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binary searches for the same element in multiple sorted arrays. Searching each array separately requires O(k \log n) time, where k is the number of arrays. Fractional cascading reduces this to O(k + \log n) by storing specific information in each array about each element and its position in the other arrays.
Fractional cascading was originally developed to efficiently solve various computational geometry problems. Fractional cascading has been applied elsewhere, such as in data mining and Internet Protocol routing.
=== Generalization to graphs ===
Binary search has been generalized to work on certain types of graphs, where the target value is stored in a vertex instead of an array element. Binary search trees are one such generalization—when a vertex (node) in the tree is queried, the algorithm either learns that the vertex is the target, or otherwise which subtree the target would be located in. However, this can be further generalized as follows: given an undirected, positively weighted graph and a target vertex, the algorithm learns upon querying a vertex that it is equal to the target, or it is given an incident edge that is on the shortest path from the queried vertex to the target. The standard binary search algorithm is | Binary search algorithm | [
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simply the case where the graph is a path. Similarly, binary search trees are the case where the edges to the left or right subtrees are given when the queried vertex is unequal to the target. For all undirected, positively weighted graphs, there is an algorithm that finds the target vertex in O(\log n) queries in the worst case.
=== Noisy binary search ===
Noisy binary search algorithms solve the case where the algorithm cannot reliably compare elements of the array. For each pair of elements, there is a certain probability that the algorithm makes the wrong comparison. Noisy binary search can find the correct position of the target with a given probability that controls the reliability of the yielded position. Every noisy binary search procedure must make at least (1 - \tau)\frac{\log_2 (n)}{H(p)} - \frac{10}{H(p)} comparisons on average, where H(p) = -p \log_2 (p) - (1 - p) \log_2 (1 - p) is the binary entropy function and \tau is the probability that the procedure yields the wrong position. The noisy binary search problem can be considered as a case of the Rényi-Ulam game, a variant of Twenty Questions where the answers may be wrong.
=== Quantum binary search ===
Classical computers are | Binary search algorithm | [
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bounded to the worst case of exactly \lfloor \log_2 n + 1 \rfloor iterations when performing binary search. Quantum algorithms for binary search are still bounded to a proportion of \log_2 n queries (representing iterations of the classical procedure), but the constant factor is less than one, providing for a lower time complexity on quantum computers. Any exact quantum binary search procedure—that is, a procedure that always yields the correct result—requires at least \frac{1}{\pi}(\ln n - 1) \approx 0.22 \log_2 n queries in the worst case, where \ln is the natural logarithm. There is an exact quantum binary search procedure that runs in 4 \log_{605} n \approx 0.433 \log_2 n queries in the worst case. In comparison, Grover's algorithm is the optimal quantum algorithm for searching an unordered list of elements, and it requires O(\sqrt{n}) queries.
== History ==
The idea of sorting a list of items to allow for faster searching dates back to antiquity. The earliest known example was the Inakibit-Anu tablet from Babylon dating back to . The tablet contained about 500 sexagesimal numbers and their reciprocals sorted in lexicographical order, which made searching for a specific entry easier. In addition, several lists of names that were sorted by | Binary search algorithm | [
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their first letter were discovered on the Aegean Islands. Catholicon, a Latin dictionary finished in 1286 CE, was the first work to describe rules for sorting words into alphabetical order, as opposed to just the first few letters.
In 1946, John Mauchly made the first mention of binary search as part of the Moore School Lectures, a seminal and foundational college course in computing. In 1957, William Wesley Peterson published the first method for interpolation search. Every published binary search algorithm worked only for arrays whose length is one less than a power of two until 1960, when Derrick Henry Lehmer published a binary search algorithm that worked on all arrays. In 1962, Hermann Bottenbruch presented an ALGOL 60 implementation of binary search that placed the comparison for equality at the end, increasing the average number of iterations by one, but reducing to one the number of comparisons per iteration. The uniform binary search was developed by A. K. Chandra of Stanford University in 1971. In 1986, Bernard Chazelle and Leonidas J. Guibas introduced fractional cascading as a method to solve numerous search problems in computational geometry.
== Implementation issues ==
When Jon Bentley assigned binary search as a problem in a course | Binary search algorithm | [
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for professional programmers, he found that ninety percent failed to provide a correct solution after several hours of working on it, mainly because the incorrect implementations failed to run or returned a wrong answer in rare edge cases. A study published in 1988 shows that accurate code for it is only found in five out of twenty textbooks. Furthermore, Bentley's own implementation of binary search, published in his 1986 book Programming Pearls, contained an overflow error that remained undetected for over twenty years. The Java programming language library implementation of binary search had the same overflow bug for more than nine years.
In a practical implementation, the variables used to represent the indices will often be of fixed size (integers), and this can result in an arithmetic overflow for very large arrays. If the midpoint of the span is calculated as \frac{L+R}{2}, then the value of L+R may exceed the range of integers of the data type used to store the midpoint, even if L and R are within the range. If L and R are nonnegative, this can be avoided by calculating the midpoint as L+\frac{R-L}{2}.
An infinite loop may occur if the exit conditions for the loop are not | Binary search algorithm | [
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] |
defined correctly. Once L exceeds R, the search has failed and must convey the failure of the search. In addition, the loop must be exited when the target element is found, or in the case of an implementation where this check is moved to the end, checks for whether the search was successful or failed at the end must be in place. Bentley found that most of the programmers who incorrectly implemented binary search made an error in defining the exit conditions.
== Library support ==
Many languages' standard libraries include binary search routines:
* C provides the function bsearch() in its standard library, which is typically implemented via binary search, although the official standard does not require it so.
* C++'s Standard Template Library provides the functions binary_search(), lower_bound(), upper_bound() and equal_range().
* D's standard library Phobos, in std.range module provides a type SortedRange (returned by sort() and assumeSorted() functions) with methods contains(), equaleRange(), lowerBound() and trisect(), that use binary search techniques by default for ranges that offer random access.
* COBOL provides the SEARCH ALL verb for performing binary searches on COBOL ordered tables.
* Go's sort standard library package contains the functions Search, SearchInts, SearchFloat64s, and SearchStrings, which implement general binary search, as well | Binary search algorithm | [
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] |
as specific implementations for searching slices of integers, floating-point numbers, and strings, respectively.
* Java offers a set of overloaded binarySearch() static methods in the classes and in the standard java.util package for performing binary searches on Java arrays and on Lists, respectively.
* Microsoft's .NET Framework 2.0 offers static generic versions of the binary search algorithm in its collection base classes. An example would be System.Array's method BinarySearch<T>(T[] array, T value).
* For Objective-C, the Cocoa framework provides the NSArray -indexOfObject:inSortedRange:options:usingComparator: method in Mac OS X 10.6+. Apple's Core Foundation C framework also contains a CFArrayBSearchValues() function.
* Python provides the bisect module.
* Ruby's Array class includes a bsearch method with built-in approximate matching.
== See also ==
* – the same idea used to solve equations in the real numbers
*
== Notes and references ==
=== Notes ===
=== Citations ===
=== Sources ===
==External links==
* NIST Dictionary of Algorithms and Data Structures: binary search
* Comparisons and benchmarks of a variety of binary search implementations in C
Category:Articles with example pseudocode
Category:Search algorithms
Category:2 (number) | Binary search algorithm | [
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Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.
The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown. In the Bayesian view, a probability is assigned to a hypothesis, whereas under frequentist inference, a hypothesis is typically tested without being assigned a probability.
Bayesian probability belongs to the category of evidential probabilities; to evaluate the probability of a hypothesis, the Bayesian probabilist specifies a prior probability. This, in turn, is then updated to a posterior probability in the light of new, relevant data (evidence). The Bayesian interpretation provides a standard set of procedures and formulae to perform this calculation.
The term Bayesian derives from the 18th-century mathematician and theologian Thomas Bayes, who provided the first mathematical treatment of a non-trivial problem of statistical data analysis using what is now known as Bayesian inference. Mathematician Pierre-Simon Laplace pioneered and popularized what is now called Bayesian probability.
==Bayesian methodology==
Bayesian methods are characterized by concepts and procedures as | Bayesian probability | [
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follows:
* The use of random variables, or more generally unknown quantities, to model all sources of uncertainty in statistical models including uncertainty resulting from lack of information (see also aleatoric and epistemic uncertainty).
* The need to determine the prior probability distribution taking into account the available (prior) information.
* The sequential use of Bayes' theorem: as more data become available, calculate the posterior distribution using Bayes' theorem; subsequently, the posterior distribution becomes the next prior.
* While for the frequentist, a hypothesis is a proposition (which must be either true or false) so that the frequentist probability of a hypothesis is either 0 or 1, in Bayesian statistics, the probability that can be assigned to a hypothesis can also be in a range from 0 to 1 if the truth value is uncertain.
==Objective and subjective Bayesian probabilities==
Broadly speaking, there are two interpretations of Bayesian probability. For objectivists, who interpret probability as an extension of logic, probability quantifies the reasonable expectation that everyone (even a "robot") who shares the same knowledge should share in accordance with the rules of Bayesian statistics, which can be justified by Cox's theorem. For subjectivists, probability corresponds to a personal belief. Rationality and coherence allow for substantial variation | Bayesian probability | [
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within the constraints they pose; the constraints are justified by the Dutch book argument or by decision theory and de Finetti's theorem. The objective and subjective variants of Bayesian probability differ mainly in their interpretation and construction of the prior probability.
==History==
The term Bayesian derives from Thomas Bayes (1702–1761), who proved a special case of what is now called Bayes' theorem in a paper titled "An Essay towards solving a Problem in the Doctrine of Chances". In that special case, the prior and posterior distributions were beta distributions and the data came from Bernoulli trials. It was Pierre-Simon Laplace (1749–1827) who introduced a general version of the theorem and used it to approach problems in celestial mechanics, medical statistics, reliability, and jurisprudence. Early Bayesian inference, which used uniform priors following Laplace's principle of insufficient reason, was called "inverse probability" (because it infers backwards from observations to parameters, or from effects to causes). After the 1920s, "inverse probability" was largely supplanted by a collection of methods that came to be called frequentist statistics.
In the 20th century, the ideas of Laplace developed in two directions, giving rise to objective and subjective currents in Bayesian practice.
Harold Jeffreys' Theory of Probability (first published in 1939) | Bayesian probability | [
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played an important role in the revival of the Bayesian view of probability, followed by works by Abraham Wald (1950) and Leonard J. Savage (1954). The adjective Bayesian itself dates to the 1950s; the derived Bayesianism, neo-Bayesianism is of 1960s coinage. In the objectivist stream, the statistical analysis depends on only the model assumed and the data analysed. No subjective decisions need to be involved. In contrast, "subjectivist" statisticians deny the possibility of fully objective analysis for the general case.
In the 1980s, there was a dramatic growth in research and applications of Bayesian methods, mostly attributed to the discovery of Markov chain Monte Carlo methods and the consequent removal of many of the computational problems, and to an increasing interest in nonstandard, complex applications. While frequentist statistics remains strong (as demonstrated by the fact that much of undergraduate teaching is based on it ), Bayesian methods are widely accepted and used, e.g., in the field of machine learning.
==Justification of Bayesian probabilities==
The use of Bayesian probabilities as the basis of Bayesian inference has been supported by several arguments, such as Cox axioms, the Dutch book argument, arguments based on decision theory and de Finetti's theorem.
===Axiomatic approach===
Richard T. Cox showed that | Bayesian probability | [
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] |
Bayesian updating follows from several axioms, including two functional equations and a hypothesis of differentiability. The assumption of differentiability or even continuity is controversial; Halpern found a counterexample based on his observation that the Boolean algebra of statements may be finite. Other axiomatizations have been suggested by various authors with the purpose of making the theory more rigorous.
===Dutch book approach===
Bruno de Finetti proposed the Dutch book argument based on betting. A clever bookmaker makes a Dutch book by setting the odds and bets to ensure that the bookmaker profits—at the expense of the gamblers—regardless of the outcome of the event (a horse race, for example) on which the gamblers bet. It is associated with probabilities implied by the odds not being coherent.
However, Ian Hacking noted that traditional Dutch book arguments did not specify Bayesian updating: they left open the possibility that non-Bayesian updating rules could avoid Dutch books. For example, Hacking writesHacking (1967), Section 3, page 316Hacking (1988, page 124) "And neither the Dutch book argument, nor any other in the personalist arsenal of proofs of the probability axioms, entails the dynamic assumption. Not one entails Bayesianism. So the personalist requires the dynamic assumption to be Bayesian. It is true | Bayesian probability | [
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that in consistency a personalist could abandon the Bayesian model of learning from experience. Salt could lose its savour."
In fact, there are non-Bayesian updating rules that also avoid Dutch books (as discussed in the literature on "probability kinematics" following the publication of Richard C. Jeffrey's rule, which is itself regarded as Bayesian). The additional hypotheses sufficient to (uniquely) specify Bayesian updating are substantial and not universally seen as satisfactory.
===Decision theory approach===
A decision-theoretic justification of the use of Bayesian inference (and hence of Bayesian probabilities) was given by Abraham Wald, who proved that every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures. Conversely, every Bayesian procedure is admissible.
==Personal probabilities and objective methods for constructing priors==
Following the work on expected utility theory of Ramsey and von Neumann, decision-theorists have accounted for rational behavior using a probability distribution for the agent. Johann Pfanzagl completed the Theory of Games and Economic Behavior by providing an axiomatization of subjective probability and utility, a task left uncompleted by von Neumann and Oskar Morgenstern: their original theory supposed that all the agents had the same probability distribution, as a convenience.Pfanzagl (1967, 1968) Pfanzagl's axiomatization was endorsed by Oskar Morgenstern: "Von | Bayesian probability | [
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Neumann and I have anticipated ... [the question whether probabilities] might, perhaps more typically, be subjective and have stated specifically that in the latter case axioms could be found from which could derive the desired numerical utility together with a number for the probabilities (cf. p. 19 of The Theory of Games and Economic Behavior). We did not carry this out; it was demonstrated by Pfanzagl ... with all the necessary rigor".Morgenstern (1976, page 65)
Ramsey and Savage noted that the individual agent's probability distribution could be objectively studied in experiments. Procedures for testing hypotheses about probabilities (using finite samples) are due to Ramsey (1931) and de Finetti (1931, 1937, 1964, 1970). Both Bruno de Finetti and Frank P. Ramsey acknowledge their debts to pragmatic philosophy, particularly (for Ramsey) to Charles S. Peirce.
