Analysis of Results of Digital Electroencephalography and Digital Vectors of Coronavirus Images upon Applying the Theory of Covariance Functions

The paper analyses the intensity changes of three pollution parameter vectors in space and time. The RGB raster pollution data of the Lithuanian territory used for the research were prepared according to the digital images of the Sentinel-2 Earth satellites. The numerical vectors of environmental pollution parameters CH4 (methane), NO2 (nitrogen dioxide) and for direct comparison O2 (oxygen gas) were used for the calculations. The covariance function theory was used to perform the analysis of intensity changes in digital vectors. Estimates of the covariance functions of the numerical vectors of pollution parameters and O2 or the auto-covariance functions of single vectors are calculated from random functions consisting of arrays of measurement parameters of all parameters vectors. Correlation between parameters vectors depends on the density of parameters and their structure. Estimates of covariance functions were calculated by changing the quantization interval on a time scale and using a compiled computer program using the Matlab procedure package. The probability dependence between the environmental pollution parameter vectors and trace gas of the territory in Lithuania and their change in time scale was determined.

Analysis variations in the intensity of vectors estimating indoor air pollution (PM2.5, PM10 and CO2) and noise levels are presented. The research was conducted in an office room during COVID-19. The theory of covariance functions was used to analyse changes in the intensity of the vectors of determined parameters. The estimates of the cross-covariance functions of digital vectors and the autocovariance functions of the individual vectors of air pollution and noise recording sensor parameters were calculated in line with the random functions of data arrays measuring the vectors of air pollution sensor parameters. The approximations of covariance functions were calculated by changing the quantisation interval on a time scale and applying software created based on the Matlab procedure package. The stochastic interdependence of the vectors of air pollution and noise level recording sensor parameters and variations in vectors on the time scale was established.

An adaptive target detection algorithm for forward-looking infrared (FLIR) imagery is proposed, which is based on measuring differences between structural information within a target and its surrounding background. At each pixel in the image a dual window is opened, where the inner window (inner image vector) represents a possible target signature and the outer window (consisting of a number of outer image vectors) represents the surrounding scene. These image vectors are then preprocessed by two directional highpass filters to obtain the corresponding image gradient vectors. The target detection problem is formulated as a statistical hypotheses testing problem by mapping these image gradient vectors into two linear transformations, P1 and P2, via principal component analysis (PCA) and eigenspace separation transform (EST), respectively. The first transformation P1 is only a function of the inner image gradient vector. The second transformation P2 is a function of both the inner and outer image gradient vectors. For the hypothesis H1 (target), the difference of the two functions is small. For the hypothesis H0 (clutter), the difference of the two functions is large. Results of testing the proposed target detection algorithm on two large FLIR image databases are presented.

In this paper, an adaptive target detection algorithm for FLIR imagery is proposed that is based on measuring differences between structural information within a target and its surrounding background. At each pixel in the image a dual window is opened where the inner window (inner image vector) represents a possible target signature and the outer window (consisting of a number of outer image vectors) represents the surrounding scene. These image vectors are preprocessed by two directional highpass filters to obtain the corresponding image edge vectors. The target detection problem is formulated as a statistical hypotheses testing problem by mapping these image edge vectors into two transformations, P 1 and P 2 , via Eigenspace Separation Transform (EST) and Principal Component Analysis (PCA). The first transformation P 1 is a function of the inner image edge vector. The second transformation P 2 is a function of both the inner and outer image edge vectors. For the hypothesis H 1 (target): the difference of the two functions is small. For the hypothesis H 0 (clutter): the difference of the two functions is large. Results of testing the proposed target detection algorithm on two large FLIR image databases are presented.

This paper discusses about the scatter of the intensity of vibration signals of paper prints and analyses their mechanical parameters applying the theory of covariance functions. It is an important practical problem, before starting printing process of colour prints, expecting the correct position of fixed raster points, to adjust the paper sheet tension between printing machine sections. The results of measuring the intensity of vibration signals at the fixed points were presented on a time scale in the form of arrays (matrices). The estimates of cross-covariance functions between digital arrays result in measuring the intensity of vibrations, and the estimates of auto-covariance functions of single arrays were calculated upon changing the quantization interval on the time scale. Application of normed auto-covariance and cross-covariance functions enables reduction of preprinting experimental measurements, which saves time (what is actual for industry). Tension force depends on the mechanical properties of the paper sheet and print. These characteristics depend on paper type, layers of printing colors and positioning of the coverage. In the calculation, the software Matlab 7 in batch statement environment was applied.

