Interpretation of protein structure and dynamics from the statistics of the open and closed times measured in a single ion-channel protein

Ion channels are proteins in the lipid cell membrane. They spontaneously fluctuate between conformational shapes that are open or closed to the passage of ions. The ionic currents through an individual channel can be resolved by the patch clamp technique. Thus, the time sequence of open and closed conformational states can be measured in one channel molecule. The probability density function of the dwell times in the open and closed states displays scaling functions that may arise from: (1) a large number of conformational substates having a continuous distribution of activation energy barriers, (2) time-dependent changes in the energy barriers between states, or (3) local interactions that constrain local structures which interact hierarchically to form global structure.     

Impact of Colored Noise on Population Model with Allee Effect

We study a population model with strong and weak Allee effect driven by internal noise and external noise.Firstly, a single-species population model with Allee effect under environmental colored noise is established, then stable and unstable states are analyzed and interpreted in biology. After that, stationary probability distribution(SPD) of population is derived based on Fokker-Planck equation. Next, mean first-passage time(MFPT) is defined in order to quantify the transition between extinction state and survival state with Allee effect. It is found that population will not extinct when weak Allee effect exists. It is not beneficial to survival of the population with the increase of Allee threshold no matter whether strong Allee effect or weak Allee effect. When strong Allee effect occurs, the correlation time of multiplicative noise plays a positive role in survival of population, while the correlation time of additive noise has a negative effect. Crucially, the phenomenon of resonant activation is firstly discovered in population dynamics with Allee effect. The conclusions we obtain can be applied to the further research of population dynamics in ecology.     

Dynamics of DNA replication in yeast

We present a mathematical model for the spatial dynamics of DNA replication. Using this model we determine the probability distribution for the time at which each chromosomal position is replicated. From this we show, contrary to previous reports, that mean replication time curves cannot be used to directly determine origin parameters. We demonstrate that the stochastic nature of replication dynamics leaves a clear signature in experimentally measured population average data, and we show that the width of the activation time probability distribution can be inferred from this data. Our results compare favorably with experimental measurements in Saccharomyces cerevisae.     

等概率符号化样本熵应用于脑电分析

样本熵(或近似熵)以信息增长率刻画时间序列的复杂性,能应用于短时序列,因而在生理信号分析中被广泛采用.然而,一方面由于传统样本熵采用与标准差线性相关的容限,使得熵值易受非平稳突变干扰的影响,另一方面传统样本熵还受序列概率分布的影响,从而导致其并非单纯反映序列的信息增长率.针对上述两个问题,将符号动力学与样本熵结合,提出等概率符号化样本熵方法,并对其物理意义、数学推导及参数选取都做了详细阐述.通过对噪声数据的仿真计算,验证了该方法的正确性及其区分不同强度时间相关的有效性.此方法应用于脑电信号分析的结果表明,在不对信号做人工伪迹去除的前提下,只需要1.25 s的脑电信号即可有效地区分出注意力集中和注意力发散两种状态.这进一步证明了该方法可很好地抵御非平稳突变干扰,能快速获得短时序列的潜在动力学特性,对脑电生物反馈技术具有很大的应用价值.     

A psychophysical model of decision making

Herein we develop a psychophysical model of decision making based on the difference between objective clock time and the human brain’s perception of time. In this model the utility function is given by the survival probability, which is shown to be a generalized hyperbolic distribution. The parameters of the utility function are fit to intertemporal choice model experimental data and decision making is determined to be a 1/f-noise process.     

A continuous model of human dynamics

Ideas and tools from statistical physics have recently been applied to the investigation of human dynamics. The timing of human activities, in particular, has been studied both experimentally and analytically. Empirical data show that, in many different situations, the time interval separating two consecutive tasks executed by an individual follows a heavy-tailed probability distribution rather than Poisson statistics. To account for this data, human behaviour has been viewed as a decision-based queuing system where individuals select and execute tasks belonging to a finite list of items as an increasing function of a task priority parameter. It is then possible to obtain analytically the empirical result P(τ)∼1/τ, where P(τ) is the waiting time probability distribution.Here a continuous model of human dynamics is introduced using instead an infinite queuing list. In contrast with the results obtained by other models in the finite case we find a waiting time distribution explicitly depending on the priority distribution density function ρ. The power-law scaling P(τ)∼1/τ is then recovered when ρ is exponentially distributed.     

