title: Opera (company)

text: Opera was involved in a years-long feud with Microsoft dating back to 2001. On at least three separate occasions, Opera accused Microsoft of deliberately breaking interoperability of its MSN services and the Opera browser or other non Internet Explorer browsers. Microsoft denied that it was intentionally shutting out Opera users. In response, Opera released the "Bork Edition" of its web browser, causing MSN to display only the phrase, "Bork, bork, bork!" which was popularized by The Muppet Show character, Swedish Chef. In 2004, Opera received a confidential $12.75 million payment from an "international corporation" reported to be Microsoft.


title: Opera (company)

text: In 2013, Opera switched from its rendering engine, Presto, to Chrome's Webkit, a decision described as a "sad day for the web."


title: Opera (company)

text: From 2018 to 2020, Opera was involved in the incubation of Kenyan loan companies OKash and Opesa. In January 2020, the then Opera-owned businesses were accused of offering predatory terms with interest rates of up to 876 percent per annum and employing unethical debt recovery practices such as debt shaming and abusing customer privacy. In October 2020, Okash along with over 300 other digital mobile lenders were barred by the Central Bank of Kenya from accessing Kenya's credit information sharing (CIS) mechanism due to "misuse of the CIS (credit information sharing) by unregulated digital and credit-only lenders, and particularly their poor responsiveness to customer complaints." In August 2020, Opera announced its divestment from majority ownership of its microlending holdings.


title: Futoshi Matsunaga

text: Matsunaga's crimes were so atrocious that most Japanese media were not willing to report the details. "The Japan Times" reported that prosecutors said the case is without comparison in the criminal history of Japan. Several writers, including Ryūzō Saki, published the details of the crimes.


title: Futoshi Matsunaga

text: Futoshi Matsunaga was born in Kokurakita Ward of the city of Kitakyūshū in Fukuoka Prefecture, and grew up in Yanagawa. Matsunaga received good grades in school and had a charming personality, but tended to exhibit disciplinary problems. He was transferred to another high school after engaging in a relationship with a junior high school girl. He married at 19 and had a son.


title: Futoshi Matsunaga

text: Despite being married, Matsunaga was involved with at least ten mistresses. In October 1982, during his marriage, he became involved with Junko Ogata, one of his former schoolmates from Yanagawa. In 1984, Matsunaga promised to marry Junko, but her mother, Shizumi Ogata, did not approve of the relationship because of Matsunaga's abuse of her daughter. Matsunaga raped Shizumi as a result. In 1985, Matsunaga convinced Junko that her family hated her because of a suicide attempt and persuaded her to move in with him.


title: Futoshi Matsunaga

text: That same year, Matsunaga also purchased a building in which he could operate a futon business. Afterwards, he began to electrically shock employees on the third floor. Matsunaga would sometimes suddenly shout towards other men, saying things like, "There is a spirit behind you! It is sucking away your fortune!" He also made references to religious terms like "saṃsāra" and "kami". By 1992, Matsunaga had stolen 180 million yen (about US$2.2 million) through fraud or blackmail. He and Junko evaded police capture and were put on Japan's most wanted list.


title: Futoshi Matsunaga

text: Matsunaga lived in a condominium in Kokurakita-ku. His first victim was a married woman with three children. In April 1993, he convinced her to leave her husband and run away with him, telling the woman that Junko was his sister. One of her children died under mysterious circumstances in September 1993. Her two other children went to live with their father and grandfather the following month. During their relationship, Matsunaga defrauded the woman for 11.8 million yen (about US$145,510). She died mysteriously in March 1994, and the police were unable to prove that Matsunaga had killed the woman or her child.


title: Futoshi Matsunaga

text: Later that year, Matsunaga began victimizing Kumio Toraya and his daughter. Kumio had previously confided to Matsunaga about his previous criminal history; Matsunaga used this information to blackmail Kumio. Kumio and his daughter were held captive in Matsunaga's apartment, where Matsunaga tortured him with electric shocks, forced him to eat his own feces, and forced his daughter to bite her father. Kumio died as a result of this abuse on February 26, 1996. Matsunaga convinced Kumio's daughter that she had murdered her father. He told Junko and the girl to dispose of the remains, which were thrown into the sea near the Kunisaki Peninsula after being pulverized.


title: Futoshi Matsunaga

text: Soon after, Matsunaga found another target in a female acquaintance of Kumio. He convinced the woman that he was a graduate of Kyoto University and promised to marry her. Instead, he defrauded her of 5.6 million yen (about US$69,066). As before, the woman and her daughter were confined to Matsunaga's apartment. The woman escaped by jumping from the second floor in March 1997. She was put into the care of a mental hospital and her daughter was released.


title: Futoshi Matsunaga

text: The following month, Junko left for work and did not return. Matsunaga contacted her family, threatening them and blackmailing Shizumi over the 1985 rape. Matsunaga then faked his own suicide, prompting Junko to return, whereupon she was subjected to continued abuse. He also raped Junko's married sister, Rieko. Junko's family gave 63 million yen (about US$777,116) to Matsunaga, after which he held them captive and psychologically controlled them in ways similar to the methods of cult-leader Shoko Asahara.


title: Futoshi Matsunaga

text: On December 21, 1997, Matsunaga coerced Junko to shock her 61-year-old father, Takashige, to the point of death. When Shizumi's mental state began to deteriorate, Matsunaga commanded Rieko and her husband, Kazuya, to strangle her on January 20, 1998. Several weeks later, he commanded Kazuya to strangle Rieko while their 10-year-old daughter, Aya, held her down. Matsunaga and Junko then confined Kazuya to a bathroom, where he starved to death on April 13, 1998. Matsunaga then forced Junko and Aya to kill Rieko's 5-year-old son, Yuki. During the trial, Kumio's daughter testified that Matsunaga and Junko had tortured Aya with electricity. Junko's testimony differed, saying the girl's recollections might have been inaccurate because of guilty feelings about committing her first murder. Kumio's daughter strangled Aya on June 7, 1998. Matsunaga and Junko dismembered and boiled their victims' remains in pots, then finally disposed of them in washrooms or into the sea. Matsunaga blamed the murders on Junko, who, with their two children, were the only survivors in her family.


title: Futoshi Matsunaga

text: In July 2000, Matsunaga convinced another woman to go away with him, lured by the prospect of marriage. In August 2001, she gave her twin children to him and Junko. Matsunaga and Junko then convinced the woman to give them 20 million yen (about US$246,580), telling her that they would need the money to bring up her children.


title: Futoshi Matsunaga

text: Kumio's daughter, who was being held captive, escaped from Matsunaga on January 30, 2002, but Matsunaga found the girl on February 15 and took her back into captivity. He then tortured the girl with electric shocks. On March 6, the girl escaped from Matsunaga again and reported the crimes to the police. She was 17 years old. The police arrested Matsunaga and Junko the next day when they tried to retrieve the girl. The twins and the couple's two children were taken into police protection.


title: Futoshi Matsunaga

text: The media initially reported only that Matsunaga and Junko had held their victims captive, similar to the case of Fusako Sano, until details of the couple's murders emerged.


title: Futoshi Matsunaga

text: The pair were charged with Aya's murder on September 18, 2002; Takashige's murder on October 12, 2002; Shizumi's murder on December 6, 2002; Yuki's murder on January 11, 2003; Kumio's murder on February 3, 2003; Rieko's murder on February 25, 2003; and Kazuya's murder on May 30, 2003. No murder charges were brought against Kumio's daughter. Junko calmly confessed to her part in the murders, but Matsunaga insisted that the women had fabricated their stories about him. Police never recovered any human remains and found no physical evidence, so they relied primarily upon the testimonies of Kumio's and Junko's daughters during the investigation.


title: Futoshi Matsunaga

text: On September 28, 2005, a district court in Fukuoka sentenced Matsunaga and Junko to die by hanging. The court tried six cases, but considered that they had not killed Takashige directly, but had only injured him by electric shocks which later resulted in his death.


title: Futoshi Matsunaga

text: The pair appealed the verdict. On September 26, 2007, the Fukuoka High Court upheld Matsunaga's original sentence, but Junko's sentence was changed from death to life imprisonment because Matsunaga had exerted control over Junko to force her to kill the victims.


title: Futoshi Matsunaga

text: In 2019, Sion Sono announced the making of his project "The Forest of Love", which is based on Matsunaga's crimes. It was released by Netflix on October 11, 2019.


title: Fifth disease

text: Erythema infectiosum, fifth disease, or slapped cheek syndrome is one of several possible manifestations of infection by parvovirus B19. Fifth disease typically presents as a rash and is more common in children. While parvovirus B19 can affect humans of all ages, only two out of ten individuals will present with physical symptoms.


title: Fifth disease

text: The name "fifth disease" comes from its place on the standard list of rash-causing childhood diseases, which also includes measles (first), scarlet fever (second), rubella (third), Dukes' disease (fourth, but is no longer widely accepted as distinct from scarlet fever), and roseola (sixth). Treatment is mostly supportive.


title: Fifth disease

text: Fifth disease starts with a low-grade fever, headache, rash, and cold-like symptoms, such as a runny or stuffy nose. These symptoms pass, then a few days later, the rash appears. The bright red rash most commonly appears in the face, particularly the cheeks. This is a defining symptom of the infection in children (hence the name "slapped cheek disease"). Occasionally, the rash will extend over the bridge of the nose or around the mouth. In addition to red cheeks, children often develop a red, lacy rash on the rest of the body, with the upper arms, torso, and legs being the most common locations. The rash typically lasts a few days and may itch; some cases have been known to last for several weeks. Patients are usually no longer infectious once the rash has appeared.


title: Fifth disease

text: Teenagers and adults may present with a self-limited arthritis. It manifests in painful swelling of the joints that feels similar to arthritis. Older children and adults with fifth disease may have difficulty in walking and in bending joints such as wrists, knees, ankles, fingers, and shoulders.


title: Fifth disease

text: The disease is usually mild, but in certain risk groups and rare circumstances, it can have serious consequences:


title: Fifth disease

text: Fifth disease, also known as erythema infectiosum, is caused by parvovirus B19, which only infects humans. Infection by parvovirus B19 can lead to multiple clinical manifestations, but the most common is fifth disease.


