title: Hazard ratio

text: Hazard ratios do not reflect a time unit of the study. The difference between hazard-based and time-based measures is akin to the difference between the odds of winning a race and the margin of victory. When a study reports one hazard ratio per time period, it is assumed that difference between groups was proportional. Hazard ratios become meaningless when this assumption of proportionality is not met.


title: Hazard ratio

text: If the proportional hazard assumption holds, a hazard ratio of one means equivalence in the hazard rate of the two groups, whereas a hazard ratio other than one indicates difference in hazard rates between groups. The researcher indicates the probability of this sample difference being due to chance by reporting the probability associated with some test statistic. For instance, the formula_10 from the Cox-model or the log-rank test might then be used to assess the significance of any differences observed in these survival curves.


title: Hazard ratio

text: Conventionally, probabilities lower than 0.05 are considered significant and researchers provide a 95% confidence interval for the hazard ratio, e.g. derived from the standard deviation of the Cox-model regression coefficient, i.e. formula_10. Statistically significant hazard ratios cannot include unity (one) in their confidence intervals.


title: Hazard ratio

text: The proportional hazards assumption for hazard ratio estimation is strong and often unreasonable. Complications, adverse effects and late effects are all possible causes of change in the hazard rate over time. For instance, a surgical procedure may have high early risk, but excellent long term outcomes.


title: Hazard ratio

text: If the hazard ratio between groups remain constant, this is not a problem for interpretation. However, interpretation of hazard ratios become impossible when selection bias exists between groups. For instance, a particularly risky surgery might result in the survival of a systematically more robust group who would have fared better under any of the competing treatment conditions, making it look as if the risky procedure was better. Follow-up time is also important. A cancer treatment associated with better remission rates might on follow-up be associated with higher relapse rates. The researchers' decision about when to follow up is arbitrary and may lead to very different reported hazard ratios.


title: Hazard ratio

text: Hazard ratios are often treated as a ratio of death probabilities. For example, a hazard ratio of 2 is thought to mean that a group has twice the chance of dying than a comparison group. In the Cox-model, this can be shown to translate to the following relationship between group survival functions: formula_13 (where "r" is the hazard ratio). Therefore, with a hazard ratio of 2, if formula_14 (20% survived at time "t"), formula_15 (4% survived at "t"). The corresponding death probabilities are 0.8 and 0.96. It should be clear that the hazard ratio is a relative measure of effect and tells us nothing about absolute risk.


title: Hazard ratio

text: While hazard ratios allow for hypothesis testing, they should be considered alongside other measures for interpretation of the treatment effect, e.g. the ratio of median times (median ratio) at which treatment and control group participants are at some endpoint. If the analogy of a race is applied, the hazard ratio is equivalent to the odds that an individual in the group with the higher hazard reaches the end of the race first. The probability of being first can be derived from the odds, which is the probability of being first divided by the probability of not being first:


title: Hazard ratio

text: In the previous example, a hazard ratio of 2 corresponds to a 67% chance of an early death. The hazard ratio does not convey information about how soon the death will occur.


title: Hazard ratio

text: Treatment effect depends on the underlying disease related to survival function, not just the hazard ratio. Since the hazard ratio does not give us direct time-to-event information, researchers have to report median endpoint times and calculate the median endpoint time ratio by dividing the control group median value by the treatment group median value.


title: Hazard ratio

text: While the median endpoint ratio is a relative speed measure, the hazard ratio is not. The relationship between treatment effect and the hazard ratio is given as formula_9. A statistically important, but practically insignificant effect can produce a large hazard ratio, e.g. a treatment increasing the number of one-year survivors in a population from one in 10,000 to one in 1,000 has a hazard ratio of 10. It is unlikely that such a treatment would have had much impact on the median endpoint time ratio, which likely would have been close to unity, i.e. mortality was largely the same regardless of group membership and clinically insignificant.


title: Hazard ratio

text: By contrast, a treatment group in which 50% of infections are resolved after one week (versus 25% in the control) yields a hazard ratio of two. If it takes ten weeks for all cases in the treatment group and half of cases in the control group to resolve, the ten-week hazard ratio remains at two, but the median endpoint time ratio is ten, a clinically significant difference.


title: Atiba Hutchinson

text: Atiba Hutchinson (born 8 February 1983) is a Canadian professional soccer player who plays as a midfielder and captains both Süper Lig club Beşiktaş and the Canada national team. While playing in Denmark he won the Danish Super Liga Player of the Year, becoming the first North American player to receive the award. That same season, Hutchinson won the first of six Canadian Player of the Year awards. Between 2010 and 2013, he played for PSV Eindhoven in the Dutch Eredivisie.


title: Atiba Hutchinson

text: In 2012 as part of the Canadian Soccer Association's centennial celebration, he was named to the all-time Canada XI men's team. Hutchinson is Canada's record cap holder and the first male Canadian soccer player to reach over 100 caps.


title: Atiba Hutchinson

text: Hutchinson was born in Brampton, Ontario, to Trinidadian parents. He began playing youth soccer at age four for Brampton Youth SC and later played youth soccer for North Scarborough SC and Woodbridge Strikers. Following a March 2001 trial at Schalke 04 in Germany, Hutchinson began his professional career in the 2002 summer season, playing briefly with the York Region Shooters of the Canadian Professional Football League before signing with the Toronto Lynx of the then A-League in mid-season, on 26 July, and playing in the team's final four games.


title: Atiba Hutchinson

text: In January 2003 he signed with Östers IF, newly promoted to the Swedish Allsvenskan. Hutchinson scored six times for Öster during the 2003 season. With the club relegated out of the Allsvenskan, Hutchinson was granted a transfer for an estimated £1.32 million and signed with Helsingborgs IF in January 2004.


title: Atiba Hutchinson

text: Expectations were high for him the first season in Helsingborg, but they were ultimately unsatisfied. However, in the 2005 season he was consistently the team's best player, scoring six goals from a primarily defensive midfield position.


title: Atiba Hutchinson

text: Hutchinson moved to Danish club F.C. Copenhagen, where, for the first half of the year, he played alongside Swedish international Tobias Linderoth in central midfield, latterly being used around the midfield and as a striker. Manager Ståle Solbakken said in an interview with the football paper "TIPS-bladet", that he saw Hutchinson's attacking talents as being too impressive for a central midfielder, saying that he would be used more often as winger. He was linked with Premier League clubs several times.


title: Atiba Hutchinson

text: After Hutchinson had left Denmark for his new team in the Eredivisie he was awarded Danish Super Liga Player of the Year for his last season with Copenhagen. This award was given on 15 November 2010 by Franz Beckenbauer at the annual Danish Football Association award show. This was the first time a Canadian had won this award in the Danish League.


title: Atiba Hutchinson

text: In 2014, 32,000 fans participated in a fan vote selecting their 11 all-time favourite Copenhagen players, selecting Hutchinson in the midfield.


title: Atiba Hutchinson

text: On 22 April 2010, Hutchinson signed a three-year contract with PSV Eindhoven joining them on a free transfer. Atiba made his PSV debut in a 6–0 home victory against De Graafschap on 14 August 2010. Four days later he made his European debut for the team in a surprising 1-0 first leg defeat to FC Sibir Novosibirsk in the Europa League, however PSV won the second leg 5–0 making it to the next stage of the competition. Atiba scored his first goal with the Dutch side on 23 January 2011, his goal came in the 46th minute of a 3–0 away victory against VVV-Venlo. Hutchinson started the 2010 season playing a defensive role as a right back, however with the mid-season transfer of Ibrahim Afellay to Barcelona allowed Hutchinson to move into his more natural position of the central midfield. Atiba continued to impress through the winter scoring his second goal of the season in a 3–2 away victory against Excelsior on 5 March 2011. Atiba also help lead PSV to the Quarter Finals of the Europa League before being knocked out by Benfica in mid-April losing 6–3 on aggregate.


title: Atiba Hutchinson

text: Hutchinson was forced to miss the beginning of the 2011–12 Eredivisie due to his knee injury sustained with Canada at the Gold Cup that summer. After missing the first two games of the season Hutchinson made his return on 21 August 2011 as a second-half substitute for Zakaria Labyad against ADO Den Haag, the game ended in a 3–0 away victory for PSV. Weeks later Hutchinson sustained yet another knee injury during a 2014 FIFA World Cup qualification against Saint Lucia forcing him to have his third knee operation in 18 months. Despite this, he started the KNVB Cup final for PSV against Heracles Almelo, which PSV won.


title: Atiba Hutchinson

text: With PSV's summer addition of Mark van Bommel Hutchinson was moved back to defense playing right back. On 26 August 2012, he scored his first goal of the new season courtesy of a Dries Mertens through ball in the 38th minute, the game ended in a 3–1 away victory over FC Groningen.


title: Atiba Hutchinson

text: With a desire to sign for a Premier League club, Hutchinson let his contract run out with PSV and went into the summer of 2013 looking for a new team, but on 31 July it was announced that he had joined Beşiktaş in the Süper Lig on a two-year deal. Hutchinson scored his first goal for the club on 23 March 2014 in a 3–0 victory over Akhisar Belediyespor. After missing the first leg in the 2014–15 UEFA Champions League play-off round Hutchinson had a standout performance against Arsenal in which Arsène Wenger said Hutchinson was the most impressive Besiktas player; the game ended in a 1–0 away defeat for the Turkish side.


title: Atiba Hutchinson

text: During the summer of 2015, Hutchinson signed a two-year extension with Beşiktaş. In the 2015–16 Süper Lig season, Hutchinson was rewarded with another hard fought honour as Beşiktaş triumphed in the league campaign, which was successfully repeated in the 2016–17 Süper Lig season, again with Hutchinson in a key playmaking defensive midfielder role.


title: Atiba Hutchinson

text: In August 2018, Hutchinson signed a one-year new contract with the club, which had a clause to extend the contract a further season if certain performance criteria are met. During the 2019–20 season, Hutchinson reached 200 league appearances with Beşiktaş.


title: Atiba Hutchinson

text: On 15 August 2020, Hutchinson signed another extension with Beşiktaş that will keep him with the club through the end of the 2020–21 season.


title: Atiba Hutchinson

text: On 6 July 2021, Hutchinson signed another 1-year extension with Beşiktaş. In July 2022, he signed a further 1-year extension.


