Adaptive resource allocation in wireless communication systems is crucial in order to support the diverse QoS needs of the services and optimize resource utilization. The design of resource allocation schemes should consider the service type for which it is intended. Moreover, due to feedback delay and channel estimation error, the Channel Quality Indicator (CQI) reported to the transmitter may not be a perfect measure of the channel quality and its use for resource allocation may severely degrade the systems performance. In this thesis, we study resource allocation and CQI reporting for wireless networks while taking the aforementioned factors into consideration. First, we consider resource allocation and adaptive modulation in uplink SC-FDMA systems. This is a combinatorial problem whose optimal solution is exponentially complex. We use canonical duality theory to derive a polynomial complexity resource allocation algorithm that provides a nearly optimal solution to the problem. Then, we focus on resource allocation for video streaming in wireless networks with time-varying interference. To this end, by using risk-sensitive control approach, we develop a cross-layer optimization framework that performs power control at the PHY/MAC layer and rate adaptation at the APPLICATION layer jointly and provides fairness among nodes. Finally, by using stochastic control and game theory, we design a robust best-M CQI reporting scheme for multi-carrier and multi-user systems which takes into account the impact of feedback delay and error in CQI computation. Performing resource allocation on the basis of the proposed CQI reporting can significantly improve the system performance.

Future cellular networks are expected to support extremely high data rates and user capacities. This thesis investigates the downlink of a wireless cellular system that takes advantage of multiple antennas at base stations and mobile stations, frequency reuse across all cells, and cooperation among base stations. We identify asynchronous interference resulting from multi-cell communication as a key challenge, prove the existence of a downlink/uplink duality in that case, and present a linear precoding scheme that exploits this duality. Since this result is not directly extendable to orthogonal frequency division multiplexing (OFDM), we propose a `hybrid' algorithm for two cooperating base stations, which combines linear and nonlinear precoding. This algorithm minimizes the sum mean squared error of the system and is extendable to OFDM. Finally, we consider the problem of user selection for multiuser precoding in OFDM-based systems. We extend an available single-cell user selection scheme to multiple cooperating cells.

