An understanding of protein folding/unfolding processes has important implications for all biological processes, in- eluding protein degradation, protein translocation, aging, and diseases. All-atom molecular dynamics...An understanding of protein folding/unfolding processes has important implications for all biological processes, in- eluding protein degradation, protein translocation, aging, and diseases. All-atom molecular dynamics （MD） simulations are uniquely suitable for it because of their atomic level resolution and accuracy. However, limited by computational ca- pabilities, nowadays even for small and fast-folding proteins, all-atom MD simulations of protein folding still presents a great challenge. An alternative way is to study unfolding process using MD simulations at high temperature. High temper- ature provides more energy to overcome energetic barriers to unfolding, and information obtained from studying unfolding can shed light on the mechanism of folding. In the present study, a 1000-ns MD simulation at high temperature （500 K） was performed to investigate the unfolding process of a small protein, chicken villin headpiece （HP-35）. To infer the folding mechanism, a Markov state model was also built from our simulation, which maps out six macrostates during the folding/unfolding process as well as critical transitions between them, revealing the folding mechanism unambiguously.展开更多
Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is propo...Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.展开更多
This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2, two kinds of period of a state are introdnced ...This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2, two kinds of period of a state are introdnced and it is obtained that the period is a 'class property',i.e. two states x and y belong to same class implies the period of x is equal to the period of y.展开更多
This paper is a continuation of [8] and [9]. The author obtains the decomposition of state space X of an Markov chain in random environment by making use of the results in [8] and [9], gives three examples, random wal...This paper is a continuation of [8] and [9]. The author obtains the decomposition of state space X of an Markov chain in random environment by making use of the results in [8] and [9], gives three examples, random walk in random environment, renewal process in random environment and queue process in random environment, and obtains the decompositions of the state spaces of these three special examples.展开更多
The feature of finite state Markov channel probability distribution is discussed on condition that original I/O are known. The probability is called posterior condition probability. It is also proved by Bayes formula ...The feature of finite state Markov channel probability distribution is discussed on condition that original I/O are known. The probability is called posterior condition probability. It is also proved by Bayes formula that posterior condition probability forms stationary Markov sequence if channel input is independently and identically distributed. On the contrary, Markov property of posterior condition probability isn’t kept if the input isn’t independently and identically distributed and a numerical example is utilized to explain this case. The properties of posterior condition probability will aid the study of the numerical calculated recurrence formula of finite state Markov channel capacity.展开更多
In this paper, we will illustrate the use and power of Hidden Markov models in analyzing multivariate data over time. The data used in this study was obtained from the Organization for Economic Co-operation and Develo...In this paper, we will illustrate the use and power of Hidden Markov models in analyzing multivariate data over time. The data used in this study was obtained from the Organization for Economic Co-operation and Development (OECD. Stat database url: https://stats.oecd.org/) and encompassed monthly data on the employment rate of males and females in Canada and the United States (aged 15 years and over;seasonally adjusted from January 1995 to July 2018). Two different underlying patterns of trends in employment over the 23 years observation period were uncovered.展开更多
First of all, we introduces the concept of m-irreducible of Markov chain in random environment. Then under the condition of m-irreducible, the relationship of recurrent and positive recurrent between two states is stu...First of all, we introduces the concept of m-irreducible of Markov chain in random environment. Then under the condition of m-irreducible, the relationship of recurrent and positive recurrent between two states is studied. We also give several conditions that can imply a state is recurrent and positive recurrent. And then the period of a state is discussed and we obtained that under the condition of m-irreducible, for any two states in x, they have the same period.展开更多
