The coevolution of costly heterogeneities and cooperation in the prisoner's dilemma game

This paper discusses the co-evolution of social strategies and an efficiency trait in spatial evolutionary games. The continuous efficiency trait determines how well a player can convert gains from a prisoner's dilemma game into evolutionary fitness. It is assumed to come at a cost proportional to its magnitude and this cost is deducted from payoff. We demonstrate that cost ranges exist such that the regime in which cooperation can persist is strongly extended by the co-evolution of efficiencies and strategies. We find that cooperation typically associates with large efficiencies while defection tends to pair with lower efficiencies. The simulations highlight that social dilemma situations in structured populations can be resolved in a natural way: the nature of the dilemma itself leads to differential pressures for efficiency improvement in cooperator and defector populations. Cooperators benefit by larger improvements which allow them to survive even in the face of inferior performance in the social dilemma. Importantly, the mechanism is possible with and without the presence of noise in the evolutionary replication process

Generalized Householder Transformations for the Complex Symmetric Eigenvalue Problem

We present an intuitive and scalable algorithm for the diagonalization of complex symmetric matrices, which arise from the projection of pseudo--Hermitian and complex scaled Hamiltonians onto a suitable basis set of "trial" states. The algorithm diagonalizes complex and symmetric (non--Hermitian) matrices and is easily implemented in modern computer languages. It is based on generalized Householder transformations and relies on iterative similarity transformations T -> T' = Q^T T Q, where Q is a complex and orthogonal, but not unitary, matrix, i.e, Q^T equals Q^(-1) but Q^+ is different from Q^(-1). We present numerical reference data to support the scalability of the algorithm. We construct the generalized Householder transformations from the notion that the conserved scalar product of eigenstates Psi_n and Psi_m of a pseudo-Hermitian quantum mechanical Hamiltonian can be reformulated in terms of the generalized indefinite inner product [integral of the product Psi_n(x,t) Psi_m(x,t) over dx], where the integrand is locally defined, and complex conjugation is avoided. A few example calculations are described which illustrate the physical origin of the ideas used in the construction of the algorithm.Comment: 14 pages; RevTeX; font mismatch in Eqs. (3) and (15) is eliminate

Analytic studies in the learning and memory of skilled performance second semi-annual report, oct. 1, 1964 - mar. 30, 1965

Analytic studies in learning and memory of skilled performanc

Improved bounds for the number of forests and acyclic orientations in the square lattice

In a recent paper Merino and Welsh (1999) studied several counting problems on the square lattice $L_n$. The authors gave the following bounds for the asymptotics of $f(n)$, the number of forests of $L_n$, and $\alpha(n)$, the number of acyclic orientations of $L_n$: $3.209912 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.84161$ and $22/7 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.70925$. In this paper we improve these bounds as follows: $3.64497 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.74101$ and $3.41358 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.55449$. We obtain this by developing a method for computing the Tutte polynomial of the square lattice and other related graphs based on transfer matrices