title: Reality (David Bowie album)

text: "Never Get Old" features a catchy guitar hook with echoing percussion and an elegant bassline. Lyrically, it presents a reflection on ageing and an expression on both desperation and denial. The music and lyrics recall the themes and styles of "Heathen", and the Berlin albums "Low" and ""Heroes"" (both 1977). Additionally, the thought of "never getting old" has been a mainstay in Bowie's songwriting, in tracks from "Changes" (1971) to "The Pretty Things Are Going to Hell" (1999). Pegg describes the line "I think about this and I think about personal history" as a "key line" for the entire "Reality" album. Described by Bowie as "a very despairing piece of work", "The Loneliest Guy" is the quietest and most reflective track on the album, which Pegg analyses as a "haunting meditation on memory, fortune and happiness". Its subject is a loner who realises he is lucky, as he has no one else to look out for but himself. Bowie revealed that the imagery was inspired by the modernist city of Brasília; in his words, "a city taken over by weeds".


title: Reality (David Bowie album)

text: "Looking for Water" is straightforward rock number that combines Slick's "discordant guitar squeals" with a repetitive bassline and "metronomic" drums. Both Pegg and O'Leary found echoes of "Never Let Me Down" tracks, particularly "Glass Spider". Similar to "New Killer Star", the song concerns post-9/11 nihilism. Bowie elaborated in 2003: "When I wrote it, I just had this image of somebody crawling through the desert looking for water[...] But then that made me think, well, the only thing he be looking at would be the oil pumps.[...] This must be about a military, industrial situation[...] That's kind of what was on my mind." Likewise, Perone analyses it as symbolic of the basic necessities of life while the narrator is surrounded by the trappings of modern technology. Bowie described "She'll Drive the Big Car" as "a tragic little story about a lady and her family. And she lives in the wrong part of town, but she wants to live in an even badder, wronger part of town – but her would-be affair, her boyfriend, doesn't turn up." Like several of the album's tracks, it eavesdrops onto a wretched and despaired life in which a woman dreams of wealth but is stuck being a mundane house wife. Musically, it is a funkier number reminiscent of Bowie's soul era, particularly tracks like "Golden Years" (1975). O'Leary writes that Bowie's harmonica can be heard for the first time since "Never Let Me Down" (1987).


title: Reality (David Bowie album)

text: "Days" is a love song that continues the album's sub-themes of "weary retrospection and aging regret". Bowie uses the same vocal style as "The Loneliest Guy" to present, in Pegg's words, "a simple and poignant plea for forgiveness". Bowie stated during a concert in Melbourne that "I sometimes feel I wrote this song for so many people". It is musically simple, boasting a "faux-naif arrangement of low-tech synthesisers and twanging guitars against a jogging beat", which Pegg compares to the 1980s works of Soft Cell and Depeche Mode. According to Bowie, the title of "Fall Dog Bombs the Moon" came from a Kellogg Brown & Root article and was subtle commentary on the then-emerging Iraq War. He further described it as "an ugly song sung by an ugly man", whom he hinted as being then-US vice-president Dick Cheney. In "The Complete David Bowie", Pegg writes: "It's a lament for the circumstances that have brought us to 'these blackest of years'. Cocking a contemptuous snook at the increasing predilection of political parties to find 'someone to hate' while jumping into bed with business corporations." Musically, the song contains similar rhythms of "New Killer Star", and the melodic motives that permeated "Heathen".


title: Reality (David Bowie album)

text: "Try Some, Buy Some" was written by George Harrison for Ronnie Spector, who released it as a single in April 1971; Harrison later released his own version on his 1973 album "Living in the Material World". Bowie, a longtime admirer of the track, wanted to cover it as far back as 1979 before finally doing so for "Reality". Pegg states that it unwittingly became a tribute to Harrison, who died in November 2001. The arrangement on Bowie's version mostly stays true to the original, although in the artist's words, "the overall atmosphere is somewhat different". Pegg and Perone contend that the "retrospective, older-and-wiser lyric" is appropriate for both "Reality" and Bowie himself. The hard rock title track is the album's loudest and rockiest moment, recalling the assault of "Hallo Spaceboy" (1995) and Bowie's works with the rock band Tin Machine. The song's message concerning how the quest for meaning in life is always doomed to fail lies at the heart of the album's loose theme; as Bowie stated, "The basis is more an all-pervasive influence of contingency than a defined structure of absolutes". The track also adopts the artificial narrative that real life has no narrative. Perone opines that it sees Bowie acknowledge that he hid behind personas and drugs throughout the early 1970s and his now facing reality.


title: Reality (David Bowie album)

text: Pegg calls "Bring Me the Disco King" "one of the most idiosyncratic and strikingly dramatic numbers in the entire Bowie songbook". After being shorthanded for several earlier albums, Bowie and Garson stripped the song down to a four-bar drum loop, vocal and piano, which the former felt worked best. Almost eight minutes in length, the song adopts a New York jazz sound that sees Garson playing an improvised piano solo similar to his one on "Aladdin Sane" (1973). Representing a culmination of the album's lyrical themes, the song offers fragmented images of, in Pegg's words, "creeping age, squandered opportunities, thwarted lives and impending dissolution". According to O'Leary, it marked Garson's final performance on a Bowie record. The outtake "Fly" features guitar playing by Bowie's longtime guitarist Carlos Alomar, marking the final collaboration between the two. Concerning a middle-class family man who suffers from anxiety and depression, it lyrically forestalls the "domestic American angst" of "Reality" tracks "New Killer Star" and "She'll Drive the Big Car". Its funky guitar riff was based on Devo's "Whip It" (1980).


title: Reality (David Bowie album)

text: In June 2002, Bowie announced the album title as "Reality" and described it to "Blender" magazine as "a bit thrusty." Reflecting the ideal that reality has become an abstract concept, Bowie explained in 2004 that "the title encapsulate[s] the prosaic nature of the project itself". The cover artwork was designed by Jonathan Barnbrook in collaboration with graphic artist Rex Ray; Barnbrook previously created the typography for "Heathen", while Ray designed the artworks for "Hours" and the "Best of Bowie" compilation (2002). Ditching the airbrushed intellectualism of the "Heathen" artwork, Ray's artwork for "Reality" depicts Bowie in a cartoon, anime-style persona, with features typical of Japanese animation, including an exaggerated hairstyle, oversized eyes and simplified lines. He steps forward against a background of various shapes, ink blobs, balloons and stars. Bowie compared it to "Hello Kitty" and bluntly stated in an interview that "The whole thing has a subtext of 'I'm taking the piss, this is not supposed to be reality'."


title: Reality (David Bowie album)

text: In the weeks prior to its release, the album was promoted on Bowie's website BowieNet via the release of excerpts of each track, titled ""Reality" jukebox", while the "Sunday Times" released various CD-ROM featurettes. ISO and Columbia officially issued "Reality" in Europe and other territories on 15September 2003, and in America the following day. Like "Heathen", it appeared in two CD formats: a single disc and a two-disc version with the outtakes "Fly" and "Queen of All the Tarts (Overture)", along with a studio re-recording of Bowie's 1974 single "Rebel Rebel"; the Japanese CD included "Waterloo Sunset" as a bonus track. In the ensuing months other versions appeared, including a "Tour Edition" to coincide with the A Reality Tour in each territory the tour travelled to; the November European release included "Waterloo Sunset" and a DVD containing a complete performance of "Reality" from 8 September at Riverside Studios.


title: Reality (David Bowie album)

text: Meanwhile, the SACD release came in December; EMI also issued a remixed SACD in September, which was packaged with three Bowie albums: "Ziggy Stardust" (1972), "Scary Monsters" (1980) and "Let's Dance" (1983). In February 2004, Columbia issued "Reality" on the new DualDisc format, containing the standard album on one side and the 5.1 mix in DVD-Audio format on the other. This release was initially restricted to the Boston and Seattle areas of the United States, with a worldwide release 12 months later. "Reality" did not receive an official release on vinyl until 2014 by the label Music on Vinyl.


title: Reality (David Bowie album)

text: "Reality" entered the UK Albums Chart at number three, becoming Bowie's highest charting album in the UK since "Black Tie White Noise" ten years prior. However, sales quickly fell after only four weeks. The album topped the charts in Denmark and the Czech Republic, and entered "Billboard" European Top 100 Albums at number one. Across Europe, "Reality" peaked at number two in France, Norway and Scotland, number three in Austria, Belgium Wallonia and Germany, number four in Belgium Flanders and Italy, number five in Sweden and Switzerland, number six in Ireland and Portugal, and number eight in Finland. It also peaked at number nine in Canada.


title: Reality (David Bowie album)

text: It fared worse in other European countries, reaching number 14 in the Netherlands and number 25 in Spain. Outside Europe, "Reality" reached number 13 in Australia, number 14 in New Zealand, and number 47 in Japan. In the US, "Reality" peaked at number 29 on the "Billboard" 200, failing to replicate the success of "Heathen", but outperforming "Earthling" and "Hours".


title: Reality (David Bowie album)

text: "Reality" was not supported through conventional single releases. Pegg opines that in the advent of Apple's iTunes, which was launched in April 2003, it was "already clear" that CD singles were becoming obsolete. As such, the music video for "New Killer Star" was released as a DVD-only single in the UK, US and other territories on 29September 2003. An audio-only version was issued as a conventional CD single in Canada, while the full-length album version appeared in Italy. Both releases were backed by "Love Missile F1-11". As the debut single, "New Killer Star" received extensive airplay during Bowie's promotional television appearances for the album.


title: Reality (David Bowie album)

text: "Never Get Old" was first previewed in France as early as June 2003 through a television advertisement for Vittel mineral water that featured Bowie himself. It was also posted online to BowieNet. The song was originally scheduled to be released as the album's second single to coincide with Bowie's UK tour dates, but it was shelved at the last minute, similar to "Slow Burn" the previous year. Promotional CDs continuing an edited version, backed by "Waterloo Sunset", appeared in Europe while in Britain, the two tracks appeared as digital downloads on Sony Music's UK site in November. "Never Get Old" also appeared as a Japanese A-side in March 2004. A mash-up of "Never Get Old" and "Rebel Rebel", created by Endless Noise in March 2004 and titled "Rebel Never Gets Old", appeared in an ad campaign for Audi in America. This release appeared as a conventional single in June and peaked at number 47 in the UK.


