In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTR...In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...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
A general formulation of the stochastic model for random walk in time-random environment and an equivalent definition is established in this paper.Moreover,some basic probability relations similar to the classical cas...A general formulation of the stochastic model for random walk in time-random environment and an equivalent definition is established in this paper.Moreover,some basic probability relations similar to the classical case which are very useful in the corresponding research of fractal properties are given.At the end,a typical example is provided to show the recurrence and transience.展开更多
The water exchange matrix is an efficient tool to study the water exchange among the sub-areas in large-scale bays. The application of the random walk method to calculate the water exchange matrix is studied. Compared...The water exchange matrix is an efficient tool to study the water exchange among the sub-areas in large-scale bays. The application of the random walk method to calculate the water exchange matrix is studied. Compared with the advection-diffusion model, the random walk model is more flexible to calculate the water exchange matrix. The forecast matrix suggested by Thompson et al. is used to evaluate the water exchange characteristics among the sub-areas fast. According to the theoretic analysis, it is found that the precision of the predicted results is mainly affected by three factors, namely, the particle number, the generated time of the forecast matrix, and the number of the sub-areas. The impact of the above factors is analyzed based on the results of a series of numerical tests. The results show that the precision of the forecast matrix increases with the increase of the generated time of the forecast matrix and the number of the particles. If there are enough particles in each sub-area, the precision of the forecast matrix will increase with the number of the sub-areas. Moreover, if the particles in each sub-area are not enough, the excessive number of the sub-areas can result in the decrease of the precision of the forecast matrix.展开更多
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
Complex networks display community structures. Nodes within groups are densely connected but among groups are sparsely connected. In this paper, an algorithm is presented for community detection named Markov Random Wa...Complex networks display community structures. Nodes within groups are densely connected but among groups are sparsely connected. In this paper, an algorithm is presented for community detection named Markov Random Walks Ants(MRWA). The algorithm is inspired by Markov random walks model theory, and the probability of ants located in any node within a cluster will be greater than that located outside the cluster.Through the random walks, the network structure is revealed. The algorithm is a stochastic method which uses the information collected during the traverses of the ants in the network. The algorithm is validated on different datasets including computer-generated networks and real-world networks. The outcome shows the algorithm performs moderately quickly when providing an acceptable time complexity and its result appears good in practice.展开更多
In the present paper, the behavior of a single polymer chain under various solvent conditions was modeled by self-avoiding walks (SAW) with nearest neighbors attraction Ae on a simple cubic lattice. Determination of t...In the present paper, the behavior of a single polymer chain under various solvent conditions was modeled by self-avoiding walks (SAW) with nearest neighbors attraction Ae on a simple cubic lattice. Determination of the 0-condition was based on the numerical results of the mean square radius of gyration and end-to-end distance. It was found that at the 0 temperature Delta epsilon /kT equals -0.27. The exponents a in the Mark-Houwink equation with different interaction parameters are consistent with the results of experiments: under 0-condition, alpha= 0.5, and for a good solvent alpha =0.74-0.84, respectively.展开更多
Using 3-dimensional Langevin dynamics simulations, we investigated the dynamics of loop formation of chains with excluded volume interactions, and the stability of the formed loop. The mean looping time ι1/scales wit...Using 3-dimensional Langevin dynamics simulations, we investigated the dynamics of loop formation of chains with excluded volume interactions, and the stability of the formed loop. The mean looping time ι1/scales with chain length N and corresponding scaling exponent α increases linearly with the capture radius scaled by the Kuhn length a/l due to the effect of finite chain length. We also showed that the probability density function of the looping time is well fitted by a single exponential. Finally, we found that the mean unlooping time ιu hardly depends on chain length N for a given a/l and that the stability of a formed loop is enhanced with increasing a/l.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
Attributed graph clustering plays a vital role in uncovering hidden network structures,but it presents significant challenges.In recent years,various models have been proposed to identify meaningful clusters by integr...Attributed graph clustering plays a vital role in uncovering hidden network structures,but it presents significant challenges.In recent years,various models have been proposed to identify meaningful clusters by integrating both structural and attribute-based information.However,these models often emphasize node proximities without adequately balancing the efficiency of clustering based on both structural and attribute data.Furthermore,they tend to neglect the critical fuzzy information inherent in attributed graph clusters.To address these issues,we introduce a new framework,Markov lumpability optimization,for efficient clustering of large-scale attributed graphs.Specifically,we define a lumped Markov chain on an attribute-augmented graph and introduce a new metric,Markov lumpability,to quantify the differences between the original and lumped Markov transition probability matrices.To minimize this measure,we propose a conjugate gradient projectionbased approach that ensures the partitioning closely aligns with the intrinsic structure of fuzzy clusters through conditional optimization.Extensive experiments on both synthetic and real-world datasets demonstrate the superior performance of the proposed framework compared to existing clustering algorithms.This framework has many potential applications,including dynamic community analysis of social networks,user profiling in recommendation systems,functional module identification in biological molecular networks,and financial risk control,offering a new paradigm for mining complex patterns in high-dimensional attributed graph data.展开更多
基金Supported by the National Natural Science Foundation of China (10771185 and 10871200)
文摘In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...
