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In recent years the extremal behaviour of log-correlated spatial Gaussian processes has drawn a lot of attention. Among many other results, it is known for the lattice discrete Gaussian free field (DGFF) in d=2 as well as for general log-correlated Gaussian fields, that the limiting law of the centred maximum is a randomly shifted Gumbel distribution. While for Gaussian fields the picture is rather complete, many difficulties arise when the field of interest in non-Gaussian. In this thesis, we study the extreme values of the non-Gaussian sine-Gordon field and P(φ)₂ field on the unit torus in dimension d=2. Our analysis includes the φ⁴₂ field. To this end, we develop tools, which we subsequently use to establish results for their extreme values, which are analogous to the known results for the Gaussian free field in d=2. In particular, we prove that the centred global maximum of the non-Gaussian fields of interest converges in distribution to a randomly shifted Gumbel distribution, which confirms the conjectured behaviour of these fields. For the sine-Gordon field, we extend the scope of the extreme values to the local extremal process, which also includes information about the local extrema of the field. More precisely, we prove that this random measure converges to a certain Poisson point process with random intensity measure. For both the sine-Gordon field and the P(φ)₂ field, the main tool is a coupling result between the well-studied Gaussian free field and the field of interest. This allows to represent the non-Gaussian field as a sum of the Gaussian free field and a difference field for which further probabilistic regularity estimates are established using renormalisation group and stochastic control techniques, in particular the Polchinski renormalisation group approach and the Boué-Dupuis variational formula.

Soybean [Glycine max (L.) Merr.] grain yields greater than three times the national average have been reported in yield contests. Characterization of soybean in a maximum yield environment is necessary to provide empirical data to support those yield claims and to provide an understanding of the physiological processes at that yield level. From 2011 to 2013, research characterized biomass and N accumulation rates, radiation use efficiency (RUE), leaf N dynamics, the rate of harvest index increase (dry matter allocation coefficient, DMAC), seedfill period (SFP), and grain yield components from Mr. Kip Cullers' contest fields and in small plots at the University of Arkansas in Fayetteville. The greatest cultivar mean yield was 7953 kg ha-1, which occurred in 2013 when biomass and N accumulation rates and RUE values as high as 64.3 g m-2 d-1, 2.08 g N m-2 d-1, and 1.89 g MJ-1 were observed, respectively. These observed crop growth characteristics were near or above the maximum values previously reported in the literature. The DMAC and SFP values were also abnormally slow and long, respectively. This coupled with the enhanced growth rates provide empirical data and insights into the production of yields >6419 kg ha-1 (100 bushels acre-1). Additional research in Fayetteville evaluated the yield effects of several of Mr. Cullers' alternative management practices. Management practices evaluated included various seed treatments, intentional herbicide injury, uniform plant spacing and emergence, lodging prevention, and a proprietary foliar-applied product. None of these alternative practices were effective in increasing yields beyond the high input practices utilized within this maximum yield environment. The feasibility of several of these high input maximum yield management practices in large production fields in eastern Arkansas were evaluated. Enhanced management including additional inputs of poultry litter, irrigation, supplemental N, and pest control were evaluated on the field scale. Two cultivars had average yields of 6931 and 6986 kg ha-1 at the England location in 2013. Economic analysis suggested that even this scaled down maximum yield management was less profitable than the growers' normal production practices. Finally, a simple soybean crop model was used to simulate crops grown within maximum yield environments at Fayetteville and Mr. Cullers' contest fields. Sensitivity analyses were also conducted to examine the effects of varying values of RUE, N accumulation, specific leaf N (SLN), and DMAC. The most accurate dataset was for Fayetteville in 2012 and 2013 and the default parameters in the model predicted yields 34.0% less than observed over all cultivars. Modifying the model with the observed parameters for RUE, N accumulation, and SLN resulted in yield predictions that averaged 3.4% greater than the observed for all the cultivars in Fayetteville in 2012 and 2013. Sensitivity analyses indicated that yield could be increased with decreased DMAC values, increased RUE values, increased SLN values when coupled with greater N accumulation rates, and with increasing N accumulation when coupled with increasing RUE values.

