Статті в журналах: "Second-order autocorrelation"

1

Mashiko, H., A. Suda, and K. Midorikawa. "Second-order autocorrelation functions for all-reflective interferometric autocorrelator." Applied Physics B 87, no. 2 (February 17, 2007): 221–26. http://dx.doi.org/10.1007/s00340-006-2574-6.

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2

Ouyang Xiaoping, 欧阳小平, 张福领 Zhang Fuling, 张攀政 Zhang Panzheng, 谢兴龙 Xie Xinglong, and 朱健强 Zhu Jianqiang. "Second Order Autocorrelation Applied to Femtosecond Laser." Chinese Journal of Lasers 36, no. 3 (2009): 742–45. http://dx.doi.org/10.3788/cjl20093603.0742.

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3

Tzallas, P., D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris. "Second-order autocorrelation measurements of attosecond XUV pulse trains." Journal of Modern Optics 52, no. 2-3 (January 20, 2005): 321–38. http://dx.doi.org/10.1080/09500340412331301533.

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4

COLLIER, J., C. HERNANDEZ-GOMEZ, R. ALLOTT, C. DANSON, and A. HALL. "A single-shot third-order autocorrelator for pulse contrast and pulse shape measurements." Laser and Particle Beams 19, no. 2 (April 2001): 231–35. http://dx.doi.org/10.1017/s0263034601192116.

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We present the design of a single-shot third-order autocorrelator that can be used to measure optical pulse lengths of ultrashort pulses within a fixed time window on a single-shot basis. It has a number of advantages over traditional second-order autocorrelation devices, namely a more direct and accurate measurement of pulse shape, the ability to differentiate temporal activity ahead and behind the pulse, and an increased dynamic range. The design is linear and is, in principle, no more difficult to construct and operate than a second-order autocorrelator.

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5

Dittrich, Dino, Roger Th A. J. Leenders, and Joris Mulder. "Network Autocorrelation Modeling: Bayesian Techniques for Estimating and Testing Multiple Network Autocorrelations." Sociological Methodology 50, no. 1 (May 29, 2020): 168–214. http://dx.doi.org/10.1177/0081175020913899.

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The network autocorrelation model has been the workhorse for estimating and testing the strength of theories of social influence in a network. In many network studies, different types of social influence are present simultaneously and can be modeled using various connectivity matrices. Often, researchers have expectations about the order of strength of these different influence mechanisms. However, currently available methods cannot be applied to test a specific order of social influence in a network. In this article, the authors first present flexible Bayesian techniques for estimating network autocorrelation models with multiple network autocorrelation parameters. Second, they develop new Bayes factors that allow researchers to test hypotheses with order constraints on the network autocorrelation parameters in a direct manner. Concomitantly, the authors give efficient algorithms for sampling from the posterior distributions and for computing the Bayes factors. Simulation results suggest that frequentist properties of Bayesian estimators on the basis of noninformative priors for the network autocorrelation parameters are overall slightly superior to those based on maximum likelihood estimation. Furthermore, when testing statistical hypotheses, the Bayes factors show consistent behavior with evidence for a true data-generating hypothesis increasing with the sample size. Finally, the authors illustrate their methods using a data set from economic growth theory.

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6

de Chatellus, H., S. Montant, E. Freysz, V. Bagnoud, and F. Salin. "Thermally poled fused silica as a second-order autocorrelation crystal." Applied Physics B 70, S1 (June 2000): S95—S98. http://dx.doi.org/10.1007/s003400000311.

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7

Ludkovski, Michael, and Guang Gong. "New Families of Ideal 2-Level Autocorrelation Ternary Sequences From Second Order DHT." Electronic Notes in Discrete Mathematics 6 (April 2001): 375–84. http://dx.doi.org/10.1016/s1571-0653(04)00189-1.

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8

Melamed, Benjamin. "The empirical TES methodology: modeling empirical time series." Journal of Applied Mathematics and Stochastic Analysis 10, no. 4 (January 1, 1997): 333–53. http://dx.doi.org/10.1155/s1048953397000403.

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TES (Transform-Expand-Sample) is a versatile class of stochastic sequences defined via an autoregressive scheme with modulo-1 reduction and additional transformations. The scope of TES encompasses a wide variety of sample path behaviors, which in turn give rise to autocorrelation functions with diverse functional forms - monotone, oscillatory, alternating, and others. TES sequences are readily generated on a computer, and their autocorrelation functions can be numerically computed from accurate analytical formulas at a modest computational cost.This paper presents the empirical TES modeling methodology which uses TES process theory to model empirical records. The novel feature of the TES methodology is that it expressly aims to simultaneously capture the empirical marginal distribution (histogram) and autocorrelation function. We draw attention to the non-parametric nature of TES modeling in that it always guarantees an exact match to the empirical marginal distribution. However, fitting the corresponding autocorrelation function calls for a heuristic search for a TES model over a large parametric space. Consequently, practical TES modeling of empirical records must currently rely on software assistance. A visual interactive software environment, called TEStool, has been designed and implemented to support TES modeling. The paper describes the empirical TES modeling methodology as implemented in TEStool and provides numerically-computable formulas for TES autocorrelations. Two examples illustrate the efficacy of the TES modeling approach. These examples serve to highlight the ability of TES models to capture first-order and second-order properties of empirical sample paths and to mimic their qualitative appearance.

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9

Floris, Claudio. "Stochastic Stability Criteria for Second-Order Oscillator Parametrically Excited by Colored Noise." Fluctuation and Noise Letters 16, no. 01 (February 2017): 1750003. http://dx.doi.org/10.1142/s0219477517500031.

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A second-order oscillator is considered having a random perturbation in its stiffness. This is given by a colored Gaussian or non-Gaussian process. In this way, the oscillator may be stochastically stable or unstable according to the intensity of the excitation. The almost sure (sample) stochastic stability and the stability in the first three response statistical moments are compared for different excitation processes: process with exponential autocorrelation, second-order Gaussian process, bounded noise process. Notable differences in the stability boundaries are found either according to the stability criteria or to the type of excitation. These comparisons are lacking in literature.

