AI News, Artificial Intelligence in Motion

Artificial Intelligence in Motion

Here is the source code I've used to minimize the De Jong's Sphere function (Special thanks to Christian Perone who inspired me to do this work) : To make things more interesting, i've decided to put a simple graphic mode, when the user can choose to see the simulation in graphics mode or console mode.

Each point is a particle and they're updating their position through the simulation and since the best optimal solution of the problem is the point (0,0), in the end of the simulation, the particles will be close to the best solution.

Doc:2.6/Tutorials/Simulation/Hair/Using the Particle Mode

Here I have for you a simple tutorial for a simple technique to make very efficient hair for stills, but it can be used also for animation.

Hair children are hairs that use the deformations of the hairs we drew above, and have some cool utilities that let us make complex hair like curly or wavy.

Now after setting the number of children we want in render (I use the same also in view, but you need a good computer), the two most important ones overall are the clump factor, and the radius: on it the roundness and the uniform are pretty useful.

Kink, well this is how you make curly, round or whatever hairs, you can play around with the settings to generate very cool effects.

If I click 'interpolate' the new hair will follow the already existing ones, and this will avoid me from needing to comb all the new hairs, and risk messing up what I've already done.

To do this, like during the modeling edit mode you can select hair points, just choose which selection mode you want to use and with G you can move vert by vert;

Be careful with these last tools, you can mess up the whole thing if you, for example, comb a head without fixed roots.

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.

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).

In application to space and oil exploration problems, Monte Carlo–based predictions of failure, cost overruns and schedule overruns are routinely better than human intuition or alternative 'soft' methods.[2] In principle, Monte Carlo methods can be used to solve any problem having a probabilistic interpretation.

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).[8][9] 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.[9][10] A natural way to simulate these sophisticated nonlinear Markov processes is to sample a large number of copies of the process, replacing in the evolution equation the unknown distributions of the random states by the sampled empirical measures.

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.

He recounts his inspiration as follows: Being secret, the work of von Neumann and Ulam required a code name.[citation needed] A colleague of von Neumann and Ulam, Nicholas Metropolis, suggested using the name Monte Carlo, which refers to the Monte Carlo Casino in Monaco where Ulam's uncle would borrow money from relatives to gamble.[12] Using lists of 'truly random' random numbers was extremely slow, but von Neumann developed a way to calculate pseudorandom numbers, using the middle-square method.

The origins of these mean field computational techniques can be traced to 1950 and 1954 with the work of Alan Turing on genetic type mutation-selection learning machines[17] and the articles by Nils Aall Barricelli at the Institute for Advanced Study in Princeton, New Jersey.[18][19] 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.[20][21][22][23][24][25][26] The origins of Quantum Monte Carlo methods are often attributed to Enrico Fermi and Robert Richtmyer who developed in 1948 a mean field particle interpretation of neutron-chain reactions,[27] but the first heuristic-like and genetic type particle algorithm (a.k.a.

From 1950 to 1996, 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.

Sawilowsky[47] distinguishes between a simulation, a Monte Carlo method, and a Monte Carlo simulation: a simulation is a fictitious representation of reality, a Monte Carlo method is a technique that can be used to solve a mathematical or statistical problem, and a Monte Carlo simulation uses repeated sampling to obtain the statistical properties of some phenomenon (or behavior).

Monte Carlo simulations are typically characterized by a large number of unknown parameters, many of which are difficult to obtain experimentally.[48] Monte Carlo simulation methods do not always require truly random numbers to be useful (although, for some applications such as primality testing, unpredictability is vital).[49] Many of the most useful techniques use deterministic, pseudorandom sequences, making it easy to test and re-run simulations.

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.

No statistically-significant difference was found between models generated with typical pseudorandom number generators and RdRand for trials consisting of the generation of 107 random numbers.[50] There are ways of using probabilities that are definitely not Monte Carlo simulations — for example, deterministic modeling using single-point estimates.

The results are analyzed to get probabilities of different outcomes occurring.[52] For example, a comparison of a spreadsheet cost construction model run using traditional “what if” scenarios, and then running the comparison again with Monte Carlo simulation and triangular probability distributions shows that the Monte Carlo analysis has a narrower range than the “what if” analysis.[example needed] This is because the “what if” analysis gives equal weight to all scenarios (see quantifying uncertainty in corporate finance), while the Monte Carlo method hardly samples in the very low probability regions.

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.[53][54][55] In statistical physics Monte Carlo molecular modeling is an alternative to computational molecular dynamics, and Monte Carlo methods are used to compute statistical field theories of simple particle and polymer systems.[28][56] Quantum Monte Carlo methods solve the many-body problem for quantum systems.[8][9][20] In radiation materials science, the binary collision approximation for simulating ion implantation is usually based on a Monte Carlo approach to select the next colliding atom.[57] In experimental particle physics, Monte Carlo methods are used for designing detectors, understanding their behavior and comparing experimental data to theory.

We currently do not have ERF estimates for some forcing mechanisms: ozone, land use, solar, etc.[67] 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,[68] or membranes.[69] The systems can be studied in the coarse-grained or ab initio frameworks depending on the desired accuracy.

A black box simulator represents the opponent's moves.[73] The Monte Carlo tree search (MCTS) method has four steps:[74] The net effect, over the course of many simulated games, is that the value of a node representing a move will go up or down, hopefully corresponding to whether or not that node represents a good move.

Monte Carlo Tree Search has been used successfully to play games such as Go,[75] Tantrix,[76] Battleship,[77] Havannah,[78] and Arimaa.[79] Monte Carlo methods are also efficient in solving coupled integral differential equations of radiation fields and energy transport, and thus these methods have been used in global illumination computations that produce photo-realistic images of virtual 3D models, with applications in video games, architecture, design, computer generated films, and cinematic special effects.[80] The US Coast Guard utilizes Monte Carlo methods within its computer modeling software SAROPS in order to calculate the probable locations of vessels during search and rescue operations.

Each simulation can generate as many as ten thousand data points which are randomly distributed based upon provided variables.[81] Search patterns are then generated based upon extrapolations of these data in order to optimize the probability of containment (POC) and the probability of detection (POD), which together will equal an overall probability of success (POS).

Monte Carlo simulation allows the business risk analyst to incorporate the total effects of uncertainty in variables like sales volume, commodity and labour prices, interest and exchange rates, as well as the effect of distinct risk events like the cancellation of a contract or the change of a tax law.

The study ran trials which varied these variables to come up with an overall estimate of the success level of the proposed program as a whole.[86] In general, the Monte Carlo methods are used in mathematics to solve various problems by generating suitable random numbers (see also Random number generation) and observing that fraction of the numbers that obeys some property or properties.

As a result, to determine our optimal path we would want to use simulation - optimization to first understand the range of potential times it could take to go from one point to another (represented by a probability distribution in this case rather than a specific distance) and then optimize our travel decisions to identify the best path to follow taking that uncertainty into account.

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