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Ampere

The ampere (, ;   symbol: A), often shortened to amp, is the unit of electric current in the International System of Units (SI). One ampere is equal to 1 coulomb (C) moving past a point per second. It is named after French mathematician and physicist André-Marie Ampère (1775–1836), considered the father of electromagnetism along with Danish physicist Hans Christian Ørsted.

As of the 2019 redefinition of the SI base units, the ampere is defined by fixing the elementary charge e to be exactly, which means an ampere is an electric current equivalent to $$ elementary charges moving every $1.602$ seconds or $6.242$ elementary charges moving in a second. Prior to the redefinition the ampere was defined as the current passing through two parallel wires 1 metre apart that produces a magnetic force of $2$ newtons per metre.

The earlier CGS system has two units of current, one structured similarly to the SI's and the other using Coulomb's law as a fundamental relationship, with the CGS unit of charge defined by measuring the force between two charged metal plates. The CGS unit of current is then defined as one unit of charge per second.

History
The ampere is named for French physicist and mathematician André-Marie Ampère (1775–1836), who studied electromagnetism and laid the foundation of electrodynamics. In recognition of Ampère's contributions to the creation of modern electrical science, an international convention, signed at the 1881 International Exposition of Electricity, established the ampere as a standard unit of electrical measurement for electric current.

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 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 $0.001 grams$ of silver per second from a silver nitrate solution. Later, more accurate measurements revealed that this current is $1 A$.

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 A = 1 W/V. Current can be measured by a multimeter, a device that can measure electrical voltage, current, and resistance.

Former definition in the SI
Until 2019, the SI defined the 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 equal to $2$ 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, was then defined as "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:
 * $$\rm 1\ A=1\frac C s.$$

In general, charge $Q$ was determined by steady current $I$ flowing for a time $t$ as $Q = It$.

This definition of the ampere was most accurately realised using a Kibble balance, but in practice the unit was maintained via Ohm's law from the units of electromotive force and resistance, the volt and the ohm, since the latter two could be tied to physical phenomena that are relatively easy to reproduce, the Josephson effect and the quantum Hall effect, respectively.

Techniques to establish the realisation of an ampere had a relative uncertainty of approximately a few parts in 10$7$, and involved realisations of the watt, the ohm and the volt.

Present definition
The 2019 redefinition of the SI base units defined the ampere by taking the fixed numerical value of the elementary charge $e$ to be when expressed in the unit C, which is equal to A⋅s, where the second is defined in terms of $∆ν_{Cs}$, the unperturbed ground state hyperfine transition frequency of the caesium-133 atom.

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:
 * $$\rm 1\ A=1\,\text{C/s}.$$

In general, charge $Q$ is determined by steady current $I$ flowing for a time $t$ as $Q = I t$.

Constant, instantaneous and average current 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 $30,000 C$"). The relation of the ampere (C/s) to the coulomb is the same as that of the watt (J/s) to the joule.

Units derived from the ampere
The international system of units (SI) is based on seven SI base units the second, metre, kilogram, kelvin, ampere, mole, and candela representing seven fundamental types of physical quantity, or "dimensions", (time, length, mass, temperature, electric current, amount of substance, and luminous intensity respectively) with all other SI units being defined using these. These SI derived units can either be given special names e.g. watt, volt, lux, etc. or defined in terms of others, e.g. metre per second. The units with special names derived from the ampere are:

There are also some SI units that are frequently used in the context of electrical engineering and electrical appliances, but are defined independently of the ampere, notably the hertz, joule, watt, candela, lumen, and lux.

SI prefixes
Like other SI units, the ampere can be modified by adding a prefix that multiplies it by a power of 10.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Ampere


text:
Talk:American football

Wrong Wrong Wrong
American football is NOT referred to as "Gridiron" -- not anywhere in the U.S., anyway. Whoever entered that reference in the main article either must not be from this country or has no interest in or knowledge of the game. The gridiron is another name for the FIELD on which the game is played, a holdover from the early days when, in addition to the 5 or 10 yard stripes, lines were also laid down from end zone to endzone, running perpendicular to the yard stripes, thus forming a grid. References are sometimes made to play "on the gridiron," yes, but is the sport ever referred to as Gridiron? That is a distinct and hearty "no way." 138.207.186.136 (talk) 13:26, 16 October 2023 (UTC)
 * In the U.K. it is routinely called gridiron football.Jeff in CA (talk) 21:50, 17 October 2023 (UTC)
 * A few people in the UK may refer to it as this but not routinely. This because in the UK American football doesn't even rank as a minor sport. — Preceding unsigned comment added by 93.204.186.108 (talk) 16:30, 10 November 2023 (UTC)
 * This term is not used in the U.S. when referring to the game. However, it is correct in its use as a differentiator from other firms of football (Association-, Australian Rules-, Rugby-, etc.), even if it IS only derivative. For that purpose, it's important that it be left unchanged.
 * More to the point, any semi-knowledgeable fan of the sport understands exactly what you mean when you say gridiron football. Ploobus (talk) 13:28, 15 December 2023 (UTC)

Authorized player numbers now include the number 0
On March 28, 2023, NFL owners approved the use of the number zero for all non-linemen beginning in the 2023-2024 NFL season.

The article currently States that the NFL only allows the use of numbers 1-99. This needs to be changed to 0-99

https://www.nfl.com/news/nfl-owners-approve-proposal-to-allow-players-to-wear-no-0 Ploobus (talk) 13:21, 15 December 2023 (UTC)

Semi-protected edit request on 1 January 2024
Reference 160 is not a relevant reference for the said article but purely a backlink attempt. Nothing about the reference provides value to the article. Should be removed as it purely for advertisement purposes. Alphape1 (talk) 19:39, 1 January 2024 (UTC)

 * Red information icon with gradient background.svg Not done: If you are talking about this reference, then I think it's pretty relevant here and I don't see any good reason to remove it.  Delta  space 42 (talk • contribs) 16:38, 2 January 2024 (UTC)

Decimals over fractions?
In the field and equipment section I see a TON of fractions that make it a bit harsh on the eyes. I know in general Wiki prefers to use of decimals to fractions and I'm think that this is a section that would benefit from that change. Lindsey40186 (talk) 19:45, 19 April 2024 (UTC)
 * The rules define them by fractions, not decimals, and since American units don't really use decimals it's the most natural way to use them, imo. AFAIK, only SI units are supposed to 100% use decimals here. Toa Nidhiki05 19:48, 19 April 2024 (UTC)
 * Fair enough :) Lindsey40186 (talk) 18:28, 13 May 2024 (UTC)

Semi-protected edit request on 13 May 2024
BennettDT (talk) 15:17, 13 May 2024 (UTC)

 * Red information icon with gradient background.svg Not done: this is not the right page to request additional user rights. You may reopen this request with the specific changes to be made and someone may add them for you, or if you have an account, you can wait until you are autoconfirmed and edit the page yourself. Myrealnamm-alt (talk) 15:27, 13 May 2024 (UTC)

For a project

title: Talk:American football


text:
Algorithm

In mathematics and computer science, an algorithm is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually. Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus".

