Today, as computer systems are ubiquitous in our everyday life, there is no need to argue that their correctness is of capital importance. In order to prove (in a mathematical sense) that a given system satisfies a given property, formal methods have been introduced. They include concepts such as model checking and synthesis. Roughly speaking, when considering synthesis, we aim at building a model of the system which is correct by construction. In order to do so, models are mainly borrowed from game theory. During the last decades, there has been a shift from two-player qualitative zero-sum games (used to model antagonistic interactions between a system and its environment) to multiplayer quantitative games (used to model complex systems composed of several agents whose objectives are not necessarily antagonistic). In the latter setting, the solution concepts of interest include numerous equilibria, such as Nash equilibrium (NE) and subgame perfect equilibrium (SPE). While the existence of equilibria is widely studied, it is also well known that several equilibria may coexist in the same game. Nevertheless, some equilibria are more relevant than others. For example, if we consider a game in which each player aims at satisfying a given qualitative objective, it is possible to have both an equilibrium in which no player satisfies his objective and another one in which each player satisfies it. In this case one prefers the latter equilibrium which is more relevant.In this thesis, we focus on multiplayer turn-based games played on graphs either with qualitative or quantitative objectives. Our contributions are twofold: (i) we provide equilibria characterizations and (ii) we use these characterizations to solve decision problems related to the existence of relevant equilibria; and characterize their complexities. Firstly, we provide a characterization of a weaker notion of SPE (weak SPE) in multiplayer games with omega-regular objectives based on the payoff profiles which are realizable by a weak SPE. We then adopt another point of view by characterizing the outcomes of equilibria instead of their payoff profiles. In particular we focus on weak SPE outcome characterization. As for some kinds of games (e.g. multiplayer quantitative Reachability games), weak SPEs and SPEs are equivalent, this characterization is useful in order to study SPEs in these games.Secondly, we use those different equilibrium characterizations to provide the exact complexity classes of different decision problems related to the existence of relevant equilibria. We mainly focus on the constrained existence problem: if each player aims at maximizing his gain, this problem asks whether there exists an equilibrium such that each resulting player’s gain is greater than a threshold (one per player). We also consider variants of relevant equilibria based on the social welfare and the Pareto optimality of the players’ payoff. In this way, we prove the exact complexity classes for (i) the weak SPE constrained existence problem in multiplayer games with classical qualitative objectives such as Büchi, co-Büchi and Safety and (ii) the NE and SPE constrained existence problems (and variants) for qualitative and quantitative reachability games. In the latter case, the upper bounds on the required memory for such relevant equilibria are studied and proved to be finite. Studying memory requirements of strategies is important since with the synthesis process those strategies have to be implemented.Finally, we consider multiplayer, non zero-sum, turn-based timed games with qualitative Reachability objectives together with the concept of SPE. We prove that the SPE constrained existence problem is EXPTIME-complete for qualitative Reachability timed games. In order to obtain an EXPTIME algorithm, we proceed in different steps. In the first step, we prove that the game variant of the classical region graph is a good abstraction for the SPE constrained existence problem. In fact, we identify conditions on bisimulations under which the study of SPE in a given game can be reduced to the study of its quotient. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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In recent years, the Brigham Young University (BYU) Radio Astronomy Systems group has developed phased-array feeds and the data acquisition processing systems necessary to perform radio astronomy observations. This thesis describes the development and testing of a real-time digital beamforming system that reduces both the time required to process phased-array feed data and the disk space used to record this data compared to post-processing beamforming systems. A real-data experiment is also discussed in this thesis, which focuses on some of the data post-processing required for one of BYU's data acquisition systems.Radio-frequency interference mitigation techniques for phased-array feed radio astronomy have been studied for several years, but the effect that these techniques have on weak-signal detection is not well understood. This thesis provides analysis of a simulated weak-source observation for the Green Bank 20-meter telescope and BYU 19 element phasedarray feed with radio-frequency interference present. Interference mitigation techniques are shown to reduce the detectability of weak sources compared with the no interference case, but it is also shown that a weak source can be detected that would otherwise be masked by interference.

Composite cascode stages have been used in operational amplifier designs to achieve ultra-high gain at very low power. The flexibility and simplicity of the stage makes it an appealing choice for low power op-amp designs. Op-amp design using the composite cascode stage is often made more difficult through the lack of a design process. A design process to aid in the selection of the MOSFET dimensions is provided in this thesis. This process includes a table-based method for selection of the widths and lengths of the MOSFETs used in the composite cascode stage. Equations are also derived for the gain, bandwidth, and noise of the composite cascode stage with each of the devices operating in the various regions of inversion.

