Autocorrelation Function Analysis Research Articles

Joint ambient noise autocorrelation and receiver function analysis of the Moho

SUMMARYIn the field of seismic interferometry, cross-correlations are used to extract Green’s function from ambient noise data. By applying a single station variation of the method, using autocorrelations, we are in principle able to retrieve zero-offset reflections in a stratified Earth. These reflections are valuable as they do not require an active seismic source and, being zero-offset, are better constrained in space than passive earthquake based measurements. However, studies that target Moho signals with ambient noise autocorrelations often give ambiguous results with unclear Moho reflections. Using a modified processing scheme and phase-weighted stacking, we determine the Moho P-wave reflection time from vertical autocorrelation traces for a test station with a known simple crustal structure (HYB in Hyderabad, India). However, in spite of the simplicity of the structure, the autocorrelation traces show several phases not related to direct reflections. Although we are able to match some of these additional phases in a qualitative way with synthetic modelling, their presence makes it hard to identify the reflection phases without prior knowledge. This prior knowledge can be provided by receiver functions. Receiver functions (arising from mode conversions) are sensitive to the same boundaries as autocorrelations, so should have a high degree of comparability and opportunity for combined analysis but in themselves are not able to independently resolve VP, VS and Moho depth. Using the timing suggested by the receiver functions as a guide, we observe the Moho S-wave reflection on the horizontal autocorrelation of the north component but not on the east component. The timing of the S reflection is consistent with the timing of the PpSs–PsPs receiver function multiple, which also depends only on the S velocity and Moho depth. Finally, we combine P receiver functions and autocorrelations from HYB in a depth–velocity stacking scheme that gives us independent estimates for VP, VS and Moho depth. These are found to be in good agreement with several studies that also supplement receiver functions to obtain unique crustal parameters. By applying the autocorrelation method to a portion of the EASI transect crossing the Bohemian Massif in central Europe, we find approximate consistency with Moho depths determined from receiver functions and spatial coherence between stations, thereby demonstrating that the method is also applicable for temporary deployments. Although application of the autocorrelation method requires great care in phase identification, it has the potential to resolve both average crustal P and S velocities alongside Moho depth in conjunction with receiver functions.

Analysis of autocorrelation function of stochastic processes by F-transform of higher degree

The autocorrelation function of a stochastic process is one of the essential mathematical tools in the description of variability that is successfully applied in many scientific fields such as signal processing or financial time series analysis and forecasting. The aim of the paper is to provide an analysis of fuzzy transform of higher degree applied to stochastic processes with a focus on its autocorrelation function. We introduce a higher-degree fuzzy transform of a stochastic process and investigate its basic properties. Further, we introduce a higher-degree fuzzy transform of bivariate functions in the tensor product of polynomial spaces and demonstrate its approximation ability. In addition, we show that the bivariate higher-degree fuzzy transform of multiplicative separable functions is a product of univariate fuzzy transform of the respective functions, which is a desirable property in the processing of functions of higher dimensions. The obtained results are used to demonstrate an interesting identity between the autocorrelation function of the fuzzy transform of a stochastic process and the bivariate fuzzy transform of the autocorrelation function of the stochastic process. This identity provides two ways to determine the autocorrelation function of the fuzzy transform of a stochastic process, which can be useful, especially in a situation where its direct calculation becomes complex or even impossible, for example, the calculation of a sample autocorrelation function.

On the statistical analysis of the harmonic signal autocorrelation function

On the statistical analysis of the harmonic signal autocorrelation function

Analysis and resistance of dynamic degradation of digital chaos via functional graphs

To analyze the effects of finite computational precision on the dynamical degradation of digital chaotic maps, we designed a periodic orbit detection algorithm that is based on a functional graph. The algorithm can calculate the transient length of each chaotic orbit, weak secret keys, fixed points and the period distribution of digital chaotic systems with various limited computational precisions accurately. Furthermore, an effective method based on quadratic congruential generator is proposed to counteract the performance degradation of digital chaos. Based on the method, a new chaotic model can be constructed with full cycle. Numerical experiments are carried out to evaluate the feasibility of the proposed scheme in terms of phase portrait, autocorrelation function, complexity and periodicity analysis. Finally, as an application, a pseudorandom bit generator with satisfactory performance is designed for chaotic secure communication.