This work is concerned with the characterization of certain classes of stochastic processes via duality formulae. In particular we consider reciprocal processes with jumps, a subject up to now neglected in the literature. In the first part we introduce a new formulation of a characterization of processes with independent increments. This characterization is based on a duality formula satisfied by processes with infinitely divisible increments, in particular Lévy processes, which is well known in Malliavin calculus. We obtain two new methods to prove this duality formula, which are not based on the chaos decomposition of the space of square-integrable function- als. One of these methods uses a formula of partial integration that characterizes infinitely divisible random vectors. In this context, our characterization is a generalization of Stein’s lemma for Gaussian random variables and Chen’s lemma for Poisson random variables. The generality of our approach permits us to derive a characterization of infinitely divisible random measures. The second part of this work focuses on the study of the reciprocal classes of Markov processes with and without jumps and their characterization. We start with a resume of already existing results concerning the reciprocal classes of Brownian diffusions as solutions of duality formulae. As a new contribution, we show that the duality formula satisfied by elements of the reciprocal class of a Brownian diffusion has a physical interpretation as a stochastic Newton equation of motion. Thus we are able to connect the results of characterizations via duality formulae with the theory of stochastic mechanics by our interpretation, and to stochastic optimal control theory by the mathematical approach. As an application we are able to prove an invariance property of the reciprocal class of a Brownian diffusion under time reversal. In the context of pure jump processes we derive the following new results. We describe the reciprocal classes of Markov counting processes, also called unit jump processes, and obtain a characterization of the associated reciprocal class via a duality formula. This formula contains as key terms a stochastic derivative, a compensated stochastic integral and an invariant of the reciprocal class. Moreover we present an interpretation of the characterization of a reciprocal class in the context of stochastic optimal control of unit jump processes. As a further application we show that the reciprocal class of a Markov counting process has an invariance property under time reversal. Some of these results are extendable to the setting of pure jump processes, that is, we admit different jump-sizes. In particular, we show that the reciprocal classes of Markov jump processes can be compared using reciprocal invariants. A characterization of the reciprocal class of compound Poisson processes via a duality formula is possible under the assumption that the jump-sizes of the process are incommensurable. / Diese Arbeit befasst sich mit der Charakterisierung von Klassen stochastischer Prozesse durch Dualitätsformeln. Es wird insbesondere der in der Literatur bisher unbehandelte Fall reziproker Klassen stochastischer Prozesse mit Sprungen untersucht. Im ersten Teil stellen wir eine neue Formulierung einer Charakterisierung von Prozessen mit unabhängigen Zuwächsen vor. Diese basiert auf der aus dem Malliavinkalkül bekannten Dualitätsformel für Prozesse mit unendlich oft teilbaren Zuwächsen. Wir präsentieren zusätzlich zwei neue Beweismethoden dieser Dualitätsformel, die nicht auf der Chaoszerlegung des Raumes quadratintegrabler Funktionale beruhen. Eine dieser Methoden basiert auf einer partiellen Integrationsformel fur unendlich oft teilbare Zufallsvektoren. In diesem Rahmen ist unsere Charakterisierung eine Verallgemeinerung des Lemma fur Gaußsche Zufallsvariablen von Stein und des Lemma fur Zufallsvariablen mit Poissonverteilung von Chen. Die Allgemeinheit dieser Methode erlaubt uns durch einen ähnlichen Zugang die Charakterisierung unendlich oft teilbarer Zufallsmaße. Im zweiten Teil der Arbeit konzentrieren wir uns auf die Charakterisierung reziproker Klassen ausgewählter Markovprozesse durch Dualitätsformeln. Wir beginnen mit einer Zusammenfassung bereits existierender Ergebnisse zu den reziproken Klassen Brownscher Bewegungen mit Drift. Es ist uns möglich die Charakterisierung solcher reziproken Klassen durch eine Dualitätsformel physikalisch umzudeuten in eine Newtonsche Gleichung. Damit gelingt uns ein Brückenschlag zwischen derartigen Charakterisierungsergebnissen und der Theorie stochastischer Mechanik durch den Interpretationsansatz, sowie der Theorie stochastischer optimaler Steuerung durch den mathematischen Ansatz. Unter Verwendung der Charakterisierung reziproker Klassen durch Dualitätsformeln beweisen wir weiterhin eine Invarianzeigenschaft der reziproken Klasse Browscher Bewegungen mit Drift unter Zeitumkehrung. Es gelingt uns weiterhin neue Resultate im Rahmen reiner Sprungprozesse zu beweisen. Wir beschreiben reziproke Klassen Markovscher Zählprozesse, d.h. Sprungprozesse mit Sprunghöhe eins, und erhalten eine Charakterisierung der reziproken Klasse vermöge einer Dualitätsformel. Diese beinhaltet als Schlüsselterme eine stochastische Ableitung nach den Sprungzeiten, ein kompensiertes stochastisches Integral und eine Invariante der reziproken Klasse. Wir präsentieren außerdem eine Interpretation der Charakterisierung einer reziproken Klasse im Rahmen der stochastischen Steuerungstheorie. Als weitere Anwendung beweisen wir eine Invarianzeigenschaft der reziproken Klasse Markovscher Zählprozesse unter Zeitumkehrung. Einige dieser Ergebnisse werden fur reine Sprungprozesse mit unterschiedlichen Sprunghöhen verallgemeinert. Insbesondere zeigen wir, dass die reziproken Klassen Markovscher Sprungprozesse vermöge reziproker Invarianten unterschieden werden können. Eine Charakterisierung der reziproken Klasse zusammengesetzter Poissonprozesse durch eine Dualitätsformel gelingt unter der Annahme inkommensurabler Sprunghöhen.