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10

Chesi, Giovanni, Alessia Allevi, and Maria Bondani. "Autocorrelation functions: a useful tool for both state and detector characterisation." Quantum Measurements and Quantum Metrology 6, no. 1 (January 1, 2019): 1–6. http://dx.doi.org/10.1515/qmetro-2019-0001.

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Abstract The calculation of autocorrelation functions represents a routinely used tool to characterise quantum states of light. In this paper, we evaluate the g(2) function for detected photons in the case of mesoscopic multi-mode twin-beam states in order to fully investigate their statistical properties starting from measurable quantities. Moreover, we show that the second-order autocorrelation function is also useful to estimate the spurious effects affecting the employed Silicon-photomultiplier detectors.

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11

Salman, Mohammad Shukri, Alaa Eleyan, and Bahaa Al-Sheikh. "Discrete-wavelet-transform recursive inverse algorithm using second-order estimation of the autocorrelation matrix." TELKOMNIKA (Telecommunication Computing Electronics and Control) 18, no. 6 (December 1, 2020): 3073. http://dx.doi.org/10.12928/telkomnika.v18i6.16191.

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12

Xu, Chris, Winfried Denk, Jeffrey Guild, and Watt W. Webb. "Determination of absolute two-photon excitation cross sections by in situ second-order autocorrelation." Optics Letters 20, no. 23 (December 1, 1995): 2372. http://dx.doi.org/10.1364/ol.20.002372.

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13

Pereira, Janser Moura, Joel Augusto Muniz, and Carlos Alberto Silva. "Nonlinear models to predict nitrogen mineralization in an Oxisol." Scientia Agricola 62, no. 4 (August 2005): 395–400. http://dx.doi.org/10.1590/s0103-90162005000400014.

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This work was carried out to evaluate the statistical properties of eight nonlinear models used to predict nitrogen mineralization in soils of the Southern Minas Gerais State, Brazil. The parameter estimations for nonlinear models with and without structure of autoregressive errors was made by the least squares method. First, a structure of second order autoregressive errors, AR(2) was considered for all nonlinear models and then the significance of the autocorrelation parameters was verified. Among the models, the Juma presented an autocorrelation of second order, and the model of Broadbent presented one of first order. In summary, these models presented significant autocorrelation parameters. To estimate the parameters of nonlinear models, the SAS procedure MODEL was used (SAS). The comparison of the models was made by measuring the fitted parameters: adjusted R-square, mean square error and mean predicted error. The Juma model with AR(2) best fitted for nitrogen mineralization without liming, followed by Cabrera, Stanford & Smith without autoregressive errors, for both with and without soil acidity correction.

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14

Mulokozi, Eneliko, and Hualiang (Harry) Teng. "Investigating the Existence of Second Order Spatial Autocorrelation in Crash Frequency across Adjacent Freeway Segments." Journal of Transportation Technologies 06, no. 05 (2016): 286–96. http://dx.doi.org/10.4236/jtts.2016.65026.

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15

Takeyasu, Kazuhiro. "Simplified Machine Diagnosis Techniques with Absolute Deterioration Factor by Utilizing the Second Order Autocorrelation Function." Business and Management Research 8, no. 1 (January 7, 2019): 1. http://dx.doi.org/10.5430/bmr.v8n1p1.

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Among many amplitude parameters, Kurtosis and Bicoherence are recognized to be the sensitive good parameters for machine diagnosis. In this paper, simplified calculation method of coefficient of autocorrelation function of 1st order lag is introduced, and new deterioration factor of correlation of four variables is introduced consecutively. New deterioration factor is an absolute index of deterioration factor. Three cases in which the rolling elements number is nine, twelve and sixteen are examined and compared. Varying N, the number of data, its characteristics are examined. When N is smaller, sensitivity is better. Therefore this parameter can be used as an index for the machine diagnosis of early failure stage especially.

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16

Panyukov, Ivan V., Vladislav Yu Shishkov, and Evgeny S. Andrianov. "Second‐Order Autocorrelation Function of Spectrally Filtered Light From an Incoherently Pumped Two‐Level System." Annalen der Physik 534, no. 2 (January 4, 2022): 2100286. http://dx.doi.org/10.1002/andp.202100286.

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17

Narimousa, Mojtaba, Mohammad Sabaeian, Seyed Mehdi Mousavi Ghahfarrokhi, and Omid Panahi. "Second-order interferometric autocorrelation for measuring group velocity dispersion and pulse broadening of femtosecond pulses." Applied Optics 57, no. 18 (June 12, 2018): 5011. http://dx.doi.org/10.1364/ao.57.005011.

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18

Soundy, Andy W. R., Bradley J. Panckhurst, Phillip Brown, Andrew Martin, Timothy C. A. Molteno, and Daniel Schumayer. "Comparison of Enhanced Noise Model Performance Based on Analysis of Civilian GPS Data." Sensors 20, no. 21 (October 24, 2020): 6050. http://dx.doi.org/10.3390/s20216050.

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We recorded the time series of location data from stationary, single-frequency (L1) GPS positioning systems at a variety of geographic locations. The empirical autocorrelation function of these data shows significant temporal correlations. The Gaussian white noise model, widely used in sensor-fusion algorithms, does not account for the observed autocorrelations and has an artificially large variance. Noise-model analysis—using Akaike’s Information Criterion—favours alternative models, such as an Ornstein–Uhlenbeck or an autoregressive process. We suggest that incorporating a suitable enhanced noise model into applications (e.g., Kalman Filters) that rely on GPS position estimates will improve performance. This provides an alternative to explicitly modelling possible sources of correlation (e.g., multipath, shadowing, or other second-order physical phenomena).

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19

Moshammer, R., Th Pfeifer, A. Rudenko, Y. H. Jiang, L. Foucar, M. Kurka, K. U. Kühnel, et al. "Second-order autocorrelation of XUV FEL pulses via time resolved two-photon single ionization of He." Optics Express 19, no. 22 (October 19, 2011): 21698. http://dx.doi.org/10.1364/oe.19.021698.

