# Browsing by Subject "Size"

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Item An analytical approach to computing step sizes for finite-difference derivatives(2012-05) Mathur, Ravishankar; Ocampo, Cesar; Hull, David G.; Fowler, Wallace T.; Marchand, Belinda; Senent, JuanShow more Finite-difference methods for computing the derivative of a function with respect to an independent variable require knowledge of the perturbation step size for that variable. Although rules of thumb exist for determining the magnitude of the step size, their effectiveness diminishes for complicated functions or when numerically solving difficult optimization problems. This dissertation investigates the problem of determining the step size that minimizes the total error associated with finite-difference derivative approximations. The total error is defined as the sum of errors from numerical sources (roundoff error) and mathematical approximations (truncation error). Several finite-difference approximations are considered, and expressions are derived for the errors associated with each approximation. Analysis of these errors leads to an algorithm that determines the optimal perturbation step size that minimizes the total error. A benefit of this algorithm is that the computed optimal step size, when used with neighboring values of the independent variable, results in approximately the same magnitude of error in the derivative. This allows the same step size to be used for several successive iterations of the independent variable in an optimization loop. A range of independent variable values for which the optimal step size can safely remain constant is also computed. In addition to roundoff and truncation errors within the finite-difference method, numerical errors within the actual function implementation are also considered. It is shown that the optimal step size can be used to compute an upper bound for these condition errors, without any prior knowledge of the function implementation. Knowledge of a function's condition error is of great assistance during the debugging stages of simulation design. Although the fundamental analysis assumes a scalar function of a scalar independent variable, it is later extended to the general case of a vector function of a vector independent variable. Several numerical examples are shown, ranging from simple polynomial and trigonometric functions to complex trajectory optimization problems. In each example, the step size is computed using the algorithm developed herein, a rule-of-thumb method, and an alternative statistical algorithm, and the resulting finite-difference derivatives are compared to the true derivative where available.Show more Item Bioaccumulation of mercury in pelagic fishes in NW Gulf of Mexico(Texas A&M University, 2006-08-16) Cai, YanShow more Total mercury (Hg) levels were determined in the tissues of ten taxa of pelagic fishes, with a special emphasis on apex predators (large vertebrates). Highest Hg levels were observed in blue marlin (Makaira nigricans), carcharhinid sharks (Genus Carcharhinus) and little tunny (Euthynnus alletteratus), ranging from 1.08 to 10.52 ppm. Moderate to low concentrations (<1.0 ppm) were observed in blackfin tuna (Thunnus atlanticus), cobia (Rachycentron canadum), dolphinfish (Coryphaena hippurus), greater amberjack (Seriola dumerili), king mackerel (Scomberomorus cavalla), wahoo (Acanthocybium solandri) and yellowfin tuna (Thunnus albacares). For the majority of species examined, Hg level did not vary significantly between locations (Texas and Louisiana) and years (2002 and 2003). The relationship between Hg level and fish size/weight was also explored and six taxa (blackfin tuna, carcharhinid sharks, dolphinfish, king mackerel, wahoo, yellowfin tuna) showed significant positive relationships between Hg level and body size and/or weight. Natural dietary tracers, stable isotopes (15N, 13C) and fatty acids were used to evaluate the relationship between Hg and trophic position and the relationship between Hg and dietary history. Stable nitrogen isotope analysis showed that Hg levels in fish tissues were positively associated with trophic position. Based on the 13C and 15N values of pelagic consumers examined in this study, three natural groups were identified with cluster analysis, and the same groupings were detected based on fatty acid profiles. This not only confirmed the existence of these natural groupings, but also indicated that the distinguishing factors for the grouping was likely connected with the dietary history of these fishes. The classification tree based on the fatty acid profiles of pelagic fishes readily separated fishes from different regions, suggesting that diets of pelagic taxa within the same region are similar or these consumers share a common source of organic matter in their food web. Findings from this study complement other Hg investigations conducted in the Gulf and also furthered our understanding of the link between feeding ecology and Hg accumulation. Moreover, the combined use of stable isotope and fatty acid techniques provided new insights on the dietary history of pelagic fishes in the Gulf of Mexico.Show more Item Ontogenic Morphometry and Genetic Diversity of Lygus hesperus (Hemiptera: Miridae)(2011-05) Shrestha, Ram B.; Parajulee, Megha N.; Francisco, Michael J. D. S.; Densmore, Llewellyn D.; Holaday, A. Scott; Strauss, Richard E.; Burow, Mark D.Show more Lygus hesperus Knight (Hemiptera: Miridae) is an economically important pest of many field crops, including cotton, in the United States. Lygus hesperus is commonly found in the western United States, hence, it is commonly known as Western Tarnished Plant Bug. Lygus hesperus populations from different geographic regions respond differently to the identical pest management practices. Population-specific pest management strategy is required for successful management of this pest. Morphological or molecular techniques or biological assays could be used to differentiate these Lygus populations. But scientific information on ontogenic morphometry and genetic diversity of this species is mostly lacking. Therefore, ontogenic morphometry, and genetic diversity studies were conducted in the cotton entomology laboratory at Texas AgriLife Research Center, Lubbock, Texas. Lygus hesperus has allometric ontogenic growth patterns and there was no significant difference between ontogenic shape and size trajectories between male and female. The discriminant function analysis revealed significant differences in pattern of ontogenic shape and size between Lygus hesperus and Lygus lineolaris. Thus, the morphometric technique can be used to differentiate nymphal stages of two species when they are hard to differentiate by visual observation of their morphology. Ten polymorphic microsatellite markers were developed and used in a genetic diversity study of eight Lygus hesperus populations from the Texas High Plains. Lygus hesperus population from this region showed a high degree of genetic diversity. Lygus hesperus from the Texas high Plains showed significant genetic population structure and they were differentiated into three genetically distinct populations. The molecular marker comparison study showed Simple Sequence Repeat (SSR) and Amplified Fragment Length Polymorphism (AFLP) markers are potential markers for genetic diversity study of this species when the capillary electrophoresis facility is available but Inter Simple Sequence Repeat (ISSR) markers can be next alternative when the capillary electrophoresis facility is not available. Morphometric and molecular biology knowledge and techniques developed in these studies will be useful in identification of pest management units and development of population specific precision pest management technology for Lygus hesperus.Show more