No abstract

Let ∇ be a meromorphic connection on a vector bundle over a compact Riemann surface Γ . An automorphism σ : Γ → Γ is called a symmetry of ∇ if the pullback bundle and the pullback connection can be identified with ∇. We study the symmetries by means of what we call the Fano group; and, under the hypothesis that ∇ has a unimodular reductive Galois group, we relate the differential Galois group, the Fano group and the symmetries by means of an exact sequence.

No abstract

The males of the species of frogs Engystomops pustulosus produce simple and complex calls to lure females, as a way of intersexual selection. Complex calls lead males to a greater reproductive success than what simple calls do. However, the complex calls are also more attractive to their main predator, the bat Trachops cirrhosus. Therefore, as M. Ryan suggests in (The túngara frog: a study in sexual selection and communication. University of Chicago Press, Chicago, 1985), the complexity of the calls lets the frogs keep a trade-off between reproductive success and predation. In this paper, we verify this trade-off from the perspective of game theory. We first model the proportion of simple calls as a symmetric game of two strategies. We also model the effect of adding a third strategy, males that keep quiet and intercept females, which would play a role of intrasexual selection. Under the assumption that the decision of the males takes into account this trade-off between reproductive success and predation, our model reproduces the observed behavior reported in the literature with minimal assumption on the parameters. From the model with three strategies, we verify that the quiet strategy could only coexists with the simple and complex strategies if the rate at which quiet males intercept females is high, which explains the rarity of the quiet strategy. We conclude that the reproductive strategy of the male frog E. pustulosus is rational.

No abstract