title: Zoran Milanović

text: Due to the ongoing civil war in Syria, in February 2012 Milanović called on Croatian companies working in Syria to withdraw from the country. On 18 January 2013 Croatian Foreign Ministry declared that Croatia, as well as the entire European Union, recognizes the National Coalition for Syrian Revolutionary and Opposition Forces as the only "legitimate representatives of the aspirations of the Syrian people". In February 2013 Milanović announced that Croatia is withdrawing its troops from the Golan Heights that are participating in the UN's peacekeeping mission after it was reported that Croatia sold their old weapons to the Syrian opposition.


title: Zoran Milanović

text: When demonstrations and riots started in Bosnia and Herzegovina in 2014, Milanović visited Mostar, a city with a Croat majority, where the seat of HDZ BiH was damaged in the riots. Sarajevo criticized his move, saying he should have visited the capital first. Milanović later called the protest quasi-civic on ethnic and religious vertical. The Croatian Government refused to accept indictments from Sarajevo labeled as political due to unacceptable claims about the character of the Croat–Bosniak War.


title: Zoran Milanović

text: On 22 July 2015 a major scandal occurred during the arbitration procedure of the Croatian–Slovenian border dispute, when it was discovered that the Slovenian representative has been lobbying other judges to rule in Slovenia's favor. Three days later Milanović announced the withdrawal of Croatia from arbitration after a meeting with the leaders of parliamentary groups.


title: Zoran Milanović

text: Beginning on 16 September 2015, migrants and refugees from the Middle East, South Asia and Africa began entering Croatia from Serbia in large numbers after the construction of the Hungary-Serbia barrier. On 17 September Croatia closed its border with Serbia. After initial efforts to register all migrant entrances into Croatia, registration ceased on 18 September and migrants began to be transported toward Slovenia and Hungary. By 23 September 2015 over 40,000 had entered Croatia from Serbia, with main acceptance centers set up in Opatovac and Zagreb, while migrants were also held in Beli Manastir, Ilača, Tovarnik, Ježevo and Sisak. Milanović criticized Serbia for sending migrants only towards the Croatian border, while sparing Hungary and Romania and stated that his country "will not become a migrant hotspot". Tensions escalated between Serbia and Croatia and on 24 September Serbia banned imports from Croatia to protest against Croatia's decision to close the border to cargo, while Croatia responded by banning all Serbian-registered vehicles from entering the country. On 25 September Croatia lifted the blockade on its border and Serbia lifted its ban on imports from Croatia, but Milanović said that he is ready to block the border again if necessary. With winter approaching a new, more permanent refugee acceptance center was built in Slavonski Brod in late 2015.


title: Zoran Milanović

text: For the 2015 parliamentary election the Kukuriku Coalition changed its name to Croatia is Growing. It consists of three out of four original members: the Social Democratic Party, Croatian People's Party – Liberal Democrats (HNS-LD), Croatian Party of Pensioners (HSU), as well as three new ones: Croatian Labourists – Labour Party, Authentic Croatian Peasant Party (A-HSS) and Zagorje Party. Istrian Democratic Assembly left the coalition. The campaign of the Coalition, led by Milanović, was based on rhetoric against austerity measures and emphasizing the government's policies during its mandate.


title: Zoran Milanović

text: After 76 days of negotiations, the Patriotic Coalition and the Bridge of Independent Lists party formed the 13th Croatian Government with Tihomir Orešković as the new prime minister. Milanović formally handed over office to Orešković in the late hours of 22 January 2016, after a lengthy parliamentary debate on the new government's program and the subsequent vote of confidence.


title: Zoran Milanović

text: On 2 April 2016, elections were held for the party's leadership. Milanović's opposing candidate was Zlatko Komadina, the prefect of Primorje-Gorski Kotar County, who advocated for a "much more social democratic" SDP. Milanović was again re-elected president of SDP for the next four years.


title: Zoran Milanović

text: In July 2016, SDP, HNS-LD and HSU formed the "People's Coalition" () for the 2016 parliamentary election. They were joined by the Croatian Peasant Party (HSS), while the Croatian Labourists left the coalition.


title: Zoran Milanović

text: Leaked taped conversations from a meeting with representatives of veterans association, published on 24 and 25 August 2016 by Jutarnji list, in which Milanović made controversial statements against the neighboring countries of Serbia and Bosnia and Herzegovina, have caused criticism. While commenting on Serbia's accession to the EU and their law on universal jurisdiction for war crimes prosecution on the whole territory of former Yugoslavia, Milanović stated that the Serbian government was acting arrogantly, and that he was willing to block Serbia's EU accession negotiations and also adopt a special law which would allow Croatia to prosecute Serbian citizens who committed war crimes in Kosovo, adding that "Serbs want to be rulers of the Balkans, but are actually a handful of misery". While commenting on Bosnia and Herzegovina, Milanović stated that he wasn't "thrilled with the situation there" and complained that "there was no one he could talk to in Sarajevo", adding that he would like for Bosnia and Herzegovina to enter the EU even without all the preconditions being met, since "it's a country without law and order". In addition, he stated that he did not care about "Za dom spremni" salute but urged veterans not to use it because it is harmful to Croatia. Milanović's rhetoric during the 2016 electoral campaign was described by some observers as populist.


title: Zoran Milanović

text: The HDZ won a majority of seats in the parliament and formed a governing majority with Most, with HDZ leader Andrej Plenković becoming the new Prime Minister. Milanović announced that he would not run for another term as SDP president. On 26 November he was succeeded by Davor Bernardić as the president of SDP.


title: Zoran Milanović

text: After leaving politics, Milanović entered the consulting business and founded a consulting firm called EuroAlba Advisory. Since 2017, he was an advisor to Albanian Prime Minister Edi Rama, and president of the Diplomatic Council of the Dag Hammarskjöld University College of International Relations and Diplomacy.


title: Zoran Milanović

text: On 17 June 2019, Milanović confirmed that he will be running in the country's upcoming presidential election as SDP's candidate, with the campaign slogan "A president with character". While announcing his candidacy, Milanović said that he wanted to be the "president of a modern, progressive, inquisitive and open Croatia". The SDP main committee, as well as the HSS presidency, gave support to Milanović's bid for president. He was subsequently endorsed by several centre-left and centrist parties, including the HSU, PGS, NS-R, Democrats, IDS, HL, SU, Glas, MDS, SNAGA, and ZS.


title: Zoran Milanović

text: The first round of the election took place on 22 December 2019, with Milanović winning a plurality of 29.55% of the vote, ahead of Kolinda Grabar-Kitarović, who received 26.65% of the vote. Miroslav Škoro, who was running as an independent candidate, narrowly failed to reach the run-off election, managing to attract the support of 24.45% of voters. Therefore, this election marked the first time in Croatian history that the incumbent president did not receive the highest number of votes in the first round. Furthermore, Milanović attained both the lowest number of votes (562,779) and the lowest percentage of the vote of any winning candidate in the first round of a presidential election. Milanović received a plurality of the vote in Croatia's three largest cities: 33.02% in Zagreb, 30.79% in Split and 41.87% in Rijeka, and finished second (25.61%) in the fourth largest city, Osijek, which was won by Škoro (33.33%).


title: Zoran Milanović

text: A run-off election took place between Milanović and Grabar-Kitarović on 5 January 2020. Milanović won by a margin of close to 105,000 votes, thereby becoming the 5th President of Croatia since independence and the second president to have been officially nominated by the Social Democratic Party, after Ivo Josipović (2010–2015).


title: Zoran Milanović

text: Since his electoral victory, the newly elected president Zoran Milanović has made his first public appearance at an official event in Rijeka. There he attended the inaugural ceremony of Rijeka as the European Capital of Culture 2020. He met with the mayor Vojko Obersnel, commended the artists, the day-long programme and the opening ceremony. Milanović also praised the founders of punk rock in Rijeka and its 44-year-old tradition, stating that, "By the time when the Paraf were having their first concert, Sid Vicious hadn’t been singing in the Sex Pistols yet. These facts are of crucial importance regarding the cultural map of Europe".


title: Zoran Milanović

text: The inauguration of Milanović as the 5th president of Croatia took place on 18 February 2020. This was the first time that a presidential inauguration ceremony in Croatia was not held at St. Mark's Square in the city center of Zagreb, where the parliament and government buildings are located. Instead, Milanović decided to forgo the usual pomp of the ceremony by inviting merely some 40 guests, including state officials, former presidents, his family and members of his campaign team. This was also the first time that party leaders, diplomats and church dignitaries did not attend a presidential inauguration. The ceremony began with the performance of the national anthem by renowned Croatian pop and jazz diva Josipa Lisac, accompanied by pianist Zvjezdan Ružić, whose alternative rendition of Croatia's national anthem struck a different tone to the national anthem's usual sombre, bombastic delivery. This caused a lot of positive comments and negative reactions, which resulted in an unprecedented public debate about the national anthem and artistic freedom.


title: Zoran Milanović

text: On 24 February 2020, Milanović strongly condemned the burning of an effigy showing a same-sex couple with their child at a festival in Imotski, describing the incident as an “inhumane, totally unacceptable act”, demanded an apology from the organizers of the event and stated that they "deserve the strongest condemnation of the public because hatred for others, intolerance and inhumanity are not and will not be a Croatian tradition". He also demanded a reaction from the relevant institutions especially as the event was observed by many children who could witness the spreading of hatred and inciting to violence.


title: Zoran Milanović

text: Milanović made his first trip abroad as president on 27 February 2020 to Otočec ob Krki, Slovenia, where he met with president Borut Pahor. The two of them firmly concluded that they would do everything to improve and make the relations between the two countries excellent, pointing out that they had known each other for over 16 years. They also discussed about the border issue between the two countries, Croatian accession to the Schengen Area and about the border controls implemented by the Croatian government due to the COVID-19 pandemic. Milanović also addressed the European perspective of Montenegro, Albania and North Macedonia.


