A Super Fast Algorithm for Estimating Sample Entropy

Sample entropy, an approximation of the Kolmogorov entropy, was proposed to characterize complexity of a time series, which is essentially defined as −log(B/A), where B denotes the number of matched template pairs with length m and A denotes the number of matched template pairs with m+1, for a predetermined positive integer m. It has been widely used to analyze physiological signals. As computing sample entropy is time consuming, the box-assisted, bucket-assisted, x-sort, assisted sliding box, and kd-tree-based algorithms were proposed to accelerate its computation. These algorithms require O(N2) or O(N2−1m+1) computational complexity, where N is the length of the time series analyzed. When N is big, the computational costs of these algorithms are large. We propose a super fast algorithm to estimate sample entropy based on Monte Carlo, with computational costs independent of N (the length of the time series) and the estimation converging to the exact sample entropy as the number of repeating experiments becomes large. The convergence rate of the algorithm is also established. Numerical experiments are performed for electrocardiogram time series, electroencephalogram time series, cardiac inter-beat time series, mechanical vibration signals (MVS), meteorological data (MD), and 1/f noise. Numerical results show that the proposed algorithm can gain 100–1000 times speedup compared to the kd-tree and assisted sliding box algorithms while providing satisfactory approximate accuracy.     

热化学非平衡流动的DSMC-ME算法研究

将最大熵方法(Maximum Entropy,缩写为ME)引入Direct Simulation Monte Carlo(DSMC)模拟热化学非平衡流动过程中,构造一个计算非平衡条件下化学反应几率和反应碰撞能量分配的最大熵模型.在DSMC-ME的模拟过程中,对分子间的非反应碰撞,采用传统的Larsen-Borgnakke唯象论模型模拟碰撞分子内能的激发与松弛;对分子间反应碰撞,采用最大熵模型模拟分子间的化学反应和能量交换.通过模拟高空高超声速绕圆柱和低密度高焓绕钝头锥体流动,并与DSMC算法和HEG实验结果比较,论证了DSMC-ME算法的有效性.     

A geometrical model for the double octahedral group based on a genus two Riemann surface

Geometrical models of double point groups are provided by double-sheeted Riemann surfaces of nonzero genus. This avoids the geometrically confusing picture of the doubling operation R as a rotation by 2π (i.e. 360°), which should instead be the identity operation E. In this manner a Riemann surface of genus 2 doubly covering a sphere and platonically tessellated b 16 equilateral triangles provides a geometrical model for the double octahedral group ²O_h. Stretching this Riemann surface along one axis to convert the 16 equilateral triangles to isosceles triangles and the underlying sphere to a prolate ellipsoid provides a model for the ²D_4h double group arising from the Jahn-Teller elongation of the regular octahedron into a prolate tetragonal bipyramid.     

Magnetocaloric effect and magnetic properties in NdMnO3 perovskite: A Monte Carlo approach

The magnetic properties and magnetocaloric effect in $\text{NdMn}{\text{O}}_3$ have been investigated, as well as the effect of magnetic anisotropy in the magnetocaloric properties of the perovskite-type compound. A classical Heisenberg Hamiltonian with nearest and next-nearest neighbors interactions was implemented. Hamiltonian parameters were fitted in order to reproduce experimental results. Magnetic field dependence on the magnetization, for isothermal processes, was performed. In this way, the magnetic entropy change $\left(\mathrm{\Delta }{S}_m\right)$ was computed as well as the relative cooling power (RCP). Results show that as the magnetic anisotropy constant increases, there was not only a sharpening, but also an increase in peak height of $?\mathrm{\Delta }{S}_m$. Finally, the magnetic field and anisotropy dependences on the RCP were obtained, showing that the highest values of the RCP were found for low anisotropy values.     

Monte Carlo Study on Spontaneous Recoil of Confined DNA Chain

在外加电场作用下,长链DNA分子的一部分链段进入构象熵较小的受限区域,其余部分仍滞留在高熵区. 电场撤除后,位于受限区域的DNA链段将自发回弹到高熵区域. 采用键涨落算法对这一动力学过程进行了模拟研究. 链段的回弹速度逐渐增大,这与实验结果是一致的. 模拟结果揭显示,增加受限区域的障碍物的尺寸或缩小间距都会导致DNA链段回弹速度的增加. 进一步的分析表明链单元在受限区域内的有效熵正比于其在受限区所能到达部分占总受限区域面积的比例.     

