Optimization and control theory are well developed techniques to quantize, model, understand and optimize real world systems and they have been widely used in engineering, economics, and science. In this thesis, we focus on applications in biomedical systems ranging from cells to microbial communities, and to something as complex as the human body. The first problem we consider is that of medication dosage control for drugs delivered intravenously to the patient. We focus specifically on a blood thinner (called bivalirudin) used in the post cardiac surgery Intensive Care Unit (ICU). We develop two approaches (a model-free and a model-based one) that predict the effect of bivalirudin. After obtaining the model and its best fit parameters by solving a non-linear optimization problem, we develop automatic dosage controllers that adaptively regulate its effect to desired levels. Our algorithms are validated using actual data from a large hospital in the Boston area. In the second problem, we introduce a cellular objective function inference mechanism in metabolic networks. We develop an inverse optimization method, called InvFBA (Inverse Flux Balance Analysis), to infer the objective functions of growing cells by using their reaction fluxes. InvFBA can be seen as an inverse version of FBA (Flux Balance Analysis) which predicts the distribution of the cell's reaction fluxes by using a hypothetical objective function. The objective functions can be linear, quadratic and non-parametric. The efficiency of the InvFBA approach matches the structure of the FBA and ensures scalability to large networks and optimality of the solution. After testing our algorithm on simulated E. coli data and time-dependent S. oneidensis fluxes inferred from gene expression data, we apply our inverse approach to flux measurements in long-term evolved E. coli strains, revealing objective functions that provide insight into metabolic adaptation trajectories. In the final problem in this thesis, we formulate a novel resource allocation problem in microbial ecosystems. We consider a given number of microbial species living symbiotically in a community and a list of all metabolic reactions present in the community, expressed in terms of the metabolite proportions involved in each reaction. We are interested in allocating reactions to organisms so that each organism maintains a minimal level of growth and the community optimizes certain objectives, such as maximizing growth and/or the uptake of specific compounds from the common environment. We leverage tools from Flux Balance Analysis (FBA) and formulate the problem as a mixed integer linear programming problem. We test our method in a toy model involving two organisms that can only survive through cross-feeding, demonstrating that the method can recover this interaction. We also test the method in a community of two simplified bacteria described in terms of their core, simplified metabolic network. We demonstrate that the method can obtain syntrophic cross-feeding species that would be very difficult to design manually.

Modelos algébricos para prever o comprimento de uma chama turbulenta têm sido foco de estudo de diversos grupos de pesquisa por suas aplicações na área de engenharia. O método experimental para obter o modelo varia desde visualizações simples, até técnicas fotográficas, este último com parâmetros fotográficos variando entre os autores. Técnicas fotográficas são usadas para estimar a altura de levantamento da base da chama, (Lift-Off) e o comprimento médio visível de chama (Visible Flame Length, VFL). Duas técnicas comuns que podem ser encontradas na literatura: por imagens de chama com baixo tempo de exposição e longo tempo de exposição, são comparados com um terceiro que se baseia na intensidade luminosa e na frequência de imagens de chama que ocupam um pixel. O melhor método foi utilizado para caracterizar o comportamento das chamas turbulentas de gás natural para diferentes regimes de velocidade do escoamento. Modelos algébricos que preveem o comprimento de chama, altura de levantamento e a velocidade crítica de extinção de chama são avaliados com os novos resultados experimentais. Logo após, os coeficientes numéricos dos melhores modelos algébricos são reajustados Finalmente, foram obtidos mapas de estabilidade relacionados à altura de levantamento e à velocidade crítica de extinção de chama para cada diâmetro em função da diluição com CO2 e do número adimensional de Reynolds. A terceira parte deste trabalho está focada no estudo da distribuição de radiação térmica. Em particular, foram consideradas três distâncias radiais medidas em comprimentos de chama (0,5 Lf, 1 Lf, 2 Lf) visando obter a distribuição do fluxo radiante experimental ao longo de um eixo vertical adjacente às chamas. Finalmente, os dados experimentais foram utilizados como dados de entrada em uma análise inversa com o objetivo de calcular os fatores de ponderação do modelo das múltiplas fontes ponderadas (por suas siglas em inglês WMPS). Nesta última parte, são apresentados frações radiantes e distribuições de fluxo de calor radiante de chamas de gás natural diluídas para diversas diluições com dióxido de carbono e diâmetros do queimador. / Predicting models for turbulent diffusion flame lengths have several applications driven the attention of many research groups. Since several studies use photographs to measure the flame length, with photographic parameters varying among authors, in other cases simple visualizations were used. It is important to explore possible discrepancies among measurement technics that could affect the results. Optical visualizations of turbulent diffusion flames are used to estimate the visible average flame length (VFL) and the lift-off. The study presents a study of three different methods to measure the VFL using optical techniques. The effect on the image of the main optic parameters such as focus, exposure time and ISO sensibility are analyzed. The VFL obtained with images in low exposure