The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch

Recent and forthcoming advances in instrumentation, and giant new surveys, are creating astronomical data sets that are not amenable to the methods of analysis familiar to astronomers. Traditional methods are often inadequate not merely because of the size in bytes of the data sets, but also because of the complexity of modern data sets. Mathematical limitations of familiar algorithms and techniques in dealing with such data sets create a critical need for new paradigms for the representation, analysis and scientific visualization (as opposed to illustrative visualization) of heterogeneous, multiresolution data across application domains. Some of the problems presented by the new data sets have been addressed by other disciplines such as applied mathematics, statistics and machine learning and have been utilized by other sciences such as space-based geosciences. Unfortunately, valuable results pertaining to these problems are mostly to be found only in publications outside of astronomy. Here we offer brief overviews of a number of concepts, techniques and developments, some "old" and some new. These are generally unknown to most of the astronomical community, but are vital to the analysis and visualization of complex datasets and images. In order for astronomers to take advantage of the richness and complexity of the new era of data, and to be able to identify, adopt, and apply new solutions, the astronomical community needs a certain degree of awareness and understanding of the new concepts. One of the goals of this paper is to help bridge the gap between applied mathematics, artificial intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in Astronomy, special issue "Robotic Astronomy

A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

Combinatorial synthesis and screening of fuel cell catalysts

Polymer electrolyte membrane fuel cells (PEMFCs) are compact power sources that can operate with high efficiencies and low emission of environmentally harmful gases. One of the major barriers impeding the development of PEMFCs as a competitive energy source is the inability of existing anode catalysts to oxidize fuels other than hydrogen at sufficient levels due to catalyst deactivation by carbon monoxide (CO) and other partial oxidation products. The focus of this research is the development and application of combinatorial strategies to construct and interrogate electrooxidation (anode) catalysts pertaining to PEMFCs to discover catalysts with enhanced performance in catalyst deactivating environments. A novel method (known as the gel-transfer method) for synthesizing catalyst composition gradient libraries for combinatorial catalyst discovery was developed. This method involved transferring a spatial concentration gradient of precursor metal salts created within a polymer gel on to a solid conducting substrate by electrochemical reduction. Chemically sensitive surface-imaging techniques, namely, scanning electrochemical microscopy (SECM) and optical screening with a pH-dependent fluorescence probe were used to characterize the combinatorial catalyst samples. The utility of SECM as a screening tool to measure the activity of multicomponent catalyst libraries towards fuel cell electrooxidation reactions was established with simple catalyst libraries including a platinum coverage gradient and platinum-ruthenium and platinum-ruthenium-molybdenum arrays. A platinum-ruthenium surface composition gradient was constructed through the gel-transfer method and its reactivity towards hydrogen oxidation in the presence of a catalyst poison (CO) was mapped using the SECM. Ruthenium composition between 20 and 30% exhibited superior performance than the rest of the binary. The gel-transfer method was extended to construct a ternary platinum-ruthenium-rhodium catalyst library and its reactivity towards several electrooxidation reactions including oxidation of hydrogen, CO, methanol and ethanol was mapped using a pH-sensitive fluorescent probe. Trends in reactivity for these reactions as a function of catalyst composition were determined. Future directions of this research are also presented

Theory of measurement-based quantum computing

In the study of quantum computation, data is represented in terms of linear operators which form a generalized model of probability, and computations are most commonly described as products of unitary transformations, which are the transformations which preserve the quality of the data in a precise sense. This naturally leads to "unitary circuit models", which are models of computation in which unitary operators are expressed as a product of "elementary" unitary transformations. However, unitary transformations can also be effected as a composition of operations which are not all unitary themselves: the "one-way measurement model" is one such model of quantum computation. In this thesis, we examine the relationship between representations of unitary operators and decompositions of those operators in the one-way measurement model. In particular, we consider different circumstances under which a procedure in the one-way measurement model can be described as simulating a unitary circuit, by considering the combinatorial structures which are common to unitary circuits and two simple constructions of one-way based procedures. These structures lead to a characterization of the one-way measurement patterns which arise from these constructions, which can then be related to efficiently testable properties of graphs. We also consider how these characterizations provide automatic techniques for obtaining complete measurement-based decompositions, from unitary transformations which are specified by operator expressions bearing a formal resemblance to path integrals. These techniques are presented as a possible means to devise new algorithms in the one-way measurement model, independently of algorithms in the unitary circuit model.Comment: Ph.D. thesis in Combinatorics and Optimization. 199 pages main text, 26 PDF figures. Official electronic version available at http://hdl.handle.net/10012/413

