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🔗 Mathematics 🔗 Television 🔗 Statistics 🔗 Game theory 🔗 Television/Television game shows

The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975 (Selvin 1975a), (Selvin 1975b). It became famous as a question from a reader's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990 (vos Savant 1990a):

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Vos Savant's response was that the contestant should switch to the other door (vos Savant 1990a). Under the standard assumptions, contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their initial choice have only a 1/3 chance.

The given probabilities depend on specific assumptions about how the host and contestant choose their doors. A key insight is that, under these standard conditions, there is more information about doors 2 and 3 than was available at the beginning of the game when door 1 was chosen by the player: the host's deliberate action adds value to the door he did not choose to eliminate, but not to the one chosen by the contestant originally. Another insight is that switching doors is a different action than choosing between the two remaining doors at random, as the first action uses the previous information and the latter does not. Other possible behaviors than the one described can reveal different additional information, or none at all, and yield different probabilities. Yet another insight is that your chance of winning by switching doors is directly related to your chance of choosing the winning door in the first place: if you choose the correct door on your first try, then switching loses; if you choose a wrong door on your first try, then switching wins; your chance of choosing the correct door on your first try is 1/3, and the chance of choosing a wrong door is 2/3.

Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong (Tierney 1991). Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy (vos Savant 1991a). Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating vos Savant’s predicted result (Vazsonyi 1999).

The problem is a paradox of the veridical type, because the correct choice (that one should switch doors) is so counterintuitive it can seem absurd, but is nevertheless demonstrably true. The Monty Hall problem is mathematically closely related to the earlier Three Prisoners problem and to the much older Bertrand's box paradox.

🔗 Mathematics 🔗 Statistics

Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential equations.

The central concept is the Itô stochastic integral, a stochastic generalization of the Riemann–Stieltjes integral in analysis. The integrands and the integrators are now stochastic processes:

${\displaystyle Y_{t}=\int _{0}^{t}H_{s}\,dX_{s},}$

where H is a locally square-integrable process adapted to the filtration generated by X (Revuz & Yor 1999, Chapter IV), which is a Brownian motion or, more generally, a semimartingale. The result of the integration is then another stochastic process. Concretely, the integral from 0 to any particular t is a random variable, defined as a limit of a certain sequence of random variables. The paths of Brownian motion fail to satisfy the requirements to be able to apply the standard techniques of calculus. So with the integrand a stochastic process, the Itô stochastic integral amounts to an integral with respect to a function which is not differentiable at any point and has infinite variation over every time interval. The main insight is that the integral can be defined as long as the integrand H is adapted, which loosely speaking means that its value at time t can only depend on information available up until this time. Roughly speaking, one chooses a sequence of partitions of the interval from 0 to t and constructs Riemann sums. Every time we are computing a Riemann sum, we are using a particular instantiation of the integrator. It is crucial which point in each of the small intervals is used to compute the value of the function. The limit then is taken in probability as the mesh of the partition is going to zero. Numerous technical details have to be taken care of to show that this limit exists and is independent of the particular sequence of partitions. Typically, the left end of the interval is used.

Important results of Itô calculus include the integration by parts formula and Itô's lemma, which is a change of variables formula. These differ from the formulas of standard calculus, due to quadratic variation terms.

In mathematical finance, the described evaluation strategy of the integral is conceptualized as that we are first deciding what to do, then observing the change in the prices. The integrand is how much stock we hold, the integrator represents the movement of the prices, and the integral is how much money we have in total including what our stock is worth, at any given moment. The prices of stocks and other traded financial assets can be modeled by stochastic processes such as Brownian motion or, more often, geometric Brownian motion (see Black–Scholes). Then, the Itô stochastic integral represents the payoff of a continuous-time trading strategy consisting of holding an amount H_t of the stock at time t. In this situation, the condition that H is adapted corresponds to the necessary restriction that the trading strategy can only make use of the available information at any time. This prevents the possibility of unlimited gains through clairvoyance: buying the stock just before each uptick in the market and selling before each downtick. Similarly, the condition that H is adapted implies that the stochastic integral will not diverge when calculated as a limit of Riemann sums (Revuz & Yor 1999, Chapter IV).

🔗 Computing 🔗 Computer science 🔗 Computing/Software 🔗 Computing/Computer science

Timsort is a hybrid stable sorting algorithm, derived from merge sort and insertion sort, designed to perform well on many kinds of real-world data. It was implemented by Tim Peters in 2002 for use in the Python programming language. The algorithm finds subsequences of the data that are already ordered (runs) and uses them to sort the remainder more efficiently. This is done by merging runs until certain criteria are fulfilled. Timsort has been Python's standard sorting algorithm since version 2.3. It is also used to sort arrays of non-primitive type in Java SE 7, on the Android platform, in GNU Octave, on V8, and Swift.

It uses techniques from Peter McIlroy's 1993 paper "Optimistic Sorting and Information Theoretic Complexity".

