scholarly journals On Estimating the Cross Correlation and Least Squares Fit of One Data Set to Another With Time Shift

2019 ◽  
Vol 6 (8) ◽  
pp. 1409-1415 ◽  
Author(s):  
B. F. Chao ◽  
C. H. Chung
Keyword(s):  
Least Squares ◽  
Cross Correlation ◽  
Time Shift ◽  
Data Set ◽  
Least Squares Fit ◽  
The Cross

scholarly journals Analysis of the transmembrane potential of embryos exposed to action of nickel, cobalt, tin and zinc

2018 ◽  
Vol 9 (2) ◽  
pp. 216-222
Author(s):  
G. V. Galyk ◽  
Z. Y. Fedorovych ◽  
E. I. Lychkovsky ◽  
D. I. Sanagursky
Keyword(s):  
Correlation Functions ◽  
Cross Correlation ◽  
Transmembrane Potential ◽  
Development Stage ◽  
Time Shift ◽  
Transmembrane Potentials ◽  
Nickel Cobalt ◽  
Cross Correlation Analysis ◽  
The Cross ◽  
Degree Of Similarity

Germ cells of aquatic organisms are complex systems whose growth and development depends on many factors, one of which is the composition of the aquatic environment. We used parameters in our analysis from aggregate data available from published literature. They are data of the transmembrane potential of the germinal cells of Misgurnus fossilis (Linnaeus, 1758) at the development stage from 180th to 360th minutes. Embryos were incubated in an environment with nickel, cobalt, tin, and zinc ions and without them. Plotted lines of the transmembrane potential were digitized and calibrated at intervals of 10 minutes. Rows of numerical values of the transmembrane potentials were obtained. These rows were used for calculation of autocorrelation and cross-cross-correlation functions. It was established that the transmembrane potential describes nonperiodic and quasi-periodic oscillations. The higher statistically significant values of the autocorrelation coefficients were observed in the first lags. Autocorrelation analysis indicates that the periods of oscillations of the transmembrane potential increase with the action of nickel, cobalt, tin and zinc on the germ. The phenomena and processes that occur in the germ cell are well reflected at the initial stages of the auto-correction and are lost when the magnitude of the lag increases. The degree of similarity of transmembrane potentials with the help of cross-correlation analysis is quantitatively characterized. The distribution of fluctuations of cross-correlation functions with complex dynamics, which arise with time shifts both in the forward and reverse directions, were established. It is established that for large values of time shifts, the cross-correlation coefficient is a low-informative indicator, since information about the influence of the factor on the living system is lost. A graph for a given time shift was constructed. The connection between the nodes is the magnitude of the cross-correlation coefficients between the vapor of the transmembrane potentials, which indicate the degree of similarity of the bioelectric processes. Graphs will be used for qualitative and quantitative study of system dynamics. The obtained results confirm the existence of a close relationship between environmental nickel, cobalt, tin, and zinc and the oscillation of transmembrane potential during early embryogenesis.

scholarly journals Advantages of the Broadening Function (BF) over the Cross-Correlation Function (CCF)

2004 ◽  
Vol 215 ◽  
pp. 17-18 ◽  
Author(s):  
Slavek M. Rucinski
Keyword(s):  
Correlation Function ◽  
Least Squares ◽  
Cross Correlation ◽  
Cross Correlation Function ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
The Cross ◽  
The Many

Performance of the cross-correlation function (CCF) is compared with the linear, algebraic equations, least-squares deconvolution directly giving the broadening function (BF). The many disadvantages of the CCF do not outweigh its simplicity so that the BF approach is strongly advocated.

scholarly journals Continuous non‐contact respiratory rate and tidal volume monitoring using a Depth Sensing Camera

2021 ◽  
Author(s):  
Paul S. Addison ◽  
Philip Smit ◽  
Dominique Jacquel ◽  
Anthony P. Addison ◽  
Cyndy Miller ◽  
...  
Keyword(s):  
Tidal Volume ◽  
Respiratory Rate ◽  
Least Squares ◽  
Clinical Setting ◽  
Pearson Correlation ◽  
Pearson Correlation Coefficient ◽  
Depth Sensing ◽  
Data Set ◽  
Least Squares Fit ◽  
High Degree

