Application of maximum entropy methods in NQR data processing

The superiority of maximum entropy method (MEM) over the traditional fast Fourier transform (FFT) method is demonstrated in NQR spectral analyses. Using computersimulated and real spectral data, a comparative study was made between the maximum entropy and the conventional discrete Fourier transform methods. It is concluded that use of MEM in NQR spectroscopy can lead to sensitivity improvements, reduction of instrumental artifacts and truncation errors, shortened data acquisition times and automatic suppression of noise, while at the same time increasing the resolution. A property of MEM which is particularly significant for two-dimensional NQR spectroscopy is its ability to produce spectral estimates from the short data records, free of truncation artifacts. The use of MEM in two-dimensional NQR studies can lead to reduction of the time necessary to acquire two-dimensional set.     

信息论在粉末衍射结构分析中的应用—最大熵方法

从粉末衍射数据直接测定晶体结构介材料和晶体学研究的热门课题之一。文章介绍了粉末衍射结构的最大熵法。最大熵法是基于信息论的最大熵原理和最大似然原理的一种方法。由于其独特的优点，最大熵法是最有前景的粉末衍射结构分析方法之一。     

Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking

Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated N₂ atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. These results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.

Graphical Abstract

     

Electron density distribution in Si and Ge using multipole, maximum entropy method and pair distribution function analysis

The local, average and electronic structure of the semiconducting materials Si and Ge has been studied using multipole, maximum entropy method (MEM) and pair distribution function (PDF) analyses, using X-ray powder data. The covalent nature of bonding and the interaction between the atoms are clearly revealed by the two-dimensional MEM maps plotted on (100) and (110) planes and one-dimensional density along [100], [110] and [111] directions. The mid-bond electron densities between the atoms are 0.554 e/?³ and 0.187 e/?³ for Si and Ge respectively. In this work, the local structural information has also been obtained by analyzing the atomic pair distribution function. An attempt has been made in the present work to utilize the X-ray powder data sets to refine the structure and electron density distribution using the currently available versatile methods, MEM, multipole analysis and determination of pair distribution function for these two systems.      

最大熵法在风廓线雷达谱分析中的应用研究

为了解现代谱分析技术在风廓线雷达中应用的可行性,通过采用实测的和模拟的风廓线雷达回波信号,对比研究了FFT法与最大熵法的谱分析效果。结果表明:(1)当回波信号比较强时,两者都可以得到较好的谱分析效果;但是当回波信号较弱时,最大熵法分析效果优于FFT法,最大熵法对地杂波具有较好的抑制能力。(2)最大熵谱比较光滑,表明最大熵法对随机白噪声也有一定的抑制作用。(3)最大熵法的递推阶数对谱分析结果有一定影响,最终预测误差准则确定的递推阶数一般偏小,采用15阶的递推阶数进行最大熵法分析取得了较好结果。由于风廓线雷达回波通常都较弱,因此研究结果可望用于改善信号处理效果。     

Electron density distribution in GaAs using MEM

Electron density distribution of GaAs is determined by means of the maximum entropy method (MEM) using reasonably good X-ray data collected at room temperature and 200 K. The bonding electron distributions are clearly visible in the MEM map and the mixed covalent-ionic character in GaAs is evidenced. The density distributions at 200 K show more condensed electronic clouds as compared to the room temperature map, preserving the trend in the bonding characters. The electron densities at the middle of the bond are 0.79 and 0.70 e/ų at 200 K and at room temperature, respectively. The refined harmonic thermal factors are in good agreement with the published values.     

An investigation on the bonding in MgO,CaO, SrO and BaO from the MEM electron density distributions

The bonding in MgO, CaO, SrO and BaO has been studied using the electron density distribution maps obtained utilizing the reported X-ray data by the statistical approach maximum entropy method (MEM). The ionic/covalent nature of the bonding and the interaction between the atoms are clearly revealed by the maps. The bonding in these systems is shown two-dimensionally on the (100) and (110) planes and the one-dimensional electron density profiles along (100), (110) and (111) directions have also been plotted using MEM electron densities. The electron density at the saddle point between the ions has been estimated using these profiles and compared with the available reported results. The resolution of these maps is high and hence these maps can be regarded as the most precise electron density distributions seen inside the chosen materials. The electron content of the doubly ionic oxygen and the cations are estimated from the three-dimensional MEM electron densities by assuming spheres of various radii. The histograms drawn with [F_Mem(k)−F_Obs(k)]/σ(k) versus the number of reflections show the validity of the approach and the appropriateness of the Gaussian weighting scheme used in the analysis.     

