For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional estimation techniques can be seen as variable selection that leads to a smaller set of variables (a “submodel”) where classical linear regression applies. We analyze linear regression estimators resulting from model selection by proving estimation error and linear representation bounds uniformly over sets of submodels. Based on deterministic inequalities, our results provide “good” rates when applied to both independent and dependent data. These results are useful in meaningfully interpreting the linear regression estimator obtained after exploring and reducing the variables and also in justifying post-model-selection inference. All results are derived under no model assumptions and are nonasymptotic in nature.

Utilizing the similarity between the spinor representation of the Dirac and the Maxwell equations that has been recognized since the early days of relativistic quantum mechanics, a quantum lattice algorithm (QLA) representation of unitary collision-stream operators of Maxwell's equations is derived for both homogeneous and inhomogeneous media. A second-order accurate 4-spinor scheme is developed and tested successfully for two-dimensional (2-D) propagation of a Gaussian pulse in a uniform medium whereas for normal (1-D) incidence of an electromagnetic Gaussian wave packet onto a dielectric interface requires 8-component spinors because of the coupling between the two electromagnetic polarizations. In particular, the well-known phase change, field amplitudes and profile widths are recovered by the QLA asymptotic profiles without the imposition of electromagnetic boundary conditions at the interface. The QLA simulations yield the time-dependent electromagnetic fields as the wave packet enters and straddles the dielectric boundary. QLA involves unitary interleaved non-commuting collision and streaming operators that can be coded onto a quantum computer: the non-commutation being the very reason why one perturbatively recovers the Maxwell equations.

There is no published information on the impact of volunteer barley on wheat yield loss or on the economics of controlling barley with a herbicide. With the registration of imazamox-resistant wheat, it is now possible to control volunteer barley in wheat. Thus, the likelihood of growing wheat in rotation with barley may increase. Field experiments were conducted in 2003 and 2004 at Beaverlodge, Lacombe, and Edmonton, AB, Canada, and Saskatoon, SK, Canada, to determine the impact of volunteer barley on yield of imazamox-resistant spring wheat seeded at relatively low (100 kg ha−1) and high (175 kg ha−1) rates. Barley was seeded at different densities to simulate volunteer barley infestations. Regression analysis indicated that wheat-plant density influenced the effects of volunteer barley interference on wheat yield loss, economic threshold values, and volunteer barley fecundity among locations and years. Economic thresholds varied from as few volunteer barley plants as 3 m−2 at Beaverlodge in 2003 and 2004 to 48 m−2 at Lacombe in 2003. In most cases, wheat yield loss and volunteer barley fecundity were lower and economic thresholds were higher when wheat was seeded at the higher rate. For example, averaged over both years at Beaverlodge initial slope values (percentage of wheat yield loss at low barley density) were 4.5 and 1.7%, and economic threshold values of volunteer barley plants were 3 m−2 and 8 m−2 at low and high wheat seeding rates, respectively. Results indicate that volunteer barley can be highly competitive in wheat, but yield losses and wheat seed contamination due to volunteer barley can be alleviated by seeding wheat at a relatively high rate.

Field experiments were conducted at Vegreville and Lacombe, AB, to determine the influence of barley (Hordeum vulgare) variety and seeding rate on interference of wild oat (Avena fatua) with barley. Barley variety and seeding rate affected barley density, height at maturity, and seed yield, as well as wild oat shoot dry weight and seed yield in most experiments, but there was no variety by seeding rate interaction. As expected, the semidwarf varieties Falcon and CDC Earl were the shortest. Barley seedling emergence and subsequent plant densities varied among varieties, locations, and years. The hull-less varieties Falcon and CDC Dawn had the poorest emergence in most cases, whereas AC Lacombe and Seebe had the highest emergence. Wild oat shoot dry matter and seed production was highest in the Falcon, CDC Dawn, and CDC Earl plots, suggesting that these were the least competitive with wild oat. Barley yield loss from wild oat interference also tended to be highest in these varieties. Poor emergence of Falcon and CDC Dawn and the shorter stature of Falcon and CDC Earl likely contributed to their relatively poor competitiveness with wild oat. Increasing the seeding rate improved the competitiveness of all varieties, as evidenced by reduced wild oat shoot dry matter and seed production and, in some cases, improved barley yields.

