Have a deep view into what people are curious about.

🔗 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.

🔗 Computing 🔗 Computing/Computer hardware

PLATO (Programmed Logic for Automatic Teaching Operations) was the first generalized computer-assisted instruction system. Starting in 1960, it ran on the University of Illinois' ILLIAC I computer. By the late 1970s, it supported several thousand graphics terminals distributed worldwide, running on nearly a dozen different networked mainframe computers. Many modern concepts in multi-user computing were originally developed on PLATO, including forums, message boards, online testing, e-mail, chat rooms, picture languages, instant messaging, remote screen sharing, and multiplayer video games.

PLATO was designed and built by the University of Illinois and functioned for four decades, offering coursework (elementary through university) to UIUC students, local schools, and other universities. Courses were taught in a range of subjects, including Latin, chemistry, education, music, and primary mathematics. The system included a number of features useful for pedagogy, including text overlaying graphics, contextual assessment of free-text answers, depending on the inclusion of keywords, and feedback designed to respond to alternative answers.

Rights to market PLATO as a commercial product were licensed by Control Data Corporation (CDC), the manufacturer on whose mainframe computers the PLATO IV system was built. CDC President William Norris planned to make PLATO a force in the computer world, but found that marketing the system was not as easy as hoped. PLATO nevertheless built a strong following in certain markets, and the last production PLATO system did not shut down until 2006, coincidentally just a month after Norris died.

🔗 Shakespeare

The Shakespeare Programming Language (SPL) is an esoteric programming language designed by Jon Åslund and Karl Hasselström. Like the Chef programming language, it is designed to make programs appear to be something other than programs; in this case, Shakespearean plays.

A character list in the beginning of the program declares a number of stacks, naturally with names like "Romeo" and "Juliet". These characters enter into dialogue with each other in which they manipulate each other's topmost values, push and pop each other, and do I/O. The characters can also ask each other questions which behave as conditional statements. On the whole, the programming model is very similar to assembly language but much more verbose.

🔗 Sociology 🔗 Culture

The Inglehart–Welzel cultural map of the world is a map, or more precisely, a scatter plot created by political scientists Ronald Inglehart and Christian Welzel based on the World Values Survey. It depicts closely linked cultural values that vary between societies in two predominant dimensions: traditional versus secular-rational values on the vertical y-axis and survival versus self-expression values on the horizontal x-axis. Moving upward on this map reflects the shift from traditional values to secular-rational ones and moving rightward reflects the shift from survival values to self-expression values.

According to the authors: "These two dimensions explain more than 70 percent of the cross-national variance in a factor analysis of ten indicators—and each of these dimensions is strongly correlated with scores of other important orientations."

The authors stress that socio-economic status is not the sole factor determining a country's location, as their religious and cultural historical heritage is also an important factor.

🔗 Netherlands 🔗 Speed Skating 🔗 Frisia

The Elfstedentocht (Dutch pronunciation: [ɛlf'steːdə(n)tɔxt]; West Frisian: Alvestêdetocht [ɔlvəˈstɛːdətɔχt], English: Eleven cities tour) is a long-distance tour skating event on natural ice, almost 200 kilometres (120 mi) long, which is held both as a speed skating competition (with 300 contestants) and a leisure tour (with 16,000 skaters). It is held in the province of Friesland in the north of the Netherlands, leading past all eleven historical cities of the province. The tour is held at most once a year, only when the natural ice along the entire course is at least 15 centimetres (6 in) thick; sometimes on consecutive years, other times with gaps that may exceed 20 years. When the ice is suitable, the tour is announced and starts within 48 hours.

🔗 Lists 🔗 Libraries

This is a list of other articles that are lists of list articles on the English Wikipedia. In other words, each of the articles linked here is an index to multiple lists on a topic. Some of the linked articles are themselves lists of lists of lists. This article is also a list of lists, and also a list itself.

🔗 Religion 🔗 Africa 🔗 Ancient Egypt 🔗 Mythology 🔗 Africa/Ancient Egypt

In Ancient Egyptian religion, Medjed is a minor and obscure god mentioned in the Book of the Dead. His ghost-like portrayal in illustrations on the Greenfield papyrus earned him popularity in modern Japanese culture, including as a character in video games and anime.

🔗 United States 🔗 Medicine 🔗 Sociology 🔗 United States/Hispanic and Latino Americans

The Hispanic paradox is an epidemiological finding that Hispanic Americans tend to have health outcomes that "paradoxically" are comparable to, or in some cases better than, those of their U.S. non-Hispanic White counterparts, even though Hispanics have lower average income and education. Low socioeconomic status is almost universally associated with worse population health and higher death rates everywhere in the world. The paradox usually refers in particular to low mortality among Hispanics in the United States relative to non-Hispanic Whites. According to the Center for Disease Control's 2015 Vital Signs report, Hispanics in the United States had a 24% lower risk of mortality, as well as lower risk for nine of the fifteen leading causes of death as compared to Whites.

There are multiple hypotheses which aim to determine the reason for the existence of this paradox. Some attribute the Hispanic paradox to biases created by patterns or selection in migration. One such hypothesis is the Salmon Bias, which suggests that Hispanics tend to return home towards the end of their lives, ultimately rendering an individual "statistically immortal" and thus artificially lowering mortality for Hispanics in the United States. Another hypothesis in this group is that of the Healthy Migrant, which attributes the better health of Hispanics to the assumption that the healthiest and strongest members of a population are most likely to migrate.

Other hypotheses around the Hispanic paradox maintain that the phenomenon is real, and is caused by sociocultural factors which characterize the Hispanic population. Many of these factors can be described under the more broad categories of cultural values, interpersonal context, and community context. Some health researchers attribute the Hispanic paradox to different eating habits, especially the relatively high intake of legumes such as beans and lentils.

🔗 Physics

In physics and cosmology, digital physics is a collection of theoretical perspectives based on the premise that the universe is describable by information. It is a form of digital ontology about the physical reality. According to this theory, the universe can be conceived of as either the output of a deterministic or probabilistic computer program, a vast, digital computation device, or mathematically isomorphic to such a device.

🔗 Mathematics

Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely often. The idea was introduced by David Hilbert in a 1924 lecture "Über das Unendliche", reprinted in (Hilbert 2013, p.730), and was popularized through George Gamow's 1947 book One Two Three... Infinity.