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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. Immediately after Ulam's breakthrough, John von Neumann understood its importance and programmed the ENIAC computer to carry out Monte Carlo calculations. Introduction[edit]

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What is a bodhisattva? Bodhipaksa What is a bodhisattva? The word “bodhisattva” is a compound word formed from bodhi (spiritual awakening, enlightenment) and sattva (a being, essence, spirit). The word can then be translated as “A being set upon enlightenment,” “One whose essence is perfect knowledge,” or “A being whose essence is enlightenment.” The word, however, has several shades of meaning, and we will explore these below.

Birth–death process The birth–death process is a special case of continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable by one and "deaths", which decrease the state by one. The model's name comes from a common application, the use of such models to represent the current size of a population where the transitions are literal births and deaths. Birth–death processes have many applications in demography, queueing theory, performance engineering, epidemiology or in biology. Dr Hannah Fry: the mathematical models that underpin our sexual success 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. But all the same, being able to estimate quantities that you have no hope of verifying is an important skill for any scientist. 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. And the idea is the same: break the problem into smaller and smaller pieces until it’s possible to make an educated guess.

Multidisciplinary design optimization - Wikipedia, the free ency MDO allows designers to incorporate all relevant disciplines simultaneously. The optimum of the simultaneous problem is superior to the design found by optimizing each discipline sequentially, since it can exploit the interactions between the disciplines. However, including all disciplines simultaneously significantly increases the complexity of the problem. These techniques have been used in a number of fields, including automobile design, naval architecture, electronics, architecture, computers, and electricity distribution.

SHARANAGATI: The True Meaning of Surrender from the Bhakti Yoga Tradition KK Sah has been a close family friend of Ram Dass since he first met Maharaji in 1967. It was KK who translated for Ram Dass in his meetings with Maharaj-ji and who also took Ram Dass into his home and introduced him to Indian family life. When the other westerners arrived in India during Ram Dass second trip KK served as mentor, friend and brother to all and showed them true compassion and love… In the West the word “surrender” means the act of yielding to the power of another or the acknowledgement of defeat. This does not, in any way, reflect the true meaning of the process of surrender in the Hindu spiritual tradition.

Astronomers discover complex organic matter exists throughout the universe Astronomers report in the journal Nature that organic compounds of unexpected complexity exist throughout the Universe. The results suggest that complex organic compounds are not the sole domain of life but can be made naturally by stars. Prof. Sun Kwok and Dr. Yong Zhang of The University of Hong Kong show that an organic substance commonly found throughout the Universe contains a mixture of aromatic (ring-like) and aliphatic (chain-like) components. 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".

Computational geometry Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. Computational complexity is central to computational geometry, with great practical significance if algorithms are used on very large datasets containing tens or hundreds of millions of points. For such sets, the difference between O(n2) and O(n log n) may be the difference between days and seconds of computation. The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing (CAD/CAM), but many problems in computational geometry are classical in nature, and may come from mathematical visualization. The main branches of computational geometry are: