Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples

This paper presents a novel power spectral density estimation technique for band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and incorporates the advantages of compressed sensing (CS) when the power spectrum is sparse, but applies to sparse and nonsparse power spectra alike. The estimates are consistent piecewise constant approximations whose resolutions (width of the piecewise constant segments) are controlled by the periodicity of the multi-coset sampling. We show that compressive estimates exhibit better tradeoffs among the estimator's resolution, system complexity, and average sampling rate compared to their noncompressive counterparts. For suitable sampling patterns, noncompressive estimates are obtained as least squares solutions. Because of the non-negativity of power spectra, compressive estimates can be computed by seeking non-negative least squares solutions (provided appropriate sampling patterns exist) instead of using standard CS recovery algorithms. This flexibility suggests a reduction in computational overhead for systems estimating both sparse and nonsparse power spectra because one algorithm can be used to compute both compressive and noncompressive estimates.Comment: 26 pages, single spaced, 9 figure

Adaptations to iron deficiency: cardiac functional responsiveness to norepinephrine, arterial remodeling, and the effect of beta-blockade on cardiac hypertrophy.

BackgroundIron deficiency (ID) results in ventricular hypertrophy, believed to involve sympathetic stimulation. We hypothesized that with ID 1) intravenous norepinephrine would alter heart rate (HR) and contractility, 2) abdominal aorta would be larger and more distensible, and 3) the beta-blocker propanolol would reduce hypertrophy.Methods1) 30 CD rats were fed an ID or replete diet for 1 week or 1 month. Norepinephrine was infused via jugular vein; pressure was monitored at carotid artery. Saline infusions were used as a control. The pressure trace was analyzed for HR, contractility, systolic and diastolic pressures. 2) Abdominal aorta catheters inflated the aorta, while digital microscopic images were recorded at stepwise pressures to measure arterial diameter and distensibility. 3) An additional 10 rats (5 ID, 5 control) were given a daily injection of propanolol or saline. After 1 month, the hearts were excised and weighed.ResultsEnhanced contractility, but not HR, was associated with ID hypertrophic hearts. Systolic and diastolic blood pressures were consistent with an increase in arterial diameter associated with ID. Aortic diameter at 100 mmHg and distensibility were increased with ID. Propanolol was associated with an increase in heart to body mass ratio.ConclusionsID cardiac hypertrophy results in an increased inotropic, but not chronotropic response to the sympathetic neurotransmitter, norepinephrine. Increased aortic diameter is consistent with a flow-dependent vascular remodeling; increased distensibility may reflect decreased vascular collagen content. The failure of propanolol to prevent hypertrophy suggests that ID hypertrophy is not mediated via beta-adrenergic neurotransmission

Quantization via Empirical Divergence Maximization

Empirical divergence maximization (EDM) refers to a recently proposed strategy for estimating f-divergences and likelihood ratio functions. This paper extends the idea to empirical vector quantization where one seeks to empirically derive quantization rules that maximize the Kullback-Leibler divergence between two statistical hypotheses. We analyze the estimator's error convergence rate leveraging Tsybakov's margin condition and show that rates as fast as 1/n are possible, where n equals the number of training samples. We also show that the Flynn and Gray algorithm can be used to efficiently compute EDM estimates and show that they can be efficiently and accurately represented by recursive dyadic partitions. The EDM formulation have several advantages. First, the formulation gives access to the tools and results of empirical process theory that quantify the estimator's error convergence rate. Second, the formulation provides a previously unknown derivation for the Flynn and Gray algorithm. Third, the flexibility it affords allows one to avoid a small-cell assumption common in other approaches. Finally, we illustrate the potential use of the method through an example.Comment: 26 single column, single spaced pages, 4 figure

FAD binding, cobinamide binding and active site communication in the corrin reductase (CobR)

Adenosylcobalamin, the coenzyme form of vitamin B12, is one Nature's most complex coenzyme whose de novo biogenesis proceeds along either an anaerobic or aerobic metabolic pathway. The aerobic synthesis involves reduction of the centrally chelated cobalt metal ion of the corrin ring from Co(II) to Co(I) before adenosylation can take place. A corrin reductase (CobR) enzyme has been identified as the likely agent to catalyse this reduction of the metal ion. Herein, we reveal how Brucella melitensis CobR binds its coenzyme FAD (flavin dinucleotide) and we also show that the enzyme can bind a corrin substrate consistent with its role in reduction of the cobalt of the corrin ring. Stopped-flow kinetics and EPR reveal a mechanistic asymmetry in CobR dimer that provides a potential link between the two electron reduction by NADH to the single electron reduction of Co(II) to Co(I)

Reconciling Compressive Sampling Systems for Spectrally-sparse Continuous-time Signals

The Random Demodulator (RD) and the Modulated Wideband Converter (MWC) are two recently proposed compressed sensing (CS) techniques for the acquisition of continuous-time spectrally-sparse signals. They extend the standard CS paradigm from sampling discrete, finite dimensional signals to sampling continuous and possibly infinite dimensional ones, and thus establish the ability to capture these signals at sub-Nyquist sampling rates. The RD and the MWC have remarkably similar structures (similar block diagrams), but their reconstruction algorithms and signal models strongly differ. To date, few results exist that compare these systems, and owing to the potential impacts they could have on spectral estimation in applications like electromagnetic scanning and cognitive radio, we more fully investigate their relationship in this paper. We show that the RD and the MWC are both based on the general concept of random filtering, but employ significantly different sampling functions. We also investigate system sensitivities (or robustness) to sparse signal model assumptions. Lastly, we show that "block convolution" is a fundamental aspect of the MWC, allowing it to successfully sample and reconstruct block-sparse (multiband) signals. Based on this concept, we propose a new acquisition system for continuous-time signals whose amplitudes are block sparse. The paper includes detailed time and frequency domain analyses of the RD and the MWC that differ, sometimes substantially, from published results.Comment: Corrected typos, updated Section 4.3, 30 pages, 8 figure

In situ process quality monitoring and defect detection for direct metal laser melting

Quality control and quality assurance are challenges in Direct Metal Laser Melting (DMLM). Intermittent machine diagnostics and downstream part inspections catch problems after undue cost has been incurred processing defective parts. In this paper we demonstrate two methodologies for in-process fault detection and part quality prediction that can be readily deployed on existing commercial DMLM systems with minimal hardware modification. Novel features were derived from the time series of common photodiode sensors along with standard machine control signals. A Bayesian approach attributes measurements to one of multiple process states and a least squares regression model predicts severity of certain material defects.Comment: 16 pages, 4 figure

Useful Facts about the Kullback-Leibler Discrimination Distance

This report contains a list of some of the more prominent properties and theorems concerning the Kullback-Leibler (KL) discrimination distance. A brief discussion is also provided indicating the type of problems in which the KL distance has been applied. References are provided for the reader's convenience

Remembering John Napier and His Logarithms

ReportThis article describes John Napier's original defintion of logarithms and presents his method of tabulation for the first logarithmic table. Napier's logarithms are found to have an intimate relationship with the natural exponential function but predates the work of Euler by about a hundred years