title: Pristina

text: According to the Kosovo Agency of Statistics (KAS) estimate from the 2011 census, there were 198,897 people residing in Pristina Municipality, representing the most populous city and municipality of Kosovo. The urban population of Pristina Municipality was approximately 160,000, while the rural population was around 37,000. With a population density of 380,3 people per square kilometre, Pristina is the third most densely populated municipality of Kosovo.


title: Pristina

text: In terms of ethnicity, Pristina Municipality was 97.77% Albanian, 1.08% Turkish, 0.28% Ashkali, 0.22% Serbian, 0.2% Bosniak, 0.1% Gorani and 0.03% Romani. By language, 98.09% spoke Albanian as a first language. Other spoken languages in Pristina Municipality were Turkish (1.04%), Serbian (0.25%) and Romani (0.03%). By religion, there were 193,474 (97.27%) Muslims, 1,170 (0.59%) Roman Catholics, 480 (0.24%) Orthodox, 344 (0.17%) of other religions and 660 (0.33%) irreligious.


title: Pristina

text: Kosovo is a secular state with no state religion. The freedom of belief, conscience and religion is explicitly guaranteed in the Constitution of Kosovo. Islam and Christianity are the most widely practiced religions among the people of Pristina. The remaining 1.9% of the population reported having no religion, or another religion, or did not provide an adequate answer. Pristina has centres of worship for a multitude of faiths for its population. The Cathedral of Pristina is perhaps the largest cathedral in Kosovo and is named in honour of the Albanian Roman Catholic nun and missionary, Mother Teresa. Some of the mosques of Pristina, among others the Imperial Mosque and Çarshi Mosque, are centuries old and were built during the Middle Ages by the Ottomans.


title: Pristina

text: As the capital city of the Republic of Kosovo, it is the center of cultural and artistic development of all Albanians that live in Kosovo. Pristina is home to the largest cultural institutions of the country, such as the National Theatre of Kosovo, National Archaeology, Ethnography and Natural science Museum, National Art Gallery and the Ethnological Museum. The National Library of Kosovo has than 1.8 million books, periodicals, maps, atlases, microfilms and other library materials.


title: Pristina

text: There are many foreign cultural institutions in Pristina, including the Albanian Albanological Institute,


title: Pristina

text: Starting in 1945, the Yugoslav authorities began constructing a modern Pristina with the idea of "destroy the old, build the new". This modernization led to major changes in the structure of the buildings, their function and their surrounding environment.


title: Pristina

text: However, numerous types of monuments have been preserved, including four mosques, a restored orthodox church, an Ottoman bath, a public fountain, a clock tower, several traditional houses as well as European-influenced architecture buildings such as Kosovo Museum. These symbolize the historical and cultural character of Pristina as it was developed throughout centuries in the spirit of conquering empires (Roman, Byzantine, Ottoman and Austro-Hungarian).


title: Pristina

text: The "Hivzi Sylejmani" library was founded 70 years ago and it is one of the largest libraries regarding the number of books in its inventory which is nearly 100.000. All of those books are in service for the library's registered readers.


title: Pristina

text: The "Mbretëresha e Dardanisë" "(Queen of Dardania)" or "Hyjnesha ne Fron" "(The Goddess on the Throne)" is an artifact that was found during some excavations in 1955 in the area of Ulpiana, a suburb of Pristina. It dates back to 3500 BC in the Neolithic Era and it is made of clay. In Pristina there is also "Hamami i Qytetit"(The City Bath) and the house of Emin Gjika which has been transformed to the Ethnographic Museum. Pristina also has its municipal archive which was established in the 1950s and holds all the records of the city, municipality and the region.


title: Pristina

text: Albanian music is considered to be very rich in genres and their development. But before talking about genre development, a key point that has to be mentioned is without doubt the rich folklore of Kosovo most of which unfortunately has not been digitalized and saved in archives. The importance of folklore is reflected in two main keys, it is considered a treasure" of cultural heritage of our country and it helps to enlighten the Albanian history of that time, and the importance of that is of a high level especially when mentioning the circumstances of our territory in that time.


title: Pristina

text: Folklore has also served as inspiration and influence in many fields including music composition in the next generations


title: Pristina

text: One of the most notable and very first composers, Rexho Mulliqi in whose work, folklore inspiration and influence is very present.


title: Pristina

text: When highlighting the music creativity and its starts in Kosovo and the relation between it and the music creativity in Albania even though they have had their development in different circumstances, it is proved that they share some characteristics in a very natural way. This fact shows that they belong to one "Cultural Tree".


title: Pristina

text: Some of few international music artists of Albanian heritage are born and raised in the city including Rita Ora, Dua Lipa and Era Istrefi.


title: Pristina

text: The city of Pristina hosts only three active theatres such as the National Theater, Oda and Dodona Theatre placed in center of Pristina. They offers live performances every week. The National Theatre is placed in the middle downtown of the city, near the main government building and was founded in 1946. ODA Theatre is situated in the Youth Centre Building and Dodona Theatre is placed in Vellusha district, which is near Ibrahim Rugova Square.


title: Pristina

text: The National Theater of Kosovo is the highest ranked theater institution in the country which has the largest number of productions. The theater is the only public theater in Kosovo and therefore it is financed by Ministry of Culture, Youth and Sport. This theater has produced more than 400 premieres which have been watched by more than 3 million spectators.


title: Pristina

text: Festivals and events are one of some things that people in Pristina enjoy properly, without rushing to get it over with. Despite having quite a small territorial space, Pristina has a pleasant number of festivals and events. The diversity of festivals makes it possible for people of different tastes to find themselves in a city this small.


title: Pristina

text: The Prishtina International Film Festival screens prominent international cinema productions in the Balkan region and beyond, and draws attention to the Kosovar film industry. It was created after the 2008 Kosovo declaration of independence. After its independence in 2008, Kosovo looked for ways to promote its cultural and artistic image.


title: Pristina

text: One of major festivals include the Chopin Piano Fest Pristina that was established for the first time on the occasion of the 200th birth anniversary of Frédéric Chopin in 2010 by the Kosovo Chopin Association. The festival is becoming a traditional piano festival held in spring every year. It is considered to be a national treasure. In its 5 years of formation it has offered interpretations by both world-famous pianists such as Peter Donohoe, Janina Fialkowska, Kosovo-Albanian musicians of international renown like Ardita Statovci, Alberta Troni and local talents. The Festival strives to promote the art of interpretation, the proper value of music and the technicalities that accompany it. The Festival has served as inspiration for the formation of other music festivals like Remusica and Kamerfest.


title: Pristina

text: The DAM Festival Pristina is one of the most prominent cultural events taking place in the capital. It is an annual music festival which gathers young and talented national and international musicians from all over the world. This festival works on enriching the Kosovar cultural scene with the collision of the traditional and the contemporary. The festival was founded by back then art student, now well known TV producer, musician, journalist and manager of the Kosovo's Philharmonic Orchestra, Dardan Selimaj.


title: Pristina

text: Pristina had always a development in trading due to its position of the Balkan trade routes. Fairs started since the medieval period, at the time when it was famous for its annual trade fairs and its goat hide and goat hair articles. Despite that fact Pristina, or Kosovo in general is not known for occurrence of fairs. With the development of culture and especially after the last war in 1999, Pristina had a progress on holding these kinds of events. Every year various types of trade fairs take place in the capital city. The essence of these fairs is usually temporary; some last only an afternoon while others may last around 3 days, a week or even longer. They have grown in size and importance over the years. These fairs are organized annually and are open to trade visitors and public. The number of exhibitors and visitors is usually very high.


title: Pristina

text: Pristina is the center of sport in Kosovo, where activity is organized across amateur and professional levels, sport organizations and clubs, regulated by the Kosovo Olympic Committee and the Ministry of Culture, Youth and Sport. Sport is organized in units called Municipal Leagues. There are seven Municipal Leagues in Pristina. The Football Municipal consists of 18 clubs, the Basketball Municipal 5 clubs, the Handball Municipal 2 clubs, Table Tennis and Chess 6 clubs each, the Karate Municipal 15 and the Tennis Municipal 2 clubs.


title: Pristina

text: Football is the most popular sport in the city. It is represented by FC Prishtina, which plays their home games in the Fadil Vokrri Stadium. Basketball has been also one of the most popular sports in Pristina and is represented by KB Prishtina. It is the most successful basketball club in Kosovo and is part of the Balkan League. Joining it in the Superleague is another team from Pristina, RTV 21.


title: Pristina

text: Streetball is a traditionally organised sport and cultural event at the Germia Park since 2000. Apart from indoor basketball success, Che Bar team has been crowned the champion of the national championship in 2013. This victory coincided with Streetball Kosovo's acceptance in FIBA. Handball is also very popular. Pristina's representatives are recognised internationally and play international matches.


title: Alessandra Mussolini

text: Alessandra Mussolini (born 30 December 1962) is an Italian politician, the granddaughter of Benito Mussolini, and a former actress and model who served as a Member of the European Parliament for Forza Italia. In 2004, she became the first woman to lead a political party in Italy. She was a member of the Chamber of Deputies from 2008 to 2013 and the Italian Senate from 2013 to 2014, she was elected under The People of Freedom which is now part of Forza Italia. She was elected to the European Parliament in 2014.


title: Alessandra Mussolini

text: She was the founder and leader of the national conservative political party Social Action; from 2004 until 2008, Mussolini also served as a Member of the European Parliament, and she has been a member of the Chamber of Deputies, the lower house of the Italian Parliament, for The People of Freedom. Mussolini left politics, temporarily, in December 2020.


title: Alessandra Mussolini

text: In November 2022 she returned as MEP, succeeding Antonio Tajani, after his election to the Chamber of Deputies.


title: Alessandra Mussolini

text: Alessandra Mussolini was born in Rome, the daughter of Romano Mussolini, the fourth son of Benito Mussolini, fascist dictator of Italy from 1922 to 1943, and Anna Maria Villani Scicolone (born 11 May 1938, Rome). Actress Sophia Loren is her maternal aunt.


