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2901 | A few tribes were on friendly terms with the other Americans, but most Indians opposed the union of the Colonies as a potential threat to their territory. Approximately 13,000 Indians fought on the British side, with the largest group coming from the Iroquois tribes, who fielded around 1,500 men. The powerful Iroquois Confederacy was shattered as a result of the conflict, whatever side they took; the Seneca, Onondaga, and Cayuga nations sided with the British. Members of the Mohawk nation fought on both sides. Many Tuscarora and Oneida sided with the colonists. The Continental Army sent the Sullivan Expedition on | "American Revolutionary War" | [
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2902 | raids throughout New York to cripple the Iroquois tribes that had sided with the British. Mohawk leaders Joseph Louis Cook and Joseph Brant sided with the Americans and the British respectively, and this further exacerbated the split. Early in July 1776, a major action occurred in the fledgling conflict when the Cherokee allies of Britain attacked the western frontier areas of North Carolina. Their defeat resulted in a splintering of the Cherokee settlements and people, and was directly responsible for the rise of the Chickamauga Cherokee, bitter enemies of the Colonials who carried on a frontier war for decades following | "American Revolutionary War" | [
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2903 | the end of hostilities with Britain. Creek and Seminole allies of Britain fought against Americans in Georgia and South Carolina. In 1778, a force of 800 Creeks destroyed American settlements along the Broad River in Georgia. Creek warriors also joined Thomas Brown's raids into South Carolina and assisted Britain during the Siege of Savannah. Many Indians were involved in the fighting between Britain and Spain on the Gulf Coast and up the Mississippi River—mostly on the British side. Thousands of Creeks, Chickasaws, and Choctaws fought in major battles such as the Battle of Fort Charlotte, the Battle of Mobile, and | "American Revolutionary War" | [
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2904 | the Siege of Pensacola. Pybus (2005) estimates that about 20,000 slaves defected to or were captured by the British, of whom about 8,000 died from disease or wounds or were recaptured by the Patriots. The British took some 12,000 at the end of the war; of these 8000 remained in slavery. Including those who left during the war, a total of about 8000 to 10,000 slaves gained freedom. About 4000 freed slaves went to Nova Scotia and 1200 blacks remained slaves. Baller (2006) examines family dynamics and mobilization for the Revolution in central Massachusetts. He reports that warfare and the | "American Revolutionary War" | [
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2905 | farming culture were sometimes incompatible. Militiamen found that living and working on the family farm had not prepared them for wartime marches and the rigors of camp life. Rugged individualism conflicted with military discipline and regimentation. A man's birth order often influenced his military recruitment, as younger sons went to war and older sons took charge of the farm. A person's family responsibilities and the prevalent patriarchy could impede mobilization. Harvesting duties and family emergencies pulled men home regardless of the sergeant's orders. Some relatives might be Loyalists, creating internal strains. On the whole, historians conclude the Revolution's effect on | "American Revolutionary War" | [
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2906 | patriarchy and inheritance patterns favored egalitarianism. McDonnell (2006) shows a grave complication in Virginia's mobilization of troops was the conflicting interests of distinct social classes, which tended to undercut a unified commitment to the Patriot cause. The Assembly balanced the competing demands of elite slave-owning planters, the middling yeomen (some owning a few slaves), and landless indentured servants, among other groups. The Assembly used deferments, taxes, military service substitute, and conscription to resolve the tensions. Unresolved class conflict, however, made these laws less effective. There were violent protests, many cases of evasion, and large-scale desertion, so that Virginia's contributions came | "American Revolutionary War" | [
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2907 | at embarrassingly low levels. With the British invasion of the state in 1781, Virginia was mired in class division as its native son, George Washington, made desperate appeals for troops. These are some of the standard works about the war in general that are not listed above; books about specific campaigns, battles, units, and individuals can be found in those articles. American Revolutionary War The American Revolutionary War (17751783), also known as the American War of Independence, was an 18th-century war between Great Britain and its Thirteen Colonies (allied with France) which declared independence as the United States of America. | "American Revolutionary War" | [
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2908 | Ampere The ampere (; symbol: A), often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics. The International System of Units defines the ampere in terms of other base units by measuring the electromagnetic force between electrical conductors carrying electric current. The earlier CGS measurement system had two different definitions of current, one essentially the same as the SI's and the other using electric charge as the base unit, with the unit of charge defined by | Ampere | [
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2909 | measuring the force between two charged metal plates. The ampere was then defined as one coulomb of charge per second. In SI, the unit of charge, the coulomb, is defined as the charge carried by one ampere during one second. New definitions, in terms of invariant constants of nature, specifically the elementary charge, will take effect on 20 May 2019. SI defines ampere as follows: The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in vacuum, would produce between these conductors a force | Ampere | [
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2910 | equal to newtons per metre of length. Ampère's force law states that there is an attractive or repulsive force between two parallel wires carrying an electric current. This force is used in the formal definition of the ampere. The SI unit of charge, the coulomb, "is the quantity of electricity carried in 1 second by a current of 1 ampere". Conversely, a current of one ampere is one coulomb of charge going past a given point per second: In general, charge "Q" is determined by steady current "I" flowing for a time "t" as . Constant, instantaneous and average current | Ampere | [
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2911 | are expressed in amperes (as in "the charging current is 1.2 A") and the charge accumulated, or passed through a circuit over a period of time is expressed in coulombs (as in "the battery charge is "). The relation of the ampere (C/s) to the coulomb is the same as that of the watt (J/s) to the joule. The ampere was originally defined as one tenth of the unit of electric current in the centimetre–gram–second system of units. That unit, now known as the abampere, was defined as the amount of current that generates a force of two dynes per | Ampere | [
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2912 | centimetre of length between two wires one centimetre apart. The size of the unit was chosen so that the units derived from it in the MKSA system would be conveniently sized. The "international ampere" was an early realization of the ampere, defined as the current that would deposit of silver per second from a silver nitrate solution. Later, more accurate measurements revealed that this current is . Since power is defined as the product of current and voltage, the ampere can alternatively be expressed in terms of the other units using the relationship I=P/V, and thus 1 ampere equals 1 | Ampere | [
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2913 | W/V. Current can be measured by a multimeter, a device that can measure electrical voltage, current, and resistance. The standard ampere is most accurately realized using a Kibble balance, but is in practice maintained via Ohm's law from the units of electromotive force and resistance, the volt and the ohm, since the latter two can be tied to physical phenomena that are relatively easy to reproduce, the Josephson junction and the quantum Hall effect, respectively. At present, techniques to establish the realization of an ampere have a relative uncertainty of approximately a few parts in 10, and involve realizations of | Ampere | [