title: Atiba Hutchinson

text: The early years of Hutchinson's international career included appearances at both the 2001 and 2003 FIFA World Youth Championships. He made his senior debut for Canada in a January 2003 friendly match against the United States. That same year, he appeared in the 2003 edition of the CONCACAF Gold Cup and would go on to appear in five subsequent editions in the following two decades (2005, 2007, 2009, 2011 and 2019).


title: Atiba Hutchinson

text: Canada reached the semi-finals of the 2007 CONCACAF Gold Cup, another match against the United States, which was the site of one of the most controversial moments in Hutchinson's career. With Canada down 2–1 in regulation time, Hutchinson scored a goal in the final minute of stoppage time, having received a ball that bounced off the head of American defender Oguchi Onyewu. However, the goal was ruled offside by referee Benito Archundia, as a result of which the United States won the game and proceeded to the final. Both then and subsequently, many believed that Archundia's call was incorrect.


title: Atiba Hutchinson

text: On 17 December 2010, Hutchinson was awarded the Canadian Men's Player of the Year by the CSA for the first time in his career. Hutchinson was heavily favoured for this award in 2010 for his play with the national team, joining a well-known European club and becoming the first Canadian to win the Danish Superliga Player of the Year. Selected to the 2011 CONCACAF Gold Cup squad, Hutchinson exited the tournament following a 0–2 loss to the Americans at Ford Field after sustaining a knee injury. He was forced to miss the rest of the tournament.


title: Atiba Hutchinson

text: For much of Hutchinson's career, Canada was not able to field a genuinely competitive international team, and qualification to the FIFA World Cup persistently eluded them. As part of the CONCACAF qualification process for the 2014 FIFA World Cup in Brazil, Canada was on the verge of reaching the final stage of CONCACAF qualification for the first time since 1998. Going into its final game of the third round against Honduras in San Pedro Sula on October 16, 2012, Canada needed only a draw to reach the fourth and final stage of qualification. Instead, the team was routed in an 8–1 victory for Honduras, its worst loss in almost thirty years. That game would come to be regarded as the lowest point in the team's history by many. Hutchinson was again named Canada Soccer's male player of the year to end 2012, and affirmed that he hoped to pursue another World Cup qualification, saying "It would still mean everything to me if I could be part of the team and give another go at it."


title: Atiba Hutchinson

text: Hutchinson was once again awarded the 2015 Canadian Men's Player of the Year by the CFA, marking his fourth straight award and fifth in the last six years. He went on to win the title again in 2016 and 2017. However, Canada would not fare any better in attempting to qualify for the 2018 FIFA World Cup, failing to advance to the fifth round of CONCACAF qualification. Disillusioned and believing that his best years had been wasted with the team, Hutchinson would later say that "in my head, I was done. I wasn't coming back to Canada, I swear."


title: Atiba Hutchinson

text: After declining to participate in 2016 and 2017 friendly matches and missing the 2017 CONCACAF Gold Cup, Hutchinson was persuaded to rejoin by coach John Herdman, newly arrived from Canada's much more successful women's national team. Herdman believed Hutchinson would add a valuable veteran presence to a team of up-and-coming talents like Alphonso Davies and Jonathan David. Upon his recall to the team in October 2018, he indicated he was looking to retire from the Canadian national team after the 2019 CONCACAF Gold Cup. He was named to the squad for that tournament on 30 May 2019.


title: Atiba Hutchinson

text: Hutchinson however remained active for Canada, and in March 2021 he accepted a call-up for 2022 FIFA World Cup qualifiers against Bermuda and the Cayman Islands. This new cycle was far more successful than any he had seen before, and they reached the final stage for the first time in a quarter century. Hutchinson said "this time around we've got a team that is full of talent." On November 16, 2021, Hutchinson captained Canada to a 2–1 victory over Mexico at Commonwealth Stadium in Edmonton, which also marked his 90th appearance for his country, surpassing Julian De Guzman as the all-time appearance leader for the men's national team. On March 27, Canada officially qualified for the World Cup with a 4–0 victory over Jamaica at BMO Field in Toronto.


title: Atiba Hutchinson

text: After he suffered a bone bruise that scuppered the beginning of his club season in the fall of 2022, there was doubt as to whether Hutchinson would be ready to participate in the World Cup. Herdman said it was "a tough situation for him. Because I think for all of us he just means so much to the team." However, he recovered sufficiently and in November 2022 he was named to Canada's 26-man squad for the 2022 FIFA World Cup. Acknowledging Hutchinson's importance to the national team through the preceding twenty years, TSN remarked that "the country's return to the World Cup is the crowning achievement in his incomparable career." On 27 November, he played his 100th match for Canada in a 4–1 defeat against Croatia during the World Cup, becoming the first male Canadian to achieve this feat. In Canada's last match of the tournament, having already been eliminated, a would-be equalizing header from Hutchinson was tucked under the crossbar but failed to cross the goal line, as Canada were eventually defeated 2–1 by Morocco, failing to take any points from their group matches.


title: Atiba Hutchinson

text: Atiba Hutchinson is married to a French-Iranian woman named Sarah, whom he met while playing in Denmark. Together they have three sons, Noah (born 2015), Nava (born 2016) and Ayo Siyah (2017), all of whom were born in Istanbul. In April 2022, he joined the ownership group of League1 Ontario club Simcoe County Rovers FC.


title: StockX

text: StockX is an online marketplace and clothing reseller, primarily of sneakers. Since November 2020, it has also opened up to electronic products such as game consoles, smartphones and computer hardware. The Detroit-based company was founded by Dan Gilbert, Josh Luber, Greg Schwartz, and Chris Kaufman in 2015–2016. StockX has more than 800 employees in Downtown Detroit. StockX currently has international offices in London, UK, in Eindhoven, the Netherlands, and has authentication facilities in Detroit's Corktown neighborhood, Moonachie, NJ, and Tempe, AZ. Scott Cutler and Schwartz serve as chief executive officer and chief operating officer, respectively, and Deena Bahri became the company's first chief marketing officer in 2019.


title: StockX

text: The startup company was founded by Dan Gilbert, Josh Luber, Greg Schwartz, and Chris Kaufman starting in 2015, and launched in February 2016. Luber had previously founded StockX's predecessor website about rare sneakers called Campless (established during 2012–2013), a site which was featured in Josh Luber's TED Talk on the sneaker market. After Gilbert acquired Campless from Luber, Luber relocated from Philadelphia to work from Gilbert's One Campus Martius building in Downtown Detroit as chief executive officer. StockX opened its first international headquarters in London in October 2018. Scott Cutler was appointed chief executive officer in June 2019.


title: StockX

text: The company has more than 800 employees, as of August 2019. StockX is among the fastest-growing startups in Detroit and Michigan, as of late 2018.


title: StockX

text: In addition to the One Campus Martius office, StockX has an authentication facility in Detroit's Corktown neighborhood. Prior to the authentication center's relocation in June 2018, the company had a team of 15 employees authenticating thousands of pairs of shoes daily. The larger Corktown facility increased the number of authentications. StockX opened a second authentication center in Tempe, Arizona, in late 2018, followed by two more in Moonachie, New Jersey, and West London. In 2019, the company opened a fifth authentication center in Eindhoven, Netherlands. StockX maintains a catalog of all fake items received.


title: StockX

text: The company's first "StockX Day" event in Detroit, which invited resellers, platform users, and industry influencers to meet employees and see operations, was held in October 2017 and attended by approximately 200 people. 150 buyers and sellers were selected from 3,000–5,000 applicants to attend the second "StockX Day" in April 2018. In May 2019, the company held a third "StockX Day" event for an audience of 300 and announced the opening of its first permanent location in New York City along with several major product updates.


title: StockX

text: StockX has collaborated with numerous celebrities and companies on charitable initiatives. In 2017, Eminem collaborated with the company to raffle off his Air Jordan sneakers designed in collaboration with Carhartt to raise funds for the Greater Houston Community Foundation Hurricane Harvey Relief Fund and Team Rubicon to support relief efforts in Texas and Florida following Hurricane Harvey. Nike Inc.'s debut of LeBron James' first retro sneaker via StockX marked the first time the brand bypassed retail and went directly to the secondary market. In 2018, StockX and Wu-Tang Clan collaborated on the Charity Rules Everyone Around Me (C.R.E.A.M.) campaign; proceeds from nine exclusive products benefitted the Wu-Tang Foundation to support children in underserved communities.


title: StockX

text: StockX suffered a data breach in mid-2019. In September, the company and Bleacher Report reached a multiyear advertising agreement, and Deena Bahri became StockX's first chief marketing officer.


title: StockX

text: In November 2021, StockX announced that it had signed UConn basketball superstar Paige Bueckers as its primary spokesperson for its basketball and women's sports lines.


title: StockX

text: StockX serves as an online marketplace, facilitating auctions between sellers and buyers, then collecting transaction and payment fees. Sellers send purchased items to StockX facilities for inspection and verification, then authenticated products are shipped to buyers. StockX features a "stock market-like" variable pricing framework and discloses price histories for specific items. StockX is most known for sneakers and streetwear but also carries other clothing and accessories such as handbags and watches. StockX surpassed eBay in total sneaker transactions in 2017. Counterfeit items are returned to sellers, and buyers are refunded.


title: StockX

text: StockX charges a 3 percent processing fee for all resellers, and a 9.5 percent transaction fee for new users, which decreases with experience. Prior to the company's expansion into Europe, StockX only advertised in the United States and accepted U.S dollars. Fifteen percent of the company's buyers were international, as of September 2018.


title: StockX

text: In January 2019, StockX partnered with celebrity jeweler and influencer Ben Baller to sell 800 pairs of black and red slides directly to the public, marking the company's first "initial product offering" ("I.P.O."). The shoes were printed with the phrase "Ben Baller did the chain", a lyric from ASAP Ferg's song "Plain Jane" (2017).


title: StockX

text: StockX has received financial backing from Gilbert, investment companies Battery Ventures and GV, as well as Scooter Braun, Jon Buscemi, Eminem, Joe Haden, Ted Leonsis, and Mark Wahlberg. The company raised $6 million in February 2017. StockX received $44 million in a second venture round in September 2018. In addition to Battery and GV, investors included Steve Aoki, Marc Benioff, Don C, and Karlie Kloss. The investment helped fund StockX's international expansion.


title: StockX

text: In June 2019, StockX raised $110 million and was valued at $1 billion in another venture round. Investors included General Atlantic, GGV Capital, and Yuri Milner's firm DST Global, in addition to Battery Ventures and GV.