The "Ramsey test" for evaluating probability distributions is implementable in theory, and has kept experimental psychologists occupied for a half century.Davidson et al. (1957)
This work demonstrates that Bayesian-probability propositions can be falsified, and so meet an empirical criterion of Charles S. Peirce, whose work inspired Ramsey. (This falsifiability-criterion was popularized by Karl Popper. (translation of 1935 original, in German).)
Modern work on the experimental evaluation of personal probabilities uses the | Bayesian probability | [
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randomization, blinding, and Boolean-decision procedures of the Peirce-Jastrow experiment.Peirce & Jastrow (1885)
Since individuals act according to different probability judgments, these agents' probabilities are "personal" (but amenable to objective study).
Personal probabilities are problematic for science and for some applications where decision-makers lack the knowledge or time to specify an informed probability-distribution (on which they are prepared to act). To meet the needs of science and of human limitations, Bayesian statisticians have developed "objective" methods for specifying prior probabilities.
Indeed, some Bayesians have argued the prior state of knowledge defines the (unique) prior probability-distribution for "regular" statistical problems; cf. well-posed problems. Finding the right method for constructing such "objective" priors (for appropriate classes of regular problems) has been the quest of statistical theorists from Laplace to John Maynard Keynes, Harold Jeffreys, and Edwin Thompson Jaynes. These theorists and their successors have suggested several methods for constructing "objective" priors (Unfortunately, it is not clear how to assess the relative "objectivity" of the priors proposed under these methods):
* Maximum entropy
* Transformation group analysis
* Reference analysis
Each of these methods contributes useful priors for "regular" one-parameter problems, and each prior can handle some challenging statistical models (with "irregularity" or several parameters). Each of these methods has | Bayesian probability | [
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been useful in Bayesian practice. Indeed, methods for constructing "objective" (alternatively, "default" or "ignorance") priors have been developed by avowed subjective (or "personal") Bayesians like James Berger (Duke University) and José-Miguel Bernardo (Universitat de València), simply because such priors are needed for Bayesian practice, particularly in science. The quest for "the universal method for constructing priors" continues to attract statistical theorists.
Thus, the Bayesian statistician needs either to use informed priors (using relevant expertise or previous data) or to choose among the competing methods for constructing "objective" priors.
==See also==
* An Essay towards solving a Problem in the Doctrine of Chances
* Bayesian epistemology
* Bertrand paradox—a paradox in classical probability
* Credal network
* De Finetti's game—a procedure for evaluating someone's subjective probability
* Monty Hall problem
* QBism—an interpretation of quantum mechanics based on subjective Bayesian probability
* Reference class problem
==References==
==Bibliography==
*
*
*
*
*
*
* (translation of de Finetti, 1931)
* (translation of de Finetti, 1937, above)
* , , two volumes.
* Goertz, Gary and James Mahoney. 2012. A Tale of Two Cultures: Qualitative and Quantitative Research in the Social Sciences. Princeton University Press.
*.
* Partly reprinted in
*
*
*
*
*
* (
*
*
*
*
*
*
*
*
*
* | Bayesian probability | [
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Probability
Category:Justification (epistemology)
Category:Probability interpretations
Category:Philosophy of mathematics
Category:Philosophy of science | Bayesian probability | [
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Telecommunications in Cambodia include telephone, radio, television, and Internet services, which are regulated by the Ministry of Posts and Telecommunications. Transport and posts were restored throughout most of the country in the early 1980s during the People's Republic of Kampuchea regime after being disrupted under Democratic Kampuchea (Khmer Rouge).
In January 1987, the Soviet-aided Intersputnik space communications station began operation in Phnom Penh and established two-way telecommunication links between the Cambodian capital and the cities of Moscow, Hanoi, Vientiane and Paris. The completion of the earth satellite station restored the telephone and telex links among Phnom Penh, Hanoi, and other countries for the first time since 1975. Although telecommunications services were initially limited to the government, these advances in communications helped break down the country's isolation, both internally and internationally.
Today, with the availability of mobile phones, communications are open to all, though the country's Prime Minister Hun Sen decreed that 3G mobile phones would not be allowed to support video calling.
==Telephones==
As of Q1 2020, Cambodia's mobile connection is at 21.4 million. Smart Axiata, a leading telecommunications company, in 2019 conducted a live trial of its 5G network with support from China's Huawei. The company said it expects to begin rolling out | Telecommunications in Cambodia | [
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] |
5G services in Cambodia by the end of 2019.
GSMA predicted that by 2025, Cambodia will have approximately 24.3 million total mobile connections with smartphone connections up to 69%. The market is predicted to adopt 1.6 million of 5G connections within 5 years from 2020. Though so, it's believed that 4G still have room for growth and will continue to be the majority network connection.
The government state communications corporation is Telecom Cambodia, founded in 2006 as an expansion of the telecom operating department of the Ministry of Posts and Telecommunications.
===Mobile networks===
{| class="wikitable"
|-
! Network !! Company !! Notes
|-
|
Smart
||
Smart Axiata Co., Ltd
||
* Incorporates the former Hello Axiata and Star-Cell
* Smart, website. Retrieved 24 October 2013.
|-
|
Mobitel
||
CamGSM Co., Ltd.
||
* Also known as Cellcard
* Incorporates the former Mfone
* Cellcard, website. Retrieved 24 October 2013.
|-
|
CooTel
||
Xinwei (Cambodia) Telecom Co., Ltd
||
* CooTel, website. Retrieved 24 October 2013.Xinwei, website. Retrieved 24 October 2013.
|-
|
SEATEL
||
Southeast Asia Telecom (Cambodia) Co., Ltd.
||
*Incorporates the former GT-TEL
* SEATEL, website. Retrieved 1 January 2015.
|-
|
Metfone
||
Viettel (Cambodia) Pte., Ltd.
||
* Incorporates the former Beeline
* Metfone, website. Retrieved 24 October 2013.
|-
|
qb
||
Cambodia Advance Communications Co., Ltd. (CADCOMMS)
||
* qb, website. Retrieved 24 October 2013.
|}
==Radio and television==
As of 2019, Cambodian broadcasters were a mixture of state-owned, joint public-private, and privately owned companies.
===Radio stations===
As of | Telecommunications in Cambodia | [
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2019, there were roughly 84 radio broadcast stations: 1 state-owned broadcaster with multiple stations and a large mixture of public and private broadcasters. Several international broadcasters are also available.
====Phnom Penh====
* Apsara Radio FM 97
* Angel Radio 96.3Mhz Kampot
* BBC World Service 100.0 MHz
* Dance Radio 96.6Mhz
* DAP Radio FM 93.75
* Family FM 99.5
* Hang Meas Radio FM 104.5
* Koh Santepheap Daily FM 87.75
* National Radio Kampuchea
* Phnom Penh Radio FM 103
* Radio FM 90.5
* Radio Beehive FM 105
* DaunPenh eFM 87.50Mhz
* ABC News FM 107.5
* Lotus Radio FM 100.5hz
* Radio Free Asia
* Radio Khmer FM 107
* Radio Love FM 97.5
* Radio Town FM 102.3 MHz
* Raksmey Hang Meas Radio FM 95.7000
* Royal Cambodia Armed Forces Radio FM 98
* Voice of America Khmer
* Women's Media Centre of Cambodia (WMC) Radio FM 102
====Provincial stations====
There are radio stations in each of the following provinces: Banteay Meanchey, Battambang, Kampong Cham, Kampong Thom, Kampot, Kandal, Pailin, Preah Vihear, Siem Reap, Sihanoukville and Svay Rieng.
===Television===
Cambodia has 27 TV broadcast stations with most operating on multiple channels, including 1 state-operated station broadcasting from multiple locations, 11 stations either jointly operated or privately owned with some broadcasting from several locations. Multi-channel cable and satellite systems are also available. There | Telecommunications in Cambodia | [
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] |
is one Chinese joint venture television station with the Ministry of Interior. Several television and radio operators broadcast online only (often via Facebook).
====Broadcast and cable networks====
* PNN TV
* Apsara Television (TV11)
* Bayon Television
* Bayon News Television
* Cambodia Cable Television (CCTV)
* Cambodian News Channel (CNC)
* Cambodian Television Network (CTN)
* CTV 8 HD
* Hang Meas HDTV
* Khmer Television 9 HDTV (TV9 HDTV)
* My TV
* National Television of Cambodia (TVK)
* One TV (Royal Media Entertainment Corporation, LTD)
* Phnom Penh Municipal Cable Television (PPCTV Co., LTD)
* Phnom Penh Television (TV3)
* TV5 Cambodia
* One News
====Provincial television stations====
* Kandal Province - Broadcasting on channel 27, Bayon Television is Cambodia's only UHF channel. A private television company belonging to Prime Minister Hun Sen, it also operates Bayon Radio FM 95 MHz. It was established in January 1998.
* Mondulkiri - Established in 1999, relays TVK on channel 10.
* Preah Vihear - Established in 2006, broadcasts on channel 7.
* Ratanakiri - Established in 1993, relays TVK on channel 7.
* Siem Reap - Established in 2002, relays TV3 on channel 12.
===Most viewed channels===
{| class="wikitable" style="font-size: 90%"
|-
! Position !! Channel !! Share of total viewing (%)
|-
| 1 || Hang Meas || 22.1
|-
| 2 || CTN || 18.3
|-
| 3 || MyTV || 10.5
|-
| | Telecommunications in Cambodia | [
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] |
4 || PNN TV || 8.1
|-
| 5 || TV5 || 4.4
|-
| 6 || Bayon TV || 2.6
|-
| 7 || CTV 8 || 2.0
|-
| 8 || SEATV || 1.4
|-
| 9 || TV9 || 1.2
|-
| 10 || TV11 || 1.0
|-
| 11 || TV3 || 0.9
|-
| 12 || CNC || 0.8
|-
| 13 || ETV || 0.6
|-
| 14 || TVK || 0.4
|}
==Internet==
the number of internet users in Cambodia rose to 15.8 million, about 98.5% of the population. According to the Telecommunications Regulator of Cambodia (TRC), the number of registered SIM cards rose by 9.4 percent during the first half of the year, reaching 20.8 million. The SIM card market is saturated, with Cambodia now having more active SIM cards than people. According to TRC, there are six telecommunications firms in the country: Cellcard, Smart Axiata, Metfone, Seatel, Cootel, and qb. Three companies, Metfone, Cellcard, and Smart, account for 90% of users. TRC noted that, as of February 2019, Facebook had seven million users in Cambodia.
List of Internet service providers
* AngkorNet
* AZ (Online)
* Cambo Technology (ISP) Co., Ltd.
* Cambodia Internet Corp
* Cambotech
* Camintel
* Camnet (Telecom Cambodia)
* CB (Cambodian Broadband)
* CDC
* Cellcard (Mobitel)
* CooTel
* Chuan Wei
* CIDC IT
* Citylink
* Digi ISP
* Dragon Royal Telecom
* | Telecommunications in Cambodia | [
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] |
EmCom
* Everyday
* Ezecom
* GTD
* Hiway Telecom
* Home Internet
* Kingtel Communications Limited
* MaxBIT
* MekongNet (Angkor Data Communication Group)
* Metfone
* Mobilastic
* Neocom ISP (NTC)
* NTC - NeocomISP Limited
* Open Net
* PCP
* PP Net Phone
* PPCTV Broadband Internet Service
* SingMeng Telemedia
* yes SEATEL Cambodia
* SINET(S.I Group Co., Ltd)
* Smart @Home
* TeleSURF
* Telecom Cambodia
* TODAY ISP (Today Communication Co., Ltd)
* Turbotech
* Vimean Seile
* Wicam
* WIP
* Wireless Internet Provider
* WirelessIP
* Y5Net (BDKTel Co,LTD)
===Internet censorship and surveillance===
In its Freedom on the Net 2013 report, Freedom House gives Cambodia a "Freedom on the Net Status" of "partly free".
Compared to traditional media in Cambodia, new media, including online news, social networks and personal blogs, enjoy more freedom and independence from government censorship and restrictions. However, the government does proactively block blogs and websites, either on moral grounds, or for hosting content deemed critical of the government. The government restricts access to sexually explicit content, but does not systematically censor online political discourse. Since 2011 three blogs hosted overseas have been blocked for perceived antigovernment content. In 2012, government ministries threatened to shutter internet cafes too near schools—citing moral concerns—and instituted surveillance of cafe premises and cell phone subscribers as a security measure."Cambodia country report", Freedom on the Net | Telecommunications in Cambodia | [
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2013, Freedom House, 3 October 2013. Retrieved 24 October 2013.
Early in 2011, very likely at the urging of the Ministry of Posts and Telecommunications, all Cambodian ISPs blocked the hosting service Blogspot, apparently in reaction to a December 2010 post on KI-Media, a blog run by Cambodians from both inside and outside the country. The site, which is often critical of the administration, described the prime minister and other officials as "traitors" after opposition leader Sam Rainsy alleged they had sold land to Vietnam at a contested national border. All ISPs but one subsequently restored service to the sites following customer complaints. In February 2011, however, multiple ISPs reinstated blocks on individual Blogspot sites, including KI-Media, Khmerization—another critical citizen journalist blog—and a blog by the Khmer political cartoonist Sacrava.
