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It was clear the crowd was ready to be teased and seduced in style at this sold-out event. Announced by the MC of the night, comedian and singer Jonny McGovern, the first act on stage was by Dita Von Teese herself, surprisingly no less than her legendary yet brand new version of the "Martini Glass" act.

After a slow and teasing striptease of high designer clothing and being accompanied by her "Vontourage" of two exquisitely handsome young men - which jokingly by the MC had one of the best qualities in life: It is instantly clear why Dita Von Teese receives an international high appraisal.

If it was during her tribute to the art of ballet in the "Swan Lake Striptease" act en pointe, or her musical striptease "Lazy", she glided gently and seductively over the stage, expressing her most beautiful features every single moment and keeping the viewer captivated.

Though kindly asked not to at the beginning of the show, the audience could not help themselves but sneak in a picture - and it wouldn't be surprising if every photo taken would come out magnificently.

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Opéra et Casino de Monte-CarloConstructed in , the Salle Garnier embodied the excess and boldness that characterized the show, as Dita strutted her stuff in sensational haute-couture costumes ordained with hundreds and thousands of Swarovski crystals.

However, not only Dita Von Teese was dressed for the occasion. As guests gathered in the foyer of the famous Monte-Carlo Casino, the glamour and beauty of the evening's dress could not go unnoticed.

It was clear the crowd was ready to be teased and seduced in style at this sold-out event. Announced by the MC of the night, comedian and singer Jonny McGovern, the first act on stage was by Dita Von Teese herself, surprisingly no less than her legendary yet brand new version of the "Martini Glass" act.

After a slow and teasing striptease of high designer clothing and being accompanied by her "Vontourage" of two exquisitely handsome young men - which jokingly by the MC had one of the best qualities in life: It is instantly clear why Dita Von Teese receives an international high appraisal.

If it was during her tribute to the art of ballet in the "Swan Lake Striptease" act en pointe, or her musical striptease "Lazy", she glided gently and seductively over the stage, expressing her most beautiful features every single moment and keeping the viewer captivated.

Though kindly asked not to at the beginning of the show, the audience could not help themselves but sneak in a picture - and it wouldn't be surprising if every photo taken would come out magnificently.

In the s, Enrico Fermi first experimented with the Monte Carlo method while studying neutron diffusion, but did not publish anything on it.

The modern version of the Markov Chain Monte Carlo method was invented in the late s by Stanislaw Ulam , while he was working on nuclear weapons projects at the Los Alamos National Laboratory.

In , physicists at Los Alamos Scientific Laboratory were investigating radiation shielding and the distance that neutrons would likely travel through various materials.

Despite having most of the necessary data, such as the average distance a neutron would travel in a substance before it collided with an atomic nucleus, and how much energy the neutron was likely to give off following a collision, the Los Alamos physicists were unable to solve the problem using conventional, deterministic mathematical methods.

Ulam had the idea of using random experiments. He recounts his inspiration as follows:. Being secret, the work of von Neumann and Ulam required a code name.

Though this method has been criticized as crude, von Neumann was aware of this: Monte Carlo methods were central to the simulations required for the Manhattan Project , though severely limited by the computational tools at the time.

In the s they were used at Los Alamos for early work relating to the development of the hydrogen bomb , and became popularized in the fields of physics , physical chemistry , and operations research.

The Rand Corporation and the U. Air Force were two of the major organizations responsible for funding and disseminating information on Monte Carlo methods during this time, and they began to find a wide application in many different fields.

The theory of more sophisticated mean field type particle Monte Carlo methods had certainly started by the mids, with the work of Henry P.

Harris and Herman Kahn, published in , using mean field genetic -type Monte Carlo methods for estimating particle transmission energies.

Metaheuristic in evolutionary computing. The origins of these mean field computational techniques can be traced to and with the work of Alan Turing on genetic type mutation-selection learning machines [18] and the articles by Nils Aall Barricelli at the Institute for Advanced Study in Princeton, New Jersey.

Quantum Monte Carlo , and more specifically Diffusion Monte Carlo methods can also be interpreted as a mean field particle Monte Carlo approximation of Feynman - Kac path integrals.

Resampled or Reconfiguration Monte Carlo methods for estimating ground state energies of quantum systems in reduced matrix models is due to Jack H.

Hetherington in [27] In molecular chemistry, the use of genetic heuristic-like particle methodologies a. The use of Sequential Monte Carlo in advanced signal processing and Bayesian inference is more recent.

It was in , that Gordon et al. The authors named their algorithm 'the bootstrap filter', and demonstrated that compared to other filtering methods, their bootstrap algorithm does not require any assumption about that state-space or the noise of the system.

Particle filters were also developed in signal processing in the early by P. From to , all the publications on Sequential Monte Carlo methodologies including the pruning and resample Monte Carlo methods introduced in computational physics and molecular chemistry, present natural and heuristic-like algorithms applied to different situations without a single proof of their consistency, nor a discussion on the bias of the estimates and on genealogical and ancestral tree based algorithms.

