The Amazon River in South America is the largest river by discharge volume of water in the world, by some definitions it is the longest. The headwaters of the Apurímac River on Nevado Mismi had been considered for nearly a century as the Amazon's most distant source, until a 2014 study found it to be the headwaters of the Mantaro River on the Cordillera Rumi Cruz in Peru; the Mantaro and Apurímac join, with other tributaries form the Ucayali River, which in turn meets the Marañón River upstream of Iquitos, Peru, to form what countries other than Brazil consider to be the main stem of the Amazon. Brazilians call this section the Solimões River above its confluence with the Rio Negro to form what Brazilians call the Amazon at the Meeting of Waters at Manaus, the river's largest city. At an average discharge of about 209,000 cubic metres per second —approximately 6,591 cubic kilometres per annum, greater than the next seven largest independent rivers combined—the Amazon represents 20% of the global riverine discharge to the ocean.
The Amazon basin is the largest drainage basin in the world, with an area of 7,050,000 square kilometres. The portion of the river's drainage basin in Brazil alone is larger than any other river's basin; the Amazon enters Brazil with only one-fifth of the flow it discharges into the Atlantic Ocean, yet has a greater flow at this point than the discharge of any other river. The river was known by Europeans as the Marañón and the Peruvian part of the river is still known by that name today, it became known as the Rio Amazonas in Spanish and Portuguese, or The Amazon in English. The name Rio Amazonas was given after native warriors attacked a 16th-century expedition by Francisco de Orellana; the warriors were led by women, reminding de Orellana of the Amazon warriors, a tribe of women warriors related to Iranian Scythians and Sarmatians mentioned in Greek mythology. The word Amazon itself may be derived from the Iranian compound *ha-maz-an- " fighting together" or ethnonym *ha-mazan- "warriors", a word attested indirectly through a derivation, a denominal verb in Hesychius of Alexandria's gloss "ἁμαζακάραν· πολεμεῖν.
Πέρσαι", where it appears together with the Indo-Iranian root *kar- "make". During what many archaeologists call the formative stage, Amazonian societies were involved in the emergence of South America's highland agrarian systems; the trade with Andean civilisations in the terrains of the headwaters in the Andes, formed an essential contribution to the social and religious development of the higher altitude civilisations of among others the Muisca and Incas. Early human settlements were based on low-lying hills or mounds. Shell mounds were the earliest evidence of habitation, they are associated with ceramic age cultures. Artificial earth platforms for entire villages are the second type of mounds, they are best represented by the Marajoara culture. Figurative mounds are the most recent types of occupation. There is ample evidence that the areas surrounding the Amazon River were home to complex and large-scale indigenous societies chiefdoms who developed large towns and cities. Archaeologists estimate that by the time the Spanish conquistador De Orellana traveled across the Amazon in 1541, more than 3 million indigenous people lived around the Amazon.
These pre-Columbian settlements created developed civilizations. For instance, pre-Columbian indigenous people on the island of Marajó may have developed social stratification and supported a population of 100,000 people. In order to achieve this level of development, the indigenous inhabitants of the Amazon rainforest altered the forest's ecology by selective cultivation and the use of fire. Scientists argue that by burning areas of the forest repetitiously, the indigenous people caused the soil to become richer in nutrients; this created dark soil areas known as terra preta de índio. Because of the terra preta, indigenous communities were able to make land fertile and thus sustainable for the large-scale agriculture needed to support their large populations and complex social structures. Further research has hypothesized; some say that its effects on forest ecology and regional climate explain the otherwise inexplicable band of lower rainfall through the Amazon basin. Many indigenous tribes engaged in constant warfare.
