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Graph representation learning serves as the core of many important tasks on graphs, ranging from friendship recommendation, name disambiguation, drug discovery, and fraud detection. Recently, deep learning has revolutionized various domains such as computer vision, natural language processing, speech recognition, etc. Inspired by the success of deep neural networks, there has been an increasing interest to learn graph representations with deep learning models such as autoencoders, convolutional neural networks, etc. However, graphs in real-life applications usually have complex structures such as sparse connections, task-irrelevant information, and rapidly evolving structures. The complexity poses great challenges to the existing frameworks, such as network embedding models with random walks and graph neural networks based on the neighborhood aggregation. In this dissertation, we propose several deep learning frameworks to tackle the aforementioned problems of graph representation learning on complex graphs. We propose a novel model to learn network representations with adversarially regularized autoencoders to overcome the sparse sampling issue of random walks on graphs. To resolve the task-irrelevant noise, we propose a general framework that is trained to simultaneously select task-relevant edges and learn graph representations by the feedback signals from downstream tasks. To learn from the dynamic evolving graphs, we propose to extract local features by performing convolutions in nodes' neighborhoods defined in joint temporal-structural space. The methodologies presented in these frameworks span different research areas, including deep network embedding, graph representation learning, temporal graph modeling, and node classification on graphs. As a result, these methodologies not only tackle specific challenges in the graph learning tasks mentioned above but also shed light on other applications like social network analysis.

Nearly 50% of global energy consumption is associated with meeting thermal requirements. Whilst some of this is heat goes to low temperature applications like hot water supply, there is also a huge demand for the supply of 100-250oC thermal energy for industrial and commercial applications which is currently met by gas and electricity. However, using innovative optical and thermal technologies, it can also (potentially) be met by concentrated sunlight from urban rooftop collectors, eliminating billions of kg of CO2 emissions per year. Hence, it may be possible to develop new, advanced collectors to substantially increase the amount of commercial rooftop solar energy harvesting. At present, though, there are still some barriers to overcome to successfully collect large scale of 100-250oC thermal energy from rooftops. One key barrier for most concentrated solar systems is that integration with rooftops is relatively complex and cumbersome in comparison with photovoltaic (PV) panels. This requires a new type of concentrator which is efficient, low-cost and has a low-wind/aesthetic profile. These criteria point to thin concentrators that can be rack-mounted or laid flat on the roof with minimal balance of system requirements. The system should have similar geometrical features and appearance to PV panels and non-concentrating solar hot water collection panels, which are by far the most widely deployed solar collection systems to date. Such a concentrating collector has yet to be demonstrated. As such, this study aims to advancing rooftop solar concentrating technology for commercial and industrial applications via the development of thin optical elements which avoid rotational tracking. During the course of the research, several innovative low-profile optical concentrators (

We consider the orbits {pu(n^{1+γ})|n ∈ N} in Γ\PSL(2,R), where Γ is a nonuniform lattice in PSL(2,R) and {u(t)} is the standard unipotent one-parameter subgroup in PSL(2,R). Under a Diophantine condition on the intial point p, we can prove that the trajectory {pu(n^{1+γ})|n ∈ N} is equidistributed in Γ\PSL(2,R) for small γ > 0, which generalizes a result of Venkatesh [V10]. In Chapter 2, we will compute Hausdorff dimensions of subsets of non-Diophantine points in Γ\PSL(2,R), using results of lattice counting problem. In Chapter 3 we will use the exponential mixing property of a semisimple flow to prove the effective equidistribution of horospherical orbits. In Chapter 4, we will give a definition of Diophantine points of type γ for γ ≥ 0 in a homogeneous space Γ\G and compute the Hausdorff dimension of the subset of points which are not Diophantine of type γ when G is a semisimple Lie group of real rank one. As an application, we will deduce a Jarnik-Besicovitch Theorem on Diophantine approximation in Heisenberg groups.

The solar photovoltaic (PV) technology was an expensive niche energy source only for satellite applications, hallmarked by the Bell Lab's launch of the Telstar satellite with PV cells in 1962. Over the past decades, the accumulation of vast amount of effort across various disciplines in science, engineering, and policy has enabled the phenomenal growth of the solar PV industry into a global enterprise with about 140 gigawatt (GW) of cumulative installations by the end of 2013. Further cost reduction through innovation holds the promise in deploying terawatt (TW)-scale solar PV systems globally in both developed and developing countries, meeting growing energy demand and mitigating climate change. Chapter 1 presents a big picture view of the unsustainable path, heavily relying on fossil fuels, in the current global energy landscape. The main body of the dissertation examines the solar PV technology from a holistic and interdisciplinary perspective: from the basic research, to innovations in manufacturing and installing PV modules, to the driving energy policies. Chapter 2 offers a fundamental understanding of the PV technology and a review on recent scientific advances in improving PV efficiency (W/m2). Chapter 3 reviews the state-of-the-art process flow in manufacturing commercial PV modules. In the context of pursuing further reduction in manufacturing cost ($/m2), the thin Si film concept and its recent research effort are reviewed. Aiming to explore novel ways to produce high-quality seed crystals for thin Si film deposition, the key findings of the laser crystallization experiment is presented in Chapter 4. The fundamental thermophysics of nucleation and crystal growth is first reviewed, which highlights the importance of temperature evolution and heat transport in modelling the ultrafast laser crystallization process. Laser crystallization of a range of Si nanostructures are then carried out to study the nucleation and crystal growth behavior under some novel conditions, such as suspended narrow Si membranes and Si nanoparticles confined on top of oxide nanostructures.The cost of a PV module ($/W) is determined by both its rated efficiency (W/m2) and its manufacturing cost ($/m2). However, the same PV module with the same cost can lead to significantly different levelized cost of electricity (LCOE) in $/kWh, depending on the location and configuration of the installed PV system. Chapter 5 starts with an overview of the geographic distribution of solar resources and retail electricity rates, which yield a range of grid parity points across the world. Then, energy yield simulations for different PV panel tilt configurations are carried out using the angle-and-wavelength-resolved solar irradiance data, to examine the effect of angular and spectral variations in the solar spectrum on system performance.Energy policies have been the driving forces for the phenomenal progress of the PV technology: the continuing reduction in cost and the rapid growth in deployment. Chapter 6 first reviews major policy instruments for PV, and then discusses about a few important policy lessons from the rapid development of the global PV industry during 2000-2013. Concerned with the mounting fiscal pressure from deployment incentives and focused on further cost reductions, an innovation-focused policy framework is proposed to revive the PV manufacturing sector and to pursue an innovation-driven global PV industry moving forward.