There are no government restrictions on access to the Internet or credible reports that the government monitors e-mail or Internet chat rooms without appropriate legal authority. During 2012 NGOs expressed concern about potential online restrictions. In February and November, the government published two circulars, which, if implemented fully, would require Internet cafes to install surveillance cameras and restrict operations within major urban centers. Activists also reported concern about a draft “cybercrimes” law, | Telecommunications in Cambodia | [
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noting that it could be used to restrict online freedoms. The government maintained it would only regulate criminal activity."Cambodia", Country Reports on Human Rights Practices for 2012, Bureau of Democracy, Human Rights and Labor, U.S. Department of State, 21 March 2013. Retrieved 24 October 2013.
The constitution provides for freedom of speech and press; however, these rights were not always respected in practice. The 1995 press law prohibits prepublication censorship or imprisonment for expressing opinions; however, the government uses the penal code to prosecute citizens on defamation, disinformation, and incitement charges. The penal code does not prescribe imprisonment for defamation, but does for incitement or spreading disinformation, which carry prison sentences of up to three years. Judges also can order fines, which may lead to jail time if not paid. The constitution requires that free speech not adversely affect public security.
The constitution declares that the king is “inviolable,” and a Ministry of Interior directive conforming to the defamation law reiterates these limits and prohibits publishers and editors from disseminating stories that insult or defame government leaders and institutions. The continued criminalization of defamation and disinformation and a broad interpretation of criminal incitement constrains freedom of expression.
The law provides for the privacy | Telecommunications in Cambodia | [
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of residence and correspondence and prohibits illegal searches; however, NGOs report that police routinely conduct searches and seizures without warrants.
Corruption remains pervasive and governmental human rights bodies are generally ineffective. A weak judiciary that sometimes fails to provide due process or fair trial procedures is a serious problem. The courts lack human and financial resources and, as a result, are not truly independent and are subject to corruption and political influence.
On 17 February 2021, the Cambodian government announced its plans to launch a censorship scheme called "National Internet Gateway" which heavily resembles China's Great Firewall, and it will get launched in February 2022.
==See also==
* Media of Cambodia
* Ministry of Posts and Telecommunications (Cambodia)
==References==
==External links==
* Networks: Cambodia
* Ministry of Posts and Telecommunications
* Telecom Cambodia
* Television stations in Cambodia
* "3G phones banned in anti-porn drive", China Daily (Associated Press), 26 May 2006. Retrieved 24 October 2013. | Telecommunications in Cambodia | [
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Telecommunications in Cameroon include radio, television, fixed and mobile telephones, and the Internet.
== History ==
During German rule, It was set up in the protectorate of Kamerun the first telegraph line, the first telephone line, and the first wireless telegraph. However, the country remained undeveloped in telecommunications. During First World War, Germans followed a scorched-earth policy that meant the destruction of communication lines, included telephone and telegraph.
In British Cameroon, from 1916 to 1950s, communications in the country relied on flag post runners that had been described as "human telephone lines". Paths followed by the runners served as a base of the development of telegraph lines in the territory. For instance, the line from Buea-Kumba to Ossidinge used the same paths that the mail runners. In the mid-1930s, the wiring of British Cameroon received more support.
==Radio and television==
* Radio stations:
** state-owned Cameroon Radio Television (CRTV); one private radio broadcaster; about 70 privately owned, unlicensed radio stations operating, but subject to closure at any time; foreign news services are required to partner with a state-owned national station (2007);
** 2 AM, 9 FM, and 3 shortwave stations (2001).
* Television stations:
** state-owned Cameroon Radio Television (CRTV), 2 private TV broadcasters (2007);
** one station (2001).
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Service radio is available via local relays (98.4 FM in Yaounde, the capital)."Cameroon profile: Media", BBC News, 14 August 2012. Retrieved 8 February 2014.
The government maintains tight control over broadcast media. State-owned Cameroon Radio Television (CRTV), operates both a TV and a radio network. It was the only officially recognized and fully licensed broadcaster until August 2007 when the government issued licenses to two private TV and one private radio broadcasters.
Approximately 375 privately owned radio stations were operating in 2012, three-fourths of them in Yaounde and Douala. The government requires nonprofit rural radio stations to submit applications to broadcast, but they were exempt from licensing fees. Commercial radio and television broadcasters must submit a licensing application and pay an application fee and thereafter pay a high annual licensing fee. Several rural community radio stations function with foreign funding. The government prohibits these stations from discussing politics.
In spite of the government's tight control, Reporters Without Borders reported in its 2011 field survey that "[i]t is clear from the diversity of the media and the outspoken reporting style that press freedom is a reality".
==Telephones==
* Calling code: +237"Communications: Cameroon", World Factbook, U.S. Central Intelligence Agency, 28 January 2014. Retrieved 8 February 2014.
* International | Telecommunications in Cameroon | [
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] |
call prefix: 00Dialing Procedures (International Prefix, National (Trunk) Prefix and National (Significant) Number) (in Accordance with ITY-T Recommendation E.164 (11/2010)), Annex to ITU Operational Bulletin No. 994-15.XII.2011, International Telecommunication Union (ITU, Geneva), 15 December 2011. Retrieved 2 January 2014.
* Main lines:
** 737,400 lines in use, 88th in the world (2012);
** 130,700 lines in use (2006).
* Mobile cellular:
** 13.1 million lines, 64th in the world (2012);
** 4.5 million lines (2007).
* Telephone system: system includes cable, microwave radio relay, and tropospheric scatter; Camtel, the monopoly provider of fixed-line service, provides connections for only about 3 per 100 persons; equipment is old and outdated, and connections with many parts of the country are unreliable; mobile-cellular usage, in part a reflection of the poor condition and general inadequacy of the fixed-line network, has increased sharply, reaching a subscribership base of 50 per 100 persons (2011).
* Communications cables: South Atlantic 3/West Africa Submarine Cable (SAT-3/WASC) fiber-optic cable system provides connectivity to Europe and Asia (2011); Africa Coast to Europe (ACE), cable system connecting countries along the west coast of Africa to each other and to Portugal and France, is planned."ACE: Africa Coast to Europe", Orange SA. Retrieved 8 February 2014.
* Satellite earth stations: 2 Intelsat | Telecommunications in Cameroon | [
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(Atlantic Ocean) (2011).
==Internet==
* Top-level domain: .cm
* Internet users:
** 1.1 million users, 113th in the world; 5.7% of the population, 184th in the world (2012).Calculated using penetration rate and population data from "Countries and Areas Ranked by Population: 2012" , Population data, International Programs, U.S. Census Bureau, retrieved 26 June 2013"Percentage of Individuals using the Internet 2000-2012", International Telecommunication Union (Geneva), June 2013, retrieved 22 June 2013
** 985,565 users (2011);
** 749,600 users, 106th in the world (2009).
* Fixed broadband: 1,006 subscriptions, 180th in the world; less than 0.05% of the population, 190th in the world (2012)."Fixed (wired)-broadband subscriptions per 100 inhabitants 2012", Dynamic Report, ITU ITC EYE, International Telecommunication Union. Retrieved on 29 June 2013.
* Wireless broadband: Unknown (2012)."Active mobile-broadband subscriptions per 100 inhabitants 2012", Dynamic Report, ITU ITC EYE, International Telecommunication Union. Retrieved on 29 June 2013.
* Internet hosts:
** 10,207 hosts, 134th in the world (2012);
** 69 hosts (2008).
* IPv4: 137,728 addresses allocated, less than 0.05% of the world total, 6.8 addresses per 1000 people (2012).Select Formats , Country IP Blocks. Accessed on 2 April 2012. Note: Site is said to be updated daily.Population, The World Factbook, United States Central Intelligence Agency. Accessed on 2 April 2012. Note: Data | Telecommunications in Cameroon | [
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are mostly for 1 July 2012.
* Internet service providers (ISPs):
** Creolink Communications"Creolink Communications", website. Retrieved 8 February 2014.
A number of projects are underway that will improve Internet access, telecommunications, and Information and communications technology (ICT) in general:"Ministry of Posts and Telecommunications, Cameroon", Telecom World, International Telecommunication Union, 19–22 November 2013. Retrieved 8 February 2014.
* Implementation of the e-post project, connecting 234 post offices throughout the country;
* Extension of the national optical fiber network, installation of the initial 3,200 km of fiber is complete and studies for the installation of an additional 3,400 km are underway;
* Construction of multipurpose community telecentres, some 115 telecentres are operating with an additional 205 under construction;
* Construction of metropolitan optical loops, the urban optical loop of Douala is complete and construction of the Yaounde loop is underway;
* Construction of submarine cable landing points;
* Establishment of public key infrastructure (PKI);
* Construction of a regional technology park to support the development of ICTs.
===Internet censorship and surveillance===
There are no government restrictions on access to the Internet or reports that the government monitors e-mail or Internet chat rooms."Cameroon", Country Reports on Human Rights Practices for 2012, Bureau of Democracy, Human Rights and Labor, U.S. Department of State, 22 March 2013. | Telecommunications in Cameroon | [
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] |
Retrieved 8 February 2014.
Although the law provides for freedom of speech and press, it also criminalizes media offenses, and the government restricts freedoms of speech and press. Government officials threaten, harass, arrest, and deny equal treatment to individuals or organizations that criticize government policies or express views at odds with government policy. Individuals who criticize the government publicly or privately sometimes face reprisals. Press freedom is constrained by strict libel laws that suppress criticism. These laws authorize the government, at its discretion and the request of the plaintiff, to criminalize a civil libel suit or to initiate a criminal libel suit in cases of alleged libel against the president and other high government officials. Such crimes are punishable by prison terms and heavy fines.
Although the constitution and law prohibit arbitrary interference with privacy, family, home, or correspondence, these rights are subject to restriction for the "higher interests of the state", and there are credible reports that police and gendarmes harass citizens, conduct searches without warrants, and open or seize mail with impunity.
==See also==
* Cameroon Radio Television, government-controlled national broadcaster.
* Commonwealth Telecommunications Organisation
* List of terrestrial fibre optic cable projects in Africa
* Media of Cameroon
* Cameroon
==References==
*
*
==External links==
* Antic.cm, top-level | Telecommunications in Cameroon | [
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domain registry for Cameroon (.cm).
* Ministry of Posts and Telecommunications, Cameroon (MINPOSTEL) . English translation. | Telecommunications in Cameroon | [
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Communications in the Cayman Islands
== Telephone ==
Telephones – main lines in use: 37,400 (2009)
Telephones – mobile cellular: 99,900 (2004)
Telephone system:
:Domestic: Reasonably good overall telephone system with a high fixed-line teledensity. Liberalization of telecom market in 2003; introduction of competition in the mobile-cellular market in 2004. FLOW Cayman, Digicel
: International: The Cayman Islands have landing points for the MAYA-1, and the Cayman-Jamaica Fiber System submarine cables that provide links to the US and parts of Central and South America. Service on both of these cables are controlled by Liberty Latin America.
Satellite earth station – 1 Intelsat (Atlantic Ocean) (2007) Intelsat (Atlantic Ocean)
== Radio ==
Radio broadcast stations: AM 0, FM 17, shortwave 0 (2006)
* List of radio stations in Cayman Islands
Radios: 36,000 (1997)
== Television ==
Television broadcast stations: Cayman27
== Internet ==
Internet Service Providers (ISPs):Four companies offer internet service in the islands with in fixed configurations or mobile or both:
* Liberty Latin America d/b/a FLOW
* Digicel
* Logic - Fibre based service. Founded in 2004 as WestTel when it was granted a telecommunications license. Purchased TeleCayman in 2013
* C3
Country code (Top-level domain): .ky
== References ==
Cayman Islands
Cayman | Telecommunications in the Cayman Islands | [
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] |
Telecommunications in the Central African Republic includes radio, television, fixed and mobile telephones, and the Internet as well as the postal system.
Persistent conflict has hampered telecommunication and media development in the Central African Republic. There are active television services, radio stations, internet service providers, and mobile phone carriers. Radio is the most-popular communications medium."Central African Republic profile: Media", BBC News, 20 September 2013. Retrieved 23 January 2014.
Socatel is the leading provider for both Internet and mobile phone access throughout the country. The primary governmental regulating bodies of telecommunications are the Ministère des Postes (Ministry of Posts), and Télécommunications et des Nouvelles Technologies (Telecommunications and New Technologies). Support is received from the ITU Telecommunication Development Sector (ITU-D) within the International Telecommunication Union to improve telecommunications infrastructure.
==Radio and television==
* Radio stations: the State-owned radio network, Radio Centrafrique, is supplemented by a small number of privately owned broadcast stations as well as a few community radio stations; transmissions of at least 2 international broadcasters are available (2007)."Communications: Central African Republic", World Factbook, U.S. Central Intelligence Agency, 13 January 2014. Retrieved 23 January 2014.
* The BBC World Service (90.2 FM), Radio France Internationale, and the Voice of America are available via local relays in | Telecommunications in the Central African Republic | [
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the capital, Bangui.
* Radios: 283,000 (1997).
* Television stations: Government-owned network, Radiodiffusion Television Centrafricaine (Central Television Broadcasting), provides domestic TV broadcasting; licenses for 2 private TV stations were pending (2007).
* Television sets: 18,000 (1997).
In Bangui, UN-sponsored Radio Ndeke Luka ("bird of luck") provides balanced output, and rebroadcasts international news programming. Other radio and TV stations are run by the state-run Radiodiffusion-Television Centrafricaine and provide little coverage of the political opposition. There are about two dozen privately owned radio stations. Many, such as Radio Notre Dame, run by religious organisations.
Starting 24 November 2011 La Radio et la Télévision nationale centrafricaine (TVCA) (Central African Radio (CAR) and National Television) are available via satellite. This move brought state-run national radio and television coverage to the entire country."La Radio et la télévision centrafricaine enfin sur satellite!" , La diplomatie de Centrafrique à Paris, CAR Embassy in Paris. English translation. Retrieved 24 January 2014.