title: Fifth disease

text: Parvovirus B19 (B19V) is a small, single-stranded, non-enveloped DNA virus. Binding of B19V capsid to the cellular receptor globoside (Gb4Cer) results in a cascade of structural changes and subsequent signal transduction processes facilitating the entry of parvovirus B19 into the host cell. After gaining access to the host cell, B19V binds to glycosphingolipid globoside (blood group P antigen) targeting erythroid lineage in the bone marrow. Replication of viral genome and release of virus from infected cells lead to various complex effects on host's cellular environment such as induction of DNA damage, hijack of cell cycle and apoptosis (killing of infected cells).


title: Fifth disease

text: B19V DNA has been found in a wide range of tissues in healthy and diseased individuals indicates the persistence of B19V infection. According to a clinical microbiology review published by Jianming Qiu "Persistence of viral DNA has been detected in up to 50% of biopsy specimens of the spleen, lymph nodes, tonsils, liver, heart, synovial tissues, skin, brain, and testes, for decades after infection."


title: Fifth disease

text: Recovery from parvovirus B19 infection is achieved by production of IgM antibodies which are specific for virus and are generated 10–12 days after infection. After day 16, when signs of fifth disease (red rashes) and arthralgia (pain in joints) becomes apparent, specific anti B19 IgG is produced by immune cells. Production of serum anti B19 IgG keeps infection under control and facilitates the recovery of erythroid cell production in erythroid lineage cells that were targeted by parvovirus B19.


title: Fifth disease

text: The "slapped cheek" appearance of the rash can be suggestive of fifth disease, however, the rash can be mistaken with other skin related disease or infections. Blood samples testing can be definitive in confirming diagnosis. Anti-parvovirus B19 IgM antibody serum assay is the preferred method to detect previous infection. An antibody assay uses antibodies designed to detect parvovirus antigen or protein in blood circulation. The assay can result positive one week after initial infection. Negative results may prompt retesting in the future to rule out early sampling of blood serum. A positive result can also be indicative of an infection within the past two to six months. People acquire lifetime immunity if IgG antibodies are produced in response to parvovirus B19 exposure. Infection by parvovirus B19 can also be confirmed by isolation of viral DNA detected by PCR or direct hybridization. PCR Is considered significantly more sensitive to detecting viral antigen compared direct DNA hybridization. DNA hybridization assay can better detect variants of the parvovirus B19. There exists 3 biological similar genotypes of parvovirus B19, numbered one through three. The most common genotype circulating is genotype one. Laboratory tests can indicate complications of infection, including anemia, liver damage, and low platelet count.


title: Fifth disease

text: Fifth disease is transmitted primarily by respiratory secretions (saliva, mucus, etc.), but can also be spread by contact with infected blood. The incubation period (the time between the initial infection and the onset of symptoms) is usually between 4 and 21 days. Individuals with fifth disease are most infectious before the onset of symptoms. Typically, school children, day-care workers, teachers, and parents are most likely to be exposed to the virus. When symptoms are evident, the risk of transmission is small; therefore, symptomatic individuals do not need to be isolated. Vertical transmission from maternal infection may also occur, which can lead to hydrops fetalis due to the infection's detrimental effects on red blood cell production.


title: Fifth disease

text: Treatment is supportive, as the infection is frequently self-limiting. No specific therapy is recommended. Antipyretics are commonly used to reduce fevers. In cases of arthropathy, such as those with arthritis or arthralgia, non-steroidal anti-inflammatories (NSAIDs) or other ant-inflammatories can be used. The rash usually does not itch, but can be mildly painful. The rash itself is not considered contagious. The infection generally lasts about 5 to 10 days. Stress, hot temperatures, exercise, and exposure to sunlight can contribute to reoccurrence within months of the initial infection. Upon resolution, immunity is considered life-long. Populations at greater risk of complications (see below) may need referral to a specialist. Anemia is a more severe complication that could result from parvovirus B19 infection and requires a blood transfusion as part of therapy.


title: Fifth disease

text: Fifth Disease is a viral illness caused by Parvovirus B19. The illness is very common and self-limiting. The modes of transmission include respiratory droplets, blood, or mother to fetus. Fifth Disease is most prevalent in children aged 5 to 15 years old. Fifth disease occurs at lower rates in adults. The virus spreads easily and once contracted, the body will begin developing lasting immunity to reinfection. The prevalence of antibodies is 50% in children and 70% to 85% in adults. The virus affects both men and women equally. During the spring and winter, epidemic outbreaks are most likely to occur. In the summer and fall, sporadic cases and outbreaks occur. The outbreaks most commonly occur in daycares and schools. The periodicity of the outbreak cycle is three-to-seven years. The risk of acquiring the viral illness increases when exposed to an infected person or contaminated blood. Individuals who have an occupation that requires close contact with infected people such as healthcare workers and teachers are at an increased risk of acquiring the viral illness. Another risk factor of fifth disease are immunocompromised individuals, those with anemia are at a higher risk of developing complications. Pregnant women are at risk for acquiring viral illness, especially during the first half of pregnancy. Though, complications are very rare and less than 5% of these cases will experience serious complications. The most common complication among pregnant women is anemia. In rare cases, severe anemia can occur, and a buildup of fluid can develop. A buildup of fluid can cause congestive heart failure or death. A blood infusion or induction may be necessary. No vaccine is available for human parvovirus B19, though attempts have been made to develop one.


title: Fifth disease

text: Parvovirus, the virus causing the fifth disease, was first discovered in 1975 by Yvonne Cossart. It, or a disease presenting similarly, was first described by Robert Willan in his book called On Cutaneous Diseases in 1808 as "rubeola, sine catarrho". It was better defined by Anton Tschamer in 1889 as a rubella variant ("Ortliche Rotheln") and described it as abortive rubella, identified as a distinct condition in 1896 by Theodor Escherich, and given the name "erythema infectiosum" in 1899. The term "Fifth disease" was coined in 1905 by the Russian-French physician Léon Cheinisse (1871-1924), who proposed a numbered classification of the six most common childhood exanthems. The virus was first described in 1957 at the University of Pennsylvania by Werner, Brachman et al.


title: Fifth disease

text: A 2019 systematic review examined the rates of parvovirus B19 infection among daycare workers. Since transmission typically occurs through respiratory secretions, it was thought that daycare workers would be at an increased risk of infection because young children can spread saliva through drool. The systematic review indicates that daycare workers are at an increased risk for infection. Another review also supports the finding that daycare workers have an increased risk of contracting parvovirus B19 infection. A 2019 meta-analysis examined rates of parvovirus B19 infection among those with Sickle Cell Disease (SCD) using IgG and IgM antibody detection. Pooled data from Africa, Asia, and the Americas revealed a 48.8% parvovirus B19 infection prevalence among persons with SCD. Prevalence of infection was also determined by geographic location, where areas with reduced access to adequate housing had higher prevalence (Africa was 55.5%). A 2020 literature review also supports the finding that persons with SCD, as well as those with the blood disorder beta thalassemia, are at a higher risk of parvovirus B19 infection.


title: Fifth disease

text: There are some known complications associated with Fifth Disease relating to pregnancy. While parvovirus B19 is typically transmitted via respiratory secretions or hand to mouth contact, it has also been known to be passed from pregnant mothers to fetuses. Roughly 50-75% of all pregnant women are immune to parvovirus B19 while the remainder of women are susceptible to mild illness. A majority of fetuses who do contract parvovirus B19 show either no significant symptoms or complete resolution of the virus. However, the following serious complications are rare but possible: miscarriage, stillbirth, fetal anemia, hepatic failure, and abnormal neurodevelopment outcome. In some cases, fetuses would develop hydrops fetalis due to congenital parvovirus B19. This condition was studied as a determinant of later fetal outcomes, such as miscarriage or perinatal death, in 2016 systematic review. The review showed that those born with parvovirus B19 that caused hydrops fetalis did have an association with higher mortality risk and higher risk of complications. While the potential consequences of erythema infectiosum can be quite serious in pregnancy, mothers can be tested for immunity via the presence of IgG and IgM antibodies.


title: Fifth disease

text: In addition to fetuses, parvovirus B19 infection and its effects has been studied in adults as well. The virus has also been associated with the development of neurological complications, as identified in a systematic review in 2014. This analysis included a total of 89 studies covering complications in both the central and nervous system such as encephalitis, meningitis, and peripheral neuropathy. However, the specific pathophysiology of these complications has yet to be discovered but the review does encourage the use of antibody testing to determine a patient's risk. Infection of this virus is not limited to the nervous system. Parvovirus B19 has also been linked to cases of cardiac inflammation that can cause structural damage to the heart over time. If the damage progresses and is significant, cardiac cell death may occur.


title: Fifth disease

text: Individuals that are living with HIV are also susceptible to complications if infected due to being immunocompromised. While relatively rare, those who live with both HIV and parvovirus B19 infection will be unable to fight off the B19 virus. This can result in substantial loss of red blood cells and cause anemia.


title: Relative risk

text: The relative risk (RR) or risk ratio is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group. Together with risk difference and odds ratio, relative risk measures the association between the exposure and the outcome.


title: Relative risk

text: Relative risk is used in the statistical analysis of the data of ecological, cohort, medical and intervention studies, to estimate the strength of the association between exposures (treatments or risk factors) and outcomes. Mathematically, it is the incidence rate of the outcome in the exposed group, formula_1, divided by the rate of the unexposed group, formula_2. As such, it is used to compare the risk of an adverse outcome when receiving a medical treatment versus no treatment (or placebo), or for environmental risk factors. For example, in a study examining the effect of the drug apixaban on the occurrence of thromboembolism, 8.8% of placebo-treated patients experienced the disease, but only 1.7% of patients treated with the drug did, so the relative risk is .19 (1.7/8.8): patients receiving apixaban had 19% the disease risk of patients receiving the placebo. In this case, apixaban is a protective factor rather than a risk factor, because it reduces the risk of disease.


