Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow

This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise $\epsilon_j$. The goals are to understand the effect of the sparsity of $x$ on the estimation precision and to construct a computationally feasible estimator to achieve the optimal rates. Inspired by the Wirtinger Flow [12] proposed for noiseless and non-sparse phase retrieval, a novel thresholded gradient descent algorithm is proposed and it is shown to adaptively achieve the minimax optimal rates of convergence over a wide range of sparsity levels when the $a_j$'s are independent standard Gaussian random vectors, provided that the sample size is sufficiently large compared to the sparsity of $x$.Comment: 28 pages, 4 figure

Interference suppression and diversity for CDMA systems

In code-division multiple-access (CDMA) systems, due to non-orthogonality of the spreading codes and multipath channels, the desired signal suffers interference from other users. Signal fading due to multipath propagation is another source of impairment in wireless CDMA systems, often severely impacting performance. In this dissertation, reduced-rank minimum mean square error (MMSE) receiver and reduced-rank minimum variance receiver are investigated to suppress interference; transmit diversity is applied to multicarrier CDMA (MC-CDMA) systems to combat fading; packet combing is studied to provide both interference suppression and diversity for CDMA random access systems. The reduced-rank MMSE receiver that uses a reduced-rank estimated covariance matrix is studied to improve the performance of MMSE receiver in CDMA systems. It is shown that the reduced-rank MMSE receiver has much better performance than the full-rank MMSE receiver when the covariance matrix is estimated by using a finite number of data samples and the desired signal is in a low dimensional subspace. It is also demonstrated that the reduced-rank minimum variance receiver outperforms the full-rank minimum variance receiver. The probability density function of the output SNR of the full-rank and reduced-rank linear MMSE estimators is derived for a general linear signal model under the assumption that the signals and noise are Gaussian distributed. Space-time coding that is originally proposed for narrow band systems is applied to an MC-CDMA system in order to get transmit diversity for such a wideband system. Some techniques to jointly decode the space-time code and suppress interference are developed. The channel estimation using either pilot channels or pilot symbols is studied for MC-CDMA systems with space-time coding. Performance of CDMA random access systems with packet combining in fading channels is analyzed. By combining the current retransmitted packet with all its previous transmitted copies, the receiver obtains a diversity gain plus an increased interference and noise suppression gain. Therefore, the bit error rate dramatically decreases with the number of transmissions increasing, which in turn improves the system throughput and reduces the average delay

Global testing against sparse alternatives in time-frequency analysis

In this paper, an over-sampled periodogram higher criticism (OPHC) test is proposed for the global detection of sparse periodic effects in a complex-valued time series. An explicit minimax detection boundary is established between the rareness and weakness of the complex sinusoids hidden in the series. The OPHC test is shown to be asymptotically powerful in the detectable region. Numerical simulations illustrate and verify the effectiveness of the proposed test. Furthermore, the periodogram over-sampled by $O(\log N)$ is proven universally optimal in global testing for periodicities under a mild minimum separation condition.Comment: Published at http://dx.doi.org/10.1214/15-AOS1412 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Weighted next reaction method and parameter selection for efficient simulation of rare events in biochemical reaction systems

The weighted stochastic simulation algorithm (wSSA) recently developed by Kuwahara and Mura and the refined wSSA proposed by Gillespie et al. based on the importance sampling technique open the door for efficient estimation of the probability of rare events in biochemical reaction systems. In this paper, we first apply the importance sampling technique to the next reaction method (NRM) of the stochastic simulation algorithm and develop a weighted NRM (wNRM). We then develop a systematic method for selecting the values of importance sampling parameters, which can be applied to both the wSSA and the wNRM. Numerical results demonstrate that our parameter selection method can substantially improve the performance of the wSSA and the wNRM in terms of simulation efficiency and accuracy

Robust and Computationally Feasible Community Detection in the Presence of Arbitrary Outlier Nodes

Community detection, which aims to cluster NN nodes in a given graph into rr distinct groups based on the observed undirected edges, is an important problem in network data analysis. In this paper, the popular stochastic block model (SBM) is extended to the generalized stochastic block model (GSBM) that allows for adversarial outlier nodes, which are connected with the other nodes in the graph in an arbitrary way. Under this model, we introduce a procedure using convex optimization followed by k-means algorithm with k=r. Both theoretical and numerical properties of the method are analyzed. A theoretical guarantee is given for the procedure to accurately detect the communities with small misclassification rate under the setting where the number of clusters can grow with N. This theoretical result admits to the best-known result in the literature of computationally feasible community detection in SBM without outliers. Numerical results show that our method is both computationally fast and robust to different kinds of outliers, while some popular computationally fast community detection algorithms, such as spectral clustering applied to adjacency matrices or graph Laplacians, may fail to retrieve the major clusters due to a small portion of outliers. We apply a slight modification of our method to a political blogs data set, showing that our method is competent in practice and comparable to existing computationally feasible methods in the literature. To the best of the authors’ knowledge, our result is the first in the literature in terms of clustering communities with fast growing numbers under the GSBM where a portion of arbitrary outlier nodes exist

Quasiparticle interference of C2-symmetric surface states in LaOFeAs parent compound

We present scanning tunneling microscopy studies of the LaOFeAs parent compound of iron pnictide superconductors. Topographic imaging reveals two types of atomically flat surfaces, corresponding to the exposed LaO layer and FeAs layer respectively. On one type of surface, we observe strong standing wave patterns induced by quasiparticle interference of two-dimensional surface states. The distribution of scattering wavevectors exhibits pronounced two-fold symmetry, consistent with the nematic electronic structure found in the Ca(Fe1-xCox)2As2 parent state.Comment: 13 pages, 4 figure

Polyphonic Poetics: Translating Lady Chatterley’s Lover

Since the cultural turn of translation studies, the focus of the researches has switched from on the pure language within the text to the influences exerted by exterior elements outside the text, neglecting such interior factors as poetics, the theory about the creation of literature and about the value and the meaning of the works. The research, through the case study of literary translation, Zhao Susu’s Chinese version of Lady Chatterley’s Lover, has explored the poetics of the literary translation from polyphonic perspective. It has been found that polyphonic poetics can be mainly classified into two independent and correlated levels, the visible one at the textual level, and the invisible one, at the subjective. In the translation process, as the organizer and the executor, the translator takes both the poetics of the author and that of the target reader into consideration. What’s more, the translator should also pay equal attention to the dominant poetics of the target culture and that of their own. The significance of research on polyphonic poetics not only lies on helping readers better understand foreign languages and cultures, but globally promoting the dialogues and communication in the domain of the education and culture among countries in the new era