Autocorrelation Function Method Research Articles

Existence of memory in membrane channels: analysis of ion current through a voltage‐dependent potassium single channel

Ion current fluctuation of voltage-dependent potassium channel in LβT2 cells has been investigated by autocorrelation function and DFA (detrended fluctuation analysis) methods. The calculation of the autocorrelation function exponent and DFA exponent of the sample was based on the digital signals or the 0-1 series corresponding to closing and opening of channels after routine evolution, rather than the sequence of sojourn times. The persistent character of the correlation of the time series was evident from the slow decay of the autocorrelation function. DFA exponent α was significantly greater than 0.5. The main outcome has been the demonstration of the existence of memory in this ion channel. Thus, the ion channel current fluctuation provided information about the kinetics of the channel protein. The result suggests the correlation character of the ion channel protein non-linear kinetics indicates whether the channel is open or not.

초음파 탄성 영상 알고리듬

초음파를 사용해 음속도, 감쇠 계수, 밀도, 비선형 B/A 파라미터 등을 측정하여 인체 조직의 특성을 정량적으로 영상화하고자 하는 연구가 1980년대부터 많이 진행되어 왔으나 아직 상용화 단계에는 도달하지 못했다. 하지만 1990년대 초에 시작된 탄성 영상법은 최근 들어 초음파 진단기에 상용화되어 임상에서 B-모드 영상법과 함께 전립선, 유방, 갑상선, 간, 혈관 등을 진단하기 위한 보완적이며 더 정량적인 모드로 사용되고 있는 단계에 진입하였다. 본고에서는 주로 준정적 또는 정적탄성 영상법에 사용되는 여러 가지 알고리듬을 소개하고 특성을 비교하고자 한다. 대부분의 알고리듬은 상호상관함수 또는 자기상관함수 방법에 그 기반을 두고 있으며 전자는 래그를 변화시켜가면서 시간 이동량을 찾지만 후자는 보간 과정 없이 고정된 래그에서의 위상차로부터 시간 이동량을 바로 구해 변위를 추정하는 점이다. Since the 1980s, there have been many research activities devoted to quantitatively characterizing and imaging human tissues based on sound speed, attenuation coefficient, density, nonlinear B/A parameter, etc., but those efforts have not yet reached the stage of commercialization. However, a new imaging technology termed elastography, which was proposed in the early 1980s, has recently been implemented in commercial clinical ultrasound scanners, and is now being used to diagnose prostates, breasts, thyroids, livers, blood vessels, etc., more quantitatively as a complementary adjunct modality to the conventional B-mode imaging. The purpose of this article is to introduce and review various elastographic algorithms for use in quasistatic or static compression type elasticity imaging modes. Most of the algorithms are based on the crosscorrelation or autocorrelation function methods, and the fundamental difference is that the time shift is estimated by changing the lag variable in the former, while it is directly obtained from the phase shift at a fixed lag in the latter.

Blast Furnace System Modeling by Multivariate Phase Space Reconstruction and Neural Networks

AbstractTime series data collected from a medium‐size blast furnace (BF) is analyzed using the phase space reconstruction. To achieve better reconstruction, multivariate correlation analysis is first applied to screen out correlated variables, which shows that three important variables, i.e., silicon content in hot metal ([Si]), permeability index (FF), and coal injection (PM), are most appropriate for multivariate reconstruction. The time delay and embedding dimension are determined via the autocorrelation function and false nearest neighbor method. With the reconstructed time series, the neural networks model is applied to construct the predictive model for silicon content in hot metal. The simulation shows that the models based on multivariate reconstruction give better predictions than those obtained by univariate reconstruction. Moreover, it reveals that multivariate reconstruction can greatly mitigate the drawbacks caused by insufficiency of data.