Field experiments were conducted at Vegreville, Alberta, in 1997, 1998, and 1999 and in Lacombe, Alberta, in 1997 and 1998, to determine if barley row spacing (20 and 30 cm) and seeding rate (75, 125, and 175 kg ha−1) influenced the effects of variable tralkoxydim rates on barley seed yield, net economic returns, and wild oat seed production. In most cases, barley seed yield was unaffected by row spacing or seeding rate. Where no herbicide was applied, the presence of wild oat reduced barley yield at each location each year. When the herbicide was applied at 50, 75, or 100% of the recommended rate, barley yields were not affected by the presence of wild oat. Results were more variable at 25% of the recommended rate, especially at Lacombe, where yield losses occurred both years at this rate. The lowest net economic returns consistently occurred in the absence of herbicide application; however, the influence of herbicide rate on net returns varied among years and locations. Net returns were either higher at the lower herbicide rates or were unaffected by herbicide rate. Seeding rate and herbicide rate affected wild oat seed production at each location each year and also the amount of seeds in the soil seedbank at Vegreville in 1999. Row spacing had little or no effect on wild oat seed production. There was a consistent and highly significant seeding rate by herbicide rate interaction on wild oat seed production. The effects of tralkoxydim on wild oat seed production, especially at relatively low rates, were superior at the higher barley seeding rates. The results suggest that seeding barley at relatively high rates can result in optimum barley yields, undiminished economic returns, and effective wild oat management when tralkoxydim is used at lower than recommended rates.

Objective: In this study, we examined 204 older depressed individuals for up to 64 months to determine factors related to depression outcome. We hypothesized that both presence of vascular brain lesions seen on baseline magnetic resonance imaging (MRI) scans and lower baseline social support measures would be related to worse depression outcome.

Method: At study entry, all subjects were at least 59 years old, had a diagnosis of major depression, and were free of other major psychiatric illness and primary neurological illness, including dementia and stroke. Depression was diagnosed via structured interview and clinical assessment by a geriatric psychiatrist who completed a Montgomery Asberg Depression Rating Scale (MADRS) to determine severity of depression. Subjects provided self-report data on social support variables and ability to perform basic and instrumental activities of daily living (ADL, IADL). All subjects agreed to have a baseline standardized MRI brain scan. Ratings of severity of hyperintensities were determined for the periventricular white matter, deep white matter, and subcortical gray matter by two readers who decided by consensus. Treatment was provided by geropsychiatrists following clinical guidelines. Using mixed models to analyze the data, we determined the effect of a variety of demographic, social and imaging variables on the trajectory of MADRS score, the outcome variable of interest.

Results: MADRS scores decreased steadily over time. In a final HLM model, in which time since entry, a baseline time indicator, age, gender, education and Mini-mental State Examination score were controlled, subjective social support, instrumental ADL impairment, subcortical gray matter severity, and the interactions of time with social network and with subcortical gray matter lesions remained significantly associated with MADRS score.

Conclusions: Both social and biological factors at baseline are associated with longitudinal depression severity in geriatric depression.

Post-traumatic stress disorder (PTSD) was studied in the Piedmont region of North Carolina. Among 2985 subjects, the lifetime and six month prevalence figures for PTSD were 1·30 and 0·44 % respectively. In comparison to non-PTSD subjects, those with PTSD had significantly greater job instability, family history of psychiatric illness, parental poverty, child abuse, and separation or divorce of parents prior to age 10. PTSD was associated with greater psychiatric co-morbidity and attempted suicide, increased frequency of bronchial asthma, hypertension, peptic ulcer and with impaired social support. Differences were noted between chronic and acute PTSD on a number of measures, with chronic PTSD being accompanied by more frequent social phobia, reduced social support and greater avoidance symptoms.

Duke Epidemiologic Catchment Area (ECA) data were used to examine the relationships between: (a) early childhood maternal death, paternal death, and parental separation/divorce, and (b) six-month DIS/DSM-III diagnoses of agoraphobia with and without panic attacks, simple phobia, social phobia, panic disorder, generalised anxiety disorder, and obsessive-compulsive disorder. Associations were found between: (a) maternal death and agoraphobia with panic attacks, and (b) parental separation/divorce and agoraphobia with panic attacks and panic disorder. The associations could not be explained by the effects of potentially confounding socio-demographic factors.