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2914 | the watt, the ohm and the volt. Rather than a definition in terms of the force between two current-carrying wires, it has been proposed that the ampere should be defined in terms of the rate of flow of elementary charges. Since a coulomb is approximately equal to elementary charges (such as those carried by protons, or the negative of those carried by electrons), one ampere is approximately equivalent to elementary charges moving past a boundary in one second. ( is the reciprocal of the value of the elementary charge in coulombs.) The proposed change would define 1 A as being | Ampere | [
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2915 | the current in the direction of flow of a particular number of elementary charges per second. In 2005, the International Committee for Weights and Measures (CIPM) agreed to study the proposed change. The new definition was discussed at the 25th General Conference on Weights and Measures (CGPM) in 2014 but for the time being was not adopted. The current drawn by typical constant-voltage energy distribution systems is usually dictated by the power (watt) consumed by the system and the operating voltage. For this reason the examples given below are grouped by voltage level. A typical motor vehicle has a 12 | Ampere | [
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2916 | V battery. The various accessories that are powered by the battery might include: Most Canada, Mexico and United States domestic power suppliers run at 120 V. Household circuit breakers typically provide a maximum of 15 A or 20 A of current to a given set of outlets. Most European domestic power supplies run at 230 V, and most Commonwealth domestic power supplies run at 240 V. For the same amount of power (in watts), the current drawn by a particular European or Commonwealth appliance (in Europe or a Commonwealth country) will be less than for an equivalent North American appliance. | Ampere | [
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2917 | Typical circuit breakers will provide 16 A. The current drawn by a number of typical appliances are: Ampere The ampere (; symbol: A), often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics. The International System of Units defines the ampere in terms of other base units by measuring the electromagnetic force between electrical conductors carrying electric current. The earlier CGS measurement system had two different definitions of current, one essentially the same as the SI's | Ampere | [
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2918 | Algorithm In mathematics and computer science, an algorithm () is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing, and automated reasoning tasks. As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state | Algorithm | [
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2919 | to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input. The concept of algorithm has existed for centuries. Greek mathematicians used algorithms in, for example, the sieve of Eratosthenes for finding prime numbers and the Euclidean algorithm for finding the greatest common divisor of two numbers. The word "algorithm" itself derives from the 9th century mathematician Muḥammad ibn Mūsā al-Khwārizmī, Latinized "Algoritmi". A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem (decision problem) posed by David Hilbert in 1928. Later formalizations were framed as | Algorithm | [
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2920 | attempts to define "effective calculability" or "effective method". Those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, and Alan Turing's Turing machines of 1936–37 and 1939. The word 'algorithm' has its roots in Latinizing the name of Muhammad ibn Musa al-Khwarizmi in a first step to "algorismus". Al-Khwārizmī ((, , c. 780–850) was a Persian mathematician, astronomer, geographer, and scholar in the House of Wisdom in Baghdad, whose name means 'the native of Khwarezm', a region that was part of Greater Iran and is now | Algorithm | [
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2921 | in Uzbekistan. About 825, al-Khwarizmi wrote an Arabic language treatise on the Hindu–Arabic numeral system, which was translated into Latin during the 12th century under the title "Algoritmi de numero Indorum". This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name. Al-Khwarizmi was the most widely read mathematician in Europe in the late Middle Ages, primarily through another of his books, the Algebra. In late medieval Latin, "algorismus", English 'algorism', the corruption of his name, simply meant the "decimal number system". In the 15th century, under the influence of the Greek | Algorithm | [
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2922 | word ἀριθμός 'number' ("cf." 'arithmetic'), the Latin word was altered to "algorithmus", and the corresponding English term 'algorithm' is first attested in the 17th century; the modern sense was introduced in the 19th century. In English, it was first used in about 1230 and then by Chaucer in 1391. English adopted the French term, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English. Another early use of the word is from 1240, in a manual titled "Carmen de Algorismo" composed by Alexandre de Villedieu. It begins thus: which translates | Algorithm | [
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2923 | as: The poem is a few hundred lines long and summarizes the art of calculating with the new style of Indian dice, or Talibus Indorum, or Hindu numerals. An informal definition could be "a set of rules that precisely defines a sequence of operations." which would include all computer programs, including programs that do not perform numeric calculations. Generally, a program is only an algorithm if it stops eventually. A prototypical example of an algorithm is the Euclidean algorithm to determine the maximum common divisor of two integers; an example (there are others) is described by the flowchart above and | Algorithm | [
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2924 | as an example in a later section. No human being can write fast enough, or long enough, or small enough† ( †"smaller and smaller without limit ...you'd be trying to write on molecules, on atoms, on electrons") to list all members of an enumerably infinite set by writing out their names, one after another, in some notation. But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give "explicit instructions for determining the nth member of the set", for arbitrary finite "n". Such instructions are to be given quite explicitly, in a form | Algorithm | [
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2925 | in which "they could be followed by a computing machine", or by a "human who is capable of carrying out only very elementary operations on symbols." An "enumerably infinite set" is one whose elements can be put into one-to-one correspondence with the integers. Thus, Boolos and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an "arbitrary" "input" integer or integers that, in theory, can be arbitrarily large. Thus an algorithm can be an algebraic equation such as "y = m + n" – two arbitrary "input variables" "m" and "n" that produce | Algorithm | [
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2926 | an output "y". But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of (for the addition example): The concept of "algorithm" is also used to define the notion of decidability. That notion is central for explaining how formal systems come into being starting from a small set of axioms and rules. In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related to our customary physical dimension. From such uncertainties, that characterize ongoing work, stems the unavailability of a definition | Algorithm | [
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0.21106010675430298,
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0.149134457... |
2927 | of "algorithm" that suits both concrete (in some sense) and abstract usage of the term. Algorithms are essential to the way computers process data. Many computer programs contain algorithms that detail the specific instructions a computer should perform (in a specific order) to carry out a specified task, such as calculating employees' paychecks or printing students' report cards. Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system. Authors who assert this thesis include Minsky (1967), Savage (1987) and Gurevich (2000): Typically, when an algorithm is associated with processing information, | Algorithm | [