Automatic Identification of Fundamental Frequency for Tied Arch Bridge Suspender Tension Monitoring

For the reliable assessment of bridge health and safety conditions, it is crucial to identify fundamental frequencies of suspender real time and automatically from random vibration signal that is weak and interfered with noise when suspender tension is measured online by frequency method. According to the characteristics of vibration signal spectrum, auto-power spectrum combined with autocorrelation function method which result was periodic distribution of spectral information in frequency domain. Plus from the spectrum the resonant peak of suspender was highlighted to reduce the noise disturbance which helped identify fundamental frequency and improved identification effect and result precision. In addition a field experiment in a tied arch bridge was carried out to analyze the collected vibration data. The practical application shows that this kind of measurement method is feasible and useful.

Methods for the Quasi-Periodic Variability Analysis in Blazars

In this work, four methods are introduced to analyse the unevenly sampled data. The four methods are power spectral density, auto-correlation function, structure function and Jurkevich method. Some interesting mathematical links are derived amongst the four methods. These links show that the four methods have the same performance. For the Jurkevich method, the effect of the width of bins is apparent. If the width is half the time scale, the method has better performance.

Gait symmetry and regularity in transfemoral amputees assessed by trunk accelerations

BackgroundThe aim of this study was to evaluate a method based on a single accelerometer for the assessment of gait symmetry and regularity in subjects wearing lower limb prostheses.MethodsTen transfemoral amputees and ten healthy control subjects were studied. For the purpose of this study, subjects wore a triaxial accelerometer on their thorax, and foot insoles. Subjects were asked to walk straight ahead for 70 m at their natural speed, and at a lower and faster speed. Indices of step and stride regularity (Ad1 and Ad2, respectively) were obtained by the autocorrelation coefficients computed from the three acceleration components. Step and stride durations were calculated from the plantar pressure data and were used to compute two reference indices (SI1 and SI2) for step and stride regularity.ResultsRegression analysis showed that both Ad1 well correlates with SI1 (R2 up to 0.74), and Ad2 well correlates with SI2 (R2 up to 0.52). A ROC analysis showed that Ad1 and Ad2 has generally a good sensitivity and specificity in classifying amputee's walking trial, as having a normal or a pathologic step or stride regularity as defined by means of the reference indices SI1 and SI2. In particular, the antero-posterior component of Ad1 and the vertical component of Ad2 had a sensitivity of 90.6% and 87.2%, and a specificity of 92.3% and 81.8%, respectively.ConclusionsThe use of a simple accelerometer, whose components can be analyzed by the autocorrelation function method, is adequate for the assessment of gait symmetry and regularity in transfemoral amputees.

Frequency-Dependent Diffusion Constant of Quantum Fluids from Path Integral Monte Carlo and Tikhonov's Regularizing Functional.

We present a novel implementation of the analytic continuation of the velocity autocorrelation function method that has been developed to study the transport properties of quantum liquids at finite temperatures. To invert the ill-posed linear Fredholm integral equation of the first kind, we combine Tikhonov's first-order regularizing functional with several methods used for automatic selection of the regularization parameter. Taking into account our results, we recommend two methods for automatic selection of the regularization parameter, namely: L-curve and quasi-optimality criterion. We found that the frequency-dependent diffusion power spectrum of normal liquid (4)He at T = 4 K and ρ = 0.01873 Å(-3) (ρ = 31.1 mmol cm(-3)) is characterized by a single asymmetric peak. The predicted self-diffusion coefficient of (4)He at this state point of 0.57-0.58 Å(2)/ps is in excellent agreement with previous works. We demonstrate that, within proposed mathematical treatment of the quantum transport at finite temperatures, the entire real-time frequency-dependent diffusion power spectrum of liquid normal (4)He, can be successfully reconstructed from the limited number of Trotter slices and without the knowledge of covariance matrix. Moreover, the small values of regularization parameters (i.e., order of 10(-7)) indicate that the information about quantum dynamics of normal liquid (4)He can be easily withdrawn from the high quality imaginary-time correlation function collected in the standard path integral Monte Carlo simulation.

