Open, type-level functions are a recent innovation in Haskell that move Haskell towards the expressiveness of dependent types, while retaining the look and feel of a practical programming language. This paper shows how to increase expressiveness still further, by adding closed type functions whose equations may overlap, and may have non-linear patterns over an open type universe. Although practically useful and simple to implement, these features go be- yond conventional dependent type theory in some respects, and have a subtle metatheory

Eisenberg, Richard A.

Vytiniotis, Dimitrios

Jones, Simon Peyton

Weirich, Stephanie

English

Previous simulations using a realistic model of a cerebellar Purkinje cell suggested that synaptic control of somatic spiking in this cell type is mediated by voltage-gated intrinsic conductances and that inhibitory rather than excitatory synaptic inputs are more influential in controlling spike timing. In this paper, we have tested these predictions physiologically using dynamic current clamping to apply model-derived synaptic conductances to Purkinje cells in vitro. As predicted by the model, this input transformed thein vitro pattern of spiking into a different spike pattern typically observed in vivo. A net inhibitory synaptic current was required to achieve such spiking, indicating the presence of strong intrinsic depolarizing currents. Spike-triggered averaging confirmed that the length of individual intervals between spikes was correlated to the amplitude of the inhibitory conductance but was not influenced by excitatory inputs. Through repeated presentation of identical stimuli, we determined that the output spike rate was very sensitive to the relative balance of excitation and inhibition in the input conductances. In contrast, the accuracy of spike timing was dependent on input amplitude and was independent of spike rate. Thus, information could be encoded in Purkinje cell spiking in a precise spike time code and a rate code at the same time. We conclude that Purkinje cell responses to synaptic input are strongly dependent on active somatic and dendritic properties and that theories of cerebellar function likely need to incorporate single-cell dynamics to a greater degree than is customary

Jaeger, Dieter

Bower, James M.

Caltech Authors - Main

Synaptic Control of Spiking in Cerebellar Purkinje Cells: Dynamic Current Clamp Based on Model Conductances

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Closed Type Families with Overlapping Equations

https://authors.library.caltech.edu/99489/1/6090.full.pdf

Closed Type Families with Overlapping Equations

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