交叉电磁场中氢原子外势阱态的有效布居

在交叉的电场和磁场中,氢原子势能面具有双阱结构.本文通过施加时变的电场,将库伦内阱量子态绝热转移到外阱的叠加态.使用量子力学方法对制备方案开展了数值模拟,研究了电场的非绝热效应对末态波函数几率分布、原子存活几率、波函数位置期望值及能级分布的影响.结果表明,较大的时间参数能够更加高效的将电子波包布居到外阱中能级较低且能量分布较窄的叠加态,且末态原子表现出巨大的电偶极矩.     

Principle of Maximum Entropy and Reduced Dynamics

A new method to obtain a series of reduced dynamics at various stages of coarse-graining is proposed. This ranges from the most coarse-grained one which agrees with the deterministic time evolution equation for averages of the relevant variables to the least coarse-grained one which is the generalized Fokker-Planck equation for the probability distribution function of the relevant variables. The method is based on the extention of the Kawasaki-Gunton operator with the help of the principle of maximum entropy.     

Stochastic aspects of pattern formation during the catalytic oxidation of CO on Pd(111) surfaces

We present experimental results on rare transitions between two states due to intrinsic noise between two states in a bistable surface reaction, namely the catalytic oxidation of CO on Pd(111) surfaces. The mean time scales involved are typically of order 10⁴ s and the probability distribution shows two peaks over a large part of the bistable regime of this surface reaction. We use measurements of the resulting CO₂ rate as well as photoelectron emission microscopy (PEEM) to characterize these rare transitions. From our dynamic data we can extract probability distributions for the CO₂ rate. We use x-t plots from PEEM measurements to describe the transitions, which are-as we demonstrate-characterized by one wall moving through the field of view in PEEM measurements. The resulting probability distributions for the CO₂ rate are shown to depend strongly on the value, Y, of the CO fraction in the reactant flux inside the bistable regime. We find that the probability distribution is strongly asymmetric indicating that the two basins of attraction are rather different in depth and width. This is also concluded from the PEEM measurements, which show in one case a rather sharp and narrow domain wall going one way, while it is rather wide and diffuse for the motion in the opposite direction. To have two basins of attraction in the bistable regime, which are rather different in nature is reminiscent of other bistable systems such as, for example, optical bistability, although the time scales involved in the present system are entirely different.     

Dynamics of morphological changes for mitochondrial fission and fusion

Mitochondria experience continuous fusion and fission in a living cell, but their dynamics remains poorly quantified. Here a theoretical model was developed, upon a simplified population balance equation (PBE), to predict the morphological changes induced by mitochondrial fission and fusion. Assuming that both fission and fusion events are statistically independent, the survival probability of mitochondria staying in the fission or fusion state was formulated as an exponentially-decayed function with time, ...     

隧穿量子点分子模型与光场相互作用系统中光场的相位特性

应用Pegg-Barnett相位理论,研究了隧穿量子点分子模型与光场相互作用系统中光场的相位特性,着重分析了光场的相位概率分布及相位涨落,并讨论了平均光子数和失谐量以及时间对相位概率分布的影响．结果发现：光场相位概率分布在零附近的概率分布最大,且涨落最小,而其它范围内概率分布小且容易振荡,适当调节平均光子数和时间,能使相位概率分布由单峰结构向对称的三峰高斯分布转化,且能调节峰值的大小．     

GaN光电阴极表面势垒对电子逸出几率的影响

针对GaN光电阴极表面势垒对电子逸出几率的影响问题,应用玻尓兹曼分布和基于Airy函数的传递矩阵法计算了GaN光电阴极的电子逸出几率,发现电子逸出几率主要由I势垒决定,II势垒对电子逸出几率的影响有限.利用自行研制的GaN光电阴极激活评估实验系统,测试了透射式GaN光电阴极样品的激活光电流.实验发现,Cs单独激活引起电子逸出几率的显著增加,而Cs单独充分激活后的Cs/O交替激活对电子逸出几率的影响有限.理论计算结果与激活光电流测试结果一致,其原因是Cs单独激活对降低真空能级的贡献远大于Cs/O共同激活.     

Decay of a thermofield-double state in chaotic quantum systems

Scrambling in interacting quantum systems out of equilibrium is particularly effective in the chaotic regime. Under time evolution, initially localized information is said to be scrambled as it spreads throughout the entire system. This spreading can be analyzed with the spectral form factor, which is defined in terms of the analytic continuation of the partition function. The latter is equivalent to the survival probability of a thermofield double state under unitary dynamics. Using random matrices from the Gaussian unitary ensemble (GUE) as Hamiltonians for the time evolution, we obtain exact analytical expressions at finite N for the survival probability. Numerical simulations of the survival probability with matrices taken from the Gaussian orthogonal ensemble (GOE) are also provided. The GOE is more suitable for our comparison with numerical results obtained with a disordered spin chain with local interactions. Common features between the random matrix and the realistic disordered model in the chaotic regime are identified. The differences that emerge as the spin model approaches a many-body localized phase are also discussed.     