title: Reality (David Bowie album)

text: "Reality" received largely positive reviews from music critics on release. Like many of the artist's most recent releases, several reviewers considered it his best since "Scary Monsters", although many were quick to recognise the reception "Heathen" earned the year prior and made positive comparisons. One reviewer for the "Miami Herald" stated that "with each listen, "Reality" feels stronger than "Heathen". That's two good ones in a row". Another review from John Mulvey of "Dotmusic" considered the songs on "Reality" stronger than "Heathen": "If "Heathen" was a little overpraised by relieved critics, then "Reality" is a more deserving case." "Pitchfork" Eric Carr further contested that "what last year's "Heathen" implied, and what "Reality" seems to prove, is that... Bowie has finally joined us all in the present, mind-young as ever but old enough not to make a show of it." He ultimately called the album "pretty good" and believed it cemented his status as a modern artist. John Aizlewood of the "Evening Standard" found the album more cohesive than "Heathen" and named it the publication's CD of the week. Comparing it to Bowie's previous works, he argued that it stands on its own and with "Reality", the artist has "rediscovered" himself and "regained his dignity". Several also considered "Reality" a return to form for the artist.


title: Reality (David Bowie album)

text: Some critics highlighted the lyrics and vocal performances as showcasing a maturity absent from previous works. Several also commented on the music. In the "Miami Herald", Howard Cohen commended the artist for playing to his musical strengths rather than "hopping aboard some inappropriate youthful bandwagon". In "The Mail on Sunday", Tim De Lisle wrote that "this record pulsates with creative vigour", offering "a gleaming showcase for his voice, or rather voices. Bowie has always been several people and most of them are here." Anthony DeCurtis praised the covers in "Rolling Stone" and felt the guitar work on "New Killer Star" was reminiscent of Mick Ronson's work on Lou Reed's 1972 album "Transformer". He ultimately believed Bowie succeeded in searching for "reality", to the artist's "mixed dismay and amusement". Senior AllMusic editor Stephen Thomas Erlewine complimented the modernisation of Bowie and Visconti's former 1970s sound. While he called its predecessor an amalgamation of "Hunky Dory" to ""Heroes"", he found "Reality" picks up where its predecessor left off, creating a blend of ""Heroes"" to "Scary Monsters". Making further comparisons to "Heathen", Erlewine felt "Reality" was "artier", but "similar in feel" and "just as satisfying". He concluded: "Both records are testaments to the fact that veteran rockers can make satisfyingly classicist records without resulting in nostalgia or getting too comfortable." Remarking on the lyrics, Ryan Lenz of "Associated Press" described the album as "an exercise in introspection" and analysed "Reality" as not "a vehicle for commentary on contemporary times", but rather encapsulating an artist "nearing 60 and finding the world disappointingly clear and never what it seemed".


title: Reality (David Bowie album)

text: Several reviewers praised the album as a whole. "Uncut" Chris Roberts hailed "Reality" as "a very, very good sexy-angst album" filled with "lovely, left-handed songs, rich with unexpected angles, daring detours and words which muse over mortality yet emerge seeming upbeat", further summarising the lyrics as "mournful" and the music as "euphoric". Andy Gill of "The Independent" described the album as a "satisfying, chunk solidity of songs" that starts on a high point but ends on a "draggy" note. Nevertheless, he highlighted the two covers and "New Killer Star". On the other hand, "NME" Tim Wild signalled out "Bring Me the Disco King" as "a true thing of beauty" among a "sweet collection of songs". Caroline Sullivan of "The Guardian" praised "Reality" as "touching [and] intelligent" and that it "gels unexpectedly well". Reviewing "Reality" for the BBC, Darryl Easlea called it "a proper album, with a beginning, a middle and an end. It's direct, warm, emotional honest, even and the surfeit of pleasingly deceptive musical simplicity allows the irony of the central concept – that there is no such thing as reality anymore – an opportunity to filter through. It's also rather lively and convincing." Meanwhile, "The Observer" Kitty Empire cited "how wonderfully unforced it all sounds" as the album's defining feature. Although she found it inferior to the artist's Berlin-era works, she deemed "Reality" "the first sequence of Bowie songs that bears repeated listening in years", concluding that "it is a pleasure, rather than a grim duty done out of respect for the memory of Ziggy Stardust." "The New York Times" writer Mim Udovitch praising Visconti's production as "impeccable" and remarked on the sense of immediacy that "makes you feel that Mr Bowie and his spectacularly hard-rocking band might be about to materialize in your living room ready for an encore." In a review for the 2007 limited-edition box set "David Bowie Box", critic Thom Jurek described "Reality" as a "schizophrenic recording", on which the covers of "Try Some, Buy Some" and "Pablo Picasso" "[distinguish] this set more than anything else".


title: Reality (David Bowie album)

text: Nevertheless, some reviewers expressed more mixed assessments. "Entertainment Weekly" Mark Weingarten cited the production as continuing to hinder Bowie's work since "Black Tie White Noise", but nevertheless called the writing an improvement over his previous records. In "The Austin Chronicle", Marc Savlov contended that "While "Reality" isn't a failure by anyone's standards, there's precious few moments that you can recall, much less hum, an hour after listening to it."


title: Reality (David Bowie album)

text: Having become revitatilised for performing following the Heathen Tour, Bowie embarked on a world tour to support "Reality" that would become his most extensive tour since the mid-1990s. It also surpassed the 1983 Serious Moonlight, 1987 Glass Spider and 1990 Sound+Vision tours to become, on the basis of individual dates, the longest tour of his career. Labelled "A Reality Tour", Pegg states that "the indefinite article emphasi[ses] the album's dalliance with the notion that there can be no absolute definition of reality." The same personnel as the Heathen Tour and "Reality"–Slick, Garson, Dorsey, Russell and Campbell–returned for the new shows, with Leonard taking Plati's place as bandleader. Rehearsals began in July 2003 before the tour commenced on 19 August with a small warm-up gig for BowieNet members only.


title: Reality (David Bowie album)

text: Most of September 2003 was spent playing various gigs to promote the upcoming release of "Reality". One of the biggest was on 8September, when the band performed the entire "Reality" album to various celebrities and BowieNet members at London's Riverside Studios. The event was broadcast live to more than 80 cinemas in 22 countries worldwide, although many suffered issues related to audio syncing and time delays. Nevertheless, the event was deemed a success and was followed by a Q&A session with fans. Several television appearances followed before the first official show in Copenhagen on 7October.


title: Reality (David Bowie album)

text: The shows on A Reality Tour were more theatrical compared to preceding tours, being dominated by LED lights, raised catwalks and staircases. According to Buckley, the band prepared more than 50 songs for the shows, although Garson later contested to learning around 60 to 70. Beginning with the "Reality" outtake "Queen of All the Tarts (Overture)" before the curtain-up, the setlist contained a variety of material across Bowie's entire career, ranging from classic hits to more obscure tracks. Numerous tracks from both "Reality" and "Heathen" were included, while tracks like "Lodger" "Fantastic Voyage" (1979) made their live debut and others, such as "Tonight" "Loving the Alien" (1984), were given radical reworkings. The band also swapped out songs throughout the shows and by the start of 2004, the band had performed over 50 songs total.


title: Reality (David Bowie album)

text: A Reality Tour received critical acclaim throughout its run. However, the long setlists began taking a toll on Bowie in mid-November 2003, resulting the cancellation of a concert in Toulouse after he contracted laryngitis, but he quickly recovered and was back on stage two days later. Two shows in Dublin were later released in 2010 on the "A Reality Tour" album and DVD. Nevertheless, Bowie encountered more health problems in early December with a bout of influenza, resulting in the postponement of five US dates. Further tragedy struck on 3May 2004 when a lighting technician fell to his death during the support act, after which the show was immediately cancelled. On 23June, Bowie was forced to end the show early due to what medical personnel deemed a pinched shoulder nerve. Although he was back on stage two days later at the Hurricane Festival in Germany, his condition worsened and on 30June, all 14 remaining dates were cancelled and A Reality Tour became his final concert tour. Pegg later described it as one of his best concert tours.


title: Reality (David Bowie album)

text: Bowie underwent a procedure for a blocked artery known as angioplasty on 26June, which was announced to the public in July 2004. Two days later, a tour insider stated that he suffered a heart attack backstage. Following the incident, Bowie withdrew from the public eye. Over the following years he was spotted at local New York venues and made occasional appearances at concerts by artists such as Franz Ferdinand, Arcade Fire and David Gilmour, with his final live public performance taking place on 9November 2006 at the Hammerstein Ballroom, where he performed "Changes". He occasionally contributed to various studio recordings by artists such as TV on the Radio and Scarlett Johansson, but did not release another studio album until "The Next Day" in 2013, making "Reality" his final album of original material for ten years.


title: Reality (David Bowie album)

text: Bowie's biographers have given "Reality" mixed to positive assessments. In "Strange Fascination", Buckley finds "Reality" lacks both a "coherent musical identity" and "any thematic trajectory", furthermore observing a general feeling of "laxity" and underwritten songs: "whilst around a third of the songs on "Reality" are Bowie near top form, the remainder vary from good to merely pleasant." O'Leary considers it "overlong" and following the release of "The Next Day", "Reality" reestablished itself as "a minor album whose songs were built to be blasted on stage". On the other hand, Perone finds it a "strong album", detecting and commending the consistent themes throughout and highlights the covers. Meanwhile, Marc Spitz called "Reality" superior to "Heathen" in "", remarking that the addition of Slick makes it more of a guitar record. Published in 2009 before the release of "The Next Day", Spitz found it worthy as a swan song to Bowie's long career. Author Paul Trynka gave the album three out of four stars, citing a familiar sound but overall, he writes the record proves that, with the likes of tracks like "Bring Me the Disco King", Bowie "has the potential to conjure up pleasures as yet unknown".


title: Reality (David Bowie album)

text: In "The Complete David Bowie", Pegg states that one of the album's successes is that it emerges with a "reinvigorated sense of rock attack" following the "delicate, self-consciously artful[ness]" of its predecessor, equating both records to the relationships between "Hunky Dory" and "Ziggy Stardust", or "Outside" (1995) and "Earthling". Further comparing the two albums, he writes that "Reality" offers "less complexity and fewer sonic layers" than "Heathen" in exchange for "a greater abundance of catchy hooks and buoyant pop-rock atmospherics". Nevertheless, despite having a more accessible atmosphere, he states that "Reality" "sacrifices none of "Heathen"s artistic sensibility" and "its lasting value lies not just in its infectious melodies and evocative lyrics, but in the exquisitely judged oddness of its sonic textures". In 2016, Bryan Wawzenek of "Ultimate Classic Rock" placed "Reality" at number 16 out of 26 in a list ranking Bowie's studio albums from worst to best, praising Bowie's comfortability on the record and his version of "Pablo Picasso". Including Bowie's two albums with Tin Machine, "Consequence of Sound" ranked "Reality" number 24 out of 28 in a 2018 list, with Pat Levy highlighting the covers but ultimately called it "a decent record in the pantheon of Bowie, nothing more, nothing less".


