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Structured Sparse Optimization
No full textIn the age of high-dimensional data-driven science, sparse optimization techniques play a vital role. Sparse optimization aims to discover solutions with compact representations in low-dimensional spaces, i.e., solutions with relatively few nonzero entries. These techniques have succeeded in areas like signal processing, statistics, and model compression. As data becomes increasingly complex, the challenges mount. Classical sparse optimization techniques use l1 regularization to obtain sparse solution estimates, which may be inadequate if a more complicated solution structure is required. Hence, the need arises for structured sparsity, which follows distinct patterns, to produce more interpretable and meaningful solutions.The development of structured sparse optimization algorithms faces many challenges, such as efficiency, scalability, noise management, and support estimation (correctly identifying the zero/nonzero structure of an exact solution). This dissertation addresses these challenges by analyzing new support identification and subspace optimization techniques.The dissertation is structured into two parts. The first part focuses on developing deterministic algorithms. In particular, Chapter 2 focuses on non-overlapping group-sparse problems. It utilizes the exact proximal operator evaluation to achieve support identification. By further integrating Newton\u27s method into the subspace optimization procedure, i.e., only optimizing groups of variables that are predicted to be in the support, the method achieves a fast local convergence rate. Numerical results validate that the proposed method achieves state-of-art performance on regularized regression problems. Chapter 3 exploits a challenging overlapping group-sparse structure and establishes the support identification property of iterates computed as particular inexact estimates of the proximal operator. By properly managing the errors incurred from the inexact proximal operator evaluation and performing special projections, our analysis provides an upper bound on the number of iterations before the support is identified, which is new to the literature.The second part of the dissertation considers the stochastic setting. Chapter 4 presents a stochastic algorithm for non-overlapping group-sparse problems. It enjoys a consistent support identification property with high probability (i.e., with high probability, the correct support is identified for all sufficiently large iterations), avoiding the reliance on exact gradient evaluation or the explicit storage of historical gradient information. Chapter 5 extends this success to overlapping group-sparse structured problems. Borrowing the tools developed in Chapter 3 and Chapter 4, we proposed a method to achieve consistent support identification with high probability with the presence of noise from both inexact proximal operator evaluation and stochastic gradient approximation. Lastly, Chapter 6 applies the idea of subspace optimization to the training of deep neural networks. Armed with a carefully designed subspace projection mechanism, we designed a method that consistently recovers high group-sparse neural networks while maintaining high task-relevant performance. This is beneficial for deploying deep neural networks for inference in devices with low computing resources since the number of parameters and the computation cost are greatly reduced
Towards Creating A Laboratory Twin Of High-Energy Tidal Sites
No full textAn emerging sector in the field of renewable energy is that of the highly predictable, highly reliable, yet largely untapped resource of tidal flow. Tidal flows at highly energetic sites are inherently turbulent and directly influence the available energy extraction, operation, and maintenance of tidal energy converters. Field studies and demonstration projects in these environments are often cost, risk, time, and resource-intensive. Lehigh University\u27s Tidal Turbulence Testing Facility has the unique capability of reproducing tidal energy site conditions in its laboratory-scale water channel. This capability is made possible by the facility\u27s active grid turbulence generator; currently, the only such device made for use in water in the United States. Through a detailed parametric study, the active grid and channel inflow parameters were tested such that desired turbulence statistics could be produced in the water tunnel, including statistics found at a particular tidal energy site. Results suggest the three most influential parameters on the turbulent flow generation include the winglet blockage ratio, mesh Reynolds number, and van Rossby number. Fine-tuning these operating parameters has produced flows with turbulence intensity values of ~30%, mimicking the upper bounds of what is found at highly energetic tidal sites. In addition to the experimental campaign, an analysis of in situ flow characteristics from actual tidal energy sites is presented. Herein, the author reviews and compares turbulence metrics applied for turbulent inflow characterization derived from published acoustic Doppler velocimeter (ADV) measurements at six energetic tidal sites spanning the globe. These metrics include turbulence intensity, turbulent kinetic energy, integral length scales, velocity spectra, vertical profiles of the streamwise velocity, and temporal variation within the tidal cycle. A consistent procedure for ADV data processing is applied to ensure a congruent comparison of these metrics between sites. Of the locations studied, frequent turbulence intensity levels span from ~7% at lower energy sites to greater than 20% at high-energy sites, such as New York City\u27s East River. The flow structures at each of these sites are heavily influenced by unique site characteristics such as bathymetry, seafloor surface roughness, nearby headlands, and physical structures such as upstream bridge piers. In this work, the key turbulence properties gathered from the Nodule Point tidal site are directly compared with those from Lehigh\u27s Tidal Turbulence Testing Facility laboratory water tunnel. Features such as mean velocities, turbulence intensity values, anisotropic ratios, and power spectra will be discussed in determining the successes and ongoing challenges of recreating turbulent flow innate to tidal currents via a laboratory twin water channel. Of note, the facility was capable of reproducing 99% of the turbulence levels measured at Nodule Point, while the facility yielded just 40% of the mean velocities seen at the site due to the current infrastructure limitations of the test facility. Development and benchmarking of a laboratory twin will allow early-stage developers (TRL: 1-5) to perform design iterations and structural health monitoring in a framework of tidal site-specific turbulence. Developers can identify failure modes and perform design iterations at lower TRL (?5) levels that would make the design more robust and provide additional confidence before open water testing (TRL>6). The ability of the active grid turbulence generator to supply these true environmental conditions necessary for this testing is thoroughly explored in this study
Design & Application of an Instructional Intervention for Introductory Programming Aimed to Address the Gender Gap in Computing