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20

HOLM, DARRYL D. "Kármán–Howarth theorem for the Lagrangian-averaged Navier–Stokes–alpha model of turbulence." Journal of Fluid Mechanics 467 (September 24, 2002): 205–14. http://dx.doi.org/10.1017/s002211200200160x.

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The Lagrangian averaged Navier–Stokes–alpha (LANS-α) model of turbulence is found to possess a Kármán–Howarth (KH) theorem for the dynamics of its second-order autocorrelation functions in homogeneous isotropic turbulence. This KH result implies that alpha-filtering in the LANS-α model of turbulence does not affect the exact Navier–Stokes relation between second and third moments at separation distances large compared to the model's length scale α. Moreover, at separations r that are smaller than α, the KH scaling between energy dissipation rate and longitudinal third-order autocorrelation changes to match the scaling found in two-dimensional incompressible flow. This is consistent with the corresponding change in scaling of the kinetic energy spectrum from k−5/3 for larger scales with kα < 1, which switches to k−3 for smaller scales with kα > 1, as discovered in Foias, Holm & Titi (2001).

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21

Thijssen, J. M., B. J. Oosterveld, and R. L. Romijn. "Phase-Derivative Imaging III: Theoretical Derivation of First and Second Order Statistics." Ultrasonic Imaging 12, no. 1 (January 1990): 17–34. http://dx.doi.org/10.1177/016173469001200102.

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The echo signal obtained from a homogenous and isotropically scattering medium can be described as a Poisson time series which is convolved with the transmission pulse of the transducer. The probability density function (pdf) of this signal approximates to a Gaussian pdf for a narrowband pulse waveform. Methods to derive the phase-derivative (PD) signal from the complex envelope and the preenvelope of the echo signal are described. The first order pdf of the PD asymptotically becomes a Gaussian pdf by smoothing. Since the rectified PD is employed to obtain 2-dimensional grey scale images, the first order pdf as well as the signal-to-noise ratio (SNR) of this signal are also derived. The rectified PD is further smoothed by a cosine time window prior to the imaging. The SNR and the autocorrelation function (in the axial direction) of this latter signal can be derived under the assumption of a Gaussian spectrum of the transmission pulse. These first and second order characteristics of the PD images are calculated for the conditions employed in simulations and experiments reported previously and are quantitatively compared to the values obtained from these.

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22

Wibun, Anuchit, and Pipat Chaiwiwatworakul. "An Estimation of Thailand's Hourly Solar Radiation Using Markov Transition Matrix Method." Applied Mechanics and Materials 839 (June 2016): 29–33. http://dx.doi.org/10.4028/www.scientific.net/amm.839.29.

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To estimate global solar radiation from easy available weather forecast data (sky condition), Markov model is used for this estimation. The five-year (1996-2000) global radiation data that are taken at an hour intervals from Nakhon Pathom station, Thailand (latitude 13.81ºN and longitude 100.04ºE) are used to construct the Markov transition matrices. The global radiation sequences in 2000 will be generated by based on the characteristic probability of moving global radiation values which were observed from the obtained data during 1996-1999. The autocorrelation function is used for checking the order of probability of moving obtained data. In this study, the five first and five second-order Markov transition matrices (MTMs), which are selected from the autocorrelation functions, are constructed, each MTMs will be used for generating global radiation values in each day with different sky conditions (clear, partly cloudy, mostly cloudy, cloudy and overcast). From the results of comparison between the statistical characteristics of observed and two synthetic generated data, global radiation data behavior slightly improved by the second order Markov model.

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23

SÖKÜT AÇAR, Tuğba. "Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation." Journal of New Theory, no. 41 (December 31, 2022): 1–17. http://dx.doi.org/10.53570/jnt.1139885.

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The sensitivity of the least-squares estimation in a regression model is impacted by multicollinearity and autocorrelation problems. To deal with the multicollinearity, Ridge, Liu, and Ridge-type biased estimators have been presented in the statistical literature. The recently proposed Kibria-Lukman estimator is one of the Ridge-type estimators. The literature has compared the Kibria-Lukman estimator with the others using the mean square error criterion for the linear regression model. It was achieved in a study conducted on the Kibria-Lukman estimator's performance under the first-order autoregressive erroneous autocorrelation. When there is an autocorrelation problem with the second-order, evaluating the performance of the Kibria-Lukman estimator according to the mean square error criterion makes this paper original. The scalar mean square error of the Kibria-Lukman estimator under the second-order autoregressive error structure was evaluated using a Monte Carlo simulation and two real examples, and compared with the Generalized Least-squares, Ridge, and Liu estimators. The findings revealed that when the variance of the model was small, the mean square error of the Kibria-Lukman estimator gave very close values with the popular biased estimators. As the model variance grew, Kibria-Lukman did not give fairly similar values with popular biased estimators as in the model with small variance. However, according to the mean square error criterion the Kibria-Lukman estimator outperformed the Generalized Least-Squares estimator in all possible cases.

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24

He, Ruying, Wennian Yu, Zaigang Chen, Yimin Shao, and Yilin Yuan. "Study on the chatter vibration of a steel plate mill based on second order cyclic autocorrelation demodulation." International Journal of Design Engineering 4, no. 4 (2011): 351. http://dx.doi.org/10.1504/ijde.2011.048132.

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25

Li, Xin Bo, Nan Nan Liu, Nan Jiang, Xiao Bo Long, and Xiao Yang Jiao. "Second-Order Statistics-Based Multi-Parameter Estimation of Near-Field Acoustic Sources." Applied Mechanics and Materials 461 (November 2013): 977–83. http://dx.doi.org/10.4028/www.scientific.net/amm.461.977.

