Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing

Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool in a variety of applications, the non-commutative nature of the quaternion product has been prohibitive to the development of quaternion uncorrelating transforms. To this end, we introduce novel techniques for a simultaneous decomposition of the covariance and complementary covariance matrices in the quaternion domain, whereby the quaternion version of the Takagi factorisation is explored to diagonalise symmetric quaternion-valued matrices. This gives new insights into the quaternion uncorrelating transform (QUT) and forms a basis for the proposed quaternion approximate uncorrelating transform (QAUT) which simultaneously diagonalises all four covariance matrices associated with improper quaternion signals. The effectiveness of the proposed uncorrelating transforms is validated by simulations on both synthetic and real-world quaternion-valued signals.Comment: 41 pages, single column, 10 figure

Soy Isoflavone Reduces Lps-Induced Acute Lung Injury via Increasing Aquaporin 1 and Aquaporin 5 in Rats

Acute lung injury (ALI) followed with severe inflammation and oxidative stress. Anti-inflammatory and antioxidant are the properties of aquaporin 1 (AQP1) and aquaporin 5 (AQP5). The goal of this study was to see if soy isoflavone can diminish lipopolysaccharide (LPS)-induced ALI and the underling mechanism. LPS-induced ALI was given to Sprague-Dawley rats 14 days following oophorectomy. One hour before the LPS challenge, estradiol (1 mg/kg) was administered subcutaneously as positive control and soy isoflavone was intragastric administration for 14 days prior to LPS challenge with different doses. Six hours after LPS challenge, the pulmonary edema, pathophysiology, inflammation, and the oxidative stress in lung tissues of rats were discovered. We found that soy isoflavone can reduce pulmonary edema and the lung pathology in a dose-dependent manner. Furthermore, tumor necrosis factor-alpha, interleukin-1β, and interleukin-6 were decreased in rats treated with soy isoflavone. Meanwhile, soy isoflavone reduced pulmonary oxidative stress by decreasing malondialdehyde levels, while increasing superoxide dismutase levels in lung tissues in a dose-dependent manner. Mechanically, we found that the mRNA and protein level of AQP1 and AOP5 were increased in lung tissues of rats treated with soy isoflavone compared the LPS-treated rats. Thus, soy isoflavone alleviates LPS-induced ALI through inducing AQP1 and AQP5

The HR-Calculus: Enabling Information Processing with Quaternion Algebra

From their inception, quaternions and their division algebra have proven to be advantageous in modelling rotation/orientation in three-dimensional spaces and have seen use from the initial formulation of electromagnetic filed theory through to forming the basis of quantum filed theory. Despite their impressive versatility in modelling real-world phenomena, adaptive information processing techniques specifically designed for quaternion-valued signals have only recently come to the attention of the machine learning, signal processing, and control communities. The most important development in this direction is introduction of the HR-calculus, which provides the required mathematical foundation for deriving adaptive information processing techniques directly in the quaternion domain. In this article, the foundations of the HR-calculus are revised and the required tools for deriving adaptive learning techniques suitable for dealing with quaternion-valued signals, such as the gradient operator, chain and product derivative rules, and Taylor series expansion are presented. This serves to establish the most important applications of adaptive information processing in the quaternion domain for both single-node and multi-node formulations. The article is supported by Supplementary Material, which will be referred to as SM

Collaborative adaptive filtering in the complex domain

A novel hybrid filter combining the complex least mean square (CLMS) and augmented CLMS (ACLMS) algorithms for complex domain adaptive filtering is introduced. The ACLMS has been shown to have improved performance in terms of prediction of non–circular complex data compared to that of the CLMS. By taking advantage of this along with the faster convergence of the CLMS, the hybrid filter is shown to give improved performance over both algorithms for both cir-cular and non–circular data. Simulations on complex–valued synthetic and real world data support the effectiveness of this approach. 1