This dissertation explores the spatial-temporal patterns of diurnal temperature range (DTR) and its component variables, maximum temperature (Tmax) and minimum temperature (Tmin). The influences on DTR, Tmin, and Tmax variability from several environmental variables are also examined. Gridded time-series data from the Climate Research Unit (CRU TS 2.1) are used along with gridded Palmer Drought Severity Index (PDSI) data and nine teleconnection indices. The study focuses on the continental United States and surrounding land areas in southern Canada and northern Mexico. Data were converted to annual and seasonal averages to reduce the impact of the annual temperature cycle. Rotated principal components analyses (RPCA) of DTR data produced five or six geographic regions of similar DTR variability for each season and annually that were used in subsequent analysis. Regionally-averaged time-series of the locally measured variables Tmin, Tmax, DTR, cloud cover, precipitation, vapor pressure, and PDSI were examined for patterns and compared across regions and seasons. Stepwise multiple linear regression (SMLR) analyses were conducted with Tmin, Tmax, and DTR as the dependent variables and the other local variables (cloud cover, precipitation, vapor pressure, and PDSI) and teleconnection indices as independent variables to determine how the dependent variables impact Tmin, Tmax, and DTR variability. Results indicate regions of similar DTR variability occur annually and in most seasons in the west coast, southwest, central, northeast, and southeast United States. Other regions did emerge between the Great Plains and Rocky Mountains and in eastern Canada, but they were not seasonally consistent. Tmin generally showed an upward trend while the Tmax trends were usually near zero or downward. The DTR, which is the difference between Tmax and Tmin, had downward trends in many regions. SMLR analyses reveal that vapor pressure and cloud cover are the most influential variables on Tmin, Tmax, and DTR. Vapor pressure increases Tmin and Tmax, but the effect on Tmin is greater, so it tends to reduce DTR. Cloud cover increases Tmin and decrease Tmax making its impact on DTR greater than vapor pressure. Precipitation and PDSI had moderate impacts on Tmin, Tmax, and DTR but were not as consistent or influential as cloud cover and vapor pressure. The teleconnection indices used in the analysis generally had little effect on Tmin, Tmax, or DTR explaining very little (if any) of their variance.

We prove that every positive solution of the difference equation x[subscript n] = max[A[subscript i] ⁄ x[subscript n-i] | i ∈ [1,k]] is eventually periodic, and that the prime period is bounded for all positive initial points. A lower bound, growing faster than polynomially, on the maximum prime period for a system of size k is given, based on a model designed to generate long periods. Conditions for systems to have unbounded preperiods are given. All cases of nonpositive systems, with either the A values and/or initial x values allowed to be negative, are analyzed. For all cases conditions are given for solutions to exist, for the solution to be bounded, and for it to be eventually periodic. Finally, we examine several other difference systems, to see if the methods developed in this paper can be applied to them.

This dissertation develops a novel method for classifying short vegetation using synthetic aperature radar. Underlying this problem is the problem of distinguishing fine differences in geometry and dielectric constant based on the polarization, magnitude, and phase response of electromagnetic reflections. We take a statistical approach, beginning by developing a novel method of solving the entropy-moment problem for maximum-entropy density estimation. The technique works in higher dimensions and is computationally efficient and numerically accurate. We combined this density estimation technique with Bayesian methods and hierarchical classification techniques to come up with what we call a Bayesian-Hierarchical classifier for short vegetation. The overall accuracy, when applying this technique the data we have available is 93% for the classification of short vegetation. We have used a large data set, with ground-truth information, and independent training and testing data sets. These points are significant, because if any of these factors is not part of the analysis, it is possible to obtain a high classification accuracies that do not reflect the actual performance of the classifier when used with real data. Finally, we discuss and demonstrate the application of the aforementioned statistical techniques above to represent the non-stationarity in a vegetation target. This representation is applied to perform a simple form of biophysical parameter estimation. We further demonstrate the application of the classification principles to point target detection, applying a deconvolution technique that proves useful for modeling point target statistics in a vegetated background.

A Roe-type Riemann solver is used to solve the spherical harmonics and maximum entropy approximations to the time-dependent neutron transport equation. The maximum entropy closure for the two-moment approximation of the transport equation is presented. It is based on the use of the most likely form of the distribution, restricted by certain constraints, to close the equations. It is designed to have a wider range of applicability than a linear two-moment closure. The spherical harmonics expansion of the transport equation is also reviewed. The high-resolution interpolation scheme of standard Riemann solvers has been modified to work with these closures. Three boundary conditions for use with the Riemann solver and the two closures have been developed and are described. They essentially provide the Mark and Marshak boundary conditions, and an extension of the Marshak boundary conditions. The maximum entropy closure does well in deep penetration problems but has difficulties if there is more than one special direction in the problem. For a pulsed isotropic line source the spherical harmonics produce a negative scalar flux at very early times. For less severe problems, or after a few collision times, even low-order spherical harmonics approximations yield excellent results. The Riemann solver provides an exceptionally robust method for numerically solving the resulting equations.