In contrast, a heuristic is an approach to problem-solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. For example, social media recommender systems rely on heuristics in such a way that, although widely characterized as "algorithms" in 21st-century popular media, cannot deliver correct results due to the nature of the problem.

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 to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.

Etymology
Around 825 AD, Persian scientist and polymath Muḥammad ibn Mūsā al-Khwārizmī wrote kitāb al-ḥisāb al-hindī ("Book of Indian computation") and kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī ("Addition and subtraction in Indian arithmetic"). In the early 12th century, Latin translations of said al-Khwarizmi texts involving the Hindu–Arabic numeral system and arithmetic appeared, for example Liber Alghoarismi de practica arismetrice, attributed to John of Seville, and Liber Algorismi de numero Indorum, attributed to Adelard of Bath. Hereby, alghoarismi or algorismi is the Latinization of Al-Khwarizmi's name; the text starts with the phrase Dixit Algorismi, or "Thus spoke Al-Khwarizmi". Around 1230, the English word algorism is attested and then by Chaucer in 1391, English adopted the French term. In the 15th century, under the influence of the Greek word ἀριθμός (arithmos, "number"; cf. "arithmetic"), the Latin word was altered to algorithmus.

Definition
One informal definition is "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), and (for example) any prescribed bureaucratic procedure or cook-book recipe. In general, a program is an algorithm only if it stops eventually —even though infinite loops may sometimes prove desirable. define an algorithm to be a set of instructions for determining an output, given explicitly, in a form that can be followed by either a computing machine or a human who could only carry out specific elementary operations on symbols.

The concept of algorithm is also used to define the notion of decidability—a notion that 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 the customary physical dimension. From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete (in some sense) and abstract usage of the term.

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.

Ancient algorithms
Since antiquity, step-by-step procedures for solving mathematical problems have been attested. This includes in Babylonian mathematics (around 2500 BC), Egyptian mathematics (around 1550 BC), Indian mathematics (around 800 BC and later), The Ifa Oracle (around 500 BC), Greek mathematics (around 240 BC), and Arabic mathematics (around 800 AD).

The earliest evidence of algorithms is found in the Babylonian mathematics of ancient Mesopotamia (modern Iraq). A Sumerian clay tablet found in Shuruppak near Baghdad and dated to c. 2500 BC described the earliest division algorithm. During the Hammurabi dynasty c. 1800, Babylonian clay tablets described algorithms for computing formulas. Algorithms were also used in Babylonian astronomy. Babylonian clay tablets describe and employ algorithmic procedures to compute the time and place of significant astronomical events.

Algorithms for arithmetic are also found in ancient Egyptian mathematics, dating back to the Rhind Mathematical Papyrus c. 1550 BC. Algorithms were later used in ancient Hellenistic mathematics. Two examples are the Sieve of Eratosthenes, which was described in the Introduction to Arithmetic by Nicomachus, and the Euclidean algorithm, which was first described in Euclid's Elements (c. 300 BC). Examples of ancient Indian mathematics included the Shulba Sutras, the Kerala School, and the Brāhmasphuṭasiddhānta.

The first cryptographic algorithm for deciphering encrypted code was developed by Al-Kindi, a 9th-century Arab mathematician, in A Manuscript On Deciphering Cryptographic Messages. He gave the first description of cryptanalysis by frequency analysis, the earliest codebreaking algorithm.

Weight-driven clocks
Bolter credits the invention of the weight-driven clock as "The key invention [of Europe in the Middle Ages]". In particular, he credits the verge escapement mechanism 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 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.

Electromechanical relay
Bell and Newell (1971) indicate that the Jacquard loom (1801), a 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 (c. 1870s) was in use, as was the use of Hollerith cards in the 1890 U.S. census. Then came the teleprinter (c. 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". The mathematician Martin Davis supported the particular importance of the electromechanical relay.

Formalization

In 1928, a partial formalization of the modern concept of algorithms began with attempts to solve the Entscheidungsproblem (decision problem) posed by David Hilbert. Later formalizations were framed as 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.

Representations
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 statements based on natural language. Programming languages are primarily intended for expressing algorithms in a form that can be executed by a computer, but they are also often used as a way to define or document algorithms.

Turing machines
There is a wide variety of representations possible and one can express a given Turing machine program as a sequence of machine tables (see finite-state machine, state-transition table, and control table for more), as flowcharts and drakon-charts (see state diagram for more), or as a form of rudimentary machine code or assembly code called "sets of quadruples" (see Turing machine for more). Representations of algorithms can also be classified into three accepted levels of Turing machine description: high-level description, implementation description, and formal description. A high-level description describes qualities of the algorithm itself, ignoring how it is implemented on the Turing machine. An implementation description describes the general manner in which the machine moves its head and stores data in order to carry out the algorithm, but doesn't give exact states. In the most detail, a formal description gives the exact state table and list of transitions of the Turing machine.

Flowchart representation
The graphical aid called a flowchart offers a way to describe and document an algorithm (and a computer program corresponding to it). 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 diagram.

Algorithmic analysis
It is frequently 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, an algorithm that adds up the elements of a list of n numbers would have a time requirement of $O(n)$, using big O notation. At all times the algorithm only needs to remember two values: the sum of all the elements 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 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.

Formal versus empirical
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 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 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.

Execution efficiency
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 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.

Design
Algorithm design refers to a method or a mathematical process for problem-solving and engineering algorithms. The design of algorithms is part of many solution theories, such as divide-and-conquer or dynamic programming within operation research. Techniques for designing and implementing algorithm designs are also called algorithm design patterns, with examples including the template method pattern and the decorator pattern. One of the most important aspects of algorithm design is resource (run-time, memory usage) efficiency; the big O notation is used to describe e.g., an algorithm's run-time growth as the size of its input increases.

