A Data-Driven McMillan Degree Lower Bound

Given measurements of a linear time-invariant system, the McMillan degree is the dimension of the smallest such system that reproduces these observed dynamics. Using impulse response measurements where the system has been started in some (unknown) state and then allowed to evolve freely, a classical result by Ho and Kalman reveals the McMillan degree as the rank of a Hankel matrix built from these measurements. However, if measurements are contaminated by noise, this Hankel matrix will almost surely be full rank. Hence practitioners often estimate the rank of this matrix---and thus the McMillan degree---by manually setting a threshold between the large singular values that correspond to the non-zero singular values of the noise-free Hankel matrix and the small singular values that are pertubations of the zero singular values. Here we introduce a probabilistic upper bound on the perturbation of the singular values of this Hankel matrix when measurements are corrupted by additive Gaussian noise, and hence provide guidance on setting the threshold to obtain a lower bound on the McMillan degree. This result is powered by a new, probabilistic bound on the 2-norm of a random Hankel matrix with normally distributed entries. Unlike existing results for random Hankel matrices, this bound features no unknown constants and, moreover, is within a small factor of the empirically observed bound when entries are independent and identically distributed. This bound on the McMillan degree provides an inexpensive alternative to more general model order selection techniques such as the Akaike Information Criteria (AIC)

Magnetic damping of an elastic conductor

Many applications call for a design that maximizes the rate of energy decay. Typical problems of this class include one dimensional damped wave operators, where energy dissipation is caused by a damping operator acting on the velocity. Two damping operators are well understood: a multiplication operator (known as viscous damping) and a scaled Laplacian (known as Kelvin---Voigt damping). Paralleling the analysis of viscous damping, this thesis investigates energy decay for a novel third operator known as magnetic damping, where the damping is expressed via a rank-one self-adjoint operator, dependent on a function a. This operator describes a conductive monochord embedded in a spatially varying magnetic field perpendicular to the monochord and proportional to a. Through an analysis of the spectrum, this thesis suggests that unless a has a singularity at one boundary for any finite time, there exist initial conditions that give arbitrarily small energy decay at any time

A near-stationary subspace for ridge approximation

Response surfaces are common surrogates for expensive computer simulations in engineering analysis. However, the cost of fitting an accurate response surface increases exponentially as the number of model inputs increases, which leaves response surface construction intractable for high-dimensional, nonlinear models. We describe ridge approximation for fitting response surfaces in several variables. A ridge function is constant along several directions in its domain, so fitting occurs on the coordinates of a low-dimensional subspace of the input space. We review essential theory for ridge approximation---e.g., the best mean-squared approximation and an optimal low-dimensional subspace---and we prove that the gradient-based active subspace is near-stationary for the least-squares problem that defines an optimal subspace. Motivated by the theory, we propose a computational heuristic that uses an estimated active subspace as an initial guess for a ridge approximation fitting problem. We show a simple example where the heuristic fails, which reveals a type of function for which the proposed approach is inappropriate. We then propose a simple alternating heuristic for fitting a ridge function, and we demonstrate the effectiveness of the active subspace initial guess applied to an airfoil model of drag as a function of its 18 shape parameters

Development of quality metrics for ambulatory pediatric cardiology: Chest pain

ObjectiveAs part of the American College of Cardiology Adult Congenital and Pediatric Cardiology Section effort to develop quality metrics (QMs) for ambulatory pediatric practice, the chest pain subcommittee aimed to develop QMs for evaluation of chest pain.DesignA group of 8 pediatric cardiologists formulated candidate QMs in the areas of history, physical examination, and testing. Consensus candidate QMs were submitted to an expert panel for scoring by the RAND‐UCLA modified Delphi process. Recommended QMs were then available for open comments from all members.PatientsThese QMs are intended for use in patients 5–18 years old, referred for initial evaluation of chest pain in an ambulatory pediatric cardiology clinic, with no known history of pediatric or congenital heart disease.ResultsA total of 10 candidate QMs were submitted; 2 were rejected by the expert panel, and 5 were removed after the open comment period. The 3 approved QMs included: (1) documentation of family history of cardiomyopathy, early coronary artery disease or sudden death, (2) performance of electrocardiogram in all patients, and (3) performance of an echocardiogram to evaluate coronary arteries in patients with exertional chest pain.ConclusionsDespite practice variation and limited prospective data, 3 QMs were approved, with measurable data points which may be extracted from the medical record. However, further prospective studies are necessary to define practice guidelines and to develop appropriate use criteria in this population.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140026/1/chd12509.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/140026/2/chd12509_am.pd