This dissertation deals with the derivation of the standard errors of the coefficients in a discriminant function between two populations, when in addition to complete samples from the two populations, one has a sample from one of the populations on a subset of the variables only. The maximum likelihood estimates (M.L.E.) of the means of the two populations and the common variance-covariance matrix are first derived. Using these, the M.L.E.'s of the discriminant function coefficients are derived. These require the estimates of the inverse of the variance-covariance matrix. For deriving the standard errors, several methods are presented. Exact results are given in the bivariate case. These are then generalized to the p-variate case. This generalization is achieved through the use of vectorization of a matrix and the related Vec operator. Properties of Wishart matrices and inverses of Wishart matrices, as derived by Haff (1979), Magnus and Neudecker (1979), are used repeatedly for this purpose. Almost exact results have been obtained in this case also. The delta technique of deriving asymptotic variances and covariances is also presented. In addition, the information theory approach of Smith and Hocking (1968) for the estimated variance-covariance matrix is extended to its inverse in this dissertation. Information matrices from independent observations are additive but variance-covariance matrices are not. Fisher's information matrix is the inverse of the large sample variance-covariance matrix of the M.L.E.'s of the parameters. Smith and Hocking use this concept to get the large sample variances and covariances, and we have extended this to the discriminant function coefficients. The decrease in the variances of the discriminant function coefficients due to the use of the extra partial information is examined in this dissertation. This decrease is a measure of the gain in efficiency resulting from the additional observations. Some numerical values are computed and presented in order to assess this gain in precision. Finally, the problem of estimation of the mean vectors and the variance-covariance matrix of more than two populations with extra partial information is considered briefly.

The primary objective of this work was to understand the time-dependent dynamics of high-latitude thermospheric neutral winds. To do this, a unique 70-orbit December-solstice dataset of Dynamics Explorer 2 (DE-2) satellite data was established, with coverage of both polar caps during the same orbit. Analysis of this data led to the characterization of four basic high-latitude neutral-wind signature categories for each hemisphere under various interplanetary-magnetic-field (IMF) configurations. In addition, neutral-gas forcing simulations for the same solar-maximum December-solstice conditions using the NCAR thermospheric general circulation model (TGCM) showed that the orientation of the pressure-gradient force in the winter northern hemisphere was different from the summer southern hemisphere, explaining the differences in neutral-wind flow patterns systematically observed by DE-2 in opposite hemispheres. The variations in the pressure-gradient forces in opposite hemispheres were ascribed to density variations and temperature gradients, resulting from a superposition of solar-EUV, Joule and cusp heating. The DE-2 dataset was then used to conduct two different time-dependent tests of the NCAR-TGCM. The first test compared TGCM-simulated neutral winds to DE-2 measured neutral winds. The results indicated that the NCAR-TGCM provides good first-order simulated neutral winds. However, the TGCM time-dependent neutral winds differed from the measured neutral wind velocities by an average of 10-40%, primarily due to the inability to accurately model the ion-drag neutral-gas momentum source. The second test used DE-2 ion-drift data as a means of providing a realistic time-dependent prescription of ion-convection parameters. Results showed that under selected geophysical conditions, use of satellite data to constrain model boundary conditions brought simulated neutral winds closer to observed values. Finally, a technique for short-range forecasting of the high-latitude ion-convection parameters was noted. While techniques of this type show promise, more combined ion drift and neutral wind data is needed for a comprehensive evaluation.

Investigation of dynamic balance control during voluntary movements is important to provide more insights into fall prevention in the elderly. Previous research has focused on movements in the sagittal plane and the change in the position of the body center of mass (COM). To improve balance during movement, however, dynamic balance response to different movement parameters need to be better understood. This dissertation tested the hypothesis that dynamic balance control is affected by age, reach direction, initial posture, movement velocity, and acceleration of the body center of mass. Two experiments were conducted to achieve these research objectives. In the first experiment, twelve elderly and twelve young adults reached to a target in four different directions (0°, 45°, 90°, and 120°). In the second experiment, eighteen young adults performed maximum reach while initial posture (preferred vs. matched-elderly), movement velocity (fast vs. matched-elderly), and reach task (reach-hold vs. reach-reversal) were manipulated. Results of the first study showed that functional reach distance and center of pressure (COP) excursion decreased with age for the forward reach direction, suggesting that age-related differences in initial posture might affect the dynamic balance. Functional reach distance decreased with reach direction, but COP excursion did not, suggesting that dynamic balance results for the sagittal plane motion may not apply to other directions. Results of the second study showed that initial posture significantly affected functional reach distance, center of pressure (COP) excursion, and safety margin, but not absolute reach distance, indicating that initial posture may confound the age differences in dynamic balance measures. Movement velocity, however, affected functional reach distance and absolute reach distance, but not COP excursion or safety margin. The increased COP excursion but smaller functional reach distance in the reach-reversal tasks was consistent with the greater COM acceleration compared to the reach-hold task. It is concluded that the functional reach distance, COP excursion, safety margin measure different aspects of dynamic balance. Simulating elderly movement characteristics in young adults provides a new technique for investigating age effects on dynamic balance control.