title: Chronology of the universe

text: The October 2010 discovery of UDFy-38135539, the first observed galaxy to have existed during the following reionization epoch, gives us a window into these times. Subsequently, Leiden University's Rychard J. Bouwens and Garth D. Illingworth from UC Observatories/Lick Observatory found the galaxy UDFj-39546284 to be even older, at a time some 480 million years after the Big Bang or about halfway through the Dark Ages 13.2 billion years ago. In December 2012 the first candidate galaxies dating to before reionization were discovered, when UDFy-38135539, EGSY8p7 and GN-z11 galaxies were found to be around 380–550 million years after the Big Bang, 13.4 billion years ago and at a distance of around .


title: Chronology of the universe

text: Quasars provide some additional evidence of early structure formation. Their light shows evidence of elements such as carbon, magnesium, iron and oxygen. This is evidence that by the time quasars formed, a massive phase of star formation had already taken place, including sufficient generations of Population III stars to give rise to these elements.


title: Chronology of the universe

text: As the first stars, dwarf galaxies and quasars gradually form, the intense radiation they emit reionizes much of the surrounding universe; splitting the neutral hydrogen atoms back into a plasma of free electrons and protons for the first time since recombination and decoupling.


title: Chronology of the universe

text: Reionization is evidenced from observations of quasars. Quasars are a form of active galaxy, and the most luminous objects observed in the universe. Electrons in neutral hydrogen have specific patterns of absorbing ultraviolet photons, related to electron energy levels and called the Lyman series. Ionized hydrogen does not have electron energy levels of this kind. Therefore, light travelling through ionized hydrogen and neutral hydrogen shows different absorption lines. Ionized hydrogen in the intergalactic medium (particularly electrons) can scatter light through Thomson scattering as it did before recombination, but the expansion of the universe and clumping of gas into galaxies resulted in a concentration too low to make the universe fully opaque by the time of reionization. Because of the immense distance travelled by light (billions of light years) to reach Earth from structures existing during reionization, any absorption by neutral hydrogen is redshifted by various amounts, rather than by one specific amount, indicating when the absorption of then-ultraviolet light happened. These features make it possible to study the state of ionization at many different times in the past.


title: Chronology of the universe

text: Reionization began as "bubbles" of ionized hydrogen which became larger over time until the entire intergalactic medium was ionized, when the absorption lines by neutral hydrogen become rare. The absorption was due to the general state of the universe (the intergalactic medium) and not due to passing through galaxies or other dense areas. Reionization might have started to happen as early as "z" = 16 (250 million years of cosmic time) and was mostly complete by around "z" = 9 or 10 (500 million years), with the remaining neutral hydrogen becoming fully ionized "z" = 5 or 6 (1 billion years), when Gunn-Peterson troughs that show the presence of large amounts of neutral hydrogen disappear. The intergalactic medium remains predominantly ionized to the present day, the exception being some remaining neutral hydrogen clouds, which cause Lyman-alpha forests to appear in spectra.


title: Chronology of the universe

text: These observations have narrowed down the period of time during which reionization took place, but the source of the photons that caused reionization is still not completely certain. To ionize neutral hydrogen, an energy larger than 13.6 eV is required, which corresponds to ultraviolet photons with a wavelength of 91.2 nm or shorter, implying that the sources must have produced significant amount of ultraviolet and higher energy. Protons and electrons will recombine if energy is not continuously provided to keep them apart, which also sets limits on how numerous the sources were and their longevity. With these constraints, it is expected that quasars and first generation stars and galaxies were the main sources of energy. The current leading candidates from most to least significant are currently believed to be Population III stars (the earliest stars) (possibly 70%), dwarf galaxies (very early small high-energy galaxies) (possibly 30%), and a contribution from quasars (a class of active galactic nuclei).


title: Chronology of the universe

text: However, by this time, matter had become far more spread out due to the ongoing expansion of the universe. Although the neutral hydrogen atoms were again ionized, the plasma was much more thin and diffuse, and photons were much less likely to be scattered. Despite being reionized, the universe remained largely transparent during reionization due how sparse the intergalactic medium was. Reionization gradually ended as the intergalactic medium became virtually completely ionized, although some regions of neutral hydrogen do exist, creating Lyman-alpha forests.


title: Chronology of the universe

text: Matter continues to draw together under the influence of gravity, to form galaxies. The stars from this time period, known as Population II stars, are formed early on in this process, with more recent Population I stars formed later. Gravitational attraction also gradually pulls galaxies towards each other to form groups, clusters and superclusters. Hubble Ultra Deep Field observations has identified a number of small galaxies merging to form larger ones, at 800 million years of cosmic time (13 billion years ago). (This age estimate is now believed to be slightly overstated).


title: Chronology of the universe

text: Using the 10-metre Keck II telescope on Mauna Kea, Richard Ellis of the California Institute of Technology at Pasadena and his team found six star forming galaxies about 13.2 billion light-years away and therefore created when the universe was only 500 million years old. Only about 10 of these extremely early objects are currently known. More recent observations have shown these ages to be shorter than previously indicated. The most distant galaxy observed as of October 2016, GN-z11, has been reported to be 32 billion light-years away, a vast distance made possible through spacetime expansion ("z" = 11.1; comoving distance of 32 billion light-years; lookback time of 13.4 billion years).


title: Chronology of the universe

text: The universe has appeared much the same as it does now, for many billions of years. It will continue to look similar for many more billions of years into the future.


title: Chronology of the universe

text: Based upon the emerging science of nucleocosmochronology, the Galactic thin disk of the Milky Way is estimated to have been formed 8.8 ± 1.7 billion years ago.


title: Chronology of the universe

text: From about 9.8 billion years of cosmic time, the universe's large-scale behavior is believed to have gradually changed for the third time in its history. Its behavior had originally been dominated by radiation (relativistic constituents such as photons and neutrinos) for the first 47,000 years, and since about 370,000 years of cosmic time, its behavior had been dominated by matter. During its matter-dominated era, the expansion of the universe had begun to slow down, as gravity reined in the initial outward expansion. But from about 9.8 billion years of cosmic time, observations show that the expansion of the universe slowly stops decelerating, and gradually begins to accelerate again, instead.


title: Chronology of the universe

text: While the precise cause is not known, the observation is accepted as correct by the cosmologist community. By far the most accepted understanding is that this is due to an unknown form of energy which has been given the name "dark energy". "Dark" in this context means that it is not directly observed, but can currently only be studied by examining the effect it has on the universe. Research is ongoing to understand this dark energy. Dark energy is now believed to be the single largest component of the universe, as it constitutes about 68.3% of the entire mass-energy of the physical universe.


title: Chronology of the universe

text: Dark energy is believed to act like a cosmological constant—a scalar field that exists throughout space. Unlike gravity, the effects of such a field do not diminish (or only diminish slowly) as the universe grows. While matter and gravity have a greater effect initially, their effect quickly diminishes as the universe continues to expand. Objects in the universe, which are initially seen to be moving apart as the universe expands, continue to move apart, but their outward motion gradually slows down. This slowing effect becomes smaller as the universe becomes more spread out. Eventually, the outward and repulsive effect of dark energy begins to dominate over the inward pull of gravity. Instead of slowing down and perhaps beginning to move inward under the influence of gravity, from about 9.8 billion years of cosmic time, the expansion of space starts to slowly accelerate "outward" at a gradually "increasing" rate.


title: Chronology of the universe

text: There are several competing scenarios for the long-term evolution of the universe. Which of them will happen, if any, depends on the precise values of physical constants such as the cosmological constant, the possibility of proton decay, the energy of the vacuum (meaning, the energy of "empty" space itself), and the natural laws beyond the Standard Model.


title: Chronology of the universe

text: If the expansion of the universe continues and it stays in its present form, eventually all but the nearest galaxies will be carried away from us by the expansion of space at such a velocity that the observable universe will be limited to our own gravitationally bound local galaxy cluster. In the very long term (after many trillions—thousands of billions—of years, cosmic time), the Stelliferous Era will end, as stars cease to be born and even the longest-lived stars gradually die. Beyond this, all objects in the universe will cool and (with the possible exception of protons) gradually decompose back to their constituent particles and then into subatomic particles and very low-level photons and other fundamental particles, by a variety of possible processes.


title: Chronology of the universe

text: Ultimately, in the extreme future, the following scenarios have been proposed for the ultimate fate of the universe:


title: Chronology of the universe

text: In this kind of extreme timescale, extremely rare quantum phenomena may also occur that are extremely unlikely to be seen on a timescale smaller than trillions of years. These may also lead to unpredictable changes to the state of the universe which would not be likely to be significant on any smaller timescale. For example, on a timescale of millions of trillions of years, black holes might appear to evaporate almost instantly, uncommon quantum tunnelling phenomena would appear to be common, and quantum (or other) phenomena so unlikely that they might occur just once in a trillion years may occur many times.


title: Kayden Kross

text: Kayden Kross (born 1985) is an American pornographic actress and director. She is a member of the AVN and XRCO Halls of Fame.


title: Kayden Kross

text: Kross grew up in the foothills between Sacramento and Placerville. She has described herself as "the book nerd" during her time as a high school student. Kross began stripping at Rick's Showgirls in Rancho Cordova, California when she was eighteen years old to earn extra money to rescue a pony from a slaughter house, which she kept for eight months. She was later contacted by an agent, whose business relationship provided Kross with the opportunity of modeling in adult magazines.


title: Kayden Kross

text: Her movies with Vivid included "Kayden's First Time", "Hard Time", and "Be Here Now". Unhappy with the company, she became a free agent one year later when she did not renew her contract. She signed an exclusive contract with Adam & Eve after one month of being a free agent.


title: Kayden Kross

text: She was named "Penthouse" Pet of the Month for September 2008. Kross' official website, ClubKayden.com, was launched on September 2, 2008. Kross has hosted a blog at UnKrossed.com, and has written regular updates and opinion columns for MikeSouth.com, an adult industry gossip blog, among other sites.


title: Kayden Kross

text: Kross became exclusive to Digital Playground under a multi-year contract on January 1, 2010. Her first movie with the company, "The Smiths", topped sales charts immediately and has continued to be a best seller. She was given the lead in their big budget feature, "Body Heat", in her third month in contract. She won two Best Actress Awards for the role.


