STUDIES TOWARD TETRAHYDROFURAN-CONTAINING NATURAL PRODUCTS: TOTAL SYNTHESIS OF AMPHIDINOLIDE C AND OXYLIPIDS

Tetrahydrofurans (thf) and tetrahydropyrans (thp) are important structural motifs found in a broad array of biologically relevant natural products such as polyether antibiotics and acetogenins. Classic methods used for thf- or thp-ring synthesis have their own advantages and disadvantages which tend to be substrate specific. Therefore, development of new and efficient methods is imperative especially to address the issue of diastereoselectivity when attainment of both cis- and trans-2,5-thf (or 2,6-thp) is highly desirable. Herein, a strategy of cross-metathesis and Pd(0)-catalyzed cyclization, useful for obtaining both cis- and trans-2,5-disubstituted thf (or 2,6-disubstituted thp), will be discussed along with its application in the synthesis of amphidinolide C and oxylipids. Amphidinolide C, a complex macrolide isolated from Okinawan marine dinoflagellates, exhibits in vitro cytotoxicity against human skin cancer cells at a low nano-molar range. Oxylipids isolated from Australian brown algae show strong activity against parasitic nematodes. This dissertation embodies investigations, synthetic efforts, and insights in achieving the total synthesis of these marine natural products

Micro-macro transition and simplified contact models for wet granular materials

Wet granular materials in a quasi-static steady state shear flow have been studied with discrete particle simulations. Macroscopic quantities, consistent with the conservation laws of continuum theory, are obtained by time averaging and spatial coarse-graining. Initial studies involve understanding the effect of liquid content and liquid properties like the surface tension on the macroscopic quantities. Two parameters of the liquid bridge contact model have been studied as the constitutive parameters that define the structure of this model (i) the rupture distance of the liquid bridge model, which is proportional to the liquid content, and (ii) the maximum adhesive force, as controlled by the surface tension of the liquid. Subsequently a correlation is developed between these micro parameters and the steady state cohesion in the limit of zero confining pressure. Furthermore, as second result, the macroscopic torque measured at the walls, which is an experimentally accessible parameter, is predicted from our simulation results as a dependence on the micro-parameters. Finally, the steady state cohesion of a realistic non-linear liquid bridge contact model scales well with the steady state cohesion for a simpler linearized irreversible contact model with the same maximum adhesive force and equal energy dissipated per contact

Inferring Concept Prerequisite Relations from Online Educational Resources

The Internet has rich and rapidly increasing sources of high quality educational content. Inferring prerequisite relations between educational concepts is required for modern large-scale online educational technology applications such as personalized recommendations and automatic curriculum creation. We present PREREQ, a new supervised learning method for inferring concept prerequisite relations. PREREQ is designed using latent representations of concepts obtained from the Pairwise Latent Dirichlet Allocation model, and a neural network based on the Siamese network architecture. PREREQ can learn unknown concept prerequisites from course prerequisites and labeled concept prerequisite data. It outperforms state-of-the-art approaches on benchmark datasets and can effectively learn from very less training data. PREREQ can also use unlabeled video playlists, a steadily growing source of training data, to learn concept prerequisites, thus obviating the need for manual annotation of course prerequisites.Comment: Accepted at the AAAI Conference on Innovative Applications of Artificial Intelligence (IAAI-19

Graded components of local cohomology modules of C\mathfrak{C}-monomial ideals in characteristic zero

Let $A$ be a commutative Noetherian ring of characteristic zero and $R=A[X_1, \ldots, X_d]$ be a polynomial ring over $A$ with the standard $\mathbb{N}^d$-grading. Let $I\subseteq R$ be an ideal which can be generated by elements of the form $aU$ where $a \in A$ (possibly nonunit) and $U$ is a monomial in $X_i$'s. We call such an ideal as a `$\mathfrak{C}$-monomial ideal'. Local cohomology modules supported on monomial ideals gain a great deal of interest due to their applications in the context of toric varieties. It was observed that for $\underline{u} \in \mathbb{Z}^d$, their $\underline{u}^{th}$ components depend only on which coordinates of $\underline{u}$ are negative. In this article, we show that this statement holds true in our general setting, even for certain invariants of the components. We mainly focus on the Bass numbers, injective dimensions, dimensions, associated primes, Bernstein-type dimensions, and multiplicities of the components. Under the extra assumption that $A$ is regular, we describe the finiteness of Bass numbers of each component and bound its injective dimension by the dimension of its support. Finally, we present a structure theorem for the components when $A$ is the ring of formal power series in one variable over a characteristic zero field