems over complicated domains, when the domain changes, when the desired precision varies over the entire domain, or when the solution lacks smoothness. For instance, in a crash simulation it is possible to increase prediction accuracy in important areas like the front of the car. Another example would be in weather prediction, where it is more important to have accurate predictions over developing highly nonlinear phenomena rather than relatively calm areas
29.
Robust statistics
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Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have developed for many common problems, such as estimating location, scale. One motivation is to produce statistical methods that are not unduly affected by outliers, another motivation is to provide methods with good performance when there are small departures from parametric distributions. For example, robust methods work well for mixtures of two normal distributions with different standard-deviations, under this model, non-robust methods like a t-test work poorly. Robust statistics seek to provide methods that emulate popular statistical methods, in statistics, classical estimation methods rely heavily on assumptions which are often not met in practice. In particular, it is assumed that the data errors are normally distributed, at least approximately. Unfortunately, when there are outliers in the data, classical estimators often have poor performance, when judged using the breakdown point. For instance, one may use a mixture of 95% a normal distribution, the median is a robust measure of central tendency, while the mean is not. The median has a point of 50%, while the mean has a breakdown point of 0%. The median absolute deviation and interquartile range are robust measures of statistical dispersion, while the standard deviation, trimmed estimators and Winsorised estimators are general methods to make statistics more robust. There are various definitions of a robust statistic, strictly speaking, a robust statistic is resistant to errors in the results, produced by deviations from assumptions. One of the most important cases is distributional robustness, classical statistical procedures are typically sensitive to longtailedness. Thus, in the context of robust statistics, distributionally robust, for one perspective on research in robust statistics up to 2000, see Portnoy & He. A related topic is that of resistant statistics, which are resistant to the effect of extreme scores, gelman et al. in Bayesian Data Analysis consider a data set relating to speed-of-light measurements made by Simon Newcomb. The data sets for that book can be found via the Classic data sets page, although the bulk of the data look to be more or less normally distributed, there are two obvious outliers. These outliers have an effect on the mean, dragging it towards them. Thus, if the mean is intended as a measure of the location of the center of the data, it is, in a sense, also, the distribution of the mean is known to be asymptotically normal due to the central limit theorem. However, outliers can make the distribution of the mean non-normal even for large data sets
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Journal of the ACM
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The Journal of the ACM is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects. It is a journal of the Association for Computing Machinery. Its current editor-in-chief is Victor Vianu, the journal was established in 1954 and computer scientists universally hold the Journal of the ACM in high esteem. Communications of the ACM Official website
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Jean-Claude Falmagne
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After finishing high school, Falmagne spent two years in the Belgian army, where he became an officer. Military service was mandatory in Belgium at the time, in 1954, he enrolled at the University of Brussels as a student in the psychology department. He received his degree in 1959 and was hired as an assistant at the University of Brussels. He obtained his Ph. D. degree in 1965 from the same institution, while working on his doctoral dissertation, which dealt with reaction times, Falmagne became interested in the applications of mathematics to the cognitive sciences. In 1964, he was invited by Patrick Suppes to spend the summer at Stanford University, Suppes, Luce, and Aczél had a strong influence on Falmagne’s choice of scientific career and on his approach to solving scientific problems. His visit to Stanford convinced him that he needed to continue his education in the United States and his interests grew to include psychophysics, measurement theory, and probabilistic models of ordering and algebraic measurement. After short teaching stints back in Europe at the University of Brussels, in 1989, he joined the faculty of University of California, Irvine, accepting an appointment at the Department of Cognitive Sciences and the Institute for Mathematical Behavioral Sciences. He remained there until his retirement in 2004, currently, Falmagne is Chairman of ALEKS Corporation, a web-based educational software company that he founded with some of his graduate students. He is also a Professor Emeritus at the University of California, in 1978, Falmagne solved a well-known problem, posed in 1960 by the economists H. D. In 1985, Falmagne, along with Jean-Paul Doignon, wrote “Spaces for the Assessment of Knowledge”, in this article, they presented a formal framework for the assessment of knowledge in various academic subjects, such as arithmetic, algebra, and chemistry. This early framework was combinatoric in character, and as such insufficient for a practical assessment, in time, they created a stochastic framework for the description of the evolution of an assessment, question by question. Falmagne and Doignons 2011 book, Learning Spaces, contains the most current presentation, Learning spaces are specific kinds of knowledge spaces, whose best applications are to situations where assessments guide efficient learning. Learning spaces are a part of the concept of Media Theory, more generally, these lines of research are collectively called Knowledge Space Theory and are being pursued by many investigators, mostly in Austria, Germany, and the Netherlands. In dimensional analysis, this invariance is implicit and captured by the concept of quantities and they proposed a more powerful framework making this invariance explicit in the notation. This approach was generalized by Falmagne in Meaningfulness and Order Invariance, Two Fundamental Principles for Scientific Laws, the monograph Elements of Psychophysical Theory presents the mathematical foundation of psychophysics and includes an introduction to measurement theory and functional equations. Falmagnes work in philosophy of science concerns foundational issues in algebraic measurement, a distinctive feature of his research lies in the use of functional equations in order to achieve generality. Falmagne is the recipient of Fulbright and Guggenheim Fellowships and of a von Humboldt Award, in 1994, he was recognized as a Friend of NSERC by the Natural Sciences and Engineering Research Council of Canada and János D. Aczél. That same year, he was elected as a member of the New York Academy of Sciences and he is also a fellow of the Society of Experimental Psychologists
