This paper proposes a k-means type clustering algorithm that can automatically calculate variable weights. A new step is introduced to the k-means clustering process to iteratively update variable weights based on the current partition of data and a formula for weight calculation is proposed. The convergency theorem of the new clustering process is given. The variable weights produced by the algorithm measure the importance of variables in clustering and can be used in variable selection in data mining applications where large and complex real data are often involved. Experimental results on both synthetic and real data have shown that the new algorithm outperformed the standard k-means type algorithms in recovering clusters in data.

The sustainable production of chemically recyclable polymers presents a significant opportunity to polymer scientists to tackle the growing environmental and energy problems of current petroleum-based plastics. Despite recent advances, however, there are still pressing needs for an expanded horizon of chemically recyclable polymers. Herein, we introduce a new paradigm of biosourced polythioesters (PTEs) with high polymerizability and complete recyclability under mild and economical conditions. The thiolactone monomers with a high ring strain can be easily prepared in a two-step process from 4-hydroxyproline. Controlled ring-opening polymerizations (ROP) using inexpensive and weak bases afford PTEs with high molar masses (M n) up to 259 kg mol–1 and narrow dispersities generally below 1.15. The properties of PTEs can be readily adjusted by copolymerization and/or pre/post-functionalization on the side chains. Selective and complete depolymerizations of the PTEs in dilute solution at ambient to modest temperatures recycle clean monomers. Density functional theory (DFT) calculation of model reactions provides mechanistic insights and highlights the importance of judicious molecular design. Taken together, the unique ROP/depolymerization chemistry of such PTEs may offer a sustainable solution for creating and manufacturing high-value materials such as optical/photochemical plastics, self-immolative polymers, and degradable biomaterials under situations where recycle and reuse are indispensable.

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Novel ionic liquid-soluble ionic copolymers containing imidazolium ionic liquidlike units have been synthesized. Rhodium nanoparticles stabilized by the ionic copolymer in ionic liquids have been successfully obtained. The nanoparticles showed unprecedented lifetime and activity in arene hydrogenation under forcing conditions (a temperature of 75 degrees C and a hydrogen pressure of 40 bar) with a total turnover (TTO) of 20 000 (in five total recycles of 4000 TTOs each) and a turnover frequency of 250 h-1, demonstrating that the combination of ionic liquids with ionic liquidlike stabilizers is a pathway towards highly stable and active nanoparticle catalysts.