Multiple-Level Power Allocation Strategy for Secondary Users in Cognitive Radio Networks

In this paper, we propose a multiple-level power allocation strategy for the secondary user (SU) in cognitive radio (CR) networks. Different from the conventional strategies, where SU either stays silent or transmit with a constant/binary power depending on the busy/idle status of the primary user (PU), the proposed strategy allows SU to choose different power levels according to a carefully designed function of the receiving energy. The way of the power level selection is optimized to maximize the achievable rate of SU under the constraints of average transmit power at SU and average interference power at PU. Simulation results demonstrate that the proposed strategy can significantly improve the performance of SU compared to the conventional strategies.Comment: 12 page

Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation

We consider testing for two-sample means of high dimensional populations by thresholding. Two tests are investigated, which are designed for better power performance when the two population mean vectors differ only in sparsely populated coordinates. The first test is constructed by carrying out thresholding to remove the non-signal bearing dimensions. The second test combines data transformation via the precision matrix with the thresholding. The benefits of the thresholding and the data transformations are showed by a reduced variance of the test thresholding statistics, the improved power and a wider detection region of the tests. Simulation experiments and an empirical study are performed to confirm the theoretical findings and to demonstrate the practical implementations.Comment: 64 page

Rotationally symmetric harmonic diffeomorphisms between surfaces

In this paper, we show that the nonexistence of rotationally symmetric harmonic diffeomorphism between the unit disk without the origin and a punctured disc with hyperbolic metric on the target.Comment: Minor typos correcte

Coupled effects of local movement and global interaction on contagion

By incorporating segregated spatial domain and individual-based linkage into the SIS (susceptible-infected-susceptible) model, we investigate the coupled effects of random walk and intragroup interaction on contagion. Compared with the situation where only local movement or individual-based linkage exists, the coexistence of them leads to a wider spread of infectious disease. The roles of narrowing segregated spatial domain and reducing mobility in epidemic control are checked, these two measures are found to be conducive to curbing the spread of infectious disease. Considering heterogeneous time scales between local movement and global interaction, a log-log relation between the change in the number of infected individuals and the timescale $\tau$ is found. A theoretical analysis indicates that the evolutionary dynamics in the present model is related to the encounter probability and the encounter time. A functional relation between the epidemic threshold and the ratio of shortcuts, and a functional relation between the encounter time and the timescale $\tau$ are found