title: Digoxin

text: Cardiac glycosides, particularly digoxin, have been conventionally used for treatment of common cardiac problems, mainly heart failure and cardiac arrhythmias. The interaction of digoxin and cancer has also been studied. Despite existence of numerous preclinical studies that investigated the anticancer effects of digoxin, there are no solid and conclusive results so far.


title: Digoxin

text: Digoxin, as a cardiac glycoside, has a chemical structure basically similar to that of estradiol. Digoxin has the ability to bind oestrogen receptors, and therefore it has been proposed that it might increase the risk of oestrogen-sensitive breast and uterine cancers. A large Danish study found a complicated picture, with slightly increased risk of breast cancer amongst women taking digoxin, but better prognostic features. The Nurses' Health Study found a similar slight increase of risk.


title: Digoxin

text: Digoxin inhibits the proliferation of many cancerous cell lines "in vitro", but its relevance to cancer "in vivo" remains unclear.


title: Kullback–Leibler divergence

text: In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted formula_1, is a type of statistical distance: a measure of how one probability distribution "P" is different from a second, reference probability distribution "Q". A simple interpretation of the KL divergence of "P" from "Q" is the expected excess surprise from using "Q" as a model when the actual distribution is "P". While it is a distance, it is not a metric, the most familiar type of distance: it is not symmetric in the two distributions (in contrast to variation of information), and does not satisfy the triangle inequality. Instead, in terms of information geometry, it is a type of divergence, a generalization of squared distance, and for certain classes of distributions (notably an exponential family), it satisfies a generalized Pythagorean theorem (which applies to squared distances).


title: Kullback–Leibler divergence

text: In the simple case, a relative entropy of 0 indicates that the two distributions in question have identical quantities of information. Relative entropy is a nonnegative function of two distributions or measures. It has diverse applications, both theoretical, such as characterizing the relative (Shannon) entropy in information systems, randomness in continuous time-series, and information gain when comparing statistical models of inference; and practical, such as applied statistics, fluid mechanics, neuroscience and bioinformatics.


title: Kullback–Leibler divergence

text: Consider two probability distributions formula_2 and formula_3. Usually, formula_2 represents the data, the observations, or a measured probability distribution. Distribution formula_3 represents instead a theory, a model, a description or an approximation of formula_2. The Kullback–Leibler divergence is then interpreted as the average difference of the number of bits required for encoding samples of formula_2 using a code optimized for formula_3 rather than one optimized for formula_2. Note that the roles of formula_2 and formula_3 can be reversed in some situations where that is easier to compute, such as with the Expectation–maximization (EM) algorithm and Evidence lower bound (ELBO) computations.


title: Kullback–Leibler divergence

text: The relative entropy was introduced by Solomon Kullback and Richard Leibler in as "the mean information for discrimination between formula_12 and formula_13 per observation from formula_14", where one is comparing two probability measures formula_15, and formula_16 are the hypotheses that one is selecting from measure formula_15 (respectively). They denoted this by formula_18, and defined the "'divergence' between formula_14 and formula_20" as the symmetrized quantity formula_21, which had already been defined and used by Harold Jeffreys in 1948. In , the symmetrized form is again referred to as the "divergence", and the relative entropies in each direction are referred to as a "directed divergences" between two distributions; Kullback preferred the term discrimination information. The term "divergence" is in contrast to a distance (metric), since the symmetrized divergence does not satisfy the triangle inequality. Numerous references to earlier uses of the symmetrized divergence and to other statistical distances are given in . The asymmetric "directed divergence" has come to be known as the Kullback–Leibler divergence, while the symmetrized "divergence" is now referred to as the Jeffreys divergence.


title: Kullback–Leibler divergence

text: For discrete probability distributions formula_2 and formula_3 defined on the same probability space, formula_24, the relative entropy from formula_3 to formula_2 is defined to be


title: Kullback–Leibler divergence

text: In other words, it is the expectation of the logarithmic difference between the probabilities formula_2 and formula_3, where the expectation is taken using the probabilities formula_2.


title: Kullback–Leibler divergence

text: Relative entropy is defined so only if for all formula_32, formula_33 implies formula_34 (absolute continuity). Else it is often defined as formula_35, but the value formula_35 is possible even if formula_37 everywhere, provided that formula_24 is infinite. Analogous comments apply to the continuous and general measure cases defined below.


title: Kullback–Leibler divergence

text: Whenever formula_39 is zero the contribution of the corresponding term is interpreted as zero because


title: Kullback–Leibler divergence

text: For distributions formula_2 and formula_3 of a continuous random variable, relative entropy is defined to be the integral:


title: Kullback–Leibler divergence

text: More generally, if formula_2 and formula_3 are probability measures on a measurable space formula_50, and formula_2 is absolutely continuous with respect to formula_3, then the relative entropy from formula_3 to formula_2 is defined as


title: Kullback–Leibler divergence

text: where formula_56 is the Radon–Nikodym derivative of formula_2 with respect to formula_3,ie. the unique formula_3-almost everywhere defined function formula_60 on formula_24 such that formula_62 which exists because formula_2 is absolutely continuous with respect to formula_3. Also we assume the expression on the right-hand side exists. Equivalently (by the chain rule), this can be written as


title: Kullback–Leibler divergence

text: which is the entropy of formula_2 relative to formula_3. Continuing in this case, if formula_68 is any measure on formula_24 for which densities formula_44 and formula_45 with formula_72 and formula_73 exist (meaning that formula_2 and formula_3 are both absolutely continuous with respect to formula_68), then the relative entropy from formula_3 to formula_2 is given as


title: Kullback–Leibler divergence

text: Note that such a measure formula_68 for which densities can be defined always exists, since one can take formula_81 although in practice it will usually be one that in the context like counting measure for discrete distributions, or Lebesgue measure or a convenient variant thereof like Gaussian measure or the uniform measure on the sphere, Haar measure on a Lie group etc. for continuous distributions.


title: Kullback–Leibler divergence

text: The logarithms in these formulae are usually taken to base 2 if information is measured in units of bits, or to base formula_82 if information is measured in nats. Most formulas involving relative entropy hold regardless of the base of the logarithm.


title: Kullback–Leibler divergence

text: Various conventions exist for referring to formula_1 in words. Often it is referred to as the divergence "between" formula_2 and formula_3, but this fails to convey the fundamental asymmetry in the relation. Sometimes, as in this article, it may be described as the divergence of formula_2 "from" formula_3 or as the divergence "from" formula_3 "to" formula_2. This reflects the asymmetry in Bayesian inference, which starts "from" a prior formula_3 and updates "to" the posterior formula_2. Another common way to refer to formula_1 is as the relative entropy of formula_2 "with respect to" formula_3 or the information gain from formula_2 over formula_3.


title: Kullback–Leibler divergence

text: Kullback gives the following example (Table 2.1, Example 2.1). Let and be the distributions shown in the table and figure. is the distribution on the left side of the figure, a binomial distribution with formula_97 and formula_98. is the distribution on the right side of the figure, a discrete uniform distribution with the three possible outcomes formula_99 , , (i.e. formula_100), each with probability formula_101.


title: Kullback–Leibler divergence

text: Relative entropies formula_1 and formula_103 are calculated as follows. This example uses the natural log with base "e", designated to get results in nats (see units of information).


title: Kullback–Leibler divergence

text: In the field of statistics the Neyman-Pearson lemma states that the most powerful way to distinguish between the two distributions formula_2 and formula_3 based on an observation formula_108 (drawn from one of them) is through the log of the ratio of their likelihoods: formula_109. The KL divergence is the expected value of this statistic if formula_108 is actually drawn from formula_2. Kullback motivated the statistic as an expected log likelihood ratio.


title: Kullback–Leibler divergence

text: In the context of coding theory, formula_1 can be constructed by measuring the expected number of extra bits required to code samples from formula_2 using a code optimized for formula_3 rather than the code optimized for formula_2.


title: Kullback–Leibler divergence

text: In the context of machine learning, formula_1 is often called the information gain achieved if formula_2 would be used instead of formula_3 which is currently used. By analogy with information theory, it is called the "relative entropy" of formula_2 with respect to formula_3.


title: Kullback–Leibler divergence

text: Expressed in the language of Bayesian inference, formula_1 is a measure of the information gained by revising one's beliefs from the prior probability distribution formula_3 to the posterior probability distribution formula_2. In other words, it is the amount of information lost when formula_3 is used to approximate formula_2.


title: Kullback–Leibler divergence

text: In applications, formula_2 typically represents the "true" distribution of data, observations, or a precisely calculated theoretical distribution, while formula_3 typically represents a theory, model, description, or approximation of formula_2. In order to find a distribution formula_3 that is closest to formula_2, we can minimize the KL divergence and compute an information projection.


title: Kullback–Leibler divergence

text: While it is a statistical distance, it is not a metric, the most familiar type of distance, but instead it is a divergence. While metrics are symmetric and generalize "linear" distance, satisfying the triangle inequality, divergences are asymmetric and generalize "squared" distance, in some cases satisfying a generalized Pythagorean theorem. In general formula_1 does not equal formula_103, and the asymmetry is an important part of the geometry. The infinitesimal form of relative entropy, specifically its Hessian, gives a metric tensor that equals the Fisher information metric; see . Relative entropy satisfies a generalized Pythagorean theorem for exponential families (geometrically interpreted as dually flat manifolds), and this allows one to minimize relative entropy by geometric means, for example by information projection and in maximum likelihood estimation.


title: Kullback–Leibler divergence

text: Relative entropy is a special case of a broader class of statistical divergences called "f"-divergences as well as the class of Bregman divergences, and it is the only such divergence over probabilities that is a member of both classes.


title: Kullback–Leibler divergence

text: This is a special case of a much more general connection between financial returns and divergence measures.


title: Kullback–Leibler divergence

text: In information theory, the Kraft–McMillan theorem establishes that any directly decodable coding scheme for coding a message to identify one value formula_133 out of a set of possibilities formula_134 can be seen as representing an implicit probability distribution formula_135 over formula_134, where formula_137 is the length of the code for formula_133 in bits. Therefore, relative entropy can be interpreted as the expected extra message-length per datum that must be communicated if a code that is optimal for a given (wrong) distribution formula_3 is used, compared to using a code based on the true distribution formula_2: it is the "excess" entropy.