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International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
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K shortest path routing
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The K shortest path routing algorithm is an extension algorithm of the shortest path routing algorithm in a given network. It is sometimes crucial to have more than one path between two nodes in a given network, in the event there are additional constraints, other paths different from the shortest path can be computed. To find the shortest path one can use shortest path algorithms such as Dijkstra’s algorithm or Bellman Ford algorithm, the K shortest path routing algorithm is a generalization of the shortest path problem. The algorithm not only finds the shortest path, but also K-1 other paths in non-decreasing order of cost, K is the number of shortest paths to find. The problem can be restricted to have the K shortest path without loops or with loop, since 1957 there have been many papers published on the K shortest path routing algorithm problem. Most of the works on not just finding the single shortest path between a pair of nodes, but instead listing a sequence of the K shortest paths, were done between the 1960s and up to 2001. Since then, most of the recent research has been about the applications of the algorithm, in 2010, Michael Gunter et al. published a book on Symbolic calculation of K-shortest paths and related measures with the stochastic process algebra tool CASPA. Important works on the K shortest paths problem, The BibTeX database contains more articles, the Dijkstra algorithm can be generalized to find the K shortest paths. In the second variant, attributed to Jin Y, yen, the paths are required to be loopless. Yens algorithm is used where only simple paths are considered, whereas Eppsteins algorithm is used when non-simple paths are allowed or where loops are not possible, in all that follows, m is the number of edges and n is the number of vertices. Eppsteins algorithm provides the best results, Eppsteins model finds the K shortest paths connecting a given pair of vertices in a digraph, in time O. This algorithm uses a transformation technique. This model can find the K shortest paths from a given source s to each vertex in the graph. The best running time for this model is attributed to Jin. Y, yens algorithm finds the lengths of all shortest paths from a fixed node to all other nodes in an n-node non negative-distance network. This technique only requires 2n2 additions and n2 comparisons - which is less than other algorithms require. The running time complexity is O, which is pseudo-polynomial, M represents the number of edges and n is the number of vertices. The following example makes use of Yen’s model to find the first K shortest paths between communicating end nodes and that is, it finds the first, second, third, etc. up to the Kth shortest path. More details can be found here, the technique implements a multiple object tracker based on the K shortest paths routing algorithm
34.
Google Scholar
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Google Scholar is a freely accessible web search engine that indexes the full text or metadata of scholarly literature across an array of publishing formats and disciplines. This estimate also determined how many documents were available on the web. Google Scholar is similar in function to the freely available CiteSeerX and it also resembles the subscription-based tools, Elseviers Scopus and Thomson Reuters Web of Science. Google Scholar arose out of a discussion between Alex Verstak and Anurag Acharya, both of whom were working on building Googles main web index. Their goal was to make the worlds problem solvers 10% more efficient by allowing easier, Scholar has gained a range of features over time. In 2006, a citation importing feature was implemented supporting bibliography managers, in 2011, Google removed Scholar from the toolbars on its search pages, making it both less easily accessible and less discoverable for users not already aware of its existence. Around this period, sites with features such as CiteSeer, Scirus. All three of these are now defunct, a major enhancement was rolled out in 2012, with the possibility for individual scholars to create personal Scholar Citations profiles, public author profiles that are editable by authors themselves. Individuals, logging on through a Google account with a bona fide address usually linked to an institution, can now create their own page giving their fields of interest. Google Scholar automatically calculates and displays the individuals total citation count, h-index, according to Google, three quarters of Scholar search results pages show links to the authors public profiles as of August 2014. A feature introduced in November 2013 allows logged-in users to search results into the Google Scholar library. A metrics feature now supports viewing the impact of academic journals and this reveals the top journals in a field of interest, and the articles generating these journals impact can also be accessed. Google Scholar allows users to search for digital or physical copies of articles and it indexes full-text journal articles, technical reports, preprints, theses, books, and other documents, including selected Web pages that are deemed to be scholarly. Using its group of feature, it shows the links to journal articles. Through its cited by feature, Google Scholar provides access to abstracts of articles that have cited the article being viewed and it is this feature in particular that provides the citation indexing previously only found in CiteSeer, Scopus and Web of Science. As of July 2013, Google Scholar is not yet available to the Google AJAX API, Google Scholars legal database of US cases is extensive. Google Scholar embeds clickable citation links within the case and the How Cited tab allows lawyers to research prior case law, the Google Scholar Legal Content Star Paginator extension inserts Westlaw and LexisNexis style page numbers in line with the text of the case. Research has shown that Google Scholar puts high weight especially on citation counts, as a consequence, the first search results are often highly cited articles