title: A Perfect Ending

text: Meanwhile, one of the three Westridge children finds the medical report of inoperable cancer that Mason Westridge has been hiding in his office desk. They all confront Rebecca and ask whether she had known about it all along. The children assume that the report refers to their father, and Rebecca tells her children that and they are not to mention it. Rebecca contacts another escort, Paris' friend, and gives her an envelope of money to help Paris leave the escort world and pursue her artistic talents. She reveals that she is the one who has cancer, and that she is dying. Afterwards, Rebecca makes the courageous decision to say goodbye to Paris.


title: A Perfect Ending

text: Towards the end of the movie, Rebecca is seen as a butterfly, beautiful girl and such a kind human. Someone who has learned to spread her wings because of her relationship with Paris. In the final scene, Paris has her own art exhibition after Rebecca's funeral. Jessica approaches Paris and introduces herself, as the two lesbian best friends watch, and says, "I want to learn about my mother at the end."


title: Bert Kaempfert

text: Bert Kaempfert (born Berthold Heinrich Kämpfert; 16 October 1923 – 21 June 1980) was a German orchestra leader, multi-instrumentalist, music producer, arranger, and composer. He made easy listening and jazz-oriented records and wrote the music for a number of well-known songs, including "Strangers in the Night", “Danke Schoen” and "Moon Over Naples".


title: Bert Kaempfert

text: Kaempfert was born in Hamburg, Germany, where he received his lifelong nickname, Fips, and studied at the local school of music. A multi-instrumentalist, he was hired by Hans Busch to play with his orchestra, before serving as a bandsman in the German Navy during World War II. He later formed his own big band and toured with them, following that by working as an arranger and producer, making hit records with Freddy Quinn and Ivo Robić. Kaempfert met his future wife, Hannelore, in 1945. They married a year later, on 14 August 1946. They had two daughters, Marion and Doris.


title: Bert Kaempfert

text: Kaempfert's first hit with his orchestra was "Wonderland by Night". Recorded in July 1959, the song could not get released in Germany, so Kaempfert took the track to Decca Records in New York, which released it in America in the fall of 1960. With its haunting solo trumpet by Charles Tabor, muted brass, and lush strings, the single topped the American pop charts and turned Bert Kaempfert and Orchestra into international stars. Over the next few years, he revived such pop tunes as "Tenderly", "Red Roses for a Blue Lady", "Three O'Clock in the Morning", and "Bye Bye Blues", as well as composing pieces of his own, including "Spanish Eyes" (a.k.a. "Moon Over Naples"), "Danke Schoen", and "Wooden Heart", which were recorded by, respectively, Al Martino, Wayne Newton, and Elvis Presley. For Kaempfert, little brought him more personal satisfaction than Nat King Cole recording his "L-O-V-E".


title: Bert Kaempfert

text: Kaempfert's orchestra made extensive use of horns. A couple of numbers that featured brass prominently, "Magic Trumpet" and "The Mexican Shuffle", were played by both Kaempfert's orchestra and by Herb Alpert & the Tijuana Brass. The Brass covered "Magic Trumpet", and Kaempfert returned the favor by covering Brass compadre Sol Lake's number "The Mexican Shuffle". The latter tune evolved into a TV ad, "The Teaberry Shuffle".


title: Bert Kaempfert

text: In his capacity as record producer, Kaempfert played a part in the rise of the Beatles. In 1961, he hired the Beatles to back Tony Sheridan on an album called "My Bonnie". Sheridan had been performing in Hamburg, and needed to recruit a band to play behind him on the proposed tracks. Kaempfert auditioned and signed the Beatles, and recorded two tracks with them during his sessions for Sheridan: "Ain't She Sweet" (sung by rhythm guitarist John Lennon) and "Cry for a Shadow" (an instrumental written by Lennon and lead guitarist George Harrison). The album and its singles, released by Polydor Records, were the Beatles' first commercially released recordings.


title: Bert Kaempfert

text: On 28 October 1961, a customer walked into the Liverpool music store owned by Brian Epstein and asked for a copy of "My Bonnie", a song recorded by the Beatles but credited to Tony Sheridan. The store did not have it, but Epstein noted the request. He was so intrigued by the idea of a Liverpool band releasing a record that he investigated. That event led to his discovery of the Beatles and, through his efforts, their signing by George Martin to Parlophone Records after Kaempfert helped them avoid any contractual claim from Polydor.


title: Bert Kaempfert

text: In 1963, jazz trumpeter Bobby Hackett recorded a complete album with 12 Kaempfert compositions, "Bobby Hackett Plays the Music of Bert Kaempfert". It has now been re-released in the United States under the Sony Records label in the "Collectable Jazz Classics" series, along with the album "Bobby Hackett Plays The Music of Henry Mancini" on a "2-in-1" CD.


title: Bert Kaempfert

text: In 1967, jazz clarinetist Pete Fountain recorded the album "Pete Fountain Plays Bert Kaempfert" in Hamburg, Germany, with musicians from Kaempfert's orchestra. It featured Kaempfert's signature hits.


title: Bert Kaempfert

text: In 1967, the Anita Kerr Singers released the LP "Bert Kaempfert Turns Us On!", a tribute to Kaempfert, featuring the standard hits.


title: Bert Kaempfert

text: In 1967, Jimi Hendrix included the melody of "Strangers in the Night" in his improvised guitar solo for his famous guitar-burning version of "Wild Thing" at the Monterey Pop Festival.


title: Bert Kaempfert

text: In 1968, jazz trumpeter Al Hirt recorded the album "Al Hirt Plays Bert Kaempfert". It too featured Kaempfert's major hits. That year, BMI awarded accolades to five of Kaempfert's songs: "Lady", "Spanish Eyes", "Strangers in the Night", "The World We Knew", and "Sweet Maria". Many of his hits during the 1960s were composed and arranged with the help of German Herb Rehbein, who became a successful bandleader in his own right. Rehbein's death in 1979 shook Kaempfert deeply. Both Kaempfert and Rehbein were posthumously inducted into the Songwriters Hall of Fame.


title: Bert Kaempfert

text: In 1970, Johnny Mathis issued a double-LP album set, "Sings the Music of Bacharach & Kaempfert", for Columbia. It consisted of a total 21 tracks in a heavyweight gatefold picture sleeve. The Kaempfert tracks were done in his arrangement style, and the Bacharach tracks were done in the American's unique upbeat style. The same year Kaempfert composed the score for the war film "You Can't Win 'Em All", starring Tony Curtis and Charles Bronson.


title: Bert Kaempfert

text: By the 1970s, sales of Kaempfert's music had declined, but he continued to record. His version of the "Theme from Shaft" was admired by composer Isaac Hayes and remained popular with audiences. He expanded the musical scope of his band and recorded in a wide variety of styles. He also began to play live concerts with his orchestra, beginning in 1974, with an appearance at the Royal Albert Hall in London.


title: Bert Kaempfert

text: Kaempfert is sampled in the 1998 song "One Week" by the Barenaked Ladies. The song's lyrics also declare that "Bert Kaempfert's got the mad hits".


title: Bert Kaempfert

text: Kaempfert used many musicians who were available in Germany and other parts of Europe, including many of the same players who played for James Last, Kai Warner, and Roberto Delgado. He featured such top soloists as trumpeters Charly Tabor, Werner Gutterer, Manfred Moch, and Ack van Rooyen, trombonists Åke Persson, and Jiggs Whigham, and sax/flute player Herb Geller. Drummer Rolf Ahrens supplied the characteristically simple but steady beat, often playing just a snare drum with brushes.


title: Bert Kaempfert

text: Another contributor to Kaempfert's music was guitarist/bassist Ladislav "Ladi" Geisler, who popularized the famous "knackbass" (crackling bass) sound, using the Fender Telecaster Bass Guitar, which became the most distinctive feature of many Kaempfert recordings — a treble staccato bass guitar sound in which the bass string was plucked with a pick and immediately suppressed to cancel out any sustain. An acoustic bass played a simple pattern in unison with this staccato electric bass, which created a unique sound. It was Geisler who lent his guitar amplifier to The Beatles for their recording session with Tony Sheridan, after the band's own equipment proved to be inadequate for recording purposes.


title: Bert Kaempfert

text: Kaempfert died suddenly following a stroke at his home in Majorca on 21 June 1980, at the age of 56, shortly after a successful appearance in the United Kingdom.


title: Hamzah bin Hussein

text: Hamzah bin Hussein, (; born 29 March 1980) is the fourth son of King Hussein bin Talal of Jordan overall and the first by his American-born fourth wife, Queen Noor. He was named Crown Prince of Jordan in 1999, a position he held until his older half-brother, King Abdullah II, rescinded it in 2004. He is a member of the Hashemite dynasty, the royal family of Jordan since 1921, and is a 41st-generation direct descendant of Muhammad. Hamzah is currently believed to be under house arrest since April 2021, after being accused of attempting to destabilise the Kingdom of Jordan and fomenting unrest. Hamzah renounced his title of prince in April 2022.


title: Hamzah bin Hussein

text: Born on 29 March 1980, Hamzah Bin Al Hussein claims ancestry with the Islamic prophet Muhammad through the Hashemite family. Queen Noor states in her autobiography that she and King Hussein named Hamzah after Hamza ibn Abd al-Muttalib.


title: Hamzah bin Hussein

text: Hamzah received his elementary education in Jordan and Amman, and then attended Harrow School in England. He then joined the Royal Military Academy Sandhurst, passing out as a commissioned officer in the Jordan Arab Legion in December 1999, with a number of prizes including the Sandhurst Overseas Sword, granted to the best overseas cadet and the HRH Prince Saud Abdullah Prize, presented to the cadet with the best aggregate mark in academic subjects.


title: Hamzah bin Hussein

text: Serving then as an officer in the Jordan Arab Army's 40th Armored Brigade, Hamzah attended a number of military courses and attachments in Jordan, the UK, Poland, Germany and the US. Currently holding the rank of Brigadier in the Jordan Arab Army, he served with the Jordan-United Arab Emirates force operating in former Yugoslavia under the umbrella of international peacekeepers. In the year 2006, he graduated from Harvard University.


title: Hamzah bin Hussein

text: Hamzah was sworn in as Regent on numerous occasions and deputized for King Abdullah II on a number of missions in the Kingdom and abroad. He headed the Royal Advisory Committee on the Energy Sector. He is also the Honorary President of the Jordan Basketball Federation, and is the chairman of the board of trustees of the Royal Automobile Museum, the President of the Royal Aero sports Club of Jordan and the President of Al-Shajarah (Tree) Protection Society.


