Degenerate Kalman filter error covariances and their convergence onto the unstable subspace

The characteristics of the model dynamics are critical in the performance of (ensemble) Kalman filters. In particular, as emphasized in the seminal work of Anna Trevisan and coauthors, the error covariance matrix is asymptotically supported by the unstable-neutral subspace only, i.e., it is spanned by the backward Lyapunov vectors with nonnegative exponents. This behavior is at the core of algorithms known as assimilation in the unstable subspace, although a formal proof was still missing. This paper provides the analytical proof of the convergence of the Kalman filter covariance matrix onto the unstable-neutral subspace when the dynamics and the observation operator are linear and when the dynamical model is error free, for any, possibly rank-deficient, initial error covariance matrix. The rate of convergence is provided as well. The derivation is based on an expression that explicitly relates the error covariances at an arbitrary time to the initial ones. It is also shown that if the unstable and neutral directions of the model are sufficiently observed and if the column space of the initial covariance matrix has a nonzero projection onto all of the forward Lyapunov vectors associated with the unstable and neutral directions of the dynamics, the covariance matrix of the Kalman filter collapses onto an asymptotic sequence which is independent of the initial covariances. Numerical results are also shown to illustrate and support the theoretical findings

Nitrogen Use Efficiency of Potato

University of Minnesota M.S. thesis. July 2019. Major: Applied Plant Sciences. Advisor: Thomas Michaels. 1 computer file (PDF); v, 78 pages.Potato (Solanum tuberosum) production typically occurs on sandy soils with only 40-60% of the applied nitrogen (N) acquired by the crop. Nitrogen fertilization rates in potato are upwards of 336 kg N ha-1. Increased N use efficiency (NUE) and its component parts, N utilization efficiency (NUtE) and N uptake efficiency (NUpE), could drastically reduce fertilizer rates and losses to the environment. We grew 12 advanced breeding selections from the University of Minnesota red potato breeding population and two elite checks under two N rates, 101 kg N ha-1 and 202 kg N ha-1. We compared NUE, NUpE and NUtE in low and high N using 45 day after planting (DAP) root phenotypes and harvest yield and skin quality metrics. We found that NUtE correlated with NUE and yield in low N and NUpE correlated with NUE and yield in high N. Low N favored smaller tubers <6.35 cm in diameter (USDA small), while high N favored tubers between 6.35cm to 8.26cm diameter (USDA medium). Nitrogen did not significantly affect skinning and redness but did significantly affect skin lightness, with low N resulting in slightly lighter skin color. Finally, we found that greater total root mass, stolon root, or basal root, correlated with greater yield and NUE, but did not correlate with measures of N uptake

MPC of constrained discrete-time linear periodic systems — A framework for asynchronous control: Strong feasibility, stability and optimality via periodic invariance

State-feedback model predictive control (MPC) of discrete-time linear periodic systems with time-dependent state and input dimensions is considered. The states and inputs are subject to periodically time-dependent, hard, convex, polyhedral constraints. First, periodic controlled and positively invariant sets are characterized, and a method to determine the maximum periodic controlled and positively invariant sets is derived. The proposed periodic controlled invariant sets are then employed in the design of least-restrictive strongly feasible reference-tracking MPC problems. The proposed periodic positively invariant sets are employed in combination with well-known results on optimal unconstrained periodic linear-quadratic regulation (LQR) to yield constrained periodic LQR control laws that are stabilizing and optimal. One motivation for systems with time-dependent dimensions is efficient control law synthesis for discrete-time systems with asynchronous inputs, for which a novel modeling framework resulting in low dimensional models is proposed. The presented methods are applied to a multirate nano-positioning system

Mortality study of 18 000 patients treated with omeprazole.

Background: The long term safety of potent gastric acid suppressive therapy has yet to be established. Method: General practice record review at a median interval of 26 months followed by retrieval of details of all deaths within four years using the UK National Health Service Central Registers in 17 936 patients prescribed omeprazole in 1993–1995. Death rates were compared with general population rates. Results: Records of 17 489 patients (97.5%) were examined. A total of 12 703 patients received further scripts for antisecretory drugs, 8097 for omeprazole only (65.6%): 3097 patients have died. All cause mortality was higher in the first year (observed/expected (O/E) 1.44 (95% confidence intervals (CI) 1.34–1.55); p<0.0001) but had fallen to population expectation by the fourth year. There were significant mortality increases in the first year, falling to or below population expectation by the fourth year, for deaths ascribed to neoplasms (1.82 (95% CI 1.58–2.08); p<0.0001), circulatory diseases (1.27 (95% CI 1.13–1.43); p<0.0001), and respiratory diseases (1.37 (95% CI 1.12–1.64); p<0.001). Increased mortality ascribed to digestive diseases (2.56 (95% CI 1.87–3.43); p<0.0001) persisted, although reduced. Increased mortality rates for cancers of the stomach (4.06 (95% CI 2.60–6.04); p<0.0001), colon and rectum (1.40 (95% CI 0.84–2.18); p=0.075), and trachea, bronchus, and lung (1.64 (95% CI 1.19–2.19); p<0.01) seen in the first year had disappeared by the fourth year but that for cancer of the oesophagus had not (O/E 7.35 (95% CI 5.20–10.09) (p<0.0001) in year 1; 2.88 (95% CI 1.62–4.79) (p<0.001) in year 4). Forty of 78 patients dying of oesophageal cancer had the disease present at registration. Twenty seven of those remaining cases had clinical evidence of Barrett’s disease, stricture, ulcer, or oesophagitis at registration (O/E 3.30 (95% CI 2.17–4.80)). Six deaths occurred in patients with hiatal hernia or reflux only (O/E 1.02 (95% CI 0.37–2.22)) and five in patients without oesophageal disease (O/E 0.77 (95% CI 0.25–1.80)). No relationships were detected with numbers of omeprazole scripts received. Conclusions: Increases in mortality associated with treatment are due to pre- existing illness, including pre-existing severe oesophageal disease. There was no evidence of an increased risk of oesophageal adenocarcinoma in those without oesophageal mucosal damage recorded at registration