Epidemiology, genetics, and subtyping of preserved ratio impaired spirometry (PRISm) in COPDGene.

BackgroundPreserved Ratio Impaired Spirometry (PRISm), defined as a reduced FEV1 in the setting of a preserved FEV1/FVC ratio, is highly prevalent and is associated with increased respiratory symptoms, systemic inflammation, and mortality. Studies investigating quantitative chest tomographic features, genetic associations, and subtypes in PRISm subjects have not been reported.MethodsData from current and former smokers enrolled in COPDGene (n = 10,192), an observational, cross-sectional study which recruited subjects aged 45-80 with ≥10 pack years of smoking, were analyzed. To identify epidemiological and radiographic predictors of PRISm, we performed univariate and multivariate analyses comparing PRISm subjects both to control subjects with normal spirometry and to subjects with COPD. To investigate common genetic predictors of PRISm, we performed a genome-wide association study (GWAS). To explore potential subgroups within PRISm, we performed unsupervised k-means clustering.ResultsThe prevalence of PRISm in COPDGene is 12.3%. Increased dyspnea, reduced 6-minute walk distance, increased percent emphysema and decreased total lung capacity, as well as increased segmental bronchial wall area percentage were significant predictors (p-value <0.05) of PRISm status when compared to control subjects in multivariate models. Although no common genetic variants were identified on GWAS testing, a significant association with Klinefelter's syndrome (47XXY) was observed (p-value < 0.001). Subgroups identified through k-means clustering include a putative "COPD-subtype", "Restrictive-subtype", and a highly symptomatic "Metabolic-subtype".ConclusionsPRISm subjects are clinically and genetically heterogeneous. Future investigations into the pathophysiological mechanisms behind and potential treatment options for subgroups within PRISm are warranted.Trial registrationClinicaltrials.gov Identifier: NCT000608764

Association studies of up to 1.2 million individuals yield new insights into the genetic etiology of tobacco and alcohol use.

Tobacco and alcohol use are leading causes of mortality that influence risk for many complex diseases and disorders1. They are heritable2,3 and etiologically related4,5 behaviors that have been resistant to gene discovery efforts6-11. In sample sizes up to 1.2 million individuals, we discovered 566 genetic variants in 406 loci associated with multiple stages of tobacco use (initiation, cessation, and heaviness) as well as alcohol use, with 150 loci evidencing pleiotropic association. Smoking phenotypes were positively genetically correlated with many health conditions, whereas alcohol use was negatively correlated with these conditions, such that increased genetic risk for alcohol use is associated with lower disease risk. We report evidence for the involvement of many systems in tobacco and alcohol use, including genes involved in nicotinic, dopaminergic, and glutamatergic neurotransmission. The results provide a solid starting point to evaluate the effects of these loci in model organisms and more precise substance use measures

Assessment of risk of insect-resistant transgenic crops to nontarget arthropods

An international initiative is developing a scientifically rigorous approach to evaluate the potential risks to nontarget arthropods (NTAs) posed by insect-resistant, genetically modified (IRGM) crops. It adapts the tiered approach to risk assessment that is used internationally within regulatory toxicology and environmental sciences. The approach focuses on the formulation and testing of clearly stated risk hypotheses, making maximum use of available data and using formal decision guidelines to progress between testing stages (or tiers). It is intended to provide guidance to regulatory agencies that are currently developing their own NTA risk assessment guidelines for IRGM crops and to help harmonize regulatory requirements between different countries and different regions of the world