title: Zoran Milanović

text: During the summer he visited Montenegro and met with president Milo Đukanović. He also canceled his planned trip to Russia, where president Vladimir Putin invited him to attend the 2020 Victory Day parade. In September and October, he got involved in a verbal confrontation with a number of prominent Croatian politicians, political analysts and journalists, including the prime minister Andrej Plenković. He voiced his opposition to lockdown and curfew, as he said he would arrest and put in a police van those wanting curfew and lockdown.


title: Zoran Milanović

text: In January 2021, he refused to participate in a ceremony commemorating the 1993 Operation Maslenica because the Croatian Defence Forces′ symbols were to be displayed.


title: Zoran Milanović

text: In September 2021, Milanović publicly voiced his opinion that Bunjevci are Croatians. The national council of Bunjevci responded harshly to his statements, stating that Bunjevci had been living in Subotica for 350 years and that the difference between Bunjevci and Croats was clearly attested by historical sources.


title: Zoran Milanović

text: In November 2021, Austria′s foreign ministry summoned the Croatian ambassador in Vienna, Daniel Glunčić, to give an explanation, after Milanović compared the lockdown in Austria to the methods employed in the era of Nazism.


title: Zoran Milanović

text: In December 2021, Milanović criticised prime minister Plenković’s visit to Ukraine made at the start of a new escalation of the crisis over Ukraine calling it “plain charlatanism”. The prime minister responded by saying that the government sought to maintain good relations with Russia too.


title: Zoran Milanović

text: Harsh reaction from Ukraine′s government followed Milanović′s statements made on 25 January 2022 about Ukraine being not fit to join NATO as well the country being corrupt and Russia deserving to be given a way to have its security demands met. Milanović also referred to the 2014 Maidan Revolution in Ukraine as a "coup d'état". The foreign ministry of Ukraine summoned Croatian ambassador Anica Djamić, whereafter the ministry issued a comment that said, "[...] Zoran Milanović's statements retransmit Russian propaganda narratives, do not correspond to Croatia's consistent official position in support of Ukraine's sovereignty and territorial integrity, harm bilateral relations and undermine unity within the EU and NATO in the face of current security threats in Europe. The Ministry of Foreign Affairs of Ukraine demands a public refutation of these insulting statements by the President of Croatia, as well as non-repetition in the future." The same day, he was included in the blacklist of Myrotvorets. Russia′s pro-government media outlets gave Milanović′s pronouncements much publicity, presenting them as a sign of a split in the ranks of the EU and NATO and predicting that other EU leaders would follow suit. Croatia′s prime minister Plenković reacted by saying that on hearing Milanović′s statements he thought it was being said "by some Russian official"; he also offered apologies to Ukraine and reiterated that Croatia supported Ukraine′s territorial integrity. In an interview with the RTL television network shortly after, Milanović refused to apologise and re-affirmed his stance on Ukraine and went on to say that he thought that prime minister Andrej Plenković "behaved like an agent of Ukraine". On 1 March 2022, Milanović stated: "one has to be concerned when Ukraine threatens to use nuclear weapons, or when Russia threatens to use nuclear weapons."


title: Zoran Milanović

text: On 1 February 2022, as the UK defence secretary Ben Wallace was in Zagreb for a meeting with his Croatian counterpart, Mario Banožić, to discuss the security situation caused by the crisis over Ukraine, Milanović told the press he thought Britain was “misleading Ukraine, inciting it, and holding it hostage to the relationship between London, which ha[d] become a second-order power, and Washington”; he also said Ukraine would "not make itself happy if it listen[ed] to London" and voiced his opinion that the EU could not enjoy stability without settlement with Russia. Shortly after, former Russian ambassador to Croatia Anvar Azimov welcomed "the reasonable statements of president Zoran Milanović about Ukraine", while Croatian weekly "Globus" opined that Milanović proved to be the only statesman in the EU and NATO, who "so openly demonstrated his acceptance of Russia, relativised its actions, and criticised America, Britain and other NATO allies for the current tensions". When being asked by journalists about Bucha massacre, Milanović responded: That is far away, I know nothing about that. The Russians withdrew. What was found there, who found it, from Croatian experience, don't ask me about that, be careful." On the same occasion, he said that Ukraine isn't a democratic state "otherwise they would [already] start negotiations with the EU or had some status". On 10 June Milanović again commented the War in Ukraine by saying: "Zelenskyy's words lead to defeat, once Russian boot arrives somewhere, it never leaves. It is a powerful military force. Russia is not like us, they are not a democracy. As an enemy, they are indestructible." In September 2022, Milanović said that EU's policy towards Ukraine is "stupid" and not in interest of Croatia, nor Germany. He went on to say that: "we're currently watching how Russia is mincing Ukraine with very small number of soldiers". He further said that West for 8 years couldn't tell Ukraine to respect its peace treaty with Russia.


title: Zoran Milanović

text: In the aftermath of Tu-141 drone crash in Zagreb, Milanović issued the order to ban NATO's aircraft flights over Zagreb and other Croatian cities, claiming that the flights "disturb the citizens". By doing so, he continued his conflict with prime minister Plenković, who said that these flights are supposed to send the message of "strategic partnership and safety of Croatian citizens". After EU announced the possibility of training Ukrainian troops on its territory, including in Croatia, Milanović announced blocking this decision because, according to him that would bring the war to Croatia.


title: Zoran Milanović

text: Milanovic, with his wife, attended the state funeral of Queen Elizabeth II in Westminster Abbey, London, on 19 September, 2022.


title: Zoran Milanović

text: In April 2022, Milanović suggested blocking Finnish and Swedish accession to NATO, until the electoral law in Bosnia and Herzegovina, which allows Bosniaks the option of electing a Croat member of the Presidency and Croat representatives in the House of Peoples of the Federation of Bosnia and Herzegovina, is changed. He went on to say that he will label every MP in Croatian Sabor who refuses to vote against expansion of NATO as a national traitor. After Finland's foreign minister Pekka Haavisto stated that his country was shocked by Milanović's statements, Milanović responded by saying: “Welcome to the club, mister foreign minister. We have been shocked for several years already by your ignorance and rudeness”.


title: Zoran Milanović

text: However, the Finnish Minister for European Affairs and Ownership Steering Tytti Tuppurainen later commented that, although the citizens of Finland were confused by Milanović's statements, Finland understands the Croatian concern about the reforms of the electoral law in Bosnia and Herzegovina and that Finland supports the international efforts regarding the changes of the electoral law. Despite his earlier rhetoric, Milanović did not veto Finnish and Swedish NATO accession at the 2022 NATO Madrid summit.


title: Linear discriminant analysis

text: Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.


title: Linear discriminant analysis

text: LDA is closely related to analysis of variance (ANOVA) and regression analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements. However, ANOVA uses categorical independent variables and a continuous dependent variable, whereas discriminant analysis has continuous independent variables and a categorical dependent variable ("i.e." the class label). Logistic regression and probit regression are more similar to LDA than ANOVA is, as they also explain a categorical variable by the values of continuous independent variables. These other methods are preferable in applications where it is not reasonable to assume that the independent variables are normally distributed, which is a fundamental assumption of the LDA method.


title: Linear discriminant analysis

text: LDA is also closely related to principal component analysis (PCA) and factor analysis in that they both look for linear combinations of variables which best explain the data. LDA explicitly attempts to model the difference between the classes of data. PCA, in contrast, does not take into account any difference in class, and factor analysis builds the feature combinations based on differences rather than similarities. Discriminant analysis is also different from factor analysis in that it is not an interdependence technique: a distinction between independent variables and dependent variables (also called criterion variables) must be made.


title: Linear discriminant analysis

text: LDA works when the measurements made on independent variables for each observation are continuous quantities. When dealing with categorical independent variables, the equivalent technique is discriminant correspondence analysis.


title: Linear discriminant analysis

text: Discriminant analysis is used when groups are known a priori (unlike in cluster analysis). Each case must have a score on one or more quantitative predictor measures, and a score on a group measure. In simple terms, discriminant function analysis is classification - the act of distributing things into groups, classes or categories of the same type.


title: Linear discriminant analysis

text: The original dichotomous discriminant analysis was developed by Sir Ronald Fisher in 1936. It is different from an ANOVA or MANOVA, which is used to predict one (ANOVA) or multiple (MANOVA) continuous dependent variables by one or more independent categorical variables. Discriminant function analysis is useful in determining whether a set of variables is effective in predicting category membership.


title: Linear discriminant analysis

text: Consider a set of observations formula_1 (also called features, attributes, variables or measurements) for each sample of an object or event with known class formula_2. This set of samples is called the training set. The classification problem is then to find a good predictor for the class formula_2 of any sample of the same distribution (not necessarily from the training set) given only an observation formula_4.


title: Linear discriminant analysis

text: LDA approaches the problem by assuming that the conditional probability density functions formula_5 and formula_6 are both the normal distribution with mean and covariance parameters formula_7 and formula_8, respectively. Under this assumption, the Bayes optimal solution is to predict points as being from the second class if the log of the likelihood ratios is bigger than some threshold T, so that:


title: Linear discriminant analysis

text: Without any further assumptions, the resulting classifier is referred to as quadratic discriminant analysis (QDA).


title: Linear discriminant analysis

text: LDA instead makes the additional simplifying homoscedasticity assumption ("i.e." that the class covariances are identical, so formula_10) and that the covariances have full rank.


title: Linear discriminant analysis

text: This means that the criterion of an input formula_17 being in a class formula_2 is purely a function of this linear combination of the known observations.


title: Linear discriminant analysis

text: It is often useful to see this conclusion in geometrical terms: the criterion of an input formula_17 being in a class formula_2 is purely a function of projection of multidimensional-space point formula_17 onto vector formula_22 (thus, we only consider its direction). In other words, the observation belongs to formula_2 if corresponding formula_17 is located on a certain side of a hyperplane perpendicular to formula_22. The location of the plane is defined by the threshold c.


title: Linear discriminant analysis

text: The assumptions of discriminant analysis are the same as those for MANOVA. The analysis is quite sensitive to outliers and the size of the smallest group must be larger than the number of predictor variables.