title: Relative risk

text: Assuming the causal effect between the exposure and the outcome, values of relative risk can be interpreted as follows:


title: Relative risk

text: As always, correlation does not mean causation; the causation could be reversed, or they could both be caused by a common confounding variable. The relative risk of having cancer when in the hospital versus at home, for example, would be greater than 1, but that is because having cancer causes people to go to the hospital. Also, for example, the relative risk of having lung cancer when you have smoker's cough versus no cough, would be greater than 1, but that is because they are both caused by a common confounder, smoking.


title: Relative risk

text: Relative risk is commonly used to present the results of randomized controlled trials. This can be problematic if the relative risk is presented without the absolute measures, such as absolute risk, or risk difference. In cases where the base rate of the outcome is low, large or small values of relative risk may not translate to significant effects, and the importance of the effects to the public health can be overestimated. Equivalently, in cases where the base rate of the outcome is high, values of the relative risk close to 1 may still result in a significant effect, and their effects can be underestimated. Thus, presentation of both absolute and relative measures is recommended.


title: Relative risk

text: The sampling distribution of the formula_4is closer to normal than the distribution of RR, with standard error


title: Relative risk

text: where formula_9 is the standard score for the chosen level of significance. To find the confidence interval around the RR itself, the two bounds of the above confidence interval can be exponentiated.


title: Relative risk

text: In regression models, the exposure is typically included as an indicator variable along with other factors that may affect risk. The relative risk is usually reported as calculated for the mean of the sample values of the explanatory variables.


title: Relative risk

text: The relative risk is different from the odds ratio, although the odds ratio asymptotically approaches the relative risk for small probabilities of outcomes. If IE is substantially smaller than "IN", then IE/(IE + IN) formula_10 IE/IN. Similarly, if CE is much smaller than CN, then CE/(CN + CE) formula_10 CE/CN. Thus, under the rare disease assumption


title: Relative risk

text: In practice the odds ratio is commonly used for case-control studies, as the relative risk cannot be estimated.


title: Relative risk

text: In fact, the odds ratio has much more common use in statistics, since logistic regression, often associated with clinical trials, works with the log of the odds ratio, not relative risk. Because the (natural log of the) odds of a record is estimated as a linear function of the explanatory variables, the estimated odds ratio for 70-year-olds and 60-year-olds associated with the type of treatment would be the same in logistic regression models where the outcome is associated with drug and age, although the relative risk might be significantly different.


title: Relative risk

text: Since relative risk is a more intuitive measure of effectiveness, the distinction is important especially in cases of medium to high probabilities. If action A carries a risk of 99.9% and action B a risk of 99.0% then the relative risk is just over 1, while the odds associated with action A are more than 10 times higher than the odds with B.


title: Relative risk

text: In statistical modelling, approaches like Poisson regression (for counts of events per unit exposure) have relative risk interpretations: the estimated effect of an explanatory variable is multiplicative on the rate and thus leads to a relative risk. Logistic regression (for binary outcomes, or counts of successes out of a number of trials) must be interpreted in odds-ratio terms: the effect of an explanatory variable is multiplicative on the odds and thus leads to an odds ratio.


title: Relative risk

text: We could assume a disease noted by formula_13, and no disease noted by formula_14, exposure noted by formula_15, and no exposure noted by formula_16. The relative risk can be written as


title: Relative risk

text: This way the relative risk can be interpreted in Bayesian terms as the posterior ratio of the exposure (i.e. after seeing the disease) normalized by the prior ratio of exposure. If the posterior ratio of exposure is similar to that of the prior, the effect is approximately 1, indicating no association with the disease, since it didn't change beliefs of the exposure. If on the other hand, the posterior ratio of exposure is smaller or higher than that of the prior ratio, then the disease has changed the view of the exposure danger, and the magnitude of this change is the relative risk.


title: Aliphatic compound

text: In organic chemistry, hydrocarbons (compounds composed solely of carbon and hydrogen) are divided into two classes: aromatic compounds and aliphatic compounds (; G. "aleiphar", fat, oil). Aliphatic compounds can be saturated, like hexane, or unsaturated, like hexene and hexyne. Open-chain compounds, whether straight or branched, and which contain no rings of any type, are always aliphatic. Cyclic compounds can be aliphatic if they are not aromatic.


title: Aliphatic compound

text: Aliphatic compounds can be saturated, joined by single bonds (alkanes), or unsaturated, with double bonds (alkenes) or triple bonds (alkynes). If other elements (heteroatoms) are bound to the carbon chain, the most common being oxygen, nitrogen, sulfur, and chlorine, it is no longer a hydrocarbon, and therefore no longer an aliphatic compound.


title: Aliphatic compound

text: Most aliphatic compounds are flammable, allowing the use of hydrocarbons as fuel, such as methane in Bunsen burners and as liquefied natural gas (LNG), and ethyne (acetylene) in welding.


title: Aliphatic compound

text: Important examples of low-molecular aliphatic compounds can be found in the list below (sorted by the number of carbon-atoms):


title: CS50

text: CS50 (Computer Science 50) is an on-campus and online introductory course on computer science taught at Harvard University and Yale University. In 2016, CS50 became available to high school students as an Advanced Placement Computer Science course. The on-campus version is Harvard's largest class with 800 students, 102 staff and up to 2,200 participants in their regular hackathons.


title: CS50

text: The course material is available online for free on the EdX platform, with a range of certificates available for a fee. this online version, called CS50x, teaches the languages C, Python, SQL, HTML, CSS, and JavaScript. It also teaches fundamental computer-science concepts including arrays and data structures, and the Flask web framework. The 2021 iteration of the course introduced three new additional lectures on computer security, artificial Intelligence, and the ethics of technology.


title: CS50

text: The lead instructor is Harvard professor David Malan. Doug Lloyd and Brian Yu is also a former member of CS50 and was one of the lecturers. Facebook co-founder Mark Zuckerberg and former Microsoft Chief Executive Officer Steve Ballmer have given guest lectures. The CS50 course first appeared on-campus in 1989.


title: CS50

text: Several follow-on programs exist, focusing on web programming, artificial intelligence, game development, and mobile apps.


title: CS50

text: Lectures are recorded and uploaded to several services including iTunes U, EdX, and YouTube. Additional video "walkthroughs" are recorded with professors and volunteer students. Course questions, called problem sets, or "psets" for short, are available in both PDF and HTML format. Students can upload problem set answers, and some questions are graded by automation. Students can also use special software to check their code in the cloud. In 2016, CS50 became the first university course to offer students the possibility to watch all lectures entirely in virtual reality. In 2022, the course shifted from CS50 IDE to a web based version of VS Code based on GitHub codespaces and now the lectures are available in 4K HDR and SDR.


title: CS50

text: CS50 also provides courses for people who are new to programming or who want to understand more about technology.


title: Eliaquim Mangala

text: Eliaquim Hans Mangala (born 13 February 1991) is a French professional footballer who plays as a centre-back.


title: Eliaquim Mangala

text: Born in France, he moved to Belgium as a child and began his career there at Standard Liège, going onto Porto in 2011 where he won consecutive Primeira Liga titles before joining Manchester City in 2014 for £32 million. He played 79 matches for City, won the Premier League in 2017–18, and had loans at Valencia and Everton, before joining the former on a free transfer in 2019.


title: Eliaquim Mangala

text: Mangala made his debut with the France national team on 6 June 2013 against Uruguay. He was included in the nation's squads for the 2014 FIFA World Cup and UEFA Euro 2016, helping them finish as runners-up in the latter tournament.


title: Eliaquim Mangala

text: Mangala was born in the northwestern Parisian suburb of Colombes to Congolese parents, but moved to Belgium at the age of five to live in the French-speaking city of Namur. At the same age, he joined local club "Athletic Club Lustin" as a youth player and spent six years at the club before moving to "CS Wépionnais" in nearby Wépion. After two years in Wépion, Mangala joined the biggest club in the city, UR Namur, and quickly impressed. While at Namur, Mangala was utilised as a striker and his positive displays at youth level led to interest from Standard Liège. In 2007, Mangala and Standard reached an agreement on a three-year youth contract.


title: Eliaquim Mangala

text: Mangala joined Standard Liège and, upon his arrival, was converted into a left back and inserted into the club's under-17 team for the 2007–08 season. Mangala's admirable play with the team led to the player being promoted to Standard's under-19 team in January 2008, where he again switched positions, this time moving into central defence. During his time with the under-19 team, Mangala made the bench several times for Standard's under-21 team, despite being only 17 years old.


title: Eliaquim Mangala

text: For the 2008–09 season, Mangala was given the opportunity to train and play with the first team. On 23 October 2008, he signed his first professional contract, agreeing to a five-year deal with the club. Mangala was officially promoted to the senior team and assigned the number 22 shirt. On 9 November, he made his professional debut as an 89th-minute substitute in a 3–1 victory over Germinal Beerschot. He made another late appearance against Gent before earning his first career league start against Dender on 17 January 2009. In the match, Mangala provided the assist on the opening goal scored by Milan Jovanović in the 3rd minute of play. Standard won the match 3–2 with Mangala playing the entire match. He finished the season with 11 league appearances as Standard Liège were crowned champions. He also appeared in UEFA Cup matches against Italian club Sampdoria, German club Stuttgart, and Portuguese team Sporting CP, starting the match against the latter.


title: Eliaquim Mangala

text: Mangala was inserted as a starter for the 2009–10 season making his debut in the club's 2–0 victory over Genk in the Belgian Supercup on 25 July 2009. On 12 September, Mangala scored his first professional goal in a league match against Mechelen in a 3–0 victory. Four days later, Mangala scored another goal against English club Arsenal in the club's opening UEFA


title: Eliaquim Mangala

text: In what proved to be his final league match for Standard, Mangala converted a Steven Defour free-kick to give his team a 1–0 lead over KRC Genk at half-time, but striker Kennedy Ugoala Nwanganga earned a 1–1 draw for Genk, securing the league title by just half a point over Standard. In his final appearance for the club on 21 May 2011, Mangala scored Standard's first goal in their 2–0 victory over K.V.C. Westerlo in the final of the Belgian Cup, ending an 18-year cup drought.


