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🔗 Mathematics 🔗 Statistics

The secretary problem is a problem that demonstrates a scenario involving optimal stopping theory. The problem has been studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem.

The basic form of the problem is the following: imagine an administrator who wants to hire the best secretary out of ${\displaystyle n}$ rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator gains information sufficient to rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy (stopping rule) to maximize the probability of selecting the best applicant. If the decision can be deferred to the end, this can be solved by the simple maximum selection algorithm of tracking the running maximum (and who achieved it), and selecting the overall maximum at the end. The difficulty is that the decision must be made immediately.

The shortest rigorous proof known so far is provided by the odds algorithm (Bruss 2000). It implies that the optimal win probability is always at least ${\displaystyle 1/e}$ (where e is the base of the natural logarithm), and that the latter holds even in a much greater generality (2003). The optimal stopping rule prescribes always rejecting the first ${\displaystyle \sim n/e}$ applicants that are interviewed and then stopping at the first applicant who is better than every applicant interviewed so far (or continuing to the last applicant if this never occurs). Sometimes this strategy is called the ${\displaystyle 1/e}$ stopping rule, because the probability of stopping at the best applicant with this strategy is about ${\displaystyle 1/e}$ already for moderate values of ${\displaystyle n}$. One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) is simple and selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants.

🔗 Apple Inc./Macintosh 🔗 Apple Inc.

Miller columns (also known as cascading lists) are a browsing/visualization technique that can be applied to tree structures. The columns allow multiple levels of the hierarchy to be open at once, and provide a visual representation of the current location. It is closely related to techniques used earlier in the Smalltalk browser, but was independently invented by Mark S. Miller in 1980 at Yale University. The technique was then used at Project Xanadu, Datapoint, and NeXT.

While at Datapoint, Miller generalized the technique to browse directed graphs with labeled nodes and arcs. In all cases, the technique is appropriate for structures with high degree (large fanout). For low-degree structures, outline editors or graph viewers are more effective.

🔗 Business

The bullwhip effect is a supply chain phenomenon where orders to suppliers tend to have a larger variability than sales to buyers, which results in an amplified demand variability upstream. In part, this results in increasing swings in inventory in response to shifts in consumer demand as one moves further up the supply chain. The concept first appeared in Jay Forrester's Industrial Dynamics (1961) and thus it is also known as the Forrester effect. It has been described as "the observed propensity for material orders to be more variable than demand signals and for this variability to increase the further upstream a company is in a supply chain".

Research at Stanford University helped incorporate the concept into supply chain vernacular using a story about Volvo. Suffering a glut in green cars, sales and marketing developed a program to sell the excess inventory. While successful in generating the desired market pull, manufacturing did not know about the promotional plans. Instead, they read the increase in sales as an indication of growing demand for green cars and ramped up production.

Research indicates a fluctuation in point-of-sale demand of five percent will be interpreted by supply chain participants as a change in demand of up to forty percent. Much like cracking a whip, a small flick of the wrist - a shift in point of sale demand - can cause a large motion at the end of the whip - manufacturers' responses.

🔗 Germany 🔗 Disaster management 🔗 Politics 🔗 European history 🔗 Crime and Criminal Biography 🔗 Firefighting

The Reichstag fire (German: Reichstagsbrand, pronounced [ˈʁaɪçstaːksˌbʁant] ) was an arson attack on the Reichstag building, home of the German parliament in Berlin, on Monday, 27 February 1933, precisely four weeks after Adolf Hitler was sworn in as Chancellor of Germany. Marinus van der Lubbe, a Dutch council communist, was said to be the culprit; the Nazis attributed the fire to a group of Communist agitators, used it as a pretext to claim that Communists were plotting against the German government, and induced President Paul von Hindenburg to issue the Reichstag Fire Decree, suspending civil liberties, and pursue a "ruthless confrontation" with the Communists. This made the fire pivotal in the establishment of Nazi rule in Germany.

The first report of the fire came shortly after 9:00 p.m., when a Berlin fire station received an alarm call. By the time police and firefighters arrived, the structure was engulfed in flames. The police conducted a thorough search inside the building and found Van der Lubbe, who was arrested.

