The construction of general basis functions in reweighting ensemble dynamics simulations: Reproduce equilibrium distribution in complex systems from multiple short simulation trajectories

Ensemble simulations, which use multiple short independent trajectories from dispersive initial conformations, rather than a single long trajectory as used in traditional simulations, are expected to sample complex systems such as biomolecules much more efficiently. The re-weighted ensemble dynamics（RED） is designed to combine these short trajectories to reconstruct the global equilibrium distribution. In the RED, a number of conformational functions, named as basis functions,are applied to relate these trajectories to each other, then a detailed-balance-based linear equation is built, whose solution provides the weights of these trajectories in equilibrium distribution. Thus, the sufficient and efficient selection of basis functions is critical to the practical application of RED. Here, we review and present a few possible ways to generally construct basis functions for applying the RED in complex molecular systems. Especially, for systems with less priori knowledge, we could generally use the root mean squared deviation（RMSD） among conformations to split the whole conformational space into a set of cells, then use the RMSD-based-cell functions as basis functions. We demonstrate the application of the RED in typical systems, including a two-dimensional toy model, the lattice Potts model, and a short peptide system. The results indicate that the RED with the constructions of basis functions not only more efficiently sample the complex systems, but also provide a general way to understand the metastable structure of conformational space.

Management Model of Resources Equilibrium Distribution among Overlapping-Generations

The overlapping generation models the western scholars have designed from various perspectives to address different kinds of issues do not reflect Chinese emerging political and economic problems, and cannot be entirely and blindly applied to Chinese practical situation. In this paper the authors endeavor to incorporate some western scholars' research results into their own research findings to present overlapping generations model theory in a new perspective through establishing an overlapping generations theory on population including articulation of concepts and theorems of biological generation, economic generation and social generation and the overlapping periods in biological generation and two overlapping periods in economic generation among three generations. This management model with equilibrium distribution of resource wealth includes overlapping generations length model (6), equilibrium transfer model (θ) and a complete model on equilibrium distribution among generations (δ-θ). The model

Distributed Nash Equilibrium Seeking Strategies Under Quantized Communication

This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.

THE QUEUE-LENGTH DISTRIBUTION FOR M^x/G/1 QUEUE WITH SINGLE SERVER VACATION

This paper studies the bulk-arrival M-x/G/1 queue with single server vacation. By introducing the server busy period and using the Laplace transform, the recursion expression of the Laplace transform of the transient queue-length distribution is derived. Furthermore, the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are obtained. Especially some results for the single-arrival M/G/1 queue with single server vacation and bulk-arrival M-x/G/1 queue but with no server vacation can be derived directly by the results obtained in this paper.

Distribution of Phosphorus between CaO-CaF2 Slag and Fe-C-P Melt

The equilibrium distribution ratio of phosphorus between CaO-CaF2 molten slag and Fe-C-P melt at 1450 ℃ was measured.The phosphate capacity of slag and the activity coefficient of phosphorus oxide were calculated.

Equilibrium Analysis for Anycast in WDM Networks

In this paper, the wavelength-routed WDM network was analyzed for the dynamic case where the arrival of anycast requests was modeled by a state-dependent Poisson process. The equilibrium analysis was also given with the UWNC algorithm.

Thermodynamics Behavior of Titanium for BOF Smelting Bearing Steel

When titanium element appears in bearing steel, it is very easy to create titanium nitride inclusion, which reduces the fatigue life of bearing steel. Based on the production data of bearing steel produced by BOF, it is found that the titanium takes its source in bearing steel; the factors-affecting titanium content, and the thermodynamics behavior of titanium under smelting condition were studied. The results show that the prime reasons of titanium content increment are the soluble aluminum content and the titanium oxide of slag. The comparison between the experimental data and theoretical ones shows that there is a big declination when the soluble aluminum content of steel is higher, which is caused by the nonequilibrium reaction of slag and steel. The apparent equilibrium distribution coefficient of titanium between slag and steel is Obtained by use of experimental data.

Comparative Study of Decomposition of CCl_4 in Different Atmosphere Thermal Plasmas

Decomposition of carbon tetrachloride was studied theoretically in the most commonly used thermal plasma atmosphere such as H2, N2, O2 and water steam. A code developed by the National Aeronautics and Space Administration （NASA） was adopted to calculate the chemical equilibrium distribution and energy consumption of the decomposition of CC;4 in the H2, N2, O2 and water steam atmosphere thermal plasma respectively, with a temperature range of 500 K to 5000 K. In the neutral condition （H2, N2, atmosphere） formation of solid carbon was observed and in the oxygen-atmosphere （O2 and water steam） solid carbon formation disappeared through controlling the ratio of C/O. This indicates that the formation of polycyclic aromatic hydrocarbons （PAHs） is impossible theoretically. The energy consumption in the N2 atmosphere was much higher than that in the H2, O2 and water steam atmosphere at 1500 K.