Structured programming
Per the Church–Turing thesis, any algorithm can be computed by a model known to be Turing complete. In fact, it has been demonstrated that Turing completeness requires only four instruction types—conditional GOTO, unconditional GOTO, assignment, HALT. However, 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.

Legal status
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), so 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 curing of synthetic rubber was deemed patentable. The patenting of software is controversial, and there are criticized patents involving algorithms, especially data compression algorithms, such as Unisys's LZW patent. Additionally, some cryptographic algorithms have export restrictions (see export of cryptography).

Classification
There are various ways to classify algorithms, each with its own merits.

By implementation
One way to classify algorithms is by implementation means.

 * Recursion
 * A recursive algorithm is one that invokes (makes reference to) itself repeatedly until a certain condition (also known as termination condition) matches, which is a method common to functional programming. Iterative algorithms use repetitive constructs like loops and sometimes additional data structures like stacks to solve the given problems. Some problems are naturally suited for one implementation or the other. For example, towers of Hanoi is well understood using recursive implementation. Every recursive version has an equivalent (but possibly more or less complex) iterative version, and vice versa.

 * Serial, parallel or distributed
 * Algorithms are usually discussed with the assumption that computers execute one instruction of an algorithm at a time. Those computers are sometimes called serial computers. An algorithm designed for such an environment is called a serial algorithm, as opposed to parallel algorithms or distributed algorithms. Parallel algorithms are algorithms that take advantage of computer architectures where multiple processors can work on a problem at the same time. Distributed algorithms are algorithms that use multiple machines connected to a computer network. Parallel and distributed algorithms divide the problem into more symmetrical or asymmetrical subproblems and collect the results back together. For example, a CPU would be an example of a parallel algorithm. The resource consumption in such algorithms is not only processor cycles on each processor but also the communication overhead between the processors. Some sorting algorithms can be parallelized efficiently, but their communication overhead is expensive. Iterative algorithms are generally parallelizable, but some problems have no parallel algorithms and are called inherently serial problems.

 * Deterministic or non-deterministic
 * Deterministic algorithms solve the problem with exact decision at every step of the algorithm whereas non-deterministic algorithms solve problems via guessing although typical guesses are made more accurate through the use of heuristics.

 * Exact or approximate
 * While many algorithms reach an exact solution, approximation algorithms seek an approximation that is closer to the true solution. The approximation can be reached by either using a deterministic or a random strategy. Such algorithms have practical value for many hard problems. One of the examples of an approximate algorithm is the Knapsack problem, where there is a set of given items. Its goal is to pack the knapsack to get the maximum total value. Each item has some weight and some value. The total weight that can be carried is no more than some fixed number X. So, the solution must consider weights of items as well as their value.

 * Quantum algorithm
 * Quantum algorithms run on a realistic model of quantum computation. The term is usually used for those algorithms which seem inherently quantum, or use some essential feature of Quantum computing such as quantum superposition or quantum entanglement.

By design paradigm
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 common paradigms are:

 * Brute-force or exhaustive search
 * Brute force is a method of problem-solving that involves systematically trying every possible option until the optimal solution is found. This approach can be very time-consuming, as it requires going through every possible combination of variables. However, it is often used when other methods are not available or too complex. Brute force can be used to solve a variety of problems, including finding the shortest path between two points and cracking passwords.

 * Divide and conquer
 * A divide-and-conquer algorithm repeatedly reduces an instance of a problem to one or more smaller instances of the same problem (usually recursively) until the instances are small enough to solve easily. One such example of divide and conquer is merge sorting. Sorting can be done on each segment of data after dividing data into segments and sorting of entire data can be obtained in the conquer phase by merging the segments. A simpler variant of divide and conquer is called a decrease-and-conquer algorithm, which solves an identical subproblem and uses the solution of this subproblem to solve the bigger problem. Divide and conquer divides the problem into multiple subproblems and so the conquer stage is more complex than decrease and conquer algorithms. An example of a decrease and conquer algorithm is the binary search algorithm.

 * Search and enumeration
 * Many problems (such as playing chess) can be modeled as problems on graphs. A graph exploration algorithm specifies rules for moving around a graph and is useful for such problems. This category also includes search algorithms, branch and bound enumeration, and backtracking.

 * Randomized algorithm
 * Such algorithms make some choices randomly (or pseudo-randomly). They can be very useful in finding approximate solutions for problems where finding exact solutions can be impractical (see heuristic method below). For some of these problems, it is known that the fastest approximations must involve some randomness. Whether randomized algorithms with polynomial time complexity can be the fastest algorithm for some problems is an open question known as the P versus NP problem. There are two large classes of such algorithms:
 * 1) Monte Carlo algorithms return a correct answer with high-probability. E.g. RP is the subclass of these that run in polynomial time.
 * 2) Las Vegas algorithms always return the correct answer, but their running time is only probabilistically bound, e.g. ZPP.
 * Reduction of complexity
 * This technique involves solving a difficult problem by transforming it into a better-known problem for which we have (hopefully) asymptotically optimal algorithms. The goal is to find a reducing algorithm whose complexity is not dominated by the resulting reduced algorithms. For example, one selection algorithm for finding the median in an unsorted list involves first sorting the list (the expensive portion) and then pulling out the middle element in the sorted list (the cheap portion). This technique is also known as transform and conquer.

 * Back tracking
 * In this approach, multiple solutions are built incrementally and abandoned when it is determined that they cannot lead to a valid full solution.

Optimization problems
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:

 * Linear programming
 * When searching for optimal solutions to a linear function bound to linear equality and inequality constraints, the constraints of the problem can be used directly in producing the optimal solutions. There are algorithms that can solve any problem in this category, such as the popular simplex algorithm. Problems that can be solved with linear programming include the maximum flow problem for directed graphs. If a problem additionally requires that one or more of the unknowns must be an integer then it is classified in integer programming. A linear programming algorithm can solve such a problem if it can be proved that all restrictions for integer values are superficial, i.e., the solutions satisfy these restrictions anyway. In the general case, a specialized algorithm or an algorithm that finds approximate solutions is used, depending on the difficulty of the problem.
 * Dynamic programming
 * When a problem shows optimal substructures—meaning the optimal solution to a problem can be constructed from optimal solutions to subproblems—and overlapping subproblems, meaning the same subproblems are used to solve many different problem instances, a quicker approach called dynamic programming avoids recomputing solutions that have already been computed. For example, Floyd–Warshall algorithm, the shortest path to a goal from a vertex in a weighted graph can be found by using the shortest path to the goal from all adjacent vertices. Dynamic programming and memoization go together. The main difference between dynamic programming and divide and conquer is that subproblems are more or less independent in divide and conquer, whereas subproblems overlap in dynamic programming. The difference between dynamic programming and straightforward recursion is in caching or memoization of recursive calls. When subproblems are independent and there is no repetition, memoization does not help; hence dynamic programming is not a solution for all complex problems. By using memoization or maintaining a table of subproblems already solved, dynamic programming reduces the exponential nature of many problems to polynomial complexity.