time and long exposure time are compared with a third optical method that is based on the luminous intensity and the frequency of flame images occupying a pixel. One method was used to characterize the behavior of turbulent diffusion flames of natural gas for a range of flames in function of the flow velocity. Universal non-dimensional models that describe the VFL, lift-off and the blow-out stability limit of gaseous jet diffusion flames in the still air have been compared with new experimental data. The numerical coefficients of the best models are adjusted. Finally, maps of stability related to lift-off and blow-out were obtained for each diameter in function of the dilution with CO2 and flow exit velocity expressed in non-dimensional Reynolds number The third part of this work focuses on the estimation of the thermal distribution of radiative flux from turbulent diffusion flames in laboratory-scale. The experimental measurements were gotten from the previous stability study. In particular, was considered three radial distances measured in flame lengths (0,5 Lf, 1 Lf, 2 Lf) aiming at obtaining the experimental radiant flux along a vertical axis adjacent to the flames. Finally, the experimental data was used as input data in an inverse analysis with the purpose of computing weight coefficients of the weighted multi-point source (WMPS) model. Then, experimental data that include: radiant fractions and radiative heat flux are presents for several flames with different dilutions with carbon dioxide and burner´s diameters.

Modelos algébricos para prever o comprimento de uma chama turbulenta têm sido foco de estudo de diversos grupos de pesquisa por suas aplicações na área de engenharia. O método experimental para obter o modelo varia desde visualizações simples, até técnicas fotográficas, este último com parâmetros fotográficos variando entre os autores. Técnicas fotográficas são usadas para estimar a altura de levantamento da base da chama, (Lift-Off) e o comprimento médio visível de chama (Visible Flame Length, VFL). Duas técnicas comuns que podem ser encontradas na literatura: por imagens de chama com baixo tempo de exposição e longo tempo de exposição, são comparados com um terceiro que se baseia na intensidade luminosa e na frequência de imagens de chama que ocupam um pixel. O melhor método foi utilizado para caracterizar o comportamento das chamas turbulentas de gás natural para diferentes regimes de velocidade do escoamento. Modelos algébricos que preveem o comprimento de chama, altura de levantamento e a velocidade crítica de extinção de chama são avaliados com os novos resultados experimentais. Logo após, os coeficientes numéricos dos melhores modelos algébricos são reajustados Finalmente, foram obtidos mapas de estabilidade relacionados à altura de levantamento e à velocidade crítica de extinção de chama para cada diâmetro em função da diluição com CO2 e do número adimensional de Reynolds. A terceira parte deste trabalho está focada no estudo da distribuição de radiação térmica. Em particular, foram consideradas três distâncias radiais medidas em comprimentos de chama (0,5 Lf, 1 Lf, 2 Lf) visando obter a distribuição do fluxo radiante experimental ao longo de um eixo vertical adjacente às chamas. Finalmente, os dados experimentais foram utilizados como dados de entrada em uma análise inversa com o objetivo de calcular os fatores de ponderação do modelo das múltiplas fontes ponderadas (por suas siglas em inglês WMPS). Nesta última parte, são apresentados frações radiantes e distribuições de fluxo de calor radiante de chamas de gás natural diluídas para diversas diluições com dióxido de carbono e diâmetros do queimador. / Predicting models for turbulent diffusion flame lengths have several applications driven the attention of many research groups. Since several studies use photographs to measure the flame length, with photographic parameters varying among authors, in other cases simple visualizations were used. It is important to explore possible discrepancies among measurement technics that could affect the results. Optical visualizations of turbulent diffusion flames are used to estimate the visible average flame length (VFL) and the lift-off. The study presents a study of three different methods to measure the VFL using optical techniques. The effect on the image of the main optic parameters such as focus, exposure time and ISO sensibility are analyzed. The VFL obtained with images in low exposure time and long exposure time are compared with a third optical method that is based on the luminous intensity and the frequency of flame images occupying a pixel. One method was used to characterize the behavior of turbulent diffusion flames of natural gas for a range of flames in function of the flow velocity. Universal non-dimensional models that describe the VFL, lift-off and the blow-out stability limit of gaseous jet diffusion flames in the still air have been compared with new experimental data. The numerical coefficients of the best models are adjusted. Finally, maps of stability related to lift-off and blow-out were obtained for each diameter in function of the dilution with CO2 and flow exit velocity expressed in non-dimensional Reynolds number The third part of this work focuses on the estimation of the thermal distribution of radiative flux from turbulent diffusion flames in laboratory-scale. The experimental measurements were gotten from the previous stability study. In particular, was considered three radial distances measured in flame lengths (0,5 Lf, 1 Lf, 2 Lf) aiming at obtaining the experimental radiant flux along a vertical axis adjacent to the flames. Finally, the experimental data was used as input data in an inverse analysis with the purpose of computing weight coefficients of the weighted multi-point source (WMPS) model. Then, experimental data that include: radiant fractions and radiative heat flux are presents for several flames with different dilutions with carbon dioxide and burner´s diameters.