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In this paper, a new approach based on the second-order statistics (SOS) and acoustic vector sensor (AVS) array is proposed, for localization estimation of near-field acoustic narrowband sources. Firstly, we choose the centrosymmetric uniform linear-array as the AVS arrangement, and the array is consistent with the coordinate axis direction of the acoustic vector-sensor. This estimation method makes good use of the acquisition information from the AVS, such as one-dimensional sound pressure and three-dimensional particle velocity, and has shown preferable performance for the parameter estimation of direction-of-arrival (DOA) and range of target acoustic sources in the near field. The estimation algorithm expands the near-ﬁeld array manifold of one single acoustic vector sensor to the acoustic vector-sensor’s uniform linear-array, and the near-ﬁeld acoustic vector sensor linear array output model is deduced. The autocorrelation and cross-correlation function of the velocity field and the pressure field are used to construct the rotational invariance frame, which helps to extract the expected information. Consequently, the closed-form solutions of the incident source’s DOA and range are derived explicitly through the parameter pairing operation. The proposed method reduces the computational burden and has good spatial recognition ability and high resolution in the case of limited array elements. It also has better engineering application prospect. Eventually, the performance of the method is verified by Monte Carlo simulation experiments.

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26

Shi, Huaitao, and Yajun Shang. "Initial Fault Diagnosis of Rolling Bearing Based on Second-Order Cyclic Autocorrelation and DCAE Combined With Transfer Learning." IEEE Transactions on Instrumentation and Measurement 71 (2022): 1–18. http://dx.doi.org/10.1109/tim.2021.3132065.

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27

Indrawati, Luvera Deva Intan, Rina Dwi Indriana, and Irham Nurwidyanto. "Comparative Results of Regional and Residual Anomalies with the Upward Continuation, Moving Average, and Polynomial Methods for Magnetic Data." Journal of Physics and Its Applications 2, no. 2 (May 15, 2020): 90–93. http://dx.doi.org/10.14710/jpa.v2i2.7673.

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Geophysics programing of regional and residual anomaly separation on Magnetic data has been carried out with the results compared with the upward continuation method in the OasisMontaj software. Separation of anomalies with moving average and polynomial methods is processed using Matlab programming. The orders used in the polynomial method are first-order, second-order and third-order. Comparison is done by calculating the match value. The chosen matching method is autocorrelation. Correlation of residual magnetic anomalies resulting from upward continuation (Magpick) to moving averages, 1st-order polynomials, 2nd-order polynomials and 3rd-order polynomials. Correlation values obtained for the moving average method are 0.9604, first order polynomial 0.9072, 2nd order polynomial 0.9482 and third order polynomial 0.6057. The moving average and second order polynomial methods can be used as a substitute method if we do not use the upward continuation method.

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28

He, Changli, and Timo Terasvirta. "Properties of the Autocorrelation Function of Squared Observations for Second-order Garch Processes Under Two Sets of Parameter Constraints." Journal of Time Series Analysis 20, no. 1 (January 1999): 23–30. http://dx.doi.org/10.1111/1467-9892.00123.

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29

Sun, Yixiao, Peter C. B. Phillips, and Sainan Jin. "POWER MAXIMIZATION AND SIZE CONTROL IN HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS WITH EXPONENTIATED KERNELS." Econometric Theory 27, no. 6 (May 17, 2011): 1320–68. http://dx.doi.org/10.1017/s0266466611000077.

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Using the power kernels of Phillips, Sun, and Jin (2006, 2007), we examine the large sample asymptotic properties of the t-test for different choices of power parameter (ρ). We show that the nonstandard fixed-ρ limit distributions of the t-statistic provide more accurate approximations to the finite sample distributions than the conventional large-ρ limit distribution. We prove that the second-order corrected critical value based on an asymptotic expansion of the nonstandard limit distribution is also second-order correct under the large-ρ asymptotics. As a further contribution, we propose a new practical procedure for selecting the test-optimal power parameter that addresses the central concern of hypothesis testing: The selected power parameter is test-optimal in the sense that it minimizes the type II error while controlling for the type I error. A plug-in procedure for implementing the test-optimal power parameter is suggested. Simulations indicate that the new test is as accurate in size as the nonstandard test of Kiefer and Vogelsang (2002a, 2002b), and yet it does not incur the power loss that often hurts the performance of the latter test. The results complement recent work by Sun, Phillips, and Jin (2008) on conventional and bT HAC testing.

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30

Dow, Ximeng Y., Christopher M. Dettmar, Emma L. DeWalt, Justin A. Newman, Alexander R. Dow, Shatabdi Roy-Chowdhury, Jesse D. Coe, Christopher Kupitz, Petra Fromme, and Garth J. Simpson. "Second harmonic generation correlation spectroscopy for characterizing translationally diffusing protein nanocrystals." Acta Crystallographica Section D Structural Biology 72, no. 7 (June 23, 2016): 849–59. http://dx.doi.org/10.1107/s205979831600841x.

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Second harmonic generation correlation spectroscopy (SHG-CS) is demonstrated as a new approach to protein nanocrystal characterization. A novel line-scanning approach was performed to enable autocorrelation analysis without sample damage from the intense incident beam. An analytical model for autocorrelation was developed, which includes a correction for the optical scattering forces arising when focusing intense, infrared beams. SHG-CS was applied to the analysis of BaTiO3nanoparticles ranging from 200 to ∼500 nm and of photosystem I nanocrystals. A size distribution was recovered for each sample and compared with the size histogram measured by scanning electron microscopy (SEM). Good agreement was observed between the two independent measurements. The intrinsic selectivity of the second-order nonlinear optical process provides SHG-CS with the ability to distinguish well ordered nanocrystals from conglomerates and amorphous aggregates. Combining the recovered distribution of particle diameters with the histogram of measured SHG intensities provides the inherent hyperpolarizability per unit volume of the SHG-active nanoparticles. Simulations suggest that the SHG activity per unit volume is likely to exhibit relatively low sensitivity to the subtle distortions within the lattice that contribute to resolution loss in X-ray diffraction, but high sensitivity to the presence of multi-domain crystals.

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31

Akyuz, Dilek Eren, Mehmetcik Bayazit, and Bihrat Onoz. "Markov Chain Models for Hydrological Drought Characteristics." Journal of Hydrometeorology 13, no. 1 (February 1, 2012): 298–309. http://dx.doi.org/10.1175/jhm-d-11-019.1.