Some financial problems as minimizing the shortfall risk when hedging in incomplete markets lead to problems belonging to test theory. This paper considers a generalization of the Neyman-Pearson lemma. With methods of convex duality we deduce the structure of an optimal randomized test when testing a compound hypothesis against a simple alternative. We give necessary and sufficient optimality conditions for the problem.

Traditionellt har HR-arbetet främst varit fokuserat på administrativa uppgifter och inte ansetts vara tillräckligt effektivt och värdeskapande. För att HR-arbetet ska bli mer strategiskt behöver funktionen organiseras så att den tillgodoser dessa behov (Boglind et al, 2013). Vi menar att HR-funktionens relation till ledare och linjechefer är avgörande för hur framgångsrikt deras arbete blir. Syftet med detta arbete är därför att undersöka hur chefer uppfattar HR-funktionens förändrade roll och vilken typ av stöd de förväntar sig av den. Vi vill också undersöka om uppfattningen av HR-funktionen skiljer sig åt beroende på hur den är organiserad. Undersökningen är baserad på en multipel fallstudie utförd på Falu och Avesta kommun. Totalt har tretton djupintervjuer genomförts, där fem personer representerar HR-avdelningarna och åtta personer representerar linjecheferna. Falu kommun började genomföra en HR-transformation vid årsskiftet 2013/2014, Avesta kommun har inte genomfört en HR-transformation utan har funktionen uppdelad i två team. Av empirin framkommer att linjecheferna i båda kommunerna har en ganska vag uppfattning om HR-funktionens organisation och trots de strukturella skillnaderna mellan kommunerna efterfrågar linjecheferna något mer. I Avesta är samtliga respondenter överens om att en samsyn kring HR-funktionens arbetsuppgifter inte finns på grund av att en tydlig strategi för HR-funktionen saknas. Cheferna i Avesta efterfrågar ett arbete med personalfrågor från grunden samt ett mer strategiskt arbete. I Falun visar empirin att linjechefer och HR-personer har olika åsikter kring huruvida det finns en samsyn. Även om flera linjechefer i Falun anser att HR-funktionen fungerar bättre efter transformationen efterfrågar samtliga en kontakt med en specifik HR-person istället för att kontakta ett HR-center. Trots att de organisationer vi studerat har HR-funktioner som skiljer sig åt i storlek och struktur kan vi konstatera många likheter. Vi drar därför slutsatsen att de problem som linjecheferna beskriver inte är relaterade till HR-avdelningens organisering, utan snarare kan kopplas till en obalans i HR-arbetets inneboende dualitet som uppstått i och med ett mer strategiskt fokus. Vi anser att båda kommunernas HR-funktioner bör ha en tydlig och kontinuerlig dialog med linjecheferna för att maximera värdeskapandet dem emellan. Sammanfattningsvis menar vi att kommunerna bör lägga fokus på att identifiera vilka aspekter av personalarbetet som är värdefulla och unika för just deras organisation samt arbeta strategiskt utifrån dessa. / Traditionally, HR work has not been considered sufficiently effective and value creating because of its main focus on administrative tasks. For HR work to become more strategic the function has to organize in a way that meet the new needs (Boglind et al, 2013). We believe that the success of the HR function depends on their relationships to leaders and line managers. The purpose of this essay is to examine how line managers perceive the changing role of the HR function and what kind of support they expect from them. We also want to investigate whether the perception of the HR function is related to how it’s organized. The survey is based on a multiple case study conducted in Falu and Avesta municipality. A total of thirteen in-depth interviews were conducted where five respondents represented the HR departments and eight respondents represented the line managers. Falun municipality began implementing an HR transformation at the turn of 2013/2014. Avesta municipality has an HR function divided into two teams and hasn’t performed an HR transformation. Our empirical data reveals that line managers in both municipalities have a rather vague idea of the HR function and its organization. Despite structural differences between the municipalities line managers in both organizations demand something more. All respondents in Avesta municipality agree to a lack of consensus regarding the duties of the HR function, due to an absence of a distinct strategy. The line managers of Avesta requests a more fundamental and strategic HR management. Empirical data from Falun municipality reveals that line managers and HR respondents disagree on whether there is a consensus regarding the tasks of the HR function. Although several line managers in Falun mentions that the HR function have improved from the transformation, they still prefer close relations to a specific HR person over contacting the HR call center. Although the studied HR functions differ in size and structure, we observe many similarities. We therefore conclude that the difficulties described by line managers isn’t related to the structure of the HR function, but instead relates to an imbalance in the immanent duality of the HR work that emerge from a more strategic focus. We believe that the HR function in both municipalities should have a consistent and continuous dialogue with line managers to maximize the exchange of value. In conclusion we suggest that the municipalities should focus on identifying the aspects of HR work that is most valuable and unique to their organization and build their strategies from these.