title: Frogmore Cottage

text: Frogmore Cottage is a historic Grade II listed home on the Frogmore estate, which is part of Home Park in Windsor, England. Built in 1801 at the direction of Queen Charlotte in the gardens near Frogmore House, Frogmore Cottage is part of the Crown Estate, the monarch's public estate. The cottage is the official residence of the Duke and Duchess of Sussex in the United Kingdom, and was their primary residence before they moved to Montecito, California in the United States. In 2020 the Frogmore Cottage was described as a ten-bedroom single-residence Grade-II listed house.


title: Frogmore Cottage

text: The cottage was originally known as Double Garden Cottage and was listed in Queen Charlotte's 1801 accounts for her garden as having been built for £450 by a Mr Bowen. Queen Victoria had breakfast at the cottage on 28 June 1875 and noted an "immense number of little frogs" which she found "quite disgusting". The cottage has been listed Grade II on the National Heritage List for England since October 1975. The listing provides little of the history: "Early C19 plain 2 storey house with parapet. Centre break with porch. Glazing bar sashes. Stucco faced."


title: Frogmore Cottage

text: The cottage was a retreat for Charlotte, the queen consort of George III, and her unmarried daughters. The theologian Henry James Sr. and his family lived at the cottage in the 1840s. A personal secretary of Queen Victoria's, Abdul Karim, moved to Frogmore Cottage in 1897 with his wife and father. Grand Duchess Xenia Alexandrovna in exile from her native Russia after the Russian Revolution stayed there in the 1920s. In the early 21st century, the cottage was a series of five separate units housing Windsor estate workers.


title: Frogmore Cottage

text: In 2019, the house was converted into a four-bedroom-and-nursery single-family home at a reported cost of £2.4 million from the Sovereign Grant for the Duke and Duchess of Sussex prior to the birth of their son, Archie Mountbatten-Windsor, in May 2019. As a property of a royal palace of state and designated heritage site, Frogmore Cottage was always scheduled to be renovated, regardless of occupant. However, after the Duke and Duchess of Sussex announced in January 2020 that they intended to step down as senior working members of the royal family and move to North America, they "shared their wish to repay Sovereign Grant expenditure for the refurbishment of Frogmore Cottage". In September, that sum was reportedly settled in full by the Duke and his lease on the property was extended to March 2022.


title: Frogmore Cottage

text: Princess Eugenie and her husband, Jack Brooksbank, took up residence at the cottage in November 2020, and resided there with their son. In February 2022, it was announced that Prince Harry planned to renew the lease on the cottage, which would allow him to remain domiciled in the UK. In May 2022, it was reported that Harry's lease of the property had been renewed, while Eugenie had moved out of the property to divide her time between London and Portugal.


title: Navid Negahban

text: Navid Negahban (; born June 2, 1968) is an Iranian-American actor. He has appeared on "24", "Homeland", "Mistresses" and as Amahl Farouk / Shadow King in the second and third seasons of FX's "Legion." He has also starred as The Sultan in the live-action remake of "Aladdin".


title: Navid Negahban

text: Negahban was born in Mashhad, Iran. He took a liking to the theater when he was eight years old, while provoking laughter from a large audience by portraying an old man on stage. He left Iran in 1985 when he was 17 for Turkey and then Germany, where he spent eight years. In Germany, he worked for a theater company, and then in 1993 he moved to the United States. He is fluent in English, German and Persian. He also began learning French for his role on "Legion".


title: Navid Negahban

text: He has appeared in "The Shield", "The West Wing", "Lost", and "". He has collaborated twice with Iranian-American actress Necar Zadegan, once in "24", where her on-screen husband ordered his interrogation and the torturing of his family, and also in "CSI: Miami", where, as his wife, she killed him.


title: Navid Negahban

text: Negahban also had two collaborations with another Iranian-American actress, Mozhan Marnò, in the TV series "The Unit" and the movie "The Stoning of Soraya M.", where he plays the husband of Soraya (Marnò). In 2008, Negahban voiced and provided his likeness to the character Dr. Challus Mercer in the survival horror game "Dead Space". Negahban also appeared as terrorist mastermind Abu Nazir in the critically acclaimed TV series "Homeland". In 2011 he won the Best Actor Award for the 2009 Iranian short film, "Liberation" at the Noor Iranian Film Festival, and in 2012, he returned to serve as an official festival judge.


title: Navid Negahban

text: In February 2015, "The Hollywood Reporter" and "Variety" confirmed that Negahban had begun shooting the spy thriller, "Damascus Cover", based on the novel by Howard Kaplan, alongside Jonathan Rhys Meyers, Olivia Thirlby and John Hurt. Negahban played the role of Syrian General Sarraj. Negahban appeared as General Abdul Rashid Dostum in the 2018 war drama, "12 Strong", and also starred as the Sultan in the 2019 live-action adaptation of "Aladdin". In 2022, he appears in the American crime drama television series "The Cleaning Lady" as Hayak Barsamian, an Armenian Mob Boss.


title: Wicket

text: The origin of the word is from wicket gate, a small gate. Originally, cricket wickets had only two stumps and one bail and looked like a gate, much like the wicket used in the North American game of wicket. The third (middle) stump was introduced in 1775, after Lumpy Stevens bowled three successive deliveries to John Small that went straight through the two stumps rather than hitting them.


title: Wicket

text: The size and shape of the wicket has changed several times during the last 300 years; its dimensions and placing is now determined by Law 8 in the "Laws of Cricket", thus:


title: Wicket

text: There are also specified lengths for the barrel and spigots of the bail. There are different specifications for the wickets and bails for junior cricket. The umpires may dispense with the bails if conditions are unfit (e.g., if it is windy they might fall off by themselves). Further details on the specifications of the wickets are contained in Appendix D to the laws.


title: Wicket

text: The wicket can be thought of as the target of the fielding team, as the bowler and fielders alike can dismiss the batter by hitting the wicket with the ball, and in particular, can prevent run-scoring (off a ball that has not reached the boundary) by managing or threatening to run out batters.


title: Wicket

text: For a batsman to be dismissed by being bowled, run out, stumped or hit wicket, his wicket needs to be put down, potentially when neither batsman is in the ground of the wicket. This generally occurs when a fielder throws the ball at the wicket, or hits it with ball in hand. What this means is defined by Law 29. A wicket is put down if:


title: Wicket

text: If the umpires have agreed to dispense with bails, because, for example, it is too windy for the bails to remain on the stumps, the decision as to whether the wicket has been put down is one for the umpire concerned to decide. After a decision to play without bails, the wicket has been put down if the umpire concerned is satisfied that the wicket has been struck by the ball, by the striker's bat, person, or items of his clothing or equipment separated from his person as described above, or by a fielder with the hand holding the ball or with the arm of the hand holding the ball.


title: Wicket

text: As per the ICC Playing Conditions, when using the LED wickets, "the moment at which the wicket has been put down [...] shall be deemed to be the first frame in which the LED lights are illuminated and subsequent frames show the bail permanently removed from the top of the stumps." The manufacturer is reviewing the LED wicket's performance after a number of international cricketers criticized the Zing bails during the 2019 Cricket World Cup.


title: Wicket

text: The dismissal of a batsman is known as the "taking of a wicket". The batsman is said to have "lost his wicket", the batting side is said to have "lost a wicket", the fielding side to have "taken a wicket", and the bowler is also said to have "taken his" (i.e. the batsman's) "wicket", if the dismissal is one of the types for which the bowler receives credit. This language is used even if the dismissal did not actually involve the stumps and bails in any way (for example, a catch). The other four of the five most common methods of dismissal (bowled, LBW, run out, and stumped) involve the stumps and bails being put down (in the case of LBW, theoretically).


title: Wicket

text: A team's score is described in terms of the total number of runs scored and the total number of wickets lost.


title: Wicket

text: The number of wickets taken is a primary measure of an individual bowler's ability, and a key part of a bowling analysis.


title: Wicket

text: The sequence of time over which two particular batsmen bat together, a partnership, is referred to as a specifically numbered wicket when discriminating it from other partnerships in the innings. This can be thought of as saying "this was the number of runs scored while this team had lost ["n"-1] wickets and had yet to lose their "n"th wicket."


title: Wicket

text: A team can win a match by a certain number of wickets. This means that they were batting last, and reached the winning target with a certain number of batsmen still not dismissed. For example, if the side scored the required number of runs to win with only three batsmen dismissed, they are said to have won by seven wickets (as a team's innings ends when ten batsmen are dismissed).


title: Wicket

text: The word "wicket" is also sometimes used to refer to the cricket pitch itself. According to the "Laws of Cricket", this usage is incorrect, but it is in common usage and commonly understood by cricket followers.


title: Wicket

text: The term "sticky wicket" refers to a situation in which the pitch has become damp, typically due to rain or high humidity. This makes the path of the ball more unpredictable thus making the job of defending the stumps that much more difficult. The full phrase is thought to have originally been "to bat on a sticky wicket." Such pitches were commonplace at all levels of the game (i.e. up to Test match level) until the late 1950s.


title: Wicket

text: Even though it's a cricket term, the arches used in croquet and roque are sometimes referred to as "wickets", especially in American English. These arches descend from the ancestral game of ground billiards (which may also be related to cricket), and were formerly called the "hoop", "arch" or "port". The port remained a prominent feature of indoor table billiards until well into the 18th century.


title: Wicket

text: In baseball, the strike zone is similar to the wicket, in that a batter who fails to hit a ball that is going towards the strike zone is at risk of being out.


title: Nickname

text: A nickname is a substitute for the proper name of a familiar person, place or thing. Commonly used to express affection, a form of endearment, and sometimes amusement, it can also be used to express defamation of character. As a concept, it is distinct from both pseudonym and stage name, and also from a title (for example, City of Fountains), although there may be overlap in these concepts.


title: Nickname

text: The compound word "ekename", literally meaning "additional name", was attested as early as 1303. This word was derived from the Old English phrase "eac" "also", related to "eacian" "to increase". By the 15th century, the misdivision of the syllables of the phrase "an ekename" led to its rephrasing as "a nekename". Though the spelling has changed, the pronunciation and meaning of the word have remained relatively stable ever since.


