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Monte Carlo method

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; typically one runs simulations many times over in order to obtain the distribution of an unknown probabilistic entity. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to obtain a closed-form expression, or infeasible to apply a deterministic algorithm. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration and generation of draws from a probability distribution. The modern version of the Monte Carlo method was invented in the late 1940s by Stanislaw Ulam, while he was working on nuclear weapons projects at the Los Alamos National Laboratory. Introduction[edit] Monte Carlo method applied to approximating the value of π. Monte Carlo methods vary, but tend to follow a particular pattern: History[edit] Definitions[edit] Related:  mathematics

BBC Four - Climate Change by Numbers Dr Hannah Fry: the mathematical models that underpin our sexual success | Science What are the odds? Or how mathematician Peter Backus weighed up his chances of finding love… Just as it’s not possible to calculate precisely how many alien life forms there are, it’s also not possible to calculate exactly how many potential partners you may have. It also applies to maths student Peter Backus’s well-publicised quest to see whether there were intelligent, socially advanced women of the same species out there for him to date. 1. 2. 3. 4. 5. 6. 7. Leaving him with just 26 women in the whole world he would be willing to date. Personally, I think that he is being a little picky. I think there’s room to be a bit more generous. 1. 5. 6. 7. Almost a thousand potential partners across a city, then. But there is another issue. Strangely though, opening our minds to all potential partners seems to be the opposite of what we do when we’re single. The statistics of sex In 1996 Swedish scientists asked 2,810 people how many sexual partners they’d had. The happily ever after

Ding Dong Bell The sound of bells In East Anglia, as you look across the fens, villages appear almost like little islands (indeed some of them were islands before the fens were drained) and these villages are dominated by big churches with tall towers. In the past people regulated their lives and passed messages by ringing church bells, which could be heard for miles around, telling the time of day, and giving news of births, marriages and deaths in a parish. The following quotation comes from the ringer's rules from Southhill in Bedfordshire "When mirth and pleasure is on the wing we ring; at the departure of a soul we toll". Bell ringing is good exercise for the body and mind, the bells are heavy and the bellringers have to remember the changes. The mathematics of the changes With four bells there are of course many more possibilities; there are twenty four different permutations or orders in which the bells can be rung and there are four bell ringing changes. Find the vertex labelled 1234.

learn morse code Bach and the mathematics of genius The unmistakeable handwriting of J S Bach What does this formula mean to you? If you’ve studied mathematics, you may recognise it as “Euler’s identity”. As it happens, I’ve studied maths. If, however, you’re a professional mathematician, then it's quite a turn-on. Sing? Despite my almost total ignorance of maths, that doesn’t surprise me. At the end of his life, Johann Sebastian Bach wrote a short set of organ variations on the Christmas hymn tune Von Himmel hoch. Bach’s variations chase tunes at different pitches or intervals; they alternate between three and four voices; they find ingenious ways of weaving the original hymn tune into the texture; they turn the melody upside-down; they play intricate games with rhythm; and towards the end the composer sneaks in the notes B, A, C and H (which is what Germans call B flat). The deeper you dig into the Canonic Variations, the more you discover about their kaleidoscopic symmetry. This makes me angry, because it could so easily be put right.

Revolutions: data science by Sherri RoseAssistant Professor of Health Care PolicyHarvard Medical School Targeted learning methods build machine-learning-based estimators of parameters defined as features of the probability distribution of the data, while also providing influence-curve or bootstrap-based confidence internals. The theory offers a general template for creating targeted maximum likelihood estimators for a data structure, nonparametric or semiparametric statistical model, and parameter mapping. These estimators of causal inference parameters are double robust and have a variety of other desirable statistical properties. Targeted maximum likelihood estimation built on the loss-based “super learning” system such that lower-dimensional parameters could be targeted (e.g., a marginal causal effect); the remaining bias for the (low-dimensional) target feature of the probability distribution was removed. Of key importance are the two R packages SuperLearner and tmle.

Conway's Game of Life - Javascript/Canvas Implementation What is this? This page contains a Javascript implementation of the well know John Conway's Game of Life. It uses the List Life algorithm (by Tony Finch) and a Canvas interface for drawing. This is a work in progress and I will add some new features in the near future: Zoom controls Canvas navigation controls More patterns Proper benchmark support ... Previous versions 1.0.0 - First public release. Source Code Javascript source code is available here: game-of-life-v3.1.1.js. License This work is licenced under a MIT license (except any 3rd party code). 3rd Party Powered by CSS Browser Selector and JSON Sans Eval. Video The following video demonstrates some features of this program. What is this? This page contains a Javascript implementation of the well know John Conway's Game of Life. This is a work in progress and I will add some new features in the near future: Zoom controls Canvas navigation controls More patterns Proper benchmark support ... Previous versions 1.0.0 - First public release. License

Divide By Zero About To Divide by Zero is an internet slang term describing an action that leads to an epic failure or theoretically unlikely disaster, such as an earth-shattering apocalypse or a wormhole in the time-space continuum. The concept of division by zero is also associated with the phrase “OH SHI-,” which represents the response of someone that is cut off mid-sentence as a result of the disaster. Origin The earliest known reference to division by zero can be found in a YTMND site titled “1/0 !!!!!!!!!!!!” uploaded on October 3rd, 2005, which featured an artist’s illustration of a black hole. However, according to Encyclopedia Dramatica, the phrase is said to have originated on 4chan’s /b/ (random) board, with its earliest dating to December 8th, 2006. In Mathematics In math with real numbers, values that represent quantities along a continuous line, division by zero is an undefined operation, meaning it is impossible to have a real number answer to the equation. Spread Mr. Notable Examples

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