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🔗 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.

🔗 Board and table games

18XX is the generic term for a series of board games that, with a few exceptions, recreate the building of railroad corporations during the 19th century; individual games within the series use particular years in the 19th century as their title (usually the date of the start of railway development in the area of the world they cover), or "18" plus a two or more letter geographical designator (such as 18EU for a game set in the European Union). The games 2038, set in the future, and Poseidon and Ur, 1830 BC, both set in ancient history, are also regarded as 18XX titles as their game mechanics and titling nomenclature are similar despite variance from the common railroad/stock-market theme.

The 18XX series has its origins in the game 1829, first produced by Francis Tresham in the mid-1970s. 1829 was chosen as it was the year of the Rainhill Trials. 1830 was produced by Avalon Hill in 1986, and was the first game of the series widely available in the United States; it is seen as the basic 18XX game by the U.S. audience.

In addition to traditionally published games, the 18XX series has spawned self-published variants and games published by low-volume game companies.

With few exceptions (such as 2038), 18XX titles are multiplayer board games without random variables in their game mechanics.

🔗 Genetics

Cephalization is an evolutionary trend in which, over many generations, the mouth, sense organs, and nerve ganglia become concentrated at the front end of an animal, producing a head region. This is associated with movement and bilateral symmetry, such that the animal has a definite head end. This led to the formation of a highly sophisticated brain in three groups of animals, namely the arthropods, cephalopod molluscs, and vertebrates.

🔗 Climate change 🔗 Environment 🔗 Antarctica 🔗 Glaciers

The Western Antarctic Ice Sheet (WAIS) is the segment of the continental ice sheet that covers West Antarctica, the portion of Antarctica on the side of the Transantarctic Mountains that lies in the Western Hemisphere. The WAIS is classified as a marine-based ice sheet, meaning that its bed lies well below sea level and its edges flow into floating ice shelves. The WAIS is bounded by the Ross Ice Shelf, the Ronne Ice Shelf, and outlet glaciers that drain into the Amundsen Sea.

🔗 Soviet Union 🔗 Russia 🔗 Russia/technology and engineering in Russia 🔗 Spaceflight 🔗 Dogs 🔗 Russia/science and education in Russia 🔗 Russia/history of Russia

Laika (Russian: Лайка; c. 1954 – 3 November 1957) was a Soviet space dog who was one of the first animals in space and the first to orbit the Earth. A stray mongrel from the streets of Moscow, she flew aboard the Sputnik 2 spacecraft, launched into low orbit on 3 November 1957. As the technology to de-orbit had not yet been developed, Laika's survival was never expected. She died of overheating hours into the flight, on the craft's fourth orbit.

Little was known about the impact of spaceflight on living creatures at the time of Laika's mission, and animal flights were viewed by engineers as a necessary precursor to human missions. The experiment, which monitored Laika's vital signs, aimed to prove that a living organism could survive being launched into orbit and continue to function under conditions of weakened gravity and increased radiation, providing scientists with some of the first data on the biological effects of spaceflight.

Laika died within hours from overheating, possibly caused by a failure of the central R‑7 sustainer to separate from the payload. The true cause and time of her death were not made public until 2002; instead, it was widely reported that she died when her oxygen ran out on day six or, as the Soviet government initially claimed, she was euthanised prior to oxygen depletion. In 2008, a small monument to Laika depicting her standing atop a rocket was unveiled near the military research facility in Moscow that prepared her flight. She also appears on the Monument to the Conquerors of Space in Moscow.

🔗 Computing 🔗 Computing/Computer hardware 🔗 Computing/Software 🔗 Java

Jazelle DBX (direct bytecode execution) is an extension that allows some ARM processors to execute Java bytecode in hardware as a third execution state alongside the existing ARM and Thumb modes. Jazelle functionality was specified in the ARMv5TEJ architecture and the first processor with Jazelle technology was the ARM926EJ-S. Jazelle is denoted by a "J" appended to the CPU name, except for post-v5 cores where it is required (albeit only in trivial form) for architecture conformance.

Jazelle RCT (Runtime Compilation Target) is a different technology based on ThumbEE mode; it supports ahead-of-time (AOT) and just-in-time (JIT) compilation with Java and other execution environments.

The most prominent use of Jazelle DBX is by manufacturers of mobile phones to increase the execution speed of Java ME games and applications. A Jazelle-aware Java virtual machine (JVM) will attempt to run Java bytecode in hardware, while returning to the software for more complicated, or lesser-used bytecode operations. ARM claims that approximately 95% of bytecode in typical program usage ends up being directly processed in the hardware.

The published specifications are very incomplete, being only sufficient for writing operating system code that can support a JVM that uses Jazelle. The declared intent is that only the JVM software needs to (or is allowed to) depend on the hardware interface details. This tight binding facilitates the hardware and JVM evolving together without affecting other software. In effect, this gives ARM Holdings considerable control over which JVMs are able to exploit Jazelle. It also prevents open source JVMs from using Jazelle. These issues do not apply to the ARMv7 ThumbEE environment, the nominal successor to Jazelle DBX.

🔗 Poetry 🔗 Bible

An acrostic is a poem (or other form of writing) in which the first letter (or syllable, or word) of each line (or paragraph, or other recurring feature in the text) spells out a word, message or the alphabet. The word comes from the French acrostiche from post-classical Latin acrostichis, from Koine Greek ἀκροστιχίς, from Ancient Greek ἄκρος "highest, topmost" and στίχος "verse". As a form of constrained writing, an acrostic can be used as a mnemonic device to aid memory retrieval.

