In this thesis direct numerical simulations are used to investigate two phenomenain shear flows: laminar-turbulent transition over a flat plate and periodicvortex shedding induced by a jet in cross flow. The emphasis is on understanding and controlling the flow dynamics using tools from dynamical systems and control theory. In particular, the global behavior of complex flows is describedand low-dimensional models suitable for control design are developed; this isdone by decomposing the flow into global modes determined from spectral analysisof various linear operators associated with the Navier–Stokes equations.Two distinct self-sustained global oscillations, associated with the sheddingof vortices, are identified from direct numerical simulations of the jet incrossflow. The investigation is split into a linear stability analysis of the steadyflow and a nonlinear analysis of the unsteady flow. The eigenmodes of theNavier–Stokes equations, linearized about an unstable steady solution revealthe presence of elliptic, Kelvin-Helmholtz and von K´arm´an type instabilities.The unsteady nonlinear dynamics is decomposed into a sequence of Koopmanmodes, determined from the spectral analysis of the Koopman operator. Thesemodes represent spatial structures with periodic behavior in time. A shearlayermode and a wall mode are identified, corresponding to high-frequency andlow-frequency self-sustained oscillations in the jet in crossflow, respectively.The knowledge of global modes is also useful for transition control, wherethe objective is to reduce the growth of small-amplitude disturbances to delaythe transition to turbulence. Using a particular basis of global modes, knownas balanced modes, low-dimensional models that capture the behavior betweenactuator and sensor signals in a flat-plate boundary layer are constructed andused to design optimal feedback controllers. It is shown that by using controltheory in combination with sensing/actuation in small, localized, regionsnear the rigid wall, the energy of disturbances may be reduced by an order of magnitude.

While moment matching can effectively reduce the dimension of a linear, time-invariant system, it can simultaneously fail to improve the stable time-step for the forward Euler scheme. In the context of a semi-discrete heat equation with spatially smooth forcing, the high frequency modes are virtually insignificant. Eliminating such modes dramatically improves the stable time-step without sacrificing output accuracy. This is accomplished by modal filtration, whose computational cost is relatively palatable when applied following an initial reduction stage by moment matching. A bound on the norm of the difference between the transfer functions of the moment-matched system and its modally-filtered counterpart yields an intelligent choice for the mode of truncation. The dual-stage algorithm disappoints in the context of highly nonnormal semi-discrete convection-diffusion equations. There, moment matching can be ineffective in dimension reduction, precluding a cost-effective modal filtering step.

We present a new method for the computation of low rank approximations to the solution of large, sparse, stable Lyapunov equations. It is based on a generalization of the classical Smith method and profits by the usual low rank property of the right hand side matrix. The requirements of the method are moderate with respect to both computational cost and memory. Hence, it provides a possibility to tackle large scale control problems. Besides the efficient solution of the matrix equation itself, a thorough integration of the method into several control algorithms can improve their performance to a high degree. This is demonstrated for algorithms for model reduction and optimal control. Furthermore, we propose a heuristic for determining a set of suboptimal ADI shift parameters. This heuristic, which is based on a pair of Arnoldi processes, does not require any a priori knowledge on the spectrum of the coefficient matrix of the Lyapunov equation. Numerical experiments show the efficiency of the iterative scheme combined with the heuristic for the ADI parameters.

