The thesis mainly studies two problems in Algebraic Geometry and Hodge Theory. The first problem deals with the geometric realizations of certain Hermitian symmetric domains as moduli space of algebraic varieties, notably the Abelian varieties and Calabi-Yau varieties. The study of the first problem occupies most of the thesis. In section 1.3; we study the second problem, namely, the L2 Higgs cohomology of polarized variation of Hodge structures over Hermitian symmetric domains. / Sheng Mao. / "December 2005." / Advisers: Shing-Tung Yau; Nai-Chung Conan Leung. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6442. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 108-113). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Model selection criteria frequently arise from constructing estimators of discrepancy measures used to assess the disparity between the data generating model and a fitted approximating model. The widely known Akaike information criterion (AIC) results from utilizing Kullback's directed divergence (KDD) as the targeted discrepancy. Under appropriate conditions, AIC serves as an asymptotically unbiased estimator of KDD. The directed divergence is an asymmetric measure of separation between two statistical models, meaning that an alternate directed divergence may be obtained by reversing the roles of the two models in the definition of the measure. The sum of the two directed divergences is Kullback's symmetric divergence (KSD). A comparison of the two directed divergences indicates an important distinction between the measures. When used to evaluate fitted approximating models that are improperly specified, the directed divergence which serves as the basis for AIC is more sensitive towards detecting overfitted models, whereas its counterpart is more sensitive towards detecting underfitted models. Since KSD combines the information in both measures, it functions as a gauge of model disparity which is arguably more balanced than either of its individual components. With this motivation, we propose three estimators of KSD for use as model selection criteria in the setting of generalized linear models: KICo, KICu, and QKIC. These statistics function as asymptotically unbiased estimators of KSD under different assumptions and frameworks. As with AIC, KICo and KICu are both justified for large-sample maximum likelihood settings; however, asymptotic unbiasedness holds under more general assumptions for KICo and KICu than for AIC. KICo serves as an asymptotically unbiased estimator of KSD in settings where the distribution of the response is misspecified. The asymptotic unbiasedness of KICu holds when the candidate model set includes underfitted models. QKIC is a modification of KICo. In the development of QKIC, the likelihood is replaced by the quasi-likelihood. QKIC can be used as a model selection tool when generalized estimating equations, a quasi-likelihood-based method, are used for parameter estimation. We examine the performance of KICo, KICu, and QKIC relative to other relevant criteria in simulation experiments. We also apply QKIC in a model selection problem for a randomized clinical trial investigating the effect of antidepressants on the temporal course of disability after stroke.

Block ciphers are widely used building blocks for secure communication systems; their purpose is to ensure confidentiality of the data exchanged through such systems, while achieving high performance. In this context, a variety of aspects must be taken into account. Primarily, they must be secure. The security of a block cipher is usually assessed by testing its resistance against known attacks. However as attacks may exist that are currently unknown, generic security proofs are also tried to be obtained. On the other hand, another attack methodology is also worth considering. Contrary to the others, it aims at the implementation of the algorithm rather than the cipher itself. It is known as side-channel analysis. Finally, performance of a block cipher in terms of throughput is very important as well. More than any other cryptographic primitive, block ciphers allow a tradeoff to be made between security and performance. In this thesis, contributions are given regarding these various topics. In the first part of the thesis, we deal with two particular types of attacks, namely the square attack and key schedule cryptanalysis. We also consider security proofs in the so-called Luby-Rackoff model, which deals with adversaries having unbounded computation capabilities. More precisely, we are interested in the Misty structure, when the round functions are assumed to be involutions. The second part of the thesis is devoted to design and implementation aspects. First, we present a fault attack on substitution-permutation networks, which requires as few as two faulty ciphertexts to retrieve the key. We also study the security of DeKaRT, which is an algorithm intended to protect smart cards against probing attacks. Finally we present the design of ICEBERG, a block cipher deliberately oriented towards good performance in hardware, and give an adequate analysis of its security.