title: Linear discriminant analysis

text: It has been suggested that discriminant analysis is relatively robust to slight violations of these assumptions, and it has also been shown that discriminant analysis may still be reliable when using dichotomous variables (where multivariate normality is often violated).


title: Linear discriminant analysis

text: Discriminant analysis works by creating one or more linear combinations of predictors, creating a new latent variable for each function. These functions are called discriminant functions. The number of functions possible is either formula_26 where formula_27 = number of groups, or formula_28 (the number of predictors), whichever is smaller. The first function created maximizes the differences between groups on that function. The second function maximizes differences on that function, but also must not be correlated with the previous function. This continues with subsequent functions with the requirement that the new function not be correlated with any of the previous functions.


title: Linear discriminant analysis

text: Given group formula_29, with formula_30 sets of sample space, there is a discriminant rule such that if formula_31, then formula_32. Discriminant analysis then, finds “good” regions of formula_30 to minimize classification error, therefore leading to a high percent correct classified in the classification table.


title: Linear discriminant analysis

text: An eigenvalue in discriminant analysis is the characteristic root of each function. It is an indication of how well that function differentiates the groups, where the larger the eigenvalue, the better the function differentiates. This however, should be interpreted with caution, as eigenvalues have no upper limit.


title: Linear discriminant analysis

text: Some suggest the use of eigenvalues as effect size measures, however, this is generally not supported. Instead, the canonical correlation is the preferred measure of effect size. It is similar to the eigenvalue, but is the square root of the ratio of "SS" and "SS". It is the correlation between groups and the function.


title: Linear discriminant analysis

text: Canonical discriminant analysis (CDA) finds axes ("k" − 1 canonical coordinates, "k" being the number of classes) that best separate the categories. These linear functions are uncorrelated and define, in effect, an optimal "k" − 1 space through the "n"-dimensional cloud of data that best separates (the projections in that space of) the "k" groups. See “Multiclass LDA” for details below.


title: Linear discriminant analysis

text: The terms "Fisher's linear discriminant" and "LDA" are often used interchangeably, although Fisher's original article actually describes a slightly different discriminant, which does not make some of the assumptions of LDA such as normally distributed classes or equal class covariances.


title: Linear discriminant analysis

text: Suppose two classes of observations have means formula_38 and covariances formula_39. Then the linear combination of features formula_40 will have means formula_41 and variances formula_42 for formula_43. Fisher defined the separation between these two distributions to be the ratio of the variance between the classes to the variance within the classes:


title: Linear discriminant analysis

text: This measure is, in some sense, a measure of the signal-to-noise ratio for the class labelling. It can be shown that the maximum separation occurs when


title: Linear discriminant analysis

text: Be sure to note that the vector formula_46 is the normal to the discriminant hyperplane. As an example, in a two dimensional problem, the line that best divides the two groups is perpendicular to formula_46.


title: Linear discriminant analysis

text: Generally, the data points to be discriminated are projected onto formula_46; then the threshold that best separates the data is chosen from analysis of the one-dimensional distribution. There is no general rule for the threshold. However, if projections of points from both classes exhibit approximately the same distributions, a good choice would be the hyperplane between projections of the two means, formula_49 and formula_50. In this case the parameter c in threshold condition formula_14 can be found explicitly:


title: Linear discriminant analysis

text: Otsu's method is related to Fisher's linear discriminant, and was created to binarize the histogram of pixels in a grayscale image by optimally picking the black/white threshold that minimizes intra-class variance and maximizes inter-class variance within/between grayscales assigned to black and white pixel classes.


title: Linear discriminant analysis

text: In the case where there are more than two classes, the analysis used in the derivation of the Fisher discriminant can be extended to find a subspace which appears to contain all of the class variability. This generalization is due to C. R. Rao. Suppose that each of C classes has a mean formula_53 and the same covariance formula_54. Then the scatter between class variability may be defined by the sample covariance of the class means


title: Linear discriminant analysis

text: where formula_56 is the mean of the class means. The class separation in a direction formula_57 in this case will be given by


title: Linear discriminant analysis

text: This means that when formula_57 is an eigenvector of formula_60 the separation will be equal to the corresponding eigenvalue.


title: Linear discriminant analysis

text: If formula_60 is diagonalizable, the variability between features will be contained in the subspace spanned by the eigenvectors corresponding to the "C" − 1 largest eigenvalues (since formula_62 is of rank "C" − 1 at most). These eigenvectors are primarily used in feature reduction, as in PCA. The eigenvectors corresponding to the smaller eigenvalues will tend to be very sensitive to the exact choice of training data, and it is often necessary to use regularisation as described in the next section.


title: Linear discriminant analysis

text: If classification is required, instead of dimension reduction, there are a number of alternative techniques available. For instance, the classes may be partitioned, and a standard Fisher discriminant or LDA used to classify each partition. A common example of this is "one against the rest" where the points from one class are put in one group, and everything else in the other, and then LDA applied. This will result in C classifiers, whose results are combined. Another common


title: Linear discriminant analysis

text: method is pairwise classification, where a new classifier is created for each pair of classes (giving "C"("C" − 1)/2 classifiers in total), with the individual classifiers combined to produce a final classification.


title: Linear discriminant analysis

text: The typical implementation of the LDA technique requires that all the samples are available in advance. However, there are situations where the entire data set is not available and the input data are observed as a stream. In this case, it is desirable for the LDA feature extraction to have the ability to update the computed LDA features by observing the new samples without running the algorithm on the whole data set. For example, in many real-time applications such as mobile robotics or on-line face recognition, it is important to update the extracted LDA features as soon as new observations are available. An LDA feature extraction technique that can update the LDA features by simply observing new samples is an "incremental LDA algorithm", and this idea has been extensively studied over the last two decades. Chatterjee and Roychowdhury proposed an incremental self-organized LDA algorithm for updating the LDA features. In other work, Demir and Ozmehmet proposed online local learning algorithms for updating LDA features incrementally using error-correcting and the Hebbian learning rules. Later, Aliyari "et a"l. derived fast incremental algorithms to update the LDA features by observing the new samples.


title: Linear discriminant analysis

text: In practice, the class means and covariances are not known. They can, however, be estimated from the training set. Either the maximum likelihood estimate or the maximum a posteriori estimate may be used in place of the exact value in the above equations. Although the estimates of the covariance may be considered optimal in some sense, this does not mean that the resulting discriminant obtained by substituting these values is optimal in any sense, even if the assumption of normally distributed classes is correct.


title: Linear discriminant analysis

text: Another complication in applying LDA and Fisher's discriminant to real data occurs when the number of measurements of each sample (i.e., the dimensionality of each data vector) exceeds the number of samples in each class. In this case, the covariance estimates do not have full rank, and so cannot be inverted. There are a number of ways to deal with this. One is to use a pseudo inverse instead of the usual matrix inverse in the above formulae. However, better numeric stability may be achieved by first projecting the problem onto the subspace spanned by formula_62.


title: Linear discriminant analysis

text: Another strategy to deal with small sample size is to use a shrinkage estimator of the covariance matrix, which


title: Linear discriminant analysis

text: where formula_65 is the identity matrix, and formula_66 is the "shrinkage intensity" or "regularisation parameter".


title: Linear discriminant analysis

text: Also, in many practical cases linear discriminants are not suitable. LDA and Fisher's discriminant can be extended for use in non-linear classification via the kernel trick. Here, the original observations are effectively mapped into a higher dimensional non-linear space. Linear classification in this non-linear space is then equivalent to non-linear classification in the original space. The most commonly used example of this is the kernel Fisher discriminant.


title: Linear discriminant analysis

text: LDA can be generalized to multiple discriminant analysis, where "c" becomes a categorical variable with "N" possible states, instead of only two. Analogously, if the class-conditional densities formula_67 are normal with shared covariances, the sufficient statistic for formula_68 are the values of "N" projections, which are the subspace spanned by the "N" means, affine projected by the inverse covariance matrix. These projections can be found by solving a generalized eigenvalue problem, where the numerator is the covariance matrix formed by treating the means as the samples, and the denominator is the shared covariance matrix. See “Multiclass LDA” above for details.


title: Linear discriminant analysis

text: In bankruptcy prediction based on accounting ratios and other financial variables, linear discriminant analysis was the first statistical method applied to systematically explain which firms entered bankruptcy vs. survived. Despite limitations including known nonconformance of accounting ratios to the normal distribution assumptions of LDA, Edward Altman's 1968 model is still a leading model in practical applications.


title: Linear discriminant analysis

text: In computerised face recognition, each face is represented by a large number of pixel values. Linear discriminant analysis is primarily used here to reduce the number of features to a more manageable number before classification. Each of the new dimensions is a linear combination of pixel values, which form a template. The linear combinations obtained using Fisher's linear discriminant are called "Fisher faces", while those obtained using the related principal component analysis are called "eigenfaces".


title: Linear discriminant analysis

text: In marketing, discriminant analysis was once often used to determine the factors which distinguish different types of customers and/or products on the basis of surveys or other forms of collected data. Logistic regression or other methods are now more commonly used. The use of discriminant analysis in marketing can be described by the following steps:


title: Linear discriminant analysis

text: The main application of discriminant analysis in medicine is the assessment of severity state of a patient and prognosis of disease outcome. For example, during retrospective analysis, patients are divided into groups according to severity of disease – mild, moderate and severe form. Then results of clinical and laboratory analyses are studied in order to reveal variables which are statistically different in studied groups. Using these variables, discriminant functions are built which help to objectively classify disease in a future patient into mild, moderate or severe form.


title: Linear discriminant analysis

text: In biology, similar principles are used in order to classify and define groups of different biological objects, for example, to define phage types of Salmonella enteritidis based on Fourier transform infrared spectra, to detect animal source of "Escherichia coli" studying its virulence factors etc.


title: Linear discriminant analysis

text: This method can be used to . For example, when different data from various zones are available, discriminant analysis can find the pattern within the data and classify it effectively.