A Novel Approach To Intelligent Navigation Of A Mobile Robot In A Dynamic And Cluttered Indoor Environment

The need and rationale for improved solutions to indoor robot navigation is increasingly driven by the influx of domestic and industrial mobile robots into the market. This research has developed and implemented a novel navigation technique for a mobile robot operating in a cluttered and dynamic indoor environment. It divides the indoor navigation problem into three distinct but interrelated parts, namely, localization, mapping and path planning. The localization part has been addressed using dead-reckoning (odometry). A least squares numerical approach has been used to calibrate the odometer parameters to minimize the effect of systematic errors on the performance, and an intermittent resetting technique, which employs RFID tags placed at known locations in the indoor environment in conjunction with door-markers, has been developed and implemented to mitigate the errors remaining after the calibration. A mapping technique that employs a laser measurement sensor as the main exteroceptive sensor has been developed and implemented for building a binary occupancy grid map of the environment. A-r-Star pathfinder, a new path planning algorithm that is capable of high performance both in cluttered and sparse environments, has been developed and implemented. Its properties, challenges, and solutions to those challenges have also been highlighted in this research. An incremental version of the A-r-Star has been developed to handle dynamic environments. Simulation experiments highlighting properties and performance of the individual components have been developed and executed using MATLAB. A prototype world has been built using the WebotsTM robotic prototyping and 3-D simulation software. An integrated version of the system comprising the localization, mapping and path planning techniques has been executed in this prototype workspace to produce validation results

Quantum Hamiltonian Complexity

Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. Over the past decade and a half, this field has witnessed fundamental breakthroughs, ranging from the establishment of a "Quantum Cook-Levin Theorem" to deep insights into the structure of 1D low-temperature quantum systems via so-called area laws. Our aim here is to provide a computer science-oriented introduction to the subject in order to help bridge the language barrier between computer scientists and physicists in the field. As such, we include the following in this survey: (1) The motivations and history of the field, (2) a glossary of condensed matter physics terms explained in computer-science friendly language, (3) overviews of central ideas from condensed matter physics, such as indistinguishable particles, mean field theory, tensor networks, and area laws, and (4) brief expositions of selected computer science-based results in the area. For example, as part of the latter, we provide a novel information theoretic presentation of Bravyi's polynomial time algorithm for Quantum 2-SAT.Comment: v4: published version, 127 pages, introduction expanded to include brief introduction to quantum information, brief list of some recent developments added, minor changes throughou

Developing Time-Resolved Synchrotron Infrared Spectroscopy for Spectroelectrochemical Measurements

This thesis details my work in developing spectroelectrochemical platforms utilizing synchrotron infrared radiation (SIR) and time-resolved FTIR to study the kinetics of electrochemical reactions on second to millisecond scale with high chemical sensitivity. It will cover development of spectroelectrochemical cells and procedures compatible with the mid-IR beamline at the Canadian Light Source to study irreversible electrocatalytic processes with rapid scan FTIR in reflection mode. The thesis demonstrates application of SIR-based rapid scan FTIR to spatially map catalytic activity on heterogenous PtNi electrode and provides proof-of-principle for its capability for combinatorial screening for binary electrocatalysts. The thesis discusses the development of time-resolved step scan FTIR in attenuated total reflection - surface enhancing infrared absorption spectroscopy configuration (ATR-SEIRAS) to improve signal-to-noise of the measurement for increased detection limits and time-resolution, before demonstrating the utility of the developed step scan ATR-SEIRAS platform by investigation of the kinetics of conformational changes within self-assembled monolayers (SAM) of ferrocene alkanethiols. Overall, the work described in this thesis outlines the advancement of SIR-based spectroelectrochemical platforms within the group to a point, where they can be directly applied to investigation of dynamics processes within electrochemical reaction