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The goal of this thesis is to first give an overview of the modern approach, using the paper of A. Vershik and A. Okounkov, to inductively parametrizing all irreducible representations of the symmetric groups. This theory is then used to answer questions concerning to central projections in the group algebra. We index units first by partitions, and then by so called standard tableaux. We also present a new result and discuss future research exploring the connections between this theory and Quantum Information.

The goal of this thesis is to first give an overview of the modern approach, using the paper of A. Vershik and A. Okounkov, to inductively parametrizing all irreducible representations of the symmetric groups. This theory is then used to answer questions concerning to central projections in the group algebra. We index units first by partitions, and then by so called standard tableaux. We also present a new result and discuss future research exploring the connections between this theory and Quantum Information.

In this master thesis, the goal was to devise design patterns and a fabrication processfor manufacturing a 3-D rotationally symmetric converging-diverging cold gasmicronozzle in silicon.The report explains the theory of etching and the methods involved. The work beginswith calculations and simulations of the etching processes. The chosen etch techniqueutilizes so called microloading and reactive ion etching lag effects, which essentially arephenomena where the etch rate can be adjusted by breaking up mask features intosubpatterns, and the etch depth for a given recipe and time can be made to differlocally. The subpatterns consisted of very small rectangles and triangles withalternating concentration. Five different recipes for the reactive ion etching weretried, where the coil power, platen power, pressure, temperature and time wasvaried.Etch rates could be made to differ locally depending on the concentration ofsubpatterns within the mask feature. The etch rates were also affected by the recipeparameters such as coil power, platen power, and pressure. High coil and platenpower increased the etch rate, while high pressure reduced the etch rate. The platenpower also affected the surface roughness.A solution for reducing misalignment problems in the future for the fusion bondingprocess resulted in the proposed moiré patterns that were made to showmisalignments down to 0.2 μm.Through scanning electron microscopy, the Nozzle 5_4_2 was concluded to have themost rotationally symmetric cross section at both the throat and the outlet. It hasthroat diameter of 31.1 μm with a depth of 34.2 μm and an outlet diameter of146.4 μm with a depth of 113.2 μm

Owing to the fast progress of mobile communication technologies and the ubiquity of mobile networks, users can communicate with each other anytime and anywhere as long as they carry their smart and tiny mobile phones. This convenient communication service is quite popular and gradually joins in the people¡¦s life. Nevertheless, lots of attacks, such as the men-in-the-middle attacks and the replay attacks, are seriously threatening the security of the mobile networks and affecting the quality of the service simultaneously. Many security mechanisms for mobile communication have been introduced in the literature. Among these mechanisms, authentication plays a very important role in the entire mobile network system and acts as the first defense against the attackers since it can ensure the correctness of the identities of communication entities before they engage in any other communication activities. Therefore, to guarantee the quality of this advanced service, an efficient (especially, user efficient) and secure authentication scheme is urgently desired. In this thesis, we will propose a robust authentication scheme for mobile communication systems. Not only does the proposed scheme achieve mutual authentication, but also it greatly reduces the computation and communication cost of mobile users as compared with the existing authentication schemes.

A mixture experiment is an experiments in which the q-ingredients are nonnegative and subject to the simplex restriction on the (q-1)-dimentional probability simplex. In this work , we investigate the robust A-optimal designs for mixture experiments with uncertainty on the linear, quadratic models considered by Scheffe' (1958). In Chan (2000), a review on the optimal designs including A-optimal designs are presented for each of the Scheffe's linear and quadratic models. We will use these results to find the robust A-optimal design for the linear and quadratic models under some robust A-criteria. It is shown with the two types of robust A-criteria defined here, there exists a convex combination of the individual A-optimal designs for linear and quadratic models respectively to be robust A-optimal. In the end, we compare efficiencies of these optimal designs with respect to different A-criteria.