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🔗 Mathematics 🔗 Statistics

Local regression or local polynomial regression, also known as moving regression, is a generalization of the moving average and polynomial regression. Its most common methods, initially developed for scatterplot smoothing, are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing), both pronounced . They are two strongly related non-parametric regression methods that combine multiple regression models in a k-nearest-neighbor-based meta-model. In some fields, LOESS is known and commonly referred to as Savitzky–Golay filter (proposed 15 years before LOESS).

LOESS and LOWESS thus build on "classical" methods, such as linear and nonlinear least squares regression. They address situations in which the classical procedures do not perform well or cannot be effectively applied without undue labor. LOESS combines much of the simplicity of linear least squares regression with the flexibility of nonlinear regression. It does this by fitting simple models to localized subsets of the data to build up a function that describes the deterministic part of the variation in the data, point by point. In fact, one of the chief attractions of this method is that the data analyst is not required to specify a global function of any form to fit a model to the data, only to fit segments of the data.

The trade-off for these features is increased computation. Because it is so computationally intensive, LOESS would have been practically impossible to use in the era when least squares regression was being developed. Most other modern methods for process modeling are similar to LOESS in this respect. These methods have been consciously designed to use our current computational ability to the fullest possible advantage to achieve goals not easily achieved by traditional approaches.

A smooth curve through a set of data points obtained with this statistical technique is called a loess curve, particularly when each smoothed value is given by a weighted quadratic least squares regression over the span of values of the y-axis scattergram criterion variable. When each smoothed value is given by a weighted linear least squares regression over the span, this is known as a lowess curve; however, some authorities treat lowess and loess as synonyms.

🔗 Caribbean 🔗 Football 🔗 Caribbean/Barbados 🔗 Grenada

On January 27, 1994, the national football teams of Barbados and Grenada played against each other as part of the qualification round for the 1994 Caribbean Cup. Barbados won 4-2 in extra time. In the last minutes of regular time, both teams attempted to score own goals. The result has been described as "one of the strangest matches ever".

In the 1994 Caribbean Cup, the tournament organisers implemented a variant of the golden goal rule: the first goal scored in extra-time not only won the match, but was also worth two goals. Barbados needed to win the match by a margin of at least two goals to qualify for the final tournament over Grenada. Barbados led the game 2-0 until Grenada scored at the 83rd minute, bringing the score to 2-1. Barbados then deliberately scored an own goal, tying the game at 2-2, to force extra-time so that they could take advantage of the golden goal rule to achieve their needed two-goal margin. This resulted in an unusual situation: for the last three minutes of the match, Grenada tried to score in both goals. Either outcome (3–2 on points, or 2–3 via goal difference) would have advanced them to the finals, while Barbados had to defend both goals. Ultimately, Barbados was able to prevent Grenada from scoring, forcing extra-time. Barbados then scored the golden goal to win the match.

The outcome of the match was criticised by Grenadian coach James Clarkson, who felt that his team had been unfairly prevented from advancing to the finals. However, given the fact that the unusual tournament rules had not been broken, FIFA cleared Barbados of any wrongdoing.

🔗 Law 🔗 Sexology and sexuality 🔗 Pornography

The Miller test, also called the three-prong obscenity test, is the United States Supreme Court's test for determining whether speech or expression can be labeled obscene, in which case it is not protected by the First Amendment to the United States Constitution and can be prohibited.

🔗 Cetaceans 🔗 Energy

Spermaceti is a waxy substance found in the head cavities of the sperm whale (and, in smaller quantities, in the oils of other whales). Spermaceti is created in the spermaceti organ inside the whale's head. This organ may contain as much as 1,900 litres (500 US gal) of spermaceti. It has been extracted by whalers since the 17th century for human use in cosmetics, textiles, and candles.

Theories for the spermaceti organ's biological function suggest that it may control buoyancy, may act as a focusing apparatus for the whale's sense of echolocation, or possibly both. There has been concrete evidence to support both theories. The buoyancy theory holds that the sperm whale is capable of heating the spermaceti, lowering its density and thus allowing the whale to float; in order for the whale to sink again, it must take water into its blowhole which cools the spermaceti into a denser solid. This claim has been called into question by recent research which indicates a lack of biological structures to support this heat exchange, as well as the fact that the change in density is too small to be meaningful until the organ grows to huge size. Measurement of the proportion of wax esters retained by a harvested sperm whale accurately described the age and future life expectancy of a given individual. The proportion of wax esters in the spermaceti organ increases with the age of the whale: 38–51% in calves, 58–87% in adult females, and 71–94% in adult males.