 * The greedy method
 * A greedy algorithm is similar to a dynamic programming algorithm in that it works by examining substructures, in this case not of the problem but of a given solution. Such algorithms start with some solution, which may be given or have been constructed in some way, and improve it by making small modifications. For some problems they can find the optimal solution while for others they stop at local optima, that is, at solutions that cannot be improved by the algorithm but are not optimum. The most popular use of greedy algorithms is for finding the minimal spanning tree where finding the optimal solution is possible with this method. Huffman Tree, Kruskal, Prim, Sollin are greedy algorithms that can solve this optimization problem.

 * The heuristic method
 * In optimization problems, heuristic algorithms can be used to find a solution close to the optimal solution in cases where finding the optimal solution is impractical. These algorithms work by getting closer and closer to the optimal solution as they progress. In principle, if run for an infinite amount of time, they will find the optimal solution. Their merit is that they can find a solution very close to the optimal solution in a relatively short time. Such algorithms include local search, tabu search, simulated annealing, and genetic algorithms. Some of them, like simulated annealing, are non-deterministic algorithms while others, like tabu search, are deterministic. When a bound on the error of the non-optimal solution is known, the algorithm is further categorized as an approximation algorithm.

Examples
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:
 * 1) If there are no numbers in the set, then there is no highest number.
 * 2) Assume the first number in the set is the largest number in the set.
 * 3) For each remaining number in the set: if this number is larger than the current largest number, consider this number to be the largest number in the set.
 * 4) When there are no numbers left in the set to iterate over, consider the current largest number to be the largest number of the set.

(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:

Input: A list of numbers L. Output: The largest number in the list L.

if L.size = 0 return null largest ← L[0] for each item in L, do if item > largest, then largest ← item return largest

title: Algorithm


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Annual plant

An annual plant is a plant that completes its life cycle, from germination to the production of seeds, within one growing season, and then dies. Globally, 6% of all plant species and 15% of herbaceous plants (excluding trees and shrubs) are annuals. The annual life cycle has independently emerged in over 120 different plant families throughout the entire angiosperm phylogeny.

The evolutionary and ecological drivers of the annual life cycle
Traditionally, there has been a prevailing assumption that annuals have evolved from perennial ancestors. However, recent research challenges this notion, revealing instances where perennials have evolved from annual ancestors. Intriguingly, models propose that transition rates from an annual to a perennial life cycle are twice as fast as the reverse transition.

The life-history theory posits that annual plants are favored when adult mortality is higher than seedling (or seed) mortality, i.e., annuals will dominate environments with disturbances or high temporal variability, reducing adult survival. This hypothesis finds support in observations of increased prevalence of annuals in regions with hot-dry summers, with elevated adult mortality and high seed persistence. Furthermore, the evolution of the annual life cycle under hot-dry summer in different families makes it one of the best examples of convergent evolution. Additionally, annual prevalence is also positively affected by year-to-year variability.

Globally, the prevalence of annual plants shows an upward trend with an increasing human footprint. Moreover, domestic grazing has been identified as contributing to the heightened abundance of annuals in grasslands. Disturbances linked to activities like grazing and agriculture, particularly following European settlement, have facilitated the invasion of annual species from Europe and Asia into the New World.

In various ecosystems, the dominance of annual plants is often a temporary phase during secondary succession, particularly in the aftermath of disturbances. For instance, after fields are abandoned, annuals may initially colonize them but are eventually replaced by long-lived species. However, in certain Mediterranean systems, a unique scenario unfolds: when annuals establish dominance, perennials do not necessarily supplant them. This peculiarity is attributed to alternative stable states in the system—both annual dominance and perennial states prove stable, with the ultimate system state dependent on the initial conditions.

Traits of annuals and their implication for agriculture
Annual plants commonly exhibit a higher growth rate, allocate more resources to seeds, and allocate fewer resources to roots than perennials. In contrast to perennials, which feature long-lived plants and short-lived seeds, annual plants compensate for their lower longevity by maintaining a higher persistence of soil seed banks. These differences in life history strategies profoundly affect ecosystem functioning and services. For instance, annuals, by allocating less resources belowground, play a minor role in reducing erosion, storing organic carbon, and achieving lower nutrient- and water-use efficiencies than perennials.

The distinctions between annual and perennial plants are notably evident in agricultural contexts. Despite constituting a minor part of global biomass, annual species stand out as the primary food source for humankind, likely owing to their greater allocation of resources to seed production, thereby enhancing agricultural productivity. In the Anthropocene epoch, marked by human impact on the environment, there has been a substantial increase in the global cover of annuals. This shift is primarily attributed to the conversion of natural systems, often dominated by perennials, into annual cropland. Currently, annual plants cover approximately 70% of croplands and contribute to around 80% of worldwide food consumption.

Molecular genetics
In 2008, it was discovered that the inactivation of only two genes in one species of annual plant leads to its conversion into a perennial plant. Researchers deactivated the SOC1 and FUL genes (which control flowering time) of Arabidopsis thaliana. This switch established phenotypes common in perennial plants, such as wood formation.

title: Annual plant


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Anthophyta

The anthophytes are a paraphyletic grouping of plant taxa bearing flower-like reproductive structures. The group, once thought to be a clade, 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 320-300 mya.

Some more recent studies have used the word anthophyte to describe a hypothetical group which includes the angiosperms and a variety of extinct seed plant groups (with various suggestions including at least some of the following groups: glossopterids, corystosperms, Petriellales Pentoxylales, Bennettitales and Caytoniales), but not the Gnetales.

title: Anthophyta


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Atlas (disambiguation)

An atlas is a collection of maps.

