6,115 research outputs found
Unitary Equivalence of Quantum Walks
A simple coined quantum walk in one dimension can be characterized by a
operator with three parameters which represents the coin toss. However,
different such coin toss operators lead to equivalent dynamics of the quantum
walker. In this manuscript we present the unitary equivalence classes of
quantum walks and show that all the nonequivalent quantum walks can be
distinguished by a single parameter. Moreover, we argue that the electric
quantum walks are equivalent to quantum walks with time dependent coin toss
operator
Dynamic Contests
Considering several main types of dynamic contests (the race, the tug-of-war, elimination contests and iterated incumbency fights) we identify a common pattern: the discouragement effect. This effect explains why the sum of rentseeking efforts often falls considerably short of the prize that is at stake. It may cause violent conflict in early rounds, but may also lead to long periods of peaceful interaction
Playing with parameters: structural parameterization in graphs
When considering a graph problem from a parameterized point of view, the
parameter chosen is often the size of an optimal solution of this problem (the
"standard" parameter). A natural subject for investigation is what happens when
we parameterize such a problem by various other parameters, some of which may
be the values of optimal solutions to different problems. Such research is
known as parameterized ecology. In this paper, we investigate seven natural
vertex problems, along with their respective parameters: the size of a maximum
independent set, the size of a minimum vertex cover, the size of a maximum
clique, the chromatic number, the size of a minimum dominating set, the size of
a minimum independent dominating set and the size of a minimum feedback vertex
set. We study the parameterized complexity of each of these problems with
respect to the standard parameter of the others.Comment: 17 page
- …