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.

城市漫步体验中的移动端导识系统设计探索

目的城市漫步活动作为一种新型的旅游活动正在受到越来越多人的关注和参与,导识系统在旅游活动中非常重要,而应用在传统旅游活动中的导识系统并不适用于城市漫步体验,应当针对城市漫步活动的特征,构建适用于城市漫步的导识系统设计策略。方法基于城市漫步的特点和游客的体验需求,结合普适性的城市导识系统设计策略,从路线、标识、信息、体验四个方面得出适用于城市漫步的导识系统设计策略,并应用在城市漫步活动“悠栽逛中轴”中。结论基于移动端的城市漫步导识系统的功能不仅限于协助到达目的地,更应当提供丰富的文化信息和趣味性体验,让游客充分体验到漫步的乐趣和城市文化魅力。

Surgical intervention combined with weight-bearing walking training promotes recovery in patients with chronic spinal cord injury:a randomized controlled study

For patients with chronic spinal cord injury,the co nventional treatment is rehabilitation and treatment of spinal cord injury complications such as urinary tract infection,pressure sores,osteoporosis,and deep vein thrombosis.Surgery is rarely perfo rmed on spinal co rd injury in the chronic phase,and few treatments have been proven effective in chronic spinal cord injury patients.Development of effective therapies fo r chronic spinal co rd injury patients is needed.We conducted a randomized controlled clinical trial in patients with chronic complete thoracic spinal co rd injury to compare intensive rehabilitation(weight-bearing walking training)alone with surgical intervention plus intensive rehabilitation.This clinical trial was registered at ClinicalTrials.gov(NCT02663310).The goal of surgical intervention was spinal cord detethering,restoration of cerebrospinal fluid flow,and elimination of residual spinal cord compression.We found that surgical intervention plus weight-bearing walking training was associated with a higher incidence of American Spinal Injury Association Impairment Scale improvement,reduced spasticity,and more rapid bowel and bladder functional recovery than weight-bearing walking training alone.Overall,the surgical procedures and intensive rehabilitation were safe.American Spinal Injury Association Impairment Scale improvement was more common in T7-T11 injuries than in T2-T6 injuries.Surgery combined with rehabilitation appears to have a role in treatment of chronic spinal cord injury patients.

Diverse experiences by active travel for carbon neutrality:A longitudinal study of residential context,daily travel and experience types

Two key goals for sustainable spatial planning are to promote low-carbon travel in daily life and to enhance human wellbeing through diverse human-environment interactions.Yet,the integration of these goals has been underexplored.This study investigates the potential for experiential diversity via active travel in different resi-dential contexts within the Gävle city-region,Sweden.Over 15 months,we collected spatiotemporal data from 165 participants,analyzing 4,362 reported experiences and 13,192 GPS-derived travel trajectories.Our analysis uncovered a significant spatial discrepancy:while the travelled distances to locations of positive experiences typ-ically ranged from 1.5 km to 5 km,active travel predominated only within 1.5 km.This discrepancy persisted across urban,suburban,and peripheral contexts.Although residents in different contexts reported the same types of experiences,urban dwellers travelled about 50%farther for nature experiences compared with other positive experiences,whereas peripheral dwellers travelled twice the distance for urbanicity experiences compared with other positive experiences.Consequently,urban residents mostly relied on active travel for urbanicity experiences and motorised travel for nature experiences,with the reverse trend observed among peripheral dwellers.These results illustrate the importance of spatial scale for promoting diverse positive experiences via active travel,re-gardless of residential context.Effective planning strategies may include enhancing environmental diversity near homes and developing infrastructure that favours active over motorised travel for short to moderate distances.

ON THE EMPTY BALLS OF A CRITICAL OR SUBCRITICAL BRANCHING RANDOM WALK

Let{Z_(n)}_(n)≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure on R^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈R^(d):∣x∣<u})=0}the radius of the largest empty ball centered at the origin of Z_(n).In this work,we prove that after suitable renormalization,Rn converges in law to some non-degenerate distribution as n→∞.Furthermore,our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk.This completes the results of Révész[13]for the critical binary branching Wiener process.

