Quantitative Structural Analysis Research Articles

Diffusion of Technology in Strategic HR Practices and their Impact Over Productivity of Small Firms

With the change in time, the practices of HR also get changed to support the businesses in the highly competitive market like by incorporating the technology in daily workplace activities. Although the incorporation of new techniques and methodologies in HR was very limited in past few decades but after analyzing the benefits in every area, HR department incorporate these into their daily functioning like the use of SHRM, HRIS. HRIS system is an application of technology where big data can be managed, retrieved easily by replacing the heavy filing paper work and gives error free result. In this paper after the deep review of literature, the researcher selected six human factors based on infusion of technology in HR practices and their impact over the productivity. This study is conducted to put some light over the technology benefits in small firms, which are lacking in the previous studies. Maximization of profit, high production, good quality and customer satisfaction are the current requirements of every company and to fulfill these requirements technology plays a vital role. Analysis of the information collected from the sample in this research study clearly revealed that requirements of a company could be fulfilled by choosing some selective HR practices along with the strategic point of view for optimization of productivity. PLS-SEM software is used to calculate the statistical value of variables in precise form to analyze this new combination of technology and HR. So, this paper applying quantitative structural analysis method of PLS software to find out the rationale of the study by supporting the concept of right selection of innovative information system in HR practices based on human factor leads to great result

Integrating deep convolutional neural networks with marker-controlled watershed for overlapping nuclei segmentation in histopathology images

Nuclei segmentation in histopathology images plays a crucial role in the morphological quantitative analysis of tissue structure and has become a hot research topic. Though numerous efforts have been tried in this research area, the overlapping and touching nuclei segmentation remains a challenging problem. In this paper, we present a novel and effective instance segmentation method for tackling this challenge by integrating Deep Convolutional Neural Networks with Marker-controlled Watershed. Firstly, we design a novel network architecture with multiple segmentation tasks, called Deep Interval-Marker-Aware Network, for learning the foreground, marker, and interval of nuclei, simultaneously. Then the learned interval between overlapping nuclei is used to refine the foreground result of nuclei by using the logical operators. Finally, the learned marker result and the nuclei segmentation result refined by interval are transmitted into the Marker-controlled Watershed for splitting the touching nuclei. The experiments on the standard public datasets demonstrate that our method achieves a substantial improvement compared with state-of-the-art methods. Source codes are available at https://github.com/appiek/Nuclei_Segmentation_Experiments_Demo.

Optical and magnetic properties of Gd1−xSrxCrO3 (0 ⩽ x ⩽ 0.15)

Optical and magnetic properties of Gd1−xSrxCrO3 (0 ⩽ x ⩽ 0.15) polycrystalline samples have been investigated to identify the role of Sr2+ ion in GdCrO3 compound. Quantitative structural analysis using Rietveld refinement suggests the formation of single orthorhombic phase up to x = 0.1 composition, and in addition, a secondary monazite-type structure of SrCrO4 arises for x = 0.15 composition. Raman and Fourier transform infrared spectra also confirm the presence of SrCrO4 component for higher concentration of Sr2+ ion. Mixed valence state of Cr such as Cr3+ and Cr4+ is obtained from x-ray photoelectron spectroscopy. The presence of Cr4+ ion induces a reduction of optical band gap with increase of Sr content. The unoccupied states originate from Cr4+ modify d–d transitions. Larger cell volume and breaking of magnetic exchange pathways through nonmagnetic element (Sr) weaken the strength of interaction and consequently lower Néel and spin reorientation temperatures.

Real-time Observation of Interface Atomic Structures by an Energy-Dispersive Surface X-ray Diffraction

Surface X-ray diffraction is a powerful tool for studying the atomic structure of buried interfaces nondestructively. The analysis is often limited to the static structures, since the acquisition of crystal truncation rod (CTR) profile dataset is lengthy. Recently, high-speed methods have been developed by several groups, aiming for the in operando study of interface phenomena. Our method uses energy-dispersive convergent X-rays and area detector, and allows the quantitative structure analysis during irreversible phenomena in a typical time frame of 1 s. In this review, the energy-dispersive method is compared with the other high-speed methods which use high-energy X-rays with a grazing incidence geometry and transmission geometry, and then two examples of the real-time monitoring are presented, the photo-induced wettability transition of the rutile-TiO2(110) surface and an electrochemical reaction on the Pt(111) electrode surface, to show the capability of the energy-dispersive method.

