No description available.

No description available.

Die hier dargelegte Dissertation ist motiviert durch die Vorschläge von Joyce, Doan und Walpuski zur Definitionen enumerativer Invarianten für G2-Mannigfaltigkeit, durch das Zählen gewisser kalibrierter Untermannigfaltigkeiten, sogenannter assoziativen Untermannigfaltigkeiten. In Kapitel 1, werde ich Definitionen und grundlegende Fakten über G2-Mannigfaltigkeit und deren assoziative Untermannigfaltigkeit wiederholen. Darüber hinaus erläutere ich die Konstruktion von G2-Mannigfaltigkeit als verdrehte verbundener Summe. Kapitel 2 schafft die nötige Grundlage für das darauf folgende dritte Kapitel. Hier definiere ich den Modul-Raum der asymptotisch zylindrischen assoziativen Untermannigfaltigkeiten zusammen mit seiner natürlichen Topologie und zeige, dass der Modul-Raum lokal homeomorph zur Urbild-Menge der Null einer glatten Abbildung zwischen zwei endlich-dimensionalen Räu- men ist. In besonderen Fällen ist dieser Modul-Raum eine Lagrangesche Untermannigfaltigkeit des Modul Raums der holomorphen Kurven einer asymptotisch zylindrischen Calabi-Yau Man- nigfaltigkeit. In Kapitel 3 beweise ich ein Klebe-Theorem für ein Paar von asymptotisch zylindrischen as- soziativen Untermannigfaltigkeiten in einem zusammenpassenden Paar von asymptotisch zylin- drischen G2-Mannigfaltigkeiten. Hiermit konstruiere ich neue geschlossene und starre (rigid) assoziative Untermannigfaltigkeiten in verdrehten verbundenen Summe G2-Mannigfaltigkeiten. In Kapitel 4 untersuche ich den Modul-Raum der konisch singulären assoziativen Un- termannigfaltigkeiten in G2-Mannigfaltigkeiten. Durch das Umformulieren des Indexes des Operators, der die Deformationstheorie kontrolliert, in bestimmte Stabilität-Indizes des zu- grundeliegenden assoziativen Kegels begründe ich, dass in einem generischen Pfad in dem Raum der ko-geschlossenen G2-Strukturen keine asymptotisch konischen assoziative Unter- mannigfaltigkeiten existieren, die mindestens eine Singularität besitzen, die auf einem Kegel mit Stabiltätsindex größer als eins modeliert werden. Dieses Resultat lässt sich auf alle speziellen Lagrangesche-Kegel außer den Harvey-Lawson-T2-Kegel und die Vereinigung zweier speziellen Lagrangesche-Flächen anwenden. Zusätzlich lässt sich das Ergebnis auch auf alle konischen assoziativen Untermannigfaltigkeiten anwenden, deren zugrundeliegende Verschlingung (link) holomorphe Kurven mit Null-Torsion in S6 sind. Des Weiteren dienen Teile des vierten Kapitels als Grundlage für das darauf folgende Kapitel 5. Aufgrund einiger Übergangsphänomene entlang eines generischen Pfades von G2-Strukturen, führt das naive Zählen von assoziativen Untermannigfaltigkeiten zu keiner Invariante. Tat- sächlich wurde vermutet, dass a) eine assoziative Untermannigfaltigkeit aus einer assoziativen Untermannigfaltigkeit mit Selbstsschnitt (self-intersection) geboren werden kann, und, dass b) drei assoziative Untermannigfaltigkeiten aus einer konisch singulären assoziativen Un- termannigfaltigkeit, deren Singularität durch den Harvey-Lawson-T2-Kegel modelliert wird, entspringen. In Kapitel 5, beweise ich ein Desingularitätstheorem für konisch singulären assoziative Untermannigfaltigkeit entlang eines Pfades von ko-geschlossenen G2-Strukturen. Somit verifiziere ich Vermutung b) bewiesen und teilweise auch Vermutung a). / The dissertation presented here is motivated from the proposals made by Joyce, Doan and Walpuski to define enumerative invariants of G2-manifolds by counting certain calibrated submanifolds, called associative submanifolds. In Chapter 1, I review the definitions and basic facts of G2-manifolds and associative submanifolds. Moreover, I explain the construction of G2-manifolds as twisted connected sums. Chapter 2 serves