Spermaceti wax is extracted from sperm oil by crystallisation at 6 °C (43 °F), when treated by pressure and a chemical solution of caustic alkali. Spermaceti forms brilliant white crystals that are hard but oily to the touch, and are devoid of taste or smell, making it very useful as an ingredient in cosmetics, leatherworking, and lubricants. The substance was also used in making candles of a standard photometric value, in the dressing of fabrics, and as a pharmaceutical excipient, especially in cerates and ointments.

The whaling industry in the 17th and 18th centuries was developed to find, harvest and refine the contents of the head of a sperm whale. The crews seeking spermaceti routinely left on three-year tours on several oceans. Cetaceous lamp oil was a commodity that created many maritime fortunes. The light produced by a single pure spermaceti source (candle) became the standard measurement of "candlepower" for another century. Candlepower, a photometric unit defined in the United Kingdom Act of Parliament Metropolitan Gas Act 1860 and adopted at the International Electrotechnical Conference of 1883, was based on the light produced by a pure spermaceti candle.

🔗 Physics

In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter ${\displaystyle \varepsilon }$. The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of ${\displaystyle \varepsilon }$ usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction.

Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The field in general remains actively and heavily researched across multiple disciplines.

🔗 Computer science 🔗 Statistics

The Jaccard index, also known as the Jaccard similarity coefficient, is a statistic used for gauging the similarity and diversity of sample sets. It was developed by Grove Karl Gilbert in 1884 as his ratio of verification (v) and now is frequently referred to as the Critical Success Index in meteorology. It was later developed independently by Paul Jaccard, originally giving the French name coefficient de communauté, and independently formulated again by T. Tanimoto. Thus, the Tanimoto index or Tanimoto coefficient are also used in some fields. However, they are identical in generally taking the ratio of Intersection over Union. The Jaccard coefficient measures similarity between finite sample sets, and is defined as the size of the intersection divided by the size of the union of the sample sets:

${\displaystyle J(A,B)={{|A\cap B|} \over {|A\cup B|}}={{|A\cap B|} \over {|A|+|B|-|A\cap B|}}.}$

Note that by design, ${\displaystyle 0\leq J(A,B)\leq 1.}$ If A intersection B is empty, then J(A,B) = 0. The Jaccard coefficient is widely used in computer science, ecology, genomics, and other sciences, where binary or binarized data are used. Both the exact solution and approximation methods are available for hypothesis testing with the Jaccard coefficient.

Jaccard similarity also applies to bags, i.e., Multisets. This has a similar formula, but the symbols mean bag intersection and bag sum (not union). The maximum value is 1/2.

${\displaystyle J(A,B)={{|A\cap B|} \over {|A\uplus B|}}={{|A\cap B|} \over {|A|+|B|}}.}$

The Jaccard distance, which measures dissimilarity between sample sets, is complementary to the Jaccard coefficient and is obtained by subtracting the Jaccard coefficient from 1, or, equivalently, by dividing the difference of the sizes of the union and the intersection of two sets by the size of the union:

${\displaystyle d_{J}(A,B)=1-J(A,B)={{|A\cup B|-|A\cap B|} \over |A\cup B|}.}$

An alternative interpretation of the Jaccard distance is as the ratio of the size of the symmetric difference ${\displaystyle A\triangle B=(A\cup B)-(A\cap B)}$ to the union. Jaccard distance is commonly used to calculate an n × n matrix for clustering and multidimensional scaling of n sample sets.

This distance is a metric on the collection of all finite sets.

There is also a version of the Jaccard distance for measures, including probability measures. If ${\displaystyle \mu }$ is a measure on a measurable space ${\displaystyle X}$, then we define the Jaccard coefficient by

${\displaystyle J_{\mu }(A,B)={{\mu (A\cap B)} \over {\mu (A\cup B)}},}$

and the Jaccard distance by

${\displaystyle d_{\mu }(A,B)=1-J_{\mu }(A,B)={{\mu (A\triangle B)} \over {\mu (A\cup B)}}.}$

Care must be taken if ${\displaystyle \mu (A\cup B)=0}$ or ${\displaystyle \infty }$, since these formulas are not well defined in these cases.

The MinHash min-wise independent permutations locality sensitive hashing scheme may be used to efficiently compute an accurate estimate of the Jaccard similarity coefficient of pairs of sets, where each set is represented by a constant-sized signature derived from the minimum values of a hash function.