title: Kayden Kross

text: Kross hosted the 2010 AVN Awards show, along with porn actress Kirsten Price and comedian Dave Attell. She was "Penthouse" magazine's "Cover Girl" for September 2008 and 2010. Kross starred in the 2010 AVN Best Feature "The 8th Day" and portrayed the role of Elin Nordegren, wife of Tiger Woods, in Adam & Eve Pictures' film "Tyler's Wood".


title: Kayden Kross

text: In 2012, she hosted the Xbiz awards for the second time, and appeared in the ceremony alongside Wicked Pictures/Wicked.com contract star, Jessica Drake, and on the AVN red carpet with co-hosts Jesse Jane and guitarist Dave Navarro.


title: Kayden Kross

text: Kross has made appearances in the FX's comedy series "The League", the G4 reality series "The Block", and "Family Jewels".


title: Kayden Kross

text: In 2011, she was cast as Tara in Gregory Hatanaka's drama "Blue Dream" briefly co-hosted a regular videocast, "Kayden's Review", for Triggla TV alongside the comedian Dane Hanson. From 2012 - 2013, Kross portrayed a main character in the second season of Tucky Williams' lesbian-themed web series "Girl/Girl Scene". Starting from January 2013 Kross hosts the weekly call-in show "Krossfire" on Playboy Radio.


title: Kayden Kross

text: In 2013, Kross also appeared in the featurette "Chicks 'N Guns" on the "Breaking Bad" 5th season DVD as a stripper. The scene takes place during the season 5 episode "Gliding Over All". Kross also appeared in two music videos from the band Nekrogoblikon, "No One Survives" in 2012 and "We Need a Gimmick" in 2015.


title: Kayden Kross

text: Kross writes columns regularly for publications such as "Complex" magazine, "XBIZ" magazine, and a blog for xcritic.com. She has also contributed to "Timothy McSweeney's Internet Tendency", and her short story "Plank" appeared in the 2012 short story collection "Forty Stories: New Writing from Harper Perennial", an e-book. As of August 2012, she was writing an autobiographical book about the porn industry.


title: Kayden Kross

text: In 2008, she was among those testifying against a proposed tax in California on all producers and distributors of adult entertainment. In February 2012, she and conservative pundit Wendy Murphy appeared on "Stossel", with host John Stossel, to discuss legislation in California that would require that condoms be used during the production of adult movies.


title: Kayden Kross

text: In October 2008, Kross was charged with grand theft and violations of the California Civil Code, involving contracts for purchases of home equity mortgages. In July 2009, the grand-theft charge was dismissed, and the real-estate-fraud charge was reduced to a misdemeanor; Kross pleaded no contest to the resulting charges and was sentenced to one day in custody and three years of probation. She blamed her involvement in the situation on her naïveté and being scammed by the broker and mortgage lender.


title: Kayden Kross

text: Kross and her French partner Manuel Ferrara have one daughter, born in January 2014. In 2013, Ferrara asked her to no longer perform with other men. Ferrara continues to shoot scenes with other women, occasionally scenes which are directed by Kross. They acknowledged the seeming double standard of their arrangement but agreed that his work would stay professional and that Kross maintains "veto" power over who performs with Manuel. He also related that if she wished for him to stop performing altogether, he would.


title: Random forest

text: Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that operates by constructing a multitude of decision trees at training time. For classification tasks, the output of the random forest is the class selected by most trees. For regression tasks, the mean or average prediction of the individual trees is returned. Random decision forests correct for decision trees' habit of overfitting to their training set. Random forests generally outperform decision trees, but their accuracy is lower than gradient boosted trees. However, data characteristics can affect their performance.


title: Random forest

text: The first algorithm for random decision forests was created in 1995 by Tin Kam Ho using the random subspace method, which, in Ho's formulation, is a way to implement the "stochastic discrimination" approach to classification proposed by Eugene Kleinberg.


title: Random forest

text: An extension of the algorithm was developed by Leo Breiman and Adele Cutler, who registered "Random Forests" as a trademark in 2006 (, owned by Minitab, Inc.). The extension combines Breiman's "bagging" idea and random selection of features, introduced first by Ho and later independently by Amit and Geman in order to construct a collection of decision trees with controlled variance.


title: Random forest

text: Random forests are frequently used as "blackbox" models in businesses, as they generate reasonable predictions across a wide range of data while requiring little configuration.


title: Random forest

text: The general method of random decision forests was first proposed by Ho in 1995. Ho established that forests of trees splitting with oblique hyperplanes can gain accuracy as they grow without suffering from overtraining, as long as the forests are randomly restricted to be sensitive to only selected feature dimensions. A subsequent work along the same lines concluded that other splitting methods behave similarly, as long as they are randomly forced to be insensitive to some feature dimensions. Note that this observation of a more complex classifier (a larger forest) getting more accurate nearly monotonically is in sharp contrast to the common belief that the complexity of a classifier can only grow to a certain level of accuracy before being hurt by overfitting. The explanation of the forest method's resistance to overtraining can be found in Kleinberg's theory of stochastic discrimination.


title: Random forest

text: tree. The idea of random subspace selection from Ho was also influential in the design of random forests. In this method a forest of trees is grown,


title: Random forest

text: Decision trees are a popular method for various machine learning tasks. Tree learning "come[s] closest to meeting the requirements for serving as an off-the-shelf procedure for data mining", say Hastie "et al.", "because it is invariant under scaling and various other transformations of feature values, is robust to inclusion of irrelevant features, and produces inspectable models. However, they are seldom accurate".


title: Random forest

text: In particular, trees that are grown very deep tend to learn highly irregular patterns: they overfit their training sets, i.e. have low bias, but very high variance. Random forests are a way of averaging multiple deep decision trees, trained on different parts of the same training set, with the goal of reducing the variance. This comes at the expense of a small increase in the bias and some loss of interpretability, but generally greatly boosts the performance in the final model.


title: Random forest

text: Forests are like the pulling together of decision tree algorithm efforts. Taking the teamwork of many trees thus improving the performance of a single random tree. Though not quite similar, forests give the effects of a k-fold cross validation.


title: Random forest

text: The training algorithm for random forests applies the general technique of bootstrap aggregating, or bagging, to tree learners. Given a training set = , ..., with responses = , ..., , bagging repeatedly ("B" times) selects a random sample with replacement of the training set and fits trees to these samples:


title: Random forest

text: After training, predictions for unseen samples can be made by averaging the predictions from all the individual regression trees on :


title: Random forest

text: This bootstrapping procedure leads to better model performance because it decreases the variance of the model, without increasing the bias. This means that while the predictions of a single tree are highly sensitive to noise in its training set, the average of many trees is not, as long as the trees are not correlated. Simply training many trees on a single training set would give strongly correlated trees (or even the same tree many times, if the training algorithm is deterministic); bootstrap sampling is a way of de-correlating the trees by showing them different training sets.


title: Random forest

text: Additionally, an estimate of the uncertainty of the prediction can be made as the standard deviation of the predictions from all the individual regression trees on :


title: Random forest

text: The number of samples/trees, , is a free parameter. Typically, a few hundred to several thousand trees are used, depending on the size and nature of the training set. An optimal number of trees can be found using cross-validation, or by observing the "out-of-bag error": the mean prediction error on each training sample , using only the trees that did not have in their bootstrap sample.


title: Random forest

text: The above procedure describes the original bagging algorithm for trees. Random forests also include another type of bagging scheme: they use a modified tree learning algorithm that selects, at each candidate split in the learning process, a random subset of the features. This process is sometimes called "feature bagging". The reason for doing this is the correlation of the trees in an ordinary bootstrap sample: if one or a few features are very strong predictors for the response variable (target output), these features will be selected in many of the trees, causing them to become correlated. An analysis of how bagging and random subspace projection contribute to accuracy gains under different conditions is given by Ho.


title: Random forest

text: Typically, for a classification problem with features, (rounded down) features are used in each split. For regression problems the inventors recommend (rounded down) with a minimum node size of 5 as the default. In practice, the best values for these parameters should be tuned on a case-to-case basis for every problem.


title: Random forest

text: Adding one further step of randomization yields "extremely randomized trees", or ExtraTrees. While similar to ordinary random forests in that they are an ensemble of individual trees, there are two main differences: first, each tree is trained using the whole learning sample (rather than a bootstrap sample), and second, the top-down splitting in the tree learner is randomized. Instead of computing the locally "optimal" cut-point for each feature under consideration (based on, e.g., information gain or the Gini impurity), a "random" cut-point is selected. This value is selected from a uniform distribution within the feature's empirical range (in the tree's training set). Then, of all the randomly generated splits, the split that yields the highest score is chosen to split the node. Similar to ordinary random forests, the number of randomly selected features to be considered at each node can be specified. Default values for this parameter are formula_3 for classification and formula_4 for regression, where formula_4 is the number of features in the model.


title: Random forest

text: Random forests can be used to rank the importance of variables in a regression or classification problem in a natural way. The following technique was described in Breiman's original paper and is implemented in the R package "randomForest".


title: Random forest

text: The first step in measuring the variable importance in a data set formula_6 is to fit a random forest to the data. During the fitting process the out-of-bag error for each data point is recorded and averaged over the forest (errors on an independent test set can be substituted if bagging is not used during training).


title: Random forest

text: To measure the importance of the formula_7-th feature after training, the values of the formula_7-th feature are permuted among the training data and the out-of-bag error is again computed on this perturbed data set. The importance score for the formula_7-th feature is computed by averaging the difference in out-of-bag error before and after the permutation over all trees. The score is normalized by the standard deviation of these differences.


title: Random forest

text: Features which produce large values for this score are ranked as more important than features which produce small values. The statistical definition of the variable importance measure was given and analyzed by Zhu "et al."


title: Random forest

text: This method of determining variable importance has some drawbacks. For data including categorical variables with different number of levels, random forests are biased in favor of those attributes with more levels. Methods such as partial permutations


title: Random forest

text: and growing unbiased trees can be used to solve the problem. If the data contain groups of correlated features of similar relevance for the output, then smaller groups are favored over larger groups.


