The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.     

New relations for excited baryons in large-N(c) QCD

We show that excited baryons in large-N(c) QCD form multiplets, within which masses are first split at O(1/N(c)). The dominant couplings of resonances to various mesons are highly constrained: The N(1535) decays at leading 1/N(c) order exclusively to eta-N rather than pi-N, and vice versa for the N(1650). This multiplet structure is reproduced by a simple large-N(c) quark model, well studied in the literature, that describes resonances as single-quark excitations.     

Theoretical models for the interpretation of E.S.C.A. spectra

Three features of E.S.C.A. spectra are discussed: the chemical shift, multiplet splitting, and satellite bands. In the chemical shift effect a perturbation theory treatment shows that the electronic relaxation energy in the hole state of the molecules can be attributed to a flow of electrons on to the ionized atom. Thus the relative abilities of surrounding atoms to “feed” electrons to the ionized atom determines the relative importance of the relaxation energy contribution to the chemical shift. This explains why neutral atom charges don't always determine the direction of the chemical shift. In multiplet splitting the same perturbation treatment shows that the sign and magnitude of the relaxation energy contribution to the multiplet splitting is determined by the direction and magnitude of flow of majority electron spin density in going to the relaxed hole state. Unrestricted Hartree-Fock calculations on the series MF ₂, with M first row transition metals, are compared with E.S.C.A. experiments on the corresponding octahedral complexes to show that complex ion formation has only a very small effect on core level multiplet splitting. Relaxed hole state calculations on a series of first row atom (C,N,O,F) containing radicals leads to the conclusion that in these cases correlation energy effects are larger for the high spin multiplets than for the low spin multiplets. The assignments of satellite structure in transition metal complexes is reviewed and multiconfiguration self-consistent field results are presented and discussed for the satellite structure     

Research of SU(3) 27-plet

Exotics belong to high multiplet of SU(3), so one can understand them by researching their non-exotic partners in the same multiplet. Here the possible 27-plet from flavor SU(3) symmetry are investigated. By fitting the mass spectrum and calculating the two-body partial hadronic decay widths of members, two set of 27-plet baryons with different parities are found. For the mass spectrum, all non-exotic members have their candidates in PDG except for a new Λ(1780). For the decay widths, the computing results show the approximate flavor SU(3) symmetry. The further analyzing and comparing with the results from other theoretical models can support the rationality of the 27-plet assignment.     

基于SU(3)对称性的27重态研究

奇特重子属于味SU(3)的高维表示, 可以通过研究与其属于同一多重态的非奇特伴子来了解其性质. 本文研究了PDG粒子数据表中可能的27重态. 通过经典SU(3)方法所采用的质量拟合和两体强衰变部分宽度的计算预言出具有不同宇称的两套27重态. 质量谱的拟合预言了新的非奇特态Λ(1780), 其他非奇特伴子都能在PDG中找到候选者; 衰变宽度的计算结果表明存在近似味SU(3)对称性. 进一步分析和对比其他理论模型的研究结果可以支持27重态指定的合理性.     

Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Cr, Mn, Fe, Co and Ni

Chemical state X-ray photoelectron spectroscopic analysis of first row transition metals and their oxides and hydroxides is challenging due to the complexity of their 2p spectra resulting from peak asymmetries, complex multiplet splitting, shake-up and plasmon loss structure, and uncertain, overlapping binding energies. Our previous paper [M.C. Biesinger et al., Appl. Surf. Sci. 257 (2010) 887-898.] in which we examined Sc, Ti, V, Cu and Zn species, has shown that all the values of the spectral fitting parameters for each specific species, i.e. binding energy (eV), full wide at half maximum (FWHM) value (eV) for each pass energy, spin-orbit splitting values and asymmetric peak shape fitting parameters, are not all normally provided in the literature and data bases, and are necessary for reproducible, quantitative chemical state analysis. A more consistent, practical and effective approach to curve fitting was developed based on a combination of (1) standard spectra from quality reference samples, (2) a survey of appropriate literature databases and/or a compilation of literature references and (3) specific literature references where fitting procedures are available. This paper extends this approach to the chemical states of Cr, Mn, Fe, Co and Ni metals, and various oxides and hydroxides where intense, complex multiplet splitting in many of the chemical states of these elements poses unique difficulties for chemical state analysis. The curve fitting procedures proposed use the same criteria as proposed previously but with the additional complexity of fitting of multiplet split spectra which has been done based on spectra of numerous reference materials and theoretical XPS modeling of these transition metal species. Binding energies, FWHM values, asymmetric peak shape fitting parameters, multiplet peak separation and peak area percentages are presented. The procedures developed can be utilized to remove uncertainties in the analysis of surface states in nano-particles, corrosion, catalysis and surface-engineered materials.     

Quantum Mechanical Algorithm for Solving Quadratic Residue Equation

We propose a quantum mechanical algorithm for solving quadratic residue equation z ²=b (mod M) based on Grover quantum search. The quantum algorithm will take O( ?M\sqrt{M} ) steps for finding the solutions to the equation by exploiting the properties of quantum superposition and interference effect, while classical algorithm to the same problem will take O(M) steps. The success probability of the algorithm approaches to unity and the cost of the algorithm mainly depends on the calculations of quadratic residue modulo M and the number of iterations. Furthermore, we show that the algorithm can be used to solve the prime factorization problem, and the computing complexity is O( ?N\sqrt{N} ).     

Ultraviolet photoemission and 4d core reflectance spectra of SmSe(100)

Ultraviolet photoemission (UPS) and inner core reflectance spectra have been measured on SmSe(100) surface with synchrotron radiation. Besides the multiplet structures observed in UPS spectra for the Sm 4f, 5p and 5s excitations, the reflectance spectrum has revealed a multiplet structure associated with the Sm 4d→4f excitation. Each band of the UPS spectra has shown remarkably different hν dependence and the resonant behavior of the cross section. Sm 4f- and Se 4p-derived valence band features are unambiguously identified by the angle resolved UPS.     

Minimum state for high Reynolds and Péclet number turbulent flows

Direct numerical simulations (DNS) or experiments for the very high Reynolds (Re) and Péclet (Pe) number flows commonly exceed the resolution possible even when use is made of the most advanced computer capability or most sophisticated diagnostics and physical capabilities of advanced laboratory facilities. In practice use is made of statistical flow data bases developed at the highest Re and Pe levels achievable within the currently available facility limitations. In addition, there is presently no metric to indicate whether and how much of the fully resolved physics of the flow of interest has been captured within the facilities available. In this Letter the authors develop the necessary metric criteria for homogeneous, isotropic and shear layer flows. It is based on establishing a smaller subset of the total range of dynamic scale interactions that will still faithfully reproduce all of the essential, significant, influences of the larger range of scale interactions. The work identifies a minimum significant Re and Pe level that must be obtained by DNS or experiment in order to capture all of the significant dynamic influences in data which is then scaleable to flows of interest. Hereafter this is called the minimum state. Determination of the minimum state is based on finding a minimum scale separation for the energy-containing scales of the flow and scalar fields sufficient to prevent contamination by interaction with the (non-universal) velocity dissipation and scalar diffusivity inertial range scale limits.     

Effects of viscous fluid on wave propagation in carbon nanotubes

In this Letter, the effects of the viscous fluid on the propagation characteristics of elastic waves in carbon nanotubes are studied. Based on the nonlocal continuum theory, the small scales effects are also considered. The equations of wave motion are derived and the dispersion relation is presented. Numerical simulations are performed with the consideration of different scale coefficients to discuss the influence of the viscous fluid. From the results, it can be observed that the dispersion relation can be changed by the fluid viscosity obviously. Moreover, due to the fluid viscosity, the wave frequency will be reduced to a low region and the elastic wave behaviors can be significantly influenced by the viscous fluid velocity.     