title: Linear discriminant analysis

text: Discriminant function analysis is very similar to logistic regression, and both can be used to answer the same research questions. Logistic regression does not have as many assumptions and restrictions as discriminant analysis. However, when discriminant analysis’ assumptions are met, it is more powerful than logistic regression. Unlike logistic regression, discriminant analysis can be used with small sample sizes. It has been shown that when sample sizes are equal, and homogeneity of variance/covariance holds, discriminant analysis is more accurate. Despite all these advantages, logistic regression has none-the-less become the common choice, since the assumptions of discriminant analysis are rarely met.


title: Linear discriminant analysis

text: Geometric anomalies in higher dimensions lead to the well-known curse of dimensionality. Nevertheless, proper utilization of concentration of measure phenomena can make computation easier. An important case of these "blessing of dimensionality" phenomena was highlighted by Donoho and Tanner: if a sample is essentially high-dimensional then each point can be separated from the rest of the sample by linear inequality, with high probability, even for exponentially large samples. These linear inequalities can be selected in the standard (Fisher's) form of the linear discriminant for a rich family of probability distribution. In particular, such theorems are proven for log-concave distributions including multidimensional normal distribution (the proof is based on the concentration inequalities for log-concave measures) and for product measures on a multidimensional cube (this is proven using Talagrand's concentration inequality for product probability spaces). Data separability by classical linear discriminants simplifies the problem of error correction for artificial intelligence systems in high dimension.


title: Female body shape

text: Female body shape or female figure is the cumulative product of a woman's skeletal structure and the quantity and distribution of muscle and fat on the body.


title: Female body shape

text: There is a wide range of normality of female body shapes. Female figures are typically narrower at the waist than at the bust and hips. The bust, waist, and hips are called inflection points, and the ratios of their circumferences are used to define basic body shapes.


title: Female body shape

text: Reflecting the wide range of individual beliefs on what is best for physical health and what is preferred aesthetically, as well as disagreements on the social standing and purported "purpose" of women in society, there is no universally acknowledged ideal female body shape. Cultural ideals, however, have developed and continue to exert influence over how a woman relates to her own body, as well as how others in her society may perceive and treat her.


title: Female body shape

text: Estrogens, which are primary female sex hormones, have a significant impact on a female's body shape. They are produced in both men and women, but their levels are significantly higher in women, especially in those of reproductive age. Besides other functions, estrogens promote the development of female secondary sexual characteristics, such as breasts and hips. As a result of estrogens, during puberty, girls develop breasts and their hips widen. Working against estrogen, the presence of testosterone in a pubescent female inhibits breast development and promotes muscle and facial hair development.


title: Female body shape

text: Estrogen levels also rise significantly during pregnancy. A number of other changes typically occur during pregnancy, including enlargement and increased firmness of the breasts, mainly due to hypertrophy of the mammary gland in response to the hormone prolactin. The size of the nipples may increase noticeably. These changes may continue during breastfeeding. Breasts generally revert to approximately their previous size after pregnancy, although there may be some increased sagging.


title: Female body shape

text: Estrogens can also affect the female body shape in a number of other ways, including increasing fat stores, accelerating metabolism, reducing muscle mass, and increasing bone formation.


title: Female body shape

text: Estrogens cause higher levels of fat to be stored in a female body than in a male body. They also affect body fat distribution, causing fat to be stored in the buttocks, thighs, and hips in women, but generally not around their waists, which will remain about the same size as they were before puberty. The hormones produced by the thyroid gland regulate the rate of metabolism, controlling how quickly the body uses energy, and controls how sensitive the body should be to other hormones. Body fat distribution may change from time to time, depending on food habits, activity levels and hormone levels.


title: Female body shape

text: When women reach menopause and the estrogen produced by ovaries declines, fat migrates from their buttocks, hips and thighs to their waists; later fat is stored at the abdomen.


title: Female body shape

text: Body fat percentage recommendations are higher for females, as this fat may serve as an energy reserve for pregnancy. Males have less subcutaneous fat in their faces due to the effects of testosterone; testosterone also reduces fat by aiding fast metabolism. The lack of estrogen in males generally results in more fat being deposited around the waist and abdomen (producing an "apple shape").


title: Female body shape

text: Testosterone is a steroid hormone which helps build and maintain muscles with physical activity, such as exercise. The amount of testosterone produced varies from one individual to another, but, on average, an adult female produces around one-tenth of the testosterone of an adult male, but females are more sensitive to the hormone. The muscles most likely to be affected are the pectoral muscles, biceps and the triceps in the arms and quadriceps in the thighs.


title: Female body shape

text: On the other hand, estrogens reduce muscle mass . Muscle mass changes over time as a result of changes in testosterone and estrogen levels and exercise, besides other factors.


title: Female body shape

text: The aging process has an inevitable impact on a person's body shape. A woman's sex hormone levels will affect the fat distribution on her body. According to Dr. Devendra Singh, "Body shape is determined by the nature of body fat distribution that, in turn, is significantly correlated with women's sex hormone profile, risk for disease, and reproductive capability." Concentrations of estrogen will influence where body fat is stored.


title: Female body shape

text: Before puberty both males and females have a similar waist–hip ratio. At puberty, a girl's sex hormones, mainly estrogen, will promote breast development and a wider pelvis tilted forward for child bearing, and until menopause a woman's estrogen levels will cause her body to store excess fat in the buttocks, hips and thighs, but generally not around her waist, which will remain about the same size as it was before puberty. These factors result in women's waist–hip ratio (WHR) being lower than for males, although males tend to have a greater upper-body to waist–hip ratio (WHR) giving them a V shape look because of their greater muscle mass (e.g., they generally have much larger, more muscular and broader shoulders, pectoral muscles, teres major muscles and latissimus dorsi muscles).


title: Female body shape

text: During and after pregnancy, a woman experiences body shape changes. After menopause, with the reduced production of estrogen by the ovaries, there is a tendency for fat to redistribute from a female's buttocks, hips and thighs to her waist or abdomen.


title: Female body shape

text: The breasts of girls and women in early stages of development commonly are "high" and rounded, dome- or cone-shaped, and protrude almost horizontally from a female's chest wall. Over time, the sag on breasts tends to increase due to their natural weight, the relaxation of support structures, and aging.


title: Female body shape

text: Body shapes are often categorised in the fashion industry into one of four elementary geometric shapes, though there are very wide ranges of actual sizes within each shape:


title: Female body shape

text: A study of the shapes of over 6,000 women, carried out by researchers at the North Carolina State University circa 2005, for apparel, found that 46% were rectangular, just over 20% spoon, just under 14% inverted triangle, and 8% hourglass. Another study has found "that the average woman's waistline had expanded by six inches since the 1950s" and that women in 2004 were taller and had bigger busts and hips than those of the 1950s. Note however that a 2021 study found that slight changes in measurement placement definition can recategorise up to 40% of women into different body shapes, meaning cross-research comparisons may be flawed unless the exact measurement definitions are used.


title: Female body shape

text: The "Female Figure Identification Technique for Apparel" uses the following formula to identify an individual's body type:


title: Female body shape

text: The Chinese clothing size standards give codes to clothing designed for different ratios between chest and waist. They adapt for a linear scale between inverted triangle/hourglass and rectangular.


title: Female body shape

text: The Japanese and South Korean clothing size standards give codes to women's clothing designed for different ratios between hips and chest. The German standards similarly use hip and bust measures. They all adapt for a linear scale between rectangular and spoon shapes.


title: Female body shape

text: The German sizing system also has height categories for short, regular and tall women, which combine with the shape categories to produce 9 categories.


title: Female body shape

text: The circumferences of bust, waist, and hips (BWH) and the ratios between them are a widespread method of identifying different female body shapes. As noted above, descriptive terms used include "rectangle", "spoon", "inverted triangle", and "hourglass".


title: Female body shape

text: The waist is typically smaller than the bust and hips, unless there is a high proportion of body fat distributed around it. How much the bust or hips inflect inward, towards the waist, determines a woman's structural shape. The hourglass shape is present in only about 8% of women.


title: Female body shape

text: A woman's dimensions are often expressed by the circumference around the three inflection points. For example, "36–29–38" in US customary units would mean a bust, waist and hips.


title: Female body shape

text: Height will also affect the appearance of the figure. A woman who is 36–24–36 (91–61–91 cm) at height will look different from a woman who is 36–24–36 at height. If both are the same weight, the taller woman has a much lower body mass index; if they have the same BMI, the weight is distributed around a greater volume.


title: Female body shape

text: A woman's bust measure is a combination of her rib cage and breast size. For convenience, a woman's bra measurements are often used as a proxy. Conventionally, measurement for the band of a bra is taken around the torso immediately below the breasts, with the tape measure parallel to the floor. Bra cup size is determined by measuring across the crest of the breasts and calculating the difference between that measurement and the band measurement. The waist is measured at the midpoint between the bottom of the rib cage and the top of the 'front' hip bones. The hips are measured at the largest circumference of the hips and buttocks.


title: Female body shape

text: The British Fashion Model Agents Association (BFMA) says that female models should be at least tall and proportionately around 34–24–34" (86–61–86 cm). Laws "aimed at preventing anorexia by stopping the promotion of inaccessible ideals of beauty" have been introduced in a number of European countries, to regulate the minimum actual or apparent BMI of fashion models. "Under World Health Organisation guidelines an adult with a BMI below 18.5 is considered underweight, 18 malnourished, and 17 severely malnourished. The average model measuring 1.75m (5ft 9in) and weighing 50kg (7st 12lb) [110lb] has a BMI of 16".


title: Female body shape

text: According to Camille Paglia, the ideal body type as envisioned by members of society has changed throughout history. She states that Stone Age Venus figurines show the earliest body type preference, dramatic steatopygia; and that the emphasis on protruding belly, breasts, and buttocks is likely a result of both the aesthetic of being well fed and aesthetic of being fertile, traits that were more difficult to achieve at the time. In sculptures from Classical Greece and Ancient Rome the female bodies are more tubular and regularly proportioned. There is essentially no emphasis given to any particular body part, not the breasts, buttocks, or belly.


