The asymptotic behavior of rarely visited edges of the simple random walk

In this paper, we study the asymptotic behavior of the number of rarely visited edges (i.e., edges that visited only once) of a simple symmetric random walk on $\mathbb{Z}$. Let $\alpha(n)$ be the number of rarely visited edges up to time $n$. First, we evaluate $\mathbb{E}(\alpha(n))$, show that $n\to \mathbb{E}(\alpha(n))$ is non-decreasing in $n$ and that $\lim\limits_{n\to+\infty}\mathbb{E}(\alpha(n))=2$. Then we study the asymptotic behavior of $\mathbb{P} (\alpha(n)>a(\log n)^2)$ for any $a>0$ and use it to show that there exists a constant $C\in(0,+\infty)$ such that $\limsup\limits_{n\to+\infty}\frac{\alpha(n)}{(\log n)^2}=C$ almost surely

Off-diagonal low-rank preconditioner for difficult PageRank problems

PageRank problem is the cornerstone of Google search engine and is usually stated as solving a huge linear system. Moreover, when the damping factor approaches 1, the spectrum properties of this system deteriorate rapidly and this system becomes difficult to solve. In this paper, we demonstrate that the coefficient matrix of this system can be transferred into a block form by partitioning its rows into special sets. In particular, the off-diagonal part of the block coefficient matrix can be compressed by a simple low-rank factorization, which can be beneficial for solving the PageRank problem. Hence, a matrix partition method is proposed to discover the special sets of rows for supporting the low rank factorization. Then a preconditioner based on the low-rank factorization is proposed for solving difficult PageRank problems. Numerical experiments are presented to support the discussions and to illustrate the effectiveness of the proposed methods. (C) 2018 Elsevier B.V. All rights reserved

Research on the Electromagnetic-Heat-Flow Coupled Modeling and Analysis for In-Wheel Motor

In this paper, a 15 KW in-wheel motor (IWM) is taken as the research object, and the coupling factors among the electromagnetic field, temperature field and flow field are analyzed, and the strong and weak coupling factors between the three fields are clarified, and by identifying the strong and weak coupling factors between the three fields, a three-field coupling analysis model for IWM with appropriate complexity is established, and the validity of the model is verified. In a certain driving condition, the electromagnetic field, temperature field and flow field characteristics of IWM are analyzed with the multi-field coupling model. The result shows that, after the IWM runs 8440 s under driving conditions, in this paper, the IWM electromagnetic torque of the rated working condition is 134.2 Nm, and IWM the electromagnetic torque of the peak working condition is 451.36 Nm, and the power requirement of the motor can be guaranteed. The highest temperature of the IWM is 150 &deg C, which does not exceed the insulation grade requirements of the motor (155 &deg C), the highest temperature of the permanent magnet (PM) is 65.6 &deg C, and it does not exceed the highest operating temperature of the PM, and ensures the accurate calculation of components loss and the temperature of the motor. It can be found, through research, that the electromagnetic torque difference between unidirectional coupling and bidirectional coupling is 3.2%, the maximum temperature difference is 7.98% in the three-field coupling analysis of IWM under rated working conditions. Therefore, it is necessary to consider the influence of coupling factors on the properties of motor materials when analyzing the electromagnetic field, temperature field and flow field of IWM it also provides some reference value for the simulation analysis of IWM in the future. Document type: Articl

Interactions between food hazards and intestinal barrier: impact on foodborne diseases

The intestine is an important digestive organ of the human body, and its barrier is the guardian of the body from the external environment. The impairment of the intestinal barrier is believed to be an important determinant in various foodborne diseases. Food hazards can lead to the occurrence of many foodborne diseases represented by inflammation. Therefore, understanding the mechanisms of the impact of the food hazards on intestinal barriers is essential for promoting human health. This review examined the relationship between food hazards and the intestinal barrier in three aspects: apoptosis, imbalance of gut microbiota, and pro-inflammatory cytokines. The mechanism of dysfunctional gut microbiota caused by food hazards was also discussed. This review discusses the interaction among food hazards, intestinal barrier, and foodborne diseases and, thus, offers a new thought to deal with foodborne disease

Experimental Implementation of Noncyclic and Nonadiabatic Geometric Quantum Gates in a Superconducting Circuit

Quantum gates based on geometric phases possess intrinsic noise-resilience features and therefore attract much attention. However, the implementations of previous geometric quantum computation typically require a long pulse time of gates. As a result, their experimental control inevitably suffers from the cumulative disturbances of systematic errors due to excessive time consumption. Here, we experimentally implement a set of noncyclic and nonadiabatic geometric quantum gates in a superconducting circuit, which greatly shortens the gate time. And also, we experimentally verify that our universal single-qubit geometric gates are more robust to both the Rabi frequency error and qubit frequency shift-induced error, compared to the conventional dynamical gates, by using the randomized benchmarking method. Moreover, this scheme can be utilized to construct two-qubit geometric operations, while the generation of the maximally entangled Bell states is demonstrated. Therefore, our results provide a promising routine to achieve fast, high-fidelity, and error-resilient quantum gates in superconducting quantum circuits

The influence of age and gender on skin-associated microbial communities in urban and rural human populations

© The Author(s), 2015. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in PLoS One (10): e0141842, doi:10.1371/journal.pone.0141842.Differences in the bacterial community structure associated with 7 skin sites in 71 healthy people over five days showed significant correlations with age, gender, physical skin parameters, and whether participants lived in urban or rural locations in the same city. While body site explained the majority of the variance in bacterial community structure, the composition of the skin-associated bacterial communities were predominantly influenced by whether the participants were living in an urban or rural environment, with a significantly greater relative abundance of Trabulsiella in urban populations. Adults maintained greater overall microbial diversity than adolescents or the elderly, while the intragroup variation among the elderly and rural populations was significantly greater. Skin-associated bacterial community structure and composition could predict whether a sample came from an urban or a rural resident ~5x greater than random.This work was supported by a grant from Johnson & Johnson (China)

Early afterglows from radially structured outflows and the application to X-ray shallow decays

In the fireball model, it is more physically realistic that gamma-ray burst (GRB) ejecta have a range of bulk Lorentz factors (assuming $M\propto \Gamma^{-s}$). The low Lorentz factor part of the ejecta will catch up with the high Lorentz factor part when the latter is decelerated by the surrounding medium to a comparable Lorentz factor. Such a process will develop a long-lasting weak reverse shock until the whole ejecta are shocked. Meanwhile, the forward shocked materials are gradually supplied with energy from the ejecta that are catching-up, and thus the temporal decay of the forward shock emission will be slower than that without an energy supply. However, the reverse shock may be strong. Here, we extend the standard reverse-forward shock model to the case of radially nonuniform ejecta. We show that this process can be classified into two cases: the thick shell case and the thin shell case. In the thin shell case, the reverse shock is weak and the temporal scaling law of the afterglow is the same as that in Sari & Mesz (2000). However, in the thick shell case, the reverse shock is strong and thus its emission dominates the afterglow in the high energy band. Our results also show slower decaying behavior of the afterglow due to the energy supply by low Lorentz factor materials, which may help the understanding of the plateau observed in the early optical and X-ray afterglows