AbstractThe monitoring of respiratory parameters is important across many areas of care within the hospital. Here we report on the performance of a depth-sensing camera system for the continuous non-contact monitoring of Respiratory Rate (RR) and Tidal Volume (TV), where these parameters were compared to a ventilator reference. Depth sensing data streams were acquired and processed over a series of runs on a single volunteer comprising a range of respiratory rates and tidal volumes to generate depth-based respiratory rate (RRdepth) and tidal volume (TVdepth) estimates. The bias and root mean squared difference (RMSD) accuracy between RRdepth and the ventilator reference, RRvent, across the whole data set was found to be -0.02 breaths/min and 0.51 breaths/min respectively. The least squares fit regression equation was determined to be: RRdepth = 0.96 × RRvent + 0.57 breaths/min and the resulting Pearson correlation coefficient, R, was 0.98 (p < 0.001). Correspondingly, the bias and root mean squared difference (RMSD) accuracy between TVdepth and the reference TVvent across the whole data set was found to be − 0.21 L and 0.23 L respectively. The least squares fit regression equation was determined to be: TVdepth = 0.79 × TVvent—0.01 L and the resulting Pearson correlation coefficient, R, was 0.92 (p < 0.001). In conclusion, a high degree of agreement was found between the depth-based respiration rate and its ventilator reference, indicating that RRdepth is a promising modality for the accurate non-contact respiratory rate monitoring in the clinical setting. In addition, a high degree of correlation between depth-based tidal volume and its ventilator reference was found, indicating that TVdepth may provide a useful monitor of tidal volume trending in practice. Future work should aim to further test these parameters in the clinical setting.

Polarity Change Extraction of GPR Data for Under-road Cavity Detection: Application on Sudeoksa Testbed Data

2019 ◽  
Vol 24 (3) ◽  
pp. 419-431
Author(s):  
Jongha Hwang ◽  
Donggeon Kim ◽  
Xiangyue Li ◽  
Dong-Joo Min
Keyword(s):  
Phase Shift ◽  
Power Spectrum ◽  
Cross Correlation ◽  
Survey Methods ◽  
Time Lag ◽  
Background Signal ◽  
Data Set ◽  
Air Ground Interface ◽  
The Cross ◽  
Polarity Change

Ground penetrating radar (GPR) is one of the most widely used geophysical survey methods to locate cavities under roads due to its speedy exploration and high-resolution imaging. To locate underground cavities using GPR, we need to distinguish between cavity-induced reflections and other reflections, which can be achieved by examining the polarity change in reflections compared to the polarity of the transmitted signal. The polarity change can be measured from the phase shift between the target and first reflections. To estimate the phase shift in reflections, the method of computing the power spectrum difference between the original trace and background signal was proposed, but the method has a limitation for shallow reflectors. As an alternative method to avoid this limitation, we propose using only one component of the power spectrum difference, the cross-correlation between the target reflection and background signal. The cross-correlation has its maximum peak at a time lag between the target and first reflection (from the air-ground interface). Additionally, the phase at that time lag represents a phase shift between the two reflections. We compare our cross-correlation-based method with the conventional method of computing the whole power spectrum difference and investigate the feasibility of our method for distinguishing cavity-induced reflections using a 2D field data set acquired in a testbed in Sudeoksa, Korea.

Simultaneous multivintage time-shift estimation

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. V109-V121 ◽  
Author(s):  
Ehsan Zabihi Naeini ◽  
Henning Hoeber ◽  
Gordon Poole ◽  
Hamid R. Siahkoohi
Keyword(s):  
Continental Shelf ◽  
Least Squares ◽  
Least Squares Method ◽  
Synthetic Data ◽  
Time Lapse ◽  
Time Shift ◽  
Data Sets ◽  
Data Set ◽  
Time Alignment ◽  
Multiple Repeat

Time-shift estimation is a key step in seismic time-lapse processing as well as in many other signal-processing applications. We consider the time-shift problem in the setting of multiple repeat surveys that must be aligned consistently. We introduce an optimized least-squares method based on the Taylor expansion for estimating two-vintage time shifts and compare it to crosscorrelation. The superiority of the proposed algorithm is demonstrated with synthetic data and residual time-lapse matching on a U. K. continental shelf data set. We then discuss the shortcomings of cascaded time alignment in multiple repeat monitor surveys and propose an approach to estimate simultaneous multivintage time shifts that uses a constrained least-squares technique combined with elements of network theory. The resulting time shifts are consistent across all vintages in a least-squares sense, improving overall alignment when compared to the classical flow of alignment in a cascaded manner. The method surpasses the cascaded approach, as noted with sample synthetic and three-vintage U. K. continental shelf time-lapse data sets.

Is the stabilization of quiet upright stance in humans driven by synchronized modulations of the activity of medial and lateral gastrocnemius muscles?

2010 ◽  
Vol 108 (1) ◽  
pp. 85-97 ◽  
Author(s):  
Taian M. M. Vieira ◽  
Uwe Windhorst ◽  
Roberto Merletti
Keyword(s):  
Cross Correlation ◽  
Center Of Pressure ◽  
The Body ◽  
Quiet Standing ◽  
Time Shift ◽  
Data Set ◽  
Lateral Gastrocnemius ◽  
Surface Potentials ◽  
Emg Signal ◽  
Gastrocnemius Muscles