title: Nickname

text: English nicknames are generally represented in quotes between the bearer's first and last names (e.g., "Dwight David "Ike" Eisenhower", "Daniel Lamont "Bubba" Franks", etc.). However, it is also common for the nickname to be identified after a comma following the full real name or later in the body of the text, such as in an obituary (e.g., "Frankie Frisch, "The Fordham Flash""). Any middle name is generally omitted, especially in speech. Like English, German uses (German-style) quotation marks between the first and last names (e.g., "Andreas Nikolaus „Niki“ Lauda"). Other languages may use other conventions; for example, Italian writes the nickname after the full name followed by "detto" "called" (e.g., "Salvatore Schillaci detto Totò"), in Spanish the nickname is written in formal contexts at the end in quotes following "alias" (e.g. "Alfonso Tostado, alias «el Abulense»"), in Portuguese the nickname is written after the full name followed by "vulgo" or between parenthesis (e.g. Edson Arantes do Nascimento, vulgo Pelé / Edson Arantes do Nascimento (Pelé)) and Slovenian represents nicknames after a dash or hyphen (e.g., "Franc Rozman – Stane"). The latter may cause confusion because it resembles an English convention sometimes used for married and maiden names.


title: Nickname

text: In Viking societies, many people had "heiti", "viðrnefni", or "kenningarnöfn" (Old Norse terms for nicknames) which were used in addition to, or instead of, the first name. In some circumstances, the giving of a nickname had a special status in Viking society in that it created a relationship between the name maker and the recipient of the nickname, to the extent that the creation of a nickname also often entailed a formal ceremony and an exchange of gifts known in Old Norse as "nafnfestr" ('fastening a name').


title: Nickname

text: In Bengali society, for example, people will often have two names: a "daknam" (pet name) which is the name used by family and friends and a "bhalonam" which is their formal name.


title: Nickname

text: In England, some nicknames are traditionally associated with a person's surname. A man with the surname 'Clark' will be nicknamed 'Nobby': the surname 'Miller' will have the nickname 'Dusty' (alluding to the flour dust of a miller at work): the surname 'Adams' has the nickname 'Nabby'. There are several other nicknames linked traditionally with a person's surname, including Chalky White, Bunny Warren, Tug Wilson, and Spud Baker. Other English nicknames allude to a person's origins. A Scotsman may be nicknamed 'Jock', an Irishman 'Paddy' (alluding to Saint Patrick, the patron saint of Ireland) or 'Mick' (alluding to the preponderance of Roman Catholicism in Ireland), and a Welshman may be nicknamed 'Taffy' (from Welsh "Dafydd", David). Some nicknames referred ironically to a person's physical characteristics, such as 'Lofty' for a short person, or 'Curly' for a bald man. Traditional English nicknaming was common through the first half of the 20th century, and was frequently used in the armed services during World War I and World War II, but has become less common since then.


title: Nickname

text: In Chinese culture, nicknames are frequently used within a community among relatives, friends, and neighbours. A typical southern Chinese nickname often begins with a "阿" followed by another character, usually, the last character of the person's given name. For example, Taiwanese politician Chen Shui-bian (陳水扁) is sometimes referred as "阿扁" (A-Bian). In many Chinese communities of Southeast Asia, nicknames may also connote one's occupation or status. For example, the landlord might be known simply as "" () Hokkien for "boss") to his tenants or workers while a bread seller would be called "Mianbao Shu" 面包叔 (literally, Uncle Bread). Among Cantonese-speaking communities, the character "仔" (pronounced "Zai") may be used in a similar context of "Junior" in Western naming practices.


title: Nickname

text: In the context of information technology, a nickname (usually called a nick) is a common synonym for the "screen name" or "handle" of a user. In computer networks it has become a common practice for every person to also have one or more nicknames for pseudonymity, to avoid ambiguity, or simply because the natural name or technical address would be too long to type or take too much space on the screen.


title: Nickname

text: Nicknames are usually applied to a person and they are not always chosen by the recipient themselves. Some nicknames are derogatory name calls.


title: Nickname

text: Many geographical places have titles, or alternative names, which have positive implications. Paris, for example, is the "City of Light", Rome is the "Eternal City", Venice is "La Serenissima", and New Jersey is the "Garden State". These alternative names are often used to boost the status of such places, contrary to the usual role of a nickname.


title: Nickname

text: Many places or communities, particularly in the US, adopt titles because they can help in establishing a civic identity, help outsiders recognize a community or attract people to a community, promote civic pride, and build community unity. Titles and slogans that successfully create a new community "ideology or myth" are also believed to have economic value. Their economic value is difficult to measure, but there are anecdotal reports of cities that have achieved substantial economic benefits by "branding" themselves by adopting new slogans.


title: Nickname

text: By contrast, older city nicknames may be critical: London is still occasionally referred to as "The Smoke" in memory of its notorious "pea-souper" smogs (smoke-filled fogs) of the 19th and early 20th centuries, and Edinburgh was "Auld Reekie" for the same reason, as countless coal fires polluted its atmosphere.


title: Nickname

text: Besides or replacing the demonym, some places have collective nicknames for their inhabitants. Many examples of this practice are found in Wallonia and in Belgium in general, where such a nickname is referred to in French as "blason populaire".


title: 1995 NBA Finals

text: The 1995 NBA Finals was the championship round of the 1994–95 National Basketball Association (NBA) season. The series pitted the Eastern Conference champion Orlando Magic against the defending NBA champion and Western Conference champion Houston Rockets. The pre-series hype and buildup of the Finals was centered on the meeting of the two centers opposing each other: Shaquille O'Neal of the Magic and Hakeem Olajuwon of the Rockets. Going into the series the matchup was compared to the Bill Russell–Wilt Chamberlain matchup of the 1960s.


title: 1995 NBA Finals

text: The Rockets became the first team in NBA history to beat four 50-win teams in a single postseason en route to the championship. The Rockets would win a playoff-record nine road games in the 1995 playoffs. It was the second NBA Finals sweep in the 2–3–2 Finals format (after the Detroit Pistons did so against the Los Angeles Lakers in 1989). The Rockets also became the first repeat NBA Champion in history to keep the title with a sweep. In addition, the Rockets became the first team in NBA history to win the title without having home-court advantage in any of the four playoff rounds since the playoffs was expanded to a 16 team format in 1984. Coincidentally, this feat would also be achieved in the NHL by the New Jersey Devils that same year, when they won the Stanley Cup over the Detroit Red Wings.


title: 1995 NBA Finals

text: The Orlando Magic, making their first NBA Finals appearance, began the series at home, hosting the defending champion Houston Rockets. With the Magic up 110–107 late in Game 1, Nick Anderson missed four consecutive free throws in the closing seconds of the game, and Kenny Smith hit a three-pointer, tying the game and sending it to overtime as well as setting a new record at the time, with the most three-pointers in an NBA Finals game with seven. The more experienced Rockets went on to win in overtime and eventually swept the Magic, winning their second consecutive NBA Championship. In achieving this, they earned the distinction of being the only team to win both championships during Michael Jordan's first retirement (although Jordan did return in the closing months of the 1994–95 season), in addition to being the only team other than the Chicago Bulls to win multiple championships in the 1990s.


title: 1995 NBA Finals

text: The season-ending documentary "Double Clutch" by Hal Douglas, was released by NBA Entertainment to coincide with the Rockets' championship season.


title: 1995 NBA Finals

text: The Rockets entered the 1994–95 season as defending champions. They had won their first eight games of the season, the first defending champions to have won their first eight games of their season since the 1987-88 Lakers. However, they struggled to maintain last season's form due to injuries and off-court-distractions. On February 14, the Rockets acquired Clyde Drexler from the Portland Trail Blazers, but the trade of a hometown hero (Drexler was a teammate of Olajuwon at the University of Houston) did not improve matters, and the Rockets settled for the sixth seed with a 47–35 record.


title: 1995 NBA Finals

text: However, Houston once again lived up to its Clutch City reputation come playoff time. En route to the Finals, the Rockets defeated three teams with 55 or more victories. They began by ousting the Utah Jazz in five games (the Rockets trailed 2–1 after three games), then repeating last season's comeback effort over the Phoenix Suns (wherein the Rockets trailed 3–1 after four games). In Game 7 of that series, Phoenix led Houston 51-42 after the first half before Houston mounted a comeback to get the series win, 115-114. After dispatching the Suns, the Rockets outclassed the top-seeded San Antonio Spurs in six games of the conference finals. They also became the first team in NBA History to have lost all their home games of the series but won all road games of that certain series thus advancing to the next round.


title: 1995 NBA Finals

text: The Magic were only in their sixth season of existence, but they were a team on the rise. Led by All-Stars Shaquille O'Neal and Penny Hardaway, new acquisition Horace Grant, and franchise cornerstones Nick Anderson and Dennis Scott, the Magic rolled through the Eastern Conference, winding up with a then-franchise best 57–25 mark.


title: 1995 NBA Finals

text: Orlando's road to the Finals began with a convincing 3–1 series win over the Boston Celtics. They followed it up with a six-game ouster of Michael Jordan (returning from an 18-month retirement) and the Chicago Bulls in the second round, and in the conference finals, they vanquished the Indiana Pacers in a tough seven-game series.


title: 1995 NBA Finals

text: This was one of only two NBA Finals in which the team who did not have home court advantage swept the series, (the other being the 1975 Finals, in which the Golden State Warriors swept the Washington Bullets).


title: 1995 NBA Finals

text: Orlando led 110-107 with 10.5 seconds left, when Nick Anderson was intentionally fouled to send him to the free-throw line. Normally a respectable free-throw shooter (70.4 percent in the regular season), Anderson missed both of his free throws, but was able to grab the offensive rebound after the second miss and was fouled again. Anderson shockingly missed the next two free throws, and Houston grabbed the rebound, and would tie the game with 1.6 seconds left on Kenny Smith's 3-point shot. The shot was one of Smith's seven made 3-point shots, setting a then-Finals record. In overtime, Hakeem Olajuwon tipped in a missed finger roll by Clyde Drexler with three-tenths of a second left to win the game. Hakeem Olajuwon finished the game with 31 points, 6 rebounds, 7 assists and 4 blocks while Kenny Smith recorded 23 points and 9 assists. The four consecutive missed free-throws by Nick Anderson would haunt him for the rest of his career. After the Finals, Anderson would shoot only 60.5% on free-throws for the rest of his career.


title: 1995 NBA Finals

text: Hakeem Olajuwon recorded a double-double with 34 points and 11 rebounds to lead the Rockets to a 117-106 victory and a 2-0 series lead. The Magic, on the other hand, became the 2nd team in NBA Finals history to lose the first two of their four home games.