title: Alessandra Mussolini

text: From 1976 to 1980 she went to high school at the American Overseas School of Rome. She graduated in 1994 from Sapienza University of Rome, where she got her Master of Science in medicine and surgery.


title: Alessandra Mussolini

text: She married customs policeman Mauro Floriani on 28 October 1989. Contrary to tradition, she proposed to him. Together they have three children, Caterina, Clarissa, and Romano — the last named after his grandfather. Later, the children adopted their mother's surname, but she went through a complex legal process to allow them to do so. She has since campaigned for Italian law to be changed to allow all children to take their mother's last name if they wish.


title: Alessandra Mussolini

text: Her husband was one of the accused scheduled to appear in court for a child prostitution trial in 2015. In 2013, around 50 men—among them professionals, priests, and politicians—were accused of paying two teenage girls, aged 14 and 15, for sexual services in Rome.


title: Alessandra Mussolini

text: She is first cousin once-removed to Caio Giulio Cesare Mussolini, Benito Mussolini's great-grandson, who ran for the Fratelli d’Italia party in the 2019 European Parliament election. She considers herself Roman Catholic, although she does not attend Mass regularly.


title: Alessandra Mussolini

text: In 2001, Mussolini was involved in a physical altercation while filming for a Porta a Porta talk show episode on sexual harassment. She was verbally attacked by Katia Bellillo, then Minister for Equal Opportunities, who got up and approached menacingly versus Mussolini, who called her an "ugly communist" who should "go and live in Cuba."


title: Alessandra Mussolini

text: Mussolini was taken under the wing of her aunt Sophia Loren for a while and started a career as an actress in the Italian film industry during the 1970s. "A Special Day" (1977), in which she had a minor role as "Maria Luisa," won an American Golden Globe Award for Best Foreign Language Film and was nominated for an Academy Award for Best Foreign Language Film.


title: Alessandra Mussolini

text: During 1982, Mussolini released a pop music album of romantic songs under the title "Amore" on Alfa Records; the album was released only in Japan and has since become something of a collectors item.


title: Alessandra Mussolini

text: Mussolini also appeared as a glamour model, including on the cover of two European editions of "Playboy", in Italy (August 1983) and Germany (November 1983). "When you are an actress, you are dealing with the body. Every actress does topless and stuff like this; you have to," she has said.


title: Alessandra Mussolini

text: Mussolini continued as an actress into the 1980s. Some of the films she featured in were made for Italian television. However, she still acted in standard cinematic films, such as "The Assisi Underground" in which she played a nun; the movie focused on the Roman Catholic Church rescuing Italian Jews from the Nazis in 1943. She starred in her final film in 1990 and then left the film industry to continue studying after a producer asked her to change her name.


title: Alessandra Mussolini

text: In 1992, Alessandra Mussolini was elected to parliament in a Naples constituency as a member of the Movimento Sociale Italiano (MSI).


title: Alessandra Mussolini

text: After the Italian general elections of April 2008, Mussolini served as a member of the Italian parliament within Silvio Berlusconi's alliance of right wing parties, The People of Freedom.


title: Alessandra Mussolini

text: In the Italian general election of February 2013, she was elected to the Senate of the Republic as a member of The People of Freedom. The party was transformed into a new Forza Italia in November 2013. In the 2014 European Parliament election, Mussolini was elected to the EP for Forza Italia.


title: Alessandra Mussolini

text: Mussolini was a candidate for the post of mayor of Naples, but was defeated by Antonio Bassolino. She claimed that her relations with Gianfranco Fini, leader of the Alleanza Nazionale, never were very good; she then later withdrew, resigning over differences with him at least once. She unsuccessfully challenged him for the leadership of the party when he withdrew support for Mussolini in a television interview in January 2002.


title: Alessandra Mussolini

text: Mussolini suddenly left the National Alliance on 28 November 2003, following the visit of party leader and the Deputy Prime Minister Gianfranco Fini to Israel, where he described fascism as part "the absolute evil" with regard to the Holocaust as he apologised for Italy's role as an Axis Power during the Second World War. Mussolini, however, defended the right of Israel to exist and declared that the world "should beg forgiveness of Israel."


title: Alessandra Mussolini

text: Following her resignation, Mussolini formed her Social Action party, originally named "Freedom of Action," and organised a coalition named Social Alternative. This made her the first female leader of an Italian political party. The move was read in the Italian media as surprising because of Mussolini's "progressive" stances on many issues, including abortion, artificial insemination, gay rights and civil unions. She has been an outspoken feminist and has been described by conservative commentators as a "socialist" and a "left-winger."


title: Alessandra Mussolini

text: In the 2004 European Parliament election, Social Alternative, gained 1.2% of the electoral list vote. Mussolini herself received 133,000 preference votes.


title: Alessandra Mussolini

text: In response to a comment made by UKIP MEP Godfrey Bloom in which he said that "No self-respecting small businessman with a brain in the right place would ever employ a lady of child-bearing age. That isn't politically correct, is it, but it's a fact of life. The more women's rights you have, it's actually a bar to their employment." and: "I just don't think [women] clean behind the fridge enough," Mussolini responded by saying


title: Alessandra Mussolini

text: In March 2005, Mussolini was banned by a local court from regional elections held the following month for presenting fraudulent signatures. "This is an affront to democracy, if they're going to exclude the Social Alternative they will have to exclude all the parties, because all the signature lists are false," Mussolini told Reuters. Mussolini went on a hunger strike to protest the decision. However, at the end of the month Italy's top administrative court, the Council of State, annulled the decision and she stood for election.


title: Alessandra Mussolini

text: In November 2007, remarks by Mussolini triggered the collapse of the far-right Identity, Tradition, Sovereignty grouping within the European Parliament. Mussolini declared that all Romanians were criminals in remarks regarding immigration policy. This prompted delegates from the Greater Romania Party to quit the group, bringing the group below the minimum number of members to qualify as a caucus and receive Parliamentary funding. In the 2019 European Parliament election, she lost her bid for re-election to the European Parliament.


title: Alessandra Mussolini

text: In 2006, she responded to claims by the transgender Italian parliamentary candidate Vladimir Luxuria that she was a "fascist" by saying that it would be better to be a fascist than it would be to be gay.


title: Alessandra Mussolini

text: Mussolini condemned the Vatican's comparison of homosexuality with pedophilia, stating "You can't link sexual orientation to pedophilia … this link risks becoming dangerously misleading for the protection of children."


title: Alessandra Mussolini

text: She left Forza Italia in 2018, following the party's decision to be in opposition to the Conte government. She has used Twitter to defend the memory of her grandfather from critics such as actor Jim Carrey, and fans of Scottish football club Celtic F.C.


title: Alessandra Mussolini

text: In November 2022, Mussolini returned to politics to replace Antonio Tajani as a Forza Italia MEP after his election to the Chamber of Deputies.


title: Molluscum contagiosum

text: Molluscum contagiosum (MC), sometimes called water warts, is a viral infection of the skin that results in small raised pink lesions with a dimple in the center. They may become itchy or sore, and occur singularly or in groups. Any area of the skin may be affected, with abdomen, legs, arms, neck, genital area, and face being the most common. Onset of the lesions is around seven weeks after infection. They usually go away within a year without scarring.


title: Molluscum contagiosum

text: The infection is caused by a poxvirus called the "molluscum contagiosum virus" (MCV). The virus is spread either by direct contact, including sexual activity, or via contaminated objects such as towels. The condition can also be spread to other areas of the body by the person themselves. Risk factors include a weak immune system, atopic dermatitis, and crowded living conditions. Following one infection, it is possible to get re-infected. Diagnosis is typically based on the appearance of the lesions.


title: Molluscum contagiosum

text: Prevention includes hand washing and not sharing personal items. While treatment is not necessary, some may wish to have the lesions removed for cosmetic reasons or to prevent spread. Removal may occur with freezing, laser therapy, or opening up the lesion and scraping the inside. Scraping the lesion can, however, result in scarring. The oral medication cimetidine, or podophyllotoxin cream applied to the skin, may also be used for treatment.


title: Molluscum contagiosum

text: Approximately 122 million people globally were affected by molluscum contagiosum as of 2010 (1.8% of the population). It is more common in children between the ages of one and ten years old. The condition has become more common in the United States since 1966. But having an infection is not a reason to keep a child out of school or daycare.


title: Molluscum contagiosum

text: Molluscum contagiosum lesions are flesh-colored, dome-shaped, and pearly in appearance. They are often 1–5 mm in diameter, with a dimpled center. Molluscum lesions are most commonly found on the face, arms, legs, torso, and armpits in children. Adults typically have molluscum lesions in the genital region and this is considered to be a sexually transmitted infection; because of this, if genital lesions are found on a child, sexual abuse should be suspected. These lesions are generally not painful, but they may itch or become irritated. Picking or scratching the bumps may lead to a spread of the viral infection responsible for molluscum contagiosum, an additional bacterial infection, and scarring. In some cases, eczema develops around the lesions.


title: Molluscum contagiosum

text: Individual molluscum lesions may go away on their own within two months and generally clear completely without treatment or scarring in six to twelve months. Mean durations for an outbreak are variously reported from eight to about 18 months, but durations are reported as widely as six months to five years, lasting longer in immunosuppressed individuals.


title: Molluscum contagiosum

text: As the name implies, molluscum contagiosum is extremely contagious. Transmission of the molluscum contagiosum virus can occur many different ways including direct skin contact (e.g., contact sports or sexual activity), contact with an infected surface (fomite), or autoinoculation (self-infection) by scratching or picking molluscum lesions and then touching other parts of the skin not previously affected by the virus. Children are particularly susceptible to autoinoculation and may have widespread clusters of lesions.


title: Molluscum contagiosum

text: The viral infection is limited to a localized area on the topmost layer of the superficial layer of the skin. Once the virus-containing head of the lesion has been destroyed, the infection is gone. The central waxy core contains the virus.


title: Molluscum contagiosum

text: Diagnosis is made on the appearance; the virus cannot routinely be cultured. The diagnosis can be confirmed by excisional biopsy.