==Telephones==
* Calling code: +236
* International call prefix: 00Dialing Procedures (International Prefix, National (Trunk) Prefix and National (Significant) Number) (in Accordance with ITY-T Recommendation E.164 (11/2010)), Annex to ITU Operational Bulletin No. 994-15.XII.2011, International Telecommunication Union (ITU, Geneva), 15 December 2011. Retrieved 2 January 2014.
* Main lines: 5,600 lines in use, 209th in the | Telecommunications in the Central African Republic | [
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world (2012).
* Mobile cellular: 1.1 million lines, 157th in the world (2012).
* Telephone system: The network consists principally of microwave radio relay and low-capacity, low-powered radiotelephone communication; limited telephone service with less than one fixed-line connection per 100 persons; spurred by the presence of multiple mobile-cellular service providers, cellular usage is increasing from a low base; most fixed-line and mobile-cellular telephone services are concentrated in the capital, Bangui (2011).
* Satellite earth stations: 1 Intelsat (Atlantic Ocean) (2011).
GSM coverage was for a long time limited to the capital area. But in June 2006 coverage was expanded at least to Berberati in the western part of the country. There are currently two GSM-900 mobile operators, Telecel CAR and NationLink Telecom RCA. A third network, Centrafrique Telecom Plus closed down in late 2005 after failing to attract more than 5,000 subscribers and failing to renew its license, in accordance with the then new Bozize government policies.
==Internet==
* Top-level domain: .cf
* Internet users:
** 151,716 users, 160th in the world; 3.0% of the population, 195th in the world (2012).Calculated using penetration rate and population data from "Countries and Areas Ranked by Population: 2012" , Population data, International Programs, U.S. Census Bureau, retrieved 26 June 2013"Percentage of | Telecommunications in the Central African Republic | [
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Individuals using the Internet 2000–2012", International Telecommunication Union (Geneva), June 2013, retrieved 22 June 2013
** 22,600 users, 192nd in the world (2009).
* Internet hosts: 20 hosts, 221st in the world (2012).
* IPv4: 4,352 addresses allocated, less than 0.05% of the world total, 0.9 addresses per 1000 people (2012).Select Formats , Country IP Blocks. Accessed on 2 April 2012. Note: Site is said to be updated daily.Population, The World Factbook, United States Central Intelligence Agency. Accessed on 2 April 2012. Note: Data are mostly for 1 July 2012.
* Internet Service Providers (ISPs): Moov, Orange, Socatel, and Telecel.
===Internet censorship and surveillance===
There are no government restrictions on access to the Internet or credible reports that the government monitors e-mail or Internet chat rooms without judicial oversight."Central African Republic", Country Reports on Human Rights Practices for 2012, Bureau of Democracy, Human Rights and Labor, U.S. Department of State, 28 March 2013. Retrieved 23 January 2014.
Although the constitution and law provide for freedom of speech and press, authorities occasionally arrest journalists critical of the government and in some cases the government impedes individuals’ right to free speech. Imprisonment for defamation and censorship were abolished in 2005; however, journalists found guilty of libel or slander | Telecommunications in the Central African Republic | [
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face fines of 100,000 to eight million CFA francs ($200 to US$16,000). The law provides for imprisonment and fines of as much as one million CFA francs (US$2,000) for journalists who use the media to incite disobedience among security forces or incite persons to violence, hatred, or discrimination. Similar fines and imprisonment of six months to two years may be imposed for the publication or broadcast of false or fabricated information that "would disturb the peace."
== Postal system==
L'Office National de la Poste et de l'Épargne (ONPE) is the government organization responsible for the postal service.
==See also==
* Media of the Central African Republic
* Economy of the Central African Republic
* Central African Republic
==References==
*
*
==External links==
* Central African Republic profile, BBC News.
Category:Communications in the Central African Republic | Telecommunications in the Central African Republic | [
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The technical regulator of communications in Chile is the Ministry of Transportation and Telecommunications, through the Undersecretariat of Telecommunications (Subtel).
==Telephone==
=== History ===
Telephone and telegraph services started in Chile in 1879, three years after Alexander Graham Bell, presented his patent for a telephonic system. José Dottin Husbands, an associate of Thomas Edison, arrived into the port of Valparaiso carrying the first set of switching equipment and telephones. By 1880 the first telephone company of the country is born (Compañia Chilena de Telefonos de Edison), while in 1893, after a rapid expansion in the northern regions of Chile, telephone services started operating in the south, thanks to the founding of Telefonica del Sur (current day Grupo GTD), a company created by a group of German inmigrants that had previously settled in the area of Valdivia, Region de los Rios.
*Main lines in use: 3.379 million (2007)
*Mobile cellular: 24.130.754 (2012) (devices)
**Pre-paid: 17.283.257
**Post-paid: 6.847.497
*System: privatization began in 1988; advanced telecommunications infrastructure; modern system based on extensive microwave radio relay facilities; fixed-line connections have dropped in recent years as mobile-cellular usage continues to increase, reaching a level of 85 telephones per 100 persons
**Domestic: extensive microwave radio relay links; domestic satellite system with 3 earth | Telecommunications in Chile | [
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stations
**international: country code - 56; submarine cables provide links to the US and to Central and South America; satellite earth stations - 2 Intelsat (Atlantic Ocean) (2007)
==Radio==
*Broadcast stations: 1,490 (175 AM; 1,315 FM) (2006)Compendio Estadístico 2006, INE.
==Television==
*Broadcast stations: 63 (plus 121 repeaters) (1997)
*Broadcast television system: NTSC
*Pay television: 4.158.874 (2012)Articulo 2012, Cambio21.
==Internet==
*Internet hosts: 847,215 (2008)
*Internet users: 5.57 million (2007)
*Internet mobile users: 4.921.587
*Internet country code: .cl
==Other technical details==
*Voltage: 220 volts AC, 50 Hz
==References==
Chile | Telecommunications in Chile | [
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] |
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularity to some time between and seconds after the singularity. Following the inflationary period, the universe continued to expand, but at a slower rate. The acceleration of this expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago).
Inflation theory was developed in the late 1970s and early 80s, with notable contributions by several theoretical physicists, including Alexei Starobinsky at Landau Institute for Theoretical Physics, Alan Guth at Cornell University, and Andrei Linde at Lebedev Physical Institute. Alexei Starobinsky, Alan Guth, and Andrei Linde won the 2014 Kavli Prize "for pioneering the theory of cosmic inflation." It was developed further in the early 1980s. It explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe (see galaxy formation and evolution and structure formation).Tyson, Neil deGrasse and Donald Goldsmith (2004), Origins: Fourteen Billion Years of Cosmic Evolution, | Inflation (cosmology) | [
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W. W. Norton & Co., pp. 84–5. Many physicists also believe that inflation explains why the universe appears to be the same in all directions (isotropic), why the cosmic microwave background radiation is distributed evenly, why the universe is flat, and why no magnetic monopoles have been observed.
The detailed particle physics mechanism responsible for inflation is unknown. The basic inflationary paradigm is accepted by most physicists, as a number of inflation model predictions have been confirmed by observation;
however, a substantial minority of scientists dissent from this position. The hypothetical field thought to be responsible for inflation is called the inflaton.
In 2002 three of the original architects of the theory were recognized for their major contributions; physicists Alan Guth of M.I.T., Andrei Linde of Stanford, and Paul Steinhardt of Princeton shared the prestigious Dirac Prize "for development of the concept of inflation in cosmology". In 2012 Guth and Linde were awarded the Breakthrough Prize in Fundamental Physics for their invention and development of inflationary cosmology.
== Overview ==
Around 1930, Edwin Hubble discovered that light from remote galaxies was redshifted; the more remote, the more shifted. This was quickly interpreted as meaning galaxies were receding from Earth. If Earth is not in some | Inflation (cosmology) | [
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special, privileged, central position in the universe, then it would mean all galaxies are moving apart, and the further away, the faster they are moving away. It is now understood that the universe is expanding, carrying the galaxies with it, and causing this observation. Many other observations agree, and also lead to the same conclusion. However, for many years it was not clear why or how the universe might be expanding, or what it might signify.
Based on a huge amount of experimental observation and theoretical work, it is now believed that the reason for the observation is that space itself is expanding, and that it expanded very rapidly within the first fraction of a second after the Big Bang. This kind of expansion is known as a "metric" expansion. In the terminology of mathematics and physics, a "metric" is a measure of distance that satisfies a specific list of properties, and the term implies that the sense of distance within the universe is itself changing. Today, metric variation is far too small an effect to see on less than an intergalactic scale.
The modern explanation for the metric expansion of space was proposed by physicist Alan Guth in 1979, while investigating | Inflation (cosmology) | [
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the problem of why no magnetic monopoles are seen today. He found that if the universe contained a field in a positive-energy false vacuum state, then according to general relativity it would generate an exponential expansion of space. It was very quickly realized that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look like it does today, the Universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation theory largely resolves these problems as well, thus making a universe like ours much more likely in the context of Big Bang theory.
No physical field has yet been discovered that is responsible for this inflation. However such a field would be scalar and the first relativistic scalar field proven to exist, the Higgs field, was only discovered in 2012–2013 and is still being researched. So it is not seen as problematic that a field responsible for cosmic inflation and the metric expansion of space has not yet been discovered. The proposed field and its quanta (the subatomic particles related to it) have been named the inflaton. If this field did not exist, scientists would | Inflation (cosmology) | [
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have to propose a different explanation for all the observations that strongly suggest a metric expansion of space has occurred, and is still occurring (much more slowly) today.
== Theory ==
An expanding universe generally has a cosmological horizon, which, by analogy with the more familiar horizon caused by the curvature of Earth's surface, marks the boundary of the part of the Universe that an observer can see. Light (or other radiation) emitted by objects beyond the cosmological horizon in an accelerating universe never reaches the observer, because the space in between the observer and the object is expanding too rapidly.
The observable universe is one causal patch of a much larger unobservable universe; other parts of the Universe cannot communicate with Earth yet. These parts of the Universe are outside our current cosmological horizon. In the standard hot big bang model, without inflation, the cosmological horizon moves out, bringing new regions into view. Yet as a local observer sees such a region for the first time, it looks no different from any other region of space the local observer has already seen: its background radiation is at nearly the same temperature as the background radiation of other regions, and its space-time curvature | Inflation (cosmology) | [
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is evolving lock-step with the others. This presents a mystery: how did these new regions know what temperature and curvature they were supposed to have? They couldn't have learned it by getting signals, because they were not previously in communication with our past light cone.Using Tiny Particles To Answer Giant Questions. Science Friday, 3 April 2009.See also Faster than light#Universal expansion.
Inflation answers this question by postulating that all the regions come from an earlier era with a big vacuum energy, or cosmological constant. A space with a cosmological constant is qualitatively different: instead of moving outward, the cosmological horizon stays put. For any one observer, the distance to the cosmological horizon is constant. With exponentially expanding space, two nearby observers are separated very quickly; so much so, that the distance between them quickly exceeds the limits of communications. The spatial slices are expanding very fast to cover huge volumes. Things are constantly moving beyond the cosmological horizon, which is a fixed distance away, and everything becomes homogeneous.
As the inflationary field slowly relaxes to the vacuum, the cosmological constant goes to zero and space begins to expand normally. The new regions that come into view during the normal expansion phase are | Inflation (cosmology) | [
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exactly the same regions that were pushed out of the horizon during inflation, and so they are at nearly the same temperature and curvature, because they come from the same originally small patch of space.
The theory of inflation thus explains why the temperatures and curvatures of different regions are so nearly equal. It also predicts that the total curvature of a space-slice at constant global time is zero. This prediction implies that the total ordinary matter, dark matter and residual vacuum energy in the Universe have to add up to the critical density, and the evidence supports this. More strikingly, inflation allows physicists to calculate the minute differences in temperature of different regions from quantum fluctuations during the inflationary era, and many of these quantitative predictions have been confirmed.
===Space expands===
In a space that expands exponentially (or nearly exponentially) with time, any pair of free-floating objects that are initially at rest will move apart from each other at an accelerating rate, at least as long as they are not bound together by any force. From the point of view of one such object, the spacetime is something like an inside-out Schwarzschild black hole—each object is surrounded by a spherical event | Inflation (cosmology) | [
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horizon. Once the other object has fallen through this horizon it can never return, and even light signals it sends will never reach the first object (at least so long as the space continues to expand exponentially).
In the approximation that the expansion is exactly exponential, the horizon is static and remains a fixed physical distance away. This patch of an inflating universe can be described by the following metric:
:
ds^2=- (1- \Lambda r^2) \, c^2dt^2 + {1\over 1-\Lambda r^2} \, dr^2 + r^2 \, d\Omega^2.
This exponentially expanding spacetime is called a de Sitter space, and to sustain it there must be a cosmological constant, a vacuum energy density that is constant in space and time and proportional to Λ in the above metric. For the case of exactly exponential expansion, the vacuum energy has a negative pressure p equal in magnitude to its energy density ρ; the equation of state is p=−ρ.
Inflation is typically not an exactly exponential expansion, but rather quasi- or near-exponential. In such a universe the horizon will slowly grow with time as the vacuum energy density gradually decreases.
===Few inhomogeneities remain===
Because the accelerating expansion of space stretches out any initial variations in density or | Inflation (cosmology) | [
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temperature to very large length scales, an essential feature of inflation is that it smooths out inhomogeneities and anisotropies, and reduces the curvature of space. This pushes the Universe into a very simple state in which it is completely dominated by the inflaton field and the only significant inhomogeneities are tiny quantum fluctuations. Inflation also dilutes exotic heavy particles, such as the magnetic monopoles predicted by many extensions to the Standard Model of particle physics. If the Universe was only hot enough to form such particles before a period of inflation, they would not be observed in nature, as they would be so rare that it is quite likely that there are none in the observable universe. Together, these effects are called the inflationary "no-hair theorem"Kolb and Turner (1988). by analogy with the no hair theorem for black holes.
