Exploring Faculty Perceptions of a Case Library as an Online Teaching Resource

Professors need alternative programs to support their online teaching. This dissertation reports an initial study in a long-term research agenda for developing a faculty online teaching solution. The primary purpose of the study is to explore faculty perceptions of a case library to help decision makers and researchers determine whether they would pursue the use of such a tool to support faculty online teaching. The secondary purpose of the study is to generate design knowledge to inform future development of and research on this or similar case libraries. The methodology of this study includes three components: development research, rapid prototyping, and qualitative methods. Development research and rapid prototyping provided a three-stage framework for this study: conceptualization, development, and research. I synthesized the literature to create conceptual models of an Online Teaching Case Library (OTCL) at the conceptualization stage, built a prototype to implement the models at the development stage, and conducted research to evaluate the prototype at the research stage. Qualitative methods guided data gathering and analysis. I recruited seven faculty participants based on a purposeful sampling technique. To gather the data, I followed a three-step data collection process: initial interviews, contextual interviews, and final interviews. This process allowed me to observe and interview faculty participants while they were exploring the prototype. I analyzed the data by following an 11-step procedure synthesized from the works of Miles and Huberman (1994) as well as LeCompte and Schensul (1999a). This study found that on one hand, faculty members might use an OTCL, because they perceived that this tool could support their apprenticeship approach to learning to teach. On the other hand, however, their perceived decision to use an OTCL would also be influenced by the perceptions of the usefulness and usability of the tool. The study identified the initial evidence supporting an OTCL as an online teaching resource and the challenges involved in developing and implementing such a solution. It provides a base for decision makers to determine whether they would adopt this tool. It also offers some design guidance for those who do want to pursue this solution to faculty development

Spectral Method and Regularized MLE Are Both Optimal for Top-KK Ranking

This paper is concerned with the problem of top-$K$ ranking from pairwise comparisons. Given a collection of $n$ items and a few pairwise comparisons across them, one wishes to identify the set of $K$ items that receive the highest ranks. To tackle this problem, we adopt the logistic parametric model --- the Bradley-Terry-Luce model, where each item is assigned a latent preference score, and where the outcome of each pairwise comparison depends solely on the relative scores of the two items involved. Recent works have made significant progress towards characterizing the performance (e.g. the mean square error for estimating the scores) of several classical methods, including the spectral method and the maximum likelihood estimator (MLE). However, where they stand regarding top-$K$ ranking remains unsettled. We demonstrate that under a natural random sampling model, the spectral method alone, or the regularized MLE alone, is minimax optimal in terms of the sample complexity --- the number of paired comparisons needed to ensure exact top-$K$ identification, for the fixed dynamic range regime. This is accomplished via optimal control of the entrywise error of the score estimates. We complement our theoretical studies by numerical experiments, confirming that both methods yield low entrywise errors for estimating the underlying scores. Our theory is established via a novel leave-one-out trick, which proves effective for analyzing both iterative and non-iterative procedures. Along the way, we derive an elementary eigenvector perturbation bound for probability transition matrices, which parallels the Davis-Kahan $\sin\Theta$ theorem for symmetric matrices. This also allows us to close the gap between the $\ell_2$ error upper bound for the spectral method and the minimax lower limit.Comment: Add discussions on the setting of the general condition numbe

Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often require proper regularization (e.g. trimming, regularized cost, projection) in order to guarantee fast convergence. For vanilla procedures such as gradient descent, however, prior theory either recommends highly conservative learning rates to avoid overshooting, or completely lacks performance guarantees. This paper uncovers a striking phenomenon in nonconvex optimization: even in the absence of explicit regularization, gradient descent enforces proper regularization implicitly under various statistical models. In fact, gradient descent follows a trajectory staying within a basin that enjoys nice geometry, consisting of points incoherent with the sampling mechanism. This "implicit regularization" feature allows gradient descent to proceed in a far more aggressive fashion without overshooting, which in turn results in substantial computational savings. Focusing on three fundamental statistical estimation problems, i.e. phase retrieval, low-rank matrix completion, and blind deconvolution, we establish that gradient descent achieves near-optimal statistical and computational guarantees without explicit regularization. In particular, by marrying statistical modeling with generic optimization theory, we develop a general recipe for analyzing the trajectories of iterative algorithms via a leave-one-out perturbation argument. As a byproduct, for noisy matrix completion, we demonstrate that gradient descent achieves near-optimal error control --- measured entrywise and by the spectral norm --- which might be of independent interest.Comment: accepted to Foundations of Computational Mathematics (FOCM