基于伊辛模型的Fe0.5Mn0.1Al0.4 合金磁化强度和磁熵变蒙特卡洛模拟

基于伊辛模型的单自旋反转蒙特卡洛算法,考虑了粒子间的最近邻以及次近邻相互作用,研究了无序 合金的磁化强度和磁熵变。首先,强调了粒子间的次近邻相关作用对体系的磁性和热力学性质的影响,明确了次近邻相互作用系数,证实了低温合金阻挫的存在;其次,研究了在相变温度处(不同磁场下)磁化强度随外加磁场（温度）的变化情况以及磁性粒子对磁化强度的贡献,发现反铁磁性粒子Mn在低温区对 合金的相变起了主要作用,而高温区体系的相变是由铁磁性粒子Fe贡献的;最后,分析了体系在相变温度处磁熵变数值随外加磁场的变化情况以及磁熵变在不同的外磁场下随温度的变化情况,当外加磁场h=0.14时,Mn粒子在冻结温度处的平均磁化强度为零,体系处于最无序的状态,对应的磁熵变 达到了正向最大值,极值的位置对应于体系的相变温度。     

基于伊辛模型的Fe_(0.5)Mn_(0.1)Al_(0.4)合金磁化强度和磁熵变蒙特卡洛模拟

基于伊辛模型的单自旋反转蒙特卡洛算法,考虑了粒子间的最近邻以及次近邻相互作用,研究了无序Fe0.5Mn0.1Al0.4合金的磁化强度和磁熵变.首先,强调了粒子间的次近邻相关作用对体系的磁性和热力学性质的影响,明确了次近邻相互作用系数,证实了低温合金阻挫的存在;其次,研究了在相变温度处(不同磁场下)磁化强度随外加磁场(温度)的变化情况以及磁性粒子对磁化强度的贡献,发现反铁磁性粒子Mn在低温区对Fe0.5Mn0.1Al0.4合金的相变起了主要作用,而高温区体系的相变是由铁磁性粒子Fe贡献的;最后,分析了体系在相变温度处磁熵变数值随外加磁场的变化情况以及磁熵变在不同的外磁场下随温度的变化情况,当外加磁场H=0.14(a.u.)时,Mn粒子在冻结温度处的平均磁化强度为零,体系处于最无序的状态,对应的磁熵变ΔS(0.1,0.14)达到了正向最大值,极值的位置对应于体系的相变温度.     

Simulation of coupon bond European and barrier options in quantum finance

Coupon bond European and barrier options are studied in the framework of quantum finance. The prices of European and barrier options are analyzed by generating sample values of the forward interest rates f(t,x) using a two-dimensional Gaussian quantum field A(t,x). The strong correlations of forward interest rates are described by the stiff propagator of the quantum field A(t,x). Using the Cholesky decomposition, A(t,x) is expressed in terms of white noise. The simulation results for European coupon bond and barrier options are compared with approximate formulas, which are obtained as power series in the volatility of the forward interest rates. The simulation shows that the simulated price deviates from the approximate value for large volatilities. The numerical algorithm is flexible and can be used for pricing any kind of option. It is shown that the three-factor HJM model can be derived from the quantum finance formulation.     

Study of neutron response for two hybrid RPC setups using the GEANT4 MC simulation approach

The present article describes a detailed neutron simulation study in the energy range 10^-10 MeV to 1.0 GeV for two different RPC configurations. The simulation studies were taken by using the GEANT4 MC code. Aluminum was utilized on the GND and readout strips for the （a） Bakelite-based and （b） glass-based RPCs. For the former type of RPC setup the neutron sensitivity for the isotropic source was Sn = 2.702 × 10^-2 at En = 1.0 GeV, while for the latter type of RPC, the neutron sensitivity for the same source was evaluated as Sn = 4.049 × 10^-2 at En = 1.0 GeV. These results were further compared with the previous RPC configuration in which copper was used for ground and pickup pads. Additionally A1 was employed at （GND＋strips） of the phosphate glass RPC setup and compared with the copper-based phosphate glass RPC. Good agreement with sensitivity values was obtained with the current and previous simulation results.     

Study of neutron response for two hybrid RPC setups using the GEANT4 MC simulation approach

The present article describes a detailed neutron simulation study in the energy range 10~(-10) MeV to 1.0 GeV for two different RPC configurations.The simulation studies were taken by using the GEANT4 MC code.Aluminum was utilized on the GND and readout strips for the (a) Bakelite-based and (b) glass-based RPCs.For the former type of RPC setup the neutron sensitivity for the isotropic source was S_n=2.702×10~(-2) at E_n=1.0 GeV, while for the latter type of RPC, the neutron sensitivity for the same source was evaluated as S_n=4.049×10~(-2) at E_n=1.0 geV.These results were further compared with the previous RPC configuration in which copper was used for ground and pickup pads.Additionally A1 was employed at (GND+strips) of the phosphate glass RPC setup and compared with the copper-based phosphate glass RPC.Good agreement with sensitivity values was obtained with the current and previous simulation results.     

聚乙烯-碘化铯中子阴极的最佳化

本文的中子阴级由聚乙烯、导电基底(Al)和碘化铯二次电子发射体组成.文中建立了一个此中子阴级的新的物理模型,并采用Monte Carlo方法模拟了中子同阴极作用产生低能二次电子的物理过程.模拟得到的出射二次电子能谱和产额与实验结果和理论分析符合得较好.我们还得到了最大探测效率时各中子阴极组分的最佳厚度.     

