Optimal uncertainty quantification via convex optimization and relaxation

Many engineering applications face the problem of bounding the expected value of a quantity of interest (performance, risk, cost, etc.) that depends on stochastic uncertainties whose probability distribution is not known exactly. Optimal uncertainty quantification (OUQ) is a framework that aims at obtaining the best bound in these situations by explicitly incorporating available information about the distribution. Unfortunately, this often leads to non-convex optimization problems that are numerically expensive to solve.

This thesis emphasizes on efficient numerical algorithms for OUQ problems. It begins by investigating several classes of OUQ problems that can be reformulated as convex optimization problems. Conditions on the objective function and information constraints under which a convex formulation exists are presented. Since the size of the optimization problem can become quite large, solutions for scaling up are also discussed. Finally, the capability of analyzing a practical system through such convex formulations is demonstrated by a numerical example of energy storage placement in power grids.

When an equivalent convex formulation is unavailable, it is possible to find a convex problem that provides a meaningful bound for the original problem, also known as a convex relaxation. As an example, the thesis investigates the setting used in Hoeffding's inequality. The naive formulation requires solving a collection of non-convex polynomial optimization problems whose number grows doubly exponentially. After structures such as symmetry are exploited, it is shown that both the number and the size of the polynomial optimization problems can be reduced significantly. Each polynomial optimization problem is then bounded by its convex relaxation using sums-of-squares. These bounds are found to be tight in all the numerical examples tested in the thesis and are significantly better than Hoeffding's bounds.

The control of indirect effects of biomanipulation

Results from long-term investigations on biomanipulation show that indirect effects are at least as important as direct effects are for the stability of biomanipulation. Three types of indirect effects can be distinguished: (1) a change in quantity or quality of the resource base, (2) behavioural change of the prey, and (3) development of anti-predator traits. Although indirect effects of type (2), (e.g. a change in the pattern of vertical migration of zooplankton), and type (3), (e.g. development of helmets and neck teeth in Daphnia), are important mechanisms, the most essential indirect effects regarding biomanipulation belong to type (1). An example of the latter will be demonstrated: the complex of indirect effects of enhanced grazing by large herbivores on the phosphorus metabolism of the lake. It is concluded that control of the indirect effects is absolutely necessary to stabilize biomanipulation measures, but this is much more difficult than the control of direct effects and needs deeper insights into the structuring mechanisms of food webs. Proper management of fish stocks, in combination with the control of phosphorus load and/or the physical conditions, seems to be the most promising way of controlling the indirect effects of biomanipulation.

Desajuste interno e desadaptação marginal de sistemas restauradores estéticos usados em restaurações inlays indiretas

O objetivo é comparar o ajuste interno e marginal cervical de dois sistemas de compósito e um de cerâmica prensada. O Material e Métodos foi elaborado a partir de um modelo mestre metálico com preparo para inlay MOD, 15 troquéis de gesso tipo IV foram obtidos e distribuídos randomicamente em três grupos (n=5), a saber: Grupo Empress, Grupo Sinfony e Grupo Z350. Após a confecção das restaurações, cada peça foi posicionada no modelo mestre e fotografada nas faces mesial e distal para através de um programa de computador fazer a análise da desadaptação marginal cervical. Depois, a peça foi cimentada no modelo mestre usando silicone de adição de ultrabaixa viscosidade para preencher o espaço entre as restaurações e o preparo. Após a remoção das inlays, cada réplica foi pesada em balança de precisão para posterior obtenção de seu volume. Nos Resultados temos a interface paredes do preparo/paredes da restauração: houve diferença estatística entre o grupo Empress, que apresentou volume até 137% maior que os demais grupos, que foram considerados iguais entre si. Área de desadaptação marginal cervical: Houve diferença entre todos os grupos com o grupo Empress apresentando os maiores valores, seguido pelo grupo Sinfony e pelo grupo Z350. Os grupos Empress e o Sinfony apresentaram respectivamente áreas de desadaptação 450% e 200% maiores que o grupo Z350. Maior distância entre as bordas da restauração e as margens do preparo os grupos Empress e Sinfony foram iguais estatisticamente e diferentes do grupo Z350 que apresentou os menores valores. Entretanto, o grupo Empress apresentou uma desadaptação linear 43% maior que o grupo Sinfony. Concluímos que quanto ao desajuste interno, o grupo Empress apresentou os maiores valores no volume da interface dente/restauração, com diferença estatística significativa (P<0,05) em relação aos demais grupos. Para o cálculo da área, a desadaptação marginal foi menor no grupo Z350, seguido dos grupos Sinfony e Empress, todos mostrando diferença estatística significativa entre si (P<0,05). Considerando a medida linear, a desadaptação marginal foi menor no grupo Z350, indicando diferença estatística significativa (P<0,05) deste para os demais grupos.