The "no-hair" theorem works essentially because the cosmological horizon is no different from a black-hole horizon, except for philosophical disagreements about what is on the other side. The interpretation of the no-hair theorem is that the Universe (observable and unobservable) expands by an enormous factor during inflation. In an expanding universe, energy densities generally fall, or get diluted, as the volume of | Inflation (cosmology) | [
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the Universe increases. For example, the density of ordinary "cold" matter (dust) goes down as the inverse of the volume: when linear dimensions double, the energy density goes down by a factor of eight; the radiation energy density goes down even more rapidly as the Universe expands since the wavelength of each photon is stretched (redshifted), in addition to the photons being dispersed by the expansion. When linear dimensions are doubled, the energy density in radiation falls by a factor of sixteen (see the solution of the energy density continuity equation for an ultra-relativistic fluid). During inflation, the energy density in the inflaton field is roughly constant. However, the energy density in everything else, including inhomogeneities, curvature, anisotropies, exotic particles, and standard-model particles is falling, and through sufficient inflation these all become negligible. This leaves the Universe flat and symmetric, and (apart from the homogeneous inflaton field) mostly empty, at the moment inflation ends and reheating begins.
===Duration===
A key requirement is that inflation must continue long enough to produce the present observable universe from a single, small inflationary Hubble volume. This is necessary to ensure that the Universe appears flat, homogeneous and isotropic at the largest observable scales. This requirement is | Inflation (cosmology) | [
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generally thought to be satisfied if the Universe expanded by a factor of at least during inflation.
===Reheating===
Inflation is a period of supercooled expansion, when the temperature drops by a factor of 100,000 or so. (The exact drop is model-dependent, but in the first models it was typically from K down to K.
Guth, Phase transitions in the very early universe, in The Very Early Universe, eds. Hawking, Gibbon & Siklos
) This relatively low temperature is maintained during the inflationary phase. When inflation ends the temperature returns to the pre-inflationary temperature; this is called reheating or thermalization because the large potential energy of the inflaton field decays into particles and fills the Universe with Standard Model particles, including electromagnetic radiation, starting the radiation dominated phase of the Universe. Because the nature of the inflation is not known, this process is still poorly understood, although it is believed to take place through a parametric resonance.
See Kolb and Turner (1988) or Mukhanov (2005).
==Motivations==
Inflation resolves several problems in Big Bang cosmology that were discovered in the 1970s.Much of the historical context is explained in chapters 15–17 of Peebles (1993). Inflation was first proposed by Alan Guth in 1979 while investigating the problem of why | Inflation (cosmology) | [
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no magnetic monopoles are seen today; he found that a positive-energy false vacuum would, according to general relativity, generate an exponential expansion of space. It was very quickly realised that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look like it does today, the Universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation attempts to resolve these problems by providing a dynamical mechanism that drives the Universe to this special state, thus making a universe like ours much more likely in the context of the Big Bang theory.
===Horizon problem===
The horizon problem is the problem of determining why the Universe appears statistically homogeneous and isotropic in accordance with the cosmological principle. For example, molecules in a canister of gas are distributed homogeneously and isotropically because they are in thermal equilibrium: gas throughout the canister has had enough time to interact to dissipate inhomogeneities and anisotropies. The situation is quite different in the big bang model without inflation, because gravitational expansion does not give the early universe enough time to equilibrate. In a big bang with only the matter and radiation known in | Inflation (cosmology) | [
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the Standard Model, two widely separated regions of the observable universe cannot have equilibrated because they move apart from each other faster than the speed of light and thus have never come into causal contact. In the early Universe, it was not possible to send a light signal between the two regions. Because they have had no interaction, it is difficult to explain why they have the same temperature (are thermally equilibrated). Historically, proposed solutions included the Phoenix universe of Georges Lemaître,, English in Gen. Rel. Grav. 29:641–680, 1997. the related oscillatory universe of Richard Chase Tolman, Reissued (1987) New York: Dover . and the Mixmaster universe of Charles Misner. Lemaître and Tolman proposed that a universe undergoing a number of cycles of contraction and expansion could come into thermal equilibrium. Their models failed, however, because of the buildup of entropy over several cycles. Misner made the (ultimately incorrect) conjecture that the Mixmaster mechanism, which made the Universe more chaotic, could lead to statistical homogeneity and isotropy.
===Flatness problem===
The flatness problem is sometimes called one of the Dicke coincidences (along with the cosmological constant problem).
It became known in the 1960s that the density of matter in the Universe was comparable to | Inflation (cosmology) | [
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the critical density necessary for a flat universe (that is, a universe whose large scale geometry is the usual Euclidean geometry, rather than a non-Euclidean hyperbolic or spherical geometry).
Therefore, regardless of the shape of the universe the contribution of spatial curvature to the expansion of the Universe could not be much greater than the contribution of matter. But as the Universe expands, the curvature redshifts away more slowly than matter and radiation. Extrapolated into the past, this presents a fine-tuning problem because the contribution of curvature to the Universe must be exponentially small (sixteen orders of magnitude less than the density of radiation at Big Bang nucleosynthesis, for example). This problem is exacerbated by recent observations of the cosmic microwave background that have demonstrated that the Universe is flat to within a few percent.
===Magnetic-monopole problem===
The magnetic monopole problem, sometimes called the exotic-relics problem, says that if the early universe were very hot, a large number of very heavy, stable magnetic monopoles would have been produced. This is a problem with Grand Unified Theories, which propose that at high temperatures (such as in the early universe) the electromagnetic force, strong, and weak nuclear forces are not actually fundamental forces but arise | Inflation (cosmology) | [
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] |
due to spontaneous symmetry breaking from a single gauge theory.
These theories predict a number of heavy, stable particles that have not been observed in nature. The most notorious is the magnetic monopole, a kind of stable, heavy "charge" of magnetic field.
Monopoles are predicted to be copiously produced following Grand Unified Theories at high temperature,
and they should have persisted to the present day, to such an extent that they would become the primary constituent of the Universe.
Not only is that not the case, but all searches for them have failed, placing stringent limits on the density of relic magnetic monopoles in the Universe.See, e.g.
A period of inflation that occurs below the temperature where magnetic monopoles can be produced would offer a possible resolution of this problem: monopoles would be separated from each other as the Universe around them expands, potentially lowering their observed density by many orders of magnitude. Though, as cosmologist Martin Rees has written, "Skeptics about exotic physics might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical. Preventive medicine can readily seem 100 percent effective against a disease that doesn't exist!"
==History==
===Precursors===
In the early days of General Relativity, Albert | Inflation (cosmology) | [
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Einstein introduced the cosmological constant to allow a static solution, which was a three-dimensional sphere with a uniform density of matter. Later, Willem de Sitter found a highly symmetric inflating universe, which described a universe with a cosmological constant that is otherwise empty.
It was discovered that Einstein's universe is unstable, and that small fluctuations cause it to collapse or turn into a de Sitter universe.
In the early 1970s Zeldovich noticed the flatness and horizon problems of Big Bang cosmology; before his work, cosmology was presumed to be symmetrical on purely philosophical grounds. In the Soviet Union, this and other considerations led Belinski and Khalatnikov to analyze the chaotic BKL singularity in General Relativity. Misner's Mixmaster universe attempted to use this chaotic behavior to solve the cosmological problems, with limited success.
====False vacuum====
In the late 1970s, Sidney Coleman applied the instanton techniques developed by Alexander Polyakov and collaborators to study the fate of the false vacuum in quantum field theory. Like a metastable phase in statistical mechanics—water below the freezing temperature or above the boiling point—a quantum field would need to nucleate a large enough bubble of the new vacuum, the new phase, in order to make a transition. Coleman found the | Inflation (cosmology) | [
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] |
most likely decay pathway for vacuum decay and calculated the inverse lifetime per unit volume. He eventually noted that gravitational effects would be significant, but he did not calculate these effects and did not apply the results to cosmology.
The universe could have been spontaneously created from nothing (no space, time, nor matter) by quantum fluctuations of metastable false vacuum causing an expanding bubble of true vacuum.
====Starobinsky inflation====
In the Soviet Union, Alexei Starobinsky noted that quantum corrections to general relativity should be important for the early universe. These generically lead to curvature-squared corrections to the Einstein–Hilbert action and a form of f(R) modified gravity. The solution to Einstein's equations in the presence of curvature squared terms, when the curvatures are large, leads to an effective cosmological constant. Therefore, he proposed that the early universe went through an inflationary de Sitter era.
<br/>
This resolved the cosmology problems and led to specific predictions for the corrections to the microwave background radiation, corrections that were then calculated in detail. Starobinsky used the action
:
S=\frac{1}{2} \int d^4 x \left(R + \frac{R^2}{6M^2} \right)
which corresponds to the potential
:\quad V(\phi)=\Lambda^4 \left(1 - e^{-\sqrt{2/3} \phi/M^2_p} \right)^2
in the Einstein frame. This results in the observables:
n_s=1 - \frac{2}{N}, \quad \quad | Inflation (cosmology) | [
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r=\frac{12}{N^2}.
====Monopole problem====
In 1978, Zeldovich noted the monopole problem, which was an unambiguous quantitative version of the horizon problem, this time in a subfield of particle physics, which led to several speculative attempts to resolve it. In 1980 Alan Guth realized that false vacuum decay in the early universe would solve the problem, leading him to propose a scalar-driven inflation. Starobinsky's and Guth's scenarios both predicted an initial de Sitter phase, differing only in mechanistic details.
===Early inflationary models===
Guth proposed inflation in January 1981 to explain the nonexistence of magnetic monopoles;SLAC seminar, " seconds after the Big Bang", 23 January 1980. see Guth (1997), pg 186
it was Guth who coined the term "inflation".Chapter 17 of Peebles (1993). At the same time, Starobinsky argued that quantum corrections to gravity would replace the initial singularity of the Universe with an exponentially expanding de Sitter phase.
In October 1980, Demosthenes Kazanas suggested that exponential expansion could eliminate the particle horizon and perhaps solve the horizon problem,
while Sato suggested that an exponential expansion could eliminate domain walls (another kind of exotic relic).
In 1981 Einhorn and Sato
published a model similar to Guth's and showed that it would resolve the puzzle of the magnetic monopole abundance in | Inflation (cosmology) | [
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Grand Unified Theories. Like Guth, they concluded that such a model not only required fine tuning of the cosmological constant, but also would likely lead to a much too granular universe, i.e., to large density variations resulting from bubble wall collisions.
Guth proposed that as the early universe cooled, it was trapped in a false vacuum with a high energy density, which is much like a cosmological constant. As the very early universe cooled it was trapped in a metastable state (it was supercooled), which it could only decay out of through the process of bubble nucleation via quantum tunneling. Bubbles of true vacuum spontaneously form in the sea of false vacuum and rapidly begin expanding at the speed of light. Guth recognized that this model was problematic because the model did not reheat properly: when the bubbles nucleated, they did not generate any radiation. Radiation could only be generated in collisions between bubble walls. But if inflation lasted long enough to solve the initial conditions problems, collisions between bubbles became exceedingly rare. In any one causal patch it is likely that only one bubble would nucleate.
===Slow-roll inflation===
The bubble collision problem was solved by Linde and independently by Andreas Albrecht and | Inflation (cosmology) | [
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Paul Steinhardt in a model named new inflation or slow-roll inflation (Guth's model then became known as old inflation). In this model, instead of tunneling out of a false vacuum state, inflation occurred by a scalar field rolling down a potential energy hill. When the field rolls very slowly compared to the expansion of the Universe, inflation occurs. However, when the hill becomes steeper, inflation ends and reheating can occur.
===Effects of asymmetries===
Eventually, it was shown that new inflation does not produce a perfectly symmetric universe, but that quantum fluctuations in the inflaton are created. These fluctuations form the primordial seeds for all structure created in the later universe. These fluctuations were first calculated by Viatcheslav Mukhanov and G. V. Chibisov in analyzing Starobinsky's similar model.See Linde (1990) and Mukhanov (2005). In the context of inflation, they were worked out independently of the work of Mukhanov and Chibisov at the three-week 1982 Nuffield Workshop on the Very Early Universe at Cambridge University.See Guth (1997) for a popular description of the workshop, or The Very Early Universe, eds Hawking, Gibbon & Siklos for a more detailed report The fluctuations were calculated by four groups working separately over the course of the | Inflation (cosmology) | [
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workshop: Stephen Hawking; Starobinsky; Guth and So-Young Pi; and Bardeen, Steinhardt and Turner.
==Observational status==
Inflation is a mechanism for realizing the cosmological principle, which is the basis of the standard model of physical cosmology: it accounts for the homogeneity and isotropy of the observable universe. In addition, it accounts for the observed flatness and absence of magnetic monopoles. Since Guth's early work, each of these observations has received further confirmation, most impressively by the detailed observations of the cosmic microwave background made by the Planck spacecraft. This analysis shows that the Universe is flat to within 0.5 percent, and that it is homogeneous and isotropic to one part in 100,000.
Inflation predicts that the structures visible in the Universe today formed through the gravitational collapse of perturbations that were formed as quantum mechanical fluctuations in the inflationary epoch. The detailed form of the spectrum of perturbations, called a nearly-scale-invariant Gaussian random field is very specific and has only two free parameters. One is the amplitude of the spectrum and the spectral index, which measures the slight deviation from scale invariance predicted by inflation (perfect scale invariance corresponds to the idealized de Sitter universe).
The other free parameter is the tensor to scalar ratio. | Inflation (cosmology) | [
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The simplest inflation models, those without fine-tuning, predict a tensor to scalar ratio near 0.1.
