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The approximate nearest neighbor(ANN) search over high dimensional data has become an unavoidable service for online applications. Fast and high-quality results of unknown queries are the largest challenge that most algorithms faced with. Locality Sensitive Hashing(LSH) is a well-known ANN search algorithm while suffers from inefficient index structure, poor accuracy in distributed scheme. The traditional index structures have most significant bits(MSB) problem, which is their indexing strategies have an implicit assumption that the bits from one direction in the hash value have higher priority. In this thesis, we propose a new content-based index called Random Draw Forest(RDF), which not only uses an adaptive tree structure by applying the dynamic length of compound hash functions to meet the different cardinality of data, but also applies the shuffling permutations to solve the MSB problem in the traditional LSH-based index. To raise the accuracy in the distributed scheme, we design a variable steps lookup strategy to search the multiple step sub-indexes which are most likely to hold the mistakenly partitioned similar objects. By analyzing the index, we show that RDF has a higher probability to retrieve the similar objects compare to the original index structure. In the experiment, we first learn the performance of different hash functions, then we show the effect of parameters in RDF and the performance of RDF compared with other LSH-based methods to meet the ANN search. / Thesis / Master of Science (MSc)

Nonlinear Galerkin methods utilize approximate inertial manifolds to reduce the spatial error of the standard Galerkin method. For certain scenarios, where a rough forcing term is used, a simple postprocessing step yields the same improvements that can be observed with nonlinear Galerkin. We show that this improvement is mainly due to the information about the forcing term that is neglected by standard Galerkin. Moreover, we construct a simple postprocessing scheme that uses only this neglected information but gives the same increase in accuracy as nonlinear or postprocessed Galerkin methods. / Master of Science

Yes / This article presents the homotopy perturbation method (HPM) employed to investigate the effects of inclination on the thermal behavior of a porous fin heat sink. The study aims to review the thermal characterization of heat sink with the inclined porous fin of rectangular geometry. The study establishes that heat sink of an inclined porous fin shows a higher thermal performance compared to a heat sink of equal dimension with a vertical porous fin. In addition, the study also shows that the performance of inclined or tilted fin increases with decrease in length–thickness aspect ratio. The study further reveals that increase in the internal heat generation variable decreases the fin temperature gradient, which invariably decreases the heat transfer of the fin. The obtained results using HPM highlights the accuracy of the present method for the analysis of nonlinear heat transfer problems, as it agrees well with the established results of Runge–Kutta. / Supported in part by the Tertiary Education Trust Fund of Federal Government of Nigeria, and the European Union’s Horizon 2020 research and innovation programme under grant agreement H2020-MSCA-ITN-2016SECRET-722424.