After the Fire Decree was issued, the police – now controlled by Hitler's Nazi Party – made mass arrests of communists, including all of the communist Reichstag delegates. This severely crippled communist participation in the 5 March elections. After the 5 March elections, the absence of the communists allowed the Nazi Party to expand their plurality in the Reichstag, greatly assisting the Nazi seizure of total power. On 9 March 1933 the Prussian state police arrested Bulgarians Georgi Dimitrov, Vasil Tanev, and Blagoy Popov, who were known Comintern operatives (though the police did not know it then, Dimitrov was head of all Comintern operations in Western Europe). Ernst Torgler, chairman of the KPD Reichstag faction, had surrendered to police on 28 February.

Van der Lubbe and the four communists were the defendants in a trial that started in September 1933. It ended in the acquittal of the four communists and the conviction of Van der Lubbe, who was then executed. In 2008, Germany posthumously pardoned Van der Lubbe under a law introduced in 1998 to lift unjust verdicts from the Nazi era. The responsibility for the Reichstag fire remains a topic of debate, as while Van der Lubbe was found guilty, it is unclear whether he acted alone. The consensus amongst historians is the Reichstag was set ablaze by Van der Lubbe; some consider it to have been a part of a Nazi plot, a view Richard J. Evans labels a conspiracy theory.

🔗 Technology 🔗 Physics 🔗 Radio 🔗 Astronomy 🔗 Engineering

In engineering, the terahertz gap is a frequency band in the terahertz region of the electromagnetic spectrum between radio waves and infrared light for which practical technologies for generating and detecting the radiation do not exist. It is defined as 0.1 to 10 THz (wavelengths of 3 mm to 30 µm). Currently, at frequencies within this range, useful power generation and receiver technologies are inefficient and unfeasible.

Mass production of devices in this range and operation at room temperature (at which energy k·T is equal to the energy of a photon with a frequency of 6.2 THz) are mostly impractical. This leaves a gap between mature microwave technologies in the highest frequencies of the radio spectrum and the well developed optical engineering of infrared detectors in their lowest frequencies. This radiation is mostly used in small-scale, specialized applications such as submillimetre astronomy. Research that attempts to resolve this issue has been conducted since the late 20th century.

🔗 Automobiles

The Electro Gyro-Cator was claimed to be the world's first automated commercially available automotive navigation system. It was co-developed by Honda, Alpine, and Stanley Electric Co..

Unlike most navigation systems of today, it did not use GPS Satellites to maintain its position and discern movement of the vehicle. Rather, it was an Inertial navigation system, because it contained a helium gas gyroscope that could detect both rotation and movement. A special servo gear was also attached to the transmission housing to feed information to the Gyro-Cator to help maintain position, map speed and distance traveled.

Transparent maps were placed inside the unit and it would scroll them past a 6 inch monochrome CRT illuminated screen as the car traveled along. The monitor would indicate by a series of circles (or cross hairs) on the screen to show the vehicle's current location or display lines for path of travel. A marking pen was also included to help make personal indicators on the map if needed. Adjustments could be made to change the display scale, position, rotation, brightness, and contrast. In its only year of production in 1981, it was announced as an option on that year's Honda Accord and Honda Vigor, but at ¥300,000 ($2,746 USD), it was almost a quarter of the value of the car. It is not clear how many units were actually sold to customers as a "dealer option". A patent for gyroscope design was introduced to the US in design patent D274332.

Documented weight for the unit was roughly 20 lb (9 kg). A display unit, with a cutaway of the Gyroscope, is currently shown at the Honda Collection Hall at Twin Ring Motegi, Japan.

🔗 Computer science

In computing, aspect-oriented programming (AOP) is a programming paradigm that aims to increase modularity by allowing the separation of cross-cutting concerns. It does so by adding behavior to existing code (an advice) without modifying the code itself, instead separately specifying which code is modified via a "pointcut" specification, such as "log all function calls when the function's name begins with 'set'". This allows behaviors that are not central to the business logic (such as logging) to be added to a program without cluttering the code core to the functionality.

AOP includes programming methods and tools that support the modularization of concerns at the level of the source code, while aspect-oriented software development refers to a whole engineering discipline.

Aspect-oriented programming entails breaking down program logic into distinct parts (so-called concerns, cohesive areas of functionality). Nearly all programming paradigms support some level of grouping and encapsulation of concerns into separate, independent entities by providing abstractions (e.g., functions, procedures, modules, classes, methods) that can be used for implementing, abstracting and composing these concerns. Some concerns "cut across" multiple abstractions in a program, and defy these forms of implementation. These concerns are called cross-cutting concerns or horizontal concerns.

Logging exemplifies a crosscutting concern because a logging strategy necessarily affects every logged part of the system. Logging thereby crosscuts all logged classes and methods.

