A simple analytical framework to study the molecular quasispecies evolution of finite populations is proposed, in which the population is assumed to be a random combination of the constituent molecules in each generation, i.e., linkage disequilibrium at the population level is neglected. In particular, for the single-sharp-peak replication landscape we investigate the dependence of the error threshold on the population size and find that the replication accuracy at the threshold increases linearly with the reciprocal of the population size for sufficiently large populations. Furthermore, in the deterministic limit our formulation yields the exact steady-state of the quasispecies model, indicating then that the population composition is a random combination of the molecules.

Given a sequence of N positive real numbers {a 1 , a 2 , . . . , a N }, the number partitioning problem consists of partitioning them into two sets such that the absolute value of the difference of the sums of a j over the two sets is minimized. In the case that the a j 's are statistically independent random variables uniformly distributed in the unit interval, this NP-complete problem is equivalent to the problem of finding the ground state of an infinite-range, random anti-ferromagnetic Ising model. We employ the annealed approximation to derive analytical lower bounds to the average value of the difference for the best constrained and unconstrained partitions in the large N limit. Furthermore, we calculate analytically the fraction of metastable states, i.e. states that are stable against all single spin flips, and found that it vanishes like N −3/2 .

The notion that cooperation can aid a group of agents to solve problems more efficiently than if those agents worked in isolation is prevalent in computer science and business circles. Here we consider a primordial form of cooperation – imitative learning – that allows an effective exchange of information between agents, which are viewed as the processing units of a social intelligence system or collective brain. In particular, we use agent-based simulations to study the performance of a group of agents in solving a cryptarithmetic problem. An agent can either perform local random moves to explore the solution space of the problem or imitate a model agent – the best performing agent in its influence network. There is a trade-off between the number of agents and the imitation probability , and for the optimal balance between these parameters we observe a thirtyfold diminution in the computational cost to find the solution of the cryptarithmetic problem as compared with the independent search. If those parameters are chosen far from the optimal setting, however, then imitative learning can impair greatly the performance of the group.