3-Deoxy-D-arabino heptulosonate 7-phosphate synthase (DAH7PS) catalyses the first step of the shikimate pathway, responsible for the biosynthesis of aromatic amino acids. This pathway is found in microorganisms, plants and apicomplexan parasites and its absence in mammals makes it a viable target for antimicrobial drug design. DAH7PS enzymes differ in the regulatory machinery that decorates the catalytic (β/α)8 barrel. Some DAH7PS enzymes are fused to chorismate mutase (CM), another enzyme in the shikimate pathway. This fusion protein is allosterically regulated by chorismate (CA) or prephenate (PA), the precursor of tyrosine and phenylalanine. It has been suggested that DAH7PS enzymes evolved these extensions to the core barrel for the sole purpose of regulation. Geobacillus sp DAH7PS (GspDAH7PSWT) is a thermophilic type Iβ DAH7PS enzyme with an N-terminal CM domain fused through a linker region. This thesis describes the functional characterisation work carried out on GspDAH7PSWT, in attempt to help determine how DAH7PS enzymes evolved such diverse methods of regulation. Chapter 2 describes the functional characterisation work carried out on the catalytic and regulatory domains of GspDAH7PSWT. The enzyme demonstrated both DAH7PS and CM activities with the DAH7PS domain determined to be metal dependent and most activated by Cd2+. PA completely inhibited the catalytic activity of GspDAH7PSWT, and AUC demonstrated an equilibrium exists between the dimeric and tetrameric quaternary states of the enzyme in solution. Chapter 3 describes the domain truncation of GspDAH7PSWT carried out at the linker region in order to obtain two separate protein domains, the catalytic domain lacking the N-terminal domain (GspDAH7PSDAH7PS) and the regulatory domain without the catalytic domain (GspDAH7PSCM). Both variants were fully characterised, and information obtained from each domain was compared to the respective catalytic and regulatory domains of the wild-type enzyme, which was also characterised. Like GspDAH7PSWT, GspDAH7PSDAH7PS showed greatest activation in the presence of Cd2+, with other metals having varying effects on activation rates and stability of the enzyme. Both truncated variants followed Michaelis-Menten kinetics where GspDAH7PSDAH7PS was found to be more active than GspDAH7PSWT and unaffected by PA, whereas GspDAH7PSCM was a less efficient catalyst than the CM domain of GspDAH7PSWT. AUC demonstrated that in solution an equilibrium occurs between the monomeric and tetrameric oligomeric states of GspDAH7PSDAH7PS. Chapter 4 summarises the findings of the thesis along with future directions of this research, combining the results obtained and expanding upon them. It is concluded that the catalytic regulatory CM domain supports both protein structure and allosteric regulation of GspDAH7PSWT

3-Deoxy-D-arabino heptulosonate 7-phosphate synthase (DAH7PS) catalyses the first step of the shikimate pathway, responsible for the biosynthesis of aromatic amino acids. This pathway is found in microorganisms, plants and apicomplexan parasites and its absence in mammals makes it a viable target for antimicrobial drug design. DAH7PS enzymes differ in the regulatory machinery that decorates the catalytic (β/α)8 barrel. Some DAH7PS enzymes are fused to chorismate mutase (CM), another enzyme in the shikimate pathway. This fusion protein is allosterically regulated by chorismate (CA) or prephenate (PA), the precursor of tyrosine and phenylalanine. It has been suggested that DAH7PS enzymes evolved these extensions to the core barrel for the sole purpose of regulation. Geobacillus sp DAH7PS (GspDAH7PSWT) is a thermophilic type Iβ DAH7PS enzyme with an N-terminal CM domain fused through a linker region. This thesis describes the functional characterisation work carried out on GspDAH7PSWT, in attempt to help determine how DAH7PS enzymes evolved such diverse methods of regulation. Chapter 2 describes the functional characterisation work carried out on the catalytic and regulatory domains of GspDAH7PSWT. The enzyme demonstrated both DAH7PS and CM activities with the DAH7PS domain determined to be metal dependent and most activated by Cd2+. PA completely inhibited the catalytic activity of GspDAH7PSWT, and AUC demonstrated an equilibrium exists between the dimeric and tetrameric quaternary states of the enzyme in solution. Chapter 3 describes the domain truncation of GspDAH7PSWT carried out at the linker region in order to obtain two separate protein domains, the catalytic domain lacking the N-terminal domain (GspDAH7PSDAH7PS) and the regulatory domain without the catalytic domain (GspDAH7PSCM). Both variants were fully characterised, and information obtained from each domain was compared to the respective catalytic and regulatory domains of the wild-type enzyme, which was also characterised. Like GspDAH7PSWT, GspDAH7PSDAH7PS showed greatest activation in the presence of Cd2+, with other metals having varying effects on activation rates and stability of the enzyme. Both truncated variants followed Michaelis-Menten kinetics where GspDAH7PSDAH7PS was found to be more active than GspDAH7PSWT and unaffected by PA, whereas GspDAH7PSCM was a less efficient catalyst than the CM domain of GspDAH7PSWT. AUC demonstrated that in solution an equilibrium occurs between the monomeric and tetrameric oligomeric states of GspDAH7PSDAH7PS. Chapter 4 summarises the findings of the thesis along with future directions of this research, combining the results obtained and expanding upon them. It is concluded that the catalytic regulatory CM domain supports both protein structure and allosteric regulation of GspDAH7PSWT