title: Random forest

text: A relationship between random forests and the -nearest neighbor algorithm (-NN) was pointed out by Lin and Jeon in 2002. It turns out that both can be viewed as so-called "weighted neighborhoods schemes". These are models built from a training set formula_10 that make predictions formula_11 for new points by looking at the "neighborhood" of the point, formalized by a weight function :


title: Random forest

text: Here, formula_13 is the non-negative weight of the 'th training point relative to the new point in the same tree. For any particular , the weights for points formula_14 must sum to one. Weight functions are given as follows:


title: Random forest

text: Since a forest averages the predictions of a set of trees with individual weight functions formula_17, its predictions are


title: Random forest

text: This shows that the whole forest is again a weighted neighborhood scheme, with weights that average those of the individual trees. The neighbors of in this interpretation are the points formula_14 sharing the same leaf in any tree formula_7. In this way, the neighborhood of depends in a complex way on the structure of the trees, and thus on the structure of the training set. Lin and Jeon show that the shape of the neighborhood used by a random forest adapts to the local importance of each feature.


title: Random forest

text: As part of their construction, random forest predictors naturally lead to a dissimilarity measure among the observations. One can also define a random forest dissimilarity measure between unlabeled data: the idea is to construct a random forest predictor that distinguishes the "observed" data from suitably generated synthetic data.


title: Random forest

text: The observed data are the original unlabeled data and the synthetic data are drawn from a reference distribution. A random forest dissimilarity can be attractive because it handles mixed variable types very well, is invariant to monotonic transformations of the input variables, and is robust to outlying observations. The random forest dissimilarity easily deals with a large number of semi-continuous variables due to its intrinsic variable selection; for example, the "Addcl 1" random forest dissimilarity weighs the contribution of each variable according to how dependent it is on other variables. The random forest dissimilarity has been used in a variety of applications, e.g. to find clusters of patients based on tissue marker data.


title: Random forest

text: Instead of decision trees, linear models have been proposed and evaluated as base estimators in random forests, in particular multinomial logistic regression and naive Bayes classifiers. In cases that the relationship between the predictors and the target variable is linear, the base learners may have an equally high accuracy as the ensemble learner.


title: Random forest

text: In machine learning, kernel random forests (KeRF) establish the connection between random forests and kernel methods. By slightly modifying their definition, random forests can be rewritten as kernel methods, which are more interpretable and easier to analyze.


title: Random forest

text: Leo Breiman was the first person to notice the link between random forest and kernel methods. He pointed out that random forests which are grown using i.i.d. random vectors in the tree construction are equivalent to a kernel acting on the true margin. Lin and Jeon established the connection between random forests and adaptive nearest neighbor, implying that random forests can be seen as adaptive kernel estimates. Davies and Ghahramani proposed Random Forest Kernel and show that it can empirically outperform state-of-art kernel methods. Scornet first defined KeRF estimates and gave the explicit link between KeRF estimates and random forest. He also gave explicit expressions for kernels based on centered random forest and uniform random forest, two simplified models of random forest. He named these two KeRFs Centered KeRF and Uniform KeRF, and proved upper bounds on their rates of consistency.


title: Random forest

text: Centered forest is a simplified model for Breiman's original random forest, which uniformly selects an attribute among all attributes and performs splits at the center of the cell along the pre-chosen attribute. The algorithm stops when a fully binary tree of level formula_21 is built, where formula_22 is a parameter of the algorithm.


title: Random forest

text: Uniform forest is another simplified model for Breiman's original random forest, which uniformly selects a feature among all features and performs splits at a point uniformly drawn on the side of the cell, along the preselected feature.


title: Random forest

text: Given a training sample formula_23 of formula_24-valued independent random variables distributed as the independent prototype pair formula_25, where formula_26. We aim at predicting the response formula_27, associated with the random variable formula_28, by estimating the regression function formula_29. A random regression forest is an ensemble of formula_30 randomized regression trees. Denote formula_31 the predicted value at point formula_32 by the formula_7-th tree, where formula_34 are independent random variables, distributed as a generic random variable formula_35, independent of the sample formula_36. This random variable can be used to describe the randomness induced by node splitting and the sampling procedure for tree construction. The trees are combined to form the finite forest estimate formula_37.


title: Random forest

text: For regression trees, we have formula_38, where formula_39 is the cell containing formula_32, designed with randomness formula_41 and dataset formula_36, and formula_43.


title: Random forest

text: Thus random forest estimates satisfy, for all formula_44, formula_45. Random regression forest has two levels of averaging, first over the samples in the target cell of a tree, then over all trees. Thus the contributions of observations that are in cells with a high density of data points are smaller than that of observations which belong to less populated cells. In order to improve the random forest methods and compensate the misestimation, Scornet defined KeRF by


title: Random forest

text: which is equal to the mean of the formula_47's falling in the cells containing formula_32 in the forest. If we define the connection function of the formula_30 finite forest as formula_50, i.e. the proportion of cells shared between formula_32 and formula_52, then almost surely we have formula_53, which defines the KeRF.


title: Random forest

text: The construction of Centered KeRF of level formula_21 is the same as for centered forest, except that predictions are made by formula_55, the corresponding kernel function, or connection function is


title: Random forest

text: Uniform KeRF is built in the same way as uniform forest, except that predictions are made by formula_55, the corresponding kernel function, or connection function is


title: Random forest

text: Predictions given by KeRF and random forests are close if the number of points in each cell is controlled:


title: Random forest

text: When the number of trees formula_30 goes to infinity, then we have infinite random forest and infinite KeRF. Their estimates are close if the number of observations in each cell is bounded:


title: Random forest

text: Assume that formula_68, where formula_69 is a centered Gaussian noise, independent of formula_28, with finite variance formula_71. Moreover, formula_28 is uniformly distributed on formula_73 and formula_74 is Lipschitz. Scornet proved upper bounds on the rates of consistency for centered KeRF and uniform KeRF.


title: Random forest

text: Providing formula_75 and formula_76, there exists a constant formula_77 such that, for all formula_78,


title: Random forest

text: While random forests often achieve higher accuracy than a single decision tree, they sacrifice the intrinsic interpretability present in decision trees. Decision trees are among a fairly small family of machine learning models that are easily interpretable along with linear models, rule-based models, and attention-based models. This interpretability is one of the most desirable qualities of decision trees. It allows developers to confirm that the model has learned realistic information from the data and allows end-users to have trust and confidence in the decisions made by the model. For example, following the path that a decision tree takes to make its decision is quite trivial, but following the paths of tens or hundreds of trees is much harder. To achieve both performance and interpretability, some model compression techniques allow transforming a random forest into a minimal "born-again" decision tree that faithfully reproduces the same decision function. If it is established that the predictive attributes are linearly correlated with the target variable, using random forest may not enhance the accuracy of the base learner. Furthermore, in problems with multiple categorical variables, random forest may not be able to increase the accuracy of the base learner.


title: Live Free or Die Hard

text: Live Free or Die Hard (released as Die Hard 4.0 outside North America) is a 2007 American action-thriller film directed by Len Wiseman, and serves as the fourth installment in the "Die Hard" film series. It is based on the 1997 article "A Farewell to Arms" written for "Wired" magazine by John Carlin. The film's name is adapted from New Hampshire's state motto, "Live Free or Die".


title: Live Free or Die Hard

text: In the film, NYPD Detective John McClane (Bruce Willis) attempts to stop a cyber-terrorist (Timothy Olyphant) who hacks into government and commercial computers across the United States with the goal of starting a "fire sale" that would disable key elements of the nation's infrastructure. Justin Long, Cliff Curtis, and Maggie Q also star.


title: Live Free or Die Hard

text: "Live Free or Die Hard" was released in the United States on June 27, 2007. The film grossed $388 million worldwide, making it the highest-grossing installment in the "Die Hard" series. It received generally positive reviews from critics, who called the film a return to form for the series. It is the only "Die Hard" film to be theatrically released with a PG-13 rating from the MPAA, although an unrated edition would later be made available on home media. A fifth film, "A Good Day to Die Hard", was released in 2013.


title: Live Free or Die Hard

text: Responding to a brief computer outage at its Cyber-Security Division by tracking down top computer hackers, the FBI, led by Deputy Director Miguel Bowman, asks NYPD detective John McClane to go to New Jersey to bring in hacker Matthew Farrell. McClane arrives just in time to save him from assassins sent by Mai Linh, who is the lover and accomplice of Thomas Gabriel, a hacker and leader of the terrorists.


title: Live Free or Die Hard

text: On the way to D.C., Farrell tells McClane he had written an algorithm for Linh to crack a specific security system for white hat purposes. Meanwhile, Gabriel orders his crew of hackers to take over transportation grids and the stock market, while nationally broadcasting a threatening message to the U.S. government. Farrell realizes this is the start of a "fire sale", a cyber attack designed to disable the nation's infrastructure. As McClane and Farrell are driven to DHS headquarters, Linh, posing as a dispatcher, reroutes them into a helicopter ambush. McClane fends off the attackers, destroying the helicopter and all but one of the terrorists.


title: Live Free or Die Hard

text: Desperate, McClane asks Farrell what would be Gabriel's next move. He deduces Gabriel's next target is the power grid, so they drive to a utility superstation in West Virginia. They find the superstation under control by a team led by Linh. McClane kills all but Linh. After an intense, violent struggle between the two, Linh, trapped in a car, is killed when the vehicle falls down an elevator shaft.


title: Live Free or Die Hard

text: While Farrell is working on the hub computer to slow down the damage done, he is able to trace Gabriel and uploads his picture. He then sends it to Bowman at the FBI. McClane is shocked to learn that Bowman and Gabriel once worked together at the U.S. Department of Defense. Gabriel was the chief programmer for infrastructural security. He warned the department of weaknesses that made America's network infrastructure vulnerable to cyberwarfare, but he was ignored and his unorthodox methods got him fired, and he is out for revenge. Enraged over Linh's death, Gabriel redirects large amounts of natural gas to the superstation to kill McClane and Farrell, and they barely escape.


title: Live Free or Die Hard

text: McClane and Farrell then travel by helicopter to the home of super hacker, Frederick "Warlock" Kaludis in Baltimore. Warlock identifies the piece of code Farrell wrote for Linh as a means to access data at a Social Security Administration building at Woodlawn, Maryland. He confirms Gabriel's former ties as a government employee. Doing a traceroute, Warlock locates Gabriel.


title: Live Free or Die Hard

text: The Woodlawn building is actually an NSA facility intended to back up the nation's personal and financial records in the event of a cyber attack and designed by Gabriel himself. The attack on the FBI triggered a download of financial data to Woodlawn, data which Gabriel plans to steal. Meanwhile, ordered by Gabriel, one of his top men kills all but one of his computer hackers after they've outlived their usefulness. Gabriel then taps into the connection they made, which reveals the location of McClane's estranged daughter Lucy, whom he kidnaps. McClane and Gabriel then meet - virtually - McClane telling him he will lose.


