Active Clinical Trials for Personalized Medicine

Individualized treatment rules (ITRs) tailor treatments according to individual patient characteristics. They can significantly improve patient care and are thus becoming increasingly popular. The data collected during randomized clinical trials are often used to estimate the optimal ITRs. However, these trials are generally expensive to run, and, moreover, they are not designed to efficiently estimate ITRs. In this paper, we propose a cost-effective estimation method from an active learning perspective. In particular, our method recruits only the "most informative" patients (in terms of learning the optimal ITRs) from an ongoing clinical trial. Simulation studies and real-data examples show that our active clinical trial method significantly improves on competing methods. We derive risk bounds and show that they support these observed empirical advantages.Comment: 48 Page, 9 Figures. To Appear in JASA--T&

Theory of variational quantum simulation

The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and simulating real and imaginary time dynamics. In this work, we first review the conventional variational principles, including the Rayleigh-Ritz method for solving static problems, and the Dirac and Frenkel variational principle, the McLachlan's variational principle, and the time-dependent variational principle, for simulating real time dynamics. We focus on the simulation of dynamics and discuss the connections of the three variational principles. Previous works mainly focus on the unitary evolution of pure states. In this work, we introduce variational quantum simulation of mixed states under general stochastic evolution. We show how the results can be reduced to the pure state case with a correction term that takes accounts of global phase alignment. For variational simulation of imaginary time evolution, we also extend it to the mixed state scenario and discuss variational Gibbs state preparation. We further elaborate on the design of ansatz that is compatible with post-selection measurement and the implementation of the generalised variational algorithms with quantum circuits. Our work completes the theory of variational quantum simulation of general real and imaginary time evolution and it is applicable to near-term quantum hardware.Comment: 41 pages, accepted by Quantu

Development of a Rapid and Confirmatory Method to Identify Ganoderic Acids in Ganoderma Mushrooms

To examine the composition of lanostanoids in Ganoderma lucidum, we have developed a liquid chromatography–mass spectrometry (LC–MS) method by using the ganoderic acids isolated in our laboratory as reference standards. The identity of 14 peaks in the high performance liquid chromatogram (HPLC) of G. lucidum has been confirmed. By using the HPLC retention times of these ganoderic acids and their mass fragmentation patterns established in this paper, one can use LC–MS to analyze G. lucidum without requiring the reference standards of these 14 ganoderic acids. Subsequently, only the HPLC–UV method would be needed to analyze routine samples of G. lucidum