This dissertation studies a class of path-dependent stochastic control problems with applications to Finance. In particular, we solve the open problem of the continuous time expected utility maximization with addictive consumption habit formation in incomplete markets under two independent scenarios. In the first project, we study the continuous time utility optimization problem with consumption habit formation in general incomplete semimartingale financial markets. Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into an abstract time-separable utility maximization problem with a shadow random endowment on the product space. We establish existence and uniqueness of the optimal solution using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living. We also provide market independent sufficient conditions both on the stochastic discounting processes of the habit formation process and on the utility function for the well-posedness of our original optimization problem. Under the same assumptions, we can carefully modify the classical proofs in the approach of convex duality analysis when the auxiliary dual process is not necessarily integrable. In the second project, we examine an example of the optimal investment and consumption problem with both habit-formation and partial observations in incomplete markets driven by It\^{o} processes. The individual investor develops addictive consumption habits gradually while only observing the market stock prices but not the instantaneous rates of return, which follow an Ornstein-Uhlenbeck process. Applying the Kalman-Bucy filtering theorem and Dynamic Programming arguments, we solve the associated Hamilton-Jacobi-Bellman(HJB) equation fully explicitly for this path dependent stochastic control problem in the case of power utility preferences. We provide the optimal investment and consumption policy in explicit feedback form using rigorous verification arguments. / text

The future smart grid is envisioned as a large scale cyber-physical system encompassing advanced power, computing, communications and control technologies. This work provides comprehensive accounts of the application with optimization methods, probability theory, commitment and dispatching technologies for addressing open problems in three emerging areas that pertain to the smart grid: unit commitment, service restoration problems in microgrid systems, and charging services for the plug-in hybrid electric vehicle (PHEV) markets. The work on the short-term scheduling problem in renewable-powered islanded microgrids is to determine the least-cost unit commitment (UC) and the associated dispatch, while meeting electricity load, environmental and system operating requirements. A novel probability-based concept, {\em probability of self-sufficiency}, is introduced to indicate the probability that the microgrid is capable of meeting local demand in a self-sufficient manner. Furthermore, we make the first attempt in approaching the mixed-integer UC problem from a convex optimization perspective, which leads to an analytical closed-form characterization of the optimal commitment and dispatch solutions. The extended research of the renewable-powered microgrid in the connection mode is the second part of this work. In this situation, the role of microgrid is changed to be either an electricity provider selling energy to the main grid or a consumer purchasing energy from the main grid. This interaction with the main grid completes work on the scheduling schemes. Third, a microgrid should be connected with the main grid most of the time. However, when a blackout of the main grid occurs, how to guarantee reliability in a microgrid as much as possible becomes an immediate question, which motivates us to investigate the service restoration in a microgrid, driven islanded by an unscheduled breakdown from the main grid. The objective is to determine the maximum of the expected restorative loads by choosing the best arrangement of the power network configurations immediately from the beginning of the breakdown all the way to the end of the island mode. Lastly, the work investigating the pricing strategy in future PHEV markets considers a monopoly market with two typical service classes. The unique characteristics of battery charging result in a piecewise linear quality of service model. Resorting to the concept of subdifferential, some theoretical results, including the existence and uniqueness of the subscriber equilibrium as well as the convergence of the corresponding subscriber dynamics are established. In the course of developing revenue-maximizing pricing strategies for both service classes, a general tradeoff has been identi ed between monetization and customer acquisition. / Graduate