A matrix of 120 electromyogram (EMG) electrodes (8 rows and 15 columns) was used to investigate individual activation patterns of the medial (MG) and lateral gastrocnemius (LG) muscles during forward sways of the body in human quiet stance. This matrix was positioned on the right calf of eight subjects after identification of the MG and LG contours with ultrasound scanning. Gray-scale images were generated with the maxima and minima of the cross-correlation function between the envelope of each EMG signal and the body center of pressure (CoP) for individual forward sways. These images were automatically segmented to reduce the data set into representative and local values of EMG-CoP cross-correlation for each muscle. On average, modulations in EMG amplitude preceded the onset of forward sways with a variable timing, with both gastrocnemius muscles being similarly and synchronously modulated in 193 out of 236 sways. Variations in the timing of activation between muscles were less frequent, although consistent across subjects and significantly correlated with changes in the direction and velocity of body sways. Interestingly, the time shift between EMG and CoP traces sometimes varied consistently along different channels of the same column of electrodes, either in proximal-to-distal or distal-to-proximal direction. The variable EMG-CoP cross-correlation delay was not congruent with the delay expected for the propagation of surface potentials along muscle fibers. Comparison of surface EMGs with intramuscular EMGs recorded from six subjects demonstrated that surface potentials provide high spatial selectivity, thus supporting the notion of selective activation of motor units during quiet standing. Hence, the stabilization of the quiet standing posture likely relies on flexible rather than stereotyped mechanisms of control.

scholarly journals Joint Multifractal Analysis and Source Testing of River Level Records Based on Multifractal Detrended Cross-Correlation Analysis

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Liang Wu ◽  
Manling Wang ◽  
Tongzhou Zhao
Keyword(s):  
Correlation Analysis ◽  
Multifractal Analysis ◽  
Cross Correlation ◽  
Source Analysis ◽  
Data Set ◽  
River Level ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
The Cross ◽  
Joint Multifractal Analysis

The joint multifractal analysis is usually conducted in two different variables for their cross-correlations but rarely used for two records of one variable collected at two different places. It is important for the detection of change in multifractality in space. Besides, the cross-correlations in two analyzed series make the analysis of sources of joint multifractality difficult. There are few studies on the source of joint multifractality. We focus on the two issues for two level records at pairs of adjacent sites along one river and carry out an extension of our previous work which is about the single multifractality of one record with the same data set. The data set is collected from 10 observation stations of a northern China river and contains about two million high-frequency river level records. Results of joint multifractal analysis via multifractal detrended cross-correlation analysis show that the change in joint multifractality at pairs of adjacent sites caused by weak cross-correlations can be detected by comparing the single generalized Hurst exponent with the joint scaling exponent function and reveal the effects of human activities on joint multifractality. This analysis provides an approach for detecting the change in multifractality. Following the idea of our previous work, two robust hypothesis tests via a set of pairs of surrogate series are proposed for the source testing of joint multifractality. The analysis of the effects of cross-correlations is carried out via a proposed simultaneously half-shifting technique which can both minimize the cross-correlations between original series and make full use of records. Results of source analysis show not only the effects of autocorrelations in series and probability distribution of river levels but also the effects of cross-correlations between series.

scholarly journals Statistical Analysis of Mixed Model Factorial Experiments with Missing Factor Combinations: The Case of Asynchronous Cyclic Drought Data

2006 ◽  
Vol 131 (2) ◽  
pp. 201-208
Author(s):  
Dawn M. VanLeeuwen ◽  
Rolston St. Hilaire ◽  
Emad Y. Bsoul
Keyword(s):  
Statistical Analysis ◽  
Least Squares ◽  
Mixed Models ◽  
Repeated Measures ◽  
Fixed Effects ◽  
Information Criteria ◽  
Covariance Structures ◽  
Data Set ◽  
Nested Models ◽  
The Cross

Statistical analysis of data from repeated measures experiments with missing factor combinations encounters multiple complications. Data from asynchronous cyclic drought experiments incorporate unequal numbers of drought cycles for different sources and provide an example of data both with repeated measures and missing factor combinations. Repeated measures data are problematic because typical analyses with PROC GLM do not allow the researcher to compare candidate covariance structures. In contrast, PROC MIXED allows comparison of covariance structures and several options for modeling serial correlation and variance heterogeneity. When there are missing factor combinations, the cross-classified model traditionally used for synchronized trials is inappropriate. For asynchronous data, some least squares means estimates for treatment and source main effects, and treatment by source interaction effects are inestimable. The objectives of this paper were to use an asynchronous drought cycle data set to 1) model an appropriate covariance structure using mixed models, and 2) compare the cross-classified fixed effects model to drought cycle nested within source models. We used a data set of midday water potential measurements taken during a cyclic drought study of 15 half-siblings of bigtooth maples (Acer grandidentatum Nutt.) indigenous to Arizona, New Mexico, Texas, and Utah. Data were analyzed using SAS PROC MIXED software. Information criteria lead to the selection of a model incorporating separate compound symmetric covariance structures for the two irrigation treatment groups. When using nested models in the fixed portion of the model, there are no missing factors because drought cycle is not treated as a crossed experimental factor. Nested models provided meaningful F tests and estimated all the least squares means, but the cross-classified model did not. Furthermore, the nested models adequately compared the treatment effect of sources subjected to asynchronous drought events. We conclude that researchers wishing to analyze data from asynchronous drought trials must consider using mixed models with nested fixed effects.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

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