Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates

With a view toward fractal spaces, by using a Korevaar-Schoen space approach, we introduce the class of bounded variation (BV) functions in a general framework of strongly local Dirichlet spaces with a heat kernel satisfying sub-Gaussian estimates. Under a weak Bakry-\'Emery curvature type condition, which is new in this setting, this BV class is identified with a heat semigroup based Besov class. As a consequence of this identification, properties of BV functions and associated BV measures are studied in detail. In particular, we prove co-area formulas, global $L^1$ Sobolev embeddings and isoperimetric inequalities. It is shown that for nested fractals or their direct products the BV class we define is dense in $L^1$. The examples of the unbounded Vicsek set, unbounded Sierpinski gasket and unbounded Sierpinski carpet are discussed.Comment: The notes arXiv:1806.03428 will be divided in a series of papers. This is the third paper. v2: Final versio

Microscaled and nanoscaled platinum sensors

We show small and robust platinum resistive heaters and thermometers that are defined by microlithography on silicon substrates. These devices can be used for a wide range of applications, including thermal sensor arrays, programmable thermal sources, and even incandescent light emitters. To explore the miniaturization of such devices, we have developed microscaled and nanoscaled platinum resistor arrays with wire widths as small as 75 nm, fabricated lithographically to provide highly localized heating and accurate resistance (and hence temperature) measurements. We present some of these potential applications of microfabricated platinum resistors in sensing and spectroscopy

Enhanced multi-source data analysis for personalized sleep-wake pattern recognition and sleep parameter extraction

The file attached to this record is the author's final peer reviewed version.Sleep behavior is traditionally monitored with polysomnography, and sleep stage patterns are a key marker for sleep quality used to detect anomalies and diagnose diseases. With the growing demand for personalized healthcare and the prevalence of the Internet of Things, there is a trend to use everyday technologies for sleep behavior analysis at home, having the potential to eliminate expensive in-hospital monitoring. In this paper, we conceived a multi-source data mining approach to personalized sleep-wake pattern recog-nition which uses physiological data and personal information to facilitate fine-grained detection. Physiological data includes actigraphy and heart rate variability and personal data makes use of gender, health status and race infor-mation which are known influence factors. Moreover, we developed a personal-ized sleep parameter extraction technique fused with the sleep-wake approach, achieving personalized instead of static thresholds for decision-making. Results show that the proposed approach improves the accuracy of sleep and wake stage recognition, therefore, offers a new solution for personalized sleep-based health monitoring