In the first part of this dissertation, we show how to execute range queries securely and efficiently on encrypted databases in the cloud. Current methods provide either security or efficiency, but not both. Many schemes even reveal the ordering of encrypted tuples, which, as we show, allows adversaries to estimate plaintext values accurately.

We present the R̂-tree, a hierarchical encrypted index that may be securely placed in the cloud, and searched efficiently. It is based on a mechanism we design for encrypted halfspace range queries in Rd, using Asymmetric Scalar-product Preserving Encryption. Data owners can tune the R̂-tree parameters to achieve desired security-efficiency tradeoffs. We also present extensive experiments to evaluate R̂-tree performance. Our results show that R̂-tree queries are efficient on encrypted databases, and reveal far less information than competing methods. In the second part, we propose a new query obfuscation scheme to protect user privacy in key word search. Text-based search queries reveal user intent to the search engine, compromising privacy. Topical Intent Obfuscation (TIO) is a promising new approach to preserving user privacy. TIO masks topical intent by mixing real user queries with dummy queries matching various different topics. Dummy queries are generated using a Dummy Query Generation Algorithm (DGA).

We demonstrate various shortcomings in current TIO schemes, and show how to correct them. Current schemes assume that DGA details are unknown to the adversary. We argue that this is a flawed assumption, and show how DGA details can be used to construct efficient attacks on TIO schemes, using an iterative DGA as an example. Our extensive experiments on real data sets show that our attacks can flag up to 80% of dummy queries. We also propose HDGA, a new DGA that we prove to be immune to the attacks based on DGA semantics that we describe.

Tetracyclines are a group of natural products produced by soil-borne Actinobacteria. Their broad-spectrum biological activities such as antibiotic, anticancer, and novel activity against tetracycline resistant bacteria are attributed to their signature linearly fused four ring structure. However, the extensive use of tetracyclines during the last sixty years has led to emergence of resistance mechanisms among microorganism communities, resulting in dramatically decreased effectiveness of tetracyclines as first line antibiotic agents. Therefore, new generation of tetracyclines is highly demanded to overcome current resistance mechanisms. To obtain new generation of tetracyclines, fundamental understanding of tetracycline biosynthesis and establishment of robust manipulation platform are required. The biosynthetic pathways of three natural tetracycline, including oxytetracycline, SF2575, and dactylocycline, were investigated by using genetic, biochemical, and protein structure based analysis.

Oxytetracycline represents an important example of natural tetracyclines featuring a signature C5 hydroxyl group. Unveiling of oxytetracycline biosynthetic pathway will establish a cornerstone to understand and engineer tetracycline biosynthesis. After a decade investigations, the biosynthetic pathway of a key intermediate anhydrotetracycline has been revealed; however, the longstanding missing link involved in the final transformations from anhydrotetracycline to oxytetracycline remains elusive since the first discovery of oxytetracycline in 1950. Two redox enzymes OxyS and OxyR were unravelled to catalyze the mysterious final transformations by using flavin adenine dinucleotide (FAD) and F420 as coenzymes respectively. The protein structure of OxyS has been determined and provided valuable insights into the enzymology unique to tetracycline biosynthesis.

SF2575 stands out from tetracycline family due to its fully substituted tetracycline aglycone and novel potent anticancer activity. Cascade transformations are catalyzed by a set of new tetracycline tailoring enzymes involved in SF2575 biosynthesis, including four methyltransferases, a glycosyltransferase, and three redox enzymes. To decipher the biosynthesis and understand the chemical reactions catalyzed by these dedicated tailoring enzymes, the corresponding encoding genes were inactivated in heterologous expression host Streptomyces lividans K4-114. The functions of the tailoring enzymes were elucidated by isolation and structural characterization of intermediates accumulated from the corresponding gene-inactivation mutants. The production of fourteen tetracycline analogs from ten mutants led to functional assignment of SF2575 tailoring enzymes and elucidation of SF2575 biosynthetic pathway. Most interestingly the redundancy of the methyltransferase SsfM3 demonstrates an evolutionary event in which combinatorial biosynthesis strategy has been employed by nature to generate novel tetracycline compounds.