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-0.0664608478... |
2928 | data can be read from an input source, written to an output device and stored for further processing. Stored data are regarded as part of the internal state of the entity performing the algorithm. In practice, the state is stored in one or more data structures. For some such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise. That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable). Because an algorithm is a precise list of precise | Algorithm | [
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2929 | steps, the order of computation is always crucial to the functioning of the algorithm. Instructions are usually assumed to be listed explicitly, and are described as starting "from the top" and going "down to the bottom", an idea that is described more formally by "flow of control". So far, this discussion of the formalization of an algorithm has assumed the premises of imperative programming. This is the most common conception, and it attempts to describe a task in discrete, "mechanical" means. Unique to this conception of formalized algorithms is the assignment operation, setting the value of a variable. It derives | Algorithm | [
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2930 | from the intuition of "memory" as a scratchpad. There is an example below of such an assignment. For some alternate conceptions of what constitutes an algorithm see functional programming and logic programming. Algorithms can be expressed in many kinds of notation, including natural languages, pseudocode, flowcharts, drakon-charts, programming languages or control tables (processed by interpreters). Natural language expressions of algorithms tend to be verbose and ambiguous, and are rarely used for complex or technical algorithms. Pseudocode, flowcharts, drakon-charts and control tables are structured ways to express algorithms that avoid many of the ambiguities common in natural language statements. Programming languages | Algorithm | [
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2931 | are primarily intended for expressing algorithms in a form that can be executed by a computer but are often used as a way to define or document algorithms. There is a wide variety of representations possible and one can express a given Turing machine program as a sequence of machine tables (see more at finite-state machine, state transition table and control table), as flowcharts and drakon-charts (see more at state diagram), or as a form of rudimentary machine code or assembly code called "sets of quadruples" (see more at Turing machine). Representations of algorithms can be classed into three accepted | Algorithm | [
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0.1648589223... |
2932 | levels of Turing machine description: For an example of the simple algorithm "Add m+n" described in all three levels, see Algorithm#Examples. Algorithm design refers to a method or mathematical process for problem-solving and engineering algorithms. The design of algorithms is part of many solution theories of operation research, such as dynamic programming and divide-and-conquer. Techniques for designing and implementing algorithm designs are also called algorithm design patterns, such as the template method pattern and decorator pattern. One of the most important aspects of algorithm design is creating an algorithm that has an efficient run-time, also known as its Big O. | Algorithm | [
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0.03783653303980... |
2933 | Typical steps in the development of algorithms: Most algorithms are intended to be implemented as computer programs. However, algorithms are also implemented by other means, such as in a biological neural network (for example, the human brain implementing arithmetic or an insect looking for food), in an electrical circuit, or in a mechanical device. In computer systems, an algorithm is basically an instance of logic written in software by software developers, to be effective for the intended "target" computer(s) to produce "output" from given (perhaps null) "input". An optimal algorithm, even running in old hardware, would produce faster results than | Algorithm | [
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0.0044849500991... |
2934 | a non-optimal (higher time complexity) algorithm for the same purpose, running in more efficient hardware; that is why algorithms, like computer hardware, are considered technology. ""Elegant" (compact) programs, "good" (fast) programs ": The notion of "simplicity and elegance" appears informally in Knuth and precisely in Chaitin: Chaitin prefaces his definition with: "I'll show you can't prove that a program is 'elegant—such a proof would solve the Halting problem (ibid). "Algorithm versus function computable by an algorithm": For a given function multiple algorithms may exist. This is true, even without expanding the available instruction set available to the programmer. Rogers observes | Algorithm | [
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2935 | that "It is . . . important to distinguish between the notion of "algorithm", i.e. procedure and the notion of "function computable by algorithm", i.e. mapping yielded by procedure. The same function may have several different algorithms". Unfortunately, there may be a tradeoff between goodness (speed) and elegance (compactness)—an elegant program may take more steps to complete a computation than one less elegant. An example that uses Euclid's algorithm appears below. "Computers (and computors), models of computation": A computer (or human "computor") is a restricted type of machine, a "discrete deterministic mechanical device" that blindly follows its instructions. Melzak's and | Algorithm | [
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0.02341217920184... |
2936 | Lambek's primitive models reduced this notion to four elements: (i) discrete, distinguishable "locations", (ii) discrete, indistinguishable "counters" (iii) an agent, and (iv) a list of instructions that are "effective" relative to the capability of the agent. Minsky describes a more congenial variation of Lambek's "abacus" model in his "Very Simple Bases for Computability". Minsky's machine proceeds sequentially through its five (or six, depending on how one counts) instructions, unless either a conditional IF–THEN GOTO or an unconditional GOTO changes program flow out of sequence. Besides HALT, Minsky's machine includes three "assignment" (replacement, substitution) operations: ZERO (e.g. the contents of location | Algorithm | [
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0.0709401220083... |
2937 | replaced by 0: L ← 0), SUCCESSOR (e.g. L ← L+1), and DECREMENT (e.g. L ← L − 1). Rarely must a programmer write "code" with such a limited instruction set. But Minsky shows (as do Melzak and Lambek) that his machine is Turing complete with only four general "types" of instructions: conditional GOTO, unconditional GOTO, assignment/replacement/substitution, and HALT. "Simulation of an algorithm: computer (computor) language": Knuth advises the reader that "the best way to learn an algorithm is to try it . . . immediately take pen and paper and work through an example". But what about a simulation | Algorithm | [
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2938 | or execution of the real thing? The programmer must translate the algorithm into a language that the simulator/computer/computor can "effectively" execute. Stone gives an example of this: when computing the roots of a quadratic equation the computor must know how to take a square root. If they don't, then the algorithm, to be effective, must provide a set of rules for extracting a square root. This means that the programmer must know a "language" that is effective relative to the target computing agent (computer/computor). But what model should be used for the simulation? Van Emde Boas observes "even if we | Algorithm | [
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2939 | base complexity theory on abstract instead of concrete machines, arbitrariness of the choice of a model remains. It is at this point that the notion of "simulation" enters". When speed is being measured, the instruction set matters. For example, the subprogram in Euclid's algorithm to compute the remainder would execute much faster if the programmer had a "modulus" instruction available rather than just subtraction (or worse: just Minsky's "decrement"). "Structured programming, canonical structures": Per the Church–Turing thesis, any algorithm can be computed by a model known to be Turing complete, and per Minsky's demonstrations, Turing completeness requires only four instruction | Algorithm | [