The chronostratigraphy of a Holocene Barrier Estuary: Lake Illawarra NSW

Valley-fill sequences, preserved in topographic lows associated with incised valley systems, potentially preserve a record of Holocene sea level fluctuations. A detailed litho- and biostratigraphy of the Holocene barrier estuary, Lake Illawarra, New South Wales has been constructed. Forty kilometres of seismic surveys, forty-one vibracores, supplemented by auger drill holes and trenches, and faunal analysis provides the data for this investigation. A detailed chronology of the infilling of the barrier estuary has been established using 115 aspartic acid derived ages and six radiocarbon ages. The results provide a detailed chronology for the deposition of marine transgressive deposits, barrier growth, and the subsequent development of the estuarine back-barrier environment. The results from Lake Illawarra indicate that the generalised evolution of the barrier estuary occurred in five geomorphologically distinct phases associated with rising sea levels following the last glacial maximum (LGM)

Polymeric IgA and immune complex concentrations in IgA-related renal disease

Polymeric IgA and immune complex concentrations in IgA-related renal disease. Polymeric IgA (PIgA) and immune complex concentrations in IgA-related renal disease were measured in cross sectional and longitudinal studies to establish the relationship between these parameters and both mucosal infection and renal dysfunction. These studies were performed in 50 patients with IgA nephropathy (IgAN), 17 patients with Henoch Schönlein purpura nephritis (HSPN), 11 control patients with IgA negative, diffuse mesangial proliferative glomerulonephritis (DMPGN) and 50 healthy controls. Total PIgA (PIgAT) and PIgA subclass concentrations were measured using a secretory component binding enzyme immunoassay and isotype specific immune complex concentrations were measured using conglutinin (K) binding immunoassays. In cross sectional studies patients with IgAN were found to have increased concentrations of PIgAT, PIgA1, K-IgA1 and K-IgA2 compared to controls. In the longitudinal studies controls and patients had significant increases in PIgAT and PIgA1 concentrations during infection. However, in patients with IgAN, the increases were greater, persisted for longer, and PIgA2 concentrations were also increased. K-IgA1 and K-IgA2 concentrations increased significantly during episodes of infection in IgAN patients in contrast to controls. Patients with HSPN had results similar to those of IgAN patients. No significant correlation was found between PIgA or K-IgA concentrations, and either serum creatinine concentrations or the degree of hematuria. The results indicate that patients with IgA-related renal disease have abnormal regulation of PIgA and immune complexed IgA, and that these abnormalities are exaggerated during mucosal infection

Data assimilation using adaptive, non-conservative, moving mesh models

Numerical models solved on adaptive moving meshes have become increasingly prevalent in recent years. Motivating problems include the study of fluids in a Lagrangian frame and the presence of highly localized structures such as shock waves or interfaces. In the former case, Lagrangian solvers move the nodes of the mesh with the dynamical flow; in the latter, mesh resolution is increased in the proximity of the localized structure. Mesh adaptation can include remeshing, a procedure that adds or removes mesh nodes according to specific rules reflecting constraints in the numerical solver. In this case, the number of mesh nodes will change during the integration and, as a result, the dimension of the model's state vector will not be conserved. This work presents a novel approach to the formulation of ensemble data assimilation (DA) for models with this underlying computational structure. The challenge lies in the fact that remeshing entails a different state space dimension across members of the ensemble, thus impeding the usual computation of consistent ensemble-based statistics. Our methodology adds one forward and one backward mapping step before and after the ensemble Kalman filter (EnKF) analysis, respectively. This mapping takes all the ensemble members onto a fixed, uniform reference mesh where the EnKF analysis can be performed. We consider a high-resolution (HR) and a low-resolution (LR) fixed uniform reference mesh, whose resolutions are determined by the remeshing tolerances. This way the reference meshes embed the model numerical constraints and are also upper and lower uniform meshes bounding the resolutions of the individual ensemble meshes. Numerical experiments are carried out using 1-D prototypical models: Burgers and Kuramoto–Sivashinsky equations and both Eulerian and Lagrangian synthetic observations. While the HR strategy generally outperforms that of LR, their skill difference can be reduced substantially by an optimal tuning of the data assimilation parameters. The LR case is appealing in high dimensions because of its lower computational burden. Lagrangian observations are shown to be very effective in that fewer of them are able to keep the analysis error at a level comparable to the more numerous observers for the Eulerian case. This study is motivated by the development of suitable EnKF strategies for 2-D models of the sea ice that are numerically solved on a Lagrangian mesh with remeshing