Modelos algébricos para prever o comprimento de uma chama turbulenta têm sido foco de estudo de diversos grupos de pesquisa por suas aplicações na área de engenharia. O método experimental para obter o modelo varia desde visualizações simples, até técnicas fotográficas, este último com parâmetros fotográficos variando entre os autores. Técnicas fotográficas são usadas para estimar a altura de levantamento da base da chama, (Lift-Off) e o comprimento médio visível de chama (Visible Flame Length, VFL). Duas técnicas comuns que podem ser encontradas na literatura: por imagens de chama com baixo tempo de exposição e longo tempo de exposição, são comparados com um terceiro que se baseia na intensidade luminosa e na frequência de imagens de chama que ocupam um pixel. O melhor método foi utilizado para caracterizar o comportamento das chamas turbulentas de gás natural para diferentes regimes de velocidade do escoamento. Modelos algébricos que preveem o comprimento de chama, altura de levantamento e a velocidade crítica de extinção de chama são avaliados com os novos resultados experimentais. Logo após, os coeficientes numéricos dos melhores modelos algébricos são reajustados Finalmente, foram obtidos mapas de estabilidade relacionados à altura de levantamento e à velocidade crítica de extinção de chama para cada diâmetro em função da diluição com CO2 e do número adimensional de Reynolds. A terceira parte deste trabalho está focada no estudo da distribuição de radiação térmica. Em particular, foram consideradas três distâncias radiais medidas em comprimentos de chama (0,5 Lf, 1 Lf, 2 Lf) visando obter a distribuição do fluxo radiante experimental ao longo de um eixo vertical adjacente às chamas. Finalmente, os dados experimentais foram utilizados como dados de entrada em uma análise inversa com o objetivo de calcular os fatores de ponderação do modelo das múltiplas fontes ponderadas (por suas siglas em inglês WMPS). Nesta última parte, são apresentados frações radiantes e distribuições de fluxo de calor radiante de chamas de gás natural diluídas para diversas diluições com dióxido de carbono e diâmetros do queimador. / Predicting models for turbulent diffusion flame lengths have several applications driven the attention of many research groups. Since several studies use photographs to measure the flame length, with photographic parameters varying among authors, in other cases simple visualizations were used. It is important to explore possible discrepancies among measurement technics that could affect the results. Optical visualizations of turbulent diffusion flames are used to estimate the visible average flame length (VFL) and the lift-off. The study presents a study of three different methods to measure the VFL using optical techniques. The effect on the image of the main optic parameters such as focus, exposure time and ISO sensibility are analyzed. The VFL obtained with images in low exposure time and long exposure time are compared with a third optical method that is based on the luminous intensity and the frequency of flame images occupying a pixel. One method was used to characterize the behavior of turbulent diffusion flames of natural gas for a range of flames in function of the flow velocity. Universal non-dimensional models that describe the VFL, lift-off and the blow-out stability limit of gaseous jet diffusion flames in the still air have been compared with new experimental data. The numerical coefficients of the best models are adjusted. Finally, maps of stability related to lift-off and blow-out were obtained for each diameter in function of the dilution with CO2 and flow exit velocity expressed in non-dimensional Reynolds number The third part of this work focuses on the estimation of the thermal distribution of radiative flux from turbulent diffusion flames in laboratory-scale. The experimental measurements were gotten from the previous stability study. In particular, was considered three radial distances measured in flame lengths (0,5 Lf, 1 Lf, 2 Lf) aiming at obtaining the experimental radiant flux along a vertical axis adjacent to the flames. Finally, the experimental data was used as input data in an inverse analysis with the purpose of computing weight coefficients of the weighted multi-point source (WMPS) model. Then, experimental data that include: radiant fractions and radiative heat flux are presents for several flames with different dilutions with carbon dioxide and burner´s diameters.

