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🔗 Electronics

A Wallace tree is an efficient hardware implementation of a digital circuit that multiplies two integers. It was devised by the Australian computer scientist Chris Wallace in 1964.

The Wallace tree has three steps:

1. Multiply (that is – AND) each bit of one of the arguments, by each bit of the other, yielding ${\displaystyle n^{2}}$ results. Depending on position of the multiplied bits, the wires carry different weights, for example wire of bit carrying result of ${\displaystyle a_{4}b_{3}}$ is 128 (see explanation of weights below).
2. Reduce the number of partial products to two by layers of full and half adders.
3. Group the wires in two numbers, and add them with a conventional adder.

The second step works as follows. As long as there are three or more wires with the same weight add a following layer:-

• Take any three wires with the same weights and input them into a full adder. The result will be an output wire of the same weight and an output wire with a higher weight for each three input wires.
• If there are two wires of the same weight left, input them into a half adder.
• If there is just one wire left, connect it to the next layer.

The benefit of the Wallace tree is that there are only ${\displaystyle O(\log n)}$ reduction layers, and each layer has ${\displaystyle O(1)}$ propagation delay. As making the partial products is ${\displaystyle O(1)}$ and the final addition is ${\displaystyle O(\log n)}$, the multiplication is only ${\displaystyle O(\log n)}$, not much slower than addition (however, much more expensive in the gate count). Naively adding partial products with regular adders would require ${\displaystyle O(\log ^{2}n)}$ time. From a complexity theoretic perspective, the Wallace tree algorithm puts multiplication in the class NC¹.

These computations only consider gate delays and don't deal with wire delays, which can also be very substantial.

The Wallace tree can be also represented by a tree of 3/2 or 4/2 adders.

It is sometimes combined with Booth encoding.

🔗 Computing 🔗 Computing/Software

Max, also known as Max/MSP/Jitter, is a visual programming language for music and multimedia developed and maintained by San Francisco-based software company Cycling '74. Over its more than thirty-year history, it has been used by composers, performers, software designers, researchers, and artists to create recordings, performances, and installations.

The Max program is modular, with most routines existing as shared libraries. An application programming interface (API) allows third-party development of new routines (named external objects). Thus, Max has a large user base of programmers unaffiliated with Cycling '74 who enhance the software with commercial and non-commercial extensions to the program. Because of this extensible design, which simultaneously represents both the program's structure and its graphical user interface (GUI), Max has been described as the lingua franca for developing interactive music performance software.

🔗 Mathematics 🔗 Physics

The finite element method (FEM) is the most widely used method for solving problems of engineering and mathematical models. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a particular numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretisation in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. The FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.

Studying or analyzing a phenomenon with FEM is often referred to as finite element analysis (FEA).

🔗 Biography 🔗 Literature 🔗 Women writers 🔗 Biography/arts and entertainment

Barbara Newhall Follett (March 4, 1914 – disappeared December 7, 1939) was an American child prodigy novelist. Her first novel, The House Without Windows, was published in January 1927, when she was twelve years old. Her next novel, The Voyage of the Norman D.w, received critical acclaim when she was fourteen.

In December 1939, aged 25, Follett reportedly became depressed with her marriage and walked out of her apartment, never to be seen again.

🔗 Spaceflight 🔗 Environment 🔗 Disaster management

The Kessler syndrome (also called the Kessler effect, collisional cascading, or ablation cascade), proposed by NASA scientist Donald J. Kessler in 1978, is a theoretical scenario in which the density of objects in low Earth orbit (LEO) due to space pollution is high enough that collisions between objects could cause a cascade in which each collision generates space debris that increases the likelihood of further collisions. One implication is that the distribution of debris in orbit could render space activities and the use of satellites in specific orbital ranges difficult for many generations.

🔗 Fishes 🔗 Psychoactive and Recreational Drugs 🔗 Altered States of Consciousness

Several species of fish are claimed to produce hallucinogenic effects when consumed. For example, Sarpa salpa, a species of sea bream, is commonly claimed to be hallucinogenic. These widely distributed coastal fish are normally found in the Mediterranean and around Spain, and along the west and south coasts of Africa. Occasionally they are found in British waters. They may induce hallucinogenic effects that are purportedly LSD-like if eaten. In 2006, two men who apparently ate the fish experienced hallucinations lasting for several days. The likelihood of hallucinations depends on the season. Sarpa salpa is known as "the fish that makes dreams" in Arabic.

Other species claimed to be capable of producing hallucinations include several species of sea chub from the genus Kyphosus. It is unclear whether the toxins are produced by the fish themselves or by marine algae in their diet. Other hallucinogenic fish are Siganus spinus, called "the fish that inebriates" in Reunion Island, and Mulloidichthys flavolineatus (formerly Mulloidichthys samoensis), called "the chief of ghosts" in Hawaii.