title: 1995 NBA Finals

text: Robert Horry hit a three-pointer to give Houston a 104-100 lead with 14.1 seconds left. Orlando's Anfernee Hardaway then missed a three-pointer, and the rebound deflected off Dennis Scott and out of bounds with 6.8 seconds left, turning the ball over to Houston. Clyde Drexler was immediately fouled. He missed his first free throw and made the second for a 105-100 Rockets lead with 5.9 seconds left. Nick Anderson hit a three-pointer with 2.7 seconds left to bring the Magic within two points, and then Sam Cassell was immediately fouled. He needed to make both free throws to likely seal it, but missed the first. He made the second to give the Rockets a three-point lead with 2.2 seconds left. After a timeout to advance the ball to midcourt, the Magic had one last chance to tie the game and force overtime, but Hardaway missed a three-pointer as the buzzer sounded. The Rockets held on for a 106-103 win in Game 3 to take a 3-0 series lead and were one win away from their second consecutive NBA title.


title: 1995 NBA Finals

text: At the end of the first half, the Magic had a 4-point advantage of the home team, Rockets. However, the Rockets have another notable comeback as they outscored the Magic 66-50 in the second half, thus winning their second consecutive NBA championship. Olajuwon outscores O'Neal by 10 points and caps off the sweep by hitting a memorable yet uncharacteristic 3-pointer in front of O'Neal. When accepting the Larry O'Brien Trophy on the floor of The Summit, Rockets head coach Rudy Tomjanovich said "Don't ever underestimate the heart of a champion!" Olajuwon, with his 35 point and 15 rebound performance, was named Finals MVP for the second straight year.


title: 1995 NBA Finals

text: Although both centers played well, Olajuwon outscored O'Neal in every game of the series and became one of the few players in NBA history to score at least 30 points in every game of an NBA Finals series:


title: 1995 NBA Finals

text: By winning his second straight NBA Finals MVP award, Hakeem Olajuwon became the sixth player to win the award on multiple occasions, joining Willis Reed, Kareem Abdul-Jabbar, Magic Johnson, Larry Bird, and Michael Jordan. Jordan and Olajuwon at the time were the only players to win the award consecutively.


title: 1995 NBA Finals

text: In the United States, the NBA Finals was broadcast on NBC television, with Marv Albert, Matt Guokas and Bill Walton calling the action. Ahmad Rashad, Hannah Storm, and Jim Gray served as sideline reporters, and studio coverage was handled by Bob Costas, Julius Erving and Peter Vecsey.


title: 1995 NBA Finals

text: National radio coverage was provided by the NBA Radio Network, with Joe McConnell and Wes Unseld on the call. After the season, NBA Radio was dissolved and subsequent national radio broadcasts of the NBA Finals would be handled by ESPN Radio.


title: 1995 NBA Finals

text: The Rockets' title reign ended in 1996, when they were swept by the Seattle SuperSonics in the second round. The Sonics were also the last team to beat the Rockets in the playoffs prior to their championship run, having eliminated them in the second round in 1993. That year, the Rockets won 48 games and achieved the fourth seed. The following offseason, they acquired former NBA MVP Charles Barkley in a trade, but age and injuries would take its toll and the closest the Rockets would achieve after their two-year championship reign was a six-game loss to the Utah Jazz in the 1997 Western Conference Finals.


title: 1995 NBA Finals

text: The Magic won a franchise-record 60 games in the 1995–96 NBA season, but were swept by the Chicago Bulls in the 1996 Eastern Conference Finals. During the offseason, Shaquille O'Neal signed with the Los Angeles Lakers, with whom he went on to win three championships; he later added a fourth title to his resume with the Miami Heat in . The Magic would not return to the Finals until , which they lost to the Lakers in five games.


title: Catalan number

text: In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after the French-Belgian mathematician Eugène Charles Catalan (1814–1894).


title: Catalan number

text: which is equivalent to the expression given above because formula_4. This expression shows that "C" is an integer, which is not immediately obvious from the first formula given. This expression forms the basis for a proof of the correctness of the formula.


title: Catalan number

text: in the sense that the quotient of the "n"th Catalan number and the expression on the right tends towards 1 as "n" approaches infinity. This can be proved by using the asymptotic growth of the central binomial coefficients, by Stirling's approximation for formula_8, or via generating functions.


title: Catalan number

text: The only Catalan numbers "C" that are odd are those for which "n" = 2 − 1; all others are even. The only prime Catalan numbers are "C" = 2 and "C" = 5.


title: Catalan number

text: The latter representation is closely connected to Wigner's semicircle law for eigenvalue distribution of random symmetric matrices.


title: Catalan number

text: Consider a random walk on the integer line, starting at 0. Let -1 be a "trap" state, such that if the walker arrives at -1, it will remain there. The walker can arrive at the trap state at times 1, 3, 5, 7..., and the number of ways the walker can arrive at the trap state at time formula_11 is formula_12. Since the 1D random walk is recurrent, the probability that the walker eventually arrives at -1 is formula_13.


title: Catalan number

text: There are many counting problems in combinatorics whose solution is given by the Catalan numbers. The book "Enumerative Combinatorics: Volume 2" by combinatorialist Richard P. Stanley contains a set of exercises which describe 66 different interpretations of the Catalan numbers. Following are some examples, with illustrations of the cases "C" = 5 and "C" = 14.


title: Catalan number

text: Also, the interior of the correctly matching closing Y for the first X of a Dyck word contains the description of the left subtree, with the exterior describing the right subtree.


title: Catalan number

text: solves the combinatorial problems listed above. The first proof below uses a generating function. The other proofs are examples of bijective proofs; they involve literally counting a collection of some kind of object to arrive at the correct formula.


title: Catalan number

text: We first observe that all of the combinatorial problems listed above satisfy Segner's recurrence relation


title: Catalan number

text: The recurrence relation given above can then be summarized in generating function form by the relation


title: Catalan number

text: in other words, this equation follows from the recurrence relation by expanding both sides into power series. On the one hand, the recurrence relation uniquely determines the Catalan numbers; on the other hand, interpreting as a quadratic equation of "c" and using the quadratic formula, the generating function relation can be algebraically solved to yield two solution possibilities


title: Catalan number

text: This is a special case of Newton's generalized binomial theorem; as with the general theorem, it can be proved by computing derivatives to produce its Taylor series.


title: Catalan number

text: We count the number of paths which start and end on the diagonal of a "n" × "n" grid. All such paths have "n" right and "n" up steps. Since we can choose which of the 2"n" steps are up or right, there are in total formula_37 monotonic paths of this type. A "bad" path crosses the main diagonal and touches the next higher diagonal (red in the illustration).


title: Catalan number

text: The part of the path after the higher diagonal is flipped about that diagonal, as illustrated with the red dotted line. This swaps all the right steps to up steps and vice versa. In the section of the path that is not reflected, there is one more up step than right steps, so therefore the remaining section of the bad path has one more right step than up steps. When this portion of the path is reflected, it will have one more up step than right steps.


title: Catalan number

text: Since there are still 2"n" steps, there are now "n" + 1 up steps and "n" − 1 right steps. So, instead of reaching ("n","n"), all bad paths after reflection end at ("n" − 1, "n" + 1). Because every monotonic path in the ("n" − 1) × ("n" + 1) grid meets the higher diagonal, and because the reflection process is reversible, the reflection is therefore a bijection between bad paths in the original grid and monotonic paths in the new grid.


title: Catalan number

text: and the number of Catalan paths (i.e. good paths) is obtained by removing the number of bad paths from the total number of monotonic paths of the original grid,


title: Catalan number

text: In terms of Dyck words, we start with a (non-Dyck) sequence of "n" X's and "n" Y's and interchange all X's and Y's after the first Y that violates the Dyck condition. After this Y, note that there is exactly one more Y than there are Xs.


title: Catalan number

text: This bijective proof provides a natural explanation for the term "n" + 1 appearing in the denominator of the formula for "C". A generalized version of this proof can be found in a paper of Rukavicka Josef (2011).


title: Catalan number

text: Given a monotonic path, the exceedance of the path is defined to be the number of vertical edges above the diagonal. For example, in Figure 2, the edges above the diagonal are marked in red, so the exceedance of this path is 5.


title: Catalan number

text: Given a monotonic path whose exceedance is not zero, we apply the following algorithm to construct a new path whose exceedance is "1" less than the one we started with.


title: Catalan number

text: In Figure 3, the black dot indicates the point where the path first crosses the diagonal. The black edge is "X", and we place the last lattice point of the red portion in the top-right corner, and the first lattice point of the green portion in the bottom-left corner, and place X accordingly, to make a new path, shown in the second diagram.


title: Catalan number

text: The exceedance has dropped from "3" to "2". In fact, the algorithm causes the exceedance to decrease by "1" for any path that we feed it, because the first vertical step starting on the diagonal (at the point marked with a black dot) is the unique vertical edge that passes from above the diagonal to below it - all the other vertical edges stay on the same side of the diagonal.


title: Catalan number

text: It is also not difficult to see that this process is "reversible": given any path "P" whose exceedance is less than "n", there is exactly one path which yields "P" when the algorithm is applied to it. Indeed, the (black) edge "X", which originally was the first horizontal step ending on the diagonal, has become the "last" horizontal step "starting" on the diagonal. Alternatively, reverse the original algorithm to look for the first edge that passes "below" the diagonal.


title: Catalan number

text: This implies that the number of paths of exceedance "n" is equal to the number of paths of exceedance "n" − 1, which is equal to the number of paths of exceedance "n" − 2, and so on, down to zero. In other words, we have split up the set of "all" monotonic paths into "n" + 1 equally sized classes, corresponding to the possible exceedances between 0 and "n". Since there are formula_40 monotonic paths, we obtain the desired formula formula_41


title: Catalan number

text: Figure 4 illustrates the situation for "n" = 3. Each of the 20 possible monotonic paths appears somewhere in the table. The first column shows all paths of exceedance three, which lie entirely above the diagonal. The columns to the right show the result of successive applications of the algorithm, with the exceedance decreasing one unit at a time. There are five rows, that is, "C" = 5, and the last column displays all paths no higher than the diagonal.


title: Catalan number

text: Using Dyck words, start with a sequence from formula_42. Let formula_43 be the first that brings an initial subsequence to equality, and configure the sequence as formula_44. The new sequence is formula_45.


title: Catalan number

text: This proof uses the triangulation definition of Catalan numbers to establish a relation between "C" and "C".


title: Catalan number

text: Given a polygon "P" with "n" + 2 sides and a triangulation, mark one of its sides as the base, and also orient one of its 2"n" + 1 total edges. There are (4"n" + 2)"C" such marked triangulations for a given base.