Atlas may also refer to:

Mythology

 * Atlas (mythology), an Ancient Greek Titanic deity
 * Atlas of Atlantis, the first legendary king of Atlantis
 * Atlas of Mauretania, a legendary king

United States

 * Atlas, Illinois
 * Atlas, Texas
 * Atlas, West Virginia
 * Atlas, Wisconsin
 * Atlas District, in Washington, D.C.
 * Atlas Peak AVA, a California wine region
 * Atlas Township, Michigan

Other places

 * Atlas Cinema, a historic movie theatre in Istanbul, Turkey
 * Atlas Mountains, a set of mountain ranges in northwestern Africa
 * Atlas, Nilüfer, a village in Bursa Province, Turkey

People with the name

 * Atlas (given name)
 * Atlas (graffiti artist)
 * Atlas DaBone, American wrestler and football player
 * Charles Atlas (1892–1972), Italian-American bodybuilder
 * Charles Atlas (artist)
 * David Atlas (born 1924), American meteorologist
 * James Atlas (1949-2019), American writer, editor and publisher
 * Meir Atlas (1848–1926), Lithuanian rabbi
 * Natacha Atlas (born 1964), Belgian singer
 * Nava Atlas, American book artist and author
 * Omar Atlas (born 1938), former Venezuelan professional wrestler
 * Scott Atlas (born 1955), American conservative health care policy advisor
 * Teddy Atlas (born 1956), American boxing trainer and commentator
 * Tony Atlas (born 1954), American wrestler and bodybuilder

Comics

 * Atlas (comic book series), by Dylan Horrocks
 * Agents of Atlas, a Marvel Comics mini-series
 * Atlas Comics (1950s), a publisher
 * Atlas/Seaboard Comics, a 1970s line of comics

Fictional characters

 * Atlas (DC Comics), any of several fictional characters
 * Atlas (Teen Titans)
 * Atlas, an Astro Boy (1980) character
 * Atlas (BioShock)
 * Atlas, a BattleMech in the BattleTech universe
 * Atlas, an antagonist in Mega Man ZX Advent
 * Atlas, a Portal 2 character
 * Atlas, a PS238 character
 * Erik Josten, a.k.a. Atlas, a Marvel Comics supervillain
 * The Atlas, a strong driving force from No Man's Sky

Literature

 * Atlas, a photography book by Gerhard Richter
 * ATLAS of Finite Groups, a group theory book
 * Atlas Shrugged, a novel by Ayn Rand
 * The Atlas (novel), by William T. Vollmann

Groups

 * Atlas (band), a New Zealand rock band
 * Atlas Sound, the solo musical project of Deerhunter lead singer and guitarist Bradford Cox

Musicians

 * Black Atlass, a Canadian musician

Albums

 * Atlas (Kinky album)
 * Atlas (Laurel Halo album)
 * Atlas (Parkway Drive album)
 * Atlas (Real Estate album)
 * Atlas (RÜFÜS album)
 * Atlas (The Score album)

Operas

 * Atlas (opera), 1991, by Meredith Monk
 * Atlas: An Opera in Three Parts, a 1993 recording of Monk's opera

Songs

 * "Atlas" (Battles song), 2007
 * "Atlas" (Bicep song), 2020
 * "Atlas" (Coldplay song), 2013
 * "Atlas", a song by Caligula's Horse from the album The Tide, the Thief & River's End
 * "Atlas", by Parkway Drive
 * "Atlas", a song by Man Overboard from Man Overboard
 * "Atlas", a song by Jake Chudnow, used as the main theme in the YouTube series Mind Field
 * “Atlas”, a song by Coheed and Cambria
 * “Atlas”, a song by Good Kid

Periodicals

 * Atlas (magazine)
 * The Atlas (newspaper), published in England from 1826 to 1869

Other uses in arts, entertainment, and media

 * Atlas (1961 film), an action-adventure film
 * Atlas (2024 film), an American science fiction thriller film
 * Atlas (statue), iconic statue by Lee Lawrie in Rockefeller Center
 * Atlas, a book about flora and/or fauna of a region, such as atlases of the flora and fauna of Britain and Ireland
 * Atlas Entertainment, a film production company
 * Atlas folio, a book size
 * Atlas Media Corp., a non-fiction entertainment company
 * Atlas Press, a UK publisher
 * RTV Atlas, a broadcaster in Montenegro
 * The Atlas (video game), a 1991 multiplatform strategy video game
 * Atlas (video game), a massively-multiplayer online video game released for early access in 2018
 * Atlas Corporation, a fictional arms manufacturer in the video game series Borderlands
 * Atlas Corporation, a fictional private military company in the game Call of Duty: Advanced Warfare

Brands and enterprises

 * Atlas (appliance company), in Belarus
 * Atlas (restaurant), a Michelin-starred restaurant in Atlanta
 * Atlas Consortium, a group of technology companies
 * Atlas Copco, a Swedish company founded in 1873
 * Atlas Corporation, an investment company
 * Atlas Elektronik, a German naval/marine electronics and systems business
 * Atlas Group, a Pakistani business group
 * Atlas Mara Limited, formerly Atlas Mara Co-Nvest Limited, a financial holding company that owns banks in Africa
 * Atlas Model Railroad, American maker of model trains and accessories
 * Atlas Network, formerly Atlas Economic Research Foundation
 * Atlas Press (tool company)
 * Atlas Solutions, an online advertising subsidiary of Meta Platforms
 * Atlas Van Lines, a moving company
 * Atlas-Imperial, an American diesel engine manufacturer
 * Dresser Atlas, a provider of oilfield and factory automation services
 * Tele Atlas, a Dutch mapping company
 * Western Atlas, an oilfield services company
 * Atlas Powder Company, American explosives and chemicals company

Computing and technology

 * Atlas (computer), a 1960s supercomputer
 * Atlas Supervisor, its operating system
 * Atlas (robot)
 * ATLAS (software), a tool to scan American citizenship records for candidates for denaturalization
 * Atlas, a computer used at the Lawrence Livermore National Laboratory in 2006
 * Abbreviated Test Language for All Systems (ATLAS), a computer language for equipment testing
 * Advanced Technology Leisure Application Simulator (ATLAS), a hydraulic motion simulator used in theme parks
 * ASP.NET AJAX (formerly "Atlas"), a set of ASP.NET extensions
 * ATLAS Transformation Language, a programming language for model transformation
 * Atlas.ti, a qualitative analysis program
 * Automatically Tuned Linear Algebra Software (ATLAS)
 * Texture atlas, in computer graphics, a large image containing multiple smaller images
 * UNIVAC 1101, a 1950s American computer

