Multivalued solutions to the eikonal equation in stratified media

In the present paper we study the geometric properties of the multivalued solutions to the eikonal equation and we give the appropriate classification theorems. Our motivation stems from geometrical optics for approximating high frequency waves in stratified media. We consider the case of a fixed Hamiltonian imposed by the medium, and we present the geometric framework that describes the geometric solutions, using the notion of Legendrian immersions with an initial point source or an initial smooth front. · Then, we study the singularities of the solutions in the case of a smooth or piecewise Hamiltonian in a boundaryless stratified medium. Finally, we study the singularities of the solutions in a domain with a boundary that describes the propagating field in a waveguide

Monolingual Biases in Simulations of Cultural Transmission

Recent research suggests that the evolution of language is affected by the inductive biases of its learners. I suggest that there is an implicit assumption that one of these biases is to expect a single linguistic system in the input. Given the prevalence of bilingual cultures, this may not be a valid abstraction. This is illustrated by demonstrating that the ‘minimal naming game’ model, in which a shared lexicon evolves in a population of agents, includes an implicit mutual exclusivity bias. Since recent research suggests that children raised in bilingual cultures do not exhibit mutual exclusivity, the individual learning algorithm of the agents is not as abstract as it appears to be. A modification of this model demonstrates that communicative success can be achieved without mutual exclusivity. It is concluded that complex cultural phenomena, such as bilingualism, do not necessarily result from complex individual learning mechanisms. Rather, the cultural process itself can bring about this complexity