A forecasting the consumer price index using time series model

This article examines the behavior of the consumer price index in Ukraine for the period from January 2010 to September 2020. The characteristics of the initial time series, the analysis of autocorrelation functions made it possible to reveal the tendency of their development and the presence of annual seasonality. To model the behavior of the consumer price index and forecast for the next months, two types of models were used: the additive ARIMA*ARIMAS model, better known as the model of Box-Jenkins and the exponential smoothing model with the seasonality estimate of Holt-Winters. As a result of using the STATISTICA package, the most adequate models were built, reflecting the monthly dynamics of the consumer price index in Ukraine. The inflation forecast was carried out on the basis of the Holt-Winters model, which has a minimum error.

Forecast and trend analysis of gold prices in India using auto regressive integrated moving average model

Autoregressive Integrated Moving Average (ARIMA) is one of the powerful statistical method to forecast the timeseries data. Forecasting plays a key role in estimating the future prices. Keeping in view that we have selected the prices of Gold in India from 1964 to 2019 through different secondary sources. Many factors are responsible for rise of gold price in India such as traditional demand, no liability on the investors, inflation proof, low interest rate on most of the saving schemes, safe investment tool. In the present study we mainly focused on estimating the prices of Gold from the year 2020 to 2029, observed the sudden increase of gold price in 2020 due to various reasons and its impact on forecasting prices of gold using ARIMA model. Identifying the suitable ARIMA model (0,2,3) by conducting the analysis of Autocorrelation function (ACF) and Partial autocorrelation function (PACF) to the selected differenced series and present the forecasting prices of gold. The selected secondary source data exhibits the positive trends for the quantitative analysis.

Forecast and trend analysis of gold prices in India using auto regressive integrated moving average model

Autoregressive Integrated Moving Average (ARIMA) is one of the powerful statistical method to forecast the timeseries data. Forecasting plays a key role in estimating the future prices. Keeping in view that we have selected the prices of Gold in India from 1964 to 2019 through different secondary sources. Many factors are responsible for rise of gold price in India such as traditional demand, no liability on the investors, inflation proof, low interest rate on most of the saving schemes, safe investment tool. In the present study we mainly focused on estimating the prices of Gold from the year 2020 to 2029, observed the sudden increase of gold price in 2020 due to various reasons and its impact on forecasting prices of gold using ARIMA model. Identifying the suitable ARIMA model (0,2,3) by conducting the analysis of Autocorrelation function (ACF) and Partial autocorrelation function (PACF) to the selected differenced series and present the forecasting prices of gold. The selected secondary source data exhibits the positive trends for the quantitative analysis.

An information-theoretical analysis of gene nucleotide sequence structuredness for a selection of aging and cancer-related genes.

We provide an algorithm for the construction and analysis of autocorrelation (information) functions of gene nucleotide sequences. As a measure of correlation between discrete random variables, we use normalized mutual information. The information functions are indicative of the degree of structuredness of gene sequences. We construct the information functions for selected gene sequences. We find a significant difference between information functions of genes of different types. We hypothesize that the features of information functions of gene nucleotide sequences are related to phenotypes of these genes.

Estimation of total dissolved solids, electrical conductivity, salinity and groundwater levels using novel learning machines

In this study, the groundwater parameters including electrical conductivity (EC), salinity, total dissolved solids (TDS) and groundwater level (GWL) for a 15-year time series (from 2002 to 2017) of the Mighan Plain, located in Markazi Province, Iran, were simulated using a hybrid meta heuristic artificial intelligence (AI) model called “wavelet self-adaptive extreme learning machine” (WSAELM) for the first time. Initially, the detection of the most significant lags of the time-series data was conducted using the autocorrelation function (ACF) and the partial autocorrelation function (PACF) analyses. By using these lags, four WSAELM models were defined and then the superior models in simulating the TDS, EC, salinity and GWL were introduced. The values of the determination coefficient (R2), Variance Accounted for (VAF) and the Nash–Sutcliffe efficiency coefficient (NSC) for the superior model simulating salinity were computed to be 0.991, 98.124 and 0.980, respectively. Also, approximately 44% of the TDS values modeled by the best model had an error less than 10%, while roughly a third of the TDS values estimated by the model had an error more than 15%. The findings indicated that the proposed hybrid model underestimated the GWL parameter, while it performed in an overestimate way for other parameters. The results of the uncertainty analysis showed the low width of uncertainty for GWL (WUB = ± 0.798), TDS (WUB = ± 5.035), EC (WUB = ± 6.425) and salinity (WUB = ± 66.650).

