Reversals of fortune: path dependency, problem solving, and temporal cases

Historical reversals highlight a basic methodological problem: is it possible to treat two successive periods both as independent cases to compare for causal analysis and as parts of a single historical sequence? I argue that one strategy for doing so, using models of path dependency, imposes serious limits on explanation. An alternative model which treats successive periods as contrasting solutions for recurrent problems offers two advantages. First, it more effectively combines analytical comparisons of different periods with narratives of causal sequences spanning two or more periods. Second, it better integrates scholarly accounts of historical reversals with actors’ own narratives of the past

Population density models of integrate-and-fire neurons with jumps: well-posedness

International audienceIn this paper we study the well-posedness of different models of population of leaky integrate- and- re neurons with a population density approach. The synaptic interaction between neurons is modeled by a potential jump at the reception of a spike. We study populations that are self excitatory or self inhibitory. We distinguish the cases where this interaction is instantaneous from the one where there is a repartition of conduction delays. In the case of a bounded density of delays both excitatory and inhibitory population models are shown to be well-posed. But without conduction delay the solution of the model of self excitatory neurons may blow up. We analyze the di erent behaviours of the model with jumps compared to its di usion approximation