Finite horizon optimal stopping of time-discontinuous functionals with applications to impulse control with delay

We study finite horizon optimal stopping problems for continuous-time Feller–Markov processes. The functional depends on time, state, and external parameters and may exhibit discontinuities with respect to the time variable. Both left- and right-hand discontinuities are considered. We investigate the dependence of the value function on the parameters, on the initial state of the process, and on the stopping horizon. We construct $\varepsilon$-optimal stopping times and provide conditions under which an optimal stopping time exists. We demonstrate how to approximate this optimal stopping time by solutions to discrete-time problems. Our results are applied to the study of impulse control problems with finite time horizon, decision lag, and execution delay

Importance of spike timing in touch: an analogy with hearing?

Touch is often conceived as a spatial sense akin to vision. However, touch also involves the transduction and processing of signals that vary rapidly over time, inviting comparisons with hearing. In both sensory systems, first order afferents produce spiking responses that are temporally precise and the timing of their responses carries stimulus information. The precision and informativeness of spike timing in the two systems invites the possibility that both implement similar mechanisms to extract behaviorally relevant information from these precisely timed responses. Here, we explore the putative roles of spike timing in touch and hearing and discuss common mechanisms that may be involved in processing temporal spiking patterns

Temporal structure in spiking patterns of ganglion cells defines perceptual thresholds in rodents with subretinal prosthesis

Abstract Subretinal prostheses are designed to restore sight in patients blinded by retinal degeneration using electrical stimulation of the inner retinal neurons. To relate retinal output to perception, we studied behavioral thresholds in blind rats with photovoltaic subretinal prostheses stimulated by full-field pulsed illumination at 20 Hz, and measured retinal ganglion cell (RGC) responses to similar stimuli ex-vivo. Behaviorally, rats exhibited startling response to changes in brightness, with an average contrast threshold of 12%, which could not be explained by changes in the average RGC spiking rate. However, RGCs exhibited millisecond-scale variations in spike timing, even when the average rate did not change significantly. At 12% temporal contrast, changes in firing patterns of prosthetic response were as significant as with 2.3% contrast steps in visible light stimulation of healthy retinas. This suggests that millisecond-scale changes in spiking patterns define perceptual thresholds of prosthetic vision. Response to the last pulse in the stimulation burst lasted longer than the steady-state response during the burst. This may be interpreted as an excitatory OFF response to prosthetic stimulation, and can explain behavioral response to decrease in illumination. Contrast enhancement of images prior to delivery to subretinal prosthesis can partially compensate for reduced contrast sensitivity of prosthetic vision