High resolution electron density mapping for LiF and NaF by maximum entropy method (MEM)

High resolution maximum entropy method (MEM) electron density maps have been elucidated for LiF and NaF using reported X-ray structure factors. The ionic nature of the bonding between constituent atoms in both the systems is found to be well pronounced and clearly seen from the electron density maps. The resolution of the present MEM maps is 0.063 Å per pixel for LiF and 0.072 Å per pixel for NaF along the three crystallographic axes. The electron density at the middle of the bond along [111] is found to be 0.0673 e/ų for LiF and 0.003 e/ų for NaF showing the different ionic strengths of the bonding. The electron density along [100] and [110] has also been drawn and analyzed. The inequality in the ionicity for the individual atoms and the electron content for different ionic radii have also been analyzed and compared with already published results. The wR_MEM obtained from MEM analysis is 0.3% for LiF and 0.79% for NaF.     

Comparison of some resolution enhancement methods applied to35Cl-NQR nutation spectroscopy

The³⁵Cl nuclear quadrupole resonance spin echo nutation spectroscopy method was used to determine asymmetry parameters,η, of the electric field gradient tensor in cyanuric chloride, 1,3,5-trichloro-cyanuric acid and 1,3-dichloro-5,5-dimethylhydantoin. For comparison of advantages and drawbacks of some data processing methods we have tried integral transforms of nutation interferogram (pseudo-FID) data (Hankel and Hartley transforms) alternative to the Fourier transform. Another processing method, which provides a power spectrum estimated from time-domain data, is the maximum entropy method (MEM), and we applied the Burg algorithm version of it. We found that MEM gives the best enhancement of the nutation spectrum resolution and the signal-to-noise ratio, provided the number of autocorrelation coefficients is chosen for optimum performance of the Burg algorithm, otherwise estimated singularities in the nutation spectrum can be obscured by multiple spurious peaks or the spectrum resolution is low. In the Hankel transform with the first-order Bessel functions the improvement in resolution is achieved at the expense of the overall signal-to-noise ratio and for noisy experimental data this transform did not show reliable results. The Hartley transform gives a resolution better than the Fourier transform but worse than the two other methods. Unlike the Hankel transform after the Hartley transform the signal-to-noise ratio is not degraded. Theη parameter determined by MEM for cyanuric chloride was 18%, which is close to previously reported values. For 1,3,5-trichloro-cyanuric acidη = 20% and for the two chlorine sites in 1,3-dichloro-5,5-dimethylhydantoinη = 0 and 12% respectively. These values are in substantial agreement with the anticipated double bond character of N-Cl bonds in the two last compounds.     

Maximum entropy: a complement to Tikhonov regularization for determination of pair distance distributions by pulsed ESR

Tikhonov regularization (TIKR) has been demonstrated as a powerful and valuable method for the determination of distance distributions of spin-pairs in bi-labeled biomolecules directly from pulsed ESR signals. TIKR is a direct method, which requires no iteration, and, therefore, provides a rapid and unique solution. However, the distribution obtained tends to exhibit oscillatory excursions with negative portions in the presence of finite noise, especially in the peripheral regions of the distribution. The Shannon-Jaynes entropy of a probability distribution provides an intrinsic non-negativity constraint on the probability distribution and an unbiased way of obtaining information from incomplete data. We describe how the maximum entropy regularization method (MEM) may be applied to solve the ill-posed nature of the dipolar signal in pulsed ESR. We make use of it to suppress the negative excursions of the distance distribution and to increase the tolerance to noise in the dipolar signal. Model studies and experimental data are investigated, and they show that, with the initial or "seed" probability distribution that is required for MEM taken as the TIKR result, then MEM is able to provide a regularized solution, subject to the non-negativity constraint, and it is effective in dealing with noise that is problematic for TIKR. In addition we have incorporated into our MEM method the ability to extract the intermolecular dipolar component, which is embedded in the raw experimental data. We find that MEM minimization, which is implemented iteratively, is greatly accelerated using the TIKR result as the seed, and it converges more successfully. Thus we regard the MEM method as a complement to TIKR by securing a positive pair distance distribution and enhancing the accuracy of TIKR.     

