Go is a traditional strategy-based board game originating from China circa 4th century BCE.  It involves two players placing  black and white playing pieces called stones on a 19×19 grid. The relatively new field of Computer Go is a field of Artificial Intelligence that focuses on creating creating computer programs to autonomously play Go.

Monte Carlo […]

In my first post I wrote about a team at Stanford University that created a raytracing algorithm called the Hybrid Particle Level Set Method for rendering images, treating the object when appropriate as either a liquid or as composed of tiny metaballs. Although this method was groundbreaking enough to win an Oscar, the bounds of […]

Automatic music transcription is a unique problem to which Monte Carlo methods can be applied. It is sometimes desirable to extract human-readable music scores from a performance by musicians, but it is not a simple task. The basic difficulties of extracting the information are, perhaps, somewhat obvious, but there also lie more subtle issues. For […]

Monte Carlo methods are used in many areas including random number generations, nuclear reactor designs, traffic flows, oil-well explorations, economics etc.
PEREGRINE is a software/hardware system that implements the Monte Carlo method for the specific purpose of simulating medical radiation delivery. The major goals in its development have been to design a system specifically tailored to […]

http://www.youtube.com/watch?v=qaPuPouEfbM
Browsing on youtube, I found a game named after the two German mathematicians Carl Runge and Martin Kutta.  The author of the game says he used the Runge Kutta method to simulate the spring in the game.
He says he uses RK4 with a frame timestep of t = t + 0.1, when running at 60fps.  […]

Enrico Fermi in the 1930’s used Monte Carlo in the calculation of neutron diffusion. He would later design a Monte Carlo mechanical device used in calculating criticality in nuclear reactors. That device was called the Fermiac.John Louis von Neumann in the 1940’s established the mathematical basis for PDF’s, CDF’s, and pseudorandom number generators. […]

Although we have never covered this in class, splines are a very important component in numerical analysis and computer graphics.  A spline is a special piecewise defined function.  To go along with what we have learned in class, polynomial interpolation can be executed by spline interpolation.  In more specific areas of computer graphics, spline functions […]

Computational physics is one branch of physics that solves problems in physics by implementing computational algorithms. Especially in theoretical physics, the study of numerical physics is significantly useful and often used for simulations.
One of the most exiting branches of computational physics is numerical relativity. It is the astrophysical study to simulate objects in space-time […]

      In Eric Veach of Stanford University’s dissertation Robust Monte Carlo Methods for Light Transport Simulation, he describes how newly developed Monte Carlo techniques can extend the range of input models for which light transport simulations are practical. This includes brand spanking new theoretical models, statistical methods and rendering algorithms. For the theoretical basis for […]

In the article Topology Testing of Phylogenies Using Least Squares methods, Aleksandra Czarna et al. use the least squares method to analyze data from a variety of biology topics including mammalian mitochondrial protein sequences, nucleotides, Hepatitis C, and DNA hybridization. The researchers found that the weighted least squares method provides a computationally efficient approximation to […]