title: Flag of Slovakia

text: The current form of the national flag of the Slovak Republic () was adopted by Slovakia's Constitution, which came into force on 3 September 1992. The flag, like many other flags of Slavic nations, uses Pan-Slavic colors (red, white, and blue). Pictured in the centre of the flag is the Slovakia's national coat of arms.


title: Flag of Slovakia

text: Slovakia's flag in its current form (but with another coat of arms on it or without any arms) can be dated back to the revolutionary year 1848. It was also used semi-officially in Czechoslovakia before World War II, by the Slovak Republic during World War II.


title: Flag of Slovakia

text: In 1990, the interior ministry tasked Ladislav Čisárik, a painter and heraldic artist, and Ladislav Vrtel, an expert in heraldry, with creating a new coat of arms and national flag. Čisárik and Vrtel based their designs for a modern coat of arms and flag on an existing 14th century coat of arms. However, Čisárik and Vrtel chose to enlarge the double cross three times to emphasize it as a national symbol. In addition to the national coat of arms and the national flag, the duo also designed a new presidential standard, which incorporates the double cross as well.


title: Flag of Slovakia

text: The new flag was finally adopted (initially without Čisárik's and Vrtel's coat of arms) on 1 March 1990 as the flag of the Slovak Republic within Czechoslovakia. The coat of arms was added on 3 September 1992 and a special law describing the details of the flag followed in February 1993, after Slovakia became an independent country.


title: Flag of Slovakia

text: Since the Slovak flag without the coat of arms is identical to the current flag of the Russian Federation, and can also be compared to the modern flag of Slovenia, the Constitution of Slovakia added the national coat of arms to it in September 1992.


title: Stochastic matrix

text: In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov at the beginning of the 20th century, and has found use throughout a wide variety of scientific fields, including probability theory, statistics, mathematical finance and linear algebra, as well as computer science and population genetics. There are several different definitions and types of stochastic matrices:


title: Stochastic matrix

text: In the same vein, one may define a stochastic vector (also called probability vector) as a vector whose elements are nonnegative real numbers which sum to 1. Thus, each row of a right stochastic matrix (or column of a left stochastic matrix) is a stochastic vector. A common convention in English language mathematics literature is to use row vectors of probabilities and right stochastic matrices rather than column vectors of probabilities and left stochastic matrices; this article follows that convention. In addition, a substochastic matrix is a real square matrix whose row sums are all formula_1


title: Stochastic matrix

text: The stochastic matrix was developed alongside the Markov chain by Andrey Markov, a Russian mathematician and professor at St. Petersburg University who first published on the topic in 1906. His initial intended uses were for linguistic analysis and other mathematical subjects like card shuffling, but both Markov chains and matrices rapidly found use in other fields.


title: Stochastic matrix

text: Stochastic matrices were further developed by scholars like Andrey Kolmogorov, who expanded their possibilities by allowing for continuous-time Markov processes. By the 1950s, articles using stochastic matrices had appeared in the fields of econometrics and circuit theory. In the 1960s, stochastic matrices appeared in an even wider variety of scientific works, from behavioral science to geology to residential planning. In addition, much mathematical work was also done through these decades to improve the range of uses and functionality of the stochastic matrix and Markovian processes more generally.


title: Stochastic matrix

text: From the 1970s to present, stochastic matrices have found use in almost every field that requires formal analysis, from structural science to medical diagnosis to personnel management. In addition, stochastic matrices have found wide use in land change modeling, usually under the term Markov matrix.


title: Stochastic matrix

text: If the probability of moving from to in one time step is , the stochastic matrix is given by using as the -th row and -th column element, e.g.,


title: Stochastic matrix

text: The above elementwise sum across each row of may be more concisely written as , where is the -dimensional column vector of all ones. Using this, it can be seen that the product of two right stochastic matrices and is also right stochastic: . In general, the -th power of a right stochastic matrix is also right stochastic. The probability of transitioning from to in two steps is then given by the -th element of the square of :


title: Stochastic matrix

text: In general, the probability transition of going from any state to another state in a finite Markov chain given by the matrix in steps is given by .


title: Stochastic matrix

text: An initial probability distribution of states, specifying where the system might be initially and with what probabilities, is given as a row vector.


title: Stochastic matrix

text: A "stationary" probability vector is defined as a distribution, written as a row vector, that does not change under application of the transition matrix; that is, it is defined as a probability distribution on the set which is also a row eigenvector of the probability matrix, associated with eigenvalue 1:


title: Stochastic matrix

text: It can be shown that the spectral radius of any stochastic matrix is one. By the Gershgorin circle theorem, all of the eigenvalues of a stochastic matrix have absolute values less than or equal to one. Additionally, every right stochastic matrix has an "obvious" column eigenvector associated to the eigenvalue 1: the vector , whose coordinates are all equal to 1 (just observe that multiplying a row of times equals the sum of the entries of the row and, hence, it equals 1). As left and right eigenvalues of a square matrix are the same, every stochastic matrix has, at least, a row eigenvector associated to the eigenvalue 1 and the largest absolute value of all its eigenvalues is also 1. Finally, the Brouwer Fixed Point Theorem (applied to the compact convex set of all probability distributions of the finite set ) implies that there is some left eigenvector which is also a stationary probability vector.


title: Stochastic matrix

text: On the other hand, the Perron–Frobenius theorem also ensures that every irreducible stochastic matrix has such a stationary vector, and that the largest absolute value of an eigenvalue is always 1. However, this theorem cannot be applied directly to such matrices because they need not be irreducible.


title: Stochastic matrix

text: In general, there may be several such vectors. However, for a matrix with strictly positive entries (or, more generally, for an irreducible aperiodic stochastic matrix), this vector is unique and can be computed by observing that for any we have the following limit,


title: Stochastic matrix

text: where is the -th element of the row vector . Among other things, this says that the long-term probability of being in a state is independent of the initial state . That both of these computations give the same stationary vector is a form of an ergodic theorem, which is generally true in a wide variety of dissipative dynamical systems: the system evolves, over time, to a stationary state.


title: Stochastic matrix

text: Intuitively, a stochastic matrix represents a Markov chain; the application of the stochastic matrix to a probability distribution redistributes the probability mass of the original distribution while preserving its total mass. If this process is applied repeatedly, the distribution converges to a stationary distribution for the Markov chain.


title: Stochastic matrix

text: Suppose there is a timer and a row of five adjacent boxes. At time zero, a cat is in the first box, and a mouse is in the fifth box. The cat and the mouse both jump to a random adjacent box when the timer advances. E.g. if the cat is in the second box and the mouse is in the fourth, the probability that "the cat will be in the first box and the mouse in the fifth after the timer advances" is one fourth. If the cat is in the first box and the mouse is in the fifth, the probability that "the cat will be in box two and the mouse will be in box four after the timer advances" is one. The cat eats the mouse if both end up in the same box, at which time the game ends. Let the random variable "K" be the time the mouse stays in the game.


title: Stochastic matrix

text: The Markov chain that represents this game contains the following five states specified by the combination of positions (cat,mouse). Note that while a naive enumeration of states would list 25 states, many are impossible either because the mouse can never have a lower index than the cat (as that would mean the mouse occupied the cat's box and survived to move past it), or because the sum of the two indices will always have even parity. In addition, the 3 possible states that lead to the mouse's death are combined into one:


title: Stochastic matrix

text: We use a stochastic matrix, formula_7 (below), to represent the transition probabilities of this system (rows and columns in this matrix are indexed by the possible states listed above, with the pre-transition state as the row and post-transition state as the column). For instance, starting from state 1 – 1st row – it is impossible for the system to stay in this state, so formula_8; the system also cannot transition to state 2 – because the cat would have stayed in the same box – so formula_9, and by a similar argument for the mouse, formula_10. Transitions to states 3 or 5 are allowed, and thus formula_11 .


title: Stochastic matrix

text: No matter what the initial state, the cat will eventually catch the mouse (with probability 1) and a stationary state π = (0,0,0,0,1) is approached as a limit. To compute the long-term average or expected value of a stochastic variable formula_13, for each state formula_14 and time formula_15 there is a contribution of formula_16. Survival can be treated as a binary variable with formula_17 for a surviving state and formula_18 for the terminated state. The states with formula_18 do not contribute to the long-term average.


title: Stochastic matrix

text: As State 5 is an absorbing state, the distribution of time to absorption is discrete phase-type distributed. Suppose the system starts in state 2, represented by the vector formula_20. The states where the mouse has perished don't contribute to the survival average so state five can be ignored. The initial state and transition matrix can be reduced to,


title: Stochastic matrix

text: where formula_23 is the identity matrix, and formula_24 represents a column matrix of all ones that acts as a sum over states.


title: Stochastic matrix

text: Since each state is occupied for one step of time the expected time of the mouse's survival is just the sum of the probability of occupation over all surviving states and steps in time,


title: Gianluca Busio

text: Gianluca Cristiano Busio (born May 28, 2002) is an American professional soccer player who plays as a midfielder for club Venezia and the United States national team.


title: Gianluca Busio

text: Born in Greensboro, North Carolina, Busio joined the Sporting Kansas City academy in 2016 from North Carolina Fusion.


title: Gianluca Busio

text: On August 25, 2017, Busio signed a Homegrown Player contract with Sporting Kansas City, making him the youngest player to sign with a Major League Soccer club since Freddy Adu joined D.C. United in 2004.


title: Gianluca Busio

text: He made his professional debut on April 4, 2018, appearing for Sporting Kansas City's United Soccer League affiliate side, Swope Park Rangers, starting in a 1–0 win over Colorado Springs Switchbacks. Busio went on to make his first Major League Soccer appearance for Sporting Kansas City on July 28 as a 77th-minute substitute in a 3–2 loss against FC Dallas. One week later, on August 4, Busio made his first league start for Sporting Kansas City against the Houston Dynamo, which saw three red cards, eight yellow cards, and 28 total fouls. He provided his first career assist on a 74th-minute goal for teammate Diego Rubio, which proved to be the winner in a 1–0 match. Busio was the third-youngest player to start a match in Major League Soccer history.


title: Gianluca Busio

text: On August 9, 2021, Busio moved to Serie A side Venezia for a club-record transfer fee. The fee was reported to be $6.5 million rising to $10.5 million in potential add-ons. He made his debut for the club on August 27 in a 0–3 defeat to Udinese. He scored his first goal for the club, a last minute equalizer, in a 1–1 draw with Cagliari on October 1.


title: Gianluca Busio

text: In October 2019, he was named to the United States squad for the 2019 FIFA U-17 World Cup in Brazil. On July 11, 2021, Busio made his senior national team debut, substituting for Jackson Yueill in the 62nd minute of the U.S.'s CONCACAF Gold Cup group match against Haiti.


title: Gianluca Busio

text: Busio is of Italian descent through his Brescia-born father and holds Italian citizenship. His mother is African American. He has an older sister, Ilaria, and an older brother, Matteo, who plays soccer at UNC-Charlotte and whom Gianluca lists as his biggest inspiration.


title: Goodbye (Cream album)

text: Goodbye (also called Goodbye Cream) is the fourth and final studio album by Cream, with three tracks recorded live, and three recorded in the studio. It was released in Europe by Polydor Records and by Atco Records in the United States, debuting in "Billboard" on 15 February 1969. It reached number one in the United Kingdom and number two in the United States. A single, "Badge", was subsequently released from the album a month later. The album was released after Cream disbanded in November 1968.


title: Goodbye (Cream album)

text: Just before Cream's third album, "Wheels of Fire", was to be released, the group's manager Robert Stigwood announced that the group were going to disband after a farewell tour and a final concert at the Royal Albert Hall in November. Just before the start of their farewell tour in October 1968, Cream recorded three songs at IBC Studios in London with producer Felix Pappalardi and engineer Damon Lyon-Shaw. The songs "Badge" and "Doing That Scrapyard Thing" featured Eric Clapton using a Leslie speaker, while all three recordings featured keyboard instruments played by either Jack Bruce or Felix Pappalardi. The group started their farewell tour on 4 October 1968 in Oakland, California and 15 days later on 19 October the group performed at The Forum in Los Angeles where the three live recordings on "Goodbye" were recorded with Felix Pappalardi and engineers Adrian Barber and Bill Halverson.


title: Goodbye (Cream album)

text: The original plan for "Goodbye" was to make it a double album, with one disc featuring studio recordings and the other with live performances like "Wheels of Fire". With a lack of quality material on hand, however, the album was only one disc with three live recordings and three studio recordings.


title: Goodbye (Cream album)

text: The original LP release of the album was packaged in a gatefold sleeve with art direction handled by Haig Adishian. The outer sleeve featured photography by Roger Phillips with a cover design by the Alan Aldridge ink Studios, while the inner sleeve featured an illustration of a cemetery by Roger Hane that had the song titles on tombstones. A Compact Disc reissue of the album for the Cream Remasters series in 1998 featured an inlay photograph and had the inner-sleeve illustration in the liner notes of the album.


title: Goodbye (Cream album)

text: In a contemporary review for "Rolling Stone", music critic Ray Rezos felt Cream deserved to depart with a better album. He wrote that most of the live songs sounded inferior to the original recordings and that the studio tracks were marred by the same flaw as on "Wheels of Fire", namely the presence of blues playing on songs whose compositions were not blues in his opinion. Nonetheless, "Goodbye" was voted the 148th best rock album of all time in Paul Gambaccini's 1978 poll of 50 prominent American and English rock critics.


title: Goodbye (Cream album)

text: In a retrospective review for AllMusic, senior editor Stephen Thomas Erlewine called "Goodbye" a work of "hard, heavy rock" and "strong moments" rather than cohesiveness, with live music that is generally better than on "Wheels of Fire" and a side of studio recordings that also found Cream "at something of a peak". Robert Christgau also reacted favourably to the album, citing it as his favorite record from the group. J. D. Considine was less impressed in "The Rolling Stone Album Guide" (1992), deeming "Goodbye" an incomplete record with "exquisite studio work" but mediocre live performances.


title: Mdina

text: Mdina ( ; ; ; ; ), also known by its Italian-language titles ' ("Old City") and ' ("Notable City"), is a fortified city in the Northern Region of Malta which served as the island's capital from antiquity to the medieval period. The city is still confined within its walls, and has a population of just under 300, but it is contiguous with the town of Rabat, which takes its name from the Arabic word for suburb, and has a population of over 11,000 (as of March 2014).


title: Mdina

text: The city was founded as Maleth in around the 8th century BC by Phoenician settlers, and was later renamed Melite by the Romans. Ancient Melite was larger than present-day Mdina, and it was reduced to its present size during the Byzantine or Arab occupation of Malta. During the latter period, the city adopted its present name, which derives from the Arabic word . The city remained the capital of Malta throughout the Middle Ages, until the arrival of the Order of St. John in 1530, when Birgu became the administrative centre of the island. Mdina experienced a period of decline over the following centuries, although it saw a revival in the early 18th century. At this point, it acquired several Baroque features, although it did not lose its medieval character.


title: Mdina

text: Mdina remained the centre of the Maltese nobility and religious authorities (and property continues to largely be passed down from families and from generation to generation), but it never regained its pre-1530 importance, giving rise to the popular nickname the "Silent City" by both locals and visitors. Mdina is on the tentative list of UNESCO World Heritage Sites, and it is now one of the main tourist attractions in Malta.


title: Mdina

text: The plateau on which Mdina is built has been inhabited since prehistory, and by the Bronze Age it was a place of refuge since it was naturally defensible. The Phoenicians colonized Malta around the 8th century BC, and they founded the city of Maleth on this plateau. It was taken over by the Roman Republic in 218 BC, becoming known as Melite. The Punic-Roman city was about three times the size of present-day Mdina, extending into a large part of modern Rabat.


title: Mdina

text: According to Early Modern interpretation the Acts of the Apostles, when Paul the Apostle was shipwrecked on Malta in 60 AD, he was greeted by Publius, the governor of Melite, and he cured his sick father. According to tradition, the population of Melite converted to Christianity, and Publius became the first Bishop of Malta and then Bishop of Athens before being martyred in 112 AD.


title: Mdina

text: Very few remains of the Punic-Roman city survive today. The most significant are the ruins of the Domvs Romana, in which several well-preserved mosaics, statues and other remains were discovered. Remains of the podium of a Temple of Apollo, fragments of the city walls and some other sites have also been excavated.


title: Mdina

text: At some point following the fall of the Western Roman Empire, a retrenchment was built within the city, reducing it to its present size. This was done to make the city's perimeter more easily defensible, and similar reductions in city sizes were common around the Mediterranean region in the early Middle Ages. Although it was traditionally assumed that the retrenchment was built by the Arabs, it has been suggested that it was actually built by the Byzantine Empire in around the 8th century, when the threat from the Arabs increased.


title: Mdina

text: In 870, Byzantine Melite, which was ruled by governor Amros (probably Ambrosios), was besieged by Aghlabids led by Halaf al-Hādim. He was killed in the fighting, and Sawāda Ibn Muḥammad was sent from Sicily to continue the siege following his death. The duration of the siege is unknown, but it probably lasted for some weeks or months. After Melite fell to the invaders, the inhabitants were massacred, the city was destroyed and its churches were looted. Marble from Melite's churches was used to build the castle of Sousse.


title: Mdina

text: According to Al-Himyarī, Malta remained almost uninhabited until it was resettled in 1048 or 1049 by a Muslim community and their slaves, who built a settlement called Medina on the site of Melite. Archaeological evidence suggests that the city was already a thriving Muslim settlement by the beginning of the 11th century, so 1048–49 might be the date when the city was officially founded and its walls were constructed. The layout of the new city was completely different to that of ancient Melite. Mdina still has features typical of a medina, a legacy of the period of Arab rule.


title: Mdina

text: The Byzantines besieged Medina in 1053–54, but were repelled by its defenders. The city surrendered peacefully to Roger I of Sicily after a short siege in 1091, and Malta was subsequently incorporated into the County and later the Kingdom of Sicily, being dominated by a succession of feudal lords. A castle known as the "Castellu di la Chitati" was built on the southeast corner of the city near the main entrance, probably on the site of an earlier Byzantine fort.


title: Mdina

text: The population of Malta during the fifteenth century was about 10,000, with town life limited to Mdina, Birgu and the Gozo Citadel. Mdina was comparatively small and partly uninhabited and by 1419, it was already outgrown by its suburb, Rabat. Under Aragonese rule, local government rested on the "Università", a communal body based in Mdina, which collected taxation and administered the islands' limited resources. At various points during the fifteenth century, this town council complained to its Aragonese overlords that the islands were at the mercy of the sea and the saracens.


title: Mdina

text: The city withstood a siege by Hafsid invaders in 1429. While the exact number of casualties or Maltese who were carried into slavery is unknown, the islands suffered depopulation in this raid.


title: Mdina

text: When the Order of Saint John took over in Malta in 1530, the nobles ceremoniously handed over the keys of the city to Grand Master Philippe Villiers de L'Isle-Adam, but the Order settled in Birgu and Mdina lost its status as capital city. In the 1540s, the fortifications began to be upgraded during the magistracy of Juan de Homedes y Coscon, and in 1551 the city withstood a brief Ottoman attack.


title: Mdina

text: During the Great Siege of Malta in 1565, Mdina was the base of the Order's cavalry, which made occasional sorties on the invading Ottomans. On 7 August 1565, the cavalry attacked the unprotected Ottoman field hospital, which led in the invaders abandoning a major assault on the main fortifications in Birgu and Senglea. The Ottomans attempted to take Mdina in September so as to winter there, but abandoned their plans when the city fired its cannon, leading them to believe that it had ammunition to spare. After the siege, Maltese military engineer Girolamo Cassar drew up plans to reduce Mdina's size by half and turning it into a fortress, but these were never implemented due to protests by the city's nobles. The fortifications were again upgraded in the mid-17th century, when the large De Redin Bastion was built at the centre of the land front.


title: Mdina

text: Mdina suffered severe damage during the 1693 Sicily earthquake, although no casualties were reported the 13th-century Cathedral of St. Paul was partially destroyed, and it was rebuilt by Lorenzo Gafà in the Baroque style between 1697 and 1703.