James Stuart Olson wrote: "The Munduruku expansion dislocated and displaced the Kawahíb, breaking the tribe down into much smaller groups... first came to the attention of Europeans in 1770 when they began a series of widespread attacks on Brazilian settlements along the Amazon River." In March 1500, Spanish conquistador Vicente Yáñez Pinzón was the first documented European to sail up the Amazon River. Pinzón called the stream Río Santa María del Mar Dulce shortened to Mar Dulce sweet sea, because of its fresh water pushing out into the ocean. Another Spanish explorer, Francisco de Orellana, was the first European to travel from the origins of the upstream river basins, situated in the Andes, to the mouth of the river. In this journey, Orellana baptised some of the affluents of the Amazonas like Rio Negro and Jurua; the name Amazonas is taken from the native warriors that attacked this expedition women, that reminded De Orellana of the mythical female Amazon warriors from the
Philippe Flajolet was a French computer scientist. A former student of École Polytechnique, Philippe Flajolet received his Ph. D. in computer science from University Paris Diderot in 1973 and state doctorate from Paris-Sud 11 University in 1979. Most of Philippe Flajolet's research work was dedicated towards general methods for analyzing the computational complexity of algorithms, including the theory of average-case complexity, he introduced the theory of analytic combinatorics. With Robert Sedgewick of Princeton University, he wrote the first book-length treatment of the topic, the 2009 book entitled Analytic Combinatorics. A summary of his research up to 1998 can be found in the article "Philippe Flajolet's research in Combinatorics and Analysis of Algorithms" by H. Prodinger and W. Szpankowski, Algorithmica 22, 366-387. At the time of his death from a serious illness, Philippe Flajolet was a research director at INRIA in Rocquencourt. From 1994 to 2003 he was a corresponding member of the French Academy of Sciences, was a full member from 2003 on.
He was a member of the Academia Europaea. The HyperLogLog commands of Redis, released in April 2014, are prefixed with "PF" in honor of Philippe Flajolet. With Robert Sedgewick: An Introduction to the Analysis of Algorithms. 2nd edition, Addison-Wesley, Mass. 1995, ISBN 0-201-40009-X with Robert Sedgewick: Analytic Combinatorics. CUP, Cambridge 2009, ISBN 978-0-521-89806-5 Random tree models in the analysis of algorithms. INRIA, Rocquencourt 1987 with Andrew Odlyzko: Singularity analysis of generating functions. University Press, Calif. 1988 Philippe Flajolet's Home Page Philippe Flajolet and Analytic Combinatorics, Conference in the memory of Philippe Flajolet Luc Devroye, Philippe Flajolet, 1 December 1948--22 March 2011
An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial "axiom" string from which to begin construction, a mechanism for translating the generated strings into geometric structures. L-systems were introduced and developed in 1968 by Aristid Lindenmayer, a Hungarian theoretical biologist and botanist at the University of Utrecht. Lindenmayer used L-systems to describe the behaviour of plant cells and to model the growth processes of plant development. L-systems have been used to model the morphology of a variety of organisms and can be used to generate self-similar fractals; as a biologist, Lindenmayer worked with yeast and filamentous fungi and studied the growth patterns of various types of bacteria, such as the cyanobacteria Anabaena catenula. The L-systems were devised to provide a formal description of the development of such simple multicellular organisms, to illustrate the neighbourhood relationships between plant cells.
On, this system was extended to describe higher plants and complex branching structures. The recursive nature of the L-system rules leads to self-similarity and thereby, fractal-like forms are easy to describe with an L-system. Plant models and natural-looking organic forms are easy to define, as by increasing the recursion level the form slowly'grows' and becomes more complex. Lindenmayer systems are popular in the generation of artificial life. L-system grammars are similar to the semi-Thue grammar. L-systems are now known as parametric L systems, defined as a tuple G =,where V is a set of symbols containing both elements that can be replaced and those which cannot be replaced ω is a string of symbols from V defining the initial state of the system P is a set of production rules or productions defining the way variables can be replaced with combinations of constants and other variables. A production consists of the predecessor and the successor. For any symbol A, a member of the set V which does not appear on the left hand side of a production in P, the identity production A → A is assumed.
