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🔗 Mathematics

In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is completely inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear.

For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the extended Euclidean plane. Monge's theorem states that the three such points given by the three pairs of circles always lie in a straight line. In the case of two of the circles being of equal size, the two external tangent lines are parallel. In this case Monge's theorem asserts that the other two intersection points must lie on a line parallel to those two external tangents. In other words, if the two external tangents are considered to intersect at the point at infinity, then the other two intersection points must be on a line passing through the same point at infinity, so the line between them takes the same angle as the external tangent.

🔗 United States 🔗 California 🔗 Companies 🔗 California/San Francisco Bay Area 🔗 Internet 🔗 Internet culture 🔗 Business 🔗 Crime and Criminal Biography 🔗 Project-independent assessment

The eBay stalking scandal was a campaign conducted in 2019 by eBay and contractors. The scandal involved the aggressive stalking and harassment of two e-commerce bloggers, Ina and David Steiner, who wrote frequent commentary about eBay on their website EcommerceBytes. Seven eBay employees pleaded guilty to charges involving criminal conspiracies. The seven employees included two senior members of eBay’s corporate security team. Two members of eBay's Executive Leadership Team who were implicated in the scandal were not charged.

🔗 Psychology 🔗 Museums

Museum fatigue is a state of physical or mental fatigue caused by the experience of exhibits in museums and similar cultural institutions. The collection of phenomena that characterize museum fatigue was first described in 1916, and has since received widespread attention in popular and scientific contexts.

The first known description of museum fatigue was made by Benjamin Ives Gilman in the January 1916 edition of The Scientific Monthly. Gilman mainly focused on the efforts of museum fatigue on how the viewing displays are placed. Gilman went on to say that the way the displays were presented caused museum fatigue. In other later studies, Edward Robinson in 1928 spoke more about museum fatigue, specifically of four museums that showed a lot of characteristics of museum fatigue because of how the displays were placed. Arthur Melton provided more proof for Robinson by observing visitors' interest in the displays decreased as the number of displays increased.

In a more recent study of the phenomenon, Falk, Koran, Direking, and Dreblow studied museum fatigue at the Florida Museum of Natural History in 1985. While observing visitors they noticed a pattern of high interest in anything in the museum for about 30 minutes and then a decrease in interest. In 1997–1998, Beverly Serrell in her research determined that in less than 20 minutes people became apathetic towards the museum. Museum fatigue has also been applied in zoos to see if they had the same effect. In one study in 1986, Bitgood, Patterson, and Benefeld observed the reptile house of the Birmingham Zoo. While observing they noticed that the pattern was different from museum fatigue.

🔗 Death 🔗 Iran 🔗 Archaeology

The Hasanlu Lovers are a pair of human remains found at the Teppe Hasanlu archaeological site, located in the Naqadeh in the West Azerbaijan Province of Iran. Around 800 BCE, the city of Hasanlu, located in north-western Iran, was destroyed by an unknown invader. Inhabitants were slain and left where they fell. In 1973, the lovers were discovered by a team of archaeologists from the University of Pennsylvania led by Robert H. Dyson.

The two human skeletons were found together in a bin during excavations, seemingly embracing at the time of death, with no other objects except a stone slab under the head of one skeleton. They died together around 800 BCE, during the last destruction of the Hasanlu. Approximately 246 skeletons were found at the site altogether. How the lovers died and ended up in the bin is still under speculation but both skeletons lack evidence of injury near the time of death and possibly died of asphyxiation. They were exhibited at the Penn Museum from 1974 until the mid-1980s.

The right skeleton, referred to as HAS 73-5-799 (SK 335), is lying on its back and the left skeleton, referred to as HAS 73-5-800 (SK 336), is lying on its left side facing SK 335. When excavated, the skeletons were tested to determine various characteristics. Dental evidence suggest SK 335 was a young adult, possibly 19–22 years of age. Researchers identified the skeleton as male largely based on the pelvis. The skeleton had no apparent evidence of disease or healed lifetime injuries. Skeleton SK 336 appeared to have been healthy in life; the skeleton had no apparent evidence of healed lifetimes injuries, and was estimated to have been aged to about 30–35 years. Sex determination of the left skeleton was less definitive. Evidence suggests SK 336 was also male after being originally identified as female. The skeletons have been a subject of debate since they were first excavated.

🔗 Companies 🔗 Korea 🔗 Food and drink 🔗 Korea/North Korea

Pyongyang (Chosongul: 평양관) is a restaurant chain named after the capital of North Korea, with around 130 locations worldwide. The restaurants are owned and operated by the Haedanghwa Group, an organization of the government of North Korea.