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2940 | types—conditional GOTO, unconditional GOTO, assignment, HALT. Kemeny and Kurtz observe that, while "undisciplined" use of unconditional GOTOs and conditional IF-THEN GOTOs can result in "spaghetti code", a programmer can write structured programs using only these instructions; on the other hand "it is also possible, and not too hard, to write badly structured programs in a structured language". Tausworthe augments the three Böhm-Jacopini canonical structures: SEQUENCE, IF-THEN-ELSE, and WHILE-DO, with two more: DO-WHILE and CASE. An additional benefit of a structured program is that it lends itself to proofs of correctness using mathematical induction. "Canonical flowchart symbols": The graphical aide called | Algorithm | [
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2941 | a flowchart, offers a way to describe and document an algorithm (and a computer program of one). Like the program flow of a Minsky machine, a flowchart always starts at the top of a page and proceeds down. Its primary symbols are only four: the directed arrow showing program flow, the rectangle (SEQUENCE, GOTO), the diamond (IF-THEN-ELSE), and the dot (OR-tie). The Böhm–Jacopini canonical structures are made of these primitive shapes. Sub-structures can "nest" in rectangles, but only if a single exit occurs from the superstructure. The symbols, and their use to build the canonical structures are shown in the | Algorithm | [
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0.026994664... |
2942 | diagram. One of the simplest algorithms is to find the largest number in a list of numbers of random order. Finding the solution requires looking at every number in the list. From this follows a simple algorithm, which can be stated in a high-level description in English prose, as: "High-level description:" "(Quasi-)formal description:" Written in prose but much closer to the high-level language of a computer program, the following is the more formal coding of the algorithm in pseudocode or pidgin code: Euclid's algorithm to compute the greatest common divisor (GCD) to two numbers appears as Proposition II in Book | Algorithm | [
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2943 | VII ("Elementary Number Theory") of his "Elements". Euclid poses the problem thus: "Given two numbers not prime to one another, to find their greatest common measure". He defines "A number [to be] a multitude composed of units": a counting number, a positive integer not including zero. To "measure" is to place a shorter measuring length "s" successively ("q" times) along longer length "l" until the remaining portion "r" is less than the shorter length "s". In modern words, remainder "r" = "l" − "q"×"s", "q" being the quotient, or remainder "r" is the "modulus", the integer-fractional part left over after | Algorithm | [
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0.0560033656... |
2944 | the division. For Euclid's method to succeed, the starting lengths must satisfy two requirements: (i) the lengths must not be zero, AND (ii) the subtraction must be “proper”; i.e., a test must guarantee that the smaller of the two numbers is subtracted from the larger (alternately, the two can be equal so their subtraction yields zero). Euclid's original proof adds a third requirement: the two lengths must not be prime to one another. Euclid stipulated this so that he could construct a reductio ad absurdum proof that the two numbers' common measure is in fact the "greatest". While Nicomachus' algorithm | Algorithm | [
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0.0909389033913... |
2945 | is the same as Euclid's, when the numbers are prime to one another, it yields the number "1" for their common measure. So, to be precise, the following is really Nicomachus' algorithm. Only a few instruction "types" are required to execute Euclid's algorithm—some logical tests (conditional GOTO), unconditional GOTO, assignment (replacement), and subtraction. The following algorithm is framed as Knuth's four-step version of Euclid's and Nicomachus', but, rather than using division to find the remainder, it uses successive subtractions of the shorter length "s" from the remaining length "r" until "r" is less than "s". The high-level description, shown in | Algorithm | [
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2946 | boldface, is adapted from Knuth 1973:2–4: INPUT: E0: [Ensure "r" ≥ "s".] E1: [Find remainder]: Until the remaining length "r" in R is less than the shorter length "s" in S, repeatedly subtract the measuring number "s" in S from the remaining length "r" in R. E2: [Is the remainder zero?]: EITHER (i) the last measure was exact, the remainder in R is zero, and the program can halt, OR (ii) the algorithm must continue: the last measure left a remainder in R less than measuring number in S. E3: [Interchange "s" and "r"]: The nut of Euclid's algorithm. Use | Algorithm | [
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0.0544418916106224... |
2947 | remainder "r" to measure what was previously smaller number "s"; L serves as a temporary location. OUTPUT: DONE: The following version of Euclid's algorithm requires only six core instructions to do what thirteen are required to do by "Inelegant"; worse, "Inelegant" requires more "types" of instructions. The flowchart of "Elegant" can be found at the top of this article. In the (unstructured) Basic language, the steps are numbered, and the instruction is the assignment instruction symbolized by ←. The following version can be used with Object Oriented languages: "How "Elegant" works": In place of an outer "Euclid loop", "Elegant" shifts | Algorithm | [
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2948 | back and forth between two "co-loops", an A > B loop that computes A ← A − B, and a B ≤ A loop that computes B ← B − A. This works because, when at last the minuend M is less than or equal to the subtrahend S ( Difference = Minuend − Subtrahend), the minuend can become "s" (the new measuring length) and the subtrahend can become the new "r" (the length to be measured); in other words the "sense" of the subtraction reverses. Does an algorithm do what its author wants it to do? A few test | Algorithm | [
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0.048864666372537... |
2949 | cases usually suffice to confirm core functionality. One source uses 3009 and 884. Knuth suggested 40902, 24140. Another interesting case is the two relatively prime numbers 14157 and 5950. But exceptional cases must be identified and tested. Will "Inelegant" perform properly when R > S, S > R, R = S? Ditto for "Elegant": B > A, A > B, A = B? (Yes to all). What happens when one number is zero, both numbers are zero? ("Inelegant" computes forever in all cases; "Elegant" computes forever when A = 0.) What happens if "negative" numbers are entered? Fractional numbers? If | Algorithm | [
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2950 | the input numbers, i.e. the domain of the function computed by the algorithm/program, is to include only positive integers including zero, then the failures at zero indicate that the algorithm (and the program that instantiates it) is a partial function rather than a total function. A notable failure due to exceptions is the Ariane 5 Flight 501 rocket failure (June 4, 1996). "Proof of program correctness by use of mathematical induction": Knuth demonstrates the application of mathematical induction to an "extended" version of Euclid's algorithm, and he proposes "a general method applicable to proving the validity of any algorithm". Tausworthe | Algorithm | [
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2951 | proposes that a measure of the complexity of a program be the length of its correctness proof. "Elegance (compactness) versus goodness (speed)": With only six core instructions, "Elegant" is the clear winner, compared to "Inelegant" at thirteen instructions. However, "Inelegant" is "faster" (it arrives at HALT in fewer steps). Algorithm analysis indicates why this is the case: "Elegant" does "two" conditional tests in every subtraction loop, whereas "Inelegant" only does one. As the algorithm (usually) requires many loop-throughs, "on average" much time is wasted doing a "B = 0?" test that is needed only after the remainder is computed. "Can | Algorithm | [
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2952 | the algorithms be improved?": Once the programmer judges a program "fit" and "effective"—that is, it computes the function intended by its author—then the question becomes, can it be improved? The compactness of "Inelegant" can be improved by the elimination of five steps. But Chaitin proved that compacting an algorithm cannot be automated by a generalized algorithm; rather, it can only be done heuristically; i.e., by exhaustive search (examples to be found at Busy beaver), trial and error, cleverness, insight, application of inductive reasoning, etc. Observe that steps 4, 5 and 6 are repeated in steps 11, 12 and 13. Comparison | Algorithm | [
