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This thesis aims at developing efficient algorithms for solving some fundamental engineering problems in data science and machine learning. We investigate a variety of acceleration techniques for improving the convergence times of optimization algorithms.  First, we investigate how problem structure can be exploited to accelerate the solution of highly structured problems such as generalized eigenvalue and elastic net regression. We then consider Anderson acceleration, a generic and parameter-free extrapolation scheme, and show how it can be adapted to accelerate practical convergence of proximal gradient methods for a broad class of non-smooth problems. For all the methods developed in this thesis, we design novel algorithms, perform mathematical analysis of convergence rates, and conduct practical experiments on real-world data sets. / <p>QC 20191105</p>

<p>In the field of Tracking and Data Fusion most, if not all, computations executed by a computer are carried out serially. The sole part of the process that is not entirely serial is the collection of data from multiple sensors, which can be executed in parallel. However, once the data is to be filtered the most likely candidate is a serial algorithm. This is due in large part to the algorithms themselves that have been developed over the last several decades for use on conventional computers that have been left void of parallel computing capabilities, until now. With the arrival of graphical processing units, or GPUs, the tracking community is in a favourable position to exploit the functionality of parallel processing in order to track a growing number of targets. The problem, however, begins with the sheer labour of having to convert all the pre-existing serial tracking algorithms into parallel ones. This is clearly a daunting task when one considers the extent to which the tracking community has gone to develop modern day filters such as Alpha Beta filters, Probabilistic Data Association filters, Interacting Multiple Model filters, and several dozen, if not hundred, variants of the aforementioned. It is most likely that these filters will find some kind of a parallelization in the near future as ever more sensors are dispersed throughout society and even more targets are monitored with these sensors. The volume of targets then becomes simply too unmanageable for a serial algorithm and more focus is placed iv on parallel ones. Yet, before the parallel algorithms can be utilized they have to be derived. It is the derivation of these parallel algorithms which is the focus of this thesis. However, it should be made clear that it would be impossible to formulate a parallelization for every filter found in the literature, and so the goal here is to direct the attention onto one filter in particular, the Kalman filter.</p> / Master of Applied Science (MASc)

Over the past two decades, vibrational sum-frequency generation (VSFG) has been applied as a versatile technique for probing the structure and dynamics of molecules at surfaces and interfaces. The excellent surface specificity of the SFG allows for probing different kinds of liquid interfaces with no or negligible contribution from adjacent and much deeper bulk phase. VSFG spectroscopy has provided evidence that the structure of the water at interfaces is different from the bulk. With the ultrafast pulses, VSFG can also be used as a probe of ultrafast vibrational dynamics at interfaces. However, apart from a few pioneering studies, the extension of VSFG into time domain has not been explored extensively. Here VSFG is used as a probe of ultrafast vibrational dynamics of water at silica interfaces. Silica is an excellent model system for the solid phase where one can systematically vary the surface charge via bulk pH adjustment. The extension of the surface electric field, the interfacial thickness and surface accumulation of ions at a charged silica surface were studied using IR pump-VSFG probe spectroscopy. A vibrational lifetime (T1) of about 250 fs, similar to bulk H2O, was observed for the O-H stretch of H2O/silica interface when the silica surface is negatively charged. At the neutral surface, where the thickness of interfacial water is smaller than at the charged surface, the vibrational lifetime of O-H stretch becomes more than two times longer (T1~ 600 fs) due to the decreased number of neighboring water molecules, probed by SFG. The fast T1 at negatively charged surface begins to slow down by screening of the penetration of surface electric field via adding salt which suggests the primary reason for similar vibrational dynamics of water at charged interface with bulk water is the penetration of electric field. By decoupling of OH of HDO in D2O, a frequency dependent vibrational lifetime is observed with faster T1 at the red compared to the blue side of the hydrogen bond spectral region. This correlates with the redshift of the SFG spectra with increasing charged surface and is consistent with a theoretical model that relates the vibrational lifetime to the strength of the hydrogen bond network. / Chemistry