title: Molluscum contagiosum

text: Histologically, molluscum contagiosum is characterized by "molluscum bodies" (also known as Henderson-Patersen bodies) in the epidermis, above the "stratum basale", which consist of cells with abundant large granular eosinophilic cytoplasmic inclusion bodies (accumulated virions) and a small nucleus that has been pushed to the periphery.


title: Molluscum contagiosum

text: Because molluscum contagiosum usually resolves without treatment and treatment options can cause discomfort to children, initial recommendations are often to simply wait for the lesions to resolve on their own. Of the treatments available, a meta-analysis of randomized controlled trials suggested that there is no difference between treatments in short term improvement, and no single treatment is significantly better than natural resolution of the condition.


title: Molluscum contagiosum

text: Bumps located in the genital area may be treated in an effort to prevent them from spreading. When treatment has resulted in the elimination of all bumps, the infection has been effectively cured and will not reappear unless the person is reinfected.


title: Molluscum contagiosum

text: For mild cases, over-the-counter wart medicines, such as salicylic acid may shorten infection duration. Daily topical application of tretinoin cream may also trigger resolution.


title: Molluscum contagiosum

text: Studies have found cantharidin to be an effective and safe treatment for removing molluscum contagiosum. This medication is usually well tolerated though mild side effects such as pain or blistering are common.


title: Molluscum contagiosum

text: There is no high-quality evidence for cimetidine. However, oral cimetidine has been used as an alternative treatment for the pediatric population as it is generally well tolerated and less invasive.


title: Molluscum contagiosum

text: Imiquimod is a form of immunotherapy initially proposed as a treatment for molluscum based on promising results in small case series and clinical trials. However, two large randomized controlled trials, specifically requested by the U.S. Food and Drug Administration under the Best Pharmaceuticals for Children Act both demonstrated that imiquimod cream applied three times per week was no more effective than placebo cream for treating molluscum after 18 weeks of treatment in a total of 702 children aged 2–12 years. In 2007, results from those trials—which remain unpublished—were incorporated into FDA-approved prescribing information for imiquimod, which states: "Limitations of Use: Efficacy was not demonstrated for molluscum contagiosum in children aged 2–12." In 2007, the FDA also updated imiquimod's label concerning safety issues raised in the two large trials and an FDA-requested pharmacokinetic study (the latter of which was published). The updated safety label reads as follows:


title: Molluscum contagiosum

text: Surgical treatments include cryosurgery, in which liquid nitrogen is used to freeze and destroy lesions, as well as scraping them off with a curette. Application of liquid nitrogen may cause burning or stinging at the treated site, which may persist for a few minutes after the treatment. With liquid nitrogen, a blister may form at the treatment site, but it will slough off in two to four weeks. Cryosurgery and curette scraping can be painful procedures and can result in residual scarring.


title: Molluscum contagiosum

text: A 2014 systematic review of case reports and case series concluded that the limited available data suggest pulsed dye laser therapy is a safe and effective treatment for molluscum contagiosum and is generally well tolerated by children. Side effects seen with pulsed dye laser therapy included mild temporary pain at the site of therapy, bruising (lasting up to 2–3 weeks), and temporary discoloration of the treated skin (as long as 1–6 months). No cases of permanent scarring have been reported. As of 2009, however, there is no evidence for genital lesions.


title: Molluscum contagiosum

text: Most cases of molluscum contagiosum will clear up naturally within two years (usually within nine months). So long as the skin growths are present, there is a possibility of transmitting the infection to another person. When the growths are gone, the possibility of spreading the infection is ended.


title: Molluscum contagiosum

text: Unlike herpesviruses, which can remain inactive in the body for months or years before reappearing, molluscum contagiosum does not remain in the body when the growths are gone from the skin and will not reappear on their own.


title: Molluscum contagiosum

text: As of 2010, approximately 122 million people were affected worldwide by molluscum contagiosum (1.8% of the population).


title: Oleg Penkovsky

text: Oleg Vladimirovich Penkovsky (; 23 April 1919 – 16 May 1963), codenamed HERO, was a Soviet military intelligence (GRU) colonel during the late 1950s and early 1960s. Penkovsky informed the United States and the United Kingdom about Soviet military secrets, most importantly, the appearance and footprint of Soviet intermediate-range ballistic missile (IRBM) installations and the weakness of the Soviet intercontinental ballistic missile (ICBM) program. This information was decisive in allowing the US to recognize that the Soviets were placing IRBMs in Cuba before most of the missiles were operational. It also gave US President John F. Kennedy, during the Cuban Missile Crisis that followed, valuable information about Soviet weakness that allowed him to face down Soviet leader Nikita Khrushchev and resolve the crisis without a nuclear war.


title: Oleg Penkovsky

text: Penkovsky was the highest-ranking Soviet official to provide intelligence for the West up until that time, and is one of several individuals credited with altering the course of the Cold War. He was arrested by the Soviets in October 1962, then tried and executed the following year.


title: Oleg Penkovsky

text: Penkovsky never knew his father, who was killed fighting as an officer in the White Army in the Russian Civil War when he was a baby. Brought up in the North Caucasus, Penkovsky graduated from the Kiev Artillery Academy with the rank of lieutenant in 1939. After taking part in the Winter War against Finland and in World War II, he reached the rank of lieutenant-colonel. In 1944, he was assigned to the headquarters of Colonel-General Sergei Varentsov, commander of artillery on the 1st Ukrainian front, who became his patron. Penkovsky was wounded in action in 1944, at about the same time as Varentsov, who appointed him his Liaison Officer. In 1945, Penkovsky married the teenage daughter of Lieutenant-General Dmitri Gapanovich, thus acquiring another high-ranking patron. On Varentsov's recommendation, he studied at the Frunze Military Academy in 1945-48, then worked as a staff officer.


title: Oleg Penkovsky

text: Penkovsky joined the GRU as an officer, in 1953. In 1955 Penkovsky was appointed military attaché in Ankara, Turkey, but was recalled after he had reported his superior officer, and later other GRU personnel for a breach of regulations, which made him unpopular in the department. Relying once again on Varentsov's patronage, he spent nine months studying rocket artillery at Dzerzhinsky Military Academy. He was selected for the post of military attache in India, but the KGB had uncovered the story of his father's death, and he was suspended, investigated, and assigned in November 1960 to the State Committee for Science and Technology. He later worked at the Soviet Committee for Scientific Research.


title: Oleg Penkovsky

text: Penkovsky approached American students on the Bolshoy Moskvoretsky Bridge in Moscow in July 1960 and gave them a package in which he offered to spy for the U.S. He asked them to deliver it to an intelligence officer at the U.S. Embassy. The Central Intelligence Agency delayed in contacting him. When the U.S. Embassy in Moscow refused to cooperate, fearing an international incident, the CIA contacted MI6 for assistance.


title: Oleg Penkovsky

text: A British salesman of industrial equipment to countries behind the Iron Curtain, Greville Wynne, was recruited by MI6 to communicate with Penkovksy. In his autobiography, Wynne says that he was carefully developed by British intelligence over many years with the specific task of making contact with Penkovsky.


title: Oleg Penkovsky

text: The first meeting between Penkovsky and two American and two British intelligence officers occurred during a visit by Penkovsky to London in April 1961. For the following 18 months, Penkovsky supplied a tremendous amount of information to the CIA–MI6 team of handlers, including documents demonstrating that the Soviet nuclear arsenal was much smaller than Nikita Khrushchev claimed or the CIA had thought and that the Soviets were not yet capable of producing a large number of ICBMs. This information was invaluable to President John F. Kennedy in negotiating with Nikita Khrushchev for the removal of the Soviet IRBMs from Cuba.


title: Oleg Penkovsky

text: Peter Wright, a former British MI5 officer known for his scathing condemnation of the leadership of British intelligence during most of the Cold War, believed that Penkovsky was a fake defection. Wright noted that, unlike Igor Gouzenko and other earlier defectors, Penkovsky did not reveal the names of any Soviet agents in the West but only provided organisational detail, much of which was known already. Some of the documents provided were originals, which Wright thought could not have been easily taken from their sources. Wright was bitter towards British intelligence, reportedly believing that it should have adopted his proposed methods to identify British/Soviet agents. In Wright's view, the failure of British intelligence leaders to listen to him caused them to become paralysed when British/Soviet agents defected to the Soviet Union; in his book, "Spycatcher", he suggests that his hypothesis had to be true, and that the Soviets were aware of this paralysis and planted Penkovsky.


title: Oleg Penkovsky

text: In his memoir "Spycatcher: The Candid Autobiography of a Senior Intelligence Officer" (1987), written with journalist Paul Greengrass, Wright says:


title: Oleg Penkovsky

text: Former KGB major-general Oleg Kalugin does not mention Penkovsky in his comprehensive memoir about his career in intelligence against the West. The KGB defector Vladimir N. Sakharov suggests Penkovsky was genuine, saying: "I knew about the ongoing KGB reorganisation precipitated by Oleg Penkovsky's case and Yuri Nosenko's defection. The party was not satisfied with KGB performance ... I knew many heads in the KGB had rolled again, as they had after Stalin". While the weight of opinion seems to be that Penkovsky was genuine, the debate underscores the difficulty faced by all intelligence agencies of determining information offered from the enemy. In a meeting with Secretary of Defense Leon Panetta, the head of Russia's foreign intelligence service, Mikhail Fradkov named Penkovsky as Russia's biggest intelligence failure.


title: Oleg Penkovsky

text: The Soviet leadership began the deployment of nuclear missiles, in the belief that Washington would not detect the Cuban missile sites until it was too late to do anything about them. Penkovsky provided plans and descriptions of the nuclear rocket launch sites in Cuba to the West. This information allowed the West to identify the missile sites from the low-resolution pictures provided by US U-2 spy planes. The documents provided by Penkovsky showed that the Soviet Union was not prepared for war in the area, which emboldened Kennedy to risk the operation in Cuba. Former GRU captain Viktor Suvorov, who defected to the UK in 1978, later wrote in his book on Soviet intelligence, "historians will remember with gratitude the name of the GRU Colonel Oleg Penkovsky. Thanks to his priceless information the Cuban crisis was not transformed into a last World War".