🔗 United States 🔗 Biography 🔗 Women scientists 🔗 Biography/science and academia 🔗 Women's History 🔗 History of Science 🔗 Austria 🔗 Jewish Women 🔗 Biography/Actors and Filmmakers

Hedy Lamarr (), born Hedwig Eva Maria Kiesler (November 9, 1914 – January 19, 2000), was an Austrian-born American actress, inventor and film producer. She was part of 30 films in an acting career spanning 28 years, and co-invented an early version of frequency-hopping spread spectrum.

After a brief early film career in Czechoslovakia, including the controversial Ecstasy (1933), she fled from her husband, a wealthy Austrian ammunition manufacturer, and secretly moved to Paris. Traveling to London, she met Louis B. Mayer, head of Metro-Goldwyn-Mayer (MGM) studio, who offered her a movie contract in Hollywood, where he began promoting her as the "world's most beautiful woman".

She became a star with her performance in Algiers (1938), her first film made in the United States. Her MGM films include Lady of the Tropics (1939), Boom Town (1940), H.M. Pulham, Esq. (1941), and White Cargo (1942). Dismayed with her MGM contract, Lamarr co-founded a new production studio and starred in its films including The Strange Woman (1946), and Dishonored Lady (1947). Her greatest success was as Delilah in Cecil B. DeMille's Samson and Delilah (1949). She also acted on television before the release of her final film, The Female Animal (1958). She was honored with a star on the Hollywood Walk of Fame in 1960.

At the beginning of World War II, Lamarr and composer George Antheil developed a radio guidance system for Allied torpedoes, intended to use frequency-hopping spread spectrum technology to defeat the threat of jamming by the Axis powers. She also helped to improve aviation designs for Howard Hughes while they dated during the war. Although the US Navy did not adopt Lamarr and Antheil's invention until 1957, various spread-spectrum techniques are incorporated into Bluetooth technology and are similar to methods used in legacy versions of Wi-Fi. Recognition of the value of their work resulted in the pair being posthumously inducted into the National Inventors Hall of Fame in 2014.

🔗 United States 🔗 Mass surveillance 🔗 Espionage 🔗 Companies 🔗 Military history 🔗 Military history/North American military history 🔗 Military history/United States military history 🔗 Military history/Military science, technology, and theory 🔗 Military history/Intelligence 🔗 Cryptography 🔗 Cryptography/Computer science 🔗 Switzerland 🔗 Military history/Cold War 🔗 Sweden

Crypto AG was a Swiss company specialising in communications and information security. It was secretly jointly owned by the American Central Intelligence Agency (CIA) and West German Federal Intelligence Service (BND) from 1970 until about 1993, with the CIA continuing as sole owner until about 2018. With headquarters in Steinhausen, the company was a long-established manufacturer of encryption machines and a wide variety of cipher devices.

The company had about 230 employees, had offices in Abidjan, Abu Dhabi, Buenos Aires, Kuala Lumpur, Muscat, Selsdon and Steinhausen, and did business throughout the world. The owners of Crypto AG were unknown, supposedly even to the managers of the firm, and they held their ownership through bearer shares.

The company has been criticised for selling backdoored products to benefit the American, British and German national signals intelligence agencies, the National Security Agency (NSA), the Government Communications Headquarters (GCHQ), and the BND, respectively. On 11 February 2020, The Washington Post, ZDF and SRF revealed that Crypto AG was secretly owned by the CIA in a highly classified partnership with West German intelligence, and the spy agencies could easily break the codes used to send encrypted messages. The operation was known first by the code name "Thesaurus" and later "Rubicon".

🔗 Mathematics

A person's Erdős–Bacon number is the sum of one's Erdős number—which measures the "collaborative distance" in authoring academic papers between that person and Hungarian mathematician Paul Erdős—and one's Bacon number—which represents the number of links, through roles in films, by which the person is separated from American actor Kevin Bacon. The lower the number, the closer a person is to Erdős and Bacon, which reflects a small world phenomenon in academia and entertainment.

To have a defined Erdős–Bacon number, it is necessary to have both appeared in a film and co-authored an academic paper, although this in and of itself is not sufficient.

🔗 Biography 🔗 Medicine 🔗 COVID-19 🔗 China 🔗 Biography/science and academia

Li Wenliang (Chinese: 李文亮; pinyin: Lǐ Wénliàng; 12 October 1986 – 7 February 2020) was a Chinese ophthalmologist who worked as a physician at Wuhan Central Hospital. Li warned his colleagues in December 2019 about a possible outbreak of an illness that resembled severe acute respiratory syndrome (SARS), later acknowledged as COVID-19. He became a whistleblower when his warnings were later shared publicly. On 3 January 2020, Wuhan police summoned and admonished him for "making false comments on the Internet". Li returned to work, later contracted the virus from an infected patient (who had been originally treated for glaucoma) and died from the disease on 7 February 2020, at age 33. A subsequent Chinese official inquiry exonerated him and the Communist Party formally offered a "solemn apology" to his family and revoked its admonishment of him.