Heat Kernel Estimates on Simple Random Walks and On-Diagonal Upper Bounds

We primarily provide several estimates for the heat kernel defined on the 2-dimensional simple random walk. Additionally, we offer an estimate for the heat kernel on high-dimensional random walks, demonstrating that the heat kernel in higher dimensions converges rapidly. We also compute the constants involved in the estimate for the 1-dimensional heat kernel. Furthermore, we discuss the general case of on-diagonal estimates for the heat kernel.

Stationary Measures of Three-State Quantum Walks with Defect on the One-Dimension Lattice

In this paper, we focus on the space-inhomogeneous three-state on the one-dimension lattice, a one-phase model and a two-phase model include. By using the transfer matrices method by Endo et al., we calculate the stationary measure for initial state concrete eigenvalue. Finally we found the transfer matrices method is more effective for the three-state quantum walks than the method obtained by Kawai et al.

基于Random Walks算法的心脏双源CT左心房分割

针对在传统的CT介入式治疗过程中,胸腔中软组织较多软组织的厚度和注射的造影剂在心脏中呈现的不均匀分布,导致在采用CT成像的图像中胸腔内部各组织之间存在边界模糊或者确实等状况,本文提出一种采用形态重构和随机行走相结合的分割方法。首先利用形态学开闭运算对图像进行化简,并使得心脏CT腔体边界分离,进而使得各个组织组织分离,再结合Random walks算法。从而使得不需要标记太多种子点的情况下提高了分割的速度和准确性,实验证明该方法能够达到预期的目标。

Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap

In this paper, we study the scaling for the mean first-passage time （MFPT） of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from a triangle to a polygon, we obtain the exact scaling for the MFPT. We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order. In addition, we determine the exponents of scaling efficiency characterizing the random walks. Our results are the generalizations of those derived for the Koch network, which shed light on the analysis of random walks over various fractal networks.

Efficient quantum private comparison protocol based on one direction discrete quantum walks on the circle

We propose an efficient quantum private comparison protocol firstly based on one direction quantum walks.With the help of one direction quantum walk,we develop a novel method that allows the semi-honest third party to set a flag to judge the comparing result,which improves the qubit efficiency and the maximum quantity of the participants’secret messages.Besides,our protocol can judge the size of the secret messages,not only equality.Furthermore,the quantum walks particle is disentangled in the initial state.It only requires a quantum walks operator to move,making our proposed protocol easy to implement and reducing the quantum resources.Through security analysis,we prove that our protocol can withstand well-known attacks and brute-force attacks.Analyses also reveal that our protocol is correct and practical.

文本类型理论视角下She Walks in Beauty的两个汉译本

She Walks in Beauty是英国著名诗人拜伦脍炙人口的一首抒情诗,塑造了温柔、善良、理想的美的女性形象,表达了诗人自己对于美好事物的追求。该文拟选取德国功能翻译派的文本类型理论这一新视角,对该诗的两个汉译本《她身披美丽而行》和《伊人倩影》做出对比分析,从而得出赖斯提出的文本类型理论不仅可以指导诗歌翻译的翻译策略和方法,也对诗歌不同译本的评析具有重要的意义。

基于多模态话语分析的诗篇解读——以She Walks in Beauty为例

文章突破以往仅从语言层面对诗歌进行分析研究的状况,以韩礼德系统功能语法为基础的多模态话语分析方法来解读英诗She Walks in Beauty及其汉译本中所呈现出的听觉美、视觉美与感官美,并探索双语诗篇所实现的概念功能与人际功能,从而为英诗欣赏与汉译本的可行性解读提供新思路。

The entanglement of deterministic aperiodic quantum walks

We study the entanglement between the internal(coin)and the external(position)degrees of freedom in the dynamic and the static deterministic aperiodic quantum walks(QWs).For the dynamic(static)aperiodic QWs,the coin depends on the time(position)and takes two coins C(α)and C(β)arranged in the two classes of generalized Fibonacci(GF)and the Thue–Morse(TM)sequences.We found that for the dynamic QWs,the entanglement of three kinds of the aperiodic QWs are close to the maximal value,which are all much larger than that of the homogeneous QWs.Further,the first class of GF(1st GF)QWs can achieve the maximum entangled state,which is similar to that of the dynamic disordered QWs.And the entanglement of 1st GF QWs is greater than that of the TM QWs,being followed closely by the entanglement of the second class of GF(2nd GF)QWs.For the static QWs,the entanglement of three kinds of the aperiodic QWs are also close to the maximal value and 1st GF QWs can achieve the maximum entangled state.The entanglement of the TM QWs is between1st GF QWs and 2nd GF QWs.However,the entanglement of the static disordered QWs is less than that of three kinds of the aperiodic QWs.This is different from those of the dynamic QWs.From these results,we can conclude that the dynamic and static 1st GF QWs can also be considered as maximal entanglement generators.

Localization of quantum walks on finite graphs

We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probability distribution vectors of quantum walks in infinite and finite graphs in the presence of static disorder respectively, and get the distance between these two vectors. We find that when the steps taken are small and the boundary condition is tight, the localization between the infinite and finite cases is greatly different. However, the difference is negligible when the steps taken are large or the boundary condition is loose. It means quantum walks on a one-dimensional finite graph may also suffer from localization in the presence of static disorder. Our approach and results can be generalized to analyze the localization of quantum walks in higher-dimensional cases.

THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS

Suppose {Xn} is a random walk in time-random environment with state space Z^d, ｜Xn｜ approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index α. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.

