Data mining student activity patterns in an interactive activity-based STEM learning environment

Jupyter Notebook is gaining in popularity for STEM instruction and activity-based learning. This platform for sharing interactive documents via a web interface allows instructors to combine a variety of media together with interactive and editable code, providing rich opportunities for an active learning pedagogy. Other online learning environments, such as Canvas and Moodle, provide or integrate learning analytics for the use of administrators, educators, and students to improve learning outcomes; however, these platforms lack the rich learning environment of Jupyter Notebook. Also, with increasing interest in online learning, research communities have arisen for Learning Analytics and Educational Data Mining. Unfortunately, these research communities have not yet begun to address the Jupyter Notebook learning environment. The University of Missouri College of Engineering offers a Program of Study in Data Science (PSDS) under contract with the National Geospatial Intelligence Agency (NGA.) This program is delivered online, making heavy use of Jupyter notebooks served by JupyterHub for active engagement with course content. The PSDS infrastructure uses the Graylog log management program to collect Jupyter logs, which are stored in an integrated Elasticsearch document store for a period of months. The PSDS program provides an excellent case study for a proof-of-concept in applying learning analytics to the Jupyter learning environment. This thesis consists of two major parts. (1) Mining the Graylog system to extract useful log messages, transformation of those messages into student-activities features, and loading the data into a PostgreSQL database for long-term storage. (2) Developing a variety of visualizations of student activity for administrators, instructors and students. The pedological structure of PSDS courses allows unique insights into student engagement with the course material. Finally, recommendations are made for the development of a more comprehensive logging system and additional analyses that could be performed.Includes bibliographical reference

Composite lacunary polynomials and the proof of a conjecture of Schinzel

Let $g(x)$ be a fixed non-constant complex polynomial. It was conjectured by Schinzel that if $g(h(x))$ has boundedly many terms, then h(x)\in \C[x] must also have boundedly many terms. Solving an older conjecture raised by R\'enyi and by Erd\"os, Schinzel had proved this in the special cases $g(x)=x^d$; however that method does not extend to the general case. Here we prove the full Schinzel's conjecture (actually in sharper form) by a completely different method. Simultaneously we establish an "algorithmic" parametric description of the general decomposition $f(x)=g(h(x))$, where $f$ is a polynomial with a given number of terms and $g,h$ are arbitrary polynomials. As a corollary, this implies for instance that a polynomial with $l$ terms and given coefficients is non-trivially decomposable if and only if the degree-vector lies in the union of certain finitely many subgroups of $\Z^l$.Comment: 9 page

Exportin-5, a novel karyopherin, mediates nuclear export of double-stranded RNA binding proteins

We have identified a novel human karyopherin (Kap)β family member that is related to human Crm1 and the Saccharomyces cerevisiae protein, Msn5p/Kap142p. Like other known transport receptors, this Kap binds specifically to RanGTP, interacts with nucleoporins, and shuttles between the nuclear and cytoplasmic compartments. We report that interleukin enhancer binding factor (ILF)3, a double-stranded RNA binding protein, associates with this Kap in a RanGTP-dependent manner and that its double-stranded RNA binding domain (dsRBD) is the limiting sequence required for this interaction. Importantly, the Kap interacts with dsRBDs found in several other proteins and binding is blocked by double-stranded RNA. We find that the dsRBD of ILF3 functions as a novel nuclear export sequence (NES) in intact cells, and its ability to serve as an NES is dependent on the expression of the Kap. In digitonin-permeabilized cells, the Kap but not Crm1 stimulated nuclear export of ILF3. Based on the ability of this Kap to mediate the export of dsRNA binding proteins, we named the protein exportin-5. We propose that exportin-5 is not an RNA export factor but instead participates in the regulated translocation of dsRBD proteins to the cytoplasm where they interact with target mRNAs

The role of colloidal organic matter in the marine geochemistry of PCB's

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric and Planetary Sciences and the Woods Hole Oceanographic Institution, 1986.Microfiche copy available in Archives and Science.Vita.Bibliography: leaves 271-297.by Bruce J. Brownawell.Ph.D

A Weil-Barsotti formula for Drinfeld modules

We study the group of extensions in the category of Drinfeld modules and Anderson's t-modules, and we show in certain cases that this group can itself be given the structure of a t-module. Our main result is a Drinfeld module analogue of the Weil-Barsotti formula for abelian varieties. Extensions of general t-modules are also considered, in particular extensions of tensor powers of the Carlitz module. We motivate these results from various directions and compare to the situation of elliptic curves.Comment: 20 pages, latex file. To appear in Journal of Number Theor

