Intrinsic energy conversion mechanism via telescopic extension and retraction of concentric carbon nanotubes

The conversion of other forms of energy into mechanical work through the geometrical extension and retraction of nanomaterials has a wide variety of potential applications, including for mimicking biomotors. Here, using molecular dynamic simulations, we demonstrate that there exists an intrinsic energy conversion mechanism between thermal energy and mechanical work in the telescopic motions of double-walled carbon nanotubes (DWCNTs). A DWCNT can inherently convert heat into mechanical work in its telescopic extension process, while convert mechanical energy into heat in its telescopic retraction process. These two processes are thermodynamically reversible. The underlying mechanism for this reversibility is that the entropy changes with the telescopic overlapping length of concentric individual tubes. We find also that the entropy effect enlarges with the decreasing intertube space of DWCNTs. As a result, the spontaneously telescopic motion of a condensed DWCNT can be switched to extrusion by rising the system temperature above a critical value. These findings are important for fundamentally understanding the mechanical behavior of concentric nanotubes, and may have general implications in the application of DWCNTs as linear motors in nanodevices

Label Embedding by Johnson-Lindenstrauss Matrices

We present a simple and scalable framework for extreme multiclass classification based on Johnson-Lindenstrauss matrices (JLMs). Using the columns of a JLM to embed the labels, a $C$-class classification problem is transformed into a regression problem with \cO(\log C) output dimension. We derive an excess risk bound, revealing a tradeoff between computational efficiency and prediction accuracy, and further show that under the Massart noise condition, the penalty for dimension reduction vanishes. Our approach is easily parallelizable, and experimental results demonstrate its effectiveness and scalability in large-scale applications