Local Kernels and the Geometric Structure of Data

We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the generator of a continuous Markov process, which converges in the limit of large data. We explicitly connect the drift and diffusion coefficients of the process to the moments of the kernel. Moreover, when the kernel is symmetric, the generator is the Laplace-Beltrami operator with respect to a geometry which is influenced by the embedding geometry and the properties of the kernel. In particular, this allows us to generate any Riemannian geometry by an appropriate choice of local kernel. In this way, we continue a program of Belkin, Niyogi, Coifman and others to reinterpret the current diverse collection of kernel-based data analysis methods and place them in a geometric framework. We show how to use this framework to design local kernels invariant to various features of data. These data-driven local kernels can be used to construct conformally invariant embeddings and reconstruct global diffeomorphisms

Kalman-Takens filtering in the presence of dynamical noise

The use of data assimilation for the merging of observed data with dynamical models is becoming standard in modern physics. If a parametric model is known, methods such as Kalman filtering have been developed for this purpose. If no model is known, a hybrid Kalman-Takens method has been recently introduced, in order to exploit the advantages of optimal filtering in a nonparametric setting. This procedure replaces the parametric model with dynamics reconstructed from delay coordinates, while using the Kalman update formulation to assimilate new observations. We find that this hybrid approach results in comparable efficiency to parametric methods in identifying underlying dynamics, even in the presence of dynamical noise. By combining the Kalman-Takens method with an adaptive filtering procedure we are able to estimate the statistics of the observational and dynamical noise. This solves a long standing problem of separating dynamical and observational noise in time series data, which is especially challenging when no dynamical model is specified

MICROBIAL CONTROLS ON THE ENVIRONMENTAL FATE OF CARBON NANOMATERIALS

Since the synthesis of the first carbon nanomaterials (CNM) 30 years ago, researchers and manufacturers have recognized the potential of these materials to transform the world. The unique physical properties and incredible resilience of these materials gives them countless applications and has led to significant increases in their production over the last decade. However, despite their growing prevalence, the properties and processes controlling the degradation of CNM in the environment remain poorly understood. The primary purpose of this dissertation is to examine the role of environmental microorganisms in degrading CNM and to elucidate which CNM properties and environmental processes represent important controls on this degradation. To accomplish this, a series of incubation studies were conducted in which pure fungal cultures and soils were exposed to a CNM

Contextual Pedagogy: A Praxis Engaging Black Male High School Students Toward Eliminating the Achievement Gap

Problems facing black male students in K-12 education are as multiple as they are complex. Regarding this issue, the research literature revealed three major themes that came to the foreground: 1) the lack of school engagement, 2) academic achievement gaps, and 3) racism. In response, the purpose of this qualitative research study was to explore the contextual pedagogical influences of Project-Based Learning (PBL) on school engagement, creativity, and problem solving for fourteen black male students in a suburban Minnesota high school. The methodology for this was an instrumental case study (i.e., seeking understanding of phenomena beyond the case itself). Findings in this case revealed that the PBL process in several ways engaged black males. Critical Race Theory combined with contextual pedagogic practice was found to be vital to engaging these students. This study indicated that educators would benefit by examining how to define achievement of black males in light of antiracist teaching practices to foster more opportunities for them to succeed. There was no disruptive behavior observed during the PBL sessions. However, the issue of racial disparity in school suspensions did surface during the study, leading toward discourse about antiracist teaching practice, and policy for school leaders. More research is needed to explore how these approaches can work within the structure of public schools

Persuasion and instructional media: the use of a fear provoking videotape to change attitudes toward smoking in field dependent/independent college students

http://www.worldcat.org/oclc/955912

Working Definitions Council of Deans

The underpinnings of what it means for higher education to support diversity, equity and inclusion is often problematized by different interpretations of key terms necessary to work systematically. Inspired by efforts in both the office of Diversity, Equity and Inclusion and Academic Affairs, we will use the following working definitions in its efforts to increase awareness, understanding and collective action as we work toward our vision and mission