Efficiently computing weighted proximity relationships in spatial databases

Spatial data mining recently emerges from a number of real applications, such as real-estate marketing, urban planning, weather forecasting, medical image analysis, road traffic accident analysis, etc. It demands for efficient solutions for many new, expensive, and complicated problems. In this paper, we investigate the problem of evaluating the top k distinguished “features” for a “cluster” based on weighted proximity relationships between the cluster and features. We measure proximity in an average fashion to address possible nonuniform data distribution in a cluster. Combining a standard multi-step paradigm with new lower and upper proximity bounds, we presented an efficient algorithm to solve the problem. The algorithm is implemented in several different modes. Our experiment results not only give a comparison among them but also illustrate the efficiency of the algorithm.

Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Dispersion and size control of layered double hydroxide nanoparticles in aqueous solutions

We report a simple but efficient method to prepare stable homogeneous suspensions containing monodispersed MgAl layered double hydroxide (LDH) nanoparticles that have wide promising applications in cellular drug ( gene) delivery, polymer/LDH nanocomposites, and LDH thin films for catalysis, gas separation, sensing, and electrochemical materials. This new method involves a fast coprecipitation followed by controlled hydrothermal treatment under different conditions and produces stable homogeneous LDH suspensions under variable hydrothermal treatment conditions. Moreover, the relationship between the LDH particle size and the hydrothermal treatment conditions ( time, temperature, and concentration) has been systematically investigated, which indicates that the LDH particle size can be precisely controlled between 40 and 300 nm by adjusting these conditions. The reproducibility of making the identical suspensions under identical conditions has been confirmed with a number of experiments. The dispersion of agglomerated LDH aggregates into individual LDH crystallites during the hydrothermal treatment has been further discussed. This method has also been successfully applied to preparing stable homogeneous LDH suspensions containing various other metal ions such as Ni2+, Fe2+, Fe3+, Co2+, Cd2+, and Gd3+ in the hydroxide layers and many inorganic anions such as Cl-, CO32-, NO3-, and SO42-.