Scaled Toda-like flows

AbstractThis paper discusses the class of isospectral flows Ẋ = [X, A ∘ X], where ∘ denotes the Hadamard product and [., .] is the Lie bracket. The presence of A allows arbitrary and independent scaling for each element in the matrix X. The time-1 mapping of the scaled Toda-like flow still enjoys a QR-like iteration. The scaled structure includes the classical Toda flow, Brockett's double bracket flow, and other interesting flows as special cases. Convergence proof is thus unified and simplified. The effect of scaling on a variety of applications is demonstrated by examples

Differences in carotid arterial morphology and composition between individuals with and without obstructive coronary artery disease: A cardiovascular magnetic resonance study

Objective: We sought to determine differences with cardiovascular magnetic resonance (CMR) in the morphology and composition of the carotid arteries between individuals with angiographically-defined obstructive coronary artery disease (CAD, = 50% stenosis, cases) and those with angiographically normal coronaries (no lumen irregularities, controls). Methods and results: 191 participants (50.3% female; 50.8% CAD cases) were imaged with a multi-sequence, carotid CMR protocol at 1.5T. For each segment of the carotid, lumen area, wall area, total vessel area (lumen area + wall area), mean wall thickness and the presence or absence of calcification and lipid-rich necrotic core were recorded bilaterally. In male CAD cases compared to male controls, the distal bulb had a significantly smaller lumen area (60.0 [plus or minus] 3.1 vs. 79.7 [plus or minus] 3.2 mm[super]2, p less than 0.001) and total vessel area (99.6 [plus or minus] 4.0 vs. 119.8 [plus or minus] 4.1 mm[super]2; p less than 0.001), and larger mean wall thickness (1.25 [plus or minus] 0.03 vs. 1.11 [plus or minus] 0.03 mm; p = 0.002). Similarly, the internal carotid had a smaller lumen area (37.5 [plus or minus] 1.8 vs. 44.6 [plus or minus] 1.8 mm[super]2; p = 0.006) and smaller total vessel area (64.0 [plus or minus] 2.3 vs. 70.9 [plus or minus] 2.4 mm[super]2; p = 0.04). These metrics were not significantly different between female groups in the distal bulb and internal carotid or for either gender in the common carotid. Male CAD cases had an increased prevalence of lipid-rich necrotic core (49.0% vs. 19.6%; p = 0.003), while calcification was more prevalent in both male (46.9% vs. 17.4%; p = 0.002) and female (33.3% vs. 14.6%; p = 0.031) CAD cases compared to controls. Conclusion: Males with obstructive CAD compared to male controls had carotid bulbs and internal carotid arteries with smaller total vessel and lumen areas, and an increased prevalence of lipid-rich necrotic core. Carotid calcification was related to CAD status in both males and females. Carotid CMR identifies distinct morphological and compositional differences in the carotid arteries between individuals with and without angiographically-defined obstructive CAD.Carotid Atherosclerosis (MRI) Progression Study (CAMPS, HL076378) and Cardiovascular Research Training Program (T-32, HL07838); and the General Clinical Research Center at the Wake Forest University School of Medicine (M01 RR-07122)

Revisiting QRS detection methodologies for portable, wearable, battery-operated, and wireless ECG systems

Cardiovascular diseases are the number one cause of death worldwide. Currently, portable battery-operated systems such as mobile phones with wireless ECG sensors have the potential to be used in continuous cardiac function assessment that can be easily integrated into daily life. These portable point-of-care diagnostic systems can therefore help unveil and treat cardiovascular diseases. The basis for ECG analysis is a robust detection of the prominent QRS complex, as well as other ECG signal characteristics. However, it is not clear from the literature which ECG analysis algorithms are suited for an implementation on a mobile device. We investigate current QRS detection algorithms based on three assessment criteria: 1) robustness to noise, 2) parameter choice, and 3) numerical efficiency, in order to target a universal fast-robust detector. Furthermore, existing QRS detection algorithms may provide an acceptable solution only on small segments of ECG signals, within a certain amplitude range, or amid particular types of arrhythmia and/or noise. These issues are discussed in the context of a comparison with the most conventional algorithms, followed by future recommendations for developing reliable QRS detection schemes suitable for implementation on battery-operated mobile devices.Mohamed Elgendi, Björn Eskofier, Socrates Dokos, Derek Abbot

On a differential equation approach to the weighted orthogonal Procrustes problem

The weighted orthogonal Procrustes problem, an important class of data matching problems in multivariate data analysis, is reconsidered in this paper. It is shown that a steepest descent flow on the manifold of orthogonal matrices can naturally be formulated. This formulation has two important implications: that the weighted orthogonal Procrustes problem can be solved as an initial value problem by any available numerical integrator and that the first order and the second order optimality conditions can also be derived. The proposed approach is illustrated by numerical examples