Wavelength coincidence of allowed and intercombination multiplets in N III and O IV: A density and/or temperature diagnostic

Two multiplets of N III with different intensity dependence on source conditions fall in the same wavelength interval near 1750 Å, and the analogous multiplets in O IV also lie close together. It is suggested that the multiplet pair can be useful for diagnostic purposes. The calculated ratios are consistent with available observations. A preliminary inspection of solar flare spectra shows the presence of the higher-density-indicating allowed multiplet in O IV.     

基于背景最佳滤波尺度的红外图像复杂度评价准则

提出一种基于背景最佳滤波尺度的红外图像复杂度评价准则来解决传统方法评价背景效果较差的问题. 同时, 这种方法还可以为红外图像滤波提供最佳高通滤波尺度信息, 从而对红外图像进行性能最佳滤波. 首先, 生成高斯仿真目标并与红外图像进行融合, 获得包含仿真目标及真实红外背景的图像. 然后, 在不同高斯滤波尺度下对图像滤波, 并计算滤波后仿真目标的信噪比. 最后, 取滤波后目标信噪比最大时的滤波尺度作为背景最佳滤波尺度, 使用该尺度可评价红外图像的复杂度. 另外, 本文还使用数学模型推导了红外图像最佳滤波尺度, 得出最佳滤波尺度的数学表达式. 大量实验表明: 1) 本文推导的最佳滤波尺度数学表达式与实验曲线吻合. 2) 这种方法在评价红外图像复杂度方面比传统的基于信息熵的方法效果要好很多. 并且这种方法获取的红外背景复杂度为滤波最佳尺度, 可以直接利用这项指标对图像进行最佳滤波从而更好地检测弱小目标. 3) 仿真目标尺度越大, 最佳滤波尺度也会相应增大. 因此, 在评价图像复杂度时, 应使用相同尺度的仿真目标, 不同图像之间才具备可比性. 同时, 最佳滤波尺度与仿真目标的强度无关. 4) 本文算法使用的滤波器宜用高斯及Butterworth高通滤波器实现. 5) 本文提出的方法不仅可以有效分析红外视频的复杂度, 并且可以通过复杂度的变化分析图像内容的突变.     

Slow-time acceleration for modeling multiple-time-scale problems

The numerical simulation of a system exhibiting a broad range of time scales can be very expensive because the time discretization will in general need to resolve the smallest time scale, and the simulation will have to extend over many times the longest time scale. However, it is common that not all the time scales are of interest for a particular problem. When the long time scales are of primary interest, a number of techniques are available to eliminate the unwanted short time scales from consideration. When the short time scales are of primary interest, a technique for mitigating the consequences of anomalously long time scales is needed. The “slow-time acceleration” technique presented here has been developed to address this problem. In the slow-time acceleration technique, a modified evolution equation is developed in which the longest time scale is much shorter than that of the original system, and which has the same multi-time scale asymptotic structure as the original system. As an example, this approach is applied to the numerical simulation of solid-propellant rockets in which the long time scale is associated with the regression of the burning propellant.     

Relaxation and lyapunov time scales in a one-dimensional gravitating sheet system

The relation between relaxation, the time scale of Lyapunov instabilities, and the Kolmogorov-Sinai time in a one-dimensional gravitating sheet system is studied. Both the maximum Lyapunov exponent and the Kolmogorov-Sinai entropy decrease as proportional to N(-1/5). The time scales determined by these quantities evidently differ from any type of relaxation time found in the previous investigations. The relaxation time to quasiequilibria (microscopic relaxation) is found to have the same N dependence as the inverse of the minimum positive Lyapunov exponent. The relaxation time to the final thermal equilibrium differs from the inverse of the Lyapunov exponents and the Kolmogorov-Sinai time.     

