1000003900010@unknown@formal@none@1@S@⌊δInformationδ⌋@@@@1@1@@oe@26-8-2013 1000003900020@unknown@formal@none@1@S@⌊∗Information∗⌋ as a ⌊>concept>⌋ has a diversity of meanings, from everyday usage to technical settings.@@@@1@15@@oe@26-8-2013 1000003900030@unknown@formal@none@1@S@Generally speaking, the concept of information is closely related to notions of ⌊>constraint>⌋, ⌊>communication>⌋, ⌊>control>⌋, ⌊>data>⌋, ⌊>form>⌋, ⌊>instruction>⌋, ⌊>knowledge>⌋, ⌊>meaning>⌋, ⌊>mental stimulus>⌋, ⌊>pattern>⌋, ⌊>perception>⌋, and ⌊>representation>⌋.@@@@1@26@@oe@26-8-2013 1000003900040@unknown@formal@none@1@S@Many people speak about the ⌊>Information Age>⌋ as the advent of the Knowledge Age or ⌊>knowledge society>⌋, the ⌊>information society>⌋, the ⌊>Information revolution>⌋, and ⌊>information technologies>⌋, and even though ⌊>informatics>⌋, ⌊>information science>⌋ and ⌊>computer science>⌋ are often in the spotlight, the word "information" is often used without careful consideration of the various meanings it has acquired.@@@@1@56@@oe@26-8-2013 1000003900050@unknown@formal@none@1@S@⌊=Etymology¦2=⌋@@@@1@1@@oe@26-8-2013 1000003900060@unknown@formal@none@1@S@According to the ⌊>Oxford English Dictionary>⌋, the earliest historical meaning of the word ⌊/information/⌋ in ⌊>English>⌋ was the act of ⌊/informing/⌋, or giving form or shape to the mind, as in education, instruction, or training.@@@@1@35@@oe@26-8-2013 1000003900070@unknown@formal@none@1@S@A quote from 1387: "Five books come down from heaven for information of mankind."@@@@1@14@@oe@26-8-2013 1000003900080@unknown@formal@none@1@S@It was also used for an ⌊/item/⌋ of training, ⌊/e.g./⌋ a particular instruction.@@@@1@13@@oe@26-8-2013 1000003900090@unknown@formal@none@1@S@"Melibee had heard the great skills and reasons of Dame Prudence, and her wise information and techniques."@@@@1@17@@oe@26-8-2013 1000003900100@unknown@formal@none@1@S@(1386)@@@@1@1@@oe@26-8-2013 1000003900110@unknown@formal@none@1@S@The English word was apparently derived by adding the common "noun of action" ending "⌊/-ation/⌋" (descended through Francais from Latin "⌊/-tio/⌋") to the earlier verb ⌊/to inform/⌋, in the sense of to give form to the mind, to discipline, instruct, teach: "Men so wise should go and inform their kings."@@@@1@50@@oe@26-8-2013 1000003900120@unknown@formal@none@1@S@(1330) ⌊/Inform/⌋ itself comes (via French) from the Latin verb ⌊/informare/⌋, to give form to, to form an idea of.@@@@1@20@@oe@26-8-2013 1000003900130@unknown@formal@none@1@S@Furthermore, Latin itself already even contained the word ⌊/informatio/⌋ meaning concept or idea, but the extent to which this may have influenced the development of the word ⌊/information/⌋ in English is unclear.@@@@1@32@@oe@26-8-2013 1000003900140@unknown@formal@none@1@S@As a final note, the ancient Greek word for ⌊/form/⌋ was [eidos], and this word was famously used in a technical philosophical sense by [Plato] (and later Aristotle) to denote the ideal identity or essence of something (see [Theory of forms]).@@@@1@41@@oe@26-8-2013 1000003900150@unknown@formal@none@1@S@"Eidos" can also be associated with [thought], [proposition] or even [concept].@@@@1@11@@oe@26-8-2013 1000003900160@unknown@formal@none@1@S@⌊=Information as a message¦2=⌋@@@@1@4@@oe@26-8-2013 1000003900170@unknown@formal@none@1@S@⌊∗Information∗⌋ is the state of a system of interest.@@@@1@9@@oe@26-8-2013 1000003900180@unknown@formal@none@1@S@Message is the information materialized.@@@@1@5@@oe@26-8-2013 1000003900190@unknown@formal@none@1@S@Information is a quality of a ⌊>message>⌋ from a ⌊>sender>⌋ to one or more receivers.@@@@1@15@@oe@26-8-2013 1000003900200@unknown@formal@none@1@S@Information is always ⌊/about/⌋ something (size of a parameter, occurrence of an event, etc).@@@@1@14@@oe@26-8-2013 1000003900210@unknown@formal@none@1@S@Viewed in this manner, information does not have to be accurate.@@@@1@11@@oe@26-8-2013 1000003900220@unknown@formal@none@1@S@It may be a truth or a lie, or just the sound of a falling tree.@@@@1@16@@oe@26-8-2013 1000003900230@unknown@formal@none@1@S@Even a disruptive noise used to inhibit the flow of communication and create misunderstanding would in this view be a form of information.@@@@1@23@@oe@26-8-2013 1000003900240@unknown@formal@none@1@S@However, generally speaking, if the ⌊/amount/⌋ of information in the received message increases, the message is more accurate.@@@@1@18@@oe@26-8-2013 1000003900250@unknown@formal@none@1@S@This model assumes there is a definite ⌊>sender>⌋ and at least one receiver.@@@@1@13@@oe@26-8-2013 1000003900260@unknown@formal@none@1@S@Many refinements of the model assume the existence of a common language understood by the sender and at least one of the receivers.@@@@1@23@@oe@26-8-2013 1000003900270@unknown@formal@none@1@S@An important variation identifies information as that which would be communicated by a message if it were sent from a sender to a receiver capable of understanding the message.@@@@1@29@@oe@26-8-2013 1000003900280@unknown@formal@none@1@S@Notably, it is not required that the sender be capable of understanding the message, or even cognizant that there is a message.@@@@1@22@@oe@26-8-2013 1000003900290@unknown@formal@none@1@S@Thus, information is something that can be extracted from an environment, e.g., through observation, reading or measurement.@@@@1@17@@oe@26-8-2013 1000003900300@unknown@formal@none@1@S@Information is a term with many meanings depending on context, but is as a rule closely related to such concepts as meaning, knowledge, instruction, communication, representation, and mental stimulus.@@@@1@29@@oe@26-8-2013 1000003900310@unknown@formal@none@1@S@Simply stated, information is a message received and understood.@@@@1@9@@oe@26-8-2013 1000003900320@unknown@formal@none@1@S@In terms of data, it can be defined as a collection of facts from which conclusions may be drawn.@@@@1@19@@oe@26-8-2013 1000003900330@unknown@formal@none@1@S@There are many other aspects of information since it is the knowledge acquired through study or experience or instruction.@@@@1@19@@oe@26-8-2013 1000003900340@unknown@formal@none@1@S@But overall, information is the result of processing, manipulating and organizing data in a way that adds to the knowledge of the person receiving it.@@@@1@25@@oe@26-8-2013 1000003900350@unknown@formal@none@1@S@⌊>Communication theory>⌋ provides a numerical measure of the uncertainty of an outcome.@@@@1@12@@oe@26-8-2013 1000003900360@unknown@formal@none@1@S@For example, we can say that "the signal contained thousands of bits of information".@@@@1@14@@oe@26-8-2013 1000003900370@unknown@formal@none@1@S@Communication theory tends to use the concept of ⌊>information entropy>⌋, generally attributed to ⌊>C.E. Shannon>⌋ (see below).@@@@1@17@@oe@26-8-2013 1000003900380@unknown@formal@none@1@S@Another form of information is ⌊>Fisher information>⌋, a concept of ⌊>R.A. Fisher>⌋.@@@@1@12@@oe@26-8-2013 1000003900390@unknown@formal@none@1@S@This is used in application of statistics to ⌊>estimation theory>⌋ and to science in general.@@@@1@15@@oe@26-8-2013 1000003900400@unknown@formal@none@1@S@Fisher information is thought of as the amount of information that a message carries about an unobservable parameter.@@@@1@18@@oe@26-8-2013 1000003900410@unknown@formal@none@1@S@It can be computed from knowledge of the ⌊>likelihood function>⌋ defining the system.@@@@1@13@@oe@26-8-2013 1000003900420@unknown@formal@none@1@S@For example, with a normal likelihood function, the Fisher information is the reciprocal of the variance of the law.@@@@1@19@@oe@26-8-2013 1000003900430@unknown@formal@none@1@S@In the absence of knowledge of the likelihood law, the Fisher information may be computed from normally distributed score data as the reciprocal of their second moment.@@@@1@27@@oe@26-8-2013 1000003900440@unknown@formal@none@1@S@Even though information and data are often used interchangeably, they are actually very different.@@@@1@14@@oe@26-8-2013 1000003900450@unknown@formal@none@1@S@Data is a set of unrelated information, and as such is of no use until it is properly evaluated.@@@@1@19@@oe@26-8-2013 1000003900460@unknown@formal@none@1@S@Upon evaluation, once there is some significant relation between data, and they show some relevance, then they are converted into information.@@@@1@21@@oe@26-8-2013 1000003900470@unknown@formal@none@1@S@Now this same data can be used for different purposes.@@@@1@10@@oe@26-8-2013 1000003900480@unknown@formal@none@1@S@Thus, till the data convey some information, they are not useful.@@@@1@11@@oe@26-8-2013 1000003900490@unknown@formal@none@1@S@⌊=Measuring information entropy¦3=⌋@@@@1@3@@oe@26-8-2013 1000003900500@unknown@formal@none@1@S@The view of information as a message came into prominence with the publication in 1948 of an influential paper by ⌊>Claude Shannon>⌋, "⌊>A Mathematical Theory of Communication>⌋."@@@@1@27@@oe@26-8-2013 1000003900510@unknown@formal@none@1@S@This paper provides the foundations of ⌊>information theory>⌋ and endows the word ⌊/information/⌋ not only with a technical meaning but also a measure.@@@@1@23@@oe@26-8-2013 1000003900520@unknown@formal@none@1@S@If the sending device is equally likely to send any one of a set of ⌊×N×⌋ messages, then the preferred measure of "the information produced when one message is chosen from the set" is the base two ⌊>logarithm>⌋ of ⌊×N×⌋ (This measure is called ⌊/⌊>self-information>⌋/⌋).@@@@1@45@@oe@26-8-2013 1000003900530@unknown@formal@none@1@S@In this paper, Shannon continues:@@@@1@5@@oe@26-8-2013 1000003900540@unknown@formal@none@1@S@⌊"The ⌊>choice>⌋ of a logarithmic base corresponds to the choice of a ⌊>unit for measuring information>⌋.@@@@1@16@@oe@26-8-2013 1000003900550@unknown@formal@none@1@S@If the base 2 is used the resulting units may be called binary digits, or more briefly ⌊>bit>⌋s, a word suggested by ⌊>J. W. Tukey>⌋. A device with two stable positions, such as a relay or a flip-flop circuit, can store one bit of information.@@@@1@45@@oe@26-8-2013 1000003900560@unknown@formal@none@1@S@N such devices can store N bits…"⌋@@@@1@7@@oe@26-8-2013 1000003900570@unknown@formal@none@1@S@A complementary way of measuring information is provided by ⌊>algorithmic information theory>⌋.@@@@1@12@@oe@26-8-2013 1000003900580@unknown@formal@none@1@S@In brief, this measures the information content of a list of symbols based on how predictable they are, or more specifically how easy it is to compute the list through a ⌊>program>⌋: the information content of a sequence is the number of bits of the shortest program that computes it.@@@@1@50@@oe@26-8-2013 1000003900590@unknown@formal@none@1@S@The sequence below would have a very low algorithmic information measurement since it is a very predictable pattern, and as the pattern continues the measurement would not change.@@@@1@28@@oe@26-8-2013 1000003900600@unknown@formal@none@1@S@Shannon information would give the same information measurement for each symbol, since they are ⌊>statistically random>⌋, and each new symbol would increase the measurement.@@@@1@24@@oe@26-8-2013 1000003900610@unknown@formal@none@1@S@⌊⇥123456789101112131415161718192021⇥⌋@@@@1@1@@oe@26-8-2013 1000003900620@unknown@formal@none@1@S@It is important to recognize the limitations of traditional information theory and algorithmic information theory from the perspective of human meaning.@@@@1@21@@oe@26-8-2013 1000003900630@unknown@formal@none@1@S@For example, when referring to the meaning content of a message Shannon noted “Frequently the messages have ⌊/meaning…/⌋ these semantic aspects of communication are irrelevant to the engineering problem.@@@@1@29@@oe@26-8-2013 1000003900640@unknown@formal@none@1@S@The significant aspect is that the actual message is one selected ⌊/from a set of possible messages/⌋” (emphasis in original).@@@@1@20@@oe@26-8-2013 1000003900650@unknown@formal@none@1@S@In information theory signals are part of a process, not a substance; they do something, they do not contain any specific meaning.@@@@1@22@@oe@26-8-2013 1000003900660@unknown@formal@none@1@S@Combining algorithmic information theory and information theory we can conclude that the most random signal contains the most information as it can be interpreted in any way and cannot be compressed.@@@@1@31@@oe@26-8-2013 1000003900670@unknown@formal@none@1@S@Michael Reddy noted that "'signals' of the ⌊>mathematical theory>⌋ are 'patterns that can be exchanged'.@@@@1@15@@oe@26-8-2013 1000003900680@unknown@formal@none@1@S@There is no message contained in the signal, the signals convey the ability to select from a set of possible messages."@@@@1@21@@oe@26-8-2013 1000003900690@unknown@formal@none@1@S@In information theory "the system must be designed to operate for each possible selection, not just the one which will actually be chosen since this is unknown at the time of design".@@@@1@32@@oe@26-8-2013 1000003900700@unknown@formal@none@1@S@⌊=Information as a pattern¦2=⌋@@@@1@4@@oe@26-8-2013 1000003900710@unknown@formal@none@1@S@Information is any represented ⌊>pattern>⌋.@@@@1@5@@oe@26-8-2013 1000003900720@unknown@formal@none@1@S@This view assumes neither accuracy nor directly communicating parties, but instead assumes a separation between an object and its representation.@@@@1@20@@oe@26-8-2013 1000003900730@unknown@formal@none@1@S@Consider the following example: ⌊>economic statistics>⌋ represent an ⌊>economy>⌋, however inaccurately.@@@@1@11@@oe@26-8-2013 1000003900740@unknown@formal@none@1@S@What are commonly referred to as data in ⌊>computing>⌋, ⌊>statistics>⌋, and other fields, are forms of information in this sense.@@@@1@20@@oe@26-8-2013 1000003900750@unknown@formal@none@1@S@The ⌊>electro-magnetic>⌋ patterns in a ⌊>computer network>⌋ and connected ⌊>device>⌋s are related to something other than the pattern itself, such as ⌊>text characters>⌋ to be displayed and ⌊>keyboard>⌋ input.@@@@1@29@@oe@26-8-2013 1000003900760@unknown@formal@none@1@S@⌊>Signal>⌋s, ⌊>sign>⌋s, and ⌊>symbol>⌋s are also in this category.@@@@1@9@@oe@26-8-2013 1000003900770@unknown@formal@none@1@S@On the other hand, according to ⌊>semiotics>⌋, data is symbols with certain syntax and information is data with a certain semantic.@@@@1@21@@oe@26-8-2013 1000003900780@unknown@formal@none@1@S@⌊>Painting>⌋ and ⌊>drawing>⌋ contain information to the extent that they represent something such as an assortment of objects on a table, a ⌊>profile>⌋, or a ⌊>landscape>⌋.@@@@1@26@@oe@26-8-2013 1000003900790@unknown@formal@none@1@S@In other words, when a pattern of something is transposed to a pattern of something else, the latter is information.@@@@1@20@@oe@26-8-2013 1000003900800@unknown@formal@none@1@S@This would be the case whether or not there was anyone to perceive it.@@@@1@14@@oe@26-8-2013 1000003900810@unknown@formal@none@1@S@But if information can be defined merely as a pattern, does that mean that neither ⌊>utility>⌋ nor meaning are necessary components of information?@@@@1@23@@oe@26-8-2013 1000003900820@unknown@formal@none@1@S@Arguably a distinction must be made between raw unprocessed data and information which possesses utility, ⌊>value>⌋ or some quantum of meaning.@@@@1@21@@oe@26-8-2013 1000003900830@unknown@formal@none@1@S@On this view, information may indeed be characterized as a pattern; but this is a ⌊>necessary>⌋ condition, not a ⌊>sufficient>⌋ one.@@@@1@21@@oe@26-8-2013 1000003900840@unknown@formal@none@1@S@An individual entry in a telephone book, which follows a specific pattern formed by name, address and telephone number, does not become "informative" in some sense unless and until it possesses some degree of utility, value or meaning.@@@@1@38@@oe@26-8-2013 1000003900850@unknown@formal@none@1@S@For example, someone might look up a girlfriend's number, might order a take away etc.@@@@1@15@@oe@26-8-2013 1000003900860@unknown@formal@none@1@S@The vast majority of numbers will never be construed as "information" in any meaningful sense.@@@@1@15@@oe@26-8-2013 1000003900870@unknown@formal@none@1@S@The gap between data and information is only closed by a behavioral bridge whereby some value, utility or meaning is added to transform mere data or pattern into information.@@@@1@29@@oe@26-8-2013 1000003900880@unknown@formal@none@1@S@When one constructs a representation of an object, one can selectively extract from the object (⌊>sampling>⌋) or use a ⌊>system>⌋ of signs to replace (⌊>encoding>⌋), or both.@@@@1@27@@oe@26-8-2013 1000003900890@unknown@formal@none@1@S@The sampling and encoding result in representation.@@@@1@7@@oe@26-8-2013 1000003900900@unknown@formal@none@1@S@An example of the former is a "sample" of a product; an example of the latter is "verbal description" of a product.@@@@1@22@@oe@26-8-2013 1000003900910@unknown@formal@none@1@S@Both contain information of the product, however inaccurate.@@@@1@8@@oe@26-8-2013 1000003900920@unknown@formal@none@1@S@When one interprets representation, one can predict a broader pattern from a limited number of observations (inference) or understand the relation between patterns of two different things (⌊>decoding>⌋).@@@@1@28@@oe@26-8-2013 1000003900930@unknown@formal@none@1@S@One example of the former is to sip a ⌊>soup>⌋ to know if it is spoiled; an example of the latter is examining footprints to determine the animal and its condition.@@@@1@31@@oe@26-8-2013 1000003900940@unknown@formal@none@1@S@In both cases, information sources are not constructed or presented by some "sender" of information.@@@@1@15@@oe@26-8-2013 1000003900950@unknown@formal@none@1@S@Regardless, information is dependent upon, but usually unrelated to and separate from, the medium or media used to express it.@@@@1@20@@oe@26-8-2013 1000003900960@unknown@formal@none@1@S@In other words, the position of a theoretical series of bits, or even the output once interpreted by a ⌊>computer>⌋ or similar device, is unimportant, except when someone or something is present to interpret the information.@@@@1@36@@oe@26-8-2013 1000003900970@unknown@formal@none@1@S@Therefore, a quantity of information is totally distinct from its medium.