🔗 Biography

Pieter Hintjens (3 December 1962 – 4 October 2016) was a Belgian software developer, author, and past president of the Foundation for a Free Information Infrastructure (FFII), an association that fights against software patents. In 2007, he was nominated one of the "50 most influential people in IP" by Managing Intellectual Property magazine.

🔗 Lists 🔗 Food and drink 🔗 Plants

This is a list of vegetables which are grown or harvested primarily for the consumption of their leafy parts, either raw or cooked. Many plants with leaves that are consumed in small quantities as a spice such as oregano, for medicinal purposes such as lime, or used in infusions such as tea, are not included in this list.

🔗 Lists 🔗 Science Fiction 🔗 Transhumanism 🔗 Sociology 🔗 Futures studies 🔗 Science 🔗 Popular Culture

This is a list of fictional stories that, when written, were set in the future, but the future they predicted is now present or past. The list excludes works that were alternate histories, which were composed after the dates they depict, alternative futures, as depicted in time travel fiction, as well as any works that make no predictions of the future, such as those focusing solely on the future lives of specific fictional characters, or works which, despite their claimed dates, are contemporary in all but name. Entries referencing the current year may be added if their month and day were not specified or have already occurred.

🔗 Software 🔗 Software/Computing

Waterfox is an open-source web browser for x64, ARM64, and PPC64LE systems. It is intended to be speedy and ethical, and maintain support for legacy extensions dropped by Firefox, from which it is forked. There are official releases for Windows (including a portable version), Mac OS, Linux and Android.

Waterfox is based on Firefox and is compiled using various compilers and using Intel's Math Kernel Library, Streaming SIMD Extensions 3 and Advanced Vector Extensions. Linux builds are built with Clang on all architectures other than PPC64LE. Waterfox is continuing to support the long-standing XUL and XPCOM add-on capability that Firefox removed in version 57.

🔗 Cryptography 🔗 Cryptography/Computer science

A physical unclonable function (sometimes also called physically unclonable function, which refers to a weaker security metric), or PUF, is a physical object that for a given input and conditions (challenge), provides a physically-defined "digital fingerprint" output (response) that serves as a unique identifier, most often for a semiconductor device such as a microprocessor. PUFs are most often based on unique physical variations which occur naturally during semiconductor manufacturing. A PUF is a physical entity embodied in a physical structure. Today, PUFs are usually implemented in integrated circuits and are typically used in applications with high security requirements, more specifically cryptography.

🔗 United States/U.S. Government 🔗 United States 🔗 Medicine 🔗 Economics 🔗 Politics 🔗 Geography

Universal healthcare (also called universal health coverage, universal coverage, or universal care) is a health care system in which all residents of a particular country or region are assured access to health care. It is generally organized around providing either all residents or only those who cannot afford on their own, with either health services or the means to acquire them, with the end goal of improving health outcomes.

Universal healthcare does not imply coverage for all cases and for all people – only that all people have access to healthcare when and where needed without financial hardship. Some universal healthcare systems are government-funded, while others are based on a requirement that all citizens purchase private health insurance. Universal healthcare can be determined by three critical dimensions: who is covered, what services are covered, and how much of the cost is covered. It is described by the World Health Organization as a situation where citizens can access health services without incurring financial hardship. The Director General of WHO describes universal health coverage as the “single most powerful concept that public health has to offer” since it unifies “services and delivers them in a comprehensive and integrated way”. One of the goals with universal healthcare is to create a system of protection which provides equality of opportunity for people to enjoy the highest possible level of health.

As part of Sustainable Development Goals, United Nations member states have agreed to work toward worldwide universal health coverage by 2030.

🔗 Astronomy 🔗 Astronomy/Astronomical objects

Wolf 359 is a red dwarf star located in the constellation Leo, near the ecliptic. At a distance of approximately 7.9 light years from Earth, it has an apparent magnitude of 13.54 and can only be seen with a large telescope. Wolf 359 is one of the nearest stars to the Sun; only the Alpha Centauri system (including Proxima Centauri), Barnard's Star and the brown dwarfs Luhman 16 and WISE 0855−0714 are known to be closer. Its proximity to Earth has led to its mention in several works of fiction.

Wolf 359 is one of the faintest and lowest-mass stars known. At the light-emitting layer called the photosphere, it has a temperature of about 2,800 K, which is low enough for chemical compounds to form and survive. The absorption lines of compounds such as water and titanium(II) oxide have been observed in the spectrum. The surface has a magnetic field that is stronger than the average magnetic field on the Sun. As a result of magnetic activity caused by convection, Wolf 359 is a flare star that can undergo sudden increases in luminosity for several minutes. These flares emit strong bursts of X-ray and gamma ray radiation that have been observed by space telescopes. Wolf 359 is a relatively young star with an age of less than a billion years. Two planetary companions are suspected but as yet no debris disks have been unmasked.