Differing preferential ion binding to the peptide bond in ionic environment from classical and first principles molecular dynamics simulations

The interactions of ions with N-methylacetamide (NMA) in hydrated ionic liquid (IL), methylammonium formate (MAF), with varying concentrations were studied by molecular dynamics simulations. As the interactions depend on the choice of potential, the current study aims to compare the preferential binding of cation and anion of MAF to peptide bond of NMA utilizing force field-based classical molecular dynamics (CMD) and first principles molecular dynamics (FPMD) simulations. NMA forms a stable hydrogen bonding network with anion. First principles molecular dynamics simulations predict hydrogen bonding interaction with both anion and cation in pure IL. In contrast, the classical molecular dynamics simulations provide evidence of the strong interaction of NMA with anion only. However, NMA interacts with cation in the presence of water as a co-solvent. Water molecules facilitate the more significant cation-anion distance, which decreases the electrostatic interaction between ions. In aqueous solutions, the self-diffusivity of the entities increases as compared to pure IL. The value of residence time rises with an increase in the concentration of IL. The analysis of hydrogen bond auto-correlation function reveals that with increasing IL concentration, the short-range force increases, and simultaneously, the lifetime of intermolecular hydrogen bonds increases. Between NMA-cation and NMA-anion, the strength of the NMA-anion hydrogen bond is stronger than the former. The preferential solvation is due to nature of predefined classical potential as compared to FPMD simulations.

Systematic Quantification of Synapses in Primary Neuronal Culture.

SummaryMost neurological disorders display impaired synaptic connectivity. Hence, modulation of synapse formation may have therapeutic relevance. However, the high density and small size of synapses complicate their quantification. To improve synapse-oriented screens, we analyzed the labeling performance of synapse-targeting antibodies on neuronal cell cultures using segmentation-independent image analysis based on sliding window correlation. When assessing pairwise colocalization, a common readout for mature synapses, overlap was incomplete and confounded by spurious signals. To circumvent this, we implemented a proximity ligation-based approach that only leads to a signal when two markers are sufficiently close. We applied this approach to different marker combinations and demonstrate its utility for detecting synapse density changes in healthy and compromised cultures. Thus, segmentation-independent analysis and exploitation of resident protein proximity increases the sensitivity of synapse quantifications in neuronal cultures and represents a valuable extension to the analytical toolset for in vitro synapse screens.

Technique for Rapid Mass Determination of Airborne Microparticles Based on Release and Recapture from an Optical Dipole Force Trap

We describe a new method for the rapid determination of the mass of particles confined in a free-space optical dipole-force trap. The technique relies on direct imaging of drop-and-restore experiments without the need for a vacuum environment. In these experiments, the trapping light is rapidly shuttered with an acousto-optic modulator causing the particle to be released from and subsequently recaptured by the trapping force. The trajectories of both the falls and restorations, imaged using a high-speed CMOS sensor, are combined to determine the particle mass. We corroborate these measurements using an analysis of position autocorrelation functions of the trapped particles. We report a statistical uncertainty of less than 2% for masses on the order of $5\times10^{-14}$ kg using a data acquisition time of approximately 90 seconds.

ASSESSMENT OF THE FLIGHT QUALITY IN VERTICAL PLANE

This article discusses the problem of the quality assessing of the crew An-148 piloting technique, taking into account the human factor. The calculations showed that the statistical distribution of the pitch angle does not contradict the normal distribution. It is known that the normal law of the distribution of parameters indicates a good quality piloting technique. An analysis of autocorrelation functions and its spectrum is proposed to quickly solve this problem. The assessment of the quality of the piloting technique by analyzing the autocorrelation function of the pitch angle and its spectrum is consistent with the estimation method according to the distribution laws. A good technique was established for piloting the An-148 pilot under normal piloting technique. It also offers a scheme of a warning system for failures of systems for displaying the values of the angle of attack or speed and an algorithm of actions in such cases.

Modelling qualitative and quantitative parameters of groundwater using a new wavelet conjunction heuristic method: wavelet extreme learning machine versus wavelet neural networks