The rules of the L-system grammar are applied iteratively starting from the initial state. As many rules as possible are applied per iteration; the fact that each iteration employs as many rules as possible differentiates an L-system from a formal language generated by a formal grammar, which applies only one rule per iteration. If the production rules were to be applied only one at a time, one would quite generate a language, rather than an L-system. Thus, L-systems are strict subsets of languages. An L-system is context-free if each production rule refers only to an individual symbol and not to its neighbours. Context-free L-systems are thus specified by a context-free grammar. If a rule depends not only on a single symbol but on its neighbours, it is termed a context-sensitive L-system. If there is one production for each symbol the L-system is said to be deterministic. If there are several, each is chosen with a certain probability during each iteration it is a stochastic L-system. Using L-systems for generating graphical images requires that the symbols in the model refer to elements of a drawing on the computer screen.
For example, the program Fractint uses turtle graphics to produce screen images. It interprets each constant in an L-system model as a turtle command. Lindenmayer's original L-system for modelling the growth of algae. Variables: A B constants: none axiom: A rules:, which produces: n = 0: A n = 1: AB n = 2: ABA n = 3: ABAAB n = 4: ABAABABA n = 5: ABAABABAABAAB n = 6: ABAABABAABAABABAABABA n = 7: ABAABABAABAABABAABABAABAABABAABAAB n=0: A start / \ n=1: A B the initial single A spawned into AB by rule, rule couldn't be applied /| \ n=2: A B A former string AB with all rules applied, A spawned into AB again, former B turned into A / | | | \ n=3: A B A A B note all A's producing a copy of themselves in the first place a B, which turns... / | | | \ | \ \ n=4: A B A A B A B A... into an A one generation starting to spawn/repeat/recurse The result is the sequence of Fibonacci words. If we count the length of each string, we obtain the famous Fibonacci sequence of numbers: 1 2 3 5 8 13 21 34 55 89...
For each string, if we count the k-th position from the left end of the string, the value is determined by whether a multiple of the golden ratio falls within the interval. The ratio of A to B converges to the golden mean; this example yields the same result if the rule is replaced with, except that the strings are mirrored. This sequence is a locally catenative sequence because G = G G, where
In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child. A recursive definition using just set theory notions is that a binary tree is a tuple, where L and R are binary trees or the empty set and S is a singleton set; some authors allow the binary tree to be the empty set as well. From a graph theory perspective, binary trees as defined here are arborescences. A binary tree may thus be called a bifurcating arborescence—a term which appears in some old programming books, before the modern computer science terminology prevailed, it is possible to interpret a binary tree as an undirected, rather than a directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of binary tree to emphasize the fact that the tree is rooted, but as defined above, a binary tree is always rooted. A binary tree is a special case of an ordered K-ary tree, where k is 2.
In mathematics, what is termed binary tree can vary from author to author. Some use the definition used in computer science, but others define it as every non-leaf having two children and don't order the children either. In computing, binary trees are used in two different ways: First, as a means of accessing nodes based on some value or label associated with each node. Binary trees labelled this way are used to implement binary search trees and binary heaps, are used for efficient searching and sorting; the designation of non-root nodes as left or right child when there is only one child present matters in some of these applications, in particular it is significant in binary search trees. However, the arrangement of particular nodes into the tree is not part of the conceptual information. For example, in a normal binary search tree the placement of nodes depends entirely on the order in which they were added, can be re-arranged without changing the meaning. Second, as a representation of data with a relevant bifurcating structure.
