Local-set-based Graph Signal Reconstruction

Signal processing on graph is attracting more and more attentions. For a graph signal in the low-frequency subspace, the missing data associated with unsampled vertices can be reconstructed through the sampled data by exploiting the smoothness of the graph signal. In this paper, the concept of local set is introduced and two local-set-based iterative methods are proposed to reconstruct bandlimited graph signal from sampled data. In each iteration, one of the proposed methods reweights the sampled residuals for different vertices, while the other propagates the sampled residuals in their respective local sets. These algorithms are built on frame theory and the concept of local sets, based on which several frames and contraction operators are proposed. We then prove that the reconstruction methods converge to the original signal under certain conditions and demonstrate the new methods lead to a significantly faster convergence compared with the baseline method. Furthermore, the correspondence between graph signal sampling and time-domain irregular sampling is analyzed comprehensively, which may be helpful to future works on graph signals. Computer simulations are conducted. The experimental results demonstrate the effectiveness of the reconstruction methods in various sampling geometries, imprecise priori knowledge of cutoff frequency, and noisy scenarios.Comment: 28 pages, 9 figures, 6 tables, journal manuscrip

Follow Whom? Chinese Users Have Different Choice

Sina Weibo, which was launched in 2009, is the most popular Chinese micro-blogging service. It has been reported that Sina Weibo has more than 400 million registered users by the end of the third quarter in 2012. Sina Weibo and Twitter have a lot in common, however, in terms of the following preference, Sina Weibo users, most of whom are Chinese, behave differently compared with those of Twitter. This work is based on a data set of Sina Weibo which contains 80.8 million users' profiles and 7.2 billion relations and a large data set of Twitter. Firstly some basic features of Sina Weibo and Twitter are analyzed such as degree and activeness distribution, correlation between degree and activeness, and the degree of separation. Then the following preference is investigated by studying the assortative mixing, friend similarities, following distribution, edge balance ratio, and ranking correlation, where edge balance ratio is newly proposed to measure balance property of graphs. It is found that Sina Weibo has a lower reciprocity rate, more positive balanced relations and is more disassortative. Coinciding with Asian traditional culture, the following preference of Sina Weibo users is more concentrated and hierarchical: they are more likely to follow people at higher or the same social levels and less likely to follow people lower than themselves. In contrast, the same kind of following preference is weaker in Twitter. Twitter users are open as they follow people from levels, which accords with its global characteristic and the prevalence of western civilization. The message forwarding behavior is studied by displaying the propagation levels, delays, and critical users. The following preference derives from not only the usage habits but also underlying reasons such as personalities and social moralities that is worthy of future research.Comment: 9 pages, 13 figure

Trauma Recovery of Tara Westover in Educated: A Memoir

Educated: A Memoir is an autobiographical novel of Tara Westover. This paper analyzes the protagonist Tara Westover’s trauma experiences and recovery process based on trauma theory. Combining trauma theory with this book can help readers better understand Tara’s experiences and deeply reveal the themes of this novel

New technologies accelerate the exploration of non-coding RNAs in horticultural plants.

Non-coding RNAs (ncRNAs), that is, RNAs not translated into proteins, are crucial regulators of a variety of biological processes in plants. While protein-encoding genes have been relatively well-annotated in sequenced genomes, accounting for a small portion of the genome space in plants, the universe of plant ncRNAs is rapidly expanding. Recent advances in experimental and computational technologies have generated a great momentum for discovery and functional characterization of ncRNAs. Here we summarize the classification and known biological functions of plant ncRNAs, review the application of next-generation sequencing (NGS) technology and ribosome profiling technology to ncRNA discovery in horticultural plants and discuss the application of new technologies, especially the new genome-editing tool clustered regularly interspaced short palindromic repeat (CRISPR)/CRISPR-associated protein 9 (Cas9) systems, to functional characterization of plant ncRNAs