A mass spectrometric stochastic dynamic diffusion approach to selective quantitative and 3D structural analyses of native cyclodextrins by electrospray ionization and atmospheric pressure chemical ionization methods

The paper addressed shortcoming with highly precise and selective 3D structural analysis of native cyclodextrins in mixture using ions observable at low m/z–region by ESI– and APCI–mass spectrometry. Because of, the quantitative and structural analyses of CDs, in general, are vexed by a set of complications. The study outlines our own stochastic dynamic approaches to the latter issues based on new model relations, quantifing the measurable MS outcome intensity. They introduce the so–called stochastic dynamic mass spectrometric diffusion “DSD” parameter, exhibiting high accuracy, precision, sensitivity and selectivity, respectively. It is linearly connected with the so–called quantum chemical diffusion parameter “DQC” according to Arrhenius’s theory. The most important upshot is that statistical parameters r = 0.99639–0.99981 has been obtained correlating between DSD and DQC parameters. Therefore, we determine high accurately 3D molecular and electronic structures of analytes by mass spectrometry. Fragment peaks at m/z 313, 279, 272, 252, 231, 214, 198, 171, 158 and 141 are examined. Mixtures of CDs and monomeric and acyclic oligomer carbohydrates glucose (1), sucrose (2), raffinose (3), melezitose (4) and cellotriose (5) are also studied. Our method is able to account precisely for the effect of the temperature under ESI– and APCI–MS conditions, as well. Correlative analysess between DSD parameters of ESI– and APCI–MS measurements under different temperatures is also shown. Chemometric tests are used. Another important results and conclusions, among others, to draw from this research are: (i) excellent linear correlation between DSD and DQC parameters of r = 0.99636 is found looking at common ions at m/z 141, 158 and 171, belonging to 2-formyl-3,4-dihydroxy-pyranylium, 4,5,6-trihydroxy-6H-pyran-2-carbaldehyde and 3,4,5-trihydroxy-6-oxo-6H-pyran-2-ylmethylidyne-oxonium ions. Thus, we distinguish precisely between the last structure and 3-formyl-4,5-dihydroxy-2,7-dioxa-8-oxonia-bicyclo[4.2.0]octa-1(8),3,5-triene cation. In the case of ion at m/z 141 subtle electronic effects are distinguished between the mentioned structure and the charged 3,4-dihydroxy-6H-pyran-2-carbaldehyde one. The method determines precisely very similar structurally poly–OH–substituted derivatives. Because of, (ii) absolute reproducibility (r = 1) of DSD parameters of ESI–MS spectra is obtained studying the shown in point (i) MS peaks of β-CD between jth and jth numbers of experiments. The statistical equation is DiSD = (0.51 ± 3.1.10−5) × DjSD; (iii) the APCI– and ESI–MS provide identical results studying common MS ions of CDs and the correlation between DAPCISD and DESISD parameters excludes from error, due to, experiment; and (iv) The correlation between theory and experiment accounting for the factor temperature within our model equations shows r = 0.9828 looking at the MS peaks at m/z 313 280, 279, 274 and 252, respectively. The effect of the temperature under both ESI– and APCI–MS conditions on the 3D molecular and electronic structures of CDs is precisely studied, respectively.

ALTIS: A fast and automatic lung and trachea CT-image segmentation method.

The automated segmentation of each lung and trachea in CT scans is commonly taken as a solved problem. Indeed, existing approaches may easily fail in the presence of some abnormalities caused by a disease, trauma, or previous surgery. For robustness, we present ALTIS (implementation is available at http://lids.ic.unicamp.br/downloads) - a fast automatic lung and trachea CT-image segmentation method that relies on image features and relative shape- and intensity-based characteristics less affected by most appearance variations of abnormal lungs and trachea. ALTIS consists of a sequence of image foresting transforms (IFTs) organized in three main steps: (a) lung-and-trachea extraction, (b) seed estimation inside background, trachea, left lung, and right lung, and (c) their delineation such that each object is defined by an optimum-path forest rooted at its internal seeds. We compare ALTIS with two methods based on shape models (SOSM-S and MALF), and one algorithm based on seeded region growing (PTK). The experiments involve the highest number of scans found in literature - 1255 scans, from multiple public data sets containing many anomalous cases, being only 50 normal scans used for training and 1205 scans used for testing the methods. Quantitative experiments are based on two metrics, DICE and ASSD. Furthermore, we also demonstrate the robustness of ALTIS in seed estimation. Considering the test set, the proposed method achieves an average DICE of 0.987 for both lungs and 0.898 for the trachea, whereas an average ASSD of 0.938 for the right lung, 0.856 for the left lung, and 1.316 for the trachea. These results indicate that ALTIS is statistically more accurate and considerably faster than the compared methods, being able to complete segmentation in a few seconds on modern PCs. ALTIS is the most effective and efficient choice among the compared methods to segment left lung, right lung, and trachea in anomalous CT scans for subsequent detection, segmentation, and quantitative analysis of abnormal structures in the lung parenchyma and pleural space.