title: Oleg Penkovsky

text: Penkovsky's activities were revealed by Jack Dunlap, a National Security Agency (NSA) employee and Soviet spy working for the KGB. Top KGB officers had known for more than a year that Penkovsky was a British agent, but they protected their source, a highly placed mole in MI6. Jack Dunlap was just another source they had to protect. They worked hard, shadowing British diplomats, to build up a "discovery case" against Penkovsky so that they could arrest him without throwing suspicion on their moles. Their caution in this matter may have led to the missiles being discovered earlier than the Soviets would have preferred. After a West German agent overheard a remark at Stasi headquarters, paraphrased as "I wonder how things are going in Cuba" he passed it on to the CIA.


title: Oleg Penkovsky

text: Penkovsky was arrested on 22 October 1962. This was prior to President Kennedy's address to the US revealing that U-2 spy plane photographs had confirmed intelligence reports that the Soviets were installing medium-range nuclear missiles in Cuba, in what was known as Operation Anadyr. President Kennedy was deprived of information from a potentially important intelligence agent, such as reporting that Nikita Khrushchev was already looking for ways to defuse the situation, which might have lessened the tension during the ensuing 13-day stand-off. That information might have reduced the pressure on Kennedy to launch an invasion of the island, which could have risked Soviet use of "9K52 Luna-M"-class tactical nuclear weapons against U.S. troops.


title: Oleg Penkovsky

text: Penkovsky's American contacts received a letter from Penkovsky notifying them that a Moscow dead drop had been loaded. Upon servicing the dead drop, the American handler was arrested, signaling that Penkovsky had been apprehended by Soviet authorities. Penkovsky was executed but there are conflicting reports about the manner of his death. Alexander Zagvozdin, Chief KGB interrogator for the investigation, stated that Penkovsky had been "questioned perhaps a hundred times" and that he had been shot and cremated. The noted Soviet sculptor Ernst Neizvestny said that he had been told by the director of the Donskoye Cemetery crematorium "how Penkovsky [had been] executed by 'fire'". A similar description was later included in Ernest Volkman's popular history book about spies, Tom Clancy's novel "Red Rabbit" and in Viktor Suvorov's book "Aquarium". In a 2010 interview, Suvorov denied that the man in the film was Penkovsky and said that he had been shot. Greville Wynne, in his book "The Man from Odessa," claimed that Penkovsky killed himself. Wynne had worked as both Penkovsky's contact and courier; both men were arrested by the Soviets in October 1962.


title: Oleg Penkovsky

text: The Soviet public was first told of Penkovsky's arrest more than seven weeks later, when "Pravda" named Wynne and Jacobs as his contacts, without naming anyone else. In May 1963, after his trial, "Izvestya" reported that Varentsov, who had since achieved the rank of Chief Marshal of Artillery and Commander in Chief of Rocket Forces and candidate member of the Central Committee had been demoted to the rank of Major General. In June he was expelled from the Central Committee for 'having relaxed his political vigilance.' Three other officers were also disciplined. The head of the GRU, Ivan Serov was sacked during the same period. He was reputedly on friendly terms with Penkovsky, which is very likely to have been a cause of his fall.


title: Oleg Penkovsky

text: Penkovsky was portrayed by Christopher Rozycki in the 1985 BBC Television serial "Wynne and Penkovsky". His spying career was the subject of episode 1 of the 2007 BBC Television docudrama "Nuclear Secrets", titled "The Spy from Moscow" in which he was portrayed by Mark Bonnar. The programme featured original covert KGB footage showing Penkovsky photographing classified information and meeting up with Janet Chisholm, a British MI6 agent stationed in Moscow. It was broadcast on 15 January 2007.


title: Oleg Penkovsky

text: Penkovsky was referred to in four of Tom Clancy's Jack Ryan espionage novels: "The Hunt for Red October" (1984), "The Cardinal of the Kremlin" (1988), ‘’The Bear and the Dragon’’ (2000) and "Red Rabbit" (2002). In the Jack Ryan universe, he is described as the agent who recruited Colonel Mikhail Filitov as a CIA agent (code-name CARDINAL) and had urged Filitov to betray him to solidify his position as the West's top spy in the Soviet hierarchy. The "cremated alive" hypothesis appears in several Clancy novels, though Clancy never identified Penkovsky as the executed spy. Penkovsky's fate is also mentioned in the Nelson DeMille spy novel "The Charm School" (1988).


title: Oleg Penkovsky

text: Penkovsky was portrayed by Eduard Bezrodniy in the 2014 Polish thriller "Jack Strong", about Ryszard Kukliński, another Cold War spy. His character's execution was the opening scene for the movie. Penkovsky was portrayed by Merab Ninidze in the 2020 British film "The Courier", in which Benedict Cumberbatch played Greville Wynne.


title: Lara Logan

text: Lara Logan (born 29 March 1971) is a South African television and radio journalist and war correspondent. Logan's career began in South Africa with various news organizations in the 1990s. Her profile rose due to reporting around the American invasion of Afghanistan in 2001. She was hired as a correspondent for CBS News in 2002, eventually becoming Chief Foreign Affairs Correspondent.


title: Lara Logan

text: In 2013, a story of Logan's on the 2012 Benghazi attack caused significant controversy due to factual errors and was retracted, resulting in a leave of absence. Logan left CBS in 2018. After her departure from CBS, Logan began to make wide-ranging claims on a variety of conspiracy theories regarding topics such as the AIDS virus or the Rothschild family. In 2019, she joined the Sinclair Broadcast Group, a conservative media company. In January 2020, she joined Fox Nation, a subscription streaming service run by Fox News. In March 2022, she said she had been "dumped" by the network.


title: Lara Logan

text: Logan was born in Durban, South Africa, and attended high school at Durban Girls' College. She graduated from the University of Natal in Durban in 1992 with a degree in commerce. She earned a diploma in French language, culture and history at Alliance Française in Paris.


title: Lara Logan

text: Logan worked as a news reporter for the "Sunday Tribune" in Durban during her studies (1988–1989), then for the city's "Daily News" (1990–1992). In 1992, she joined Reuters Television in Africa, primarily as a senior producer. After four years she branched out into freelance journalism, obtaining assignments as a reporter and editor/producer with ITN and Fox/SKY, CBS News, ABC News (in London), NBC, and the European Broadcasting Union. She worked for CNN, reporting on incidents such as the 1998 United States embassy bombings in Nairobi and Tanzania, the conflict in Northern Ireland, and the Kosovo war.


title: Lara Logan

text: Logan was hired in 2000 by GMTV Breakfast Television (in the UK) as a correspondent; she also worked with CBS News Radio as a freelance correspondent. Days after the September 11 attacks, she asked a clerk at the Russian Embassy in London to give her a visa to travel to Afghanistan. In November 2001, while in Afghanistan working for GMTV, she infiltrated the American-British-backed Northern Alliance and interviewed their commander, General Babajan, at the Bagram Air Base.


title: Lara Logan

text: CBS News offered her a full-fledged correspondent position in 2002. She spent much of the next four years reporting from the battlefield, including war zones in Afghanistan and Iraq, often embedded with the United States Armed Forces. But she also interviewed famous figures and explorers such as Robert Ballard, discoverer of the wreck of the . Many of her reports were for "60 Minutes II". She was also a regular contributor to the "CBS Evening News", "The Early Show" and "Face the Nation". In February 2006, Logan was promoted to "Chief foreign affairs correspondent" for CBS News.


title: Lara Logan

text: Logan left CBS News in August 2018. The following year, she joined the Sinclair Broadcast Group on a temporary basis, as a correspondent reporting on the United States-Mexico border.


title: Lara Logan

text: In October 2022, Logan was banned from right-wing television network Newsmax for what the network described as "reprehensible statements" during an interview where she said that "the open [United States-Mexico] border is Satan’s way of taking control of the world through all of these people who are his stooges and his servants ... You know, the ones who want us eating insects, cockroaches and that while they dine on the blood of children?"


title: Lara Logan

text: In late January 2007, Logan filed a report of fighting along Haifa Street in Baghdad, but the "CBS Evening News" did not run the report, deeming it "a bit strong". To reverse the decision, Logan enlisted public support, asking people to watch the story and pass the link to as many of their friends and acquaintances as possible, saying, "It should be seen".


title: Lara Logan

text: Logan was criticized in June 2010 for her remarks about another journalist, Michael Hastings, and her view that reporters who embed with the military ought not to write about the general banter they hear. An article by Hastings in "Rolling Stone" that month quoted General Stanley A. McChrystal and his staff—comments Hastings overheard while traveling with McChrystal—criticizing then U.S. Vice President Joe Biden and other officials, after which President Barack Obama fired McChrystal as his commander in Afghanistan. Logan told CNN that Hastings's reporting had violated an unspoken agreement between reporters who travel with military personnel not to report casual comments that pass between them.


title: Lara Logan

text: Quoting her statement, "I mean, the question is, really, is what General McChrystal and his aides are doing so egregious, that they deserved to end a career like McChrystal's? I mean, Michael Hastings has never served his country the way McChrystal has." CNN's former chief military correspondent Jamie McIntyre said that what they did was indeed egregious, and that her comments "unfortunately reinforced the worst stereotype of reporters who 'embed' with senior military officers but are actually 'in bed' with them." He went on to quote Admiral Mike Mullen's statement that military personnel must be neutral and should not criticize civilian leaders.


title: Lara Logan

text: Glenn Greenwald, commenting on the incident for "Salon", wrote that Logan's segment was an example of what journalism had "degenerated into". Greenwald said that Logan had done courageous reporting over the years, but had come to see herself as part of the government and military.


title: Lara Logan

text: Logan and her CBS crew were arrested and detained for one night by the Egyptian Army on 3 February 2011, while covering the Egyptian revolution. She said the crew was blindfolded and handcuffed at gunpoint, and their driver beaten. They were advised to leave the country, but were later released.


