The problem this paper focuses on is the classical problem of unsupervised clustering of a data-set. In particular, the bisecting divisive clustering approach is here considered. This approach consists in recursively splitting a cluster into two sub-clusters, starting from the main data-set. This is one of the more basic and common problems in fields like pattern analysis, data mining, document...

In the real-time strategy game Pluckmin 3, Captain Ottomar needs to move his troop of Pluckmin through hazardous terrain full of obstacles and predators. He has determined that when Pluckmin are traveling through predator-infested areas, there is a maximum number of Pluckmin that can safely travel along each edge without getting eaten. In addition to predators, some “lock” nodes have obstacles ...

EXTRA CREDIT: This problem set is not required, but can be turned in on the last day of classes or earlier, for up to three points of extra credit. The problem set includes 35 points of problems, which will be credited by muliplying your score by 3/35 and then increasing your final course grade by this amount. This extra credit assignment is an alternative to the extra credit paper that has alr...

We apply a piecewise constant level set method to elliptic inverse problems. The discontinuity of the coefficients is represented implicitly by a piecewise constant level set function, which allows to use one level set function to represent multiple phases. The inverse problem is solved using a variational penalization method with the total variation regularization of the coefficients. An opera...

In this work, we calculate the limit distribution of the total cost incurred by splitting a tree selected at random from the set of all finite free trees. This total cost is considered to be an additive functional induced by a toll equal to the square of the size of tree. The main tools used are the recent results connecting the asymptotics of generating functions with the asymptotics of...

Alstromeria has beautiful flowers that is popular in the world. One of the most problem in commercial of this flower is ethylene sensitivity and bacterial contamination in stem end of cut flowers. In this experiment, effect of essential oils of bitter orange (0, 25 and 50 mg l-1) and lawson cypress (0, 100 and 200 mg l-1) and nonchemical treatment (with and without) with 18 treatments, 3 replic...

We discuss iterative operator-splitting methods for convection-diffusion and wave equations motivated from the eigenvalue problem to decide the splitting process. The operator-splitting methods are well-know to solve such complicated multi-dimensional and multi-physical problems. Often the problem, how to decouple the underlying operators, is not understood well enough. We propose a method base...