This dissertation concerns the model reduction of linear periodic descriptor systems both in continuous and discrete-time case. In this dissertation, mainly the projection based approaches are considered for model order reduction of linear periodic time varying descriptor systems. Krylov based projection method is used for large continuous-time periodic descriptor systems and balancing based projection technique is applied to large sparse discrete-time periodic descriptor systems to generate the reduce systems. For very large dimensional state space systems, both the techniques produce large dimensional solutions. Hence, a recycling technique is used in Krylov based projection methods which helps to compute low rank solutions of the state space systems and also accelerate the computational convergence. The outline of the proposed model order reduction procedure is given with more details. The accuracy and suitability of the proposed method is demonstrated through different examples of different orders. Model reduction techniques based on balance truncation require to solve matrix equations. For periodic time-varying descriptor systems, these matrix equations are projected generalized periodic Lyapunov equations and the solutions are also time-varying. The cyclic lifted representation of the periodic time-varying descriptor systems is considered in this dissertation and the resulting lifted projected Lyapunov equations are solved to achieve the periodic reachability and observability Gramians of the original periodic systems. The main advantage of this solution technique is that the cyclic structures of projected Lyapunov equations can handle the time-varying dimensions as well as the singularity of the period matrix pairs very easily. One can also exploit the theory of time-invariant systems for the control of periodic ones, provided that the results achieved can be easily re-interpreted in the periodic framework. Since the dimension of cyclic lifted system becomes very high for large dimensional periodic systems, one needs to solve the very large scale periodic Lyapunov equations which also generate very large dimensional solutions. Hence iterative techniques, which are the generalization and modification of alternating directions implicit (ADI) method and generalized Smith method, are implemented to obtain low rank Cholesky factors of the solutions of the periodic Lyapunov equations. Also the application of the solvers in balancing-based model reduction of discrete-time periodic descriptor systems is discussed. Numerical results are given to illustrate the effciency and accuracy of the proposed methods.

New techniques,languages and paradigms have facilitated the creation of distributed applications in several areas. Perhaps the most promising paradigm is the one that incorporates the mobile agent concept. A mobile agent in a large scale network can be viewed as a software program that travels through a heterogeneous network, crossing various security domains and executing autonomously in its destination. Mobile agent technology extends the traditional network communication model by including mobile processes, which can autonomously migrate to new remote servers. This basic idea results in numerous benefits including flexible, dynamic customisation of the behavior of clients and servers and robust interaction over unreliable networks. In spite of its advantages, widespread adoption of the mobile agent paradigm is being delayed due to various security concerns. Currently available mechanisms for reducing the security risks of this technology do not e±ciently cover all the existing threats. Due to the characteristics of the mobile agent paradigm and the threats to which it is exposed, security mechanisms must be designed to protect both agent hosting servers and agents. Protection to agent-hosting servers' security is a reasonably well researched issue, and many viable mechanisms have been developed to address it. Protecting agents is technically more challenging and solutions to do so are far less developed. The primary added complication is that, as an agent traverses multiple servers that are trusted to different degrees, the agent's owner has no control over the behaviors of the agent-hosting servers. Consequently the hosting servers can subvert the computation of the passing agent. Since it is infeasible to enforce the remote servers to enact the security policy that may prevent the server from corrupting agent's data, cryptographic mechanisms defined by the agent's owner may be one of the feasible solutions to protect agent's data.Hence the focus of this thesis is the development and deployment of cryptographic mechanisms for securing mobile agents in an open environment. Firstly, requirements for securing mobile agents' data are presented. For a sound mobile agent application, the data in an agent that is collected from each visiting server must be provided integrity. In some applications where servers intend to keep anonymous and will reveal their identities only under certain cir- cumstances, privacy is also necessitated. Aimed at these properties, four new schemes are designed to achieve different security levels: two schemes direct at preserving integrity for the agent's data, the other two focus on attaining data privacy. There are four new security techniques designed to support these new schemes. The first one is joint keys to discourage two servers from colluding to forge a victim server's signature. The second one is recoverable key commitment to enable detection of any illegal operation of hosting servers on an agent's data. The third one is conditionally anonymous digital signature schemes, utilising anonymous public-key certificates, to allow any server to digitally sign a document without leaking its identity. The fourth one is servers' pseudonyms that are analogues of identities, to enable servers to be recognised as legitimate servers while their identities remain unknown to anyone. Pseudonyms can be deanonymised with the assistance of authorities. Apart from these new techniques, other mechanisms such as hash chaining relationship and mandatory verification process are adopted in the new schemes. To enable the inter-operability of these mechanisms, a security architecture is therefore developed to integrate compatible techniques to provide a generic solution for securing an agent's data. The architecture can be used independently of the particular mobile agent application under consideration. It can be used for guiding and supporting developers in the analysis of security issues during the design and implementation of services and applications based on mobile agents technology.