Inflation predicts that the observed perturbations should be in thermal equilibrium with each other (these are called adiabatic or isentropic perturbations). This structure for the perturbations has been confirmed by the Planck spacecraft, WMAP spacecraft and other cosmic microwave background (CMB) experiments, and galaxy surveys, especially the ongoing Sloan Digital Sky Survey. These experiments have shown that the one part in 100,000 inhomogeneities observed have exactly the form predicted by theory. There is evidence for a slight deviation from scale invariance. The spectral index, ns is one for a scale-invariant Harrison–Zel'dovich spectrum. The simplest inflation models predict that ns is between 0.92 and 0.98. This is the range that is possible without fine-tuning of the parameters related to energy. From Planck data it can be inferred that ns=0.968 ± 0.006, and a tensor to scalar ratio that is less than 0.11. These are considered an important confirmation of the theory of inflation.
Various inflation theories have been proposed that make radically different predictions, but they generally have much more fine tuning than should be necessary. As a physical model, however, inflation is most valuable in that it | Inflation (cosmology) | [
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robustly predicts the initial conditions of the Universe based on only two adjustable parameters: the spectral index (that can only change in a small range) and the amplitude of the perturbations. Except in contrived models, this is true regardless of how inflation is realized in particle physics.
Occasionally, effects are observed that appear to contradict the simplest models of inflation. The first-year WMAP data suggested that the spectrum might not be nearly scale-invariant, but might instead have a slight curvature. However, the third-year data revealed that the effect was a statistical anomaly. Another effect remarked upon since the first cosmic microwave background satellite, the Cosmic Background Explorer is that the amplitude of the quadrupole moment of the CMB is unexpectedly low and the other low multipoles appear to be preferentially aligned with the ecliptic plane. Some have claimed that this is a signature of non-Gaussianity and thus contradicts the simplest models of inflation. Others have suggested that the effect may be due to other new physics, foreground contamination, or even publication bias.See cosmic microwave background#Low multipoles for details and references.
An experimental program is underway to further test inflation with more precise CMB measurements. In particular, high precision measurements of the so-called | Inflation (cosmology) | [
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] |
"B-modes" of the polarization of the background radiation could provide evidence of the gravitational radiation produced by inflation, and could also show whether the energy scale of inflation predicted by the simplest models (– GeV) is correct. In March 2014, the BICEP2 team announced B-mode CMB polarization confirming inflation had been demonstrated. The team announced the tensor-to-scalar power ratio r was between 0.15 and 0.27 (rejecting the null hypothesis; r is expected to be 0 in the absence of inflation). However, on 19 June 2014, lowered confidence in confirming the findings was reported; on 19 September 2014, a further reduction in confidence was reported and, on 30 January 2015, even less confidence yet was reported. By 2018, additional data suggested, with 95% confidence, that r is 0.06 or lower: consistent with the null hypothesis, but still also consistent with many remaining models of inflation.
Other potentially corroborating measurements are expected from the Planck spacecraft, although it is unclear if the signal will be visible, or if contamination from foreground sources will interfere. Other forthcoming measurements, such as those of 21 centimeter radiation (radiation emitted and absorbed from neutral hydrogen before the first stars formed), may measure the power spectrum with even | Inflation (cosmology) | [
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greater resolution than the CMB and galaxy surveys, although it is not known if these measurements will be possible or if interference with radio sources on Earth and in the galaxy will be too great.
==Theoretical status==
In Guth's early proposal, it was thought that the inflaton was the Higgs field, the field that explains the mass of the elementary particles. It is now believed by some that the inflaton cannot be the Higgs field
although the recent discovery of the Higgs boson has increased the number of works considering the Higgs field as inflaton.
One problem of this identification is the current tension with experimental data at the electroweak scale,
which is currently under study at the Large Hadron Collider (LHC). Other models of inflation relied on the properties of Grand Unified Theories. Since the simplest models of grand unification have failed, it is now thought by many physicists that inflation will be included in a supersymmetric theory such as string theory or a supersymmetric grand unified theory. At present, while inflation is understood principally by its detailed predictions of the initial conditions for the hot early universe, the particle physics is largely ad hoc modelling. As such, although predictions of inflation have | Inflation (cosmology) | [
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been consistent with the results of observational tests, many open questions remain.
===Fine-tuning problem===
One of the most severe challenges for inflation arises from the need for fine tuning. In new inflation, the slow-roll conditions must be satisfied for inflation to occur. The slow-roll conditions say that the inflaton potential must be flat (compared to the large vacuum energy) and that the inflaton particles must have a small mass.Technically, these conditions are that the logarithmic derivative of the potential, \epsilon=(1/2)(V'/V)^2 and second derivative \eta=V/V are small, where V is the potential and the equations are written in reduced Planck units. See, e.g. Liddle and Lyth (2000), pg 42–43. New inflation requires the Universe to have a scalar field with an especially flat potential and special initial conditions. However, explanations for these fine-tunings have been proposed. For example, classically scale invariant field theories, where scale invariance is broken by quantum effects, provide an explanation of the flatness of inflationary potentials, as long as the theory can be studied through perturbation theory.
Linde proposed a theory known as chaotic inflation in which he suggested that the conditions for inflation were actually satisfied quite generically. Inflation will occur in virtually any universe that begins in a | Inflation (cosmology) | [
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chaotic, high energy state that has a scalar field with unbounded potential energy. However, in his model the inflaton field necessarily takes values larger than one Planck unit: for this reason, these are often called large field models and the competing new inflation models are called small field models. In this situation, the predictions of effective field theory are thought to be invalid, as renormalization should cause large corrections that could prevent inflation.
This problem has not yet been resolved and some cosmologists argue that the small field models, in which inflation can occur at a much lower energy scale, are better models.See, e.g. While inflation depends on quantum field theory (and the semiclassical approximation to quantum gravity) in an important way, it has not been completely reconciled with these theories.
Brandenberger commented on fine-tuning in another situation. The amplitude of the primordial inhomogeneities produced in inflation is directly tied to the energy scale of inflation. This scale is suggested to be around GeV or times the Planck energy. The natural scale is naïvely the Planck scale so this small value could be seen as another form of fine-tuning (called a hierarchy problem): the energy density given by the | Inflation (cosmology) | [
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scalar potential is down by compared to the Planck density. This is not usually considered to be a critical problem, however, because the scale of inflation corresponds naturally to the scale of gauge unification.
===Eternal inflation===
In many models, the inflationary phase of the Universe's expansion lasts forever in at least some regions of the Universe. This occurs because inflating regions expand very rapidly, reproducing themselves. Unless the rate of decay to the non-inflating phase is sufficiently fast, new inflating regions are produced more rapidly than non-inflating regions. In such models, most of the volume of the Universe is continuously inflating at any given time.
All models of eternal inflation produce an infinite, hypothetical multiverse, typically a fractal. The multiverse theory has created significant dissension in the scientific community about the viability of the inflationary model.
Paul Steinhardt, one of the original architects of the inflationary model, introduced the first example of eternal inflation in 1983. He showed that the inflation could proceed forever by producing bubbles of non-inflating space filled with hot matter and radiation surrounded by empty space that continues to inflate. The bubbles could not grow fast enough to keep up with the inflation. Later that same year, Alexander Vilenkin | Inflation (cosmology) | [
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showed that eternal inflation is generic.
Although new inflation is classically rolling down the potential, quantum fluctuations can sometimes lift it to previous levels. These regions in which the inflaton fluctuates upwards expand much faster than regions in which the inflaton has a lower potential energy, and tend to dominate in terms of physical volume. It has been shown that any inflationary theory with an unbounded potential is eternal. There are well-known theorems that this steady state cannot continue forever into the past. Inflationary spacetime, which is similar to de Sitter space, is incomplete without a contracting region. However, unlike de Sitter space, fluctuations in a contracting inflationary space collapse to form a gravitational singularity, a point where densities become infinite. Therefore, it is necessary to have a theory for the Universe's initial conditions.
In eternal inflation, regions with inflation have an exponentially growing volume, while regions that are not inflating don't. This suggests that the volume of the inflating part of the Universe in the global picture is always unimaginably larger than the part that has stopped inflating, even though inflation eventually ends as seen by any single pre-inflationary observer. Scientists disagree about how to assign a probability distribution to this | Inflation (cosmology) | [
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hypothetical anthropic landscape. If the probability of different regions is counted by volume, one should expect that inflation will never end or applying boundary conditions that a local observer exists to observe it, that inflation will end as late as possible.
Some physicists believe this paradox can be resolved by weighting observers by their pre-inflationary volume. Others believe that there is no resolution to the paradox and that the multiverse is a critical flaw in the inflationary paradigm. Paul Steinhardt, who first introduced the eternal inflationary model, later became one of its most vocal critics for this reason.
===Initial conditions===
Some physicists have tried to avoid the initial conditions problem by proposing models for an eternally inflating universe with no origin. These models propose that while the Universe, on the largest scales, expands exponentially it was, is and always will be, spatially infinite and has existed, and will exist, forever.
Other proposals attempt to describe the ex nihilo creation of the Universe based on quantum cosmology and the following inflation. Vilenkin put forth one such scenario. Hartle and Hawking offered the no-boundary proposal for the initial creation of the Universe in which inflation comes about naturally.; See also Hawking (1998).
Guth described the inflationary universe | Inflation (cosmology) | [
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as the "ultimate free lunch":Hawking (1998), p. 129.Wikiquote new universes, similar to our own, are continually produced in a vast inflating background. Gravitational interactions, in this case, circumvent (but do not violate) the first law of thermodynamics (energy conservation) and the second law of thermodynamics (entropy and the arrow of time problem). However, while there is consensus that this solves the initial conditions problem, some have disputed this, as it is much more likely that the Universe came about by a quantum fluctuation. Don Page was an outspoken critic of inflation because of this anomaly.; see also Roger Penrose's book The Road to Reality: A Complete Guide to the Laws of the Universe. He stressed that the thermodynamic arrow of time necessitates low entropy initial conditions, which would be highly unlikely. According to them, rather than solving this problem, the inflation theory aggravates it – the reheating at the end of the inflation era increases entropy, making it necessary for the initial state of the Universe to be even more orderly than in other Big Bang theories with no inflation phase.
Hawking and Page later found ambiguous results when they attempted to compute the probability of inflation in the Hartle-Hawking initial | Inflation (cosmology) | [
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state. Other authors have argued that, since inflation is eternal, the probability doesn't matter as long as it is not precisely zero: once it starts, inflation perpetuates itself and quickly dominates the Universe. However, Albrecht and Lorenzo Sorbo argued that the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state is much higher than that of a non-inflationary cosmos. This is because the "seed" amount of non-gravitational energy required for the inflationary cosmos is so much less than that for a non-inflationary alternative, which outweighs any entropic considerations.
Another problem that has occasionally been mentioned is the trans-Planckian problem or trans-Planckian effects. Since the energy scale of inflation and the Planck scale are relatively close, some of the quantum fluctuations that have made up the structure in our universe were smaller than the Planck length before inflation. Therefore, there ought to be corrections from Planck-scale physics, in particular the unknown quantum theory of gravity. Some disagreement remains about the magnitude of this effect: about whether it is just on the threshold of detectability or completely undetectable.
===Hybrid inflation===
Another kind of inflation, called hybrid inflation, is an extension of new inflation. It introduces additional | Inflation (cosmology) | [
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scalar fields, so that while one of the scalar fields is responsible for normal slow roll inflation, another triggers the end of inflation: when inflation has continued for sufficiently long, it becomes favorable to the second field to decay into a much lower energy state.
In hybrid inflation, one scalar field is responsible for most of the energy density (thus determining the rate of expansion), while another is responsible for the slow roll (thus determining the period of inflation and its termination). Thus fluctuations in the former inflaton would not affect inflation termination, while fluctuations in the latter would not affect the rate of expansion. Therefore, hybrid inflation is not eternal. When the second (slow-rolling) inflaton reaches the bottom of its potential, it changes the location of the minimum of the first inflaton's potential, which leads to a fast roll of the inflaton down its potential, leading to termination of inflation.
===Relation to dark energy===
Dark energy is broadly similar to inflation and is thought to be causing the expansion of the present-day universe to accelerate. However, the energy scale of dark energy is much lower, GeV, roughly 27 orders of magnitude less than the scale of inflation.
===Inflation and string cosmology===
The discovery of | Inflation (cosmology) | [
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flux compactifications opened the way for reconciling inflation and string theory. Brane inflation suggests that inflation arises from the motion of D-branes in the compactified geometry, usually towards a stack of anti-D-branes. This theory, governed by the Dirac-Born-Infeld action, is different from ordinary inflation. The dynamics are not completely understood. It appears that special conditions are necessary since inflation occurs in tunneling between two vacua in the string landscape. The process of tunneling between two vacua is a form of old inflation, but new inflation must then occur by some other mechanism.
===Inflation and loop quantum gravity===
When investigating the effects the theory of loop quantum gravity would have on cosmology, a loop quantum cosmology model has evolved that provides a possible mechanism for cosmological inflation. Loop quantum gravity assumes a quantized spacetime. If the energy density is larger than can be held by the quantized spacetime, it is thought to bounce back.
==Alternatives and adjuncts==
Other models have been advanced that are claimed to explain some or all of the observations addressed by inflation.
=== Big bounce ===
The big bounce hypothesis attempts to replace the cosmic singularity with a cosmic contraction and bounce, thereby explaining the initial conditions that led to the big bang.
The | Inflation (cosmology) | [
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flatness and horizon problems are naturally solved in the Einstein-Cartan-Sciama-Kibble theory of gravity, without needing an exotic form of matter or free parameters.
This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between torsion and Dirac spinors generates a spin-spin interaction that is significant in fermionic matter at extremely high densities. Such an interaction averts the unphysical Big Bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. The rapid expansion immediately after the Big Bounce explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic. As the density of the Universe decreases, the effects of torsion weaken and the Universe smoothly enters the radiation-dominated era.