基于分布鲁棒优化的环境博弈建模研究

本文讨论一类含有随机变量的环境博弈建模问题,在这类问题中随机变量的概率分布不是可以精确得知的,而是假设可以在一定范围内波动。分布式鲁棒优化的环境博弈模型既不同于不确定数据概率分布已被精准给出的传统博弈,也不同于用紧凸集代表不确定数据的模型。鲁棒博弈忽略了概率性信息,故总是得到过度保守的解决方案。本文利用分布式鲁棒优化法来处理环境博弈中的随机变量,从而得到分布鲁棒环境博弈模型。在一定的假设条件下,文章证明了分布鲁棒环境博弈中均衡的存在的合理性。在概率分布的一阶距和二阶距已知的情况下,文章指出均衡的求解可以转化为一类半定规划问题。通过数值实验进一步验证了上述方法的有效性。

Characterizations on Heavy-tailed Distributions by Means of Hazard Rate

Abstract Let F(x) be a distribution function supported on [0,X), with an equilibrium distribution function Fe(x). In this paper we shall study the function $r_e(x)( - {\rm ln}{\overline F}_e ( x ))\prime = {\overline F}( x )/\int_x^\infty {\overline F}( u )du $, which is called the equilibrium hazard rate of F. By the limiting behavior of re(x) we give a criterion to identify F to be heavy-tailed or light-tailed. Two broad classes of heavy-tailed distributions are also introduced and studied.

The Queue Length Distribution for M/G/1 Queue with Delay Single Server Vacation

In this paper we study the transient and equilibrium distributions of the queue length for the M/G/1 queueing system with delay single server vacation.By the server busy period and the Laplace transformation we directly obtain the recursion formula of the L transformation of the transient queue length distribution at any time t , as well as the recursion formula of the equilibrium distribution for calculating conveniently.Furthermore we obtain the stochastic decompositions of the queue length and waiting time in equilibrium.

A distributed normalized Nash equilibrium seeking algorithm for power allocation among micro-grids

In this paper, a power allocation problem based on the Cournot game and generalized Nash game is proposed. After integrating dynamic average consensus algorithm and distributed projection neural network through singular perturbation systems, a normalized Nash equilibrium seeking algorithm is presented to solve the proposed power allocation problem in a distributed way.Combine Lyapunov stability with the singular perturbation analysis, the convergence of the proposed algorithm is analyzed. A simulation on IEEE 118-bus confirms that the proposed distributed algorithm can adjust the power allocation according to different situations, while keeping the optimal solution within the feasible set.

Uneven Distribution of Primary and Middle Schools:A Case Study of Changchun,China

Providing further knowledge to and refinement of public facility location theory,this paper focuses on the distribution of basic educational facilities in China.The aim towards an equilibrium in the distribution of education resources has captured widespread attention in recent years.The basis of an education equilibrium is the balanced distribution of teaching facilities.Using the spatial analysis function of ArcGIS,this article discusses the evolution characteristics of education equilibrium and explores its dynamics with reference to primary and middle schools in Changchun City,Jilin Province from 2007 to 2013.The study found the spatial distribution of primary and middle schools in Changchun was uneven and the characteristic of close internal but sparse external has not changed.Low-level equilibrium of primary and middle schools in Changchun has been basically realized,but high-level equilibrium is far from being realized.Although there has been a trend towards suburbanization of these schools in recent years,the high entrance threshold has determined that high-quality school opportunity(schools with high-level resource allocation)has not increased for people.The spatial distribution of primary and middle schools is related to the factors of population,real estate,transportation and the education system itself.Education space,living space,and traffic space all interact and together affect urban spatial structure.

An M/G/1 Queueing System with Delay Server Vacations

In this paper we study the transient property of the queue length for the M/G/1 queueing system with delay server vacations.Using the server busy period and the Laplace transformation we directly obtain the recursion formula of the L transformation of the transient queue length distribution at time t , and also the recursion formula of the equilibrium distribution for calculating conveniently.As will be seen, this paper provides an intuitive and elegant method for studying transient properties of M/G/1 type queueing systems.

M^x/M/c Queue with catastrophes and state-dependent control at idle time

We consider an MX/M/c queue with catastrophes and state- dependent control at idle time. Properties of the queues which terminate when the servers become idle are first studied. Recurrence, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no catastrophes. All of these properties and the first effective catastrophe occurrence time are then investigated for the case of resurrection and catastrophes. In particular, we obtain the Laplace transform of the transition probability for the absorbing MX/M/c queue.