Solving physics-driven inverse problems via structured least squares

Numerous physical phenomena are well modeled by partial differential equations (PDEs); they describe a wide range of phenomena across many application domains, from model- ing EEG signals in electroencephalography to, modeling the release and propagation of toxic substances in environmental monitoring. In these applications it is often of interest to find the sources of the resulting phenomena, given some sparse sensor measurements of it. This will be the main task of this work. Specifically, we will show that finding the sources of such PDE-driven fields can be turned into solving a class of well-known multi-dimensional structured least squares prob- lems. This link is achieved by leveraging from recent results in modern sampling theory – in particular, the approximate Strang-Fix theory. Subsequently, numerical simulation re- sults are provided in order to demonstrate the validity and robustness of the proposed framework

On a dynamic reaction-diffusion mechanism: The spatial patterning of teeth primordia in the alligator

It is now well established both theoretically and, more recently, experimentally, that steady-state spatial chemical concentration patterns can be formed by a number of specific reaction–diffusion systems. Reaction–diffusion models have been widely applied to biological pattern formation problems. Here we propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator, Alligator mississippiensis, which, from a reaction–diffusion theory, introduces, among other things, a new element, namely the effect of domain growth on dynamic spatial pattern formation. Detailed embryological studies by Westergaard and Ferguson (B. Westergaard and M. W. J. Ferguson, J. Zool. Lond., 1986, 210, 575; 1987, 212, 191; Am. J. Anatomy, 1990, 187, 393) show that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. Based on biological data we develop a reaction–diffusion mechanism, which crucially includes domain growth. The model can reproduce the spatial pattern development of the first seven teeth primordia in the lower half jaw of A. mississippiensis. The results for the precise spatio temporal sequence compare well with detailed developmental experiments

Lubricant life tests on ball bearings for space applications Final report

Ball bearing life tests in vacuum using molybdenum sulfide solid films with high vacuum oils as lubricant

The U wave in atrial fibrillation

The U wave in ECGs of patients is difficult to observe because it is hidden under the atrial fibrillatory wave. Measurement and characteristics of the U wave in atrial fibrillation have not previously been described. Beat averaging was used to reveal the U waves in 12-lead ECGs of 8 patients with atrial fibrillation taking account of heart rate dependency of U wave characteristics. U wave polarity and amplitude in 12-lead ECG and the amplitude ratio of U wave to atrial fibrillatory wave in lead VI were measured. U waves were measureable in all patients. U waves were predominantly positive in leads 1. 11. aVF. V2. V3, V4, V5 and V6, negative in leads aVR. Amplitudes were largest in the precordial leads measuring up to 55 fJ V. In lead VI the U wave amplitude was on average 0.17 (range 0.1 to 0.4) times the amplitude of the atrial fibrillatory wave. U waves can be measured by ventricular beat averaging in AF patients. U waves were normal in this small group of patients

Using parallel computation to improve Independent Metropolis--Hastings based estimation

In this paper, we consider the implications of the fact that parallel raw-power can be exploited by a generic Metropolis--Hastings algorithm if the proposed values are independent. In particular, we present improvements to the independent Metropolis--Hastings algorithm that significantly decrease the variance of any estimator derived from the MCMC output, for a null computing cost since those improvements are based on a fixed number of target density evaluations. Furthermore, the techniques developed in this paper do not jeopardize the Markovian convergence properties of the algorithm, since they are based on the Rao--Blackwell principles of Gelfand and Smith (1990), already exploited in Casella and Robert (1996), Atchade and Perron (2005) and Douc and Robert (2010). We illustrate those improvements both on a toy normal example and on a classical probit regression model, but stress the fact that they are applicable in any case where the independent Metropolis-Hastings is applicable.Comment: 19 pages, 8 figures, to appear in Journal of Computational and Graphical Statistic

Principal component analysis of atrial fibrillation: Inclusion of posterior ECG leads does not improve correlation with left atrial activity

Background Lead V? is routinely analysed due to its large amplitude AF waveform. V? correlates strongly with right atrial activity but only moderately with left atrial activity. Posterior lead V? correlates strongest with left atrial activity. Aims (1) To establish whether surface dominant AF frequency (DAF) calculated using principal component analysis (PCA) of a modified 12-lead ECG (including posterior leads) has a stronger correlation with left atrial activity compared to the standard ECG. (2) To assess the contribution of individual ECG leads to the AF principal component in both ECG configurations. Methods Patients were assigned to modified or standard ECG groups. In the modified ECG, posterior leads V? and V? replaced V? and V?. AF waveform was extracted from one-minute surface ECG recordings using PCA. Surface DAF was correlated with intracardiac DAF from the high right atrium (HRA), coronary sinus (CS) and pulmonary veins (PVs). Results 96 patients were studied. Surface DAF from the modified ECG did not have a stronger correlation with left atrial activity compared to the standard ECG. Both ECG configurations correlated strongly with HRA, CS and right PVs but only moderately with left PVs. V? contributed most to the AF principal component in both ECG configurations

A Bayesian partial identification approach to inferring the prevalence of accounting misconduct

This paper describes the use of flexible Bayesian regression models for estimating a partially identified probability function. Our approach permits efficient sensitivity analysis concerning the posterior impact of priors on the partially identified component of the regression model. The new methodology is illustrated on an important problem where only partially observed data is available - inferring the prevalence of accounting misconduct among publicly traded U.S. businesses