Disorder in parity-time symmetric quantum walks

We experimentally investigate the impact of static disorder and dynamic disorder on the non-unitary dynamics of parity-time(PT)-symmetric quantum walks.Via temporally alternating photon losses in an interferometric network,we realize the passive PT-symmetric quantum dynamics for single photons.Controllable coin operations allow us to simulate different environmental influences,which result in three different behaviors of quantum walkers:a standard ballistic spread,a diffusive behavior,and a localization,respectively,in a PT-symmetric quantum walk architecture.

Non-Markovian decoherent quantum walks

Quantum walks act in obviously different ways from their classical counterparts, but decoherence will lessen and close this gap between them. To understand this process, it is necessary to investigate the evolution of quantum walks under different decoherence situations. In this article, we study a non-Markovian decoherent quantum walk on a line. In a short time regime, the behavior of the walk deviates from both ideal quantum walks and classical random walks. The position variance as a measure of the quantum walk collapses and revives for a short time, and tends to have a linear relation with time. That is, the walker’s behavior shows a diffusive spread over a long time limit, which is caused by non-Markovian dephasing affecting the quantum correlations between the quantum walker and his coin. We also study both quantum discord and measurement-induced disturbance as measures of the quantum correlations, and observe both collapse and revival in the short time regime, and the tendency to be zero in the long time limit. Therefore, quantum walks with non-Markovian decoherence tend to have diffusive spreading behavior over long time limits, while in the short time regime they oscillate between ballistic and diffusive spreading behavior, and the quantum correlation collapses and revives due to the memory effect.

A Controlled Quantum Dialogue Protocol Based on Quantum Walks

In order to enable two parties to exchange their secret information equally,we propose a controlled quantum dialogue protocol based on quantum walks,which implements the equal exchange of secret information between the two parties with the help of the controller TP.The secret information is transmitted via quantum walks,by using this method,the previously required entangled particles do not need to be prepared in the initial phase,and the entangled particles can be produced spontaneously via quantum walks.Furthermore,to resist TP’s dishonest behavior,we use a hash function to verify the correctness of the secret information.The protocol analysis shows that it is safe and reliable facing some attacks,including intercept-measure-resend attack,entanglement attack,dishonest controller’s attack and participant attack.And has a slightly increasing efficiency comparing with the previous protocols.Note that the proposed protocol may be feasible because quantum walks prove to be implemented in different physical systems and experiments.

Quantum walks with coins undergoing different quantum noisy channels

Quantum walks have significantly different properties compared to classical random walks, which have potential applications in quantum computation and quantum simulation. We study Hadamard quantum walks with coins undergoing different quantum noisy channels and deduce the analytical expressions of the first two moments of position in the long- time limit. Numerical simulations have been done, the results are compared with the analytical results, and they match extremely well. We show that the variance of the position distributions of the walks grows linearly with time when enough steps are taken and the linear coefficient is affected by the strength of the quantum noisy channels.

变动社会中的晚清佛门实录——基于Walks in the city of Canton:with an itinerary一书的考察

晚清来华耶稣会士的论著是研究晚清社会宗教的重要文献资料。英国传教士约翰·亨利·格雷Walks in the City of Canton:with an Itinerary一书以观赏者的视角描述了晚清广州城的历史面貌,尤其是对广州城的佛寺有浓墨重彩的描述。不仅如实记录了佛教道场的历史传承,且重点探析了变动社会中佛门的真实转向。从中可以窥探社会经济背景与宗教文化之间的动态互动关系,进而藉此加深对晚清社会的理解。

Effect of Quantum Coins on Two-Particle Quantum Walks

We numerically study the effect of the quantum coins on the two-particle quantum walks on an infinite line. Both non-interacting and interacting particles are considered. The joint probability as well as the bunching or anti- bunching behavior are greatly affected by the phase factors in the coin operation. Further, the spatial correlation can be maximized by choosing appropriate coin parameters. The entanglement between the two particles can be adjusted in the same manner.

Quantum Statistics of Random Walks

The paper dealt with quantum canonical ensembles by random walks, where state transitions are triggered by the connections between labels, not by elements, which are transferred. The balance conditions of such walks lead to emission rates of the labels. The labels with emission rates definitely lower than 1 are like modes. For labels with emission rates very close to 1, the quantum numbers are concentrated around a mean value. As an application I consider the role of the zero label in a quantum gas in equilibrium.

Efficiency-Controllable Random Walks on a Class of Recursive Scale-Free Trees with a Deep Trap

Controls, especially effficiency controls on dynamical processes, have become major challenges in many complex systems. We study an important dynamical process, random walk, due to its wide range of applications for modeling the transporting or searching process. For lack of control methods for random walks in various structures, a control technique is presented for a class of weighted treelike scale-free networks with a deep trap at a hub node. The weighted networks are obtained from original models by introducing a weight parameter. We compute analytically the mean first passage time （MFPT） as an indicator for quantitatively measurinM the et^ciency of the random walk process. The results show that the MFPT increases exponentially with the network size, and the exponent varies with the weight parameter. The MFPT, therefore, can be controlled by the weight parameter to behave superlinearly, linearly, or sublinearly with the system size. This work provides further useful insights into controllinM eftlciency in scale-free complex networks.

Disorder and decoherence in coined quantum walks

This article aims to provide a review on quantum walks. Starting form a basic idea of discrete-time quantum walks, we will review the impact of disorder and decoherence on the properties of quantum walks. The evolution of the standard quantum walks is deterministic and disorder introduces randomness to the whole system and change interference pattern leading to the localization effect. Whereas, decoherence plays the role of transmitting quantum walks to classical random walks.