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Abstract Estimation of drought characteristics such as probabilities and return periods of droughts of various lengths is of major importance in drought forecast and management and in solving water resources problems related to water quality and navigation. This study aims at applying first- and second-order Markov chain models to dry and wet periods of annual streamflow series to reproduce the stochastic structure of hydrological droughts. Statistical evaluation of drought duration and intensity is usually carried out using runs analysis. First-order Markov chain model (MC1) for dry and wet periods is not adequate when autocorrelation of the original hydrological series is high. A second-order Markov chain model (MC2) is proposed to estimate the probabilities and return periods of droughts. Results of these models are compared with those of a simulation study assuming a lag-1 autoregressive [AR(1)] process widely used to model annual streamflows. Probability distribution and return periods of droughts of various lengths are estimated and compared with the results of MC1 and MC2 models using efficacy evaluation statistics. It is found that the MC2 model in general gives results that are in better agreement with simulation results as compared with the MC1 model. Skewness is found to have little effect on return periods except when autocorrelation is very high. MC1 and MC2 models are applied to droughts observed in some annual streamflow series, with the result that the MC2 model has a relatively good agreement considering the limited duration of the records.

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32

Ameer-Beg, S., A. J. Langley, I. N. Ross, W. Shaikh, and P. F. Taday. "An achromatic lens for focusing femtosecond pulses: direct measurement of femtosecond pulse front distortion using a second-order autocorrelation technique." Optics Communications 122, no. 4-6 (January 1996): 99–104. http://dx.doi.org/10.1016/0030-4018(95)00483-1.

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33

Phojanamongkolkij, Nipa, Seiji Kato, Bruce A. Wielicki, Patrick C. Taylor, and Martin G. Mlynczak. "A Comparison of Climate Signal Trend Detection Uncertainty Analysis Methods." Journal of Climate 27, no. 9 (April 23, 2014): 3363–76. http://dx.doi.org/10.1175/jcli-d-13-00400.1.

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Abstract Two climate signal trend analysis methods are the focus of this paper. The uncertainty of trend estimate from these two methods is investigated using Monte Carlo simulation. Several theoretically and randomly generated series of white noise, first-order autoregressive and second-order autoregressive, are explored. The choice of method that is most appropriate for the time series of interest depends upon the autocorrelation structure of the series. If the structure has its autocorrelation coefficients decreased with increasing lags (i.e., an exponential decay pattern), then the method of Weatherhead et al. is adequate. If the structure exhibits a decreasing sinusoid pattern of coefficient with lags (or a damped sinusoid pattern) or a mixture of both exponential decay and damped sinusoid patterns, then the method of Leroy et al. is recommended. The two methods are then applied to the time series of monthly and globally averaged top-of-the-atmosphere (TOA) irradiances for the reflected solar shortwave and emitted longwave regions, using radiance observations made by Clouds and the Earth’s Radiant Energy System (CERES) instruments during March 2000 through June 2011. Examination of the autocorrelation structures indicates that the reflected shortwave region has an exponential decay pattern, while the longwave region has a mixture of exponential decay and damped sinusoid patterns. Therefore, it is recommended that the method of Weatherhead et al. is used for the series of reflected shortwave irradiances and that the method of Leroy et al. is used for the series of emitted longwave irradiances.

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Núñez-González, Solange, Estefania Bedoya, Daniel Simancas-Racines, and Christopher Gault. "Spatial clusters and temporal trends of malignant melanoma mortality in Ecuador." SAGE Open Medicine 8 (January 2020): 205031212091828. http://dx.doi.org/10.1177/2050312120918285.

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Objective: The aim of this study is two fold. First, it describes the temporal trends of malignant melanoma mortality from 2000 to 2016 in Ecuador. Second, it analyzes the spatial clusters of high mortality rates due to malignant melanoma in the country, from 2011 to 2016. Methods: This is an ecological study; we included all death certificates of malignant melanoma from the National Institute of Statistics and Census database in Ecuador from 2000 to 2016. We calculated crude mortality rates and age-standardized mortality rates, all rates are expressed as deaths per 100,000 population. In order to assess the trend of malignant melanoma rates, we obtained average annual percent changes through Joinpoint regression analysis. Spatial scan statistics were used to identify high-risk clusters and the spatial autocorrelation was evaluated through a global Moran index. Results: In Ecuador, between 2000 and 2016, malignant melanoma caused a total of 958 deaths. Crude mortality rates increased significantly (annual percent change = 4.8%; 95% confidence interval: 2.6–7.0), the age-standardized mortality rate also increased (annual percent change: 2.9%; 95% confidence interval: 0.5–5.4). The most likely cluster included 19 cantons and the second most likely cluster included 10 cantons, located in the Highlands region. The Global Moran I index for the study period shows a positive spatial autocorrelation (0.32; p = 0.001). Conclusion: Mortality due to malignant melanoma in Ecuador significantly increased over the 17-year study period; the spatial analysis and spatial autocorrelation indicates the presence of high-risk occurrence clusters in the Highlands region of the country.

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35

Kuc, Roman, and Hilda Li. "Reduced-Order Autoregressive Modeling for Center-Frequency Estimation." Ultrasonic Imaging 7, no. 3 (July 1985): 244–51. http://dx.doi.org/10.1177/016173468500700304.

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The center frequency of a narrowband, discrete-time random process, such as a reflected ultrasound signal, is estimated from the parameter values of a reduced, second-order autoregressive (AR) model. This approach is proposed as a fast estimator that performs better than the zero-crossing count estimate for determining the center-frequency location. The parameter values are obtained through a linear prediction analysis on the correlated random process, which in this case is identical to the maximum entropy method for spectral estimation. The frequency of the maximum of the second-order model spectrum is determined from these parameters and is used as the center-frequency estimate. This estimate can be computed very efficiently, requiring only the estimates of the first three terms of the process autocorrelation function. The bias and variance properties of this estimator are determined for a random process having a Gaussian-shaped spectrum and compared to those of the ideal FM frequency discriminator, zero-crossing count estimator and a correlation estimator. It is found that the variance values for the reduced-order AR model center-frequency estimator lie between those for the ideal FM frequency discriminator and the zero-crossing count estimator.