@@@@1@11@@oe@26-8-2013 1000003900980@unknown@formal@none@1@S@⌊=Information as sensory input¦2=⌋@@@@1@4@@oe@26-8-2013 1000003900990@unknown@formal@none@1@S@Often information is viewed as a type of ⌊>input>⌋ to an ⌊>organism>⌋ or designed device.@@@@1@15@@oe@26-8-2013 1000003901000@unknown@formal@none@1@S@Inputs are of two kinds.@@@@1@5@@oe@26-8-2013 1000003901010@unknown@formal@none@1@S@Some inputs are important to the function of the organism (for example, food) or device (⌊>energy>⌋) by themselves.@@@@1@18@@oe@26-8-2013 1000003901020@unknown@formal@none@1@S@In his book ⌊/Sensory Ecology,/⌋ Dusenbery called these causal inputs.@@@@1@10@@oe@26-8-2013 1000003901030@unknown@formal@none@1@S@Other inputs (information) are important only because they are associated with causal inputs and can be used to predict the occurrence of a causal input at a later time (and perhaps another place).@@@@1@33@@oe@26-8-2013 1000003901040@unknown@formal@none@1@S@Some information is important because of association with other information but eventually there must be a connection to a causal input.@@@@1@21@@oe@26-8-2013 1000003901050@unknown@formal@none@1@S@In practice, information is usually carried by weak stimuli that must be detected by specialized sensory systems and amplified by energy inputs before they can be functional to the organism or device.@@@@1@32@@oe@26-8-2013 1000003901060@unknown@formal@none@1@S@For example, light is often a causal input to plants but provides information to animals.@@@@1@15@@oe@26-8-2013 1000003901070@unknown@formal@none@1@S@The colored light reflected from a flower is too weak to do much photosynthetic work but the visual system of the bee detects it and the bee's nervous system uses the information to guide the bee to the flower, where the bee often finds nectar or pollen, which are causal inputs, serving a nutritional function.@@@@1@55@@oe@26-8-2013 1000003901080@unknown@formal@none@1@S@Information is any type of sensory input.@@@@1@7@@oe@26-8-2013 1000003901090@unknown@formal@none@1@S@When an organism with a ⌊>nervous system>⌋ receives an input, it transforms the input into an electrical signal.@@@@1@18@@oe@26-8-2013 1000003901100@unknown@formal@none@1@S@This is regarded information by some.@@@@1@6@@oe@26-8-2013 1000003901110@unknown@formal@none@1@S@The idea of representation is still relevant, but in a slightly different manner.@@@@1@13@@oe@26-8-2013 1000003901120@unknown@formal@none@1@S@That is, while ⌊>abstract painting>⌋ does not represent anything concretely, when the viewer sees the painting, it is nevertheless transformed into electrical signals that create a representation of the painting.@@@@1@30@@oe@26-8-2013 1000003901130@unknown@formal@none@1@S@Defined this way, information does not have to be related to truth, communication, or representation of an object.@@@@1@18@@oe@26-8-2013 1000003901140@unknown@formal@none@1@S@⌊>Entertainment>⌋ in general is not intended to be informative.@@@@1@9@@oe@26-8-2013 1000003901150@unknown@formal@none@1@S@⌊>Music>⌋, the ⌊>performing arts>⌋, ⌊>amusement park>⌋s, works of ⌊>fiction>⌋ and so on are thus forms of information in this sense, but they are not necessarily forms of information according to some definitions given above.@@@@1@34@@oe@26-8-2013 1000003901160@unknown@formal@none@1@S@Consider another example: food supplies both nutrition and taste for those who eat it.@@@@1@14@@oe@26-8-2013 1000003901170@unknown@formal@none@1@S@If information is equated to sensory input, then nutrition is not information but taste is.@@@@1@15@@oe@26-8-2013 1000003901180@unknown@formal@none@1@S@⌊=Information as an influence which leads to a transformation¦2=⌋@@@@1@9@@oe@26-8-2013 1000003901190@unknown@formal@none@1@S@Information is any type of pattern that influences the formation or transformation of other patterns.@@@@1@15@@oe@26-8-2013 1000003901200@unknown@formal@none@1@S@In this sense, there is no need for a conscious mind to perceive, much less appreciate, the pattern.@@@@1@18@@oe@26-8-2013 1000003901210@unknown@formal@none@1@S@Consider, for example, ⌊>DNA>⌋.@@@@1@4@@oe@26-8-2013 1000003901220@unknown@formal@none@1@S@The sequence of ⌊>nucleotide>⌋s is a pattern that influences the formation and development of an organism without any need for a conscious mind.@@@@1@23@@oe@26-8-2013 1000003901230@unknown@formal@none@1@S@⌊>Systems theory>⌋ at times seems to refer to information in this sense, assuming information does not necessarily involve any conscious mind, and patterns circulating (due to ⌊>feedback>⌋) in the system can be called information.@@@@1@34@@oe@26-8-2013 1000003901240@unknown@formal@none@1@S@In other words, it can be said that information in this sense is something potentially perceived as representation, though not created or presented for that purpose.@@@@1@26@@oe@26-8-2013 1000003901250@unknown@formal@none@1@S@When ⌊>Marshall McLuhan>⌋ speaks of ⌊>media>⌋ and their effects on human cultures, he refers to the structure of ⌊>artifacts>⌋ that in turn shape our behaviors and mindsets.@@@@1@27@@oe@26-8-2013 1000003901260@unknown@formal@none@1@S@Also, ⌊>pheromone>⌋s are often said to be "information" in this sense.@@@@1@11@@oe@26-8-2013 1000003901270@unknown@formal@none@1@S@(See also ⌊>Gregory Bateson>⌋.)@@@@1@4@@oe@26-8-2013 1000003901280@unknown@formal@none@1@S@⌊=Information as a property in physics¦2=⌋@@@@1@6@@oe@26-8-2013 1000003901290@unknown@formal@none@1@S@In 2003, J. D. Bekenstein claimed there is a growing trend in ⌊>physics>⌋ to define the physical world as being made of information itself (and thus information is defined in this way).@@@@1@32@@oe@26-8-2013 1000003901300@unknown@formal@none@1@S@Information has a well defined meaning in physics.@@@@1@8@@oe@26-8-2013 1000003901310@unknown@formal@none@1@S@Examples of this include the phenomenon of ⌊>quantum entanglement>⌋ where particles can interact without reference to their separation or the speed of light.@@@@1@23@@oe@26-8-2013 1000003901320@unknown@formal@none@1@S@Information itself cannot travel faster than light even if the information is transmitted indirectly.@@@@1@14@@oe@26-8-2013 1000003901330@unknown@formal@none@1@S@This could lead to the fact that all attempts at physically observing a particle with an "entangled" relationship to another are slowed down, even though the particles are not connected in any other way other than by the information they carry.@@@@1@41@@oe@26-8-2013 1000003901340@unknown@formal@none@1@S@Another link is demonstrated by the ⌊>Maxwell's demon>⌋ thought experiment.@@@@1@10@@oe@26-8-2013 1000003901350@unknown@formal@none@1@S@In this experiment, a direct relationship between information and another physical property, ⌊>entropy>⌋, is demonstrated.@@@@1@15@@oe@26-8-2013 1000003901360@unknown@formal@none@1@S@A consequence is that it is impossible to destroy information without increasing the entropy of a system; in practical terms this often means generating heat.@@@@1@25@@oe@26-8-2013 1000003901370@unknown@formal@none@1@S@Another, more philosophical, outcome is that information could be thought of as interchangeable with ⌊>energy>⌋.@@@@1@15@@oe@26-8-2013 1000003901380@unknown@formal@none@1@S@Thus, in the study of ⌊>logic gates>⌋, the theoretical lower bound of thermal energy released by an ⌊/AND gate/⌋ is higher than for the ⌊/NOT gate/⌋ (because information is destroyed in an ⌊/AND gate/⌋ and simply converted in a ⌊/NOT gate/⌋).@@@@1@41@@oe@26-8-2013 1000003901390@unknown@formal@none@1@S@Physical information is of particular importance in the theory of ⌊>quantum computers>⌋.@@@@1@12@@oe@26-8-2013 1000003901400@unknown@formal@none@1@S@⌊=Information as records¦2=⌋@@@@1@3@@oe@26-8-2013 1000003901410@unknown@formal@none@1@S@Records are a specialized form of information.@@@@1@7@@oe@26-8-2013 1000003901420@unknown@formal@none@1@S@Essentially, records are information produced consciously or as by-products of business activities or transactions and retained because of their value.@@@@1@20@@oe@26-8-2013 1000003901430@unknown@formal@none@1@S@Primarily their value is as evidence of the activities of the organization but they may also be retained for their informational value.@@@@1@22@@oe@26-8-2013 1000003901440@unknown@formal@none@1@S@Sound ⌊>records management>⌋ ensures that the integrity of records is preserved for as long as they are required.@@@@1@18@@oe@26-8-2013 1000003901450@unknown@formal@none@1@S@The international standard on records management, ISO 15489, defines records as "information created, received, and maintained as evidence and information by an organization or person, in pursuance of legal obligations or in the transaction of business".@@@@1@36@@oe@26-8-2013 1000003901460@unknown@formal@none@1@S@The International Committee on Archives (ICA) Committee on electronic records defined a record as, "a specific piece of recorded information generated, collected or received in the initiation, conduct or completion of an activity and that comprises sufficient content, context and structure to provide proof or evidence of that activity".@@@@1@49@@oe@26-8-2013 1000003901470@unknown@formal@none@1@S@Records may be retained because of their business value, as part of the ⌊>corporate memory>⌋ of the organization or to meet legal, fiscal or accountability requirements imposed on the organization.@@@@1@30@@oe@26-8-2013 1000003901480@unknown@formal@none@1@S@Willis (2005) expressed the view that sound management of business records and information delivered "…six key requirements for good ⌊>corporate governance>⌋…transparency; accountability; due process; compliance; meeting statutory and common law requirements; and security of personal and corporate information."@@@@1@38@@oe@26-8-2013 1000003901490@unknown@formal@none@1@S@⌊=Information and semiotics¦2=⌋@@@@1@3@@oe@26-8-2013 1000003901500@unknown@formal@none@1@S@Beynon-Davies explains the multi-faceted concept of information in terms of that of signs and sign-systems.@@@@1@15@@oe@26-8-2013 1000003901510@unknown@formal@none@1@S@Signs themselves can be considered in terms of four inter-dependent levels, layers or branches of ⌊>semiotics>⌋: pragmatics, semantics, syntactics and empirics.@@@@1@21@@oe@26-8-2013 1000003901520@unknown@formal@none@1@S@These four layers serve to connect the social world on the one hand with the physical or technical world on the other.@@@@1@22@@oe@26-8-2013 1000003901530@unknown@formal@none@1@S@⌊>Pragmatics>⌋ is concerned with the purpose of communication.@@@@1@8@@oe@26-8-2013 1000003901540@unknown@formal@none@1@S@Pragmatics links the issue of signs with that of intention.@@@@1@10@@oe@26-8-2013 1000003901550@unknown@formal@none@1@S@The focus of pragmatics is on the intentions of human agents underlying communicative behaviour.@@@@1@14@@oe@26-8-2013 1000003901560@unknown@formal@none@1@S@In other words, intentions link language to action.@@@@1@8@@oe@26-8-2013 1000003901570@unknown@formal@none@1@S@⌊>Semantics>⌋ is concerned with the meaning of a message conveyed in a communicative act.@@@@1@14@@oe@26-8-2013 1000003901580@unknown@formal@none@1@S@Semantics considers the content of communication.@@@@1@6@@oe@26-8-2013 1000003901590@unknown@formal@none@1@S@Semantics is the study of the meaning of signs - the association between signs and behaviour.@@@@1@16@@oe@26-8-2013 1000003901600@unknown@formal@none@1@S@Semantics can be considered as the study of the link between symbols and their referents or concepts; particularly the way in which signs relate to human behaviour.@@@@1@27@@oe@26-8-2013 1000003901610@unknown@formal@none@1@S@Syntactics is concerned with the formalism used to represent a message.@@@@1@11@@oe@26-8-2013 1000003901620@unknown@formal@none@1@S@Syntactics as an area studies the form of communication in terms of the logic and grammar of sign systems.@@@@1@19@@oe@26-8-2013 1000003901630@unknown@formal@none@1@S@Syntactics is devoted to the study of the form rather than the content of signs and sign-systems.@@@@1@17@@oe@26-8-2013 1000003901640@unknown@formal@none@1@S@Empirics is the study of the signals used to carry a message; the physical characteristics of the medium of communication.@@@@1@20@@oe@26-8-2013 1000003901650@unknown@formal@none@1@S@Empirics is devoted to the study of communication channels and their characteristics, e.g., sound, light, electronic transmission etc.@@@@1@18@@oe@26-8-2013 1000003901660@unknown@formal@none@1@S@Communication normally exists within the context of some social situation.@@@@1@10@@oe@26-8-2013 1000003901670@unknown@formal@none@1@S@The social situation sets the context for the intentions conveyed (pragmatics) and the form in which communication takes place.@@@@1@19@@oe@26-8-2013 1000003901680@unknown@formal@none@1@S@In a communicative situation intentions are expressed through messages which comprise collections of inter-related signs taken from a language which is mutually understood by the agents involved in the communication.@@@@1@30@@oe@26-8-2013 1000003901690@unknown@formal@none@1@S@Mutual understanding implies that agents involved understand the chosen language in terms of its agreed syntax (syntactics) and semantics.@@@@1@19@@oe@26-8-2013 1000003901700@unknown@formal@none@1@S@The sender codes the message in the language and sends the message as signals along some communication channel (empirics).@@@@1@19@@oe@26-8-2013 1000003901710@unknown@formal@none@1@S@The chosen communication channel will have inherent properties which determine outcomes such as the speed with which communication can take place and over what distance.@@@@1@25@@oe@26-8-2013 1000004000010@unknown@formal@none@1@S@⌊δInformation extractionδ⌋@@@@1@2@@oe@26-8-2013 1000004000020@unknown@formal@none@1@S@In ⌊>natural language processing>⌋, ⌊∗information extraction∗⌋ (IE) is a type of ⌊>information retrieval>⌋ whose goal is to automatically extract structured information, i.e. categorized and contextually and semantically well-defined data from a certain domain, from unstructured ⌊>machine-readable>⌋ documents.@@@@1@37@@oe@26-8-2013 1000004000030@unknown@formal@none@1@S@An example of information extraction is the extraction of instances of corporate mergers, more formally ⌊×MergerBetween(company_1, company_2, date)×⌋, from an online news sentence such as: "Yesterday, New-York based Foo Inc. announced their acquisition of Bar Corp."@@@@1@36@@oe@26-8-2013 1000004000040@unknown@formal@none@1@S@A broad goal of IE is to allow computation to be done on the previously unstructured data.@@@@1@17@@oe@26-8-2013 1000004000050@unknown@formal@none@1@S@A more specific goal is to allow logical reasoning to draw inferences based on the logical content of the input data.@@@@1@21@@oe@26-8-2013 1000004000060@unknown@formal@none@1@S@The significance of IE is determined by the growing amount of information available in unstructured (i.e. without ⌊>metadata>⌋) form, for instance on the Internet.@@@@1@24@@oe@26-8-2013 1000004000070@unknown@formal@none@1@S@This knowledge can be made more accessible by means of transformation into ⌊>relational form>⌋, or by marking-up with ⌊>XML>⌋ tags.@@@@1@20@@oe@26-8-2013 1000004000080@unknown@formal@none@1@S@An intelligent agent monitoring a news data feed requires IE to transform unstructured data into something that can be reasoned with.@@@@1@21@@oe@26-8-2013 1000004000090@unknown@formal@none@1@S@A typical application of IE is to scan a set of documents written in a ⌊>natural language>⌋ and populate a database with the information extracted.@@@@1@25@@oe@26-8-2013 1000004000100@unknown@formal@none@1@S@Current approaches to IE use ⌊>natural language processing>⌋ techniques that focus on very restricted domains.@@@@1@15@@oe@26-8-2013 1000004000110@unknown@formal@none@1@S@For example, the ⌊/⌊>Message Understanding Conference>⌋/⌋ (MUC) is a competition-based conference that focused on the following domains in the past:@@@@1@20@@oe@26-8-2013 1000004000120@unknown@formal@none@1@S@⌊•⌊#MUC-1 (1987), MUC-2 (1989): Naval operations messages.#⌋@@@@1@7@@oe@26-8-2013 1000004000130@unknown@formal@none@1@S@⌊#MUC-3 (1991), MUC-4 (1992): Terrorism in Latin American countries.#⌋@@@@1@9@@oe@26-8-2013 1000004000140@unknown@formal@none@1@S@⌊#MUC-5 (1993): Joint ventures and microelectronics domain.#⌋@@@@1@7@@oe@26-8-2013 1000004000150@unknown@formal@none@1@S@⌊#MUC-6 (1995): News articles on management changes.#⌋@@@@1@7@@oe@26-8-2013 1000004000160@unknown@formal@none@1@S@⌊#MUC-7 (1998): Satellite launch reports.#⌋•⌋@@@@1@5@@oe@26-8-2013 1000004000170@unknown@formal@none@1@S@Natural Language texts may need to use some form of a ⌊>Text simplification>⌋ to create a more easily machine readable text to extract the sentences.@@@@1@25@@oe@26-8-2013 1000004000180@unknown@formal@none@1@S@Typical subtasks of IE are:@@@@1@5@@oe@26-8-2013 1000004000190@unknown@formal@none@1@S@⌊•⌊#⌊>Named Entity Recognition>⌋: recognition of entity names (for people and organizations), place names, temporal expressions, and certain types of numerical expressions.#⌋@@@@1@21@@oe@26-8-2013 1000004000200@unknown@formal@none@1@S@⌊#⌊>Coreference>⌋: identification chains of ⌊>noun phrase>⌋s that refer to the same object.@@@@1@12@@oe@26-8-2013 1000004000210@unknown@formal@none@1@S@For example, ⌊>anaphora>⌋ is a type of coreference.#⌋@@@@1@8@@oe@26-8-2013 1000004000220@unknown@formal@none@1@S@⌊#⌊>Terminology extraction>⌋: finding the relevant terms for a given ⌊>corpus>⌋#⌋@@@@1@10@@oe@26-8-2013 1000004000230@unknown@formal@none@1@S@⌊#Relation Extraction: identification of relations between entities, such as:@@@@1@9@@oe@26-8-2013 1000004000240@unknown@formal@none@1@S@⌊•⌊#PERSON works for ORGANIZATION (extracted from the sentence "Bill works for IBM.")#⌋@@@@1@12@@oe@26-8-2013 1000004000250@unknown@formal@none@1@S@⌊#PERSON located in LOCATION (extracted from the sentence "Bill is in France.")#⌋•⌋#⌋•⌋@@@@1@12@@oe@26-8-2013 1000004100010@unknown@formal@none@1@S@⌊δInformation retrievalδ⌋@@@@1@2@@oe@26-8-2013 1000004100020@unknown@formal@none@1@S@⌊∗Information retrieval∗⌋ (⌊∗IR∗⌋) is the science of searching for documents, for ⌊>information>⌋ within documents and for ⌊>metadata>⌋ about documents, as well as that of searching ⌊>relational database>⌋s and the ⌊>World Wide Web>⌋.