Dactylocycline offers us the third example of natural tetracycline with novel activity against tetracycline resistant bacteria. This promising activity is due to a unique hydroxylamino sugar modification at C6 hydroxyl group of dactylocyclinone which shows cross resistance with tetracycline. Identification of dactylocycline biosynthetic gene cluster led to a proposed biosynthetic pathway and expanded enzymatic tools to synthesize both dactylocycline aglycone and the hydroxylamino sugar moiety. To validate this gene cluster, the dac gene cluster was heterologously expressed in Streptomyces lividans K4-114 resulting in the production of dactylocyclinone.

Given three natural tetracycline biosynthetic pathways and an accommodating heterologous host, we are able to generate new tetracycline analogs by using combinatorial biosynthesis approaches.

Graphene's planar structure and unique low energy spectrum make it an intriguing material to study its electronic properties. Recent progresses in stacking graphene (G) on high quality hexagonal boron nitride (hBN) greatly advanced the electronic performance of graphene devices, pproaching the intrinsic properties of graphene. This thesis reports transport studies of graphene on hBN, including graphene/hBN moiré superlattice at small rotation angle and ballistic transport in short/wide encapsulated BN/G/BN structures.

Chapter 1 will introduce the basic properties of graphene, including the unique low energy electronic spectrum and the unconventional integer quantum Hall effect. The concept of Berry's phase and pseudospin winding number and their connection to the quantum Hall effect are also discussed. Chapter 2 reviews the properties of graphene on hBN, especially the long wavelength moiré superlattice at small rotation angle which modulates graphene's low energy spectrum. It also discusses the Hofstadter's butterfly and its realization in the graphene/hBN heterostructure.

Chapter 3 addresses some of the essential techniques used to fabricate graphene/hBN devices measured in this thesis, including the layer stacking techniques and fabrication of graphene field effect transistors.

Chapter 4 reports the measurements of Hofstadter's butterfly spectrum focusing at the large doping region where the Fermi level is above the secondary Dirac points generated by the moiré superlattice. At large electron doping, we observed a novel π phase shift in the magneto-oscillations. At large hole doping, inversion symmetry breaking generates a distinct hexagonal pattern.

Chapter 5 discusses measurements of short BN/G/BN cavities. The high quality BN/G/BN devices exhibit ballistic transport behavior - Fabry-Pérot oscillations.The effects of magnetic field on the system are also investigated, showing signatures of "pseudodiffussive" transport at the charge neutrality point for finite fields.

This dissertation studies first a distributed algorithm to solve general convex optimization

problems and then designs distributed algorithms to solve special optimization problems

related to a system of linear equations.

First, a wider selection of step sizes is explored for the distributed subgradient

algorithm for multi-agent optimization problems with time-varying and balanced commu-

nication topologies. The square summable requirement of the step sizes commonly adopted

in the literature is removed. The step sizes are only required to be positive, vanishing

and non-summable, which provides the possibility for better convergence rates. Both un-

constrained and constrained optimization problems are considered. It is proved that the

agents’ estimates reach a consensus and converge to the minimizer of the global objective

function with the more general choice of step sizes. The best convergence rate is shown to

be the reciprocal of the square root of iterations for the best record of the function value at

the average of the agents’ estimates for the unconstrained case with the wider selection of

step sizes.

Then we design a distributed algorithm for a special optimization problem to find

the solution of the linear equations Ax = b with minimum energy, i.e. the minimum weighted

norm associated with the weighted inner product. We first prove that for a special case

when the norm is two-norm, the algorithm can make multiple agents reach the minimum

two-norm solution of the global linear equations Ax = b if the agents are initialized at

the minimum two-norm solutions of their local equations. We then prove that if there are

bounded initialization errors, the final convergence of the algorithm is also bounded away

from the minimum two-norm solution of the global linear equations. Next, we prove the

case with the two-norm replaced with a weighted norm associated with the weighted inner

product.