title: Kullback–Leibler divergence

text: where formula_142 is the cross entropy of formula_2 and formula_3, and formula_145 is the entropy of formula_2 (which is the same as the cross-entropy of P with itself).


title: Kullback–Leibler divergence

text: The relative entropy formula_1 can be thought of geometrically as a statistical distance, a measure of how far the distribution "Q" is from the distribution "P". Geometrically it is a divergence: an asymmetric, generalized form of squared distance. The cross-entropy formula_148 is itself such a measurement (formally a loss function), but it cannot be thought of as a distance, since formula_149 isn't zero. This can be fixed by subtracting formula_150 to make formula_1 agree more closely with our notion of distance, as the "excess" loss. The resulting function is asymmetric, and while this can be symmetrized (see ), the asymmetric form is more useful. See for more on the geometric interpretation.


title: Kullback–Leibler divergence

text: Arthur Hobson proved that relative entropy is the only measure of difference between probability distributions that satisfies some desired properties, which are the canonical extension to those appearing in a commonly used characterization of entropy. Consequently, mutual information is the only measure of mutual dependence that obeys certain related conditions, since it can be defined in terms of Kullback–Leibler divergence.


title: Kullback–Leibler divergence

text: In particular, if formula_155 and formula_73, then formula_157 formula_68-almost everywhere. The entropy formula_145 thus sets a minimum value for the cross-entropy formula_160, the expected number of bits required when using a code based on formula_3 rather than formula_2; and the Kullback–Leibler divergence therefore represents the expected number of extra bits that must be transmitted to identify a value formula_32 drawn from formula_134, if a code is used corresponding to the probability distribution formula_3, rather than the "true" distribution formula_2.


title: Kullback–Leibler divergence

text: The following result, due to Donsker and Varadhan, is known as Donsker and Varadhan's variational formula.


title: Kullback–Leibler divergence

text: Suppose that we have two multivariate normal distributions, with means formula_192 and with (non-singular) covariance matrices formula_193 If the two distributions have the same dimension, formula_194, then the relative entropy between the distributions is as follows:


title: Kullback–Leibler divergence

text: The logarithm in the last term must be taken to base "e" since all terms apart from the last are base-"e" logarithms of expressions that are either factors of the density function or otherwise arise naturally. The equation therefore gives a result measured in nats. Dividing the entire expression above by formula_196 yields the divergence in bits.


title: Kullback–Leibler divergence

text: In a numerical implementation, it is helpful to express the result in terms of the Cholesky decompositions formula_197 such that formula_198 and formula_199. Then with formula_200 and formula_201 solutions to the triangular linear systems formula_202, and formula_203,


title: Kullback–Leibler divergence

text: A special case, and a common quantity in variational inference, is the relative entropy between a diagonal multivariate normal, and a standard normal distribution (with zero mean and unit variance):


title: Kullback–Leibler divergence

text: While relative entropy is a statistical distance, it is not a metric on the space of probability distributions, but instead it is a divergence. While metrics are symmetric and generalize "linear" distance, satisfying the triangle inequality, divergences are asymmetric in general and generalize "squared" distance, in some cases satisfying a generalized Pythagorean theorem. In general formula_1 does not equal formula_103, and while this can be symmetrized (see ), the asymmetry is an important part of the geometry.


title: Kullback–Leibler divergence

text: It generates a topology on the space of probability distributions. More concretely, if formula_209 is a sequence of distributions such that


title: Kullback–Leibler divergence

text: Relative entropy is directly related to the Fisher information metric. This can be made explicit as follows. Assume that the probability distributions formula_2 and formula_3 are both parameterized by some (possibly multi-dimensional) parameter formula_215. Consider then two close by values of formula_216 and formula_217 so that the parameter formula_215 differs by only a small amount from the parameter value formula_219. Specifically, up to first order one has (using the Einstein summation convention)


title: Kullback–Leibler divergence

text: with formula_221 a small change of formula_215 in the formula_223 direction, and formula_224 the corresponding rate of change in the probability distribution. Since relative entropy has an absolute minimum 0 for formula_154, i.e. formula_226, it changes only to "second" order in the small parameters formula_227. More formally, as for any minimum, the first derivatives of the divergence vanish


title: Kullback–Leibler divergence

text: must be positive semidefinite. Letting formula_219 vary (and dropping the subindex 0) the Hessian formula_232 defines a (possibly degenerate) Riemannian metric on the parameter space, called the Fisher information metric.


title: Kullback–Leibler divergence

text: Another information-theoretic metric is variation of information, which is roughly a symmetrization of conditional entropy. It is a metric on the set of partitions of a discrete probability space.


title: Kullback–Leibler divergence

text: Many of the other quantities of information theory can be interpreted as applications of relative entropy to specific cases.


title: Kullback–Leibler divergence

text: The self-information, also known as the information content of a signal, random variable, or event is defined as the negative logarithm of the probability of the given outcome occurring.


title: Kullback–Leibler divergence

text: is the relative entropy of the probability distribution formula_239 from a Kronecker delta representing certainty that formula_240 — i.e. the number of extra bits that must be transmitted to identify formula_241 if only the probability distribution formula_239 is available to the receiver, not the fact that formula_240.


title: Kullback–Leibler divergence

text: is the relative entropy of the product formula_245 of the two marginal probability distributions from the joint probability distribution formula_246 — i.e. the expected number of extra bits that must be transmitted to identify formula_134 and formula_108 if they are coded using only their marginal distributions instead of the joint distribution. Equivalently, if the joint probability formula_246 "is" known, it is the expected number of extra bits that must on average be sent to identify formula_108 if the value of formula_134 is not already known to the receiver.


title: Kullback–Leibler divergence

text: is the number of bits which would have to be transmitted to identify formula_134 from formula_254 equally likely possibilities, "less" the relative entropy of the uniform distribution on the random variates of formula_134, formula_256, from the true distribution formula_257 — i.e. "less" the expected number of bits saved, which would have had to be sent if the value of formula_134 were coded according to the uniform distribution formula_256 rather than the true distribution formula_257. This definition of Shannon entropy forms the basis of E.T. Jaynes's alternative generalization to continuous distributions, the limiting density of discrete points (as opposed to the usual differential entropy), which defines the continuous entropy as


title: Kullback–Leibler divergence

text: is the number of bits which would have to be transmitted to identify formula_134 from formula_254 equally likely possibilities, "less" the relative entropy of the product distribution formula_266 from the true joint distribution formula_246 — i.e. "less" the expected number of bits saved which would have had to be sent if the value of formula_134 were coded according to the uniform distribution formula_256 rather than the conditional distribution formula_270 of formula_134 given formula_108.


title: Kullback–Leibler divergence

text: When we have a set of possible events, coming from the distribution , we can encode them (with a lossless data compression) using entropy encoding. This compresses the data by replacing each fixed-length input symbol with a corresponding unique, variable-length, prefix-free code (e.g.: the events (A, B, C) with probabilities p = (1/2, 1/4, 1/4) can be encoded as the bits (0, 10, 11)). If we know the distribution in advance, we can devise an encoding that would be optimal (e.g.: using Huffman coding). Meaning the messages we encode will have the shortest length on average (assuming the encoded events are sampled from ), which will be equal to Shannon's Entropy of (denoted as formula_273). However, if we use a different probability distribution () when creating the entropy encoding scheme, then a larger number of bits will be used (on average) to identify an event from a set of possibilities. This new (larger) number is measured by the cross entropy between and .


title: Kullback–Leibler divergence

text: The cross entropy between two probability distributions ( and ) measures the average number of bits needed to identify an event from a set of possibilities, if a coding scheme is used based on a given probability distribution , rather than the "true" distribution . The cross entropy for two distributions and over the same probability space is thus defined as follows.


title: Kullback–Leibler divergence

text: Under this scenario, relative entropies (kl-divergence) can be interpreted as the extra number of bits, on average, that are needed (beyond formula_273) for encoding the events because of using for constructing the encoding scheme instead of .


title: Kullback–Leibler divergence

text: In Bayesian statistics, relative entropy can be used as a measure of the information gain in moving from a prior distribution to a posterior distribution: formula_276. If some new fact formula_277 is discovered, it can be used to update the posterior distribution for formula_134 from formula_279 to a new posterior distribution formula_280 using Bayes' theorem:


title: Kullback–Leibler divergence

text: which may be less than or greater than the original entropy formula_283. However, from the standpoint of the new probability distribution one can estimate that to have used the original code based on formula_279 instead of a new code based on formula_285 would have added an expected number of bits:


title: Kullback–Leibler divergence

text: to the message length. This therefore represents the amount of useful information, or information gain, about formula_134, that has been learned by discovering formula_277.


title: Kullback–Leibler divergence

text: If a further piece of data, formula_289, subsequently comes in, the probability distribution for formula_32 can be updated further, to give a new best guess formula_291. If one reinvestigates the information gain for using formula_292 rather than formula_293, it turns out that it may be either greater or less than previously estimated:


title: Kullback–Leibler divergence

text: A common goal in Bayesian experimental design is to maximise the expected relative entropy between the prior and the posterior. When posteriors are approximated to be Gaussian distributions, a design maximising the expected relative entropy is called Bayes d-optimal.


title: Kullback–Leibler divergence

text: Relative entropy formula_299 can also be interpreted as the expected discrimination information for formula_12 over formula_301: the mean information per sample for discriminating in favor of a hypothesis formula_12 against a hypothesis formula_301, when hypothesis formula_12 is true. Another name for this quantity, given to it by I. J. Good, is the expected weight of evidence for formula_12 over formula_301 to be expected from each sample.


title: Kullback–Leibler divergence

text: The expected weight of evidence for formula_12 over formula_301 is not the same as the information gain expected per sample about the probability distribution formula_309 of the hypotheses,


title: Kullback–Leibler divergence

text: Either of the two quantities can be used as a utility function in Bayesian experimental design, to choose an optimal next question to investigate: but they will in general lead to rather different experimental strategies.


title: Kullback–Leibler divergence

text: On the entropy scale of "information gain" there is very little difference between near certainty and absolute certainty—coding according to a near certainty requires hardly any more bits than coding according to an absolute certainty. On the other hand, on the logit scale implied by weight of evidence, the difference between the two is enormous – infinite perhaps; this might reflect the difference between being almost sure (on a probabilistic level) that, say, the Riemann hypothesis is correct, compared to being certain that it is correct because one has a mathematical proof. These two different scales of loss function for uncertainty are "both" useful, according to how well each reflects the particular circumstances of the problem in question.


