Grade information has been considered in Yuan et al. (2007) wherein they proposed a Quasi-CRM method to incorporate the grade toxicity information in phase I trials. A potential problem with the Quasi-CRM model is that the choice of skeleton may dramatically vary the performance of the CRM model, which results in similar consequences for the Quasi-CRM model. In this paper, we propose a new model by utilizing bayesian model selection approach – Robust Quasi-CRM model – to tackle the above-mentioned pitfall with the Quasi-CRM model. The Robust Quasi-CRM model literally inherits the BMA-CRM model proposed by Yin and Yuan (2009) to consider a parallel of skeletons for Quasi-CRM. The superior performance of Robust Quasi-CRM model was demonstrated by extensive simulation studies. We conclude that the proposed method can be freely used in real practice.
By successively assembling genetic parts such as BioBrick according to grammatical models, complex genetic constructs composed of dozens of functional blocks can be built. However, usually every category of genetic parts includes a few or many parts. With increasing quantity of genetic parts, the process of assembling more than a few sets of these parts can be expensive, time consuming and error prone. At the last step of assembling it is somewhat difficult to decide which part should be selected. Based on statistical language model, which is a probability distribution P(s) over strings S that attempts to reflect how frequently a string S occurs as a sentence, the most commonly used parts will be selected. Then, a dynamic programming algorithm was designed to figure out the solution of maximum probability. The algorithm optimizes the results of a genetic design based on a grammatical model and finds an optimal solution. In this way, redundant operations can be reduced and the time and cost required for conducting biological experiments can be minimized.
A feasible interior point method is proposed for solving the NP-hard absolute value equation (AVE) when the singular values of A exceed one. We formulate the NP-hard AVE as linear complementary problem, and prove that the solution to AVE is existent and unique under suitable assumptions. Then we present a feasible interior point algorithm for AVE based on the Newton direction and centering direction. We show that this algorithm has the polynomial complexity. Preliminary numerical results show that this method is promising.
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