Off-the-Grid Line Spectrum Denoising and Estimation with Multiple Measurement Vectors

Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is the spectrally-sparse signal, which is composed of a small number of spectral atoms with arbitrary frequencies on the unit interval. In this paper we study the problem of line spectrum denoising and estimation with an ensemble of spectrally-sparse signals composed of the same set of continuous-valued frequencies from their partial and noisy observations. Two approaches are developed based on atomic norm minimization and structured covariance estimation, both of which can be solved efficiently via semidefinite programming. The first approach aims to estimate and denoise the set of signals from their partial and noisy observations via atomic norm minimization, and recover the frequencies via examining the dual polynomial of the convex program. We characterize the optimality condition of the proposed algorithm and derive the expected convergence rate for denoising, demonstrating the benefit of including multiple measurement vectors. The second approach aims to recover the population covariance matrix from the partially observed sample covariance matrix by motivating its low-rank Toeplitz structure without recovering the signal ensemble. Performance guarantee is derived with a finite number of measurement vectors. The frequencies can be recovered via conventional spectrum estimation methods such as MUSIC from the estimated covariance matrix. Finally, numerical examples are provided to validate the favorable performance of the proposed algorithms, with comparisons against several existing approaches.Comment: 14 pages, 10 figure

Super-Resolution of Mutually Interfering Signals

We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional super-resolution single-molecule imaging, neural spike sorting, multi-user channel identification, among others. We propose a novel algorithm, based on convex programming, and establish its near-optimal performance guarantee for exact recovery by exploiting the sparsity of the point source model as well as incoherence between the point spread functions. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.Comment: ISIT 201

Impact of International Sport Events in Promoting International Attention of Cities：Evidence from Google Trends

In order to raise the international attention and gain more competitive advantages, many Chinese cities are aiming at holding international sport events to promote urban development. However, previous studies indicated that international sport events have attracted international attention for hosting cities, but only stay at theoretical level of interpretation, empirical studies are scarce and needed. Therefore, the major purpose of this study was to investigate the impact of international sport events on urban development from the perspective of cities’ international attention, and to provide new dimensions and ideas for the relationship between sport events and urban development. This study used Google Trends corpus as the data source and used the Google Trends Index to measure five cities’ (Beijing, Shanghai, Nanjing, Chengdu, Wuhan) international attention in order to analyze the impact of international sport events on hosting cities in China. Through data mining, this study collected weekly data of international attention (time range is from January 1st, 2014 to December 31th, 2018) of five cities and compared with major media events in the corresponding period when highest international attention appeared in each city. Using Pearson Correlation, correlation analysis of international attention (all categories) and international attention (sports categories) of five cities was tested. Valuable information was obtained through the relevant keyword search function of the search volume ranking to provide more comprehensive evidence for the empirical results. There was a significant correlation between the international attention (all categories) and international attention (sports categories) in these five cities, and Nanjing\u27s data were the strongest (P=0.987). Through empirical analysis, the peak time of international attention in Beijing, Shanghai, Nanjing, Chengdu and Wuhan in recent five years was highly consistent with the major international sport events (Beijing IAAF World Championships, 2015; ATP1000 Shanghai Masters, 2018; Nanjing Summer Youth Olympics, 2014; ATP250 Chengdu Open ,2018; Wuhan Open ,2018), but the effect was negligible as the events ended. International sport events are an important dynamic attraction for hosting cities to gain more international attention, which can produce intense impulsive impact on each city\u27s international attention. The effect of international sport events on hosting city\u27s international attention is relatively short and concentrated, and there is no obvious long term effect. Finally, the international attention of cities has a relatively stable level from a long time perspective

From centralization to cooperation: The development and reform process of sports venues in China from 1949 to 2022

The management of sports venues has undergone a series of reforms since the People's Republic of China's establishment in 1949. The reform of management right is especially significant. It reflects the government–enterprise relationship and logic of government action. Utilizing the perspective of the government–enterprise relationship, this study systematically reviews the reform model for sports venues to incorporate Chinese characteristics. The aim of this study is to understand the relationship between the People's Republic of China's government and the market through the reforms implemented for the operation and management of sports venues. According to the study, the development and reform of sports venues in China has experienced government centralization, devolution, decentralization, and cooperation. The reform of sports venues' operation and management follows a “market-oriented government-led” model which reflects the government's logic. It is concluded that a “market-oriented government-led” model is essential for the promotion of comprehensive reforms for sports venues with Chinese characteristics

Investigations on the light hadron decays of Zb(10610)Z_b(10610) and Zb(10650)Z_b(10650)

The light hadron decay processes of $Z_b(10610)/Z_b(10650)$ provide us a way to study their nature and decay mechanism. In this work, we evaluate the branching ratios of $Z_b(10610)/Z_b(10650) \to VP$ ($V$ and $P$ stand for light vector and pseudoscalar mesons, respectively) using an effective Lagrangian approach, in which the contributions of intermediate bottomed meson triangle loops are considered. In our calculations, the $Z_b(10610)$ and $Z_b(10650)$ are regarded as $B\bar{B}^*+c.c.$ and $B^*\bar{B}^*$ molecular states, respectively. The predicted branching ratios of $Z_b(10610)\rightarrow VP$ are about in the order of $10^{-2}$, while the branching ratios of $Z_b(10650)\rightarrow VP$ are in the order of $10^{-3}$. Furthermore, the dependence of these ratios between different decay modes of $Z_b(10610)/Z_b(10650)$ on the mixing $\eta-\eta^\prime$ angle $\theta_P$ is investigated, which may be a good quantity for the experiments. It is hoped that the calculations here could be tested by future experiments.Comment: 7 pages, 8 figures and 1 tabl