title: Live Free or Die Hard

text: McClane and Farrell race to the Woodlawn facility. Farrell finds the facility's main server and encrypts the data Gabriel's men downloaded before getting captured. Gabriel then takes Farrell and Lucy with him as he flees. McClane pursues them, hijacking their semi mobile base. Accessing the communication system of an F-35B Lightning II, Gabriel orders the pilot to attack the truck McClane is driving, but the jet is destroyed by falling debris. McClane barely survives and sees Gabriel's vehicle pull into a nearby hangar. He contacts the FBI and orders the director to storm the facility where Gabriel is situated and rescue his daughter if he doesn't make it out alive.


title: Live Free or Die Hard

text: There, Gabriel demands that Farrell decrypt the financial data. When he refuses, Gabriel shoots him in the knee and threatens to kill Lucy. McClane arrives, killing two of Gabriel's men, but he is shot in the shoulder by Gabriel's last man, Emerson. Gabriel positions himself behind McClane, putting the barrel of the gun in his shoulder wound. McClane then pulls the trigger. The bullet travels through McClane's shoulder and hits Gabriel in the chest, killing him instantly. Farrell then grabs a pistol and kills Emerson as the FBI arrives. Afterwards, McClane thanks Farrell for saving Lucy's life, who takes a romantic interest in him.


title: Live Free or Die Hard

text: Additional characters include Gabriel's henchmen: Chris Palmero as Del, Andrew Friedman as Casper and Bryon Weiss as Robinson. Chris Ellis appears as Jack Sclavino, McClane's superior officer. Sung Kang makes an appearance as Raj, a desk officer of FBI's cyber division. Matt O'Leary appears as Clay, a hacker who unwittingly gives Gabriel a code, allowing his house to be destroyed. Jake McDorman plays a small role as Jim, Lucy's boyfriend. Tim Russ appears as an NSA agent. Rosemary Knower has a cameo as Mrs. Kaludis, Frederick's mother.


title: Live Free or Die Hard

text: After the success they had with "Die Hard With a Vengeance", and after many discussions with Bruce Willis, 20th Century Fox started working on the fourth "Die Hard" film. As they did with original scripts for the previous three films, Fox and Willis decided to pick a script which was not written as a "Die Hard" film and then have it changed into the next sequel. In 1997, they picked up a script titled "Tears of the Sun", an action-adventure written by Alan B. McElroy, which Willis really liked and wanted to turn into "Die Hard 4". The script was about a group of people who go to set up a radio relay station deep inside the Amazon jungle; due to a severe storm, they land in a small mining town where they hire a guide. However, they are soon captured by a drug lord and his gang, who force them to work as slaves in his mine. They manage to escape and have to survive both the jungle and drug dealers who are chasing them.


title: Live Free or Die Hard

text: At the time Fox decided to rework the story into "Die Hard 4", "Tears of the Sun" had been in development since the early 1990s. Around 1994, it was one of several projects to which John Woo was attached as a director, but which never got made. Besides McElroy, some of the other writers who worked on the "Tears of the Sun" script over the years included Ronald Bass, Chris Gerolmo, Larry Ferguson, Robert Mark Kamen and Joel Gross. It was also at one point considered to be re-written into a new modern adaptation of "Tarzan", before Fox got the script.


title: Live Free or Die Hard

text: Interestingly, one of the first rejected scripts for the third "Die Hard" film, written by John Milius, also took place in the jungle. As with that script, the "Tears of the Sun" version of "Die Hard 4" was never made.


title: Live Free or Die Hard

text: Willis liked the "Tears of the Sun" title so much that he requested that one of his films, made in 2002, be re-titled "Tears of the Sun" (instead of "Hostile Rescue" or "Man of War") in exchange for starring in another "Die Hard" film. This is why it is often mistakenly reported that "Tears of the Sun" was originally going to be the fourth "Die Hard" film.


title: Live Free or Die Hard

text: The film's plot is based on an earlier script entitled "WW3.com" by David Marconi, screenwriter of the 1998 film "Enemy of the State". Using John Carlin's "Wired" magazine article entitled "A Farewell to Arms", Marconi crafted a screenplay about a cyber-terrorist attack on the United States. The attack procedure is known as a "fire sale", depicting a three-stage coordinated attack on a country's transportation, telecommunications, financial, and utilities infrastructure systems. After the September 11, 2001 attacks, the project was stalled, only to be resurrected several years later and rewritten into "Live Free or Die Hard" by Doug Richardson and eventually by Mark Bomback.


title: Live Free or Die Hard

text: Willis said in 2005 that the film would be called "Die Hard 4.0", as it revolves around computers and cyber-terrorism. IGN later reported the film was to be called "Die Hard: Reset" instead. 20th Century Fox later announced the title as "Live Free or Die Hard" and set a release date of June 29, 2007 with filming to begin in September 2006. The title is based on New Hampshire's state motto, "Live Free or Die", which is attributed to a quote from General John Stark. International trailers use the "Die Hard 4.0" title, as the film was released outside North America with that title. Early into the film's DVD commentary, both Wiseman and Willis note a preference for the title "Die Hard 4.0".


title: Live Free or Die Hard

text: For the visual effects used throughout the film, actor Bruce Willis and director Len Wiseman stated that they wanted to use a limited amount of computer-generated imagery (CGI). One VFX producer said that "Len was insisting on the fact that, because we’ve got "Transformers" and other big CG movies coming out, this one has to feel more real. It has to be embedded in some kind of practical reality in order to give it that edge of being a "Die Hard"." Companies such as Digital Dimension, The Orphanage, R!ot, Pixel Magic, and Amalgamated Pixels assisted in the film's visual effects.


title: Live Free or Die Hard

text: Digital Dimension worked on 200 visual effects shots in the film, including the sequence that shows characters John McClane and Matt Farrell crouching between two cars as another car lands on top of the other cars. To achieve this effect, a crane yanked the car and threw it in the air onto the two cars that were also being pulled by cables. The shot was completed when the two characters were integrated into the footage of the car stunt after the lighting was adjusted and CGI glass and debris were added. In the same sequence, John McClane destroys a helicopter that several of Gabriel's henchman are riding in by ramming it with a car. This was accomplished by first filming one take where one of Gabriel's henchman, Rand, jumps from the helicopter, and in the next take the car is propelled into the stationary helicopter as it is hoisted by wires. The final view of the shot overlays the two takes, with added CGI for the debris and moving rotor blades. The company also assisted in adding cars for traffic collisions and masses of people for evacuations from several government buildings.


title: Live Free or Die Hard

text: The Orphanage developed a multi-level freeway interchange for use in one of the film's final scenes by creating a digital environment and a long spiral ramp that was built in front of a bluescreen. When a F-35 jet is chasing McClane on the freeway, a miniature model and a full-size prop were both built to assist in digitally adding the jet into the scene. The nine-foot model was constructed from November 2006 through February 2007. When the jet is shown hovering near the freeway, editors used the software 3D graphics program Maya to blur the background and create a heat ripple effect.


title: Live Free or Die Hard

text: Filming for "Live Free or Die Hard" started in downtown Baltimore, Maryland on September 23, 2006. Eight different sets were built on a large soundstage for filming many scenes throughout the film. When recording the sound for the semi trailer used in one of the film's final scenes, 18 microphones were used to record the engine, tires, and damage to the vehicle. Post-production for the film only took 16 weeks, when it was more common for similar films to use 26 weeks.


title: Live Free or Die Hard

text: In order to prevent possible injuries and be in peak condition for the film, Willis worked out almost daily for several months prior to filming. Willis was injured on January 24, 2007 during a fight scene, when he was kicked above his right eye by a stunt double for actress Maggie Q who was wearing stiletto heels. Willis described the event as "no big deal" but when Len Wiseman inspected his injury, he noticed that the situation was much more serious than previously thought—in the DVD commentary, Wiseman indicates in inspecting the wound that he could see bone. Willis was hospitalized and received seven stitches which ran through his right eyebrow and down into the corner of his eye. Due to the film's non-linear production schedule, these stitches can accidentally be seen in the scene where McClane first delivers Farrell to Bowman.


title: Live Free or Die Hard

text: Throughout filming, between 200 and 250 stunt people were used. Bruce Willis' stunt double, Larry Rippenkroeger, was knocked unconscious when he fell from a fire escape to the pavement. Rippenkroeger suffered broken bones in his face, several broken ribs, a punctured lung, and fractures in both wrists. Due to his injuries, production was temporarily shut down. Willis personally paid the hotel bills for Rippenkroeger's parents and visited him a number of times at the hospital.


title: Live Free or Die Hard

text: Kevin Smith recalls rewriting scenes on the set of "Live Free or Die Hard" in his spoken word film "".


title: Live Free or Die Hard

text: The score for "Live Free or Die Hard", written by Marco Beltrami, was released on July 2, 2007 by Varèse Sarabande (which also released the soundtracks for the first two "Die Hard" films), several days after the United States release of the film. This was the first film not to be scored by Michael Kamen, due to his death in 2003; Beltrami incorporates Kamen's thematic material into his score, but Kamen is not credited on the film or the album. Other songs in the film include "Rock & Roll Queen" by The Subways, "Fortunate Son" by Creedence Clearwater Revival and "I'm So Sick" by Flyleaf. Eric Lichtenfeld, reviewing from Soundtrack.net, said of the score: "The action cues, in which the entire orchestra seems percussive, flow well together."


title: Live Free or Die Hard

text: In the United States, the first three films in the "Die Hard" series were rated R by the Motion Picture Association of America. "Live Free or Die Hard", however, was edited to obtain a PG-13 rating. In some cases, alternate profanity-free dialogue was shot and used or swearing was cut out in post-production to reduce profanity. Director Len Wiseman commented on the rating, saying "It was about three months into it [production], and I hadn't even heard that it was PG-13... But in the end, it was just trying to make the best "Die Hard" movie, not really thinking so much about what the rating would be."


title: Live Free or Die Hard

text: Bruce Willis was upset with the studio's decision, stating, "I really wanted this one to live up to the promise of the first one, which I always thought was the only really good one. That's a studio decision that is becoming more and more common, because they’re trying to reach a broader audience. It seems almost a courageous move to give a picture an R rating these days. But we still made a pretty hardcore, smashmouth film." Willis said he thought that viewers unaware that it was not an R-rated film would not suspect so due to the level and intensity of the action as well as the usage of some profanity, although he admitted these elements were less intense than in the previous films. He also said that this film was the best of the four: "It's unbelievable. I just saw it last week. I personally think, it's better than the first one."