@@@@1@32@@oe@26-8-2013 1000004100030@unknown@formal@none@1@S@There is overlap in the usage of the terms data retrieval, ⌊>document retrieval>⌋, information retrieval, and ⌊>text retrieval>⌋, but each also has its own body of literature, theory, ⌊>praxis>⌋ and technologies.@@@@1@31@@oe@26-8-2013 1000004100040@unknown@formal@none@1@S@IR is ⌊>interdisciplinary>⌋, based on ⌊>computer science>⌋, ⌊>mathematics>⌋, ⌊>library science>⌋, ⌊>information science>⌋, ⌊>information architecture>⌋, ⌊>cognitive psychology>⌋, ⌊>linguistics>⌋, ⌊>statistics>⌋ and ⌊>physics>⌋.@@@@1@20@@oe@26-8-2013 1000004100050@unknown@formal@none@1@S@Automated information retrieval systems are used to reduce what has been called "⌊>information overload>⌋".@@@@1@14@@oe@26-8-2013 1000004100060@unknown@formal@none@1@S@Many universities and ⌊>public libraries>⌋ use IR systems to provide access to books, journals and other documents.@@@@1@17@@oe@26-8-2013 1000004100070@unknown@formal@none@1@S@Web ⌊>search engine>⌋s are the most visible ⌊>IR applications>⌋.@@@@1@9@@oe@26-8-2013 1000004100080@unknown@formal@none@1@S@⌊=History¦2=⌋@@@@1@1@@oe@26-8-2013 1000004100090@unknown@formal@none@1@S@The idea of using computers to search for relevant pieces of information was popularized in an article ⌊/⌊>As We May Think>⌋/⌋ by ⌊>Vannevar Bush>⌋ in 1945.@@@@1@26@@oe@26-8-2013 1000004100100@unknown@formal@none@1@S@First implementations of information retrieval systems were introduced in the 1950s and 1960s.@@@@1@13@@oe@26-8-2013 1000004100110@unknown@formal@none@1@S@By 1990 several different techniques had been shown to perform well on small text corpora (several thousand documents).@@@@1@18@@oe@26-8-2013 1000004100120@unknown@formal@none@1@S@In 1992 the US Department of Defense, along with the ⌊>National Institute of Standards and Technology>⌋ (NIST), cosponsored the ⌊>Text Retrieval Conference>⌋ (TREC) as part of the TIPSTER text program.@@@@1@30@@oe@26-8-2013 1000004100130@unknown@formal@none@1@S@The aim of this was to look into the information retrieval community by supplying the infrastructure that was needed for evaluation of text retrieval methodologies on a very large text collection.@@@@1@31@@oe@26-8-2013 1000004100140@unknown@formal@none@1@S@This catalyzed research on methods that ⌊>scale>⌋ to huge corpora.@@@@1@10@@oe@26-8-2013 1000004100150@unknown@formal@none@1@S@The introduction of web ⌊>search engine>⌋s has boosted the need for very large scale retrieval systems even further.@@@@1@18@@oe@26-8-2013 1000004100160@unknown@formal@none@1@S@The use of digital methods for storing and retrieving information has led to the phenomenon of ⌊>digital obsolescence>⌋, where a digital resource ceases to be readable because the physical media, the reader required to read the media, the hardware, or the software that runs on it, is no longer available.@@@@1@50@@oe@26-8-2013 1000004100170@unknown@formal@none@1@S@The information is initially easier to retrieve than if it were on paper, but is then effectively lost.@@@@1@18@@oe@26-8-2013 1000004100180@unknown@formal@none@1@S@⌊=Timeline¦3=⌋@@@@1@1@@oe@26-8-2013 1000004100190@unknown@formal@none@1@S@⌊•⌊#1890: Hollerith tabulating machines were used to analyze the US census.@@@@1@11@@oe@26-8-2013 1000004100200@unknown@formal@none@1@S@(⌊>Herman Hollerith>⌋).#⌋@@@@1@2@@oe@26-8-2013 1000004100210@unknown@formal@none@1@S@⌊#1945: ⌊>Vannevar Bush>⌋'s ⌊/⌊>As We May Think>⌋/⌋ appeared in ⌊/⌊>Atlantic Monthly>⌋/⌋#⌋@@@@1@11@@oe@26-8-2013 1000004100220@unknown@formal@none@1@S@⌊#Late 1940s: The US military confronted problems of indexing and retrieval of wartime scientific research documents captured from Germans.#⌋@@@@1@19@@oe@26-8-2013 1000004100230@unknown@formal@none@1@S@⌊#1947: ⌊>Hans Peter Luhn>⌋ (research engineer at IBM since 1941) began work on a mechanized, punch card based system for searching chemical compounds.#⌋@@@@1@23@@oe@26-8-2013 1000004100240@unknown@formal@none@1@S@⌊#1950: The term "information retrieval" may have been coined by ⌊>Calvin Mooers>⌋.#⌋@@@@1@12@@oe@26-8-2013 1000004100250@unknown@formal@none@1@S@⌊#1950s: Growing concern in the US for a "science gap" with the USSR motivated, encouraged funding, and provided a backdrop for mechanized literature searching systems (⌊>Allen Kent>⌋ et al) and the invention of citation indexing (⌊>Eugene Garfield>⌋).#⌋@@@@1@37@@oe@26-8-2013 1000004100260@unknown@formal@none@1@S@⌊#1955: Allen Kent joined ⌊>Case Western Reserve University>⌋, and eventually becomes associate director of the Center for Documentation and Communications Research.@@@@1@21@@oe@26-8-2013 1000004100270@unknown@formal@none@1@S@That same year, Kent and colleagues publish a paper in American Documentation describing the precision and recall measures, as well as detailing a proposed "framework" for evaluating an IR system, which includes statistical sampling methods for determining the number of relevant documents not retrieved.#⌋@@@@1@44@@oe@26-8-2013 1000004100280@unknown@formal@none@1@S@⌊#1958: International Conference on Scientific Information Washington DC included consideration of IR systems as a solution to problems identified.@@@@1@19@@oe@26-8-2013 1000004100290@unknown@formal@none@1@S@See: Proceedings of the International Conference on Scientific Information, 1958 (National Academy of Sciences, Washington, DC, 1959)#⌋@@@@1@17@@oe@26-8-2013 1000004100300@unknown@formal@none@1@S@⌊#1959: Hans Peter Luhn published "Auto-encoding of documents for information retrieval."#⌋@@@@1@11@@oe@26-8-2013 1000004100310@unknown@formal@none@1@S@⌊#1960: Melvin Earl (Bill) Maron and J. L. Kuhns published "On relevance, probabilistic indexing, and information retrieval" in Journal of the ACM 7(3):216-244, July 1960.#⌋@@@@1@25@@oe@26-8-2013 1000004100320@unknown@formal@none@1@S@⌊#Early 1960s: ⌊>Gerard Salton>⌋ began work on IR at Harvard, later moved to Cornell.#⌋@@@@1@14@@oe@26-8-2013 1000004100330@unknown@formal@none@1@S@⌊#1962: ⌊>Cyril W. Cleverdon>⌋ published early findings of the Cranfield studies, developing a model for IR system evaluation.@@@@1@18@@oe@26-8-2013 1000004100340@unknown@formal@none@1@S@See: Cyril W. Cleverdon, "Report on the Testing and Analysis of an Investigation into the Comparative Efficiency of Indexing Systems".@@@@1@20@@oe@26-8-2013 1000004100350@unknown@formal@none@1@S@Cranfield Coll. of Aeronautics, Cranfield, England, 1962.#⌋@@@@1@7@@oe@26-8-2013 1000004100360@unknown@formal@none@1@S@⌊#1962: Kent published Information Analysis and Retrieval#⌋@@@@1@7@@oe@26-8-2013 1000004100370@unknown@formal@none@1@S@⌊#1963: Weinberg report "Science, Government and Information" gave a full articulation of the idea of a "crisis of scientific information."@@@@1@20@@oe@26-8-2013 1000004100380@unknown@formal@none@1@S@The report was named after Dr. ⌊>Alvin Weinberg>⌋.#⌋@@@@1@8@@oe@26-8-2013 1000004100390@unknown@formal@none@1@S@⌊#1963: ⌊>Joseph Becker>⌋ and ⌊>Robert M. Hayes>⌋ published text on information retrieval.@@@@1@12@@oe@26-8-2013 1000004100400@unknown@formal@none@1@S@Becker, Joseph; Hayes, Robert Mayo.@@@@1@5@@oe@26-8-2013 1000004100410@unknown@formal@none@1@S@Information storage and retrieval: tools, elements, theories.@@@@1@7@@oe@26-8-2013 1000004100420@unknown@formal@none@1@S@New York, Wiley (1963).#⌋@@@@1@4@@oe@26-8-2013 1000004100430@unknown@formal@none@1@S@⌊#1964: ⌊>Karen Spärck Jones>⌋ finished her thesis at Cambridge, ⌊/Synonymy and Semantic Classification/⌋, and continued work on ⌊>computational linguistics>⌋ as it applies to IR#⌋@@@@1@24@@oe@26-8-2013 1000004100440@unknown@formal@none@1@S@⌊#1964: The ⌊>National Bureau of Standards>⌋ sponsored a symposium titled "Statistical Association Methods for Mechanized Documentation."@@@@1@16@@oe@26-8-2013 1000004100450@unknown@formal@none@1@S@Several highly significant papers, including G. Salton's first published reference (we believe) to the SMART system.#⌋@@@@1@16@@oe@26-8-2013 1000004100460@unknown@formal@none@1@S@⌊#Mid-1960s: National Library of Medicine developed ⌊>MEDLARS>⌋ Medical Literature Analysis and Retrieval System, the first major machine-readable database and batch retrieval system#⌋@@@@1@22@@oe@26-8-2013 1000004100470@unknown@formal@none@1@S@⌊#Mid-1960s: Project Intrex at MIT#⌋@@@@1@5@@oe@26-8-2013 1000004100480@unknown@formal@none@1@S@⌊#1965: ⌊>J. C. R. Licklider>⌋ published ⌊/Libraries of the Future/⌋#⌋@@@@1@10@@oe@26-8-2013 1000004100490@unknown@formal@none@1@S@⌊#1966: ⌊>Don Swanson>⌋ was involved in studies at University of Chicago on Requirements for Future Catalogs#⌋@@@@1@16@@oe@26-8-2013 1000004100500@unknown@formal@none@1@S@⌊#1968: Gerard Salton published ⌊/Automatic Information Organization and Retrieval/⌋.#⌋@@@@1@9@@oe@26-8-2013 1000004100510@unknown@formal@none@1@S@⌊#1968: ⌊>J. W. Sammon>⌋'s RADC Tech report "Some Mathematics of Information Storage and Retrieval..." outlined the vector model.#⌋@@@@1@18@@oe@26-8-2013 1000004100520@unknown@formal@none@1@S@⌊#1969: Sammon's "A nonlinear mapping for data structure analysis" (IEEE Transactions on Computers) was the first proposal for visualization interface to an IR system.#⌋@@@@1@24@@oe@26-8-2013 1000004100530@unknown@formal@none@1@S@⌊#Late 1960s: ⌊>F. W. Lancaster>⌋ completed evaluation studies of the MEDLARS system and published the first edition of his text on information retrieval#⌋@@@@1@23@@oe@26-8-2013 1000004100540@unknown@formal@none@1@S@⌊#Early 1970s: first online systems--NLM's AIM-TWX, MEDLINE; Lockheed's Dialog; SDC's ORBIT#⌋@@@@1@11@@oe@26-8-2013 1000004100550@unknown@formal@none@1@S@⌊#Early 1970s: ⌊>Theodor Nelson>⌋ promoting concept of ⌊>hypertext>⌋, published Computer Lib/Dream Machines#⌋@@@@1@12@@oe@26-8-2013 1000004100560@unknown@formal@none@1@S@⌊#1971: ⌊>N. Jardine>⌋ and ⌊>C. J. Van Rijsbergen>⌋ published "The use of hierarchic clustering in information retrieval", which articulated the "cluster hypothesis."@@@@1@22@@oe@26-8-2013 1000004100570@unknown@formal@none@1@S@(Information Storage and Retrieval, 7(5), pp. 217-240, Dec 1971)#⌋@@@@1@9@@oe@26-8-2013 1000004100580@unknown@formal@none@1@S@⌊#1975: Three highly influential publications by Salton fully articulated his vector processing framework and term discrimination model:@@@@1@17@@oe@26-8-2013 1000004100590@unknown@formal@none@1@S@⌊•⌊#A Theory of Indexing (Society for Industrial and Applied Mathematics)#⌋@@@@1@10@@oe@26-8-2013 1000004100600@unknown@formal@none@1@S@⌊#"A theory of term importance in automatic text analysis", (JASIS v. 26)#⌋@@@@1@12@@oe@26-8-2013 1000004100610@unknown@formal@none@1@S@⌊#"A vector space model for automatic indexing", (CACM 18:11)#⌋•⌋#⌋@@@@1@9@@oe@26-8-2013 1000004100620@unknown@formal@none@1@S@⌊#1978: The First ⌊>ACM>⌋ ⌊>SIGIR>⌋ conference.#⌋@@@@1@6@@oe@26-8-2013 1000004100630@unknown@formal@none@1@S@⌊#1979: C. J. Van Rijsbergen published ⌊/Information Retrieval/⌋ (Butterworths).@@@@1@9@@oe@26-8-2013 1000004100640@unknown@formal@none@1@S@Heavy emphasis on probabilistic models.#⌋@@@@1@5@@oe@26-8-2013 1000004100650@unknown@formal@none@1@S@⌊#1980: First international ACM SIGIR conference, joint with British Computer Society IR group in Cambridge#⌋@@@@1@15@@oe@26-8-2013 1000004100660@unknown@formal@none@1@S@⌊#1982: ⌊>Belkin>⌋, Oddy, and Brooks proposed the ASK (Anomalous State of Knowledge) viewpoint for information retrieval.@@@@1@16@@oe@26-8-2013 1000004100670@unknown@formal@none@1@S@This was an important concept, though their automated analysis tool proved ultimately disappointing.#⌋@@@@1@13@@oe@26-8-2013 1000004100680@unknown@formal@none@1@S@⌊#1983: Salton (and M. McGill) published Introduction to Modern Information Retrieval (McGraw-Hill), with heavy emphasis on vector models.#⌋@@@@1@18@@oe@26-8-2013 1000004100690@unknown@formal@none@1@S@⌊#Mid-1980s: Efforts to develop end user versions of commercial IR systems.#⌋@@@@1@11@@oe@26-8-2013 1000004100700@unknown@formal@none@1@S@⌊#1985-1993: Key papers on and experimental systems for visualization interfaces.#⌋@@@@1@10@@oe@26-8-2013 1000004100710@unknown@formal@none@1@S@⌊#Work by ⌊>D. B. Crouch>⌋, ⌊>Robert R. Korfhage>⌋, ⌊>M. Chalmers>⌋, ⌊>A. Spoerri>⌋ and others.#⌋@@@@1@14@@oe@26-8-2013 1000004100720@unknown@formal@none@1@S@⌊#1989: First ⌊>World Wide Web>⌋ proposals by ⌊>Tim Berners-Lee>⌋ at ⌊>CERN>⌋.#⌋@@@@1@11@@oe@26-8-2013 1000004100730@unknown@formal@none@1@S@⌊#1992: First TREC conference.#⌋@@@@1@4@@oe@26-8-2013 1000004100740@unknown@formal@none@1@S@⌊#1997: Publication of ⌊>Korfhage>⌋'s ⌊/Information Storage and Retrieval/⌋ with emphasis on visualization and multi-reference point systems.#⌋@@@@1@16@@oe@26-8-2013 1000004100750@unknown@formal@none@1@S@⌊#Late 1990s: Web ⌊>search engine>⌋ implementation of many features formerly found only in experimental IR systems#⌋•⌋@@@@1@16@@oe@26-8-2013 1000004100760@unknown@formal@none@1@S@⌊=Overview¦2=⌋@@@@1@1@@oe@26-8-2013 1000004100770@unknown@formal@none@1@S@An information retrieval process begins when a user enters a query into the system.@@@@1@14@@oe@26-8-2013 1000004100780@unknown@formal@none@1@S@Queries are formal statements of ⌊>information need>⌋s, for example search strings in web search engines.@@@@1@15@@oe@26-8-2013 1000004100790@unknown@formal@none@1@S@In information retrieval a query does not uniquely identify a single object in the collection.@@@@1@15@@oe@26-8-2013 1000004100800@unknown@formal@none@1@S@Instead, several objects may match the query, perhaps with different degrees of ⌊>relevancy>⌋.@@@@1@13@@oe@26-8-2013 1000004100810@unknown@formal@none@1@S@An object is an entity which keeps or stores information in a database.@@@@1@13@@oe@26-8-2013 1000004100820@unknown@formal@none@1@S@User queries are matched to objects stored in the database.@@@@1@10@@oe@26-8-2013 1000004100830@unknown@formal@none@1@S@Depending on the ⌊>application>⌋ the data objects may be, for example, text documents, images or videos.@@@@1@16@@oe@26-8-2013 1000004100840@unknown@formal@none@1@S@Often the documents themselves are not kept or stored directly in the IR system, but are instead represented in the system by document surrogates.@@@@1@24@@oe@26-8-2013 1000004100850@unknown@formal@none@1@S@Most IR systems compute a numeric score on how well each object in the database match the query, and rank the objects according to this value.@@@@1@26@@oe@26-8-2013 1000004100860@unknown@formal@none@1@S@The top ranking objects are then shown to the user.@@@@1@10@@oe@26-8-2013 1000004100870@unknown@formal@none@1@S@The process may then be iterated if the user wishes to refine the query.@@@@1@14@@oe@26-8-2013 1000004100880@unknown@formal@none@1@S@⌊=Performance measures¦2=⌋@@@@1@2@@oe@26-8-2013 1000004100890@unknown@formal@none@1@S@Many different measures for evaluating the performance of information retrieval systems have been proposed.@@@@1@14@@oe@26-8-2013 1000004100900@unknown@formal@none@1@S@The measures require a collection of documents and a query.@@@@1@10@@oe@26-8-2013 1000004100910@unknown@formal@none@1@S@All common measures described here assume a ground truth notion of relevancy: every document is known to be either relevant or non-relevant to a particular query.@@@@1@26@@oe@26-8-2013 1000004100920@unknown@formal@none@1@S@In practice queries may be ⌊>ill-posed>⌋ and there may be different shades of relevancy.@@@@1@14@@oe@26-8-2013 1000004100930@unknown@formal@none@1@S@⌊=Precision¦3=⌋@@@@1@1@@oe@26-8-2013 1000004100940@unknown@formal@none@1@S@Precision is the fraction of the documents retrieved that are ⌊>relevant>⌋ to the user's information need.@@@@1@16@@oe@26-8-2013 1000004100950@unknown@formal@none@1@S@⌊⇥⌊×\\mbox{precision}=\\frac{|\\{\\mbox{relevant documents}\\}\\cap\\{\\mbox{retrieved documents}\\}|}{|\\{\\mbox{retrieved documents}\\}|}×⌋⇥⌋@@@@1@4@@oe@26-8-2013 1000004100960@unknown@formal@none@1@S@In ⌊>binary classification>⌋, precision is analogous to ⌊>positive predictive value>⌋.@@@@1@10@@oe@26-8-2013 1000004100970@unknown@formal@none@1@S@Precision takes all retrieved documents into account.@@@@1@7@@oe@26-8-2013 1000004100980@unknown@formal@none@1@S@It can also be evaluated at a given cut-off rank, considering only the topmost results returned by the system.@@@@1@19@@oe@26-8-2013 1000004100990@unknown@formal@none@1@S@This measure is called ⌊/precision at n/⌋ or ⌊/P\sn/⌋.@@@@1@9@@oe@26-8-2013 1000004101000@unknown@formal@none@1@S@Note that the meaning and usage of "precision" in the field of Information Retrieval differs from the definition of ⌊>accuracy and precision>⌋ within other branches of science and technology.@@@@1@29@@oe@26-8-2013 1000004101010@unknown@formal@none@1@S@⌊=Recall¦3=⌋@@@@1@1@@oe@26-8-2013 1000004101020@unknown@formal@none@1@S@Recall is the fraction of the documents that are relevant to the query that are successfully retrieved.@@@@1@17@@oe@26-8-2013 1000004101030@unknown@formal@none@1@S@⌊⇥⌊×\\mbox{recall}=\\frac{|\\{\\mbox{relevant documents}\\}\\cap\\{\\mbox{retrieved documents}\\}|}{|\\{\\mbox{relevant documents}\\}|}×⌋⇥⌋@@@@1@4@@oe@26-8-2013 1000004101040@unknown@formal@none@1@S@In binary classification, recall is called ⌊>sensitivity>⌋.@@@@1@7@@oe@26-8-2013 1000004101050@unknown@formal@none@1@S@So it can be looked at as ⌊/the probability that a relevant document is retrieved by the query/⌋.@@@@1@18@@oe@26-8-2013 1000004101060@unknown@formal@none@1@S@It is trivial to achieve recall of 100% by returning all documents in response to any query.@@@@1@17@@oe@26-8-2013 1000004101070@unknown@formal@none@1@S@Therefore recall alone is not enough but one needs to measure the number of non-relevant documents also, for example by computing the precision.@@@@1@23@@oe@26-8-2013 1000004101080@unknown@formal@none@1@S@⌊=Fall-Out¦3=⌋@@@@1@1@@oe@26-8-2013 1000004101090@unknown@formal@none@1@S@The proportion of non-relevant documents that are retrieved, out of all non-relevant documents available:@@@@1@14@@oe@26-8-2013 1000004101100@unknown@formal@none@1@S@⌊⇥⌊×\\mbox{fall-out}=\\frac{|\\{\\mbox{non-relevant documents}\\}\\cap\\{\\mbox{retrieved documents}\\}|}{|\\{\\mbox{non-relevant documents}\\}|}×⌋⇥⌋@@@@1@4@@oe@26-8-2013 1000004101110@unknown@formal@none@1@S@In binary classification, fall-out is closely related to ⌊>specificity>⌋.