title: Female body shape

text: Moving forward there is more evidence that fashion somewhat dictated what people believed were the proper female body proportions. This is the case because the body is primarily seen through clothing, which always changes the way the underlying structures are conceived. The first representations of truly fashionable women appear in the 14th century. Between the 14th and 16th centuries in northern Europe, bulging bellies were again desirable, however the stature of the rest of the figure was generally thin. This is most easily visible in paintings of nudes from the time. When looking at clothed images, the belly is often visible through a mass of otherwise concealing, billowing, loose robes. Since the stomach was the only visible anatomical feature, it became exaggerated in nude depictions while the rest of the body remained minimal. In southern Europe, around the time of the renaissance, this was also true. Though the classical aesthetic was being revived and very closely studied, the art produced in the time period was influenced by both factors. This resulted in a beauty standard that reconciled the two aesthetics by using classically proportioned figures who had non-classical amounts of flesh and soft, padded skin.


title: Female body shape

text: In the nude paintings of the 17th century, such as those by Rubens, the naked women appear quite plump. Upon closer inspection however, most of the women have fairly normal statures, Rubens has simply painted their flesh with rolls and ripples that otherwise would not be there. This may be a reflection of the female style of the day: a long, cylindrical, gown with rippling satin accents, tailored over a figure in stays. Thus Rubens' women have a tubular body with rippling embellishments. While stays continued to be fashionable into the 18th century, they were shortened, became more conical, and consequently began to emphasize the waist. It also lifted and separated the breasts as opposed to the 17th century corsets which compressed and minimized the breasts. Consequently, depictions of nude women in the 18th century tend to have a very narrow waist and high, distinct breasts, almost as if they were wearing an invisible corset. La maja desnuda is a clear example of this aesthetic. The 19th century maintained the general figure of the 18th century. Examples can be seen in the works of many contemporary artists, both academic artists, such as Cabanel, Ingres, and Bouguereau, and Impressionists, such as Degas, Renoir, and Toulouse-Lautrec. As the 20th century began, the rise of athletics resulted in a drastic slimming of the female figure. This culminated in the 1920s flapper look, which has informed modern fashion ever since.


title: Female body shape

text: The last 100 years envelop the time period in which that overall body type has been seen as attractive, though there have been small changes within the period as well. The 1920s was the time in which the overall silhouette of the ideal body slimmed down. There was dramatic flattening of the entire body resulting in a more youthful aesthetic. As the century progressed, the ideal size of both the breasts and buttocks increased. From the 1950s to 1960 that trend continued with the interesting twist of cone shaped breasts as a result of the popularity of the bullet bra. In the 1960s, the invention of the miniskirt as well as the increased acceptability of pants for women, prompted the idealization of the long leg that has lasted to this day. Following the invention of the push-up bra in the 1970s the ideal breast has been a rounded, fuller, and larger breast. In the past 20 years the average American bra size has increased from 34B to 34DD, although this may be due to the increase in obesity within the United States in recent years. Additionally, the ideal figure has favored an ever-lower waist–hip ratio, especially with the advent and progression of digital editing software such as Adobe Photoshop.


title: Female body shape

text: Each society develops a general perception of what an ideal female body shape would be like. These ideals are generally reflected in the art and literature produced by or for a society, as well as in popular media such as films and magazines. The ideal or preferred female body size and shape has varied over time and continues to vary among cultures; but a preference for a small waist has remained fairly constant throughout history. A low waist–hip ratio has often been seen as a sign of good health and reproductive potential.


title: Female body shape

text: A low waist–hip ratio has also often been regarded as an indicator of attractiveness of a woman, but recent research suggests that attractiveness is more correlated to body mass index than waist–hip ratio, contrary to previous belief. According to Dr. Devendra Singh of the University of Texas, who studied the representations of women, historically found there was a trend for slightly overweight women in the 17th and 18th centuries, as typified by the paintings of Rubens, but that in general there has been a preference for a slimmer waist in Western culture. He notes that "The finding that the writers describe a small waist as beautiful suggests instead that this body part – a known marker of health and fertility – is a core feature of feminine beauty that transcends ethnic differences and cultures."


title: Female body shape

text: New research suggests that apple-shaped women have the highest risk of developing heart disease, while hourglass-shaped women have the lowest. Diabetes professionals advise that a waist measurement for a woman of over increases the risk of heart disease, but that ethnic background also plays a factor. This is because body fat buildup around the waist (the apple shape) poses a higher health risk than a fat buildup at the hips (the pear shape).


title: Female body shape

text: Compared to males, females generally have relatively narrow waists and large buttocks, and this along with wide hips make for a wider hip section and a lower waist–hip ratio.


title: Female body shape

text: Research shows that a waist–hip ratio (WHR) for a female very strongly correlates to the perception of attractiveness. Women with a 0.7 WHR (waist circumference that is 70% of the hip circumference) are rated more attractive by men in various cultures. Such diverse beauty icons as Marilyn Monroe, Sophia Loren and the Venus de Milo have ratios around 0.7; this is a typical ratio in Western art. In other cultures, preferences vary, ranging from 0.6 in China, to 0.8 or 0.9 in parts of South America and Africa, and divergent preferences based on ethnicity, rather than nationality, have also been noted.


title: Female body shape

text: Anthropologists and behaviorists have discovered evidence that the WHR is a significant measure for female attractiveness.


title: Female body shape

text: Many studies indicate that WHR correlates with female fertility, leading some to speculate that its use as a sexual selection cue by men has an evolutionary basis. However it is also suggested that the evident relationships between WHR-influencing hormones and survival-relevant traits such as competitiveness and stress tolerance may give a preference for higher waist–hip ratios its own evolutionary benefit. That, in turn, may account for the cross-cultural variation observed in actual average waist–hip ratios and culturally preferred waist-to-hip ratios for women.


title: Female body shape

text: WHR has been found to be a more efficient predictor of mortality in older people than waist circumference or body mass index (BMI).


title: Female body shape

text: Over the past several hundred years, there has been a shift towards viewing the body as part of one's identity – not in a purely physical way, but as a means of deeper self-expression. David Gauntlett, in his 2008 book, recognizes the importance of malleability in physical identity, stating, "the body is the outer expression of our self, to be improved and worked upon". One of the more key factors in creating the desire for a particular body shape – most notably for females – is the media, which has promoted a number of so-called "ideal" body shapes. Fashionable figures are often unattainable for the majority of the population, and their popularity tends to be short-lived due to their arbitrary nature.


title: Female body shape

text: During the 1950s, the fashion model and celebrity were two separate entities, allowing the body image of the time to be shaped more by television and film rather than high fashion advertisements. While the fashion model of the 1950s, such as Jean Patchett and Dovima, were very thin, the ideal image of beauty was still a larger one. As the fashion houses in the early 1950s still catered to a specific, elite clientele, the image of the fashion model at that time was not as sought after or looked up to as was the image of the celebrity. While the models that graced the covers of Vogue Magazine and Harper's Bazaar in the 1950s were in line with the thin ideal of the day, the most prominent female icon was Marilyn Monroe. Monroe, who was more curvaceous, fell on the opposite end of the feminine ideal spectrum in comparison to high fashion models. Regardless of their sizes, however, both fashion of the time and depictions of Monroe emphasize a smaller waist and fuller bottom half. The late 1950s, however, brought about the rise of ready-to-wear fashion, which implemented a standardized sizing system for all mass-produced clothing. While fashion houses, such as Dior and Chanel, remained true to their couture, tailor-made garments, the rise of these rapidly-produced, standardized garments led to a shift in location from Europe to America as the epicenter of fashion. Along with that shift came the standardization of sizes, in which garments weren't made to fit the body anymore, but instead the body must be altered to fit the garment.


title: Female body shape

text: During the 1960s, the popularity of the model Twiggy meant that women favoured a thinner body, with long, slender limbs. This was a drastic change from the former decade's ideal, which saw curvier icons, such as Marilyn Monroe, to be considered the epitome of beautiful. These shifts in what was seen to be the "fashionable body" at the time followed no logical pattern, and the changes occurred so quickly that one shape was never in vogue for more than a decade. As is the case with fashion itself in the post-modern world, the premise of the ever-evolving "ideal" shape relies on the fact that it will soon become obsolete, and thus must continue changing to prevent itself from becoming uninteresting.


title: Female body shape

text: An early example of the body used as an identity marker occurred in the Victorian era, when women wore corsets to help themselves attain the body they wished to possess. Having a tiny waist was a sign of social status, as the wealthier women could afford to dress more extravagantly and sport items such as corsets to increase their physical attractiveness. By the 1920s, the cultural ideal had changed significantly as a result of the suffrage movement, and "the fashion was for cropped hair, flat (bound) breasts and a slim androgynous shape".


title: Female body shape

text: More recently, magazines and other popular media have been criticized for promoting an unrealistic trend of thinness. David Gauntlett states that the media's "repetitive celebration of a beauty 'ideal' which most women will not be able to match … will eat up readers' time and money—and perhaps good health—if they try". Additionally, the impact that this has on women and their self-esteem is often a very negative one, and resulted in the diet industry taking off in the 1960s – something that would not have occurred "had bodily appearance not been so closely associated with identity for women". Melissa Oldman states, "Nowhere is the thin female ideal more evident than in popular media."


title: Female body shape

text: The importance of "the body as a work zone", as Myra MacDonald asserts, further perpetuates the link between fashion and identity, with the body being used as a means of creating a visible and unavoidable image for oneself. The tools with which to create the final copy of such a project range from the extreme—plastic surgery—to the more tame, such as diet and exercise.


title: Female body shape

text: A study at Brigham Young University using MRI technology suggested that women experience more anxiety about weight gain than do men, while aggregated research has been used to claim that images of thin women in popular media may induce psychological stress. A study of 52 older adults found that females may think more about their body shape and endorse thinner figures than men even into old age.


title: Female body shape

text: Various strategies, including exercise, are sometimes employed in an attempt to temporarily or permanently alter the shape of a body. Dieting is also sometimes used, but is generally not effective in the long term.