title: Catalan number

text: Given a polygon "Q" with "n" + 3 sides and a (different) triangulation, again mark one of its sides as the base. Mark one of the sides other than the base side (and not an inner triangle edge). There are ("n" + 2)"C" such marked triangulations for a given base.


title: Catalan number

text: There is a simple bijection between these two marked triangulations: We can either collapse the triangle in "Q" whose side is marked (in two ways, and subtract the two that cannot collapse the base), or, in reverse, expand the oriented edge in "P" to a triangle and mark its new side.


title: Catalan number

text: This proof is based on the Dyck words interpretation of the Catalan numbers, so "C" is the number of ways to correctly match "n" pairs of brackets. We denote a (possibly empty) "correct" string with "c" and its inverse (where "[" and "]" are exchanged) with "c". Since any "c" can be uniquely decomposed into "c" = [ "c" ] "c", summing over the possible spots to place the closing bracket immediately gives the recursive definition


title: Catalan number

text: Let "b" stand for a "balanced" string of length 2"n"—that is, containing an equal number of "[" and "]", so formula_52. As before, any balanced string can be uniquely decomposed into either [ "c" ] "b" or ] "c" [ "b", so


title: Catalan number

text: This proof is based on the Dyck words interpretation of the Catalan numbers and uses the Cycle lemma of Dvoretzky and Motzkin.


title: Catalan number

text: We call a sequence of X's and Y's "dominating" if, reading from left to right, the number of X's is always strictly greater than the number of Y's. The Cycle lemma states that any sequence of formula_59 X's and formula_60 Y's, where formula_61, has precisely formula_62 dominating cyclic permutations. To see this, arrange the given sequence of formula_63 X's and Y's in a circle. Repeatedly removing XY pairs leaves exactly formula_62 X's. Each of these X's was the start of a dominating cyclic permutation before anything was removed.


title: Catalan number

text: For example, consider formula_65. This is dominating, but none of its cyclic permutations formula_66, formula_67, formula_68 and formula_69 are.


title: Catalan number

text: In particular, when formula_70, there is exactly one dominating cyclic permutation. Removing the leading X from it (a dominating sequence must begin with X) leaves a Dyck sequence. Since there are formula_71 in total, and each one belongs to an equivalence class of size "2n+1" (because "n", "m" and "2n+1" are pairwise coprime), we have formula_72 distinct cycles of formula_73 X's and formula_60 Y's, each of which corresponds to exactly one Dyck sequence, hence formula_75 counts Dyck sequences.


title: Catalan number

text: The "n"×"n" Hankel matrix whose ("i", "j") entry is the Catalan number "C" has determinant 1, regardless of the value of "n". For example, for "n" = 4 we have


title: Catalan number

text: Moreover, if the indexing is "shifted" so that the ("i", "j") entry is filled with the Catalan number "C" then the determinant is still 1, regardless of the value of "n".


title: Catalan number

text: Another feature unique to the Catalan–Hankel matrix is the determinant of the "n"×"n" submatrix starting at "2" has determinant "n" + 1.


title: Catalan number

text: The Catalan sequence was described in the 18th century by Leonhard Euler, who was interested in the number of different ways of dividing a polygon into triangles. The sequence is named after Eugène Charles Catalan, who discovered the connection to parenthesized expressions during his exploration of the Towers of Hanoi puzzle. The reflection counting trick (second proof) for Dyck words was found by Désiré André in 1887.


title: Catalan number

text: In 1988, it came to light that the Catalan number sequence had been used in China by the Mongolian mathematician Mingantu by 1730. That is when he started to write his book "Ge Yuan Mi Lu Jie Fa" "[The Quick Method for Obtaining the Precise Ratio of Division of a Circle]", which was completed by his student Chen Jixin in 1774 but published sixty years later. Peter J. Larcombe (1999) sketched some of the features of the work of Mingantu, including the stimulus of Pierre Jartoux, who brought three infinite series to China early in the 1700s.


title: Catalan number

text: For instance, Ming used the Catalan sequence to express series expansions of formula_82 and formula_83 in terms of formula_84.


title: Catalan number

text: The Catalan numbers can be interpreted as a special case of the Bertrand's ballot theorem. Specifically, formula_14 is the number of ways for a candidate A with "n+1" votes to lead candidate B with "n" votes.


title: Catalan number

text: is a generalization of the Catalan numbers. These are named super-Catalan numbers, per Ira Gessel. These should not confused with the Schröder–Hipparchus numbers, which sometimes are also called super-Catalan numbers.


title: Catalan number

text: For formula_87, this is just two times the ordinary Catalan numbers, and for formula_88, the numbers have an easy combinatorial description.


title: Catalan number

text: Sergey Fomin and Nathan Reading have given a generalized Catalan number associated to any finite crystallographic Coxeter group, namely the number of fully commutative elements of the group; in terms of the associated root system, it is the number of anti-chains (or order ideals) in the poset of positive roots. The classical Catalan number formula_14 corresponds to the root system of type formula_92. The classical recurrence relation generalizes: the Catalan number of a Coxeter diagram is equal to the sum of the Catalan numbers of all its maximal proper sub-diagrams.


title: Aimee Semple McPherson

text: Aimee Elizabeth Semple McPherson (née Kennedy; October 9, 1890 – September 27, 1944), also known as Sister Aimee or Sister, was a Canadian Pentecostal evangelist and media celebrity in the 1920s and 1930s, famous for founding the Foursquare Church. McPherson pioneered the use of broadcast mass media for wider dissemination of both religious services and appeals for donations, using radio to draw in both additional audience and revenue with the growing appeal of popular entertainment and incorporating stage techniques into her weekly sermons at Angelus Temple, an early megachurch.


title: Aimee Semple McPherson

text: In her time, she was the most publicized Protestant evangelist, surpassing Billy Sunday and other predecessors. She conducted public faith healing demonstrations involving tens of thousands of participants. McPherson's view of the United States as a nation founded and sustained by divine inspiration influenced later pastors.


title: Aimee Semple McPherson

text: National news coverage focused on events surrounding her family and church members, including accusations that she fabricated her reported kidnapping. McPherson's preaching style, extensive charity work and ecumenical contributions were a major influence on 20th century Charismatic Christianity.


title: Aimee Semple McPherson

text: McPherson was born Aimee Elizabeth Kennedy in Salford, Ontario, Canada, to James Morgan and Mildred Ona (Pearce) Kennedy (1871–1947). She had early exposure to religion through her mother, Mildred, who worked with the poor in Salvation Army soup kitchens. As a child she would play "Salvation Army" with classmates and preach sermons to dolls.


title: Aimee Semple McPherson

text: As a teenager, McPherson strayed from her mother's teachings by reading novels and attending movies and dances, activities disapproved of by the Salvation Army and her father's Methodist religion. In high school, she was taught the Theory of Evolution. She began to ask questions about faith and science, but was unsatisfied with the answers. She wrote to a Canadian newspaper, questioning the taxpayer-funded teaching of evolution. This was her first exposure to fame, as people nationwide responded to her letter, and the beginning of a lifelong anti-evolution crusade.


title: Aimee Semple McPherson

text: While attending a revival meeting in 1907, McPherson met Robert James Semple, a Pentecostal missionary from Ireland. She dedicated her life to Jesus and converted to Pentecostalism. At the meeting, she became enraptured by Semple and his message. After a short courtship, they were married in an August 1908 Salvation Army ceremony. Semple supported them as a foundry worker and preached at the local Pentecostal mission. They studied the Bible together, then moved to Chicago and joined William Durham's Full Gospel Assembly. Durham instructed her in the practice of interpretation of tongues.


title: Aimee Semple McPherson

text: After embarking on an evangelistic tour to China, both contracted malaria. Semple also contracted dysentery, of which he died in Hong Kong. McPherson recovered and gave birth to their daughter, Roberta Star Semple. On board a ship returning to the United States, she held religious services and classes.


title: Aimee Semple McPherson

text: After her recuperation in the United States, McPherson joined her mother Mildred working with the Salvation Army. While in New York City, she met accountant Harold Stewart McPherson. They were married in 1912, moved to Providence, Rhode Island, and had a son, Rolf Potter Kennedy McPherson, in 1913.


title: Aimee Semple McPherson

text: During this time, McPherson felt as though she denied her "calling" to go preach. Struggling with emotional distress and obsessive–compulsive disorder, she would weep and pray. In 1914, she fell seriously ill with appendicitis. McPherson later stated that after a failed operation, she heard a voice asking her to go preach. After accepting the voice's challenge, she said, she was able to turn over in bed without pain. In 1915, her husband returned home and discovered that McPherson had left him and taken the children. A few weeks later, he received a note inviting him to join her in evangelistic work.


title: Aimee Semple McPherson

text: Harold McPherson followed her to bring her home, but changed his mind after seeing her preaching, and joined her in evangelism, setting up tents for revival meetings and preaching. The couple sold their house and lived out of their "Gospel Car". Harold McPherson, despite his initial enthusiasm, wanted a more stable and predictable life, and returned to Rhode Island. In 1918 he filed for separation, then petitioned for divorce, citing abandonment; the divorce was granted in 1921.


title: Aimee Semple McPherson

text: McPherson remarried in 1932 to actor and musician David Hutton. After she fell and fractured her skull, she visited Europe to recover. While there, she was angered to learn Hutton was billing himself as "Aimee's man" in his cabaret singing act and was frequently photographed with scantily clad women. Hutton's personal scandals were damaging the reputation of the Foursquare Gospel Church and its leader. McPherson and Hutton separated in 1933 and divorced in 1934. McPherson later publicly repented of the marriage for both theological and personal reasons and later rejected gospel singer Homer Rodeheaver when he proposed marriage in 1935.


title: Aimee Semple McPherson

text: As part of William Durham's Full Gospel Assembly in Chicago, McPherson became known for interpreting glossolalia, translating the words of people speaking in tongues. Unable to find fulfillment as a housewife, in 1913, McPherson began evangelizing, holding tent revivals across the Sawdust Trail. McPherson quickly amassed a large following, often having to relocate to larger buildings to accommodate growing crowds. She emulated the enthusiasm of Pentecostal meetings but avoided their unbridled chaos, in which participants would shout, tremble on the floor, and speak in tongues. McPherson set up a separate tent area for such displays of religious fervor, which could be off-putting to larger audiences.