title: Hamzah bin Hussein

text: Hamzah is a qualified rotor and fixed wing aircraft pilot, and participates in other sports such as Jujitsu and target-shooting.


title: Hamzah bin Hussein

text: On 7 February 1999, King Hussein died and his eldest son Prince Abdullah bin Hussein ascended to the throne of Jordan, having two weeks previously been designated to succeed his father as ruler in place of the king's brother, Crown Prince Hassan bin Talal. On the same day, in compliance with his father's wish, King Abdullah II decreed that he, in turn, would be succeeded not by a son of his own but by his half-brother, Hamzah, who was therefore accorded the title of crown prince.


title: Hamzah bin Hussein

text: Nearly six years later, on 28 November 2004, King Abdullah removed Hamzah as crown prince. In a letter from Abdullah to Hamzah, read on Jordanian state television, he said, "Your holding this symbolic position has restrained your freedom and hindered our entrusting you with certain responsibilities that you are fully qualified to undertake."


title: Hamzah bin Hussein

text: No successor to the title was named at the time, but some analysts believed it probable that Abdullah intended to name his own son, Prince Hussein, to succeed him at some point in the future. Article 28(B) of Jordan's constitution provides that the king's eldest son automatically succeeds to the crown upon the monarch's death unless the king has designated one of his brothers to inherit the throne as crown prince, but Abdullah II confirmed that his son Hussein would succeed him by designating him as crown prince on 2 July 2009.


title: Hamzah bin Hussein

text: On 3 April 2021, the BBC published a video of Hamzah in which he reported that he has been placed under house arrest as part of a crackdown on critics. It was stated that the video had been passed to the BBC through Hamzah's lawyer. On 7 April 2021, King Abdullah II publicly hinted that his tension with Hamzah, who had pledged loyalty to him two days after his house arrest began, was ending and that Hamzah was now "in his palace under my protection." Abdullah also stated that the crisis which resulted in Hamzah's house arrest started when Jordan's military chief of staff visited Hamzah and warned him to stop attending meetings with critics of the government. In April 2022, Hamzah relinquished his royal title of prince, stating his "personal convictions" were not in line with "the approaches, trends and modern methods of our institutions". A month earlier, he had reportedly apologized to the King in a letter, wishing to "turn the page on this chapter in our country's and our family's history". In May 2022, the King formally announced that Hamzah had been put under house arrest and his communications and movements were limited due to his "erratic behavior and aspirations".


title: Hamzah bin Hussein

text: Hamzah married his second cousin, Princess Noor bint Asem bin Nayef, at Al Baraka Palace in Amman on 29 August 2003. The official wedding was held on 27 May 2004. Hamzah and Noor divorced on 9 September 2009. The couple had a daughter:


title: Sreejita De

text: Sreejita De (born 19 July 1989) is an Indian actress and model who works in Hindi television. She is best known for portraying Mukta Rathore in Colors TV's serial "Uttaran" which ranks among the longest-running show and Dilruba in Star Plus's supernatural thriller "Nazar". In 2022, she was a contestant on the reality TV show "Bigg Boss 16".


title: Sreejita De

text: She made her debut on TV with "Kasautii Zindagii Kay", playing the role of Gargi Tushar Bajaj. At the same time Ekta Kapoor offered her the role of Aastha in "Karam Apna Apna". In 2008, she appeared in the Bollywood film "Tashan" as Paravati. In the same year, she played the lead role in the soap opera "Annu Ki Ho Gayee Waah Bhai Waah" as Annu. In 2012 she bagged the lead character of Mukta Raghuvendra Pratap Rathore, Tapasya's daughter, in "Uttaran" on Colors TV"."


title: Sreejita De

text: She played the lead role of Shreya Bhushan Pethewala in "Tum Hi Ho Bandhu Sakha Tumhi", which is aired on Zee TV. In 2016 she joined the cast of "Piya Rangrezz" as Aradhya Shamsher Singh, which aired on Life Ok. She was seen in the Star Plus show "Koi Laut Ke Aaya Hai" as Kavya.


title: Sreejita De

text: Apart from that, she has done episodic roles in shows like "Savdhaan India", "Aahat", "Ssshhhh...Koi Hai", "Aye Zindagi, Mahima Shani Dev Ki" and "Chakradhari Ajay Krishna."


title: Sreejita De

text: From 2018 to 2020, she was seen in "Nazar" as Dilruba. In 2019, she join "Yehh Jadu Hai Jinn Ka!" Where she portrayed the role of Aliya.


title: Sreejita De

text: In 2022, she currently is participating in Colors TV's popular reality show "Bigg Boss 16". She was evicted on Day 13 but later returned as a wild-card on Day 69, Week 10.


title: Dionysius the Areopagite

text: Dionysius the Areopagite (; "Dionysios ho Areopagitēs") was an Athenian judge at the Areopagus Court in Athens, who lived in the first century. A convert to Christianity, he is venerated as a saint by multiple denominations.


title: Dionysius the Areopagite

text: Blessed Anne Catherine Emmerich says that he studied at Heliopolis, on the Nile, in Egypt, where there was also a Jewish community.


title: Dionysius the Areopagite

text: As related in the "Acts of the Apostles" (), he was converted to Christianity by the preaching of Paul the Apostle


title: Dionysius the Areopagite

text: After his conversion, Dionysius became the first Bishop of Athens, though he is sometimes counted as the second after Hierotheus. He is venerated as a saint in the Catholic and the Eastern Orthodox churches. He is the patron saint of Athens and is venerated as the protector of the Judges and the Judiciary. His memory is celebrated on October 3.


title: Dionysius the Areopagite

text: In the early sixth century the so-called "Corpus Dionysiacum", a series of writings of a mystical nature, employing Neoplatonic language to elucidate Christian theological and mystical ideas, was ascribed to the Areopagite.


title: Dionysius the Areopagite

text: Dionysius has been misidentified with the martyr Dionysius, the first Bishop of Paris. However, this mistake by a ninth century writer is ignored and each saint is commemorated on his respective day.


title: Dionysius the Areopagite

text: In Athens there are two large churches bearing his name, one in Kolonaki on Skoufa Street, while the other is the Catholic Metropolis of Athens, on Panepistimiou Street. The pedestrian walkway around the Acropolis, which passes through the rock of the Areios Pagos, also bears his name.


title: Dionysius the Areopagite

text: Dionysius is the patron saint of the Gargaliani of Messenia, as well as in the village of Dionysi in the south of the prefecture of Heraklion. The village was named after him and is the only village of Crete with a church in honor of Saint Dionysios Areopagitis.


title: Code coverage

text: In computer science, test coverage is a percentage measure of the degree to which the source code of a program is executed when a particular test suite is run. A program with high test coverage has more of its source code executed during testing, which suggests it has a lower chance of containing undetected software bugs compared to a program with low test coverage. Many different metrics can be used to calculate test coverage. Some of the most basic are the percentage of program subroutines and the percentage of program statements called during execution of the test suite.


title: Code coverage

text: Test coverage was among the first methods invented for systematic software testing. The first published reference was by Miller and Maloney in "Communications of the ACM", in 1963.


title: Code coverage

text: To measure what percentage of code has been executed by a test suite, one or more "coverage criteria" are used. These are usually defined as rules or requirements, which a test suite must satisfy.


title: Code coverage

text: Condition coverage does not necessarily imply branch coverage. For example, consider the following code fragment:


title: Code coverage

text: However, this set of tests does not satisfy branch coverage since neither case will meet the codice_6 condition.


title: Code coverage

text: Fault injection may be necessary to ensure that all conditions and branches of exception-handling code have adequate coverage during testing.


title: Code coverage

text: A combination of function coverage and branch coverage is sometimes also called decision coverage. This criterion requires that every point of entry and exit in the program has been invoked at least once, and every decision in the program has taken on all possible outcomes at least once. In this context, the decision is a boolean expression comprising conditions and zero or more boolean operators. This definition is not the same as branch coverage, however, the term "decision coverage" is sometimes used as a synonym for it.


title: Code coverage

text: Condition/decision coverage requires that both decision and condition coverage be satisfied. However, for safety-critical applications (such as avionics software) it is often required that modified condition/decision coverage (MC/DC) be satisfied. This criterion extends condition/decision criteria with requirements that each condition should affect the decision outcome independently.


title: Code coverage

text: However, the above tests set will not satisfy modified condition/decision coverage, since in the first test, the value of 'b' and in the second test the value of 'c' would not influence the output. So, the following test set is needed to satisfy MC/DC:


title: Code coverage

text: This criterion requires that all combinations of conditions inside each decision are tested. For example, the code fragment from the previous section will require eight tests:


title: Code coverage

text: Parameter value coverage (PVC) requires that in a method taking parameters, all the common values for such parameters be considered. The idea is that all common possible values for a parameter are tested. For example, common values for a string are: 1) null, 2) empty, 3) whitespace (space, tabs, newline), 4) valid string, 5) invalid string, 6) single-byte string, 7) double-byte string. It may also be appropriate to use very long strings. Failure to test each possible parameter value may result in a bug. Testing only one of these could result in 100% code coverage as each line is covered, but as only one of seven options are tested, there is only 14.2% PVC.


title: Code coverage

text: Safety-critical or dependable applications are often required to demonstrate 100% of some form of test coverage.


title: Code coverage

text: For example, the ECSS-E-ST-40C standard demands 100% statement and decision coverage for two out of four different criticality levels; for the other ones, target coverage values are up to negotiation between supplier and customer.


title: Code coverage

text: However, setting specific target values - and, in particular, 100% - has been criticized by practitioners for various reasons (cf.)


title: Code coverage

text: Martin Fowler writes: "I would be suspicious of anything like 100% - it would smell of someone writing tests to make the coverage numbers happy, but not thinking about what they are doing".


title: Code coverage

text: Some of the coverage criteria above are connected. For instance, path coverage implies decision, statement and entry/exit coverage. Decision coverage implies statement coverage, because every statement is part of a branch.


title: Code coverage

text: Full path coverage, of the type described above, is usually impractical or impossible. Any module with a succession of formula_1 decisions in it can have up to formula_2 paths within it; loop constructs can result in an infinite number of paths. Many paths may also be infeasible, in that there is no input to the program under test that can cause that particular path to be executed. However, a general-purpose algorithm for identifying infeasible paths has been proven to be impossible (such an algorithm could be used to solve the halting problem). Basis path testing is for instance a method of achieving complete branch coverage without achieving complete path coverage.