title: Female body shape

text: At times artificial devices are used or surgery is employed. In 2019, 92% of all cosmetic procedures in the US were undertaken by women, with the most popular being a breast augmentation. Breast size can be artificially increased or decreased. Falsies, breast prostheses or padded bras may be used to increase the apparent size of a woman's breasts, while minimiser bras may be used to reduce the apparent size. Breasts can be surgically enlarged using breast implants or reduced by the systematic removal of parts of the breasts. Hormonal breast enhancement may be another option.


title: Female body shape

text: Historically, boned corsets have been used to reduce waist sizes. The corset reached its climax during the Victorian era. In twentieth century these corsets were mostly replaced with more flexible/comfortable foundation garments. Where corsets are used for waist reduction, they may cause temporary reduction through occasional use or permanent reduction through constant and continuous use. Those who use corsets for permanent reduction are often referred to as tightlacers. Liposuction and liposculpture are common surgical methods for reducing the waist line.


title: Female body shape

text: Padded control briefs or hip and buttock padding may be used to increase the apparent size of hips and buttocks. Buttock augmentation surgery may be used to increase the size of hips and buttocks to make them look more rounded.


title: Female body shape

text: In the a 2012 experiment, researchers Crossley, Cornelissen and Tovée asked men and women to depict an attractive female body and the majority of them chose the same ideal. The women who participated in this experiment drew their ideal bodies with enlarged busts and narrowed the rest of their bodies. The male participants also depicted their ideal partner with the same image. The researchers state, "For both sexes, the primary predictor of female beauty is a relatively low BMI combined with a relatively curvaceous body". However the generality of their conclusions was limited given their small sample size and single ethnicity of participants.


title: Casual (TV series)

text: Casual is an American television comedy-drama series that premiered on October 7, 2015, on Hulu. Created by Zander Lehmann and directed by Jason Reitman, it centers on Valerie (Michaela Watkins), a newly divorced single mother living with her brother Alex (Tommy Dewey) and her daughter Laura (Tara Lynne Barr). The cast also includes Frances Conroy and Nyasha Hatendi.


title: Casual (TV series)

text: In advance of its premiere on Hulu, the first two episodes received a preview screening at the 2015 Toronto International Film Festival as part of the festival's new "Primetime" platform of selected television projects.


title: Casual (TV series)

text: On October 19, 2017, Hulu renewed the series for a fourth and final season with all eight episodes released simultaneously on July 31, 2018.


title: Casual (TV series)

text: On June 23, 2016, Hulu renewed the series for a 13-episode third season. The season premiered on May 23, 2017.


title: Casual (TV series)

text: On October 19, 2017, Hulu renewed the series for a fourth and final season with all 8 episodes being released simultaneously on July 31, 2018.


title: Casual (TV series)

text: The first season received critical acclaim. On Metacritic the first season holds a rating of 77 out of 100 based on 20 critic reviews, indicating 'generally favorable reviews'. Rotten Tomatoes gave the first season a 93% 'certified fresh' rating based on 28 critic reviews, with the critical consensus "Jason Reitman's Casual is a funny -- albeit very specific -- look at modern dating, sharpened by edgy dialogue and self-assured performances." For the 73rd Golden Globe Awards, the series was nominated in the category for Best Television Series - Musical or Comedy.


title: Casual (TV series)

text: The second season received similar acclaim. It holds an 87% approval rating on review aggregator website Rotten Tomatoes, based on 15 reviews, with an average rating of 8.8/10. The site's critical consensus reads, "Well-written and solidly acted, Casual offers a profane -- yet profound -- take on life's many challenges". On Metacritic, the season holds a rating of 88 out of 100, based on 7 critics, indicating "Universal acclaim".


title: Rifling

text: In firearms, rifling is machining helical grooves into the internal (bore) surface of a gun's barrel for the purpose of exerting torque and thus imparting a spin to a projectile around its longitudinal axis during shooting to stabilize the projectile longitudinally by conservation of angular momentum, improving its aerodynamic stability and accuracy over smoothbore designs.


title: Rifling

text: Rifling is characterized by its twist rate, which indicates the distance the rifling takes to complete one full revolution, such as "1 turn in 10 inches" (1:10 inches), "1 turn in 254 mm" ("1:254 mm" or "1:25.4 cm)", or the like. Normally, an experienced shooter can infer the units of measurement from the numbers alone. A shorter distance indicates a faster twist, meaning that for a given velocity the projectile will rotate at a higher spin rate.


title: Rifling

text: The combination of length, weight, and shape of a projectile determines the twist rate needed to gyroscopically stabilize it – barrels intended for short, large-diameter projectiles such as spherical lead balls require a very low twist rate, such as 1 turn in 48 inches (122 cm). Barrels intended for long, small-diameter projectiles, such as the ultra-low-drag 80-grain 0.223 inch bullets (5.2 g, 5.56 mm), use twist rates of 1 turn in 8 inches (20 cm) or faster.


title: Rifling

text: In some cases, rifling will increase the twist rate as the projectile travels down the length of the barrel, called a "gain twist" or "progressive twist"; a twist rate that decreases from breech to muzzle is undesirable because it cannot reliably stabilize the projectile as it travels down the bore.


title: Rifling

text: An extremely long projectile, such as a flechette, requires impractically high twist rates to stabilize; they are often stabilized aerodynamically instead. An aerodynamically stabilized projectile can be fired from a smoothbore barrel without a reduction in accuracy.


title: Rifling

text: Muskets were smoothbore, large caliber weapons using ball-shaped ammunition fired at relatively low velocity. Due to the high cost, great difficulty of precision manufacturing, and the need to load readily and speedily from the muzzle, musket balls were generally a loose fit in the barrels. Consequently, on firing the balls would often bounce off the sides of the barrel when fired and the final destination after leaving the muzzle was less predictable. This was countered when accuracy was more important, for example when hunting, by using a tighter-fitting combination of a closer-to-bore-sized ball and a patch. The accuracy was improved, but still not reliable for precision shooting over long distances.


title: Rifling

text: Like the invention of gunpowder itself, the inventor of barrel rifling is not yet definitely known. Straight grooving had been applied to small arms since at least 1480, originally intended as "soot grooves" to collect gunpowder residue.


title: Rifling

text: Some of the earliest recorded European attempts of spiral-grooved musket barrels were of Gaspard Kolner, a gunsmith of Vienna in 1498 and Augustus Kotter of Nuremberg in 1520. Some scholars allege that Kollner’s works at the end of the 15th century only used straight grooves, and it wasn’t until he received help from Kotter that a working spiral-grooved firearm was made. There may have been attempts even earlier than this, as the main inspiration of rifled firearms came from archers and crossbowmen who realized that their projectiles flew far faster and more accurately when they imparted rotation through twisted fletchings.


title: Rifling

text: Though true rifling dates from the 16th century, it had to be engraved by hand and consequently did not become commonplace until the mid-19th century. Due to the laborious and expensive manufacturing process involved, early rifled firearms were primarily used by wealthy recreational hunters, who did not need to fire their weapons many times in rapid succession and appreciated the increased accuracy. Rifled firearms were not popular with military users since they were difficult to clean, and loading projectiles presented numerous challenges. If the bullet was of sufficient diameter to take up the rifling, a large mallet was required to force it down the bore. If, on the other hand, it was of reduced diameter to assist in its insertion, the bullet would not fully engage the rifling and accuracy was reduced.


title: Rifling

text: The first practical military weapons using rifling with black powder were breech loaders such as the Queen Anne pistol.


title: Rifling

text: The grooves most commonly used in modern rifling have fairly sharp edges. More recently, polygonal rifling, a throwback to the earliest types of rifling, has become popular, especially in handguns. Polygonal barrels tend to have longer service lives because the reduction of the sharp edges of the land (the grooves are the spaces that are cut out, and the resulting ridges are called lands) reduces erosion of the barrel. Supporters of polygonal rifling also claim higher velocities and greater accuracy. Polygonal rifling is currently seen on pistols from CZ, Heckler & Koch, Glock, Tanfoglio, and Kahr Arms, as well as the Desert Eagle.


title: Rifling

text: For tanks and artillery pieces, the extended range, full bore (ERFB) concept developed by Gerald Bull for the GC-45 howitzer reverses the normal rifling idea by using a projectile with small nubs that ride in the grooves, instead of having a slightly oversized driving band which is forced into the grooves. This imparts spin but eliminates the friction required to deform the driving band into the grooves; a soft and low-friction silicon rubber ring is used to achieve a seal between the projectile and the walls of the tube. Guns capable of firing these projectiles have achieved significant increases in muzzle velocity and range. Unlike a shell narrower than the gun's bore with a sabot, ERFB shells use the full bore, permitting a larger payload. Examples include the South African G5 and the German PzH 2000. ERFB may be combined with base bleed.


title: Rifling

text: A gain-twist or progressive rifling begins with a slow twist rate that gradually increases down the bore, resulting in very little initial change in the projectile's angular momentum during the first few inches of bullet travel after it enters the throat. This enables the bullet to remain essentially undisturbed and trued to the case mouth. After engaging the rifling at the throat, the bullet is progressively subjected to accelerated angular momentum as it gets propelled down the barrel. The theoretical advantage is that by gradually increasing the spin rate, torque gets imparted along a much longer bore length, allowing thermomechanical stress to be spread over a larger area rather than being focused predominantly at the throat, which typically wears out much faster than other parts of the barrel.


title: Rifling

text: Gain-twist rifling was used prior to and during the American Civil War (1861–65). Colt Army and Navy revolvers both employed gain-twist rifling. Gain-twist rifling, however, is more difficult to produce than uniform rifling, and therefore is more expensive. The military has used gain-twist rifling in a variety of weapons such as the M61 Vulcan Gatling gun used in some current fighter jets and the larger GAU-8 Avenger Gatling gun used in the A10 Thunderbolt II close air support jet. In these applications it allows lighter construction of the barrels by decreasing chamber pressures through the use of low initial twist rates but ensuring the projectiles have sufficient stability once they leave the barrel. It is seldom used in commercially available products, though notably on the Smith & Wesson Model 460 (X-treme Velocity Revolver).


