We study Maker/Breaker games on the edges of the complete graph, as introduced by Chvátal and Erdős. We show that in the (m : b) clique game played on KN , the complete graph on N vertices, Maker can achieve a Kq for q = ( m log 2 (b+1) − o(1) ) · logN , which partially solves an open problem by Beck. Moreover, we show that in the (1:1) clique game played on KN for a sufficiently large N , Make...

We prove that in the biased (1 : b) Hamiltonicity Maker-Breaker game, played on the edges of the complete graph Kn, Maker has a winning strategy for b(n) ≤ ( 1− 30 ln n ) n lnn , for all large enough n.

We study Cournot competition among firms in a networked marketplace that is centrally managed by a market maker. In particular, we study a situation in which a market maker facilitates trade between geographically separate markets via a constrained transport network. Our focus is on understanding the consequences of the design of the market maker and on providing tools for optimal design. To th...

We consider a tic-tac-toe game played on the d-dimensional integer lattice. The game that we investigate is a Maker–Breaker version of tic-tac-toe. In a Maker– Breaker game, the first player, Maker, only tries to occupy a winning line and the second player, Breaker, only tries to stop Maker from occupying a winning line. We consider the bounded number of directions game, in which we designate a...

In the present work we deal with the concept of alpha-fair resource allocation in the situation where the decision maker (in our case, the base station) does not have complete information about environment. Namely, we develop a concept of α-fairness under uncertainty to allocate power resource in the presence of a jammer under two types of uncertainty: (a) the decision maker does not have compl...

Advancing age is associated with albuminuria and vascular changes. This review will explore the putative links between the two. Vascular ageing involves endothelial dysfunction as well as increased arterial diameter, wall thickness and stiffness, ultimately leading to arterial sclerosis. This process is accelerated by a defective vascular repair process. Endothelial dysfunction is likely to be ...

C-reactive protein (CRP) has emerged as an interesting novel and potentially clinically useful marker for increased cardiovascular risk.1,2 This is an attractive concept because atherosclerosis is a disease characterized by chronic arterial inflammation3,4 and suggests the possibility that subclinical states of atherosclerosis can be identified by an increase in circulating markers of inflammat...