Testing of Multifractional Brownian Motion

Fractional Brownian motion (FBM) is a generalization of the classical Brownian motion. Most of its statistical properties are characterized by the self-similarity (Hurst) index 0<H<1. In nature one often observes changes in the dynamics of a system over time. For example, this is true in single-particle tracking experiments where a transient behavior is revealed. The stationarity of increments of FBM restricts substantially its applicability to model such phenomena. Several generalizations of FBM have been proposed in the literature. One of these is called multifractional Brownian motion (MFBM) where the Hurst index becomes a function of time. In this paper, we introduce a rigorous statistical test on MFBM based on its covariance function. We consider three examples of the functions of the Hurst parameter: linear, logistic, and periodic. We study the power of the test for alternatives being MFBMs with different linear, logistic, and periodic Hurst exponent functions by utilizing Monte Carlo simulations. We also analyze mean-squared displacement (MSD) for the three cases of MFBM by comparing the ensemble average MSD and ensemble average time average MSD, which is related to the notion of ergodicity breaking. We believe that the presented results will be helpful in the analysis of various anomalous diffusion phenomena.     

多分辨分形理论在高分辨力遥感图像分割中的应用

针对遥感图像的高分辨力特性,提出了基于多分辨分形的遥感图像分割方法。改进了多分辨结构的建立方法,提出了基于Laplacian金字塔的多分辨结构的分形分割法。实验表明,改进的多分辨分形图像分割方法在减少信息冗余度的同时,提高了数据利用率,可有效地对高分辨力遥感图像进行分割分类。     

Non-zero total correlation means non-zero quantum correlation

We investigated the super quantum discord based on weak measurements. The super quantum discord is an extension of the standard quantum discord defined by projective measurements and also describes the quantumness of correlations. We provide some equivalent conditions for zero super quantum discord by using quantum discord, classical correlation and mutual information. In particular, we find that the super quantum discord is zero only for product states, which have zero mutual information. This result suggests that non-zero correlations can always be detected using the quantum correlation with weak measurements. As an example, we present the assisted state-discrimination method.     

Two-particle correlation function and dihadron correlation approach

It is shown that, in the case of asymmetric nuclear interactions, the application of the traditional dihadron correlation approach to determining a two-particle correlation function C may lead to a form distorted in relation to the canonical pair correlation function _C². This result was obtained both by means of exact analytic calculations of correlation functions within a simple string model for proton–nucleus and deuteron–nucleus collisions and by means of Monte Carlo simulations based on employing the HIJING event generator. It is also shown that the method based on studying multiplicity correlations in two narrow observation windows separated in rapidity makes it possible to determine correctly the canonical pair correlation function C₂ for all cases, including the case where the rapidity distribution of product particles is not uniform.     

量子关联

量子纠缠是量子信息处理过程中的重要资源,也是量子力学与经典力学本质区别的一个重要特征.最近随着量子信息理论的不断发展,人们发现可分态中也可以存在非经典的量子关联,量子纠缠只是量子关联的一部分.而且这种非纠缠的量子关联可能在一些量子信息处理过程中起到重要的作用.文章介绍了量子关联最近所取得的一些研究进展,特别是量子关联在各种消相干环境下的演化规律等.     

Dynamic correlation

From a knowledge of the Hartree-Fock and exact non-relativistic energies of atoms, the correlation energy E_c, as defined by Lowdin, may be calculated. For atoms this correlation is defined as dynamic correlation. The separate like-spin and unlike-spin contributions, E_cσσ, E_cαβ, may be calculated as a sum of pair energies from quantum chemistry; we have used the unrestricted M?ller-Plesset second-order algorithm, and then scaled them to give E_c. These three values may also be computed using dynamic correlation functionals, with the Stoll partitioning. The VWN, LYP and P91 functionals were studied for the atoms from H to Ar. Although the total correlation energies of LYP and P91 are similar, only P91 gives a semi-sensible breakdown into the E_cσσ, and E_cαβ components. It is immediately apparent that a new functional, OPTC, derived from the P91 components as 0.6625 x E_cσσ, + 1. 1015 x E_cαβ is an improvement (its mean absolute error is only 0.006 E_h). Using the recently introduced improved exchange functional OPTX (obtained through a fit to the HF energies of atoms), Kohn-Sham calculations were performed on the atoms using the OPT(=OPTX + OPTC) functional. The total energies have a mean absolute error of 0.006 E_h. The study then moves to molecules. First it is shown that the dynamic correlation energy contribution to the dissociation energies is very similar (within 2kcalmol^?1 in most cases), whether it is calculated with LYP, P91 or OPTC. A calculation is then made of the HF contribution, the dynamic contribution through OPTC and the left-right contribution through OPTX, to molecular binding. In many cases the sum agrees with the observed value, but in some cases the prediction is significantly in error, e.g. O₂ is overbound by 10 kcal mol^?1. Thus either OPTX or OPTC or both are inadequate. An attempt was made to determine improved local exchange and correlation functionals by fitting to both atomic and molecular data, but this was unsuccessful. The conclusion is that the method is close to the limit of accuracy achievable from separately optimized local exchange and correlation functionals. Finally, a new hybrid functional O3LYP, which is a substantial improvement on B3LYP, is presented.     

