Singular degenerate parabolic equations with applications to geometric evolutions

We prove a comparison theorem for viscosity solutions of degenerate parabolic equations which is singular at finite directions of derivatives. We apply our theorem to construct a global generalized evolution for interfaces equations with a certain class of the interface energy not necessarily 02

Inhibitory Effects of Heavy Metal Ions on Endolymphatic DC Potential and Cochlear Microphonics in the Guinea Pig

Endocochlear DC potential (EP) and cochlear microphonics (CM) were investigated in the guinea pig under the influence of the following heavy metal ions; manganese, nickel, cobalt, cadmium and lanthanum. The scala tympani and scala vestibuli were perfused with control and test solutions. CM decreased gradually to 50-80%, but EP showed no change after perfusion with a solution containing 1 mM of metal ions. At a concentration of 10 mM, EP decreased from +80 mV to +11-+48 mV and CM decreased to 15-55%. These decreases in EP and CM were irreversible, and perfusion of the area with the standard solution for 20 min had no effect

3D Histogram Based Anomaly Detection for Categorical Sensor Data in Internet of Things

The applications of Internet-of-things (IoT) deploy massive number of sensors to monitor the system and environment. Anomaly detection on streaming sensor data is an important task for IoT maintenance and operation. In real IoT applications, many sensors report categorical values rather than numerical readings. Unfortunately, most existing anomaly detection methods are designed only for numerical sensor data. They cannot be used to monitor the categorical sensor data. In this study, we design and develop a 3D Histogram based Categorical Anomaly Detection (HCAD) solution to monitor categorical sensor data in IoT. HCAD constructs the histogram model by three dimensions: categorical value, event duration, and frequency. The histogram models are used to profile normal working states of IoT devices. HCAD automatically determines the range of normal data and anomaly threshold. It only requires very limit parameter setting and can be applied to a wide variety of different IoT devices. We implement HCAD and integrate it into an online monitoring system. We test the proposed solution on real IoT datasets such as telemetry data from satellite sensors, air quality data from chemical sensors, and transportation data from traffic sensors. The results of extensive experiments show that HCAD achieves higher detecting accuracy and efficiency than state-of-the-art methods

Singular degenerate parabolic equations with applications to geometric evolutions

We prove a comparison theorem for viscosity solutions of degenerate parabolic equations which is singular at finite directions of derivatives. We apply our theorem to construct a global generalized evolution for interfaces equations with a certain class of the interface energy not necessarily 02