Next, we solve a system of linear equations Ax = b in a distributed way motivated

by a special subgradient algorithm. A discrete-time distributed algorithm to solve a system

of linear equations Ax = b is proposed. The algorithm can find a solution of Ax = b from

arbitrary initializations at a geometric rate when Ax = b has either unique or multiple

solutions. When Ax = b has a unique solution, the geometric convergence rate of the

algorithm is proved by analyzing the mixed norm of homogeneous M-Fejer type mappings

from the subgradient update. Then when Ax = b has multiple solutions, the geometric

convergence rate is proved through orthogonal decompositions of the agents’ estimates onto

the row space and null space of A, and the relationship between the initializations and the

final convergence point is also specified. Quantitative upper bounds of the convergence rate

for two special cases are given.

Finally, we investigate communication efficient distributed algorithm to solve Ax =

b for matrices with a similar sparsity structure to that of the Laplacian matrix of communi-

cation topology. We propose the algorithm based on gradient descent method with constant

step size and prove the convergence in finite time or at a linear rate. We also provide a way

to select the step sizes in a distributed way.

Human are interpolating the visual world with very rich understanding. For example, when observing the world through eyes, we not only understand the high level semantic meaning of each region/pixel, more importantly, we also understand the 3D properties like how far away each object is and how the 3D shape of each object is in order to do interaction with the world. In the field of computer vision, however, visual understanding are separated into multiple tasks, e.g. segmentation, 3D reconstruction or object detection etc., due to its high complexity. However, this induces the problem that the results from different strategies are lack of compatibility among different tasks. For example, semantic object detection can not take care of the 3D occlusion regions, while 3D reconstruction does not consider overall semantic context. Thus, in order to have good visual understanding, it is critical to joint understand different tasks while maintaining their compatibility.

Luckily, thanks to the raising technique of deep learning, (a.k.a. convolutional neural network (CNN)), which dramatically beats the other traditional strategies in many visual tasks based on hierarchical learned features with a nearly single framework, we are able to unify different understandings in a more compact and efficient way by designing reasonable output and interaction terms.

However, CNN is not a magic key of solving all problems, and one obvious limitation of CNN is that it contains arbitrarily selected convolutional kernel size and layers, yielding non-adaptive receptive fields to match the variance of object scales. In addition, it is not strait-forward to add arbitrary connections inside each layer based on intuition. Thus, we further embed the conditional random field (CRF) into the system in order to compensate the deficiency in order to unify different cues and perform multiple tasks simultaneously.

In this thesis, we prove the concept through estimating multiple tasks jointly including joint part and object segmentation, joint segmentation and geometry estimation etc. We first show that we can fit deep convolutional network into many different tasks to acquire superior performance compare to traditional shallow features. Secondly, by unifying different tasks with our designed compatibility constrains, we make different tasks mutually regularized and beneficial. Finally, to evaluate the results, we perform our experiments over the standard evaluating benchmarks like PASCAL for segmentation and the NYU v2 dataset for depth estimation. Last but not the least, we not only apply the existing metrics to show the performance gain from our design, but also introduce reasonable new metrics in order to better show the aspect that improved.