In such cases the particular arrangement of nodes under and/or to the left or right of other nodes is part of the information. Common examples occur with Huffman coding and cladograms; the everyday division of documents into chapters, paragraphs, so on is an analogous example with n-ary rather than binary trees. To define a binary tree in general, we must allow for the possibility that only one of the children may be empty. An artifact, which in some textbooks is called an extended binary tree is needed for that purpose. An extended binary tree is thus recursively defined as: the empty set is an extended binary tree if T1 and T2 are extended binary trees denote by T1 • T2 the extended binary tree obtained by adding a root r connected to the left to T1 and to the right to T2 by adding edges when these sub-trees are non-empty. Another way of imagining this construction is to consider instead of the empty set a different type of node—for instance square nodes if the regular ones are circles. A binary tree is a rooted tree, an ordered tree in which every node has at most two children.
A rooted tree imparts a notion of levels, thus for every node a notion of children may be defined as the nodes connected to it a level below. Ordering of these children makes possible to distinguish left child from right child, but this still doesn't distinguish between a node with left but not a right child from a one with right but no left child. The necessary distinction can be made by first partitioning the edges, i.e. defining the binary tree as triplet, where is a rooted tree and E1 ∩ E2 is empty, requiring that for all j ∈ every node has at most one Ej child. A more informal way of making the distinction is to say, quoting the Encyclopedia of Mathematics, that "every node has a left child, a right child, neither, or both" and to specify that these "are all different" binary trees. Tree terminology so varies in the literature. A rooted binary tree has a root node and every node has at most two children. A full binary tree is a tree in which every node has 2 children. Another way of defining a full binary tree is a recursive definition.
A full binary tree is either:A single vertex. A tree whose root note has two subtrees. In a complete binary tree every level, except the last, is filled, all nodes in the last level are as far left as possible, it can have between 2h nodes at the last level h. An alternative definition is a perfect tree; some authors use the term complete to refer instead to a perfect binary tree as defined above, in which case they call this type of tree an complete binary tree or nearly complete binary tree. A complete binary tree can be efficiently represented using an array. A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level. An example of a perfect binary tree is the ancestry chart of a person to a given depth, as each person has two biological parents. In the infinite complete binary tree, every node has two children; the set of all nodes is countably infinite, but the set of all infinite paths from the root
The Ohio River is a 981-mile long river in the midwestern United States that flows southwesterly from western Pennsylvania south of Lake Erie to its mouth on the Mississippi River at the southern tip of Illinois. It is the second largest river by discharge volume in the United States and the largest tributary by volume of the north-south flowing Mississippi River that divides the eastern from western United States; the river flows through or along the border of six states, its drainage basin includes parts of 15 states. Through its largest tributary, the Tennessee River, the basin includes several states of the southeastern U. S, it is the source of drinking water for three million people. The lower Ohio River just below Louisville is obstructed by rapids known as the Falls of the Ohio where the water level falls 26ft. in 2 miles and is impassible for navigation. The McAlpine Locks and Dam, a shipping canal bypassing the rapids, now allows commercial navigation from the Forks of the Ohio at Pittsburgh to the Port of New Orleans at the mouth of the Mississippi on the Gulf of Mexico.
The name "Ohio" comes from the Ohi: yo', lit. "Good River". Discovery of the Ohio River may be attributed to English explorers from Virginia in the latter half of the 17th century. In his Notes on the State of Virginia published in 1781–82, Thomas Jefferson stated: "The Ohio is the most beautiful river on earth, its current gentle, waters clear, bosom smooth and unbroken by rocks and rapids, a single instance only excepted." In the late 18th century, the river was the southern boundary of the Northwest Territory. It became a primary transportation route for pioneers during the westward expansion of the early U. S; the river is sometimes considered as the western extension of the Mason–Dixon Line that divided Pennsylvania from Maryland, thus part of the border between free and slave territory, between the Northern and Southern United States or Upper South. Where the river was narrow, it was the way to freedom for thousands of slaves escaping to the North, many helped by free blacks and whites of the Underground Railroad resistance movement.