Pressure dependence of the electron density in solid iodine by the maximum-entropy method

Abstract

A direct observation of the electron density of solid iodine has been attempted in order to study the electron-density delocalization process due to pressure-induced metallization. A high-accuracy x-ray powder diffraction measurement was carried out with a diamond anvil cell and an imaging plate on a synchrotron-radiation source. The maximum entropy method was employed to analyze the data and to obtain electron-density maps under pressures up to 20 GPa. The electron density between adjacent iodine molecules has been shown to gradually increase with increasing pressure; also, a two-dimensional network is formed at a density level of 0.2 e/ų at around 16 GPa.     

The thermoelectric power of MEM(TCNQ)2

MEM(TCNQ)₂ undergoes a first order semiconductor to metal transition at 340.8 K. We have measured the thermoelectric power (TEP) of MEM(TCNQ)₂ in the temperature range above 335 K. Above the transition the TEP is ?65 μV/°K, in the low temperature phase it is strongly temperature dependent and approaches zero near the transition. The indicated loss of spin entropy at the transition is discussed.     

Scattering mechanism in a step-modulated subwavelength metal slit: a multi-mode multi-reflection analysis

In this paper, the scattering/transmission inside a step-modulated subwavelength metal slit is investigated in detail. We firstly investigate the scattering in a junction structure by two types of structural changes. The variation of transmission and reflection coefficients depending on structural parameters are analysed. Then a multi-mode multi-reflection model based on ray theory is proposed to illustrate the transmission in the step-modulated slit explicitly. The key parts of this model are the multi-mode excitation and the superposition procedure of the scatterings from all possible modes, which represent the interference and energy transfer occurring at the interfaces. The method we use is an improved modal expansion method (MEM), which is a more practical and efficient version compared with the previous one [C. Li, Y.S. Zhou, H.Y. Wang, F.H. Wang, Opt. Express 19, 10073 (2011)]. In addition, some commonly used methods including FDTD, scattering matrix method and improved characteristic impedance method are compared with MEM to highlight the accuracy of these methods.     

Two-dimensional on- and off-resonance nutation FFT/MEM NQR spectroscopy

The new two-dimensional nuclear quadrupole resonance experiments based on the principle of nutation spectroscopy, which can be used to determine the asymmetry parameter, and thus the full quadrupolar tensor of spin-3/2 nuclei at zero applied magnetic field are discussed. The problems of reconstructing 2D-nutation NQR spectra using conventional methods and the advantages of using implementation of the maximum entropy method (MEM) are analyzed. Use of the MEM in 2D-NQR spectroscopy can lead to sensitivity improvement, reduction of instrumental artifacts and truncation errors, shortened data acquisition times and automatic suppression of noise, while at the same time increasing the resolution. The possibilities of off-resonance irradiation in nutation experiments are demonstrated experimentally and theoretically. It is shown that the off-resonance nutation spectroscopy is a useful extension of the conventional on-resonance experiments thus facilitating the determination of asymmetry parameters in multiple spectrum. The methods have been successfully demonstrated for the³⁵Cl on-and off-resonance 2D-nutation spectra in polycrystalline 2,4,6-trichloro-1,3,5-triazine.     

CO2 motion in carbon dioxide deuterohydrate determined by applying maximum entropy method to neutron powder diffraction data

Crystal structures of carbon dioxide deuterohydrate were studied by neutron powder diffraction at temperatures from 10 to 200 K. Maps of scattering length density distribution were obtained using a maximum entropy method (MEM), which clarified the motion of CO₂ molecules in the hydrate. In small cages, the carbon atom of the CO₂ molecule is at the center of the cage, and the oxygen atoms of CO₂ revolve freely around the carbon atom. In large cages, the carbon atom also is at the center of the cage, but the oxygen atoms tend to revolve around the carbon atom along the plane parallel to the hexagonal facets of the cage.     