as a necessary groundwork for Chapter 3. Here, I define the moduli space of asymptotically cylindrical associative submanifolds with its natural topology and prove that the moduli space is locally homeomorphic to the zero set of a smooth map between two finite-dimensional spaces. In the best scenario, this moduli space is a Lagrangian submanifold of the moduli space of holomorphic curves in the asymptotic Calabi-Yau 3-fold. In Chapter 3, I prove a gluing theorem for a pair of asymptotically cylindrical associative submanifolds in a matching pair of asymptotically cylindrical G2-manifolds. Using this I construct new closed and rigid associative submanifolds of twisted connected sum G2-manifolds. In Chapter 4, I study the moduli space of conically singular associative submanifolds in G2-manifolds. By reformulating the index of the operator that controls the deformation theory in terms of certain stability-index of the associative cones, I establish that in a generic path of co-closed G2-structures there are no conically singular associative submanifolds that have at least one singularity modeled on a cone of stability-index greater than one. This result applies to all special Lagrangian cones, except the Harvey-Lawson T2-cone and a union of two special Lagrangian planes. Additionally, it applies to all associative cones whose links are null-torsion holomorphic curves in S6. Furthermore, parts of Chapter 4 also serve as a necessary groundwork for Chapter 5. The naive counting of associative submanifolds does not lead to an invariant due to several transitions that may occur along a generic path of G2-structures. In fact it was conjectured that a) an associative submanifold born out of an associative submanifold with self intersection, and b) three associative submanifolds arise from a conically singular associative submanifold whose singularity is modeled on Harvey-Lawson T2-cone. In Chapter 5, I prove a desingularization theorem for conically singular associative submanifolds along a path of co-closed G2-structures. Consequently, I verify conjecture b) and partially confirm conjecture a).

Diese Arbeit beginnt mit einer Analyse von stochastischen Rückwärtsdifferentialgleichungen (BSDEs) mit Sprüngen, getragen von zufälligen Maßen mit ggf. unendlicher Aktivität und zeitlich inhomogenem Kompensator. Unter konkreten, in Anwendungen leicht verifizierbaren Bedingungen liefern wir Existenz-, Eindeutigkeits- und Vergleichsergebnisse beschränkter Lösungen für eine Klasse von Generatorfunktionen, die nicht global Lipschitz-stetig im Sprungintegranden sein brauchen. Der übrige Teil der Arbeit behandelt robuste Bewertung und Hedging in unvollständigen Märkten. Wir verfolgen den No-Good-Deal-Ansatz, der Good-Deal-Grenzen liefert, indem nur eine Teilmenge der risikoneutralen Maße mit ökonomischer Bedeutung betrachtet wird (z.B. Grenzen für instantanen Sharpe-Ratio, optimale Wachstumsrate oder erwarteten Nutzen). Durchweg untersuchen wir ein Konzept des Good-Deal-Hedgings für welches Hedgingstrategien als Minimierer geeigneter dynamischer Risikomaße auftreten, was optimale Risikoteilung mit der Markt erlaubt. Wir zeigen, dass Hedging mindestens im-Mittel-selbstfinanzierend ist, also, dass Hedgefehler unter geeigneten A-priori-Bewertungsmaßen eine Supermartingaleigenschaft haben. Wir leiten konstruktive Ergebnisse zu Good-Deal-Bewertung und -Hedging im Rahmen von Prozessen mit Sprüngen durch BSDEs mit Sprüngen, sowie im Brown''schen Fall mit Driftunsicherheit durch klassische BSDEs und mit Volatilitätsunsicherheit durch BSDEs zweiter Ordnung her. Wir liefern neue Beispiele, die insbesondere für versicherungs- und finanzmathematische Anwendungen von Bedeutung sind. Bei Ungewissheit des Real-World-Maßes führt ein Worst-Case-Ansatz