Phenylalanine as a hydroxyl radical-specific probe in pyrite slurries

The abundant iron sulfide mineral pyrite has been shown to catalytically produce hydrogen peroxide (H2O2) and hydroxyl radical (.OH) in slurries of oxygenated water. Understanding the formation and fate of these reactive oxygen species is important to biological and ecological systems as exposure can lead to deleterious health effects, but also environmental engineering during the optimization of remediation approaches for possible treatment of contaminated waste streams. This study presents the use of the amino acid phenylalanine (Phe) to monitor the kinetics of pyrite-induced .OH formation through rates of hydroxylation forming three isomers of tyrosine (Tyr) - ortho-, meta-, and para-Tyr. Results indicate that about 50% of the Phe loss results in Tyr formation, and that these products further react with .OH at rates comparable to Phe. The overall loss of Phe appeared to be pseudo first-order in [Phe] as a function of time, but for the first time it is shown that initial rates were much less than first-order as a function of initial substrate concentration, [Phe]o. These results can be rationalized by considering that the effective concentration of .OH in solution is lower at a higher level of reactant and that an increasing fraction of .OH is consumed by Phe-degradation products as a function of time. A simplified first-order model was created to describe Phe loss in pyrite slurries which incorporates the [Phe]o, a first-order dependence on pyrite surface area, the assumption that all Phe degradation products compete equally for the limited supply of highly reactive .OH, and a flux that is related to the release of H2O2 from the pyrite surface (a result of the incomplete reduction of oxygen at the pyrite surface). An empirically derived rate constant, Kpyr, was introduced to describe a variable .OH-reactivity for different batches of pyrite. Both the simplified first-order kinetic model, and a more detailed numerical simulation, yielded results that compare well to the observed kinetic data describing the effects of variations in concentrations of both initial Phe and pyrite. This work supports the use of Phe as a useful probe to assess the formation of .OH in the presence of pyrite, and its possible utility for similar applications with other minerals

Zero Order Estimates for Analytic Functions

The primary goal of this paper is to provide a general multiplicity estimate. Our main theorem allows to reduce a proof of multiplicity lemma to the study of ideals stable under some appropriate transformation of a polynomial ring. In particular, this result leads to a new link between the theory of polarized algebraic dynamical systems and transcendental number theory. On the other hand, it allows to establish an improvement of Nesterenko's conditional result on solutions of systems of differential equations. We also deduce, under some condition on stable varieties, the optimal multiplicity estimate in the case of generalized Mahler's functional equations, previously studied by Mahler, Nishioka, Topfer and others. Further, analyzing stable ideals we prove the unconditional optimal result in the case of linear functional systems of generalized Mahler's type. The latter result generalizes a famous theorem of Nishioka (1986) previously conjectured by Mahler (1969), and simultaneously it gives a counterpart in the case of functional systems for an important unconditional result of Nesterenko (1977) concerning linear differential systems. In summary, we provide a new universal tool for transcendental number theory, applicable with fields of any characteristic. It opens the way to new results on algebraic independence, as shown in Zorin (2010).Comment: 42 page

Using Elimination Theory to construct Rigid Matrices

The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r. Since its introduction by Valiant (1977), rigidity and similar rank-robustness functions of matrices have found numerous applications in circuit complexity, communication complexity, and learning complexity. Almost all nxn matrices over an infinite field have a rigidity of (n-r)^2. It is a long-standing open question to construct infinite families of explicit matrices even with superlinear rigidity when r = Omega(n). In this paper, we construct an infinite family of complex matrices with the largest possible, i.e., (n-r)^2, rigidity. The entries of an n x n matrix in this family are distinct primitive roots of unity of orders roughly exp(n^2 log n). To the best of our knowledge, this is the first family of concrete (but not entirely explicit) matrices having maximal rigidity and a succinct algebraic description. Our construction is based on elimination theory of polynomial ideals. In particular, we use results on the existence of polynomials in elimination ideals with effective degree upper bounds (effective Nullstellensatz). Using elementary algebraic geometry, we prove that the dimension of the affine variety of matrices of rigidity at most k is exactly n^2-(n-r)^2+k. Finally, we use elimination theory to examine whether the rigidity function is semi-continuous.Comment: 25 Pages, minor typos correcte

Zero estimates with moving targets

Zero estimates have a classical history in diophantine approximation and transcendence, as well as more recent applications to counting rational points on analytic sets. We give some examples showing that the sharpest conceivable results can be false, and in some cases the natural guess has even to be doubled. A by-product is a "non-degenerate" case of the (unproved) "Zilber Nullstellensatz" in connexion with "Strong Exponential Closure"