Two-orbital Systems with Crystal Field Splitting and Interorbital Hopping

The nondegenerate two-orbital Hubbard model is studied within the dynamic mean-field theory to reveal the influence of two important factors, i.e. crystal field splitting and interorbital hopping, on orbital selective Mott transition (OSMT) and realistic compound Ca$_{2-x}$Sr$_{x}$RuO$_{4}$. A distinctive feature of the optical conductivity of the two nondegenerate bands is found in OSMT phase, where the metallic character of the wide band is indicated by a nonzero Drude peak, while the insulating narrow band has its Drude peak drop to zero in the mean time. We also find that the OSMT regime expands profoundly with the increase of interorbital hopping integrals. On the contrary, it is shown that large and negative level splitting of the two orbitals diminishes the OSMT regime completely. Applying the present findings to compound Ca$_{2-x}$Sr$_{x}$RuO$_{4}$, we demonstrate that in the doping region from $x=0.2$ to 2.0, the negative level splitting is unfavorable to the OSMT phase.Comment: 7 pages with 5 figure

Nonparametric Detection of Geometric Structures over Networks

Nonparametric detection of existence of an anomalous structure over a network is investigated. Nodes corresponding to the anomalous structure (if one exists) receive samples generated by a distribution q, which is different from a distribution p generating samples for other nodes. If an anomalous structure does not exist, all nodes receive samples generated by p. It is assumed that the distributions p and q are arbitrary and unknown. The goal is to design statistically consistent tests with probability of errors converging to zero as the network size becomes asymptotically large. Kernel-based tests are proposed based on maximum mean discrepancy that measures the distance between mean embeddings of distributions into a reproducing kernel Hilbert space. Detection of an anomalous interval over a line network is first studied. Sufficient conditions on minimum and maximum sizes of candidate anomalous intervals are characterized in order to guarantee the proposed test to be consistent. It is also shown that certain necessary conditions must hold to guarantee any test to be universally consistent. Comparison of sufficient and necessary conditions yields that the proposed test is order-level optimal and nearly optimal respectively in terms of minimum and maximum sizes of candidate anomalous intervals. Generalization of the results to other networks is further developed. Numerical results are provided to demonstrate the performance of the proposed tests.Comment: Submitted for journal publication in November 2015. arXiv admin note: text overlap with arXiv:1404.029

Secrecy Outage and Diversity Analysis of Cognitive Radio Systems

In this paper, we investigate the physical-layer security of a multi-user multi-eavesdropper cognitive radio system, which is composed of multiple cognitive users (CUs) transmitting to a common cognitive base station (CBS), while multiple eavesdroppers may collaborate with each other or perform independently in intercepting the CUs-CBS transmissions, which are called the coordinated and uncoordinated eavesdroppers, respectively. Considering multiple CUs available, we propose the round-robin scheduling as well as the optimal and suboptimal user scheduling schemes for improving the security of CUs-CBS transmissions against eavesdropping attacks. Specifically, the optimal user scheduling is designed by assuming that the channel state information (CSI) of all links from CUs to CBS, to primary user (PU) and to eavesdroppers are available. By contrast, the suboptimal user scheduling only requires the CSI of CUs-CBS links without the PU's and eavesdroppers' CSI. We derive closed-form expressions of the secrecy outage probability of these three scheduling schemes in the presence of the coordinated and uncoordinated eavesdroppers. We also carry out the secrecy diversity analysis and show that the round-robin scheduling achieves the diversity order of only one, whereas the optimal and suboptimal scheduling schemes obtain the full secrecy diversity, no matter whether the eavesdroppers collaborate or not. In addition, numerical secrecy outage results demonstrate that for both the coordinated and uncoordinated eavesdroppers, the optimal user scheduling achieves the best security performance and the round-robin scheduling performs the worst. Finally, upon increasing the number of CUs, the secrecy outage probabilities of the optimal and suboptimal user scheduling schemes both improve significantly.Comment: 16 pages, 5 figures, accepted to appear, IEEE Journal on Selected Areas in Communications, 201