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36

Collaud Coen, Martine, Elisabeth Andrews, Alessandro Bigi, Giovanni Martucci, Gonzague Romanens, Frédéric P. A. Vogt, and Laurent Vuilleumier. "Effects of the prewhitening method, the time granularity, and the time segmentation on the Mann–Kendall trend detection and the associated Sen's slope." Atmospheric Measurement Techniques 13, no. 12 (December 21, 2020): 6945–64. http://dx.doi.org/10.5194/amt-13-6945-2020.

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Abstract. The Mann–Kendall test associated with the Sen's slope is a very widely used non-parametric method for trend analysis. It requires serially uncorrelated time series, yet most of the atmospheric processes exhibit positive autocorrelation. Several prewhitening methods have therefore been designed to overcome the presence of lag-1 autocorrelation. These include a prewhitening, a detrending and/or a correction of the detrended slope and the original variance of the time series. The choice of which prewhitening method and temporal segmentation to apply has consequences for the statistical significance, the value of the slope and of the confidence limits. Here, the effects of various prewhitening methods are analyzed for seven time series comprising in situ aerosol measurements (scattering coefficient, absorption coefficient, number concentration and aerosol optical depth), Raman lidar water vapor mixing ratio, as well as tropopause and zero-degree temperature levels measured by radio-sounding. These time series are characterized by a broad variety of distributions, ranges and lag-1 autocorrelation values and vary in length between 10 and 60 years. A common way to work around the autocorrelation problem is to decrease it by averaging the data over longer time intervals than in the original time series. Thus, the second focus of this study evaluates the effect of time granularity on long-term trend analysis. Finally, a new algorithm involving three prewhitening methods is proposed in order to maximize the power of the test, to minimize the number of erroneous detected trends in the absence of a real trend and to ensure the best slope estimate for the considered length of the time series.

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37

Cunningham, Frederick L., Guiming Wang, and D. Tommy King. "Seasonal Habitat Selection by American White Pelicans." Diversity 14, no. 10 (September 30, 2022): 821. http://dx.doi.org/10.3390/d14100821.

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Resource utilization strategies of avian migrants are a major concern for conservation and management. Understanding seasonal habitat selection by migratory birds helps us explain the ongoing continental declines of migratory bird populations. Our objective was to compare the second-order and third-order habitat selection by the American White Pelican (Pelecanus erythrorhynchos; hereafter pelican) between the breeding and non-breeding grounds. We tested the Lack hypothesis that habitat selection by migratory birds is stronger on the breeding grounds than on the non-breeding grounds. We used random-effect Dirichlet-multinomial models to estimate the second-order habitat selection between the seasons with the GPS locations of 32 tracked pelicans. We used Gaussian Markov random field models to estimate the third-order habitat selection by pelicans at the breeding and non-breeding grounds, accounting for spatial autocorrelation. Pelicans strongly selected waterbodies and wetlands at both non-breeding and breeding grounds, tracking their foraging habitats between the seasons at the home range level. However, pelicans exhibited seasonal differences in the strength of the third-order selection of wetlands and waterbodies with foraging habitat selection being stronger at the breeding grounds than at the non-breeding grounds, supporting the Lack hypothesis.

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38

EL-KHAMY, S. E., M. M. HADHOUD, M. I. DESSOUKY, B. M. SALAM, and F. E. ABD EL-SAMIE. "ACQUISITION OF SARSAT INFORMATION USING AN AUTO-CORRELATION BASED ADAPTIVE LINE ENHANCER." International Journal of Information Acquisition 02, no. 04 (December 2005): 291–302. http://dx.doi.org/10.1142/s0219878905000659.

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This paper develops a new approach to the detection of the emergency locator transmitter (ELT) signal using an adaptive line enhancer (ALE). The input signal to the ALE is replaced by its autocorrelation function (ACF) because noise affects the central samples of the autocorrelation function only while it affects all samples of the noisy signal. This gives the ALE the ability to get rid of noise, easily. The output ACF is then used in the spectral estimation and detection of the ELT signal. This approach is related to the signal processing using Higher Order Statistics (HOS) since the ACF is the used input. The paper also compares the results of the new approach to other different previously used methods foe ELT signal detection. The first method uses the signal xk as an input to the ALE, and the second method uses [Formula: see text]. Results illustrate the superiority of the proposed method over the other two methods. A comparison study between the performance of two types of ALE; Fixed pole radius and variable pole radius ALEs in detecting the ELT signal, is introduced.

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39

LIPPERT, THOMAS. "LATTICE QUANTUM ELECTRODYNAMICS NEAR THE PHASE TRANSITION." International Journal of Modern Physics C 04, no. 01 (February 1993): 163–79. http://dx.doi.org/10.1142/s0129183193000185.

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Numerical simulations of quantum electrodynamics near the phase transition suffer from an extreme slowing down on large lattices. The two leading terms of the decaying autocorrelation function can be attributed to the influence of first-order phase transition effects, called supercritical slowing down, and second-order phase transition effects, called critical slowing down, respectively. We show that we can bypass supercritical slowing down using a conventional local updating algorithm based on a phenomenological weight ratio fixing method. As for critical slowing down, we apply a new global multi-scale updating algorithm which removes critical slowing down completely. We compare the structure of the local vs. the global algorithm as well as their implementation on the Connection Machine CM-2, analyze their computational complexity and present actual performance measurements.

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40

BECKUS, SIEGFRIED, and FELIX POGORZELSKI. "Delone dynamical systems and spectral convergence." Ergodic Theory and Dynamical Systems 40, no. 6 (October 22, 2018): 1510–44. http://dx.doi.org/10.1017/etds.2018.116.

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In the realm of Delone sets in locally compact, second countable Hausdorff groups, we develop a dynamical systems approach in order to study the continuity behavior of measured quantities arising from point sets. A special focus is both on the autocorrelation, as well as on the density of states for random bounded operators. It is shown that for uniquely ergodic limit systems, the latter measures behave continuously with respect to the Chabauty–Fell convergence of hulls. In the special situation of Euclidean spaces, our results complement recent developments in describing spectra as topological limits: we show that the measured quantities under consideration can be approximated via periodic analogs.

