We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk （SAW）, which violates the detailed balance condition and satisfies tile balance condition. Its performance improves signific...We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk （SAW）, which violates the detailed balance condition and satisfies tile balance condition. Its performance improves significantly compared to that of the Berretti-Sokal algorithm, which is a variant of the Metropolis Hastings method. The gained efficiency increases with spatial dimension （D）, from approximately 10 times in 2D to approximately 40 times in 5D. We simulate the SAW on a 5D hypercubic lattice with periodic boundary conditions, for a linear system with a size up to L = 128, and confirm that as for the 5D Ising model, the finite-size scaling of the SAW is governed by renormalized exponents, υ^＊ = 2/d and γ/υ^＊ = d/2. The critical point is determined, which is approximately 8 times more precise than the best available estimate.展开更多
The self-avoiding walk (SAW) is an important model greatly different from the normalrandom walk in mathematics. Since a site that has been occupied once cannot be visitedagain by the walker, the SAW is not a Markov ch...The self-avoiding walk (SAW) is an important model greatly different from the normalrandom walk in mathematics. Since a site that has been occupied once cannot be visitedagain by the walker, the SAW is not a Markov chain. Generally speaking, it is difficult togive an accurate analytical expression of the problem dealing with the SAW. It is wellknown that the SAW model is widely used in physics, chemistry and biology. For exam-展开更多
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 th...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.展开更多
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 wit...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).展开更多
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 m...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.展开更多
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∈...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.展开更多
This research paper presents a comprehensive investigation into the effectiveness of the DeepSurNet-NSGA II(Deep Surrogate Model-Assisted Non-dominated Sorting Genetic Algorithm II)for solving complex multiobjective o...This research paper presents a comprehensive investigation into the effectiveness of the DeepSurNet-NSGA II(Deep Surrogate Model-Assisted Non-dominated Sorting Genetic Algorithm II)for solving complex multiobjective optimization problems,with a particular focus on robotic leg-linkage design.The study introduces an innovative approach that integrates deep learning-based surrogate models with the robust Non-dominated Sorting Genetic Algorithm II,aiming to enhance the efficiency and precision of the optimization process.Through a series of empirical experiments and algorithmic analyses,the paper demonstrates a high degree of correlation between solutions generated by the DeepSurNet-NSGA II and those obtained from direct experimental methods,underscoring the algorithm’s capability to accurately approximate the Pareto-optimal frontier while significantly reducing computational demands.The methodology encompasses a detailed exploration of the algorithm’s configuration,the experimental setup,and the criteria for performance evaluation,ensuring the reproducibility of results and facilitating future advancements in the field.The findings of this study not only confirm the practical applicability and theoretical soundness of the DeepSurNet-NSGA II in navigating the intricacies of multi-objective optimization but also highlight its potential as a transformative tool in engineering and design optimization.By bridging the gap between complex optimization challenges and achievable solutions,this research contributes valuable insights into the optimization domain,offering a promising direction for future inquiries and technological innovations.展开更多
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 t...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.展开更多
Objective:The purpose of this study was to determine the effectiveness of brisk walking as an intervention for self-care agency and care dependency in patients with permanent colorectal cancer stoma.Method:This study ...Objective:The purpose of this study was to determine the effectiveness of brisk walking as an intervention for self-care agency and care dependency in patients with permanent colorectal cancer stoma.Method:This study adopted a quasi-experimental research design,specifically a non-equivalent control group pre-test and post-test design.Utilizing the Exercise of Self-Care Agency Scale(ESCA)and Care Dependency Scale(CDS),a survey was administered to 64 patients from a hospital in Shandong Province.The statistical methods used for analyzing data included frequency,mean,standard deviation(SD),independent t-test,P-value calculation,and dependent t-test.Result:After two months of a brisk walking exercise program,participants in the experimental group had a higher level of self-care agency than before the experiment(P<0.05),and their level of care dependency was significantly reduced(P<0.05).Participants in the control group also showed higher levels of self-care agency(P<0.05)and lower levels of care dependency(P<0.05)after two months compared to their levels before the two months.Conclusion:The brisk walking program had a positive impact on patients’self-care agency and reduced their care dependency.展开更多
The catalysis of olefin polymerization through the chain-walking process is a subject of great interest. In this contribution, the successful synthesis of a Brookhart-type unsymmetrical α-diimine nickel catalyst Ni, ...The catalysis of olefin polymerization through the chain-walking process is a subject of great interest. In this contribution, the successful synthesis of a Brookhart-type unsymmetrical α-diimine nickel catalyst Ni, which contains both dibenzhydryl and phenyl groups, was determined by X-ray crystallography. The compound has a pseudo-tetrahedral geometry at the Ni center, showing pseudo-C2-symmetry. Upon activation with modified methylaluminoxane (MMAO), Ni1 exhibits high catalytic activity up to 1.02 × 107 g PE (mol Ni h)−1 toward ethylene polymerization, enabling the synthesis of high molecular weight branched polyethylene. The molecular weights and branching densities could be tuned over a very wide range. The polymerization results indicated the possibility of precise microstructure control, depending on the polymerization temperature. The branching densities were decreased with increasing the polymerization temperature.展开更多
基金Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant Nos. 11275185 and 11625522, and the Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China （No. Y5KF191CJ1）. Y. Deng acknowledges the Ministry of Education （of China） for the Fundamental Research Funds for the Central Universities under Grant No. 2340000034.