title: Kullback–Leibler divergence

text: The idea of relative entropy as discrimination information led Kullback to propose the Principle of (MDI): given new facts, a new distribution formula_311 should be chosen which is as hard to discriminate from the original distribution formula_312 as possible; so that the new data produces as small an information gain formula_313 as possible.


title: Kullback–Leibler divergence

text: For example, if one had a prior distribution formula_314 over formula_32 and formula_316, and subsequently learnt the true distribution of formula_316 was formula_318, then the relative entropy between the new joint distribution for formula_32 and formula_316, formula_321, and the earlier prior distribution would be:


title: Kullback–Leibler divergence

text: i.e. the sum of the relative entropy of formula_323 the prior distribution for formula_316 from the updated distribution formula_318, plus the expected value (using the probability distribution formula_318) of the relative entropy of the prior conditional distribution formula_327 from the new conditional distribution formula_328. (Note that often the later expected value is called the "conditional relative entropy" (or "conditional Kullback-Leibler divergence") and denoted by formula_329


title: Kullback–Leibler divergence

text: ) This is minimized if formula_330 over the whole support of formula_318; and we note that this result incorporates Bayes' theorem, if the new distribution formula_318 is in fact a δ function representing certainty that formula_316 has one particular value.


title: Kullback–Leibler divergence

text: MDI can be seen as an extension of Laplace's Principle of Insufficient Reason, and the Principle of Maximum Entropy of E.T. Jaynes. In particular, it is the natural extension of the principle of maximum entropy from discrete to continuous distributions, for which Shannon entropy ceases to be so useful (see "differential entropy"), but the relative entropy continues to be just as relevant.


title: Kullback–Leibler divergence

text: In the engineering literature, MDI is sometimes called the Principle of Minimum Cross-Entropy (MCE) or Minxent for short. Minimising relative entropy from formula_334 to formula_44 with respect to formula_334 is equivalent to minimizing the cross-entropy of formula_44 and formula_334, since


title: Kullback–Leibler divergence

text: which is appropriate if one is trying to choose an adequate approximation to formula_44. However, this is just as often "not" the task one is trying to achieve. Instead, just as often it is formula_334 that is some fixed prior reference measure, and formula_44 that one is attempting to optimise by minimising formula_343 subject to some constraint. This has led to some ambiguity in the literature, with some authors attempting to resolve the inconsistency by redefining cross-entropy to be formula_343, rather than formula_345.


title: Kullback–Leibler divergence

text: Surprisals add where probabilities multiply. The surprisal for an event of probability formula_44 is defined as formula_347. If formula_194 is formula_349 then surprisal is in formula_350nats, bits, or formula_351 so that, for instance, there are formula_254 bits of surprisal for landing all "heads" on a toss of formula_254 coins.


title: Kullback–Leibler divergence

text: Best-guess states (e.g. for atoms in a gas) are inferred by maximizing the "average surprisal" formula_354 (entropy) for a given set of control parameters (like pressure formula_2 or volume formula_356). This constrained entropy maximization, both classically and quantum mechanically, minimizes Gibbs availability in entropy units formula_357 where formula_358 is a constrained multiplicity or partition function.


title: Kullback–Leibler divergence

text: When temperature formula_359 is fixed, free energy (formula_360) is also minimized. Thus if formula_361 and number of molecules formula_254 are constant, the Helmholtz free energy formula_363 (where formula_364 is energy and formula_354 is entropy) is minimized as a system "equilibrates." If formula_359 and formula_2 are held constant (say during processes in your body), the Gibbs free energy formula_368 is minimized instead. The change in free energy under these conditions is a measure of available work that might be done in the process. Thus available work for an ideal gas at constant temperature formula_369 and pressure formula_370 is formula_371 where formula_372 and formula_373 (see also Gibbs inequality).


title: Kullback–Leibler divergence

text: More generally the work available relative to some ambient is obtained by multiplying ambient temperature formula_369 by relative entropy or "net surprisal" formula_375 defined as the average value of formula_376 where formula_377 is the probability of a given state under ambient conditions. For instance, the work available in equilibrating a monatomic ideal gas to ambient values of formula_378 and formula_369 is thus formula_380, where relative entropy


title: Kullback–Leibler divergence

text: The resulting contours of constant relative entropy, shown at right for a mole of Argon at standard temperature and pressure, for example put limits on the conversion of hot to cold as in flame-powered air-conditioning or in the unpowered device to convert boiling-water to ice-water discussed here. Thus relative entropy measures thermodynamic availability in bits.


title: Kullback–Leibler divergence

text: For density matrices formula_2 and formula_3 on a Hilbert space, the quantum relative entropy from formula_3 to formula_2 is defined to be


title: Kullback–Leibler divergence

text: In quantum information science the minimum of formula_387 over all separable states formula_3 can also be used as a measure of entanglement in the state formula_2.


title: Kullback–Leibler divergence

text: Just as relative entropy of "actual from ambient" measures thermodynamic availability, relative entropy of "reality from a model" is also useful even if the only clues we have about reality are some experimental measurements. In the former case relative entropy describes "distance to equilibrium" or (when multiplied by ambient temperature) the amount of "available work", while in the latter case it tells you about surprises that reality has up its sleeve or, in other words, "how much the model has yet to learn".


title: Kullback–Leibler divergence

text: Although this tool for evaluating models against systems that are accessible experimentally may be applied in any field, its application to selecting a statistical model via Akaike information criterion are particularly well described in papers and a book by Burnham and Anderson. In a nutshell the relative entropy of reality from a model may be estimated, to within a constant additive term, by a function of the deviations observed between data and the model's predictions (like the mean squared deviation) . Estimates of such divergence for models that share the same additive term can in turn be used to select among models.


title: Kullback–Leibler divergence

text: When trying to fit parametrized models to data there are various estimators which attempt to minimize relative entropy, such as maximum likelihood and maximum spacing estimators.


title: Kullback–Leibler divergence

text: which they referred to as the "divergence", though today the "KL divergence" refers to the asymmetric function (see for the evolution of the term). This function is symmetric and nonnegative, and had already been defined and used by Harold Jeffreys in 1948; it is accordingly called the Jeffreys divergence.


title: Kullback–Leibler divergence

text: This quantity has sometimes been used for feature selection in classification problems, where formula_2 and formula_3 are the conditional pdfs of a feature under two different classes. In the Banking and Finance industries, this quantity is referred to as Population Stability Index (PSI), and is used to assess distributional shifts in model features through time.


title: Kullback–Leibler divergence

text: which can be interpreted as the expected information gain about formula_134 from discovering which probability distribution formula_134 is drawn from, formula_2 or formula_3, if they currently have probabilities formula_393 and formula_400 respectively.


title: Kullback–Leibler divergence

text: formula_405 can also be interpreted as the capacity of a noisy information channel with two inputs giving the output distributions formula_2 and formula_3. The Jensen–Shannon divergence, like all "f"-divergences, is "locally" proportional to the Fisher information metric. It is similar to the Hellinger metric (in the sense that it induces the same affine connection on a statistical manifold).


title: Kullback–Leibler divergence

text: Furthermore, the Jensen-Shannon divergence can be generalized using abstract statistical M-mixtures relying on an abstract mean M.


title: Kullback–Leibler divergence

text: There are many other important measures of probability distance. Some of these are particularly connected with relative entropy. For example:


title: Kullback–Leibler divergence

text: Other notable measures of distance include the Hellinger distance, "histogram intersection", "Chi-squared statistic", "quadratic form distance", "match distance", "Kolmogorov–Smirnov distance", and "earth mover's distance".


title: Kullback–Leibler divergence

text: Just as "absolute" entropy serves as theoretical background for data "compression", "relative" entropy serves as theoretical background for data "differencing" – the absolute entropy of a set of data in this sense being the data required to reconstruct it (minimum compressed size), while the relative entropy of a target set of data, given a source set of data, is the data required to reconstruct the target "given" the source (minimum size of a patch).


title: Merseyside

text: Merseyside ( ) is a metropolitan and ceremonial county in North West England, with a population of 1.38 million. It encompasses both banks of the Mersey Estuary and comprises five metropolitan boroughs: Knowsley, St Helens, Sefton, Wirral and the city of Liverpool. Merseyside, which was created on 1 April 1974 as a result of the Local Government Act 1972, takes its name from the River Mersey and sits within the historic counties of Lancashire and Cheshire.


title: Merseyside

text: Merseyside spans of land. It borders the ceremonial counties of Lancashire (to the north-east), Greater Manchester (to the east), Cheshire (to the south and south-east) and the Irish Sea to the west. North Wales is across the Dee Estuary. There is a mix of high density urban areas, suburbs, semi-rural and rural locations in Merseyside, but overwhelmingly the land use is urban. It has a focused central business district, formed by Liverpool City Centre, but Merseyside is also a polycentric county with five metropolitan districts, each of which has at least one major town centre and outlying suburbs. The Liverpool Urban Area is the fifth most populous conurbation in England and dominates the geographic centre of the county, while the Birkenhead Urban Area dominates the Wirral Peninsula in the south.


title: Merseyside

text: In the 12 years following 1974, the county had a two-tier system of local government; district councils shared power with the Merseyside County Council. The county council was abolished in 1986 and so its districts (the metropolitan boroughs) are now effectively unitary authority areas. However, the metropolitan county continues to exist in law and as a geographic frame of reference, and several county-wide services are co-ordinated by authorities and joint-boards, such as Merseytravel (for public transport), Merseyside Fire and Rescue Service and the Merseyside Police (for law-enforcement); as a ceremonial county, Merseyside has a Lord Lieutenant and a High Sheriff. As the Lancashire county palatine boundaries remain the same as the historic boundaries, the High Sheriff of Merseyside, along with those of Lancashire and Greater Manchester are appointed "within the Duchy and County Palatine of Lancaster".


title: Merseyside

text: The boroughs of Merseyside are joined by the neighbouring borough of Halton in Cheshire to form the Liverpool City Region, which is a local enterprise partnership and combined authority area.