bei Annahme mehrerer Referenzmaße zu Good-Deal-Hedging, welches robust bzgl. Unsicherheit, im Sinne von gleichmäßig über alle Referenzmaße mindestens im-Mittel-selbstfinanzierend, ist. Daher ist bei hinreichend großer Driftunsicherheit Good-Deal-Hedging zur Risikominimierung äquivalent. / This thesis starts by an analysis of backward stochastic differential equations (BSDEs) with jumps driven by random measures possibly of infinite activity with time-inhomogeneous compensators. Under concrete conditions that are easy to verify in applications, we prove existence, uniqueness and comparison results for bounded solutions for a class of generators that are not required to be globally Lipschitz in the jump integrand. The rest of the thesis deals with robust valuation and hedging in incomplete markets. The focus is on the no-good-deal approach, which computes good-deal valuation bounds by using only a subset of the risk-neutral measures with economic meaning (e.g. bounds on instantaneous Sharpe ratios, optimal growth rates, or expected utilities). Throughout we study a notion of good-deal hedging consisting in minimizing some dynamic risk measures that allow for optimal risk sharing with the market. Hedging is shown to be at least mean-self-financing in that hedging errors satisfy a supermartingale property under suitable valuation measures. We derive constructive results on good-deal valuation and hedging in a jump framework using BSDEs with jumps, as well as in a Brownian setting with drift uncertainty using classical BSDEs and with volatility uncertainty using second-order BSDEs. We provide new examples which are particularly relevant for actuarial and financial applications. Under ambiguity about the real-world measure, a worst-case approach under multiple reference priors leads to good-deal hedging that is robust w.r.t. uncertainty in that it is at least mean-self-financing uniformly over all priors. This yields that good-deal hedging is equivalent to risk-minimization if drift uncertainty is sufficiently large.

Motiviert durch das Problem der optimalen Strategie beim Handel einer großen Aktienposition, behandelt diese Arbeit ein stochastisches Kontrollproblem mit zwei besonderen Eigenschaften. Zum einen wird davon ausgegangen, dass das Kontrollproblem eine exponentielle Verzögerung in der Kontrollvariablen beinhaltet, zum anderen nehmen wir an, dass die Koeffizienten des Kontrollproblems linear in der Kontrollvariablen sind. Wir erhalten ein degeneriertes stochastisches Kontrollproblem, dessen Lösung - sofern sie existiert - Bang-Bang-Charakter hat. Die resultierende Unstetigkeit der optimalen Kontrolle führt dazu, dass die Existenz einer optimalen Lösung nicht selbstverständlich ist und bewiesen werden muss. Es wird eine Folge von stochastischen Kontrollproblemen mit Zustandsprozessen konstruiert, deren jeweilige Diffusionsmatrix invertierbar ist und die ursprüngliche degenerierte Diffusionsmatrix approximiert. Außerdem stellen die Kostenfunktionale der Folge eine konvexe Approximation des ursprünglichen linearen Kostenfunktionals dar. Um die Konvergenz der Lösungen dieser Folge zu zeigen, stellen wir die Kontrollprobleme in Form von stochastischen Vorwärts-Rückwärts-Differential-gleichungen (FBSDEs) dar. Wir zeigen, dass die zu der konstruierten Folge von Kontrollproblemen gehörigen Lösungen der Vorwärts-Rückwärtsgleichungen – zumindest für eine Teilfolge - in Verteilung konvergieren. Mit Hilfe einer Konvexitätsannahme der Koeffizienten ist es möglich, einen Kontroll-prozess auf einem passenden Wahrscheinlichkeitsraum zu konstruieren, der optimal für das ursprüngliche stochastische Kontrollproblem ist. Neben der damit bewiesenen Existenz einer optimalen (Bang-Bang-) Lösung, wird damit auch eine