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

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

Common Genetic Polymorphisms Influence Blood Biomarker Measurements in COPD

Implementing precision medicine for complex diseases such as chronic obstructive lung disease (COPD) will require extensive use of biomarkers and an in-depth understanding of how genetic, epigenetic, and environmental variations contribute to phenotypic diversity and disease progression. A meta-analysis from two large cohorts of current and former smokers with and without COPD [SPIROMICS (N = 750); COPDGene (N = 590)] was used to identify single nucleotide polymorphisms (SNPs) associated with measurement of 88 blood proteins (protein quantitative trait loci; pQTLs). PQTLs consistently replicated between the two cohorts. Features of pQTLs were compared to previously reported expression QTLs (eQTLs). Inference of causal relations of pQTL genotypes, biomarker measurements, and four clinical COPD phenotypes (airflow obstruction, emphysema, exacerbation history, and chronic bronchitis) were explored using conditional independence tests. We identified 527 highly significant (p 10% of measured variation in 13 protein biomarkers, with a single SNP (rs7041; p = 10−392) explaining 71%-75% of the measured variation in vitamin D binding protein (gene = GC). Some of these pQTLs [e.g., pQTLs for VDBP, sRAGE (gene = AGER), surfactant protein D (gene = SFTPD), and TNFRSF10C] have been previously associated with COPD phenotypes. Most pQTLs were local (cis), but distant (trans) pQTL SNPs in the ABO blood group locus were the top pQTL SNPs for five proteins. The inclusion of pQTL SNPs improved the clinical predictive value for the established association of sRAGE and emphysema, and the explanation of variance (R2) for emphysema improved from 0.3 to 0.4 when the pQTL SNP was included in the model along with clinical covariates. Causal modeling provided insight into specific pQTL-disease relationships for airflow obstruction and emphysema. In conclusion, given the frequency of highly significant local pQTLs, the large amount of variance potentially explained by pQTL, and the differences observed between pQTLs and eQTLs SNPs, we recommend that protein biomarker-disease association studies take into account the potential effect of common local SNPs and that pQTLs be integrated along with eQTLs to uncover disease mechanisms. Large-scale blood biomarker studies would also benefit from close attention to the ABO blood group

Genetic diversity fuels gene discovery for tobacco and alcohol use

Tobacco and alcohol use are heritable behaviours associated with 15% and 5.3% of worldwide deaths, respectively, due largely to broad increased risk for disease and injury(1-4). These substances are used across the globe, yet genome-wide association studies have focused largely on individuals of European ancestries(5). Here we leveraged global genetic diversity across 3.4 million individuals from four major clines of global ancestry (approximately 21% non-European) to power the discovery and fine-mapping of genomic loci associated with tobacco and alcohol use, to inform function of these loci via ancestry-aware transcriptome-wide association studies, and to evaluate the genetic architecture and predictive power of polygenic risk within and across populations. We found that increases in sample size and genetic diversity improved locus identification and fine-mapping resolution, and that a large majority of the 3,823 associated variants (from 2,143 loci) showed consistent effect sizes across ancestry dimensions. However, polygenic risk scores developed in one ancestry performed poorly in others, highlighting the continued need to increase sample sizes of diverse ancestries to realize any potential benefit of polygenic prediction.Peer reviewe

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 disorders 1 . They are heritable 2,3 and etiologically related 4,5 behaviors that have been resistant to gene discovery efforts 6–11 . 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