In this paper, an analysis of the spread of random extraneous low-frequency (50 Hz) vibrations excited in a gravimeter body is presented. Further, their influence on the gravimeter scale reference system is determined by applying the theory of covariance function. The data on the measurement of strength of random extraneous vibrations in fixed points excited in the gravimeter body were recorded on the time scale in the form of arrays using a three-axis accelerometer. High-frequency (2 and 20 kHz) noise vibrations were also used to modulate the gravimeter scale data. While processing the results of measuring the strength of random extraneous vibrations and the data arrays on the reference system, estimates of autocovariance and cross-covariance functions by changing the quantisation interval on the time scale were calculated. Software developed within the MATLAB 7 package was applied for the calculations.

The relationship between a continuous process such as the EEG of the central nervous system and a point process such as the discharge activity of a single neuron can often be profitably studied by way of the cross covariance function (CCVF). The individual events in the point process can be used to trigger an average response computer so as to obtain the average response of the continuous process to an event in the point process. Under certain circumstances it has been shown that this average response is a useful estimate of the CCVF. Because the technique is simpler to use than conventional methods for estimating the CCVF, it has been suggested that the technique be used for this purpose. However, when the point process is considered in terms of its expectation density, it can be shown that the CCVF estimate obtained by averaging is valid only when the properties of the processes are special enough as not to be encountered in many of the experimental conditions of interest. The derivation indicates explicitly how the differences between the averaging estimator and the true CCVF arise.

The paper analyses an opportunity to develop predictive models for identification of parameters of seismic vibrations by applying statistical processing of measurement data. The calculations used measurement data arrays according to vectors E, N and Z obtained from four seismic stations (India EVBH, Indonesia LUWIBH, Italy CERABN and Turkey BNHBH). The Doppler method and the theory of covariance functions were applied for analysing the measurement data arrays. The trend of seismic vibration intensity vectors was estimated by applying the least-squares method. In addition, the said procedure partially eliminates random errors of the measurement data from the stations. Using the intensity variation of seismic vibration vectors E, N and Z on the timescale, the estimates of autocovariance and cross-covariance functions of seismic vibration vectors were calculated by changing the quantised interval on the time scale. The average values of parameter z in the Doppler formula were calculated according to the created formula by applying the expressions of cross-covariance functions of the algebraic addition of the relevant vectors and a single vector. By applying the values of parameter z from the Doppler formula, the approximate value of the velocity of reciprocal movement of seismic vectors was calculated. In the calculations, the software developed on the basis of the MATLAB program package operators was applied.

An ability to construct predictive models for identifying seismic oscillation parameters by using the mathematics of covariance functions and Doppler effect phenomena is examined in this work. In the calculations, the Mars seismic oscillations measurement data from InSight Mission V2, observed in the months May, June and July of 2019, was used. To analyze the observation data arrays the Doppler phenomena and the expressions of covariance functions were employed. The seismic oscillations trend's intensity vectors were assessed by least squares method, and the random errors of measurements at the stations were eliminated partially as well. The estimates of the vector's auto-covariance and cross-covariance functions were derived by altering the quantization interval on the general time scale while varying the magnitude of the seismic oscillation vector on the same time scale. To detect the mean values of z —the main parameter of Doppler expression— we developed a formula by involving the derivatives of cross-covariance functions of a single vector and algebraic sum of the relevant vectors.

This paper explores the possibility of identifying gravitational waves by statistically processing data obtained from the experiment performed by the Laser Interferometer Gravitational-Wave Observatory (LIGO observatory). For an analysis of the measurement data arrays, the parameter z from the Doppler formula and the theory of covariance functions has been used. The trend of oscillation vectors of detectors obtained at the Hanford and Livingston observatories was assessed by applying the least square method. In addition, this procedure partially eliminates random errors in the data obtained from measurements carried out by the observatory. Upon assessment of the impact of gravitational waves on the changes in the values of the parameters of interferometer laser beams, the estimates of the auto-covariance and cross-covariance functions of vibration vectors of detectors measured at the observatories were calculated by varying the quantised interval on the time scale. The covariance of algebraic addition of relevant vectors and single vectors was used in the calculation of the estimates of covariance functions. The average value of the parameter z from the Doppler formula was calculated according to the formula created by using the expression of cross-covariance function of algebraic addition Hanford Gravitational Wave–Livingston Gravitational Wave (HGW−LGW) vector and single LGW vector. The speed and the direction of spread of the gravitational waves’ component HGW → LGW in respect of the vector of the gravitational waves were established. The calculations were performed using the author’s original software based on MATLAB procedures.