title: Mdina

text: On 3 November 1722, newly elected Grand Master António Manoel de Vilhena issued orders for the restoration and renovation of Mdina. This renovation was entrusted to the French architect and military engineer Charles François de Mondion, who introduced strong French Baroque elements into what was still a largely medieval city. At this point, large parts of the fortifications and the city entrance were completely rebuilt. The remains of the "Castellu di la Chitati" were demolished to make way for Palazzo Vilhena, while the main gate was walled up and a new Mdina Gate was built nearby. Several public buildings were also built, including the Banca Giuratale and the Corte Capitanale. The last major addition to the Mdina fortifications was Despuig Bastion, which was completed in 1746.


title: Mdina

text: On 10 June 1798, Mdina was captured by French forces without much resistance during the French invasion of Malta. A French garrison remained in the city, but a Maltese uprising broke out on 2 September of that year. The following day, rebels entered the city through a sally port and massacred the garrison of 65 men. These events marked the beginning of a two-year uprising and blockade, and the Maltese set up a National Assembly which met at Mdina's Banca Giuratale. The rebels were successful, and in 1800 the French surrendered and Malta became a British protectorate.


title: Mdina

text: Today, Mdina is one of Malta's major tourist attractions, hosting about 750,000 tourists a year. No cars (other than a limited number of residents, emergency vehicles, wedding cars and horses) are allowed in Mdina, partly why it has earned the nickname 'the Silent City' (). The city displays an unusual mix of Norman and Baroque architecture, including several palaces, most of which serve as private homes.


title: Mdina

text: Founded in 2006, the Mdina Knights F.C. play in the third division league of the Malta Football Association.


title: Stinkers Bad Movie Awards

text: The Stinkers Bad Movie Awards (formerly known as the "Hastings Bad Cinema Society") was a Los Angeles-based group of film buffs and film critics devoted to honoring the worst films of the year.


title: Stinkers Bad Movie Awards

text: The society was founded by Mike Lancaster and Ray Wright, two former ushers who met in the late 1970s at what is now the Pacific Hastings Theater in Pasadena, California (from which the society originally got its name).


title: Stinkers Bad Movie Awards

text: "The Stinkers Bad Movie Awards" have been featured in "Entertainment Weekly", "USA Today", "Los Angeles Times", and on the BBC, CNN, as well as in several newspapers and magazines.


title: Stinkers Bad Movie Awards

text: Lancaster and Wright offered the annual Stinkers Bad Movie Awards, which was a parody of the Academy Awards. The Stinkers were similar to the Golden Raspberry Awards (the "Razzies"), which debuted four years after the Stinkers. Aside from the usual categories one might expect in an Oscar parody (Worst Picture, Worst Actor, etc.), the Stinkers offered other categories such as Worst Fake Accent, Most Painfully Unfunny Comedy, Least 'Special' Special Effects and Worst On-Screen Hairstyle. Unlike the Razzies, the Stinkers did not have an awards ceremony.


title: Stinkers Bad Movie Awards

text: The Stinkers' first ballots were handed out to the public in 1997. In the years that followed, the Razzies and Stinkers rarely agreed on a list of nominees or winners. The Stinkers initially opened their balloting to the general moviegoing public but soon discovered that most people surveyed hadn't seen many of the films on the ballot and often just voted for the person they hated the most, usually someone like Mariah Carey, the Spice Girls or anyone connected with the film "Gigli".


title: Stinkers Bad Movie Awards

text: In 2001 the Stinkers created "", a list that parodied "AFI's 100 Years...100 Movies" list. The next year the Stinkers made a special trophy of a miniature flushing toilet for comedian actor Tom Green. Green's "Freddy Got Fingered" was nominated for seven awards and won Worst Film, Worst Sense of Direction, Worst Actor and Most Painfully Unfunny Comedy. That same year the Stinkers gave a special award to David Manning, the controversial Sony Pictures fictitious movie critic.


title: Stinkers Bad Movie Awards

text: The Stinkers included in 2003 another special category for Worst Performance by a Child, dedicated to child actor Spencer Breslin.


title: Stinkers Bad Movie Awards

text: In 2004, the Stinkers went to a more selective way of obtaining votes. They dismantled their membership and offered ballots by invitation only to a small, select group of film geeks and critics, who had seen a majority of the films during the year.


title: Stinkers Bad Movie Awards

text: In 2006, the Stinkers refused to nominate hotel heiress Paris Hilton for her supporting role in the horror film "House of Wax". Said Lancaster, "To get on the Stinkers ballot you are judged on your performance, not your tabloid persona. Anyone that would put Paris Hilton on a list of the five worst supporting actresses in 2005 didn't see a lot of movies in 2005. I could list twelve actresses who gave worse supporting performances than Paris Hilton."


title: Stinkers Bad Movie Awards

text: The next year, the Stinkers did nominate Hilton for Worst Actress for her performance in the barely released "National Lampoon's Pledge This!".


title: Stinkers Bad Movie Awards

text: In late January 2007, it was announced on the website that following the announcement of the year's winners, the Stinkers website would be officially closed down after ten years on the internet. On July 1, 2007, four months after the announcement of the worst of 2006 winners, the site was taken down. No reliable source or involved party gave a reason for the end of the Stinkers.


title: Stinkers Bad Movie Awards

text: Special categories have also been introduced for specific years. Some have been in multiple ballots while others were used one time.


title: Destrier

text: The destrier is the best-known war horse of the Middle Ages. It carried knights in battles, tournaments, and jousts. It was described by contemporary sources as the "Great Horse", due to its significance.


title: Destrier

text: While highly prized by knights and men-at-arms, the destrier was not very common. Most knights and mounted men-at-arms rode other war horses, such as coursers and rounceys.


title: Destrier

text: The word is first attested in Middle English around 1330, as "destrer". It was borrowed into Middle English from Anglo-Norman "destrer", whose Old French counterpart was "destrier" (from which the Modern English spelling derives). The word is also found in medieval Provençal (as "destrier") and Italian (as "destriere", "destriero"). These forms themselves derived from the Vulgar Latin "equus dextrarius", meaning "right-sided horse" (from "dextra", "right hand", the same root as "dextrous" and "dexterity"). This may refer to it being led by the squire at the knight's right side, as often before battle the destrier ran unburdened to keep it fresh for the fray; the knight rode another horse, mounting his destrier just before engaging the enemy. Alternatively, it could describe the horse's gait (leading with the right).


title: Destrier

text: The word "destrier" does not refer to a breed of horse, but to a type of horse; the finest and strongest warhorses. These horses were usually stallions, bred and raised from foalhood specifically for the needs of war. The destrier was specifically for use in battle or tournament; for everyday riding, a knight would use a palfrey, and his baggage would be carried on a sumpter horse (or packhorse), or possibly in wagons.


title: Destrier

text: They had powerful hindquarters, able to easily coil and spring to a stop, spin, turn or sprint forward quickly. They also had a short back and well-muscled loin, strong bone, and a well-arched neck. From medieval art, the head of the destrier appears to have had a straight or slightly convex profile, a strong, wide jaw, and good width between the eyes.


title: Destrier

text: The destrier was considered the most suited to the joust: coursers seem to have been preferred for other forms of warfare.


title: Destrier

text: Many well-known scholars have speculated about the nature of destriers and about the size they attained. They apparently were not enormous draft types. Recent research undertaken at the Museum of London, using literary, pictorial and archeological sources, suggests war horses (including destriers) averaged from , and differed from a riding horse in their strength, musculature and training, rather than in their size. An analysis of medieval horse armour located in the Royal Armouries indicates the equipment was originally worn by horses of , about the size and build of a modern field hunter or ordinary riding horse.


title: Destrier

text: Equestrian sculptures in Italy suggest a "Spanish" style of horse that today would be referred to as a Baroque horse, such as the Andalusian horse, Friesian horse, or even a heavy but agile warmblood breed such as the Irish Draught. Modern estimates put the height of a destrier at no more than , but with a strong and heavy physique. Though the term "Great Horse" was used to describe the destrier, leading some historians to speculate that such animals were the forerunners of modern draught horse breeds, the historical record does not support the image of the destrier as a draft horse.


title: Destrier

text: The modern Percheron draft breed may in part descend from destriers, though it is probably taller and heavier than the average destrier. Other draft breeds such as the Shire claim destrier ancestry, though proof is less certain.


title: Destrier

text: Modern attempts to reproduce the destrier type usually involve crossing an athletic riding horse with a light draft type. Outcomes of such attempts include crossbreds such as the "Spanish-Norman", a cross between the Percheron and the Andalusian; and the Warlander, a cross between the Andalusian and the Friesian horse.


title: Destrier

text: A good destrier was very costly: at the times of the Crusades, a fine destrier was valued at seven or eight times the cost of an ordinary horse. In England, the specific sum of eighty pounds (in this context a pound was 240 silver pennies, which amounted to one pound of silver by weight) was noted at the end of the thirteenth century. During the important military campaigns of King Edward III in the middle of the fourteenth century, the increased demand for warhorses brought about considerable price inflation: in 1339 William de Bohun, 1st Earl of Northampton lost a destrier valued at one hundred pounds while on campaign in Flanders. Army muster rolls included detailed inventories of the warriors' horses: less than 5% of the warhorses were classified as destriers, owned only by a small elite of the most wealthy knights. However, because of destriers' relative scarcity and consequent infrequent sale and purchase, reliable price information for the period has not often survived.


title: Cai Haoyu

text: Cai Haoyu (; born 1987) is a Chinese entrepreneur and game producer. He is the co-founder, chairman and president of the Chinese game company miHoYo. The Chinese magazine "New Fortune" ranked Cai in 73rd place on the "2022 "New Fortune" 500 Rich List" that ranks the 500 richest people in China.


title: Cai Haoyu

text: Cai was born in Jinan, Shandong, in 1987. His parents, who both work as computer subject-related instructors, began teaching him about computers after noticing his interest for it beginning when he was five years old and his aptitude for it. In 1995, Cai received second place in the animation category in the youth division of the National Computer Competition. In 1996, he received the "Top Ten Teenagers in Tianqiao District, Jinan City" award. In 1998, his "Alien Envoy" () and "Blue-Eared Spaceship" () submissions received second place in the animation category in the youth division of the National Computer Competition. In February 1999 when he was 12 years old, he was elected to the Chinese Youth Academy of Sciences in the first group of junior academicians chosen. He said in an interview, "The computer is not a dead thing. It changes all the time. I have to keep learning to keep up with it."