The Ohio River is a climatic transition area, as its water runs along the periphery of the humid subtropical and humid continental climate areas. It is inhabited by flora of both climates. In winter, it freezes over at Pittsburgh but farther south toward Cincinnati and Louisville. At Paducah, Kentucky, in the south, near the Ohio's confluence with the Mississippi, it is ice-free year-round; the name "Ohio" comes from the Seneca language, Ohi:yo', a proper name derived from ohiːyoːh, therefore translating to "Good River". "Great river" and "large creek" have been given as translations. Native Americans, including the Lenni Lenape and Iroquois, considered the Ohio and Allegheny rivers as the same, as is suggested by a New York State road sign on Interstate 86 that refers to the Allegheny River as Ohi:yo'. An earlier Miami-Illinois language name was applied to the Ohio River, Mosopeleacipi. Shortened in the Shawnee language to pelewa thiipi, spelewathiipi or peleewa thiipiiki, the name evolved through variant forms such as "Polesipi", "Peleson", "Pele Sipi" and "Pere Sipi", stabilized to the variant spellings "Pelisipi", "Pelisippi" and "Pellissippi".
Applied just to the Ohio River, the "Pelisipi" name was variously applied back and forth between the Ohio River and the Clinch River in Virginia and Tennessee. In his original draft of the Land Ordinance of 1784, Thomas Jefferson proposed a new state called "Pelisipia", to the south of the Ohio River, which would have included parts of present-day Eastern Kentucky and West Virginia; the river had great significance in the history of the Native Americans, as numerous civilizations formed along its valley. For thousands of years, Native Americans used the river as a major trading route, its waters connected communities. In the five centuries before European conquest, the Mississippian culture built numerous regional chiefdoms and major earthwork mounds in the Ohio Valley, such as Angel Mounds near Evansville, Indiana, as well as in the Mississippi Valley and the Southeast; the Osage, Omaha and Kaw lived in the Ohio Valley, but under pressure from the Iroquois to the northeast, migrated west of the Mississippi River in the 17th century to territory now defined as Missouri and Oklahoma.
The discovery and traversal of the Ohio River by Europeans admits of several possibilities, all in the latter half of the 17th century. Virginian Englishman Abraham Wood's trans-Appalachian expeditions between 1654 and 1664; the first person to traverse the length of the river, from the headwaters of the Allegheny to its mouth on the Mississippi, was a Dutch trader from New York, Arnout Viele, in 1692. In 1749, Great Britain established the Ohio Company to trade in the area. Exploration of the territory and trade with the Indians in the region near the Forks brought British colonials from both Pennsylvania and Virginia across the mountains, both colonies claimed the territory; the movement across the Allegheny Mountains of British settlers and the claims of the area near modern day Pittsburgh led to conflict with the French, who had forts in the Ohio River Valley. This conflict was called the Indian War. In 17
Luc P. Devroye is a Belgian computer scientist and mathematician and a James McGill Professor in the School of Computer Science of McGill University in Montreal, Canada. Since joining the McGill faculty in 1977 he has won numerous awards, including an E. W. R. Steacie Memorial Fellowship, a Humboldt Research Award, the Killam Prize and the Statistical Society of Canada gold medal, he received an honorary doctorate from the University of Louvain in 2002, he received an honorary doctorate from Universiteit Antwerpen on March 29, 2012. He studied at Katholieke Universiteit Leuven and subsequently at Osaka University and in 1976 received his PhD from University of Texas at Austin under the supervision of Terry Wagner. Devroye specializes in the probabilistic analysis of algorithms, random number generation, type design. Devroye is deeply interested in the history of letters and font design, his website collects a large range of information on this topic. Luc Devroye's Homepage The Mathematician Typographer
Geographic information system
A geographic information system is a system designed to capture, manipulate, analyze and present spatial or geographic data. GIS applications are tools that allow users to create interactive queries, analyze spatial information, edit data in maps, present the results of all these operations. GIS sometimes refers to geographic information science, the science underlying geographic concepts and systems. GIS can refer to a number of different technologies, processes and methods, it is attached to many operations and has many applications related to engineering, management, transport/logistics, telecommunications, business. For that reason, GIS and location intelligence applications can be the foundation for many location-enabled services that rely on analysis and visualization. GIS can relate unrelated information by using location as the key index variable. Locations or extents in the Earth space–time may be recorded as dates/times of occurrence, x, y, z coordinates representing, longitude and elevation, respectively.