title: Live Free or Die Hard

text: In the United Kingdom, the British Board of Film Classification awarded the film a 15 rating (including the unrated version, released later), the same rating as "Die Hard with a Vengeance" and "Die Hard 2", albeit both were cut for both theatrical and video release, (The first film in the series originally received an 18 certificate). All films have been re-rated 15 uncut. Die Hard 4.0 was released with no cuts made and the cinema version (i.e.,the U.S. PG-13 version) consumer advice read that it "contains frequent action violence and one use of strong language". The unrated version was released on DVD as the "Ultimate Action Edition" with the consumer advice "contains strong language and violence".


title: Live Free or Die Hard

text: In Australia, Die Hard 4.0 was released with the PG-13 cut with an M rating, the same as the others in the series (The Australian Classification Board is less strict with regards to language and to a lesser extent, violence). The unrated version was later released on DVD and Blu-ray also with an M rating. The film, notably never released in home media with its theatrical cut, has only been released in Australia as the extended edition.


title: Live Free or Die Hard

text: The Blu-ray and DVD were released on October 29, 2007, in the United Kingdom, on October 31 in Hungary, November 20 in the United States, and December 12 in Australia. The DVD topped rental and sales charts in its opening week of release in the U.S. and Canada. There is an unrated version, which retains much of the original 'R-rated' dialogue, and a theatrical version of the film. However, the unrated version has a branching error that resulted in one of the unrated changes being omitted. The film briefly switches to the PG-13 version in the airbag scene; McClane's strong language is missing from this sequence (although international DVD releases of the unrated version are unaffected). The Blu-ray release features the PG-13 theatrical cut which runs at 128 minutes, while the Collector's Edition DVD includes both the unrated and theatrical versions. "Time" magazine's Richard Corliss named it one of the Top 10 DVDs of 2007, ranking it at No. 10. In 2015, the movie was featured in the "Die Hard: Nakatomi Plaza" boxed set, which featured the unrated cut of the film on Blu-Ray for the first time in the US. In 2017, the movie was included in the "Die Hard Collection" Blu-ray set with all 5 films in it. Though unlike the DVD, the Blu-ray doesn't contain the branching error during the airbag scene.


title: Live Free or Die Hard

text: The DVD for the film was the first to include a Digital Copy of the film which could be played on a PC or Mac computer and could also be imported into several models of portable video players. Mike Dunn, a president for 20th Century Fox, stated "The industry has sold nearly 12 billion DVDs to date, and the release of "Live Free or Die Hard" is the first one that allows consumers to move their content to other devices."


title: Live Free or Die Hard

text: "Live Free or Die Hard" debuted at No. 2 behind "Ratatouille", at the U.S. box office and made $9.1 million in its first day of release in 3,172 theaters, the best opening day take of any film in the "Die Hard" series (not taking inflation into account). On its opening weekend "Live Free or Die Hard" made $33.3 million ($48.3 million counting Wednesday and Thursday). The film made $134.5 million domestically, and $249.0 million overseas for a total of $383.5 million, making it the twelfth highest-grossing film of 2007. As of 2022, it is the most successful film in the series.


title: Live Free or Die Hard

text: On Rotten Tomatoes, the film has an approval rating of 82% based on 210 reviews, and an average rating of 6.8/10. The site's critical consensus reads, ""Live Free or Die Hard" may be preposterous, but it's an efficient, action-packed summer popcorn flick with thrilling stunts and a commanding performance by Bruce Willis. Fans of the previous "Die Hard" films will not be disappointed." On Metacritic, the film has a weighted average score of 69 out of 100, based on 34 critics, indicating "generally favorable reviews". Audiences polled by CinemaScore gave the film an average grade of "A−" on an A+ to F scale.


title: Live Free or Die Hard

text: IGN stated, "Like the recent "Rocky Balboa", this new "Die Hard" works as both its own story about an over-the-hill but still vital hero and as a nostalgia trip for those who grew up with the original films." On the television show "Ebert & Roeper", film critic Richard Roeper and guest critic Katherine Tulich gave the film "two thumbs up", with Roeper stating that the film is "not the best or most exciting "Die Hard", but it is a lot of fun" and that it is his favorite among the "Die Hard" sequels. Roeper also remarked, "Willis is in top form in his career-defining role." Michael Medved gave the film three and a half out of four stars, opining, "a smart script and spectacular special effects make this the best "Die Hard" of 'em all."


title: Live Free or Die Hard

text: Conversely, Lawrence Toppman of "The Charlotte Observer" stated: "I can safely say I've never seen anything as ridiculous as "Live Free or Die Hard"." Toppman also wrote that the film had a lack of memorable villains and referred to John McClane as "just a bald Terminator with better one-liners".


title: Lexus LFA

text: The is a two-seat sports car manufactured by Lexus, the luxury car division of Toyota. It is the second model in the F marque line of performance vehicles from Lexus, following the IS F, and also the first standalone Lexus F model. Three concept versions were unveiled, each debuting at the North American International Auto Show with the LF-A designation as part of the LF Series concept line. After beginning development in the early 2000s (with a codename of TXS), the first LF-A concept premiered in 2005, followed in 2007 by a second concept with a more completely furnished interior and exterior. The third version of the LF-A, featuring a roadster body style premiered in 2008. The production model, trademarked LFA, was unveiled at the Tokyo Motor Show in October 2009. According to Lexus, the "A" in production LFA name stands for the "Apex" of the LF line of cars.


title: Lexus LFA

text: Akio Toyoda, CEO of parent company Toyota Motor Corporation (TMC) saw the LFA as an opportunity to create a global icon for the Lexus brand, embodying Toyoda's idea that the ultimate Lexus should connect with its owner.


title: Lexus LFA

text: The production version of the Lexus LFA features a V10 engine developed in collaboration with Yamaha exclusive to the car and a body made from carbon fibre-reinforced polymer (CFRP). CFRP materials account for 65 percent of the LFA's body composition by mass. The LFA went into production in late 2010. A circuit-tuned variant debuted in 2012, and was one of the most expensive Japanese road cars ever built. Production ended in December 2012 with 500 cars produced, the final car being a Nürburgring Package model.


title: Lexus LFA

text: In February 2016, Lexus' European boss Alain Uyttenhoven confirmed that there would be no new LFA replacement in the near future.


title: Lexus LFA

text: , Lexus still had four unsold LFAs after selling three LFAs in 2019. However, two were sold in March 2020 and another in September 2020, still, an LFA remains unsold even though the car's production ended in 2012.


title: Lexus LFA

text: The LF-A sports car began development with a codename of TXS, which was intended to showcase the performance capabilities of Toyota Motor Corporation and its Lexus marque. The first prototype was completed during June 2003. Prototypes of the LF-A were spotted regularly undergoing testing at the Nürburgring, the famous motorsport race track in Nürburg, Germany, since October 2004. Numerous test vehicles had been equipped with automatic retractable rear spoilers, and carbon ceramic brake discs.


title: Lexus LFA

text: In January 2005, the first LF-A concept premiered at the North American International Auto Show in Detroit, Michigan as a design study with no plans for production. The first LF-A concept had an overall length of , while its wheelbase measured The concept was nearly in height, with a width of . Some news outlets reported the concept name as referring to Lexus Future-Advance, a claim later dismissed by Chief Engineer Tanahashi. The first LF-A concept featured a glass roof and side cameras mounted in the side mirrors. Twin rear radiators were installed behind the rear wheels, and visible behind large screens. The rear bumper featured a triple exhaust placed in an inverted triangle formation. The wheels were shaped like turbines, and air-scoops were placed on the C-pillars. Following enthusiastic public reaction for the LF-A concept on the auto show circuit, development continued with a greater emphasis on a possible production model. Concurrently, Lexus was preparing for the launch of its long-rumored F marque series of performance vehicles, with a production LF-A being a possible future member of this lineup. Reports in 2006 suggested that the LF-A concept car had received the green-light for production, however these reports were not officially confirmed.


title: Lexus LFA

text: Following the original LF-A concept, development time was lengthened by the switch from an aluminum frame to a carbonfibre tub, the result of engineering efforts aimed at improving the LF-A's power-to-weight ratio. The LF-A was reported to draw engineering resources from Toyota's Formula One team. In January 2007, a restyled LF-A concept car premiered alongside the first production F marque vehicle, the IS F sports sedan. The second LF-A concept featured a more aerodynamic exterior, a near-production interior, and F marque emblems. Later that year, Lexus Great Britain director Steve Settle indicated plans for a V10 and hybrid version of the LF-A. The hybrid version, combining a petrol engine with electric motors, was to feature a V8 powertrain similar to that designed for the Lexus LS 600h L. LF-A test mules continued to be spotted at the Nürburgring, including early models with a large, fixed rear wing. In December 2007, "Auto Express" reported that the LF-A had set an unofficial 7:24 lap at the Nürburgring.


title: Lexus LFA

text: In January 2008, Lexus displayed a roadster version of the LF-A concept car designated LF-A Roadster, or LF-AR, at the North American International Auto Show. Initial specifications for the roadster were a V10 engine having a displacement of 5.0 L and rated at over . The car's top speed was reported to be over . Automotive photographers capturing the LF-A in various test guises had photographed a disguised convertible test model, dubbed LF-A Spyder, on the Nürburgring as early as October 2005. After its debut at the 2008 North American International Auto Show, the LF-A Roadster was also shown at the 2008 Pebble Beach Concours d'Elegance, the 2008 Geneva Motor Show, the United States Open Championship tournament, and at Lexus exhibits in Japan. A single LF-A racing prototype was also entered into Veranstaltergemeinschaft Langstreckenpokal Nürburgring endurance races at the Nürburgring in May 2008, competing in the SP8 class of VLN events. Media reports uncovered an LFA trademark filing with the United States Patent and Trademark Office in December 2008, with the concept LF-A name dropping its hyphen to become LFA for a possible production model.