Astronomy

 * Atlas (comet) (C/2019 Y4)
 * Atlas (crater), on the near side of the Moon
 * Atlas (moon), a satellite of Saturn
 * Atlas (star), a triple star system in the constellation of Taurus and a member of the Pleiades
 * Advanced Topographic Laser Altimeter System (ATLAS), a space-based lidar instrument on ICESat-2
 * Asteroid Terrestrial-impact Last Alert System (ATLAS)

Mathematics

 * Atlas (topology), a set of charts
 * A set of charts which covers a manifold
 * A smooth structure, a maximal smooth atlas for a topological manifold

Physics

 * Argonne Tandem Linear Accelerator System (ATLAS), at the Argonne National Laboratory
 * ATLAS experiment, a particle detector for the Large Hadron Collider at CERN
 * Atomic-terrace low-angle shadowing (ATLAS), a nanofabrication technique

Biology and healthcare

 * Atlas (anatomy), a vertebra in the cervical spine
 * Atlas personality, the personality of someone whose childhood was characterized by excessive responsibilities
 * Brain atlas, a neuroanatomical map of the brain of a human or other animal

Animals and plants

 * Atlas bear
 * Atlas beetle
 * Atlas cedar
 * Atlas moth
 * Atlas pied flycatcher, a bird
 * Atlas turtle

Sport

 * Atlas Delmenhorst, a German association football club
 * Atlas F.C., a Mexican professional football club
 * Club Atlético Atlas, an Argentine amateur football club
 * KK Atlas, a former Serbian men's professional basketball club

Aerospace

 * Atlas (rocket family)
 * SM-65 Atlas intercontinental ballistic missile (ICBM)
 * AeroVelo Atlas, a human-powered helicopter
 * Airbus A400M Atlas, a military aircraft produced from 2007–present
 * Armstrong Whitworth Atlas, a British military aeroplane produced 1927–1933
 * Atlas Air, an American cargo airline
 * Atlas Aircraft, a 1940s aircraft manufacturer
 * Atlas Aircraft Corporation, a South African military aircraft manufacturer
 * Atlas Aviation, an aircraft maintenance firm
 * Atlas Blue, a Moroccan low-cost airline
 * Atlasjet, a Turkish airline
 * Birdman Atlas, an ultralight aircraft
 * HMLAT-303, U.S. Marine Corps helicopter training squadron
 * La Mouette Atlas, a French hang glider design

Automotive

 * Atlas (1951 automobile), a French mini-car
 * Atlas (light trucks), a Greek motor vehicle manufacturer
 * Atlas (Pittsburgh automobile), produced 1906–1907
 * Atlas (Springfield automobile), produced 1907–1913
 * Atlas, a British van by the Standard Motor Company produced 1958–1962
 * Atlas Drop Forge Company, a parts subsidiary of REO Motor Car Company
 * Atlas Motor Buggy, an American highwheeler produced in 1909
 * Ford Atlas, a concept pickup truck that previewed the then-new 2015 F-150
 * General Motors Atlas engine
 * Honda Atlas Cars Pakistan, a car manufacturer
 * Nissan Atlas, a Japanese light truck
 * Volkswagen Atlas, a sport utility vehicle
 * Geely Atlas, a sport utility vehicle

Ships and boats

 * Atlas Werke, a defunct German shipbuilding company
 * Atlas (ship), any of several merchant ships
 * French ship Atlas, any of several French Navy ships
 * HMS Atlas, any of several Royal Navy ships
 * ST Atlas, a Swedish tugboat
 * USS Atlas, any of several U.S. Navy ships

Trains

 * Atlas, an 1863–1885 South Devon Railway Dido class locomotive
 * Atlas, a 1927–1962 LMS Royal Scot Class locomotive
 * Atlas Car and Manufacturing Company, a locomotive manufacturer
 * Atlas Model Railroad

Other uses

 * Atlas (architecture)
 * ATLAS (simulation) (Army Tactical Level Advanced Simulation), a Thai military system
 * Atlas (storm), which hit the Midwestern United States in October 2013, named by The Weather Channel
 * Agrupación de Trabajadores Latinoamericanos Sindicalistas (ATLAS), a 1950s Latin American trade union confederation
 * Atlas languages, Berber languages spoken in the Atlas Mountains of Morocco
 * ATLAS Network, a network of European special police units
 * Atlas Uranium Mill
 * Atlas Corporation, a private military company by Call of Duty: Advanced Warfare

title: Atlas (disambiguation)


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Mouthwash

Mouthwash, mouth rinse, oral rinse, or mouth bath is a liquid which is held in the mouth passively or swirled 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 mouth, 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 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, but is not as cost-effective as leaving the fluoride toothpaste on the teeth after brushing. 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 there was a limited evidence base for best practice.

Use
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 after brushing. Patients were told to "spit don't rinse" after toothbrushing as part of a National Health Service campaign in the UK. A fluoride mouthrinse can be used at a different time of the day to brushing.

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.

Dangerous misuse
If one drinks mouthwash, serious harm and even death can quickly result from the high alcohol content and other substances harmful to ingestion present in mouthwash. It is a common cause of death among homeless people during winter months, because a person can feel warmer after drinking it.

Effects
The most-commonly-used mouthwashes are commercial antiseptics, which are used at home as part of an oral hygiene routine. 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 their antiseptic and antiplaque mouthwashes 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 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 mouthwashes, 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 may make dry mouth and halitosis worse, as they dry out the mouth. Soreness, ulceration and redness may sometimes occur (e.g., aphthous stomatitis or 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. saltwater), 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 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 between the most common magic-mouthwash formulation, on the one hand, and commercial mouthwashes (such as chlorhexidine) or a saline/baking soda solution, on the other. Current guidelines suggest that saline solution is just as effective as magic mouthwash in pain relief and in shortening the healing time of oral mucositis from cancer therapies.

History
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. The ancient Chinese had also gargled salt water, tea and wine as a form of mouthwash after meals, due to the antiseptic properties of those liquids.

Before Europeans came to the Americas, Native North American and Mesoamerican cultures used mouthwashes, often made from plants such as Coptis trifolia. 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 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 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–creating anaerobic bacteria that live in the mouth and excrete substances that lead to bad breath and unpleasant mouth taste. For example, the number of mouthwash variants in the United States of America has grown from 15 (1970) to 66 (1998) to 113 (2012).

Research
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 solution.