glatte Approximation der unstetigen Bang-Bang-Lösung erreicht, welche man für die numerische Approximation des Problems verwenden kann. Die Ergebnisse werden schließlich dann in Form von numerischen Simulationen auf das Problem der optimalen Handels¬ausführung angewendet. / Motivated by the problem of how to optimally execute a large stock position, this thesis considers a stochastic control problem with two special properties. First, the control problem has an exponential delay in the control variable, and so the present value of the state process depends on the moving average of past control decisions. Second, the coefficients are assumed to be linear in the control variable. It is shown that a control problem with these properties generates a mathematically challenging problem. Specifically, it becomes a stochastic control problem whose solution (if one exists) has a bang-bang nature. The resulting discontinuity of the optimal solution creates difficulties in proving the existence of an optimal solution and in solving the problem with numerical methods. A sequence of stochastic control problems with state processes is constructed, whose diffusion matrices are invertible and approximate the original degenerate diffusion matrix. The cost functionals of the sequence of control problems are convex approximations of the original linear cost functional. To prove the convergence of the solutions, the control problems are written in the form of forward-backward stochastic differential equations (FBSDEs). It is then shown that the solutions of the FBSDEs corresponding to the constructed sequence of control problems converge in law, at least along a subsequence. By assuming convexity of the coefficients, it is then possible to construct from this limit an admissible control process which, for an appropriate reference stochastic system, is optimal for our original stochastic control problem. In addition to proving the existence of an optimal (bang-bang) solution, we obtain a smooth approximation of the discontinuous optimal bang-bang solution, which can be used for the numerical solution of the problem. These results are then applied to the optimal execution problem in form of numerical simulations.

A hemofilia A é uma doença ligada ao cromossomo X causada pela deficiência do fator VIII da coagulação sanguínea (FVIII). O tratamento disponível consiste na terapia de reposição da proteína do fator VIII derivada do plasma (FVIIIdp) ou recombinante (FVIIIr). Atualmente, dos 7 produtos recombinantes disponíveis no mercado, 6 são produzidos em linhagens celulares de roedores. A expressão dessa proteína em sistemas celulares não-humanos pode gerar uma molécula com perfil de modificações diferente do endógeno, podendo levar a reações imunogênicas e geração de inibidores anti-FVIIIr. Em função disso, novas estratégias de produção têm sido avaliadas, como a utilização de células hospedeiras mais eficientes no que diz respeito ao potencial de expressão da proteína de interesse. Dentre as linhagens de interesse, a linhagem hepática SK-HEP-1 tem se destacado por apresentar altos níveis de expressão do FVIIIr e potencial para o cultivo em suspensão em meios livres de soro fetal bovino (SFB). Dessa forma, o objetivo deste trabalho foi avaliar a produção de FVIIIr na linhagem celular humana SK-Hep-1 comparando duas estratégias para o estabelecimento de processos de produção em condições livres de soro e em suspensão: Estratégia 1 - adaptação para tais condições da linhagem já modificada geneticamente e Estratégia 2 - modificação gênica para a expressão da proteína já em células previamente adaptadas à tais condições. Para a estratégia 1, foram geradas duas linhagens recombinantes produtoras de FVIIIr, SK-HEP-F8/Neo-E1 e SK-HEP-F8/GFP-E1 