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🔗 Statistics

In probability theory, although simple examples illustrate that linear uncorrelatedness of two random variables does not in general imply their independence, it is sometimes mistakenly thought that it does imply that when the two random variables are normally distributed. This article demonstrates that assumption of normal distributions does not have that consequence, although the multivariate normal distribution, including the bivariate normal distribution, does.

To say that the pair ${\displaystyle (X,Y)}$ of random variables has a bivariate normal distribution means that every linear combination ${\displaystyle aX+bY}$ of ${\displaystyle X}$ and ${\displaystyle Y}$ for constant (i.e. not random) coefficients ${\displaystyle a}$ and ${\displaystyle b}$ has a univariate normal distribution. In that case, if ${\displaystyle X}$ and ${\displaystyle Y}$ are uncorrelated then they are independent. However, it is possible for two random variables ${\displaystyle X}$ and ${\displaystyle Y}$ to be so distributed jointly that each one alone is marginally normally distributed, and they are uncorrelated, but they are not independent; examples are given below.

🔗 India 🔗 Numismatics

The Indian rupee sign (sign: ₹; code: INR) is the currency symbol for the Indian rupee, the official currency of India. Designed by Udaya Kumar, it was presented to the public by the Government of India on 15 July 2010, following its selection through an "open" competition among Indian residents. Before its adoption, the most commonly used symbols for the rupee were Rs, Re or, in texts in Indian languages, an appropriate abbreviation in the language used.

The design is based on the Devanagari letter "र" (ra) with a double horizontal line at the top. It also resembles the Latin capital letter "R", especially R rotunda (Ꝛ).

The Unicode character for the Indian rupee sign is U+20B9 ₹ INDIAN RUPEE SIGN. Other countries that use a rupee, such as Sri Lanka, Pakistan and Nepal, still use the generic U+20A8 ₨ RUPEE SIGN character.

🔗 Computer science

In computer science, a succinct data structure is a data structure which uses an amount of space that is "close" to the information-theoretic lower bound, but (unlike other compressed representations) still allows for efficient query operations. The concept was originally introduced by Jacobson to encode bit vectors, (unlabeled) trees, and planar graphs. Unlike general lossless data compression algorithms, succinct data structures retain the ability to use them in-place, without decompressing them first. A related notion is that of a compressed data structure, in which the size of the data structure depends upon the particular data being represented.

Suppose that ${\displaystyle Z}$ is the information-theoretical optimal number of bits needed to store some data. A representation of this data is called:

• implicit if it takes ${\displaystyle Z+O(1)}$ bits of space,
• succinct if it takes ${\displaystyle Z+o(Z)}$ bits of space, and
• compact if it takes ${\displaystyle O(Z)}$ bits of space.

For example, a data structure that uses ${\displaystyle 2Z}$ bits of storage is compact, ${\displaystyle Z+{\sqrt {Z}}}$ bits is succinct, ${\displaystyle Z+\lg Z}$ bits is also succinct, and ${\displaystyle Z+3}$ bits is implicit.

Implicit structures are thus usually reduced to storing information using some permutation of the input data; the most well-known example of this is the heap.

🔗 Crime 🔗 Africa 🔗 Squatting 🔗 Africa/Ghana

Agbogbloshie is a nickname of a commercial district on the Korle Lagoon of the Odaw River, near the center of Accra, Ghana's capital city. Near the slum called "Old Fadama", the Agbogbloshie site became known as a destination for externally generated automobile and electronic scrap collected from mostly the western world. It was alleged to be at the center of a legal and illegal exportation network for the environmental dumping of electronic waste (e-waste) from industrialized nations. The Basel Action Network, a small NGO based in Seattle, has referred to Agbogbloshie as a "digital dumping ground", where they allege millions of tons of e-waste are processed each year.

However, repeated international studies have failed to confirm the allegations, which have been labelled an "e-waste hoax" by international reuse advocate WR3A. The most exhaustive study of the trade in used electronics in Nigeria, funded by UNEP and Basel Convention, revealed that from 540 000 tonnes of informally processed waste electronics, 52% of the material was recovered.

