Bilinear pairings on elliptic curves have many cryptographic applications such as identity based encryption, one-round three-party key agreement protocols, and short signature schemes. The elliptic curves which are suitable for pairing-based cryptography are called pairing friendly curves. The prime-order pairing friendly curves with embedding degrees k=3,4 and 6 were characterized by Miyaji, Nakabayashi and Takano. We study this characterization of MNT curves in details. We present explicit algorithms to obtain suitable curve parameters and to construct the corresponding elliptic curves. We also give a heuristic lower bound for the expected number of isogeny classes of MNT curves. Moreover, the related theoretical findings are compared with our experimental results.

Harnessing the power of DNA microarray technology requires the existence of analysis methods that accurately interpret microarray data. Current literature abounds with algorithms meant for the investigation of microarray data. However, there is need for an efficient approach that combines different techniques of microarray data analysis and provides a viable solution to dimensionality reduction of microarray data. Reducing the high dimensionality of microarray data is one approach in striving to better understand the information contained within the data. We propose a novel approach for dimensionality reduction of microarray data that effectively combines different techniques in the study of DNA microarrays. Our method, <strong><em>KAS</em></strong> (<em>kernel alignment with semidefinite embedding</em>), aids the visualization of microarray data in two dimensions and shows improvement over existing dimensionality reduction methods such as PCA, LLE and Isomap.

Bilinear pairings on elliptic curves have many cryptographic applications such as identity based encryption, one-round three-party key agreement protocols, and short signature schemes. The elliptic curves which are suitable for pairing-based cryptography are called pairing friendly curves. The prime-order pairing friendly curves with embedding degrees k=3,4 and 6 were characterized by Miyaji, Nakabayashi and Takano. We study this characterization of MNT curves in details. We present explicit algorithms to obtain suitable curve parameters and to construct the corresponding elliptic curves. We also give a heuristic lower bound for the expected number of isogeny classes of MNT curves. Moreover, the related theoretical findings are compared with our experimental results.

Harnessing the power of DNA microarray technology requires the existence of analysis methods that accurately interpret microarray data. Current literature abounds with algorithms meant for the investigation of microarray data. However, there is need for an efficient approach that combines different techniques of microarray data analysis and provides a viable solution to dimensionality reduction of microarray data. Reducing the high dimensionality of microarray data is one approach in striving to better understand the information contained within the data. We propose a novel approach for dimensionality reduction of microarray data that effectively combines different techniques in the study of DNA microarrays. Our method, <strong><em>KAS</em></strong> (<em>kernel alignment with semidefinite embedding</em>), aids the visualization of microarray data in two dimensions and shows improvement over existing dimensionality reduction methods such as PCA, LLE and Isomap.

Network virtualization can offer more flexibility and better manageability for the future Internet by allowing multiple heterogeneous virtual networks (VN) to coexist on a shared infrastructure provider (InP) network. A major challenge in this respect is the VN embedding problem that deals with the efficient mapping of virtual resources on InP network resources. Previous research focused on heuristic algorithms for the VN embedding problem assuming that the InP network remains operational at all times. In this thesis, we remove that assumption by formulating the survivable virtual network embedding (SVNE) problem and developing baseline policy heuristics and an efficient hybrid policy heuristic to solve it. The hybrid policy is based on a fast re-routing strategy and utilizes a pre-reserved quota for backup on each physical link. Our evaluation results show that our proposed heuristic for SVNE outperforms baseline heuristics in terms of long term business profit for the InP, acceptance ratio, bandwidth efficiency, and response time.

Noise and linearity are the two key concerns in RF transceiver systems. However, the impact of circuit topology and device technology on systems noise and linearity behaviors is poorly understood because of the complexity and diversity involved. There are two general questions that are addressed by the RF device and circuit designers: for a given device technology, how best to optimize the circuit topology; and for a given circuit topology, how best to optimize the device technology to improve the noise and linearity performance. In this dissertation, a systematic noise and linearity calculation method is proposed. This approach offers simple and analytical solutions to optimize the noise and linearity characteristics of integrated circuits. Supported by this approach, the physics of state-of-the-art SiGe HBT technology devices can be decoupled and studied. The corresponding impact on noise and linearity is investigated. New optimization methodologies for noise and linearity at both the device and circuit level are presented. In addition, this thesis demonstrates a technique that accurately extracts ac and noise parameters of devices/circuits in the millimeter-wave range. The extraction technique supports and verifies the device/circuit noise analysis from a measurement standpoint.