title: Rifling

text: An early method of introducing rifling to a pre-drilled barrel was to use a cutter mounted on a square-section rod, accurately twisted into a spiral of the desired pitch, mounted in two fixed square-section holes. As the cutter was advanced through the barrel it twisted at a uniform rate governed by the pitch. The first cut was shallow. The cutter points were gradually expanded as repeated cuts were made. The blades were in slots in a wooden dowel which were gradually packed out with slips of paper until the required depth was obtained. The process was finished off by casting a slug of molten lead into the barrel, withdrawing it and using it with a paste of emery and oil to smooth the bore.


title: Rifling

text: The "grooves" are the spaces that are cut out, and the resulting ridges are called "lands". These lands and grooves can vary in number, depth, shape, direction of twist (right or left), and twist rate. The spin imparted by rifling significantly improves the stability of the projectile, improving both range and accuracy. Typically rifling is a constant rate down the barrel, usually measured by the length of travel required to produce a single turn. Occasionally firearms are encountered with a "gain twist", where the rate of spin increases from chamber to muzzle. While intentional gain twists are rare, due to manufacturing variance, a slight gain twist is in fact fairly common. Since a reduction in twist rate is very detrimental to accuracy, gunsmiths who are machining a new barrel from a rifled blank will often measure the twist carefully so they may put the faster rate, no matter how minute the difference is, at the muzzle end.


title: Rifling

text: A barrel of circular bore cross-section is not capable of imparting a spin to a projectile, so a rifled barrel has a non-circular cross-section. Typically the rifled barrel contains one or more grooves that run down its length, giving it a cross-section resembling an internal gear, though it can also take the shape of a polygon, usually with rounded corners. Since the barrel is not circular in cross-section, it cannot be accurately described with a single diameter. Rifled bores may be described by the bore diameter (the diameter across the "lands" or high points in the rifling), or by groove diameter (the diameter across the "grooves" or low points in the rifling). Differences in naming conventions for cartridges can cause confusion; for example, the projectiles of the .303 British are actually slightly larger in diameter than the projectiles of the .308 Winchester, because the ".303" refers to the bore diameter in inches (bullet is .312), while the ".308" refers to the bullet diameter in inches (7.92 mm and 7.82 mm, respectively).


title: Rifling

text: Despite differences in form, the common goal of rifling is to deliver the projectile accurately to the target. In addition to imparting the spin to the bullet, the barrel must hold the projectile securely and concentrically as it travels down the barrel. This requires that the rifling meet a number of tasks:


title: Rifling

text: Rifling may not begin immediately forward of the chamber. There may be an unrifled throat ahead of the chamber so a cartridge may be chambered without pushing the bullet into the rifling. This reduces the force required to load a cartridge into the chamber, and prevents leaving a bullet stuck in the rifling when an unfired cartridge is removed from the chamber. The specified diameter of the throat may be somewhat greater than groove diameter, and may be enlarged by use if hot powder gas melts the interior barrel surface when the rifle is fired. Freebore is a groove-diameter length of smoothbore barrel without lands forward of the throat. Freebore allows the bullet to transition from static friction to sliding friction and gain linear momentum prior to encountering the resistance of increasing rotational momentum. Freebore may allow more effective use of propellants by reducing the initial pressure peak during the minimum volume phase of internal ballistics before the bullet starts moving down the barrel. Barrels with freebore length exceeding the rifled length have been known by a variety of trade names including paradox.


title: Rifling

text: When the projectile is swaged into the rifling, it takes on a mirror image of the rifling, as the lands push into the projectile in a process called "engraving". Engraving takes on not only the major features of the bore, such as the lands and grooves, but also minor features, like scratches and tool marks. The relationship between the bore characteristics and the engraving on the projectile are often used in forensic ballistics.


title: Rifling

text: The original firearms were loaded from the muzzle by forcing a ball from the muzzle to the chamber. Whether using a rifled or smooth bore, a good fit was needed to seal the bore and provide the best possible accuracy from the gun. To ease the force required to load the projectile, these early guns used an undersized ball, and a patch made of cloth, paper, or leather to fill the "windage" (the gap between the ball and the walls of the bore). The patch acted as a wadding and provided some degree of pressure sealing, kept the ball seated on the charge of black powder, and kept the ball concentric to the bore. In rifled barrels, the patch also provided a means to transfer the spin from the rifling to the bullet, as the patch is engraved rather than the ball. Until the advent of the hollow-based Minié ball, which expands and obturates upon firing to seal the bore and engage the rifling, the patch provided the best means of getting the projectile to engage the rifling.


title: Rifling

text: In breech-loading firearms, the task of seating the projectile into the rifling is handled by the "throat" of the chamber. Next is the "freebore", which is the portion of the throat down which the projectile travels before the rifling starts. The last section of the throat is the "throat angle", where the throat transitions into the rifled barrel.


title: Rifling

text: The throat is usually sized slightly larger than the projectile, so the loaded cartridge can be inserted and removed easily, but the throat should be as close as practical to the groove diameter of the barrel. Upon firing, the projectile expands under the pressure from the chamber, and obturates to fit the throat. The bullet then travels down the throat and engages the rifling, where it is engraved, and begins to spin. Engraving the projectile requires a significant amount of force, and in some firearms there is a significant amount of freebore, which helps keep chamber pressures low by allowing the propellant gases to expand before being required to engrave the projectile. Minimizing freebore improves accuracy by decreasing the chance that a projectile will distort before entering the rifling.


title: Rifling

text: For best performance, the barrel should have a twist rate sufficient to spin stabilize any bullet that it would reasonably be expected to fire, but not significantly more. Large diameter bullets provide more stability, as the larger radius provides more gyroscopic inertia, while long bullets are harder to stabilize, as they tend to be very backheavy and the aerodynamic pressures have a longer arm ("lever") to act on. The slowest twist rates are found in muzzle-loading firearms meant to fire a round ball; these will have twist rates as low as 1 in , or slightly longer, although for a typical multi-purpose muzzleloader rifle, a twist rate of 1 in is very common. The M16A2 rifle, which is designed to fire the 5.56×45mm NATO SS109 ball and L110 tracer bullets, has a 1 in or 32 calibers twist. Civilian AR-15 rifles are commonly found with 1 in or 54.8 calibers for older rifles and 1 in or 41.1 calibers for most newer rifles, although some are made with 1 in or 32 calibers twist rates, the same as used for the M16 rifle. Rifles, which generally fire longer, smaller diameter bullets, will in general have higher twist rates than handguns, which fire shorter, larger diameter bullets.


title: Rifling

text: The, traditionally speaking, most common method expresses the twist rate in terms of the 'travel' (length) required to complete one full projectile revolution in the rifled barrel. This method does not give an easy or straightforward understanding of whether a twist rate is "relatively" slow or fast when bores of different diameters are compared.


title: Rifling

text: The second method describes the 'rifled travel' required to complete one full projectile revolution in calibers or bore diameters.


title: Rifling

text: Note that the twist travel L and the bore diameter D must be expressed in a consistent unit of measure, i.e. metric (mm) "or" imperial (in).


title: Rifling

text: The third method simply reports the angle of the grooves relative to the bore axis, measured in degrees.


title: Rifling

text: Note that the latter two methods have the inherent advantage of expressing twist rate as a ratio and give an easy understanding if a twist rate is "relatively" slow or fast even when comparing bores of differing diameters.


title: Rifling

text: In 1879, George Greenhill, a professor of mathematics at the Royal Military Academy (RMA) at Woolwich, London, UK developed a rule of thumb for calculating the optimal twist rate for lead-core bullets. This shortcut uses the bullet's length, needing no allowances for weight or nose shape. The eponymous "Greenhill Formula", still used today, is:


title: Rifling

text: The original value of C was 150, which yields a twist rate in inches per turn, when given the diameter D and the length L of the bullet in inches. This works to velocities of about 840 m/s (2800 ft/s); above those velocities, a C of 180 should be used. For instance, with a velocity of 600 m/s (2000 ft/s), a diameter of and a length of , the Greenhill formula would give a value of 25, which means 1 turn in .


title: Rifling

text: Improved formulas for determining stability and twist rates include the Miller Twist Rule and the McGyro program developed by Bill Davis and Robert McCoy.


title: Rifling

text: If an insufficient twist rate is used, the bullet will begin to yaw and then tumble; this is usually seen as "keyholing", where bullets leave elongated holes in the target as they strike at an angle. Once the bullet starts to yaw, any hope of accuracy is lost, as the bullet will begin to veer off in random directions as it precesses.


title: Rifling

text: Conversely, too high a rate of twist can also cause problems. The excessive twist can cause accelerated barrel wear, and coupled with high velocities also induce a very high spin rate which can cause projectile jacket ruptures causing high velocity spin stabilized projectiles to disintegrate in flight. Projectiles made out of mono metals cannot practically achieve flight and spin velocities such that they disintegrate in flight due to their spin rate. Smokeless powder can produce muzzle velocities of approximately for spin stabilized projectiles and more advanced propellants used in smoothbore tank guns can produce muzzle velocities of approximately . A higher twist than needed can also cause more subtle problems with accuracy: Any inconsistency within the bullet, such as a void that causes an unequal distribution of mass, may be magnified by the spin. Undersized bullets also have problems, as they may not enter the rifling exactly concentric and coaxial to the bore, and excess twist will exacerbate the accuracy problems this causes.


title: Rifling

text: A bullet fired from a rifled barrel can spin at over 300,000 rpm (5 kHz), depending on the bullet's muzzle velocity and the barrel's twist rate.


title: Rifling

text: The general definition of the spin formula_3 of an object rotating around a single axis can be written as


title: Rifling

text: where formula_5 is the linear velocity of a point in the rotating object (in units of distance/time) and formula_6 refers to the circumference of the circle that this measuring point performs around the axis of rotation.


title: Rifling

text: For example, an M4 Carbine with a twist rate of 1 in and a muzzle velocity of will give the bullet a spin of 930 m/s / 0.1778 m = 5.2 kHz (314,000 rpm).


title: Rifling

text: Excessive rotational speed can exceed the bullet's designed limits and the resulting centrifugal force can cause the bullet to disintegrate radially during flight.