Spatial search weighting information contained in cell velocity distribution

Cell migration plays a significant role in physiological and pathological processes.Understanding the characteristics of cell movement is crucial for comprehending biological processes such as cell functionality,cell migration,and cell–cell interactions.One of the fundamental characteristics of cell movement is the specific distribution of cell speed,containing valuable information that still requires comprehensive understanding.This article investigates the distribution of mean velocities along cell trajectories,with a focus on optimizing the efficiency of cell food search in the context of the entire colony.We confirm that the specific velocity distribution in the experiments corresponds to an optimal search efficiency when spatial weighting is considered.The simulation results indicate that the distribution of average velocity does not align with the optimal search efficiency when employing average spatial weighting.However,when considering the distribution of central spatial weighting,the specific velocity distribution in the experiment is shown to correspond to the optimal search efficiency.Our simulations reveal that for any given distribution of average velocity,a specific central spatial weighting can be identified among the possible central spatial weighting that aligns with the optimal search strategy.Additionally,our work presents a method for determining the spatial weights embedded in the velocity distribution of cell movement.Our results have provided new avenues for further investigation of significant topics,such as relationship between cell behavior and environmental conditions throughout their evolutionary history,and how cells achieve collective cooperation through cell-cell communication.

Characteristics of cell motility during cell collision

Quantitative examination of cellular motion and intercellullar interactions possesses substantial relevance for both biology and medicine.However,the effects of intercellular interactions during cellular locomotion remain under-explored in experimental research.As such,this study seeks to bridge this research gap,adopting Dictyostelium discoideum(Dicty)cells as a paradigm to investigate variations in cellular motion during reciprocal collisions.We aim to attain a comprehensive understanding of how cell interactions influence cell motion.By observing and processing the motion trajectories of colliding cells under diverse chemical environments,we calculated the diffusion coefficient(D)and the persistence time(τ),using mean square displacement.Our analysis of the relationship dynamics between D andτprior to the collisions reveals intricate and non-monotonic alterations in cell movements during collisions.By quantitatively scrutinizing theτtrend,we were able to categorize the cellular responses to interactions under different conditions.Importantly,we ascertained that the effect of cell interactions during collisions in Dicty cells emulates a classical sigmoid function.This discovery suggests that cellular responses might comply with a pattern akin to the Weber–Fechner law.

Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

We construct a one-dimensional quasiperiodic quantum walk to investigate the localization–delocalization transition.The inverse participation ratio and Lyapunov exponent are employed as two indexes to determine the mobility edge, a critical energy to distinguish the energy regions of extended and localized states. The analytical solution of mobility edge is obtained by the Lyapunov exponents in global theory, and the consistency of the two indexes is confirmed. We further study the dynamic characteristics of the quantum walk and show that the probabilities are localized to some specific lattice sites with time evolution. This phenomenon is explained by the effective potential of the Hamiltonian which corresponds to the phase in the coin operator of the quantum walk.

Strong invariance principle for a counterbalanced random walk

We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as follows.For n≥2,X_(n) is a new independent sample from some fixed law̸=0 with a fixed probability p,andX_(n)=−X_(v(n))with probability 1−p,where v(n)is a uniform random variable on{1;…;n−1}.We apply martingale method to obtain a strong invariance principle forS_(n).

Enhancing personalized exercise recommendation with student and exercise portraits

The exercise recommendation system is emerging as a promising application in online learning scenarios,providing personalized recommendations to assist students with explicit learning directions.Existing solutions generally follow a collaborative filtering paradigm,while the implicit connections between students(exercises)have been largely ignored.In this study,we aim to propose an exercise recommendation paradigm that can reveal the latent connections between student-student(exercise-exercise).Specifically,a new framework was proposed,namely personalized exercise recommendation with student and exercise portraits(PERP).It consists of three sequential and interdependent modules:Collaborative student exercise graph(CSEG)construction,joint random walk,and recommendation list optimization.Technically,CSEG is created as a unified heterogeneous graph with students’response behaviors and student(exercise)relationships.Then,a joint random walk to take full advantage of the spectral properties of nearly uncoupled Markov chains is performed on CSEG,which allows for full exploration of both similar exercises that students have finished and connections between students(exercises)with similar portraits.Finally,we propose to optimize the recommendation list to obtain different exercise suggestions.After analyses of two public datasets,the results demonstrated that PERP can satisfy novelty,accuracy,and diversity.