title: Merseyside

text: Merseyside is an amalgamation of 22 former local government districts from the former administrative counties of Lancashire, Cheshire and six autonomous county boroughs centred on Birkenhead, Bootle, Liverpool, Southport, St Helens and Wallasey.


title: Merseyside

text: Merseyside was designated as a "Special Review" area in the Local Government Act 1958, and the Local Government Commission for England started a review of this area in 1962, based around the core county boroughs of Liverpool, Bootle, Birkenhead and Wallasey. Further areas, including Widnes and Runcorn, were added to the Special Review Area by Order in 1965. Draft proposals were published in 1965, but the commission never completed its final proposals as it was abolished in 1966.


title: Merseyside

text: Instead, a Royal Commission was set up to review English local government entirely, and its report (known as the Redcliffe-Maud Report) proposed a much wider Merseyside metropolitan area covering southwest Lancashire and northwest Cheshire, extending as far south as Chester and as far north as the River Ribble. This would have included four districts: Southport/Crosby, Liverpool/Bootle, St Helens/Widnes and Wirral/Chester. In 1970 the Merseyside Passenger Transport Executive (which operates today under the "Merseytravel" brand) was set up, covering Liverpool, Sefton, Wirral and Knowsley, but excluding Southport and St Helens.


title: Merseyside

text: The Redcliffe-Maud Report was rejected by the incoming Conservative Party government, but the concept of a two-tier metropolitan area based on the Mersey area was retained. A White Paper was published in 1971. The Local Government Bill presented to Parliament involved a substantial trimming from the White Paper, excluding the northern and southern fringes of the area, excluding Chester, Ellesmere Port (and, unusually, including Southport, whose council had requested to be included). Further alterations took place in Parliament, with Skelmersdale being removed from the area, and a proposed district including St Helens and Huyton being subdivided into what are now the metropolitan boroughs of St Helens and Knowsley.


title: Merseyside

text: Merseyside was created on 1 April 1974 from areas previously part of the administrative counties of Lancashire and Cheshire, along with the county boroughs of Birkenhead, Wallasey, Liverpool, Bootle, and St Helens. Following the creation of Merseyside, Merseytravel expanded to take in St Helens and Southport.


title: Merseyside

text: Between 1974 and 1986 the county had a two-tier system of local government with the five boroughs sharing power with the Merseyside County Council. However, in 1986 the government of Margaret Thatcher abolished the county council along with all other metropolitan county councils, and so its boroughs are now effectively unitary authorities.


title: Merseyside

text: Merseyside is divided into two parts by the Mersey Estuary; the Wirral is located on the west side of the estuary, upon the Wirral Peninsula and the rest of the county is located on the east side of the estuary. The eastern part of Merseyside borders onto Lancashire to the north, Greater Manchester to the east, with both parts of the county bordering Cheshire to the south. The territory comprising the county of Merseyside previously formed part of the administrative counties of Lancashire (east of the River Mersey) and Cheshire (west of the River Mersey). The two parts are linked by the two Mersey Tunnels, the Wirral Line of Merseyrail, and the Mersey Ferry.


title: Merseyside

text: Merseyside contains green belt interspersed throughout the county, surrounding the Liverpool urban area, as well as across the Mersey in the Wirral area, with further pockets extending towards and surrounding Southport, as part of the western edge of the North West Green Belt. It was first drawn up from the 1950s. All the county's districts contain some portion of belt.


title: Merseyside

text: Ipsos MORI polls in the boroughs of Sefton and Wirral in the 2000s showed that in general, residents of these boroughs identified slightly more strongly to Merseyside than to Lancashire or Cheshire respectively, but their affinity to Merseyside was more likely to be "fairly strong" than "very strong".


title: Merseyside

text: Following the abolition of the county council some local services are run by joint-boards of the five metropolitan boroughs; these include the:


title: Merseyside

text: The Liverpool City Region Combined Authority, which includes the five boroughs and the Borough of Halton headed by a mayor, Steve Rotheram, elected in May 2017.


title: Merseyside

text: This is a chart of the trend of regional gross value added of Merseyside at current basic prices published (pp. 240–253) by "Office for National Statistics" with figures in millions of British Pounds Sterling.


title: Merseyside

text: Transport in Merseyside consists of travel by roads, rail, air and water. Motorways serving Merseyside include M53 motorway in Wirral, M57 motorway, M58 motorway and M62 motorway. Rail travel is provided by Merseyrail, Network Rail and Wirral Tramway (since 1995) with major stations at Liverpool Lime Street, Liverpool Central, Liverpool James Street and Birkenhead Hamilton Square.


title: Merseyside

text: Aviation and air travel is provided by Liverpool John Lennon Airport, the oldest provincial airport in the United Kingdom. Major cycling routes on the National Cycle Network (such as National Cycle Route 56 and National Cycle Route 62) pass through the region too such as New Brighton and the Wirral Way. Major bus companies are Stagecoach Merseyside and Arriva North West. Liverpool One bus station serves as a terminus for national coach travel.


title: Merseyside

text: Liverpool Cruise Terminal provides long-distance passenger cruises, Fred. Olsen Cruise Lines and Cruise & Maritime Voyages using the terminal to depart to Iceland, France, Spain and Norway.


title: Merseyside

text: Prince's Landing Stage, Pier Head, Liverpool serves Isle of Man Steam Packet Company summer service to the Isle of Man (and Mersey Ferries).


title: Merseyside

text: Twelve Quays, Birkenhead ferry port serves winter Isle of Man ferry service and Stena Line to Belfast, Northern Ireland.


title: Merseyside

text: The Port of Liverpool handles most commercial shipping, but several other ports on the Wirral peninsula, such as Great Float and Queen Elizabeth II Dock, operate too.


title: Merseyside

text: The Mersey Ferry has operated since the 1200s, currently between Seacombe, Woodside and Liverpool Pier Head. Leeds and Liverpool Canal and Manchester Ship Canal are the main canal systems.


title: Merseyside

text: Merseyside is host to several football league football clubs including Liverpool F.C., Everton F.C., Tranmere Rovers F.C. and Southport F.C. Golf courses include Royal Liverpool Golf Club, Royal Birkdale Golf Club and Southport and Ainsdale Golf Club. Cricket clubs include the historic Aigburth Cricket Ground, Liverpool. Aintree Motor Racing Circuit hosted the British Grand Prix. Aintree Racecourse hosts the Grand National and there is also Haydock Park Racecourse. Totally Wicked Stadium hosts Rugby League and Hoylake hosts sailing (such as Southport 24 Hour Race) and is Britain's premier location for sand yachting. A ski slope facility is found at The Oval (Wirral).


title: Old Henry (film)

text: Old Henry is a 2021 American Western film written and directed by Potsy Ponciroli. It stars Tim Blake Nelson as the titular character, a farmer who must protect his son from outlaws, with Scott Haze, Gavin Lewis, Trace Adkins, and Stephen Dorff in supporting roles. The film had its world premiere at the Venice Film Festival on September 7, 2021, and was theatrically released in the United States by Shout! Studios on October 1. It was critically acclaimed, with praise to the story, Ponciroli's direction, and Nelson's performance. The National Board of Review selected the film in its annual list of the of the year.


title: Old Henry (film)

text: Widower Henry and his son Wyatt live on a farm in Oklahoma Territory in 1906 near Henry's brother-in-law Al, with Wyatt chafing at their simple existence. After Henry and Wyatt find a lost horse with blood on the saddle, Henry goes to investigate and finds a near-dead man named Curry. Seeing that the man has a gunshot wound, a revolver and a satchel full of cash, he is hesitant at first, but decides to help Curry. He covers their tracks and brings Curry back to the farm, treating his injuries and removing the bullet. Henry uses the surgery as a chance to interrogate Curry, who claims to be a lawman and the sole survivor of a posse that confronted a gang of outlaws.


title: Old Henry (film)

text: Henry goes to fetch a doctor, and in the meantime, Wyatt sneaks into Henry's room and finds his documents, as well as a fine revolver and some bullets. Wyatt takes Curry's gun and goes target shooting outside, allowing Curry to escape. Curry overpowers Wyatt, but Henry returns just in time to intervene and ties Curry up again. Henry had turned back after spotting three men investigating the spot where he first found Curry, narrowly escaping being caught by them after he spied on them from a wheat field nearby.


title: Old Henry (film)

text: Soon after, the trio, led by a man named Ketchum, come to the farm in search of Curry. They claim to be lawmen from Woods County and that Curry is the outlaw, but arouse Henry's suspicions when Ketchum begins asking questions about Henry's own identity and family. Henry does not give up Curry, and the men leave after a tense standoff. That evening, Henry has a conversation with Curry in which Curry reveals detailed knowledge of people known to Henry, which leads Henry to trust his claims and undo some of his restraints. Curry then tells Henry about his experience as a young ranch hand who witnessed the death of Billy the Kid. The house is suddenly attacked by Duggan, one of Ketchum's men. After a game of cat-and-mouse in which Duggan crawls underneath the house to ambush them, Henry rousts him out with a shotgun and then strangles him in the mud as Wyatt watches.


title: Old Henry (film)

text: The next morning, Ketchum returns with the rest of his gang, greatly outnumbering Curry, Henry and Wyatt. Curry encourages Henry to surrender and turn him over, telling Henry that they should not die for his sake. However, Ketchum has captured Henry's brother-in-law Al and, when Henry refuses to surrender, shoots him in cold blood. Wyatt emerges, enraged, and opens fire, and he and Henry manage to duck back into the house. Henry goes into his room and retrieves his gear, saying "Keep your damn head down, you'll be alright" to Wyatt. Curry recognizes the phrase as something Billy the Kid said to him when he was a young boy and realizes that Henry is in fact Billy the Kid, who faked his own death with the help of Pat Garrett.


title: Old Henry (film)

text: Henry pretends to surrender, and then draws his revolver and shoots Ketchum in the face, killing several other outlaws before diving back into the house and slipping out of the back door. Whilst Curry and Wyatt hold off the remaining gang members, Henry stealthily eliminates several more until only Stilwell, the gang's tracker, is left. Stilwell pretends to surrender but tries to kill Henry with a throwing knife and is shot through the eye.