Random walks in a random field of decaying traps

We study random walks on ^d (d 1) containing traps subject to decay. The initial trap distribution is random. In the course of time, traps decay independently according to a given lifetime distribution. We derive a necessary and sufficient condition under which the walk eventually gets trapped with probability 1. We prove bounds and asymptotic estimates for the survival probability as a function of time and for the average trapping time. These are compared with some well-known results for nondecaying traps.     

Characteristic periodicities of collective behavior at the foreign exchange market

The Battle of the Sexes describes asymmetric conflicts in mating behavior of males and females. Males can be philanderer or faithful, while females are either fast or coy, leading to a cyclic dynamics. The adjusted replicator equation predicts stable coexistence of all four strategies. In this situation, we consider the effects of fluctuations stemming from a finite population size. We show that they unavoidably lead to extinction of two strategies in the population. However, the typical time until extinction occurs strongly prolongs with increasing system size. In the emerging time window, a quasi-stationary probability distribution forms that is anomalously flat in the vicinity of the coexistence state. This behavior originates in a vanishing linear deterministic drift near the fixed point. We provide numerical data as well as an analytical approach to the mean extinction time and the quasi-stationary probability distribution.     

虚时间分裂算符方法研究溶剂电子转移动力学

在Sumi-Marcus理论中，采用虚时间分裂算符方法研究电子转移动力学．此方法具体应用于计算嗪-1和N,N-二甲基苯胺分子之间的电子转移速率常数．通过计算得到的两种反应物态的平均速率常数和一个长时间的速率常数，揭示了不同的sink函数时的电子转移动力学．在数值模拟过程中还发现了一些新的电子转移特性．     

Analysis of the impact of agglomeration and surface chemistry models on soot formation and oxidation

Models for soot aggregation that account for the influence of soot surface chemistry on mass growth and oxidation are still at the formative stage. Past studies have considered techniques ranging from the method of moments to stochastic approaches and significantly different sensitivities to chemical processes such as mass growth and oxidation have been reported. The method of moments is computationally efficient and can yield encouraging results for laminar flames as well as for turbulent flames when combined with transported probability density function (PDF) methods. However, an assessment of the sensitivity to constituent model assumptions is not trivial and information regarding the soot size distribution is incomplete. In the current work, the ability of a sectional method to reproduce population dynamics data has been evaluated along with the sensitivity of predictions to closure elements associated with soot nucleation, agglomeration, surface growth and oxidation. A detailed chemistry model with 285 chemical species and 1520 reactions was used for the gas phase. It is shown that the approach to the fuel lean sooting limit can be reproduced with reasonable accuracy and that the inclusion of fractal aggregates and surface chemistry effects improve agreement with experimental data.     

Noise-induced multilevel Landau–Zener transitions: Density matrix investigation

The generalised multilevel Landau–Zener problem is solved by applying the density matrix technique within the framework of nonstationary perturbation theory. The exact survival probability is achieved as a proof of the Brundobler–Elzer hypothesis (Brundobler and Elzer (1993) [38]). The effect of classical Gaussian noise is investigated by averaging the solution over the noise realisation. A generalised formula for slow noise-induced transition probability is obtained and found to agree exactly with all known results. Exact results are reported for the Demkov–Osherov model in the slow and fast noise limits. Thermal transition probabilities are obtained via the activation Arrhenius law and observed to tailor a qubit from thermal decoherence.     

基于社交网络的观点传播动力学研究

社交网络和微博是重要的Web2.0应用模式, 其观点传播模式与其他网络媒体以及传统媒体相比有很大差异. 本文提出一种基于在线社交网络的观点传播模型, 研究社交网络中舆论观点扩散的形式与特征. 仿真结果表明: 模型中信息传播的速度与六度分割理论的结论十分符合; 一个带强烈倾向性的观点在固有观点均匀分布的网络中传播的情况下, 稳定时网络中不会出现相反的观点; 稳定时的观点分布与源节点的度和回溯深度有关, 并不受信任界限的限制, 这与Deffuant模型和Hegselmann-Krause模型不同. 同时, 本文还分析了传播意愿、观点变更率和信任界限对弛豫时间的影响.