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Huoxue Huayu therapy (HXHY) has been widely used to treat cardiovascular diseases in traditional Chinese medicine (TCM), such as hypertension, and coronary heart disease (CHD). This study describes a meta-analysis of a series of prospective randomized, double-blind, placebo-controlled trials conducted to evaluate the effect of HXHY on patients with CHD after percutaneous coronary intervention (PCI).The Cochrane Library, PubMed, EMBASE, the China National Knowledge Infrastructure (CNKI), the Chinese Biomedical Literature database and the Wanfang database were searched up until June 2018. A series of randomized controlled clinical trials were included and the subjects were patients with CHD who had undergone PCI. The experimental group was treated with HXHY therapy, and the control group was treated with placebo; meanwhile, all the patients accepted conventional Western medicine. Review Manager 5.3 software was used for the statistical analysis. Ten trials were included in the final study. The overall risk of bias assessment was low. HXHY had a greater beneficial effect on reducing the in-stent restenosis (ISR) rate (RR=0.57, 95% CI [0.40, 0.80], P=0.001) and the degree of restenosis (MD=-8.89, 95% CI [-10.62, -7.17], P<0.00001) compared with Placebo. Moreover, HXHY was determined to be more effective in improving Seattle Angina Questionnaires (SAQ) and the revascularization rate (RR=0.54, 95% CI [0.32, 0.90], P=0.02) compared with Placebo, whereas the rate of death and MI of patients treated with HXHY were no different from those treated with the placebo (P>0.05). Therefore, HXHY is an effective and safe therapy for CHD 1# These authors contributed equally to this work.

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Complex polynomial optimization has recently gained more and more attention in both theory and practice. In this paper, we study the optimization of a real-valued general conjugate complex form over various popular constraint sets including the m-th roots of complex unity, the complex unit circle, and the complex unit sphere. A real-valued general conjugate complex form is a homogenous polynomial function of complex variables as well as their conjugates, and always takes real values. General conjugate form optimization is a wide class of complex polynomial optimization models, which include many homogenous polynomial optimization in the real domain with either discrete or continuous variables, and Hermitian quadratic form optimization as well as its higher degree extensions. All the problems under consideration are NP-hard in general and we focus on polynomial-time approximation algorithms with worst-case performance ratios. These approximation ratios improve previous results when restricting our problems to some special classes of complex polynomial optimization, and improve or equate previous results when restricting our problems to some special classes of polynomial optimization in the real domain. These algorithms are based on tensor relaxation and random sampling. Our novel technical contributions are to establish the first set of probability lower bounds for random sampling over the m-th root of unity, the complex unit circle, and the complex unit sphere, and propose the first polarization formula linking general conjugate forms and complex multilinear forms.

Conjugate partial-symmetric (CPS) tensors are the high-order generalization of Hermitian matrices. As the role played by Hermitian matrices in matrix theory and quadratic optimization, CPS tensors have shown growing interest recently in tensor theory and optimization, particularly in many application-driven complex polynomial optimization problems. In this paper, we study CPS tensors with a focus on ranks, rank-one decompositions and approximations, as well as their applications. The analysis is conducted along side with a more general class of complex tensors called partial-symmetric tensors. We prove constructively that any CPS tensor can be decomposed into a sum of rank-one CPS tensors, which provides an alternative definition of CPS tensors via linear combinations of rank-one CPS tensors. Three types of ranks for CPS tensors are defined and shown to be different in general. This leads to the invalidity of the conjugate version of Comon's conjecture. We then study rank-one approximations and matricizations of CPS tensors. By carefully unfolding CPS tensors to Hermitian matrices, rank-one equivalence can be preserved. This enables us to develop new convex optimization models and algorithms to compute best rank-one approximation of CPS tensors. Numerical experiments from various data are performed to justify the capability of our methods.