Relatively simple acrostics may merely spell out the letters of the alphabet in order; such an acrostic may be called an 'alphabetical acrostic' or abecedarius. These acrostics occur in the first four of the five chapters that make up the Book of Lamentations, in the praise of the good wife in Proverbs 31:10-31, and in Psalms 25, 34, 37, 111, 112, 119 and 145 of the Hebrew Bible. Notable among the acrostic Psalms is the long Psalm 119, which typically is printed in subsections named after the 22 letters of the Hebrew alphabet, each section consisting of 8 verses, each of which begins with the same letter of the alphabet and the entire psalm consisting of 22 x 8 = 176 verses; and Psalm 145, which is recited three times a day in the Jewish services. Some acrostic psalms are technically imperfect. E.g. Psalm 9 and Psalm 10 appear to constitute a single acrostic psalm together, but the length assigned to each letter is unequal and five of the 22 letters of the Hebrew alphabet are not represented and the sequence of two letters is reversed. In Psalm 25 one Hebrew letter is not represented, the following letter (Resh) repeated. In Psalm 34 the current final verse, 23, does fit verse 22 in content, but adds an additional line to the poem. In Psalms 37 and 111 the numbering of verses and the division into lines are interfering with each other; as a result in Psalm 37, for the letters Daleth and Kaph there is only one verse, and the letter Ayin is not represented. Psalm 111 and 112 have 22 lines, but 10 verses. Psalm 145 does not represent the letter Nun, having 21 one verses, but one Qumran manuscript of this Psalm does have that missing line, which agrees with the Septuagint.

Acrostics are common in medieval literature, where they usually serve to highlight the name of the poet or his patron, or to make a prayer to a saint. They are most frequent in verse works but can also appear in prose. The Middle High German poet Rudolf von Ems for example opens all his great works with an acrostic of his name, and his world chronicle marks the beginning of each age with an acrostic of the key figure (Moses, David, etc.). In chronicles, acrostics are common in German and English but rare in other languages.

Often the ease of detectability of an acrostic can depend on the intention of its creator. In some cases an author may desire an acrostic to have a better chance of being perceived by an observant reader, such as the acrostic contained in the Hypnerotomachia Poliphili (where the key capital letters are decorated with ornate embellishments). However, acrostics may also be used as a form of steganography, where the author seeks to conceal the message rather than proclaim it. This might be achieved by making the key letters uniform in appearance with the surrounding text, or by aligning the words in such a way that the relationship between the key letters is less obvious. This is referred to as null ciphers in steganography, using the first letter of each word to form a hidden message in an otherwise innocuous text. Using letters to hide a message, as in acrostic ciphers, was popular during the Renaissance, and could employ various methods of enciphering, such as selecting other letters than initials based on a repeating pattern (equidistant letter sequences), or even concealing the message by starting at the end of the text and working backwards.

🔗 Mathematics 🔗 Physics 🔗 Systems 🔗 Systems/Dynamical systems

The Abelian sandpile model, also known as the Bak–Tang–Wiesenfeld model, was the first discovered example of a dynamical system displaying self-organized criticality. It was introduced by Per Bak, Chao Tang and Kurt Wiesenfeld in a 1987 paper.

The model is a cellular automaton. In its original formulation, each site on a finite grid has an associated value that corresponds to the slope of the pile. This slope builds up as "grains of sand" (or "chips") are randomly placed onto the pile, until the slope exceeds a specific threshold value at which time that site collapses transferring sand into the adjacent sites, increasing their slope. Bak, Tang, and Wiesenfeld considered process of successive random placement of sand grains on the grid; each such placement of sand at a particular site may have no effect, or it may cause a cascading reaction that will affect many sites.

The model has since been studied on the infinite lattice, on other (non-square) lattices, and on arbitrary graphs (including directed multigraphs). It is closely related to the dollar game, a variant of the chip-firing game introduced by Biggs.

🔗 India 🔗 India/Indian literature workgroup

The Shishupala Vadha (Sanskrit: शिशुपालवध, IAST: Śiśupāla-vadha, lit. "the slaying of Shishupala") is a work of classical Sanskrit poetry (kāvya) composed by Māgha in the 7th or 8th century. It is an epic poem in 20 sargas (cantos) of about 1800 highly ornate stanzas, and is considered one of the six Sanskrit mahakavyas, or "great epics". It is also known as the Māgha-kāvya after its author. Like other kavyas, it is admired more for its exquisite descriptions and lyrical quality than for any dramatic development of plot. Its 19th canto is noted for verbal gymnastics and wordplay; see the section on linguistic ingenuity below.

🔗 Computer science 🔗 Systems 🔗 Systems/Scientific modeling

Jackson structured programming (JSP) is a method for structured programming developed by British software consultant Michael A. Jackson and described in his 1975 book Principles of Program Design. The technique of JSP is to analyze the data structures of the files that a program must read as input and produce as output, and then produce a program design based on those data structures, so that the program control structure handles those data structures in a natural and intuitive way.

JSP describes structures (of both data and programs) using three basic structures – sequence, iteration, and selection (or alternatives). These structures are diagrammed as (in effect) a visual representation of a regular expression.