Complexity-entropy causality plane: A useful approach for distinguishing songs

Nowadays we are often faced with huge databases resulting from the rapid growth of data storage technologies. This is particularly true when dealing with music databases. In this context, it is essential to have techniques and tools able to discriminate properties from these massive sets. In this work, we report on a statistical analysis of more than ten thousand songs aiming to obtain a complexity hierarchy. Our approach is based on the estimation of the permutation entropy combined with an intensive complexity measure, building up the complexity-entropy causality plane. The results obtained indicate that this representation space is very promising to discriminate songs as well as to allow a relative quantitative comparison among songs. Additionally, we believe that the here-reported method may be applied in practical situations since it is simple, robust and has a fast numerical implementation.     

A generalized optimization of Monte Carlo particle transport schemes

Formulations and algorithms for optimizing biased random walk problems in radiation transport are described. A matrix-integral equation is constructed by coupling the second moment and its derivative with respect to the biasing parameter. The optimization is based on estimation of the second moment around the score and the Monte Carlo perturbation algorithm to treat the variation in the biasing parameter.     

A Monte Carlo method for simulating fractal surfaces

A Monte Carlo method is presented for simulating rough surfaces with the fractal behavior. The simulation is based on power-law size distribution of asperity diameter and self-affine property of roughness on surfaces. A probability model based on random number for asperity sizes is developed to generate the surfaces. By iteration, this method can be used to simulate surfaces that exhibit the aforementioned properties. The results indicate that the variation of the surface topography is related to the effects of scaling constant G and the fractal dimension D of the profile of rough surface. The larger value of D or smaller value of G signifies the smoother surface topography. This method may have the potential in prediction of the transport properties (such as friction, wear, lubrication, permeability and thermal or electrical conductivity, etc.) on rough surfaces.     

用自洽的蒙特卡罗—流体结合模型模拟溅射过程

 采用自洽的蒙特卡罗－流体结合模型对溅射过程进行模拟,以了解等离子体粒子行为与溅射参数的关系。溅射过程包括气体放电和溅射原子传输。对于气体放电,蒙特卡罗部分模拟快电子和快气体原子,而流体部分则描述离子和慢电子。对于溅射原子传输,蒙特卡罗部分模拟溅射原子的碰撞过程,而流体部分则描述溅射原子的扩散和漂移。模拟的结果包括：等离子体粒子的密度和能量分布;不同电离机制对气体原子和溅射原子电离的贡献;不同等离子体粒子对阴极溅射碰撞的贡献;溅射原子的密度分布;溅射场和溅射粒子相对于入射离子能量和角度的分布;溅射原子经碰撞后在整个等离子体区的分布。     

A bit-string model for biological aging

We present a simple model for biological aging. We study it through computer simulations and fint it to reflect some features of real populations.     

General-purpose event generators for LHC physics

We review the physics basis, main features and use of general-purpose Monte Carlo event generators for the simulation of proton-proton collisions at the Large Hadron Collider. Topics included are: the generation of hard scattering matrix elements for processes of interest, at both leading and next-to-leading QCD perturbative order; their matching to approximate treatments of higher orders based on the showering approximation; the parton and dipole shower formulations; parton distribution functions for event generators; non-perturbative aspects such as soft QCD collisions, the underlying event and diffractive processes; the string and cluster models for hadron formation; the treatment of hadron and tau decays; the inclusion of QED radiation and beyond Standard Model processes. We describe the principal features of the Ariadne, Herwig++, Pythia 8 and Sherpa generators, together with the Rivet and Professor validation and tuning tools, and discuss the physics philosophy behind the proper use of these generators and tools. This review is aimed at phenomenologists wishing to understand better how parton-level predictions are translated into hadron-level events as well as experimentalists seeking a deeper insight into the tools available for signal and background simulation at the LHC.     

横向磁场对辉光等离子体阴极区电子输运过程的影响

本文动用改进的蒙特卡罗技术，研究了横向磁场对氦气直流辉光放电阴极区电子输运过程的影响。     

Numerical investigation on atomic oxygen undercutting of the protective polymer film using Monte Carlo approach

Atomic oxygen undercutting effect of the protective polymer film in low earth orbit space environment is a potential threat to vulnerable long duration exposure facility. A Monte Carlo computational model is developed to simulate the interactions between atomic oxygen undercutting course with polyimide film. Physical process of the atomic oxygen undercutting, the definition of parameters, the affected by atomic oxygen fluence, orbit angle, protection coating thickness and thermal assimilation and the additive anti-undercutting components as well as a new three-dimensional reaction probability are discussed in detail. Simulated results are in good agreement with flight experimental data. With the increment of the atomic oxygen fluence, all the undercutting profiles, the depth and the width increased. Maximum undercutting depth is always larger than maximum undercutting width and the larger thermal assimilation coefficient causes the smaller undercutting damage. Using three-dimensional reaction probability, maximum depth decreased by approximately 20% than that of 28.5° orbit angle.