Approximation of a chaotic orbit as a cryptanalytical method on Baptista's cipher

Many cryptographic schemes based on M.S. Baptista algorithm were created. The original algorithm and some of the versions that based upon it were put to test with various cryptanalytic techniques. This Letter shows the new approach to Baptista's cipher cryptanalysis. The presumption is that the attacker knows the mapping in between the characters of the plaintext and the numbers of the ?-interval. Then, depending on the amount of the knowledge about the key possessed, the estimation of all components of the key requires a different computational complexity, however it is possible. This Letter also takes into consideration, independently, all the components of the key from the M.S. Baptista's original algorithm. The main aim is the use of the approximation of the blurred chaotic orbit's real value in Baptista-type cipher cryptanalysis.     

Perceived sound quality of reproductions with different frequency responses and sound levels

Three programs (female voice, jazz music, and pink noise) were reproduced using four different frequency responses and two different sound levels. Fourteen normal hearing subjects listened to the reproduction via earphones and judged the sound quality on seven perceptual scales (loudness, clarity, fullness, spaciousness, brightness, softness/gentleness, and nearness) and a fidelity scale. Significant differences among the reproductions appeared in all scales and could be attributed to the differences in frequency response or sound level or both. Interactions between the reproductions and the programs could be explained by the relations between the spectrum of the programs and the frequency responses used. The results for the noise program were similar to those for the jazz music program.     

滑动移除小波分析法在动力学结构突变检验中的应用

标度指数计算的即时性与准确性对相关时间序列的动力学结构突变分析至关重要,然而现有方法在即时性与准确性上一直无法兼顾.将小波分析方法与滑动移除窗口技术相融合,提出一种新的动力学结构突变检测方法——滑动移除小波分析法.通过选取不同的滑动移除窗口,分别对构建的线性、非线性理想时间序列进行动力学结构突变分析,结果表明不论是线性时间序列还是非线性时间序列,滑动移除小波分析能够准确地检测到序列的动力学结构突变点及突变区间,对于滑动移除窗口长度依赖性较小,具有很强的稳定性,而且在计算速度上明显优于滑动移除重标极差和滑动移除方差分析方法,将在大数据处理中具有一定的优势.同时分别对线性、非线性理想时间序列添加高斯白噪声,结果表明滑动移除小波分析具有很强的抗噪能力,能够准确地检测到加噪后序列的突变点.对佛坪站日最高温度实测资料的动力学结构突变的准确检测进一步验证了该方法的有效性.滑动移除小波分析法可为具有相关性的系统动力学结构突变的快速、准确检测提供一种途径.     

Gauge unification in type I/I′ models

We discuss whether the (MSSM) unification of gauge couplings can be accommodated in string theories with a low (TeV) string scale. This requires either power law running of the couplings or logarithmic running extremely far above the string scale. In both cases it is difficult to arrange for the multiplet structure to give the MSSM result. For the case of power law running there is also enhanced sensitivity to the spectrum at the unification scale. For the case of logarithmic running there is a fine tuning problem associated with the light closed string Kaluza Klein spectrum which requires gauge mediated supersymmetry breaking on the “visible” brane with a dangerously low scale of supersymmetry breaking. Evading these problems in low string scale models requires a departure from the MSSM structure, which would imply that the success of gauge unification in the MSSM is just an accident.     

Density fluctuations on mm and Mpc scales

We will in this Letter report on suggestive similarities between density fluctuation power versus wavenumber on small (mm) and large (Mpc) scales. The small scale measurements were made in fusion plasmas and compared to predictions from classical fluid turbulence theory. The data is consistent with the dissipative range of 2D turbulence. Alternatively, the results can be fitted to a functional form that cannot be explained by turbulence theory. The large scale measurements were part of the Sloan Digital Sky Survey galaxy redshift examination. We found that the equations describing fusion plasmas also hold for the galaxy data. The comparable dependency of density fluctuation power on wavenumber in fusion plasmas and galaxies might indicate a common origin of these fluctuations.