A clinical trial and laboratory studies have shown that alcohol-containing mouthwash could reduce the growth of Neisseria gonorrhoeae in the pharynx. However, subsequent trials have found that there was no difference in gonorrhoea cases among men using daily mouthwash compared to those who did not use mouthwash for 12 weeks.

Alcohol
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 may temporarily worsen halitosis in those who already have it, or, indeed, be the sole cause of halitosis in other individuals. Alcohol in mouthwashes may act as a carcinogen (cancer-inducing agent) in some cases, see. Many newer brands of mouthwash are alcohol-free, not just in response to consumer concerns about oral cancer, but also to cater for religious groups who abstain from alcohol consumption.

Benzydamine (analgesic)
In painful oral conditions such as aphthous stomatitis, analgesic mouthrinses (e.g. benzydamine mouthwash, or "Difflam") are sometimes used to ease pain, commonly used before meals to reduce discomfort while eating.

Benzoic acid
Benzoic acid acts as a buffer.

Betamethasone
Betamethasone is sometimes used as an anti-inflammatory, corticosteroid mouthwash. It may be used for severe inflammatory conditions of the oral mucosa such as the severe forms of aphthous stomatitis.

Cetylpyridinium chloride (antiseptic, antimalodor)
Cetylpyridinium chloride containing mouthwash (e.g. 0.05%) is used in some specialized mouthwashes for halitosis. Cetylpyridinium chloride mouthwash has less anti-plaque effect than chlorhexidine and may cause staining of teeth, or sometimes an oral burning sensation or ulceration.

Chlorhexidine digluconate and hexetidine (antiseptic)
Chlorhexidine digluconate is a chemical antiseptic and is used in a 0.05–0.2% solution as a mouthwash. There is no evidence to support that higher concentrations are more effective in controlling dental plaque and gingivitis. A randomized clinical trial conducted in Rabat University in Morocco found better results in plaque inhibition when chlorohexidine with alcohol base 0.12% was used, when compared to an alcohol-free 0.1% chlorhexidine mouthrinse.

Chlorhexidine has good substantivity (the ability of a mouthwash to bind to hard and soft tissues in the mouth). It has anti-plaque action, and also some anti-fungal action. It is especially effective against Gram-negative rods. The proportion of Gram-negative rods increase as gingivitis develops, so it is also used to reduce gingivitis. It is sometimes used as an adjunct to prevent dental caries and to treat periodontal disease, although it does not penetrate into periodontal pockets well. Chlorhexidine mouthwash alone is unable to prevent plaque, so it is not a substitute for regular toothbrushing and flossing. Instead, chlorhexidine mouthwash is more effective when used as an adjunctive treatment with toothbrushing and flossing. In the short term, if toothbrushing is impossible due to pain, as may occur in primary herpetic gingivostomatitis, chlorhexidine mouthwash is used as a temporary substitute for other oral hygiene measures. It is not suited for use in acute necrotizing ulcerative gingivitis, however. Rinsing with chlorhexidine mouthwash before and after a tooth extraction may reduce the risk of a dry socket. Other uses of chlorhexidine mouthwash include prevention of oral candidiasis in immunocompromised persons, treatment of denture-related stomatitis, mucosal ulceration/erosions and oral mucosal lesions, general burning sensation and many other uses.

Chlorhexidine mouthwash is known to have minor adverse effects. Chlorhexidine binds to tannins, meaning that prolonged use in persons who consume coffee, tea or red wine is associated with extrinsic staining (i.e. removable staining) of teeth. A systematic review of commercial chlorhexidine products with anti-discoloration systems (ADSs) found that the ADSs were able to reduce tooth staining without affecting the beneficial effects of chlorhexidine. Chlorhexidine mouthwash can also cause taste disturbance or alteration. Chlorhexidine is rarely associated with other issues like overgrowth of enterobacteria in persons with leukemia, desquamation, irritation, and stomatitis of oral mucosa, salivary gland pain and swelling, and hypersensitivity reactions including anaphylaxis.

Hexetidine also has anti-plaque, analgesic, astringent and anti-malodor properties, but is considered an inferior alternative to chlorhexidine.

Chlorine dioxide
In dilute concentrations, chlorine dioxide is an ingredient that acts as an antiseptic agent in some mouthwashes.

Edible oils
In traditional Ayurvedic medicine, the use of oil mouthwashes is called "Kavala" ("oil swishing") or "Gandusha", and this practice has more recently been re-marketed by the complementary and alternative medicine industry as "oil pulling". Its promoters claim it works by "pulling out" "toxins", which are known as ama in Ayurvedic medicine, and thereby reducing inflammation. Ayurvedic literature claims that oil pulling is capable of improving oral and systemic health, including a benefit in conditions such as headaches, migraines, diabetes mellitus, asthma, and acne, as well as whitening teeth.

Oil pulling has received little study and there is little evidence to support claims made by the technique's advocates. When compared with chlorhexidine in one small study, it was found to be less effective at reducing oral bacterial load, and the other health claims of oil pulling have failed scientific verification or have not been investigated. There is a report of lipid pneumonia caused by accidental inhalation of the oil during oil pulling.

The mouth is rinsed with approximately one tablespoon of oil for 10–20 minutes then spat out. Sesame oil, coconut oil and ghee are traditionally used, but newer oils such as sunflower oil are also used.

Essential oils
Phenolic compounds and monoterpenes include essential oil constituents that have some antibacterial properties, such as eucalyptol, eugenol, hinokitiol, menthol, phenol, or thymol. Essential oils are oils which have been extracted from plants. Mouthwashes based on essential oils could be more effective than traditional mouthcare as anti-gingival treatments. They have been found effective in reducing halitosis, and are being used in several commercial mouthwashes.

Fluoride (anticavity)
Anti-cavity mouthwashes use sodium fluoride to protect against tooth decay. Fluoride-containing mouthwashes are used as prevention for dental caries for individuals who are considered at higher risk for tooth decay, whether due to xerostomia related to salivary dysfunction or side effects of medication, to not drinking fluoridated water, or to being physically unable to care for their oral needs (brushing and flossing), and as treatment for those with dentinal hypersensitivity, gingival recession/ root exposure.

Flavoring agents and Xylitol
Flavoring agents include sweeteners such as sorbitol, sucralose, sodium saccharin, and xylitol, which stimulate salivary function due to their sweetness and taste and helps restore the mouth to a neutral level of acidity.

Xylitol rinses double as a bacterial inhibitor, and have been used as substitute for alcohol to avoid dryness of mouth associated with alcohol.