Xylella fastidiosa (Xf), a xylem-limited fastidious bacterium, is the causal agent of Pierce's Disease (PD) of grapevine. Xf has a very broad host range, including grapevine, citrus, almond, oleander, peach and maple. PD is a lethal disease of grapevine and understanding the disease from the perspective of molecular interactions between Xf and grapevine is very important. Pathogens often encounter reactive oxygen species (ROS) from a variety of sources during the infection process. These ROS can be toxic to the pathogen and correspondingly, the pathogen has evolved several tightly regulated mechanisms to cope with this stress. OxyR is a redox-responsive transcription factor that regulates expression of antioxidant enzymes. Interestingly. OxyR is the only known oxidative stress regulator in the Xf genome leading us to speculate that it plays a vital role in adaptation to the host environment. We constructed an oxyR mutant and found it was significantly more sensitive to H₂O₂ than wild type Xf. In addition, we found that the Xf oxyR mutant was reduced in surface attachment, cell-cell aggregation and mature biofilm formation. In planta tests indicated that the oxyR mutant was significantly compromised in the ability to colonize the host xylem, but, interestingly, no difference in virulence was observed when compared with wild type Xf.

The Type II secretion system (T2SS) is an important protein secretion system in plant pathogenic bacteria. The repertoire of proteins secreted by this system are largely involved in nutrition and include plant cell wall degrading enzymes (CWDEs). Xf employs CWDEs to degrade xylem pit membranes to facilitate systematic movement within the xylem. The majority of the demonstrated and putative CWDEs are predicted to be secreted by the T2SS. By knocking out a T2SS structure gene xpsE, which encodes a putative ATPase that provides the energy that drives the T2SS, I demonstrated that Xf requires XpsE for full virulence and establishment in the xylem vessels indicating that the T2SS is an important factor employed during the infection process.

This dissertation mainly addresses the generic types of ageostrophic instability in general continuously differentiable, interior, horizontal and vertical shear flows without special "edges" (vertical, side or equatorial boundaries or frontal outcropping). In contrast to the classic barotropic and baroclinic instabilities, whose nonlinear dynamics (geostrophic turbulence) have an ''inverse cascade" characteristic, the ageostrophic instabilities serve as a local route for the breakdown of balance in the interior ocean or atmosphere, leading to an efficient energy cascade towards small scales. For the first part of this dissertation, the linear instabilities, both momentum-balanced and unbalanced, in several different U(y) shear profiles are investigated in the rotating shallow water equations. The unbalanced instabilities are strongly ageostrophic and involve inertia-gravity wave motions, occurring only for finite Rossby (Ro) and Froude (Fr) numbers. Aside from the classic shear instability among balanced shear wave modes (i.e., B-B type), two types of ageostrophic instability (B-G and G-G) are found. Here B represents balanced shear wave mode, and G represents inertia-gravity wave mode. The B-G instability has attributes of both a balanced shear wave mode and an inertia-gravity wave mode. The G-G instability occurs as a sharp resonance between two inertia-gravity wave modes. The criterion for the occurrence of the ageostrophic instability is associated with the second stability condition of Ripa 1983, which requires a sufficiently large local Froude number. When Ro and especially Fr increase, the balanced instability is suppressed, while the ageostrophic instabilities are enhanced. The profile of the mean flow also affects the strength of the balanced and ageostrophic instabilities. For the second part of this dissertation, the linear instabilities of several rotating, stably stratified, interior vertical shear flows U(z) are solved in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in antisymmetric U(z) for intermediate Rossby number (Ro). AI1 is a stationary (zero frequency) instability, which appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate Ro values and horizontal wave numbers (k, l) that are far from l = 0 or k = 0. AI1 grows by drawing energy from the kinetic energy of the mean flow. The instability AI2 always has inertial critical layers at certain heights; and hence it is associated with an inertia-gravity wave. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (B-G), or between two inertia-gravity waves (G-G). The main energy source for an unstable B-G mode is the mean kinetic energy, while the main energy source for an unstable G-G mode is the mean available potential energy. AI1 and AI2 of the B-G type occur in the neighborhood of A-S = 0 (McWilliams et al. 1998), while AI2 of the G-G type arises beyond this condition (A-S denotes absolute vertical vorticity minus strain rate in isentropic coordinates). Both AI1 and AI2 are unbalanced instabilities, which lead to a loss of balance in 3D interior flows.