According to statistics from the World Bank, in large cities like Accra and Lagos the majority of households have owned televisions and computers for decades. The UN Report "Where are WEEE in Africa" (2012) disclosed that the majority of used electronics found in African dumps had not in fact been recently imported as scrap, but originated from these African cities. Agbogbloshie is situated on the banks of the Korle Lagoon, northwest of Accra's Central Business District. Roughly 40,000 Ghanaians inhabit the area, most of whom are migrants from rural areas. Due to its harsh living conditions and rampant crime, the area is nicknamed "Sodom and Gomorrah".

The Basel Convention prevents the transfrontier shipment of hazardous waste from developed to less developed countries. However, the Convention specifically allows export for reuse and repair under Annex Ix, B1110. While numerous international press reports have made reference to allegations that the majority of exports to Ghana are dumped, research by the US International Trade Commission found little evidence of unprocessed e-waste being shipped to Africa from the United States, a finding corroborated by the United Nations Environment Programme, MIT, Memorial University, Arizona State University, and other research. In 2013, the original source of the allegation blaming foreign dumping for the material found in Agbogbloshie recanted, or rather stated it had never made the claim that 80% of US e-waste is exported.

Whether domestically generated by residents of Ghana or imported, concern remains over methods of waste processing - especially burning - which emit toxic chemicals into the air, land and water. Exposure is especially hazardous to children, as these toxins are known to inhibit the development of the reproductive system, the nervous system, and especially the brain. Concerns about human health and the environment of Agbogbloshie continue to be raised as the area remains heavily polluted. In the 2000s, the Ghanaian government, with new funding and loans, implemented the Korle Lagoon Ecological Restoration Project (KLERP), an environmental remediation and restoration project that will address the pollution problem by dredging the lagoon and Odaw canal to improve drainage and flooding into the ocean.

🔗 Medicine 🔗 Sociology 🔗 Physiology 🔗 Medicine/Cardiology 🔗 Medicine/Society and Medicine

The Roseto effect is the phenomenon by which a close-knit community experiences a reduced rate of heart disease. The effect is named for Roseto, Pennsylvania. The Roseto effect was first noticed in 1961 when the local Roseto doctor encountered Dr. Stewart Wolf, then head of Medicine of the University of Oklahoma, and they discussed, over a couple of beers, the unusually low rate of myocardial infarction in the Italian American community of Roseto compared with other locations. Many studies followed, including a 50-year study comparing Roseto to nearby Bangor. As the original authors had predicted, as the Roseto cohort shed their Italian social structure and became more Americanized in the years following the initial study, heart disease rates increased, becoming similar to those of neighboring towns.

From 1954 to 1961, Roseto had nearly no heart attacks for the otherwise high-risk group of men 55 to 64, and men over 65 had a death rate of 1% while the national average was 2%. Widowers outnumbered widows, as well.

These statistics were at odds with a number of other factors observed in the community. They smoked unfiltered stogies, drank wine "with seeming abandon" in lieu of milk and soft drinks, skipped the Mediterranean diet in favor of meatballs and sausages fried in lard with hard and soft cheeses. The men worked in the slate quarries where they contracted illnesses from gases and dust. Roseto also had no crime, and very few applications for public assistance.

Wolf attributed Rosetans' lower heart disease rate to lower stress. "'The community,' Wolf says, 'was very cohesive. There was no keeping up with the Joneses. Houses were very close together, and everyone lived more or less alike.'" Elders were revered and incorporated into community life. Housewives were respected, and fathers ran the families.

🔗 Technology

Tensegrity, tensional integrity or floating compression is a structural principle based on a system of isolated components under compression inside a network of continuous tension, and arranged in such a way that the compressed members (usually bars or struts) do not touch each other while the prestressed tensioned members (usually cables or tendons) delineate the system spatially.

The term was coined by Buckminster Fuller in the 1960s as a portmanteau of "tensional integrity". The other denomination of tensegrity, floating compression, was used mainly by the constructivist artist Kenneth Snelson.