Simple broodstock management to control indirect selection and inbreeding: Indian carp example

Following a survey of the important traits of Indian carp broodstock at some southern Indian hatcheries, it was found that the broodstock selection was size selective, exerting strong, negative selection of prematuration growth rate and positive selection on age at first maturation. This meant that the hatchery bred inadvertently slower growing and later maturing individuals. Details are given of approaches to avoid such negative selection and minimize inbreeding.

Identification of Sex and Female’s Reproductive Stage in Commercial Fish Species through the Quantification of Ribosomal Transcripts in Gonads

The estimation of maturity and sex of fish stocks in European waters is a requirement of the EU Data Collection Framework as part of the policy to improve fisheries management. On the other hand, research on fish biology is increasingly focused in molecular approaches, researchers needing correct identification of fish sex and reproductive stage without necessarily having in house the histological know-how necessary for the task. Taking advantage of the differential gene transcription occurring during fish sex differentiation and gametogenesis, the utility of 5S ribosomal RNA (5S rRNA) and General transcription factor IIIA (gtf3a) in the molecular identification of sex and gametogenic stage was tested in different economically-relevant fish species from the Bay of Biscay. Gonads of 9 fish species (, Atlantic, Atlantic-chub and horse mackerel, blue whiting, bogue, European anchovy, hake and pilchard and megrim), collected from local commercial fishing vessels were histologically sexed and 5S and 18S rRNA concentrations were quantified by capillary electrophoresis to calculate a 5S/18S rRNA index. Degenerate primers permitted cloning and sequencing of gtf3a fragments in 7 of the studied species. 5S rRNA and gtf3a transcript levels, together with 5S/18S rRNA index, distinguished clearly ovaries from testis in all of the studied species. The values were always higher in females than in males. 5S/18S rRNA index values in females were always highest when fish were captured in early phases of ovary development whilst, in later vitellogenic stages, the values decreased significantly. In megrim and European anchovy, where gonads in different oogenesis stages were obtained, the 5S/18S rRNA index identified clearly gametogenic stage. This approach, to the sexing and the quantitative non-subjective identification of the maturity stage of female fish, could have multiple applications in the study of fish stock dynamics, fish reproduction and fecundity and fish biology in general.

Quantification of drag and lift imposed by pop-up satellite archival tags and estimation of the metabolic cost to cownose rays (Rhinoptera bonasus)

The recent development of the pop-up satellite archival tag (PSAT) has allowed the collection of information on a tagged animal, such as geolocation, pressure (depth), and ambient water temperature. The success of early studies, where PSATs were used on pelagic fishes, has spurred increasing interest in the use of these tags on a large variety of species and age groups. However, some species and age groups may not be suitable candidates for carrying a PSAT because of the relatively large size of the tag and the consequent energy cost to the study animal. We examined potential energetic costs to carrying a tag for the cownose ray (Rhinoptera bonasus). Two forces act on an animal tagged with a PSAT: lift from the PSATs buoyancy and drag as the tag is moved through the water column. In a freshwater flume, a spring scale measured the total force exerted by a PSAT at flume velocities from 0.00 to 0.60 m/s. By measuring the angle of deflection of the PSAT at each velocity, we separated total force into its constituent forces — lift and drag. The power required to carry a PSAT horizontally through the water was then calculated from the drag force and velocity. Using published metabolic rates, we calculated the power for a ray of a given size to swim at a specified velocity (i.e., its swimming power). For each velocity, the power required to carry a PSAT was compared to the swimming power expressed as a percentage, %TAX (Tag Altered eXertion). A %TAX greater than 5% was felt to be energetically significant. Our analysis indicated that a ray larger than 14.8 kg can carry a PSAT without exceeding this criterion. This method of estimating swimming power can be applied to other species and would allow a researcher to decide the suitability of a given study animal for tagging with a PSAT.