No full textAcross the computer science pipeline, a metaphor describing the potential trajectory of students from K-12 classrooms, into post-secondary programs and ultimately into the computing workforce, supporting the complex processes of teaching and learning programming are challenges that continue to elude academics and practitioners alike (Ball et al., 2017). Despite the persistence of signature pedagogical practices, introductory programming courses represent a "barrier" of entry for students into the field of computer science (CS) with historically high failure rates. Particularly affected by the challenges faced within "barrier" classes are women and students from other traditionally underrepresented groups, as exemplified by the historic lack of diversity in the field. Situated Expectancy Value Theory (SEVT) of Academic Motivation (Eccles et al., 1983) is presented as a lens through which we can understand and evaluate the experience of all students in CS classrooms, but in particular those who do not identify as male. A novel instructional intervention, known as Looping between Interactive Lecture and Authentic Context (LILAC) is presented that leverages signature pedagogies of CS instruction specifically supported through the theory of active learning and tenets of project-based learning. The present study aimed to uncover differences in how SEVT constructs (including self-efficacy, intrinsic value, attainment value, utility value and cost) and intentions to persist in CS change throughout a LILAC-centered introductory programming course for undergraduates (n=103). Findings indicated no gender differences in SEVT factors of motivation or ultimate intent to persist. Overall intent to persist and SEVT constructs changed in different ways, with two SEVT factors (intrinsic value and cost) showing statistically significant differences. Implications for future course design and research design are considered
The Oxidative Coupling of Methane: a Kinetic Model
No full textThe oxidative coupling of methane creates valuable hydrocarbons from natural gas, a low-carbon solution. Details about this reaction network are vital to the future utilization of natural gas in new areas of chemical production. A python tool was developed to model chemical reaction networks based on kinetics. Reaction rates, concentrations, and paths can be determined through this script. Further application will reveal the optimal conditions for the oxidative coupling of methane
Gendered Gaps: Landslides in Bududa, Uganda
No full textBududa is a district located in the east of Uganda that frequently suffers from the occurrence of landslides. Based on 22 interviews with community members, I investigated the roles of natural disasters in rural Uganda and the ever-changing social landscape of Bududa. Using the world-systems theory, the theory of ecologically unequal exchange, and ecofeminism, this study examines the changes in gender roles that ensue post-landslides and how this fits the frameworks stated above
The Design and Implementation of AI Partner in Supporting Foreign Language Teaching and Assessment - Supplemental File 3
No full textFundamental Aspects of Black Holes and Holography
No full textThis thesis examines the interplay between gravitational theories and quantum field theory corrections, focusing on the properties and implications of the Weak Gravity Conjecture (WGC) in the context of higher-dimensional models, black hole physics, the behavior of electric fields in Einstein-Maxwell systems, and dark energy in string theory. The study synthesizes results from four cutting-edge papers to explore repulsive black holes and higher-derivative corrections, the asymptotic behavior of dark energy within string theory frameworks, the constraints on Einstein-Maxwell theory with time delays on boosted Reissner-Nordström (RN) backgrounds, and the implications of a NUT charge WGC from dimensional reduction. The papers contribute to our understanding of how these complex theories can be bounded and related to each other, offering new perspectives on the constraints required for a consistent theory of quantum gravity and the potential role of topological charges alongside gauge charges in higher-dimensional spacetimes.</p
Some Topics in Partial Differential Equations: Exact Limit and Diffusive Limit
No full textThis dissertation addresses two types of equations. Firstly, we consider the Benjamin-Bona-Mahony-Burgers (BBMB) equation in the spatial dimensions n = 1, 2, 3. We
achieve exact limits for all orders of derivatives of the n-dimensional BBMB equation.
Leveraging these exact limits, we establish improved decay estimates with
sharp rates for all orders of derivatives of the solutions. The proof utilizes a meticulously
constructed integral and the technique of integral decomposition. Secondly,
we consider the neutron transport equation within a three-dimensional bounded
convex domain with specular-reflection boundary conditions. We study the diffusive
limits as the Knudsen number ϵ → 0+. Depending on the presence or absence of
a time variable, we discuss the steady problem and the unsteady problem separately.
Using Hilbert expansion, it is proven that solutions converge in both cases. Challenges
are addressed through an innovative approach, utilizing remainder estimates
with the L2-L6-L∞ framework.</p
Preparing Inservice High School Mathematics Teachers to Support English Learners: A Multiple Case Study
No full textRising numbers of English learners (ELs) being placed in general education high school mathematics classrooms with underprepared teachers is an increasing concern in U.S. public schools. Despite its importance, there has been little research on how to best support high school mathematics teachers in their attempt to teach both the highly specialized language and content of mathematics. To ensure equitable access to high-quality education for ELs, it is of vital importance to understand how best to educate and support teachers to successfully instruct ELs. The purpose of this mixed methods multiple case study was to investigate and address the perceived needs of high school mathematics teachers in how to better support ELs in general education classrooms. Through the use of a focus group, the perceived needs of high school mathematics teachers of ELs were established, learning modules were created to address the needs, and participants were then observed pre- and post-completion of the online learning to determine if the modules had any impact on teaching practices. The study demonstrated that the learning modules had a positive impact on the instructional strategies of all four participants, two at a statistically significant level. Participants embraced vocabulary instruction, and created other small shifts in their classroom to allow ELs to more fully engage in learning. Additionally, participants found the modules engaging and directly applicable to their classroom.
In the future, additional professional development should put more of an emphasis on individualizing accommodations and language objectives for each student, rather than focusing on strategies that are interpreted as being more universally beneficial. Emphasis should also be placed on how to incorporate support for ELs who are at the upper end of English language proficiency levels. While these students are approaching English fluency, their unique needs must still be fully supported and acknowledged. </p