Mu Columbae is a prototypical weak-wind O star for which we have obtained a high-resolution X-ray spectrum with the Chandra LETG/ACIS instrument and a low-resolution spectrum with Suzaku. This allows us, for the first time, to investigate the role of X-rays on the wind structure in a bona fide weak-wind system and to determine whether there actually is a massive hot wind. The X-ray emission measure indicates that the outflow is an order of magnitude greater than that derived from UV lines and is commensurate with the nominal wind-luminosity relationship for O stars. Therefore, the "weak-wind problem"--identified from cool wind UV/optical spectra--is largely resolved by accounting for the hot wind seen in X-rays. From X-ray line profiles, Doppler shifts, and relative strengths, we find that this weak-wind star is typical of other late O dwarfs. The X-ray spectra do not suggest a magnetically confined plasma-the spectrum is soft and lines are broadened; Suzaku spectra confirm the lack of emission above 2 keV. Nor do the relative line shifts and widths suggest any wind decoupling by ions. The He-like triplets indicate that the bulk of the X-ray emission is formed rather close to the star, within five stellar radii. Our results challenge the idea that some OB stars are "weak-wind" stars that deviate from the standard wind-luminosity relationship. The wind is not weak, but it is hot and its bulk is only detectable in X-rays.

In-situ chain extension of polymers used in the formulation of artificial tears and mild gelation are techniques to increase the residence time of eye drops on cornea. In-situ chain extension also helps to control the stability of ophthalmic emulsions both in the bottle and in the tear film. In this work, the interaction of hydrophobically modified guar and tear proteins as a method of polymer chain extension and mild gelation has been evaluated. Guar and its derivatives have been found to be very effective for ophthalmic applications. The ideal guar gelation agent is the one that turns on the gelation upon introduction onto the eye and that gelation chemistry is biocompatible and biodegradable. Controllable gelation is desirable to have relatively low viscosity eye drops for easy application and the drops form weak gels in the eye. One recent strategy to cure dry eye disease is to include emulsions in lubricant eye drops. The idea is to supplement the natural lipid layer on the exterior surface of the tear film. Formulating artificial tear emulsions is relatively complicated and must satisfy conflicting criteria. Emulsion droplets should be stable over the period of their shelf life without creaming or aggregate formation. On the other hand, in the tear film the emulsion droplets must cream fast enough and deposit onto the water/lipid film interface on the exterior surface of the tear film. Thus, the emulsion must be stable but not too stable. Initially, science-based design rules were proposed for the development of future generations of lubricant eye drops. The effect of guar molecular weight and concentration on emulsion stability was evaluated. According to the concentration-molecular weight plot, polymer solutions can be divided into stable and unstable regions. They are defined based on the critical flocculation concentration (CFC) and critical viscosity concentration (C*). Inverted QCM-D has been proposed as a simple and fast method to define the stability of oil in water emulsion systems. This technique is a promising alternative for time consuming conventional creaming experiments. Low molecular weight guar can be optimized to out-perform high molecular weight guars without the complications of formulating eye drops with high molecular weight polymers. Hydroxypropyl guar samples were oxidized and modified with linear alkyl amines to give a series of hydrophobically modified guars (MGuars). Lysozyme and human serum albumin (HSA), natural tear proteins, are able to extend the effective chain length of MGuar through polymer/protein complex formation. Hydrophobic modifications on guar enable efficient interaction with proteins, through their mutual hydrophobic characteristics. The interaction of proteins with various alkyl chain lengths, degrees of substitution and a range of molecular weights were examined. Binding and rheological measurements were employed to evaluate the interactions efficiency. Our results suggest that higher degrees of substitution and longer alkyl chain length give higher viscosity values. Lowering molecular weight allows for higher concentration, while keeping the initial viscosity constant. Higher viscosity was achieved as the chain extension occurred. The influence of hydrophobic modification and molecular weight variation on lubrication behavior of MGuars has also been determined. Hydrophobic modification enhanced the lubrication between hydrophobic surfaces. However, saturation of hydrophobes with protein abolished the lubricity. / Thesis / Doctor of Philosophy (PhD)

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