Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

A Wireless EEG Acquisition Platform based on Embedded Systems

This paper proposes a wireless EEG acquisition platform based on Open Multimedia Architecture Platform (OMAP) embedded system. A high-impedance active dry electrode was tested for improving the scalp- electrode interface. It was used the sigma-delta ADS1298 analog-to-digital converter, and developed a “kernelspace” character driver to manage the communications between the converter unit and the OMAP’s ARM core. The acquired EEG signal data is processed by a “userspace” application, which accesses the driver’s memory, saves the data to a SD-card and transmits them through a wireless TCP/IP-socket to a PC. The electrodes were tested through the alpha wave replacement phenomenon. The experimental results presented the expected alpha rhythm (8-13 Hz) reactiveness to the eyes opening task. The driver spends about 725 μs to acquire and store the data samples. The application takes about 244 μs to get the data from the driver and 1.4 ms to save it in the SD-card. A WiFi throughput of 12.8Mbps was measured which results in a transmission time of 5 ms for 512 kb of data. The embedded system consumes about 200 mAh when wireless off and 400 mAh when it is on. The system exhibits a reliable performance to record EEG signals and transmit them wirelessly. Besides the microcontroller-based architectures, the proposed platform demonstrates that powerful ARM processors running embedded operating systems can be programmed with real-time constrains at the kernel level in order to control hardware, while maintaining their parallel processing abilities in high level software applications.