title: Aimee Semple McPherson

text: In 1916, McPherson embarked on a tour of the Southern United States, and again in 1918 with Mildred Kennedy. Standing on the back seat of their convertible, McPherson preached sermons over a megaphone.


title: Aimee Semple McPherson

text: In 1917, she started a magazine, "Bridal Call", for which she wrote articles about women's roles in religion; she portrayed the link between Christians and Jesus as a marriage bond. Along with taking women's roles seriously, the magazine contributed to transforming Pentecostalism into an ongoing American religious presence.


title: Aimee Semple McPherson

text: In Baltimore in 1919 she was first "discovered" by newspapers after conducting evangelistic services at the Lyric Opera House, where she performed faith-healing demonstrations. During these events the crowds in their religious ecstasy were barely kept under control. Baltimore became a pivotal point for her early career.


title: Aimee Semple McPherson

text: She was ordained evangelist by the Assemblies of God USA in 1919. However, she ended her association with the Assemblies of God USA in 1922.


title: Aimee Semple McPherson

text: In 1918, McPherson moved to Los Angeles. Mildred Kennedy rented the 3,500-seat Philharmonic Auditorium, and people waited for hours to get into the crowded venue. Afterwards, attendees of her meetings built a home for her family. At this time, Los Angeles was a popular vacation destination. Rather than touring the United States, McPherson chose to stay in Los Angeles, drawing audiences from both visitors and the city's burgeoning population. Her ministry to tourists allowed her message to spread nationwide.


title: Aimee Semple McPherson

text: For several years, she traveled and raised money for the construction of a large, domed church in the Echo Park area of Los Angeles, named Angelus Temple, in reference to the Angelus bell and to angels. Not wanting to incur debt, McPherson found a construction firm willing to work with her as funds were raised "by faith", beginning with $5,000 for the foundation. McPherson mobilized diverse groups to fund and build the church, by means such as selling chairs for Temple seating. In his book 'Growing up in Hollywood' Robert Parrish describes in detail attending one of her services.


title: Aimee Semple McPherson

text: Raising more money than expected, McPherson altered the plans and built a "megachurch". The endeavor cost contributors around $250,000. Costs were kept down by donations of building materials and labor. The dedication took place in 1923.


title: Aimee Semple McPherson

text: Enrollment grew to over 10,000, and Angelus Temple was advertised as the largest single Christian congregation in the world. According to church records, the Temple received 40 million visitors within the first seven years.


title: Aimee Semple McPherson

text: McPherson developed a church organization to provide for physical as well as spiritual needs. McPherson mobilized people to get involved in charity and social work, saying that "true Christianity is not only to be good but to do good." The Temple collected donations for humanitarian relief including for a Japanese disaster and a German relief fund. Men released from prison were found jobs by a "brotherhood". A "sisterhood" sewed baby clothing for impoverished mothers.


title: Aimee Semple McPherson

text: In June 1925, after an earthquake in Santa Barbara McPherson interrupted a radio broadcast to request food, blankets, clothing, and emergency supplies. In 1928, after a dam failed and the ensuing flood left up to 600 dead, McPherson's church led the relief effort. In 1933, an earthquake struck and devastated Long Beach. McPherson quickly arranged for volunteers offering blankets, coffee, and doughnuts. McPherson persuaded fire and police departments to assist in distribution. Doctors, physicians, and dentists staffed her free clinic that trained nurses to treat children and the elderly. To prevent the power from being turned off to homes of overdue accounts during the winter, a cash reserve was set up with the utility company.


title: Aimee Semple McPherson

text: Drawing from her childhood experience with the Salvation Army, in 1927 McPherson opened a commissary at Angelus Temple offering food, clothing, and blankets. She became active in creating soup kitchens, free clinics, and other charitable activities during the Great Depression, and fed an estimated 1.5 million. Volunteer workers filled commissary baskets with food and other items, as well as Foursquare Gospel literature. When the government shut down the free school-lunch program, McPherson took it over. Her giving "alleviated suffering on an epic scale".


title: Aimee Semple McPherson

text: In 1932, the commissary was raided by police, allegedly to locate a still used to make brandy out of donated apricots. As a consequence, the commissary was briefly shut down, and the staff was let go. However, students from her Foursquare Gospel Church's L.I.F.E. Bible College filled in.


title: Aimee Semple McPherson

text: As McPherson refused to distinguish between the "deserving" and the "undeserving," her temple commissary became known as an effective and inclusive aid institution, assisting more families than other public or private institutions. Because her programs aided nonresidents such as migrants from other states and Mexico, she ran afoul of California state regulations. Though temple guidelines were later officially adjusted to accommodate those policies, helping families in need was a priority, regardless of their place of residence.


title: Aimee Semple McPherson

text: In August 1925, McPherson chartered a plane to Los Angeles to give her Sunday sermon. Aware of the opportunity for publicity, she arranged for followers and press at the airport. The plane failed after takeoff and the landing gear collapsed, sending the nose of the plane into the ground. McPherson used the experience as the narrative of an illustrated sermon called "The Heavenly Airplane", featuring the devil as pilot, sin as the engine, and temptation as propeller.


title: Aimee Semple McPherson

text: On another occasion, she described being pulled over by a police officer, calling the sermon "Arrested for Speeding". Dressed in a traffic cop's uniform, she sat in a police motorcycle and blared the siren. One author in attendance wrote that she drove the motorcycle across the access ramp to the pulpit, slammed the brakes, and raised a hand to shout "Stop! You're speeding to Hell!"


title: Aimee Semple McPherson

text: McPherson employed a small group of artists, electricians, decorators, and carpenters, who built sets for each service. Religious music was played by an orchestra. McPherson also worked on elaborate sacred operas. One production, "The Iron Furnace", based on the Exodus story, saw Hollywood actors assist with obtaining costumes.


title: Aimee Semple McPherson

text: Though McPherson condemned theater and film as the devil's workshop, its techniques were co-opted. She became the first woman evangelist to adopt cinematic methods to avoid dreary church services. Serious messages were delivered in a humorous tone. Animals were frequently incorporated. McPherson gave up to 22 sermons a week, including lavish Sunday night services so large that extra trolleys and police were needed to help route the traffic through Echo Park. To finance the Temple and its projects, collections were taken at every meeting.


title: Aimee Semple McPherson

text: McPherson preached a conservative gospel, but used progressive methods, taking advantage of radio, movies, and stage acts. She attracted some women associated with modernism, but others were put off by the contrast between her message and her presentation.


title: Aimee Semple McPherson

text: The battle between fundamentalists and modernists escalated after World War I. Fundamentalists generally believed their faith should influence every aspect of their lives. Despite her modern style, McPherson aligned with the fundamentalists in seeking to eradicate modernism and secularism in homes, churches, schools, and communities.


title: Aimee Semple McPherson

text: The appeal of McPherson's revival events from 1919 to 1922 surpassed any touring event of theater or politics in American history. She broke attendance records recently set by Billy Sunday and frequently used his temporary tabernacle structures to hold her meetings. One such revival was held in a boxing ring, and throughout the boxing event, she carried a sign reading "knock out the Devil". In San Diego the city called in the National Guard to control a revival crowd of over 30,000 people.


title: Aimee Semple McPherson

text: McPherson's ability to draw crowds was also greatly assisted by her faith healing presentations. According to Nancy Barr Mavity, an early McPherson biographer, the evangelist claimed that when she laid hands on sick or injured persons, they got well because of the power of God in her. During a 1916 revival in New York, a woman in advanced stages of rheumatoid arthritis was brought to the altar by friends. McPherson laid hands on her and prayed, and the woman apparently walked out of the church without crutches. McPherson's reputation as a faith healer grew as people came to her by the tens of thousands. McPherson's faith-healing practices were extensively covered in the news and were a large part of her early-career success. Over time, though, she largely withdrew from faith-healing, but still scheduled weekly and monthly healing sessions which remained popular until her death.


title: Aimee Semple McPherson

text: McPherson published the weekly "Foursquare Crusader." She began broadcasting on radio in the early 1920s. In April 1922, she became the first woman to preach a sermon wirelessly. With the opening of Foursquare Gospel-owned KFSG in 1924, she became the second woman granted a broadcast license by the Department of Commerce, which supervised broadcasting at the time.


title: Aimee Semple McPherson

text: In October 1922, she explained her vision of "Foursquare Gospel" (or "Full Gospel") in a sermon in Oakland, California. This represents the 4 aspects of the ministry of Jesus Christ; Savior, Baptizer with the Holy Ghost, Healer and King.


title: Aimee Semple McPherson

text: McPherson racially integrated her tent meetings and church services. On one occasion, as a response to integration, Ku Klux Klan members were in attendance, but after the service, their hoods and robes were found on the ground nearby. She is also credited with helping Hispanic ministries in Los Angeles.


title: Aimee Semple McPherson

text: McPherson caused concern among some Los Angeles churches. Though she shared many of their fundamentalist beliefs, her lavish sermons and faith-healing events, along with her status as a female divorcee, were unprecedented, and her style of dress was drawing emulators. Her illustrated sermons attracted criticism from some clergy members for allegedly turning the Gospel message into mundane entertainment. Faith healing was considered to be unique to Apostolic times. Rival radio evangelist Robert P. Shuler published a pamphlet titled "McPhersonism," in which he called her ministry "out of harmony with God's word." Debates such as the Bogard-McPherson debate in 1934 drew further attention to the controversy.


title: Aimee Semple McPherson

text: The newly forming Assemblies of God denomination worked with her for a time, but it encouraged her to separate her church from established Protestant faiths. McPherson resisted trends to isolate her church as a denomination and continued her evangelical coalition-building. She was helped by the establishment of L.I.F.E. Bible College adjacent to the Temple, which was intended to train ministers so they would be able to share her new "Foursquare Gospel" both nationally and internationally. Methodist minister Frank Thompson ran the college, teaching students the doctrines of John Wesley, while McPherson and others infused them with Pentecostal ideals. McPherson's efforts eventually led Pentecostals, who were previously on the periphery of Christianity, into mainstream American evangelicalism.


title: Aimee Semple McPherson

text: By early 1926, McPherson had become one of the most charismatic and influential women and ministers of her time. Her fame equaled, to name a few, Charles Lindbergh, Johnny Weissmuller, Jack Dempsey, Babe Ruth, Ty Cobb, Knute Rockne, Bobby Jones, Louise Brooks, and Rudolph Valentino. She was a major American phenomenon, who along with some other high profile preachers of the time, unlike Hollywood celebrities, could be admired by their adoring public, "without apparently compromising their souls."