Mineral oxide/aqueous interfaces play an important role in the transport of water through aquafers and streams, erosion, the formation of beaches and river deltas, nuclear waste storage, the sequestration and filtration of small ions, and are widely used in industrial scale catalysis. Unlike metal or semiconductor electrodes, the surface charge resulting from the protonation or deprotonation of insulating mineral oxides is highly localized and heterogeneous in nature. While the unique acid/base chemistry associated with different mineral oxide surfaces leads to their wide variety of applications, the extent to which surface groups found on mineral oxides partake in acid/base chemistry is still controversial due to the difficulty associated with experimentally probing them. Surface specific spectroscopic techniques, such as vibrational Sum Frequency Generation (vSFG), provide an opportunity to investigate how the surface architecture and corresponding chemical nature of various mineral oxide surfaces orient the interfacial solvent at a variety of solvent compositions and surface charges. Although vSFG has been used as a tool to measure the orientation and composition of interfacial O-H species originating from the surface and solvent for many mineral oxide/aqueous interfaces since the late 1990’s, controversy still exists in the assignment of vSFG spectra in the O-H stretching region of SiO2, Al2O3, CaF2, and TiO2/aqueous interfaces. The first section of this dissertation focuses on how the nonlinear optics and computational community’s understanding of the structure associated with mineral oxide/aqueous interfaces has evolved and where it stands now. Of particular interest is how the addition of electrolyte and variation of bulk pH allow modulation of the depth of the interfacial region and surface charge. Electrolyte solutions can vary the length of the interface by screening interfacial charges through non-specific adsorption at the interface, or generating surface charge if accumulation is facilitated by specific adsorption. The specific interaction of small ions with mineral oxide surfaces is relevant in geochemistry and filtration technology, and can also aid in prediction of contaminant mobility in ground water systems. Chapters two and three discuss the theory and application of vSFG, and the experimental setup used to capture vSFG spectra in this work, respectively. The fourth chapter investigates how monovalent or divalent cations accumulate at alpha-Al2O3(0001)/H2O interfaces and reorganize the interfacial solvent structure. The reactivity of these interfaces is strongly impacted by the presence of ions. Thus, it is critical to understand how ions alter the interfacial environment. This is achieved by measuring the changes in the structure and vibrational dynamics of interfacial water induced by the presence of ions in close vicinity to the mineral surface. The alpha-Al2O3(0001) surface represents a flexible platform to study the effect of ions on interfacial aqueous environments at positive, neutral and negative surface charge. Using vibrational sum frequency generation (vSFG) in the frequency and time domain, we investigate how monovalent and divalent cations affect the hydrogen bonding environment of the first few layers of interfacial water next to an alpha-Al2O3(0001) surface. Our results indicate that monovalent cations, such as Li+, Na+, K+, and Cs+, appear to have lower adsorption affinities for the interface compared to Ca2+, Sr2+, and Ba2+. This leads to an interfacial region that is structured in a cation valence dependent manner. Time resolved vSFG measurements reveal that the O-H vibrational lifetime (T1) of interfacial species at pH 10 conditions in the presence of NaCl and BaCl2 remains similar, but restructuring of the surface seen in steady state vSFG is manifested in the degree to which strongly hydrogen bonded species recover to their original populations post excitation. By tracking the accumulation of ions at the interface via the vSFG response, we can characterize the unique surface arrangements of interfacial water molecules induced by a range of monovalent and divalent cations at the alpha-Al2O3(0001)/water interface. In the fifth chapter the Stark active C ≡ N stretch of potassium thiocyanate is used as a molecular probe of interfacial electrostatic potential at the alpha-Al2O3(0001)/H2O interface. We confirm the presence of the thiocyanate ion in the interfacial region via reorganization of surface waters in the O-H stretching region. Changes in electrostatic potential are then tracked via Stark shifts of the vibrational frequency of the C ≡ N stretch. Our vSFG measurements show that we can simultaneously measure the SFG response of SCN- ions experiencing charged and neutral surface sites and assign a local potential of + 308 mV and -154 mV to positively and negatively charged aluminol groups, respectively. Thiocyanate anions at charged surface sites adopt similar relative orientations independent of surface charge, but adopt an opposite orientation at neutral surface sites. MD-DFT simulations of SCN- near the neutral alpha-Al2O3(0001)//H2O interface show that the vSFG response in the C ≡ N stretch region originates from a SCN-H-O-Al complex, suggesting the surface site specificity of these experiments. By tracking how this molecular probe responds to local surface charges we offer insight into the local electrostatic potential at neutral and charged surface aluminol groups. Chapter six investigates the vibrational dynamics of potassium thiocyanate at the alumina/water interface. Here, we leverage the sensitivity of the C ≡ N stretch vibrational lifetime of potassium thiocyanate to measure the local electrostatic potential at the alpha-Al2O3(0001)/H2O interface. To accomplish this, KSCN was investigated using free induction decay vSFG (FID-vSFG) and time resolved pump probe (TR-vSFG) measurements, which measure the total dephasing time and vibrational lifetime of the excited C ≡ N stretch, respectively. Our FID-vSFG spectra suggest that at all surface charges the total dephasing time of SCN- is on the order of ~300-600 fs. TR-vSFG characterizations of potassium thiocyanate report the vibrational lifetime of the excited C ≡ N stretch between ~0.5-2 ps. TR-vSFG measurements show two distinct vibrational relaxation rates, which are assigned the CN stretch and the HOH bend plus libration combination band of interfacial water. The variation in the T1 lifetime of the CN stretch with bulk pH show that changes in the SCN- net orientation measured using steady-state vSFG can be correlated to the vibrational dynamics in the interfacial region. The energy transfer to the bend plus libration combination band of water is also sensitive to the surface charge, as the lifetime of this species becomes shorter as the bulk pH is increased. Lastly, in chapter seven this thesis is summarized, and future directions of the experiments presented here are discussed. / Chemistry