title: Eliaquim Mangala

text: Mangala joined reigning Europa League champions Porto on 16 August 2011. The deal also included Porto signing his Standard teammate Steven Defour in a combined deal that totalled £11.4 million. He played his first season with Porto as a substitute behind the likes of Rolando, Maicon and Nicolás Otamendi. He made his first appearance in the 2012–13 season for Porto in the Supertaça Cândido de Oliveira against Académica on 11 August 2012, playing the full 90 minutes as Porto won the pre-season title with a 1–0 win. He made his first-team breakthrough with Porto that season, becoming the first-choice centre back and scoring four league goals, one of which was in a 2–2 draw with Benfica on 13 January 2013. Mangala featured in Porto's 2–0 win over Paços de Ferreira on 19 May 2013, leading the club to an undefeated season and a third-straight league title, by just one point over rivals Benfica.


title: Eliaquim Mangala

text: In the January 2014 transfer window, Manchester City made an offer for Mangala and his teammate Fernando, but abandoned interest when Porto held out for £50 million. On 23 February, he was sent off for a reckless challenge inside the area and Porto fell to a 1–0 defeat to Estoril as Evandro converted the spot kick. In Porto's Europa League Round of 16-second leg against Eintracht Frankfurt four days later, Mangala scored two goals, both from headers, as Porto battled back from 2–0 down to draw 3–3 and secure passage to the quarter-finals on away goals. On 3 April, he headed in the game's only goal as Porto defeated Sevilla in the first-leg of that round. His goal would not be enough to guide the Portuguese into the next round as they fell to a 4–1 loss in Spain seven days later.


title: Eliaquim Mangala

text: On 11 August 2014, Mangala signed for English club Manchester City on a five-year contract, for a reported £31.8 million transfer fee. It was however reported 18 months into his contract that the fee was more in the region of £42m due to spiralling costs as a result of Mangala's split ownership at Porto, with City having to pay in the region of £18m to two companies which owned over 40% of Mangala's economic rights. This second figure would make Mangala the most expensive defender in British transfer history at the time. He reunited with his former Porto teammate, Fernando, who had joined City earlier in the summer.


title: Eliaquim Mangala

text: Mangala made his debut in City's fifth match of the Premier League season, a 1–1 home draw against Chelsea on 21 September. Lining up alongside captain Vincent Kompany, his performance was described by BBC Sport as "colossal". Six days later, an own goal and concession of a penalty by Mangala caused City to lose a 2–0 lead against Hull City, although they eventually triumphed 4–2. Despite media criticism, manager Manuel Pellegrini said "we continue to trust him because he is a very good player who had very bad luck". On 30 November, Mangala was sent off for two yellow cards in City's 3–0 win away to Southampton.


title: Eliaquim Mangala

text: On 31 August 2016, Mangala joined Spanish club Valencia on a season-long loan. He made his debut for the "Che" on 11 September, starting alongside fellow newcomer Ezequiel Garay in a 3–2 home loss to Real Betis. On 28 February 2017, he scored his first goal to defeat Leganés at Mestalla, and on 19 March he headed the opening goal of a 4–2 away loss at FC Barcelona in which he was sent off for pulling at Luis Suárez in the penalty area.


title: Eliaquim Mangala

text: Mangala joined Premier League club Everton on loan on 31 January 2018. He made his debut against Arsenal, but in his second game against Crystal Palace he was forced off at half-time with a knee injury. He later underwent surgery and was ruled out for the remainder of the season. At the end of the season he was eligible for a Premier League winners' medal having previously made nine league appearances for Manchester City before joining Everton.


title: Eliaquim Mangala

text: On 12 August 2019, Mangala returned to former club Valencia on a permanent basis after agreeing to a two-year contract on a free transfer. He and teammates Ezequiel Garay and José Luis Gayà tested positive for COVID-19 virus during the COVID-19 pandemic in Spain.


title: Eliaquim Mangala

text: On 20 January 2022, Mangala signed for Saint-Étienne on a free transfer, on a six-month contract. He played 14 Ligue 1 matches, and scored an equaliser in a 2–1 home loss to Reims in the penultimate fixture on 14 May. He was suspended three times due to accumulating nine yellow cards, missing the first leg of the promotion/relegation playoff against Auxerre and returning in the second leg for the penalty shootout defeat.


title: Eliaquim Mangala

text: Due to being raised in Belgium, Mangala did not feature with any of France's youth football teams. In 2008, he was approached by the Royal Belgian Football Association who called the player up to the country's under-18 national team. However, due to not possessing a passport at the time, the call up was deemed futile. After excelling with Standard Liège's senior team, Mangala drew the interest of the French Football Federation with France under-21 manager Erick Mombaerts attending a match between Liège and Mouscron at the Stade Le Canonnier in November. On 5 November 2009, Mangala was selected, for the first time, to the under-21 team for a friendly match against Tunisia on 13 November and a 2011 UEFA European Under-21 Championship qualification match against Slovenia on 17 November. Mangala made his under-21 debut in the Tunisia match, but missed the match against Slovenia after withdrawing from the team due to an injury suffered the previous day in training. On 2 March 2010, he earned his second straight selection to the under-21 team and started in central defence alongside captain Mamadou Sakho in the team's 3–1 win over Croatia.


title: Eliaquim Mangala

text: Mangala made his debut with the France senior team in a 1–0 loss to Uruguay on 6 June 2013. He was included in France's squad for the 2014 FIFA World Cup but did not make an appearance during the tournament, in which "Les Bleus" reached the quarter-finals.


title: Eliaquim Mangala

text: Mangala was also included in France's squad that finished runners-up at UEFA Euro 2016 on home soil. He made one appearance in the quarter-finals on 3 July, replacing Laurent Koscielny for the final 18 minutes of a 5–2 win over Iceland at the Stade de France.


title: Linear time-invariant system

text: In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below. These properties apply (exactly or approximately) to many important physical systems, in which case the response of the system to an arbitrary input can be found directly using convolution: where is called the system's impulse response and ∗ represents convolution (not to be confused with multiplication, as is frequently employed by the symbol in computer languages). What's more, there are systematic methods for solving any such system (determining ), whereas systems not meeting both properties are generally more difficult (or impossible) to solve analytically. A good example of an LTI system is any electrical circuit consisting of resistors, capacitors, inductors and linear amplifiers.


title: Linear time-invariant system

text: Linear time-invariant system theory is also used in image processing, where the systems have spatial dimensions instead of, or in addition to, a temporal dimension. These systems may be referred to as "linear translation-invariant" to give the terminology the most general reach. In the case of generic discrete-time (i.e., sampled) systems, "linear shift-invariant" is the corresponding term. LTI system theory is an area of applied mathematics which has direct applications in electrical circuit analysis and design, signal processing and filter design, control theory, mechanical engineering, image processing, the design of measuring instruments of many sorts, NMR spectroscopy, and many other technical areas where systems of ordinary differential equations present themselves.


title: Linear time-invariant system

text: The fundamental result in LTI system theory is that any LTI system can be characterized entirely by a single function called the system's impulse response. The output of the system formula_2 is simply the convolution of the input to the system formula_1 with the system's impulse response formula_19. This is called a continuous time system. Similarly, a discrete-time linear time-invariant (or, more generally, "shift-invariant") system is defined as one operating in discrete time: formula_20 where "y", "x", and "h" are sequences and the convolution, in discrete time, uses a discrete summation rather than an integral.


title: Linear time-invariant system

text: LTI systems can also be characterized in the "frequency domain" by the system's transfer function, which is the Laplace transform of the system's impulse response (or Z transform in the case of discrete-time systems). As a result of the properties of these transforms, the output of the system in the frequency domain is the product of the transfer function and the transform of the input. In other words, convolution in the time domain is equivalent to multiplication in the frequency domain.


title: Linear time-invariant system

text: For all LTI systems, the eigenfunctions, and the basis functions of the transforms, are complex exponentials. This is, if the input to a system is the complex waveform formula_21 for some complex amplitude formula_22 and complex frequency formula_23, the output will be some complex constant times the input, say formula_24 for some new complex amplitude formula_25. The ratio formula_26 is the transfer function at frequency formula_23.


title: Linear time-invariant system

text: Since sinusoids are a sum of complex exponentials with complex-conjugate frequencies, if the input to the system is a sinusoid, then the output of the system will also be a sinusoid, perhaps with a different amplitude and a different phase, but always with the same frequency upon reaching steady-state. LTI systems cannot produce frequency components that are not in the input.


title: Linear time-invariant system

text: LTI system theory is good at describing many important systems. Most LTI systems are considered "easy" to analyze, at least compared to the time-varying and/or nonlinear case. Any system that can be modeled as a linear differential equation with constant coefficients is an LTI system. Examples of such systems are electrical circuits made up of resistors, inductors, and capacitors (RLC circuits). Ideal spring–mass–damper systems are also LTI systems, and are mathematically equivalent to RLC circuits.


title: Linear time-invariant system

text: Most LTI system concepts are similar between the continuous-time and discrete-time (linear shift-invariant) cases. In image processing, the time variable is replaced with two space variables, and the notion of time invariance is replaced by two-dimensional shift invariance. When analyzing filter banks and MIMO systems, it is often useful to consider vectors of signals.


title: Linear time-invariant system

text: A linear system that is not time-invariant can be solved using other approaches such as the Green function method.


title: Linear time-invariant system

text: The behavior of a linear, continuous-time, time-invariant system with input signal "x"("t") and output signal "y"("t") is described by the convolution integral:


title: Linear time-invariant system

text: where formula_28 is the system's response to an impulse: formula_29. formula_30 is therefore proportional to a weighted average of the input function formula_31. The weighting function is formula_32, simply shifted by amount formula_33. As formula_33 changes, the weighting function emphasizes different parts of the input function. When formula_35 is zero for all negative formula_36, formula_37 depends only on values of formula_38 prior to time formula_33, and the system is said to be causal.