In this paper an attempt will be made to offer a partial history of the three major languages of ancient Peru: Puquina, Aimara and Quechua, postulating their initial settlement from which they started spreading, until their encounter in the Central-Southern Andes during the Late Intermediate Period. It is proposed that the Incas passed through two stages of language substitution: the first from Puquina to Aimara and then from Aimara to Quechua. Linguistic, historical and archaeological evidence will be advanced to support the hypothesis. / En la presente contribución intentaremos bosquejar una parte de la historia de las tres lenguas mayores del antiguo Perú: el puquina, el aimara y el quechua, proponiendo los emplazamientos iniciales a partir de los cuales se expandieron hasta confluir en los Andes centro-sureños durante el Periodo Intermedio Tardío. Proponemos que los incas, a lo largo de su dominación, pasaron por dos etapas de mudanza idiomática: primeramente del puquina al aimara y, luego, del aimara al quechua. En apoyo de las hipótesis planteadas echamos mano de las evidencias de carácter lingüístico, histórico y arqueológico disponibles.

L’étude des vides avec flux est une étape primordiale afin de mieux comprendre la compactification en théorie des cordes ainsi que ses conséquences phénoménologiques. En présence de flux, l’espace interne ne peut plus être Calabi-Yau, mais admet tout de même une structure SU(3) qui devient un outil privilégié. Après une introduction aux notions géométriques nécessaires, cette thèse examine le rôle des flux dans la compactification supersymétrique sous différents angles. Nous considérons tout d’abord des troncations cohérentes de la supergravité IIA. Nous montrons alors que des condensats fermioniques peuvent aider à supporter des flux et générer une contribution positive à la constante cosmologique. Ces troncations admettent donc des vides de Sitter qu’il serait autrement très difficile d’obtenir, si ce n’est impossible. L’argument est tout d’abord employé avec des condensats de dilatini puis améliorer en suggérant un mécanisme pour générer des condensats de gravitini à partir d’instantons gravitationnels. Ensuite l’attention se tourne sur les branes et leur comportement sous T-dualité non abélienne. Nous calculons les configurations duales à certaines solutions avec D branes de la supergravité de type II, et examinons les flux ainsi que leurs charges afin d’identifier les branes après dualité. La solution supersymétrique avec brane D2 est étudiée plus en détails en vérifiant explicitement les équations sur les spineurs généralisés, puis en discutant de la possibilité d’une déformation massive. Le dernier chapitre fournit une construction systématique de structures SU(3) sur une large classe de variétés toriques compactes. Cette construction définit un fibré en sphère au-dessus d’une variété torique 2d quelconque, mais fonctionne tout aussi bien sur une base Kähler-Einstein / The study of flux vacua is a primordial step in the understanding of string compactifications and their phenomenological properties. In presence of flux the internal manifold ceases to be Calabi-Yau, but still admits an SU(3) structure which becomes thus the preferred framework. After introducing the relevant geometrical notions this thesis explores the role that fluxes play in supersymmetric compactification through several approaches. At first consistent truncations of type IIA supergravity are considered. It is shown that fermionic condensates can help support fluxes and generate a positive contribution to the cosmological constant. These truncations thus admit de Sitter vacua which are otherwise extremely difficult to get, if not impossible. The argument is initially performed with dilatini condensates and then improved by suggesting a mechanism to generate gravitini condensates from gravitational instantons. Then the focus shifts towards branes and their behavior under non abelian T-duality. The duals of several D-brane solutions of type II supergravity are computed and the branes are tracked down by investigating the fluxes and the charges they carry. The supersymmetric D2 brane is further studied by checking explicitly the generalized spinor equations and discussing the possibility of a massive deformation. The last chapter gives a systematic construction of SU(3) structures on a wide class of compact toric varieties. The construction defines a sphere bundle on an arbitrary two-dimensional toric variety but also works when the base is Kähler-Einstein

We present a new method for the computation of low rank approximations to the solution of large, sparse, stable Lyapunov equations. It is based on a generalization of the classical Smith method and profits by the usual low rank property of the right hand side matrix. The requirements of the method are moderate with respect to both computational cost and memory. Hence, it provides a possibility to tackle large scale control problems. Besides the efficient solution of the matrix equation itself, a thorough integration of the method into several control algorithms can improve their performance to a high degree. This is demonstrated for algorithms for model reduction and optimal control. Furthermore, we propose a heuristic for determining a set of suboptimal ADI shift parameters. This heuristic, which is based on a pair of Arnoldi processes, does not require any a priori knowledge on the spectrum of the coefficient matrix of the Lyapunov equation. Numerical experiments show the efficiency of the iterative scheme combined with the heuristic for the ADI parameters.