@@@@1@9@@oe@26-8-2013 1000004101120@unknown@formal@none@1@S@More precisely: ⌊×\\mbox{fall-out}=1-\\mbox{specificity}×⌋.@@@@1@3@@oe@26-8-2013 1000004101130@unknown@formal@none@1@S@It can be looked at as ⌊/the probability that a non-relevant document is retrieved by the query/⌋.@@@@1@17@@oe@26-8-2013 1000004101140@unknown@formal@none@1@S@It is trivial to achieve fall-out of 0% by returning zero documents in response to any query.@@@@1@17@@oe@26-8-2013 1000004101150@unknown@formal@none@1@S@⌊=F-measure¦3=⌋@@@@1@1@@oe@26-8-2013 1000004101160@unknown@formal@none@1@S@The weighted ⌊>harmonic mean>⌋ of precision and recall, the traditional F-measure or balanced F-score is:@@@@1@15@@oe@26-8-2013 1000004101170@unknown@formal@none@1@S@⌊⇥⌊×F = 2 \\cdot (\\mathrm{precision} \\cdot \\mathrm{recall}) / (\\mathrm{precision} + \\mathrm{recall}).\\,×⌋⇥⌋@@@@1@11@@oe@26-8-2013 1000004101180@unknown@formal@none@1@S@This is also known as the ⌊×F_1×⌋ measure, because recall and precision are evenly weighted.@@@@1@15@@oe@26-8-2013 1000004101190@unknown@formal@none@1@S@The general formula for non-negative real ß is:@@@@1@8@@oe@26-8-2013 1000004101200@unknown@formal@none@1@S@⌊⇥⌊×F_\\beta = (1 + \\beta^2) \\cdot (\\mathrm{precision} \\cdot \\mathrm{recall}) / (\\beta^2 \\cdot \\mathrm{precision} + \\mathrm{recall}).\\,×⌋⇥⌋@@@@1@15@@oe@26-8-2013 1000004101210@unknown@formal@none@1@S@Two other commonly used F measures are the ⌊×F_{2}×⌋ measure, which weights recall twice as much as precision, and the ⌊×F_{0.5}×⌋ measure, which weights precision twice as much as recall.@@@@1@30@@oe@26-8-2013 1000004101220@unknown@formal@none@1@S@The F-measure was derived by van Rijsbergen (1979) so that ⌊×F_\\beta×⌋ "measures the effectiveness of retrieval with respect to a user who attaches ß times as much importance to recall as precision".@@@@1@32@@oe@26-8-2013 1000004101230@unknown@formal@none@1@S@It is based on van Rijsbergen's effectiveness measure ⌊×E = 1-(1/(\\alpha/P + (1-\\alpha)/R))×⌋.@@@@1@13@@oe@26-8-2013 1000004101240@unknown@formal@none@1@S@Their relationship is ⌊×F_\\beta = 1 - E×⌋ where ⌊×\\alpha=1/(\\beta^2+1)×⌋.@@@@1@10@@oe@26-8-2013 1000004101250@unknown@formal@none@1@S@⌊=Average precision of precision and recall¦3=⌋@@@@1@6@@oe@26-8-2013 1000004101260@unknown@formal@none@1@S@The precision and recall are based on the whole list of documents returned by the system.@@@@1@16@@oe@26-8-2013 1000004101270@unknown@formal@none@1@S@Average precision emphasizes returning more relevant documents earlier.@@@@1@8@@oe@26-8-2013 1000004101280@unknown@formal@none@1@S@It is average of precisions computed after truncating the list after each of the relevant documents in turn:@@@@1@18@@oe@26-8-2013 1000004101290@unknown@formal@none@1@S@⌊⇥⌊×\\operatorname{AveP} = \\frac{\\sum_{r=1}^N (P(r) \\times \\mathrm{rel}(r))}{\\mbox{number of relevant documents}} \\!×⌋⇥⌋@@@@1@10@@oe@26-8-2013 1000004101300@unknown@formal@none@1@S@where ⌊/r/⌋ is the rank, ⌊/N/⌋ the number retrieved, ⌊/rel()/⌋ a binary function on the relevance of a given rank, and ⌊/P()/⌋ precision at a given cut-off rank.@@@@1@28@@oe@26-8-2013 1000004101310@unknown@formal@none@1@S@⌊=Model types¦2=⌋@@@@1@2@@oe@26-8-2013 1000004101320@unknown@formal@none@1@S@For the information retrieval to be efficient, the documents are typically transformed into a suitable representation.@@@@1@16@@oe@26-8-2013 1000004101330@unknown@formal@none@1@S@There are several representations.@@@@1@4@@oe@26-8-2013 1000004101340@unknown@formal@none@1@S@The picture on the right illustrates the relationship of some common models.@@@@1@12@@oe@26-8-2013 1000004101350@unknown@formal@none@1@S@In the picture, the models are categorized according to two dimensions: the mathematical basis and the properties of the model.@@@@1@20@@oe@26-8-2013 1000004101360@unknown@formal@none@1@S@⌊=First dimension: mathematical basis¦3=⌋@@@@1@4@@oe@26-8-2013 1000004101370@unknown@formal@none@1@S@⌊•⌊#⌊/Set-theoretic models/⌋ represent documents as sets of words or phrases.@@@@1@10@@oe@26-8-2013 1000004101380@unknown@formal@none@1@S@Similarities are usually derived from set-theoretic operations on those sets.@@@@1@10@@oe@26-8-2013 1000004101390@unknown@formal@none@1@S@Common models are:@@@@1@3@@oe@26-8-2013 1000004101400@unknown@formal@none@1@S@⌊•⌊#⌊>Standard Boolean model>⌋@@@@1@3@@oe@26-8-2013 1000004101410@unknown@formal@none@1@S@⌊>Extended Boolean model>⌋@@@@1@3@@oe@26-8-2013 1000004101420@unknown@formal@none@1@S@⌊>Fuzzy retrieval>⌋#⌋•⌋#⌋•⌋@@@@1@2@@oe@26-8-2013 1000004101430@unknown@formal@none@1@S@⌊•⌊#⌊/Algebraic models/⌋ represent documents and queries usually as vectors, matrices or tuples.@@@@1@12@@oe@26-8-2013 1000004101440@unknown@formal@none@1@S@The similarity of the query vector and document vector is represented as a scalar value.@@@@1@15@@oe@26-8-2013 1000004101450@unknown@formal@none@1@S@⌊•⌊#⌊>Vector space model>⌋@@@@1@3@@oe@26-8-2013 1000004101460@unknown@formal@none@1@S@⌊>Generalized vector space model>⌋#⌋@@@@1@4@@oe@26-8-2013 1000004101470@unknown@formal@none@1@S@⌊#Topic-based vector space model (literature: , )#⌋@@@@1@7@@oe@26-8-2013 1000004101480@unknown@formal@none@1@S@⌊#⌊>Extended Boolean model>⌋#⌋@@@@1@3@@oe@26-8-2013 1000004101490@unknown@formal@none@1@S@⌊#Enhanced topic-based vector space model (literature: , )#⌋@@@@1@8@@oe@26-8-2013 1000004101500@unknown@formal@none@1@S@⌊#Latent semantic indexing aka ⌊>latent semantic analysis>⌋#⌋•⌋#⌋•⌋@@@@1@7@@oe@26-8-2013 1000004101510@unknown@formal@none@1@S@⌊•⌊#⌊/Probabilistic models/⌋ treat the process of document retrieval as a probabilistic inference.@@@@1@12@@oe@26-8-2013 1000004101520@unknown@formal@none@1@S@Similarities are computed as probabilities that a document is relevant for a given query.@@@@1@14@@oe@26-8-2013 1000004101530@unknown@formal@none@1@S@Probabilistic theorems like the ⌊>Bayes' theorem>⌋ are often used in these models.@@@@1@12@@oe@26-8-2013 1000004101540@unknown@formal@none@1@S@⌊•⌊#⌊>Binary independence retrieval>⌋@@@@1@3@@oe@26-8-2013 1000004101550@unknown@formal@none@1@S@⌊>Probabilistic relevance model (BM25)>⌋#⌋@@@@1@4@@oe@26-8-2013 1000004101560@unknown@formal@none@1@S@⌊#Uncertain inference#⌋@@@@1@2@@oe@26-8-2013 1000004101570@unknown@formal@none@1@S@⌊#⌊>Language model>⌋s#⌋@@@@1@2@@oe@26-8-2013 1000004101580@unknown@formal@none@1@S@⌊#⌊>Divergence-from-randomness model>⌋@@@@1@2@@oe@26-8-2013 1000004101590@unknown@formal@none@1@S@⌊>Latent Dirichlet allocation>⌋#⌋•⌋#⌋•⌋@@@@1@3@@oe@26-8-2013 1000004101600@unknown@formal@none@1@S@⌊=Second dimension: properties of the model¦3=⌋@@@@1@6@@oe@26-8-2013 1000004101610@unknown@formal@none@1@S@⌊•⌊#⌊/Models without term-interdependencies/⌋ treat different terms/words as independent.@@@@1@8@@oe@26-8-2013 1000004101620@unknown@formal@none@1@S@This fact is usually represented in vector space models by the ⌊>orthogonality>⌋ assumption of term vectors or in probabilistic models by an ⌊>independency>⌋ assumption for term variables.#⌋•⌋@@@@1@27@@oe@26-8-2013 1000004101630@unknown@formal@none@1@S@⌊•⌊#⌊/Models with immanent term interdependencies/⌋ allow a representation of interdependencies between terms.@@@@1@12@@oe@26-8-2013 1000004101640@unknown@formal@none@1@S@However the degree of the interdependency between two terms is defined by the model itself.@@@@1@15@@oe@26-8-2013 1000004101650@unknown@formal@none@1@S@It is usually directly or indirectly derived (e.g. by ⌊>dimensional reduction>⌋) from the ⌊>co-occurrence>⌋ of those terms in the whole set of documents.#⌋•⌋@@@@1@23@@oe@26-8-2013 1000004101660@unknown@formal@none@1@S@⌊•⌊#⌊/Models with transcendent term interdependencies/⌋ allow a representation of interdependencies between terms, but they do not allege how the interdependency between two terms is defined.@@@@1@25@@oe@26-8-2013 1000004101670@unknown@formal@none@1@S@They relay an external source for the degree of interdependency between two terms.@@@@1@13@@oe@26-8-2013 1000004101680@unknown@formal@none@1@S@(For example a human or sophisticated algorithms.)#⌋•⌋@@@@1@7@@oe@26-8-2013 1000004101690@unknown@formal@none@1@S@⌊=Awards in the field¦2=⌋@@@@1@4@@oe@26-8-2013 1000004101700@unknown@formal@none@1@S@⌊•⌊#⌊>Tony Kent Strix award>⌋@@@@1@4@@oe@26-8-2013 1000004101710@unknown@formal@none@1@S@⌊>Gerard Salton Award>⌋#⌋•⌋@@@@1@3@@oe@26-8-2013 1000004200010@unknown@formal@none@1@S@⌊δInformation theoryδ⌋@@@@1@2@@oe@26-8-2013 1000004200020@unknown@formal@none@1@S@⌊∗Information theory∗⌋ is a branch of ⌊>applied mathematics>⌋ and ⌊>electrical engineering>⌋ involving the quantification of ⌊>information>⌋.@@@@1@16@@oe@26-8-2013 1000004200030@unknown@formal@none@1@S@Historically, information theory was developed to find fundamental limits on compressing and reliably ⌊>communicating>⌋ data.@@@@1@15@@oe@26-8-2013 1000004200040@unknown@formal@none@1@S@Since its inception it has broadened to find applications in many other areas, including ⌊>statistical inference>⌋, ⌊>natural language processing>⌋, ⌊>cryptography>⌋ generally, ⌊>networks>⌋ other than communication networks -- as in ⌊>neurobiology>⌋, the evolution and function of molecular codes, model selection in ecology, thermal physics, ⌊>quantum computing>⌋, plagiarism detection and other forms of ⌊>data analysis>⌋.@@@@1@53@@oe@26-8-2013 1000004200050@unknown@formal@none@1@S@A key measure of information in the theory is known as ⌊>information entropy>⌋, which is usually expressed by the average number of bits needed for storage or communication.@@@@1@28@@oe@26-8-2013 1000004200060@unknown@formal@none@1@S@Intuitively, entropy quantifies the uncertainty involved when encountering a ⌊>random variable>⌋.@@@@1@11@@oe@26-8-2013 1000004200070@unknown@formal@none@1@S@For example, a fair coin flip (2 equally likely outcomes) will have less entropy than a roll of a die (6 equally likely outcomes).@@@@1@24@@oe@26-8-2013 1000004200080@unknown@formal@none@1@S@Applications of fundamental topics of information theory include ⌊>lossless data compression>⌋ (e.g. ⌊>ZIP files>⌋), ⌊>lossy data compression>⌋ (e.g. ⌊>MP3>⌋s), and ⌊>channel coding>⌋ (e.g. for ⌊>DSL>⌋ lines).@@@@1@26@@oe@26-8-2013 1000004200090@unknown@formal@none@1@S@The field is at the intersection of ⌊>mathematics>⌋, ⌊>statistics>⌋, ⌊>computer science>⌋, ⌊>physics>⌋, ⌊>neurobiology>⌋, and ⌊>electrical engineering>⌋.@@@@1@16@@oe@26-8-2013 1000004200100@unknown@formal@none@1@S@Its impact has been crucial to the success of the ⌊>Voyager>⌋ missions to deep space, the invention of the CD, the feasibility of mobile phones, the development of the ⌊>Internet>⌋, the study of ⌊>linguistics>⌋ and of human perception, the understanding of ⌊>black hole>⌋s, and numerous other fields.@@@@1@47@@oe@26-8-2013 1000004200110@unknown@formal@none@1@S@Important sub-fields of information theory are source coding, channel coding, algorithmic complexity theory, algorithmic information theory, and measures of information.@@@@1@20@@oe@26-8-2013 1000004200120@unknown@formal@none@1@S@⌊=Overview¦2=⌋@@@@1@1@@oe@26-8-2013 1000004200130@unknown@formal@none@1@S@The main concepts of information theory can be grasped by considering the most widespread means of human communication: language.@@@@1@19@@oe@26-8-2013 1000004200140@unknown@formal@none@1@S@Two important aspects of a good language are as follows: First, the most common words (e.g., "a", "the", "I") should be shorter than less common words (e.g., "benefit", "generation", "mediocre"), so that sentences will not be too long.@@@@1@38@@oe@26-8-2013 1000004200150@unknown@formal@none@1@S@Such a tradeoff in word length is analogous to ⌊>data compression>⌋ and is the essential aspect of ⌊>source coding>⌋.@@@@1@19@@oe@26-8-2013 1000004200160@unknown@formal@none@1@S@Second, if part of a sentence is unheard or misheard due to noise -— e.g., a passing car -— the listener should still be able to glean the meaning of the underlying message.@@@@1@33@@oe@26-8-2013 1000004200170@unknown@formal@none@1@S@Such robustness is as essential for an electronic communication system as it is for a language; properly building such robustness into communications is done by ⌊>channel coding>⌋.@@@@1@27@@oe@26-8-2013 1000004200180@unknown@formal@none@1@S@Source coding and channel coding are the fundamental concerns of information theory.@@@@1@12@@oe@26-8-2013 1000004200190@unknown@formal@none@1@S@Note that these concerns have nothing to do with the ⌊/importance/⌋ of messages.@@@@1@13@@oe@26-8-2013 1000004200200@unknown@formal@none@1@S@For example, a platitude such as "Thank you; come again" takes about as long to say or write as the urgent plea, "Call an ambulance!" while clearly the latter is more important and more meaningful.@@@@1@35@@oe@26-8-2013 1000004200210@unknown@formal@none@1@S@Information theory, however, does not consider message importance or meaning, as these are matters of the quality of data rather than the quantity and readability of data, the latter of which is determined solely by probabilities.@@@@1@36@@oe@26-8-2013 1000004200220@unknown@formal@none@1@S@Information theory is generally considered to have been founded in 1948 by ⌊>Claude Shannon>⌋ in his seminal work, "⌊>A Mathematical Theory of Communication>⌋."@@@@1@23@@oe@26-8-2013 1000004200230@unknown@formal@none@1@S@The central paradigm of classical information theory is the engineering problem of the transmission of information over a noisy channel.@@@@1@20@@oe@26-8-2013 1000004200240@unknown@formal@none@1@S@The most fundamental results of this theory are Shannon's ⌊>source coding theorem>⌋, which establishes that, on average, the number of ⌊/bits/⌋ needed to represent the result of an uncertain event is given by its ⌊>entropy>⌋; and Shannon's ⌊>noisy-channel coding theorem>⌋, which states that ⌊/reliable/⌋ communication is possible over ⌊/noisy/⌋ channels provided that the rate of communication is below a certain threshold called the channel capacity.@@@@1@65@@oe@26-8-2013 1000004200250@unknown@formal@none@1@S@The channel capacity can be approached in practice by using appropriate encoding and decoding systems.@@@@1@15@@oe@26-8-2013 1000004200260@unknown@formal@none@1@S@Information theory is closely associated with a collection of pure and applied disciplines that have been investigated and reduced to engineering practice under a variety of rubrics throughout the world over the past half century or more: ⌊>adaptive system>⌋s, ⌊>anticipatory system>⌋s, ⌊>artificial intelligence>⌋, ⌊>complex system>⌋s, ⌊>complexity science>⌋, ⌊>cybernetics>⌋, ⌊>informatics>⌋, ⌊>machine learning>⌋, along with ⌊>systems science>⌋s of many descriptions.@@@@1@58@@oe@26-8-2013 1000004200270@unknown@formal@none@1@S@Information theory is a broad and deep mathematical theory, with equally broad and deep applications, amongst which is the vital field of ⌊>coding theory>⌋.@@@@1@24@@oe@26-8-2013 1000004200280@unknown@formal@none@1@S@Coding theory is concerned with finding explicit methods, called ⌊/codes/⌋, of increasing the efficiency and reducing the net error rate of data communication over a noisy channel to near the limit that Shannon proved is the maximum possible for that channel.@@@@1@41@@oe@26-8-2013 1000004200290@unknown@formal@none@1@S@These codes can be roughly subdivided into ⌊>data compression>⌋ (source coding) and ⌊>error-correction>⌋ (channel coding) techniques.@@@@1@16@@oe@26-8-2013 1000004200300@unknown@formal@none@1@S@In the latter case, it took many years to find the methods Shannon's work proved were possible.@@@@1@17@@oe@26-8-2013 1000004200310@unknown@formal@none@1@S@A third class of information theory codes are cryptographic algorithms (both ⌊>code>⌋s and ⌊>cipher>⌋s).@@@@1@14@@oe@26-8-2013 1000004200320@unknown@formal@none@1@S@Concepts, methods and results from coding theory and information theory are widely used in ⌊>cryptography>⌋ and ⌊>cryptanalysis>⌋.@@@@1@17@@oe@26-8-2013 1000004200330@unknown@formal@none@1@S@⌊/See the article ⌊>ban (information)>⌋ for a historical application./⌋@@@@1@9@@oe@26-8-2013 1000004200340@unknown@formal@none@1@S@Information theory is also used in ⌊>information retrieval>⌋, ⌊>intelligence gathering>⌋, ⌊>gambling>⌋, ⌊>statistics>⌋, and even in ⌊>musical composition>⌋.@@@@1@17@@oe@26-8-2013 1000004200350@unknown@formal@none@1@S@⌊=Historical background¦2=⌋@@@@1@2@@oe@26-8-2013 1000004200360@unknown@formal@none@1@S@The landmark event that established the discipline of information theory, and brought it to immediate worldwide attention, was the publication of ⌊>Claude E. Shannon>⌋'s classic paper "⌊>A Mathematical Theory of Communication>⌋" in the ⌊/⌊>Bell System Technical Journal>⌋/⌋ in July and October of 1948.@@@@1@43@@oe@26-8-2013 1000004200370@unknown@formal@none@1@S@Prior to this paper, limited information theoretic ideas had been developed at Bell Labs, all implicitly assuming events of equal probability.@@@@1@21@@oe@26-8-2013 1000004200380@unknown@formal@none@1@S@⌊>Harry Nyquist>⌋'s 1924 paper, ⌊/Certain Factors Affecting Telegraph Speed,/⌋ contains a theoretical section quantifying "intelligence" and the "line speed" at which it can be transmitted by a communication system, giving the relation ⌊×W = K \\log m×⌋, where ⌊/W/⌋ is the speed of transmission of intelligence, ⌊/m/⌋ is the number of different voltage levels to choose from at each time step, and ⌊/K/⌋ is a constant.@@@@1@66@@oe@26-8-2013 1000004200390@unknown@formal@none@1@S@⌊>Ralph Hartley>⌋'s 1928 paper, ⌊/Transmission of Information,/⌋ uses the word ⌊/information/⌋ as a measurable quantity, reflecting the receiver's ability to distinguish that one sequence of symbols from any other, thus quantifying information as ⌊×H = \\log S^n = n \\log S×⌋, where ⌊/S/⌋ was the number of possible symbols, and ⌊/n/⌋ the number of symbols in a transmission.@@@@1@58@@oe@26-8-2013 1000004200400@unknown@formal@none@1@S@The natural unit of information was therefore the decimal digit, much later renamed the ⌊>hartley>⌋ in his honour as a unit or scale or measure of information.