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🔗 Food and drink 🔗 Plants

Romanesco broccoli (also known as Roman cauliflower, Broccolo Romanesco, Romanesque cauliflower, or simply Romanesco) is an edible flower bud of the species Brassica oleracea. First documented in Italy in the 16th century, it is chartreuse in color, and has a form naturally approximating a fractal. When compared to a traditional cauliflower, it has a firmer texture and delicate, nutty flavor.

🔗 Philosophy 🔗 Philosophy/Social and political philosophy 🔗 Football

Three-sided football (often referred to as 3SF) is a variation of association football played with three teams instead of the usual two. It was devised by the Danish Situationist Asger Jorn to explain his notion of triolectics, his refinement on the Marxian concept of dialectics, as well as to disrupt one's everyday idea of football. Played on a hexagonal pitch [1], the game can be adapted for similarity to soccer as well as other versions of football.

Unlike conventional football, where the winner is determined by the highest scoring of the two teams, in three-sided football the winning team is that which concedes the fewest goals.

🔗 Mathematics 🔗 Statistics 🔗 Linguistics 🔗 Linguistics/Applied Linguistics

Zipf's law (, not as in German) is an empirical law formulated using mathematical statistics that refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions. Zipf distribution is related to the zeta distribution, but is not identical.

Zipf's law was originally formulated in terms of quantitative linguistics, stating that given some corpus of natural language utterances, the frequency of any word is inversely proportional to its rank in the frequency table. Thus the most frequent word will occur approximately twice as often as the second most frequent word, three times as often as the third most frequent word, etc.: the rank-frequency distribution is an inverse relation. For example, in the Brown Corpus of American English text, the word the is the most frequently occurring word, and by itself accounts for nearly 7% of all word occurrences (69,971 out of slightly over 1 million). True to Zipf's Law, the second-place word of accounts for slightly over 3.5% of words (36,411 occurrences), followed by and (28,852). Only 135 vocabulary items are needed to account for half the Brown Corpus.

The law is named after the American linguist George Kingsley Zipf (1902–1950), who popularized it and sought to explain it (Zipf 1935, 1949), though he did not claim to have originated it. The French stenographer Jean-Baptiste Estoup (1868–1950) appears to have noticed the regularity before Zipf. It was also noted in 1913 by German physicist Felix Auerbach (1856–1933).

🔗 Biography 🔗 Biography/science and academia 🔗 University of Pennsylvania

George Harry Heilmeier (May 22, 1936 – April 21, 2014) was an American engineer, manager, and a pioneering contributor to liquid crystal displays (LCDs), for which he was inducted into the National Inventors Hall of Fame. Heilmeier's work is an IEEE Milestone.

🔗 Philosophy 🔗 Politics 🔗 Psychology 🔗 Marketing & Advertising 🔗 Philosophy/Philosophy of science 🔗 Philosophy/Epistemology 🔗 Sociology 🔗 Education

Social facilitation is defined as improvement or decrease in individual performance when working with other people rather than alone.

In addition to working together with other people, social facilitation also occurs in the mere presence of other people. Previous research has found that individual performance is improved by coaction, performing a task in the presence of others who are performing a similar task, and having an audience while performing a certain task. An example of coaction triggering social facilitation can be seen in instances where a cyclist's performance is improved when cycling along with other cyclists as compared to cycling alone. An instance where having an audience triggers social facilitation can be observed where a weightlifter lifts heavier weight in the presence of an audience. Social facilitation has occasionally been attributed to the fact that certain people are more susceptible to social influence, with the argument that personality factors can make these people more aware of evaluation.

The Yerkes-Dodson law, when applied to social facilitation, states that "the mere presence of other people will enhance the performance in speed and accuracy of well-practiced tasks, but will degrade in the performance of less familiar tasks." Compared to their performance when alone, when in the presence of others they tend to perform better on simple or well-rehearsed tasks and worse on complex or new ones.

The audience effect attempts to explain psychologically why the presence of an audience leads to people performing tasks better in some cases and worse in others. This idea was further explored when some studies showed that the presence of a passive audience facilitated the better performance of a simple task, while other studies showed that the presence of a passive audience inhibited the performance of a more difficult task or one that was not well practiced, possibly due to psychological pressure or stress. (See Yerkes–Dodson law.)

🔗 Mathematics

In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix that generalizes the eigendecomposition of a square normal matrix to any ${\displaystyle m\times n}$ matrix via an extension of the polar decomposition.

Specifically, the singular value decomposition of an ${\displaystyle m\times n}$ real or complex matrix ${\displaystyle \mathbf {M} }$ is a factorization of the form ${\displaystyle \mathbf {U\Sigma V^{*}} }$, where ${\displaystyle \mathbf {U} }$ is an ${\displaystyle m\times m}$ real or complex unitary matrix, ${\displaystyle \mathbf {\Sigma } }$ is an ${\displaystyle m\times n}$ rectangular diagonal matrix with non-negative real numbers on the diagonal, and ${\displaystyle \mathbf {V} }$ is an ${\displaystyle n\times n}$ real or complex unitary matrix. If ${\displaystyle \mathbf {M} }$ is real, ${\displaystyle \mathbf {U} }$ and ${\displaystyle \mathbf {V} =\mathbf {V^{*}} }$ are real orthonormal matrices.