AbstractIn recent years, as a result of climate change as well as rainfall reduction in arid and semi‐arid regions, modelling qualitative and quantitative parameters belonging to aquifers has become crucially important. In Iran, as aquifers are treated as the most commonly used drinking water resources, modelling their qualitative and quantitative parameters is enormously important. In this paper, for the first time, values of salinity, total dissolved solids (TDS), groundwater level (GWL) and electrical conductivity (EC) of the Arak Plain, located in Markazi Province, Iran, are simulated by means of four modern artificial intelligence models including extreme learning machine (ELM), wavelet extreme learning machine (WELM), online sequential extreme learning machine (OSELM) and wavelet online sequential extreme learning machine (WOSELM) as well as the MODFLOW software for a 15‐year period monthly. To develop the hybrid artificial intelligence models, the wavelet is employed. First, the effective lags in estimating the qualitative and quantitative parameters of the groundwater are identified using the autocorrelation function (ACF) and the partial autocorrelation function (PACF) analysis. After that, four different models are developed by the selected input combinations and also the ACF and the PACF in the form of different lags for each of ELM, WAELM, OSELM and WOSELM methods. Then, the superior models in simulating the groundwater qualitative and qualitative parameters are detected by conducting a sensitivity analysis. To forecast the electrical conductivity (EC) by the best WOSELM model, the values of the Nash–Sutcliffe efficiency coefficient (NSC), Mean Absolute Error (MAE) and the scatter index (SI) are obtained to be 0.991, 18.005 and 4.28E‐03, respectively. In addition, the most effective lags in estimating these parameters are introduced. Subsequently, the results found by the MODFLOW model are compared with those of the artificial intelligence models and it is concluded that the latter are more accurate. For instance, the scatter index and Nash–Sutcliffe efficiency coefficient values calculated by WOSELM for TDS, respectively, are 5.34E‐03 and 0.991. Finally, an uncertainty analysis is conducted to evaluate the performance of different numerical models. For example, MODFLOW has an underestimated performance in simulating the salinity parameter.

DETECTING SYSTEMATIC AND RANDOM COMPONENT OFSURFACE ROUGHNESS SIGNAL

The solution of the problem of separating the initial one-dimensional signal into two components –systematic and random –has an extremely wide practical application not only in the theory of information and communication (and related disci-plines), but also in mechanical engineering disciplines. For example, mechanical engineering technology being a science discipline includes the teaching about the surface quality of the machined parts and researching the surface roughness after machining these parts by cutting and grinding. The paper shows that the theoretical and actual values of roughness parameters differ significantly (up to 20 times) due to the influence of a random component that is present in the roughness signal together with a systematic com-ponent. It is necessary to identify the share of each of these components in the specified surface quality parameters in accordance with the method proposed in the paper. This method allows detecting the systematic and random components of the signal and isbased on the analysis of the signal autocorrelation function. Practical examples of this analysis are considered in detail formilled surface profilogram obtained experimentally. Both milling, which creates irregularities on the machined surface, and measurement of these irregularities are performed on modern CNC equipment: machining center 500V/5 and computer measuring station T8000, respectively. The developed and shown by examples signal separation technique is also applicable in other fields of science, technol-ogy and manufacturing. For example, when determining the signal to noise ratio in the theory of information and communication, in the field of telecommunications and telemetry, radio engineering, etc.

Proposal of frequency‐based decomposition approach for minimization of errors in surface texture parameter calculation

In this paper, the frequency‐based decomposition approach (FBDA) for preprocessing of surface texture parameters calculation/assessment was proposed. Two types of textures were analysed: turned or grinded details. They were measured with interferometric method. For detection/minimization of high‐frequency measuring errors (HFME) the wavelets, Haar, Daubechies, Coiflet, biorthogonal or reverse‐biorthogonal approaches were proposed. Moreover, in some cases, the power spectrum density and/or autocorrelation function analysis provided an additional and/or valuable information about surface texture/features as well. It was assumed that application of various extraction methods (such as FBDA) can provide reasonable results for noise extraction in accordance to the commonly used algorithms, such as median filter, moving average (arithmetic mean) filter or other denoising procedures (e.g., Gaussian denoising filter) proposed in commercial software. The influence of proposed procedure on calculation (error minimization) of surface topography parameters (from ISO 25178 standard) was also presented. Some errors (especially those caused by false estimation of noise‐removal procedure) in surface topography parameter calculation were comprehensively studied with profile analysis; for areal HFME decomposition, the noise surface was defined. For some turned details, the HFME was observed in profiles analysis mostly. The biggest high frequencies from removed noise surface (created by noise extraction with FBDA) contained, the better results (of proposed approach) were obtained. It was also assumed that FBDA for preprocessing of both grinded and turned surfaces with various decomposition filters (in some cases the RBW) gave more ‘direct results’ that commonly used denoising approaches.

