If Σ̃ → Σ is a branched covering between closed surfaces, there are several easy relations one can establish between χ(Σ̃), χ(Σ), orientability of Σ and Σ̃, the total degree, and the local degrees at the branching points, including the classical Riemann-Hurwitz formula. These necessary relations have been shown to be also sufficient for the existence of the covering except when Σ is the sphere S (...

We clarify the explicit structure of the Hurwitz quaternion order, which is of fundamental importance in Riemann surface theory and systolic geometry. We present some properties of the associated congruence subgroups. Namely, we show that a Hurwitz group defined by a congruence subgroup associated with an odd ideal, is necessarily defined by a principal congruence subgroup. All such Hurwitz gro...

We analyze the Iterated Prisoner’s Dilemma and the performance of GRADUAL, the best behavior found so far. This behavior has the undesirable property of permanent memory, which would be detrimental for stability. As a solution to the permanent memory problem, we propose an adaptive tit-for-tat behavior that uses a self-regulated estimate of the opponent’s friendliness. On a second level, we dem...

We show that Barkhausen noise in two-dimensional disordered ferromagnets with extended domain walls is characterized by the avalanche size exponent ts51.54 at low disorder. With increasing disorder the characteristic domain size is reduced relative to the system size due to nucleation of new domains and a dynamic phase transition occurs to the scaling behavior with ts51.30. The exponents decrea...

This paper describes an alternative to the common view that explanation in the special sciences involves subsumption under laws. According to this alternative, whether or not a generalization can be used to explain has to do with whether it is invariant rather than with whether it is lawful. A generalization is invariant if it is stable or robust in the sense that it would continue to hold unde...

The present research examined the nature of stability and change in achievement goal endorsement over time, using 4 complementary data-analytic approaches (differential continuity, mean-level change, individual-level change, and ipsative continuity). Three longitudinal studies were conducted in college classrooms; in each study, achievement goals were assessed prior to a series of 3 course exam...