Contraction: A Unified Perspective of Correlation Decay and Zero-Freeness of 2-Spin Systems

We study complex zeros of the partition function of 2-spin systems, viewed as a multivariate polynomial in terms of the edge interaction parameters and the uniform external field. We obtain new zero-free regions in which all these parameters are complex-valued. Crucially based on the zero-freeness, we show the existence of correlation decay in these regions. As a consequence, we obtain an FPTAS for computing the partition function of 2-spin systems on graphs of bounded degree for these parameter settings. We introduce the contraction property as a unified sufficient condition to devise FPTAS via either Weitz's algorithm or Barvinok's algorithm. Our main technical contribution is a very simple but general approach to extend any real parameter of which the 2-spin system exhibits correlation decay to its complex neighborhood where the partition function is zero-free and correlation decay still exists. This result formally establishes the inherent connection between two distinct notions of phase transition for 2-spin systems: the existence of correlation decay and the zero-freeness of the partition function via a unified perspective, contraction.Comment: 21 pages, 3 figures. Update: two correlation decay sets were added; a discussion with an independent work by Liu with similar results was give

Deep Learning based Recommender System: A Survey and New Perspectives

With the ever-growing volume of online information, recommender systems have been an effective strategy to overcome such information overload. The utility of recommender systems cannot be overstated, given its widespread adoption in many web applications, along with its potential impact to ameliorate many problems related to over-choice. In recent years, deep learning has garnered considerable interest in many research fields such as computer vision and natural language processing, owing not only to stellar performance but also the attractive property of learning feature representations from scratch. The influence of deep learning is also pervasive, recently demonstrating its effectiveness when applied to information retrieval and recommender systems research. Evidently, the field of deep learning in recommender system is flourishing. This article aims to provide a comprehensive review of recent research efforts on deep learning based recommender systems. More concretely, we provide and devise a taxonomy of deep learning based recommendation models, along with providing a comprehensive summary of the state-of-the-art. Finally, we expand on current trends and provide new perspectives pertaining to this new exciting development of the field.Comment: The paper has been accepted by ACM Computing Surveys. https://doi.acm.org/10.1145/328502

High-resolution single-worm transcriptomics and the function of oscillating genes in mouth-form development in Pristionchus pacificus

Development is largely under the control of genes. Specific spatiotemporal gene expression can modify the development and the final phenotype of an organism. To obtain a high-resolution catalog of the developmental transcriptome in Pristionchus pacificus, I developed and implemented a single worm transcriptomic approach for the nematode model organism P. pacificus, and performed temporal transcriptome analysis over the entire postembryonic development with 38 time points. I focused on investigating oscillating gene expression patterns and found that i) nearly 3000 oscillating genes are periodically expressed during postembryonic development, ii) there is an overrepresentation of ancient gene classes among oscillatory genes, and iii) the developmental switch gene eud-1 mediates numerous oscillatory genes including collagens, indicating the potential roles of these oscillating collagens in regulating mouth-form plasticity. Mouth-form dimorphism in P. pacificus provides an ideal example to study the mechanisms of phenotype plasticity. Many previous studies focused on the regulation of mouth-form development and identified environmental influences, developmental switches, the gene regulatory network involved in mouth-form plasticity, and the associated evolutionary processes. However, the molecular and structural basis of the teeth in P. pacificus remains poorly understood. To address this fundamental question, I used two complementary approaches. First, I performed a large-scale genetic screen and obtained six mutants displaying morphological changes in both stomatal structures and body shape. Using whole genome sequencing and genome editing (CRISPR/Cas9 system) technologies, I identified Ppa-dpy-6, which encodes a mucin-type protein, as the first structural component of the nematode stoma involved in the specification of the cheilostom and cuticle. Second, I investigated the function of two chitin synthase genes (chs) in P. pacificus. Phylogenetic analysis revealed that two chitin synthase genes are highly conserved across nematodes. Mutations in the C- terminus of chs-2 in P. pacificus result in a viable but teethless phenotype. Moreover, animals with this teethless phenotype were observed after injection of the chitin-synthase inhibitor Nikkomycin Z. These results suggest that the conserved Ppa-chs-2 is essential for P. pacificus teeth formation. In addition, such teethless mutants can feed on various bacterial food sources, yet they are incapable of predation

Outage Constrained Robust Secure Transmission for MISO Wiretap Channels

In this paper we consider the robust secure beamformer design for MISO wiretap channels. Assume that the eavesdroppers' channels are only partially available at the transmitter, we seek to maximize the secrecy rate under the transmit power and secrecy rate outage probability constraint. The outage probability constraint requires that the secrecy rate exceeds certain threshold with high probability. Therefore including such constraint in the design naturally ensures the desired robustness. Unfortunately, the presence of the probabilistic constraints makes the problem non-convex and hence difficult to solve. In this paper, we investigate the outage probability constrained secrecy rate maximization problem using a novel two-step approach. Under a wide range of uncertainty models, our developed algorithms can obtain high-quality solutions, sometimes even exact global solutions, for the robust secure beamformer design problem. Simulation results are presented to verify the effectiveness and robustness of the proposed algorithms

A Literature Review of Recent Research on Transcendentalism in China and Abroad

Ralph Waldo Emerson set up a series of ideas which are called “Transcendentalism” by later generations. Transcendentalism is an important intellectual and cultural movement with a religious color in New England in the 1830s. Since the end of the nineteenth centuries, researches on transcendentalism both in America and in other countries have probed into different aspects of transcendentalism deeply. Based on the influence of transcendentalism, comments on transcendentalism, the reflection of transcendentalism in literary works and relationships between transcendentalism and other thoughts, this thesis reviews transcendentalism studies both in China and abroad

Finite Time Performance Analysis of MIMO Systems Identification

This paper is concerned with the finite time identification performance of an n dimensional discrete-time Multiple-Input Multiple-Output (MIMO) Linear Time-Invariant system, with p inputs and m outputs. We prove that the widely-used Ho-Kalman algorithm and Multivariable Output Error State Space (MOESP) algorithm are ill-conditioned for MIMO system when n/m or n/p is large. Moreover, by analyzing the Cramer-Rao bound, we derive a fundamental limit for identifying the real and stable (or marginally stable) poles of MIMO system and prove that the sample complexity for any unbiased pole estimation algorithm to reach a certain level of accuracy explodes superpolynomially with respect to n/(pm). Numerical results are provided to illustrate the ill-conditionedness of Ho-Kalman algorithm and MOESP algorithm as well as the fundamental limit on identification.Comment: 9 pages, 4 figure