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The Replicator Equation on Graphs
(Elsevier, 2006)
We study evolutionary games on graphs. Each player is represented
by a vertex of the graph. The edges denote who meets whom. A player can use any one of n strategies. Players obtain a payoff from interaction with all their ...
Synergy and Discounting of Cooperation in Social Dilemmas
(Elsevier, 2006)
The emergence and maintenance of cooperation by natural selection is an enduring conundrum in evolutionary biology, which has been studied using a variety of game theoretical models inspired by different biological situations. ...
A Symmetry of Fixation Times in Evoultionary Dynamics
(Elsevier, 2006)
In this paper, we show that for evolutionary dynamics between two types that can be described by a Moran process, the conditional fixation time of either type is the same irrespective of the selective scenario. With frequency ...
Teichmüller Curves in Genus Two: Torsion Divisors and Ratios of Sines
(Springer Verlag, 2006)
On some points-and-lines problems and configurations
(Springer Verlag, 2006)
We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.
Points of low height on elliptic curves and surfaces I: Elliptic surfaces over P1 with small d
(Springer Verlag, 2006)
For each of n = 1, 2, 3 we find the minimal height ˆh(P) of a nontorsion point P of an elliptic curve E over C(T) of discriminant degree d = 12n (equivalently, of arithmetic genus n), and exhibit all (E, P) attaining this ...
Shimura Curves for Level-3 Subgroups of the (2,3,7) Triangle Group and Some Other Examples
(Springer Verlag, 2006)
The (2,3,7) triangle group is known to be associated with a quaternion algebra A/K ramified at two of the three real places of K=Q(cos2π/7) and unramified at all other places of K. This triangle group and its congruence ...
The Mathieu group M-12 and its pseudogroup extension M-13
(AK Peters, 2006)
We study a construction of the Mathieu group M-12 using a game reminiscent of Loyd's "15-puzzle." The elements of M-12 are realized as permutations on 12 of the 13 points of the finite projective plane of order 3. There ...
Sylvester-Gallai Theorems for Complex Numbers and Quaternions
(Springer Verlag, 2006)
A Sylvester-Gallai (SG) configuration is a finite set S of points such that the line through any two points in S contains a third point of S. According to the Sylvester-Gallai theorem, an SG configuration in real projective ...
Discrete One-forms on Meshes and Applications to 3D mesh Parameterization
(Elsevier, 2006)
We describe how some simple properties of discrete one-forms directly relate to some old and new results concerning the parameterization of 3D mesh data. Our first result is an easy proof of Tutte's celebrated “spring-embedding” ...