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2953 | with "Elegant" provides a hint that these steps, together with steps 2 and 3, can be eliminated. This reduces the number of core instructions from thirteen to eight, which makes it "more elegant" than "Elegant", at nine steps. The speed of "Elegant" can be improved by moving the "B=0?" test outside of the two subtraction loops. This change calls for the addition of three instructions (B = 0?, A = 0?, GOTO). Now "Elegant" computes the example-numbers faster; whether this is always the case for any given A, B, and R, S would require a detailed analysis. It is frequently | Algorithm | [
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2954 | important to know how much of a particular resource (such as time or storage) is theoretically required for a given algorithm. Methods have been developed for the analysis of algorithms to obtain such quantitative answers (estimates); for example, the sorting algorithm above has a time requirement of O("n"), using the big O notation with "n" as the length of the list. At all times the algorithm only needs to remember two values: the largest number found so far, and its current position in the input list. Therefore, it is said to have a space requirement of "O(1)", if the space | Algorithm | [
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2955 | required to store the input numbers is not counted, or O("n") if it is counted. Different algorithms may complete the same task with a different set of instructions in less or more time, space, or 'effort' than others. For example, a binary search algorithm (with cost O(log n) ) outperforms a sequential search (cost O(n) ) when used for table lookups on sorted lists or arrays. The analysis, and study of algorithms is a discipline of computer science, and is often practiced abstractly without the use of a specific programming language or implementation. In this sense, algorithm analysis resembles other | Algorithm | [
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2956 | mathematical disciplines in that it focuses on the underlying properties of the algorithm and not on the specifics of any particular implementation. Usually pseudocode is used for analysis as it is the simplest and most general representation. However, ultimately, most algorithms are usually implemented on particular hardware/software platforms and their algorithmic efficiency is eventually put to the test using real code. For the solution of a "one off" problem, the efficiency of a particular algorithm may not have significant consequences (unless n is extremely large) but for algorithms designed for fast interactive, commercial or long life scientific usage it may | Algorithm | [
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0.00352269737... |
2957 | be critical. Scaling from small n to large n frequently exposes inefficient algorithms that are otherwise benign. Empirical testing is useful because it may uncover unexpected interactions that affect performance. Benchmarks may be used to compare before/after potential improvements to an algorithm after program optimization. Empirical tests cannot replace formal analysis, though, and are not trivial to perform in a fair manner. To illustrate the potential improvements possible even in well-established algorithms, a recent significant innovation, relating to FFT algorithms (used heavily in the field of image processing), can decrease processing time up to 1,000 times for applications like medical | Algorithm | [
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2958 | imaging. In general, speed improvements depend on special properties of the problem, which are very common in practical applications. Speedups of this magnitude enable computing devices that make extensive use of image processing (like digital cameras and medical equipment) to consume less power. There are various ways to classify algorithms, each with its own merits. One way to classify algorithms is by implementation means. Another way of classifying algorithms is by their design methodology or paradigm. There is a certain number of paradigms, each different from the other. Furthermore, each of these categories includes many different types of algorithms. Some | Algorithm | [
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2959 | common paradigms are: For optimization problems there is a more specific classification of algorithms; an algorithm for such problems may fall into one or more of the general categories described above as well as into one of the following: Every field of science has its own problems and needs efficient algorithms. Related problems in one field are often studied together. Some example classes are search algorithms, sorting algorithms, merge algorithms, numerical algorithms, graph algorithms, string algorithms, computational geometric algorithms, combinatorial algorithms, medical algorithms, machine learning, cryptography, data compression algorithms and parsing techniques. Fields tend to overlap with each other, and | Algorithm | [
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0.2124273031949... |
2960 | algorithm advances in one field may improve those of other, sometimes completely unrelated, fields. For example, dynamic programming was invented for optimization of resource consumption in industry but is now used in solving a broad range of problems in many fields. Algorithms can be classified by the amount of time they need to complete compared to their input size: Some problems may have multiple algorithms of differing complexity, while other problems might have no algorithms or no known efficient algorithms. There are also mappings from some problems to other problems. Owing to this, it was found to be more suitable | Algorithm | [
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0.013984983786... |
2961 | to classify the problems themselves instead of the algorithms into equivalence classes based on the complexity of the best possible algorithms for them. The adjective "continuous" when applied to the word "algorithm" can mean: Algorithms, by themselves, are not usually patentable. In the United States, a claim consisting solely of simple manipulations of abstract concepts, numbers, or signals does not constitute "processes" (USPTO 2006), and hence algorithms are not patentable (as in Gottschalk v. Benson). However practical applications of algorithms are sometimes patentable. For example, in Diamond v. Diehr, the application of a simple feedback algorithm to aid in the | Algorithm | [
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2962 | curing of synthetic rubber was deemed patentable. The patenting of software is highly controversial, and there are highly criticized patents involving algorithms, especially data compression algorithms, such as Unisys' LZW patent. Additionally, some cryptographic algorithms have export restrictions (see export of cryptography). Algorithms were used in ancient Greece. Two examples are the Sieve of Eratosthenes, which was described in Introduction to Arithmetic by Nicomachus, and the Euclidean algorithm, which was first described in Euclid's Elements (c. 300 BC). Babylonian clay tablets describe and employ algorithmic procedures to compute the time and place of significant astronomical events. Tally-marks: To keep track | Algorithm | [
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2963 | of their flocks, their sacks of grain and their money the ancients used tallying: accumulating stones or marks scratched on sticks or making discrete symbols in clay. Through the Babylonian and Egyptian use of marks and symbols, eventually Roman numerals and the abacus evolved (Dilson, p. 16–41). Tally marks appear prominently in unary numeral system arithmetic used in Turing machine and Post–Turing machine computations. The work of the ancient Greek geometers (Euclidean algorithm), the Indian mathematician Brahmagupta, and the Persian mathematician Al-Khwarizmi (from whose name the terms "algorism" and "algorithm" are derived), and Western European mathematicians culminated in Leibniz's notion | Algorithm | [