This project investigates the applicability of the originalversion of Markowitz’s mean-variance model for portfoliooptimization to real-world modern actively managed portfolios.The method measures the mean-variance model’s capability toaccurately capture the riskiness of given portfolios, by invertingthe mathematical formulation of the model. The inversion of themodel is carried out both for fabricated data and real-world dataand shows that in the cases of real-world data the model lackscertain accuracy for estimating risk averseness. The method hascertain errors which both originate from the proposed estimationmethods of input variables and invalid assumptions of investors. / Projektet undersöker lämpligheten att använda den ursprungliga versionen av Markowitzs ”Mean-Variance model” för portföljoptimering för moderna aktivt förvaltade portföljer. Metoden mäter modellens förmåga att tillförlitligt beräkna risken för givna portföljer genom att invert-era den matematiska formuleringen av modellen. Inversionen av modellen utförs både för simulerad data och verklig data och visar att i fallet med verkliga data saknar modellen viss noggrannhet för att uppskatta riskpreferens. Metoden har vissa fel som både uppstår från de föreslagna uppskattningsmetoderna för inputvariabler och ogiltiga antaganden för investerare. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm

Deposition of nanoscale thickness films is ubiquitous in micro- and nano-scale device manufacturing. Current techniques such as spin-coating and chemical vapor deposition are designed to create only uniform thin films, and can be wasteful in material consumption. They lack the ability to adaptively prescribe desired film thickness profiles. This dissertation presents a novel inkjet-based zero-waste polymer deposition process referred to as Jet and Coat of Adaptive Sustainable Thin Films or J-CAST. The core of this process is built on an experimentally validated multi-scale fluid evolution model, based on extensions of lubrication theory. This model involves a nano-scale fluid film sandwiched between two flat plates: a compliant superstrate and a rigid substrate, with spatial topography on both surfaces. Accounting for the flexural elasticity of the compliant superstrate, and describing the temporal evolution of the fluid film in the presence of different boundary conditions reveals that instead of seeking process equilibrium, non-equilibrium transients should be exploited to guide film deposition. This forms the first core concept behind the process. This concept also enables robust full-wafer processes for creation of uniform films as well as nanoscale films with prescribed variation of thickness at mm-scale spatial wavelengths. The use of inkjets enables zero-waste adaptive material deposition with the preferred drop volumes and locations obtained from an inverse optimization formulation. This forms the second core concept behind the process. The optimization is based on the prescribed film thickness profile and typically involves >100,000 integer parameters. Using simplifying approximations for the same, three specific applications have been discussed - gradient surfaces in combinatorial materials science and research, elliptical profiles with ~10km radius of curvature for X-ray nanoscopy applications and polishing of starting wafer surfaces for mitigation of existing nanotopography. In addition, the potential of extending the demonstrated process to high throughput roll-roll systems has also been mentioned by modifying the model to incorporate the compliance of the substrate along with that of the superstrate. / text

[pt] Demonstramos como aprender a função objetivo e as restrições de problemas de otimização enquanto observamos sua solução ótima no decorrer de múltiplas rodadas. Nossa abordagem é baseada em técnicas de Online Learning e funciona para funções objetivo lineares sob conjuntos viáveis arbitrários generalizando trabalhos anteriores. Os dois algoritmos, um para aprender a função objetivo e o outro par aprender as restrições, convergem a uma taxa de O (1 sobre raiz de T) que nos permitem produzir soluções tão boas quanto as ótimas em poucas observações. Finalmente, mostramos a eficácia e possíveis aplicações de nossos métodos em um amplo estudo computacional. / [en] We demonstrate how to learn the objective function and constraints of optimization problems while observing its optimal solution over multiple rounds. Our approach is based on Online Learning techniques and works for linear objective functions under arbitrary feasible sets by generalizing previous work. The two algorithms, one to learn objective function and other to learn constraints, converge at a rate of O (1 on t root) that allow us to produce solutions as good as the optimal in a few observations. Finally, we show the efficacy and possible applications of our methods in a significant computational study.