The diagonal entries ${\displaystyle \sigma _{i}=\Sigma _{ii}}$ of ${\displaystyle \mathbf {\Sigma } }$ are known as the singular values of ${\displaystyle \mathbf {M} }$. The number of non-zero singular values is equal to the rank of ${\displaystyle \mathbf {M} }$. The columns of ${\displaystyle \mathbf {U} }$ and the columns of ${\displaystyle \mathbf {V} }$ are called the left-singular vectors and right-singular vectors of ${\displaystyle \mathbf {M} }$, respectively.

The SVD is not unique. It is always possible to choose the decomposition so that the singular values ${\displaystyle \Sigma _{ii}}$are in descending order. In this case, Σ (but not always U and V) is uniquely determined by M.

The term sometimes refers to the compact SVD, a similar decomposition ${\displaystyle \mathbf {M} =\mathbf {U\Sigma V^{*}} }$ in which Σ is square diagonal of size ${\displaystyle r\times r}$, where ${\displaystyle r\leq \min\{m,n\}}$ is the rank of M, and has only the non-zero singular values. In this variant, ${\displaystyle \mathbf {U} }$ is an ${\displaystyle m\times r}$ matrix and ${\displaystyle \mathbf {V} }$ is an ${\displaystyle n\times r}$ matrix, such that ${\displaystyle \mathbf {U^{*}U} =\mathbf {V^{*}V} =\mathbf {I} _{r\times r}}$.

Mathematical applications of the SVD include computing the pseudoinverse, matrix approximation, and determining the rank, range, and null space of a matrix. The SVD is also extremely useful in all areas of science, engineering, and statistics, such as signal processing, least squares fitting of data, and process control.

🔗 Mathematics

Visual calculus, invented by Mamikon Mnatsakanian (known as Mamikon), is an approach to solving a variety of integral calculus problems. Many problems that would otherwise seem quite difficult yield to the method with hardly a line of calculation, often reminiscent of what Martin Gardner called "aha! solutions" or Roger Nelsen a proof without words.

🔗 Military history 🔗 Military history/North American military history 🔗 Military history/United States military history

Millennium Challenge 2002 (MC02) was a major war game exercise conducted by the United States Armed Forces in mid-2002. The exercise, which ran from 24 July to 15 August and cost US$250 million (equivalent to about $355M in 2019), involved both live exercises and computer simulations. MC02 was meant to be a test of future military "transformation"—a transition toward new technologies that enable network-centric warfare and provide more effective command and control of current and future weaponry and tactics. The simulated combatants were the United States, referred to as "Blue", and a fictitious state in the Persian Gulf, "Red", often characterized as Iran or Iraq.

🔗 Korea 🔗 Physics 🔗 Chemicals 🔗 Electrical engineering 🔗 Materials

LK-99 is a proposed ambient pressure and room-temperature superconductor with a gray‒black appearance.^: 8 LK-99 has a hexagonal structure slightly modified from lead‒apatite and is claimed to function as a superconductor below 400 K (127 °C; 260 °F).^: 1 The material was investigated by a team of Sukbae Lee et al. from the Korea Institute of Science and Technology (KIST).^: 1 As of 26 July 2023 the discovery of LK-99 has not been peer reviewed or independently replicated.

The chemical composition of LK-99 is approximately Pb₉Cu(PO₄)₆O such that—compared to pure lead-apatite (Pb₁₀(PO₄)₆O)^: 5—approximately one quarter of Pb(2) ions are replaced by Cu(II) ions.^: 9 This partial replacement of Pb²⁺ ions (measuring 133 picometre) with Cu²⁺ ions (measuring 87 picometre) is said to cause a 0.48% reduction in volume, creating internal stress inside the material.^: 8

The internal stress is claimed to cause a heterojunction quantum well between the Pb(1) and oxygen within the phosphate ([PO₄]³⁻) generating a superconducting quantum well (SQW).^: 10 Lee et al claim to show LK-99 exhibits a response to a magnetic field (Meissner effect) when chemical vapor deposition is used to apply LK-99 to a non-magnetic copper sample.^: 4 Pure lead-apatite is an insulator, but Lee et al claim copper-doped lead-apatite forming LK-99 is a superconductor, or at higher temperatures, a metal.^: 5

🔗 Military history 🔗 Military history/Military science, technology, and theory 🔗 Military history/Weaponry 🔗 Medicine 🔗 Chemicals 🔗 Occupational Safety and Health 🔗 Military history/World War I 🔗 Medicine/Toxicology

Chloropicrin, also known as PS and nitrochloroform, is a chemical compound currently used as a broad-spectrum antimicrobial, fungicide, herbicide, insecticide, and nematicide. It was used as a poison gas in World War I. Its chemical structural formula is Cl₃CNO₂.