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2964 | of the calculus ratiocinator (ca 1680): "The clock": Bolter credits the invention of the weight-driven clock as "The key invention [of Europe in the Middle Ages]", in particular, the verge escapement that provides us with the tick and tock of a mechanical clock. "The accurate automatic machine" led immediately to "mechanical automata" beginning in the 13th century and finally to "computational machines"—the difference engine and analytical engines of Charles Babbage and Countess Ada Lovelace, mid-19th century. Lovelace is credited with the first creation of an algorithm intended for processing on a computer – Babbage's analytical engine, the first device considered | Algorithm | [
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2965 | a real Turing-complete computer instead of just a calculator – and is sometimes called "history's first programmer" as a result, though a full implementation of Babbage's second device would not be realized until decades after her lifetime. "Logical machines 1870—Stanley Jevons' "logical abacus" and "logical machine"": The technical problem was to reduce Boolean equations when presented in a form similar to what is now known as Karnaugh maps. Jevons (1880) describes first a simple "abacus" of "slips of wood furnished with pins, contrived so that any part or class of the [logical] combinations can be picked out mechanically . . | Algorithm | [
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2966 | . More recently, however, I have reduced the system to a completely mechanical form, and have thus embodied the whole of the indirect process of inference in what may be called a "Logical Machine"" His machine came equipped with "certain moveable wooden rods" and "at the foot are 21 keys like those of a piano [etc] . . .". With this machine he could analyze a "syllogism or any other simple logical argument". This machine he displayed in 1870 before the Fellows of the Royal Society. Another logician John Venn, however, in his 1881 "Symbolic Logic", turned a jaundiced eye | Algorithm | [
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2967 | to this effort: "I have no high estimate myself of the interest or importance of what are sometimes called logical machines ... it does not seem to me that any contrivances at present known or likely to be discovered really deserve the name of logical machines"; see more at Algorithm characterizations. But not to be outdone he too presented "a plan somewhat analogous, I apprehend, to Prof. Jevon's "abacus" ... [And] [a]gain, corresponding to Prof. Jevons's logical machine, the following contrivance may be described. I prefer to call it merely a logical-diagram machine ... but I suppose that it could | Algorithm | [
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2968 | do very completely all that can be rationally expected of any logical machine". "Jacquard loom, Hollerith punch cards, telegraphy and telephony—the electromechanical relay": Bell and Newell (1971) indicate that the Jacquard loom (1801), precursor to Hollerith cards (punch cards, 1887), and "telephone switching technologies" were the roots of a tree leading to the development of the first computers. By the mid-19th century the telegraph, the precursor of the telephone, was in use throughout the world, its discrete and distinguishable encoding of letters as "dots and dashes" a common sound. By the late 19th century the ticker tape (ca 1870s) was | Algorithm | [
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2969 | in use, as was the use of Hollerith cards in the 1890 U.S. census. Then came the teleprinter (ca. 1910) with its punched-paper use of Baudot code on tape. "Telephone-switching networks" of electromechanical relays (invented 1835) was behind the work of George Stibitz (1937), the inventor of the digital adding device. As he worked in Bell Laboratories, he observed the "burdensome' use of mechanical calculators with gears. "He went home one evening in 1937 intending to test his idea... When the tinkering was over, Stibitz had constructed a binary adding device". Davis (2000) observes the particular importance of the electromechanical | Algorithm | [
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2970 | relay (with its two "binary states" "open" and "closed"): "Symbols and rules": In rapid succession, the mathematics of George Boole (1847, 1854), Gottlob Frege (1879), and Giuseppe Peano (1888–1889) reduced arithmetic to a sequence of symbols manipulated by rules. Peano's "The principles of arithmetic, presented by a new method" (1888) was "the first attempt at an axiomatization of mathematics in a symbolic language". But Heijenoort gives Frege (1879) this kudos: Frege's is "perhaps the most important single work ever written in logic. ... in which we see a " 'formula language', that is a "lingua characterica", a language written with | Algorithm | [
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2971 | special symbols, "for pure thought", that is, free from rhetorical embellishments ... constructed from specific symbols that are manipulated according to definite rules". The work of Frege was further simplified and amplified by Alfred North Whitehead and Bertrand Russell in their Principia Mathematica (1910–1913). "The paradoxes": At the same time a number of disturbing paradoxes appeared in the literature, in particular, the Burali-Forti paradox (1897), the Russell paradox (1902–03), and the Richard Paradox. The resultant considerations led to Kurt Gödel's paper (1931)—he specifically cites the paradox of the liar—that completely reduces rules of recursion to numbers. "Effective calculability": In an | Algorithm | [
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2972 | effort to solve the Entscheidungsproblem defined precisely by Hilbert in 1928, mathematicians first set about to define what was meant by an "effective method" or "effective calculation" or "effective calculability" (i.e., a calculation that would succeed). In rapid succession the following appeared: Alonzo Church, Stephen Kleene and J. B. Rosser's λ-calculus a finely honed definition of "general recursion" from the work of Gödel acting on suggestions of Jacques Herbrand (cf. Gödel's Princeton lectures of 1934) and subsequent simplifications by Kleene. Church's proof that the Entscheidungsproblem was unsolvable, Emil Post's definition of effective calculability as a worker mindlessly following a list | Algorithm | [
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2973 | of instructions to move left or right through a sequence of rooms and while there either mark or erase a paper or observe the paper and make a yes-no decision about the next instruction. Alan Turing's proof of that the Entscheidungsproblem was unsolvable by use of his "a- [automatic-] machine"—in effect almost identical to Post's "formulation", J. Barkley Rosser's definition of "effective method" in terms of "a machine". S. C. Kleene's proposal of a precursor to "Church thesis" that he called "Thesis I", and a few years later Kleene's renaming his Thesis "Church's Thesis" and proposing "Turing's Thesis". Emil Post | Algorithm | [
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2974 | (1936) described the actions of a "computer" (human being) as follows: His symbol space would be Alan Turing's work preceded that of Stibitz (1937); it is unknown whether Stibitz knew of the work of Turing. Turing's biographer believed that Turing's use of a typewriter-like model derived from a youthful interest: "Alan had dreamt of inventing typewriters as a boy; Mrs. Turing had a typewriter, and he could well have begun by asking himself what was meant by calling a typewriter 'mechanical'". Given the prevalence of Morse code and telegraphy, ticker tape machines, and teletypewriters we might conjecture that all were | Algorithm | [
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2975 | influences. Turing—his model of computation is now called a Turing machine—begins, as did Post, with an analysis of a human computer that he whittles down to a simple set of basic motions and "states of mind". But he continues a step further and creates a machine as a model of computation of numbers. Turing's reduction yields the following: "It may be that some of these change necessarily invoke a change of state of mind. The most general single operation must, therefore, be taken to be one of the following: A few years later, Turing expanded his analysis (thesis, definition) with | Algorithm | [
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2976 | this forceful expression of it: J. Barkley Rosser defined an 'effective [mathematical] method' in the following manner (italicization added): Rosser's footnote No. 5 references the work of (1) Church and Kleene and their definition of λ-definability, in particular Church's use of it in his "An Unsolvable Problem of Elementary Number Theory" (1936); (2) Herbrand and Gödel and their use of recursion in particular Gödel's use in his famous paper "On Formally Undecidable Propositions of Principia Mathematica and Related Systems I" (1931); and (3) Post (1936) and Turing (1936–37) in their mechanism-models of computation. Stephen C. Kleene defined as his now-famous | Algorithm | [