title: Linear time-invariant system

text: To understand why the convolution produces the output of an LTI system, let the notation formula_40 represent the function formula_41 with variable formula_42 and constant formula_36. And let the shorter notation formula_44 represent formula_45. Then a continuous-time system transforms an input function, formula_46 into an output function, formula_47. And in general, every value of the output can depend on every value of the input. This concept is represented by:


title: Linear time-invariant system

text: where formula_49 is the transformation operator for time formula_33. In a typical system, formula_37 depends most heavily on the values of formula_38 that occurred near time formula_33. Unless the transform itself changes with formula_33, the output function is just constant, and the system is uninteresting.


title: Linear time-invariant system

text: In summary, the input function, formula_44, can be represented by a continuum of time-shifted impulse functions, combined "linearly", as shown at . The system's linearity property allows the system's response to be represented by the corresponding continuum of impulse responses, combined in the same way. And the time-invariance property allows that combination to be represented by the convolution integral.


title: Linear time-invariant system

text: An eigenfunction is a function for which the output of the operator is a scaled version of the same function. That is,


title: Linear time-invariant system

text: The exponential functions formula_64, where formula_65, are eigenfunctions of a linear, time-invariant operator. A simple proof illustrates this concept. Suppose the input is formula_66. The output of the system with impulse response formula_19 is then


title: Linear time-invariant system

text: So the system's response is a scaled version of the input. In particular, for any formula_65, the system output is the product of the input formula_72 and the constant formula_73. Hence, formula_64 is an eigenfunction of an LTI system, and the corresponding eigenvalue is formula_73.


title: Linear time-invariant system

text: i.e. that a complex exponential formula_85 as input will give a complex exponential of same frequency as output.


title: Linear time-invariant system

text: The eigenfunction property of exponentials is very useful for both analysis and insight into LTI systems. The one-sided Laplace transform


title: Linear time-invariant system

text: is exactly the way to get the eigenvalues from the impulse response. Of particular interest are pure sinusoids (i.e., exponential functions of the form formula_87 where formula_88 and formula_89). The Fourier transform formula_90 gives the eigenvalues for pure complex sinusoids. Both of formula_73 and formula_92 are called the "system function", "system response", or "transfer function".


title: Linear time-invariant system

text: The Laplace transform is usually used in the context of one-sided signals, i.e. signals that are zero for all values of "t" less than some value. Usually, this "start time" is set to zero, for convenience and without loss of generality, with the transform integral being taken from zero to infinity (the transform shown above with lower limit of integration of negative infinity is formally known as the bilateral Laplace transform).


title: Linear time-invariant system

text: The Fourier transform is used for analyzing systems that process signals that are infinite in extent, such as modulated sinusoids, even though it cannot be directly applied to input and output signals that are not square integrable. The Laplace transform actually works directly for these signals if they are zero before a start time, even if they are not square integrable, for stable systems. The Fourier transform is often applied to spectra of infinite signals via the Wiener–Khinchin theorem even when Fourier transforms of the signals do not exist.


title: Linear time-invariant system

text: Due to the convolution property of both of these transforms, the convolution that gives the output of the system can be transformed to a multiplication in the transform domain, given signals for which the transforms exist


title: Linear time-invariant system

text: One can use the system response directly to determine how any particular frequency component is handled by a system with that Laplace transform. If we evaluate the system response (Laplace transform of the impulse response) at complex frequency , where , we obtain |"H"("s")| which is the system gain for frequency "f". The relative phase shift between the output and input for that frequency component is likewise given by arg("H"("s")).


title: Linear time-invariant system

text: When the Laplace transform of the derivative is taken, it transforms to a simple multiplication by the Laplace variable "s".


title: Linear time-invariant system

text: Some of the most important properties of a system are causality and stability. Causality is a necessity for a physical system whose independent variable is time, however this restriction is not present in other cases such as image processing.


title: Linear time-invariant system

text: A system is causal if the output depends only on present and past, but not future inputs. A necessary and sufficient condition for causality is


title: Linear time-invariant system

text: where formula_19 is the impulse response. It is not possible in general to determine causality from the two-sided Laplace transform. However when working in the time domain one normally uses the one-sided Laplace transform which requires causality.


title: Linear time-invariant system

text: A system is bounded-input, bounded-output stable (BIBO stable) if, for every bounded input, the output is finite. Mathematically, if every input satisfying


title: Linear time-invariant system

text: (that is, a finite maximum absolute value of formula_1 implies a finite maximum absolute value of formula_2), then the system is stable. A necessary and sufficient condition is that formula_19, the impulse response, is in L (has a finite L norm):


title: Linear time-invariant system

text: As an example, the ideal low-pass filter with impulse response equal to a sinc function is not BIBO stable, because the sinc function does not have a finite L norm. Thus, for some bounded input, the output of the ideal low-pass filter is unbounded. In particular, if the input is zero for formula_112 and equal to a sinusoid at the cut-off frequency for formula_113, then the output will be unbounded for all times other than the zero crossings.


title: Linear time-invariant system

text: In many contexts, a discrete time (DT) system is really part of a larger continuous time (CT) system. For example, a digital recording system takes an analog sound, digitizes it, possibly processes the digital signals, and plays back an analog sound for people to listen to.


title: Linear time-invariant system

text: In practical systems, DT signals obtained are usually uniformly sampled versions of CT signals. If formula_1 is a CT signal, then the sampling circuit used before an analog-to-digital converter will transform it to a DT signal:


title: Linear time-invariant system

text: where "T" is the sampling period. Before sampling, the input signal is normally run through a so-called Nyquist filter which removes frequencies above the "folding frequency" 1/(2T); this guarantees that no information in the filtered signal will be lost. Without filtering, any frequency component "above" the folding frequency (or Nyquist frequency) is aliased to a different frequency (thus distorting the original signal), since a DT signal can only support frequency components lower than the folding frequency.


title: Linear time-invariant system

text: A discrete system transforms an input sequence, formula_118 into an output sequence, formula_121 In general, every element of the output can depend on every element of the input. Representing the transformation operator by formula_122, we can write:


title: Linear time-invariant system

text: Note that unless the transform itself changes with "n", the output sequence is just constant, and the system is uninteresting. (Thus the subscript, "n".) In a typical system, "y"["n"] depends most heavily on the elements of "x" whose indices are near "n".


title: Linear time-invariant system

text: For the special case of the Kronecker delta function, formula_124 the output sequence is the impulse response:


title: Linear time-invariant system

text: In such a system, the impulse response, formula_127, characterizes the system completely. That is, for any input sequence, the output sequence can be calculated in terms of the input and the impulse response. To see how that is done, consider the identity:


title: Linear time-invariant system

text: which is the familiar discrete convolution formula. The operator formula_134 can therefore be interpreted as proportional to a weighted average of the function "x"["k"].


title: Linear time-invariant system

text: The weighting function is "h"[−"k"], simply shifted by amount "n". As "n" changes, the weighting function emphasizes different parts of the input function. Equivalently, the system's response to an impulse at "n"=0 is a "time" reversed copy of the unshifted weighting function. When "h"["k"] is zero for all negative "k", the system is said to be causal.


title: Linear time-invariant system

text: An eigenfunction is a function for which the output of the operator is the same function, scaled by some constant. In symbols,


title: Linear time-invariant system

text: The exponential functions formula_137, where formula_138, are eigenfunctions of a linear, time-invariant operator. formula_139 is the sampling interval, and formula_140. A simple proof illustrates this concept.


title: Linear time-invariant system

text: So formula_146 is an eigenfunction of an LTI system because the system response is the same as the input times the constant formula_147.


title: Linear time-invariant system

text: The eigenfunction property of exponentials is very useful for both analysis and insight into LTI systems. The Z transform


title: Linear time-invariant system

text: is exactly the way to get the eigenvalues from the impulse response. Of particular interest are pure sinusoids; i.e. exponentials of the form formula_149, where formula_88. These can also be written as formula_146 with formula_152. The discrete-time Fourier transform (DTFT) formula_153 gives the eigenvalues of pure sinusoids. Both of formula_147 and formula_155 are called the "system function", "system response", or "transfer function".


title: Linear time-invariant system

text: Like the one-sided Laplace transform, the Z transform is usually used in the context of one-sided signals, i.e. signals that are zero for t<0. The discrete-time Fourier transform Fourier series may be used for analyzing periodic signals.


title: Linear time-invariant system

text: Due to the convolution property of both of these transforms, the convolution that gives the output of the system can be transformed to a multiplication in the transform domain. That is,


title: Linear time-invariant system

text: Just as with the Laplace transform transfer function in continuous-time system analysis, the Z transform makes it easier to analyze systems and gain insight into their behavior.


title: Linear time-invariant system

text: The input-output characteristics of discrete-time LTI system are completely described by its impulse response formula_142.


title: Linear time-invariant system

text: Two of the most important properties of a system are causality and stability. Non-causal (in time) systems can be defined and analyzed as above, but cannot be realized in real-time. Unstable systems can also be analyzed and built, but are only useful as part of a larger system whose overall transfer function "is" stable.


title: Linear time-invariant system

text: A discrete-time LTI system is causal if the current value of the output depends on only the current value and past values of the input. A necessary and sufficient condition for causality is


title: Linear time-invariant system

text: where formula_142 is the impulse response. It is not possible in general to determine causality from the Z transform, because the inverse transform is not unique. When a region of convergence is specified, then causality can be determined.


title: Linear time-invariant system

text: A system is bounded input, bounded output stable (BIBO stable) if, for every bounded input, the output is finite. Mathematically, if


title: Linear time-invariant system

text: (that is, if bounded input implies bounded output, in the sense that the maximum absolute values of formula_168 and formula_169 are finite), then the system is stable. A necessary and sufficient condition is that formula_142, the impulse response, satisfies


title: Linear time-invariant system

text: In the frequency domain, the region of convergence must contain the unit circle (i.e., the locus satisfying formula_172 for complex "z").


title: Brook trout

text: The brook trout (Salvelinus fontinalis) is a species of freshwater fish in the char genus "Salvelinus" of the salmon family Salmonidae. It is native to Eastern North America in the United States and Canada, but has been introduced elsewhere in North America, as well as to Iceland, Europe, and Asia. In parts of its range, it is also known as the eastern brook trout, speckled trout, brook charr, squaretail, brookie or mud trout, among others. A potamodromous population in Lake Superior, as well as an anadromous population in Maine, is known as coaster trout or, simply, as coasters. The brook trout is the state fish of nine U.S. states: Michigan, New Hampshire, New Jersey, New York, North Carolina, Pennsylvania, Vermont, Virginia, and West Virginia, and the Provincial Fish of Nova Scotia in Canada.