title: Lara Logan

text: On 15 February 2011, CBS News released a statement that Logan had been beaten and sexually assaulted on 11 February, while covering the celebrations in Tahrir Square following Hosni Mubarak's resignation. "60 Minutes" broadcast an interview with her about it on 1 May 2011; she said she was speaking out because of the prevalence of mass sexual assault in Egypt, and to break the silence about the sexual violence women reporters are reluctant to report in case it prevents them from doing their jobs.


title: Lara Logan

text: She said the incident involved 200 to 300 men and lasted around 25 minutes. She had been reporting the celebrations for an hour without incident when her camera battery failed. One of the Egyptian CBS crew suggested they leave, telling her later he heard the crowd make inappropriate sexual comments about her. She felt hands touching her, and can be heard shouting "stop", just as the camera died. One of the crowd shouted that she was an Israeli Jew, a claim that CBS said, though false, was a "match to gasoline". She said that they tore off her clothes and, in her words, raped her with their hands, while taking photographs with their cellphones. They began pulling her body in different directions, pulling her hair so hard she said it seemed they were trying to tear off chunks of her scalp. She was dragged along the square to where the crowd was stopped by a fence, alongside which a group of women were camping. One woman wearing a chador put her arms around Logan, and the others closed ranks around her, while some men who were with the women threw water at the crowd. A group of soldiers appeared, beat back the crowd with batons, and one of them threw Logan over his shoulder. She later said she thought she was dying during the assault. She was flown back to the U.S. the next day, where she spent four days in the hospital. She was contacted by President Barack Obama when she arrived home. CBS said that the identity of the attackers remained unclear, and that it was unlikely that any would be prosecuted.


title: Lara Logan

text: In October 2012, Logan delivered a speech before the annual luncheon of the Better Government Association in which she sharply criticized the Obama administration's statements about the War in Afghanistan and other conflicts in the Arab world. In particular, Logan criticized the administration's claims that the Taliban was weakening in Afghanistan, calling such claims "a major lie" made in preparation for ending the U.S. military role in that country. She also stated that she hoped that the United States would "exact revenge" for the 2012 Benghazi attack, in which U.S. diplomatic personnel were attacked and killed in Libya.


title: Lara Logan

text: On 8 November 2013, Logan went on "CBS This Morning" to apologize for an inaccurate "60 Minutes" report about the Benghazi attack, which had aired on October 27. She indicated that an investigation uncovered that the source of much of her reporting was inaccurate and blamed it on Dylan Davies, manager of the local guard force at the U.S. Embassy in Benghazi. Logan said he lied about information and insisted they looked into his credibility and relied on such things as photographs and documents he supplied. In hindsight, Logan said they learned that the story told by Davies did not match what he told federal investigators. "You know the most important thing to every person at "60 Minutes" is the truth," she said in the on-air apology on the morning show. "And today the truth is we made a mistake. And that's ah ... that's very disappointing for any journalist. That's very disappointing for me." Logan went on to add, "Nobody likes to admit they made a mistake. But if you do, you have to stand up and take responsibility – and you have to say you were wrong. And in this case we were wrong."


title: Lara Logan

text: On 26 November 2013, Logan was forced to take a leave of absence due to the errors in the Benghazi report. Al Ortiz, executive director of Standards and Practices for CBS News, wrote in a memo, "Logan made a speech in which she took a strong public position arguing that the U.S. Government was misrepresenting the threat from Al Qaeda, and urging actions that the U.S. should take in response to the Benghazi attack. From a CBS News Standards perspective, there is a conflict in taking a public position on the government’s handling of Benghazi and Al Qaeda, while continuing to report on the story."


title: Lara Logan

text: She subsequently sued "New York Magazine" for $25 million for their reporting on the fallout. The suit was dismissed with prejudice.


title: Lara Logan

text: After leaving CBS News, Logan began to criticize the media, which she said had a liberal bias. She described journalists as "political activists" and "propagandists" against President Donald Trump. She said that making these comments was akin to "professional suicide". Shortly thereafter, she joined the Sinclair Broadcast Group, a right-wing media group. Since then, Logan has tweeted right-wing conspiracy theories, such as speculating that Representative Alexandria Ocasio-Cortez won her election to office because of some unspecified plot operated by unknown entities Logan believes control antifa activists.


title: Lara Logan

text: In 2020, Logan was hired by Fox News to do a series of shows called "Lara Logan has No Agenda". The "Los Angeles Times" observed that "Despite the 'No Agenda' slogan, Logan does plan to wade back into the topic of media bias."


title: Lara Logan

text: On 31 May 2020, Logan tweeted a picture, which she claimed was an antifa riot instruction manual. The picture actually was an updated hoax dating to the 2015 Baltimore riots. On 1 June, Logan tweeted a threat by the @ANTIFA_US Twitter account. The account turned out to be fake and linked to Identity Evropa, a white nationalist organization. After being criticized for posting the hoaxes, Logan claimed that there was a campaign to "destroy" her, including by Media Matters for America.


title: Lara Logan

text: On 4 June 2020, Logan appeared on "Hannity" to claim that antifa was leaving "pallets of bricks" at protest sites in an attempt to stoke violence and destruction. Fact-checkers found that claims of bricks being left at protest sites were without foundation, and that pictures submitted as evidence of this activity were actually taken at ordinary construction sites. No one else reported seeing antifa trucks leaving pallets of bricks. Next, Logan promoted a 5 June joke tweet which linked antifa to juggalos and a "clown hierarchy". Logan instead focused on the portion of the tweet that mentioned a "traditional command structure" and argued that anarchists thus indeed had organizational structure.


title: Lara Logan

text: In November and December 2021, Logan promoted falsehoods and conspiracy theories about AIDS and COVID-19. She shared articles that disputed the scientific consensus that HIV causes AIDS. She compared NIAID director Anthony Fauci to the Nazi scientist Josef Mengele. During a discussion of the SARS-CoV-2 Omicron variant, she said: "And so in that moment, what you see on Dr Fauci, this is what people say to me, that he doesn’t represent science to them. He represents Josef Mengele, Dr Josef Mengele, the Nazi doctor who did experiments on Jews during the second world war and in the concentration camps, and I am talking about people all across the world are saying this."


title: Lara Logan

text: Several prominent Jewish groups, including the Anti-Defamation League and the Auschwitz Museum, condemned her remarks. Logan subsequently retweeted criticisms of the Auschwitz Museum. During a December 2021 interview with MSNBC, Fauci called Logan's remarks "absolutely preposterous and disgusting", and criticized Fox News for not taking disciplinary action against her. United Talent Agency dropped Logan as a client shortly after her Mengele comment.


title: Lara Logan

text: Since making her comment, Logan has not appeared as a guest on Fox News, and there have been no new episodes of "Lara Logan has No Agenda". In March 2022, Logan said that she had been "dumped" by Fox.


title: Lara Logan

text: During the 2022 Russian invasion of Ukraine, Logan in her television appearances linked Ukrainian president Volodymyr Zelenskyy to "satanic, occult" practices, called him a "puppet" and claimed that Zelenskyy had been "selected [...], not voted in". She praised Russian President Vladimir Putin for "not going to stand by while the globalists take over the world" and accused Ukrainians of being "actual Nazis". Logan's comments were praised and taken up by Russian government propaganda.


title: Lara Logan

text: In March 2022, Logan claimed without evidence that Charles Darwin was employed by the Rothschild family to create his theory of evolution. She also promoted claims that the Rothschild family, a frequent target of antisemitic conspiracy theories, engineered the American Civil War, and the assassinations of Abraham Lincoln and John F. Kennedy.


title: Lara Logan

text: Logan married Jason Siemon, an American from Iowa playing professional basketball in the UK; the marriage ended in divorce. In 2008, she married Joseph Burkett, a U.S. government defense contractor from Texas. It was the second marriage for both. The couple live in Washington, D.C., with their two children and Burkett's daughter from his previous marriage.


title: Dynamic programming

text: Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics.


title: Dynamic programming

text: In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart recursively. Likewise, in computer science, if a problem can be solved optimally by breaking it into sub-problems and then recursively finding the optimal solutions to the sub-problems, then it is said to have "optimal substructure".


title: Dynamic programming

text: If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods are applicable, then there is a relation between the value of the larger problem and the values of the sub-problems. In the optimization literature this relationship is called the Bellman equation.


title: Dynamic programming

text: In terms of mathematical optimization, dynamic programming usually refers to simplifying a decision by breaking it down into a sequence of decision steps over time. This is done by defining a sequence of value functions "V", "V", ..., "V" taking "y" as an argument representing the state of the system at times "i" from 1 to "n". The definition of "V"("y") is the value obtained in state "y" at the last time "n". The values "V" at earlier times "i" = "n" −1, "n" − 2, ..., 2, 1 can be found by working backwards, using a recursive relationship called the Bellman equation. For "i" = 2, ..., "n", "V" at any state "y" is calculated from "V" by maximizing a simple function (usually the sum) of the gain from a decision at time "i" − 1 and the function "V" at the new state of the system if this decision is made. Since "V" has already been calculated for the needed states, the above operation yields "V" for those states. Finally, "V" at the initial state of the system is the value of the optimal solution. The optimal values of the decision variables can be recovered, one by one, by tracking back the calculations already performed.


title: Dynamic programming

text: In control theory, a typical problem is to find an admissible control formula_1 which causes the system formula_2 to follow an admissible trajectory formula_3 on a continuous time interval formula_4 that minimizes a cost function


title: Dynamic programming

text: The solution to this problem is an optimal control law or policy formula_6, which produces an optimal trajectory formula_3 and a cost-to-go function formula_8. The latter obeys the fundamental equation of dynamic programming:


title: Dynamic programming

text: a partial differential equation known as the Hamilton–Jacobi–Bellman equation, in which formula_10 and formula_11. One finds that minimizing formula_12 in terms of formula_13, formula_14, and the unknown function formula_15 and then substitutes the result into the Hamilton–Jacobi–Bellman equation to get the partial differential equation to be solved with boundary condition formula_16. In practice, this generally requires numerical techniques for some discrete approximation to the exact optimization relationship.