Evaluating Chemical Dispersant Efficacy in an Experimental Wave Tank: 1, Dispersant Effectiveness as a Function of Energy Dissipation Rate

Numerous laboratory test systems have been developed for the comparison of efficacy between various chemical oil dispersant formulations. However, for the assessment of chemical dispersant effectiveness under realistic sea state, test protocols are required to produce hydrodynamic conditions close to the mixing, transport, and dilution effects found in the natural environment. To this end, we have designed and constructed an experimental wave tank system capable of generating waves of different energy levels, ranging from regular nonbreaking waves to plunging breakers. The hydrodynamics of these wave conditions were characterized using an autocorrelation function method applied to in situ velocity measurements. We report here an investigation of the effectiveness of two chemical dispersants (Corexit 9500 and SPC 1000) on two crude oils (weathered MESA and fresh ANS) under three different wave conditions in the wave tank operated in batch mode. Corexit 9500 dispersed approximately 75% of the weathered MESA and more than 90% of the fresh ANS crude, and SPC 1000 dispersed about 53 and 64%, respectively. Under control conditions (absence of chemical dispersant), only 10 to 20% of the crude oils were dispersed. Quantitative relationships were established between dispersant effectiveness and energy dissipation rate under the different simulated wave conditions. These relationships are essential for the development of accurate predictive models on dispersant effectiveness and operational guidelines for dispersant use.

The Volatility of the Index of Shanghai Stock Market Research Based on ARCH and Its Extended Forms

The proposed ARCH and its extension model have brought a powerful tool for the study of stock market volatility as well as verify that a “high risk brings high-yield” and the “leverage effect” of stock market. This paper gives modeling analysis by using the ARCH group models; in the last ten years Shanghai's index returns, concluded that there are significant “high-yield associated with high-risk” phenomenon and the “leverage effect” in the domestic securities market. The previous studies in fitting return series of ARMA models, mostly with low accuracy have a very subjective “observation autocorrelation and partial autocorrelation function method,” and even directly use “random walk” model. That will inevitably have some impact on the accuracy of the model. While this paper adopts the Pandit-Wu formulaic modeling method, the ARMA model is built on a strong theoretical foundation.

Measuring nonlinear dependence in hydrologic time series

It has been a common practice to employ the correlation dimension method to investigate the presence of nonlinearity and chaos in hydrologic processes. Although the method is generally reliable, potential limitations that exist in its applications to hydrologic data cannot be dismissed altogether. As for these limitations, two issues have dominated the discussions thus far: small data size and presence of noise. Another issue that is equally important, but less discussed in the literature, is the selection of delay time (τd) for reconstruction of the phase-space, which is an essential first step in the correlation dimension method, or any other chaos identification and prediction method for that matter. It has also been increasingly recognized that fixing the delay time window (τw) rather than just the delay time itself could be more appropriate, since the delay time window is the one that is of actual interest at the end to represent the dynamics. To this effect, Kim et al. (1998a) [Phys Rev E 58(5):5676–5682] developed a procedure for fixing the delay time window and demonstrated its effectiveness on three artificial chaotic series, and followed it up with the development of the C–C method to estimate both the delay time and the delay time window. The purpose of the present study is to test this procedure on real hydrologic time series and, hence, to assess their nonlinear deterministic characteristics. Three hydrologic time series are studied: (1) daily streamflow series from St. Johns near Cocoa, FL, USA; (2) biweekly volume time series from the Great Salt Lake, UT, USA; and (3) daily rainfall series from Seoul, South Korea. The results are also compared with those obtained using the conventional autocorrelation function (ACF) method.