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2977 | "Thesis I" known as the Church–Turing thesis. But he did this in the following context (boldface in original): A number of efforts have been directed toward further refinement of the definition of "algorithm", and activity is on-going because of issues surrounding, in particular, foundations of mathematics (especially the Church–Turing thesis) and philosophy of mind (especially arguments about artificial intelligence). For more, see Algorithm characterizations. Algorithm In mathematics and computer science, an algorithm () is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing, and automated reasoning tasks. As an effective method, an | Algorithm | [
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2978 | Annual plant An annual plant is a plant that completes its life cycle, from germination to the production of seeds, within one year, and then dies. Summer annuals germinate during spring or early summer and mature by autumn of the same year. Winter annuals germinate during the autumn and mature during the spring or summer of the following calendar year. One seed-to-seed life cycle for an annual can occur in as little as a month in some species, though most last several months. Oilseed rapa can go from seed-to-seed in about five weeks under a bank of fluorescent lamps. This | "Annual plant" | [
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2979 | style of growing is often used in classrooms for education. Many desert annuals are therophytes, because their seed-to-seed life cycle is only weeks and they spend most of the year as seeds to survive dry conditions. In cultivation, many food plants are, or are grown as, annuals, including virtually all domesticated grains. Some perennials and biennials are grown in gardens as annuals for convenience, particularly if they are not considered cold hardy for the local climate. Carrot, celery and parsley are true biennials (divarsiya) that are usually grown as annual crops for their edible roots, petioles and leaves, respectively. Tomato, | "Annual plant" | [
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2980 | sweet potato and bell pepper are tender perennials usually grown as annuals. Ornamental perennials commonly grown as annuals are impatiens, mirabilis, wax begonia, snapdragon, "pelargonium", coleus and petunia. Examples of true annuals include corn, wheat, rice, lettuce, peas, watermelon, beans, zinnia and marigold. Summer annuals sprout, flower, produce seed, and die, during the warmer months of the year. The lawn weed crabgrass is a summer annual. Winter annuals germinate in autumn or winter, live through the winter, then bloom in winter or spring. The plants grow and bloom during the cool season when most other plants are dormant or other | "Annual plant" | [
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2981 | annuals are in seed form waiting for warmer weather to germinate. Winter annuals die after flowering and setting seed. The seeds germinate in the autumn or winter when the soil temperature is cool. Winter annuals typically grow low to the ground, where they are usually sheltered from the coldest nights by snow cover, and make use of warm periods in winter for growth when the snow melts. Some common winter annuals include henbit, deadnettle, chickweed, and winter cress. Winter annuals are important ecologically, as they provide vegetative cover that prevents soil erosion during winter and early spring when no other | "Annual plant" | [
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2982 | cover exists and they provide fresh vegetation for animals and birds that feed on them. Although they are often considered to be weeds in gardens, this viewpoint is not always necessary, as most of them die when the soil temperature warms up again in early to late spring when other plants are still dormant and have not yet leafed out. Even though they do not compete directly with cultivated plants, sometimes winter annuals are considered a pest in commercial agriculture, because they can be hosts for insect pests or fungal diseases (ovary smut – Microbotryum sp) which attack crops being | "Annual plant" | [
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2983 | cultivated. The property that they prevent the soil from drying out can also be problematic for commercial agriculture. In 2008, it was discovered that the inactivation of only two genes in one species of annual plant leads to the conversion into a perennial plant. Researchers deactivated the SOC1 and FUL genes in "Arabidopsis thaliana", which control flowering time. This switch established phenotypes common in perennial plants, such as wood formation. Annual plant An annual plant is a plant that completes its life cycle, from germination to the production of seeds, within one year, and then dies. Summer annuals germinate during | "Annual plant" | [
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2984 | Anthophyta The anthophytes were thought to be a clade comprising plants bearing flower-like structures. The group contained the angiosperms - the extant flowering plants, such as roses and grasses - as well as the Gnetales and the extinct Bennettitales. Detailed morphological and molecular studies have shown that the group is not actually monophyletic, with proposed floral homologies of the gnetophytes and the angiosperms having evolved in parallel. This makes it easier to reconcile molecular clock data that suggests that the angiosperms diverged from the gymnosperms around . Some more recent studies have used the word anthophyte to describe a group | Anthophyta | [
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2985 | which includes the angiosperms and a variety of fossils (glossopterids, "Pentoxylon", Bennettitales, and "Caytonia"), but not the Gnetales. Anthophyta The anthophytes were thought to be a clade comprising plants bearing flower-like structures. The group contained the angiosperms - the extant flowering plants, such as roses and grasses - as well as the Gnetales and the extinct Bennettitales. Detailed morphological and molecular studies have shown that the group is not actually monophyletic, with proposed floral homologies of the gnetophytes and the angiosperms having evolved in parallel. This makes it easier to reconcile molecular clock data that suggests that the angiosperms diverged | Anthophyta | [
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2986 | Mouthwash Mouthwash, mouth rinse, oral rinse, or mouth bath is a liquid which is held in the mouth passively or swilled around the mouth by contraction of the perioral muscles and/or movement of the head, and may be gargled, where the head is tilted back and the liquid bubbled at the back of the mouth. Usually mouthwashes are antiseptic solutions intended to reduce the microbial load in the oral cavity, although other mouthwashes might be given for other reasons such as for their analgesic, anti-inflammatory or anti-fungal action. Additionally, some rinses act as saliva substitutes to neutralize acid and keep | Mouthwash | [
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2987 | the mouth moist in xerostomia (dry mouth). Cosmetic mouthrinses temporarily control or reduce bad breath and leave the mouth with a pleasant taste. Rinsing with water or mouthwash after brushing with a fluoride toothpaste can reduce the availability of salivary fluoride. This can lower the anti-cavity re-mineralization and antibacterial effects of fluoride. Fluoridated mouthwash may mitigate this effect or in high concentrations increase available fluoride. A group of experts discussing post brushing rinsing in 2012 found that although there was clear guidance given in many public health advice publications to "spit, avoid rinsing with water/excessive rinsing with water" they believed | Mouthwash | [
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2988 | there was a limited evidence base for best practice. Common use involves rinsing the mouth with about 20-50 ml (2/3 fl oz) of mouthwash. The wash is typically swished or gargled for about half a minute and then spat out. Most companies suggest not drinking water immediately after using mouthwash. In some brands, the expectorate is stained, so that one can see the bacteria and debris. Mouthwash should not be used immediately after brushing the teeth so as not to wash away the beneficial fluoride residue left from the toothpaste. Similarly, the mouth should not be rinsed out with water | Mouthwash | [