title: Dynamic programming

text: Alternatively, the continuous process can be approximated by a discrete system, which leads to a following recurrence relation analog to the Hamilton–Jacobi–Bellman equation:


title: Dynamic programming

text: at the formula_18-th stage of formula_19 equally spaced discrete time intervals, and where formula_20 and formula_21 denote discrete approximations to formula_22 and formula_23. This functional equation is known as the Bellman equation, which can be solved for an exact solution of the discrete approximation of the optimization equation.


title: Dynamic programming

text: In economics, the objective is generally to maximize (rather than minimize) some dynamic social welfare function. In Ramsey's problem, this function relates amounts of consumption to levels of utility. Loosely speaking, the planner faces the trade-off between contemporaneous consumption and future consumption (via investment in capital stock that is used in production), known as intertemporal choice. Future consumption is discounted at a constant rate formula_24. A discrete approximation to the transition equation of capital is given by


title: Dynamic programming

text: where formula_26 is consumption, formula_18 is capital, and formula_22 is a production function satisfying the Inada conditions. An initial capital stock formula_29 is assumed.


title: Dynamic programming

text: Let formula_30 be consumption in period , and assume consumption yields utility formula_31 as long as the consumer lives. Assume the consumer is impatient, so that he discounts future utility by a factor each period, where formula_32 be capital in period . Assume initial capital is a given amount formula_33, and suppose that this period's capital and consumption determine next period's capital as formula_34, where is a positive constant and formula_35 subject to formula_36 for all formula_37


title: Dynamic programming

text: Written this way, the problem looks complicated, because it involves solving for all the choice variables formula_38. (The capital formula_39 is not a choice variable—the consumer's initial capital is taken as given.)


title: Dynamic programming

text: The dynamic programming approach to solve this problem involves breaking it apart into a sequence of smaller decisions. To do so, we define a sequence of "value functions" formula_40, for formula_41 which represent the value of having any amount of capital at each time . There is (by assumption) no utility from having capital after death, formula_42.


title: Dynamic programming

text: The value of any quantity of capital at any previous time can be calculated by backward induction using the Bellman equation. In this problem, for each formula_37, the Bellman equation is


title: Dynamic programming

text: This problem is much simpler than the one we wrote down before, because it involves only two decision variables, formula_30 and formula_47. Intuitively, instead of choosing his whole lifetime plan at birth, the consumer can take things one step at a time. At time , his current capital formula_48 is given, and he only needs to choose current consumption formula_30 and saving formula_47.


title: Dynamic programming

text: To actually solve this problem, we work backwards. For simplicity, the current level of capital is denoted as . formula_51 is already known, so using the Bellman equation once we can calculate formula_52, and so on until we get to formula_53, which is the "value" of the initial decision problem for the whole lifetime. In other words, once we know formula_54, we can calculate formula_55, which is the maximum of formula_56, where formula_57 is the choice variable and formula_58.


title: Dynamic programming

text: We see that it is optimal to consume a larger fraction of current wealth as one gets older, finally consuming all remaining wealth in period , the last period of life.


title: Dynamic programming

text: There are two key attributes that a problem must have in order for dynamic programming to be applicable: optimal substructure and overlapping sub-problems. If a problem can be solved by combining optimal solutions to "non-overlapping" sub-problems, the strategy is called "divide and conquer" instead. This is why merge sort and quick sort are not classified as dynamic programming problems.


title: Dynamic programming

text: "Optimal substructure" means that the solution to a given optimization problem can be obtained by the combination of optimal solutions to its sub-problems. Such optimal substructures are usually described by means of recursion. For example, given a graph "G=(V,E)", the shortest path "p" from a vertex "u" to a vertex "v" exhibits optimal substructure: take any intermediate vertex "w" on this shortest path "p". If "p" is truly the shortest path, then it can be split into sub-paths "p" from "u" to "w" and "p" from "w" to "v" such that these, in turn, are indeed the shortest paths between the corresponding vertices (by the simple cut-and-paste argument described in "Introduction to Algorithms"). Hence, one can easily formulate the solution for finding shortest paths in a recursive manner, which is what the Bellman–Ford algorithm or the Floyd–Warshall algorithm does.


title: Dynamic programming

text: "Overlapping" sub-problems means that the space of sub-problems must be small, that is, any recursive algorithm solving the problem should solve the same sub-problems over and over, rather than generating new sub-problems. For example, consider the recursive formulation for generating the Fibonacci series: "F" = "F" + "F", with base case "F" = "F" = 1. Then "F" = "F" + "F", and "F" = "F" + "F". Now "F" is being solved in the recursive sub-trees of both "F" as well as "F". Even though the total number of sub-problems is actually small (only 43 of them), we end up solving the same problems over and over if we adopt a naive recursive solution such as this. Dynamic programming takes account of this fact and solves each sub-problem only once.


title: Dynamic programming

text: Some programming languages can automatically memoize the result of a function call with a particular set of arguments, in order to speed up call-by-name evaluation (this mechanism is referred to as "call-by-need"). Some languages make it possible portably (e.g. Scheme, Common Lisp, Perl or D). Some languages have automatic memoization built in, such as tabled Prolog and J, which supports memoization with the "M." adverb. In any case, this is only possible for a referentially transparent function. Memoization is also encountered as an easily accessible design pattern within term-rewrite based languages such as Wolfram Language.


title: Dynamic programming

text: Dynamic programming is widely used in bioinformatics for tasks such as sequence alignment, protein folding, RNA structure prediction and protein-DNA binding. The first dynamic programming algorithms for protein-DNA binding were developed in the 1970s independently by Charles DeLisi in USA and Georgii Gurskii and Alexander Zasedatelev in USSR. Recently these algorithms have become very popular in bioinformatics and computational biology, particularly in the studies of nucleosome positioning and transcription factor binding.


title: Dynamic programming

text: From a dynamic programming point of view, Dijkstra's algorithm for the shortest path problem is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method.


title: Dynamic programming

text: is a paraphrasing of Bellman's famous Principle of Optimality in the context of the shortest path problem.


title: Dynamic programming

text: Using dynamic programming in the calculation of the "n"th member of the Fibonacci sequence improves its performance greatly. Here is a naïve implementation, based directly on the mathematical definition:


title: Dynamic programming

text: Notice that if we call, say, codice_1, we produce a call tree that calls the function on the same value many different times:


title: Dynamic programming

text: In particular, codice_7 was calculated three times from scratch. In larger examples, many more values of codice_8, or "subproblems", are recalculated, leading to an exponential time algorithm.


title: Dynamic programming

text: Now, suppose we have a simple map object, "m", which maps each value of codice_8 that has already been calculated to its result, and we modify our function to use it and update it. The resulting function requires only O("n") time instead of exponential time (but requires O("n") space):


title: Dynamic programming

text: This technique of saving values that have already been calculated is called "memoization"; this is the top-down approach, since we first break the problem into subproblems and then calculate and store values.


title: Dynamic programming

text: In the bottom-up approach, we calculate the smaller values of codice_8 first, then build larger values from them. This method also uses O("n") time since it contains a loop that repeats n − 1 times, but it only takes constant (O(1)) space, in contrast to the top-down approach which requires O("n") space to store the map.


title: Dynamic programming

text: In both examples, we only calculate codice_7 one time, and then use it to calculate both codice_12 and codice_13, instead of computing it every time either of them is evaluated.


title: Dynamic programming

text: Consider the problem of assigning values, either zero or one, to the positions of an matrix, with even, so that each row and each column contains exactly zeros and ones. We ask how many different assignments there are for a given formula_19. For example, when , five possible solutions are


title: Dynamic programming

text: Brute force consists of checking all assignments of zeros and ones and counting those that have balanced rows and columns ( zeros and ones). As there are formula_67 possible assignments and formula_68 sensible assignments, this strategy is not practical except maybe up to formula_69.


title: Dynamic programming

text: Backtracking for this problem consists of choosing some order of the matrix elements and recursively placing ones or zeros, while checking that in every row and column the number of elements that have not been assigned plus the number of ones or zeros are both at least . While more sophisticated than brute force, this approach will visit every solution once, making it impractical for larger than six, since the number of solutions is already 116,963,796,250 for  = 8, as we shall see.


title: Dynamic programming

text: Dynamic programming makes it possible to count the number of solutions without visiting them all. Imagine backtracking values for the first row – what information would we require about the remaining rows, in order to be able to accurately count the solutions obtained for each first row value? We consider boards, where , whose formula_18 rows contain formula_71 zeros and formula_71 ones. The function "f" to which memoization is applied maps vectors of "n" pairs of integers to the number of admissible boards (solutions). There is one pair for each column, and its two components indicate respectively the number of zeros and ones that have yet to be placed in that column. We seek the value of formula_73 (formula_19 arguments or one vector of formula_19 elements). The process of subproblem creation involves iterating over every one of formula_76 possible assignments for the top row of the board, and going through every column, subtracting one from the appropriate element of the pair for that column, depending on whether the assignment for the top row contained a zero or a one at that position. If any one of the results is negative, then the assignment is invalid and does not contribute to the set of solutions (recursion stops). Otherwise, we have an assignment for the top row of the board and recursively compute the number of solutions to the remaining board, adding the numbers of solutions for every admissible assignment of the top row and returning the sum, which is being memoized. The base case is the trivial subproblem, which occurs for a board. The number of solutions for this board is either zero or one, depending on whether the vector is a permutation of formula_77 and formula_78 pairs or not.


title: Dynamic programming

text: Links to the MAPLE implementation of the dynamic programming approach may be found among the external links.


title: Dynamic programming

text: Consider a checkerboard with "n" × "n" squares and a cost function codice_14 which returns a cost associated with square codice_15 (codice_16 being the row, codice_17 being the column). For instance (on a 5 × 5 checkerboard),


title: Dynamic programming

text: Let us say there was a checker that could start at any square on the first rank (i.e., row) and you wanted to know the shortest path (the sum of the minimum costs at each visited rank) to get to the last rank; assuming the checker could move only diagonally left forward, diagonally right forward, or straight forward. That is, a checker on codice_19 can move to codice_20, codice_21 or codice_22.


title: Dynamic programming

text: This problem exhibits optimal substructure. That is, the solution to the entire problem relies on solutions to subproblems. Let us define a function codice_23 as


title: Dynamic programming

text: Starting at rank codice_24 and descending to rank codice_25, we compute the value of this function for all the squares at each successive rank. Picking the square that holds the minimum value at each rank gives us the shortest path between rank codice_24 and rank codice_25.


title: Dynamic programming

text: The function codice_23 is equal to the minimum cost to get to any of the three squares below it (since those are the only squares that can reach it) plus codice_14. For instance:


title: Dynamic programming

text: The first line of this equation deals with a board modeled as squares indexed on codice_25 at the lowest bound and codice_24 at the highest bound. The second line specifies what happens at the first rank; providing a base case. The third line, the recursion, is the important part. It represents the codice_33 terms in the example. From this definition we can derive straightforward recursive code for codice_34. In the following pseudocode, codice_24 is the size of the board, codice_14 is the cost function, and codice_37 returns the minimum of a number of values:


title: Dynamic programming

text: This function only computes the path cost, not the actual path. We discuss the actual path below. This, like the Fibonacci-numbers example, is horribly slow because it too exhibits the overlapping sub-problems attribute. That is, it recomputes the same path costs over and over. However, we can compute it much faster in a bottom-up fashion if we store path costs in a two-dimensional array codice_38 rather than using a function. This avoids recomputation; all the values needed for array codice_38 are computed ahead of time only once. Precomputed values for codice_15 are simply looked up whenever needed.


title: Dynamic programming

text: We also need to know what the actual shortest path is. To do this, we use another array codice_41; a "predecessor array". This array records the path to any square codice_42. The predecessor of codice_42 is modeled as an offset relative to the index (in codice_38) of the precomputed path cost of codice_42. To reconstruct the complete path, we lookup the predecessor of codice_42, then the predecessor of that square, then the predecessor of that square, and so on recursively, until we reach the starting square. Consider the following pseudocode:


title: Dynamic programming

text: In genetics, sequence alignment is an important application where dynamic programming is essential. Typically, the problem consists of transforming one sequence into another using edit operations that replace, insert, or remove an element. Each operation has an associated cost, and the goal is to find the sequence of edits with the lowest total cost.


title: Dynamic programming

text: The problem can be stated naturally as a recursion, a sequence A is optimally edited into a sequence B by either:


title: Dynamic programming

text: The partial alignments can be tabulated in a matrix, where cell (i,j) contains the cost of the optimal alignment of A[1..i] to B[1..j]. The cost in cell (i,j) can be calculated by adding the cost of the relevant operations to the cost of its neighboring cells, and selecting the optimum.


title: Dynamic programming

text: The Tower of Hanoi or Towers of Hanoi is a mathematical game or puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.


title: Dynamic programming

text: where n denotes the number of disks to be moved, h denotes the home rod, t denotes the target rod, not(h,t) denotes the third rod (neither h nor t), ";" denotes concatenation, and


title: Dynamic programming

text: For n=1 the problem is trivial, namely S(1,h,t) = "move a disk from rod h to rod t" (there is only one disk left).


title: Dynamic programming

text: The number of moves required by this solution is 2 − 1. If the objective is to maximize the number of moves (without cycling) then the dynamic programming functional equation is slightly more complicated and 3 − 1 moves are required.


title: Dynamic programming

text: The following is a description of the instance of this famous puzzle involving N=2 eggs and a building with H=36 floors:


title: Dynamic programming

text: To derive a dynamic programming functional equation for this puzzle, let the state of the dynamic programming model be a pair s = (n,k), where


title: Dynamic programming

text: For instance, "s" = (2,6) indicates that two test eggs are available and 6 (consecutive) floors are yet to be tested. The initial state of the process is "s" = ("N","H") where "N" denotes the number of test eggs available at the commencement of the experiment. The process terminates either when there are no more test eggs ("n" = 0) or when "k" = 0, whichever occurs first. If termination occurs at state "s" = (0,"k") and "k" > 0, then the test failed.


title: Dynamic programming

text: with "W"("n",0) = 0 for all "n" > 0 and "W"(1,"k") = "k" for all "k". It is easy to solve this equation iteratively by systematically increasing the values of "n" and "k".


title: Dynamic programming

text: Notice that the above solution takes formula_82 time with a DP solution. This can be improved to formula_83 time by binary searching on the optimal formula_84 in the above recurrence, since formula_85 is increasing in formula_84 while formula_87 is decreasing in formula_84, thus a local minimum of formula_89 is a global minimum. Also, by storing the optimal formula_84 for each cell in the DP table and referring to its value for the previous cell, the optimal formula_84 for each cell can be found in constant time, improving it to formula_92 time. However, there is an even faster solution that involves a different parametrization of the problem:


title: Dynamic programming

text: Let formula_18 be the total number of floors such that the eggs break when dropped from the formula_18th floor (The example above is equivalent to taking formula_95).


title: Dynamic programming

text: Let formula_97 be the maximum number of values of formula_96 that are distinguishable using formula_13 tries and formula_19 eggs.


title: Dynamic programming

text: If the first egg broke, formula_96 is from formula_105 to formula_103 and distinguishable using at most formula_107 tries and formula_108 eggs.


title: Dynamic programming

text: If the first egg did not break, formula_96 is from formula_110 to formula_18 and distinguishable using formula_107 tries and formula_19 eggs.


title: Dynamic programming

text: To do so, we could compute formula_117 in order of increasing formula_13, which would take formula_119 time.


title: Dynamic programming

text: But the recurrence relation can in fact be solved, giving formula_122, which can be computed in formula_123 time using the identity formula_124 for all formula_125.


title: Dynamic programming

text: Since formula_126 for all formula_127, we can binary search on formula_13 to find formula_84, giving an formula_130 algorithm.


title: Dynamic programming

text: Matrix chain multiplication is a well-known example that demonstrates utility of dynamic programming. For example, engineering applications often have to multiply a chain of matrices. It is not surprising to find matrices of large dimensions, for example 100×100. Therefore, our task is to multiply matrices . Matrix multiplication is not commutative, but is associative; and we can multiply only two matrices at a time. So, we can multiply this chain of matrices in many different ways, for example:


title: Dynamic programming

text: and so on. There are numerous ways to multiply this chain of matrices. They will all produce the same final result, however they will take more or less time to compute, based on which particular matrices are multiplied. If matrix A has dimensions m×n and matrix B has dimensions n×q, then matrix C=A×B will have dimensions m×q, and will require m*n*q scalar multiplications (using a simplistic matrix multiplication algorithm for purposes of illustration).


title: Dynamic programming

text: For example, let us multiply matrices A, B and C. Let us assume that their dimensions are m×n, n×p, and p×s, respectively. Matrix A×B×C will be of size m×s and can be calculated in two ways shown below:


title: Dynamic programming

text: Let us assume that m = 10, n = 100, p = 10 and s = 1000. So, the first way to multiply the chain will require 1,000,000 + 1,000,000 calculations. The second way will require only 10,000+100,000 calculations. Obviously, the second way is faster, and we should multiply the matrices using that arrangement of parenthesis.


title: Dynamic programming

text: Therefore, our conclusion is that the order of parenthesis matters, and that our task is to find the optimal order of parenthesis.


title: Dynamic programming

text: At this point, we have several choices, one of which is to design a dynamic programming algorithm that will split the problem into overlapping problems and calculate the optimal arrangement of parenthesis. The dynamic programming solution is presented below.


title: Dynamic programming

text: Let's call m[i,j] the minimum number of scalar multiplications needed to multiply a chain of matrices from matrix i to matrix j (i.e. A × ... × A, i.e. i<=j). We split the chain at some matrix k, such that i <= k < j, and try to find out which combination produces minimum m[i,j].


title: Dynamic programming

text: This formula can be coded as shown below, where input parameter "chain" is the chain of matrices, i.e. :


title: Dynamic programming

text: So far, we have calculated values for all possible , the minimum number of calculations to multiply a chain from matrix "i" to matrix "j", and we have recorded the corresponding "split point". For example, if we are multiplying chain , and it turns out that and , that means that the optimal placement of parenthesis for matrices 1 to 3 is and to multiply those matrices will require 100 scalar calculations.


title: Dynamic programming

text: This algorithm will produce "tables" "m"[, ] and "s"[, ] that will have entries for all possible values of i and j. The final solution for the entire chain is m[1, n], with corresponding split at s[1, n]. Unraveling the solution will be recursive, starting from the top and continuing until we reach the base case, i.e. multiplication of single matrices.


title: Dynamic programming

text: Therefore, the next step is to actually split the chain, i.e. to place the parenthesis where they (optimally) belong. For this purpose we could use the following algorithm:


title: Dynamic programming

text: Of course, this algorithm is not useful for actual multiplication. This algorithm is just a user-friendly way to see what the result looks like.


title: Dynamic programming

text: The term "dynamic programming" was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he refined this to the modern meaning, referring specifically to nesting smaller decision problems inside larger decisions, and the field was thereafter recognized by the IEEE as a systems analysis and engineering topic. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form.


title: Dynamic programming

text: Bellman explains the reasoning behind the term "dynamic programming" in his autobiography, "Eye of the Hurricane: An Autobiography":


title: Dynamic programming

text: The word "dynamic" was chosen by Bellman to capture the time-varying aspect of the problems, and because it sounded impressive. The word "programming" referred to the use of the method to find an optimal "program", in the sense of a military schedule for training or logistics. This usage is the same as that in the phrases "linear programming" and "mathematical programming", a synonym for mathematical optimization.


title: Dynamic programming

text: The above explanation of the origin of the term is lacking. As Russell and Norvig in their book have written, referring to the above story: "This cannot be strictly true, because his first paper using the term (Bellman, 1952) appeared before Wilson became Secretary of Defense in 1953." Also, there is a comment in a speech by Harold J. Kushner, where he remembers Bellman. Quoting Kushner as he speaks of Bellman: "On the other hand, when I asked him the same question, he replied that he was trying to upstage Dantzig's linear programming by adding dynamic. Perhaps both motivations were true."