aderentes e em cultivos suplementados com SFB. Na caracterização da cinética e produção do FVIIIr as linhagens apresentaram taxas específicas máxima de crescimento (?max) de 0,064 e 0,0031h-1 produzindo 1,0 e 0,78UI/mL de FVIIIr, respectivamente. Diversos protocolos de adaptação foram empregados, entretanto, não foi possível obter sucesso na adaptação das linhagens recombinantes para condições livres de soro e em suspensão. Para a estratégia 2, as células SK-HEP-1 selvagens adaptadas ao meio de cultura livre de SFB SFMII apresentaram um valor de ?max de 0,0186h-1 e Xmax de 1,9x106cels/mL. Para as etapas de modificação gênica da linhagem selvagem foram utilizados os mesmos vetores lentivirais empregados para a geração das células recombinantes aderentes, pLVmpsvFVIII?B-Neo e pLVCMVFVIII?B-GFP. Para o primeiro, não foi possível gerar uma linhagem produtora do FVIIIr. Para o segundo, foi possível obter duas linhagens produtoras do FVIIIr com 0.14 e 0.12IU/mL de atividade pelo ensaio cromogênico. O presente trabalho mostrou que a linhagem humana Sk-Hep-1 é apropriada para a produção de altos níveis de FVIIIr. No entanto, maiores esforços devem ser voltados ao desenvolvimento de meios de cultura livres de soro específicos para a linhagem para possibilitar a produção eficiente do FVIIIr em suspensão em meios livre de soro. / Hemophilia A is a genetic X-linked disorder caused by the coagulation factor VIII (FVIII) deficiency. The current treatment is the replacement therapy with plasma derived FVIII (pdFVIII) or recombinant FVIII (rFVIII) products. Nowadays, of the seven products available in the market, six are produced in rodent expression systems, which can result in a rFVIII molecule with different post-translational modifications and may lead to immune responses to non-human epitopes. Therefore, new production strategies have been evaluated, as the use of more efficient hosts in terms of protein expression potential. Among potential cell lines, the hepatic SK-HEP-1 cell line features high levels of rFVIII production and potential for serum-free suspension culture. In face of the exposed above, the goal of this study was to evaluate rFVIII production in the SK-HEP-1 human cell line comparing two strategies for the establishment of production process in a suspension serum-free condition: strategy 1 - adaptation to these conditions of a genetic modified cell line; strategy 2 - genetic modification of an already adapted cell line to rFVIII protein expression. For strategy 1, two adherent rFVIII producer cell lines were established in serum containing medium, SK-HEP-F8/Neo-E1 e SK-HEP-F8/GFP-E1. Characterization of cell growth and rFVIII production showed a maximum specific growth rate (?max) of 0.064 and 0.00311h-1 with rFVIII production of 1.0 and 0.78UI/mL, respectively. Different adaptation protocols were used; however, it was not possible to adapt the recombinant cell lines to growth in suspension serum-free conditions. For strategy 2, the wildtype SK-HEP-1 cell line adapted growth in SFMII BSF medium, showed a ?max of 0.0186h-1 and a maximum cell concentration (Xmax) of 1.9x106cells/mL. For the genetic modification, it were employed the same lentiviral vectors used for the recombinant adherent cells generation, pLVmpsvFVIII?B-Neo and pLVCMVFVIII?B-GFP. For the first, no attempts were successful. For the second, it was possible to generate two rFVIII producer populations with 0.14 and 0.12IU/mL activity, measured by chromogenic assay. These results demonstrate that the SK-HEP-1 cell line is appropriate for the production of high levels of rFVIII. Nevertheless, efforts should be made in developing specific medium to support efficient rFVIII production in suspension and suspension serum-free conditions.