The mathematical foundations and the first rigorous analysis of these particle algorithms are due to Pierre Del Moral [32] [40] in There is no consensus on how Monte Carlo should be defined.

For example, Ripley [47] defines most probabilistic modeling as stochastic simulation , with Monte Carlo being reserved for Monte Carlo integration and Monte Carlo statistical tests.

Sawilowsky [48] distinguishes between a simulation , a Monte Carlo method, and a Monte Carlo simulation: Kalos and Whitlock [11] point out that such distinctions are not always easy to maintain.

For example, the emission of radiation from atoms is a natural stochastic process. It can be simulated directly, or its average behavior can be described by stochastic equations that can themselves be solved using Monte Carlo methods.

The main idea behind this method is that the results are computed based on repeated random sampling and statistical analysis.

The Monte Carlo simulation is in fact random experimentations, in the case that, the results of these experiments are not well known.

Monte Carlo simulations are typically characterized by a large number of unknown parameters, many of which are difficult to obtain experimentally. The only quality usually necessary to make good simulations is for the pseudo-random sequence to appear "random enough" in a certain sense.

What this means depends on the application, but typically they should pass a series of statistical tests. Testing that the numbers are uniformly distributed or follow another desired distribution when a large enough number of elements of the sequence are considered is one of the simplest, and most common ones.

Sawilowsky lists the characteristics of a high quality Monte Carlo simulation: Pseudo-random number sampling algorithms are used to transform uniformly distributed pseudo-random numbers into numbers that are distributed according to a given probability distribution.

Low-discrepancy sequences are often used instead of random sampling from a space as they ensure even coverage and normally have a faster order of convergence than Monte Carlo simulations using random or pseudorandom sequences.

Methods based on their use are called quasi-Monte Carlo methods. In an effort to assess the impact of random number quality on Monte Carlo simulation outcomes, astrophysical researchers tested cryptographically-secure pseudorandom numbers generated via Intel's RdRand instruction set, as compared to those derived from algorithms, like the Mersenne Twister , in Monte Carlo simulations of radio flares from brown dwarfs.

RdRand is the closest pseudorandom number generator to a true random number generator. No statistically-significant difference was found between models generated with typical pseudorandom number generators and RdRand for trials consisting of the generation of 10 7 random numbers.

There are ways of using probabilities that are definitely not Monte Carlo simulations — for example, deterministic modeling using single-point estimates.

Scenarios such as best, worst, or most likely case for each input variable are chosen and the results recorded.

By contrast, Monte Carlo simulations sample from a probability distribution for each variable to produce hundreds or thousands of possible outcomes. The results are analyzed to get probabilities of different outcomes occurring.

The samples in such regions are called "rare events". Monte Carlo methods are especially useful for simulating phenomena with significant uncertainty in inputs and systems with a large number of coupled degrees of freedom.

Areas of application include:. Monte Carlo methods are very important in computational physics , physical chemistry , and related applied fields, and have diverse applications from complicated quantum chromodynamics calculations to designing heat shields and aerodynamic forms as well as in modeling radiation transport for radiation dosimetry calculations.

In astrophysics , they are used in such diverse manners as to model both galaxy evolution [59] and microwave radiation transmission through a rough planetary surface.

Monte Carlo methods are widely used in engineering for sensitivity analysis and quantitative probabilistic analysis in process design.

The need arises from the interactive, co-linear and non-linear behavior of typical process simulations. The Intergovernmental Panel on Climate Change relies on Monte Carlo methods in probability density function analysis of radiative forcing.

The PDFs are generated based on uncertainties provided in Table 8. The combination of the individual RF agents to derive total forcing over the Industrial Era are done by Monte Carlo simulations and based on the method in Boucher and Haywood PDF of the ERF from surface albedo changes and combined contrails and contrail-induced cirrus are included in the total anthropogenic forcing, but not shown as a separate PDF.

We currently do not have ERF estimates for some forcing mechanisms: Monte Carlo methods are used in various fields of computational biology , for example for Bayesian inference in phylogeny , or for studying biological systems such as genomes, proteins, [69] or membranes.

Computer simulations allow us to monitor the local environment of a particular molecule to see if some chemical reaction is happening for instance.

In cases where it is not feasible to conduct a physical experiment, thought experiments can be conducted for instance: Path tracing , occasionally referred to as Monte Carlo ray tracing, renders a 3D scene by randomly tracing samples of possible light paths.

Repeated sampling of any given pixel will eventually cause the average of the samples to converge on the correct solution of the rendering equation , making it one of the most physically accurate 3D graphics rendering methods in existence.

The standards for Monte Carlo experiments in statistics were set by Sawilowsky. Monte Carlo methods are also a compromise between approximate randomization and permutation tests.

An approximate randomization test is based on a specified subset of all permutations which entails potentially enormous housekeeping of which permutations have been considered.

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