Multiple quasi-phase-matching for enhanced generation of selected high harmonics in aperiodic modulated fibers

A technique for enhanced generation of selected high harmonics in a gas medium, in a high ionization limit, is proposed in this paper. An aperiodically corrugated hollow-core fiber is employed to modulate the intensity of the fundamental laser pulse along the direction of propagation, resulting in multiple quasi-phase-matched high harmonic emissions at the cutoff region. Simulated annealing (SA) algorithm is applied for optimizing the aperiodic hollow-core fiber. Our simulation shows that the yield of selected harmonics is increased equally by up to 2 orders of magnitude compared with no modulation and this permits flexible control of the quasi-phase-matched emission of selected harmonics by appropriate corrugation. (c) 2007 Optical Society of America.

Phase-matching control of high-order harmonic generation in a two-color laser field

The phase-matching condition of high-order harmonic generation driven by intense few-cycle pulses could be controlled by adding second-harmonic pulses to change the ionization fraction of the gaseous medium. The harmonic generation efficiency could be improved by moving the phase-matching point with an all-optical control of the ionization fraction or a proper change of the confocal parameter. A specific order of harmonics could be easily controlled to reach phase matching at a fixed higher gas pressure by adding second-harmonic pulses with a suitable intensity. Such an all-optical phase-matching control was demonstrated to be dependent upon the temporal delay between the fundamental-wave and second harmonic pulses.

On parallel computing for stochastic optimization models and algorithms

167 p.

Protein structure refinement algorithms

Protein structure prediction has remained a major challenge in structural biology for more than half a century. Accelerated and cost efficient sequencing technologies have allowed researchers to sequence new organisms and discover new protein sequences. Novel protein structure prediction technologies will allow researchers to study the structure of proteins and to determine their roles in the underlying biology processes and develop novel therapeutics.

Difficulty of the problem stems from two folds: (a) describing the energy landscape that corresponds to the protein structure, commonly referred to as force field problem; and (b) sampling of the energy landscape, trying to find the lowest energy configuration that is hypothesized to be the native state of the structure in solution. The two problems are interweaved and they have to be solved simultaneously. This thesis is composed of three major contributions. In the first chapter we describe a novel high-resolution protein structure refinement algorithm called GRID. In the second chapter we present REMCGRID, an algorithm for generation of low energy decoy sets. In the third chapter, we present a machine learning approach to ranking decoys by incorporating coarse-grain features of protein structures.

Convex Relaxation for Low-Dimensional Representation: Phase Transitions and Limitations

There is a growing interest in taking advantage of possible patterns and structures in data so as to extract the desired information and overcome the curse of dimensionality. In a wide range of applications, including computer vision, machine learning, medical imaging, and social networks, the signal that gives rise to the observations can be modeled to be approximately sparse and exploiting this fact can be very beneficial. This has led to an immense interest in the problem of efficiently reconstructing a sparse signal from limited linear observations. More recently, low-rank approximation techniques have become prominent tools to approach problems arising in machine learning, system identification and quantum tomography.

In sparse and low-rank estimation problems, the challenge is the inherent intractability of the objective function, and one needs efficient methods to capture the low-dimensionality of these models. Convex optimization is often a promising tool to attack such problems. An intractable problem with a combinatorial objective can often be "relaxed" to obtain a tractable but almost as powerful convex optimization problem. This dissertation studies convex optimization techniques that can take advantage of low-dimensional representations of the underlying high-dimensional data. We provide provable guarantees that ensure that the proposed algorithms will succeed under reasonable conditions, and answer questions of the following flavor:

More specifically, i) Focusing on linear inverse problems, we generalize the classical error bounds known for the least-squares technique to the lasso formulation, which incorporates the signal model. ii) We show that intuitive convex approaches do not perform as well as expected when it comes to signals that have multiple low-dimensional structures simultaneously. iii) Finally, we propose convex relaxations for the graph clustering problem and give sharp performance guarantees for a family of graphs arising from the so-called stochastic block model. We pay particular attention to the following aspects. For i) and ii), we aim to provide a general geometric framework, in which the results on sparse and low-rank estimation can be obtained as special cases. For i) and iii), we investigate the precise performance characterization, which yields the right constants in our bounds and the true dependence between the problem parameters.

Two and Three Finger Caging of Polygons and Polyhedra

Multi-finger caging offers a rigorous and robust approach to robot grasping. This thesis provides several novel algorithms for caging polygons and polyhedra in two and three dimensions. Caging refers to a robotic grasp that does not necessarily immobilize an object, but prevents it from escaping to infinity. The first algorithm considers caging a polygon in two dimensions using two point fingers. The second algorithm extends the first to three dimensions. The third algorithm considers caging a convex polygon in two dimensions using three point fingers, and considers robustness of this cage to variations in the relative positions of the fingers.

This thesis describes an algorithm for finding all two-finger cage formations of planar polygonal objects based on a contact-space formulation. It shows that two-finger cages have several useful properties in contact space. First, the critical points of the cage representation in the hand’s configuration space appear as critical points of the inter-finger distance function in contact space. Second, these critical points can be graphically characterized directly on the object’s boundary. Third, contact space admits a natural rectangular decomposition such that all critical points lie on the rectangle boundaries, and the sublevel sets of contact space and free space are topologically equivalent. These properties lead to a caging graph that can be readily constructed in contact space. Starting from a desired immobilizing grasp of a polygonal object, the caging graph is searched for the minimal, intermediate, and maximal caging regions surrounding the immobilizing grasp. An example constructed from real-world data illustrates and validates the method.

A second algorithm is developed for finding caging formations of a 3D polyhedron for two point fingers using a lower dimensional contact-space formulation. Results from the two-dimensional algorithm are extended to three dimension. Critical points of the inter-finger distance function are shown to be identical to the critical points of the cage. A decomposition of contact space into 4D regions having useful properties is demonstrated. A geometric analysis of the critical points of the inter-finger distance function results in a catalog of grasps in which the cages change topology, leading to a simple test to classify critical points. With these properties established, the search algorithm from the two-dimensional case may be applied to the three-dimensional problem. An implemented example demonstrates the method.

This thesis also presents a study of cages of convex polygonal objects using three point fingers. It considers a three-parameter model of the relative position of the fingers, which gives complete generality for three point fingers in the plane. It analyzes robustness of caging grasps to variations in the relative position of the fingers without breaking the cage. Using a simple decomposition of free space around the polygon, we present an algorithm which gives all caging placements of the fingers and a characterization of the robustness of these cages.

Distributed Optimal Control of Cyber-Physical Systems: Controller Synthesis, Architecture Design and System Identification

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation.

The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification.

We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H-infinity optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H-infinity norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

Phase unwrapping algorithms, respectively, based on path-following and discrete cosine transform

This paper describes a path-following phase unwrapping algorithm and a phase unwrapping algorithm based on discrete cosine transform (DCT) which accelerates the Computation and suppresses the propagation of noise. Through analysis of fringe pattern with serious noises simulated in mathematic model, we make a contrast between path-following algorithm and DCT algorithm. The advantages and disadvantages or analytical fringe pattern are also given through comparison of two algorithms. Three-dimensional experimental results have been given to prove the validity of these algorithms. Despite DCT phase unwrapping technique robustness and speed in some cases, it cannot be unwrapping inconsistencies phase. The path-following algorithm can be used in automation analysis of fringe patterns with little influence of noise. (c) 2007 Elsevier GmbH. All rights reserved.

Contributions on distance-based algorithms, multi-classifier construction and pairwise classification

179 p.