The widely linear quaternion recursive total least squares

This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ICASSP.2015.7178593A widely linear quaternion recursive total least squares (WLQRTLS) algorithm is introduced for the processing of Q- improper processes contaminated by noise. The total least squares for quaternions (QTLS) is a generalisation of the real-valued total least squares and is introduced rigorously, starting from the existence condition for low-rank approximation of quaternion matrices. Then, a quaternion Rayleigh quotient (QRQ) is defined to establish the link between the QTLS solution and the minimisation of the QRQ. Finally, the rank-one update formula is employed to allow for fast iterative solution based on the QRQ. Through simulations, the WL-QRTLS was shown to exhibit superior performance, under perturbations on both input and output signals, to other adaptive filtering of the same class - the widely linear quaternion least mean squares (WL-QLMS) and the widely linear quaternion recursive least squares (WL-QRLS). The experiments on both synthetic and real-world Q-improper processes supported the analysis

Financial Stress Through Complexity Science

Financial markets typically undergo periods of prosperity followed by periods of stagnation, and this undulation makes it challenging to maintain market efficiency. The efficient market hypothesis (EMH) states that there exist differences in structural complexity in security prices between regular and abnormal situations. Yet, despite a clear link between market acceleration (cf. recession in security prices) and stress in physical systems, indices of financial stress still have significant scope for further development. The overarching aim of this work is therefore to determine the characteristics of financial indices related to financial stress, and to establish a robust metric for the extent of such 'stress'. This is achieved based on intrinsic multiscale analysis which quantifies the so called complexity-loss hypothesis in the context of financial stress. The multiscale sample entropy and our proposed Assessment of Latent Index of Stress methods have successfully assessed financial stress, and have served as a measure to establish an analogy between transitions from 'normal' (relaxed) to 'abnormal' (stressed) financial periods with the sympatho-vagal balance in humans. Four major stock indices of the US economy over the past 25 years are considered: (i) Dow Jones Industrial Average, (ii) NASDAQ Composite, (iii) Standard & Poor's 500, and (iv) Russell 2000, together with FTSE 100, CAC 40 and exchange rates. Our findings support the EMH theory and reveal high stress for both the periods of Internet bubble burst and sub-prime mortgage crisis.This work was supported by the Financial Signal Processing Laboratory (http://www.fsplab.com/) at Imperial College London. The guest editor coordinating the review of this manuscript and approving it for publication was Prof. Ali N. Akansu.Hemakom, A.; Chanwimalueang, T.; Carrión García, A.; Aufegger, L.; Constantinides, AG.; Mandic, DP. (2016). Financial Stress Through Complexity Science. IEEE Journal of Selected Topics in Signal Processing. 10(6):1112-1126. doi:10.1109/JSTSP.2016.2581299S1112112610

Statistical-Analysis of a Mixed-Layer X-Ray-Diffraction Peak

Fil: Rebollo-Neira, Laura. Department of Mathematics. Aston University. Birmingham; United KingdomFil: Constantinides, Anthony G.. Imperial College London. Department of Electrical and Electronic Engineering. London; United KingdomFil: Plastino, Ángel Luis. CONICET; ArgentinaFil: Alvarez, Alberto Guillermo. Departamento de Química. Universidad de Los Andes; ColombiaFil: Bonetto, Rita D.. Centro de Investigación y Desarrollo en Ciencias Aplicadas Dr. Jorge J. Ronco. CINDECA. Facultad de Ingeniería y de Ciencias Exactas. Universidad Nacional de La Plata; ArgentinaFil: Iñíguez Rodríguez, Adrián Mario. Centro de Investigaciones Geológicas (CIG). Facultad de Ciencias Naturales y Museo. Universidad Nacional de La Plata; Argentin

Self-contained encrypted image folding

The recently introduced approach for Encrypted Image Folding is generalized to make it self-contained. The goal is achieved by enlarging the folded image so as to embed all the necessary information for the image recovery. The need for extra size is somewhat compensated by considering a transformation with higher folding capacity. Numerical examples show that the size of the resulting cipher image may be significantly smaller than the plain text one. The implementation of the approach is further extended to deal also with color images.Instituto de Física La Plat