Diese Arbeit behandelt zwei Gebiete: stochastische partielle Rückwerts-Differentialgleichungen (BSPDEs) und Mean-Field-Games (MFGs). Im ersten Teil wird über eine stochastische Variante der De Giorgischen Iteration ein Maximumprinzip für quasilineare reflektierte BSPDEs (RBSPDEs) auf allgemeinen Gebieten bewiesen. Als Folgerung erhalten wir ein Maximumprinzip für RBSPDEs auf beschränkten, sowie für BSPDEs auf allgemeinen Gebieten. Abschließend wird das lokale Verhalten schwacher Lösungen untersucht. Im zweiten Teil zeigen wir zunächst die Existenz von Gleichgewichten in MFGs mit singulärer Kontrolle. Wir beweisen, dass die Lösung eines MFG ohne Endkosten und ohne Kosten in der singulären Kontrolle durch die Lösungen eines MFGs mit strikt regulären Kontrollen approximiert werden kann. Die vorgelegten Existenz- und Approximationsresultat basieren entscheidend auf der Wahl der Storokhod M1 Topologie auf dem Raum der Càdlàg-Funktion. Anschließend betrachten wir ein MFG optimaler Portfolioliquidierung unter asymmetrischer Information. Die Lösung des MFG charakterisieren wir über eine stochastische Vorwärts-Rückwärts-Differentialgleichung (FBSDE) mit singulärer Endbedingung der Rückwärtsgleichung oder alternativ über eine FBSDE mit endlicher Endbedingung, jedoch singulärem Treiber. Wir geben ein Fixpunktargument, um die Existenz und Eindeutigkeit einer Kurzzeitlösung in einem gewichteten Funktionenraum zu zeigen. Dies ermöglicht es, das ursprüngliche MFG mit entsprechenden MFGs ohne Zustandsendbedinung zu approximieren. Der zweite Teil wird abgeschlossen mit einem Leader-Follower-MFG mit Zustandsendbedingung im Kontext optimaler Portfolioliquidierung bei hierarchischer Agentenstruktur. Wir zeigen, dass das Problem beider Spielertypen auf singuläre FBSDEs zurückgeführt werden kann, welche mit ähnlichen Methoden wie im vorangegangen Abschnitt behandelt werden können. / The thesis is concerned with two topics: backward stochastic partial differential equations and mean filed games. In the first part, we establish a maximum principle for quasi-linear reflected backward stochastic partial differential equations (RBSPDEs) on a general domain by using a stochastic version of De Giorgi’s iteration. The maximum principle for RBSPDEs on a bounded domain and the maximum principle for BSPDEs on a general domain are obtained as byproducts. Finally, the local behavior of the weak solutions is considered. In the second part, we first establish the existence of equilibria to mean field games (MFGs) with singular controls. We also prove that the solutions to MFGs with no terminal cost and no cost from singular controls can be approximated by the solutions, respectively control rules, for MFGs with purely regular controls. Our existence and approximation results strongly hinge on the use of the Skorokhod M1 topology on the space of càdlàg functions. Subsequently, we consider an MFG of optimal portfolio liquidation under asymmetric information. We prove that the solution to the MFG can be characterized in terms of a forward backward stochastic differential equation (FBSDE) with possibly singular terminal condition on the backward component or, equivalently, in terms of an FBSDE with finite terminal value, yet singular driver. We apply the fixed point argument to prove the existence and uniqueness on a short time horizon in a weighted space. Our existence and uniqueness result allows to prove that our MFG can be approximated by a sequence of MFGs without state constraint. The final result of the second part is a leader follower MFG with terminal constraint arising from optimal portfolio liquidation between hierarchical agents. We show the problems for both follower and leader reduce to the solvability of singular FBSDEs, which can be solved by a modified approach of the previous result.

No description available.