载荷外推作为载荷谱编制的重要技术手段,当前研究缺乏对于载荷外推总体方法的全面梳理、马尔可夫稳态分布的求解方法适应性不够、缺乏不同非参频次外推方法的比较与选用原则,导致不便生成高精度载荷谱以支撑装备性能设计。围绕坦克在高...载荷外推作为载荷谱编制的重要技术手段,当前研究缺乏对于载荷外推总体方法的全面梳理、马尔可夫稳态分布的求解方法适应性不够、缺乏不同非参频次外推方法的比较与选用原则,导致不便生成高精度载荷谱以支撑装备性能设计。围绕坦克在高机动和极限工况下的载荷谱编制问题,基于某坦克行进间身管位移数据样本,分别使用基于雨流矩阵及核密度估计的非参数外推法、基于马尔可夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)的信号重构法以及Metropolis-Hastings(简称MH)直接采样法进行了载荷频次外推,并针对MCMC的信号重构法提出了一种改良马尔可夫稳态分布的求解方法。应用所提出的频次-极值相结合的载荷外推总体方法对坦克身管位移进行了频次扩充与极值预测,并结合实车试验结果验证了方法的准确性。研究结果表明:改良的马尔可夫稳态分布求解方法是有效的;在样本长度足够、外推精度要求不甚高的情况下,MH直接采样法可作为一种新的频次外推方法;运用频次-极值相结合的载荷外推总体方法所得结果精度较高;形成的频次外推法选用原则对于载荷谱编制过程中的方法选择具有一定的指导意义。研究工作为装备载荷谱的高质量编制提供了成熟的技术路线和参考。展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11175068 and 11474117)the Self-determined Research Funds of CCNU from the Colleges Basic Research and Operation of MOE,China(Grant No.230-20205170054)
文摘An understanding of protein folding/unfolding processes has important implications for all biological processes, in- eluding protein degradation, protein translocation, aging, and diseases. All-atom molecular dynamics （MD） simulations are uniquely suitable for it because of their atomic level resolution and accuracy. However, limited by computational ca- pabilities, nowadays even for small and fast-folding proteins, all-atom MD simulations of protein folding still presents a great challenge. An alternative way is to study unfolding process using MD simulations at high temperature. High temper- ature provides more energy to overcome energetic barriers to unfolding, and information obtained from studying unfolding can shed light on the mechanism of folding. In the present study, a 1000-ns MD simulation at high temperature （500 K） was performed to investigate the unfolding process of a small protein, chicken villin headpiece （HP-35）. To infer the folding mechanism, a Markov state model was also built from our simulation, which maps out six macrostates during the folding/unfolding process as well as critical transitions between them, revealing the folding mechanism unambiguously.
文摘Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.
文摘This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2, two kinds of period of a state are introdnced and it is obtained that the period is a 'class property',i.e. two states x and y belong to same class implies the period of x is equal to the period of y.
基金Supported by the National Natural Science Foundation of China (10371092) and the Foundation of Wuhan University.
文摘This paper is a continuation of [8] and [9]. The author obtains the decomposition of state space X of an Markov chain in random environment by making use of the results in [8] and [9], gives three examples, random walk in random environment, renewal process in random environment and queue process in random environment, and obtains the decompositions of the state spaces of these three special examples.
文摘The feature of finite state Markov channel probability distribution is discussed on condition that original I/O are known. The probability is called posterior condition probability. It is also proved by Bayes formula that posterior condition probability forms stationary Markov sequence if channel input is independently and identically distributed. On the contrary, Markov property of posterior condition probability isn’t kept if the input isn’t independently and identically distributed and a numerical example is utilized to explain this case. The properties of posterior condition probability will aid the study of the numerical calculated recurrence formula of finite state Markov channel capacity.
文摘In this paper, we will illustrate the use and power of Hidden Markov models in analyzing multivariate data over time. The data used in this study was obtained from the Organization for Economic Co-operation and Development (OECD. Stat database url: https://stats.oecd.org/) and encompassed monthly data on the employment rate of males and females in Canada and the United States (aged 15 years and over;seasonally adjusted from January 1995 to July 2018). Two different underlying patterns of trends in employment over the 23 years observation period were uncovered.
基金Supported by the National Natural Science Foundation of China (10371092)the Foundation of Wuhan University
文摘First of all, we introduces the concept of m-irreducible of Markov chain in random environment. Then under the condition of m-irreducible, the relationship of recurrent and positive recurrent between two states is studied. We also give several conditions that can imply a state is recurrent and positive recurrent. And then the period of a state is discussed and we obtained that under the condition of m-irreducible, for any two states in x, they have the same period.
文摘载荷外推作为载荷谱编制的重要技术手段,当前研究缺乏对于载荷外推总体方法的全面梳理、马尔可夫稳态分布的求解方法适应性不够、缺乏不同非参频次外推方法的比较与选用原则,导致不便生成高精度载荷谱以支撑装备性能设计。围绕坦克在高机动和极限工况下的载荷谱编制问题,基于某坦克行进间身管位移数据样本,分别使用基于雨流矩阵及核密度估计的非参数外推法、基于马尔可夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)的信号重构法以及Metropolis-Hastings(简称MH)直接采样法进行了载荷频次外推,并针对MCMC的信号重构法提出了一种改良马尔可夫稳态分布的求解方法。应用所提出的频次-极值相结合的载荷外推总体方法对坦克身管位移进行了频次扩充与极值预测,并结合实车试验结果验证了方法的准确性。研究结果表明:改良的马尔可夫稳态分布求解方法是有效的;在样本长度足够、外推精度要求不甚高的情况下,MH直接采样法可作为一种新的频次外推方法;运用频次-极值相结合的载荷外推总体方法所得结果精度较高;形成的频次外推法选用原则对于载荷谱编制过程中的方法选择具有一定的指导意义。研究工作为装备载荷谱的高质量编制提供了成熟的技术路线和参考。