@@@@1@27@@oe@26-8-2013 1000004200410@unknown@formal@none@1@S@⌊>Alan Turing>⌋ in 1940 used similar ideas as part of the statistical analysis of the breaking of the German second world war ⌊>Enigma>⌋ ciphers.@@@@1@24@@oe@26-8-2013 1000004200420@unknown@formal@none@1@S@Much of the mathematics behind information theory with events of different probabilities was developed for the field of ⌊>thermodynamics>⌋ by ⌊>Ludwig Boltzmann>⌋ and ⌊>J. Willard Gibbs>⌋.@@@@1@26@@oe@26-8-2013 1000004200430@unknown@formal@none@1@S@Connections between information-theoretic entropy and thermodynamic entropy, including the important contributions by ⌊>Rolf Landauer>⌋ in the 1960s, are explored in ⌊/⌊>Entropy in thermodynamics and information theory>⌋/⌋.@@@@1@26@@oe@26-8-2013 1000004200440@unknown@formal@none@1@S@In Shannon's revolutionary and groundbreaking paper, the work for which had been substantially completed at Bell Labs by the end of 1944, Shannon for the first time introduced the qualitative and quantitative model of communication as a statistical process underlying information theory, opening with the assertion that@@@@1@47@@oe@26-8-2013 1000004200450@unknown@formal@none@1@S@⌊⇥"The fundamental problem of communication is that of reproducing at one point, either exactly or approximately, a message selected at another point."⇥⌋@@@@1@22@@oe@26-8-2013 1000004200460@unknown@formal@none@1@S@With it came the ideas of@@@@1@6@@oe@26-8-2013 1000004200470@unknown@formal@none@1@S@⌊•⌊#the ⌊>information entropy>⌋ and ⌊>redundancy>⌋ of a source, and its relevance through the ⌊>source coding theorem>⌋;#⌋@@@@1@16@@oe@26-8-2013 1000004200480@unknown@formal@none@1@S@⌊#the ⌊>mutual information>⌋, and the ⌊>channel capacity>⌋ of a noisy channel, including the promise of perfect loss-free communication given by the ⌊>noisy-channel coding theorem>⌋;#⌋@@@@1@24@@oe@26-8-2013 1000004200490@unknown@formal@none@1@S@⌊#the practical result of the ⌊>Shannon–Hartley law>⌋ for the channel capacity of a Gaussian channel; and of course#⌋@@@@1@18@@oe@26-8-2013 1000004200500@unknown@formal@none@1@S@⌊#the ⌊>bit>⌋—a new way of seeing the most fundamental unit of information#⌋•⌋@@@@1@12@@oe@26-8-2013 1000004200510@unknown@formal@none@1@S@⌊=Ways of measuring information¦2=⌋@@@@1@4@@oe@26-8-2013 1000004200520@unknown@formal@none@1@S@Information theory is based on ⌊>probability theory>⌋ and ⌊>statistics>⌋.@@@@1@9@@oe@26-8-2013 1000004200530@unknown@formal@none@1@S@The most important quantities of information are ⌊>entropy>⌋, the information in a ⌊>random variable>⌋, and ⌊>mutual information>⌋, the amount of information in common between two random variables.@@@@1@27@@oe@26-8-2013 1000004200540@unknown@formal@none@1@S@The former quantity indicates how easily message data can be ⌊>compressed>⌋ while the latter can be used to find the communication rate across a ⌊>channel>⌋.@@@@1@25@@oe@26-8-2013 1000004200550@unknown@formal@none@1@S@The choice of logarithmic base in the following formulae determines the ⌊>unit>⌋ of ⌊>information entropy>⌋ that is used.@@@@1@18@@oe@26-8-2013 1000004200560@unknown@formal@none@1@S@The most common unit of information is the ⌊>bit>⌋, based on the ⌊>binary logarithm>⌋.@@@@1@14@@oe@26-8-2013 1000004200570@unknown@formal@none@1@S@Other units include the ⌊>nat>⌋, which is based on the ⌊>natural logarithm>⌋, and the ⌊>hartley>⌋, which is based on the ⌊>common logarithm>⌋.@@@@1@22@@oe@26-8-2013 1000004200580@unknown@formal@none@1@S@In what follows, an expression of the form ⌊×p \\log p \\,×⌋ is considered by convention to be equal to zero whenever ⌊×p=0.×⌋@@@@1@23@@oe@26-8-2013 1000004200590@unknown@formal@none@1@S@This is justified because ⌊×\\lim_{p \\rightarrow 0+} p \\log p = 0×⌋ for any logarithmic base.@@@@1@16@@oe@26-8-2013 1000004200600@unknown@formal@none@1@S@⌊=Entropy¦3=⌋@@@@1@1@@oe@26-8-2013 1000004200610@unknown@formal@none@1@S@The ⌊∗⌊>entropy>⌋∗⌋, ⌊×H×⌋, of a discrete random variable ⌊×X×⌋ is a measure of the amount of ⌊/uncertainty/⌋ associated with the value of ⌊×X×⌋.@@@@1@23@@oe@26-8-2013 1000004200620@unknown@formal@none@1@S@Suppose one transmits 1000 bits (0s and 1s).@@@@1@8@@oe@26-8-2013 1000004200630@unknown@formal@none@1@S@If these bits are known ahead of transmission (to be a certain value with absolute probability), logic dictates that no information has been transmitted.@@@@1@24@@oe@26-8-2013 1000004200640@unknown@formal@none@1@S@If, however, each is equally and independently likely to be 0 or 1, 1000 bits (in the information theoretic sense) have been transmitted.@@@@1@23@@oe@26-8-2013 1000004200650@unknown@formal@none@1@S@Between these two extremes, information can be quantified as follows.@@@@1@10@@oe@26-8-2013 1000004200660@unknown@formal@none@1@S@If ⌊×\\mathbb{X}\\,×⌋ is the set of all messages ⌊×x×⌋ that ⌊×X×⌋ could be, and ⌊×p(x)×⌋ is the probability of ⌊×X×⌋ given ⌊×x×⌋, then the entropy of ⌊×X×⌋ is defined:@@@@1@29@@oe@26-8-2013 1000004200670@unknown@formal@none@1@S@⌊⇥⌊×H(X) = \\mathbb{E}_{X} [I(x)] = -\\sum_{x \\in \\mathbb{X}} p(x) \\log p(x).×⌋⇥⌋@@@@1@11@@oe@26-8-2013 1000004200680@unknown@formal@none@1@S@(Here, ⌊×I(x)×⌋ is the ⌊>self-information>⌋, which is the entropy contribution of an individual message.)@@@@1@14@@oe@26-8-2013 1000004200690@unknown@formal@none@1@S@An important property of entropy is that it is maximized when all the messages in the message space are equiprobable—i.e., most unpredictable—in which case ⌊×H(X) = \\log |\\mathbb{X}|.×⌋@@@@1@28@@oe@26-8-2013 1000004200700@unknown@formal@none@1@S@The special case of information entropy for a random variable with two outcomes is the ⌊∗⌊>binary entropy function>⌋∗⌋:@@@@1@18@@oe@26-8-2013 1000004200710@unknown@formal@none@1@S@⌊⇥⌊×H_\\mbox{b}(p) = - p \\log p - (1-p)\\log (1-p).\\,×⌋⇥⌋@@@@1@9@@oe@26-8-2013 1000004200720@unknown@formal@none@1@S@⌊=Joint entropy¦3=⌋@@@@1@2@@oe@26-8-2013 1000004200730@unknown@formal@none@1@S@The ⌊∗⌊>joint entropy>⌋∗⌋ of two discrete random variables ⌊×X×⌋ and ⌊×Y×⌋ is merely the entropy of their pairing: ⌊×(X, Y)×⌋.@@@@1@20@@oe@26-8-2013 1000004200740@unknown@formal@none@1@S@This implies that if ⌊×X×⌋ and ⌊×Y×⌋ are ⌊>independent>⌋, then their joint entropy is the sum of their individual entropies.@@@@1@20@@oe@26-8-2013 1000004200750@unknown@formal@none@1@S@For example, if ⌊×(X,Y)×⌋ represents the position of a ⌊>chess>⌋ piece — ⌊×X×⌋ the row and ⌊×Y×⌋ the column, then the joint entropy of the row of the piece and the column of the piece will be the entropy of the position of the piece.@@@@1@45@@oe@26-8-2013 1000004200760@unknown@formal@none@1@S@⌊⇥⌊×H(X, Y) = \\mathbb{E}_{X,Y} [-\\log p(x,y)] = - \\sum_{x, y} p(x, y) \\log p(x, y) \\,×⌋⇥⌋@@@@1@16@@oe@26-8-2013 1000004200770@unknown@formal@none@1@S@Despite similar notation, joint entropy should not be confused with ⌊∗⌊>cross entropy>⌋∗⌋.@@@@1@12@@oe@26-8-2013 1000004200780@unknown@formal@none@1@S@⌊=Conditional entropy (equivocation)¦3=⌋@@@@1@3@@oe@26-8-2013 1000004200790@unknown@formal@none@1@S@The ⌊∗⌊>conditional entropy>⌋∗⌋ or ⌊∗conditional uncertainty∗⌋ of ⌊×X×⌋ given random variable ⌊×Y×⌋ (also called the ⌊∗equivocation∗⌋ of ⌊×X×⌋ about ⌊×Y×⌋) is the average conditional entropy over ⌊×Y×⌋:@@@@1@27@@oe@26-8-2013 1000004200800@unknown@formal@none@1@S@⌊⇥⌊×H(X|Y) = \\mathbb E_Y [H(X|y)] = -\\sum_{y \\in Y} p(y) \\sum_{x \\in X} p(x|y) \\log p(x|y) = -\\sum_{x,y} p(x,y) \\log \\frac{p(x,y)}{p(y)}.×⌋⇥⌋@@@@1@21@@oe@26-8-2013 1000004200810@unknown@formal@none@1@S@Because entropy can be conditioned on a random variable or on that random variable being a certain value, care should be taken not to confuse these two definitions of conditional entropy, the former of which is in more common use.@@@@1@40@@oe@26-8-2013 1000004200820@unknown@formal@none@1@S@A basic property of this form of conditional entropy is that:@@@@1@11@@oe@26-8-2013 1000004200830@unknown@formal@none@1@S@⌊⇥⌊×H(X|Y) = H(X,Y) - H(Y) .\\,×⌋⇥⌋@@@@1@6@@oe@26-8-2013 1000004200840@unknown@formal@none@1@S@⌊=Mutual information (transinformation)¦3=⌋@@@@1@3@@oe@26-8-2013 1000004200850@unknown@formal@none@1@S@⌊∗⌊>Mutual information>⌋∗⌋ measures the amount of information that can be obtained about one random variable by observing another.@@@@1@18@@oe@26-8-2013 1000004200860@unknown@formal@none@1@S@It is important in communication where it can be used to maximize the amount of information shared between sent and received signals.@@@@1@22@@oe@26-8-2013 1000004200870@unknown@formal@none@1@S@The mutual information of ⌊×X×⌋ relative to ⌊×Y×⌋ is given by:@@@@1@11@@oe@26-8-2013 1000004200880@unknown@formal@none@1@S@⌊⇥⌊×I(X;Y) = \\mathbb{E}_{X,Y} [SI(x,y)] = \\sum_{x,y} p(x,y) \\log \\frac{p(x,y)}{p(x)\\, p(y)}×⌋⇥⌋@@@@1@10@@oe@26-8-2013 1000004200890@unknown@formal@none@1@S@where ⌊×SI×⌋ (⌊/S/⌋pecific mutual ⌊/I/⌋nformation) is the ⌊>pointwise mutual information>⌋.@@@@1@10@@oe@26-8-2013 1000004200900@unknown@formal@none@1@S@A basic property of the mutual information is that@@@@1@9@@oe@26-8-2013 1000004200910@unknown@formal@none@1@S@⌊⇥⌊×I(X;Y) = H(X) - H(X|Y).\\,×⌋⇥⌋@@@@1@5@@oe@26-8-2013 1000004200920@unknown@formal@none@1@S@That is, knowing ⌊/Y/⌋, we can save an average of ⌊×I(X; Y)×⌋ bits in encoding ⌊/X/⌋ compared to not knowing ⌊/Y/⌋.@@@@1@21@@oe@26-8-2013 1000004200930@unknown@formal@none@1@S@Mutual information is ⌊>symmetric>⌋:@@@@1@4@@oe@26-8-2013 1000004200940@unknown@formal@none@1@S@⌊⇥⌊×I(X;Y) = I(Y;X) = H(X) + H(Y) - H(X,Y).\\,×⌋⇥⌋@@@@1@9@@oe@26-8-2013 1000004200950@unknown@formal@none@1@S@Mutual information can be expressed as the average ⌊>Kullback–Leibler divergence>⌋ (information gain) of the ⌊>posterior probability distribution>⌋ of ⌊/X/⌋ given the value of ⌊/Y/⌋ to the ⌊>prior distribution>⌋ on ⌊/X/⌋:@@@@1@30@@oe@26-8-2013 1000004200960@unknown@formal@none@1@S@⌊⇥⌊×I(X;Y) = \\mathbb E_{p(y)} [D_{\\mathrm{KL}}( p(X|Y=y) \\| p(X) )].×⌋⇥⌋@@@@1@9@@oe@26-8-2013 1000004200970@unknown@formal@none@1@S@In other words, this is a measure of how much, on the average, the probability distribution on ⌊/X/⌋ will change if we are given the value of ⌊/Y/⌋.@@@@1@28@@oe@26-8-2013 1000004200980@unknown@formal@none@1@S@This is often recalculated as the divergence from the product of the marginal distributions to the actual joint distribution:@@@@1@19@@oe@26-8-2013 1000004200990@unknown@formal@none@1@S@⌊⇥⌊×I(X; Y) = D_{\\mathrm{KL}}(p(X,Y) \\| p(X)p(Y)).×⌋⇥⌋@@@@1@6@@oe@26-8-2013 1000004201000@unknown@formal@none@1@S@Mutual information is closely related to the ⌊>log-likelihood ratio test>⌋ in the context of contingency tables and the ⌊>multinomial distribution>⌋ and to ⌊>Pearson's χ⌊^2^⌋ test>⌋: mutual information can be considered a statistic for assessing independence between a pair of variables, and has a well-specified asymptotic distribution.@@@@1@46@@oe@26-8-2013 1000004201010@unknown@formal@none@1@S@⌊=Kullback–Leibler divergence (information gain)¦3=⌋@@@@1@4@@oe@26-8-2013 1000004201020@unknown@formal@none@1@S@The ⌊∗⌊>Kullback–Leibler divergence>⌋∗⌋ (or ⌊∗information divergence∗⌋, ⌊∗information gain∗⌋, or ⌊∗relative entropy∗⌋) is a way of comparing two distributions: a "true" ⌊>probability distribution>⌋ ⌊/p(X)/⌋, and an arbitrary probability distribution ⌊/q(X)/⌋.@@@@1@29@@oe@26-8-2013 1000004201030@unknown@formal@none@1@S@If we compress data in a manner that assumes ⌊/q(X)/⌋ is the distribution underlying some data, when, in reality, ⌊/p(X)/⌋ is the correct distribution, the Kullback–Leibler divergence is the number of average additional bits per datum necessary for compression.@@@@1@39@@oe@26-8-2013 1000004201040@unknown@formal@none@1@S@It is thus defined@@@@1@4@@oe@26-8-2013 1000004201050@unknown@formal@none@1@S@⌊⇥⌊×D_{\\mathrm{KL}}(p(X) \\| q(X)) = \\sum_{x \\in X} -p(x) \\log {q(x)} \\, - \\, \\left( -p(x) \\log {p(x)}\\right) = \\sum_{x \\in X} p(x) \\log \\frac{p(x)}{q(x)}.×⌋⇥⌋@@@@1@24@@oe@26-8-2013 1000004201060@unknown@formal@none@1@S@Although it is sometimes used as a 'distance metric', it is not a true ⌊>metric>⌋ since it is not symmetric and does not satisfy the ⌊>triangle inequality>⌋ (making it a semi-quasimetric).@@@@1@31@@oe@26-8-2013 1000004201070@unknown@formal@none@1@S@⌊=Other quantities¦3=⌋@@@@1@2@@oe@26-8-2013 1000004201080@unknown@formal@none@1@S@Other important information theoretic quantities include ⌊>Rényi entropy>⌋ (a generalization of entropy) and ⌊>differential entropy>⌋ (a generalization of quantities of information to continuous distributions.)@@@@1@24@@oe@26-8-2013 1000004201090@unknown@formal@none@1@S@⌊=Coding theory¦2=⌋@@@@1@2@@oe@26-8-2013 1000004201100@unknown@formal@none@1@S@⌊>Coding theory>⌋ is one of the most important and direct applications of information theory.@@@@1@14@@oe@26-8-2013 1000004201110@unknown@formal@none@1@S@It can be subdivided into ⌊>source coding>⌋ theory and ⌊>channel coding>⌋ theory.@@@@1@12@@oe@26-8-2013 1000004201120@unknown@formal@none@1@S@Using a statistical description for data, information theory quantifies the number of bits needed to describe the data, which is the information entropy of the source.@@@@1@26@@oe@26-8-2013 1000004201130@unknown@formal@none@1@S@⌊•⌊#Data compression (source coding): There are two formulations for the compression problem:#⌋•⌋@@@@1@12@@oe@26-8-2013 1000004201140@unknown@formal@none@1@S@⌊•⌊#⌊>lossless data compression>⌋: the data must be reconstructed exactly;#⌋@@@@1@9@@oe@26-8-2013 1000004201150@unknown@formal@none@1@S@⌊#⌊>lossy data compression>⌋: allocates bits needed to reconstruct the data, within a specified fidelity level measured by a distortion function.@@@@1@20@@oe@26-8-2013 1000004201160@unknown@formal@none@1@S@This subset of Information theory is called ⌊>rate–distortion theory>⌋.#⌋•⌋@@@@1@9@@oe@26-8-2013 1000004201170@unknown@formal@none@1@S@⌊•⌊#Error-correcting codes (channel coding): While data compression removes as much ⌊>redundancy>⌋ as possible, an error correcting code adds just the right kind of redundancy (i.e. ⌊>error correction>⌋) needed to transmit the data efficiently and faithfully across a noisy channel.#⌋•⌋@@@@1@39@@oe@26-8-2013 1000004201180@unknown@formal@none@1@S@This division of coding theory into compression and transmission is justified by the information transmission theorems, or source–channel separation theorems that justify the use of bits as the universal currency for information in many contexts.@@@@1@35@@oe@26-8-2013 1000004201190@unknown@formal@none@1@S@However, these theorems only hold in the situation where one transmitting user wishes to communicate to one receiving user.@@@@1@19@@oe@26-8-2013 1000004201200@unknown@formal@none@1@S@In scenarios with more than one transmitter (the multiple-access channel), more than one receiver (the ⌊>broadcast channel>⌋) or intermediary "helpers" (the ⌊>relay channel>⌋), or more general ⌊>networks>⌋, compression followed by transmission may no longer be optimal.@@@@1@36@@oe@26-8-2013 1000004201210@unknown@formal@none@1@S@⌊>Network information theory>⌋ refers to these multi-agent communication models.@@@@1@9@@oe@26-8-2013 1000004201220@unknown@formal@none@1@S@⌊=Source theory¦3=⌋@@@@1@2@@oe@26-8-2013 1000004201230@unknown@formal@none@1@S@Any process that generates successive messages can be considered a ⌊∗⌊>source>⌋∗⌋ of information.@@@@1@13@@oe@26-8-2013 1000004201240@unknown@formal@none@1@S@A memoryless source is one in which each message is an ⌊>independent identically-distributed random variable>⌋, whereas the properties of ⌊>ergodicity>⌋ and ⌊>stationarity>⌋ impose more general constraints.@@@@1@26@@oe@26-8-2013 1000004201250@unknown@formal@none@1@S@All such sources are ⌊>stochastic>⌋.@@@@1@5@@oe@26-8-2013 1000004201260@unknown@formal@none@1@S@These terms are well studied in their own right outside information theory.@@@@1@12@@oe@26-8-2013 1000004201270@unknown@formal@none@1@S@⌊=Rate¦4=⌋@@@@1@1@@oe@26-8-2013 1000004201280@unknown@formal@none@1@S@Information ⌊>⌊∗rate∗⌋>⌋ is the average entropy per symbol.@@@@1@8@@oe@26-8-2013 1000004201290@unknown@formal@none@1@S@For memoryless sources, this is merely the entropy of each symbol, while, in the case of a stationary stochastic process, it is@@@@1@22@@oe@26-8-2013 1000004201300@unknown@formal@none@1@S@⌊⇥⌊×r = \\lim_{n \\to \\infty} H(X_n|X_{n-1},X_{n-2},X_{n-3}, \\ldots);×⌋⇥⌋@@@@1@7@@oe@26-8-2013 1000004201310@unknown@formal@none@1@S@that is, the conditional entropy of a symbol given all the previous symbols generated.@@@@1@14@@oe@26-8-2013 1000004201320@unknown@formal@none@1@S@For the more general case of a process that is not necessarily stationary, the ⌊/average rate/⌋ is@@@@1@17@@oe@26-8-2013 1000004201330@unknown@formal@none@1@S@⌊⇥⌊×r = \\lim_{n \\to \\infty} \\frac{1}{n} H(X_1, X_2, \\dots X_n);×⌋⇥⌋@@@@1@10@@oe@26-8-2013 1000004201340@unknown@formal@none@1@S@that is, the limit of the joint entropy per symbol.@@@@1@10@@oe@26-8-2013 1000004201350@unknown@formal@none@1@S@For stationary sources, these two expressions give the same result.@@@@1@10@@oe@26-8-2013 1000004201360@unknown@formal@none@1@S@It is common in information theory to speak of the "rate" or "entropy" of a language.@@@@1@16@@oe@26-8-2013 1000004201370@unknown@formal@none@1@S@This is appropriate, for example, when the source of information is English prose.@@@@1@13@@oe@26-8-2013 1000004201380@unknown@formal@none@1@S@The rate of a source of information is related to its ⌊>redundancy>⌋ and how well it can be ⌊>compressed>⌋, the subject of ⌊∗source coding∗⌋.@@@@1@24@@oe@26-8-2013 1000004201390@unknown@formal@none@1@S@⌊=Channel capacity¦3=⌋@@@@1@2@@oe@26-8-2013 1000004201400@unknown@formal@none@1@S@Communications over a channel—such as an ⌊>ethernet>⌋ wire—is the primary motivation of information theory.@@@@1@14@@oe@26-8-2013 1000004201410@unknown@formal@none@1@S@As anyone who's ever used a telephone (mobile or landline) knows, however, such channels often fail to produce exact reconstruction of a signal; noise, periods of silence, and other forms of signal corruption often degrade quality.@@@@1@36@@oe@26-8-2013 1000004201420@unknown@formal@none@1@S@How much information can one hope to communicate over a noisy (or otherwise imperfect) channel?