A hemofilia A é uma doença ligada ao cromossomo X causada pela deficiência do fator VIII da coagulação sanguínea (FVIII). O tratamento disponível consiste na terapia de reposição da proteína do fator VIII derivada do plasma (FVIIIdp) ou recombinante (FVIIIr). Atualmente, dos 7 produtos recombinantes disponíveis no mercado, 6 são produzidos em linhagens celulares de roedores. A expressão dessa proteína em sistemas celulares não-humanos pode gerar uma molécula com perfil de modificações diferente do endógeno, podendo levar a reações imunogênicas e geração de inibidores anti-FVIIIr. Em função disso, novas estratégias de produção têm sido avaliadas, como a utilização de células hospedeiras mais eficientes no que diz respeito ao potencial de expressão da proteína de interesse. Dentre as linhagens de interesse, a linhagem hepática SK-HEP-1 tem se destacado por apresentar altos níveis de expressão do FVIIIr e potencial para o cultivo em suspensão em meios livres de soro fetal bovino (SFB). Dessa forma, o objetivo deste trabalho foi avaliar a produção de FVIIIr na linhagem celular humana SK-Hep-1 comparando duas estratégias para o estabelecimento de processos de produção em condições livres de soro e em suspensão: Estratégia 1 - adaptação para tais condições da linhagem já modificada geneticamente e Estratégia 2 - modificação gênica para a expressão da proteína já em células previamente adaptadas à tais condições. Para a estratégia 1, foram geradas duas linhagens recombinantes produtoras de FVIIIr, SK-HEP-F8/Neo-E1 e SK-HEP-F8/GFP-E1 aderentes e em cultivos suplementados com SFB. Na caracterização da cinética e produção do FVIIIr as linhagens apresentaram taxas específicas máxima de crescimento (?max) de 0,064 e 0,0031h-1 produzindo 1,0 e 0,78UI/mL de FVIIIr, respectivamente. Diversos protocolos de adaptação foram empregados, entretanto, não foi possível obter sucesso na adaptação das linhagens recombinantes para condições livres de soro e em suspensão. Para a estratégia 2, as células SK-HEP-1 selvagens adaptadas ao meio de cultura livre de SFB SFMII apresentaram um valor de ?max de 0,0186h-1 e Xmax de 1,9x106cels/mL. Para as etapas de modificação gênica da linhagem selvagem foram utilizados os mesmos vetores lentivirais empregados para a geração das células recombinantes aderentes, pLVmpsvFVIII?B-Neo e pLVCMVFVIII?B-GFP. Para o primeiro, não foi possível gerar uma linhagem produtora do FVIIIr. Para o segundo, foi possível obter duas linhagens produtoras do FVIIIr com 0.14 e 0.12IU/mL de atividade pelo ensaio cromogênico. O presente trabalho mostrou que a linhagem humana Sk-Hep-1 é apropriada para a produção de altos níveis de FVIIIr. No entanto, maiores esforços devem ser voltados ao desenvolvimento de meios de cultura livres de soro específicos para a linhagem para possibilitar a produção eficiente do FVIIIr em suspensão em meios livre de soro. / Hemophilia A is a genetic X-linked disorder caused by the coagulation factor VIII (FVIII) deficiency. The current treatment is the replacement therapy with plasma derived FVIII (pdFVIII) or recombinant FVIII (rFVIII) products. Nowadays, of the seven products available in the market, six are produced in rodent expression systems, which can result in a rFVIII molecule with different post-translational modifications and may lead to immune responses to non-human epitopes. Therefore, new production strategies have been evaluated, as the use of more efficient hosts in terms of protein expression potential. Among potential cell lines, the hepatic SK-HEP-1 cell line features high levels of rFVIII production and potential for serum-free suspension culture. In face of the exposed above, the goal of this study was to evaluate rFVIII production in the SK-HEP-1 human cell line comparing two strategies for the establishment of production process in a suspension serum-free condition: strategy 1 - adaptation to these conditions of a genetic modified cell line; strategy 2 - genetic modification of an already adapted cell line to rFVIII protein expression. For strategy 1, two adherent rFVIII producer cell lines were established in serum containing medium, SK-HEP-F8/Neo-E1 e SK-HEP-F8/GFP-E1. Characterization of cell growth and rFVIII production showed a maximum specific growth rate (?max) of 0.064 and 0.00311h-1 with rFVIII production of 1.0 and 0.78UI/mL, respectively. Different adaptation protocols were used; however, it was not possible to adapt the recombinant cell lines to growth in suspension serum-free conditions. For strategy 2, the wildtype SK-HEP-1 cell line adapted growth in SFMII BSF medium, showed a ?max of 0.0186h-1 and a maximum cell concentration (Xmax) of 1.9x106cells/mL. For the genetic modification, it were employed the same lentiviral vectors used for the recombinant adherent cells generation, pLVmpsvFVIII?B-Neo and pLVCMVFVIII?B-GFP. For the first, no attempts were successful. For the second, it was possible to generate two rFVIII producer populations with 0.14 and 0.12IU/mL activity, measured by chromogenic assay. These results demonstrate that the SK-HEP-1 cell line is appropriate for the production of high levels of rFVIII. Nevertheless, efforts should be made in developing specific medium to support efficient rFVIII production in suspension and suspension serum-free conditions.