title: Cai Haoyu

text: He is from a business family background, which influenced him as a youth to "conduct business". Cai bought Xiaolingtong cordless telephones for cheap and sold them at a profit when he was in junior high school and sold watches in high school. When he reached college, he speculated in stocks, which allowed him to make over (US$) in a month.


title: Cai Haoyu

text: Cai attended Jinan Baliqiao Primary School (). Shanghai Jiaotong University admitted him as a student in 2005. He was a computer science master's student and received a master's degree from the university.


title: Cai Haoyu

text: At Shanghai Jiaotong University, he became roommates with Liu Wei and Luo Yuhao. He and his roommates became drawn to the ACG subculture of animation, comics, and games. In 2009, they made video games with ACG as the theme including as their graduation project. Cai started making his first game "FlyMe2theMoon" in 2010. Two years later, it received its first and only angel investment worth 1million RMB. After that, he started to work on "" ("Guns Girl Z") as the production director.


title: Cai Haoyu

text: Cai and his roommates secured a (US$) grant from the Shanghai Technology Innovation Center's Eagle Program. In January 2011, using the grant, they established miHoYo in a university dormitory while they were second-year graduate students. It began as a literary open source community. Cai is the chairman of miHoYo, which by 2021, made over ¥10billion (US$1.4billion) in revenue. "Chinese Business Strategy", a media company that profiles businesspeople, said Cai "tends to think intuitively, is responsible for business strategy decisions, and is meticulous about affairs management".


title: Cai Haoyu

text: In May 2022, "New Fortune", a Chinese magazine, published the "2022 "New Fortune" 500 Rich List" ranking the 500 richest people in China. Cai Haoyu made his first appearance on the list in 73rd place at ¥56billion (US$8.7billion). Of the first 100 people on the list, he was the only person who made the list through being a video game entrepreneur. He is the richest person in Jinan.


title: Fire Emblem Heroes

text: "Fire Emblem Heroes" is a tactical role-playing game. Players control a team of up to four characters ("Heroes") against enemy teams of varying sizes on an 8x6 grid map. Different characters have different movement restrictions; for example, armored units have a shorter range than cavalry units, but cavalry units cannot enter forest tiles. Flying units can enter most tiles, even ones impassable to all other units such as water or mountains. The game strictly alternates between a player phase and an enemy phase every turn. During the player's phase, Heroes can attack enemy characters when in range; if both the attacker and defender have the same range, the defender will counterattack if still alive. Heroes deal either physical or magical damage types; they also have a "color" that informs a rock paper scissors-esque system that makes it so some units have advantageous match-ups over other units. After moving and optionally attacking with all their heroes, the enemy phase occurs where the game's AI does the same for the opposing team of characters. The player, in general, seeks to lure enemy units into disadvantageous match-ups by careful character positioning on the map. Unlike other "Fire Emblem" titles, there is no element of randomness or chance in battles; an engagement between two characters is perfectly deterministic, as is the enemy AI, so a given strategy will either win or lose consistently. "Fire Emblem Heroes" has a set of "story" missions divided by chapters for the player to complete, rotating challenge missions, a training tower for increasing character's strength in random battles, fights against other players' teams (albeit controlled by the game's AI) in the "Arena" and in "Aether Raids", special challenges involving "Brigades" where teams with eight or more characters are controlled on a larger map than usual, and a variety of other content to complete.


title: Fire Emblem Heroes

text: The game's currency is known as "orbs", which can be used to acquire new heroes as well as several other quality-of-life items. Missions cost stamina to play while stamina is recovered over time; the exact cost of missions and maximum of stamina held has varied over the course of the app. Orbs are either earned by completing in-game activities or with in-app purchases.


title: Fire Emblem Heroes

text: Upon its initial release date, "Fire Emblem Heroes" players could potentially access up to 100 distinct controllable units in the game, with players beginning with access to Alfonse, Sharena, and Anna. These three members of the "Order of Heroes" were created specifically for "Heroes", with the remainder of the controllable characters being crossovers from the rest of the franchise. Since release, additional characters have been added to the list, including from games that were previously not featured. In general, most characters are gained via a "Summon" tab which works on a gacha system. Orbs are spent on randomized heroes, with some heroes being common and other heroes being rare. Other heroes are gained for free, by completing in-game missions of varying difficulty and effort. If a player gains duplicates of the same character, the duplicates can be merged to create a single more powerful character.


title: Fire Emblem Heroes

text: In March 2017, the game added "skill inheritance", which allows characters to mix skills previously reserved to other heroes: for example, a hero could gain another character's weapon or special ability. In November 2017, the game released "Book II", which included a new animated video, new story missions, added new mechanics, increased the power of some of the weapons and skills perceived as weak, and introduced a new set of "Heroes"-exclusive allies and villains. "Heroes" has continued to release new content and new characters. By December 2017, the game included more than 200 unique heroes; in August 2021, the game has more than 600 characters.


title: Fire Emblem Heroes

text: The main conflict in "Fire Emblem Heroes" is a war between the nations of Askr and Embla. The protagonist, also known as the summoner, whose name can be chosen by the player, aids the Kingdom of Askr and its Order of Heroes, whose members include its Commander Anna, Prince Alfonse, and Princess Sharena. Embla is led by Princess Veronica and Prince Bruno; Veronica is featured on the original app icon and prominently in the title artwork. Both sides use summoned heroes from other worlds, with the other worlds being the settings of other "Fire Emblem" games. In the Book II expansion, released from November 2017–September 2018, two new nations are introduced: the Kingdom of Nifl and its Princess Fjorm, who ally with Askr, and the Kingdom of Múspell and its King Surtr, Princess Laevatein, and strategist Loki, who ally with Embla. In the Book III expansion, released from December 2018–November 2019, both Askr and Embla come under invasion from the forces of Hel, the realm of the dead. The protagonist gains an ally in Eir, who is Hel's daughter. In Book IV, Askr faces the forces of Dökkálfheimr, a realm inhabited by evil fairy-like creatures of nightmares. In Book V, Askr battles the forces of Niðavellir, a country whose inhabitants have merged magic and technology. In Book VI, the previously defused conflict between Askr and Embla is reignited by Embla's eponymous patron deity.


title: Fire Emblem Heroes

text: The setting of "Heroes" includes loose references to Norse mythology; the names of the warring countries are that of Ask and Embla, the first humans, while the kingdoms introduced in later books match that of Niflheim, Muspelheim, and Hel. Place names and spell descriptions often include fragments in the Old Norse language, such as rauðr, blár, and gronn for red, blue, and green. The members of Múspell have the names of Surtr, the fire giant; Loki the trickster half-giant / half-god; and Laevatein the weapon; the members of Hel include references to Hel (the deity), Líf, and Eir.


title: Fire Emblem Heroes

text: The game was announced by Nintendo as the third mobile game made under the DeNA partnership in April 2016, alongside an "Animal Crossing" mobile game, and was originally set for release that year. Intelligent Systems, the studio within Nintendo that has produced the other games of the "Fire Emblem" series, headed up development of "Heroes" to ensure it would be a proper "Fire Emblem" game optimized for mobile devices. The game's title and gameplay details were later revealed during a "Fire Emblem" Direct presentation in January 2017. Immediately afterwards, Nintendo launched an online "choose your legend" promotion, in which players could vote for various characters from the series to be included in the game. The game was initially released in 39 countries for Android and iOS devices on February 2, 2017. As was the case with Nintendo's previously released mobile game "Super Mario Run", "Fire Emblem Heroes" requires players to have an internet connection to play.


title: Fire Emblem Heroes

text: Since release, the game has continued releasing new characters and features. Shingo Matsushita, the director of "Heroes", compared a normal "Fire Emblem" game to a movie, and "Heroes" to a television series; there would be a constant demand for new "episodes", but there would also be a feedback loop between the producers and the players that could affect the initial vision of the product.


title: Fire Emblem Heroes

text: At time of release, "Fire Emblem Heroes" received mixed reception, according to review aggregator Metacritic. One critic praised the game's casual-friendly design with its straightforward combat and character collection, but did not like the arbitrary play time constraint that stamina limit creates. Criticism of the stamina restrictions at launch were later met by an increase in the Stamina cap as well as a reduction in the Stamina spent to complete missions.


title: Fire Emblem Heroes

text: During the first day of release, Nintendo reported that the game generated more than $2.9 million. The game also ranked in third place in Japan when the game launched, also making shares skyrocket for the company. By December 2017, the game had grossed from 12million paid players. In February 2018, it was reported that "Heroes" had made roughly in its first year. By September 2018, the game had reached 14.1million downloads and grossed . By February 2019, the game had grossed worldwide, with Japan accounting for 56% (about ) of its revenue. , the game has grossed worldwide, making it Nintendo's highest-grossing mobile game.


title: Fire Emblem Heroes

text: Commentators have noted that despite having an install base smaller than "Super Mario Run", "Fire Emblem Heroes" is more financially lucrative for Nintendo. "The Verge" noted this was due both to being a "superior game" to "Super Mario Run" as well as "Heroes" targeting a somewhat older audience willing and capable of paying microtransactions for more content.


title: Fire Emblem Heroes

text: The game won the award for "Best Game of 2017" in Google Play Japan, and for "Best Mobile Game" in "Destructoid"s Game of the Year Awards 2017, and it also won the People's Choice Award for the same category in "IGN"s Best of 2017 Awards. "Polygon" ranked it 20th on their list of the 50 best games of 2017.


title: Lares

text: Lares ( , ; archaic , singular "Lar") were guardian deities in ancient Roman religion. Their origin is uncertain; they may have been hero-ancestors, guardians of the hearth, fields, boundaries, or fruitfulness, or an amalgam of these.


title: Lares

text: Lares were believed to observe, protect, and influence all that happened within the boundaries of their location or function. The statues of domestic Lares were placed at the table during family meals; their presence, cult, and blessing seem to have been required at all important family events.


title: Lares

text: Roman writers sometimes identify or conflate them with ancestor-deities, domestic Penates, and the hearth.


title: Lares

text: Because of these associations, Lares are sometimes categorised as household gods, but some had much broader domains. Roadways, seaways, agriculture, livestock, towns, cities, the state, and its military were all under the protection of their particular Lar or Lares. Those who protected local neighbourhoods ("vici") were housed in the crossroad shrines ("Compitalia"), which served as a focus for the religious, social, and political lives of their local, overwhelmingly plebeian communities. Their cult officials included freedmen and slaves, otherwise excluded by status or property qualifications from most administrative and religious offices.