title: Lexus LFA

text: The second LF-A concepts had an overall length of , and a wheelbase of ; height remained the same as the prior concept, while width grew to . While the original LF-A had been strictly a concept model, the second concept's design reflected engineering analysis for possible production. The exterior design had been restyled to take advantage of the flexibility offered by carbon-fibre construction, with improved aerodynamics and surface features aimed at improving the car's overall top speed. The reshaped exterior featured smoother lines with additional detailing, and more curved surfaces. The aft radiator cooling vents were retained, but integrated into the rear fascia, and the lower side and front air intakes were restyled, along with the forward fascia and headlamps. Designers reportedly drew inspiration from the 1965 2000GT sports coupé, which was also produced in a front-engine, rear-wheel drive layout, and represented the combination of Japanese technology and design ethics in a sports car. However, no design features on the LF-A were directly derived from the 2000GT. The second LF-A concept and accompanying LF-A Roadster were also equipped with a retractable rear wing for improved handling at speed and a two-seat interior with a two-tone colour scheme.


title: Lexus LFA

text: On 5 August 2009, Toyota's new CEO, Akio Toyoda, publicly confirmed production of the LF-A in his speech at a conference held at the Center for Automotive Research in the United States. The production vehicles were expected to carry V10 engines.


title: Lexus LFA

text: In September 2009, reports in Japanese automotive magazines indicated that the 4.8 L V10 engine for the LF-A would carry a "1LR" designation.


title: Lexus LFA

text: A subsequent television ad for the Japanese market showed the pre-production LFA testing at the Fuji Speedway.


title: Lexus LFA

text: On 21 October 2009, the production version of the Lexus LFA was unveiled on the first press day of the 41st biennial Tokyo Motor Show. The car was introduced by Akio Toyoda at a press conference, in which it was disclosed that the vehicle would be limited to 500 production copies. The car carried the same designation as the concepts, LFA, but without the hyphen. The production designation reportedly stood for Lexus Fuji Apex, another claim dismissed by Chief Engineer Tanahashi. The LFA was shown as the final vehicle of the press conference, following the LF-Ch hybrid concept.


title: Lexus LFA

text: The production announcement for the LFA marked the 20th anniversary of the launch of Lexus. Given the high cost of construction and development, analysts did not expect LFA sales to be profitable. However, the LFA was intended to serve as a testbed for new car technologies, including carbon-fibre mass-production, and related performance vehicle development. At its debut, a circuit-ready model was also indicated for a 2012 launch.


title: Lexus LFA

text: Lexus began taking orders for the LFA on 23 October 2009. Buyers were selectively chosen by Lexus in the second quarter of 2010. Production began in December 2010. Only 500 total cars were made for worldwide markets, with only 20 produced each month with a base price of $375,000 (£340,000). Each car had to be custom ordered to the customer's specifications.


title: Lexus LFA

text: Following the LFA's Introduction at the Tokyo Motor Show, Lexus unveiled a website with an 'LFA configurator', which allowed users to select exterior and interior colours, brake caliper colours, seats, steering wheel leather, and other interior designs. In total, there were over 30 billion possible combinations. Each LFA was hand-built by a dedicated production team of engineers and specialists at Toyota's Motomatchi plant in Aichi, Japan.


title: Lexus LFA

text: In the North American market, 150 cars were initially sold through a two-year lease program. This was to prevent owners from reselling the vehicle for a profit. Racing driver Scott Pruett was hired to give test drives to interested buyers, demonstrating the vehicle's capabilities at Auto Club Speedway. The Lexus division of Toyota Motors USA stopped taking orders at the end of 2009, at which time they planned to open discussions about a purchase plan for the lessees. Lexus later changed their stance and allowed outright purchase, but only on the condition that they sign an agreement giving the dealer the first right of refusal to buy back the LFA if the owner wanted to sell it within the first two years. The dealer would have the option to buy back the used LFA for either fair market value or the original sticker price, whichever is lower. In the European market, buyers could order their LFA through a single Lexus dealer located in Park Lane, London where it was purchased outright.


title: Lexus LFA

text: During the LFA's production, each vehicle received an individually numbered plaque, indicating the unit's place in the production run. Each LFA V10 engine carried the signature of the specialist who assembled it. With 20 units produced monthly, production of the LFA extended from December 2010 to December 2012. Production ended on 14 December 2012, with the last car finished in white exterior colour and equipped with the Nürburgring package. When production ended, no successor was scheduled. The LFA plant in Motomachi continued making parts with a small team.


title: Lexus LFA

text: The Lexus LFA is powered by a 72-degree bank angle V10 engine equipped with Dual VVT-i carrying the "1LR-GUE" designation with a maximum output of delivered at 8,700 rpm. Its maximum torque output of arrives at 6,800 rpm, 90 percent of which is available from 3,700 rpm. The engine redlines at 9,000 rpm, but with a fuel cutoff set at 9,500 rpm, and is constructed using forged aluminum pistons, forged titanium connecting rods, and solid titanium valves. The V-angle of the LFA's V-10 engine is set to 72-degrees to fully balance the firing force from the pistons. This 72-degree angle allows for even firing from the pistons without the use of a split-journal crankshaft, thus improving engine efficiency as well as lowering the overall weight. Dry sump lubrication prevents engine oil starvation through high-speed corners and lowers the engine's center of mass. Air is fed directly from beneath the hood through a visible slit passing into a dual-stage variable intake manifold and then into ten individual throttle bodies before finally exiting from a dual-stage titanium muffler.


title: Lexus LFA

text: The LFA's engineers selected a V10 engine over an equivalent displacement V8 engine for its ability to rev higher, and over a V12 for its lower reciprocating mass, allowing for more rapid engine response. Lexus claimed their engine could rev from idle to its redline in 0.6 seconds and an analog tachometer needle could not accurately track the LFA's changes in engine speeds. This necessitated the use of a digital tachometer which can instantly display engine speed. The engine reportedly weighs less than the manufacturer's own 3.5-litre "2GR-FE" V6 engine. Engineers attempted to make the engine sound like that of a Formula One car with high revs, while at the same time maintaining reliability and vibration control. Along with other manufacturers such as Ferrari, Toyota had produced its own F1 engines and chassis designs. The exhaust note has been described by Toyota engineers as the "roar of an angel", and a US television spot later used the engine sound to shatter a champagne glass via resonance frequency.


title: Lexus LFA

text: The powerplant gives the LFA a weight-to-power ratio of 2.67 kg/hp and enables it to reach a top speed of around . Unlike the IS F's 2UR-GSE engine, Yamaha co-developed the entire engine, and not just the cylinder heads. The engine exceeds Euro V emissions. The engine is installed with a front mid-engine placement. According to Chief Engineer Haruhiko Tanahashi a front engine layout was selected instead of a mid engine layout as it is inherently more forgiving dynamically, affording less experienced drivers a wider safety net.


title: Lexus LFA

text: The gearbox built by Aisin is a six-speed single-clutch automated manual transmission actuated with paddle-shifters.


title: Lexus LFA

text: The Lexus LFA's frame is made from an in-house designed and manufactured carbon fibre-reinforced polymer (CFRP) centre monocoque with aluminium front and rear subframes. The subframes, which can be removed and replaced minimising potential repair costs, are joined to the monocoque using a newly developed aluminum flanged collar designed to create a stronger joint. According to the manufacturer, the quality of the CFRP material matches that of aeronautical grades and is woven by a laser monitored circular loom, one of only two in the world. Overall 65% of the vehicle's total body mass is CFRP material while the remaining 35% is aluminum. Manufacturer data indicates that the use of CFRP saves over equivalent aluminum materials.


title: Lexus LFA

text: An electric power steering rack with a 14.3:1 gear ratio is used. The front suspension utilises a double-wishbone arrangement and there is a multi-link arrangement at the rear with coil-over dampers at all wheels. The dampers are a monotube design, each with a remote fluid reservoir that includes an expanding and contracting bellows: a purely mechanical system. The LFA further features six-piston front and four-piston rear Brembo monobloc brake calipers with front and rear carbon ceramic discs controlled by Toyota's Electronically Controlled Brake-by-wire system. Forged 20-inch BBS wheels fitted with front and rear Bridgestone next-generation Potenza tyres are standard. The LFA is equipped with a three-mode Vehicle Dynamics Integrated Management (VDIM) stability control system with Sport setting.


title: Lexus LFA

text: To maintain a near-ideal weight distribution, a rear transaxle is used, in addition to the mounting of the fuel tank ahead of the rear axle and the radiators at the rear. The windshield washer fluid reservoir is mounted in the center next to the fuel tank to improve further the center of weight. Overall 48% of the LFA's mass is distributed along with the front wheels with 52% at the rear. The fuel tank straddles the exhaust system keeping weight centered along the left-right axis. The engine is connected to the transaxle via a rigid carbon-fibre torque tube which the exhaust system runs directly below. This stacked driveshaft and exhaust arrangement decreases the width of the centre tunnel allowing for centrally located seating.


title: Lexus LFA

text: The LFA has an overall length of , while its wheelbase measures , with a height of and width of . Compared to the prior 2007–2008 concepts, the production model is nearly longer, with identical width, height, and nearly same wheelbase dimensions. The exterior design of the LF-A concepts and the final production model was the work of car stylists led by Lexus Design general manager Kengo Matsumoto. The overall design ethos was based on the principle of form follows function, with aesthetics secondary to aerodynamics and operation.


title: Lexus LFA

text: The LFA's body features sharp edges and cutoffs for improved aerodynamic performance, made possible by the carbon fiber body. The body was designed with an emphasis on downforce. There are air scoops located over the rear fenders which feed the aft-mounted radiators and help cool the brakes. A horizontal hood gap also feeds air to the engine. Two small aft vents expel air that is collected by an underbody air scoop and used to cool the titanium exhaust pipes. Dual hood ducts serve to move hot air away from the exhaust manifold.


title: Lexus LFA

text: The LFA's speed-sensitive rear wing incorporates a Gurney flap and deploys at speeds over . With the wing retracted the LFA's body has a drag coefficient of . The LFA body was offered with a choice of 28 standard exterior colours, along with 3 wheel colours and a matte black option. Additional special colours are available to order. The front and rear fenders, doors, roof rails, and rocker panels are made out of blast fiber reinforced sheet panels, while the tail lamps are light-emitting diode (LED) lights.


title: Lexus LFA

text: The LFA interior incorporates carbon fibre, leather, alcantara, and metallic surfaces. There are two bucket seats, and Lexus' Remote Touch controller interface. The interior design uses bespoke materials and colours. The instrument display is a digital thin-film transistor (TFT) speedometer with colour-changing background, size-changing numbers, and side-appearing submenus.