title: Aimee Semple McPherson

text: McPherson crusaded against Darwinian evolution and became a supporter of William Jennings Bryan during the 1925 Scopes trial, about local laws prohibiting the teaching of human evolution. Bryan and McPherson worked together in the Temple, and they believed that Darwinism undermined morality, "poisoning the minds of the children of the nation." McPherson organized an all-night prayer service, preceded by a Bible parade through Los Angeles."


title: Aimee Semple McPherson

text: McPherson's political alignment was undisclosed. She endorsed Herbert Hoover, but threw her support behind Franklin D. Roosevelt and his social programs after his election. She patronized organized labor, preaching that a gangster's money was "no more unclean than the dollars of the man who amasses his millions from underpaid factory workers". She was more cautious when labor strikes resulted in violent uprisings, and worried about Communism's influence in labor unions. McPherson opposed both Communism and fascism as totalitarian rule; Communism ruling without God and fascism wrongly stating to represent the power of God.


title: Aimee Semple McPherson

text: McPherson did not align herself consistently with any broad conservative or liberal political agenda. Instead, she wanted Christianity to occupy a central place in national life. The Foursquare Gospel Church currently qualifies the evangelist's views "in light of the political and religious climate of the 1920s, 30s, and 40s," drawing a contrast between her approach and "today's extreme fundamentalist, right-wing Christianity." She was also among the first prominent Christian ministers to defend the establishment of a Jewish homeland in Palestine.


title: Aimee Semple McPherson

text: The reported kidnapping of Aimee Semple McPherson caused a media frenzy and changed her life and career. After disappearing in May 1926, she reappeared in Mexico five weeks later, stating she had been held for ransom in a desert shack. Subsequent grand-jury inquiries precipitated continued public interest.


title: Aimee Semple McPherson

text: On May 18, 1926, McPherson disappeared from Ocean Park Beach in Santa Monica, CA. Presuming she had drowned, searchers combed the area. McPherson sightings were reported around the county, often many miles apart. The Temple received calls and letters claiming knowledge of McPherson, including ransom demands. After weeks of unpromising leads, Mildred Kennedy believed her daughter to be dead.


title: Aimee Semple McPherson

text: After the Temple's memorial service, three days later on June 23, Kennedy received a phone call from Douglas, Arizona. McPherson was alive in a Douglas hospital, and relating her story to officials.


title: Aimee Semple McPherson

text: McPherson said that at the beach she had been approached by a couple who wanted her to pray over their sick child. After walking with them to their car, she was shoved inside. A cloth laced with chloroform was held against her face, causing her to pass out. Eventually, she was moved to a shack in the Mexican desert. When her captors were away, McPherson escaped out a window and traveled through the desert for 11–17 hours and an estimated 17–20 miles (27–32 km), reaching Agua Prieta, Sonora, a Mexican border town, at around 1:00 a.m. Collapsing near a house, the evangelist was taken by locals to adjacent Douglas.


title: Aimee Semple McPherson

text: Her return to Los Angeles was greeted by 30,000–50,000 people, a greater turnout than President Woodrow Wilson's 1919 visit to Los Angeles.


title: Aimee Semple McPherson

text: Los Angeles prosecutors had varying theories why she disappeared, among them a publicity stunt, and finally contended that McPherson ran off with a former employee, Kenneth Ormiston, staying with him in a California resort town cottage he had rented. After leaving the cottage at the end of May, the pair traveled for the next three weeks and remained hidden. Around June 22, Ormiston drove McPherson to Mexico, dropping her off 3 miles outside of nearby Agua Prieta, where she walked the remaining distance. In contrast, McPherson consistently maintained her kidnapping story, and defense witnesses corroborated her assertions.


title: Aimee Semple McPherson

text: Much of the evidence asserted against McPherson came from reporters, who passed it on to police. The bulk of the investigation against McPherson was funded by Los Angeles-area newspapers at an estimated amount of $500,000. The secrecy of California's grand jury proceedings was ignored by both sides as the Los Angeles prosecution passed new developments to the press, while the evangelist used her radio station to broadcast her side of the story.


title: Aimee Semple McPherson

text: On November 3, the case was to be moved to jury trial set for January 1927, charging McPherson, her mother, and other defendants with criminal conspiracy, perjury and obstruction of justice. If convicted, McPherson faced a maximum prison time of 42 years. However, the prosecution's case developed credibility issues. Witnesses changed testimonies and evidence often appeared to have suspicious origins or was mishandled and lost in custody. On January 2, Ormiston identified another woman as the companion who stayed with him at the cottage. All charges against McPherson and associated parties were dropped for the lack of evidence on January 10. However, months of unfavorable news reports produced enduring public belief in McPherson's wrongdoing.


title: Aimee Semple McPherson

text: Allegations of love affairs directed against McPherson started during the 1926 kidnapping trial. Suspected lovers generally denied involvement. Alarmed by her style of dress and involvement with Hollywood, a Temple official hired detectives in 1929 to shadow McPherson. The detectives found no evidence of affairs. After McPherson's death, unsubstantiated allegations of affairs continued to emerge. Canadian journalist Gordon Sinclair claimed a 1934 affair in his autobiography. Another claim by comedian Milton Berle alleged a brief affair with the evangelist. Berle asserted that he met McPherson in Los Angeles where both were doing a charity show. Another book by Berle published during McPherson's life did not claim an affair. Biographer Matthew Sutton asserted that Berle's story of a crucifix in McPherson's bedroom was inconsistent with the coolness of Pentecostal-Catholic relations during that era. Other contradictions in Milton Berle's story were noted as well. During that period, from publications, church and travel records, the evangelist's appearances and whereabouts could be traced almost every day, and there was no record of the charity show Berle alleged. McPherson had her own charities. Moreover, she was incapacitated with illness a full five months of that year, By 1931, McPherson kept herself chaperoned to guard against allegations."


title: Aimee Semple McPherson

text: After the kidnapping, McPherson remained nationally famous and continued her ministry, but fell out of press favor. The media, which once dubbed her a "miracle worker", focused on disturbances in her household, including difficulties with her mother.


title: Aimee Semple McPherson

text: Despite this, up to 10% of the population in Los Angeles held Temple membership, and movie studios competed to offer her contracts. Believing that film had the potential to transform Christianity, McPherson explored Hollywood culture and appeared in newsreels alongside Mary Pickford, Frances Perkins, and Franklin D. Roosevelt. She lost weight, cut and dyed her hair, began to wear makeup and jewelry, and became known for stylish dress. This solicitation of fame was off-putting to some church members who preferred her former uniform of a navy cape over a white servant's dress.


title: Aimee Semple McPherson

text: In 1927, McPherson set out on a tour, taking advantage of the publicity from her kidnapping story to preach. She even visited nightclubs, including Texas Guinan's speakeasy, where she addressed the crowd. Her visits to bars added to McPherson's notoriety: newspapers reported heavily on them; and rumors erroneously implied she was drinking, smoking and dancing.


title: Aimee Semple McPherson

text: Mildred Kennedy did not agree with McPherson's strategy of tearing down barriers between the secular and religious. In 1927, Kennedy left the Temple, along with other church members including 300 members of the choir. Attempting to curtail her daughter's influence, Kennedy initiated a staff-member confidence vote against McPherson, but lost. The two had argued over management and McPherson's changing dress and appearance. Kennedy's administrative skills had been crucial to growing McPherson's ministry and maintaining Temple activities. A series of management staff replaced Kennedy, and the Temple became involved in various unsuccessful projects such as hotel building, cemetery plots, and land sales, plummeting into debt. In response to the difficulties, Kennedy returned in 1929, but because of continued disagreements with McPherson, resigned again in July 1930. The following month, McPherson had a physical and nervous breakdown. For 10 months, she was absent from the pulpit, diagnosed with acute acidosis.


title: Aimee Semple McPherson

text: When she returned, she introduced her "Attar of Roses" sermon, based on the Song of Solomon. In October 1931 McPherson held a revival in Boston, a city with large Unitarian, Episcopalian, and Catholic populations, traditionally hostile to Pentecostal messages. On opening night, McPherson spoke to fewer than 5,000 in the 22,000-seat sports arena. The following day, her campaign's tone shifted and attendance climbed sharply. The final day of afternoon and evening services saw 40,000 people attending, exceeding the stadium venue's capacity and breaking attendance records.


title: Aimee Semple McPherson

text: McPherson's revival in New York City was less fruitful due to her sensationalistic reputation. McPherson went on to Washington D.C. and Philadelphia, and visited 21 states. A full crew of musicians, scene designers, and costumers accompanied McPherson. In her last national revival tour, 1933–1934, two million persons heard 336 sermons.


title: Aimee Semple McPherson

text: McPherson was not a radical literalist. She believed that the creation story in the book of Genesis allowed great latitude of interpretation, and did not insist on Young Earth creationism. In another meeting with students, McPherson heard an assertion that Christianity had outlived its usefulness. The encounter persuaded her to travel and gain new perspectives. In 1935, McPherson embarked on a six-month world tour, partly to study the women's movement in connection with India's independence struggle and speak with Mahatma Gandhi, who gave her a sari made on his spinning wheel. Impressed with Gandhi, McPherson thought that he might secretly lean toward Christianity. Other highlights included visiting Shwedagon Pagoda in Myanmar, hearing Benito Mussolini speak in Italy, and sitting on a wrecked military vehicle on a still-uncleared battlefield in Verdun, France.


title: Aimee Semple McPherson

text: In mid-1936, a delegation associated with the 1906 Azusa Street Mission Revivals, including African-American Evangelist Emma Cotton, asked to use the Angelus Temple for their 30th anniversary celebration. Cotton and McPherson organized a series of meetings, also marking McPherson's re-identification with Pentecostalism. McPherson's experiments with celebrity had been less successful than she hoped, and alliances with other church groups were failing or defunct. Therefore, she looked to her spiritual origins and considered reintroducing Pentecostal elements into her public meetings. Temple officials were concerned that the Azusa people might bring "wildfire and Holy Rollerism."


title: Aimee Semple McPherson

text: Out of the Azusa Street Revival, black leaders and other minorities appeared on her pulpit, including Charles Harrison Mason, an African American and founder of the Churches of God in Christ, a significant Pentecostal leader. McPherson recommitted herself to the dissemination of "classic Pentecostalism", expressing concern that the Foursquare approach was in danger of becoming too "churchy". For the first time since the Temple opened, McPherson began to publicly speak in tongues.