All Earth-based spatial–temporal location and extent references should be relatable to one another and to a "real" physical location or extent. This key characteristic of GIS has begun to open new avenues of scientific inquiry; the first known use of the term "geographic information system" was by Roger Tomlinson in the year 1968 in his paper "A Geographic Information System for Regional Planning". Tomlinson is acknowledged as the "father of GIS". One of the first applications of spatial analysis in epidemiology is the 1832 "Rapport sur la marche et les effets du choléra dans Paris et le département de la Seine"; the French geographer Charles Picquet represented the 48 districts of the city of Paris by halftone color gradient according to the number of deaths by cholera per 1,000 inhabitants. In 1854 John Snow determined the source of a cholera outbreak in London by marking points on a map depicting where the cholera victims lived, connecting the cluster that he found with a nearby water source.
This was one of the earliest successful uses of a geographic methodology in epidemiology. While the basic elements of topography and theme existed in cartography, the John Snow map was unique, using cartographic methods not only to depict but to analyze clusters of geographically dependent phenomena; the early 20th century saw the development of photozincography, which allowed maps to be split into layers, for example one layer for vegetation and another for water. This was used for printing contours – drawing these was a labour-intensive task but having them on a separate layer meant they could be worked on without the other layers to confuse the draughtsman; this work was drawn on glass plates but plastic film was introduced, with the advantages of being lighter, using less storage space and being less brittle, among others. When all the layers were finished, they were combined into one image using a large process camera. Once color printing came in, the layers idea was used for creating separate printing plates for each color.
While the use of layers much became one of the main typical features of a contemporary GIS, the photographic process just described is not considered to be a GIS in itself – as the maps were just images with no database to link them to. Two additional developments are notable in the early days of GIS: Ian McHarg's publication "Design with Nature" and its map overlay method and the introduction of a street network into the U. S. Census Bureau's DIME system. Computer hardware development spurred by nuclear weapon research led to general-purpose computer "mapping" applications by the early 1960s; the year 1960 saw the development of the world's first true operational GIS in Ottawa, Canada, by the federal Department of Forestry and Rural Development. Developed by Dr. Roger Tomlinson, it was called the Canada Geographic Information System and was used to store and manipulate data collected for the Canada Land Inventory – an effort to determine the land capability for rural Canada by mapping information about soils, recreation, waterfowl and land use at a scale of 1:50,000.
A rating classification factor was added to permit analysis. CGIS was an improvement over "computer mapping" applications as it provided capabilities for overlay and digitizing/scanning, it supported a national coordinate system that spanned the continent, coded lines as arcs having a true embedded topology and it stored the attribute and locational information in separate files. As a result of this, Tomlinson has become known as the "father of GIS" for his use of overlays in promoting the spatial analysis of convergent geographic data. CGIS built a large digital land resource database in Canada, it was developed as a mainframe-based system in support of federal and provincial resource planning and management. Its strength was continent-wide analysis of complex datasets; the CGIS was never available commercially. In 1964 Howard T. Fisher formed the Laboratory for Computer Graphics and Spatial Analysis at the Harvard Graduate School of Design, where a number of important theoretical concepts in spatial data handling were developed, which by the 1970s had distributed seminal software code and systems, such as SYMAP, GRID, ODYSSEY – that served as sources for subsequent commercial development—to universities, research centers and corporations worldwide.
By the late 1970s two public domain GIS systems were in development, by the early 1980s, M&S Computing (late