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🔗 Finance & Investment 🔗 Economics 🔗 Food and drink 🔗 Food and drink/Foodservice 🔗 Retailing 🔗 Globalization

The Big Mac Index is a price index published by The Economist as an informal way of measuring the purchasing power parity (PPP) between two currencies and provides a test of the extent to which market exchange rates result in goods costing the same in different countries. It "seeks to make exchange-rate theory a bit more digestible."

The index, created in 1986, takes its name from the Big Mac, a hamburger sold at McDonald's restaurants.

🔗 Japan

In Japanese culture, a hatsuyume (Japanese: 初夢) is the first dream one has in the new year. Traditionally, the contents of such a dream would foretell the luck of the dreamer in the ensuing year. In Japan, the night of December 31 was often passed without sleeping, so the hatsuyume is often experienced during the night of January 1; the day after the night of the "first dream" is also known as the hatsuyume. This day is January 2 in the Gregorian calendar, but was different in the traditional Japanese calendar.

It is considered to be particularly good luck to dream of Mount Fuji, a hawk, and an eggplant. This belief has been in place since the early Edo period but there are various theories regarding the origins as to why this particular combination was considered to be auspicious. One theory suggests that this combination is lucky because Mount Fuji is Japan's highest mountain, the hawk is a clever and strong bird, and the word for eggplant (茄子, nasu or nasubi) suggests achieving something great (成す nasu). Another theory suggests that this combination arose because Mount Fuji, falconry, and early eggplants were favorites of the shōgun Tokugawa Ieyasu.

Although this superstition is well known in Japan, often memorized in the form ichi-Fuji, ni-taka, san-nasubi (一富士、二鷹、三茄子; 1. Fuji, 2. Hawk, 3. Eggplant), the continuation of the list is not as well known. The continuation is yon-sen, go-tabako, roku-zatō (四扇、五煙草、六座頭; 4. Fan, 5. Tobacco, 6. Blind acupressurer). The origins of this trio are less well known, and it is unclear whether they were added after the original three or whether the list of six originated at the same time.

🔗 Law 🔗 Sexology and sexuality 🔗 Pornography

The Miller test, also called the three-prong obscenity test, is the United States Supreme Court's test for determining whether speech or expression can be labeled obscene, in which case it is not protected by the First Amendment to the United States Constitution and can be prohibited.

🔗 Philosophy

The Tinkerbell effect is an American English expression describing things that are thought to exist only because people believe in them. The effect is named after Tinker Bell, the fairy in the play Peter Pan, who is revived from near death by the belief of the audience.

Another form is called the Reverse Tinkerbell effect, a term coined by David Post in 2003. It stipulates that the more you believe in something the more likely it is to vanish. For example, as more people believe that driving is safe, more people will drive carelessly, in turn making driving less safe.

🔗 Agriculture 🔗 England 🔗 Folklore

Telling the bees is a traditional custom of many European countries in which bees would be told of important events in their keeper's lives, such as births, marriages, or departures and returns in the household. If the custom was omitted or forgotten and the bees were not "put into mourning" then it was believed a penalty would be paid, such as the bees leaving their hive, stopping the production of honey, or dying. The custom is best known in England, but has also been recorded in Ireland, Wales, Germany, Netherlands, France, Switzerland, Bohemia, and the United States.

🔗 Computer science 🔗 Mathematics

A negative base (or negative radix) may be used to construct a non-standard positional numeral system. Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base b is equal to −r for some natural number r (r ≥ 2).

Negative-base systems can accommodate all the same numbers as standard place-value systems, but both positive and negative numbers are represented without the use of a minus sign (or, in computer representation, a sign bit); this advantage is countered by an increased complexity of arithmetic operations. The need to store the information normally contained by a negative sign often results in a negative-base number being one digit longer than its positive-base equivalent.

The common names for negative-base positional numeral systems are formed by prefixing nega- to the name of the corresponding positive-base system; for example, negadecimal (base −10) corresponds to decimal (base 10), negabinary (base −2) to binary (base 2), negaternary (base −3) to ternary (base 3), and negaquaternary (base −4) to quaternary (base 4).

🔗 Computing 🔗 Computing/Early computers

The IBM 7950, also known as Harvest, was a one-of-a-kind adjunct to the Stretch computer which was installed at the United States National Security Agency (NSA). Built by IBM, it was delivered in 1962 and operated until 1976, when it was decommissioned. Harvest was designed to be used for cryptanalysis.

🔗 Plants

Cyclanthera brachystachya, the exploding cucumber (but not to be confused with Ecballium elaterium), in the cucurbit or gourd family (Cucurbitaceae), is a herbaceous vine usually grown for its curiosity value, but the fruit is also edible.

🔗 Computing 🔗 Computer science 🔗 Mathematics 🔗 Physics 🔗 Statistics

Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.

In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases).

Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of risk in business and, in mathematics, evaluation of multidimensional definite integrals with complicated boundary conditions. In application to systems engineering problems (space, oil exploration, aircraft design, etc.), Monte Carlo–based predictions of failure, cost overruns and schedule overruns are routinely better than human intuition or alternative "soft" methods.

In principle, Monte Carlo methods can be used to solve any problem having a probabilistic interpretation. By the law of large numbers, integrals described by the expected value of some random variable can be approximated by taking the empirical mean (a.k.a. the sample mean) of independent samples of the variable. When the probability distribution of the variable is parameterized, mathematicians often use a Markov chain Monte Carlo (MCMC) sampler. The central idea is to design a judicious Markov chain model with a prescribed stationary probability distribution. That is, in the limit, the samples being generated by the MCMC method will be samples from the desired (target) distribution. By the ergodic theorem, the stationary distribution is approximated by the empirical measures of the random states of the MCMC sampler.

In other problems, the objective is generating draws from a sequence of probability distributions satisfying a nonlinear evolution equation. These flows of probability distributions can always be interpreted as the distributions of the random states of a Markov process whose transition probabilities depend on the distributions of the current random states (see McKean–Vlasov processes, nonlinear filtering equation). In other instances we are given a flow of probability distributions with an increasing level of sampling complexity (path spaces models with an increasing time horizon, Boltzmann–Gibbs measures associated with decreasing temperature parameters, and many others). These models can also be seen as the evolution of the law of the random states of a nonlinear Markov chain. A natural way to simulate these sophisticated nonlinear Markov processes is to sample multiple copies of the process, replacing in the evolution equation the unknown distributions of the random states by the sampled empirical measures. In contrast with traditional Monte Carlo and MCMC methodologies, these mean-field particle techniques rely on sequential interacting samples. The terminology mean field reflects the fact that each of the samples (a.k.a. particles, individuals, walkers, agents, creatures, or phenotypes) interacts with the empirical measures of the process. When the size of the system tends to infinity, these random empirical measures converge to the deterministic distribution of the random states of the nonlinear Markov chain, so that the statistical interaction between particles vanishes.

Despite its conceptual and algorithmic simplicity, the computational cost associated with a Monte Carlo simulation can be staggeringly high. In general the method requires many samples to get a good approximation, which may incur an arbitrarily large total runtime if the processing time of a single sample is high. Although this is a severe limitation in very complex problems, the embarrassingly parallel nature of the algorithm allows this large cost to be reduced (perhaps to a feasible level) through parallel computing strategies in local processors, clusters, cloud computing, GPU, FPGA, etc.

🔗 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.