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๐ History of the Monte Carlo method
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, McKeanโVlasov 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 Carloโbased 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 McKeanโVlasov 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, BoltzmannโGibbs 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.
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- "History of the Monte Carlo method" | 2022-09-18 | 94 Upvotes 26 Comments
๐ Unix time - 15:30:08 UTC on Sun, 4 December 292,277,026,596
Unix time (also known as Epoch time, POSIX time, seconds since the Epoch, or UNIX Epoch time) is a system for describing a point in time. It is the number of seconds that have elapsed since the Unix epoch, that is the time 00:00:00 UTC on 1 January 1970, minus leap seconds. Leap seconds are ignored, with a leap second having the same Unix time as the second before it, and every day is treated as if it contains exactly 86400 seconds. Due to this treatment, Unix time is not a true representation of UTC.
Unix time is widely used in operating systems and file formats. In Unix-like operating systems, date is a command which will print or set the current time; by default, it prints or sets the time in the system time zone, but with the -u flag, it prints or sets the time in UTC and, with the TZ environment variable set to refer to a particular time zone, prints or sets the time in that time zone.
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- "Unix time - 15:30:08 UTC on Sun, 4 December 292,277,026,596" | 2014-06-03 | 11 Upvotes 10 Comments
๐ Fabergรฉ Egg
A Fabergรฉ egg (Russian: ัะนัะพ ะคะฐะฑะตัะถะตฬ, romanized:ย yaytso Faberzhe) is a jewelled egg created by the jewellery firm House of Fabergรฉ, in Saint Petersburg, Russia. As many as 69 were created, of which 57 survive today. Virtually all were manufactured under the supervision of Peter Carl Fabergรฉ between 1885 and 1917. The most famous are his 52 "Imperial" eggs, 46 of which survive, made for the Russian Tsars Alexander III and Nicholas II as Easter gifts for their wives and mothers. Fabergรฉ eggs are worth millions of dollars and have become symbols of opulence.
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- "Fabergรฉ Egg" | 2023-03-12 | 52 Upvotes 37 Comments
๐ The Mother of All Demos
"The Mother of All Demos" is a name retroactively applied to a landmark computer demonstration, given at the Association for Computing Machinery / Institute of Electrical and Electronics Engineers (ACM/IEEE)โComputer Society's Fall Joint Computer Conference in San Francisco, which was presented by Douglas Engelbart on December 9, 1968.
The live demonstration featured the introduction of a complete computer hardware and software system called the oN-Line System or, more commonly, NLS. The 90-minute presentation essentially demonstrated almost all the fundamental elements of modern personal computing: windows, hypertext, graphics, efficient navigation and command input, video conferencing, the computer mouse, word processing, dynamic file linking, revision control, and a collaborative real-time editor (collaborative work). Engelbart's presentation was the first to publicly demonstrate all of these elements in a single system. The demonstration was highly influential and spawned similar projects at Xerox PARC in the early 1970s. The underlying technologies influenced both the Apple Macintosh and Microsoft Windows graphical user interface operating systems in the 1980s and 1990s.
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- "The Mother of All Demos" | 2023-07-13 | 42 Upvotes 1 Comments
- "The Mother of All Demos" | 2013-07-05 | 67 Upvotes 4 Comments
๐ 1956 Suez Crisis
The Suez Crisis or the Second ArabโIsraeli War, also referred to as the Tripartite Aggression in the Arab world and as the Sinai War in Israel, was a BritishโFrenchโIsraeli invasion of Egypt in 1956. Israel invaded on 29 October, having done so with the primary objective of re-opening the Straits of Tiran and the Gulf of Aqaba as the recent tightening of the eight-year-long Egyptian blockade further prevented Israeli passage. After issuing a joint ultimatum for a ceasefire, the United Kingdom and France joined the Israelis on 5 November, seeking to depose Egyptian president Gamal Abdel Nasser and regain control of the Suez Canal, which Nasser had earlier nationalised by transferring administrative control from the foreign-owned Suez Canal Company to Egypt's new government-owned Suez Canal Authority. Shortly after the invasion began, the three countries came under heavy political pressure from both the United States and the Soviet Union, as well as from the United Nations, eventually prompting their withdrawal from Egypt. Israel's four-month-long occupation of the Egyptian-occupied Gaza Strip and Egypt's Sinai Peninsula enabled it to attain freedom of navigation through the Straits of Tiran, but the Suez Canal itself was closed from October 1956 to March 1957. The Suez Crisis led to international humiliation for the British and the French in the wake of the Cold War, which established the Americans and the Soviets as the world's superpowers. It also strengthened Nasser's standing.
Before they were defeated, Egyptian troops had blocked all ship traffic by sinking 40 ships in the Suez Canal. It later became clear that Israel, the United Kingdom, and France had conspired to invade Egypt. Though the three allies had attained a number of their military objectives, the Suez Canal itself was useless. American president Dwight D. Eisenhower had issued a strong warning to the British if they were to invade Egypt; he threatened serious damage to the British financial system by selling the American government's bonds of pound sterling. Historians have concluded that the Suez Crisis "signified the end of Great Britain's role as one of the world's major powers" vis-ร -vis the United States and the Soviet Union.