🔗 Russia 🔗 Mathematics 🔗 Statistics 🔗 Russia/science and education in Russia

In statistics, the Gauss–Markov theorem states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. The errors do not need to be normal, nor do they need to be independent and identically distributed (only uncorrelated with mean zero and homoscedastic with finite variance). The requirement that the estimator be unbiased cannot be dropped, since biased estimators exist with lower variance. See, for example, the James–Stein estimator (which also drops linearity) or ridge regression.

The theorem was named after Carl Friedrich Gauss and Andrey Markov, although Gauss' work significantly predates Markov's. But while Gauss derived the result under the assumption of independence and normality, Markov reduced the assumptions to the form stated above. A further generalization to non-spherical errors was given by Alexander Aitken.

🔗 Computing

FRACTRAN is a Turing-complete esoteric programming language invented by the mathematician John Conway. A FRACTRAN program is an ordered list of positive fractions together with an initial positive integer input n. The program is run by updating the integer n as follows:

1. for the first fraction f in the list for which nf is an integer, replace n by nf
2. repeat this rule until no fraction in the list produces an integer when multiplied by n, then halt.

Conway 1987 gives the following formula for primes in FRACTRAN:

${\displaystyle \left({\frac {17}{91}},{\frac {78}{85}},{\frac {19}{51}},{\frac {23}{38}},{\frac {29}{33}},{\frac {77}{29}},{\frac {95}{23}},{\frac {77}{19}},{\frac {1}{17}},{\frac {11}{13}},{\frac {13}{11}},{\frac {15}{2}},{\frac {1}{7}},{\frac {55}{1}}\right)}$

Starting with n=2, this FRACTRAN program generates the following sequence of integers:

2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, ... (sequence A007542 in the OEIS)

After 2, this sequence contains the following powers of 2:

${\displaystyle 2^{2}=4,\,2^{3}=8,\,2^{5}=32,\,2^{7}=128,\,2^{11}=2048,\,2^{13}=8192,\,2^{17}=131072,\,2^{19}=524288,\,\dots }$ (sequence A034785 in the OEIS)

which are the prime powers of 2.

🔗 Computing

When writing firmware for an embedded system, immunity-aware programming refers to programming techniques which improve the tolerance of transient errors in the program counter or other modules of a program that would otherwise lead to failure. Transient errors are typically caused by single event upsets, insufficient power, or by strong electromagnetic signals transmitted by some other "source" device.

Immunity-aware programming is an example of defensive programming and EMC-aware programming. Although most of these techniques apply to the software in the "victim" device to make it more reliable, a few of these techniques apply to software in the "source" device to make it emit less unwanted noise.

🔗 Companies 🔗 Computing 🔗 United Kingdom

Andrews & Arnold Ltd (also known as AAISP) is an Internet service provider based in Bracknell in the United Kingdom founded in 1997 and launched in 1998, primarily serving businesses and "technical" home users.

In 2009 the company was judged the best niche provider in the Thinkbroadband Customer Service Awards, based on customer ratings and again in 2010.

The company's owner, Adrian Kennard (RevK), stated in a blog post that as of October 2010 the company is "xkcd/806" compliant, referring to xkcd comic number 806. This means that technical support callers who say the code word "shibboleet" will be transferred to a technical support representative who knows at least two programming languages, and presumably can offer more useful advice than a standard tech support script.

Andrews & Arnold provides IPv6 to all customers, for no additional charge.

Andrews & Arnold provides optional bonded multiple-link internet access. This allows multiple links to be used together to vastly increase speed and reliability. Special routers distribute individual IP packets between the available links in such a way that even one single download or upload operation will benefit fully from multiple speed, and it is not necessary to have several users, several running programs or computers to gain the speed benefit. Links can be of different types, each needs only to be a pipe that can carry IP packets. Multiple links can either be used together all the time, or some can be brought up as a back up if other links fail, so-called 'failover', or a combination of the two approaches can be set up.

Andrews & Arnold are strong advocates of not censoring Internet connections. Adrian Kennard has several blog posts discussing why Internet censorship as discussed in the UK is not workable, providing background for AAISP's decision.

🔗 Cryptography 🔗 Cryptography/Computer science

BB84 is a quantum key distribution scheme developed by Charles Bennett and Gilles Brassard in 1984. It is the first quantum cryptography protocol. The protocol is provably secure, relying on the quantum property that information gain is only possible at the expense of disturbing the signal if the two states one is trying to distinguish are not orthogonal (see no-cloning theorem) and an authenticated public classical channel. It is usually explained as a method of securely communicating a private key from one party to another for use in one-time pad encryption.