title: Brook trout

text: The brook trout was first scientifically described as "Salmo fontinalis" by the naturalist Samuel Latham Mitchill in 1814. The specific epithet ""fontinalis"" comes from the Latin for "of a spring or fountain", in reference to the clear, cold streams and ponds in its native habitat. The species was later moved to the char genus "Salvelinus", which in North America also includes the lake trout, bull trout, Dolly Varden, and the Arctic char.


title: Brook trout

text: There is little recognized systematic substructure in the brook trout, but two subspecies have been proposed. On the other hand, three ecological forms are distinguished.


title: Brook trout

text: The aurora trout, "S. f. timagamiensis", is a subspecies native to two lakes in the Temagami District of Ontario, Canada. The silver trout, ("Salvelinus agassizii" or "S. f. agassizii"), is an extinct trout species or subspecies last seen in Dublin Pond, New Hampshire, in 1930. It is considered by fisheries biologist Robert J. Behnke as a highly specialized form of brook trout.


title: Brook trout

text: Robert J. Behnke describes three ecological forms of the brook trout. A large lake form evolved in the larger lakes in the northern reaches of its range and are generally piscivorous as adults. A sea-run form that migrates into saltwater for short periods to feed evolved along the Atlantic coastline. Finally, a smaller generalist form evolved in the small lakes, ponds, rivers, and streams throughout most of the native range. This generalist form rarely attains sizes larger than or lives for more than three years. All three forms have the same general appearance.


title: Brook trout

text: The brook trout produces hybrids both with its congeners "Salvelinus namaycush" and "Salvelinus alpinus", and intergeneric hybrids with "Salmo trutta".


title: Brook trout

text: The splake is an intrageneric hybrid between the brook trout and lake trout ("S. namaycush"). Although uncommon in nature, they are artificially propagated in substantial numbers for stocking into brook trout or lake trout habitats. Although they are fertile, back-crossing in nature is behaviorally problematic and very little natural reproduction occurs. Splake grow more quickly than brook trout, become piscivorous sooner, and are more tolerant of competitors than brook trout.


title: Brook trout

text: The tiger trout is an intergeneric hybrid between the brook trout and the Eurasian brown trout ("Salmo trutta"). Tiger trout rarely occur naturally but are sometimes artificially propagated. Such crosses are almost always reproductively sterile. They are popular with many fish-stocking programs because they can grow quickly, and may help keep coarse fish (wild non "sport" fish) populations in check due to their highly piscivorous (fish-eating) nature.


title: Brook trout

text: The sparctic char is an intrageneric hybrid between the brook trout and the Arctic char ("S. alpinus").


title: Brook trout

text: The brook trout has a dark green to brown color, with a distinctive marbled pattern (called vermiculation) of lighter shades across the flanks and back and extending at least to the dorsal fin, and often to the tail. A distinctive sprinkling of red dots, surrounded by blue halos, occurs along the flanks. The belly and lower fins are reddish in color, the latter with white leading edges. Often, the belly, particularly of the males, becomes very red or orange when the fish are spawning.


title: Brook trout

text: Typical lengths of the brook trout vary from , and weights from . The maximum recorded length is and maximum weight . Brook trout can reach at least seven years of age, with reports of 15-year-old specimens observed in California habitats to which the species has been introduced. Growth rates are dependent on season, age, water and ambient air temperatures, and flow rates. In general, flow rates affect the rate of change in the relationship between temperature and growth rate. For example, in spring, growth increased with temperature at a faster rate with high flow rates than with low flow rates.


title: Brook trout

text: Brook trout are native to a wide area of Eastern North America, but are increasingly confined to higher elevations southward in the Appalachian Mountains to northern Georgia and northwest South Carolina, Canada from the Hudson Bay basin east, the Great Lakes–Saint Lawrence system, the Canadian maritime provinces, and the upper Mississippi River drainage as far west as eastern Iowa. Their southern historic native range has been drastically reduced, with fish being restricted to higher-elevation, remote streams due to habitat loss and introductions of brown and rainbow trout. As early as 1850, the brook trout's range started to extend west from its native range through introductions. The brook trout was eventually introduced into suitable habitats throughout the western U.S. during the late 19th and early 20th centuries at the behest of the American Acclimatization Society and by private, state, and federal fisheries authorities. Acclimatization movements in Europe, South America, and Oceania resulted in brook trout introductions throughout Europe, in Argentina, and New Zealand. Although not all introductions were successful, a great many established wild, self-sustaining populations of brook trout in non-native waters.


title: Brook trout

text: The brook trout inhabits large and small lakes, rivers, streams, creeks, and spring ponds. They prefer clear waters of high purity and a narrow pH range and are sensitive to poor oxygenation, pollution, and changes in pH caused by environmental effects such as acid rain. The typical pH range of brook trout waters is 5.0 to 7.5, with pH extremes of 3.5 to 9.8 possible. Water temperatures typically range from . Warm summer temperatures and low flow rates are stressful on brook trout populations—especially larger fish.


title: Brook trout

text: A potamodromous population of brook trout native to Lake Superior, which migrate into tributary rivers to spawn, are called "coasters". Coasters tend to be larger than most other populations of brook trout, often reaching in size. Many coaster populations have been severely reduced by overfishing and habitat loss by the construction of hydroelectric power dams on Lake Superior tributaries. In Ontario and Michigan, efforts are underway to restore and recover coaster populations.


title: Brook trout

text: When Europeans first settled in Eastern North America, semianadromous or sea-run brook trout, commonly called "salters", ranged from southern New Jersey, north throughout the Canadian maritime provinces, and west to Hudson Bay. Salters may spend up to three months at sea feeding on crustaceans, fish, and marine worms in the spring, not straying more than a few miles from the river mouth. The fish return to freshwater tributaries to spawn in the late summer or autumn. While in saltwater, salters gain a more silvery color, losing much of the distinctive markings seen in freshwater. However, within two weeks of returning to freshwater, they assume typical brook trout color and markings.


title: Brook trout

text: Brook trout have a diverse diet that includes larval, pupal, and adult forms of aquatic insects (typically caddisflies, stoneflies, mayflies, and aquatic dipterans), and adult forms of terrestrial insects (typically ants, beetles, grasshoppers, and crickets) that fall into the water, crustaceans, frogs and other amphibians, molluscs, smaller fish, invertebrates, and even small aquatic mammals such as voles and sometimes other young brook trout


title: Brook trout

text: The female constructs a depression in a location in the stream bed, sometimes referred to as a "redd", where groundwater percolates upward through the gravel. One or more males approach the female, fertilizing the eggs as the female expresses them. Most spawnings involve peripheral males, which directly influences the number of eggs that survive into adulthood. In general, the larger the number of peripheral males present, the more likely the eggs will be cannibalized. The eggs are slightly denser than water. The female then buries the eggs in a small gravel mound; they hatch in 95 to 100 days.


title: Brook trout

text: Today, many anglers practice catch-and-release tactics to preserve remaining populations. Organizations such as Trout Unlimited have been at the forefront of efforts to institute air and water quality standards sufficient to protect the brook trout. Revenues derived from the sale of fishing licenses have been used to restore many sections of creeks and streams to brook trout habitat.


title: Brook trout

text: The current world angling record brook trout was caught by Dr. W. J. Cook on the Nipigon River, Ontario, in July 1915. The trout weighed only because, at the time of weighing, it was badly decomposed after 21 days in the bush without refrigeration. A brook trout, caught in October 2006 in Manitoba, is not eligible for record status since it was released alive. This trout weighed about based on the accepted formula for calculating weight by measurements, and it currently stands as the record brook trout for Manitoba.


title: Brook trout

text: Brook trout are also commercially raised in large numbers for food production, being sold for human consumption in both fresh and smoked forms. Because of its dependence on pure water and a variety of aquatic and insect life forms, the brook trout is also used for scientific experimentation in assessing the effects of pollution and contaminated waters.


title: Brook trout

text: Brook trout are also raised commercially and sold to angling organizations or groups to stock their lakes or ponds. Some businesses hold a "U-fish license" where the public can fish at their lake or pond and buy the fish they catch.


title: Brook trout

text: Commercial fisheries do not commonly raise brook trout because they do not grow as fast as other types of fish.


title: Brook trout

text: Brook trout raised commercially are often kept in large circular tanks with a constant water flow going through them. This allows for a current to circulate through the tank and keep it clean, acting as a flush of water that takes fish waste with it. Some more elaborate systems operate on a re-circulation system where the water is filtered and reused.


title: Brook trout

text: The fish are typically fed a pelleted food consisting of 40–50% protein and 15% fat. The fish food is usually made from fish oil, animal protein, plant protein and vitamins and minerals. The protein is often sourced from soy beans.


title: Brook trout

text: Brook trout populations depend on cold, clear, well-oxygenated water of high purity. As early as the late 19th century, native brook trout in North America became extirpated from many watercourses as land development, forest clear-cutting, and industrialization took hold. Streams and creeks that were polluted, dammed, or silted up often became too warm to hold native brook trout, and were colonized by transplanted smallmouth bass and perch or other introduced salmonids such as brown and rainbow trout. The brown trout, a species not native to North America, has replaced the brook trout in much of the brook trout's native water. If already stressed by overharvesting or by temperature, brook trout populations are very susceptible to damage by the introduction of exogenous species. Many lacustrine populations of brook trout have been extirpated by the introduction of other species, particularly percids, but sometimes other spiny-rayed fishes.