All AOP implementations have some crosscutting expressions that encapsulate each concern in one place. The difference between implementations lies in the power, safety, and usability of the constructs provided. For example, interceptors that specify the methods to express a limited form of crosscutting, without much support for type-safety or debugging. AspectJ has a number of such expressions and encapsulates them in a special class, an aspect. For example, an aspect can alter the behavior of the base code (the non-aspect part of a program) by applying advice (additional behavior) at various join points (points in a program) specified in a quantification or query called a pointcut (that detects whether a given join point matches). An aspect can also make binary-compatible structural changes to other classes, like adding members or parents.

🔗 United States 🔗 Politics 🔗 LGBT studies 🔗 Sexology and sexuality 🔗 Politics/American politics 🔗 Donald Trump 🔗 Conservatism 🔗 Pornography

Project 2025 is a plan to reshape the executive branch of the U.S. federal government in the event of a Republican victory in the 2024 U.S. presidential election. Established in 2022, the project seeks to recruit tens of thousands of conservatives to Washington, D.C., to replace existing federal civil service workers it characterizes as the "deep state", to further the objectives of the next Republican president. Although participants in the project cannot promote a specific presidential candidate, many have close ties to Donald Trump and the Trump 2024 presidential campaign. The plan would perform a swift takeover of the entire executive branch under a maximalist version of the unitary executive theory — a theory proposing the president of the United States has absolute power over the executive branch — upon inauguration.

The development of the plan is led by the The Heritage Foundation, an American conservative think tank, in collaboration with over 100 partners including Turning Point USA led by Charlie Kirk; the Conservative Partnership Institute including former Trump Chief of Staff Mark Meadows as senior partner; the Center for Renewing America led by former Trump-appointee Office of Management and Budget Director Russell Vought; and America First Legal led by former Trump Senior Advisor Stephen Miller.

Project 2025 envisions widespread changes across the entire government, particularly with regard to economic and social policy and the role of the federal government and federal agencies. The plan proposes slashing U.S. Department of Justice (DOJ) funding, dismantling the FBI and the Department of Homeland Security, gutting environmental and climate change regulations to favor fossil fuel production, and eliminating the cabinet Departments of Education and Commerce. Citing an anonymous source, The Washington Post reported Project 2025 includes immediately invoking the Insurrection Act of 1807 to deploy the military for domestic law enforcement and directing the DOJ to pursue Trump adversaries. Project Director Paul Dans, a former Trump administration official, said in September 2023 that Project 2025 is "systematically preparing to march into office and bring a new army, aligned, trained, and essentially weaponized conservatives ready to do battle against the deep state."

Project 2025 consists largely of a book of policy recommendations titled Mandate for Leadership: The Conservative Promise and an accompanying personnel database open for submissions. There is also an online course called the Presidential Administration Academy, and a guide to developing transition plans. Reactions to the plan included variously describing it as authoritarian, an attempt by Trump to become a dictator, and a path leading the United States towards autocracy, with several experts in law criticizing it for violating current constitutional laws that would undermine the rule of law and the separation of powers. Additionally, some conservatives and Republicans also criticized the plan, for example in relation to climate change. The Mandate states that "freedom is defined by God, not man."

🔗 United States 🔗 Mathematics

Garfield's proof of the Pythagorean theorem is an original proof of the Pythagorean theorem discovered by James A. Garfield (November 19, 1831 – September 19, 1881), the 20th president of the United States. The proof appeared in print in the New-England Journal of Education (Vol. 3, No.14, April 1, 1876). At the time of the publication of the proof Garfield was a congressman from Ohio. He assumed the office of President on March 4, 1881, and served in that position until his death on September 19, 1881, having succumbed to injuries sustained when he was shot in an assassination in July. Garfield is thus far the only President of the United States to have contributed anything original to mathematics. The proof is nontrivial and, according to the historian of mathematics William Dunham, "Garfield's is really a very clever proof." The proof appears as the 231st proof in The Pythagorean Proposition, a compendium of 370 different proofs of the Pythagorean theorem.

🔗 Crime 🔗 Death 🔗 England 🔗 Graffiti

Who put Bella down the Wych Elm? is graffiti that appeared in 1944 following the 1943 discovery by four children of the skeletonised remains of a woman inside a wych elm in Hagley Wood, Hagley (located in the estate of Hagley Hall), in Worcestershire, England. The victim—whose murder is approximated to have occurred in 1941—remains unidentified, and the current location of her skeleton and autopsy report is unknown.