On equivariant Serre problem for principal bundles

Let $E_G$ be a $\Gamma$--equivariant algebraic principal $G$--bundle over a normal complex affine variety $X$ equipped with an action of $\Gamma$, where $G$ and $\Gamma$ are complex linear algebraic groups. Suppose $X$ is contractible as a topological $\Gamma$--space with a dense orbit, and $x_0 \in X$ is a $\Gamma$--fixed point. We show that if $\Gamma$ is reductive, then $E_G$ admits a $\Gamma$--equivariant isomorphism with the product principal $G$--bundle $X \times_{\rho} E_G(x_0)$, where $\rho\,:\, \Gamma \, \longrightarrow\, G$ is a homomorphism between algebraic groups. As a consequence, any torus equivariant principal $G$-bundle over an affine toric variety is equivariantly trivial. This leads to a classification of torus equivariant principal $G$-bundles over any complex toric variety.Comment: References added. To appear in the International Journal of Mathematic

Tannakian classification of equivariant principal bundles on toric varieties

Let $X$ be a complete toric variety equipped with the action of a torus $T$ and $G$ a reductive algebraic group, defined over an algebraically closed field $K$. We introduce the notion of a compatible $\Sigma$--filtered algebra associated to $X$, generalizing the notion of a compatible $\Sigma$--filtered vector space due to Klyachko, where $\Sigma$ denotes the fan of $X$. We combine Klyachko's classification of $T$--equivariant vector bundles on $X$ with Nori's Tannakian approach to principal $G$--bundles, to give an equivalence of categories between $T$--equivariant principal $G$--bundles on $X$ and certain compatible $\Sigma$--filtered algebras associated to $X$, when the characteristic of $K$ is $0$.Comment: 22 pages, revised version, to appear in Transform. Group

DESIGN AND EXPERIMENTAL ANALYSIS OF FURNACE FOR THE PRODUCTION OF BAMBOO CHARCOAL

This paper presents the study of carbonization systems for the production of Bamboo Charcoal which is formed on dry distillation of raw bamboo. The paper mentions the drawbacks of the conventional practices of production of Bamboo Charcoal. Design of a new charcoal production unit is aimed at eliminating the identified drawbacks in the present methodology of production making the process of production faster and more efficient by minimizing heat loss during the production process. Designing is attempted with strong consideration for manufacture, operational cost and ease of operation of the furnace as the process finds application amongst rural people with little or no technical knowhow, making simplicity of design absolutely critical for implementation of the developed technology. Results of testing and experimentation presented in this paper describe the working prototype confirming qualitative and quantitative improvements in the bamboo charcoal being produced as compared to the conventional method of production

Acceptability, safety and contraceptive efficacy of a new single-rod subdermal 3-ketodesogestrel implant in Singaporean women acceptors

Ph.DDOCTOR OF MEDICIN

Semi-supervised and Active Image Clustering with Pairwise Constraints from Humans

Clustering images has been an interesting problem for computer vision and machine learning researchers for many years. However as the number of categories increases, image clustering becomes extremely hard and is not possible to use for many practical applications. Researchers have proposed several methods that use semi-supervision from humans to improve clustering. Constrained clustering, where users indicate whether an image pair belong to the same category or not, is a well-known paradigm for semi-supervision. Past research has shown that pairwise constraints have the potential to significantly improve clustering performance. There are two major components to constrained clustering research: how pairwise constraints can be used to improve clustering (e.g: constrained clustering algorithms, distance or metric learning methods) and determining which constraints are most useful for improving clustering (e.g.: active or interactive clustering methods). In this thesis we propose three different approaches to improve pairwise constrained clustering spanning both of these components. First, we propose a distance learning method in non-vector spaces, where the triangle inequality is used to propagate the pairwise constraints to the unsupervised image pairs. This approach can work with any pairwise distance and does not require any vector representation of images. Second, we propose an algorithm for active image pair selection. A novel method is developed to choose the most useful pairs to show a person, obtaining constraints that improve clustering. Third, we study how pairwise constraints can effectively be used to cluster large image datasets. Complete clustering of large datasets requires an extremely large number of pairwise constraints and may not be feasible in practice. We propose a new algorithm to cluster a subset of the images only (we call this subclustering), which will produce a few examples from each class. Subclustering will produce smaller but purer clusters and can be used for summarization, category discovery, browsing, image search, etc.... Finally, we make use of human input in an active subclustering algorithm to further improve results. We perform experiments on several real world datasets such as faces, leaves, videos and scenes and empirically show that our approaches can advance the state-of-the-art in clustering