title: Lexus LFA

text: In operation, the TFT display shows small digits in automatic mode; larger and bolder numbers in normal mode; inverted colours, moved redline, and stark numbers in sport mode, along with a programmable redline warning colour change. The tachometer display also features an electric movable metal ring with layer acrylic plastic to create a 3D effect. The LFA further features a new driver and passenger seat-belt airbag design increases similar to the S-Class ESF safety concept car.


title: Lexus LFA

text: The steering wheel features a right-mounted start button and alloy paddle-shifters. To start the car, the driver must insert the key beside the steering wheel then press the start button. Two octaves of engine sound are channeled into the cabin via twin ducts which connect the firewall with the intake manifold, with the sound tuned in the manner of an Ovation guitar. A 12-speaker Mark Levinson sound system with compact lightweight components was also developed for the interior. Custom-made Tumi suitcases are designed for the LFA interior, with a two-piece set made from carbon-fibre style materials and inscribed with the VIN; a smaller "concourse" case is for track days and short trips, while a larger "coastal" case is for longer trips.


title: Lexus LFA

text: On 15 March 2010, Lexus detailed the circuit-tuned variant of the LFA, plans for which were first disclosed at the LFA official press launch the previous October. The variant is officially known as the LFA Nürburgring Package in reference to the similar setup employed on the LFA race cars at the 24 Hours Nürburgring.


title: Lexus LFA

text: The package features an extra from its V10 engine, bringing the total to . It also features a re-calibrated transmission with gear shifts made faster by 0.05 seconds, a front splitter, stiffer and more adjustable suspension, lightweight alloy wheels wrapped in high performance street tyres, aerodynamic canards at the sides of the front bumper, and a large fixed rear wing.


title: Lexus LFA

text: The LFA with the Nürburgring Package is a competition-focused variant and was available in four exterior colours, namely glossy black, matte black, race yellow, and whitest white. The production totals are to be included in the 500-unit total LFA planned build cycle, and although Lexus stated it would be limited to a 50-unit run, a total of 64 were produced. Buyers received training sessions at the Nordschleife, accompanied by Nürburgring chief instructors, a one-night stay at the Lindner Congress and Motorsport Hotel Nürburgring, admission to the ring°werk leisure park, a Nürburgring branded jacket, and a one-year pass to the circuit.


title: Lexus LFA

text: The Nürburgring Package LFA was tested at the Nürburgring in June 2011. Driven by Akira Iida, the LFA set a time of 7:22.85 (video confirmed), the 7th-fastest time ever for a road-legal production vehicle. Lexus confirmed that this lap video was recorded as a "warm-up" video for the "ADAC 24-hours" for exhibition purposes. The LFA hit on the last straight uphill climb, which is one of the highest speeds achieved by factory standard sports car on that segment of the track. Standard OEM Bridgestone Potenza RE70 performance street tyres were used.


title: Lexus LFA

text: On 2 September 2011 reports came from Lexus via Twitter as well as Chris Harris of Evo Magazine that the Lexus LFA Nürburgring Package completed a lap of the Nürburgring in 7:14.64 with a top speed of on the "Döttinger" uphill climb, making it the fastest road-legal production vehicle to lap the racetrack at the time. A few days later, the time was confirmed by Lexus as 7:14.64 and a video was provided. OEM Bridgestone Potenza RE070 street tyres had been used to set the record.


title: Lexus LFA

text: Tested performance specifications for the Lexus LFA from "Car and Driver", "Motor Trend", "Road & Track" and "Insideline" are as follows:


title: Lexus LFA

text: Edmunds' "Insideline" managed to acquire an LFA from Lexus for one week and tested the LFA on the track including an impromptu grudge match on the drag strip. Both cars won 2 races each making it a draw.


title: Lexus LFA

text: "Insideline" recorded a in 3.9 seconds without launch control system and achieved the 1/4-mile 11.6 seconds at . Lexus LFA circled the skidpad in 1.02 g and achieved one of the highest slalom speeds ever recorded at . "Insideline" also managed to do 3 dyno runs on a dynojet dyno on the Lexus LFA, which resulted in LFA generating a power output of to the wheels, which after factoring in RWD drivetrain loss turned out to be substantially higher than the at the crank factory specification.


title: Lexus LFA

text: "Car and Driver" track-tested the LFA in November 2010 while conducting a comparison test. The test was conducted in Wales and returned a time of 3.6 seconds using the launch control system and a quarter-mile of 11.7 seconds at . "Motor Trend" recorded a stopping distance from in less than , and pulled 1.05 g on their skidpad. "Road and Track" tested the LFA at through the slalom and 1.04 g on the skidpad.


title: Lexus LFA

text: "Motorsports France" conducted a track test on the Lexus LFA and ran a hot lap around the Circuit de Nevers Magny-Cours resulting in a lap time of 1:20.6, which was the fastest ever recorded lap time on the race track despite the test having been conducted in 0 degree freezing temperatures. It was one of the very rare track tests where an actual LFA launch control system was used resulting in a very fast 0– acceleration time of only 21.2 seconds.


title: Lexus LFA

text: "Auto Zeitung" Germany in the August 2010 edition conducted a comparison with the Lexus LFA. Around Contidrom race track in Hannover, Germany, the LFA turned a faster lap time by 1.8 seconds of 1:35.66 minutes. Although, the start sector car hit , the LFA continuously hit higher speeds in the high speed sector, dynamic sector where agility and spontaneous reactions are measured eventually turning in faster lap. AutoZeitung raved about LFA's handling, chassis control and race car-like reflexes and response.


title: Lexus LFA

text: In the LFA's "Top Gear USA" appearance in the third quarter of 2011 in the "Beating Tanner" episode, the American Stig also did a hot lap around the "Top Gear USA" testing track in 1:22.6, located at Marine Corps Air Station El Toro, which is the third quickest lap time ever on the race track.


title: Lexus LFA

text: Chief Engineer Haruhiko Tanahashi mentioned during the world's press at the Nürburgring in Germany that the LFA has lapped the Nürburgring Nordschleife in "better than 7 minutes 20 seconds", although no further specifics were given to the record lap.


title: Lexus LFA

text: "Sport Auto" in the September 2010 edition conducted an LFA supertest with a red LFA that had been used in several other tests in Europe and Horst Von Saurma conducted a hot lap of the LFA around the Nürburgring Nordschleife. The LFA clocked the Nürburgring in 7:38. The LFA was wearing temporary Bridgestone S001 street tyres since the LFA spec tyres are still under development. Although the LFA lap time is slower than the chief engineer's "better than 7:20" claim, "Sport Auto" cited LFA ran exactly the same lap time with the same driver as other major competitors. All tests were conducted by the same driver, Horst von Saurma.


title: Lexus LFA

text: "Auto Bild" Germany in the September edition of 2010 in part 1 of the comparison conducted a head-to-head Nürburgring Supercomparo (longer 20.8 km version of the track). Lexus LFA turned in the fastest Nurburgring lap time (7:38,85), The Nurburgring 20.8 km test driver Sascha Bert stated "LFA was built for the Nurburgring race track."


title: Lexus LFA

text: National Geographic's show, "Megafactories", reported a 2011 test of the Lexus LFA Nürburgring package driven by Iida Akira that achieved a record time for production vehicles of 7 minutes 14 seconds.


title: Lexus LFA

text: The LFA appeared on "Top Gear" in January 2010, where its power lap of 1.22.8 was the quickest wet test lap ever recorded on the "Top Gear" test track located at Dunsfold Aerodrome in Surrey, United Kingdom.


title: Lexus LFA

text: "Battle of the Supercars" did a head-to-head comparison with the Lexus LFA, with Tanner Foust driving the LFA at the runways of Westover Air Reserve Base. LFA comprehensively was declared the winner by the presenter where LFA lapped the short 1-mile track with a lap time of 48.9 for the LFA, despite Tanner having difficulties launching the Lexus LFA in the 1-mile road course lap and also the standing mile drag race where LFA won despite a delayed launch (no launch control used for these runs). This test also saw LFA using launch control for the first time in the 0-100-0 mph test.


title: Lexus LFA

text: LFA failed to win the brake test. However, in the behind the scenes footage, it was shown the LFA's carbon brakes meant for hardcore track usage were not warmed up properly, which is essential for carbon brakes to perform at their best. In the successive run, LFA carbon brakes were consistently getting better braking shorter in every successive run. In every 0–161 km/h (0–100 mph) sprint shown in the behind the scenes footage, LFA out-launched and out-accelerated its rival vehicle. In the top speed, rolling start run on the 3.2 km (2 mi) runway, LFA hit a speed of 296.3 km/h (184.1 mph). Tanner Foust explained there was no way to retract the LFA wing spoiler (deploys automatically at 80 km/h (50 mph)) at high speeds increasing drag substantially, which had cost him 6–10 km/h (4–6 mph).


title: Lexus LFA

text: "Car and Driver" concluded in its review of the LFA that the sports car is "hugely expensive, hugely competent". The magazine felt that car began to look like "something of a bargain" from the viewpoint that more expensive cars offered similar levels of technology and exclusivity. In May 2010, "Motor Trend" ran the LFA through several track tests and praised its driving dynamics and engine note. However, in their 2011 Best Driver's Car competition, the LFA finished ninth out of eleven cars, receiving criticism for a "nervous, twitchy chassis" that gave the judges "no confidence". The car was also criticised for its transmission, ergonomics and ride quality. "Top Gear" criticised the LFA for being sold at a price much higher than comparable sports cars.


title: Lexus LFA

text: "Autocar" complimented the LFA's engine and handling on smooth surfaces, but criticised the car's behaviour on normal roads, where they felt that "the difficulty the LFA has in coping with an uneven road" negatively impacts driving enjoyment. Pointing out that rivals such as the Ferrari 458 Italia offer "more consistent all-conditions dynamics", the magazine gave the verdict that the LFA is "an occasional car, even by supercar standards".


title: Lexus LFA

text: GTspirit.com tested the LFA in Monaco in May 2010 and gave it a positive review with quotes such as "The LFA is incredibly easy to drive. It communicates well, has a superb overall balance and the transparency of the options is an eye-opener. The choice between the racing setup and an all-day trip through a dense city is easily changed." and "the 'I want one' feeling grew considerably every single minute."