=== Ekpyrotic and cyclic models ===
The ekpyrotic and cyclic models are also considered adjuncts to inflation. These models solve the horizon problem through an expanding epoch well before the Big Bang, and then generate the required spectrum of primordial density perturbations during a contracting phase leading to a Big Crunch. The Universe passes through the Big Crunch and emerges in | Inflation (cosmology) | [
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a hot Big Bang phase. In this sense they are reminiscent of Richard Chace Tolman's oscillatory universe; in Tolman's model, however, the total age of the Universe is necessarily finite, while in these models this is not necessarily so. Whether the correct spectrum of density fluctuations can be produced, and whether the Universe can successfully navigate the Big Bang/Big Crunch transition, remains a topic of controversy and current research. Ekpyrotic models avoid the magnetic monopole problem as long as the temperature at the Big Crunch/Big Bang transition remains below the Grand Unified Scale, as this is the temperature required to produce magnetic monopoles in the first place. As things stand, there is no evidence of any 'slowing down' of the expansion, but this is not surprising as each cycle is expected to last on the order of a trillion years.
=== String gas cosmology ===
String theory requires that, in addition to the three observable spatial dimensions, additional dimensions exist that are curled up or compactified (see also Kaluza–Klein theory). Extra dimensions appear as a frequent component of supergravity models and other approaches to quantum gravity. This raised the contingent question of why four space-time dimensions became large and the rest became | Inflation (cosmology) | [
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unobservably small. An attempt to address this question, called string gas cosmology, was proposed by Robert Brandenberger and Cumrun Vafa.
This model focuses on the dynamics of the early universe considered as a hot gas of strings. Brandenberger and Vafa show that a dimension of spacetime can only expand if the strings that wind around it can efficiently annihilate each other. Each string is a one-dimensional object, and the largest number of dimensions in which two strings will generically intersect (and, presumably, annihilate) is three. Therefore, the most likely number of non-compact (large) spatial dimensions is three. Current work on this model centers on whether it can succeed in stabilizing the size of the compactified dimensions and produce the correct spectrum of primordial density perturbations. The original model did not "solve the entropy and flatness problems of standard cosmology", although Brandenburger and coauthors later argued that these problems can be eliminated by implementing string gas cosmology in the context of a bouncing-universe scenario.
=== Varying c ===
Cosmological models employing a variable speed of light have been proposed to resolve the horizon problem of and provide an alternative to cosmic inflation. In the VSL models, the fundamental constant c, denoting the speed | Inflation (cosmology) | [
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of light in vacuum, is greater in the early universe than its present value, effectively increasing the particle horizon at the time of decoupling sufficiently to account for the observed isotropy of the CMB.
==Criticisms==
Since its introduction by Alan Guth in 1980, the inflationary paradigm has become widely accepted. Nevertheless, many physicists, mathematicians, and philosophers of science have voiced criticisms, claiming untestable predictions and a lack of serious empirical support. In 1999, John Earman and Jesús Mosterín published a thorough critical review of inflationary cosmology, concluding,
: "we do not think that there are, as yet, good grounds for admitting any of the models of inflation into the standard core of cosmology."
As pointed out by Roger Penrose from 1986 on, in order to work, inflation requires extremely specific initial conditions of its own, so that the problem (or pseudo-problem) of initial conditions is not solved:
: "There is something fundamentally misconceived about trying to explain the uniformity of the early universe as resulting from a thermalization process. ... For, if the thermalization is actually doing anything ... then it represents a definite increasing of the entropy. Thus, the universe would have been even more special before the thermalization than after."
<br/>
The problem of specific | Inflation (cosmology) | [
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or "fine-tuned" initial conditions would not have been solved; it would have gotten worse. At a conference in 2015, Penrose said that
: "inflation isn't falsifiable, it's falsified. ... BICEP did a wonderful service by bringing all the Inflation-ists out of their shell, and giving them a black eye."
— This is a collation of remarks from the third day of the conference.
A recurrent criticism of inflation is that the invoked inflaton field does not correspond to any known physical field, and that its potential energy curve seems to be an ad hoc contrivance to accommodate almost any data obtainable. Paul Steinhardt, one of the founding fathers of inflationary cosmology, has recently become one of its sharpest critics. He calls 'bad inflation' a period of accelerated expansion whose outcome conflicts with observations, and 'good inflation' one compatible with them:
: "Not only is bad inflation more likely than good inflation, but no inflation is more likely than either ... Roger Penrose considered all the possible configurations of the inflaton and gravitational fields. Some of these configurations lead to inflation ... Other configurations lead to a uniform, flat universe directly – without inflation. Obtaining a flat universe is unlikely overall. Penrose's shocking | Inflation (cosmology) | [
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] |
conclusion, though, was that obtaining a flat universe without inflation is much more likely than with inflation – by a factor of 10 to the googol power!"
Together with Anna Ijjas and Abraham Loeb, he wrote articles claiming that the inflationary paradigm is in trouble in view of the data from the Planck satellite.
Counter-arguments were presented by Alan Guth, David Kaiser, and Yasunori Nomura
and by Andrei Linde,
saying that
: "cosmic inflation is on a stronger footing than ever before".
==See also==
==Notes==
==References==
==Sources==
==External links==
* Was Cosmic Inflation The 'Bang' Of The Big Bang?, by Alan Guth, 1997
*
* update 2004 by Andrew Liddle
*
*
* The Growth of Inflation Symmetry, December 2004
* Guth's logbook showing the original idea
* WMAP Bolsters Case for Cosmic Inflation, March 2006
* NASA March 2006 WMAP press release
* Max Tegmark's Our Mathematical Universe (2014), "Chapter 5: Inflation"
Category:Physical cosmology
Category:Concepts in astronomy
Category:Astronomical events
Category:1980 in science | Inflation (cosmology) | [
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] |
Telephones - main lines in use:
2.888 million (2006)
Telephones - mobile cellular:
13.075 million (2007)
Telephone system:
domestic:
86% of exchanges now digital; existing copper subscriber systems now being improved with Asymmetric Digital Subscriber Line (ADSL) equipment to accommodate Internet and other digital signals; trunk systems include fibre-optic cable and microwave radio relay
Indian Ocean regions), 1 Intelsat, 1 Eutelsat, 1 Inmarsat, 1 Globalstar
Radio broadcast stations:
AM 31, FM 304, shortwave 17 (2000)
Radios:
3,159,134 (December 2000)
Television broadcast stations:
150 (plus 1,434 repeaters) (2000)
Televisions:
3,405,834 (December 2000)
Internet Service Providers (ISPs):
more than 300 (2000)
Internet users:
4.4 million (2007)
Country code: CZ
:See also : Czech Republic | Telecommunications in the Czech Republic | [
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Chinese input methods are methods that allow a computer user to input Chinese characters. Most, if not all, Chinese input methods fall into one of two categories: phonetic readings or root shapes. Methods under the phonetic category usually are easier to learn but are less efficient, thus resulting in slower typing speeds because they typically require users to choose from a list of phonetically similar characters for input, whereas methods under the root shape category allow very precise and speedy input but have a steep learning curve because they often require a thorough understanding of a character's strokes and composition.
Other methods allow users to write characters directly onto touchscreens, such as those found on mobile phones and tablet computers.
==History==
Chinese input methods predate the computer. One of the early attempts was an electro-mechanical Chinese typewriter Ming kwai () which was invented by Lin Yutang, a prominent Chinese writer, in the 1940s. It assigned thirty base shapes or strokes to different keys and adopted a new way of categorizing Chinese characters. But the typewriter was not produced commercially and Lin soon found himself deeply in debt.中文與計算機
Before the 1980s, Chinese publishers hired teams of workers and selected a few thousand type | Chinese input methods for computers | [
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pieces from an enormous Chinese character set. Chinese government agencies entered characters using a long, complicated list of Chinese telegraph codes, which assigned different numbers to each character. During the early computer era, Chinese characters were categorized by their radicals or Pinyin romanization, but results were less than satisfactory.
In the 1970s to 1980s, large keyboards with thousands of keys were used to input Chinese. Each key was mapped to several Chinese characters. To type a character, one pressed the character key and then a selection key. There were also experimental "radical keyboards" with dozens to several hundreds keys. Chinese characters were decomposed into "radicals", each of which was represented by a key. Unwieldy and difficult to use, these keyboards became obsolete after the introduction of Cangjie input method, the first method to use only the standard keyboard and make Chinese touch typing possible.
Chu Bong-Foo invented a common input method in 1976 with his Cangjie input method, which assigns different "roots" to each key on a standard computer keyboard. With this method, for example, the character 日 is assigned to the A key, and 月 is assigned to B. Typing them together will result in the character 明 ("bright").
Despite its steeper | Chinese input methods for computers | [
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learning curve, this method remains popular in Chinese communities that use traditional Chinese characters, such as Hong Kong and Taiwan; the method allows very precise input, thus allowing users to type more efficiently and quickly, provided they are familiar with the fairly complicated rules of the method. It was the first method that allowed users to enter more than a hundred Chinese characters per minute. Its popularity is also helped by its omnipresence on traditional Chinese computer systems, since Chu has given up its patent in 1982, stating that it should be part of the cultural asset. Developers of Chinese systems can adopt it freely, and users do not have the hassle of it being absent on devices with Chinese support. Cangjie input programs supporting large CJK character set have been developed.
All methods have their strengths and weaknesses. The pinyin method can be learned rapidly but its maximum input rate is limited. The Wubi takes longer to learn, but expert typists can enter text much more rapidly with it than with phonetic methods. However, Wubi is proprietary, and a version of it has become freely available only after its inventor lost a patent lawsuit in 1997.
Due to these complexities, there | Chinese input methods for computers | [
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] |
is no "standard" method.
In mainland China, the wubi (shape-based) and pinyin methods such as Sogou Pinyin and Google Pinyin are the most popular; in Taiwan, Cangjie, Dayi, Boshiamy, and zhuyin predominate; and in Hong Kong and Macau, the Cangjie is most often taught in schools, while a few schools teach CKC Chinese Input System.
Other methods include handwriting recognition, OCR and voice recognition. The computer itself must first be "trained" before the first or second of these methods are used; that is, the new user enters the system in a special "learning mode" so that the system can learn to identify their handwriting or speech patterns. The latter two methods are used less frequently than keyboard-based input methods and suffer from relatively high error rates, especially when used without proper "training", though higher error rates are an acceptable trade-off to many users. In recent years, online IME have become more scarce, owing to the proliferation of cellphones and apps.Type in Chinese Online (IME)
== Categories ==
===Phonetic-based===
The user enters pronunciations that are converted into relevant Chinese characters. The user must select the desired character from homophones, which are common in Chinese. Modern systems, such as Sogou Pinyin and Google Pinyin, predict the desired | Chinese input methods for computers | [
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characters based on context and user preferences. For example, if one enters the sounds jicheng, the software will type 繼承 (to inherit), but if jichengche is entered, 計程車 (taxi) will appear.
Various Chinese dialects complicate the system. Phonetic methods are mainly based on standard pinyin, Zhuyin/Bopomofo, and Jyutping in China, Taiwan, and Hong Kong, respectively. Input methods based on other varieties of Chinese, like Hakka or Minnan, also exist.
While the phonetic system is easy to learn, choosing appropriate Chinese characters slows typing speed. Most users report a typing speed of fifty characters per minute, though some reach over one hundred per minute.users' Report on Pinyin Method, Sougou BBS With some phonetic IMEs (Input Method Editors), in addition to predictive input based on previous conversions, it is possible for users to create custom dictionary entries for frequently used characters and phrases, potentially lowering the number of characters required to evoke it.
==== Shuangpin ====
Shuangpin (雙拼; 双拼), literally dual spell, is a stenographical phonetic input method based on hanyu pinyin that reduces the number of keystrokes for one Chinese character to two by distributing every vowel and consonant composed of more than one letter to a specific key. In most Shuangpin layout | Chinese input methods for computers | [
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] |
schemes such as Xiaohe, Microsoft 2003 and Ziranma, the most frequently used vowels are placed on the middle layer, reducing the risk of repetitive strain injury.
Shuangpin is supported by a large number of pinyin input software including QQ, Microsoft Bing Pinyin, Sogou Pinyin and Google Pinyin.
=== Shape-based ===
* Cangjie input method (倉頡; 仓颉; Tsang-chieh)
* Simplified Cangjie (簡易倉頡, known as 速成 or 'Quick' on Windows systems and 'Sucheng' on Mac OS X systems)
* CKC Chinese Input System (縱橫輸入法)
* Boshiamy method (嘸蝦米)
* Dayi method (大易)
* Array input method (行列)
* Four-Corner Method (四角碼; 四角码)
* Oxis Chinese Character Finder
* Q9 method (九方)
* Shouwei method (首尾字型)
* Stroke count method (筆畫; 笔画)
* Stroke method (筆劃; 笔划)
* Wubi method (五筆字型; 五笔字型)
* Wubihua method (五筆畫; 五笔画)
* Zhengma method (鄭碼; 郑码)
* Biaoxingma method (表形碼; 表形码)
* Shou-wei Hao-ma method (首尾號碼)
* Knot DNA method (筆結碼)
=== Hybrid ===
* Tze-loi method (子來; 子来)
* (認知碼; 认知码)
* Cong Ming Da Zi (聪明打字, Released 2011)
=== Others ===
* Chinese telegraph code (中文電碼)
=== Examples of keyboard layouts ===
Image:Keyboard layout Zhuyin.svg|A typical keyboard layout for zhuyin on computers, which can be used as an input method
Image:5strokes.jpg|The Wubi keyboard which is an input method
Image:Keyboard layout cangjie.png|A typical keyboard layout for Cangjie method, which is based on United States keyboard | Chinese input methods for computers | [
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] |
layout. Note the non-standard use of Z as the collision key.