title: Code coverage

text: Methods for practical path coverage testing instead attempt to identify classes of code paths that differ only in the number of loop executions, and to achieve "basis path" coverage the tester must cover all the path classes.


title: Code coverage

text: The target software is built with special options or libraries and run under a controlled environment, to map every executed function to the function points in the source code. This allows testing parts of the target software that are rarely or never accessed under normal conditions, and helps reassure that the most important conditions (function points) have been tested. The resulting output is then analyzed to see what areas of code have not been exercised and the tests are updated to include these areas as necessary. Combined with other test coverage methods, the aim is to develop a rigorous, yet manageable, set of regression tests.


title: Code coverage

text: In implementing test coverage policies within a software development environment, one must consider the following:


title: Code coverage

text: Software authors can look at test coverage results to devise additional tests and input or configuration sets to increase the coverage over vital functions. Two common forms of test coverage are statement (or line) coverage and branch (or edge) coverage. Line coverage reports on the execution footprint of testing in terms of which lines of code were executed to complete the test. Edge coverage reports which branches or code decision points were executed to complete the test. They both report a coverage metric, measured as a percentage. The meaning of this depends on what form(s) of coverage have been used, as 67% branch coverage is more comprehensive than 67% statement coverage.


title: Code coverage

text: Generally, test coverage tools incur computation and logging in addition to the actual program thereby slowing down the application, so typically this analysis is not done in production. As one might expect, there are classes of software that cannot be feasibly subjected to these coverage tests, though a degree of coverage mapping can be approximated through analysis rather than direct testing.


title: Code coverage

text: There are also some sorts of defects which are affected by such tools. In particular, some race conditions or similar real time sensitive operations can be masked when run under test environments; though conversely, some of these defects may become easier to find as a result of the additional overhead of the testing code.


title: Code coverage

text: Most professional software developers use C1 and C2 coverage. C1 stands for statement coverage and C2 for branch or condition coverage. With a combination of C1 and C2, it is possible to cover most statements in a code base. Statement coverage would also cover function coverage with entry and exit, loop, path, state flow, control flow and data flow coverage. With these methods, it is possible to achieve nearly 100% code coverage in most software projects.


title: Code coverage

text: Test coverage is one consideration in the safety certification of avionics equipment. The guidelines by which avionics gear is certified by the Federal Aviation Administration (FAA) is documented in DO-178B and DO-178C.


title: Code coverage

text: Test coverage is also a requirement in part 6 of the automotive safety standard ISO 26262 "Road Vehicles - Functional Safety".


title: Swish Swish

text: "Swish Swish" is a song by American singer Katy Perry featuring rapper Nicki Minaj for Perry's fifth studio album, "Witness" (2017). It was written by both artists along with Duke Dumont, Sarah Hudson, PJ "Promnite" Sledge and Brittany Hazzard, while being produced by Dumont, with additional production by Sledge and Noah "Mailbox" Passovoy and vocal production by Passovoy. The song was initially released as a promotional single on May 19, 2017, and later as the album's third single. "Swish Swish" is a house-inspired EDM and hip hop song that samples "I Get Deep" by Roland Clark.


title: Swish Swish

text: The song uses basketball metaphors to address Perry's bullies and detractors. Multiple media outlets suspected that the song is about American singer-songwriter Taylor Swift and her 2015 single "Bad Blood", which was believed to be about Perry. Critics wrote mixed reviews of "Swish Swish"; some praised the track's empowering environment and Minaj's verse, while others criticized the song's lyrics.


title: Swish Swish

text: Promotion for the track began with a live debut of the track on "Saturday Night Live", with a performance that went viral. Subsequently, Perry continued to promote the track during BBC Radio 1's Big Weekend, the Glastonbury Festival 2017 and "The Voice Australia". Later, to further promote the track, a lyric video for the track, featuring Brazilian singer Gretchen, was released on July 3, 2017. The official music video, directed by Dave Meyers, premiered on August 24, 2017. Three days later, Perry and Minaj performed the track together for the first time during the 2017 MTV Video Music Awards. "Swish Swish" reached the top 10 in the Philippines and Scotland in addition to the top 20 in Canada and the United Kingdom as well as the top 30 in Australia and Ireland. It has also been certified platinum in Australia, Canada and the US, and was featured in the video game "Just Dance 2018".


title: Swish Swish

text: After Duke Dumont produced a track Perry recorded for H&M's 2015 holiday campaign called "Every Day Is a Holiday", he expressed interest in working with the singer again, adding: "I think we could switch things up a little more for the next record. Who knows what we could do?." Eventually, they paired together to work on the record, with Dumont claiming that Perry was a fan of his music and that they kept in touch, noting that "her vision for the album wasn't a million miles away from the stuff I'm making." He added: "[...] working on this project it was great seeing what her vision was for the album and being able to help with that. I am genuinely excited for the music." Dumont also said that "it was a very easy process and we made the song quickly. And then about two weeks ago I heard that [Nicki Minaj] is going to feature on it, it was very quick."


title: Swish Swish

text: Minaj's appearance on the track was only discovered when the song was released. Minaj and Perry previously worked together on Minaj's song "Get on Your Knees", with Perry writing it with the rapper. However, she did not have time to record her vocals, and Ariana Grande ended up singing the song. As Perry recalled, "We've always wanted to collaborate, we've done so many things together... we did a VH1 show. [...] I actually sent her a couple of songs before these songs were out and she loved 'Swish Swish' the most and she just did it so much justice. Honestly, I just want her to do the whole song." Perry also talked about Minaj's rap skills, commenting: "With Nicki, she's such a [boss-ass bitch] that you can send her anything and her pen game is crazy." On May 18, 2017, Perry announced on Instagram the track would be released at midnight Eastern time. "Swish Swish" was released the next day as the third single from her fifth album "Witness", and was included along with the pre-order of the album upon its debut. Its single cover features Perry's "blinged-out hand holding receipts from a place called 'Karma Coffee & Tea'." On May 26, 2017, Capitol Records confirmed it would focus on promoting "Swish Swish" to pop radio.


title: Swish Swish

text: "Swish Swish" was written by Perry with Duke Dumont, Sarah Hudson, PJ "Promnite" Sledge, Minaj, and Brittany Hazzard, while its production was done by Dumont with additional production by Sledge and Noah "Mailbox" Passovoy. The song samples "I Get Deep" by Roland Clark. "Swish Swish" was noted to have a beat similar to Maya Jane Coles' "What They Say" (2010). The song is performed in the key of F minor with a tempo of 120 beats per minute in common time. It follows a chord progression of Cm–A♭maj–Gm–Cm–A♭maj–Fm, and Perry's vocals span from E♭ to A♭. The track is four minutes and two seconds long. "Swish Swish" is a house-inspired EDM song. Raisa Bruner of "Time" defined it as a hip hop song. It starts with a sparse piano, before the "club-ready beat" kicks in. Lyrically, "Swish Swish" uses basketball metaphors to talk about getting over the haters. As added by Da'Shan Smith of "Billboard" "'Swish Swish' "is targeted towards a 'sheep' who is 'calculated' but not capable of bringing down Perry's spirits." Perry stated "Swish Swish" represents "a liberation from all the negative that doesn't serve you" as part of the "360-degree liberation" theme of her "Witness" album. She also called it a "great anthem for people to use when someone's trying to hold you down or bully you". The song starts with Perry comparing herself to a tiger, "declaring that one 'don't lose no sleep/ don't need opinions/ from a shellfish or a sheep.'" During the song, she claims herself as a "courtside killer queen," and in the chorus, Perry "sweetly" sings "'Swish swish, bish. Another one in the basket!'." Minaj's rap alludes to her "silly rap beefs" as well as Migos.


title: Swish Swish

text: Following its release, several publications suggested that "Swish Swish" was a diss track in response to Taylor Swift's "Bad Blood" (2014), which was believed to be about Perry. Before the song being released, Perry was asked if there was a reaction to "Bad Blood" on "Witness", with Perry replying: "I think [my new album is] a very empowered record. There is no one thing that's calling out any one person. One thing to note is: You can't mistake kindness for weakness and don't come for me. Anyone. Anyone. Anyone. Anyone. And that's not to any one person and don't quote me that it is, because it's not. It's not about that. Honestly, when women come together and they decide to unite, this world is going to be a better place. Period end of story. But, let me say this: Everything has a reaction or a consequence so don't forget about that, okay, honey." When asked if the song was directed at anyone in particular on "The Tonight Show Starring Jimmy Fallon", Perry simply replied that the song is an anti-bullying anthem. Additionally, Nicki Minaj's verse contains the line, "Silly rap beefs just get me more checks," which addresses Minaj's own purported "beef" with rapper Remy Ma, while also referring to her as a stan. On May 22, 2017, while appearing on the Carpool Karaoke segment on "The Late Late Show with James Corden", after singing to "Swish Swish", Corden asked Perry about a 2013 feud between her and Swift. "There's a situation. [...] Honestly, it's really like she started it, and it's time for her to finish it." She also added: "[T]here is the law of cause and effect. You do something, there's going to be a reaction, and trust me daddy, there's going to be a reaction. It's all about karma, right?."


title: Swish Swish

text: "Swish Swish" divided music critics at release. Leonie Cooper of "NME" was very positive, noting that "calling in Nicki Minaj's fast and furious flow for the Fatboy Slim-sampling 'Swish Swish', meanwhile, is something of a master stroke, turning a good song into a great one." Raisa Bruner of "Time" defined the song as "a feisty hip-hop track that lets both artists show off their respective areas of expertise". Rianne Houghton of Digital Spy called it "a sexy, shady banger, and it's all about keeping receipts." Hannah J Davies of "The Guardian" claimed that the song "is a house-fuelled banger with undeniable groove and nonsense content." Kevin O'Donnell of "Entertainment Weekly" called "Swish Swish" "one of the best party-starters of her career, destined for some killer remixes," also praising the "fiery verse" from Nicki Minaj.


title: Swish Swish

text: "Nylon" writer Sydney Gore also praised Minaj for being "absolutely ruthless when she comes in toward the end." Kitty Empire of "The Observer" also noted that "the Roland Clark sample" and "the ever-inventive Nicki Minaj, provides more top-flight, shade-throwing diva product." Sal Cinquemani of "Slant Magazine" praised that Perry "convincingly dabbles in house" in the song. Wren Graves for "Consequence of Sound" picked as the album's standout track, defining it as a "spunky, funky kiss-off track with a spellbinding beat by Duke Dumont, [where] Perry is deadly with her put-downs" and "Nicki Minaj is trotted out for punchline duty and punches gamely." Stephen Thomas Erlewine of AllMusic also selected it as a highlight from the album. Mikael Wood of "Los Angeles Times" thought the song was "a delight as Perry rhymes 'another one in the basket' with 'another one in the casket' over Duke Dumont's thrusting '90s-house beat".


