Abstract. We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity

the phase diagram of two-color QCD with the functional renormalization group. Universal aspects of deconfinement are illustrated mainly in the 2 + 1 dimensional SU(N) gauge theories with second order transition where many exact results from spin models can be exploited.

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by Utsaw Kumar The presence of inexpensive and powerful sensing and communication devices has made it possible to deploy large scale distributed systems for a variety of applications. Interactions among different components of such a system include communication of information and controlling dynamical processes, among others. Thus, it is important to blend ideas from information theory and control theory to address problems at the core of such distributed systems. This dissertation looks at communication scenarios, in which there are feedback channels available for enhancing communication and control performance over noisy forward links. Such feedback can considerably increase the reliability or reduce the complexity of coding schemes that approach capacity. Moreover, transmission schemes with feedback can be used to stabilize unstable plants over communication channels, where a sensor transmits the plant state information to

The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects related to dark energy. The first project analyzes a class of braneworld models in which multiple branes float in a five-dimensional anti-de Sitter bulk, while the second investigates a class of dark energy models from an effective field theory perspective. Investigations of models including extra dimensions have led to modifications of gravity involving a number of interesting features. In particular, the Randall-Sundrum model is well-known for achieving an amelioration of the hierarchy problem. However, the basic model relies on Minkowski branes and is subject to solar system constraints in the absence of a radion stabilization mechanism. We present a method by which a four-dimensional low-energy description can be obtained for braneworld scenarios, allowing for a number of generalizations to the original models. This method is applied to orbifolded and uncompactified N-brane models, deriving an effective four-dimensional action. The parameter space of this theory is constrained using observational evidence, and it is found that the generalizations do not weaken solar system constraints on the original model. Furthermore, we find that general

. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1-bit CS framework leads us to scenarios where it may be more appropriate to reduce bit-depth instead of sampling rate. We find

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is recoverable as the local maximum of a new maximisation criterion that generalises the K-means criterion. For this maximisation criterion results for asymptotic exact recovery for sparsity levels up toO(µ−1) and stable recovery for sparsity levels up to O(µ−2) as well as signal to noise ratios up to O( d

Caractérisation des problèmes conjoints de détection et d'estimation

ACKNOWLEDGMENTS I would like to give many thanks to Dr. Shengli Fu and Dr. Yan Huang as my advi-