In 1977, Phelim Boyle published a paper called “Options: A Monte Carlo Approach” where he explored the use of Monte Carlo simulations in pricing financial instruments known as options. Options are essentially contracts that give the contract holder the right (not obligation) to buy or sell an underlying asset at an exercise price stated on […]

Besides using Monte Carlo methods to approximate area or volume, as seen in the book, we can also use it for a more “frivolous” purpose. Many online poker calculators use Monte Carlo simulation to analyse the strength of poker hands. Given a deck of 52 cards, we introduce constraints of the 2-card holding of the player, […]

We’ve seen both in class and from previous blog posts some of the many different applications of principal component analysis - morphable face models, face recognition, mass spectrometry, financial analysis, etc. All these involve some fairly objective goals that one would naturally go about solving using matrix decomposition techniques - mainly due to the imperatively […]

Monte Carlo methods are useful in a wide variety of applications especially where a deterministic solution may be difficult or impossible to compute. In our class we specifically used it to do numerical integration but it can be used in areas are varied as finance or graphics. Despite their flexibility, MC methods can require many […]

Lots of numerical methods have parameters (i.e. tolerance, momentum …). While we would want to optimize the parameters and not use the default values (i.e. in 322 project), it is often very difficult to optimize them.
In general, what people do is prepare a test set, run your numerical methods with different parameter values, […]

Take a look at the following game:
http://video.aol.com/video-detail/runge-kutta-video-game/776097806

The game consists of a tiny grey rock that is connected to the fireball by a spring. The idea behind the game is that the player controls the tiny grey rock using the mouse and tries to steer the fireball into crashing into the […]

What constitutes a scene and how do you define a meaningful vocabulary for a scene? This is a very challenging problem that has immense importance in the field of object recognition. The following video talks about using the Max Margin Model to obtain new annotations for different images using existing annotations for other images.
http://www.youtube.com/watch?v=OLV1IIpTPow
The basic […]

Mass Spectrometry is a widely used method to determine the mass of proteins and other small molecules. It analyzes the ratio of mass to charge for small molecules. An important part of the method, which vastly improves the range of molecules that mass spec can distinguish is how large protein can be separated into component […]

abundant
Definition: The number n is abundant if the sum of all its positive divisors except itself is more than n.
First ten: 12, 18, 20, 24, 30, 36, 40, 42, 48, 54
amicable
Definition: The number n is amicable if it belongs to an amicable pair. Two numbers n and m are called an amicable pair if the […]

Source: http://graphics.ethz.ch/teaching/imagesynthesis_06/miniprojects/p3/index.html
This project is nearly similiar to the goal of our project, Partical Advection. However, the project described takes it much further than we are required to. The flame and smoke is rendered in three dimensions using velocify fields based on 3D Navier-Stokes equations. They use differential fields to not only […]