Application of quorum response and information entropy to animal collective motion modeling

“Quorum response” is a type of social interaction in which an individual's chance of choosing an option is a nonlinear function of the number of other individuals already committing to it. This interaction has been widely used to characterize collective decision‐making in animal groups. Here, we first implement it in 1D and 2D models of collective animal movement, and find that the resulting group motion shows the characteristic behaviors which were observed in previous experimental and modeling studies. Further, the analytic form of quorum response renders us an opportunity to propose a mean field theory in 1D with globally interacting particles, so we can estimate the average time period between changes in the group direction (mean switching time). We find that the theoretical results provide an upper bound to the simulation results when the interaction radius grows from local to global. Information entropy, a concept widely used to quantify the uncertainty of a random variable, is introduced here as a new order parameter to study the evolution of systems of two cases in 2D models. The explicitly formulated probability of a particle's dynamic state in the framework of quorum response makes information entropy directly computable. We find that, besides the global order, information entropy can also capture the structural features of local order of the system which previous order parameters such as alignment cannot. © 2016 Wiley Periodicals, Inc. Complexity 21: 584–592, 2016     

The incoming statistical knowledge of undergraduate majors in a department of mathematics and statistics

Studies have shown that at the end of an introductory statistics course, students struggle with building block concepts, such as mean and standard deviation, and rely on procedural understandings of the concepts. This study aims to investigate the understandings entering freshman of a department of mathematics and statistics (including mathematics education), students who are presumably better prepared in terms of mathematics and statistics than the average university student, have of introductory statistics. This case study found that these students enter college with common statistical misunderstandings, lack of knowledge, and idiosyncratic collections of correct statistical knowledge. Moreover, they also have a wide range of beliefs about their knowledge with some of the students who believe that they have the strongest knowledge also having significant misconceptions. More attention to these statistical building blocks may be required in a university introduction statistics course.     

基于分子模拟方法预测PIP2在双孔钾通道TREK-1上结合位点的研究

磷脂酰肌醇4,5-二磷酸酯(PIP₂)是一类分布在质膜内层的信号磷脂分子, 对钾、 钠和氯等离子通道和转运蛋白等多种跨膜蛋白具有调节作用. TREK-1是一类重要的背景钾通道, 受温度、 机械拉伸及胞内pH等多种因素调节, PIP₂在特定浓度范围内可激活TREK-1通道, 在内面向外膜片钳记录TREK-1通道电流中使用PIP₂抗结剂(如多聚赖氨酸)可导致TREK-1通道关闭. 利用分子对接和全原子分子动力学模拟探索了PIP₂与双孔钾通道TREK-1的相互作用. 分子对接计算结果表明, PIP₂在TREK-1通道上有两个可能的结合位点. 进一步的分子动力学模拟和均力势(PMF)计算结果表明, 其中位于螺旋M4和螺旋M1的位点可能是PIP₂激活TREK-1的优先结合位点. 模拟展示了PIP₂与TREK-1结合的可能构象. PIP₂的肌醇头部磷酸根与位于M1和M4上的碱性残基K45, K304和R311形成稳定盐桥; M1螺旋上的一系列疏水残基对稳定PIP₂的脂肪长链具有关键作用.     

Inelastic mean free path of low‐energy electrons in condensed media: beyond the standard models

The most established approach for ‘practical’ calculations of the inelastic mean free path (IMFP) of low‐energy electrons (~10 eV to ~10 keV) is based on optical‐data models of the dielectric function. Despite nearly four decades of efforts, the IMFP of low‐energy electrons is often not known with the desired accuracy. A universal conclusion is that the predictions of the most popular models are in rather fair agreement above a few hundred electron volts but exhibit considerable differences at lower energies. However, this is the energy range where their two main approximations, namely, the random‐phase approximation (RPA) and the Born approximation, may be invalid. After a short overview of the most popular optical‐data models, we present an approach to include exchange and correlation (XC) effects in IMFP calculations, thus going beyond the RPA and Born approximation. The key element is the so‐called many‐body local‐field correction (LFC). XC effects among the screening electrons are included using a time‐dependent local‐density approximation for the LFC. Additional XC effects related to the incident and struck electrons are included through the vertex correction calculated using a screened‐Hubbard formula for the LFC. The results presented for liquid water reveal that XC may increase the IMFP by 15–45% from its Born–RPA value, yielding much better agreement with available experimental data. The present work provides a manageable, yet rigorous, approach to improve upon the standard models for IMFP calculations, through the inclusion of XC effects at both the level of screening and the level of interaction. Copyright © 2015 John Wiley & Sons, Ltd.     