title: Swish Swish

text: Jillian Mapes of "Pitchfork" was less favorable, declaring: "If you're going to do something as tired as fueling this beef, at least give us the satisfaction of making it deliciously shady." Anna Gaca of "Spin" noted it as "another single that makes little sense", and "a random grab bag of Perry's vocals, obnoxious voice-altering effects, and piano flourishes, all laid over a house-inflected beat". Gavin Miller of "Drowned in Sound" was mixed in his review, calling "largely just a deep house track with Katy Perry singing a topline, which isn't a bad thing," but felt the producers were "just offering up tunes they've had on their hard drives for Perry's team to compartmentalise and see what demographics they represent." Neil McCormick of "The Daily Telegraph" felt the song was "too generic to land any blows," while Mike Wass of "Idolator" felt Minaj's verse was "generic" and that it "sounds like a rehash of every feature she has released in 2017."


title: Swish Swish

text: Retrospectively, "Glamour" called the song a "moment of brilliance" on "Witness" with its "basement rave-ready beat and cheeky lyrics". "Entertainment Weekly" called it a "vogue-worthy tribute to 90's house music, complete with hissing hi-hats, endearingly goofy lyrics" and a "gag-worthy" Nicki Minaj guest verse.


title: Swish Swish

text: In the United States, "Swish Swish" debuted and peaked at number 46 on the "Billboard" Hot 100 while reaching number 33 on the Pop Songs chart. The song fared better on the Dance Club Songs chart, becoming her 18th number-one on the chart. By having eighteen songs at the top, Perry became the fifth singer with most number-ones on the Dance Club charts and extended her record for most consecutive number-one songs on the chart. As of September 2017, it has sold 165,288 copies in the country, and has been certified Platinum by the Recording Industry Association of America (RIAA). In Canada, the song first opened at number 27 on the Canadian Hot 100. "Swish Swish" later climbed to number 13, becoming Perry's 22nd top-twenty entry in the nation. It has since been certified Platinum by Music Canada (MC) for shipments of 80,000 units.


title: Swish Swish

text: In Australia, "Swish Swish" first entered at number 37 on the ARIA Charts on June 4, 2017, before peaking at number 22 in July. In the United Kingdom, "Swish Swish" debuted at number 40 on the UK Singles Chart. It ascended to number 29 following the music video's release as well as Perry and Minaj's live performance of the track at the 2017 MTV Video Music Awards, and later reached number 19 in the nation. "Swish Swish" has also been certified Platinum by the British Phonographic Industry (BPI) for shipments of 600,000 units. In Germany, "Swish Swish" became Perry's lowest charting single, peaking at number 76; despite this, the single got certified Gold by BMVI for shipments of 200,000 units.


title: Swish Swish

text: A lyric video for the song was released on YouTube on July 3, 2017, and features Brazilian singer and reality television personality Gretchen. It was directed by Dario Vetere, and it features choreography by Fabio Duarte and CK Calasans. Two days later, Perry announced a contest titled the "#SwishSwishChallenge" for dancers to appear in the song's official music video where candidates submit videos of themselves dancing, and she would select her favorite dancer. After applicants posted their entries by the end of July 12, the video was filmed later in the month. A teaser for the official video was posted on August 21, 2017, on Perry's personal YouTube account.


title: Swish Swish

text: The official music video for the single was directed by Dave Meyers and released on August 24, 2017. It includes appearances from Russell Horning, Gaten Matarazzo, Jenna Ushkowitz, Doug the Pug, Christine Sydelko, Dexter Mayfield, Rob Gronkowski, Joey Chestnut, Molly Shannon, Hafþór Júlíus Björnsson, Karl-Anthony Towns, Rich Eisen, Bill Walton, and Terry Crews. Kia Stevens, Britney Young, Sydelle Noel, Ellen Wong, and Jackie Tohn make appearances as their characters from "GLOW". In the video, Perry plays "Kobe Perry" the captain of the basketball team "The Tigers" whose opponents are known as "The Sheep", and Minaj performs during the game's halftime show. The video also features the brief reappearance of Kathy Beth Terry, Perry's character from "Last Friday Night (T.G.I.F.)", as well as a short gameplay clip from Just Dance 2018 and a brief segment featuring the Bag Raiders song, "Shooting Stars". Stadion Narodowy in Warsaw, Poland, was used for exterior views of the venue in the video. The official music video has over 667 million views on YouTube as of October 2022.


title: Swish Swish

text: Elias Leight of "Rolling Stone" named it "goofy". Dave Holmes of "Esquire" noted that "like all great pop music videos, 'Swish Swish' leaves you exhausted, annoyed, confused, and a good seven years older than you were six minutes ago. It's a shame, too, because when Katy Perry stops trying to be your hilarious best friend, she's capable of great pop music." Jordan Sargent of "Spin" wrote that the video was "bad", though added "it does at least feel like Katy Perry in all her messy glory. Still, there's a gulf between Perry's slapstick character and the fang-toothed, confrontational song that's impossible to bridge. As such, Perry barely even performs the song during the video. Instead, it's as if 'Swish Swish' is the music playing softly behind a comedy sketch that you're not really meant to pay attention to."


title: Swish Swish

text: Perry performed "Swish Swish" solo on the "Saturday Night Live" season finale on May 20, 2017. The performance quickly went viral, with much of the attention coming towards dancer Russell Horning, dubbed the "Backpack Kid", whose arm-swinging dance move ("the Floss") became widely imitated. Perry also performed the song during her set on BBC Radio 1's Big Weekend on May 27, 2017, the Glastonbury Festival 2017 on June 24, 2017, as well as on "The Voice" finale on July 2, 2017, featuring male dancers in high heels. On June 26, Minaj performed a verse of the song at the first-ever 2017 NBA Awards. Perry also performed the song live with Minaj for the first time at the 2017 MTV Video Music Awards. As stated by "Billboard" Joe Lynch, Perry started the performance "standing atop an enormous half-basketball on stage." As Lynch wrote, "her backup dancers sport[ed] nets-for-veils on their faces", while later "the half-basketball rotated around to reveal Nicki Minaj hidden inside." Near the end of the performance, Perry flew "above the crowd and landing atop a basketball hoop just in time to end the show on a literal slam dunk while basketball balloons dropped over the crowd." The song is also performed on Perry's . Halfway through the performance, Perry invites a member from the audience onstage for a basketball shooting contest.


title: Barometric formula

text: The barometric formula, sometimes called the "exponential atmosphere" or "isothermal atmosphere", is a formula used to model how the pressure (or density) of the air changes with altitude. The pressure drops approximately by 11.3 pascals per meter in first 1000 meters above sea level.


title: Barometric formula

text: There are two different equations for computing pressure at various height regimes below 86 km (or 278,400 feet). The first equation is used when the value of standard temperature lapse rate is not equal to zero:


title: Barometric formula

text: The value of subscript "b" ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. In these equations, "g", "M" and "R" are each single-valued constants, while "P", "L," "T," and "h" are multivalued constants in accordance with the table below. The values used for "M", "g", and "R" are in accordance with the U.S. Standard Atmosphere, 1976, and the value for "R" in particular does not agree with standard values for this constant. The reference value for "P" for "b" = 0 is the defined sea level value, "P" = 101 325 Pa or 29.92126 inHg. Values of "P" of "b" = 1 through "b" = 6 are obtained from the application of the appropriate member of the pair equations 1 and 2 for the case when "h" = "h".


title: Barometric formula

text: The expressions for calculating density are nearly identical to calculating pressure. The only difference is the exponent in Equation 1.


title: Barometric formula

text: There are two different equations for computing density at various height regimes below 86 geometric km (84 852 geopotential meters or 278 385.8 geopotential feet). The first equation is used when the value of standard temperature lapse rate is not equal to zero; the second equation is used when standard temperature lapse rate equals zero.


title: Barometric formula

text: The value of subscript "b" ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. The reference value for "ρ" for "b" = 0 is the defined sea level value, "ρ" = 1.2250 kg/m or 0.0023768908 slug/ft. Values of "ρ" of "b" = 1 through "b" = 6 are obtained from the application of the appropriate member of the pair equations 1 and 2 for the case when "h" = "h".


title: Barometric formula

text: In these equations, "g", "M" and "R" are each single-valued constants, while "ρ", "L", "T" and "h" are multi-valued constants in accordance with the table below. The values used for "M", "g" and "R" are in accordance with the U.S. Standard Atmosphere, 1976, and that the value for "R" in particular does not agree with standard values for this constant.


title: Barometric formula

text: Assuming linear temperature change formula_41 and constant molar mass and gravitational acceleration, we get the first barometric formula:


title: Barometric formula

text: In this formulation, "R" is the gas constant, and the term "RT"/"Mg" gives the scale height (approximately equal to 8.4 km for the troposphere).


title: Militant

text: The English word militant is both an adjective and a noun, and it is generally used to mean vigorously active, combative and/or aggressive, especially in support of a cause, as in "militant reformers". It comes from the 15th century Latin ""warrior"" meaning "to serve as a soldier". The related modern concept of the militia as a defensive organization against invaders grew out of the Anglo-Saxon fyrd. In times of crisis, the militiaman left his civilian duties and became a soldier until the emergency was over, when he returned to his civilian occupation.


title: Militant

text: The current meaning of "militant" does not usually refer to a registered soldier: it can be anyone who subscribes to the idea of using vigorous, sometimes extreme, activity to achieve an objective, usually political. A "militant [political] activist" would be expected to be more confrontational and aggressive than an activist not described as militant.


title: Militant

text: Militance may or may not include physical violence, armed combat, terrorism, and the like. The Trotskyist Militant group in the United Kingdom published a newspaper, was active in labour disputes, moved resolutions in political meetings, but was not based on violence. The purpose of the Christian Church Militant is to struggle against sin, the devil and ". . . the rulers of the darkness of this world, against spiritual wickedness in high places" (Ephesians 6:12), but it is not a violent movement.


title: Militant

text: Militant can mean "vigorously active and aggressive, especially in support of a cause" as in 'militant reformers'. The American Heritage Dictionary of the English Language, defines "militant" as "Having a combative character; aggressive, especially in the service of a cause". The Merriam-Webster Dictionary defines "militant" as "aggressively active (as in a cause)". It says that the word "militant" might typically be used in phrases such as 'militant conservationists' or 'a militant attitude'.