The distinct structure and dynamics of interfacial water are due to a break in the extended hydrogen bonding network present in bulk water. At solid-aqueous interfaces, the presence of surface charge, which induces a static electric field, and the electrolytes, which are present in most naturally relevant systems, can additionally perturb the hydrogen bonding environment due to polarization. The interplay between the surface-charge-induced electric field and the ions in changing the structure of interfacial water has important consequences in the chemistry of processes ranging from protein-water interactions to mineral-water reactivity in oil recovery. Accessing information about the first few layers of water at buried interfaces is challenging. Vibrational sum-frequency generation (vSFG) spectroscopy is a powerful technique to study exclusively the interfacial region and is used here to investigate the role of interfacial solvent structure on surface reactivity. It is known that the rate of quartz dissolution increases on addition of salt at neat water pH. The reason for this enhancement was hypothesized to be a consequence of perturbations in interfacial water structure. The vSFG spectra, which is a measure of ordering in the interfacial water structure, shows an enhanced effect of salt (NaCl) at neat pH 6~8. The trend in the effect of salt on vSFG spectra versus the bulk pH is remarkably consistent with the enhancement of rate of quartz dissolution, providing the first experimental correlation between interfacial water structure and silica dissolution. If salt alters the structure of interfacial water, it must affect the vibrational energy transfer pathways of water, which is extremely fast in bulk water (~130 fs). Thus far, the role of ions on the vibrational dynamics of water at charged surfaces has been limited to the screening effects and reduction in the depth of the region that contributes to vSFG. Here, we measure the ultrafast vibrational relaxation of the O-H stretch of water at silica at different bulk pH, using time-resolved (TR-vSFG). The fast vibrational dynamics of water (~200 fs) observed at charged silica surfaces (pH 6 and pH 12), slows down (~600 fs) on addition of NaCl only at pH 6 and not at pH 12. On the other hand at pH 2 (neutral surface), the vibrational relaxation shows an acceleration at high ionic strengths (0.5 M NaCl). The TR-vSFG results suggest that there is a surface-charge dependence on the sensitivity of the interfacial dynamics to ions and that reduction in the probe depth of vSFG alone cannot explain the changes in the vibrational lifetime of interfacial O-H. This is further supported by the cation specific effects observed in the TR-vSFG of the silica/water interface. While the vibrational relaxation of O-H stretch slows on addition of all salts (LiCl, NaCl, RbCl, and CsCl), the degree of slowing down is sensitive to the cation identity. The vibrational lifetime of O-H stretch in the presence of different cations follows the order: Li+ &lt; Na+ &lt; Rb+, consistent with previous Hofmeister effect reported in vSFG spectroscopy as well as AFM measurements at silica/water interface. To provide molecular insight on the effect of surface charge density and ionic strength on the changes in interfacial water structure, Molecular Dynamics (MD) simulations were performed on water at different types of surfaces. It was shown that the properties of water near the interface, e.g., a net orientation and the depth to which this persists, depend on the degree of specific adsorption of the counter ions. Our vSFG results, along with the insights from MD simulations, highlight the importance of considering the role of ions on the solvent structure within the electric double layer region, beyond the screening effects predicted by classical electrochemical models. / Chemistry

