At other times you seemed to me either pitiable or contemptible, eunuchs, artificially confined to an eternal childhood, childlike and childish in your cool, tightly fenced, neatly tidied playground and kindergarten, where every nose is carefully wiped and every troublesome emotion is soothed, every dangerous thought repressed, where everyone plays nice, safe, bloodless games for a lifetime and...

2. (Iran Team Selection Test 2008/6) Suppose 799 teams participate in a tournament in which every pair of teams plays against each other exactly once. Prove that there exist two disjoint groups A and B of 7 teams each such that every team from A defeated every team from B. Solution: SampleA as a random 7-set. LetX be the number of guys that are totally dominated byA. Letting dv denote the in-de...

" Shortly after the celebration of the four thousandth anniversary of the opening of space, Angary J. Gustible discovered Gustible's planet. The discovery turned out to be a tragic mistake. Gustible's planet was inhabited by highly intelligent life forms. They had moderate telepathic powers. They immediately mind-read Angary J. Gustible's entire mind and life history, and embarrassed him very d...

On planar graphs, orientations, and contact graphs: for a planar graph where no two vertices in R 2 have the same y-coordinate, orient any edge uv so that u → v where the y-coordinate of v is greater than that of u. In the dual, orient any edge so that they run clockwise from the edges it crosses in the original graph. (Ex 1) A planar 2-connected graph has a drawing such that its inherited orie...

This paper presents Probabilistic Roadmap Method (PRM) simulation with straightline local planner [1]. I set up a simulation environment with 7-links robot, obstacles (bombs), and a goal. First of all, I generated samples in free configuration space. Second, if one sample could be connected to its neighbor samples, store these two samples in a graph with a cost (L-metric distance between two sa...

At other times you seemed to me either pitiable or contemptible, eunuchs, artificially confined to an eternal childhood, childlike and childish in your cool, tightly fenced, neatly tidied playground and kindergarten, where every nose is carefully wiped and every troublesome emotion is soothed, every dangerous thought repressed, where everyone plays nice, safe, bloodless games for a lifetime and...

In this lecture, we will study some basic principles of the probabilistic method, a combinatorial tool with many applications in computer science. This method is a powerful tool for demonstrating the existence of combinatorial objects. We introduce the basic idea through several examples drawn from early lecture notes, and follow that by a detailed study of the maximum satisfiability (MAX-SAT) ...

Bayesian Networks (BN) provides a robust probabilistic method of reasoning under uncertainty. They have been successfully applied in a variety of real-world tasks but they have received little attention in the area of load-frequency control (LFC). In practice, LFC systems use proportional-integral controllers. However since these controllers are designed using a linear model, the nonlinearities...