🔗 Visual arts 🔗 Belgium

Netherlandish Proverbs (Dutch: Nederlandse Spreekwoorden; also called Flemish Proverbs, The Blue Cloak or The Topsy Turvy World) is a 1559 oil-on-oak-panel painting by Pieter Bruegel the Elder that depicts a scene in which humans and, to a lesser extent, animals and objects, offer literal illustrations of Dutch-language proverbs and idioms.

Running themes in Bruegel's paintings are the absurdity, wickedness and foolishness of humans, and this is no exception. The painting's original title, The Blue Cloak or The Folly of the World, indicates that Bruegel's intent was not just to illustrate proverbs, but rather to catalog human folly. Many of the people depicted show the characteristic blank features that Bruegel used to portray fools.

His son, Pieter Brueghel the Younger, specialised in making copies of his father's work and painted at least 16 copies of Netherlandish Proverbs. Not all versions of the painting, by father or son, show exactly the same proverbs and they also differ in other minor details.

🔗 Computing 🔗 Computer science 🔗 Computing/Software 🔗 Computing/Computer science

Cargo cult programming is a style of computer programming characterized by the ritual inclusion of code or program structures that serve no real purpose. Cargo cult programming is symptomatic of a programmer not understanding either a bug they were attempting to solve or the apparent solution (compare shotgun debugging, deep magic). The term cargo cult programmer may apply when an unskilled or novice computer programmer (or one inexperienced with the problem at hand) copies some program code from one place to another with little understanding of how it works or whether it is required.

Cargo cult programming can also refer to the practice of applying a design pattern or coding style blindly without understanding the reasons behind that design principle. Examples being adding unnecessary comments to self-explanatory code, overzealous adherence to the conventions of a programming paradigm, or adding deletion code for objects that garbage collection automatically collect.

Obsessive and redundant checks for null values or testing whether a collection is empty before iterating its values may be a sign of cargo cult programming. Such obsessive checks make the code less readable, and often prevent the output of proper error messages, obscuring the real cause of a misbehaving program.

🔗 Mathematics

In number theory, Mills' constant is defined as the smallest positive real number A such that the floor function of the double exponential function

${\displaystyle \lfloor A^{3^{n}}\rfloor }$

is a prime number, for all natural numbers n. This constant is named after William H. Mills who proved in 1947 the existence of A based on results of Guido Hoheisel and Albert Ingham on the prime gaps. Its value is unknown, but if the Riemann hypothesis is true, it is approximately 1.3063778838630806904686144926... (sequence A051021 in the OEIS).

🔗 Mathematics

Graham's number is an immense number that arises as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is named after mathematician Ronald Graham, who used the number in conversations with popular science writer Martin Gardner as a simplified explanation of the upper bounds of the problem he was working on. In 1977, Gardner described the number in Scientific American, introducing it to the general public. At the time of its introduction, it was the largest specific positive integer ever to have been used in a published mathematical proof. The number was published in the 1980 Guinness Book of World Records, adding to its popular interest. Other specific integers (such as TREE(3)) known to be far larger than Graham's number have since appeared in many serious mathematical proofs, for example in connection with Harvey Friedman's various finite forms of Kruskal's theorem. Additionally, smaller upper bounds on the Ramsey theory problem from which Graham's number derived have since been proven to be valid.

Graham's number is much larger than many other large numbers such as Skewes' number and Moser's number, both of which are in turn much larger than a googolplex. As with these, it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number—and so forth, for a number of times far exceeding the total number of Planck volumes in the observable universe. Thus Graham's number cannot be expressed even by power towers of the form ${\displaystyle a^{b^{c^{\cdot ^{\cdot ^{\cdot }}}}}}$.

However, Graham's number can be explicitly given by computable recursive formulas using Knuth's up-arrow notation or equivalent, as was done by Graham. As there is a recursive formula to define it, it is much smaller than typical busy beaver numbers. Though too large to be computed in full, the sequence of digits of Graham's number can be computed explicitly through simple algorithms. The last 12 digits are ...262464195387. With Knuth's up-arrow notation, Graham's number is ${\displaystyle g_{64}}$, where