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In this thesis, we investigate a discretization of the optimality principle in dynamic programming based on radial basis functions and Shepard’s moving least squares approximation method. We prove the convergence of the discrete value function for increasingly dense sets of centres, develop an adaptive version of the algorithm and generalize a Dijkstra-like algorithm of Bertsekas which allows an efficient calculation of the value function. We illustrate the theory with numerous numerical experiments., Diese Arbeit beschäftigt sich mit einer Diskretisierung des Optimalitätsprinzips der dynamischen Programmierung, welche auf radialen Basisfunktionen und Shepards Methode der beweglichen Kleinste-Quadrate-Approximation basiert. Wir zeigen die Konvergenz der diskreten Wertefunktion für zunehmend dichtere Zentrenmengen, entwickeln eine adaptive Variante des Algorithmus und verallgemeinern einen Dijkstra-artigen Algorithmus von Bertsekas zur effizienten Berechnung der Wertefunktion. Wir illustrieren die Theorie anhand zahlreicher numerischer Experimente.

Salinity tolerance changes during larval development and metamorphosis in the summer flounder (Paralichthys dentatus) and other teleosts. The physiological mechanisms responsible for osmoregulation during these early stages of development are not well understood. This study characterized changes in ultrastructure, intracellular membranes and immunoreactive Na+/K+-ATPase of mitochondria-rich cells (MRCs) in the gills of summer flounder during metamorphosis. Gill ultrastructure at the start of metamorphosis revealed only one type of MRC, which had weak reactivity to osmium and lacked a well-defined apical pit. In juveniles, two types of MRCs were observed: light-staining MRCs (LMRCs) with weak reactivity to osmium, and dark-staining MRCs (DMRCs) with strong reactivity to osmium and positioned adjacent to LMRCs. Compared with MRCs at the start of metamorphosis, the mitochondria of juvenile MRCs appeared smaller, with more transverse cristae and electron-dense matrices. Changes in MRCs during metamorphosis were also accompanied by increased immunoreactive Na+/K+-ATPase. These findings suggest that gill MRCs develop during the metamorphosis of summer flounder as the gill takes on an increasingly important osmoregulatory role.

Metamorphosis in the summer flounder (Paralichthys dentatus) is controlled by thyroid hormones (TH) and takes place as the larvae move from a salinity of about 35 parts per thousand (ppt) in the ocean to salinity ranging from 0-35 ppt in estuaries. Historically, the role of TH in juvenile and adult teleost osmoregulation has been ambiguous, and it is not known if TH influences larval teleost osmoregulatory development. This study addresses the influence of thyroxine (T4) on the development of tolerance to low (5 ppt) and high salinity (45 and 50 ppt) as determined by salinity tolerance tests. In untreated larvae, tolerance to both low and high salinity was high during early premetamorphosis (early pre-M) and decreased or was very low from late prometamorphosis (late pro-M) through mid-metamorphic climax (mid-MC). Salinity tolerance increased 2-3-fold during late MC when whole-animal T4 levels are highest, and reached maximum tolerance at the juvenile stage. The early induction of metamorphosis by exposing larvae in pre-M to exogenous T4 reduced tolerance to low salinity during early and mid-MC, though tolerance of fish that had developed into juveniles was not impaired. In contrast, T4 increased high salinity tolerance during early and mid-MC, and the juvenile stage. This T4-induced heterochrony in salinity tolerance with regards to developmental stage suggests that the effects of T4 on salinity tolerance may be uncoupled from accelerated metamorphosis. Treatment of larvae with thiourea (TU, an inhibitor of T4 synthesis) inhibited metamorphosis and reduced tolerance to high salinity, but did not affect tolerance to low salinity. Reduced tolerance to high salinity by TU was only partially counteracted by T4 treatment, suggesting that TU also affects hypoosmoregulatory activity by an extrathyroidal mechanism. Our findings suggest that in the summer flounder T4 plays a more important role in the development of hypoosmoregulatory ability than hyperosmoregulatory ability

The summer flounder (Paralichthys dentatus) undergoes a true metamorphosis during which the bilaterally symmetrical larva transforms into an asymmetrical juvenile. This study addresses the influence of manipulating thyroid status on larval development and growth. Development was assessed by categorizing larvae in stages based on the position of the translocating eye and growth was assessed as a change in total length. Larvae were raised in seawater or in seawater containing thyroxinesodium salt (100 ppb, T4) or thiourea (30 ppm, TU). Ambient T4 raised whole-animal T4 concentration almost threefold, whereas treatment with TU reduced whole-animal T4 concentration by 95%. The wholeanimal T4 concentrations of untreated larvae increased during metamorphic climax (MC) and were related to developmental stage rather than age. Altering thyroid status of larvae in different stages had different consequences. T4 treatment of late premetamorphic (late pre-M) larvae accelerated their rate of development to prometamorphosis (pro-M), early MC, and mid MC, whereas TU treatment at this stage caused developmental stasis in early MC. T4 treatment of pro-M larvae accelerated development to early MC only and, unlike the response of late pre-M larvae, some of the pro-M larvae treated with TU slowly developed to late MC. TU treatment could inhibit completion of metamorphosis in early MC and mid MC, but not in late MC. Thyroid status of larvae had no effect on growth. However, starting at an age when most untreated and T4-treated larvae were in late MC, they began to grow longer than TU-treated larvae in developmental stasis at early MC and mid MC. Thus, T4 is necessary and sufficient for metamorphosis in summer flounder and, at this single dose, has a more pronounced effect on development at earlier stages.