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41

Tewari, S. P., and P. Silotia. "The effect of two dimensions on the temperature variation of displacement-displacement autocorrelation function, second-order Doppler shift and specific heat in graphite." Journal of Physics: Condensed Matter 1, no. 41 (October 16, 1989): 7535–41. http://dx.doi.org/10.1088/0953-8984/1/41/004.

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42

Ma, Yue, Weimin Huang, and Eric W. Gill. "Bistatic High Frequency Radar Ocean Surface Cross Section for an FMCW Source with an Antenna on a Floating Platform." International Journal of Antennas and Propagation 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/8675964.

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The first- and second-order bistatic high frequency radar cross sections of the ocean surface with an antenna on a floating platform are derived for a frequency-modulated continuous wave (FMCW) source. Based on previous work, the derivation begins with the general bistatic electric field in the frequency domain for the case of a floating antenna. Demodulation and range transformation are used to obtain the range information, distinguishing the process from that used for a pulsed radar. After Fourier-transforming the autocorrelation and comparing the result with the radar range equation, the radar cross sections are derived. The new first- and second-order antenna-motion-incorporated bistatic radar cross section models for an FMCW source are simulated and compared with those for a pulsed source. Results show that, for the same radar operating parameters, the first-order radar cross section for the FMCW waveform is a little lower than that for a pulsed source. The second-order radar cross section for the FMCW waveform reduces to that for the pulsed waveform when the scattering patch limit approaches infinity. The effect of platform motion on the radar cross sections for an FMCW waveform is investigated for a variety of sea states and operating frequencies and, in general, is found to be similar to that for a pulsed waveform.

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43

MILIVOJEVIC, Zoran, Bojan PRLINCEVIC, and Natasa SAVIC. "Optimization Parameter of the 1P Keys Interpolation Kernel Implemented in the Correlation Algorithm for Estimating the Fundamental Frequency of the Speech Signal." Eurasia Proceedings of Science Technology Engineering and Mathematics 16 (December 31, 2021): 153–61. http://dx.doi.org/10.55549/epstem.1068581.

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The first part of this paper describes an algorithm for estimating the fundamental frequency F0 of a speech signal, using an autocorrelation algorithm. After that, it was shown that, due to the discrete structure of the autocorrelation function, the accuracy of the fundamental frequency estimate largely depends on the sampling period TS. Then, in order to increase the accuracy of the estimation, an interpolation of the correlation function is performed. Interpolation is performed using a one parameter (1P) Keys interpolation kernel. The second part of the paper presents an experiment in which the optimization of the 1P Keys kernel parameter was performed. The experiment was performed on test Sine and Speech signals, in the conditions of ambient disturbances (N8 Babble noise, SNR = 5 to -10 dB). MSE was used as a measure of the accuracy of the fundamental frequency estimate. Kernel parameter optimization was performed on the basis of the MSE minimum. The results are presented graphically and tabularly. Finally, a comparative analysis of the results was performed. Based on the comparative analysis, the window function, in which the smallest estimation error was achieved for all ambient noise conditions, was chosen.

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44

Pérez, Isidro A., M. Luisa Sánchez, M. Ángeles García, Nuria Pardo, and Beatriz Fernández-Duque. "Statistical Analysis of the CO2 and CH4 Annual Cycle on the Northern Plateau of the Iberian Peninsula." Atmosphere 11, no. 7 (July 21, 2020): 769. http://dx.doi.org/10.3390/atmos11070769.

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Outliers are frequent in CO2 and CH4 observations at rural sites. The aim of this paper is to establish a procedure based on the lag-1 autocorrelation to form measurement groups, some of which include outliers, and the rest include regular measurements. Once observations are classified, a second objective is to determine the number of harmonics in order to suitably describe the annual evolution of both gases. Monthly CO2 and CH4 percentiles were calculated over a six-year period. Linear trends for most of the percentiles were around 2.24 and 0.0097 ppm year−1, and the interquartile ranges of residuals calculated from detrended concentrations were 6 and 0.02 ppm for CO2 and CH4, respectively. Five concentration groups were proposed for CO2 and six were proposed for CH4 from the lag-1 autocorrelation applied to detrended observations. Monthly medians were calculated in each group, and combinations of harmonics were applied in an effort to fit the annual cycle. Finally, adding annual and semi-annual harmonics successfully described the cycle where one step was observed in the concentration decrease in spring, not only for high CO2 percentiles but also for low CH4 percentiles.

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45

Střelec, Luboš, and Václav Adamec. "Exploration into power of homogeneity and serial correlation tests." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 61, no. 4 (2013): 1129–36. http://dx.doi.org/10.11118/actaun201361041129.

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Verification of regression models is primarily based on analysis of error terms and constitutes one of the most important steps in applied regression analysis. In cross-sectional models, the error terms are typically heteroskedastic, while in time series regressions the errors are often affected by serial correlation. Consequently, in this paper, we focus on Monte Carlo simulations applied to explore the power of several tests of homogeneity and tests for presence of autocorrelation. In the past decades, the computational power has increased significantly to allow the benefit of simulation from exact distributions, which are not defined explicitly. We will discuss 1) testing of homogeneity for a given number of components in the exponential mixture approximated by subpopulations and 2) simulation of power in several commonly used tests of autocorrelation. For the first case, we consider exact likelihood ratio test (ELR) and exact likelihood ratio test against the alternative with two-component subpopulation (ELR2). In the second case, we consider the Durbin-Watson, Durbin h, Breusch-Godfrey, Box-Pierce and Ljung-Box tests of 1st order serial correlation and the runs test of randomness in two different types of linear regression models.

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46

French, Andrew S., Susan H. Dick, and Douglas D. Rasmusson. "Postsynaptic Dorsal Column and Cuneate Correlations in the Raccoon: A Re-evaluation by Parallel-Cascade Analysis." Journal of Neurophysiology 88, no. 6 (December 1, 2002): 3372–76. http://dx.doi.org/10.1152/jn.00329.2002.