title: Militant

text: An example of the adjective usages is demonstrated when "The New York Times" ran an article titled "Militant Environmentalists Planning Summer Protests to Save Redwoods" describing a group that believes in "confrontational demonstrations" and "nonviolent tactics" to get across their message of preserving the environment. Another usage example includes 'a militant political activist', drawing attention to behaviours typical of those engaged in intensive political activism. The political protests headed by the Reverend Al Sharpton have been described as militant in nature in "The Washington Post".


title: Militant

text: In general usage, a "militant" person is a "confrontational" person who does not necessarily use violence.


title: Militant

text: "Militant" is often used within some religious circles to denote the continuous battle of Christians (as church members) or the Christian Church in their struggle against sin. In particular, the Roman Catholic Church differentiates between Church militant and church triumphant. Ellen G. White, one of the founders of the Seventh-day Adventist church, says "Now the church is militant. Now we are confronted with a world in darkness, almost wholly given over to idolatry."


title: Militant

text: Such religious meaning must not be confused with the word 'belligerent' used to describe extremist religious behaviours found in some who, based on their extreme religious beliefs or ideologies, take up weapons and become involved in warfare, or who commit acts of violence or terrorism in an attempt to advance their extremist religious agendas. Such extremist groups can be Christian, Muslims, Jewish, or of any other religious affiliation.


title: Militant

text: A "militant", as a noun, is a person who uses militant methods in pursuit of an objective; the term is not associated with the military. "Militant" can refer to an individual displaying aggressive behavior or attitudes.


title: Militant

text: "Militant" is sometimes used as a euphemism for "terrorist" or "armed insurgent". (For more on this, see mass media usage below.)


title: Militant

text: The word "militant" is sometimes used to describe groups that do not name or describe themselves as militants, but that advocate extreme violence. In the early 21st century, members of groups involved in Islamic terrorism such as Al-Qaeda and ISIS are usually described as militants.


title: Militant

text: Newspapers, magazines, and other information sources may deem "militant" a neutral term, whereas "terrorist" or "guerrilla" conventionally indicates disapproval of the behavior of the individual or organization so labeled, regardless of the motivations for such behavior. "Militant", at other times, can refer to anyone not a member of formal armed forces engaging in warfare or serving as a combatant.


title: Militant

text: The mass media sometimes uses the term ""militant"" in the context of terrorism. Journalists sometimes apply the term "militant" to paramilitary movements using terrorism as a tactic. The mass media also has used the term "militant groups" or "radical militants" for terrorist organizations.


title: Militant

text: Those resisting a foreign military occupation can be seen as not meriting the label "terrorists" because their acts of political violence against military targets of a foreign occupier do not violate international law. Protocol 1 of the Geneva Conventions gives lawful combatant status to those engaging in armed conflicts against alien (or foreign) occupation, colonial domination and racist régimes. Non-uniformed guerrillas also gain combatant status if they carry arms openly during military operations. Protocol 1 does not legitimize attacks on civilians by militants who fall into these categories.


title: Militant

text: In the UN General Assembly Resolution on terrorism (42/159, 7 December 1987). which condemns international terrorism and outlines measures to combat the crime, with one proviso: "that nothing in the present resolution could in any way prejudice the right to self-determination, freedom and independence, as derived from the Charter of the United Nations, of peoples forcibly deprived of that right [...], particularly peoples under colonial and racist regimes and foreign occupation or other forms of colonial domination, nor...the right of these peoples to struggle to this end and to seek and receive support [in accordance with the Charter and other principles of international law]."


title: Militant

text: Militants occur across the political spectrum, including racial or religious supremacists, separatists, abortion opponents and proponents, and environmentalists. Examples of left-wing, right-wing, and advocacy group militants include militant reformers, militant feminists, militant animal rights advocates, and militant anarchists. The phrase "militant Islam" can suggest violent and aggressive political activity by Islamic individuals, groups, movements, or governments. There are also various secret societies that are classified as militant groups.


title: Militant

text: Using the president's authority to assassinate people worldwide who pose an "imminent threat" if "capture is not feasible", the Obama administration routinely called every victim of extrajudicial killing a militant.


title: Militant

text: Among organisations that describe themselves as militants, the Ulster Young Militants are an example of a group resorting to violence (intimidation, arson, and murder) as a deliberate tactic.


title: Militant

text: Militant research is defined as a type of research that is distinct from academia while also not synonymous with the political militant. It refuses the alienating practices of academia which separate researchers from the political meaning of their activity. In recent years it has become an increasingly popular approach for doing research especially since it attempt to resolve academic concerns related to representation and auto-critique.


title: Trix (cereal)

text: Trix is an American brand of breakfast cereal made by General Mills in Minneapolis, Minnesota, for the North American market and by Cereal Partners (using the Nestlé brand) elsewhere in the world. The cereal consists of fruit-flavored, sweetened, ground-corn pieces.


title: Trix (cereal)

text: The Trix trademark is also used by Yoplait (a yogurt company, mostly owned by General Mills) for a line of similarly flavored yogurt marketed toward children.


title: Trix (cereal)

text: General Mills introduced Trix in 1954 as a sugar-coated version of its popular Kix cereal. The original Trix cereal was composed of more than 46% sugar. The original cereal included three colors: "Orangey Orange" (formerly named Orange Orange), "Lemony Yellow" (formerly named Lemon Yellow), and "Raspberry Red". Five fruit shapes and colors were added over the years: "Grapity (or Grapey) Purple" (1984–present), "Lime Green" (1991–1998, 2007–2015, 2017–present), "Wildberry Blue" (1996–2007, 2018–present), "Berry Blue" (2007–2015, 2017–present), and "Watermelon" (1998–2007, 2018–present). In 1991 and again in 1995, the cereal pieces were given a brighter, more colorful look. General Mills' Yoplait division produces a Trix-branded yogurt marketed to children with sweetened fruit flavors such as "Watermelon Burst". Later, Trix Swirls were introduced, with flavors such as "Rasp-orangey orange swirl" (a mix of the Orangey orange and Raspberry red flavors). A new flavor, "Wildberry Red Swirl", was introduced in 2011. Trix Swirls have since been discontinued, and the pieces in the original Trix were changed to their original 2007 flavor and shape lineup in 2014.


title: Trix (cereal)

text: The cereal originally used spherical cereal pieces, but in 1991 these were changed to puffed fruit-shaped pieces, presumably to avoid clashing with Berry Berry Kix when it was introduced in 1992. In 2007, Trix reverted to their original shapes in the United States, to the dismay of the fans. Mexico was the only country to maintain fruit-shaped pieces until around late 2018 when they were reintroduced globally.


title: Trix (cereal)

text: In 2015, General Mills announced it would no longer use artificial colors in its cereals, and Trix would be among the first to change. Trix would go from six colors to four because satisfactory natural alternatives were found for orange, yellow, red, and purple, but not blue or green.


title: Trix (cereal)

text: On September 21, 2017, General Mills announced that the six-color version of Trix cereal would be reintroduced back to the market and that artificial dyes and flavors would be utilized to do so. The four-color, non-artificial-dye/flavor version would continue to be sold. In that same announcement, General Mills said they would revert to the puffed fruit-shaped pieces, which happened around late 2018.


title: Trix (cereal)

text: By 1955, just one year after Trix's market debut, General Mills experimented with a rabbit puppet as a potential Trix mascot. Joe Harris, a copywriter and illustrator at the Dancer Fitzgerald Sample advertising agency, created the trademark animated "Silly Rabbit," who debuted in a 1959 television commercial for the cereal. Harris also wrote the iconic Trix tagline, "Silly rabbit! Trix are for kids!", which is still used in General Mills' commercial campaigns, it is also used at the end of every commercial when the children claim that the cereal itself is for themselves, as that's what they tell to the rabbit.


title: Trix (cereal)

text: Chet Stover, creative director of the Trix account at Dancer Fitzgerald Sample, fully credited Harris with the creation of the Trix rabbit after viewing the new character in its 1959 television commercial for the cereal. In an internal memo to Dancer Fitzgerald Sample employees, Stover wrote, "In a business where the only thing we have to sell are ideas, it is of first importance the credit is given where credit belongs — and Joe gets all the credit for this one."


title: Trix (cereal)

text: The Trix Rabbit—voiced by Mort Marshall in earlier commercials, and later by Russell Horton in later commercials—an anthropomorphic cartoon rabbit who finds children and wants to trick the children into giving him a bowl of cereal. He bursts with enthusiasm but is discovered every time. The kids always reprimand him with the signature phrase: "Silly rabbit! Trix are for kids!" at the end of the commercials These ads in the late 1960s and early 1970s sometimes closed with the Trix Rabbit following up with "And sometimes for tricky rabbits!" (This happened in case he managed to have a taste or he had a secret stash.) The Trix Rabbit originated as a puppet before he was animated. The plight of the Trix Rabbit has drawn comparisons to Sisyphus, a Greek figure who was doomed to endlessly repeat a futile task. He did succeed in obtaining and eating Trix cereal on occasion, including five times as the result of a box top mail-in contest (1968, 1976, 1980, 1984, and 1991) titled "Let The Rabbit Eat Trix". The results of the vote were overwhelmingly "yes", and the Trix Rabbit was depicted in a subsequent commercial enjoying a bowl of Trix. Children who voted received a button based upon their vote in the election. In 1991, the Trix Rabbit won a Tour de Trix Bicycle Race. At the end of the race, two judges are arguing about whether or not the Trix Rabbit should get the prize. To decide the fate of the prize, the children are called upon to send in their votes. The result was "yes" and the Trix Rabbit got the prize, much to his delight.


title: Trix (cereal)

text: In commercials from 1967, the 1970s, and the 1980s, the Trix Rabbit disguised himself to get the cereal, employing costumes as diverse as a balloon vendor, a painter and an American Indian. One alternate slogan for the cereal was, "Oranges, Lemons, and Grapes I see; the fruit taste of Trix is all for me!". Once, Bugs Bunny helped the Trix Rabbit in an attempt to get the cereal.


title: Trix (cereal)

text: The Trix Rabbit's popularity led him to appear in commercials for other products, such as a Got Milk? advertisement, in which he disguises himself as a man (played by Harland Williams) taking Trix from a grocery store but realizing he is out of milk, much to his distress.