In this paper, the boundedness properties of vector-valued intrinsic square functions and their vector-valued commutators with \(BMO(\mathbb {R}^{n})\) functions are discussed. We first show the weighted strong-type and weak-type estimates of vector-valued intrinsic square functions in the Morrey-type spaces. Then, we obtain weighted strong-type estimates of vector-valued analogues of commutators in Morrey-type spaces. In the endpoint case, we establish the weighted weak \(L\log L\)-type estimates for these vector-valued commutators in the setting of weighted Lebesgue spaces. Furthermore, we prove weighted endpoint estimates of these commutator operators in Morrey-type spaces. In particular, we can obtain strong-type and endpoint estimates of vector-valued intrinsic square functions and their commutators in the weighted Morrey spaces and the generalized Morrey spaces.

This article describes an agricultural application of remote sensing methods. The idea is to aid in eradicating an invasive plant called Sosnowskyi borscht (H. sosnowskyi). These plants contain strong allergens and can induce burning skin pain, and may displace native plant species by overshadowing them, meaning that even solitary individuals must be controlled or destroyed in order to prevent damage to unused rural land and other neighbouring land of various types (mostly violated forest or housing areas). We describe several methods for detecting H. sosnowskyi plants from Sentinel-2A images, and verify our results. The workflow is based on recently improved technologies, which are used to pinpoint exact locations (small areas) of plants, allowing them to be found more efficiently than by visual inspection on foot or by car. The results are in the form of images that can be classified by several methods, and estimates of the cross-covariance or single-vector auto-covariance functions of the contaminant parameters are calculated from random functions composed of plant pixel vector data arrays. The correlation of the pixel vectors for H. sosnowskyi images depends on the density of the chlorophyll content in the plants. Estimates of the covariance functions were computed by varying the quantisation interval on a certain time scale and using a computer programme based on MATLAB. The correlation between the pixels of the H. sosnowskyi plants and other plants was found, possibly because their structures have sufficiently unique spectral signatures (pixel values) in raster images. H. sosnowskyi can be identified and confirmed using a combination of two classification methods (using supervised and unsupervised approaches). The reliability of this combined method was verified by applying the theory of covariance function, and the results showed that H. sosnowskyi plants had a higher correlation coefficient. This can be used to improve the results in order to get rid of plants in particular areas. Further experiments will be carried out to confirm these results based on in situ fieldwork, and to calculate the efficiency of our method.

Vibrational analysis of length comparator

In this paper, we propose an embedded face verification system against image degradation using a TMS320C6711 DSP chip. Our proposed system has several advantages over general systems in terms of price, size and applicability. As well as physical merits, it has an efficient approach for degraded facial images based on noise parameter estimation under real-life environments. The proposed method linearly combines image vector and noise parameters into one vector for training. When estimating noise parameters, we calculate the optimal coefficients of linear decomposition of an input image vector only. The noise parameters can be obtained from the linear composition step using these optimal coefficients. In contrast to conventional methods, we add the estimated noises to original images instead of removing them. Finally we perform a verification step with the input and synthesized image. The experimental results of this system show that the proposed method can estimate noise parameters accurately while improving the performance of photo image verification.

In the paper, the spread of intensity of linear positioning table system vibrations is examined and an analysis of their parameters upon applying the theory of covariance functions is carried out. For the investigation, two linear positioning tables were chosen; for them, different lubricants were used: universal lubricant Loctite 8103 and lubricant Braycote 601EF for working in vacuum. The results of measurements of the vibration intensity in four fixed points upon varying the speed of the carriage were recorded on the time scale in form of arrays (matrices). The estimates of cross-covariance functions of the arrays of results of measurements of the digital vibration intensity were calculated. The estimates of auto-covariance functions of single arrays upon changing the quantization interval on the time scale were calculated too. For the calculations, the software developed upon using Matlab7 package of procedures was applied.