This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs. The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set. We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy. Then, we prove that the value function satisfies the optimality equation and there exists an optimal （or ε-optimal） stationary policy under suitable conditions by using a minimum nonnegative solution approach. Further we give some properties of optimal policies. In addition, a value iteration algorithm for computing the value function and optimal policies is developed and an example is given. Finally, it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes.
In circadian rhythm generation, intercellular signaling factors are shown to play a crucial role in both sustaining intrinsic cellular rhythmicity and acquiring collective behaviours across a population of circadian neurons. However, the physical mechanism behind their role remains to be fully understood. In this paper, we propose an indirectly coupled multicellular model for the synchronization of Drosophila circadian oscillators combining both intracellular and intercellular dynamics. By simulating different experimental conditions, we find that such an indirect coupling way can synchronize both heterogeneous self-sustained circadian neurons and heterogeneous mutational damped circadian neurons. Moreover, they can also be entrained to ambient light-dark （LD） cycles depending on intercellular signaling.