Transiting exoplanets from the CoRoT space mission

CoRoT, the first space-based transit search, provides ultra-high precision light curves with continuous time-sampling over periods, of up to 5 months. This allows the detection of transiting planets with relatively long periods, and the simultaneous study of the host star's photometric variability. In this letter, we report on the discovery of the transiting giant planet CoRoT-Exo-4b and use the CoRoT light curve to perform a detailed analysis of the transit and to determine the stellar rotation period. The CoRoT light curve was pre-processed to remove outliers and correct for orbital residuals and artefacts due to hot pixels on the detector. After removing stellar variability around each transit, the transit light curve was analysed to determine the transit parameters. A discrete auto-correlation function method was used to derive the rotation period of the star from the out-of-transit light curve. We derive periods for the planet's orbit and star's rotation of 9.20205 +/- 0.00037 and 8.87 +/- 1.12 days respectively, consistent with a synchronised system. We also derive the inclination, i = 90.00 -0.085 +0.000 in degrees, the ratio of the orbital distance to the stellar radius, a/R_s = 17.36 -0.25 +0.05, and the planet to star radius ratio R_p/R_s = 0.1047 -0.0022 +0.0041. We discuss briefly the coincidence between the orbital period of the planet and the stellar rotation period and its possible implications for the system's migration and star-planet interaction history.

이중 주파수와 코드를 이용한 초음파 위치 인식 시스템 구현

This paper presents real-time algorithm for an ultrasonic Local Positioning System(LPS). An ultrasonic LPS consists of 4 transmitters and n receivers. Each transmitter transmits an sequential ultrasonic signal to avoid interference of ultrasonic signal. This method is a noneffective application for a fast object. Because receiver detects four sequential transmissive ultrasonic signal and calculates a position. This paper proposes the method which 4 transmitters transmit simultaneous ultrasonic signal and each transmitter distinguished by frequencies and codes. And Auto-Correlation Function(ACF) method separates codes from an ultrasonic echo signal which is interference of each transmitter`s code. If the receiver uses only ACF method, it is difficult to implement real time application for increased computation. This paper implements LPS using dual frequencies and ACF method. Using dual frequencies reduces codes length. The reduced codes length save computation in ACF. To prove this algorithm by experiment, high performance DSP(digital signal processor) used. The result shows the performance of the designed system is good enough positioning.

Comparative analysis on some filters for wrapped phase maps

Some effective filtering methods for wrapped phase maps, a regularized phase-tracking method (RPT) without the regularization term, a multiple-parameter least-square method (MPLS), a windowed Fourier ridges method (WFR), an autocorrelation function method (ACF), and a sine/cosine average filter (SCAF), are analyzed in order to establish their transversal relationship. The analysis shows that principles of the RPT, MPLS, WFR, and ACF are equivalent and the SCAF also leads to the WFR by some extension, which elegantly unifies all these methods for filtering unwrapped phase maps.

Spatial autocorrelation and mean intercept length analysis of trabecular bone anisotropy applied to in vivo magnetic resonance imaging

Osteoporosis is characterized by bone loss and deterioration of the trabecular bone (TB) architecture that leads to impaired overall mechanical strength of the bone. Bone mineral density (BMD) measured by dual-energy x-ray absorptiometry is currently the standard clinical metric assessing bone integrity but it fails to capture the structural changes in the TB. Recent research suggests that structure contributes to bone strength in a manner complementary to BMD. Besides parameters of scale such as the mean TB thickness and mean bone volume fraction, parameters describing the anisotropy of the trabecular architecture play an important role in the characterization of TB since trabeculae are preferentially oriented along the direction of local loading. Therefore, the degree of structural anisotropy is of pivotal importance to the bone's mechanical competence. The most common method for measuring structural anisotropy of TB is the mean-intercept length (MIL). In this work we present a method, based on the three-dimensional spatial autocorrelation function (ACF), for mapping of the full structural anisotropy ellipsoid of both TB thickness and spacing and we examine its performance as compared to that of MIL. Not only is the ACF method faster by several orders of magnitude, it is also considerably more robust to noise. Further, it is applicable at lower spatial resolution and is relatively insensitive to image shading. The chief reason for ACF's superior performance is that it does not require binarization, which is difficult to achieve in the limited spatial regime of in vivo magnetic resonance imaging. MIL and ACF have been applied to high-resolution magnetic resonances images of the tibia in a group of ten healthy postmenopausal women by comparing the structural anisotropy and principal direction of the computed fabric tensor for each method. While there is fair agreement between the two methods, ACF analysis yielded greater anisotropy than MIL for both TB thickness and spacing. There was good agreement between the two techniques as far as the eigenvectors of the fabric ellipsoids were concerned, which parallel the bone's macroscopic axis.