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In a previous study, we reported evidence for correlations between the firing of postsynaptic dorsal column (PSDC) neurons and cuneate neurons with overlapping receptive fields on the glabrous skin of the raccoon forepaw. The evidence was based on cross-correlation and frequency response analyses of spontaneously firing neurons. However, cross-correlation without white noise Gaussian analog inputs or Poisson distributed pulse train inputs is difficult to interpret because of the inherent convolution with the autocorrelation of the unknown input signals. While the data suggested positive correlations in the spinocuneate direction for most neuron pairs, we could not estimate the temporal characteristics of these putative connections. We have now re-analyzed these data using a parallel-cascade method to estimate the first- and second-order kernels of a Volterra series approximation to the spinocuneate system. This unbiased analysis suggests that a positive correlation occurs after about 5 ms, probably followed by a negative correlation at about 12 ms. Second-order kernels also had repeatable structure, indicating dual pathways with time separations of at least 10 ms.

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Johnson, Donald R., Bradley J. Swanson, and Judith L. Eger. "Cyclic dynamics of eastern Canadian ermine populations." Canadian Journal of Zoology 78, no. 5 (May 1, 2000): 835–39. http://dx.doi.org/10.1139/z00-011.

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Based on partial autocorrelation analysis, 20 ermine (Mustela erminea) populations in Manitoba, Ontario, and Quebec demonstrated cyclic dynamics characterized by a latitudinal gradient of decreasing first-order feedback and increasing negativity of second-order feedback. Most of these populations exhibited three cyclic peaks and a 10-year interval of noncyclic dynamics during the sampling period (1915-1940). Changes in ermine density probably reflected those in the density of microtine rodents, their primary prey. Analysis of the limited number of long-term lemming and vole series from boreal North America indicated a latitudinal gradient in cyclic dynamics similar to that of microtine rodent populations in northern Europe. Complex geographic and temporal variation in ermine population dynamics, including cyclic, noncyclic, and shifting patterns of density change, supports the specialist-generalist hypothesis of predator-prey interaction at temperate latitudes.

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Sabines-Chesterking, Javier, Ivan A. Burenkov, and Sergey V. Polyakov. "In Situ Flow Cytometer Calibration and Single-Molecule Resolution via Quantum Measurement." Sensors 22, no. 3 (February 2, 2022): 1136. http://dx.doi.org/10.3390/s22031136.

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Fluorescent biomarkers are used to detect target molecules within inhomogeneous populations of cells. When these biomarkers are found in trace amounts it becomes extremely challenging to detect their presence in a flow cytometer. Here, we present a framework to draw a detection baseline for single emitters and enable absolute calibration of a flow cytometer based on quantum measurements. We used single-photon detection and found the second-order autocorrelation function of fluorescent light. We computed the success of rare-event detection for different signal-to-noise ratios (SNR). We showed high-accuracy identification of the events with occurrence rates below 10−5 even at modest SNR levels, enabling early disease diagnostics and post-disease monitoring.

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CLAYS, K., M. WU, and A. PERSOONS. "FEMTOSECOND HYPER-RAYLEIGH SCATTERING STUDY OF SPATIAL ORIENTATIONAL CORRELATIONS BETWEEN CHROMOPHORES." Journal of Nonlinear Optical Physics & Materials 05, no. 01 (January 1996): 59–71. http://dx.doi.org/10.1142/s0218863596000076.

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Since the introduction of Hyper-Rayleigh scattering (HRS) as a measurement technique for the first hyperpolarizability of molecules in solution,1 the importance of fluctuations was realized.2 For isotropic solutions, a combination of the spatial and temporal orientational fluctuations causes the instantaneous and local deviation from macroscopic centrosymmetry, necessary to observe a second-order signal. The fluctuations in the spatial orientational distribution function of nonlinear optical chromophores cause an HRS signal that fluctuates as a function of position in solid samples. The correlation length, characterizing the decay of the autocorrelation function of this fluctuating signal, indicates the degree of spatial correlation between these chromophores. The development of femtosecond HRS was instrumental for the study of orientational correlations.3

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50

Kurek, Sławomir, Mirosław Wójtowicz, and Jadwiga Gałka. "Using Spatial Autocorrelation for identification of demographic patterns of Functional Urban Areas in Poland." Bulletin of Geography. Socio-economic Series 52, no. 52 (June 1, 2021): 123–44. http://dx.doi.org/10.2478/bog-2021-0018.

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Abstract Functional Urban Areas (FUAs) leads to a better knowledge of urban spatial organisation, which may play a significant role in regional policy making and may be helpful in understanding the connection between urbanisation and demographic development. An explanation of population change in urban regions can be associated the second demographic transition comprising fertility decline below replacement level and postponement of births. The aim of this paper is to focus on establishing similarity patterns and anomalous values of selected demographic variables in the cores and peripheral areas of Functional Urban Areas. At the background of this study lies an assumption that population development of FUA's is shaped by different factors connected with second demographic transition and migrations. To achieve the aims the following demographic characteristics were used: population growth rate, dependency ratio, rate of natural increase, the net migration rate, and the dynamic economic ageing index, Spatial methods play an increasingly important role in contemporary socio-demographic research. In order to identify spatial systems Global Moran Statistics and the Local Indicators of Spatial Association (LISA) including Local Moran statistics as well as Getis-Ord Gi* statistics were used. The research showed global and local autocorrelation of demographic processes in Functional Urban Areas in Poland, namely population growth, natural increase, net migration and population ageing. The use of local Moran's I statistic and the Getis-Ord Gi* method has led to identification of spatial clusters and dispersions representing different demographic variables. Spatial autocorrelation methods can be useful in an analysis of demographic variables including changes in time. The main contribution of this study to the research on demographic processes in urban areas was an application of spatial groupings techniques not only to find out similarity and dissimilarity patterns of demographic indicators but also to apply this findings for the needs of spatial planning.

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