Inelastic scattering and energy loss of swift electron beams in biologically relevant materials

The inelastic mean free path and the stopping power of swift electrons in relevant biomaterials, such as liquid water, DNA, protein, lipid, carotene, sugar, and ice are calculated in the framework of the dielectric formalism. The Mermin Energy Loss Function – Generalized Oscillator Strength model is used to determine the energy loss function of these materials for arbitrary energy and momentum transfer using electron energy‐loss spectroscopy data as input. To ensure the consistency of the model, efforts are made so that both the Kramers–Kronig and f‐sum rules are fulfilled to better than 2%. Our findings indicate sizeable differences in the inelastic mean free path and stopping power among these biomaterials for low‐energy electrons. For example, at 100‐eV electron energy, the inelastic mean free path in protein is 25% smaller than for water and around 10% smaller than for the other biomaterials. The stopping power values of protein, DNA, and sugar are rather similar but 20% larger than for water. Taking into account these results, we conclude that electron interactions with living tissues at the nanometric scale cannot be reliably described using only liquid water as the surrogate of the biological target. Copyright © 2016 John Wiley & Sons, Ltd.     

Mean‐square stability of the backward Euler–Maruyama method for neutral stochastic delay differential equations with jumps

This paper is mainly considered whether the mean‐square stability of neutral stochastic delay differential equations (NSDDEs) with jumps is shared with that of the backward Euler–Maruyama method. Under the one‐sided Lipschitz condition and the linear growth condition, the trivial solution of NSDDEs with jumps is proved to be mean‐square stable by using the functional comparison principle and the Barbalat's lemma. It is shown that the backward Euler–Maruyama method can reproduce the mean‐square stability of the trivial solution under the same conditions. The implicit backward Euler–Maruyama method shows better characteristic than the explicit Euler–Maruyama method for the reason that it works without the linear growth condition on the drift coefficient. Compared with some existing results, our results do not need to add extra condition on the neutral part. The conclusions can be applied to NSDDEs and SDDEs with jumps. The effectiveness of the theoretical results is illustrated by an example. Copyright © 2016 John Wiley & Sons, Ltd.     

左截断右删失数据分位差估计及其渐近性质

我们研究了左截断右删失数据分位差,基于左截断右删失数据乘积限构造了分位差的经验估计,同时克服经验估计的非光滑性,提出了分位数差的核光滑估计.利用经验过程理论推导出这两个估计的渐近偏差和渐近方差,并且在左截断右删失数据下研究了这两个分位差的大样本性质,获得分位差估计的相合性和渐近正态性.同时给出计算模拟以验证光滑分位差估计的表现,在均方损失的意义下模拟结果表明光滑估计比经验估计具有更好的性质.     

关于Van Der Corput不等式双参数推广的改进

梳理了有关Van Der Corput不等式的研究成果与方法,并对Van Der Corput不等式的双参数推广作了进一步改进,建立了更强的推广式,它优于现有的相关结论.     

Random points in halfspheres

A random spherical polytope P_n in a spherically convex set as considered here is the spherical convex hull of n independent, uniformly distributed random points in K. The behaviour of P_n for a spherically convex set K contained in an open halfsphere is quite similar to that of a similarly generated random convex polytope in a Euclidean space, but the case when K is a halfsphere is different. This is what we investigate here, establishing the asymptotic behaviour, as n tends to infinity, of the expectation of several characteristics of P_n, such as facet and vertex number, volume and surface area. For the Hausdorff distance from the halfsphere, we obtain also some almost sure asymptotic estimates. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 3–22, 2017     

A strategy based on mean reverting property of markets and applications to foreign exchange trading with trailing stops

We propose a strategy for automated trading, outline theoretical justification of the profitability of this strategy, and overview the backtesting results in application to foreign currencies trading. The proposed methodology relies on the assumption that processes reflecting the dynamics of currency exchange rates are in a certain sense similar to the class of Ornstein–Uhlenbeck processes and exhibit the mean reverting property. In order to describe the quantitative characteristics of the projected return of the strategy, we derive the explicit expression for the running maximum of the Ornstein–Uhlenbeck process stopped at maximum drawdown and look at the correspondence between derived characteristics and the observed ones. Copyright © 2017 John Wiley & Sons, Ltd.