Princess Elizabeth of the United Kingdom (22 May 1770 – 10 January 1840) was the seventh child and third daughter of King George III and Charlotte of Mecklenburg-Strelitz. After marrying the Landgrave of Hesse-Homburg, Frederick VI, she took permanent residence in Germany as landgravine.


title: Princess Elizabeth of the United Kingdom

text: The Princess Elizabeth was born at Buckingham House, London on 22 May 1770. Her father was the reigning British monarch, George III, the eldest son of Frederick, Prince of Wales and Augusta of Saxe-Gotha. Her mother was Queen Charlotte (née Princess Charlotte of Mecklenburg-Strelitz). She was christened in the Great Council Chamber at St. James's Palace, on 17 June 1770 by Frederick Cornwallis, the Archbishop of Canterbury. Her godparents were The Hereditary Prince of Hesse-Cassel (her paternal first cousin once-removed, for whom The Earl of Hertford, Lord Chamberlain, stood proxy), The Princess of Nassau-Weilburg (her paternal first cousin once-removed, for whom The Dowager Countess of Effingham, former Lady of the Bedchamber to The Queen, stood proxy) and The Crown Princess of Sweden (another paternal first cousin once-removed, for whom The Countess of Holderness, Lady of the Bedchamber to The Queen, stood proxy).


text: The Princess' upbringing was very sheltered and she spent most of her time with her parents and sisters. King George and Queen Charlotte were keen to shelter their children, particularly the girls. However, in 1812, Princess Elizabeth purchased The Priory at Old Windsor in Berkshire as her private residence.


text: Elizabeth was known for her insistently optimistic attitude in spite of her stilted existence. Although she longed for marriage and a family of her own, Elizabeth was determined to enjoy her life by exploring and developing her varied interests and hobbies. Elizabeth was a talented artist, producing several books of her own engravings to benefit various charities. She was the only one of George III's children to share his interests in agriculture, running her own model farm at a rented cottage in Old Windsor. She took great delight in the products of her garden, as well as the eggs, milk, and butter from her livestock. Elizabeth's family teased her for her fondness of rich food and drink. She was very sensitive to criticism of her weight.


text: Elizabeth was also known for her well-developed sense of humor and maintained a large collection of jokes and witticisms. She had an open and plainspoken nature, and disliked excessive "politeness". She was closest to her sister Augusta and - uniquely among her sisters – her brother Edward, Duke of Kent and Strathearn. Elizabeth was also the closest daughter to their mother, which contributed to Charlotte's reluctance to let her marry.


text: It is alleged that Princess Elizabeth went through a form of marriage with George Ramus (1747–1808) and bore him a daughter, Eliza, in 1788. George Ramus was the son of Nicholas Ramus, who had been Page to Elizabeth's father King George. Any such marriage would have been null and void under the Royal Marriages Act 1772, but several of Elizabeth's brothers contracted similar alliances with commoners before marrying German princesses later in life. Eliza Ramus (1788–1869) was allegedly adopted and brought up by her uncle, Henry Ramus (1755–1822) of the East India Company. She married James Money (1770–1833), also of the East India Company, and her daughter Marian Martha (1806–1869) married George Wynyard Battye (1805–1888), a Bengal Judge. In widowhood, Eliza Ramus lived at 28 Chester Square in London, where she educated her Battye grandsons, all ten of whom became army officers, and cared for them when they were on sick or convalescent leave from India.


text: Largely denied opportunities to marry men of royal blood, several of Elizabeth's sisters embarked on romantic relationships with equerries and other high ranking men at court. Elizabeth herself may have had such a relationship with diplomat Alleyne Fitzherbert, 1st Baron St. Helens. St. Helens was much respected by George III, who created him a Lord of the Bedchamber in 1804. Seventeen years older than Elizabeth, St. Helens was a frank, practical, and sharp-witted character known to dislike court life, qualities which Elizabeth shared. She referred to him as, "a dear and valuable saint," and said of him in a letter to her companion Lady Harcourt, "There is no man I love so well, and his tenderness to me has never varied, and that is a thing I never forget." Elizabeth later wrote that she pined for St. Helens, eager to see him, "at all times, hours, minutes, days, nights, etc." Elizabeth later commissioned a portrait of St. Helens from noted enamelist Henry Pierce Bone, evidence of her great attachment to him. St. Helens in turn kept an enamel miniature of Elizabeth, also painted by Bone.


text: In 1808 Elizabeth was reluctantly obliged to decline a proposal from the exiled Duke of Orléans (later King of the French as Louis Philippe I) due to his Catholicism and her mother's opposition.


text: During a ball in the British royal court in 1814 Elizabeth got to know the German Prince Frederick of Hesse-Homburg. When Elizabeth saw the Austrian officer in his elegant Hussar's uniform, she is supposed to have said, "If he is single, I will marry him!" Four years later, Elizabeth received a letter indicating that Frederick was asking for her hand in marriage. Elizabeth was immediately interested, and her surviving sisters were supportive. Although Frederick was said to be overweight and smell constantly of tobacco from his beloved meerschaum pipes, Elizabeth was undeterred in her goal to marry him. Queen Charlotte refused to permit the union for weeks fearing Elizabeth's unavoidable move to Germany, but finally acquiesced when her daughter refused to back down.


text: Against all resistance, the wedding took place on 7 April 1818 in the private chapel in Buckingham Palace in Westminster. Elizabeth wore a dress made of silver tissue and Brussels lace with ostrich feathers adorning her hair. She was led to the altar by her second eldest brother, the Duke of York. Neither her eldest brother the Prince Regent nor her father attended the wedding, kept away by gout and severe mental illness respectively. The new couple honeymooned at the Prince Regent's house in Brighton.


text: It was not a real "love match", in spite of the mutual understanding and respect; in fact it was an agreement with which both were satisfied. Elizabeth was able to escape the constrictive environment of her home by moving to Germany with her husband, and Frederick gained many advantages by becoming allied with the British royal family. However, Frederick remarked during his honeymoon that he was surprised to be happy and content in Elizabeth's presence; Elizabeth found her new husband to be intelligent, generous, and affectionate. The marriage lasted until Frederick's death in 1829 and was described as very happy.


text: On 20 January 1820, Frederick succeeded his father as the Landgrave of Hesse-Homburg. Thanks to Elizabeth's dowry and annual allowance, he was able to remodel the palace in Homburg. For her part, Landgravine Elizabeth could bid farewell to the rigid court etiquette she had disliked in England. She also built him the Gothic House in the castle's grounds.


text: Elizabeth founded a care center and school in Hanover for children of working mothers. While she was past childbearing age herself, Elizabeth found fulfillment in working with the children attending the school.


text: She died on 10 January 1840 at age 69 in Frankfurt am Main, Hesse, Germany. She was buried in the Mausoleum of the Landgraves, Homburg, Germany.


text: As of 1789, as a daughter of the sovereign, Elizabeth had use of the arms of the kingdom, differenced by a "label argent of three points, the centre point bearing a cross gules, the outer points each bearing a rose gules".


title: Pope Urban VIII

text: Pope Urban VIII (; ; baptised 5 April 1568 – 29 July 1644), born Maffeo Vincenzo Barberini, was head of the Catholic Church and ruler of the Papal States from 6 August 1623 to his death in July 1644. As pope, he expanded the papal territory by force of arms and advantageous politicking, and was also a prominent patron of the arts and a reformer of Church missions.


title: Pope Urban VIII

text: However, the massive debts incurred during his pontificate greatly weakened his successors, who were unable to maintain the papacy's longstanding political and military influence in Europe. He was also an opponent of Copernicanism and involved in the Galileo affair. He is the last pope to date to take the pontifical name "Urban".


title: Pope Urban VIII

text: He was born Maffeo Vincenzo Barberini in April 1568 to Antonio Barberini, a Florentine nobleman, and Camilla Barbadoro. He was born at Barberino Val d'Elsa in "Tafania" house. His father died when he was only three years old and his mother took him to Rome, where he was put in the charge of his uncle, Francesco Barberini, an apostolic protonotary. At the age of 16, he became his uncle's heir. He was educated by the Society of Jesus ("Jesuits"), and received a doctorate of law from the University of Pisa in 1589.


title: Pope Urban VIII

text: In 1601, Barberini, through the influence of his uncle, was able to secure from Pope Clement VIII appointment as a papal legate to the court of King Henry IV of France. In 1604, the same pope appointed him as the Archbishop of Nazareth, an office joined with that of Bishop of the suppressed Dioceses of Canne and Monteverde, with his residence at Barletta. At the death of his uncle, he inherited his riches, with which he bought a palace in Rome, which he made into a luxurious Renaissance residence.


title: Pope Urban VIII

text: Pope Paul V also later employed Barberini in a similar capacity, afterwards raising him, in 1606, to the order of the Cardinal-Priest, with the titular church of San Pietro in Montorio and appointing him as a papal legate of Bologna.


title: Pope Urban VIII

text: Barberini was considered someone who could be elected as pope, though there were those such as Cardinal Ottavio Bandini who worked to prevent it. Despite this, throughout 29–30 July, the cardinals began an intense series of negotiations to test the numbers as to who could emerge from the conclave as pope, with Cardinal Ludovico Ludovisi dismissing Barberini's chances as long as Barberini remained a close ally of Cardinal Scipione Borghese, whose faction Barberini supported. Ludovisi had discussions with Cardinals Farnese, Medici and Aldobrandini on 30 July about seeing to Barberini's election. The three supported his candidacy and went about securing the support of others, which led to Barberini's election just over a week later. On 6 August 1623, at the papal conclave following the death of Pope Gregory XV, Barberini was chosen as Gregory XV's successor and took the name Urban VIII. His coronation had to be postponed until 29 September 1623 since the new pontiff was ill at the time of his election.


title: Pope Urban VIII

text: Urban VIII's papacy covered 21 years of the Thirty Years' War, (1618-1648) and was an eventful one, even by the standards of the day. He canonized Elizabeth of Portugal, Andrew Corsini and Conrad of Piacenza, and issued the papal bulls of canonization for Ignatius of Loyola (founder of the Society of Jesus, "Jesuits") and Francis Xavier (also a Jesuit), who had been canonized by his predecessor, Pope Gregory XV.


title: Pope Urban VIII

text: Despite an early friendship and encouragement for his teachings, Urban VIII was responsible for summoning the scientist and astronomer Galileo to Rome in 1633 to recant his work. Urban VIII was opposed to Copernican heliocentrism and he ordered Galileo's second trial after the publication of "Dialogue Concerning the Two Chief World Systems", in which Urban's point of view is argued by the character "Simplicio".