Effectiveness of the A3 robot on lower extremity motor function in stroke patients:A prospective,randomized controlled trial

BACKGROUND The results of existing lower extremity robotics studies are conflicting,and few relevant clinical trials have examined short-term efficacy.In addition,most of the outcome indicators in existing studies are scales,which are not objective enough.We used the combination of objective instrument measurement and scale to explore the short-term efficacy of the lower limb A3 robot,to provide a clinical reference.AIM To investigate the improvement of lower limb walking ability and balance in stroke treated by A3 lower limb robot.METHODS Sixty stroke patients were recruited prospectively in a hospital and randomized into the A3 group and the control group.They received 30 min of A3 robotics training and 30 min of floor walking training in addition to 30 min of regular rehabilitation training.The training was performed five times a week,once a day,for 2 wk.The t-test or non-parametric test was used to compare the threedimensional gait parameters and balance between the two groups before and after treatment.RESULTS The scores of basic activities of daily living,Stroke-Specific Quality of Life Scale,FM balance meter,Fugl-Meyer Assessment scores,Rivermead Mobility Index,Stride speed,Stride length,and Time Up and Go test in the two groups were significantly better than before treatment(19.29±12.15 vs 3.52±4.34;22.57±17.99 vs 4.07±2.51;1.21±0.83 vs 0.18±0.40;3.50±3.80 vs 0.96±2.08;2.07±1.21 vs 0.41±0.57;0.89±0.63 vs 0.11±0.32;12.38±9.00 vs 2.80±3.43;18.84±11.24 vs 3.80±10.83;45.12±69.41 vs 8.41±10.20;29.45±16.62 vs 8.68±10.74;P<0.05).All outcome indicators were significantly better in the A3 group than in the control group,except the area of the balance parameter.CONCLUSION For the short-term treatment of patients with subacute stroke,the addition of A3 robotic walking training to conventional physiotherapy appears to be more effective than the addition of ground-based walking training.

Functional Capacity of Patients with Venous Thromboembolic Disease Six to Twelve Months after Treatment

Background: Venous thromboembolism (VTE) is among the leading causes of hospital-related disability-adjusted life years lost. We aimed to determine the prevalence and determinants of functional capacity impairment six to twelve months after an acute VTE event. Methods: This was a cross-sectional study conducted between January and April 2021 in two referral hospitals of Yaoundé, including consenting adult patients admitted to these hospitals six to twelve months ago for VTE. We excluded dead patients and those with any comorbidity or symptoms limiting physical activity. The functional outcome was assessed with the six-minute walk test. Functional capacity impairment was defined as walking distance lower than the expected value. Results: We included 27 cases in this study with a mean age of 53.2 ± 14.4 years. The prevalence of functional capacity impairment was 29.6% (95% CI: 14.8 - 48.1). Factors associated with poor functional outcome were obesity (OR: 59.5;95% CI: 4.6 - 767.2;p - 207.4;p = 0.017), massive PE (OR: 30;95% CI: 2.5 - 354;p = 0.004), and poor adherence to treatment (OR: 30.3;95% CI: 2.5 - 333.3;p = 0.004). Conclusion: Functional capacity impairment is common in the medium-term after VTE and factors associated with this poor outcome are obesity, the severity of the VTE, and poor adherence to treatment.