文摘We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk （SAW）, which violates the detailed balance condition and satisfies tile balance condition. Its performance improves significantly compared to that of the Berretti-Sokal algorithm, which is a variant of the Metropolis Hastings method. The gained efficiency increases with spatial dimension （D）, from approximately 10 times in 2D to approximately 40 times in 5D. We simulate the SAW on a 5D hypercubic lattice with periodic boundary conditions, for a linear system with a size up to L = 128, and confirm that as for the 5D Ising model, the finite-size scaling of the SAW is governed by renormalized exponents, υ^＊ = 2/d and γ/υ^＊ = d/2. The critical point is determined, which is approximately 8 times more precise than the best available estimate.
基金Project supported by the National Natural Science Foundation of China.
文摘The self-avoiding walk (SAW) is an important model greatly different from the normalrandom walk in mathematics. Since a site that has been occupied once cannot be visitedagain by the walker, the SAW is not a Markov chain. Generally speaking, it is difficult togive an accurate analytical expression of the problem dealing with the SAW. It is wellknown that the SAW model is widely used in physics, chemistry and biology. For exam-
基金supported by Hong Kong Spinal Cord Injury Fund (HKSCIF),China (to HZ)。
文摘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.
基金Supported by the National Natural Science Foundation of China(11671373).
文摘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).
文摘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.
基金supported by the National Key R&D Program of China(2022YFA1006102).
文摘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.
文摘This research paper presents a comprehensive investigation into the effectiveness of the DeepSurNet-NSGA II(Deep Surrogate Model-Assisted Non-dominated Sorting Genetic Algorithm II)for solving complex multiobjective optimization problems,with a particular focus on robotic leg-linkage design.The study introduces an innovative approach that integrates deep learning-based surrogate models with the robust Non-dominated Sorting Genetic Algorithm II,aiming to enhance the efficiency and precision of the optimization process.Through a series of empirical experiments and algorithmic analyses,the paper demonstrates a high degree of correlation between solutions generated by the DeepSurNet-NSGA II and those obtained from direct experimental methods,underscoring the algorithm’s capability to accurately approximate the Pareto-optimal frontier while significantly reducing computational demands.The methodology encompasses a detailed exploration of the algorithm’s configuration,the experimental setup,and the criteria for performance evaluation,ensuring the reproducibility of results and facilitating future advancements in the field.The findings of this study not only confirm the practical applicability and theoretical soundness of the DeepSurNet-NSGA II in navigating the intricacies of multi-objective optimization but also highlight its potential as a transformative tool in engineering and design optimization.By bridging the gap between complex optimization challenges and achievable solutions,this research contributes valuable insights into the optimization domain,offering a promising direction for future inquiries and technological innovations.
文摘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.
文摘Objective:The purpose of this study was to determine the effectiveness of brisk walking as an intervention for self-care agency and care dependency in patients with permanent colorectal cancer stoma.Method:This study adopted a quasi-experimental research design,specifically a non-equivalent control group pre-test and post-test design.Utilizing the Exercise of Self-Care Agency Scale(ESCA)and Care Dependency Scale(CDS),a survey was administered to 64 patients from a hospital in Shandong Province.The statistical methods used for analyzing data included frequency,mean,standard deviation(SD),independent t-test,P-value calculation,and dependent t-test.Result:After two months of a brisk walking exercise program,participants in the experimental group had a higher level of self-care agency than before the experiment(P<0.05),and their level of care dependency was significantly reduced(P<0.05).Participants in the control group also showed higher levels of self-care agency(P<0.05)and lower levels of care dependency(P<0.05)after two months compared to their levels before the two months.Conclusion:The brisk walking program had a positive impact on patients’self-care agency and reduced their care dependency.
文摘The catalysis of olefin polymerization through the chain-walking process is a subject of great interest. In this contribution, the successful synthesis of a Brookhart-type unsymmetrical α-diimine nickel catalyst Ni, which contains both dibenzhydryl and phenyl groups, was determined by X-ray crystallography. The compound has a pseudo-tetrahedral geometry at the Ni center, showing pseudo-C2-symmetry. Upon activation with modified methylaluminoxane (MMAO), Ni1 exhibits high catalytic activity up to 1.02 × 107 g PE (mol Ni h)−1 toward ethylene polymerization, enabling the synthesis of high molecular weight branched polyethylene. The molecular weights and branching densities could be tuned over a very wide range. The polymerization results indicated the possibility of precise microstructure control, depending on the polymerization temperature. The branching densities were decreased with increasing the polymerization temperature.
