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π GaussβMarkov theorem
In statistics, the GaussβMarkov 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 JamesβStein 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.
π Now Wikipedia has an API
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- "Now Wikipedia has an API" | 2008-04-26 | 60 Upvotes 7 Comments
π A visualization of why 1/4 + 1/16 + 1/64 + 1/256 + ... = 1/3
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- "A visualization of why 1/4 + 1/16 + 1/64 + 1/256 + ... = 1/3" | 2009-07-21 | 200 Upvotes 47 Comments
π Unsafe at Any Speed
Unsafe at Any Speed: The Designed-In Dangers of the American Automobile is a non-fiction book by consumer advocate Ralph Nader, first published in 1965. Its central theme is that car manufacturers resisted the introduction of safety features (such as seat belts), and that they were generally reluctant to spend money on improving safety. This work contains substantial references and material from industry insiders. It was a best seller in non-fiction in 1966.
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- "Unsafe at Any Speed" | 2021-11-11 | 83 Upvotes 78 Comments
π Differential Power Analysis
In cryptography, power analysis is a form of side channel attack in which the attacker studies the power consumption of a cryptographic hardware device (such as a smart card, tamper-resistant "black box", or integrated circuit). The attack can non-invasively extract cryptographic keys and other secret information from the device.
Simple power analysis (SPA) involves visually interpreting power traces, or graphs of electrical activity over time. Differential power analysis (DPA) is a more advanced form of power analysis, which can allow an attacker to compute the intermediate values within cryptographic computations through statistical analysis of data collected from multiple cryptographic operations. SPA and DPA were introduced to the open cryptology community in 1998 by Paul Kocher, Joshua Jaffe and Benjamin Jun.
π Olbers' Paradox
In astrophysics and physical cosmology, Olbers' paradox, named after the German astronomer Heinrich Wilhelm Olbers (1758β1840), also known as the "dark night sky paradox", is the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. In the hypothetical case that the universe is static, homogeneous at a large scale, and populated by an infinite number of stars, any line of sight from Earth must end at the surface of a star and hence the night sky should be completely illuminated and very bright. This contradicts the observed darkness and non-uniformity of the night.
The darkness of the night sky is one of the pieces of evidence for a dynamic universe, such as the Big Bang model. That model explains the observed non-uniformity of brightness by invoking spacetime's expansion, which lengthens the light originating from the Big Bang to microwave levels via a process known as redshift; this microwave radiation background has wavelengths much longer than those of visible light, and so appears dark to the naked eye. Other explanations for the paradox have been offered, but none have wide acceptance in cosmology.
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- "Olbers' Paradox" | 2020-12-12 | 162 Upvotes 81 Comments
π Working Memory Training
Working memory training is intended to improve a person's working memory. Working memory is a central intellectual faculty, linked to IQ, ageing, and mental health. It has been claimed that working memory training programs are effective means, both for treating specific medical conditions associated with working memory deficit, and for general increase in cognitive capacity among healthy neurotypical adults.
Individual studies of the topic show different, and sometime contradictory, results, and as one meta study puts it, asking the question βDoes cognitive training improve intelligence?β is as inappropriate as asking βDoes medicine cure disease?β, since none of them specify which particular intervention (which medicine or working memory training program) is being evaluated, for alleviating which condition is it applied (ADHD, stroke, general cognitive improvement etc.), and under what circumstances is it administered (selection criteria, adherence rate, outcome variables etc.).
In an influential metastudy from 2012, highly critical to cognitive training, analysed 23 studies with 30 group comparisons, and concluded that clinical memory training programs produce reliable short-term improvements in working memory skills in children and adults with ADHD, but also that there is no evidence that such effects can be maintained long-term without additional follow-up training. Three years later, another metastudy reached the opposite conclusion, that working memory training does have consistent and useful effects, not just on the type of working memory tests that are practiced, but also at other non-trained tasks and everyday life. Since then, a range of additional clinical experiments have been completed, with larger sample sizes, clearly defined control groups, and more uniform treatment of outcome variables. While the evidence is still far from unanimous, there are several experimental studies of working memory training that have shown beneficial effects for people with ADHD, those who have suffered stroke or traumatic brain injury, children who have undergone cancer treatment, as well as for normally developing children.
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- "Working Memory Training" | 2024-07-06 | 10 Upvotes 1 Comments
π Embrace, Extend, and Extinguish
"Embrace, extend, and extinguish" (EEE), also known as "embrace, extend, and exterminate", is a phrase that the U.S. Department of Justice found was used internally by Microsoft to describe its strategy for entering product categories involving widely used standards, extending those standards with proprietary capabilities, and then using those differences in order to strongly disadvantage its competitors.
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- "Embrace, Extend, and Extinguish" | 2023-12-03 | 37 Upvotes 16 Comments
- "Embrace, Extend, and Extinguish" | 2023-08-25 | 17 Upvotes 4 Comments
- "Embrace, Extend, and Extinguish" | 2020-05-20 | 170 Upvotes 118 Comments
- "Embrace, Extend, and Extinguish" | 2019-07-15 | 12 Upvotes 1 Comments
π May Day
May Day is a public holiday in some regions, usually celebrated on 1 May or the first Monday of May. It is an ancient festival marking the first day of summer, and a current traditional spring holiday in many European cultures. Dances, singing, and cake are usually part of the festivities.
In 1889, May Day was chosen as the date for International Workers' Day by the socialists and communists of the Second International, as well as anarchists, labor activists, and leftists in general around the world, to commemorate the Haymarket affair in Chicago and the struggle for an eight-hour working day. International Workers' Day is also called "May Day", but it is a different celebration from the traditional May Day.
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- "May Day" | 2022-05-01 | 57 Upvotes 8 Comments
π Nanoscale Vacuum-Channel Transistor
A nanoscale vacuum-channel transistor (NVCT) is a theoretically visioned transistor in which the electron transport medium is a vacuum. In a traditional solid-state transistor, a semiconductor channel exists between the source and the drain, and the current flows through the semiconductor. However, in a nanoscale vacuum-channel transistor, no material exists between the source and the drain, and therefore, the current flows through the vacuum. However, experimental realization of such a transistor has not been demonstrated.
Theoretically, a vacuum-channel transistor is expected to operate faster than a traditional solid-state transistor, and have higher power output. Moreover, vacuum-channel transistors are expected to operate at higher temperature and radiation level than a traditional transistor making them suitable for space application.
The development of vacuum-channel transistors is still at a very early research stage, and there are only limited study in recent literature such as vertical field-emitter vacuum-channel transistor, gate-insulated planar electrodes vacuum-channel transistor, vertical vacuum-channel transistor, and all-around gate vacuum-channel transistor.
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- "Nanoscale Vacuum-Channel Transistor" | 2019-04-29 | 20 Upvotes 8 Comments