Human gait data can be collected using inertial measurement units (IMUs). An IMU is an electronic device that uses an accelerometer and gyroscope to capture three-axial linear acceleration and three-axial angular velocity. The data so collected are time series in nature. The major challenge associated with these data is the segmentation of signal samples into stride-specific information, that is, individual gait cycles. One empirical approach for stride segmentation is based on timestamps. However, timestamping is a manual technique, and it requires a timing device and a fixed laboratory set-up which usually restricts its applicability outside of the laboratory. In this study, we have proposed an automatic technique for stride segmentation of accelerometry data for three different walking activities. The autocorrelation function (ACF) is utilized for the identification of stride boundaries. Identification and extraction of stride-specific data are done by devising a concept of tuning parameter ( $t_{p}$ ) which is based on minimum standard deviation ( $\sigma$ ). Rigorous experimentation is done on human activities and postural transition and Osaka University – Institute of Scientific and Industrial Research gait inertial sensor datasets. Obtained mean stride duration for level walking, walking upstairs, and walking downstairs is 1.1, 1.19, and 1.02 s with 95% confidence interval [1.08, 1.12], [1.15, 1.22], and [0.97, 1.07], respectively, which is on par with standard findings reported in the literature. Limitations of accelerometry and ACF are also discussed. stride segmentation; human activity recognition; accelerometry; gait parameter estimation; gait cycle; inertial measurement unit; autocorrelation function; wearable sensors; IoT; edge computing; tinyML.

We present the preliminary analysis of clustering of a sample of 1157 radio-identified galaxies from Machalski & Condon (1999). We found that for separations 2–15 h−1 Mpc their redshift space autocorrelation function ξ(s) can be approximated by the power law with the correlation length ~3.75h−1 Mpc and slope γ ~ 1.8. The correlation length for radiogalaxies is found to be lower and the slope steeper than the corresponding parameters of the control sample of optically observed galaxies. Analysis the projected correlation function Ξ(r) displays possible differences in the clustering properties between active galactic nuclei (AGN) and starburst (SB) galaxies.

A method for measurement of the aberration status from high-resolution dark-field images is developed using scanning transmission electron microscopy (STEM), called the Segmented Image Autocorrelation function Matrix (SIAM). The method employs an autocorrelation function from the segmented area in the defocused STEM images from an aligned crystalline specimen to measure the defocus and twofold astigmatism for the probe-forming system. The values measured using this method can be fed directly back to the instrument by changing the strength of the stigmator and the objective lens of the microscope. It is successfully demonstrated that the feedback system can automatically correct the defocus and twofold astigmatism of the microscope after several iterations using practical STEM images from an actual crystalline specimen.

The paper presents the first attempt to develop parameters that are invariant to polarization, aimed at classification and recognition of complex radar objects. Both the simplest (two-point) model and multipoint models of a complex object are analyzed using the so-called emergence principle and a generalization of the interference laws. The polarization invariant parameters of scattered fields and their statistical parameters, including autocorrelation functions and space spectra, are found. The experimental validation of the analysis results is presented.

The Markovian arrival process generalizes the Poisson process by allowing for dependent and nonexponential interarrival times. We study the autocorrelation function of the two-state Markovian arrival process. Our findings show that the correlation structure of such a process has a very specific pattern, namely, it always converges geometrically to zero. Moreover, the signs of the autocorrelation coefficients are either constant or alternating.

The structural evolution in amorphous silicon and germanium thin films has been investigated by high-resolution transmission electron microscopy (HRTEM) in conjunction with autocorrelation function (ACF) analysis. The results established that the structure of as-deposited semiconductor films is of a high density of nanocrystallites embedded in the amorphous matrix. In addition, from ACF analysis, the structure of a-Ge is more ordered than that of a-Si. The density of embedded nanocrystallites in amorphous films was found to diminish with annealing temperature first, then to increase. The conclusions also corroborate well with the results of diminished medium-range order in annealed amorphous films determined previously by a variable coherence microscopy method.

Using Laplace transforms an explicit analytical expression is obtained for the autocorrelation function of the number in the system for the two-server Poisson queue. The method employed may be extended to Poisson queues with more than two servers.

An account is given of the autocorrelation theory of seasonal moving average models, using a vector representation defined by the author. It is shown that the autocorrelation structure of a seasonal moving average is reducible to that of a certain non-seasonal moving average, independently of the value of the seasonal periodicity if sufficiently large. It is pointed out that existing methods for the Cramér–Wold factorization discussed in Godolphin (1976) can easily be adapted to contend with the seasonal case.