Modulated Unit-Norm Tight Frames for Compressed Sensing

In this paper, we propose a compressed sensing (CS) framework that consists of three parts: a unit-norm tight frame (UTF), a random diagonal matrix and a column-wise orthonormal matrix. We prove that this structure satisfies the restricted isometry property (RIP) with high probability if the number of measurements $m = O(s \log^2s \log^2n)$ for $s$-sparse signals of length $n$ and if the column-wise orthonormal matrix is bounded. Some existing structured sensing models can be studied under this framework, which then gives tighter bounds on the required number of measurements to satisfy the RIP. More importantly, we propose several structured sensing models by appealing to this unified framework, such as a general sensing model with arbitrary/determinisic subsamplers, a fast and efficient block compressed sensing scheme, and structured sensing matrices with deterministic phase modulations, all of which can lead to improvements on practical applications. In particular, one of the constructions is applied to simplify the transceiver design of CS-based channel estimation for orthogonal frequency division multiplexing (OFDM) systems.Comment: submitted to IEEE Transactions on Signal Processin

Collaborative Inference of Coexisting Information Diffusions

Recently, \textit{diffusion history inference} has become an emerging research topic due to its great benefits for various applications, whose purpose is to reconstruct the missing histories of information diffusion traces according to incomplete observations. The existing methods, however, often focus only on single information diffusion trace, while in a real-world social network, there often coexist multiple information diffusions over the same network. In this paper, we propose a novel approach called Collaborative Inference Model (CIM) for the problem of the inference of coexisting information diffusions. By exploiting the synergism between the coexisting information diffusions, CIM holistically models multiple information diffusions as a sparse 4th-order tensor called Coexisting Diffusions Tensor (CDT) without any prior assumption of diffusion models, and collaboratively infers the histories of the coexisting information diffusions via a low-rank approximation of CDT with a fusion of heterogeneous constraints generated from additional data sources. To improve the efficiency, we further propose an optimal algorithm called Time Window based Parallel Decomposition Algorithm (TWPDA), which can speed up the inference without compromise on the accuracy by utilizing the temporal locality of information diffusions. The extensive experiments conducted on real world datasets and synthetic datasets verify the effectiveness and efficiency of CIM and TWPDA

BcB_c Exclusive Decays to Charmonium and a Light Meson at Next-to-Leading Order Accuracy

In this paper the next-to-leading order (NLO) corrections to $B_c$ meson exclusive decays to S-wave charmonia and light pseudoscalar or vector mesons, i.e. $\pi$, $K$, $\rho$, and $K^*$, are performed within non-relativistic (NR) QCD approach. The non-factorizable contribution is included, which is absent in traditional naive factorization (NF). And the theoretical uncertainties for their branching ratios are reduced compared with that of direct tree level calculation. Numerical results show that NLO QCD corrections markedly enhance the branching ratio with a K factor of 1.75 for $B_{c}^{\pm}\to \eta_{c} \pi^{\pm}$ and 1.31 for $B_{c}^{\pm}\to J/\psi \pi^{\pm}$. In order to investigate the asymptotic behavior, the analytic form is obtained in the heavy quark limit, i.e. $m_b \to \infty$. We note that annihilation topologies contribute trivia in this limit, and the corrections at leading order in $z= m_c/m_b$ expansion come from form factors and hard spectator interactions. At last, some related phenomenologies are also discussed.Comment: 20 pages, 7 figures and 5 table