In this thesis we focus on multiscale and multiphysics problems. We derive a posteriori error estimates for a one way coupled multiphysics problem, using the dual weighted residual method. Such estimates can be used to drive local mesh refinement in adaptive algorithms, in order to efficiently obtain good accuracy in a desired goal quantity, which we demonstrate numerically. Furthermore we prove existence and uniqueness of finite element solutions for a two way coupled multiphysics problem. The possibility of deriving dual weighted a posteriori error estimates for two way coupled problems is also addressed. For a two way coupled linear problem, we show numerically that unless the coupling of the equations is to strong the propagation of errors between the solvers goes to zero. We also apply a variational multiscale method to both an elliptic and a hyperbolic problem that exhibits multiscale features. The method is based on numerical solutions of decoupled local fine scale problems on patches. For the elliptic problem we derive an a posteriori error estimate and use an adaptive algorithm to automatically tune the resolution and patch size of the local problems. For the hyperbolic problem we demonstrate the importance of how to construct the patches of the local problems, by numerically comparing the results obtained for symmetric and directed patches.

À la fin du siècle dernier, lorsque les mouvements féministes secouèrent les milieux intellectuels, les questionnements sur le genre se sont retrouvés au cœur des débats en sciences sociales et en archéologie. L’archéologie maya n’échappa pas à la règle et les femmes, jusque là restées dans l’ombre, retrouvèrent une visibilité. Ce mémoire a pour objectif de dégager la complexité des constructions sociales, symboliques et idéologiques de genre au sein des couches sociales les plus élevées de la société maya classique, en regroupant et en confrontant une bonne partie des données archéologiques, iconographiques, épigraphiques mais aussi ethnohistoriques répertoriées dans la littérature. Nos résultats défendent l’idée selon laquelle les relations et les identités de genres au sein des élites dirigeantes, mais également non dirigeantes, étaient construites autour d'un principe fondamental de la pensée maya : la dualité complémentaire. / At the turn of the century, as feminist movements shook the foundations of academia, questions of gender were pushed to the fore front of debates in social sciences and archaeology. Mayan archaeology has followed this trend, shedding light on the previously neglected role of women in these societies. The goal of this thesis is to capture the complexity underlining the social, symbolic and ideological construction of gender in the upper echelons of classical Mayan society. This objective is pursued by compiling and confronting archaeological, iconographical, epigraphic and ethnohistorical data found in the literature. Our results support the thesis according to which relations and, identities pertaining to gender among the Mayan ruling and non-ruling elites were constructed along the lines of a fundamental principal of Mayan thought and culture: complimentary duality.

<p>The study concentrates on a particular type of state intervention in social policy. It considers whether policy reforms and subsequent provision of information with regards to the issue of parental leave and part-time work arrangements, makes an impact on gender equity in the labour market (Del Boca, 2002 / Naldini &amp / Saraceno, 2008). Giddens&rsquo / theory of structuration is the conceptual framework from which this study approaches these questions. It is thus held that agents (in this instance, women) are constrained by structures (labour policy framework and institutionalised labour practices) to achieve specific social goals. And further: that the apparent lack of power on the part of agents requires intervention on the part of the state apparatus to correct the failure (or inability) of the labour market to deliver the social justice as aspired to in the cited European Employment Strategy, as well as fostering economic efficiency (Barr, 1992). I further contend that not only are agents constrained by structural properties, but that institutional reform (in the form of labour policy reform) is constrained by the human action1 of the management of firms and enterprises as economic agents within the policy framework.</p>