Bart-Moe games, JumbleG and discrepancy

Positional games on graphs THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY by

The theory of Positional Games is an exciting and relatively young area of Combinatorics, though its origins can be traced back to Classical Game Theory. Its goal is to give a mathematical framework for analyzing games of thought. Positional games are strongly related to several other branches of Combinatorics such as Ramsey Theory, Extremal Graph and Set Theory and the Probabilistic Method. Th...

A family with Bart-Pumphrey syndrome

All member of family referred to our clinic complaining of white nails. Physical examination revealed clinical features of leukonychia totalis and also the presence of sensor ineural hearing loss (SNHL), palmoplantar keratoderma (PPK) and knuckle pads, the four essential criteria for the diagnosis of Bart Pumphrey syndrome. Three generations were affected with variable presentations in ma...

Good permutations for scrambled Halton sequences in terms of L2-discrepancy

One of the best known low-discrepancy sequences, used by many practitioners, is the Halton sequence. Unfortunately, there seems to exist quite some correlation between the points from the higher dimensions. A possible solution to this problem is the so-called scrambling. In this paper, we give an overview of known scrambling methods, and we propose a new way of scrambling which gives good resul...

On the convergence of quasi-random sampling/importance resampling

On Avoider-Enforcer Games

In the Avoider-Enforcer game on the complete graph Kn, the players (Avoider and Enforcer) each take an edge in turn. Enforcer wins the game when he can require Avoider’s graph to have a given property P . The important parameter is τE(P), the most number of rounds required for Enforcer to win if Avoider plays with an optimal strategy (τE(P) = ∞ if Avoider can finish the game without creating a ...