相关阵在抑制局部相关噪声中的应用

本文提出用阵元间互相关作为基元加权求和形成波束(相关阵)，并给出用来抑制线阵局部强相关干扰的一种权向量实现方法。海上试验数据处理结果表明，利用本文提出的权向量实现相关阵比CBF阵有较高的信噪比增益和较好的抗噪声干扰能力。     

Phase-restricted heterogeneous correlation

We introduce a new phase-restricted algorithm for producing a heterogeneous correlation filter that permits new in-class members to be added without changing the phase of the filter. This heterogeneous correlation filter uses amplitude modulation both to enhance in-class cross correlations and to suppress selected out-of-class correlations. This new algorithm should substantially improve the performance of existing class-associative correlators and improve their operation.     

Triple correlation functions

New values for double mode-mode and triple flux molecular equilibrium correlations are presented. The relevance of these results for hydrodynamics is then discussed. It is found that the divergence of Burnett coefficients has only a formal meaning.     

Finite-temperature correlation functions

Lattice measurements of the Pisa group are analyzed numerically, and the parameters of correlation functions are extracted fromthe data—both below and above the deconfinement temperature T _c. The gluon condensate is found for six temperatures in the interval (0.956–1.131)T _c, and field distributions in the deconfined phase are obtained.     

Billiards correlation functions

We discuss various experiments on the time decay of velocity autocorrelation functions in billiards. We perform new experiments and find results which are compatible with an exponential mixing hypothesis first put forward by Friedman and Martin (FM): they do not seem compatible with the stretched exponentials believed, in spite of FM and more recently of Chernov, to describe the mixing. The analysis leads to several byproducts: we obtain information about the normal diffusive nature of the motion and we consider the probability distribution of the number of collisions in timet _m (ast _m ), finding a strong dependence on some geometric characteristics of the locus of the billiard obstacles.This paper is dedicated to Philippe Choquard on his 65th birthday     

Left-right correlation energy

We first attempt to determine a local exchange functional E_x[p] which accurately reproduces the Hartree-Fock (HF) energies of the 18 first and second row atoms. E_x[p is determined from p and |δp|, and we find that we can improve significantly upon Becke's original generalized gradient approximation functional (commonly called B88X) by allowing the coefficient of the Dirac exchange term to be optimized (it is argued that molecules do not behave like the uniform electron gas). We call this new two parameter exchange functional OPTX. We find that neither δ p or t = Σ δ _i |² improve the fit to these atomic energies. These exchange functionals include not only exchange, but also left-right correlation. It is therefore proposed that this functional provides a definition for exchange energy plus left-right correlation energy when used in Kohn-Sham (KS) calculations. We call this energy the Kohn-Sham exchange (or KSX) energy. It is shown that for nearly all molecules studied these KSX energies are lower than the corresponding HF energies, thus giving values for the non-dynamic correlation energy. At stretched geometries, the KSX energies are always lower than the HF energies, and often substantially so. Furthermore all bond lengths from the KSX calculations are longer than HF bond lengths and experimental bond lengths, which again demonstrates the inclusion of left-right correlation effects in the functional. For these reasons we prefer to split the correlation energy into two parts: left-right correlation energy and dynamic correlation energy, arguing that the usage of the words ‘non-dynamic’ or ‘static’ or ‘near-degeneracy’ is less meaningful. We recognize that this definition of KSX is not precise, because the definition of a local E_x[p] can never be precise. We also recognize that these ideas are not new, but we think that their importance has been insufficiently recognized in functional determination. When we include third row atoms in our analysis, we are unable to find a local exchange functional which is a substantial improvement over B88X for the reproduction of HF energies. This must arise from the effects of the core orbitals, and therefore we do not consider that this detracts from the improved accuracy of OPTX. We report some MCSCF calculations constructed from bonding-antibonding configurations, from which we attempt to calculate ab initio left-right correlation. There is only moderate agreement between the two approaches. Finally we combine the OPTX functional with established correlation functionals (LYP, P86, P91) to form OLYP, OP86 and OP91; OLYP is a great improvement on BLYP for both energy and structure, and OP86, OP91 are an improvement over BP86, BP91 for structure. The importance of the exchange functional for molecular structure is therefore underlined.     

Dipole correlation functions

Glarum's relation between permanent dipole correlation functions for an isolated sphere and a spherical region in a continuous medium is derived by molecular response theory and relation time development operators for the two cases.     

