Exploring Bit-Difference for Approximate KNN Search in High-dimensional Databases

In this paper, we develop a novel index structure to support efficient approximate k-nearest neighbor (KNN) query in high-dimensional databases. In high-dimensional spaces, the computational cost of the distance (e.g., Euclidean distance) between two points contributes a dominant portion of the overall query response time for memory processing. To reduce the distance computation, we first propose a structure (BID) using BIt-Difference to answer approximate KNN query. The BID employs one bit to represent each feature vector of point and the number of bit-difference is used to prune the further points. To facilitate real dataset which is typically skewed, we enhance the BID mechanism with clustering, cluster adapted bitcoder and dimensional weight, named the BID⁺. Extensive experiments are conducted to show that our proposed method yields significant performance advantages over the existing index structures on both real life and synthetic high-dimensional datasets.

Coordinate-Independent Computations on Differential Equations

This project investigates the computational representation of differentiable manifolds, with the primary goal of solving partial differential equations using multiple coordinate systems on general n- dimensional spaces. In the process, this abstraction is used to perform accurate integrations of ordinary differential equations using multiple coordinate systems. In the case of linear partial differential equations, however, unexpected difficulties arise even with the simplest equations.

Biological Routes to Gold Nanoplates

Much effort has been devoted to the synthesis of gold nanoparticles with different shapes, including the zero-dimensional nanospheres, one dimensional nanorods, and two-dimensional nanoplates. Compared to zero or one dimensional nanostructures, the synthesis of two-dimensional nanostructures in high yield has always been more involved, often requiring complex and time-consuming steps such as morphology transformation from the nanospheres, or the seeded growth process. Herein we report a high yield method for gold nanoplate synthesis using the extract of unicellular green alga Chlorella vulgaris, which can be carried out under ambient conditions. More than 90% of the total nanoparticle population is of the platelet morphology, surpassing the previously reported value of 45%. The control of the anisotropic growth of different planes; as well as the lateral size, has also been partially optimized.