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.
基金Supported by the National Natural Science Foun dation of China(10371092)Foundation of Wuhan Universit
文摘A general formulation of the stochastic model for random walk in time-random environment and an equivalent definition is established in this paper.Moreover,some basic probability relations similar to the classical case which are very useful in the corresponding research of fractal properties are given.At the end,a typical example is provided to show the recurrence and transience.
基金supported by the National Natural Science Foundation of China(No.10702050)
文摘The water exchange matrix is an efficient tool to study the water exchange among the sub-areas in large-scale bays. The application of the random walk method to calculate the water exchange matrix is studied. Compared with the advection-diffusion model, the random walk model is more flexible to calculate the water exchange matrix. The forecast matrix suggested by Thompson et al. is used to evaluate the water exchange characteristics among the sub-areas fast. According to the theoretic analysis, it is found that the precision of the predicted results is mainly affected by three factors, namely, the particle number, the generated time of the forecast matrix, and the number of the sub-areas. The impact of the above factors is analyzed based on the results of a series of numerical tests. The results show that the precision of the forecast matrix increases with the increase of the generated time of the forecast matrix and the number of the particles. If there are enough particles in each sub-area, the precision of the forecast matrix will increase with the number of the sub-areas. Moreover, if the particles in each sub-area are not enough, the excessive number of the sub-areas can result in the decrease of the precision of the forecast matrix.
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the National High Technology Research and Development(863)Program of China(No.2015AA043701)
文摘Complex networks display community structures. Nodes within groups are densely connected but among groups are sparsely connected. In this paper, an algorithm is presented for community detection named Markov Random Walks Ants(MRWA). The algorithm is inspired by Markov random walks model theory, and the probability of ants located in any node within a cluster will be greater than that located outside the cluster.Through the random walks, the network structure is revealed. The algorithm is a stochastic method which uses the information collected during the traverses of the ants in the network. The algorithm is validated on different datasets including computer-generated networks and real-world networks. The outcome shows the algorithm performs moderately quickly when providing an acceptable time complexity and its result appears good in practice.
基金This work was supported by the National Natural Science Foundation of China (No. 29974019)
文摘In the present paper, the behavior of a single polymer chain under various solvent conditions was modeled by self-avoiding walks (SAW) with nearest neighbors attraction Ae on a simple cubic lattice. Determination of the 0-condition was based on the numerical results of the mean square radius of gyration and end-to-end distance. It was found that at the 0 temperature Delta epsilon /kT equals -0.27. The exponents a in the Mark-Houwink equation with different interaction parameters are consistent with the results of experiments: under 0-condition, alpha= 0.5, and for a good solvent alpha =0.74-0.84, respectively.
基金supported by the National Natural Science Foundation of China(21225421,21174140)the National Basic Research Program of China(2014CB845605)the Hundred Talents Program of the Chinese Academy of Science
文摘Using 3-dimensional Langevin dynamics simulations, we investigated the dynamics of loop formation of chains with excluded volume interactions, and the stability of the formed loop. The mean looping time ι1/scales with chain length N and corresponding scaling exponent α increases linearly with the capture radius scaled by the Kuhn length a/l due to the effect of finite chain length. We also showed that the probability density function of the looping time is well fitted by a single exponential. Finally, we found that the mean unlooping time ιu hardly depends on chain length N for a given a/l and that the stability of a formed loop is enhanced with increasing a/l.
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 the National Natural Science Foundation of China(Grant No.72571150)Beijing Natural Science Foundation(Grant No.9182015)。
文摘Attributed graph clustering plays a vital role in uncovering hidden network structures,but it presents significant challenges.In recent years,various models have been proposed to identify meaningful clusters by integrating both structural and attribute-based information.However,these models often emphasize node proximities without adequately balancing the efficiency of clustering based on both structural and attribute data.Furthermore,they tend to neglect the critical fuzzy information inherent in attributed graph clusters.To address these issues,we introduce a new framework,Markov lumpability optimization,for efficient clustering of large-scale attributed graphs.Specifically,we define a lumped Markov chain on an attribute-augmented graph and introduce a new metric,Markov lumpability,to quantify the differences between the original and lumped Markov transition probability matrices.To minimize this measure,we propose a conjugate gradient projectionbased approach that ensures the partitioning closely aligns with the intrinsic structure of fuzzy clusters through conditional optimization.Extensive experiments on both synthetic and real-world datasets demonstrate the superior performance of the proposed framework compared to existing clustering algorithms.This framework has many potential applications,including dynamic community analysis of social networks,user profiling in recommendation systems,functional module identification in biological molecular networks,and financial risk control,offering a new paradigm for mining complex patterns in high-dimensional attributed graph data.
