Ballistic transport simulation in nanodevices, which involves self-consistently solving a coupled Schrodinger-Poisson system of equations, is usually computationally intensive. Here, we propose coupling the reduced basis method with the subband decomposition method to improve the overall efficiency of the simulation. By exploiting a posteriori error estimation procedure and greedy sampling algorithm, we are able to design an algorithm where the computational cost is reduced significantly. In addition, the computational cost only grows marginally with the number of grid points in the confined direction.

The progress in electronic and computer sciences has transformed music, introducing new techniques and tools that have completely impacted the way we compose, perform, and distribute music. As creators and consumers, our experience with music has been shaped by these new technologies, resulting in a rapid evolution of the art form.

However, Western music theory has remained largely unchanged, with technology settling into the current system and formalizing its rules in each protocol and platform developed. Since Western music, and specifically its harmonic rules, were developed in a technological context that has since changed, it stands to reason that the theory should evolve as well. Several artists have expanded their artistic practice by exploring new systems, such as serialism, stochastic music, and microtonality. Composers such as Xenakis, Partch, Johnston, Tenney and Barlow have laid the foundation for a new computational system in music.

Understanding the perceived root phenomenon is essential to explain the most fundamental structures in twelve-tone equal temperament or 5-limit just intonation, as well as proposing new chords for new tunings. Through a music perception study conducted on 41 participants and 10 different tunings empirically establishes harmonic dualism, negative harmony and Barlow’s harmonicity as the key factors for the perception of the harmonic root and the origin of the major and minor triads, and proposes a model as a basis for a tuning-agnostic – trans-spatial – music theory.

As a result, a set of rules and algorithms are introduced to expand music’s harmonic system through computation. This thesis proposes a tuning-agnostic music theory, organizing and codifying the principles and rules of harmony into a systematic and recognizable form.

In this paper we present a second-order accurate adaptive algorithm for solving multiphase, incompressible flows in porous media. We assume a multiphase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting the total velocity, defined to be the sum of the phase velocities, is divergence-free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behavior of the method.

The significant impacts of climate change on extreme weather events have been widely demonstrated in past decades. As the most expensive climate disaster, the drought and its risks under the warming climate always attract people's attention. However, huge uncertainties exist in climate projections, mainly consisting of scenario uncertainty, model uncertainty, and internal variability. Moreover, drought is more difficult to assess in climate datasets, due to its long duration per event, relative to the length of a typical simulation. Meanwhile, since the infamous extreme drought of the 1960s, the climate of the Northeastern United States (NEUS) has generally trended towards warmer and wetter conditions. Nonetheless, there is mounting evidence that short-term droughts will continue to pose a significant risk for this region. Therefore, there is a growing need for a comprehensive framework with the most advanced climate techniques and datasets to investigate the impacts of climate change on drought over NEUS.

In this thesis, firstly, a comprehensive drought feature-based evaluation system, equipped with statistical hypothesis testing and Principal Feature Analysis, is put forward and is designed to be easily used for any climate datasets. With its help, people can choose climate models with fewer model uncertainties and biases in capturing droughts in the regions of interest. This system is applied to three characteristically distinct regions in the conterminous US and across several commonly employed climate datasets (CMIP5/6, LOCA, and CORDEX). As a result, insights emerge into the underlying drivers of model bias in global climate models, regional climate models, and statistically downscaled models.

Then to reduce the impacts of internal variability on drought projections, 7 large ensemble (LE) models and a novel drought index are employed to examine the changing trends of drought at different temporal scales. We find most LE models indicate the NEUS will experience a long-term wetting trend with more ``extremely wet'' months, but also more frequent short-term extreme droughts. These changes are associated with increasing precipitation, atmospheric water demand, and climate variability. We also conclude that discrepant trends in precipitation and evapotranspiration variability will lead to increasing anti-correlation of these variables, which is relevant to the intensification of rapidly developing drought -- particularly in the spring season. These changes are associated with an increase in evapotranspiration from plants, brought by an earlier emergence of the growing season and denser vegetation.

Social networks are becoming one of the most popular forms of communication between individuals worldwide. As more people start to use social networks and post more status updates, more information about the personal lives of individuals begins to leak out into cyberspace. In this thesis, we leverage the power of social networks and their Application Programming Interface (API) to data mine social networks.

Many social networks are beginning to add geo location information to status updates to show where users post updates from. Using the geo location information we gathered from Twitter and Foursquare, we are able to analyze the spatial and temporal patterns of individuals. Using studied heuristics, we are able to predict the activity of these individuals. These predictions are perfect for recommendation engines, law enforcement applications, and to track the spread of disease and exposure of harmful pollutants in the atmosphere.

We use the spatial and temporal information from the social networks in combination with UCLA's Vehicular Sensor Network. We seek to answer the questions of where people go and how long do they stay in one location. The Vehicular Test-Bed currently deployed in Macao, China tracks the concentration levels of carbon dioxide in the Macao region continuously. Using the social network information, we are able to estimate the exposure of individuals to these harmful pollutants.