title: Old Henry (film)

text: Henry suddenly comes under fire as Ketchum emerges, revealing that the shot only mangled his cheek. They engage in a running battle in which both men are wounded, but eventually Ketchum runs out of bullets and Henry shoots him in the head. Returning to the house, Henry is about to bandage up the injured Curry when he spots a brand on Curry's arm. Curry shoots Henry in the stomach, admitting that he was a lawman but was corrupt and allied with Ketchum. He had attempted to betray Ketchum after realizing the outlaws were going to kill him once his usefulness had run out. Curry apologizes to Henry, but then boasts that he'll kill Billy the Kid.


title: Old Henry (film)

text: Wyatt overhears all this as he is fetching his father's shotgun, and he kills Curry from the doorway before Curry can execute Henry. Wyatt tries to help his father, but Henry tells him that it is too late. Henry speaks earnestly to his son, telling him that the world is changing, and Henry has no place in it anymore but that he hoped his son, who raising him had given his life some meaning, would now find a place for himself in it. He dies in Wyatt's arms. Wyatt buries his father next to his mother and leaves the farm along with the cash, two horses, and their few possessions.


title: Old Henry (film)

text: In an interview, Tim Blake Nelson said starring in the 2018 Western film "The Ballad of Buster Scruggs" taught him how to handle a gun, "I was working with guns every day for about five months to be able to do the pistol tricks." On December 15, 2020, Hideout Pictures and Shout! Studios announced a partnership to produce, finance, and distribute three Westerns, including "Old Henry" from writer and director Potsy Ponciroli. According to Nelson, he was heating up his food when he came across an email that offered him the title role. He told "GQ" that his initial response was to say, "Well, it happened. You've been offered a character that's described as old."


title: Old Henry (film)

text: During pre-production, Nelson spent six months researching how his character would sound and move. He then spent another six months working on the 100-page screenplay with Ponciroli and two months physically preparing his body to handle a gun, ride a horse, and get in shape to look like a farmer. Nelson's role in the film was confirmed on January 12, 2021. On his performance, he says he "wanted for Henry by the end of the movie to be vastly different from the character he was at the beginning of the movie, and for the audience to never be able to name a single moment where the transformation happens."


title: Old Henry (film)

text: Nelson feared the public would negatively compare his role as Henry to his performance as Buster Scruggs, characters he finds to be "opposites". He spoke with Ponciroli about the issue and the pair agreed the film would not feature gunspinning; the final product features one spin during the film's finale that serves as a "punctuation". On January 14, 2021, Stephen Dorff, Trace Adkins, Scott Haze, and Gavin Lewis joined the cast. Principal photography for "Old Henry" took place in Tennessee between January and March 2021.


title: Old Henry (film)

text: "Old Henry" had its world premiere out of competition at the Venice Film Festival on September 7, 2021. It was released in around 30 theaters in the United States on October 1, 2021. In New York, Steve Buscemi hosted a Q&A session with Nelson at the Quad Cinema on its opening day. On October 8, the film was released through video on demand. It became a sleeper hit on VOD, staying in the top ten on iTunes for two consecutive months following initial release.


title: Old Henry (film)

text: The film's plot and execution received generally positive reviews. From "TheWrap", Steve Pond said he wished parts of the film were "more expansive" but overall described it as a "beautiful elegy" with a finale that feels "just right." Writing for "The Hollywood Reporter", David Rooney described the direction of the film as a "well-crafted exercise in old-fashioned but durable genre tropes" that later "evolves into a satisfying reflection on the more complicated, somber realities behind the icons of the Wild West." In a negative review, "The Guardian" Xan Brooks found it to be too familiar to other Westerns and expressed doubt that the film should have been screened at the Venice Film Festival.


title: Old Henry (film)

text: Furthermore, Tim Blake Nelson's performance as the title character received praise. Rooney said Nelson was able to "communicate with pathos both the regret and the steely resolve behind every beady-eyed squint." "Variety" Owen Gleiberman wrote that the film was "built as a kind of pedestal for Nelson's performance."


title: Old Henry (film)

text: In December 2021, the National Board of Review selected the film in its annual list of the of the year.


title: Xanthan gum

text: Xanthan gum () is a polysaccharide with many industrial uses, including as a common food additive. It is an effective thickening agent, emulsifier, and stabilizer that prevents ingredients from separating. It can be produced from simple sugars using a fermentation process and derives its name from the species of bacteria used, "Xanthomonas campestris".


title: Xanthan gum

text: Xanthan gum was discovered by Allene Rosalind Jeanes and her research team at the United States Department of Agriculture, and brought into commercial production by CP Kelco under the trade name Kelzan in the early 1960s. It was approved for use in foods in 1968 and is accepted as a safe food additive in the USA, Canada, European countries, and many other countries, with E number E415, and CAS number 11138-66-2.


title: Xanthan gum

text: Xanthan gum derives its name from the species of bacteria used during the fermentation process, "Xanthomonas campestris".


title: Xanthan gum

text: In foods, xanthan gum is common in salad dressings and sauces. It helps to prevent oil separation by stabilizing the emulsion, although it is not an emulsifier. Xanthan gum also helps suspend solid particles, such as spices. Xanthan gum helps create the desired texture in many ice creams. Toothpaste often contains xanthan gum as a binder to keep the product uniform. Xanthan gum also helps thicken commercial egg substitutes made from egg whites, to replace the fat and emulsifiers found in yolks. It is also a preferred method of thickening liquids for those with swallowing disorders, since it does not change the color or flavor of foods or beverages at typical use levels. In gluten-free baking, xanthan gum is used to give the dough or batter the stickiness that would otherwise be achieved with gluten. In most foods it is used at concentrations of 0.5% or less. Xanthan gum is used in a wide range of food products, such as sauces, dressings, meat and poultry products, bakery products, confectionery products, beverages, dairy products, others.


title: Xanthan gum

text: In the oil industry, xanthan gum is used in large quantities to thicken drilling mud. These fluids carry the solids cut by the drilling bit to the surface. Xanthan gum provides great "low end" rheology. When circulation stops, the solids remain suspended in the drilling fluid. The widespread use of horizontal drilling and the demand for good control of drilled solids has led to its expanded use. It has been added to concrete poured underwater, to increase its viscosity and prevent washout.


title: Xanthan gum

text: In cosmetics, xanthan gum is used to prepare water gels. It is also used in oil-in-water emulsions to enhance droplet coalescence. Xanthan gum is under preliminary research for its potential uses in tissue engineering to construct hydrogels and scaffolds supporting three-dimensional tissue formation.


title: Xanthan gum

text: The viscosity of xanthan gum solutions decreases with higher shear rates. This is called shear thinning or pseudoplasticity. This means that a product subjected to shear, whether from mixing, shaking or chewing will thin. When the shear forces are removed, the food will thicken again. In salad dressing, the addition of xanthan gum makes it thick enough at rest in the bottle to keep the mixture fairly homogeneous, but the shear forces generated by shaking and pouring thins it, so it can be easily poured. When it exits the bottle, the shear forces are removed and it thickens again, so it clings to the salad.


title: Xanthan gum

text: The greater the ratio of xanthan gum added to a liquid, the thicker the liquid will become. An emulsion can be formed with as little as 0.1% (by weight). Increasing the amount of gum gives a thicker, more stable emulsion up to 1% xanthan gum. A teaspoon of xanthan gum weighs about 2.5 grams and brings one cup (250ml) of water to a 1% concentration.


title: Xanthan gum

text: To make a foam, 0.2–0.8% xanthan gum is typically used. Larger amounts result in larger bubbles and denser foam. Egg white powder (0.2–2.0%) with 0.1–0.4% xanthan gum yields bubbles similar to soap bubbles.


title: Xanthan gum

text: According to a 2017 safety review by a scientific panel of the European Food Safety Authority (EFSA), xanthan gum (European food additive number E 415) is extensively digested during intestinal fermentation, and causes no adverse effects, even at high intake amounts. The EFSA panel found no concern about genotoxicity from long-term consumption. The EFSA concluded that there is no safety concern for the general population when xanthan gum is consumed as a food additive.


title: Xanthan gum

text: In 2022, scientists found that a microbe from the family Ruminococcaceae was present in human stool samples, was capable of degrading xanthan gum, and appeared to be from the microbiome of people in industrialized countries.


title: Xanthan gum

text: Xanthan gum is produced by the fermentation of glucose and sucrose. The medium is well-aerated and stirred, and the xanthan polymer is produced extracellularly into the medium. After one to four days, the polymer is precipitated from the medium by the addition of isopropyl alcohol, and the precipitate is dried and milled to give a powder that is readily soluble in water or brine.


title: Xanthan gum

text: It is composed of pentasaccharide repeat units, comprising glucose, mannose, and glucuronic acid in the molar ratio 2:2:1.


title: Xanthan gum

text: A strain of "X. campestris" has been developed that will grow on lactose - which allows it to be used to process whey, a waste product of cheese production. This can produce 30 g/L of xanthan gum for every 40 g/L of whey powder. Whey-derived xanthan gum is commonly used in many commercial products, such as shampoos and salad dressings.


title: Xanthan gum

text: Synthesis originates from glucose as substrate for synthesis of the sugar nucleotides precursors UDP-glucose, UDP-glucuronate, and GDP-mannose that are required for building the pentasaccharide repeat unit. This links the synthesis of xanthan to carbohydrate metabolism. The repeat units are built up at undecaprenylphosphate lipid carriers that are anchored in the cytoplasmic membrane.


title: Xanthan gum

text: Specific glycosyltransferases sequentially transfer the sugar moieties of the nucleotide sugar xanthan precursors to the lipid carriers. Acetyl and pyruvyl residues are added as non-carbohydrate decorations. Mature repeat units are polymerized and exported in a way resembling the Wzy-dependent polysaccharide synthesis mechanism of Enterobacteriaceae. Products of the gum gene cluster drive synthesis, polymerization, and export of the repeat unit.


title: The vulture and the little girl

text: The vulture and the little girl, also known as "The Struggling Girl", is a photograph by Kevin Carter which first appeared in "The New York Times" on 26 March 1993. It is a photograph of a frail famine-stricken boy, initially believed to be a girl, who had collapsed in the foreground with a hooded vulture eyeing him from nearby. The child was reported to be attempting to reach a United Nations feeding center about a half mile away in Ayod, Sudan (now South Sudan), in March 1993, and to have survived the incident. The picture won the Pulitzer Prize for Feature Photography award in 1994. Carter took his own life four months after winning the prize. This image has also been the subject of many criticisms for being a pornography of poverty.