Indirect validation of the age-reading method for Pacific cod (Gadus macrocephalus) using otoliths from marked and recaptured fish

Two examples of indirect validation are described for age-reading methods of Pacific cod (Gadus macrocephalus). Aging criteria that exclude faint translucent zones (checks) in counts of annuli and criteria that include faint zones were both tested. Otoliths from marked and recaptured fish were used to back-calculate the length of each fish at the time of its release by using measurements of the area of annuli. Estimated fish size at time of release and actual observed fish size were similar, supporting the assumption that translucent zones are laid down on an annual basis. A second method for validating reading criteria used otolith age and von Bertalanffy parameters, estimated from the tagging data, to predict how much each fish grew in length after tagging. We found that otolith aging criteria applied to otoliths from tagged and recovered Pacific cod predicted quite accurately the growth increments that we observed in these specimens. These results provide further evidence that the current aging criteria are not underestimating the age of the fish and support our current interpretation of checks (i.e., as subannual marks). We expect these indirect validations to advance age determination for Pacific cod, which in turn would enhance development of stock assessment methods based on age structure for this species in the eastern Bering Sea.

Ocorrência e ecotoxicidade de desreguladores endócrinos químicos em ambientes aquáticos e em sistemas de tratamento de esgoto

A aplicabilidade de um método selecionado de medição indireta de vitelogenina (Vtg) em plasma sanguíneo de peixe, baseado na quantificação de fosfato álcali-lábil (alkali-labile phosphate-ALP) para acessar estrogenicidade em água, foi investigada na presente tese. O método foi originalmente desenvolvido para a espécie de peixe Carassius carassius (Carpa cruciana) e aplicado pela primeira vez na espécie Oreochromis niloticus (Tilápia do Nilo) no presente estudo. Com o objetivo de acessar a sensibilidade do método, em uma primeira etapa da investigação foram realizados estudos laboratoriais com soluções estoques de 17-ethinylestradiol (EE2), 17-estradiol (E2), e estrona (E1). Os efeitos destes hormônios foram investigados com base tanto na concentração quanto na carga, utilizando-se para tanto, unidades experimentais com volumes distintos (2 L e 130 L). Após a validação do método de ALP, a estrogenicidade foi avaliada nas seguintes águas contaminadas: (i) afluente e efluente de uma grande estação de tratamento de esgotos convencional (ETE) e de uma estação descentralizada de tratamento de esgoto de pequeno porte (Ecossistema Engenheirado-DEE); (ii) água superficial (SW) e água subterrânea (GW) coletadas em uma área de brejo contaminada com gasolina; (iii) água de uma lagoa urbana (LRF) da cidade do Rio de Janeiro, com alta densidade populacional e descarte clandestino de esgoto. Na segunda etapa foram analisados em microalgas os efeitos (outros que não disrupção endócrina) causados pelos hormônios EE2, E2 e E1. Os hormônios foram testados individualmente e em misturas, em culturas individuais e combinada (S+) das espécies de microalgas unicelulares P. subcapitata e D. subspicatus. Com base nos níveis de ALP para a espécie de peixe e no EC50 para as espécies de algas, os resultados mostraram que o EE2 e o E2 causaram disrupção endócrina superior e foram mais tóxicos do que o E1 para peixes e microalgas respectivamente. Quando em misturas (E+) de concentrações equivalentes (EE2:E2:E1), os estrogênios resultaram em efeito aditivo para as espécies O. niloticus e P. subcapitata, e menos que aditivo para D. subspicatus e cultivo misto de algas (S+). Culturas contendo ambas as espécies de algas (S+) por um longo período de exposição (96 h) resultaram na atenuação dos efeitos tóxicos causados pela exposição, tanto individual (EE2, E2 ou E1), quanto na mistura (E+) dos estrogênios, medidos em termos de EC50 (T0h 0,07; 0,09; 0,18; e 0,06 g mL-1; e T96h 1,29; 1,87; 5,58; e 4,61 g mL-1, respectivamente). O DEE apresentou uma maior eficiência na remoção dos disrutores endócrinos do que a ETE convencional. Foi detectada estrogenicidade em amostras da LRF, e de água SW e GW em área brejosa contaminada com gasolina. Os resultados dos ensaios sugerem que as interações (efeitos aditivos ou menos que aditivo) causadas pela mistura dos estrogênios assim como, as interações entre as espécies de algas afetaram o resultado final dos ensaios ecotoxicológicos. Um fator raramente abordado em estudos ecotoxicológicos que foi destacado na presente tese refere-se à importância de considerar não somente a concentração e a dosagem, mas também a carga aplicada e o volume das unidades experimentais. Devido à boa sensibilidade do O. niloticus quando exposto às concentrações relativamente baixas dos estrogênios, a combinação do método de ALP com os biomarcadores auxiliares (particularmente MN) pode ser um protocolo adequado para a detecção de estogenicidade e genotoxicidade respectivamente em diferentes ambiente aquáticos contaminados, como parte de um programa de monitoramento ambiental