title: Lexus LFA

text: Many reviewers have placed Lexus LFA near the top of the cars they have ever driven. Chris Harris of "Evo UK" had called LFA as the "best car I have ever driven around Nurburgring. No other car inspires more confidence than the LFA". "Autoweek" Netherlands professional driver Sandor Van Ees stated "Lexus LFA - that sound, that experience. I place Lexus LFA in the top 5 best cars I have ever driven". Dutch European journalist Thomas Bangma said, "this car is an absolute gem ... It is absolutely the best car I have ever driven". "Car Magazine" editor and professional test driver Ben Barry called the LFA Nurburgring edition "the Bugatti Veyron of Japan".


title: Lexus LFA

text: The LFA appeared on "Top Gear" in January 2010, where Richard Hammond drove and raved about the car. Later in the episode, the LFA set a record for the quickest wet test lap ever recorded on the "Top Gear" test track, However, it was noted that the LFA cost 3 or more times than its rivals but not faster than it; Jeremy Clarkson also noted that the 202 mph LFA costs 6 times more than the 193 mph Nissan GT-R, but is not 6 times faster. In response, "Evo" review of the LFA pointed out that the performance of "a Bugatti Veyron is not 12 times more than the GT-R", with reviewer Chris Harris observing that no cars are 6 times more than a GT-R either. Jeremy Clarkson drove the LFA for the first time on Top Gear, describing it as "bloody brilliant". Later, in Series 19, Ep.2, Clarkson states at the start that the LFA is the best car he has ever driven and, in the end, quoted, "If I could have any car ever made given to me I'd pick a dark blue Lexus LFA." In Series 22, Episode 6, he states that he had expected to get a feeling like the LFA from the RC F sports coupé, but did not on the further comparison, concluding that the LFA was likely so perfect, not even Lexus themselves know how to remake it.


title: Lexus LFA

text: The LFA appeared on "Fifth Gear" with presenter Tiff Needell driving the car around the race track performing hot laps, powerslides, and power oversteers. Needell described in detail the high-tech engineering used in the car, and highly praised the 4.8-litre V10's power and sound. Tiff declared, "people who purchased the LFA would be very happy when they get their cars". At the conclusion of the review, he stated "for a weekend race track car, LFA is worth every penny".


title: Lexus LFA

text: In 2012, Jay Leno featured the LFA on his internet car enthusiast program "Jay Leno's Garage", where he looked at several advanced features of the car including the carbon-fibre construction, interior details, and the engine. Leno praised the LFA for its engineering, attention to detail, and quality of construction all around. Leno took the car for a test drive in the California mountains and had raving impressions of the LFA driving dynamics, handling, chassis rigidity, and engine sound. Leno stated that the LFA was "one of the greatest supercars ever built and certainly the best supercar ever to have come out Japan". Leno was very impressed with the LFA's city driving abilities and noted it was a "docile car around town". Leno summarized the LFA by saying, "certainly, there might be cars out there that could individually do things better than the LFA. Maybe a bit quicker or handling a bit better. But, no other car I know of does everything so extremely well".


title: Lexus LFA

text: A Lexus LF-A prototype was entered on 10 May 2008 on the Nürburgring 4-hour VLN endurance race. Despite being lapped 5 times and finishing 77th overall among over 200 teams, it surprisingly won the over 4,000 cc class SP8, as all other five class entrants, failed to finish. The best lap time of the Lexus, on the 24.4 km version used in VLN, was 9:06 in 3rd of 23 laps, on par with old Porsche 996 GT3 Cup (class Cup3A), while the fastest SP8 cars managed 8:20s.


title: Lexus LFA

text: Lexus also took part in the 24 Hours Nürburgring on 24/25 May 2008, with four Japanese drivers including Akira Iida leading the team. The LF-A was involved in a crash just prior to the race and was hurriedly repaired in two hours to make the race. As car #14, it qualified 27th among 223 cars, and finished 7th in the SP8 class of 11 entrants, and 121st overall, with a best lap average speed of , compared to of the fastest cars.


title: Lexus LFA

text: On 4 April 2009, an LF-A and a Lexus IS F entered by Gazoo Racing (which had already raced smaller cars in 2007 and 2008) finished first and second in the SP8 class in the ADAC-Westfalenfahrt VLN 4h endurance race, as all three other class entrants, failed to complete the race. In winning its second VLN 4h event, the LF-A improved its fastest lap time, with one driver completing 8:41 laps both in practice and in the race.


title: Lexus LFA

text: The LF-A was subsequently entered into the 24 Hours Nürburgring race for the manufacturer stated purpose of obtaining feedback for fine-tuning production versions along with training of support technicians. Gazoo registered two LF-As and a single IS F in the SP8 class (4,000 cc to 6,200 cc), as the LF-A racecars were powered by a 4.8-litre (4,805 cc) V10 engine with a 9,000 rpm redline.


title: Lexus LFA

text: At the 2009 24 Hours of Nürburgring endurance race held on 23/24 May, the No. 15 LF-A driven by Jochen Krumbach, Armin Hahne, André Lotterer, and Hiromu Naruse achieved sub-9 min laps and a best time of 8:50.458, which was the fastest time in the SP8 class, with a best lap speed of ;. The fastest times by the race leaders (SP9 class) were in the 8:40 range with a best lap speed of . About 90 minutes from race completion, the No. 15 LF-A experienced a separated driveshaft and a fire which poured white smoke from the vehicle's rear section. The No. 14 LF-A completed the race and was ranked 4th in its class and 87th overall, behind the 3rd ranked No. 16 IS F During the early portions of the race the No. 14 LF-A recorded its peak position of 14th overall. One of the drivers of the No. 14 car was Toyota's new CEO Akio Toyoda, who also met Aston Martin's President and fellow race entrant Ulrich Bez at the race before deciding to build the Aston Martin Cygnet together.


title: Lexus LFA

text: Lexus/Gazoo again entered two cars in the 2010 24 Hours of Nürburgring, in the SP8 class over 4,000 cc. The "Balance of Performance" required a minimum weight of , a restrictor diameter of 34.2 mm, and a fuel tank size of 120 litres. The No. 50 car won its class, and finished 18th overall with 142 laps, 12 laps down. The No. 50 car, with 4 Japanese drivers, did a fastest lap of 8:55.934 (average of 170.470 km/h), which was over 20 seconds slower than the top 10 challengers, and slower than last year's performance.


title: Lexus LFA

text: Chief Test Driver/Engineer Hiromu Naruse, who coached the 2010 LFA race team, died in a tragic accident on 23 June 2010 while testing the Nürburgring Edition of the Lexus LFA on the roads local to the Nordschleife in Germany. According to police reports, the traffic accident occurred when his LFA Nürburgring Edition test prototype veered into oncoming traffic, colliding head-on with a BMW 3 series near the Nürburgring, at Boos. The BMW was also a test vehicle, and both occupants were injured, one severely; both were expected to survive. All three test drivers wore helmets, but Naruse was reportedly not wearing his seatbelt, and as his LFA test vehicle was a pre-production prototype, its safety features, including airbags, were not functional at the time.


title: Lexus LFA

text: In April 2005, Lexus presented a sculptural model of the original LF-A concept at that year's Milan Design Week exhibition in Milan, Italy. Part of the marque's introductory display of its L-finesse design theme, the full-size LF-A model was presented next to a production Lexus GS model, in a design space produced by painter Hiroshi Senju, designer Junya Ishigami, and architect Kazuyo Sejima. The sculpted LF-A model followed the first introduction of the LF-A concept at the North American International Auto Show in January of that year. In contrast with the production GS sedan it shared the display space with, the LF-A model did not have interior access.


title: Lexus LFA

text: In April 2009, Lexus presented an acrylic glass sculpture LFA model, called 'Crystallised Wind', at that year's Milan Design Week exhibition at the Museo Della Permanente art gallery in Milan. Commissioned in partnership with architect Sou Fujimoto, the full-sized LFA crystal sculpture had a transparent appearance, allowing viewers to see the engine, chassis, interior, and other internal components. Although closely resembling the 2007 coupe concept, design elements on the LFA Crystallised Wind model differed from previous iterations of the coupe, with five-spoke wheels, different headlamp shapes, and other separate details. The vehicle was presented along with a collection of accessories, gadgets, and styling products all produced from the same acrylic materials used in the Crystallised Wind model.


title: Lexus LFA

text: In October 2009, the debut of the Lexus LFA was named among "Road & Track"s Best of the 2009 Tokyo Auto Show. For his role in leading its development project, "Top Gear" awarded Lexus LFA chief engineer Haruhiko Tanahashi as one of its Men of the Year for 2009. In April 2010, the LFA topped the "Stiff Magazine" list of the Top 5 V10 Road Cars. In its 2010 test of the LFA, "Car" gave the vehicle the magazine's maximum rating of five stars. The LFA was also named to the "Top Gear" 100 Sexiest Supercars of All Time list in 2010. "Top Gear" magazine in its September 2010 edition picked "5 greatest supercars of the year" and the LFA was honored as one of the greatest sports cars of the year. All 5 cars were featured in the magazine in a side-by-side comparison and LFA was picked as the "Stig's most favorite supercar".


title: Lexus LFA

text: "Evo UK" in its January 2011 edition held a "best engine of the year" selection. Lexus LFA's 4.8 litre V10 was selected as the "best engine of the year". Some of the comments regarding the Lexus LFA's V10 were "A mix of road and racing engines: Lexus LFA's utterly intoxicating 4.8 liter V10.", "There is the noise it makes, for a start, a dense shriek like a V10 F1 car's", "Then there's the wall of torque from 5,000 rpm to 9,000 rpm and a strong thrust even before that", "Lighter than an average V6 and it even meets the Euro 5 emission standards", "It is hard to imagine that such an engine's career will be over when all the LFAs are built, given the love that has gone into it. We certainly hope not".


title: Lexus LFA

text: "Car Graphic" magazine compiled a 'Best Cars of the Year 2011' in December 2011. It was based on all the cars that were tested during the year in their own respective months. The Lexus LFA won the 'Best Cars of the Year 2011' award. Lexus LFA was tested during the summer months in very wet conditions, but the track test even in the wet as well as daily city road driving warranted enough positive impressions for the magazine to award Lexus LFA the win. The Lexus LFA test numbers also reflect the implications of testing in the wet conditions. In February 2012, Singapore Car Mart awarded Lexus with "Best Car of the Year 2011" award for their LFA sports car.