title: The vulture and the little girl

text: The Hunger Triangle, a name relief organisations used in the 1990s for the area defined by the southern Sudan communities Kongor, Ayod, and Waat, was dependent on UNESCO and other aid organisations to fight famine. Forty percent of the area's children under five years old were malnourished as of January 1993, and an estimated 10 to 13 adults died of starvation daily in Ayod alone. To raise awareness of the situation, Operation Lifeline Sudan invited photojournalists and others, previously excluded from entering the country, to report on conditions. In March 1993, the government began granting visas to journalists for a 24-hour stay with severe restrictions on their travel within the country, including government supervision at all times.


title: The vulture and the little girl

text: In March 1993, Robert Hadley, a former photographer and at this time the information officer for the UN Operation Lifeline Sudan, invited João Silva and Kevin Carter to come to Sudan and report on the famine in the south of the country, travelling into southern Sudan with the rebels. Silva saw this as a chance to work more as a war photographer in the future. He started the arrangements and secured assignments for the expenses of the travel. Silva told Carter about the offer and Carter was also interested in going. According to fellow war photographer Greg Marinovich, Carter saw the trip as an opportunity to fix some problems "he felt trapped in". To take photos in Sudan was an opportunity for a better career as freelancer, and Carter was apparently "on a high, motivated and enthusiastic about the trip". To pay for the travel, Carter secured some money from the Associated Press and others, but needed to borrow money from Marinovich, for commitments back at home too. Not known to Carter and Silva was all the time that the UN Operation Lifeline Sudan did have "great difficulties in securing funding for Sudan pancake", explains Marinovich. Marinovich wrote further: "The UN hoped to publish the famine… Without publicity to show the need, it was difficult for aid organisations to sustain funding". About the political differences and fighting "João and Kevin knew none of this – they just wanted to get in and shoot pictures".


title: The vulture and the little girl

text: Silva and Carter stopped in Nairobi on their way to Sudan. The new fighting in Sudan forced them to wait there for an unspecified period of time. Carter flew with the UN for one day to Juba in south Sudan to take photos of a barge, with food aid for the region, but soon the situation changed again. The UN received permission from a rebel group to fly food aid to Ayod. Rob Hadley was flying on a UN light plane in and invited Silva and Carter to fly with him to Ayod.


title: The vulture and the little girl

text: The next day, their light aircraft touched down in the tiny hamlet of Ayod with the cargo aircraft landing shortly afterwards. The residents of the hamlet had been looked after by the UN aid station for some time. Greg Marinovich and João Silva described that in the book "The Bang Bang Club", Chapter 10 "Flies and Hungry People". Marinovich wrote that the villagers were already waiting next to the runway to get the food as quickly as possible: "Mothers who had joined the throng waiting for food left their children on the sandy ground nearby." Silva and Carter separated to take pictures of both children and adults, both the living and dead, all victims of the catastrophic famine that had arisen through the war. Carter went several times to Silva to tell him about the shocking situation he had just photographed. Witnessing the famine affected him emotionally. Silva was searching for rebel soldiers who could take him to someone in authority and when he found some soldiers Carter joined him. The soldiers did not speak English, but one was interested in Carter's watch. Carter gave him his cheap wristwatch as a gift. The soldiers became their bodyguards and followed them for their protection.


title: The vulture and the little girl

text: To stay a week with the rebels they needed the permission of a rebel commander. Their plane was due to depart in an hour and without the permission to stay they would be forced to fly out. Again they separated and Silva went to the clinic complex to ask for the rebel commander and he was told the commander was in Kongor, South Sudan. This was good news for Silva, as "their little UN plane was heading there next". He left the clinic and went back to the runway, taking pictures of children and adults on his way. He came across a child lying on his face in the hot sun, and took a picture.


title: The vulture and the little girl

text: Carter saw Silva on the runway and told him, "You won't believe what I've just shot! … I was shooting this kid on her knees, and then changed my angle, and suddenly there was this vulture right behind her! … And I just kept shooting – shot lots of film!" Silva asked him where he shot the picture and was looking around to take a photo as well. Carter pointed to a place away. Then Carter told him that he had chased the vulture away. He told Silva he was shocked by the situation he had just photographed, saying, "I see all this, and all I can think of is Megan", his young daughter. A few minutes later they left Ayod for Kongor.


title: The vulture and the little girl

text: In 2011, the child's father revealed the child was actually a boy, Kong Nyong, and had been taken care of by the UN food aid station. Nyong had died in about 2007, of "fevers", according to his family.


title: The vulture and the little girl

text: In March 1993, "The New York Times" was seeking an image to illustrate a story by Donatella Lorch about the Sudan famine. Nancy Buirski, the newspaper's picture editor on the foreign desk, called Marinovich, who told her about "an image of a vulture stalking a starving child who had collapsed in the sand." Carter's photo was published in the March 26, 1993 edition. The caption read: "A little girl, weakened from hunger, collapsed recently along the trail to a feeding center in Ayod. Nearby, a vulture waited."


title: The vulture and the little girl

text: This first publication in "The New York Times" "caused a sensation", Marinovich wrote, adding, "It was being used in posters for raising funds for aid organisations. Papers and magazines around the world had published it, and the immediate public reaction was to send money to any humanitarian organisation that had an operation in Sudan."


title: The vulture and the little girl

text: Claiming responsible ethical behaviour of photographers, publishers and the viewers of such photographs of shocking scenes, cultural writer Susan Sontag wrote in her essay "Regarding the Pain of Others" (2003): "There is shame as well as shock in looking at the close-up of a real horror. Perhaps the only people with the right to look at images of suffering of this extreme order are those who could do something to alleviate it … or those who could learn from it. The rest of us are voyeurs, whether or not we mean to be."


title: The vulture and the little girl

text: Due to the public reaction and questions about the child's condition, "The New York Times" published a special editorial in its 30 March 1993 edition, which said in part, "A picture last Friday with an article about the Sudan showed a little Sudanese girl who had collapsed from hunger on the trail to a feeding centre in Ayod. A vulture lurked behind her. Many readers have asked about the fate of the girl. The photographer reports that she recovered enough to resume her trek after the vulture was chased away. It is not known whether she reached the centre."


title: The vulture and the little girl

text: Four months after being awarded the Pulitzer Prize for Feature Photography, Carter died of suicide by carbon monoxide poisoning on July 27, 1994, at age 33. Desmond Tutu, Archbishop Emeritus of Cape Town, South Africa, wrote of Carter, "And we know a little about the cost of being traumatized that drove some to suicide, that, yes, these people were human beings operating under the most demanding of conditions."


title: Italians

text: Italians (, ) are a Romance-speaking ethnic group native to the Italian geographical region and its neighboring insular territories. Italians share a common culture, history, ancestry and language. They are the heirs of three of the most important ancient civilizations: the ancient Greeks resident in Magna Graecia (southern Italy), the Etruscans of northern Italy, and the Romans, who assimilated the former two. Legally, Italian nationals are citizens of Italy, regardless of ancestry or nation of residence (in effect, however, Italian nationality is largely based on jus sanguinis) and may be distinguished from ethnic Italians in general or from people of Italian descent without Italian citizenship and ethnic Italians living in territories adjacent to the Italian peninsula without Italian citizenship. The Latin equivalent of the term Italian had been in use for natives of the geographical region since antiquity.


title: Italians

text: The majority of Italian nationals are native speakers of the country's official language, Italian, or a variety thereof, that is regional Italian. However, many of them also speak a regional or minority language native to Italy, the existence of which predates the national language. Although there is disagreement on the total number, according to UNESCO, there are approximately 30 languages native to Italy, although many are often misleadingly referred to as "Italian dialects".


title: Italians

text: Since 2017, in addition to the approximately 55 million Italians in Italy (91% of the Italian national population), Italian-speaking autonomous groups are found in neighboring nations; about a half million are in Switzerland, as well as in France, the entire population of San Marino. In addition, there are also clusters of Italian speakers in the former Yugoslavia, primarily in Istria, located between in modern Croatia and Slovenia (see: "Istrian Italians"), and Dalmatia, located in present-day Croatia and Montenegro (see: "Dalmatian Italians"). Due to the wide-ranging diaspora following Italian unification, World War I and World War II, (with over 5 million Italian citizens that live outside of Italy) over 80 million people abroad claim full or partial Italian ancestry. This includes about 60% of Argentina’s population ("Italian Argentines"), 1/3 of Uruguayans ("Italian Uruguayans"), 15% of Brazilians ("Italian Brazilians," the largest Italian community outside Italy), more than 18 million "Italian Americans", and people in other parts of Europe (e.g. "Italians in Germany, Italians in France" and "Italians in the United Kingdom"), the American Continent (such as "Italian Venezuelans", "Italian Canadians", "Italian Colombians" and Italians in Paraguay, among others), Australasia ("Italian Australians" and "Italian New Zealanders"), and to a lesser extent in the Middle East.


title: Italians

text: Italians have influenced and contributed to fields like arts and music, science, technology, fashion, cinema, cuisine, restaurants, sports, jurisprudence, banking and business. Furthermore, Italian people are generally known for their attachment to their locale, expressed in the form of either regionalism or municipalism.


title: Italians

text: Hypotheses for the etymology of the Latin name "Italia" are numerous. One is that it was borrowed via Greek from the Oscan "Víteliú" 'land of calves' ("cf." Lat "vitulus" "calf", Umb "vitlo" "calf"). Greek historian Dionysius of Halicarnassus states this account together with the legend that Italy was named after Italus, mentioned also by Aristotle and Thucydides.


title: Italians

text: According to Antiochus of Syracuse, the term Italy was used by the Greeks to initially refer only to the southern portion of the Bruttium peninsula corresponding to the modern province of Reggio and part of the provinces of Catanzaro and Vibo Valentia in Southern Italy. Nevertheless, by his time the larger concept of Oenotria and "Italy" had become synonymous and the name also applied to most of Lucania as well. According to Strabo's "Geographica", before the expansion of the Roman Republic, the name was used by Greeks to indicate the land between the Strait of Messina and the line connecting the Gulf of Salerno and Gulf of Taranto, corresponding roughly to the current region of Calabria. The Greeks gradually came to apply the name "Italia" to a larger region In addition to the "Greek Italy" in the south, historians have suggested the existence of an "Etruscan Italy" covering variable areas of central Italy.