Piezoelektrika haben ein breit gefächertes Anwendungsspektrum in Industrie, Alltag und Forschung. Dies erfordert ein genaues Wissen über das Materialverhalten der betrachteten piezoelektrischen Elemente, was mit dem Lösen von simulationsgestützten inversen Parameteridentifikationsproblemen einhergeht. Die vorliegende Arbeit befasst sich mit der optimalen Versuchsplanung (OED) für dieses Problem. Piezoelektrische Materialien weisen die Eigenschaft auf, sich als Reaktion auf angelegte Potentiale oder Kräfte mechanisch oder elektrisch zu verändern (direkter und indirekter piezoelektrischer Effekt). Um eine Spannung anzulegen und den indirekten piezoelektrischen Effekt auszunutzen, werden Elektroden aufgebracht, deren Konfiguration einen erheblichen Einfluss auf mögliche Systemantworten hat. Daher werden das Potential, die Anzahl und die Größe der Elektroden zunächst im zweidimensionalen Fall optimiert. Das piezoelektrische Verhalten basiert im betrachteten Kleinsignalbereich auf zeitabhängigen, linearen partiellen Differentialgleichungen. Die Herleitung sowie Existenz und Eindeutigkeit der Lösungen werden gezeigt. Zur Berechnung der elektrischen Ladung und der Impedanz, die für das Materialidentifikationsproblem und damit für die Versuchsplanung relevant sind, werden zeit- und frequenzabhängige Simulationen auf Basis der Finite Elemente Methode (FEM) mit dem FEM Simulationstool FEniCS durchgeführt. Es wird auf Nachteile bei der Berechnung der Ableitungen eingegangen und erste adjungierte Gleichungen formuliert. Die Modellierung des Problems der optimalen Versuchsplanung erfolgt hauptsächlich durch die Kontrolle des Potentials der Dirichlet Randbedingungen des Randwertproblems. Anhand mehrerer numerischer Beispiele werden die resultierenden Konfigurationen gezeigt. Weitere Ansätze zur Elektrodenmodellierung, z.B. durch Kontrolle der Materialeigenschaften, werden ebenfalls vorgestellt. Schließlich wird auf mögliche Erweiterungen des vorgestellten OED Problems hingewiesen. / Piezoelectrics have a wide range of applications in industry, everyday life and research. This requires an accurate knowledge of the material behavior, which implies the solution of simulation-based inverse identification problems. This thesis focuses on the optimal design of experiments addressing this problem. Piezoelectric materials exhibit the property of mechanical or electrical changes in response to applied potentials or forces (direct and indirect piezoelectric effect). To apply voltage and to exploit the indirect piezoelectric effect, electrodes are attached whose configura- tion have a significant influence on possible system responses. Therefore, the potential, the number and the size of the electrodes are initially optimized in the two-dimensional case. The piezoelectric behavior in the considered small signal range is based on a time dependent linear partial differential equation system. The derivation as well as the exis- tence, uniqueness and regularity of the solutions of the equations are shown. Time- and frequency-dependent simulations based on the finite element method (FEM) with the FEM simulation tool FEniCS are performed to calculate the electric charge and the impedance, which are relevant for the material identification problem and thus for the experimental design. Drawbacks in the derivative calculations are pointed out and a first set of adjoint equations is formulated. The modeling of the optimal experimental design (OED) prob- lem is done mainly by controlling the potential of the Dirichlet boundary conditions of the boundary value problem. Several numerical examples are used to show the resulting configurations and to address the difficulties encountered. Further electrode modeling ap- proaches for example by controlling the material properties are then discussed. Finally, possible extensions of the presented OED problem are pointed out.