J/psi and eta(c) in the deconfined plasma from lattice QCD

Analyzing correlation functions of charmonia at finite temperature (T) on 32(3)x(32-96) anisotropic lattices by the maximum entropy method (MEM), we find that J/psi and eta(c) survive as distinct resonances in the plasma even up to T approximately 1.6T(c) and that they eventually dissociate between 1.6T(c) and 1.9T(c) (T(c) is the critical temperature of deconfinement). This suggests that the deconfined plasma is nonperturbative enough to hold heavy-quark bound states. The importance of having a sufficient number of temporal data points in MEM analyses is also emphasized.     

Comparison of maximum entropy and filtered back-projection methods to reconstruct rapid-scan EPR images

Reconstruction of two-dimensional images by filtered back-projection (FBP) and by the maximum entropy method (MEM) was compared for spectral-spatial EPR images with differing signal-to-noise ratios. Experimental projections were recorded using direct-detected rapid scans in the presence of a series of magnetic field gradients. The slow-scan absorption lineshapes were calculated by Fourier deconvolution. A Hamming filter was used in conjunction with FBP, but not for MEM. Imperfections in real experimental data, as well as random noise, contribute to discrepancies between the reconstructed image and experimental projections, which may make it impossible to achieve the customary MEM criterion for convergence. The Cambridge MEM algorithm, with allowance for imperfections in experimental data, produced images with more linear intensity scales and more accurate linewidths for weak signals than was obtained with another MEM method. The more effective elimination of noise in baseline regions by MEM made it possible to detect weak trityl (13)C trityl hyperfine lines that could not be distinguished from noise in images reconstructed by FBP. Another advantage of MEM is that projections do not need to be equally spaced. FBP has the advantages that computational time is less, the amplitude scale is linear, and there is less noise superimposed on peaks in images. It is useful to reconstruct images by both methods and compare results. Our observations indicate that FBP works well when the number of projections is large enough that the star effect is negligible. When there is a smaller number of projections, projections are unequally spaced, and/or signal-to-noise is lower MEM is advantageous.     

A comparison between MEM and FFT for the spectral analysis of geophysical signals

Summary The results obtained by the maximum entropy method (MEM) for the spectral analysis of real signals (the magnetic-field observations performed by ISEE-2 during periods of solar-wind turbulence upstream of the Earth's bow shock) are compared with those obtained by the traditional fast Fourier transform (FFT) technique. The major relative importance of the dominant wave form suddenly emerges in the MEM analysis and the total frequency excursion of peaks is often smaller than the frequency resolution allowed by the FFT. The expected occurrence of spurious peaks might be less dramatic then in other cases; however, the definite choice of the best power spectrum remains often ambiguous. This research has been supported by the Ministero per la Pubblica Istruzione (40%) and by the Gruppo Italiano di Fisica Cosmica.     

Analysis of fluorescence decay kinetics of thioflavin t by a maximum entropy method

The application of a maximum entropy method (MEM) for analysis of time-resolved fluorescence data is discussed. A developed version of MEM has been tested using simulated kinetic data. Based on computed results, practical criteria have been established to determine whether the lifetime distribution of emitting centers is described by a discrete spectrum (a set of two or three exponentials) or by a continuous one (mono- or bimodal distribution of exponentials). The proposed method has been used to analyze the fluorescence decay kinetics of thioflavin T (ThT) intercalated into amyloid fibrils. The presence of two peaks in the lifetime distribution of emitting centers has been explained by the existence in fibrils of two types of binding centers substantially differing in microenvironment rigidity. This suggestion is supported by the results of fluorescence quenching of intercalated ThT with the quencher KI.     

Monitoring Membrane Protein Conformational Heterogeneity by Fluorescence Lifetime Distribution Analysis Using the Maximum Entropy Method

Due to the inherent difficulty in crystallizing membrane proteins, approaches based on fluorescence spectroscopy have proved useful in elucidating their conformational characteristics. The ion channel peptide gramicidin serves as an excellent prototype for monitoring membrane protein conformation and dynamics due to a number of reasons. We have analyzed conformational heterogeneity in membrane-bound gramicidin using fluorescence lifetime distribution analysis of tryptophan residues by the maximum entropy method (MEM). MEM represents a model-free and robust approach for analyzing fluorescence lifetime distribution. In this paper, we show for the first time, that fluorescence lifetime distribution analysis using MEM could be a convenient approach to monitor conformational heterogeneity in membrane-bound gramicidin in particular and membrane proteins in general. Lifetime distribution analysis by MEM therefore provides a novel window to monitor conformational transitions in membrane proteins.