title: Italians

text: The borders of Roman Italy are better established. Cato the Elder's "Origines", the first work of history composed in Latin, described Italy as the entire peninsula south of the Alps. According to Cato and several Roman authors, the Alps formed the "walls of Italy". In 264 BC, Roman Italy extended from the Arno and Rubicon rivers of the centre-north to the entire south. The northern area of Cisalpine Gaul was occupied by Rome in the 220s BC and became considered geographically and "de facto" part of Italy, but remained politically and "de jure" separated. It was legally merged into the administrative unit of Italy in 42 BC by the triumvir Octavian as a ratification of Julius Caesar's unpublished acts ("Acta Caesaris"). Under Emperor Diocletian the Roman region called "Italia" was further enlarged with the addition in 292 AD of the three big islands of the western Mediterranean Sea: Sicily (with the Maltese archipelago), Sardinia and Corsica, coinciding with the whole Italian geographical region. All its inhabitants were considered "Italic" and "Roman".


title: Italians

text: The Latin term "Italicus" was used to describe "a man of Italy" as opposed to a provincial. For example, Pliny the Elder notably wrote in a letter "Italicus es an provincialis"? meaning "are you an Italian or a provincial?".


title: Italians

text: The adjective "italianus", from which are derived the Italian (and also French and English) name of the Italians, is medieval and was used alternatively with Italicus during the early modern period.


title: Italians

text: After the fall of the Western Roman Empire, which was caused by the invasion of the Ostrogoths, the Kingdom of Italy was created. After the Lombard invasions, "Italia" was retained as the name for their kingdom, and for its successor kingdom within the Holy Roman Empire, which nominally lasted until 1806, although it had "de facto" disintegrated due to factional politics pitting the empire against the ascendant city republics in the 13th century.


title: Italians

text: The Italian peninsula was divided into a multitude of tribal or ethnic territory prior to the Roman conquest of Italy in the 3rd century BC. After a series of wars between Greeks and Etruscans, the Latins, with Rome as their capital, gained the ascendancy by 272 BC, and completed the conquest of the Italian peninsula by 218 BC.


title: Italians

text: This period of unification was followed by one of conquest in the Mediterranean, beginning with the First Punic War against Carthage. In the course of the century-long struggle against Carthage, the Romans conquered Sicily, Sardinia and Corsica. Finally, in 146 BC, at the conclusion of the Third Punic War, with Carthage completely destroyed and its inhabitants enslaved, Rome became the dominant power in the Mediterranean.


title: Italians

text: The process of Italian unification, and the associated Romanization, culminated in 88 BC, when, in the aftermath of the Social War, Rome granted its fellow Italian allies full rights in Roman society, extending Roman citizenship to all fellow Italic peoples.


title: Italians

text: From its inception, Rome was a republican city-state, but four famous civil conflicts destroyed the Roman Republic: Lucius Cornelius Sulla against Gaius Marius and his son (88–82 BC), Julius Caesar against Pompey (49–45 BC), Marcus Junius Brutus and Gaius Cassius Longinus against Mark Antony and Octavian (43 BC), and Mark Antony against Octavian.


title: Italians

text: Octavian, the final victor (31 BC), was accorded the title of Augustus by the Senate and thereby became the first Roman Emperor. Augustus created for the first time an administrative region called "Italia" with inhabitants called "Italicus populus", stretching from the Alps to Sicily: for this reason historians like Emilio Gentile called him "Father of Italians".


title: Italians

text: In the 1st century BC, "Italia" was still a collection of territories with different political statuses. Some cities, called "municipia", had some independence from Rome, while others, the "coloniae", were founded by the Romans themselves. Around 7 BC, Augustus divided Italy into eleven "regiones".


title: Italians

text: During the Crisis of the Third Century, the Roman Empire nearly collapsed under the combined pressures of invasions, military anarchy and civil wars, and hyperinflation. In 284, emperor Diocletian restored political stability. The importance of Rome declined, because the city was far from the troubled frontiers. The seats of the Caesars became Augusta Treverorum (on the River Rhine frontier) for Constantius Chlorus and Sirmium (on the River Danube frontier) for Galerius, who also resided at Thessaloniki. Under Diocletian, Italy became the "Dioecesis Italiciana", subdivided into thirteen provinces, now including Raetia.


title: Italians

text: Under Constantine the Great, Italy became the Praetorian prefecture of Italy ("praefectura praetoria Italiae"), and was subdivided into two dioceses. "Diocesis Italia annonaria" (Italy of the annona, governed from Milan) and "Diocesis Italia Suburbicaria" (Italy "under the government of the "urbs"", i.e. governed from Rome). Christianity became the Roman state religion in AD 380, under Emperor Theodosius I.


title: Italians

text: The last Western emperor, Romulus Augustulus, was deposed in 476 by a Germanic foederati general in Italy, Odoacer. His defeat marked the end of the Western Roman Empire, and the end of the political unification of Italy until the establishment of the modern Kingdom of Italy in 1861.


title: Italians

text: Odoacer ruled well for 13 years after gaining control of Italy in 476. Then he was attacked and defeated by Theodoric, the king of another Germanic tribe, the Ostrogoths. Theodoric and Odoacer ruled jointly until 493, when Theodoric murdered Odoacer. Theodoric continued to rule Italy with an army of Ostrogoths and a government that was mostly Italian. After the death of Theodoric in 526, the kingdom began to grow weak. By 553, emperor Justinian I expelled the Ostrogoths, and Italy was included into the Byzantine Empire under the Justinian dynasty.


title: Italians

text: Byzantine rule in much of Italy collapsed by 572 as a result of invasions by another Germanic tribe, the Lombards. Much of the peninsula was now politically dominated by the Kingdom of the Lombards; however, remnants of Byzantine control remained, especially in Southern Italy, where the Byzantine Empire retained control into the 11th century until the Norman conquest of Southern Italy. In addition to the Normans, Arabs conquered parts of Southern Italy in the 9th century, establishing an Emirate of Sicily that lasted until it was also eventually overtaken by the Normans in the 11th century. The subsequent interaction between Latin, Byzantine, Arab, and Norman cultures resulted in the formation of a Norman-Arab-Byzantine culture in Southern Italy.


title: Italians

text: During the 5th and 6th centuries, the popes increased their influence in both religious and political matters in Italy. It was usually the popes who led attempts to protect Italy from invasion or to soften foreign rule. For about 200 years the popes opposed attempts by the Lombards, who had captured most of Italy, to take over Rome as well. The popes finally defeated the Lombards with the aid of two Frankish kings, Pepin the Short and Charlemagne. Using land won for them by Pepin in 756, the popes established political rule in what were called the Papal States in central Italy.


title: Italians

text: The Lombards remained a threat to papal power, however, until they were crushed by Charlemagne in 774. Charlemagne added the Kingdom of the Lombards to his vast realm. In recognition of Charlemagne's power, and to cement the church's alliance with him, Charlemagne was crowned emperor of the Romans by Pope Leo III in 800. After Charlemagne's death in 814, his son Louis the Pious succeeded him. Louis divided the empire among his sons, and Frankish Italy became part of Middle Francia, extending as far south as Rome and Spoleto. This Kingdom of Italy became part of the Holy Roman Empire in the 10th century, while southern Italy was under the rule of the Lombard Principality of Benevento or of the Byzantine Empire, in the 12th century absorbed into the Kingdom of Sicily.


title: Italians

text: From the 11th century on, Italian cities began to grow rapidly in independence and importance. They became centres of political life, banking, and foreign trade. Some became wealthy, and many, including Florence, Rome, Genoa, Milan, Pisa, Siena and Venice, grew into nearly independent city-states and maritime republics. Each had its own foreign policy and political life. They all resisted, with varying degrees of success, the efforts of noblemen, emperors, and larger foreign powers to control them.


title: Italians

text: The emergence of identifiable Italian dialects from Vulgar Latin, and as such the possibility of a specifically "Italian" ethnic identity, has no clear-cut date, but began in roughly the 12th century. Modern standard Italian derives from the written vernacular of Tuscan writers of the 12th century. The recognition of Italian vernaculars as literary languages in their own right began with "De vulgari eloquentia", an essay written by Dante Alighieri at the beginning of the 14th century.


title: Italians

text: During the 14th and 15th centuries, some Italian city-states ranked among the most important powers of Europe. Venice, in particular, had become a major maritime power, and the city-states as a group acted as a conduit for goods from the Byzantine and Islamic empires. In this capacity, they provided great impetus to the developing Renaissance, began in Florence in the 14th century, and led to an unparalleled flourishing of the arts, literature, music, and science.


title: Italians

text: However, the city-states were often troubled by violent disagreements among their citizens. The most famous division was between the Guelphs and Ghibellines. The Guelphs supported supreme rule by the pope, and the Ghibellines favoured the emperor. City-states often took sides and waged war against each other. During the Renaissance, Italy became an even more attractive prize to foreign conquerors. After some city-states asked for outside help in settling disputes with their neighbours, King Charles VIII of France marched into Italy in 1494; he soon withdrew, showing that the Italian peninsula's delicate equilibrium could be taken advantage of. After the Italian Wars, Spain emerged as the dominant force in the region. Venice, Milan, and other city-states retained at least some of their former greatness during this period, as did Savoy-Piedmont, protected by the Alps and well defended by its vigorous rulers.


title: Italians

text: Italian explorers and navigators from the dominant maritime republics, eager to find an alternative route to the Indies in order to bypass the Ottoman Empire, offered their services to monarchs of Atlantic countries and played a key role in ushering the Age of Discovery and the European colonization of the Americas. The most notable among them were: Christopher Columbus (), colonizer in the name of Spain, who is credited with discovering the New World and the opening of the Americas for conquest and settlement by Europeans; John Cabot (), sailing for England, who was the first European to set foot in "New Found Land" and explore parts of the North American continent in 1497; Amerigo Vespucci, sailing for Portugal, who first demonstrated in about 1501 that the New World (in particular Brazil) was not Asia as initially conjectured, but a fourth continent previously unknown to people of the Old World (America is named after him); and Giovanni da Verrazzano, at the service of France, renowned as the first European to explore the Atlantic coast of North America between Florida and New Brunswick in 1524.