Image:Keyboard layout Dayi.svg|A typical keyboard layout for Dayi method
Image:Keyboard layout Chinese Traditional.png|Chinese (traditional) keyboard layout, a US keyboard with Zhuyin, Cangjie and Dayi key labels, which can all be used to input Chinese characters into a computer
==Software==
*Microsoft IME
*Sogou Pinyin
*Google Pinyin
==Notes==
== See also ==
* List of input methods for Unix platforms
* List of CJK fonts
* Japanese language and computers
** Japanese input methods
* Korean language and computers
* Vietnamese language and computers
* Han unification
* Character amnesia
* Chinese character encodings:
** Big5
** Guobiao code (GB)
** Neima (內碼)
** Unicode
** Telegraph code (電報碼)
== External links ==
=== Information and articles ===
* What Does a Chinese Keyboard Look Like?, article by Slate.com
* Overview of Input Methods, by Sebastien Bruggeman.
* 中文輸入法世界 Chinese input method news.
* The engineering daring that led to the first Chinese personal computer. With 1,000s of Chinese characters and limited memory, inventors of the Sinotype III had to push the limits of early machines. by Tom Mullaney, June 29, 2021, techcrunch.com
* How intensive modding ushered in China’s computer revolution: Early Chinese engineers needed to constantly push against the boundaries of 'alphabetic order,'by Tom Mullaney, October 24, 2021, techcrunch.com
* The computer pioneer who built modern China, By Leila | Chinese input methods for computers | [
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McNeill, 19th February 2020, bbc website.
=== Tutorials ===
*What is an Input Method Editor and how do I use it?, a Microsoft article about Windows XP's Input Method Editor.
*IME Tutorial, tutorial on how to use Microsoft Global IME for pre-Windows 2000 systems.
* Setting Up Your Computer to Type Chinese, website cheng-tsui.com
=== Tools ===
*Microsoft Voice Recognition
*Typing Chinese Online with Optional Tone Input
*Online Cantonese Input
*Type in Chinese online (IME) Online IME using the pinyin system.
*InputKing Online Input System, an online IME with multiple input methods, supporting both simplified and traditional characters.
*G6 Chinese Input Method (preinstalled on some Android phones e.g. by HTC)
*NJStar Software Corp. (南极星 Nanjixing): Chinese, Japanese, and Korean language software solutions for use with Microsoft Windows operating systems. Solutions include keyboard & hand-written input tools, English translation tools, desktop publishing, and educational tools.
* CJKV Input Method Editors for MS Word VBA macros for input Asian characters and for text conversion.
* HanziLookupJS Free, open-source Chinese handwriting recognition in Javascript.
Category:Articles containing video clips
Category:Han character input
Category:Chinese-language computing | Chinese input methods for computers | [
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In large part thanks to international aid programs, Moroni has international telecommunications service. Telephone service, however, is largely limited to the islands' few towns.
==Overview==
Telephones – main lines in use:
5,000 (1995)
Telephones – mobile cellular:
0 (1995)
Telephone system:
sparse system of microwave radio relay and HF radiotelephone communication stations
domestic:
HF radiotelephone communications and microwave radio relay
CMDA mobile network (Huri, operated by Comores Telecom)
international:
HF radiotelephone communications to Madagascar and Réunion
Radio broadcast stations:
AM 1, FM 2, shortwave 1 (1998)
Radios:
90,000 (1997)
Television broadcast stations:
0 (1998)
Televisions:
1,000 (1997)
Internet Service Providers (ISPs): 1 (1999)
Country code (Top-level domain): KM
==Special projects==
In October 2011 the State of Qatar launched a special program for the construction of a wireless network to interconnect the three islands of the archipelago, by means of low cost, repeatable technology. The project has been developed by Qatar University and Politecnico di Torino, under the supervision of prof. Mazen Hasna and prof. Daniele Trinchero, with a major participation of local actors (Comorian Government, NRTIC, University of the Comoros). The project has been referred as an example of technology transfer and Sustainable Inclusion in developing countries
==External links==
*GSM World page on the Comoros
*PanAfriL10n page on the Comoros
==References== | Telecommunications in the Comoros | [
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Chemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials into useful products. Chemical engineering uses principles of chemistry, physics, mathematics, biology, and economics to efficiently use, produce, design, transport and transform energy and materials. The work of chemical engineers can range from the utilization of nanotechnology and nanomaterials in the laboratory to large-scale industrial processes that convert chemicals, raw materials, living cells, microorganisms, and energy into useful forms and products. Chemical engineers are involved in many aspects of plant design and operation, including safety and hazard assessments, process design and analysis, modeling, control engineering, chemical reaction engineering, nuclear engineering, biological engineering, construction specification, and operating instructions.
Chemical engineers typically hold a degree in Chemical Engineering or Process Engineering. Practicing engineers may have professional certification and be accredited members of a professional body. Such bodies include the Institution of Chemical Engineers (IChemE) or the American Institute of Chemical Engineers (AIChE). In India the body is called as Indian Institute of Chemical Engineers (IIChE) which also conducts collaborative events with AIChE and ICheE.
A degree in chemical | Chemical engineering | [
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engineering is directly linked with all of the other engineering disciplines, to various extents.
==Etymology==
A 1996 article cites James F. Donnelly for mentioning an 1839 reference to chemical engineering in relation to the production of sulfuric acid. In the same paper, however, George E. Davis, an English consultant, was credited with having coined the term. Davis also tried to found a Society of Chemical Engineering, but instead, it was named the Society of Chemical Industry (1881), with Davis as its first secretary. The History of Science in United States: An Encyclopedia puts the use of the term around 1890. "Chemical engineering", describing the use of mechanical equipment in the chemical industry, became common vocabulary in England after 1850. By 1910, the profession, "chemical engineer," was already in common use in Britain and the United States.
==History==
===New concepts and innovations===
In 1940s, it became clear that unit operations alone were insufficient in developing chemical reactors. While the predominance of unit operations in chemical engineering courses in Britain and the United States continued until the 1960s, transport phenomena started to experience greater focus. Along with other novel concepts, such as process systems engineering (PSE), a "second paradigm" was defined. Transport phenomena gave an analytical approach | Chemical engineering | [
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to chemical engineering while PSE focused on its synthetic elements, such as control system and process design. Developments in chemical engineering before and after World War II were mainly incited by the petrochemical industry; however, advances in other fields were made as well. Advancements in biochemical engineering in the 1940s, for example, found application in the pharmaceutical industry, and allowed for the mass production of various antibiotics, including penicillin and streptomycin. Meanwhile, progress in polymer science in the 1950s paved way for the "age of plastics".
===Safety and hazard developments===
Concerns regarding the safety and environmental impact of large-scale chemical manufacturing facilities were also raised during this period. Silent Spring, published in 1962, alerted its readers to the harmful effects of DDT, a potent insecticide. The 1974 Flixborough disaster in the United Kingdom resulted in 28 deaths, as well as damage to a chemical plant and three nearby villages. The 1984 Bhopal disaster in India resulted in almost 4,000 deaths. These incidents, along with other incidents, affected the reputation of the trade as industrial safety and environmental protection were given more focus. In response, the IChemE required safety to be part of every degree course that it accredited after 1982. By the 1970s, | Chemical engineering | [
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legislation and monitoring agencies were instituted in various countries, such as France, Germany, and the United States.
===Recent progress===
Advancements in computer science found applications designing and managing plants, simplifying calculations and drawings that previously had to be done manually. The completion of the Human Genome Project is also seen as a major development, not only advancing chemical engineering but genetic engineering and genomics as well. Chemical engineering principles were used to produce DNA sequences in large quantities.
==Concepts==
Chemical engineering involves the application of several principles. Key concepts are presented below.
===Plant design and construction===
Chemical engineering design concerns the creation of plans, specifications, and economic analyses for pilot plants, new plants, or plant modifications. Design engineers often work in a consulting role, designing plants to meet clients' needs. Design is limited by several factors, including funding, government regulations, and safety standards. These constraints dictate a plant's choice of process, materials, and equipment.
Plant construction is coordinated by project engineers and project managers,Herbst, Andrew; Hans Verwijs (Oct. 19-22). | Chemical engineering | [
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"Project Engineering: Interdisciplinary Coordination and Overall Engineering Quality Control". Proc. of the Annual IAC conference of the American Society for Engineering Management 1 (): 15–21 depending on the size of the investment. A chemical engineer may do the job of project engineer full-time or part of the time, which requires additional training and job skills or act as a consultant to the project group. In the USA the education of chemical engineering graduates from the Baccalaureate programs accredited by ABET do not usually stress project engineering education, which can be obtained by specialized training, as electives, or from graduate programs. Project engineering jobs are some of the largest employers for chemical engineers.
===Process design and analysis===
A unit operation is a physical step in an individual chemical engineering process. Unit operations (such as crystallization, filtration, drying and evaporation) are used to prepare reactants, purifying and separating its products, recycling unspent reactants, and controlling energy transfer in reactors. On the other hand, a unit process is the chemical equivalent of a unit operation. Along with unit operations, unit processes constitute a process operation. Unit processes (such as nitration, hydrogenation, hydrocracking and oxidation) | Chemical engineering | [
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involve the conversion of materials by biochemical, thermochemical and other means. Chemical engineers responsible for these are called process engineers.
Process design requires the definition of equipment types and sizes as well as how they are connected and the materials of construction. Details are often printed on a Process Flow Diagram which is used to control the capacity and reliability of a new or existing chemical factory.
Education for chemical engineers in the first college degree 3 or 4 years of study stresses the principles and practices of process design. The same skills are used in existing chemical plants to evaluate the efficiency and make recommendations for improvements.
===Transport phenomena===
Modeling and analysis of transport phenomena is essential for many industrial applications. Transport phenomena involve fluid dynamics, heat transfer and mass transfer, which are governed mainly by momentum transfer, energy transfer and transport of chemical species, respectively. Models often involve separate considerations for macroscopic, microscopic and molecular level phenomena. Modeling of transport phenomena, therefore, requires an understanding of applied mathematics.
==Applications and practice==
Chemical engineers "develop economic ways of using materials and energy". Chemical engineers use chemistry and engineering to turn raw materials into usable products, such as medicine, petrochemicals, and plastics on a large-scale, industrial | Chemical engineering | [
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setting. They are also involved in waste management and research. Both applied and research facets could make extensive use of computers.
Chemical engineers may be involved in industry or university research where they are tasked with designing and performing experiments to create better and safer methods for production, pollution control, and resource conservation. They may be involved in designing and constructing plants as a project engineer. Chemical engineers serving as project engineers use their knowledge in selecting optimal production methods and plant equipment to minimize costs and maximize safety and profitability. After plant construction, chemical engineering project managers may be involved in equipment upgrades, troubleshooting, and daily operations in either full-time or consulting roles.
== See also ==
=== Related topics ===
* Education for Chemical Engineers
* English Engineering units
* List of chemical engineering societies
* List of chemical engineers
* List of chemical process simulators
* Outline of chemical engineering
=== Related fields and concepts ===
*Biochemical engineering
*Bioinformatics
*Biological engineering
*Biomedical engineering
*Biomolecular engineering
*Bioprocess engineering
*Biotechnology
*Biotechnology engineering
*Catalysts
*Ceramics
*Chemical process modeling
*Chemical reactor
*Chemical technologist
*Chemical weapons
*Cheminformatics
*Computational fluid dynamics
*Corrosion engineering
*Cost estimation
*Earthquake engineering
*Electrochemistry
* Electrochemical engineering
*Environmental engineering
*Fischer Tropsch synthesis
*Fluid dynamics
*Food engineering
*Fuel cell
*Gasification
*Heat transfer
*Industrial catalysts
*Industrial chemistry
*Industrial gas
*Mass transfer
*Materials science
*Metallurgy
*Microfluidics
*Mineral processing
*Molecular engineering
*Nanotechnology
*Natural environment
*Natural gas processing
*Nuclear reprocessing
*Oil exploration
*Oil refinery
*Paper engineering
*Petroleum engineering
*Pharmaceutical engineering
*Plastics engineering
*Polymers
*Process control
*Process design
*Process development
*Process engineering
*Process miniaturization
*Safety engineering
*Semiconductor device fabrication
*Separation | Chemical engineering | [
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] |
processes (see also: separation of mixture)
**Crystallization processes
**Distillation processes
**Membrane processes
*Syngas production
*Textile engineering
*Thermodynamics
*Transport phenomena
*Unit operations
*Water technology
=== Associations ===
*American Institute of Chemical Engineers
*Chemical Institute of Canada
*European Federation of Chemical Engineering
*Indian Institute of Chemical Engineers
*Institution of Chemical Engineers
*National Organization for the Professional Advancement of Black Chemists and Chemical Engineers
==References==
==Bibliography==
*.
*.
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*.
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Category:Process engineering
Category:Engineering disciplines | Chemical engineering | [
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Colossus was a set of computers developed by British codebreakers in the years 1943–1945 to help in the cryptanalysis of the Lorenz cipher. Colossus used thermionic valves (vacuum tubes) to perform Boolean and counting operations. Colossus is thus regarded as the world's first programmable, electronic, digital computer, although it was programmed by switches and plugs and not by a stored program.
Colossus was designed by General Post Office (GPO) research telephone engineer Tommy Flowers to solve a problem posed by mathematician Max Newman at the Government Code and Cypher School (GC&CS) at Bletchley Park. Alan Turing's use of probability in cryptanalysis (see Banburismus) contributed to its design. It has sometimes been erroneously stated that Turing designed Colossus to aid the cryptanalysis of the Enigma. (Turing's machine that helped decode Enigma was the electromechanical Bombe, not Colossus.)
The prototype, Colossus Mark 1, was shown to be working in December 1943 and was in use at Bletchley Park by early 1944. An improved Colossus Mark 2 that used shift registers to quintuple the processing speed, first worked on 1 June 1944, just in time for the Normandy landings on D-Day. Ten Colossi were in use by the end of the war and an eleventh | Colossus computer | [
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