@@@@1@15@@oe@26-8-2013 1000004201430@unknown@formal@none@1@S@Consider the communications process over a discrete channel.@@@@1@8@@oe@26-8-2013 1000004201440@unknown@formal@none@1@S@A simple model of the process is shown below:@@@@1@9@@oe@26-8-2013 1000004201450@unknown@formal@none@1@S@Here ⌊/X/⌋ represents the space of messages transmitted, and ⌊/Y/⌋ the space of messages received during a unit time over our channel.@@@@1@22@@oe@26-8-2013 1000004201460@unknown@formal@none@1@S@Let ⌊×p(y|x)×⌋ be the ⌊>conditional probability>⌋ distribution function of ⌊/Y/⌋ given ⌊/X/⌋.@@@@1@12@@oe@26-8-2013 1000004201470@unknown@formal@none@1@S@We will consider ⌊×p(y|x)×⌋ to be an inherent fixed property of our communications channel (representing the nature of the ⌊∗⌊>noise>⌋∗⌋ of our channel).@@@@1@23@@oe@26-8-2013 1000004201480@unknown@formal@none@1@S@Then the joint distribution of ⌊/X/⌋ and ⌊/Y/⌋ is completely determined by our channel and by our choice of ⌊×f(x)×⌋, the marginal distribution of messages we choose to send over the channel.@@@@1@32@@oe@26-8-2013 1000004201490@unknown@formal@none@1@S@Under these constraints, we would like to maximize the rate of information, or the ⌊∗⌊>signal>⌋∗⌋, we can communicate over the channel.@@@@1@21@@oe@26-8-2013 1000004201500@unknown@formal@none@1@S@The appropriate measure for this is the ⌊>mutual information>⌋, and this maximum mutual information is called the ⌊∗⌊>channel capacity>⌋∗⌋ and is given by:@@@@1@23@@oe@26-8-2013 1000004201510@unknown@formal@none@1@S@⌊⇥⌊×C = \\max_{f} I(X;Y).\\!×⌋⇥⌋@@@@1@4@@oe@26-8-2013 1000004201520@unknown@formal@none@1@S@This capacity has the following property related to communicating at information rate ⌊/R/⌋ (where ⌊/R/⌋ is usually bits per symbol).@@@@1@20@@oe@26-8-2013 1000004201530@unknown@formal@none@1@S@For any information rate ⌊/R < C/⌋ and coding error ε > 0, for large enough ⌊/N/⌋, there exists a code of length ⌊/N/⌋ and rate ≥ R and a decoding algorithm, such that the maximal probability of block error is ≤ ε; that is, it is always possible to transmit with arbitrarily small block error.@@@@1@56@@oe@26-8-2013 1000004201540@unknown@formal@none@1@S@In addition, for any rate ⌊/R > C/⌋, it is impossible to transmit with arbitrarily small block error.@@@@1@18@@oe@26-8-2013 1000004201550@unknown@formal@none@1@S@⌊∗⌊>Channel coding>⌋∗⌋ is concerned with finding such nearly optimal ⌊>codes>⌋ that can be used to transmit data over a noisy channel with a small coding error at a rate near the channel capacity.@@@@1@33@@oe@26-8-2013 1000004201560@unknown@formal@none@1@S@⌊=Channel capacity of particular model channels¦4=⌋@@@@1@6@@oe@26-8-2013 1000004201570@unknown@formal@none@1@S@⌊•⌊#A continuous-time analog communications channel subject to Gaussian noise — see ⌊>Shannon–Hartley theorem>⌋.#⌋•⌋@@@@1@13@@oe@26-8-2013 1000004201580@unknown@formal@none@1@S@⌊•⌊#A ⌊>binary symmetric channel>⌋ (BSC) with crossover probability ⌊/p/⌋ is a binary input, binary output channel that flips the input bit with probability ⌊/ p/⌋.@@@@1@25@@oe@26-8-2013 1000004201590@unknown@formal@none@1@S@The BSC has a capacity of ⌊×1 - H_\\mbox{b}(p)×⌋ bits per channel use, where ⌊×H_\\mbox{b}×⌋ is the ⌊>binary entropy function>⌋:#⌋•⌋@@@@1@20@@oe@26-8-2013 1000004201600@unknown@formal@none@1@S@⌊•⌊#A binary erasure channel (BEC) with erasure probability ⌊/ p /⌋ is a binary input, ternary output channel.@@@@1@18@@oe@26-8-2013 1000004201610@unknown@formal@none@1@S@The possible channel outputs are ⌊/0/⌋, ⌊/1/⌋, and a third symbol 'e' called an erasure.@@@@1@15@@oe@26-8-2013 1000004201620@unknown@formal@none@1@S@The erasure represents complete loss of information about an input bit.@@@@1@11@@oe@26-8-2013 1000004201630@unknown@formal@none@1@S@The capacity of the BEC is ⌊/1 - p/⌋ bits per channel use.#⌋•⌋@@@@1@13@@oe@26-8-2013 1000004201640@unknown@formal@none@1@S@⌊=Applications to other fields¦2=⌋@@@@1@4@@oe@26-8-2013 1000004201650@unknown@formal@none@1@S@⌊=Intelligence uses and secrecy applications¦3=⌋@@@@1@5@@oe@26-8-2013 1000004201660@unknown@formal@none@1@S@Information theoretic concepts apply to ⌊>cryptography>⌋ and ⌊>cryptanalysis>⌋.@@@@1@8@@oe@26-8-2013 1000004201670@unknown@formal@none@1@S@⌊>Turing>⌋'s information unit, the ⌊>ban>⌋, was used in the ⌊>Ultra>⌋ project, breaking the German ⌊>Enigma machine>⌋ code and hastening the ⌊>end of WWII in Europe>⌋.@@@@1@25@@oe@26-8-2013 1000004201680@unknown@formal@none@1@S@Shannon himself defined an important concept now called the ⌊>unicity distance>⌋.@@@@1@11@@oe@26-8-2013 1000004201690@unknown@formal@none@1@S@Based on the ⌊>redundancy>⌋ of the ⌊>plaintext>⌋, it attempts to give a minimum amount of ⌊>ciphertext>⌋ necessary to ensure unique decipherability.@@@@1@21@@oe@26-8-2013 1000004201700@unknown@formal@none@1@S@Information theory leads us to believe it is much more difficult to keep secrets than it might first appear.@@@@1@19@@oe@26-8-2013 1000004201710@unknown@formal@none@1@S@A ⌊>brute force attack>⌋ can break systems based on ⌊>asymmetric key algorithms>⌋ or on most commonly used methods of ⌊>symmetric key algorithms>⌋ (sometimes called secret key algorithms), such as ⌊>block cipher>⌋s.@@@@1@31@@oe@26-8-2013 1000004201720@unknown@formal@none@1@S@The security of all such methods currently comes from the assumption that no known attack can break them in a practical amount of time.@@@@1@24@@oe@26-8-2013 1000004201730@unknown@formal@none@1@S@⌊>Information theoretic security>⌋ refers to methods such as the ⌊>one-time pad>⌋ that are not vulnerable to such brute force attacks.@@@@1@20@@oe@26-8-2013 1000004201740@unknown@formal@none@1@S@In such cases, the positive conditional ⌊>mutual information>⌋ between the ⌊>plaintext>⌋ and ⌊>ciphertext>⌋ (conditioned on the ⌊> key>⌋) can ensure proper transmission, while the unconditional mutual information between the plaintext and ciphertext remains zero, resulting in absolutely secure communications.@@@@1@39@@oe@26-8-2013 1000004201750@unknown@formal@none@1@S@In other words, an eavesdropper would not be able to improve his or her guess of the plaintext by gaining knowledge of the ciphertext but not of the key.@@@@1@29@@oe@26-8-2013 1000004201760@unknown@formal@none@1@S@However, as in any other cryptographic system, care must be used to correctly apply even information-theoretically secure methods; the ⌊>Venona project>⌋ was able to crack the one-time pads of the ⌊>Soviet Union>⌋ due to their improper reuse of key material.@@@@1@40@@oe@26-8-2013 1000004201770@unknown@formal@none@1@S@⌊=Pseudorandom number generation¦3=⌋@@@@1@3@@oe@26-8-2013 1000004201780@unknown@formal@none@1@S@⌊>Pseudorandom number generator>⌋s are widely available in computer language libraries and application programs.@@@@1@13@@oe@26-8-2013 1000004201790@unknown@formal@none@1@S@They are, almost universally, unsuited to cryptographic use as they do not evade the deterministic nature of modern computer equipment and software.@@@@1@22@@oe@26-8-2013 1000004201800@unknown@formal@none@1@S@A class of improved random number generators is termed ⌊>Cryptographically secure pseudorandom number generator>⌋s, but even they require external to the software ⌊>random seed>⌋s to work as intended.@@@@1@28@@oe@26-8-2013 1000004201810@unknown@formal@none@1@S@These can be obtained via ⌊>extractor>⌋s, if done carefully.@@@@1@9@@oe@26-8-2013 1000004201820@unknown@formal@none@1@S@The measure of sufficient randomness in extractors is ⌊>min-entropy>⌋, a value related to Shannon entropy through ⌊>Rényi entropy>⌋; Rényi entropy is also used in evaluating randomness in cryptographic systems.@@@@1@29@@oe@26-8-2013 1000004201830@unknown@formal@none@1@S@Although related, the distinctions among these measures mean that a ⌊>random variable>⌋ with high Shannon entropy is not necessarily satisfactory for use in an extractor and so for cryptography uses.@@@@1@30@@oe@26-8-2013 1000004201840@unknown@formal@none@1@S@⌊=Miscellaneous applications¦3=⌋@@@@1@2@@oe@26-8-2013 1000004201850@unknown@formal@none@1@S@Information theory also has applications in ⌊>gambling and investing>⌋, ⌊>black holes>⌋, ⌊>bioinformatics>⌋, and ⌊>music>⌋.@@@@1@14@@oe@26-8-2013 1000004300010@unknown@formal@none@1@S@⌊δItalian languageδ⌋@@@@1@2@@oe@26-8-2013 1000004300020@unknown@formal@none@1@S@⌊∗Italian∗⌋ (, or ⌊/lingua italiana/⌋) is a ⌊>Romance language>⌋ spoken as a ⌊>first language>⌋ by about 63 million people, primarily in ⌊>Italy>⌋.@@@@1@22@@oe@26-8-2013 1000004300030@unknown@formal@none@1@S@In ⌊>Switzerland>⌋, Italian is one of four ⌊>official language>⌋s.@@@@1@9@@oe@26-8-2013 1000004300040@unknown@formal@none@1@S@It is also the official language of ⌊>San Marino>⌋.@@@@1@9@@oe@26-8-2013 1000004300050@unknown@formal@none@1@S@It is the primary language of the ⌊>Vatican City>⌋.@@@@1@9@@oe@26-8-2013 1000004300060@unknown@formal@none@1@S@Standard Italian, adopted by the state after the ⌊>unification of Italy>⌋, is based on ⌊>Tuscan>⌋ and is somewhat intermediate between ⌊>Italo-Dalmatian languages>⌋ of the ⌊>South>⌋ and ⌊>Northern Italian dialects>⌋ of the ⌊>North>⌋.@@@@1@32@@oe@26-8-2013 1000004300070@unknown@formal@none@1@S@Unlike most other Romance languages, Italian has retained the contrast between short and ⌊>long consonants>⌋ which existed in Latin.@@@@1@19@@oe@26-8-2013 1000004300080@unknown@formal@none@1@S@As in most ⌊>Romance languages>⌋, ⌊>stress>⌋ is distinctive.@@@@1@8@@oe@26-8-2013 1000004300090@unknown@formal@none@1@S@Of the Romance languages, Italian is considered to be one of the closest resembling ⌊>Latin>⌋ in terms of ⌊>vocabulary>⌋.@@@@1@19@@oe@26-8-2013 1000004300100@unknown@formal@none@1@S@According to Ethnologue, lexical similarity is 89% with ⌊>French>⌋, 87% with ⌊>Catalan>⌋, 85% with ⌊>Sardinian>⌋, 82% with ⌊>Spanish>⌋, 78% with Rheto-Romance, and 77% with Romanian.@@@@1@25@@oe@26-8-2013 1000004300110@unknown@formal@none@1@S@It is affectionately called ⌊/il parlar gentile/⌋ (the gentle language) by its speakers.@@@@1@13@@oe@26-8-2013 1000004300120@unknown@formal@none@1@S@⌊=Writing system¦2=⌋@@@@1@2@@oe@26-8-2013 1000004300130@unknown@formal@none@1@S@Italian is written using the ⌊>Latin alphabet>⌋.@@@@1@7@@oe@26-8-2013 1000004300140@unknown@formal@none@1@S@The letters ⌊/J/⌋, ⌊/K/⌋, ⌊/W/⌋, ⌊/X/⌋ and ⌊/Y/⌋ are not considered part of the standard ⌊>Italian alphabet>⌋, but appear in loanwords (such as ⌊/jeans/⌋, ⌊/whisky/⌋, ⌊/taxi/⌋).@@@@1@26@@oe@26-8-2013 1000004300150@unknown@formal@none@1@S@⌊/X/⌋ has become a commonly used letter in genuine Italian words with the prefix ⌊/extra-/⌋.@@@@1@15@@oe@26-8-2013 1000004300160@unknown@formal@none@1@S@⌊/J/⌋ in Italian is an old-fashioned orthographic variant of ⌊/I/⌋, appearing in the first name "Jacopo" as well as in some Italian place names, e.g., the towns of ⌊>Bajardo>⌋, ⌊>Bojano>⌋, ⌊>Joppolo>⌋, ⌊>Jesolo>⌋, ⌊>Jesi>⌋, among numerous others, and in the alternate spelling ⌊/Mar Jonio/⌋ (also spelled ⌊/Mar Ionio/⌋) for the ⌊>Ionian Sea>⌋.@@@@1@51@@oe@26-8-2013 1000004300170@unknown@formal@none@1@S@⌊/J/⌋ may also appear in many words from different dialects, but its use is discouraged in contemporary Italian, and it is not part of the standard 21-letter contemporary Italian alphabet.@@@@1@30@@oe@26-8-2013 1000004300180@unknown@formal@none@1@S@Each of these foreign letters had an Italian equivalent spelling: ⌊/gi/⌋ for ⌊/j/⌋, ⌊/c/⌋ or ⌊/ch/⌋ for ⌊/k/⌋, ⌊/u/⌋ or ⌊/v/⌋ for ⌊/w/⌋ (depending on what sound it makes), ⌊/s/⌋, ⌊/ss/⌋, or ⌊/cs/⌋ for ⌊/x/⌋, and ⌊/i/⌋ for ⌊/y/⌋.@@@@1@39@@oe@26-8-2013 1000004300190@unknown@formal@none@1@S@⌊•⌊#Italian uses the ⌊>acute accent>⌋ over the letter ⌊/E/⌋ (as in ⌊/perché/⌋, why/because) to indicate a front mid-close vowel, and the ⌊>grave accent>⌋ (as in ⌊/tè/⌋, tea) to indicate a front mid-open vowel.@@@@1@33@@oe@26-8-2013 1000004300200@unknown@formal@none@1@S@The ⌊>grave accent>⌋ is also used on letters ⌊/A/⌋, ⌊/I/⌋, ⌊/O/⌋, and ⌊/U/⌋ to mark ⌊>stress>⌋ when it falls on the final vowel of a word (for instance ⌊/gioventù/⌋, youth).@@@@1@30@@oe@26-8-2013 1000004300210@unknown@formal@none@1@S@Typically, the penultimate syllable is stressed.@@@@1@6@@oe@26-8-2013 1000004300220@unknown@formal@none@1@S@If syllables other than the last one are stressed, the accent is not mandatory, unlike in ⌊>Spanish>⌋, and, in virtually all cases, it is omitted.@@@@1@25@@oe@26-8-2013 1000004300230@unknown@formal@none@1@S@In some cases, when the word is ambiguous (as ⌊/principi/⌋), the accent mark is sometimes used in order to disambiguate its meaning (in this case, ⌊/prìncipi/⌋, princes, or ⌊/princìpi/⌋, principles).@@@@1@30@@oe@26-8-2013 1000004300240@unknown@formal@none@1@S@This is, however, not compulsory.@@@@1@5@@oe@26-8-2013 1000004300250@unknown@formal@none@1@S@Rare words with three or more syllables can confuse Italians themselves, and the pronunciation of ⌊>Istanbul>⌋ is a common example of a word in which placement of stress is not clearly established.@@@@1@32@@oe@26-8-2013 1000004300260@unknown@formal@none@1@S@Turkish, like French, tends to put the accent on ultimate syllable, but Italian doesn't.@@@@1@14@@oe@26-8-2013 1000004300270@unknown@formal@none@1@S@So we can hear "Istànbul" or "Ìstanbul".@@@@1@7@@oe@26-8-2013 1000004300280@unknown@formal@none@1@S@Another instance is the American State of ⌊>Florida>⌋: the correct way to pronounce it in Italian is like in Spanish, "Florìda", but since there is an Italian word meaning the same ("flourishing"), "flòrida", and because of the influence of English, most Italians pronounce it that way.@@@@1@46@@oe@26-8-2013 1000004300290@unknown@formal@none@1@S@Dictionaries give the latter as an alternative pronunciation.#⌋•⌋@@@@1@8@@oe@26-8-2013 1000004300300@unknown@formal@none@1@S@⌊•⌊#The letter ⌊/H/⌋ at the beginning of a word is used to distinguish ⌊/ho/⌋, ⌊/hai/⌋, ⌊/ha/⌋, ⌊/hanno/⌋ (present indicative of ⌊/avere/⌋, 'to have') from ⌊/o/⌋ ('or'), ⌊/ai/⌋ ('to the'), ⌊/a/⌋ ('to'), ⌊/anno/⌋ ('year').@@@@1@33@@oe@26-8-2013 1000004300310@unknown@formal@none@1@S@In the spoken language this letter is always silent for the cases given above.@@@@1@14@@oe@26-8-2013 1000004300320@unknown@formal@none@1@S@⌊/H/⌋ is also used in combinations with other letters (see below), but no ⌊>phoneme>⌋ ⌊λ[h]¦[h]¦IPAλ⌋ exists in Italian.@@@@1@18@@oe@26-8-2013 1000004300330@unknown@formal@none@1@S@In foreign words entered in common use, like "hotel" or "hovercraft", the H is commonly silent, so they are pronounced as ⌊λ/oˈtɛl/¦/oˈtɛl/¦IPAλ⌋ and ⌊λ/ˈɔverkraft/¦/ˈɔverkraft/¦IPAλ⌋#⌋•⌋@@@@1@24@@oe@26-8-2013 1000004300340@unknown@formal@none@1@S@⌊•⌊#The letter ⌊/Z/⌋ represents ⌊λ/ʣ/¦/ʣ/¦IPAλ⌋, for example: ⌊/Zanzara/⌋ ⌊λ/dzan'dzaɾa/¦/dzan'dzaɾa/¦IPAλ⌋ (mosquito), or ⌊λ/ʦ/¦/ʦ/¦IPAλ⌋, for example: ⌊/Nazione/⌋ ⌊λ/naˈttsjone/¦/naˈttsjone/¦IPAλ⌋ (nation), depending on context, though there are few ⌊>minimal pair>⌋s.@@@@1@26@@oe@26-8-2013 1000004300350@unknown@formal@none@1@S@The same goes for ⌊/S/⌋, which can represent ⌊λ/s/¦/s/¦IPAλ⌋ or ⌊λ/z/¦/z/¦IPAλ⌋.@@@@1@11@@oe@26-8-2013 1000004300360@unknown@formal@none@1@S@However, these two phonemes are in ⌊>complementary distribution>⌋ everywhere except between two vowels in the same word, and even in such environment there are extremely few minimal pairs, so that this distinction is being lost in many varieties.#⌋•⌋@@@@1@38@@oe@26-8-2013 1000004300370@unknown@formal@none@1@S@⌊•⌊#The letters ⌊/C/⌋ and ⌊/G/⌋ represent ⌊>affricate>⌋s: ⌊>⌊λ/ʧ/¦/ʧ/¦IPAλ⌋>⌋ as in "chair" and ⌊>⌊λ/ʤ/¦/ʤ/¦IPAλ⌋>⌋ as in "gem", respectively, before the ⌊>front vowel>⌋s ⌊/I/⌋ and ⌊/E/⌋.@@@@1@24@@oe@26-8-2013 1000004300380@unknown@formal@none@1@S@They are pronounced as ⌊>plosive>⌋s ⌊λ/k/¦/k/¦IPAλ⌋, ⌊λ/g/¦/g/¦IPAλ⌋ (as in "call" and "gall") otherwise.@@@@1@13@@oe@26-8-2013 1000004300390@unknown@formal@none@1@S@Front/back vowel rules for ⌊/C/⌋ and ⌊/G/⌋ are similar in ⌊>French>⌋, ⌊>Romanian>⌋, ⌊>Spanish>⌋, and to some extent ⌊>English>⌋ (including ⌊>Old English>⌋).@@@@1@21@@oe@26-8-2013 1000004300400@unknown@formal@none@1@S@⌊>Swedish>⌋ and ⌊>Norwegian>⌋ have similar rules for ⌊/K/⌋ and ⌊/G/⌋.@@@@1@10@@oe@26-8-2013 1000004300410@unknown@formal@none@1@S@(See also ⌊>palatalization>⌋.)#⌋•⌋@@@@1@3@@oe@26-8-2013 1000004300420@unknown@formal@none@1@S@⌊•⌊#However, an ⌊/H/⌋ can be added between ⌊/C/⌋ or ⌊/G/⌋ and ⌊/E/⌋ or ⌊/I/⌋ to represent a plosive, and an ⌊/I/⌋ can be added between ⌊/C/⌋ or ⌊/G/⌋ and ⌊/A/⌋, ⌊/O/⌋ or ⌊/U/⌋ to signal that the consonant is an affricate.@@@@1@41@@oe@26-8-2013 1000004300430@unknown@formal@none@1@S@For example:#⌋•⌋@@@@1@2@@oe@26-8-2013 1000004300440@unknown@formal@none@1@S@⌊⇥Note that the ⌊/H/⌋ is ⌊>silent>⌋ in the digraphs ⌊/⌊>CH>⌋/⌋ and ⌊/⌊>GH>⌋/⌋, as also the ⌊/I/⌋ in ⌊/cia/⌋, ⌊/cio/⌋, ⌊/ciu/⌋ and even ⌊/cie/⌋ is not pronounced as a separate vowel, unless it carries the primary stress.@@@@1@36@@oe@26-8-2013 1000004300450@unknown@formal@none@1@S@For example, it is silent in ⌊/⌊>ciao>⌋/⌋ ⌊λ/ˈʧa.o/¦/ˈʧa.o/¦IPAλ⌋ and cielo ⌊λ/ˈʧɛ.lo/¦/ˈʧɛ.lo/¦IPAλ⌋, but it is pronounced in ⌊/farmacia/⌋ ⌊λ/ˌfaɾ.ma.ˈʧi.a/¦/ˌfaɾ.ma.ˈʧi.a/¦IPAλ⌋ and ⌊/farmacie/⌋ ⌊λ/ˌfaɾ.ma.ˈʧi.e/¦/ˌfaɾ.ma.ˈʧi.e/¦IPAλ⌋.⇥⌋@@@@1@21@@oe@26-8-2013 1000004300460@unknown@formal@none@1@S@⌊•⌊#There are three other special ⌊>digraphs>⌋ in Italian: ⌊/⌊>GN>⌋/⌋, ⌊/GL/⌋ and ⌊/SC/⌋.@@@@1@12@@oe@26-8-2013 1000004300470@unknown@formal@none@1@S@⌊/GN/⌋ represents ⌊>⌊λ/ɲ/¦/ɲ/¦IPAλ⌋>⌋.@@@@1@3@@oe@26-8-2013 1000004300480@unknown@formal@none@1@S@⌊/GL/⌋ represents ⌊>⌊λ/ʎ/¦/ʎ/¦IPAλ⌋>⌋ only before ⌊/i/⌋, and never at the beginning of a word, except in the ⌊>personal pronoun>⌋ and ⌊>definite article>⌋ ⌊/gli/⌋.@@@@1@23@@oe@26-8-2013 1000004300490@unknown@formal@none@1@S@(Compare with ⌊>Spanish>⌋ ⌊/ñ/⌋ and ⌊/ll/⌋, ⌊>Portuguese>⌋ ⌊/nh/⌋ and ⌊/lh/⌋.)@@@@1@10@@oe@26-8-2013 1000004300500@unknown@formal@none@1@S@⌊/SC/⌋ represents fricative ⌊>⌊λ/ʃ/¦/ʃ/¦IPAλ⌋>⌋ before ⌊/i/⌋ or ⌊/e/⌋.@@@@1@8@@oe@26-8-2013 1000004300510@unknown@formal@none@1@S@Except in the speech of some Northern Italians, all of these are normally ⌊>geminate>⌋ between vowels.