title: Italians

text: The French Revolution and Napoleon influenced Italy more deeply than they affected any other outside country of Europe. The French Revolution began in 1789 and immediately found supporters among the Italian people. The local Italian rulers, sensing danger in their own country, drew closer to the European kings who opposed France. After the French king was overthrown and France became a republic, secret clubs favouring an Italian republic were formed throughout Italy.


title: Italians

text: The armies of the French Republic began to move across Europe. In 1796, Napoleon Bonaparte led a French army into northern Italy and drove out the Austrian rulers. Once again, Italy was the scene of battle between the Habsburgs and the French. Wherever France conquered, Italian republics were set up, with constitutions and legal reforms. Napoleon made himself emperor in 1804, and part of northern and central Italy was unified under the name of the Kingdom of Italy, with Napoleon as king. The rest of northern and central Italy was annexed by France. Only Sicily, where the Bourbon king had taken refuge upon the French invasion of Naples, and the island of Sardinia, which had been ceded to the Alpine House of Savoy in 1720 and had remained under their rule ever since, were not under French control.


title: Italians

text: French domination lasted less than 20 years, and it differed from previous foreign control of the Italian peninsula. In spite of heavy taxation and frequent harshness, the French introduced representative assemblies and new laws that were the same for all parts of the country. For the first time since the days of ancient Rome, Italians of different regions used the same money and served in the same army. Many Italians began to see the possibility of a united Italy free of foreign control.


title: Italians

text: During the Napoleonic era, in 1797, the first official adoption of the Italian tricolour as a national flag by a sovereign Italian state, the Cispadane Republic, a Napoleonic sister republic of Revolutionary France, took place, on the basis of the events following the French Revolution (1789–1799) which, among its ideals, advocated the national self-determination. This event is celebrated by the Tricolour Day. The Italian national colours appeared for the first time on a tricolour cockade in 1789, anticipating by seven years the first green, white and red Italian military war flag, which was adopted by the Lombard Legion in 1796. The first red, white and green national flag of a sovereign Italian state was adopted on 7 January 1797, when the Fourteenth Parliament of the Cispadane Republic (1797), on the proposal of deputy Giuseppe Compagnoni, decreed "to make universal the ... standard or flag of three colours, green, white, and red ...": For having proposed the green, white and red tricolour flag, Giuseppe Compagnoni is considered the "father of the Italian flag".


title: Italians

text: After the Battle of Waterloo, the reaction set in with the Congress of Vienna allowed the restoration of many of the old rulers and systems under Austrian domination. The concept of nationalism continued strong, however, and sporadic outbreaks led by such inveterate reformers as Giuseppe Mazzini occurred in several parts of the peninsula down to 1848–49. In this context, in 1847, the first public performance of the song "Il Canto degli Italiani", the Italian national anthem since 1946, took place. "Il Canto degli Italiani", written by Goffredo Mameli set to music by Michele Novaro, is also known as the "Inno di Mameli", after the author of the lyrics, or "Fratelli d'Italia", from its opening line.


title: Italians

text: The unification of Italy was brought to a successful conclusion under the guidance of Camillo Benso, conte di Cavour, prime minister of Piedmont. Cavour managed to unite most of Italy under the headship of Victor Emmanuel II of the house of Savoy, and on 17 March 1861, the Kingdom of Italy was proclaimed with Victor Emmanuel II as king. Giuseppe Garibaldi, the popular republican hero of Italy, contributed much to this achievement with the Expedition of the Thousand and to the subsequent incorporation of the Papal States under the Italian monarch.


title: Italians

text: Cavour handed Savoy and Nice over to France at the Treaty of Turin, a decision that was the consequence of the Plombières Agreement, on 24 March 1860, an event that caused the Niçard exodus, which was the emigration of a quarter of the Niçard Italians to Italy.


title: Italians

text: Italian troops occupied Rome in 1870, and in July 1871, this formally became the capital of the kingdom. Pope Pius IX, a longtime rival of Italian kings, stated he had been made a "prisoner" inside the Vatican walls and refused to cooperate with the royal administration. Only in 1929 did the Roman Pope accept the unified Italy with Rome as capital.


title: Italians

text: World War I has been interpreted as completing the process of Italian unification, with the annexation of Trieste, Istria, Trentino-Alto Adige and Zara. After World War I, Italy emerged as one of the four great powers after the victory of the Allies.


title: Italians

text: In the decades following unification, Italy began creating colonies in Africa, and under Benito Mussolini's fascist regime conquered Ethiopia, founding the Italian Empire in 1936. The population of Italy grew to 45 million in 1940 and the economy, which had been based upon agriculture until that time, started its industrial development, mainly in northern Italy. World War II soon severely damaged Italy and destroyed its colonial power.


title: Italians

text: Between 1945 and 1948, the outlines of a new Italy began to appear. Victor Emmanuel III gave up the throne on 9 May 1946, and his son, Umberto II, became king. On 2 June Italy held its first free election after 20 years of Fascist rule (the so-called "Ventennio"). Italians chose a republic to replace the monarchy, which had been closely associated with Fascism. They elected a Constituent Assembly, which was formed by the representatives of all the anti-fascist forces that contributed to the defeat of Nazi and Fascist forces during the Italian Civil War, to prepare a new democratic constitution. The Assembly approved the new Italian constitution in 1947, which came into force on 1 January 1948.


title: Italians

text: Under the Treaty of Peace with Italy, 1947, Istria, Kvarner, most of the Julian March as well as the Dalmatian city of Zara was annexed by Yugoslavia causing the Istrian-Dalmatian exodus, which led to the emigration of between 230,000 and 350,000 of local ethnic Italians (Istrian Italians and Dalmatian Italians), the others being ethnic Slovenians, ethnic Croatians, and ethnic Istro-Romanians, choosing to maintain Italian citizenship.


title: Italians

text: In 1949 Italy became a member of NATO. The Marshall Plan helped to revive the Italian economy which, until the late 1960s, enjoyed a period of sustained economic growth commonly called the "Economic Miracle". In 1957, Italy was a founding member of the European Economic Community (EEC), which became the European Union (EU) in 1993.


title: Italians

text: Italy faced several terror attacks between 1992 and 1993 perpetrated by the Sicilian Mafia as a consequence of several life sentences pronounced during the "Maxi Trial", and of the new anti-mafia measures launched by the government. In 1992, two major dynamite attacks killed the judges Giovanni Falcone (23 May in the Capaci bombing) and Paolo Borsellino (19 July in the Via D'Amelio bombing). One year later (May–July 1993), tourist spots were attacked, such as the Via dei Georgofili in Florence, Via Palestro in Milan, and the Piazza San Giovanni in Laterano and Via San Teodoro in Rome, leaving 10 dead and 93 injured and causing severe damage to cultural heritage such as the Uffizi Gallery. The Catholic Church openly condemned the Mafia, and two churches were bombed and an anti-Mafia priest shot dead in Rome. Giovanni Falcone and Paolo Borsellino were named as heroes of the last 60 years in the 13 November 2006 issue of "Time".


title: Italians

text: Italy is considered one of the birthplaces of Western civilization and a cultural superpower. Italian culture is the culture of the Italians, a Romance ethnic group, and is incredibly diverse spanning the entirety of the Italian peninsula and the islands of Sardinia and Sicily. Italy has been the starting point of phenomena of international impact such as the Roman Republic, Roman Empire, the Roman Catholic Church, the Maritime republics, Romanesque art, Scholasticism, the Renaissance, the Age of Discovery, Mannerism, the Scientific revolution, the Baroque, Neoclassicism, the Risorgimento, Fascism, and European integration.


title: Italians

text: Italy also became a seat of great formal learning in 1088 with the establishment of the University of Bologna, the oldest university in continuous operation, and the first university in the sense of a higher-learning and degree-awarding institute, as the word "universitas" was coined at its foundation. Many other Italian universities soon followed. For example, the Schola Medica Salernitana, in southern Italy, was the first medical school in Europe. These great centres of learning presaged the "Rinascimento": the European Renaissance began in Italy and was fueled throughout Europe by Italian painters, sculptors, architects, scientists, literature masters and music composers. Italy continued its leading cultural role through the Baroque period and into the Romantic period, when its dominance in painting and sculpture diminished but the Italians re-established a strong presence in music.


title: Italians

text: Italian explorers and navigators in the 15th and 16th centuries left a perennial mark on human history with the modern "discovery of America", due to Christopher Columbus. In addition, the name of the American continents derives from the geographer Amerigo Vespucci's first name. Also noted, is explorer Marco Polo who travelled a great deal throughout the eastern world recording his travels.


title: Italians

text: The country boasts several world-famous cities. Rome was the ancient capital of the Roman Empire, seat of the Pope of the Catholic Church, capital of reunified Italy and artistic, cultural and cinematographic centre of world relevance. Florence was the heart of the Renaissance, a period of great achievements in the arts at the end of the Middle Ages. Other important cities include Turin, which used to be the capital of Italy, and is now one of the world's great centers of automobile engineering. Milan is the industrial and financial capital of Italy and one of the world's fashion capitals. Venice, former capital of a major financial and maritime power from the Middle Ages to the early modern period, with its intricate canal system attracts tourists from all over the world especially during the Venetian Carnival and the Biennale. Naples, with the largest historic city centre in Europe and the oldest continuously active public opera house in the world (Teatro di San Carlo). Bologna is the main transport hub of the country, as well as the home of a worldwide famous cuisine.


title: Italians

text: Due to comparatively late national unification, and the historical autonomy of the regions that comprise the Italian peninsula, many traditions and customs of the Italians can be identified by their regions of origin. Despite the political and social isolation of these regions, Italy's contributions to the cultural and historical heritage of the Western world remain immense. Famous elements of Italian culture are its opera and music, its iconic gastronomy and food, which are commonly regarded as amongst the most popular in the world, its cinema (with filmmakers such as Federico Fellini, Michelangelo Antonioni, Mario Monicelli, Sergio Leone, etc.), its collections of priceless works of art and its fashion (Milan and Florence are regarded as some of the few fashion capitals of the world).