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2989 | after brushing. Patients were told to "spit don't rinse" after toothbrushing as part of a National Health Service campaign in the UK. Gargling is where the head is tilted back, allowing the mouthwash to sit in the back of the mouth while exhaling, causing the liquid to bubble. Gargling is practiced in Japan for perceived prevention of viral infection. One commonly used way is with infusions or tea. In some cultures, gargling is usually done in private, typically in a bathroom at a sink so the liquid can be rinsed away. The most common use of mouthwash is commercial antiseptics, | Mouthwash | [
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2990 | which are used at home as part of an oral hygiene routine. Examples of commercial mouthwashes companies include Cēpacol, Colgate, Corsodyl, Dentyl pH, Listerine, , Oral-B, Sarakan, Scope, Tantum verde, and Biotene. Mouthwashes combine ingredients to treat a variety of oral conditions. Variations are common, and mouthwash has no standard formulation so its use and recommendation involves concerns about patient safety. Some manufacturers of mouthwash state that antiseptic and anti-plaque mouth rinse kill the bacterial plaque that causes cavities, gingivitis, and bad breath. It is, however, generally agreed that the use of mouthwash does not eliminate the need for both | Mouthwash | [
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2991 | brushing and flossing. The American Dental Association asserts that regular brushing and proper flossing are enough in most cases, in addition to regular dental check-ups, although they approve many mouthwashes. For many patients, however, the mechanical methods could be tedious and time-consuming and additionally some local conditions may render them especially difficult. Chemotherapeutic agents, including mouthrinses, could have a key role as adjuncts to daily home care, preventing and controlling supragingival plaque, gingivitis and oral malodor. Minor and transient side effects of mouthwashes are very common, such as taste disturbance, tooth staining, sensation of a dry mouth, etc. Alcohol-containing mouthwashes | Mouthwash | [
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2992 | may make dry mouth and halitosis worse since it dries out the mouth. Soreness, ulceration and redness may sometimes occur (e.g. aphthous stomatitis, allergic contact stomatitis) if the person is allergic or sensitive to mouthwash ingredients such as preservatives, coloring, flavors and fragrances. Such effects might be reduced or eliminated by diluting the mouthwash with water, using a different mouthwash (e.g. salt water), or foregoing mouthwash entirely. Prescription mouthwashes are used prior to and after oral surgery procedures such as tooth extraction or to treat the pain associated with mucositis caused by radiation therapy or chemotherapy. They are also prescribed | Mouthwash | [
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2993 | for aphthous ulcers, other oral ulcers, and other mouth pain. Magic mouthwashes are prescription mouthwashes compounded in a pharmacy from a list of ingredients specified by a doctor. Despite a lack of evidence that prescription mouthwashes are more effective in decreasing the pain of oral lesions, many patients and prescribers continue to use them. There has been only one controlled study to evaluate the efficacy of magic mouthwash; it shows no difference in efficacy among the most common formulation and commercial mouthwashes such as chlorhexidine or a saline/baking soda solution. Current guidelines suggest that saline solution is just as effective | Mouthwash | [
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2994 | as magic mouthwash in pain relief or shortening of healing time of oral mucositis from cancer therapies. The first known references to mouth rinsing is in Ayurveda for treatment of gingivitis. Later, in the Greek and Roman periods, mouth rinsing following mechanical cleansing became common among the upper classes, and Hippocrates recommended a mixture of salt, alum, and vinegar. The Jewish Talmud, dating back about 1,800 years, suggests a cure for gum ailments containing "dough water" and olive oil. Before Europeans came to the Americas, Native North American and Mesoamerican cultures used mouthwashes, often made from plants such as "Coptis | Mouthwash | [
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2995 | trifolia". Indeed, Aztec dentistry was more advanced than European dentistry of the age. Peoples of the Americas used salt water mouthwashes for sore throats, and other mouthwashes for problems such as teething and mouth ulcers. Anton van Leeuwenhoek, the famous 17th century microscopist, discovered living organisms (living, because they were mobile) in deposits on the teeth (what we now call dental plaque). He also found organisms in water from the canal next to his home in Delft. He experimented with samples by adding vinegar or brandy and found that this resulted in the immediate immobilization or killing of the organisms | Mouthwash | [
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2996 | suspended in water. Next he tried rinsing the mouth of himself and somebody else with a mouthwash containing vinegar or brandy and found that living organisms remained in the dental plaque. He concluded—correctly—that the mouthwash either did not reach, or was not present long enough, to kill the plaque organisms. In 1892, German Richard Seifert invented mouthwash product Odol, which was produced by company founder Karl August Lingner (1861–1916) in Dresden. That remained the state of affairs until the late 1960s when Harald Loe (at the time a professor at the Royal Dental College in Aarhus, Denmark) demonstrated that a | Mouthwash | [
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2997 | chlorhexidine compound could prevent the build-up of dental plaque. The reason for chlorhexidine's effectiveness is that it strongly adheres to surfaces in the mouth and thus remains present in effective concentrations for many hours. Since then commercial interest in mouthwashes has been intense and several newer products claim effectiveness in reducing the build-up in dental plaque and the associated severity of gingivitis, in addition to fighting bad breath. Many of these solutions aim to control the Volatile Sulfur Compound (VSC)-creating anaerobic bacteria that live in the mouth and excrete substances that lead to bad breath and unpleasant mouth taste. For | Mouthwash | [
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2998 | example, the number of mouthwash variants in the United States of America has grown from 15 (1970) to 66 (1998) to 113 (2012). Research in the field of microbiotas shows that only a limited set of microbes cause tooth decay, with most of the bacteria in the human mouth being harmless. Focused attention on cavity-causing bacteria such as "Streptococcus mutans" has led research into new mouthwash treatments that prevent these bacteria from initially growing. While current mouthwash treatments must be used with a degree of frequency to prevent this bacteria from regrowing, future treatments could provide a viable long term | Mouthwash | [
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2999 | solution. Alcohol is added to mouthwash not to destroy bacteria but to act as a carrier agent for essential active ingredients such as menthol, eucalyptol and thymol which help to penetrate plaque. Sometimes a significant amount of alcohol (up to 27% vol) is added, as a carrier for the flavor, to provide "bite". Because of the alcohol content, it is possible to fail a breathalyzer test after rinsing although breath alcohol levels return to normal after 10 minutes. In addition, alcohol is a drying agent, which encourages bacterial activity in the mouth, releasing more malodorous volatile sulfur compounds. Therefore, alcohol-containing | Mouthwash | [
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3000 | mouthwash may temporarily worsen halitosis in those who already have it, or indeed be the sole cause of halitosis in other individuals. It is hypothesized that alcohol mouthwashes acts as a carcinogen (cancer-inducing). Generally, there is no scientific consensus about this. One review stated: The same researchers also state that the risk of acquiring oral cancer rises almost five times for users of alcohol-containing mouthwash who neither smoke nor drink (with a higher rate of increase for those who do). In addition, the authors highlight side effects from several mainstream mouthwashes that included dental erosion and accidental poisoning of children. | Mouthwash | [
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... |
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