Atomic arrangement and mechanical properties of chemical-vapor-deposited amorphous boron

Amorphous boron can be synthesized by chemical vapor deposition (CVD) onto a tungsten wire substrate, and this core-shell fiber has been widely used in high-performance composites due to its superior mechanical properties. Although the amorphous boron coating makes a significant contribution to the high fracture strength, its mechanical properties have not been studied rigorously due to its thin thickness and strong adhesion to the substrate. Furthermore, the medium-range atomic ordering of CVD amorphous boron has not been clearly understood, and the determination of the closest crystalline structure has been a challenge. In this study, high-resolution transmission electron microscopy (HRTEM), nanoindentation, and in-situ micropillar compression were performed to investigate the atomic arrangement and mechanical properties. Electron diffraction and autocorrelation function analysis revealed α-rhombohedral boron ordering as the closest crystalline structure. Micropillar compression displayed near-ideal yield strength (~13 GPa), but nanoindentation a relatively moderate Young's modulus (~320 GPa), leading to a modulus of resilience (2.64 × 108 J/m3) unprecedentedly higher than most advanced engineering materials. Our structural and mechanical data will be discussed in terms of lattice point spacing and the influence of surface defects on fracture strength, respectively. Our results will be potentially useful to improve mechanical properties of amorphous boron core-shell fibers and related composites.

Drought index prediction using advanced fuzzy logic model: Regional case study over Kumaon in India.

A new version of the fuzzy logic model, called the co-active neuro fuzzy inference system (CANFIS), is introduced for predicting standardized precipitation index (SPI). Multiple scales of drought information at six meteorological stations located in Uttarakhand State, India, are used. Different lead times of SPI were computed for prediction, including 1, 3, 6, 9, 12, and 24 months, with inputs abstracted by autocorrelation function (ACF) and partial-ACF (PACF) analysis at 5% significance level. The proposed CANFIS model was validated against two models: classical artificial intelligence model (e.g., multilayer perceptron neural network (MLPNN)) and regression model (e.g., multiple linear regression (MLR)). Several performance evaluation metrices (root mean square error, Nash-Sutcliffe efficiency, coefficient of correlation, and Willmott index), and graphical visualizations (scatter plot and Taylor diagram) were computed for the evaluation of model performance. Results indicated that the CANFIS model predicted the SPI better than the other models and prediction results were different for different meteorological stations. The proposed model can build a reliable expert intelligent system for predicting meteorological drought at multi-time scales and decision making for remedial schemes to cope with meteorological drought at the study stations and can help to maintain sustainable water resources management.

Time dependence of quantum correlation functions.

In the past few years, the exponential expansion analysis of time autocorrelation functions has provided profound insight into the leading microscopic processes driving the atomic-scale dynamics and has made it possible to highlight the presence and the role of various relaxation channels through which the fundamental correlation functions decay with time. Here we apply this method to the determination of the full time dependence of a correlation function c(t) in a quantum system at nonzero temperature, by making explicit its relationship with its Kubo transform c_{K}(t), which in some cases can be approximately computed with the presently available quantum simulation techniques. We obtain an exact expression for c(t) in terms of the exponential modes that describe the time behavior of c_{K}(t). The relative importance of the various modes in determining the overall shape of c(t) can then be studied in detail. This work extends to the full time domain the results of a previous paper [Guarini et al., Phys. Rev. Lett. 123, 135301 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.135301], in which we employed the same method to calculate the zero time value of the velocity autocorrelation function, to obtain a microscopic description of the quantum mean kinetic energy in a fluid. In particular, we show that the decay constants and the frequencies of the dominant microscopic modes of c(t) are the same as those of c_{K}(t), but the dynamics of the quantum system also contains an additional term decaying on a time scale determined solely by temperature of the system.

DETECTING SYSTEMATIC AND RANDOM COMPONENT OF SURFACE ROUGHNESS SIGNAL

The solution of the problem of separating the initial one-dimensional signal into two components – systematic and random – has an extremely wide practical application not only in the theory of information and communication (and related disciplines), but also in mechanical engineering disciplines. For example, mechanical engineering technology being a science discipline includes the teaching about the surface quality of the machined parts and researching the surface roughness after machining these parts by cutting and grinding. The paper shows that the theoretical and actual values of roughness parameters differ significantly (up to 20 times) due to the influence of a random component that is present in the roughness signal together with a systematic component. It is necessary to identify the share of each of these components in the specified surface quality parameters in accordance with the method proposed in the paper. This method allows detecting the systematic and random components of the signal and is based on the analysis of the signal autocorrelation function. Practical examples of this analysis are considered in detail for milled surface profilogram obtained experimentally. Both milling, which creates irregularities on the machined surface, and measurement of these irregularities are performed on modern CNC equipment: machining center 500V/5 and computer measuring station T8000, respectively. The developed and shown by examples signal separation technique is also applicable in other fields of science, technology and manufacturing. For example, when determining the signal to noise ratio in the theory of information and communication, in the field of telecommunications and telemetry, radio engineering, etc.