As a result of the conflict, the United Nations established the United Nations Emergency Force to police and patrol the EgyptโIsrael border, while British prime minister Anthony Eden resigned from his position. For his diplomatic efforts in resolving the conflict through United Nations initiatives, Canadian external affairs minister Lester B. Pearson received a Nobel Peace Prize. Analysts have argued that the Suez Crisis may have emboldened the Soviet Union, prompting the Soviet invasion of Hungary.
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- "1956 Suez Crisis" | 2024-05-27 | 11 Upvotes 2 Comments
๐ Marine glass sponge that builds silica skeletons
The Venus' flower basket (Euplectella aspergillum) is a glass sponge in the phylum Porifera. It is a marine sponge found in the deep waters of the Pacific ocean. As other glass sponges, they build their skeletons out of silica, which is of great interest in materials science as they do not require heat to form their glass latices, which in some ways makes their properties superior to manufactured fiber optics. As other sponges, they feed by filtering sea water to capture plankton.
The sponges are often found to house glass sponge shrimp, usually a breeding pair, whom are typically unable to exit the sponge's lattice due to their size. Consequently, they live in and around these sponges, where the shrimp perform a mutuallistic relationship with the sponge until they die. This may have influenced the adoption of the sponge as a symbol of undying love in Japan, where the skeletons of these sponges are presented as nuptial gifts.
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- "Marine glass sponge that builds silica skeletons" | 2020-07-12 | 26 Upvotes 3 Comments
๐ Neskowin Ghost Forest
The Neskowin Ghost Forest is the remnants of a Sitka spruce forest on the Oregon Coast of the United States. The stumps were likely created when an earthquake of the Cascadia subduction zone abruptly lowered the trees, that were then covered by mud from landslides or debris from a tsunami. Many of the stumps are over 2,000 years old.
The stumps were unearthed when turbulent storms swept away sand during the winter of 1997โ1998. It is one of over thirty ghost forests along the Oregon and Washington Coast, though many appear as flat roots and not stumps. Most notably, Washington's ghost forest of red cedars was integral to the discovery of the Cascadia fault line. These ghost forests are evidence of significant, rapid changes in coastline โ often due to seismic events such as the 1700 Cascadia earthquake.
The stumps at Neskowin are 2,000 years old, according to carbon dating. While living, the trees that make up the Neskowin Ghost Forest were similar to present-day coastal rain forest. They stood 150โ200 feet (46โ61ย m) high and were at least 200 years old when buried. However, it's difficult to determine when or how the trees died, because it occurred before written history in the region. It was originally believed that these trees died slowly, as the roots were gradually submerged in saltwater due to changes in the sea levels. Yet research by geologists revealed that the soil, still present at the roots of the stumps, was buried abruptly โ indicating a more sudden and dramatic event, like an earthquake, as the cause.
The ghost forest is near Proposal Rock. It is part of the Neskowin Beach State Recreation Site. The best time to see the stumps is low tide, during winter (due to January, February and March bringing the lowest tides of the year.)
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- "Neskowin Ghost Forest" | 2023-10-25 | 34 Upvotes 1 Comments
๐ Arachne: a self-contained graphical web browser for DOS and Linux
Arachne is a discontinued Internet suite containing a graphical web browser, email client, and dialer. Originally, Arachne was developed by Michal Polรกk under his xChaos label, a name he later changed into Arachne Labs. It was written in C and compiled using Borland C++ 3.1. Arachne has since been released under the GPL as Arachne GPL.
Arachne primarily runs on DOS-based operating systems, but includes builds for Linux as well. The Linux version relies on SVGALib and therefore does not require a display server.
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- "Arachne: a self-contained graphical web browser for DOS and Linux" | 2015-10-20 | 41 Upvotes 13 Comments
๐ Tamagotchi Connection
The Tamagotchi Connection, known as Tamagotchi Plus in Japan and Tamagotchi Connexion in the UK, is a virtual pet in the Tamagotchi line of digital toys from Bandai. The Tamagotchi Connection is unique from prior models in that it uses infrared technology to connect and interact with other devices and was first released in 2004, 8 years after the first Tamagotchi toy. Using the device's infrared port, the virtual pet (referred to as a Tamagotchi) can make friends with other Tamagotchis, in addition to playing games, giving and receiving presents and having a baby.
Versions 1 to 4 of Tamagotchi Connection have 6 levels of friendship that can be viewed in the Friends List:
- Acquaintance (one smiley-face)
- Buddy (two smiley-faces)
- Friend (three smiley-faces)
- Good friend (four smiley-faces)
- Best friend (two love-hearts, two smiley-faces, during connection they may kiss)
- Partner (four love-hearts, during connection they will kiss and may have babies)
Versions 5 and 6 have different levels.
If the Tamagotchi cannot find a partner from another device to have babies with, a matchmaker will come, allowing the Tamagotchi to have a baby with a computer-controlled Tamagotchi character. This applies to versions 1 to 4 and 6 only. Version 5 introduces a Dating Show game in which the user must play to gain a CPU partner.
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- "Tamagotchi Connection" | 2023-09-06 | 110 Upvotes 76 Comments