title: Pope Urban VIII

text: Urban VIII practiced nepotism on a grand scale; various members of his family were enormously enriched by him, so that it seemed to contemporaries as if he were establishing a Barberini dynasty. He elevated his brother Antonio Marcello Barberini (Antonio the Elder) and then his nephews Francesco Barberini and Antonio Barberini (Antonio the Younger) to Cardinal. He also bestowed upon their brother, Taddeo Barberini, the titles "Prince of Palestrina", Gonfalonier of the Church, Prefect of Rome and "Commander of Sant'Angelo". Historian Leopold von Ranke estimated that during his reign, Urban VIII's immediate family amassed 105 million scudi in personal wealth.


title: Pope Urban VIII

text: Urban VIII was a skilled writer of Latin verse, and a collection of Scriptural paraphrases as well as original hymns of his composition have been frequently reprinted.


title: Pope Urban VIII

text: The 1638 papal bull "Commissum Nobis" protected the existence of Jesuit missions in South America by forbidding the enslavement of natives who were at the Jesuit Reductions. At the same time, Urban VIII repealed the Jesuit monopoly on missionary work in China and Japan, opening these countries to missionaries of other orders and missionary societies.


title: Pope Urban VIII

text: Urban VIII issued a 1624 papal bull that made the use of tobacco in holy places punishable by excommunication; Pope Benedict XIII repealed the ban one hundred years later.


title: Pope Urban VIII

text: Urban VIII canonized five saints during his pontificate: Stephen Harding (1623), Elizabeth of Portugal and Conrad of Piacenza (1625), Peter Nolasco (1628), and Andrea Corsini (1629). The pope also beatified 68 individuals including the Martyrs of Nagasaki (1627).


title: Pope Urban VIII

text: The pope created 74 cardinals in eight consistories throughout his pontificate, and this included his nephews Francesco and Antonio, cousin Lorenzo Magalotti, and the pope's own brother Antonio Marcello. He also created Giovanni Battista Pamphili as a cardinal, with Pamphili becoming his immediate successor Pope Innocent X. The pope also created eight of those cardinals whom he had reserved "in pectore".


title: Pope Urban VIII

text: In the papal bull "Sanctissimus Dominus Noster" of 13 March 1625, Urban instructed Catholics not to venerate the deceased or represent them in the manner of saints without Church sanction. It required a bishop’s approval for the publication of private revelations. Since the nineteenth century, it has become common for books of popular devotion to carry a disclaimer. One read in part: "In obedience to the decrees of Urban the Eighth, I declare that I have no intention of attributing any other than a purely human authority to the miracles, revelations, favours, and particular cases recorded in this book..."


title: Pope Urban VIII

text: Urban VIII's military involvement was aimed less at the restoration of Catholicism in Europe than at adjusting the balance of power to favour his own independence in Italy. In 1626, the duchy of Urbino was incorporated into the papal dominions, and, in 1627, when the direct male line of the Gonzagas in Mantua became extinct, he controversially favoured the succession of the Protestant Duke Charles of Nevers against the claims of the Catholic Habsburgs. He also launched the Wars of Castro in 1641 against Odoardo Farnese, Duke of Parma and Piacenza, whom he excommunicated. Castro was destroyed and its duchy incorporated into the Papal States.


title: Pope Urban VIII

text: Urban VIII was the last pope to extend the papal territory. He fortified Castelfranco Emilia on the Mantuan frontier and commissioned Vincenzo Maculani to fortify the Castel Sant'Angelo in Rome. Urban VIII also established an arsenal in the Vatican, an arms factory at Tivoli and fortified the harbour of Civitavecchia.


title: Pope Urban VIII

text: For the purposes of making cannon and the baldacchino in St Peters, massive bronze girders were pillaged from the portico of the Pantheon leading to the well known lampoon: "quod non fecerunt barbari, fecerunt Barberini," "what the barbarians did not do, the Barberini did."


title: Pope Urban VIII

text: Urban VIII and his family patronized art on a grand scale. He expended vast sums bringing polymaths like Athanasius Kircher to Rome and funding various substantial works by the sculptor and architect Bernini, from whom he had already commissioned "Boy with a Dragon" around 1617 and who was particularly favored during Urban VIII's reign. As well as several portrait busts of Urban, Urban commissioned Bernini to work on the family palace in Rome, the Palazzo Barberini, the College of the Propaganda Fide, the Fontana del Tritone in the Piazza Barberini, the baldacchino and "cathedra" in St Peter's Basilica and other prominent structures in the city. Numerous members of Barberini's family also had their likeness caught in stone by Bernini, such as his brothers Carlo and Antonio. Urban also had rebuilt the Church of Santa Bibiana and the Church of San Sebastiano al Palatino on the Palatine Hill.


title: Pope Urban VIII

text: The Barberini patronised painters such as Nicolas Poussin and Claude Lorrain. One of the most eulogistic of these artistic works in its celebration of his reign, is the huge "Allegory of Divine Providence and Barberini Power" painted by Pietro da Cortona on the ceiling of the large salon of the Palazzo Barberini.


title: Pope Urban VIII

text: Another such acquisition, in a vast collection, was the purchase of the 'Barberini vase'. This was allegedly found at the mausoleum of the Roman Emperor Severus Alexander and his family at Monte Del Grano. The discovery of the vase is described by Pietro Santi Bartoli and referenced on page 28 of a book on The Portland Vase. Pietro Bartoli indicates that the vase contained the ashes of the Roman Emperor. However, this together with the interpretations of the scenes depicted on it are the source of countless theories and disputed 'facts'. The vase remained in the Barberini family collection for some 150 years before passing through the hands of Sir William Hamilton Ambassador to the Royal Court in Naples. It was later sold to the Duke and Duchess of Portland, and has subsequently been known as the Portland Vase. Following catastrophic damage, this glass vase (1-25BC) has been reconstructed three times and resides in the British Museum. The Portland vase itself was borrowed and near copied by Josiah Wedgewood who appears to have added modesty drapery. The vase formed the basis of Jasperware.


title: Pope Urban VIII

text: A consequence of these military and artistic endeavours was a massive increase in papal debt. Urban VIII inherited a debt of 16 million scudi, and by 1635 had increased it to 28 million.


title: Pope Urban VIII

text: According to contemporary John Bargrave, in 1636 members of the Spanish faction of the College of Cardinals were so horrified by the conduct of Pope Urban VIII that they conspired to have him arrested and imprisoned (or killed) so that they could replace him with a new pope; namely Laudivio Zacchia. When Urban VIII travelled to Castel Gandolfo to rest, the members of the Spanish faction met in secret and discussed ways to advance their plan. But they were discovered and the pope raced back to Rome where he immediately held a consistory and demanded to know who the new pope was. To put an end to the conspiracy, the pope decreed that all Cardinal-Bishops should leave Rome and return to their own churches.


title: Pope Urban VIII

text: With the Spanish plan having failed, by 1640 the debt had reached 35 million scudi, consuming more than 80% of annual papal income in interest repayments.


title: Pope Urban VIII

text: Urban VIII's death on 29 July 1644 is said to have been hastened by chagrin at the result of the Wars of Castro. Because of the costs incurred by the city of Rome to finance this war, Urban VIII became immensely unpopular with his subjects.


title: Pope Urban VIII

text: On his death, the bust of Urban VIII that lay beside the Palace of the Conservators on the Capitoline Hill was rapidly destroyed by an enraged crowd, and only a quick-thinking priest saved the sculpture of the late pope belonging to the Jesuits from a similar fate.


title: Pope Urban VIII

text: Following his death, international and domestic machinations resulted in the papal conclave not electing Cardinal Giulio Cesare Sacchetti, who was closely associated with some members of the Barberini family. Instead, it elected Cardinal Giovanni Battista Pamphili, who took the name of Innocent X, as his successor at the papal conclave of 1644.


title: Pope Urban VIII

text: Urban VIII is a recurring character in the "Ring of Fire" alternative history hypernovel by Eric Flint et al. where he is favorably portrayed. He is especially prominent in "1634: The Galileo Affair" (in which he makes the fictional Grantville priest, Larry Mazzare, a cardinal), and in "1635: The Cannon Law", "1635: The Papal Stakes", and "1636: The Vatican Sanction". He is somewhat less favorably presented in "Galileo's Dream" by Kim Stanley Robinson.


title: Compressed sensing

text: Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Nyquist–Shannon sampling theorem. There are two conditions under which recovery is possible. The first one is sparsity, which requires the signal to be sparse in some domain. The second one is incoherence, which is applied through the isometric property, which is sufficient for sparse signals.


title: Compressed sensing

text: A common goal of the engineering field of signal processing is to reconstruct a signal from a series of sampling measurements. In general, this task is impossible because there is no way to reconstruct a signal during the times that the signal is not measured. Nevertheless, with prior knowledge or assumptions about the signal, it turns out to be possible to perfectly reconstruct a signal from a series of measurements (acquiring this series of measurements is called sampling). Over time, engineers have improved their understanding of which assumptions are practical and how they can be generalized.


title: Compressed sensing

text: An early breakthrough in signal processing was the Nyquist–Shannon sampling theorem. It states that if a real signal's highest frequency is less than half of the sampling rate, then the signal can be reconstructed perfectly by means of sinc interpolation. The main idea is that with prior knowledge about constraints on the signal's frequencies, fewer samples are needed to reconstruct the signal.


title: Compressed sensing

text: Around 2004, Emmanuel Candès, Justin Romberg, Terence Tao, and David Donoho proved that given knowledge about a signal's sparsity, the signal may be reconstructed with even fewer samples than the sampling theorem requires. This idea is the basis of compressed sensing.


title: Compressed sensing

text: Compressed sensing relies on formula_1 techniques, which several other scientific fields have used historically. In statistics, the least squares method was complemented by the formula_1-norm, which was introduced by Laplace. Following the introduction of linear programming and Dantzig's simplex algorithm, the formula_1-norm was used in computational statistics. In statistical theory, the formula_1-norm was used by George W. Brown and later writers on median-unbiased estimators. It was used by Peter J. Huber and others working on robust statistics. The formula_1-norm was also used in signal processing, for example, in the 1970s, when seismologists constructed images of reflective layers within the earth based on data that did not seem to satisfy the Nyquist–Shannon criterion. It was used in matching pursuit in 1993, the LASSO estimator by Robert Tibshirani in 1996 and basis pursuit in 1998. There were theoretical results describing when these algorithms recovered sparse solutions, but the required type and number of measurements were sub-optimal and subsequently greatly improved by compressed sensing.