title: Lares

text: Compared to Rome's major deities, Lares had limited scope and potency, but archaeological and literary evidence attests to their central role in Roman identity and religious life. By analogy, a homeward-bound Roman could be described as returning "ad Larem" (to the Lar). Despite official bans on non-Christian cults from the late fourth century AD onwards, unofficial cults to Lares persisted until at least the early fifth century AD.


title: Lares

text: Archaic Rome's Etruscan neighbours practiced domestic, ancestral, or family cults very similar to those offered by later Romans to their Lares. The word itself seems to derive from the Etruscan , , or , meaning "lord". Ancient Greek and Roman authors offer "heroes" and ""daimones"" as translations of "Lares"; the early Roman playwright Plautus ("circa" 254–184 BC) employs a " "as a guardian of treasure on behalf of a family, as a plot equivalent to the Greek playwright Menander's use of a "heroon" (as an ancestral hero-shrine). Weinstock proposes a more ancient equivalence of Lar and Greek "hero", based on his gloss of a fourth-century BC Latin dedication to the Roman ancestor-hero Aeneas as "Lare" (Lar).


title: Lares

text: No physical Lar images survive from before the Late Republican era, but literary references (such as Plautus' singular Lar, above) suggest that cult could be offered to a single Lar, and sometimes many more; in the case of the obscure "Lares Grundules", perhaps 30. By the early Imperial era, they had become paired divinities, probably through the influences of Greek religion – in particular, the heroic twin Dioscuri – and the iconography of Rome's semidivine founder-twins, Romulus and Remus. Lares are represented as two small, youthful, lively male figures clad in short, rustic, girdled tunics – made of dogskin, according to Plutarch. They take a dancer's attitude, tiptoed or lightly balanced on one leg. One arm raises a drinking horn ("rhyton") aloft as if to offer a toast or libation; the other bears a shallow libation dish ("patera"). Compitalia shrines of the same period show Lares figures of the same type. Painted shrine-images of paired Lares show them in mirrored poses to the left and right of a central figure, understood to be an ancestral genius.


title: Lares

text: Lares belonged within the "bounded physical domain" under their protection, and seem to have been as innumerable as the places they protected. Some appear to have had overlapping functions and changes of name. Some have no particular or descriptive name: for example, those invoked along with Mars in the Carmen Arvale are simply "Lases" (an archaic form of "Lares"), whose divine functions must be inferred from the wording and context of the Carmen itself. Likewise, those invoked along with other deities by the consul Publius Decius Mus as an act of "devotio" before his death in battle are simply "Lares". The titles and domains given below cannot, therefore, be taken as exhaustive or definitive.


title: Lares

text: Traditional Roman households owned at least one protective Lares-figure, housed in a shrine along with the images of the household's "penates", "genius" image and any other favoured deities. Their statues were placed at table during family meals and banquets. They were divine witnesses at important family occasions, such as marriages, births, and adoptions, and their shrines provided a religious hub for social and family life. Individuals who failed to attend to the needs of their Lares and their families should expect neither reward nor good fortune for themselves. In Plautus' comedy "Aulularia", the Lar of the miserly "paterfamilias" Euclio reveals a pot of gold long-hidden beneath his household hearth, denied to Euclio's father because of his stinginess towards his Lar. Euclio's own stinginess deprives him of the gold until he sees the error of his ways; then, he uses it to give his virtuous daughter the dowry she deserves, and all is well.


title: Lares

text: Responsibility for household cult and the behaviour of family members ultimately fell to the family head, the "paterfamilias", but he could, and indeed should on certain occasions properly delegate the cult and care of his Lares to other family members, especially his servants. The positioning of the Lares at the House of Menander suggest that the "paterfamilias" delegated this religious task to his "villicus" (bailiff).


title: Lares

text: Care and cult attendance to domestic Lares could include offerings of spelt wheat and grain-garlands, honey cakes and honeycombs, grapes and first fruits, wine, and incense. They could be served at any time and not always by intention; in addition to the formal offerings that seem to have been their due, any food that fell to the floor during house banquets was theirs. On important occasions, wealthier households may have offered their own Lares a pig. A single source describes Romulus' provision of an altar and sacrifice to "Lares Grundules" ("grunting lares") after an unusually large farrowing of 30 piglets. The circumstances of this offering are otherwise unknown, Taylor conjectures the sacrifice of a pig, possibly a pregnant sow.


title: Lares

text: By the early Imperial period, household shrines of any kind were known generically as "lararia" (s. "lararium") because they typically contained a Lares figure or two. Painted lararia from Pompeii show two Lares flanking a genius or ancestor-figure, who wears his toga in the priestly manner prescribed for sacrificers. Underneath this trio, a serpent, representing the fertility of fields or the principle of generative power, winds towards an altar. The essentials of sacrifice are depicted around and about; bowl and knife, incense box, libation vessels and parts of sacrificial animals.


title: Lares

text: In households of modest means, small Lar statuettes were set in wall-niches, sometimes merely a tile-support projecting from a painted background. In wealthier households, they tend to be found in servant's quarters and working areas. At Pompeii, the Lares and "lararium" of the sophisticated, unpretentious and artistically restrained House of Menander were associated with its servant quarters and adjacent agricultural estate. Its statuary was unsophisticated, "rustic" and probably of ancient type or make. The placing of Lares in the public or semi-public parts of a house, such as its atrium, enrolled them in the more outward, theatrical functions of household religion.


title: Lares

text: The House of the Vettii in Pompeii had two lararia; one was positioned out of public view, and was probably used in private household rites. The other was placed boldly front-of-house, among a riot of Greek-inspired mythological wall-paintings and the assorted statuary of patron divinities. Its positioning in a relatively public part of the domus would have provided a backdrop for the probably interminable "salutatio" (formal greeting) between its upwardly mobile owners and their strings of clients and "an assorted group of unattached persons who made the rounds of "salutationes" to assure their political and economic security".


title: Lares

text: Domestic Lararia were also used as a sacred, protective depository for commonplace symbols of family change and continuity. In his coming-of-age, a boy gave his personal amulet ("bulla") to his Lares before he put on his manly toga ("toga virilis"). Once his first beard had been ritually cut off, it was placed in their keeping. On the night before her wedding, a Roman girl surrendered her dolls, soft balls, and breastbands to her family Lares, as a sign she had come of age. On the day of her marriage, she transferred her allegiance to her husband's neighbourhood Lares ("Lares Compitalici") by paying them a copper coin en route to her new home. She paid another to her new domestic Lares, and one to her husband. If the marriage made her a "materfamilias", she took joint responsibility with her husband for aspects of household cult.


title: Lares

text: The city of Rome was protected by a Lar, or Lares, housed in a shrine ("sacellum") on the city's ancient, sacred boundary ("pomerium"). Each Roman "vicus" (pl. "vici" – administrative districts or wards) had its own communal Lares, housed in a permanent shrine at a central crossroads of the district. These "Lares Compitalicii" were celebrated at the Compitalia festival (from the Latin "compitum", a crossroad) just after the Saturnalia that closed the old year. In the "solemn and sumptuous" rites of Compitalia, a pig was led in celebratory procession through the streets of the "vicus", then sacrificed to the Lares at their Compitalia shrine. Cult offerings to these Lares were much the same as those to domestic Lares; in the late Republican era, Dionysius of Halicarnassus describes the contribution of a honey-cake from each household as ancient tradition.


title: Lares

text: The Compitalia itself was explained as an invention of Rome's sixth king, Servius Tullius, whose servile origins and favour towards plebeians and slaves had antagonised Rome's ruling Patrician caste and ultimately caused his downfall; he was said to have been fathered by a Lar or some other divine being, on a royal slave-girl. So although the Lares Compitalicii were held to protect all the community, regardless of social class, their festival had a distinctly plebeian ambiance, and a measure of Saturnalia's reversal of the "status quo". Tradition required that the "Lares Compitalicii" be served by men of very low legal and social status, not merely plebeians, but freedmen and slaves, to whom "even the heavy-handed Cato recommended liberality during the festival". Dionysius' explains it thus:


title: Lares

text: While the supervision of the "vici" and their religious affairs may have been charged to the Roman elite who occupied most magistracies and priesthoods, management of the day-to-day affairs and public amenities of neighbourhoods – including their religious festivals – was the responsibility of freedmen and their slave-assistants. The Compitalia was an official festival but during the Republican era, its shrines appear to have been funded locally, probably by subscription among the plebeians, freedmen and slaves of the "vici". Their support through private benefaction is nowhere attested, and official attitudes to the Republican Compitalia seem equivocal at best: The Compitalia games (Ludi Compitalicii) included popular theatrical religious performances of raucously subversive flavour: Compitalia thus offered a religiously sanctioned outlet for free speech and populist subversion. At some time between 85–82 BC, the Compitalia shrines were the focus of cult to the ill-fated popularist politician Marcus Marius Gratidianus during his praetorship. What happened – if anything – to the Compitalia festivals and games in the immediate aftermath of his public, ritualised murder by his opponents is not known but in 68 BC the games at least were suppressed as "disorderly".


title: Lares

text: As "princeps", Augustus reformed Compitalia and subdivided the "vici". From 7 BC a Lares' festival on 1 May was dedicated to the "Lares Augusti" and a new celebration of the "Genius Augusti" was held on 1 August, the inaugural day for Roman magistracies and personally auspicious for Augustus as the anniversary of his victory at Actium. Statues representing the "Genius Augusti" were inserted between the Lares of the Compitalia shrines. Whether or not Augustus substituted the public Lares with "his own" household Lares is questionable — the earliest reference to "august" Lares (58 BC, in provincial Cisalpine Gaul) anticipates Octavian's adoption of Augustus as honorific by some thirty years — but when coupled with his new cult to the "Genius Augusti", his donation of Lares Augusti statues for use at Compitalia shrines, and his association with the community Lares through the shared honorific makes the reformed Compitalia an unmistakable, local, "street level" aspect of cult to living emperors.