Novel micro patterning techniques have been developed for the patterning of volatile functional materials which cannot be conducted by conventional photolithography. First, in order to create micro patterns of volatile materials (such as bio-molecules and organic materials), micro-contact printing and shadow mask methods are investigated. A novel micro-contact printing technique was developed to generate micro patterns of volatile materials with variable size and density. A PDMS (Polydimethylsiloxane) stamp with 2-dimensional pyramidal tip arrays has been fabricated by anisotropic silicon etching and PDMS molding. The variable size of patterns was achieved by different external pressures on the PDMS stamp. A novel inking process was developed to enhance the uniformity and repeatability in micro-contact printing. The variable density of patterns could be obtained by alignment using x-y transitional stage and multiple stamping with a z-directional moving part. Second, for direct patterning of small molecule organic materials (e.g. pentacene), a novel shadow mask method has been developed with a simple and accurate alignment system. To make accurate dimensions of patterning windows, a silicon wafer was used for the shadow mask since a conventional semiconductor process gives a great advantage for accurate and repeatable fabrication processes. A sphere ball alignment system was developed for the accurate alignment between the shadow mask and the silicon substrate. In this alignment system, four matching pyramidal cavities were fabricated on each side of the shadow mask and silicon wafer substrate using an anisotropic silicon bulk etching. By placing four steel spheres in between the matching cavities, the self-alignment system could be demonstrated with 2-3um alignment accuracy in x-y directions. For OTFT (Organic thin film transistor) application, an organic semiconducting layer was directly deposited and patterned on the substrate using the developed shadow mask method. On the other hand, novel embedding techniques were developed for enabling conventional semiconductor processes including photolithography to be applied on the small substrate. The polymer embedding method was developed to provide an extended processing area as well as easy handling of the small substrate. As an application, post CMOS (Complementary metal-oxide-semiconductor) integration of a relatively large microstructure which might be even larger than the substrate was demonstrated on a VCO (Voltage-controlled oscillator) chip. In addition, micro patterning on the optical fiber was demonstrated by using a silicon wafer holder designed to surround and hold the optical fiber. The micro Fresnel lens could be successfully patterned and integrated on the optical fiber end.

We investigate the genericity of measure-preserving actions of the free group Fn, on possibly countably infinitely many generators, acting on a standard probability space. Specifically, we endow the space of all measure-preserving actions of Fn acting on a standard probability space with the weak topology and explore what properties may be verified on a comeager set in this topology. In this setting we show an analog of the classical Rokhlin Lemma. From this result we conclude that every action of Fn may be approximated by actions which factor through a finite group. Using this finite approximation we show the actions of Fn, which are rigid and hence fail to be mixing, are generic. Combined with a recent result of Kerr and Li, we obtain that a generic action of Fn is weak mixing but not mixing. We also show a generic action of Fn has sigma-entropy at most zero. With some additional work, we show the finite approximation result may be used to that show for any action of Fn, the crossed product embeds into the tracial ultraproduct of the hyperfinite II1 factor. We conclude by showing the finite approximation result may be transferred to a subspace of the space of all topological actions of Fn on the Cantor set. Within this class, we show the set of actions with sigma-entropy at most zero is generic.

Network virtualization can offer more flexibility and better manageability for the future Internet by allowing multiple heterogeneous virtual networks (VN) to coexist on a shared infrastructure provider (InP) network. A major challenge in this respect is the VN embedding problem that deals with the efficient mapping of virtual resources on InP network resources. Previous research focused on heuristic algorithms for the VN embedding problem assuming that the InP network remains operational at all times. In this thesis, we remove that assumption by formulating the survivable virtual network embedding (SVNE) problem and developing baseline policy heuristics and an efficient hybrid policy heuristic to solve it. The hybrid policy is based on a fast re-routing strategy and utilizes a pre-reserved quota for backup on each physical link. Our evaluation results show that our proposed heuristic for SVNE outperforms baseline heuristics in terms of long term business profit for the InP, acceptance ratio, bandwidth efficiency, and response time.

A main problem in machine learning is to predict the response variables of a test set given the training data and its corresponding response variables. A predictive model can perform satisfactorily only if the training data is an appropriate representative of the test data. This intuition is re???ected in the assumption that the training data and the test data are drawn from the same underlying distribution. However, the assumption may not be correct in many applications for various reasons. For example, gathering training data from the test population might not be easily possible, due to its expense or rareness. Or, factors like time, place, weather, etc can cause the difference in the distributions. I propose a method based on kernel distribution embedding and Hilbert Schmidt Independence Criteria (HSIC) to address this problem. The proposed method explores a new representation of the data in a new feature space with two properties: (i) the distributions of the training and the test data sets are as close as possible in the new feature space, (ii) the important structural information of the data is preserved. The algorithm can reduce the dimensionality of the data while it preserves the aforementioned properties and therefore it can be seen as a dimensionality reduction method as well. Our method has a closed-form solution and the experimental results on various data sets show that it works well in practice.