Hydrogen peroxide
Hydrogen peroxide can be used as an oxidizing mouthwash (e.g. Peroxyl, 1.5%). It kills anaerobic bacteria, and also has a mechanical cleansing action when it froths as it comes into contact with debris in mouth. It is often used in the short term to treat acute necrotising ulcerative gingivitis. Side effects can occur with prolonged use, including hypertrophy of the lingual papillae.

Lactoperoxidase (saliva substitute)
Enzymes and non-enzymatic proteins, such as lactoperoxidase, lysozyme, and lactoferrin, have been used in mouthwashes (e.g., Biotene) to reduce levels of oral bacteria, and, hence, of the acids produced by these bacteria.

Lidocaine/xylocaine
Oral lidocaine is useful for the treatment of mucositis symptoms (inflammation of mucous membranes) induced by radiation or chemotherapy. There is evidence that lidocaine anesthetic mouthwash has the potential to be systemically absorbed, when it was tested in patients with oral mucositis who underwent a bone marrow transplant.

Methyl salicylate
Methyl salicylate functions as an antiseptic, antiinflammatory, and analgesic agent, a flavoring, and a fragrance. Methyl salicylate has some anti-plaque action, but less than chlorhexidine. Methyl salicylate does not stain teeth.

Nystatin
Nystatin suspension is an antifungal ingredient used for the treatment of oral candidiasis.

Potassium oxalate
A randomized clinical trial found promising results in controlling and reducing dentine hypersensitivity when potassium oxalate mouthwash was used in conjugation with toothbrushing.

Povidone/iodine (PVP-I)
A 2005 study found that gargling three times a day with simple water or with a povidone-iodine solution was effective in preventing upper respiratory infection and decreasing the severity of symptoms if contracted. Other sources attribute the benefit to a simple placebo effect.

PVP-I in general covers "a wider virucidal spectrum, covering both enveloped and nonenveloped viruses, than the other commercially available antiseptics", which also includes the novel SARS-CoV-2 Virus.

Sanguinarine
Sanguinarine-containing mouthwashes are marketed as anti-plaque and anti-malodor treatments. Sanguinarine is a toxic alkaloid herbal extract, obtained from plants such as Sanguinaria canadensis (bloodroot), Argemone mexicana (Mexican prickly poppy), and others. However, its use is strongly associated with the development of leukoplakia (a white patch in the mouth), usually in the buccal sulcus. This type of leukoplakia has been termed "sanguinaria-associated keratosis", and more than 80% of people with leukoplakia in the vestibule of the mouth have used this substance. Upon stopping contact with the causative substance, the lesions may persist for years. Although this type of leukoplakia may show dysplasia, the potential for malignant transformation is unknown. Ironically, elements within the complementary and alternative medicine industry promote the use of sanguinaria as a therapy for cancer.

Sodium bicarbonate (baking soda)
Sodium bicarbonate is sometimes combined with salt to make a simple homemade mouthwash, indicated for any of the reasons that a saltwater mouthwash might be used. Pre-mixed mouthwashes of 1% sodium bicarbonate and 1.5% sodium chloride in aqueous solution are marketed, although pharmacists will easily be able to produce such a formulation from the base ingredients when required. Sodium bicarbonate mouthwash is sometimes used to remove viscous saliva and to aid visualization of the oral tissues during examination of the mouth.

Sodium chloride (salt)
Saline has a mechanical cleansing action and an antiseptic action, as it is a hypertonic solution in relation to bacteria, which undergo lysis. The heat of the solution produces a therapeutic increase in blood flow (hyperemia) to the surgical site, promoting healing. Hot saltwater mouthwashes also encourage the draining of pus from dental abscesses. In contrast, if heat is applied on the side of the face (e.g., hot water bottle) rather than inside the mouth, it may cause a dental abscess to drain extra-orally, which is later associated with an area of fibrosis on the face (see cutaneous sinus of dental origin).

Saltwater mouthwashes are also routinely used after oral surgery, to keep food debris out of healing wounds and to prevent infection. Some oral surgeons consider saltwater mouthwashes the mainstay of wound cleanliness after surgery. In dental extractions, hot saltwater mouthbaths should start about 24 hours after a dental extraction. The term mouth bath implies that the liquid is passively held in the mouth, rather than vigorously swilled around (which could dislodge a blood clot). Once the blood clot has stabilized, the mouthwash can be used more vigorously. These mouthwashes tend to be advised for use about 6 times per day, especially after meals (to remove food from the socket).

Sodium lauryl sulfate (foaming agent)
Sodium lauryl sulfate (SLS) is used as a foaming agent in many oral hygiene products, including many mouthwashes. Some may suggest that it is probably advisable to use mouthwash at least an hour after brushing with toothpaste when the toothpaste contains SLS, since the anionic compounds in the SLS toothpaste can deactivate cationic agents present in the mouthwash.

Sucralfate
Sucralfate is a mucosal coating agent, composed of an aluminum salt of sulfated sucrose. It is not recommended for use in the prevention of oral mucositis in head and neck cancer patients receiving radiotherapy or chemoradiation, due to a lack of efficacy found in a well-designed, randomized controlled trial.

Tetracycline (antibiotic)
Tetracycline is an antibiotic which may sometimes be used as a mouthwash in adults (it causes red staining of teeth in children). It is sometimes use for herpetiforme ulceration (an uncommon type of aphthous stomatitis), but prolonged use may lead to oral candidiasis, as the fungal population of the mouth overgrows in the absence of enough competing bacteria. Similarly, minocycline mouthwashes of 0.5% concentrations can relieve symptoms of recurrent aphthous stomatitis. Erythromycin is similar.

Tranexamic acid
A 4.8% tranexamic acid solution is sometimes used as an antifibrinolytic mouthwash to prevent bleeding during and after oral surgery in persons with coagulopathies (clotting disorders) or who are taking anticoagulants (blood thinners such as warfarin).

Triclosan
Triclosan is a non-ionic chlorinate bisphenol antiseptic found in some mouthwashes. When used in mouthwash (e.g. 0.03%), there is moderate substantivity, broad spectrum anti-bacterial action, some anti-fungal action, and significant anti-plaque effect, especially when combined with a copolymer or zinc citrate. Triclosan does not cause staining of the teeth. The safety of triclosan has been questioned.

Zinc
Astringents like zinc chloride provide a pleasant-tasting sensation and shrink tissues. Zinc, when used in combination with other antiseptic agents, can limit the buildup of tartar.

title: Mouthwash