🔗 Companies 🔗 Finance & Investment 🔗 Switzerland

Credit Suisse Group AG is a global investment bank and financial services firm founded and based in Switzerland. Headquartered in Zürich, it maintains offices in all major financial centers around the world and is one of the nine global "bulge bracket" banks providing services in investment banking, private banking, asset management, and shared services. It is known for strict bank–client confidentiality and banking secrecy. The Financial Stability Board considers it to be a global systemically important bank. Credit Suisse is also a primary dealer and Forex counterparty of the Federal Reserve in the United States.

Credit Suisse was founded in 1856 to fund the development of Switzerland's rail system. It issued loans that helped create Switzerland's electrical grid and the European rail system. In the 1900s, it began shifting to retail banking in response to the elevation of the middle class and competition from fellow Swiss banks UBS and Julius Bär. Credit Suisse partnered with First Boston in 1978 before buying a controlling share of the bank in 1988. From 1990 to 2000, the company purchased institutions such as Winterthur Group, Swiss Volksbank, Swiss American Securities Inc. (SASI), and Bank Leu. The biggest institutional shareholders of Credit Suisse include the Saudi National Bank (9.88%), the Qatar Investment Authority and BlackRock (about 5% each), Dodge & Cox, Norges Bank and the Saudi Olayan Group.

The company was one of the least affected banks during the global financial crisis, but afterwards began shrinking its investment business, executing layoffs and cutting costs. The bank was at the center of multiple international investigations for tax avoidance which culminated in a guilty plea and the forfeiture of US$2.6 billion in fines from 2008 to 2012. In 2021, Credit Suisse had assets under management (AuM) of over CHF 1.6 trillion.

UBS announced its intent to acquire Credit Suisse for $2 billion on March 19, 2023.

🔗 Economics

In economics, the Baumol effect, also known as Baumol's cost disease, is the rise of wages in jobs that have experienced little or no increase in labor productivity, in response to rising salaries in other jobs that have experienced higher productivity growth. The phenomenon was described by William J. Baumol and William G. Bowen in the 1960s and is an example of cross elasticity of demand.

The rise of wages in jobs without productivity gains derives from the requirement to compete for workers with jobs that have experienced productivity gains and so can naturally pay higher salaries, just as classical economics predicts. For instance, if the retail sector pays its managers low wages, they may decide to quit and get jobs in the automobile sector, where wages are higher because of higher labor productivity. Thus, retail managers' salaries increase not due to labor productivity increases in the retail sector, but due to productivity and corresponding wage increases in other industries.

🔗 Books 🔗 Writing systems

An abecedarium (also known as an abecedary or ABCs or simply an ABC) is an inscription consisting of the letters of an alphabet, almost always listed in order. Typically, abecedaria (or abecedaries) are practice exercises.

🔗 Crime 🔗 Law 🔗 England 🔗 Middle Ages 🔗 Middle Ages/History 🔗 Law Enforcement 🔗 Sociology 🔗 University of Oxford 🔗 British crime

The St Scholastica Day riot took place in Oxford, England, on 10 February 1355, Saint Scholastica's Day. The disturbance began when two students from the University of Oxford complained about the quality of wine served to them in the Swindlestock Tavern, which stood on Carfax, in the centre of the town. The students quarrelled with the taverner; the argument quickly escalated to blows. The inn's customers joined in on both sides, and the resulting melee turned into a riot. The violence started by the bar brawl continued over three days, with armed gangs coming in from the countryside to assist the townspeople. University halls and students' accommodation were raided and the inhabitants murdered; there were some reports of clerics being scalped. Around 30 townsfolk were killed, as were up to 63 members of the university.

Violent disagreements between townspeople and students had arisen several times previously, and 12 of the 29 coroners' courts held in Oxford between 1297 and 1322 concerned murders by students. The University of Cambridge was established in 1209 by scholars who left Oxford following the lynching of two students by the town's citizens.

King Edward III sent judges to the town with commissions of oyer and terminer to determine what had gone on and to advise what steps should be taken. He came down on the side of the university authorities, who were given additional powers and responsibilities to the disadvantage of the town's authorities. The town was fined 500 marks and its mayor and bailiffs were sent to the Marshalsea prison in London. John Gynwell, the Bishop of Lincoln, imposed an interdict on the town for one year, which banned all religious practices, including services (except on key feast days), burials and marriages; only baptisms of young children were allowed.

An annual penance was imposed on the town: each year, on St Scholastica's Day, the mayor, bailiffs and sixty townspeople were to attend a Mass at the University Church of St Mary the Virgin for those killed; the town was also made to pay the university a fine of one penny for each scholar killed. The practice was dropped in 1825; in 1955—the 600th anniversary of the riots—in an act of conciliation the mayor was given an honorary degree and the vice-chancellor was made an honorary freeman of the city.