Estimating the Number of Independent Samples in Reverberation Chamber Measurements From Sample Differences

Reverberation chamber measurements suffer from statistical fluctuations in the average power of a measured sequence. The standard deviation of these fluctuations depends on the number of independent samples N/sub ind/ in the sequence. A common method for estimating N/sub ind/ is based on calculating the autocorrelation function of the sequence. A method is presented here that is simpler, yet comparable in accuracy and precision. In the presented method, N/sub ind/ is calculated from the sequence of differences between neighboring measurement samples. Simulated sequences are used to compare different variants of the presented method and the autocorrelation function method. Examples with measured data are also presented.

A molecular-dynamics study of lipid bilayers: Effects of the hydrocarbon chain length on permeability

In this paper, we investigate the effects of the hydrocarbon chain length of lipid molecules on the permeation process of small molecules through lipid bilayers. We perform molecular-dynamics simulations using three kinds of lipid molecules with different chain length: dilauroylphosphatidylcholine, dimyristoylphosphatidylcholine, and dipalmiltoylphosphatidylcholine. Free-energy profiles of O2, CO, NO, and water molecules are calculated by means of the cavity insertion Widom method and the probability ratio method. We show that the lipid membrane with longer chains has a larger and wider energy barrier. The local diffusion coefficients of water across the bilayers are also calculated by the force autocorrelation function method and the velocity autocorrelation function method. The local diffusion coefficients in the bilayers are not altered significantly by the chain length. We estimate the permeability coefficients of water across the three membranes according to the solubility-diffusion model; we find that the water permeability decreases modestly with increasing chain length of the lipid molecules.

Investigation of benzene-hexafluorobenzene dynamics in liquid binary mixtures

The structure and microscopic dynamics of liquid mixtures of benzene and hexafluorobenzene at room temperature and several compositions have been studied by molecular-dynamics simulations. In this implementation we have rescaled the intermolecular H-F cross potential parameters obtained from the Lorentz-Berthelot combining rules, in order to avoid the substantial overestimation of the energy of mixing predicted by the model when the usual rules are employed. We found that a reduction in the strength of cross H-F interactions by 50% relative to the geometric mean is required in order to get a good agreement with experiments. Radial-angular pair-correlation functions between like and unlike species have been computed and analyzed, by comparing them with the correlations in the corresponding neat liquids. We have also studied the microscopic intermolecular momentum transfer, by computing the time correlation function between the initial velocity of a central molecule and later velocities of neighboring molecules. Structural and dynamical information extracted from the mentioned functions seem to be consistent with the picture of relatively long-lived benzene-hexafluorobenzene (Bz-Hf) complexes present in the mixtures, which would be responsible for the considerable perturbation of the structure in the first shell of like species, and would be moving within the liquid in a parallel face-to-face configuration. Using the tools developed originally to estimate hydrogen-bond lifetimes in liquids, we have computed the lifetimes of the Bz-Hf complexes as a function of the mixture composition, by two different methods: the direct time-averaging scheme and from the autocorrelation function of bond occupation numbers. The obtained lifetimes are strongly dependent on the scheme chosen to compute the characteristic times. We have obtained for the Bz-Hf dimer in solution, at room temperature, lifetimes in the range of 30-40 ps from averaging schemes and around 60-120 ps from autocorrelation function methods. In the latter case, the longest times correspond to the equimolar mixture.