title: Tropics

text: The tropics are the regions of Earth surrounding the Equator. They are defined in latitude by the Tropic of Cancer in the Northern Hemisphere at N and the Tropic of Capricorn in


title: Tropics

text: the Southern Hemisphere at S. The tropics are also referred to as the tropical zone and the torrid zone (see geographical zone).


title: Tropics

text: In terms of climate, the tropics receive sunlight that is more direct than the rest of Earth and are generally hotter and wetter as they aren't affected as much by the solar seasons. The word "tropical" sometimes refers to this sort of climate in the zone rather than to the geographical zone itself. The tropical zone includes deserts and snow-capped mountains, which are not tropical in the climatic sense. The tropics are distinguished from the other climatic and biomatic regions of Earth, which are the middle latitudes and the polar regions on either side of the equatorial zone.


title: Tropics

text: The tropics constitute 40% of Earth's surface area and contain 36% of Earth's landmass. , the region was home also to 40% of the world's population, and this figure was then projected to reach 50% by 2050. Because of global warming, the weather conditions of the tropics are expanding with areas in the subtropics, having more extreme weather events such as heatwaves and more intense storms. These changes in weather conditions may make certain parts of the tropics uninhabitable.


title: Tropics

text: The tropics are defined as the region between the Tropic of Cancer in the Northern Hemisphere at N and the Tropic of Capricorn in the Southern Hemisphere at S; these latitudes correspond to the axial tilt of the Earth.


title: Tropics

text: The Tropic of Cancer is the Northernmost latitude from which the Sun can ever be seen directly overhead, and the Tropic of Capricorn is the Southernmost. This means that the tropical zone includes everywhere on Earth which is a subsolar point at least once during the solar year. Thus the maximum latitudes of the tropics have equal distance from the equator on either side. Likewise, they approximate the angle of the Earth's axial tilt. This angle is not perfectly fixed, mainly due to the influence of the moon, but the limits of tropics are a geographic convention, and their variance from the true latitudes is very small.


title: Tropics

text: "Tropical" is sometimes used in a general sense and feeling for a tropical climate to mean warm to hot and moist year-round, often with the sense of lush vegetation.


title: Tropics

text: Many tropical areas, however, have both a dry and a wet season. The wet season, rainy season or green season is the time of year, ranging from one or more months, when most of the average annual rainfall in a region falls. Areas with wet seasons are disseminated across portions of the tropics and subtropics, some even in temperate regions. Under the Köppen climate classification, for tropical climates, a wet-season month is defined as one or more months where average precipitation is or more. Some areas with pronounced rainy seasons see a break in rainfall during mid-season when the intertropical convergence zone or monsoon trough moves poleward of their location during the middle of the warm season; typical vegetation in these areas ranges from moist seasonal tropical forests to savannahs.


title: Tropics

text: When the wet season occurs during the warm season, or summer, precipitation falls mainly during the late afternoon and early evening hours. The wet season is a time when air quality improves, freshwater quality improves and vegetation grows significantly due to the wet season supplementing flora, leading to crop yields late in the season. Floods and rains cause rivers to overflow their banks, and some animals to retreat to higher ground. Soil nutrients are washed away and erosion increases. The incidence of malaria increases in areas where the rainy season coincides with high temperatures. Animals have adaptation and survival strategies for the wetter regime. The previous dry season leads to food shortages into the wet season, as the crops have yet to mature.


title: Tropics

text: However, regions within the tropics may well not have a tropical climate. Under the Köppen climate classification, much of the area within the geographical tropics is classed not as "tropical" but as "dry" (arid or semi-arid), including the Sahara Desert, the Atacama Desert and Australian Outback. Also, there are alpine tundra and snow-capped peaks, including Mauna Kea, Mount Kilimanjaro, Puncak Jaya and the Andes as far south as the northernmost parts of Chile and Perú.


title: Tropics

text: Tropical plants and animals are those species native to the tropics. Tropical ecosystems may consist of tropical rainforests, seasonal tropical forests, dry (often deciduous) forests, spiny forests, deserts, savannahs, grasslands and other habitat types. There are often wide areas of biodiversity, and species endemism present, particularly in rainforests and seasonal forests. Some examples of important biodiversity and high endemism ecosystems are El Yunque National Forest in Puerto Rico, Costa Rican and Nicaraguan rainforests, Amazon Rainforest territories of several South American countries, Madagascar dry deciduous forests, the Waterberg Biosphere of South Africa, and eastern Madagascar rainforests. Often the soils of tropical forests are low in nutrient content, making them quite vulnerable to slash-and-burn deforestation techniques, which are sometimes an element of shifting cultivation agricultural systems.


title: Tropics

text: In biogeography, the tropics are divided into Paleotropics (Africa, Asia and Australia) and Neotropics (Caribbean, Central America, and South America). Together, they are sometimes referred to as the Pantropic. The system of biogeographic realms differs somewhat; the Neotropical realm includes both the Neotropics and temperate South America, and the Paleotropics correspond to the Afrotropical, Indomalayan, Oceanian, and tropical Australasian realms.


title: Tropics

text: Some well-known plants that are exclusively found or originate from the tropics or are often associated with the tropics include:


title: Tropics

text: Tropicality refers to the image of the tropics that people from outside the tropics have of the region, ranging from critical to verging on fetishism. The idea of tropicality gained renewed interest in geographical discourse when French geographer Pierre Gourou published "Les Pays Tropicaux" ("The Tropical World" in English), in the late 1940s.


title: Tropics

text: Tropicality encompassed two major images. One, is that the tropics represent a 'Garden of Eden', a heaven on Earth, a land of rich biodiversity or a tropical paradise. The alternative is that the tropics consist of wild, unconquerable nature. The latter view was often discussed in old Western literature more so than the first. Evidence suggests over time that the view of the tropics as such in popular literature has been supplanted by more well-rounded and sophisticated interpretations.


title: Tropics

text: Western scholars tried to theorise why tropical areas were relatively more inhospitable to human civilisations than colder regions of the Northern Hemisphere. A popular explanation focused on the differences in climate. Tropical jungles and rainforests have much more humid and hotter weather than colder and drier temperaments of the Northern Hemisphere, giving to a more diverse biosphere. This theme led some scholars to suggest that humid hot climates correlate to human populations lacking control over nature e.g. 'the wild Amazonian rainforests'.


title: Sharad Pawar

text: Sharad Govindrao Pawar (Marathi pronunciation: ], born 12 December 1940) is an Indian politician. He has served as the Chief Minister of Maharashtra on four occasions. He has held the posts of Minister of Defence and Minister of Agriculture in the Government of India. He is president of the Nationalist Congress Party (NCP), which he founded in 1999, after separating from the Indian National Congress. He leads the NCP delegation in the Rajya Sabha, the upper chamber of the Indian parliament. He is the chairperson of Maha Vikas Aghadi.


title: Sharad Pawar

text: Pawar comes from Baramati of Maharashtra. He is the patriarch of one of Maharashtra's most influential political families and a prominent face in Maharashtra politics. Other politicians from the family include his daughter Supriya Sule, Ajit Pawar his nephew, Rohit Rajendra Pawar a nephew's son and other members of his extended family.


title: Sharad Pawar

text: Outside of politics, Pawar served as the Chairman of the Board of Control for Cricket in India BCCI from 2005 to 2008 and as the president of the International Cricket Council from 2010 to 2012. He was the president of the Mumbai Cricket Association for many years.


title: Sharad Pawar

text: In 2017, the Indian government conferred upon him Padma Vibhushan, the second-highest civilian honour of India.


title: Sharad Pawar

text: Pawar is one of the eleven children born to Govindrao Pawar and Shardabai Pawar. The ancestors of Govindrao had moved to Baramati from the nearby Satara. Govindrao had a long career in "Sahakari Kharedi Vikri Sangh", a Baramati Farmers' Cooperative. He also managed "Shahu boarding", a students' hostel, in the 1940s. In 1950s he was instrumental in setting up cooperative sugar mills in the Baramati region. Shardabai Pawar was elected to the district local board three times between 1937 and 1952. She looked after the family farm at Katewadi, ten kilometres from Baramati.


title: Sharad Pawar

text: Pawar studied at Brihan Maharashtra College of Commerce (BMCC) in Pune. He was an average student but active in student politics. Most of his siblings were well educated and successful in their respective professions.


title: Sharad Pawar

text: Vasantrao, the eldest brother of Pawar and a lawyer, was murdered over a land deal by a man who was suspected to be a hired assassin. Pratap Pawar, Pawar's younger brother, runs the Marathi daily newspaper "Sakal". Pawar's nephew, Ajit Pawar, is a politician and served as the Deputy Chief Minister of Maharashtra. His grandnephew Rohit Rajendra Pawar represents the Karjat constituency in the Maharashtra Vidhan Sabha.


title: Sharad Pawar

text: Pawar is married to Pratibha (née Shinde), daughter of the test cricketer Sadashiv Shinde. They have a daughter, Supriya Sule, who represents the Baramati constituency in the 17th Lok Sabha.


title: Sharad Pawar

text: He is the oldest and senior most member of Pawar political dynastic family of Maharashtra. The family have 2 members of parliament and 2 members of legislative assembly in state assembly, among them Ajit Pawar was the deputy chief minister of Maharashtra. The family have their political party. It is one of the most powerful political families of not only in Maharashtra but also in India, many members have in number of authoritative positions.


title: Sharad Pawar

text: In 1999, Pawar was diagnosed with oral cancer due to the habit of chewing gutka, and had oral surgery in April 2004. In March 2021, he underwent surgery for his gallbladder problem.


title: Sharad Pawar

text: Pawar's first political activity was when he was a schoolboy, he organized a protest march for Goan Independence in "Pravaranagar" in 1956. At college he was active in student politics. Although his older lawyer brother belonged to Peasants and Workers Party, young Pawar preferred the Congress party and joined Youth Congress in 1958. He later became the president of "Poona" district (now Pune district) youth Congress in 1962. By 1964, he was one of the two secretaries of Maharashtra youth congress and in regular contact with influential leaders of the party.