title: Brook trout

text: In addition to chemical pollution and algae growth caused by runoff containing chemicals and fertilizers, air pollution has also been a significant factor in the disappearance of brook trout from their native habitats. In the U.S., acid rain caused by air pollution has resulted in pH levels too low to sustain brook trout in all but the highest headwaters of some Appalachian streams and creeks. Brook trout populations across large parts of eastern Canada have been similarly challenged; a subspecies known as the aurora trout was extirpated from the wild by the effects of acid rain. Today, in many parts of the range, efforts are underway to restore brook trout to those waters that once held native populations, stocking other trout species only in habitats that can no longer be recovered sufficiently to sustain brook trout populations.


title: Brook trout

text: Organizations such as Trout Unlimited and Trout Unlimited Canada are partnering with other organizations such as the Southern Appalachian Brook Trout Foundation, the Eastern Brook Trout Joint Venture, and state, provincial, and federal agencies to undertake projects that restore native brook trout habitat and populations.


title: Brook trout

text: Although brook trout populations are under stress in their native range, they are considered an invasive species where they have been introduced outside their historic native range. In the northern Rocky Mountains, non-native brook trout are considered a significant contributor to the decline or extirpation of native cutthroat trout ("Oncorhynchus clarki") in headwater streams. Non-native brook trout populations have been subject to eradication programs in efforts to preserve native species. In Yellowstone National Park, anglers may take an unlimited number of non-native brook trout in some watersheds. In the Lamar River watershed, a mandatory kill regulation for any brook trout caught is in effect. In Europe, introduced brook trout, once established, have had negative impacts on growth rates of native brown trout ("S. trutta").


title: Malice (1993 film)

text: Malice is a 1993 American neo-noir thriller film directed by Harold Becker, written by Aaron Sorkin and Scott Frank, and starring Alec Baldwin, Nicole Kidman, Bill Pullman, Anne Bancroft and George C. Scott. Adapted from a story by Jonas McCord, the plot follows Andy and Tracy Safian, a newlywed couple whose lives are upturned after they rent part of their Victorian home to Jed, a cavalier surgeon; things are further complicated when he removes Tracy's ovaries during an emergency surgery to save her life. The film features supporting performances from Bebe Neuwirth, Peter Gallagher, and Tobin Bell, with minor appearances from Gwyneth Paltrow and Brenda Strong.


title: Malice (1993 film)

text: Released in the fall of 1993, "Malice" grossed a total of $61 million worldwide and received mixed reviews from critics.


title: Malice (1993 film)

text: Andy and Tracy Safian are a newlywed couple living in a Victorian house that they are restoring in Western Massachusetts. He is an Associate Dean at a local women's college, while his wife teaches art to children. They hope to start a family soon. One night before making love, they notice the young boy next door at his window, seemingly watching them. They jokingly refer to him as a voyeur.


title: Malice (1993 film)

text: When a student on campus is attacked and seriously wounded by a serial rapist, Dr. Jed Hill, a brilliant surgeon who has recently joined the staff of the area hospital, operates and saves her life. Andy meets Jed to thank him for saving the student and realizes that they attended high school together. Andy and Jed quickly strike up a friendship. Money is tight, so Andy invites him to rent the third floor of their home, in order to finance the new plumbing. Tracy is unhappy that Andy has invited Jed to live with them. She describes Jed as arrogant. Jed brings home a woman and causes noise disturbance late at night, to Tracy’s annoyance.


title: Malice (1993 film)

text: Andy finds the body of one his students, who has been raped and murdered by the serial rapist. Police detective Dana Harris interviews him as a possible suspect and asks him to provide a semen sample. While leaving the police station, Andy learns that Tracy has been hospitalized for severe pain in her abdomen and is being operated on by Jed. While removing one of Tracy's ovaries, which has ruptured due to a cyst, Jed discovers Tracy is pregnant, but the surgery causes the fetus to abort. Another doctor notices that Tracy's other ovary is torsed and appears necrotic. Jed consults with Andy and advises him to agree to the removal of Tracy's second ovary, rather than risk her life. Andy painfully agrees, since this will mean that Tracy can never have children. Jed removes it, overruling the protests of other doctors that the ovary might still be healthy. After the removal, it is confirmed that the ovary was, in fact, healthy. Tracy tells Jed she's suing him for malpractice.


title: Malice (1993 film)

text: During a deposition in which Jed is accused of having a God complex, Jed delivers a monologue proudly claiming himself infallible as a surgeon, asserting "I am God," due to his ability to heal patients, then storms out. With Hill absent, Tracy's lawyer reveals that Jed had been in a bar the night of the operation. "Ask God how many shots of bourbon he had before he cut me open," Tracy tells the hospital's attorneys. Fearful of the negative publicity that would result from a civil trial, the hospital and Jed's insurance company settle with Andy and Tracy for $20 million. However, Tracy leaves Andy, telling him that she can't forgive him for the loss of her ability to have children.


title: Malice (1993 film)

text: Andy discovers that the serial rapist is a handyman at the college named Earl. After a struggle, Andy subdues him and Earl is arrested, thus clearing Andy of the crimes. In the aftermath, Dana informs Andy that his semen sample indicated that he was sterile, thereby revealing he wasn't the father of the aborted child. Andy confronts Tracy's lawyer, Dennis Riley, accusing him of having impregnated Tracy. Riley calmly asserts his innocence, but tells Andy that Tracy's mother — who she had told Andy had died 12 years ago — can answer all of his questions. Riley refuses to break lawyer-client privilege, but tells Andy to take a bottle of Scotch to her.


title: Malice (1993 film)

text: Andy tracks down Mrs. Kennsinger, who tells Andy that Tracy is a lifelong con artist. As a younger woman, she had an affair with a wealthy man, who paid for her to have an abortion; Tracy kept the money and had it done at a clinic, beginning her career as a con woman. Andy subsequently learns that Tracy and Jed had been carrying on an affair for some time. Tracy had arranged for Jed to move into the house so that he could begin overdosing her with a drug to intentionally cause the ovarian cyst. Andy confronts Tracy and tells her he wants half of the settlement money. Suspecting that she might try to murder him, Andy implies their next-door neighbor, the ten-year-old boy who's been their seeming voyeur, is named in his will as a potential police witness to her and Jed's nefarious activities.


title: Malice (1993 film)

text: Jed tells Tracy to give Andy what he wants so they can leave the country, but Tracy instead suggests murdering the boy. Jed refuses to kill a child, so Tracy shoots Jed, fatally. She then slips into the neighbor's house and attempts to suffocate the boy in his chair, only to find a dummy in his place. An enraged Tracy begins to destroy the dummy and attacks Andy after he walks in on her. They fall from the second floor, but they both survive. Detective Harris appears and arrests her, revealing that the boy's supposed agreement to testify against her was part of a sting operation to catch her in the act of attempted murder.


title: Malice (1993 film)

text: As Tracy is led away in handcuffs, the boy and his mother return home. As Tracy is taken to the police cruiser, Tracy sees that the boy is, in fact, blind. Andy leaves with Dana to have a drink of Scotch.


title: Malice (1993 film)

text: "Malice" was shot on location in Boston, Amherst, Holyoke, and Northampton in Massachusetts. Smith College was the setting used for Andy's college.


title: Malice (1993 film)

text: Michael Hirsh and Patrick Loubert, two of the co-founders of Canadian animation studio Nelvana, worked as executive producers on the film.


title: Malice (1993 film)

text: Aaron Sorkin expressed his disappointment with the film in 2017, saying, "Early on in my career, I wrote a movie that I’m not very proud of at all, it just turned into a mess." He recounted how Becker asked Sorkin to write a "steamy" sex scene between Baldwin and Kidman's character, which he refused: “I said, ‘Are you out of your mind?’ First of all, I just did a movie with her husband [Tom Cruise]. And second of all, no, I'm not going to write down what I'd like to see Nicole do and then hand the pages out to the crew and Nicole.” The scene was eventually created and filmed without the help of Sorkin.


title: Malice (1993 film)

text: "Malice" had its world premiere in Los Angeles on September 29, 1993, and opened on 1,431 screens in the U.S. on October 1, 1993 and grossed $9,232,650 during its opening weekend, ranking number 1 at the US box office. It eventually grossed a total of $46,405,336 in the U.S. and Canada and $15.2 million internationally for a worldwide total of $61.6 million,


title: Malice (1993 film)

text: On Rotten Tomatoes the film has a 57% approval rating based on 30 reviews. On Metacritic it has a score of 52% based on reviews from 17 critics, indicating "mixed or average reviews. Audiences polled by CinemaScore gave the film an average grade of "B+" on an A+ to F scale.


title: Malice (1993 film)

text: Roger Ebert of the "Chicago Sun-Times" called the film "one of the busiest movies I've ever seen, a film jampacked with characters and incidents and blind alleys and red herrings. Offhand, this is the only movie I can recall in which an entire subplot about a serial killer is thrown in simply for atmosphere." He added, "I can't go into detail without revealing vital secrets. Yet after the movie is over and you try to think through those secrets, you get into really deep molasses . . . "Malice" was directed by Harold Becker, whose credits include the splendid films "The Onion Field" and "Sea of Love", and he milks this material for a great deal more than it is worth."


title: Malice (1993 film)

text: Peter Travers of "Rolling Stone" observed, "Goaded on by writer Aaron Sorkin, who could run a red-herring factory, the actors work to keep you guessing long after you've caught on. No one shows any shame about going over the top, especially Anne Bancroft in an Oscar-begging cameo as Tracy's mother. Perhaps director Harold Becker thought flashy acting could distract us from the gaping plot holes. Becker gets so intent on confusing us, he forgets to give us characters to care about . . . It's got suspense but no staying power." Vincent Canby of The New York Times wrote: "No matter how wild the plot reversals, there's always a slightly madder one to come."


title: Malice (1993 film)

text: Timothy M. Gray of "Variety" said, "The immaculately crafted "Malice" is a virtual scrapbook of elements borrowed from other suspense pix, but no less enjoyable for being so familiar. [It] should tickle audiences who want to be entertained without being challenged . . . Some of the plotting gets plodding . . . but on the whole, the script does what it set out to do, and if the filmmakers didn't worry about these things, neither should you . . . After listless performances in such pics as "Days of Thunder" and "Far and Away", Aussie Kidman, who here uses a flawless American accent, proves her strengths as an actress, and Baldwin mixes menace, sex and humor in another terrific performance."