As time passes, change occurs. With this change comes the need for surveillance. One may be a technician on an assembly line and in need of a surveillance technique to monitor the number of defective components produced. On the other hand, one may be an administrator of a hospital in need of surveillance measures to monitor the number of patient falls in the hospital or to monitor surgical outcomes to detect changes in surgical failure rates. A natural choice for on-going surveillance is the control chart; however, the chart must be constructed in a way that accommodates the situation at hand. Two scenarios involving attribute control charting are investigated here. The first scenario involves Poisson count data where the area of opportunity changes. A modified exponentially weighted moving average (EWMA) chart is proposed to accommodate the varying sample sizes. The performance of this method is compared with the performance for several competing control chart techniques and recommendations are made regarding the best preforming control chart method. This research is a result of joint work with Dr. William H. Woodall (Department of Statistics, Virginia Tech). The second scenario involves monitoring a process where items are classified into more than two categories and the results for these classifications are readily available. A multinomial cumulative sum (CUSUM) chart is proposed to monitor these types of situations. The multinomial CUSUM chart is evaluated through comparisons of performance with competing control chart methods. This research is a result of joint work with Mr. Lee J. Wells (Grado Department of Industrial and Systems Engineering, Virginia Tech) and Dr. William H. Woodall (Department of Statistics, Virginia Tech). / Ph. D.

While the channel capacity of an isolated noise-limited wireless link is well-understood, the same is not true for the interference-limited wireless links that coexist in the same area and occupy the same frequency band(s). The performance of these wireless systems is coupled to each other due to the mutual interference. One such wireless scenario is modeled as a network of simultaneously communicating node pairs and is generally referred to as an interference channel (IC). The problem of characterizing the capacity of an IC is one of the most interesting and long-standing open problems in information theory. A popular way of characterizing the capacity of an IC is to maximize the achievable sum-rate by treating interference as Gaussian noise, which is considered optimal in low-interference scenarios. While the sum-rate of the single-band SISO IC is relatively well understood, it is not so when the users have multiple-bands and multiple-antennas for transmission. Therefore, the study of the optimal sum-rate of the multi-band MIMO IC is the main goal of this thesis. The sum-rate maximization problem for these ICs is formulated and is shown to be quite similar to the one already known for single-band MIMO ICs. This problem is reduced to the problem of finding the optimal fraction of power to be transmitted over each spatial channel in each frequency band. The underlying optimization problem, being non-linear and non-convex, is difficult to solve analytically or by employing local optimization techniques. Therefore, we develop a global optimization algorithm by extending the Reformulation and Linearization Technique (RLT) based Branch and Bound (BB) strategy to find the provably optimal solution to this problem. We further show that the spatial and spectral channels are surprisingly similar in a multi-band multi-antenna IC from a sum-rate maximization perspective. This result is especially interesting because of the dissimilarity in the way the spatial and frequency channels affect the perceived interference. As a part of this study, we also develop some rules-of-thumb regarding the optimal power allocation strategies in multi-band MIMO ICs in various interference regimes. Due to the recent popularity of Interference Alignment (IA) as a means of approaching capacity in an IC (in high-interference regime), we also compare the sum-rates achievable by our technique to the ones achievable by IA. The results indicate that the proposed power control technique performs better than IA in the low and intermediate interference regimes. Interestingly, the performance of the power control technique improves further relative to IA with an increase in the number of orthogonal spatial or frequency channels. / Master of Science

Microelectromechanical Systems are ubiquitous in modern technology, with applications ranging from accelerometers in smartphones to ultra-high precision motion stages used for atomically-precise positioning. With the appropriate selection of materials and device design, MEMS resonators with ultra-high quality factors can be fabricated at minimal cost. As the sizes of such resonators decrease, however, their mechanical, electrical, and material properties can no longer be treated as linear, as can be done for larger-scale devices. Unfortunately, adding nonlinear effects to a system changes its dynamics from exactly-solvable to only solvable in specific cases, if at all. Despite (and because of) these added complications, nonlinear effects open up an entirely new world of behaviors that can be measured or taken advantage of to create even more advanced technologies. In our resonators, oscillations are induced and measured using aluminum nitride transducers. I used this mechanism for several separate highly-sensitive experiments. In the first, I demonstrate the incredible sensitivity of these resonators by actuating a mechanical resonant mode using only the force generated by the radiation pressure of a laser at room temperature. In the following three experiments, which use similar mechanisms, I demonstrate information transfer and force measurements by taking advantage of the nonlinear behavior of the resonators. When nonlinear resonators are strongly driven, they exhibit sum and difference frequency generation, in which a large carrier signal can be mixed with a much smaller modulation to produce signals at sum and difference frequencies of the two signals. These sum and difference signals are used to detect information encoded in the modulation signal using optical radiation pressure and acoustic pressure waves. Finally, in my experiments, I probe the nonlinear nature of the piezoelectric material rather than take advantage of the nonlinear resonator behavior. The relative sizes of the linear and nonlinear portions of the piezoelectric constant can be determined because the force applied to the resonator by a transducer is independent of the dielectric constant. This method allowed me to quantify the nonlinear constants.