Markov decision processes associated with two threshold probability criteria

This paper deals with Markov decision processes with a target set for nonpositive rewards. Two types of threshold probability criteria are discussed. The first criterion is a probability that a total reward is not greater than a given initial threshold value, and the second is a probability that the total reward is less than it. Our first （resp. second） optimizing problem is to minimize the first （resp. second） threshold probability. These problems suggest that the threshold value is a permissible level of the total reward to reach a goal （the target set）, that is, we would reach this set over the level, if possible. For the both problems, we show that 1） the optimal threshold probability is a unique solution to an optimality equation, 2） there exists an optimal deterministic stationary policy, and 3） a value iteration and a policy space iteration are given. In addition, we prove that the first （resp. second） optimal threshold probability is a monotone increasing and right （resp. left） continuous function of the initial threshold value and propose a method to obtain an optimal policy and the optimal threshold probability in the first problem by using them in the second problem.

Staged-probability strategy of processing shotgun proteomic data to discover more functionally important proteins

Biologically important proteins related to membrane receptors,signal transduction,regulation,transcription,and translation are usually low in abundance and identified with low probability in mass spectroscopy(MS)-based analyses.Most valuable proteomics information on them were hitherto discarded due to the application of excessively strict data filtering for accurate identification.In this study,we present a stagedprobability strategy for assessing proteomic data for potential functionally important protein clues.MS-based protein identifications from the second(L2)and third(L3)layers of the cascade affinity fractionation using the Trans-Proteomic Pipeline software were classified into three probability stages as 1.00–0.95,0.95–0.50,and 0.50–0.20 according to their distinctive identification correctness rates(i.e.100%–95%,95%–50%,and 50%–20%,respectively).We found large data volumes and more functionally important proteins located at the previously unacceptable lower probability stages of 0.95–0.50 and 0.50–0.20 with acceptable correctness rate.More importantly,low probability proteins in L2 were verified to exist in L3.Together with some MS spectrogram examples,comparisons of protein identifications of L2 and L3 demonstrated that the stagedprobability strategy could more adequately present both quantity and quality of proteomic information,especially for researches involving biomarker discovery and novel therapeutic target screening.