Possible mechanisms of dielectric relaxation of liquid water and calculation of the temperature dependence of the complex permittivity of water

The spectra of the complex dielectric permittivity and absorption of water (H2O) in the frequency range 0–1000 cm−1 are calculated for a wide temperature interval. Using the method of autocorrelation functions, the dielectric response of dipoles rotating in potential wells of three types is found. The majority of dipoles (about 90%) rotate in a deep and comparatively narrow potential well, whose profile resembles an upside-down hat. Such a potential models a molecular structure with strongly bent and/or broken hydrogen bonds. The hat model describes the complex permittivity in the low-frequency (Debye) range and in the range 300–1000 cm−1. The remaining dipoles (∼10%) execute harmonic vibrations of two types: rotational vibrations about the equilibrium direction of a hydrogen bond and translational vibrations along this direction. These types of motion yield the dielectric response in the frequency range 10–300 cm−1. This response is described by the Lorentz lines in terms of the harmonic oscillator model and the truncated parabola model. The hat–harmonic oscillator–truncated parabola composite model provides good agreement with experimental spectra. The lifetimes of the three types of motion considered are about 10, 0.2, and 0.05 ps, respectively. They characterize (i) tetrahedral translations of molecules accompanied by their rotations, (ii) librations of dipoles in the hatlike potential well, and (iii) elastic interactions of hydrogen-bonded molecules. Based on data of independent methods of investigation, it is concluded that the temperature 300 K is a singular point with respect to the properties of liquid water.

Analytical calculation of far infrared spectra of ice in terms of a molecular model

Wideband far infrared (FIR) spectra of complex permittivity ε( ν) of ice are calculated in terms of a simple analytical theory based on the method of dipolar autocorrelation functions. The molecular model represents a revision of the model recently presented for liquid water in Adv. Chem. Phys. 127 (2003) 65. A composite two-fractional model is proposed. The model is characterised by three phenomenological potential wells corresponding to the three FIR bands observed in ice. The first fraction comprises dipoles reorienting in a rather narrow and deep hat-like well; these dipoles generate the librational band centred at the frequency ≈880 cm −1. The second fraction comprises elastically interacting particles; they generate two nearby bands placed around frequency 200 cm −1. For description of one of these bands the harmonic oscillator (HO) model is used, in which translational oscillations of two charged molecules along the H-bond are considered. The other band is produced by the H-bond stretch, which governs hindered rotation of a rigid dipole. Such a motion and its dielectric response are described in terms of a new cut parabolic (CP) model applicable for any vibration amplitude. The composite hat-HO–CP model results in a smooth ε( ν) ice spectrum, which does not resemble the noise-like spectra of ice met in the known literature. The proposed theory satisfactorily agrees with the experimental ice spectrum measured at −7 °C. The calculated longitudinal optic-transverse optic (LO–TO) splitting occurring at ≈250 cm −1 qualitatively agrees with the measured data.

Global and multi-scale image analysis using power spectra

Image analysis is currently used to study the structure of materials. In this paper, classical techniques of signal analysis such as power spectrum and autocorrelation functions are applied for this purpose. These techniques allow the detection of hidden features in complex images such as fracture surfaces, before highlighting them using spatial filtering. For that, the power spectrum allows us to locate the range of scales of peculiar texture, present but invisible to the naked eye. Thus, this study deals with the homogeneity of epoxy networks. Another way to use the method concerns aggregation phenomena. Indeed, the method allows us to assimilate several images of different magnifications, in order to characterize the aggregation on a large range of scales from the size of the particle or fibre to the full size of the sample. Then, the peculiar morphology of thermoplastic composites made from commingled fibres can be studied. The autocorrelation function method is also used to highlight features in the images of such composite materials.