title: DDR3 SDRAM

text: Double Data Rate 3 Synchronous Dynamic Random-Access Memory (DDR3 SDRAM) is a type of synchronous dynamic random-access memory (SDRAM) with a high bandwidth ("double data rate") interface, and has been in use since 2007. It is the higher-speed successor to DDR and DDR2 and predecessor to DDR4 synchronous dynamic random-access memory (SDRAM) chips. DDR3 SDRAM is neither forward nor backward compatible with any earlier type of random-access memory (RAM) because of different signaling voltages, timings, and other factors.


title: DDR3 SDRAM

text: DDR3 is a DRAM interface specification. The actual DRAM arrays that store the data are similar to earlier types, with similar performance. The primary benefit of DDR3 SDRAM over its immediate predecessor DDR2 SDRAM, is its ability to transfer data at twice the rate (eight times the speed of its internal memory arrays), enabling higher bandwidth or peak data rates.


title: DDR3 SDRAM

text: The DDR3 standard permits DRAM chip capacities of up to 8 gigabits (Gbit), and up to four ranks of 64 bits each for a total maximum of 16 gigabytes (GB) per DDR3 DIMM. Because of a hardware limitation not fixed until Ivy Bridge-E in 2013, most older Intel CPUs only support up to 4-Gbit chips for 8 GB DIMMs (Intel's Core 2 DDR3 chipsets only support up to 2 Gbit). All AMD CPUs correctly support the full specification for 16 GB DDR3 DIMMs.


title: DDR3 SDRAM

text: In February 2005, Samsung introduced the first prototype DDR3 memory chip. Samsung played a major role in the development and standardisation of DDR3. In May 2005, Desi Rhoden, chairman of the JEDEC committee, stated that DDR3 had been under development for "about 3 years".


title: DDR3 SDRAM

text: DDR3 was officially launched in 2007, but sales were not expected to overtake DDR2 until the end of 2009 or possibly early 2010, according to Intel strategist Carlos Weissenberg, speaking during the early part of their roll-out in August 2008. (The same timescale for market penetration had been stated by market intelligence company DRAMeXchange over a year earlier in April 2007, and by Desi Rhoden in 2005.) The primary driving force behind the increased usage of DDR3 has been new Core i7 processors from Intel and Phenom II processors from AMD, both of which have internal memory controllers: the former requires DDR3, the latter recommends it. IDC stated in January 2009 that DDR3 sales would account for 29% of the total DRAM units sold in 2009, rising to 72% by 2011.


title: DDR3 SDRAM

text: In September 2012, JEDEC released the final specification of DDR4. The primary benefits of DDR4 compared to DDR3 include a higher standardized range of clock frequencies and data transfer rates and significantly lower voltage.


title: DDR3 SDRAM

text: Compared to DDR2 memory, DDR3 memory uses less power. Some manufacturers further propose using "dual-gate" transistors to reduce leakage of current.


title: DDR3 SDRAM

text: According to JEDEC, 1.575 volts should be considered the absolute maximum when memory stability is the foremost consideration, such as in servers or other mission-critical devices. In addition, JEDEC states that memory modules must withstand up to 1.80 volts before incurring permanent damage, although they are not required to function correctly at that level.


title: DDR3 SDRAM

text: Another benefit is its prefetch buffer, which is 8-burst-deep. In contrast, the prefetch buffer of DDR2 is 4-burst-deep, and the prefetch buffer of DDR is 2-burst-deep. This advantage is an enabling technology in DDR3's transfer speed.


title: DDR3 SDRAM

text: DDR3 modules can transfer data at a rate of 800–2133 MT/s using both rising and falling edges of a 400–1066 MHz I/O clock. This is twice DDR2's data transfer rates (400–1066 MT/s using a 200–533 MHz I/O clock) and four times the rate of DDR (200–400 MT/s using a 100–200 MHz I/O clock). High-performance graphics was an initial driver of such bandwidth requirements, where high bandwidth data transfer between framebuffers is required.


title: DDR3 SDRAM

text: Because the hertz is a measure of "cycles" per second, and no signal cycles more often than every other transfer, describing the transfer rate in units of MHz is technically incorrect, although very common. It is also misleading because various memory timings are given in units of clock cycles, which are half the speed of data transfers.


title: DDR3 SDRAM

text: DDR3 does use the same electric signaling standard as DDR and DDR2, Stub Series Terminated Logic, albeit at different timings and voltages. Specifically, DDR3 uses SSTL_15.


title: DDR3 SDRAM

text: In February 2005, Samsung demonstrated the first DDR3 memory prototype, with a capacity of 512Mb and a bandwidth of 1.066Gbps. Products in the form of motherboards appeared on the market in June 2007 based on Intel's P35 "Bearlake" chipset with DIMMs at bandwidths up to DDR3-1600 (PC3-12800). The Intel Core i7, released in November 2008, connects directly to memory rather than via a chipset. The Core i7, i5 & i3 CPUs initially supported only DDR3. AMD's socket AM3 Phenom II X4 processors, released in February 2009, were their first to support DDR3 (while still supporting DDR2 for backwards compatibility).


title: DDR3 SDRAM

text: DDR3 dual-inline memory modules (DIMMs) have 240 pins and are electrically incompatible with DDR2. A key notch—located differently in DDR2 and DDR3 DIMMs—prevents accidentally interchanging them. Not only are they keyed differently, but DDR2 has rounded notches on the side and the DDR3 modules have square notches on the side. DDR3 SO-DIMMs have 204 pins.


title: DDR3 SDRAM

text: For the Skylake microarchitecture, Intel has also designed a SO-DIMM package named UniDIMM, which can use either DDR3 or DDR4 chips. The CPU's integrated memory controller can then work with either. The purpose of UniDIMMs is to handle the transition from DDR3 to DDR4, where pricing and availability may make it desirable to switch RAM type. UniDIMMs have the same dimensions and number of pins as regular DDR4 SO-DIMMs, but the notch is placed differently to avoid accidentally using in an incompatible DDR4 SO-DIMM socket.


title: DDR3 SDRAM

text: DDR3 latencies are numerically higher because the I/O bus clock cycles by which they are measured are shorter; the actual time interval is similar to DDR2 latencies, around 10 ns. There is some improvement because DDR3 generally uses more recent manufacturing processes, but this is not directly caused by the change to DDR3.


title: DDR3 SDRAM

text: CAS latency (ns) = 1000 × CL (cycles) ÷ clock frequency (MHz) = 2000 × CL (cycles) ÷ transfer rate (MT/s)


title: DDR3 SDRAM

text: While the typical latencies for a JEDEC DDR2-800 device were 5-5-5-15 (12.5 ns), some standard latencies for JEDEC DDR3 devices include 7-7-7-20 for DDR3-1066 (13.125 ns) and 8-8-8-24 for DDR3-1333 (12 ns).


title: DDR3 SDRAM

text: As with earlier memory generations, faster DDR3 memory became available after the release of the initial versions. DDR3-2000 memory with 9-9-9-28 latency (9 ns) was available in time to coincide with the Intel Core i7 release in late 2008, while later developments made DDR3-2400 widely available (with CL 9–12 cycles = 7.5–10 ns), and speeds up to DDR3-3200 available (with CL 13 cycles = 8.125 ns).


title: DDR3 SDRAM

text: Power consumption of individual SDRAM chips (or, by extension, DIMMs) varies based on many factors, including speed, type of usage, voltage, etc. Dell's Power Advisor calculates that 4 GB ECC DDR1333 RDIMMs use about 4 W each. By contrast, a more modern mainstream desktop-oriented part 8 GB, DDR3/1600 DIMM, is rated at 2.58 W, despite being significantly faster.


title: DDR3 SDRAM

text: DDR3-xxx denotes data transfer rate, and describes DDR chips, whereas PC3-xxxx denotes theoretical bandwidth (with the last two digits truncated), and is used to describe assembled DIMMs. Bandwidth is calculated by taking transfers per second and multiplying by eight. This is because DDR3 memory modules transfer data on a bus that is 64 data bits wide, and since a byte comprises 8 bits, this equates to 8 bytes of data per transfer.


title: DDR3 SDRAM

text: With two transfers per cycle of a quadrupled clock signal, a 64-bit wide DDR3 module may achieve a transfer rate of up to 64 times the memory clock speed. With data being transferred 64 bits at a time per memory module, DDR3 SDRAM gives a transfer rate of (memory clock rate) × 4 (for bus clock multiplier) × 2 (for data rate) × 64 (number of bits transferred) / 8 (number of bits in a byte). Thus with a memory clock frequency of 100 MHz, DDR3 SDRAM gives a maximum transfer rate of 6400 MB/s.


title: DDR3 SDRAM

text: The data rate (in MT/s) is twice the I/O bus clock (in MHz) due to the double data rate of DDR memory. As explained above, the bandwidth in MB/s is the data rate multiplied by eight.


title: DDR3 SDRAM

text: CL – CAS Latency clock cycles, between sending a column address to the memory and the beginning of the data in response


title: DDR3 SDRAM

text: Fractional frequencies are normally rounded down, but rounding up to 667 is common because of the exact number being 666 and rounding to the nearest whole number. Some manufacturers also round to a certain precision or round up instead. For example, PC3-10666 memory could be listed as PC3-10600 or PC3-10700.


title: DDR3 SDRAM

text: Note: All items listed above are specified by JEDEC as JESD79-3F.All RAM data rates in-between or above these listed specifications are not standardized by JEDEC—often they are simply manufacturer optimizations using higher-tolerance or overvolted chips. Of these non-standard specifications, the highest reported speed reached was equivalent to DDR3-2544, as of May 2010.


title: DDR3 SDRAM

text: Alternative naming: DDR3 modules are often incorrectly labeled with the prefix PC (instead of PC3), for marketing reasons, followed by the data-rate. Under this convention PC3-10600 is listed as PC1333.


title: DDR3 SDRAM

text: DDR3 memory utilizes serial presence detect. Serial presence detect (SPD) is a standardized way to automatically access information about a computer memory module, using a serial interface. It is typically used during the power-on self-test for automatic configuration of memory modules.