“具身化”理论下青年城市漫游现象兴起的社会学透视

城市漫游(City Walk)是当下流行的一种青年文化,其本质是在行走中同自我、他者与城市进行互动,积极地连接微观的身体与宏观的城市。以“具身化”为理论视角,运用参与式观察与深入访谈的方法进行研究。分别从具身节奏、具身情感与具身体验三个维度进行分析,发现青年在City Walk的实践中具有松弛感、放空感与真实感。对于现代社会中的青年来说,City Walk有三个很重要的价值:逃离技术规训、寻求自我认同和追寻生活意义。总之,City Walk是当下青年在城市诗意栖居的一场具身实践,其背后有着丰富的社会性隐喻,可以促使我们思考城市、身体与现代性的关系。

从“走向自然”到“走向城市”:休闲美学视域下的City Walk

“如何休闲”之问具有“顶天立地”的双重品格,既关乎具体可感的现实生活样态,又牵涉本己本真的存在与生命之思。以往,人们通过践履山水自然而追寻人性自然。而今,“走向自然”的休闲难以与日常生活相协调,亟待思考的是如何另辟蹊径。City Walk是一种时兴的、以徒步为主要方式来探索城市空间、感受别样趣味的休闲活动,其低成本、慢节奏、益身心等特点极大地推动了休闲的开展,其“反叛技术”“背离秩序”的超越性品格规避了休闲异化的风险,其维持身心健康、促进友好交往、建构和谐关系及回归诗意栖居的美学价值助力人们属人地生存与属人地休闲。研究其活动特质与美学价值,既可为休闲美学添砖加瓦,又可为城市生活建言献策。

Supervised vs home-based exercise program in kidney transplant recipients: A pilot pragmatic non-randomized study

BACKGROUND Although the benefits of exercise for kidney transplant recipients(KTRs)have been widely demonstrated,these patients experience several barriers in undertaking a structured exercise program in hospital and non-hospital facilities.AIM To compare the effects of a supervised moderate-intensity gym-based intervention with a home-based low-intensity walking program on exercise capacity in KTRs.METHODS KTRs were asked to choose between two six-month programs.The first group performed a low-intensity interval walking intervention at home-based exercise intervention (HBex). The second group performed a supervised training program at an adapted physical activitygym (Sgym), including aerobic and resistance training. The outcomes, collected at baseline and at the end of theprograms, included the 6-minute walking test, the peak oxygen consumption (VO_(2)peak) during a treadmill test,the 5-time sit-to-stand test, and blood pressure.RESULTSSeventeen patients agreed to participate and self-selected into the HBex (n = 9) and Sgym (n = 8) groups. Twopatients in the Sgym group dropped out because of familial problems. At baseline, patients in the HBex group weresignificantly older and had lower walking distance, VO_(2)peak, and lower limb strength. Primary outcome changeswere significantly greater in the HBex group than in the Sgym group (52 ± 23 m vs 8 ± 34;P = 0.005). No othersignificant differences between groups were observed. Both groups improved most of the outcomes in the withingroupcomparisons, with significant variations in VO_(2) peak.CONCLUSIONSix-month moderate-intensity supervised or low-intensity home-based training programs effectively improvedexercise capacity in KTRs. Gym-based programs combine aerobic and resistance training;however, in-homewalking may be proposed for frail KTRs.

A Bayesian Mixture Model Approach to Disparity Testing

The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.

The Master of Tea

His second method is more direct:“Come to my house,let’s have tea.”With this method,you are destined to follow him.Needless to say,Cha Ye’s great prestige and seniority on Old Street makes you feel it is a great privilege if he asks you to tea.It was a sultry day in July.As Cha Ye strolled down the street,he noticed a noise.It was Mr.Hu,boss of the Heshengzhai Antique Shop.Cha Ye walked into the antique shop,where he saw Hu holding onto a strong man’s arm,not letting him go.

City Walk:美好生活视域下的体文旅融合发展研究

City Walk是一种以漫步为主要途径来体验城市风景和文化氛围的新型“微旅游”方式。本文在分析City Walk的内在机理及价值的基础上,对以美好生活视域下City Walk中体文旅融合所面临的现实困境与纾困路径进行分析。研究发现,City Walk中体文旅融合的现实困境为缺乏相应科学健身知识储备、影响旅游目的地居民生活、过度商业化与文化原貌冲突、过于集中的City Walk路线。据此提出纾困路径:在人才支持方面要培育体文旅复合人才,组建专业队伍;在政策支持方面要完善法律法规,建立奖惩机制;在创新支持方面要持续探索新区域,助力体文旅高质量发展;在宣传支持方面要打造City Walk中的城市IP属性,扩大知名度。