The global solution of the minimal surface flow and translating surfaces

In this paper, we study evolved surfaces over convex planar domains which are evolving by the minimal surface flow $$u_{t}= div\left(\frac{Du}{\sqrt{1+|Du|^2}}\right)-H(x,Du).$$ Here, we specify the angle of contact of the evolved surface to the boundary cylinder. The interesting question is to find translating solitons of the form $u(x,t)=\omega t+w(x)$ where $\omega\in \mathbb R$. Under an angle condition, we can prove the a priori estimate holds true for the translating solitons (i.e., translator), which makes the solitons exist. We can prove for suitable condition on $H(x,p)$ that there is the global solution of the minimal surface flow. Then we show, provided the soliton exists, that the global solutions converge to some translator.Comment: 16 page

ResMatch: Residual Attention Learning for Local Feature Matching

Attention-based graph neural networks have made great progress in feature matching learning. However, insight of how attention mechanism works for feature matching is lacked in the literature. In this paper, we rethink cross- and self-attention from the viewpoint of traditional feature matching and filtering. In order to facilitate the learning of matching and filtering, we inject the similarity of descriptors and relative positions into cross- and self-attention score, respectively. In this way, the attention can focus on learning residual matching and filtering functions with reference to the basic functions of measuring visual and spatial correlation. Moreover, we mine intra- and inter-neighbors according to the similarity of descriptors and relative positions. Then sparse attention for each point can be performed only within its neighborhoods to acquire higher computation efficiency. Feature matching networks equipped with our full and sparse residual attention learning strategies are termed ResMatch and sResMatch respectively. Extensive experiments, including feature matching, pose estimation and visual localization, confirm the superiority of our networks

The Potential of a First LEGO League Robotics Program in Teaching 21st Century Skills: An Exploratory Study

Business and political leaders in the US call for schools to teach 21st century skills. In the meantime, researchers call for more research to develop curriculum that teach 21st century skills. In this study, the authors examine the experience of a First LEGO League (FLL) robotics team to explore the potential of FLL for teaching 21stcentury skills. We found that the program provided opportunities for learning many 21st century skills such as systems thinking, decision making, problem solving, teamwork, conflict resolution, flexibility, perseverance, and selfmanagement. We also found that instructional strategies such as modeling, coaching, scaffolding, examples and case studies were important in providing successful experience to children. For children to retain and transfer these 21stcentury skills, articulation and reflection are critical

The Ecological Effects of Ant-Aphid Mutualism on Plants at a Large Spatial Scale

The protective ant-plant interaction has been considered as a model system in studying mutualistic interactions, but we know little about the ecological effects of the mutualism at relatively larger spatial scales. In this study, by excluding an aphid-tending ant species (Lasius fuliginosus) from all host oak trees (Quercus liaotungensis) in 20x20 m plots, we evaluated the effects of ants on herbivory, fruit production and leaf toughness of the host tree. Through a two years study, we found that ants have a significant anti-herbivory effect on the host tree, with no effects on fruit production. At the end of the growing season, leaf toughness for plants without ants increased significantly. This suggests that ants are reliable and effective bodyguards for plants at larger spatial scales. For plants, the possible tradeoff between different defensive strategies at larger scale should be focused in further works

Understand Data Preprocessing for Effective End-to-End Training of Deep Neural Networks

In this paper, we primarily focus on understanding the data preprocessing pipeline for DNN Training in the public cloud. First, we run experiments to test the performance implications of the two major data preprocessing methods using either raw data or record files. The preliminary results show that data preprocessing is a clear bottleneck, even with the most efficient software and hardware configuration enabled by NVIDIA DALI, a high-optimized data preprocessing library. Second, we identify the potential causes, exercise a variety of optimization methods, and present their pros and cons. We hope this work will shed light on the new co-design of ``data storage, loading pipeline'' and ``training framework'' and flexible resource configurations between them so that the resources can be fully exploited and performance can be maximized