title: Malice (1993 film)

text: In the "30 Rock" episode "St. Valentine's Day", Jack Donaghy, portrayed by Baldwin, confesses to a priest that he once said "I am God" during a deposition. This is a reference to a famous line by Jed Hill, Baldwin's character in this film.


title: Malice (1993 film)

text: In the episode "Terms of Endearment" of the animated television series "Drawn Together", the character Wooldoor Sockbat recites the closing lines of Baldwin's speech verbatim.


title: Reef triggerfish

text: The reef triggerfish (Rhinecanthus rectangulus), also known as the rectangular triggerfish, wedgetail triggerfish or by its Hawaiian name humuhumunukunukuāpuaa (, meaning 'triggerfish with a snout like a pig', also spelled humuhumunukunukuapua'a or just humuhumu for short), is one of several species of triggerfish. It is found at reefs in the Indo-Pacific and is the state fish of Hawaii.


title: Reef triggerfish

text: The name humuhumunukunukuāpuaa serves for both singular and plural descriptions. The fish shares its Hawaiian name with the lagoon triggerfish ("R. aculeatus"), another fish also found in the Indo-Pacific.


title: Reef triggerfish

text: The triggerfish's teeth and top lip are blue and the teeth are set close together inside its relatively plump mouth.


title: Reef triggerfish

text: It has a small second dorsal spine which is used to lock its main spine into an upright position. When sheltering in a small crevice, this locking of its spine helps protect the fish against being extracted by a predator. When fleeing from predators, it sometimes makes grunting noises, possibly to warn other nearby triggerfish.


title: Reef triggerfish

text: The triggerfish can blow jets of water from its mouth to help it find benthic invertebrates buried under the substrate. It can often be seen spitting sand from its mouth to sift through the material for edible detritus or organisms.


title: Reef triggerfish

text: Reef triggers, up to in length, are fairly aggressive and generally do not tolerate conspecific individuals in their general vicinity; thus the fish is often solitary. This is particularly true in captivity. They have the ability to rapidly alter their coloration. They can fade into a relatively drab appearance when sleeping or demonstrating submission, while their coloration is often the most vivid when they are healthy and unthreatened by their surroundings. They have also been known to bite and attack swimmers in their area, often around the ankle, sometimes leaving marks.


title: Reef triggerfish

text: The reef triggerfish was originally designated the official fish of Hawaii in 1985, but due to an expiration of a Hawaiian state law after five years, it ceased to be the state fish in 1990. On April 17, 2006, bill HB1982 was presented to the Governor of Hawaii, which permanently reinstated the reef triggerfish (humuhumunukunukuāpuaa) as the state fish of Hawaii. The bill passed into law on May 2, 2006, and was effective upon its approval.


title: Reef triggerfish

text: Decades prior to official recognition, humuhumunukunukuāpuaa were considered a symbol of Hawai'i. The song "My Little Grass Shack in Kealakekua, Hawaii" includes the line " . . .where the humuhumunukunukuāpuaa go swimming by . . ."


title: Reef triggerfish

text: It is also featured prominently in the Disney Channel Original Movie "High School Musical 2" with a song of the same name.


title: Foreign key

text: A foreign key is a set of attributes in a table that refers to the primary key of another table. The foreign key links these two tables. Another way to put it: In the context of relational databases, a foreign key is a set of attributes subject to a certain kind of inclusion dependency constraints, specifically a constraint that the tuples consisting of the foreign key attributes in one relation, R, must also exist in some other (not necessarily distinct) relation, S, and furthermore that those attributes must also be a candidate key in S. In simpler words, a foreign key is a set of attributes that "references" a candidate key. For example, a table called TEAM may have an attribute, MEMBER_NAME, which is a foreign key referencing a candidate key, PERSON_NAME, in the PERSON table. Since MEMBER_NAME is a foreign key, any value existing as the name of a member in TEAM must also exist as a person's name in the PERSON table; in other words, every member of a TEAM is also a PERSON.


title: Foreign key

text: The table containing the foreign key is called the child table, and the table containing the candidate key is called the referenced or parent table. In database relational modeling and implementation, a candidate key is a set of zero or more attributes, the values of which are guaranteed to be unique for each tuple (row) in a relation. The value or combination of values of candidate key attributes for any tuple cannot be duplicated for any other tuple in that relation.


title: Foreign key

text: Since the purpose of the foreign key is to identify a particular row of referenced table, it is generally required that the foreign key is equal to the candidate key in some row of the primary table, or else have no value (the NULL value.). This rule is called a referential integrity constraint between the two tables.


title: Foreign key

text: Because violations of these constraints can be the source of many database problems, most database management systems provide mechanisms to ensure that every non-null foreign key corresponds to a row of the referenced table.


title: Foreign key

text: For example, consider a database with two tables: a CUSTOMER table that includes all customer data and an ORDER table that includes all customer orders. Suppose the business requires that each order must refer to a single customer. To reflect this in the database, a foreign key column is added to the ORDER table (e.g., CUSTOMERID), which references the primary key of CUSTOMER (e.g. ID). Because the primary key of a table must be unique, and because CUSTOMERID only contains values from that primary key field, we may assume that, when it has a value, CUSTOMERID will identify the particular customer which placed the order. However, this can no longer be assumed if the ORDER table is not kept up to date when rows of the CUSTOMER table are deleted or the ID column altered, and working with these tables may become more difficult. Many real world databases work around this problem by 'inactivating' rather than physically deleting master table foreign keys, or by complex update programs that modify all references to a foreign key when a change is needed.


title: Foreign key

text: Foreign keys play an essential role in database design. One important part of database design is making sure that relationships between real-world entities are reflected in the database by references, using foreign keys to refer from one table to another.


title: Foreign key

text: Another important part of database design is database normalization, in which tables are broken apart and foreign keys make it possible for them to be reconstructed.


title: Foreign key

text: Multiple rows in the referencing (or child) table may refer to the same row in the referenced (or parent) table. In this case, the relationship between the two tables is called a one to many relationship between the referencing table and the referenced table.


title: Foreign key

text: In addition, the child and parent table may, in fact, be the same table, i.e. the foreign key refers back to the same table. Such a foreign key is known in as a self-referencing or recursive foreign key. In database management systems, this is often accomplished by linking a first and second reference to the same table.


title: Foreign key

text: A table may have multiple foreign keys, and each foreign key can have a different parent table. Each foreign key is enforced independently by the database system. Therefore, cascading relationships between tables can be established using foreign keys.


title: Foreign key

text: A foreign key is defined as an attribute or set of attributes in a relation whose values match a primary key in another relation. The syntax to add such a constraint to an existing table is defined in as shown below. Omitting the column list in the codice_1 clause implies that the foreign key shall reference the primary key of the referenced table.


title: Foreign key

text: If the foreign key is a single column only, the column can be marked as such using the following syntax:


title: Foreign key

text: Because the database management system enforces referential constraints, it must ensure data integrity if rows in a referenced table are to be deleted (or updated). If dependent rows in referencing tables still exist, those references have to be considered. specifies 5 different referential actions that shall take place in such occurrences:


title: Foreign key

text: Whenever rows in the parent (referenced) table are deleted (or updated), the respective rows of the child (referencing) table with a matching foreign key column will be deleted (or updated) as well. This is called a cascade delete (or update).


title: Foreign key

text: A value cannot be updated or deleted when a row exists in a referencing or child table that references the value in the referenced table.


title: Foreign key

text: Similarly, a row cannot be deleted as long as there is a reference to it from a referencing or child table.


title: Foreign key

text: To understand RESTRICT (and CASCADE) better, it may be helpful to notice the following difference, which might not be immediately clear. The referential action CASCADE modifies the "behavior" of the (child) table itself where the word CASCADE is used. For example, ON DELETE CASCADE effectively says "When the referenced row is deleted from the other table (master table), then delete "also from me"". However, the referential action RESTRICT modifies the "behavior" of the master table, "not" the child table, although the word RESTRICT appears in the child table and not in the master table! So, ON DELETE RESTRICT effectively says: "When someone tries to delete the row from the other table (master table), prevent deletion "from that other table" (and of course, also don't delete from me, but that's not the main point here)."


title: Foreign key

text: NO ACTION and RESTRICT are very much alike. The main difference between NO ACTION and RESTRICT is that with NO ACTION the referential integrity check is done after trying to alter the table. RESTRICT does the check before trying to execute the UPDATE or DELETE statement. Both referential actions act the same if the referential integrity check fails: the UPDATE or DELETE statement will result in an error.


title: Foreign key

text: In other words, when an UPDATE or DELETE statement is executed on the referenced table using the referential action NO ACTION, the DBMS verifies at the end of the statement execution that none of the referential relationships are violated. This is different from RESTRICT, which assumes at the outset that the operation will violate the constraint. Using NO ACTION, the triggers or the semantics of the statement itself may yield an end state in which no foreign key relationships are violated by the time the constraint is finally checked, thus allowing the statement to complete successfully.


title: Foreign key

text: In general, the action taken by the DBMS for SET NULL or SET DEFAULT is the same for both ON DELETE or ON UPDATE: the value of the affected referencing attributes is changed to NULL for SET NULL, and to the specified default value for SET DEFAULT.


title: Foreign key

text: Referential actions are generally implemented as implied triggers (i.e. triggers with system-generated names, often hidden.) As such, they are subject to the same limitations as user-defined triggers, and their order of execution relative to other triggers may need to be considered; in some cases it may become necessary to replace the referential action with its equivalent user-defined trigger to ensure proper execution order, or to work around mutating-table limitations.


title: Foreign key

text: Another important limitation appears with transaction isolation: your changes to a row may not be able to fully cascade because the row is referenced by data your transaction cannot "see", and therefore cannot cascade onto. An example: while your transaction is attempting to renumber a customer account, a simultaneous transaction is attempting to create a new invoice for that same customer; while a CASCADE rule may fix all the invoice rows your transaction can see to keep them consistent with the renumbered customer row, it won't reach into another transaction to fix the data there; because the database cannot guarantee consistent data when the two transactions commit, one of them will be forced to roll back (often on a first-come-first-served basis.)