title: Compressed sensing

text: At first glance, compressed sensing might seem to violate the sampling theorem, because compressed sensing depends on the sparsity of the signal in question and not its highest frequency. This is a misconception, because the sampling theorem guarantees perfect reconstruction given sufficient, not necessary, conditions. A sampling method fundamentally different from classical fixed-rate sampling cannot "violate" the sampling theorem. Sparse signals with high frequency components can be highly under-sampled using compressed sensing compared to classical fixed-rate sampling.


title: Compressed sensing

text: An underdetermined system of linear equations has more unknowns than equations and generally has an infinite number of solutions. The figure below shows such an equation system formula_6 where we want to find a solution for formula_7.


title: Compressed sensing

text: In order to choose a solution to such a system, one must impose extra constraints or conditions (such as smoothness) as appropriate. In compressed sensing, one adds the constraint of sparsity, allowing only solutions which have a small number of nonzero coefficients. Not all underdetermined systems of linear equations have a sparse solution. However, if there is a unique sparse solution to the underdetermined system, then the compressed sensing framework allows the recovery of that solution.


title: Compressed sensing

text: Compressed sensing takes advantage of the redundancy in many interesting signals—they are not pure noise. In particular, many signals are sparse, that is, they contain many coefficients close to or equal to zero, when represented in some domain. This is the same insight used in many forms of lossy compression.


title: Compressed sensing

text: Compressed sensing typically starts with taking a weighted linear combination of samples also called compressive measurements in a basis different from the basis in which the signal is known to be sparse. The results found by Emmanuel Candès, Justin Romberg, Terence Tao, and David Donoho showed that the number of these compressive measurements can be small and still contain nearly all the useful information. Therefore, the task of converting the image back into the intended domain involves solving an underdetermined matrix equation since the number of compressive measurements taken is smaller than the number of pixels in the full image. However, adding the constraint that the initial signal is sparse enables one to solve this underdetermined system of linear equations.


title: Compressed sensing

text: The least-squares solution to such problems is to minimize the formula_8 norm—that is, minimize the amount of energy in the system. This is usually simple mathematically (involving only a matrix multiplication by the pseudo-inverse of the basis sampled in). However, this leads to poor results for many practical applications, for which the unknown coefficients have nonzero energy.


title: Compressed sensing

text: To enforce the sparsity constraint when solving for the underdetermined system of linear equations, one can minimize the number of nonzero components of the solution. The function counting the number of non-zero components of a vector was called the formula_9 "norm" by David Donoho.


title: Compressed sensing

text: Candès et al. proved that for many problems it is probable that the formula_1 norm is equivalent to the formula_9 norm, in a technical sense: This equivalence result allows one to solve the formula_1 problem, which is easier than the formula_9 problem. Finding the candidate with the smallest formula_1 norm can be expressed relatively easily as a linear program, for which efficient solution methods already exist. When measurements may contain a finite amount of noise, basis pursuit denoising is preferred over linear programming, since it preserves sparsity in the face of noise and can be solved faster than an exact linear program.


title: Compressed sensing

text: Total variation can be seen as a non-negative real-valued functional defined on the space of real-valued functions (for the case of functions of one variable) or on the space of integrable functions (for the case of functions of several variables). For signals, especially, total variation refers to the integral of the absolute gradient of the signal. In signal and image reconstruction, it is applied as total variation regularization where the underlying principle is that signals with excessive details have high total variation and that removing these details, while retaining important information such as edges, would reduce the total variation of the signal and make the signal subject closer to the original signal in the problem.


title: Compressed sensing

text: For the purpose of signal and image reconstruction, formula_15 minimization models are used. Other approaches also include the least-squares as has been discussed before in this article. These methods are extremely slow and return a not-so-perfect reconstruction of the signal. The current CS Regularization models attempt to address this problem by incorporating sparsity priors of the original image, one of which is the total variation (TV). Conventional TV approaches are designed to give piece-wise constant solutions. Some of these include (as discussed ahead) – constrained formula_16-minimization which uses an iterative scheme. This method, though fast, subsequently leads to over-smoothing of edges resulting in blurred image edges. TV methods with iterative re-weighting have been implemented to reduce the influence of large gradient value magnitudes in the images. This has been used in computed tomography (CT) reconstruction as a method known as edge-preserving total variation. However, as gradient magnitudes are used for estimation of relative penalty weights between the data fidelity and regularization terms, this method is not robust to noise and artifacts and accurate enough for CS image/signal reconstruction and, therefore, fails to preserve smaller structures.


title: Compressed sensing

text: Recent progress on this problem involves using an iteratively directional TV refinement for CS reconstruction. This method would have 2 stages: the first stage would estimate and refine the initial orientation field – which is defined as a noisy point-wise initial estimate, through edge-detection, of the given image. In the second stage, the CS reconstruction model is presented by utilizing directional TV regularizer. More details about these TV-based approaches – iteratively reweighted l1 minimization, edge-preserving TV and iterative model using directional orientation field and TV- are provided below.


title: Compressed sensing

text: In the CS reconstruction models using constrained formula_15 minimization, larger coefficients are penalized heavily in the formula_15 norm. It was proposed to have a weighted formulation of formula_15 minimization designed to more democratically penalize nonzero coefficients. An iterative algorithm is used for constructing the appropriate weights. Each iteration requires solving one formula_15 minimization problem by finding the local minimum of a concave penalty function that more closely resembles the formula_21 norm. An additional parameter, usually to avoid any sharp transitions in the penalty function curve, is introduced into the iterative equation to ensure stability and so that a zero estimate in one iteration does not necessarily lead to a zero estimate in the next iteration. The method essentially involves using the current solution for computing the weights to be used in the next iteration.


title: Compressed sensing

text: Early iterations may find inaccurate sample estimates, however this method will down-sample these at a later stage to give more weight to the smaller non-zero signal estimates. One of the disadvantages is the need for defining a valid starting point as a global minimum might not be obtained every time due to the concavity of the function. Another disadvantage is that this method tends to uniformly penalize the image gradient irrespective of the underlying image structures. This causes over-smoothing of edges, especially those of low contrast regions, subsequently leading to loss of low contrast information. The advantages of this method include: reduction of the sampling rate for sparse signals; reconstruction of the image while being robust to the removal of noise and other artifacts; and use of very few iterations. This can also help in recovering images with sparse gradients.


title: Compressed sensing

text: In the figure shown below, P1 refers to the first-step of the iterative reconstruction process, of the projection matrix P of the fan-beam geometry, which is constrained by the data fidelity term. This may contain noise and artifacts as no regularization is performed. The minimization of P1 is solved through the conjugate gradient least squares method. P2 refers to the second step of the iterative reconstruction process wherein it utilizes the edge-preserving total variation regularization term to remove noise and artifacts, and thus improve the quality of the reconstructed image/signal. The minimization of P2 is done through a simple gradient descent method. Convergence is determined by testing, after each iteration, for image positivity, by checking if formula_22 for the case when formula_23 (Note that formula_24 refers to the different x-ray linear attenuation coefficients at different voxels of the patient image).


title: Compressed sensing

text: This is an iterative CT reconstruction algorithm with edge-preserving TV regularization to reconstruct CT images from highly undersampled data obtained at low dose CT through low current levels (milliampere). In order to reduce the imaging dose, one of the approaches used is to reduce the number of x-ray projections acquired by the scanner detectors. However, this insufficient projection data which is used to reconstruct the CT image can cause streaking artifacts. Furthermore, using these insufficient projections in standard TV algorithms end up making the problem under-determined and thus leading to infinitely many possible solutions. In this method, an additional penalty weighted function is assigned to the original TV norm. This allows for easier detection of sharp discontinuities in intensity in the images and thereby adapt the weight to store the recovered edge information during the process of signal/image reconstruction. The parameter formula_25 controls the amount of smoothing applied to the pixels at the edges to differentiate them from the non-edge pixels. The value of formula_25 is changed adaptively based on the values of the histogram of the gradient magnitude so that a certain percentage of pixels have gradient values larger than formula_25. The edge-preserving total variation term, thus, becomes sparser and this speeds up the implementation. A two-step iteration process known as forward-backward splitting algorithm is used. The optimization problem is split into two sub-problems which are then solved with the conjugate gradient least squares method and the simple gradient descent method respectively. The method is stopped when the desired convergence has been achieved or if the maximum number of iterations is reached.


title: Compressed sensing

text: Some of the disadvantages of this method are the absence of smaller structures in the reconstructed image and degradation of image resolution. This edge preserving TV algorithm, however, requires fewer iterations than the conventional TV algorithm. Analyzing the horizontal and vertical intensity profiles of the reconstructed images, it can be seen that there are sharp jumps at edge points and negligible, minor fluctuation at non-edge points. Thus, this method leads to low relative error and higher correlation as compared to the TV method. It also effectively suppresses and removes any form of image noise and image artifacts such as streaking.


title: Compressed sensing

text: To prevent over-smoothing of edges and texture details and to obtain a reconstructed CS image which is accurate and robust to noise and artifacts, this method is used. First, an initial estimate of the noisy point-wise orientation field of the image formula_28, formula_29, is obtained. This noisy orientation field is defined so that it can be refined at a later stage to reduce the noise influences in orientation field estimation. A coarse orientation field estimation is then introduced based on structure tensor which is formulated as: formula_30. Here, formula_31 refers to the structure tensor related with the image pixel point (i,j) having standard deviation formula_32. formula_33 refers to the Gaussian kernel formula_34 with standard deviation formula_32. formula_25 refers to the manually defined parameter for the image formula_28 below which the edge detection is insensitive to noise. formula_38 refers to the gradient of the image formula_28 and formula_40 refers to the tensor product obtained by using this gradient.


title: Compressed sensing

text: The structure tensor obtained is convolved with a Gaussian kernel formula_33 to improve the accuracy of the orientation estimate with formula_25 being set to high values to account for the unknown noise levels. For every pixel (i,j) in the image, the structure tensor J is a symmetric and positive semi-definite matrix. Convolving all the pixels in the image with formula_33, gives orthonormal eigen vectors ω and υ of the formula_44 matrix. ω points in the direction of the dominant orientation having the largest contrast and υ points in the direction of the structure orientation having the smallest contrast. The orientation field coarse initial estimation formula_29 is defined as formula_29 = υ. This estimate is accurate at strong edges. However, at weak edges or on regions with noise, its reliability decreases.


title: Compressed sensing

text: To overcome this drawback, a refined orientation model is defined in which the data term reduces the effect of noise and improves accuracy while the second penalty term with the L2-norm is a fidelity term which ensures accuracy of initial coarse estimation.