#⌋•⌋@@@@1@16@@oe@26-8-2013 1000004300520@unknown@formal@none@1@S@⌊•⌊#In general, all letters or digraphs represent phonemes rather clearly, and, in standard varieties of Italian, there is little allophonic variation.@@@@1@21@@oe@26-8-2013 1000004300530@unknown@formal@none@1@S@The most notable exceptions are assimilation of /n/ in point of articulation before consonants, assimilatory voicing of /s/ to following voiced consonants, and vowel length (vowels are long in stressed open syllables, and short elsewhere) — compare with the enormous number of ⌊>allophone>⌋s of the English phoneme /t/.@@@@1@48@@oe@26-8-2013 1000004300540@unknown@formal@none@1@S@Spelling is clearly phonemic and difficult to mistake given a clear pronunciation.@@@@1@12@@oe@26-8-2013 1000004300550@unknown@formal@none@1@S@Exceptions are generally only found in foreign borrowings.@@@@1@8@@oe@26-8-2013 1000004300560@unknown@formal@none@1@S@There are fewer cases of ⌊>dyslexia>⌋ than among speakers of languages such as English , and the concept of a spelling bee is strange to Italians.#⌋•⌋@@@@1@26@@oe@26-8-2013 1000004300570@unknown@formal@none@1@S@⌊=History¦2=⌋@@@@1@1@@oe@26-8-2013 1000004300580@unknown@formal@none@1@S@The history of the Italian language is long, but the modern standard of the language was largely shaped by relatively recent events.@@@@1@22@@oe@26-8-2013 1000004300590@unknown@formal@none@1@S@The earliest surviving texts which can definitely be called Italian (or more accurately, vernacular, as opposed to its predecessor ⌊>Vulgar Latin>⌋) are legal formulae from the region of ⌊>Benevento>⌋ dating from 960-963.@@@@1@32@@oe@26-8-2013 1000004300600@unknown@formal@none@1@S@What would come to be thought of as Italian was first formalized in the first years of the 14th century through the works of ⌊>Dante Alighieri>⌋, who mixed southern Italian languages, especially ⌊>Sicilian>⌋, with his native Tuscan in his epic poems known collectively as the ⌊/⌊>Commedia>⌋,/⌋ to which ⌊>Giovanni Boccaccio>⌋ later affixed the title ⌊/Divina/⌋.@@@@1@55@@oe@26-8-2013 1000004300610@unknown@formal@none@1@S@Dante's much-loved works were read throughout Italy and his written dialect became the "canonical standard" that all educated Italians could understand.@@@@1@21@@oe@26-8-2013 1000004300620@unknown@formal@none@1@S@Dante is still credited with standardizing the Italian language and, thus, the dialect of ⌊>Tuscany>⌋ became the basis for what would become the official language of Italy.@@@@1@27@@oe@26-8-2013 1000004300630@unknown@formal@none@1@S@Italy has always had a distinctive dialect for each city since the cities were until recently thought of as ⌊>city-state>⌋s.@@@@1@20@@oe@26-8-2013 1000004300640@unknown@formal@none@1@S@The latter now has considerable ⌊>variety>⌋, however.@@@@1@7@@oe@26-8-2013 1000004300650@unknown@formal@none@1@S@As Tuscan-derived Italian came to be used throughout the nation, features of local speech were naturally adopted, producing various versions of Regional Italian.@@@@1@23@@oe@26-8-2013 1000004300660@unknown@formal@none@1@S@The most characteristic differences, for instance, between ⌊>Roman Italian>⌋ and ⌊>Milanese Italian>⌋ are the ⌊>gemination>⌋ of initial consonants and the pronunciation of stressed "e", and of "s" in some cases (e.g. ⌊/va bene/⌋ "all right": is pronounced ⌊λ[va ˈbːɛne]¦[va ˈbːɛne]¦IPAλ⌋ by a Roman, ⌊λ[va ˈbene]¦[va ˈbene]¦IPAλ⌋ by a Milanese; ⌊/a casa/⌋ "at home": Roman ⌊λ[a ˈkːasa]¦[a ˈkːasa]¦IPAλ⌋, Milanese ⌊λ[a ˈkaza]¦[a ˈkaza]¦IPAλ⌋).@@@@1@61@@oe@26-8-2013 1000004300670@unknown@formal@none@1@S@In contrast to the ⌊>dialects of northern Italy>⌋, ⌊>southern Italian>⌋ dialects were largely untouched by the Franco-⌊>Occitan>⌋ influences introduced to Italy, mainly by ⌊>bard>⌋s from ⌊>France>⌋, during the ⌊>Middle Ages>⌋.@@@@1@30@@oe@26-8-2013 1000004300680@unknown@formal@none@1@S@Even in the case of Northern Italian dialects, however, scholars are careful not to overstate the effects of outsiders on the natural indigenous developments of the languages.@@@@1@27@@oe@26-8-2013 1000004300690@unknown@formal@none@1@S@(See ⌊>La Spezia-Rimini Line>⌋.)@@@@1@4@@oe@26-8-2013 1000004300700@unknown@formal@none@1@S@The economic might and relative advanced development of ⌊>Tuscany>⌋ at the time (⌊>Late Middle Ages>⌋), gave its dialect weight, though Venetian remained widespread in medieval Italian commercial life.@@@@1@28@@oe@26-8-2013 1000004300710@unknown@formal@none@1@S@Also, the increasing cultural relevance of ⌊>Florence>⌋ during the periods of '⌊>Umanesimo (Humanism)>⌋' and the ⌊>Rinascimento (Renaissance)>⌋ made its ⌊/volgare/⌋ (dialect), or rather a refined version of it, a standard in the arts.@@@@1@33@@oe@26-8-2013 1000004300720@unknown@formal@none@1@S@The re-discovery of Dante's ⌊/⌊>De vulgari eloquentia>⌋/⌋ and a renewed interest in linguistics in the 16th century sparked a debate which raged throughout Italy concerning which criteria should be chosen to establish a modern Italian standard to be used as much as a literary as a spoken language.@@@@1@48@@oe@26-8-2013 1000004300730@unknown@formal@none@1@S@Scholars were divided into three factions: the ⌊>purists>⌋, headed by ⌊>Pietro Bembo>⌋ who in his ⌊/⌊>Gli Asolani>⌋/⌋ claimed that the language might only be based on the great literary classics (notably, ⌊>Petrarch>⌋, and Boccaccio but not Dante as Bembo believed that the Divine Comedy was not dignified enough as it used elements from other dialects), ⌊>Niccolò Machiavelli>⌋ and other ⌊>Florentine>⌋s who preferred the version spoken by ordinary people in their own times, and the ⌊>Courtesan>⌋s like ⌊>Baldassarre Castiglione>⌋ and ⌊>Gian Giorgio Trissino>⌋ who insisted that each local vernacular must contribute to the new standard.@@@@1@94@@oe@26-8-2013 1000004300740@unknown@formal@none@1@S@Eventually Bembo's ideas prevailed, the result being the publication of the first Italian dictionary in 1612 and the foundation of the ⌊>Accademia della Crusca>⌋ in Florence (1582-3), the official legislative body of the Italian language.@@@@1@35@@oe@26-8-2013 1000004300750@unknown@formal@none@1@S@Italian literature's first modern novel, ⌊>⌊/I Promessi Sposi/⌋>⌋ (The Betrothed), by ⌊>Alessandro Manzoni>⌋ further defined the standard by "rinsing" his Milanese 'in the waters of the ⌊>Arno>⌋" (⌊>Florence>⌋'s river), as he states in the Preface to his 1840 edition.@@@@1@39@@oe@26-8-2013 1000004300760@unknown@formal@none@1@S@After unification a huge number of civil servants and soldiers recruited from all over the country introduced many more words and idioms from their home dialects ("⌊>ciao>⌋" is ⌊>Venetian>⌋, "⌊>panettone>⌋" is ⌊>Milanese>⌋ etc.).@@@@1@33@@oe@26-8-2013 1000004300770@unknown@formal@none@1@S@⌊=Classification¦2=⌋@@@@1@1@@oe@26-8-2013 1000004300780@unknown@formal@none@1@S@Italian is most closely related to the other two Italo-Dalmatian languages, ⌊>Sicilian>⌋ and the extinct ⌊>Dalmatian>⌋.@@@@1@16@@oe@26-8-2013 1000004300790@unknown@formal@none@1@S@The three are part of the ⌊>Italo-Western>⌋ grouping of the ⌊>Romance languages>⌋, which are a subgroup of the ⌊>Italic>⌋ branch of ⌊>Indo-European>⌋.@@@@1@22@@oe@26-8-2013 1000004300800@unknown@formal@none@1@S@⌊=Geographic distribution¦2=⌋@@@@1@2@@oe@26-8-2013 1000004300810@unknown@formal@none@1@S@The total speakers of Italian as maternal language are between 60 and 70 million.@@@@1@14@@oe@26-8-2013 1000004300820@unknown@formal@none@1@S@The speakers who use Italian as second or cultural language are estimated around 110-120 million .@@@@1@16@@oe@26-8-2013 1000004300830@unknown@formal@none@1@S@Italian is the official language of ⌊>Italy>⌋ and ⌊>San Marino>⌋, and one of the official languages of ⌊>Switzerland>⌋, spoken mainly in ⌊>Ticino>⌋ and ⌊>Grigioni>⌋ cantons, a region referred to as ⌊>Italian Switzerland>⌋.@@@@1@32@@oe@26-8-2013 1000004300840@unknown@formal@none@1@S@It is also the second official language in some areas of ⌊>Istria>⌋, in ⌊>Slovenia>⌋ and ⌊>Croatia>⌋, where an Italian minority exists.@@@@1@21@@oe@26-8-2013 1000004300850@unknown@formal@none@1@S@It is the primary language of the ⌊>Vatican City>⌋ and is widely used and taught in ⌊>Monaco>⌋ and ⌊>Malta>⌋.@@@@1@19@@oe@26-8-2013 1000004300860@unknown@formal@none@1@S@It is also widely understood in France with over one million speakers (especially in ⌊>Corsica>⌋ and the ⌊>County of Nice>⌋, areas that historically spoke ⌊>Italian dialects>⌋ before annexation to ⌊>France>⌋), and in ⌊>Albania>⌋.@@@@1@33@@oe@26-8-2013 1000004300870@unknown@formal@none@1@S@Italian is also spoken by some in former Italian colonies in ⌊>Africa>⌋ (⌊>Libya>⌋, ⌊>Somalia>⌋ and ⌊>Eritrea>⌋).@@@@1@16@@oe@26-8-2013 1000004300880@unknown@formal@none@1@S@However, its use has sharply dropped off since the colonial period.@@@@1@11@@oe@26-8-2013 1000004300890@unknown@formal@none@1@S@In ⌊>Eritrea>⌋ ⌊>Italian>⌋ is widely understood .@@@@1@7@@oe@26-8-2013 1000004300900@unknown@formal@none@1@S@In fact, for fifty years, during the colonial period, Italian was the language of instruction, but ⌊>as of 1997>⌋, there is only one Italian language school remaining, with 470 pupils.@@@@1@30@@oe@26-8-2013 1000004300910@unknown@formal@none@1@S@In ⌊>Somalia>⌋ Italian used to be a major language but due to the civil war and lack of education only the older generation still uses it.@@@@1@26@@oe@26-8-2013 1000004300920@unknown@formal@none@1@S@Italian and ⌊>Italian dialects>⌋ are widely used by Italian immigrants and many of their descendants (see ⌊/⌊>Italians>⌋/⌋) living throughout ⌊>Western Europe>⌋ (especially ⌊>France>⌋, ⌊>Germany>⌋, ⌊>Belgium>⌋, ⌊>Switzerland>⌋, the ⌊>United Kingdom>⌋ and ⌊>Luxembourg>⌋), the ⌊>United States>⌋, ⌊>Canada>⌋, ⌊>Australia>⌋, and ⌊>Latin America>⌋ (especially ⌊>Uruguay>⌋, ⌊>Brazil>⌋, ⌊>Argentina>⌋, and ⌊>Venezuela>⌋).@@@@1@45@@oe@26-8-2013 1000004300930@unknown@formal@none@1@S@In the United States, Italian speakers are most commonly found in four cities: ⌊>Boston>⌋ (7,000), ⌊>Chicago>⌋ (12,000), ⌊>New York City>⌋ (140,000), and ⌊>Philadelphia>⌋ (15,000).@@@@1@24@@oe@26-8-2013 1000004300940@unknown@formal@none@1@S@In Canada there are large Italian-speaking communities in ⌊>Montreal>⌋ (120,000) and ⌊>Toronto>⌋ (195,000).@@@@1@13@@oe@26-8-2013 1000004300950@unknown@formal@none@1@S@Italian is the second most commonly-spoken language in Australia, where 353,605 ⌊>Italian Australian>⌋s, or 1.9% of the population, reported speaking Italian at home in the 2001 ⌊>Census>⌋.@@@@1@27@@oe@26-8-2013 1000004300960@unknown@formal@none@1@S@In 2001 there were 130,000 Italian speakers in ⌊>Melbourne>⌋, and 90,000 in ⌊>Sydney>⌋.@@@@1@13@@oe@26-8-2013 1000004300970@unknown@formal@none@1@S@⌊=Italian language education¦3=⌋@@@@1@3@@oe@26-8-2013 1000004300980@unknown@formal@none@1@S@Italian is widely taught in many schools around the world, but rarely as the first non-native language of pupils; in fact, Italian generally is the fourth or fifth most taught second-language in the world.@@@@1@34@@oe@26-8-2013 1000004300990@unknown@formal@none@1@S@In ⌊>anglophone>⌋ parts of ⌊>Canada>⌋, Italian is, after ⌊>French>⌋, the third most taught language.@@@@1@14@@oe@26-8-2013 1000004301000@unknown@formal@none@1@S@In ⌊>francophone>⌋ Canada it is third after ⌊>English>⌋.@@@@1@8@@oe@26-8-2013 1000004301010@unknown@formal@none@1@S@In the ⌊>United States>⌋ and the ⌊>United Kingdom>⌋, Italian ranks fourth (after ⌊>Spanish>⌋-French-⌊>German>⌋ and French-German-Spanish respectively).@@@@1@16@@oe@26-8-2013 1000004301020@unknown@formal@none@1@S@Throughout the world, Italian is the fifth most taught non-native language, after ⌊>English>⌋, French, Spanish, and German.@@@@1@17@@oe@26-8-2013 1000004301030@unknown@formal@none@1@S@In the ⌊>European Union>⌋, Italian is spoken as a mother tongue by 13% of the population (64 million, mainly in Italy itself) and as a second language by 3% (14 million); among EU member states, it is most likely to be desired (and therefore learned) as a second language in ⌊>Malta>⌋ (61%), ⌊>Croatia>⌋ (14%), ⌊>Slovenia>⌋ (12%), ⌊>Austria>⌋ (11%), ⌊>Romania>⌋ (8%), ⌊>France>⌋ (6%), and ⌊>Greece>⌋ (6%).@@@@1@65@@oe@26-8-2013 1000004301040@unknown@formal@none@1@S@It is also an important second language in ⌊>Albania>⌋ and ⌊>Switzerland>⌋, which are not EU members or candidates.@@@@1@18@@oe@26-8-2013 1000004301050@unknown@formal@none@1@S@⌊=Influence and derived languages¦3=⌋@@@@1@4@@oe@26-8-2013 1000004301060@unknown@formal@none@1@S@From the late 19th to the mid 20th century, thousands of Italians settled in Argentina, Uruguay and southern Brazil, where they formed a very strong physical and cultural presence (see the ⌊>Italian diaspora>⌋).@@@@1@33@@oe@26-8-2013 1000004301070@unknown@formal@none@1@S@In some cases, colonies were established where variants of ⌊>Italian dialects>⌋ were used, and some continue to use a derived dialect.@@@@1@21@@oe@26-8-2013 1000004301080@unknown@formal@none@1@S@An example is ⌊>Rio Grande do Sul>⌋, ⌊>Brazil>⌋, where ⌊>Talian>⌋ is used and in the town of ⌊>Chipilo>⌋ near Puebla, ⌊>Mexico>⌋ each continuing to use a derived form of ⌊>Venetian>⌋ dating back to the 19th century.@@@@1@36@@oe@26-8-2013 1000004301090@unknown@formal@none@1@S@Another example is ⌊>Cocoliche>⌋, an Italian-Spanish ⌊>pidgin>⌋ once spoken in ⌊>Argentina>⌋ and especially in ⌊>Buenos Aires>⌋, and ⌊>Lunfardo>⌋.@@@@1@18@@oe@26-8-2013 1000004301100@unknown@formal@none@1@S@⌊>Rioplatense Spanish>⌋, and particularly the speech of the city of Buenos Aires, has intonation patterns that resemble those of Italian dialects, due to the fact that Argentina had a constant, large influx of Italian settlers since the second half of the nineteenth century; initially primarily from Northern Italy then, since the beginning of the twentieth century, mostly from Southern Italy.@@@@1@60@@oe@26-8-2013 1000004301110@unknown@formal@none@1@S@⌊=Lingua Franca¦3=⌋@@@@1@2@@oe@26-8-2013 1000004301120@unknown@formal@none@1@S@Starting in late ⌊>medieval>⌋ times, Italian language variants replaced Latin to become the primary commercial language for much of Europe and Mediterranean Sea (especially the Tuscan and Venetian variants).@@@@1@29@@oe@26-8-2013 1000004301130@unknown@formal@none@1@S@This became solidified during the ⌊>Renaissance>⌋ with the strength of Italian banking and the rise of ⌊>humanism>⌋ in the arts.@@@@1@20@@oe@26-8-2013 1000004301140@unknown@formal@none@1@S@During the period of the Renaissance, Italy held artistic sway over the rest of Europe.@@@@1@15@@oe@26-8-2013 1000004301150@unknown@formal@none@1@S@All educated European gentlemen were expected to make the ⌊>Grand Tour>⌋, visiting Italy to see its great historical monuments and works of art.@@@@1@23@@oe@26-8-2013 1000004301160@unknown@formal@none@1@S@It thus became expected that educated Europeans would learn at least some Italian; the English poet ⌊>John Milton>⌋, for instance, wrote some of his early poetry in Italian.@@@@1@28@@oe@26-8-2013 1000004301170@unknown@formal@none@1@S@In England, Italian became the second most common modern language to be learned, after ⌊>French>⌋ (though the classical languages, ⌊>Latin>⌋ and ⌊>Greek>⌋, came first).@@@@1@24@@oe@26-8-2013 1000004301180@unknown@formal@none@1@S@However, by the late eighteenth century, Italian tended to be replaced by ⌊>German>⌋ as the second modern language on the curriculum.@@@@1@21@@oe@26-8-2013 1000004301190@unknown@formal@none@1@S@Yet Italian ⌊>loanword>⌋s continue to be used in most other ⌊>European languages>⌋ in matters of art and music.@@@@1@18@@oe@26-8-2013 1000004301200@unknown@formal@none@1@S@Today, the Italian language continues to be used as a ⌊>lingua franca>⌋ in some environments.@@@@1@15@@oe@26-8-2013 1000004301210@unknown@formal@none@1@S@Within the ⌊>Catholic church>⌋ Italian is known by a large part of the ecclesiastic hierarchy, and is used in substitution of ⌊>Latin>⌋ in some official documents.@@@@1@26@@oe@26-8-2013 1000004301220@unknown@formal@none@1@S@The presence of Italian as the primary language in the ⌊>Vatican City>⌋ indicates not only use within the ⌊>Holy See>⌋, but also throughout the world where an episcopal seat is present.@@@@1@31@@oe@26-8-2013 1000004301230@unknown@formal@none@1@S@It continues to be used in ⌊>music>⌋ and ⌊>opera>⌋.@@@@1@9@@oe@26-8-2013 1000004301240@unknown@formal@none@1@S@Other examples where Italian is sometimes used as a means communication is in some sports (sometimes in ⌊>football>⌋ and ⌊>motorsports>⌋) and in the ⌊>design>⌋ and ⌊>fashion>⌋ industries.@@@@1@27@@oe@26-8-2013 1000004301250@unknown@formal@none@1@S@⌊=Dialects¦2=⌋@@@@1@1@@oe@26-8-2013 1000004301260@unknown@formal@none@1@S@In Italy, all ⌊>Romance languages>⌋ spoken as the vernacular, other than standard Italian and other unrelated, non-Italian languages, are termed "Italian dialects".@@@@1@22@@oe@26-8-2013 1000004301270@unknown@formal@none@1@S@Many Italian dialects are, in fact, historical languages in their own right.@@@@1@12@@oe@26-8-2013 1000004301280@unknown@formal@none@1@S@These include recognized language groups such as ⌊>Friulian>⌋, ⌊>Neapolitan>⌋, ⌊>Sardinian>⌋, ⌊>Sicilian>⌋, ⌊>Venetian>⌋, and others, and regional variants of these languages such as ⌊>Calabrian>⌋.@@@@1@23@@oe@26-8-2013 1000004301290@unknown@formal@none@1@S@The division between dialect and language has been used by scholars (such as by ⌊>Francesco Bruni>⌋) to distinguish between the languages that made up the Italian ⌊>koine>⌋, and those which had very little or no part in it, such as ⌊>Albanian>⌋, ⌊>Greek>⌋, ⌊>German>⌋, ⌊>Ladin>⌋, and ⌊>Occitan>⌋, which are still spoken by minorities.@@@@1@52@@oe@26-8-2013 1000004301300@unknown@formal@none@1@S@Dialects are generally not used for general mass communication and are usually limited to native speakers in informal contexts.@@@@1@19@@oe@26-8-2013 1000004301310@unknown@formal@none@1@S@In the past, speaking in dialect was often deprecated as a sign of poor education.@@@@1@15@@oe@26-8-2013 1000004301320@unknown@formal@none@1@S@Younger generations, especially those under 35 (though it may vary in different areas), speak almost exclusively standard Italian in all situations, usually with local accents and idioms.