A recent controversy has emerged concerning the existence of long pauses, presumably reflecting bistability of membrane potential, in the cerebellar Purkinje cells (PC) of awake animals. It is generally agreed that in the anesthetized animals and in vitro, these cells switch between two stable membrane potential states: a depolarized state (the ‘up-state’) characterized by continuous firing of simple spikes (SS) and a hyperpolarized state (the ‘down-state’) characterized by long pauses in the SS activity. To address the existence of long pauses in the neural activity of cerebellar PCs in the awake and behaving animal we used extracellular recordings in cats and find that approximately half of the recorded PCs exhibit such long pauses in the SS activity and transition between activity – periods with uninterrupted SS lasting an average of 1300 ms – and pauses up to several seconds. We called these cells pausing Purkinje cells (PPC) and they can easily be distinguished from continuous firing Purkinje cells. In most PPCs, state transitions in both directions were often associated (25% of state transitions) with complex spikes (CSs). This is consistent with intracellular findings of CS-driven state transitions. In sum, we present proof for the existence of long pauses in the PC SS activity that probably reflect underlying bistability, provide the first in-depth analysis of these pauses and show for the first time that transitions in and out of these pauses are related to CS firing in the awake and behaving animal.
A model of computation over the p-adic numbers, for odd primes p, is defined following the approach of Blum, Shub, and Smale. This model employs branching on the property of being a square in Q p and unit height. The feasibility of systems of quadratic polynomials is shown to be NP-complete in this model. A polynomial time algorithm is given for feasibility of a single quadratic polynomial over Q p .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.