title: Lares

text: The iconography of these shrines celebrates their sponsor's personal qualities and achievements and evokes a real or re-invented continuity of practice from ancient times. Some examples are sophisticated, others crude and virtually rustic in style; taken as a whole, their positioning in every "vicus" (ward) of Rome symbolically extends the ideology of a "refounded" Rome to every part of the city. The Compitalia reforms were ingenious and genuinely popular; they valued the traditions of the Roman masses and won their political, social and religious support. Probably in response to this, provincial cults to the "Lares Augusti" appear soon afterwards; in Ostia, a "Lares Augusti" shrine was placed in the forum, which was ritually cleansed for the occasion. The Augustan model persisted until the end of the Western Empire, with only minor and local modifications, and the "Lares Augusti" would always be identified with the ruling emperor, the "Augustus", whatever his personal or family name.


title: Lares

text: Augustus officially confirmed the plebeian-servile character of Compitalia as essential to his "restoration" of Roman tradition, and formalised their offices; the vici and their religious affairs were now the responsibility of official "magistri vici", usually freedmen, assisted by "ministri vici" who were usually slaves. A dedication of 2 BC to the Augustan Lares lists four slaves as shrine-officials of their "vicus". Given their slave status, their powers are debatable but they clearly constitute an official body. Their inscribed names, and those of their owners, are contained within an oak-wreath cartouche. The oak-leaf chaplet was voted to Augustus as "saviour" of Rome; He was symbolic "pater" (father) of the Roman state, and though his "genius" was owed cult by his extended family, its offer seems to have been entirely voluntary. Hardly any of the reformed Compital shrines show evidence of cult to the emperor's "genius". Augustus acted with the political acumen of any responsible "patronus" (patron); his subdivision of the vici created new opportunities for his clients. It repaid honour with honours, which for the plebs meant offices, priesthood, and the respect of their peers; at least for some. In Petronius' "Satyricon", a magistrate's lictor bangs on Trimalchio's door; it causes a fearful stir but in comes Habinnas, one of Augustus' new priests, a stonemason by trade; dressed up in his regalia, perfumed and completely drunk.


title: Lares

text: From the Late Republican and early Imperial eras, the priestly records of the Arval Brethren and the speculative commentaries of a very small number of literate Romans attest to a Mother of the Lares (Mater Larum). Her children are invoked by the obscure, fragmentary opening to the Arval Hymn (Carmen Arvale); "enos Lases iuvate" ("Help us, Lares"). She is named as Mania by Varro (116–27 BC), who believes her an originally Sabine deity. The same name is used by later Roman authors with the general sense of a bogey or "evil spirit". Much later, Macrobius ("fl." AD 395–430) describes the woolen figurines hung at crossroad shrines during Compitalia as "maniae", supposed as an ingenious substitution for child sacrifices to the Mater Larum, instituted by Rome's last monarch and suppressed by its first consul, L. Junius Brutus. Modern scholarship takes the Arval rites to the Mother of the Lares as typically chthonic, and the goddess herself as a dark or terrible aspect of the earth-mother, Tellus. Ovid supplies or elaborates an origin-myth for the "Mater Larum" as a once-loquacious nymph, Lara, whose tongue is cut out as punishment for her betrayal of Jupiter's secret amours. Lara thus becomes Muta (the speechless one). Mercury leads her to the underworld abode of the dead ("ad Manes"); in this place of silence she is Dea Tacita (the silent one). En route, he impregnates her. She gives birth to twin boys as silent or speechless as she. In this context, the Lares can be understood as "manes of silence" ("taciti manes").


title: Lares

text: Ovid's poetic myth appears to draw on remnants of ancient rites to the Mater Larum, surviving as folk-cult among women at the fringes of the Feralia: an old woman sews up a fish-head, smears it with pitch then pierces and roasts it to bind hostile tongues to silence: she thus invokes Dea Tacita. If, as Ovid proposes, the lemures are an unsatiated, malevolent and wandering form of Lares, then they and their mother also find their way into Lemuralia, when the hungry Lemures gather in Roman houses and claim cult from the living. The "paterfamilias" must redeem himself and his family with the offer of midnight libations of spring-water, and black beans spat onto the floor. Any lemures dissatisfied with these offerings are scared away by the loud clashing of bronze pots. Taylor notes the chthonic character of offerings made to fall – or deliberately expelled – towards the earth. If their mother's nature connects the Lares to the earth they are, according to Taylor, spirits of the departed.


title: Lares

text: Plutarch offers a legend of Servius Tullius, sixth king of Rome, credited with the founding of the Lares' public festival, Compitalia. Servius' virginal slave mother-to-be is impregnated by a phallus-apparition arising from the hearth, or some other divine being held to be a major deity or ancestor-hero by some, a Lar by others: the latter seems to have been a strong popular tradition. During the Augustan era, Dionysius of Halicarnassus reports Servius' fathering by a Lar and his pious founding of Compitalia as common knowledge, and the Lar as equivalent to the Greek hero; semi-divine, ancestral and protective of place.


title: Lares

text: These stories connect the Lar to the hearth, the underworld, generative powers (however embodied), nourishment, forms of divine or semi-divine ancestry and the coupling of the divine with the servile, wherein those deprived by legal or birth-status of a personal gens could serve, and be served by, the cults attached to Compitalia and Larentalia. Mommsen's contention that Lares were originally field deities is not incompatible with their role as ancestors and guardians. A rural familia relied on the productivity of their estate and its soil: around the early 2nd century BC, Plautus's Lar Familiaris protects the house, and "familia" as he has always done, and safeguards their secrets.


title: Lares

text: The little mythography that belongs to the Lares seems inventive and poetic. With no traditional, systematic theology to limit their development, Lares became a single but usefully nebulous type, with many functions. In Cicero's day, one's possession of domestic Lares laid moral claim of ownership and belonging to one's domicile. Festus identifies them as "gods of the underworld" ("di inferi"). To Flaccus, they are ancestral genii (s. "genius"). Apuleius considers them benevolent ancestral spirits; they belong both to the underworld and to particular places of the human world. To him, this distinguishes them from the divine and eternal "genius" which inhabits, protects and inspires living men: and having specific physical domains, they cannot be connected with the malicious, vagrant "lemures". In the 4th century AD the Christian polemicist Arnobius, claiming among others Varro (116–27 BC) as his source, describes them as once-human spirits of the underworld, therefore ancestral manes-ghosts; but also as "gods of the air", or the upper world. He also – perhaps uniquely in the literature but still claiming Varro's authority – categorises them with the frightful larvae. The ubiquity of Lares seems to have offered considerable restraints on Christian participation in Roman public life. In the 3rd century AD, Tertullian remarks the inevitable presence of Lares in pagan households as good reason to forbid marriage between pagan men and Christian women: the latter would be "tormented by the vapor of incense each time the demons are honored, each solemn festivity in honor of the emperors, each beginning of the year, each beginning of the month." Yet their type proved remarkably persistent. In the early 5th century AD, after the official suppression of non-Christian cults, Rutilius Namatianus could write of a famine-stricken district whose inhabitants had no choice but to "abandon their Lares" (thus, to desert their rat-infested houses).


title: Violet Line (Delhi Metro)

text: The Violet Line (Line 6) is one of the lines of the Delhi Metro, a rapid transit system in Delhi, India. The line connects Kashmere Gate station in New Delhi with Raja Nahar Singh in Ballabhgarh via Faridabad. The line consists of 32 metro stations with a total length of .


title: Violet Line (Delhi Metro)

text: This line acts as a parallel link for those, who travel in the heavily used Yellow Line and connects the interior parts of South Delhi, a little of Central Delhi to the satellite town of Faridabad. The stretch between ITO metro station and Kashmere Gate metro station is popularly known as the Heritage Line.


title: Violet Line (Delhi Metro)

text: The Violet Line was originally planned to open in March 2010. On 12 July 2009, a portion of a bridge under construction collapsed when its cantilever pier collapsed on load of launching girder at Zamrudpur, near East of Kailash, on the Central Secretariat – Badarpur corridor. Six people were killed and 15 others injured. The day after, on 13 July 2009, a crane that was removing the debris collapsed, and with a bowling pin effect collapsed two other nearby cranes, injuring six.


title: Violet Line (Delhi Metro)

text: An extension from the Badarpur metro station of the line was opened on 6 September 2015 to provide connectivity to the neighbouring satellite city of Faridabad. This is the second line to cross the Delhi-Haryana border after the Yellow Line to Gurgaon. This extension runs fully elevated for 13.87 km and has 9 stations.


title: Violet Line (Delhi Metro)

text: This line has standard gauge trains manufactured by a consortium of Mitsubishi-ROTEM-BEML. A total of 196 cars were ordered for 4-car configuration (46 trains) and 6-car configuration (2 trains). These trains are used in this line and Green Line. One train was manufactured in Changwon in South Korea and rest of the trains are manufactured at BEML's facility in Bangalore. Trains are as compared to of broad gauge trains.


title: Robert Richardson (cinematographer)

text: Robert Bridge Richardson, (born August 27, 1955) is an American cinematographer. He has won the Academy Award for Best Cinematography three times, for his work on "JFK", "The Aviator", and "Hugo". Richardson is and has been a frequent collaborator for several directors, including Oliver Stone, John Sayles, Errol Morris, Quentin Tarantino, Martin Scorsese and Andy Serkis. He is one of three living persons who has won the Academy Award for Best Cinematography three times, the others being Vittorio Storaro and Emmanuel Lubezki.


title: Robert Richardson (cinematographer)

text: Richardson was born in Hyannis, Massachusetts. He graduated from the Rhode Island School of Design with a BFA in Film/Animation/Video and received his MFA from AFI Conservatory. Richardson's work began as a camera operator and 2nd unit photographer on such features as Alex Cox's "Repo Man", Dorian Walker's "Making the Grade" and Wes Craven's "A Nightmare on Elm Street" (all in 1984). At the same time he also served as cinematographer on TV documentaries and docudramas such as "America, America" for The Disney Channel, "God's Peace" for the BBC and PBS' "The Front Line: El Salvador". His television work and documentary style filmmaking led to his meeting Oliver Stone, who hired him to "shoot" "Salvador" (1986).


title: Robert Richardson (cinematographer)

text: Oliver Stone's major motion picture debut was also Richardson's first film as director of photography. "Salvador" was also filmed the same year as Stone's "Platoon". "Platoon" would earn Richardson his first Oscar nomination for Best Cinematography. In 1987, Richardson reteamed with Stone on "Wall Street". In 1988, he filmed "Eight Men Out" for John Sayles. In 1989, he earned his second Best Cinematography Oscar nomination for Stone's "Born on the Fourth of July".