Wavelet-based morphological correlation

A wavelet-based morphological correlation (WBMC) is proposed as a new architecture to improve the properties of the classical morphological correlation (MC). For the WBMC, a dilated wavelet intensity function is introduced to filter the joint power spectrum (JPS) of the MC before final inverse Fourier transform. Computer simulation results show that, as compared with the linear correlation (LC), the conventional MC and the joint wavelet transform correlation (JWTC), the WBMC provides better discrimination capability with sharp and unmistakable correlation signal and its performance metrics are more stable under input outlier noise (salt-and-pepper noise). Although the WBMC loses illumination-invariance when input illumination factor is larger than unity, considerable discrimination capability is still maintained.     

Stochastic correlation tomography

An analysis is made of the possibility of using stochastic generation of correlated quanta (random in time) to obtain rapid volume information on the state of a medium and to develop the physical principles of a real-time tomograph. Flux theory and mathematical modeling with a computer experiment are successfully used for these investigations.     

Apochromatic optical correlation

Optical correlation, or matched filtering, can now be applied more widely than before, because the light is now allowed to be totally incoherent, spatially and spectrally. Two such correlators were demonstrated recently. Their state of chromatic correction can be called achromatic, since the scaling error has two zero crossings within the visible range of wavelengths. We present a new apochromatic correlator, in which the scaling error has three zero crossings. The maximum error and the rms error are reduced by a factor of 5. Our apochromatic correlator is composed of two highly dispersive heavy flint lenses that are in contact with two diffractive lenses and two chromatic corrected refractive lenses. The uncommon combination of flint dispersion and diffractive dispersion enabled us to achieve apochromatic correction of the scaling factor of the correlator.     

Interaural correlation sensitivity

Sensitivity to differences in interaural correlation was measured for 1.3-ERB-wide bands of noise using a 2IFC task at six frequencies: 250, 500, 750, 1000, 1250, and 1500 Hz. The sensitivity index, d', was measured for discriminations between a number of fixed pairs of correlation values. Cumulative d' functions were derived for each frequency and condition. The d' for discriminating any two values of correlation may be recovered from the cumulative d' function by the difference between cumulative d's for these values. Two conditions were employed: the noisebands were either presented in isolation (narrow-band condition) or in the context of broad, contiguous flanking bands of correlated noise (fringed condition). The cumulative d' functions showed greater sensitivity to differences in correlation close to 1 than close to 0 at low frequencies, but this difference was less pronounced in the fringed condition. Also, a more linear relationship was observed when cumulative d' was plotted as a function of the equivalent signal-to-noise ratio (SNR) in dB for each correlation value, rather than directly against correlation. The equivalent SNR was the SNR at which the interaural correlation in an NoS(pi) stimulus would equal the interaural correlation of the noise used in the experiment. The maximum cumulative d' declined above 750 Hz. This decline was steeper for the fringed than for the narrow-band condition. For the narrow-band condition, the total cumulative d' was variable across listeners. All cumulative d' functions were closely fitted using a simple two-parameter function. The complete data sets, averaged across listeners, from the fringed and narrow-band conditions were fitted using functions to describe the changes in these parameters over frequency, in order to produce an interpolated family of curves that describe sensitivity at frequencies between those tested. These curves predict the spectra recovered by the binaural system when complex sounds, such as speech, are masked by noise.     

Accurate definition of correlation peak position by optical speckle-displacement correlation technique

An optical speckle-displacement correlator based on hybrid optical–digital joint transform correlator architecture with a digital first stage and an optical second stage has been used to determine the correlation peak position with subpixel accuracy, without the use of intricate interpolation algorithms. A thorough analysis and a calculation of the parameters of the second optical stage are performed in order to achieve the necessary magnification of the correlation peak, so as to obtain an accurate definition of the peak position. The experiment setup for the realization of the optical speckle-displacement technique was constructed with a digital Fourier processor as its basic component, making possible a joint power spectrum median and ring median binarization, and an optical Fourier processor. The results which were obtained demonstrate that a setup of this kind can produce sharp and narrow correlation peaks, and can provide the necessary magnification for finding the peak position with subpixel accuracy.     

相关测速声呐时空相关函数模型改进研究

相关测速声呐通过对回波的理论时空相关函数和数据时空相关函数进行最小二乘拟合或其它优化算法来解算载体速度,因此理论时空相关函数模型的准确性对速度解算是至关重要的。通过对多次海试数据的处理发现,在某些情形下,相关测速声呐的理论空间相关函数和数据空间相关函数三维俯视图形状不匹配,导致速度估计结果不准确。通过对时空相关函数理论模型进行改进,将理论空间相关函数在水平面上的投影由圆形修改为椭圆,则其与数据空间相关函数拟合得更好,从而使相关测速声呐测速准确度得到了提高,并得出相关函数的三维俯视图呈椭圆形状与部分海底表面不平整性的各向异性有关的结论。