@@@@1@27@@oe@26-8-2013 1000004301330@unknown@formal@none@1@S@Regional differences can be recognized by various factors: the openness of vowels, the length of the consonants, and influence of the local dialect (for example, ⌊/annà/⌋ replaces ⌊/andare/⌋ in the area of Rome for the infinitive "to go").@@@@1@38@@oe@26-8-2013 1000004301340@unknown@formal@none@1@S@⌊=Sounds¦2=⌋@@@@1@1@@oe@26-8-2013 1000004301350@unknown@formal@none@1@S@⌊=Vowels¦3=⌋@@@@1@1@@oe@26-8-2013 1000004301360@unknown@formal@none@1@S@Italian has seven ⌊>vowel>⌋ phonemes: ⌊λ/a/¦/a/¦IPAλ⌋, ⌊λ/e/¦/e/¦IPAλ⌋, ⌊λ/ɛ/¦/ɛ/¦IPAλ⌋, ⌊λ/i/¦/i/¦IPAλ⌋, ⌊λ/o/¦/o/¦IPAλ⌋, ⌊λ/ɔ/¦/ɔ/¦IPAλ⌋, ⌊λ/u/¦/u/¦IPAλ⌋.@@@@1@12@@oe@26-8-2013 1000004301370@unknown@formal@none@1@S@The pairs ⌊λ/e/¦/e/¦IPAλ⌋-⌊λ/ɛ/¦/ɛ/¦IPAλ⌋ and ⌊λ/o/¦/o/¦IPAλ⌋-⌊λ/ɔ/¦/ɔ/¦IPAλ⌋ are seldom distinguished in writing and often confused, even though most varieties of Italian employ both phonemes consistently.@@@@1@23@@oe@26-8-2013 1000004301380@unknown@formal@none@1@S@Compare, for example: "perché" ⌊λ[perˈkɛ]¦[perˈkɛ]¦IPAλ⌋ (why, because) and "senti" ⌊λ[ˈsenti]¦[ˈsenti]¦IPAλ⌋ (you listen, you are listening, listen!), employed by some northern speakers, with ⌊λ[perˈke]¦[perˈke]¦IPAλ⌋ and ⌊λ[ˈsɛnti]¦[ˈsɛnti]¦IPAλ⌋, as pronounced by most central and southern speakers.@@@@1@33@@oe@26-8-2013 1000004301390@unknown@formal@none@1@S@As a result, the usage is strongly indicative of a person's origin.@@@@1@12@@oe@26-8-2013 1000004301400@unknown@formal@none@1@S@The standard (Tuscan) usage of these vowels is listed in vocabularies, and employed outside Tuscany mainly by specialists, especially actors and very few (television) journalists.@@@@1@25@@oe@26-8-2013 1000004301410@unknown@formal@none@1@S@These are truly different ⌊>phonemes>⌋, however: compare ⌊λ/ˈpeska/¦/ˈpeska/¦IPAλ⌋ (fishing) and ⌊λ/ˈpɛska/¦/ˈpɛska/¦IPAλ⌋ (peach), both spelled ⌊/pesca/⌋ .@@@@1@16@@oe@26-8-2013 1000004301420@unknown@formal@none@1@S@Similarly ⌊λ/ˈbotte/¦/ˈbotte/¦IPAλ⌋ ('barrel') and ⌊λ/ˈbɔtte/¦/ˈbɔtte/¦IPAλ⌋ ('beatings'), both spelled ⌊/botte/⌋, discriminate ⌊λ/o/¦/o/¦IPAλ⌋ and ⌊λ/ɔ/¦/ɔ/¦IPAλ⌋ .@@@@1@14@@oe@26-8-2013 1000004301430@unknown@formal@none@1@S@In general, vowel combinations usually pronounce each vowel separately.@@@@1@9@@oe@26-8-2013 1000004301440@unknown@formal@none@1@S@⌊>Diphthong>⌋s exist (e.g. ⌊/uo/⌋, ⌊/iu/⌋, ⌊/ie/⌋, ⌊/ai/⌋), but are limited to an unstressed ⌊/u/⌋ or ⌊/i/⌋ before or after a stressed vowel.@@@@1@22@@oe@26-8-2013 1000004301450@unknown@formal@none@1@S@The unstressed ⌊/u/⌋ in a diphthong approximates the English semivowel ⌊/w/⌋, the unstressed ⌊/i/⌋ approximates the semivowel ⌊/y/⌋.@@@@1@18@@oe@26-8-2013 1000004301460@unknown@formal@none@1@S@E.g.: ⌊/buono/⌋ ⌊λ[ˈbwɔno]¦[ˈbwɔno]¦IPAλ⌋, ⌊/ieri/⌋ ⌊λ[ˈjɛri]¦[ˈjɛri]¦IPAλ⌋.@@@@1@5@@oe@26-8-2013 1000004301470@unknown@formal@none@1@S@⌊>Triphthong>⌋s exist in Italian as well, like "contin⌊/uia/⌋mo" ("we continue").@@@@1@10@@oe@26-8-2013 1000004301480@unknown@formal@none@1@S@Three vowel combinations exist only in the form semiconsonant (⌊λ/j/¦/j/¦IPAλ⌋ or ⌊λ/w/¦/w/¦IPAλ⌋), followed by a vowel, followed by a desinence vowel (usually ⌊λ/i/¦/i/¦IPAλ⌋), as in ⌊/miei/⌋, ⌊/suoi/⌋, or two semiconsonants followed by a vowel, as the group ⌊/-uia-/⌋ exemplified above, or ⌊/-iuo-/⌋ in the word ⌊/aiuola/⌋.@@@@1@46@@oe@26-8-2013 1000004301490@unknown@formal@none@1@S@⌊=Mobile diphthongs¦3=⌋@@@@1@2@@oe@26-8-2013 1000004301500@unknown@formal@none@1@S@Many Latin words with a short ⌊/e/⌋ or ⌊/o/⌋ have Italian counterparts with a mobile diphthong (⌊/ie/⌋ and ⌊/uo/⌋ respectively).@@@@1@20@@oe@26-8-2013 1000004301510@unknown@formal@none@1@S@When the vowel sound is stressed, it is pronounced and written as a diphthong; when not stressed, it is pronounced and written as a single vowel.@@@@1@26@@oe@26-8-2013 1000004301520@unknown@formal@none@1@S@So Latin ⌊/focus/⌋ gave rise to Italian ⌊/fuoco/⌋ (meaning both "fire" and "optical focus"): when unstressed, as in ⌊/focale/⌋ ("focal") the "o" remains alone.@@@@1@24@@oe@26-8-2013 1000004301530@unknown@formal@none@1@S@Latin ⌊/pes/⌋ (more precisely its accusative form ⌊/pedem/⌋) is the source of Italian ⌊/piede/⌋ (foot): but unstressed "e" was left unchanged in ⌊/pedone/⌋ (pedestrian) and ⌊/pedale/⌋ (pedal).@@@@1@27@@oe@26-8-2013 1000004301540@unknown@formal@none@1@S@From Latin ⌊/iocus/⌋ comes Italian ⌊/giuoco/⌋ ("play", "game"), though in this case ⌊/gioco/⌋ is more common: ⌊/giocare/⌋ means "to play (a game)".@@@@1@22@@oe@26-8-2013 1000004301550@unknown@formal@none@1@S@From Latin ⌊/homo/⌋ comes Italian ⌊/uomo/⌋ (man), but also ⌊/umano/⌋ (human) and ⌊/ominide/⌋ (hominid).@@@@1@14@@oe@26-8-2013 1000004301560@unknown@formal@none@1@S@From Latin ⌊/ovum/⌋ comes Italian ⌊/uovo/⌋ (egg) and ⌊/ovaie/⌋ (ovaries).@@@@1@10@@oe@26-8-2013 1000004301570@unknown@formal@none@1@S@(The same phenomenon occurs in ⌊>Spanish>⌋: ⌊/juego/⌋ (play, game) and ⌊/jugar/⌋ (to play), ⌊/nieve/⌋ (snow) and ⌊/nevar/⌋ (to snow)).@@@@1@19@@oe@26-8-2013 1000004301580@unknown@formal@none@1@S@⌊=Consonants¦3=⌋@@@@1@1@@oe@26-8-2013 1000004301590@unknown@formal@none@1@S@Two symbols in a table cell denote the voiceless and voiced consonant, respectively.@@@@1@13@@oe@26-8-2013 1000004301600@unknown@formal@none@1@S@Nasals undergo assimilation when followed by a consonant, e.g., when preceding a velar (⌊λ/k/¦/k/¦IPAλ⌋ or ⌊λ/g/¦/g/¦IPAλ⌋) only ⌊λ[ŋ]¦[ŋ]¦IPAλ⌋ appears, etc.@@@@1@20@@oe@26-8-2013 1000004301610@unknown@formal@none@1@S@Italian has geminate, or double, consonants, which are distinguished by ⌊>length>⌋.@@@@1@11@@oe@26-8-2013 1000004301620@unknown@formal@none@1@S@Length is distinctive for all consonants except for ⌊λ/ʃ/¦/ʃ/¦IPAλ⌋, ⌊λ/ʦ/¦/ʦ/¦IPAλ⌋, ⌊λ/ʣ/¦/ʣ/¦IPAλ⌋, ⌊λ/ʎ/¦/ʎ/¦IPAλ⌋ ⌊λ/ɲ/¦/ɲ/¦IPAλ⌋, which are always geminate, and ⌊λ/z/¦/z/¦IPAλ⌋ which is always single.@@@@1@23@@oe@26-8-2013 1000004301630@unknown@formal@none@1@S@Geminate plosives and affricates are realised as lengthened closures.@@@@1@9@@oe@26-8-2013 1000004301640@unknown@formal@none@1@S@Geminate fricatives, nasals, and ⌊λ/l/¦/l/¦IPAλ⌋ are realized as lengthened ⌊>continuant>⌋s.@@@@1@10@@oe@26-8-2013 1000004301650@unknown@formal@none@1@S@The flap consonant ⌊λ/ɾː/¦/ɾː/¦IPAλ⌋ is typically dialectal, and it is called ⌊/erre moscia/⌋.@@@@1@13@@oe@26-8-2013 1000004301660@unknown@formal@none@1@S@The correct standard pronunciation is ⌊λ[r]¦[r]¦IPAλ⌋.@@@@1@6@@oe@26-8-2013 1000004301670@unknown@formal@none@1@S@Of special interest to the linguistic study of Italian is the ⌊/⌊>Gorgia Toscana>⌋/⌋, or "Tuscan Throat", the weakening or ⌊>lenition>⌋ of certain ⌊>intervocalic>⌋ consonants in ⌊>Tuscan dialect>⌋s.@@@@1@27@@oe@26-8-2013 1000004301680@unknown@formal@none@1@S@See also ⌊>Syntactic doubling>⌋.@@@@1@4@@oe@26-8-2013 1000004301690@unknown@formal@none@1@S@⌊=Assimilation¦3=⌋@@@@1@1@@oe@26-8-2013 1000004301700@unknown@formal@none@1@S@Italian has few diphthongs, so most unfamiliar diphthongs that are heard in foreign words (in particular, those beginning with vowel "a", "e", or "o") will be assimilated as the corresponding ⌊>diaeresis>⌋ (i.e., the vowel sounds will be pronounced separately).@@@@1@39@@oe@26-8-2013 1000004301710@unknown@formal@none@1@S@Italian ⌊>phonotactics>⌋ do not usually permit polysyllabic nouns and verbs to end with consonants, excepting poetry and song, so foreign words may receive extra terminal vowel sounds.@@@@1@27@@oe@26-8-2013 1000004301720@unknown@formal@none@1@S@⌊=Grammar¦2=⌋@@@@1@1@@oe@26-8-2013 1000004301730@unknown@formal@none@1@S@⌊=Common variations in the writing systems¦3=⌋@@@@1@6@@oe@26-8-2013 1000004301740@unknown@formal@none@1@S@Some variations in the usage of the writing system may be present in practical use.@@@@1@15@@oe@26-8-2013 1000004301750@unknown@formal@none@1@S@These are scorned by educated people, but they are so common in certain contexts that knowledge of them may be useful.@@@@1@21@@oe@26-8-2013 1000004301760@unknown@formal@none@1@S@⌊•⌊#Usage of ⌊/x/⌋ instead of ⌊/per/⌋: this is very common among teenagers and in ⌊>SMS>⌋ abbreviations.@@@@1@16@@oe@26-8-2013 1000004301770@unknown@formal@none@1@S@The multiplication operator is pronounced "per" in Italian, and so it is sometimes used to replace the word "per", which means "for"; thus, for example, "per te" ("for you") is shortened to "x te" (compare with English "4 U").@@@@1@39@@oe@26-8-2013 1000004301780@unknown@formal@none@1@S@Words containing ⌊/per/⌋ can also have it replaced with ⌊/x/⌋: for example, ⌊/perché/⌋ (both "why" and "because") is often shortened as ⌊/xché/⌋ or ⌊/xké/⌋ or ⌊/x' /⌋(see below).@@@@1@28@@oe@26-8-2013 1000004301790@unknown@formal@none@1@S@This usage might be useful to jot down quick notes or to fit more text into the low character limit of an SMS, but it is considered unacceptable in formal writing.#⌋@@@@1@31@@oe@26-8-2013 1000004301800@unknown@formal@none@1@S@⌊#Usage of foreign letters such as ⌊/k/⌋, ⌊/j/⌋ and ⌊/y/⌋, especially in nicknames and SMS language: ⌊/ke/⌋ instead of ⌊/che/⌋, ⌊/Giusy/⌋ instead of ⌊/Giuseppina/⌋ (or sometimes ⌊/Giuseppe/⌋).@@@@1@27@@oe@26-8-2013 1000004301810@unknown@formal@none@1@S@This is curiously mirrored in the usage of ⌊/i/⌋ in English names such as ⌊/Staci/⌋ instead of ⌊/Stacey/⌋, or in the usage of ⌊/c/⌋ in ⌊>Northern Europe>⌋ (⌊/Jacob/⌋ instead of ⌊/Jakob/⌋).@@@@1@31@@oe@26-8-2013 1000004301820@unknown@formal@none@1@S@The use of "k" instead of "ch" or "c" to represent a plosive sound is documented in some historical texts from before the standardization of the Italian language; however, that usage is no longer standard in Italian.@@@@1@37@@oe@26-8-2013 1000004301830@unknown@formal@none@1@S@Possibly because it is associated with the ⌊>German language>⌋, the letter "k" has sometimes also been used in satire to suggest that a political figure is an authoritarian or even a "pseudo-nazi": ⌊>Francesco Cossiga>⌋ was famously nicknamed ⌊/Kossiga/⌋ by rioting students during his tenure as minister of internal affairs.@@@@1@49@@oe@26-8-2013 1000004301840@unknown@formal@none@1@S@[Cf. the ⌊>politicized spelling ⌊/Amerika/⌋>⌋ in the USA.]#⌋@@@@1@8@@oe@26-8-2013 1000004301850@unknown@formal@none@1@S@⌊#Usage of the following abbreviations is limited to the electronic communications media and is deprecated in all other cases: ⌊∗nn∗⌋ instead of ⌊/non/⌋ (not), ⌊∗cmq∗⌋ instead of ⌊/comunque/⌋ (anyway, however), ⌊∗cm∗⌋ instead of ⌊/come/⌋ (how, like, as), ⌊∗d∗⌋ instead of ⌊/di/⌋ (of), ⌊∗(io/loro) sn∗⌋ instead of ⌊/(io/loro) sono/⌋ (I am/they are), ⌊∗(io) dv∗⌋ instead of ⌊/(io) devo/⌋ (I must/I have to) or instead of ⌊/dove/⌋ (where), ⌊∗(tu) 6∗⌋ instead of ⌊/(tu) sei/⌋ (you are).#⌋@@@@1@74@@oe@26-8-2013 1000004301860@unknown@formal@none@1@S@⌊#Inexperienced typists often replace accents with apostrophes, such as in ⌊/perche'/⌋ instead of ⌊/perché/⌋.@@@@1@14@@oe@26-8-2013 1000004301870@unknown@formal@none@1@S@Uppercase ⌊/⌊>È>⌋/⌋ is particularly rare, as it is absent from the ⌊>Italian keyboard layout>⌋, and is very often written as ⌊/E/⌋' (even though there are ⌊>several ways>⌋ of producing the uppercase È on a computer).@@@@1@35@@oe@26-8-2013 1000004301880@unknown@formal@none@1@S@This never happens in books or other professionally typeset material.#⌋•⌋@@@@1@10@@oe@26-8-2013 1000004301890@unknown@formal@none@1@S@⌊=Examples¦2=⌋@@@@1@1@@oe@26-8-2013 1000004301900@unknown@formal@none@1@S@⌊•⌊#Cheers: "Salute!"#⌋@@@@1@2@@oe@26-8-2013 1000004301910@unknown@formal@none@1@S@⌊#English: ⌊/inglese/⌋ ⌊λ/iŋˈglese/¦/iŋˈglese/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004301920@unknown@formal@none@1@S@⌊#Good-bye: ⌊/arrivederci/⌋ ⌊λ/arriveˈdertʃi/¦/arriveˈdertʃi/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004301930@unknown@formal@none@1@S@⌊#Hello: ⌊/⌊>ciao>⌋/⌋ ⌊λ/ˈtʃao/¦/ˈtʃao/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004301940@unknown@formal@none@1@S@⌊#Good day: ⌊/buon giorno/⌋ ⌊λ/bwɔnˈdʒorno/¦/bwɔnˈdʒorno/¦IPAλ⌋#⌋@@@@1@5@@oe@26-8-2013 1000004301950@unknown@formal@none@1@S@⌊#Good evening: ⌊/buona sera/⌋ ⌊λ/bwɔnaˈsera/¦/bwɔnaˈsera/¦IPAλ⌋#⌋@@@@1@5@@oe@26-8-2013 1000004301960@unknown@formal@none@1@S@⌊#Yes: ⌊/sì/⌋ ⌊λ/si/¦/si/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004301970@unknown@formal@none@1@S@⌊#No: ⌊/no/⌋ ⌊λ/nɔ/¦/nɔ/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004301980@unknown@formal@none@1@S@⌊#How are you? : Come stai ⌊λ/ˈkome ˈstai/¦/ˈkome ˈstai/¦IPAλ⌋ (informal); Come sta ⌊λ/ˈkome 'sta/¦/ˈkome 'sta/¦IPAλ⌋ (formal)#⌋@@@@1@16@@oe@26-8-2013 1000004301990@unknown@formal@none@1@S@⌊#Sorry: ⌊/mi dispiace/⌋ ⌊λ/mi disˈpjatʃe/¦/mi disˈpjatʃe/¦IPAλ⌋#⌋@@@@1@6@@oe@26-8-2013 1000004302000@unknown@formal@none@1@S@⌊#Excuse me: scusa ⌊λ/ˈskuza/¦/ˈskuza/¦IPAλ⌋ (informal); scusi ⌊λ/ˈskuzi/¦/ˈskuzi/¦IPAλ⌋ (formal)#⌋@@@@1@8@@oe@26-8-2013 1000004302010@unknown@formal@none@1@S@⌊#Again: ⌊/di nuovo/⌋, /⌊λdi ˈnwɔvo¦di ˈnwɔvo¦IPAλ⌋/; ⌊/ancora/⌋ /⌊λaŋˈkora¦aŋˈkora¦IPAλ⌋/#⌋@@@@1@8@@oe@26-8-2013 1000004302020@unknown@formal@none@1@S@⌊#Always: ⌊/sempre/⌋ /⌊λˈsɛmpre¦ˈsɛmpre¦IPAλ⌋/#⌋@@@@1@3@@oe@26-8-2013 1000004302030@unknown@formal@none@1@S@⌊#When: ⌊/quando/⌋ ⌊λ/ˈkwando/¦/ˈkwando/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302040@unknown@formal@none@1@S@⌊#Where: ⌊/dove/⌋ ⌊λ/'dove/¦/'dove/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302050@unknown@formal@none@1@S@⌊#Why/Because: ⌊/perché/⌋ ⌊λ/perˈke/¦/perˈke/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302060@unknown@formal@none@1@S@⌊#How: ⌊/come/⌋ ⌊λ/'kome/¦/'kome/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302070@unknown@formal@none@1@S@⌊#How much is it?: ⌊/quanto costa?/⌋@@@@1@6@@oe@26-8-2013 1000004302080@unknown@formal@none@1@S@⌊λ/ˈkwanto/¦/ˈkwanto/¦IPAλ⌋#⌋@@@@1@1@@oe@26-8-2013 1000004302090@unknown@formal@none@1@S@⌊#Thank you!: ⌊/grazie!/⌋@@@@1@3@@oe@26-8-2013 1000004302100@unknown@formal@none@1@S@⌊λ/ˈgrattsie/¦/ˈgrattsie/¦IPAλ⌋#⌋@@@@1@1@@oe@26-8-2013 1000004302110@unknown@formal@none@1@S@⌊#Bon appetit: ⌊/buon appetito/⌋ ⌊λ/ˌbwɔn appeˈtito/¦/ˌbwɔn appeˈtito/¦IPAλ⌋#⌋@@@@1@7@@oe@26-8-2013 1000004302120@unknown@formal@none@1@S@⌊#You're welcome!: ⌊/prego!/⌋@@@@1@3@@oe@26-8-2013 1000004302130@unknown@formal@none@1@S@⌊λ/ˈprɛgo/¦/ˈprɛgo/¦IPAλ⌋#⌋@@@@1@1@@oe@26-8-2013 1000004302140@unknown@formal@none@1@S@⌊#I love you: ⌊/Ti amo/⌋ ⌊λ/ti ˈamo/¦/ti ˈamo/¦IPAλ⌋, ⌊/Ti voglio bene/⌋ ⌊λ/ti ˈvɔʎʎo ˈbɛne/¦/ti ˈvɔʎʎo ˈbɛne/¦IPAλ⌋.@@@@1@16@@oe@26-8-2013 1000004302150@unknown@formal@none@1@S@The difference is that you use "Ti amo" when you are in a romantic relationship, "Ti voglio bene" in any other occasion (to parents, to relatives, to friends...)#⌋•⌋@@@@1@28@@oe@26-8-2013 1000004302160@unknown@formal@none@1@S@Counting to twenty:@@@@1@3@@oe@26-8-2013 1000004302170@unknown@formal@none@1@S@⌊•⌊#One: ⌊/uno/⌋ ⌊λ/ˈuno/¦/ˈuno/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302180@unknown@formal@none@1@S@⌊#Two: ⌊/due/⌋ ⌊λ/ˈdue/¦/ˈdue/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302190@unknown@formal@none@1@S@⌊#Three: ⌊/tre/⌋ ⌊λ/tre/¦/tre/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302200@unknown@formal@none@1@S@⌊#Four: ⌊/quattro/⌋ ⌊λ/ˈkwattro/¦/ˈkwattro/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302210@unknown@formal@none@1@S@⌊#Five: ⌊/cinque/⌋ ⌊λ/ˈʧiŋkwe/¦/ˈʧiŋkwe/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302220@unknown@formal@none@1@S@⌊#Six: ⌊/sei/⌋ ⌊λ/ˈsɛi/¦/ˈsɛi/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302230@unknown@formal@none@1@S@⌊#Seven: ⌊/sette/⌋ ⌊λ/ˈsɛtte/¦/ˈsɛtte/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302240@unknown@formal@none@1@S@⌊#Eight: ⌊/otto/⌋ ⌊λ/ˈɔtto/¦/ˈɔtto/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302250@unknown@formal@none@1@S@⌊#Nine: ⌊/nove/⌋ ⌊λ/ˈnɔve/¦/ˈnɔve/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302260@unknown@formal@none@1@S@⌊#Ten: ⌊/dieci/⌋ ⌊λ/ˈdjɛʧi/¦/ˈdjɛʧi/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302270@unknown@formal@none@1@S@⌊#Eleven: ⌊/undici/⌋ ⌊λ/ˈundiʧi/¦/ˈundiʧi/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302280@unknown@formal@none@1@S@⌊#Twelve: ⌊/dodici/⌋ ⌊λ/ˈdodiʧi/¦/ˈdodiʧi/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302290@unknown@formal@none@1@S@⌊#Thirteen: ⌊/tredici/⌋ ⌊λ/ˈtrediʧi/¦/ˈtrediʧi/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302300@unknown@formal@none@1@S@⌊#Fourteen: ⌊/quattordici/⌋ ⌊λ/kwat'tordiʧi/¦/kwat'tordiʧi/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302310@unknown@formal@none@1@S@⌊#Fifteen: ⌊/quindici/⌋ ⌊λ/ˈkwindiʧi/¦/ˈkwindiʧi/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302320@unknown@formal@none@1@S@⌊#Sixteen: ⌊/sedici/⌋ ⌊λ/ˈsediʧi/¦/ˈsediʧi/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302330@unknown@formal@none@1@S@⌊#Seventeen: ⌊/diciassette/⌋ ⌊λ/diʧas'sɛtte/¦/diʧas'sɛtte/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302340@unknown@formal@none@1@S@⌊#Eighteen: ⌊/diciotto/⌋ ⌊λ/di'ʧɔtto/¦/di'ʧɔtto/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302350@unknown@formal@none@1@S@⌊#Nineteen: ⌊/diciannove/⌋ ⌊λ/diʧan'nɔve/¦/diʧan'nɔve/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302360@unknown@formal@none@1@S@⌊#Twenty: ⌊/venti/⌋ ⌊λ/'venti/¦/'venti/¦IPAλ⌋#⌋•⌋@@@@1@3@@oe@26-8-2013 1000004302370@unknown@formal@none@1@S@The days of the week:@@@@1@5@@oe@26-8-2013 1000004302380@unknown@formal@none@1@S@⌊•⌊#Monday: ⌊/lunedì/⌋ ⌊λ/lune'di/¦/lune'di/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302390@unknown@formal@none@1@S@⌊#Tuesday: ⌊/martedì/⌋ ⌊λ/marte'di/¦/marte'di/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302400@unknown@formal@none@1@S@⌊#Wednesday: ⌊/mercoledì/⌋ ⌊λ/merkole'di/¦/merkole'di/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302410@unknown@formal@none@1@S@⌊#Thursday: ⌊/giovedì/⌋ ⌊λ/dʒove'di/¦/dʒove'di/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302420@unknown@formal@none@1@S@⌊#Friday: ⌊/venerdì/⌋ ⌊λ/vener'di/¦/vener'di/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302430@unknown@formal@none@1@S@⌊#Saturday: ⌊/sabato/⌋ ⌊λ/ˈsabato/¦/ˈsabato/¦IPAλ⌋#⌋@@@@1@3@@oe@26-8-2013 1000004302440@unknown@formal@none@1@S@⌊#Sunday: ⌊/domenica/⌋ ⌊λ/do'menika/¦/do'menika/¦IPAλ⌋#⌋•⌋@@@@1@3@@oe@26-8-2013