The Qualitative and Quantitative Structure of Oral Microbiocenosis in Rats with Periodontitis in a Setting of Hyper- and Hypothyroidism

Abstract Background and aims. Oral microbial flora is a highly sensitive indicator system producing qualitative and quantitative responses to changes in various individual organs and systems. The aim of study was to perform a comparative analysis of qualitative and quantitative structure of oral microbiocenosis in rats with comorbidity-free periodontitis and in animals with periodontitis in a setting of hyper- and hypothyroidism. Material and methods. Experimental studies were conducted on 48 mature male white rats. Samples for microbiological tests were taken from dental surfaces (on the border between hard tissue and gums in the interdental spaces). The isolated pure cultures were identified by their morphological, tinctorial, cultural and biochemical properties and the signs of pathogenecity. Results. We found that the oral dysbiosis occurring in a setting of periodontitis in rats is chiefly characterized by increased quantity of coccal forms and by increased candidal inoculation; these organisms cumulatively inhibit the growth of normal microbial flora, such as Lactobacilli, bacteroids and Bifidobacteria. Thyroid dysfunction exacerbates changes in the qualitative and quantitative structure of oral microbiocenosis. Conclusions. The periodontitis in a setting of thyroid dysfunction increases both the species variety and the quantitative counts of oral microbial flora, with predominance of such microbial organisms as Staph. aureus, E. coli, E. faecalis, Candida albicans and P. aeruginosa.

Quantitative analysis of microscopic structure and gas seepage characteristics of low-rank coal based on CT three-dimensional reconstruction of CT images and fractal theory

The pores/fractures are places for gas migration and storage in coal. Their structure complexity will directly influence the pore structure parameters and gas seepage properties of coal. Therefore, we selected 6 low-rank coal samples and quantitatively studied these influences utilizing the high-resolution micro computed tomography (μCT) and fractal theory. The total pore structure and connected pore structure parameters of 6 samples were acquired from three-dimensional (3D) reconstruction of CT images. The fractal dimensions of total pore structures (Df), solid structures (Ds) and connected pore structures (Dc) were calculated using 3D box-counting method. The relationship between Df and porosity was analyzed through the 3D total pore model, and the relationships between Dc and connectivity as well as permeability were analyzed through the 3D connected pore model. The results show that Df, which is between 2.10 and 2.43, could accurately describe the fractal characteristics of coal and the solid structure of coal is not fractal. The porosities of the 6 samples are between 3.33% and 12.18% and their relationship with Df can be defined by a monotonically increasing power function. The larger the Df is, the larger the porosity of the tested coal sample. Dc is between 2.28 and 2.32, the connectivity is between 0.54 and 0.83, and the permeability is in the range of 1.76–11.63 × 10−8 m2 (except samples 1 and 6). Dc is negatively correlated with connectivity and permeability and its relationship with connectivity and permeability can be represented by the quadratic function and monotone decreasing power function, respectively.

Effect of bubble plume on liquid phase flow structures using PIV

In this study, particle image velocimetry (PIV) technique was used for the quantitative visualization and analysis of the liquid phase flow structure driven by a chain of air bubbles in a rectangular bubble column. So, we aimed to provide the recirculation flow pattern and turbulence characteristics in the vicinity of rising bubbles. To this aim, a simple experimental set-up was built, the liquid phase was seeded with 10 µm hallow glass particles. The illumination system consists of a 5 W argon laser source. Images were taken with a high-speed camera (Teledyne Dalsa, Falcon 1.4M100 HG CMOS). The sequence of different bubbles trajectories in water and glycerin solution of high viscosity was studied in order to understand the induced liquid phase flow structure. When the liquid viscosity increases, the instabilities of the liquid velocity field disappears showing the liquid entrainment in the bubbles wake which tends to rise in vertical alignment around the central axis of the column. Furthermore, the viscous force reduces the pseudo-turbulence induced by the rising bubbles, which increases the vertical liquid velocity.

Stability of Ligands on Nanoparticles Regulating the Integrity of Biological Membranes at the Nano-Lipid Interface.

When nanoparticles interact with cellular or organelle membranes, the coating ligands are known to affect the integrity of the membranes, which regulate cell death and inflammation. However, the molecular mechanisms of this modulation remain unresolved. Here, we use synchrotron X-ray liquid surface scattering and molecular dynamics simulations to study interface structures between phospholipids and gold nanorods (AuNRs) coated by surfactant and polyelectrolyte. These ligands are two types of widely used surface modification with different self-assembled structures and stabilities on the surface of nanoparticles. We reveal distinct mechanisms of the ligand stability in disrupting membrane integrity. We find that the cationic surfactant ligand cetyltrimethylammonium bromide detaches from the AuNRs and inserts into phospholipids, resulting in reduced membrane thickness by compressing the phospholipids to align with the shorter ligand. Conversely, the cationic polyelectrolyte ligand poly(diallyldimethylammonium chloride) is more stable on AuNRs; although it adsorbs onto the membrane, it does not cause much impairment. The distinct coating ligand interactions with phospholipids are further verified by cellular responses including impaired lysosomal membranes and triggered inflammatory effects in macrophages. Together, the quantitative analysis of interface structures elucidates key bio-nano interactions and highlights the importance of surface ligand stability for safety and rational design of nanoparticles.

Investigation of nicotinamide and isonicotinamide derivatives: A quantitative and qualitative structural analysis

An anhydrous nature of benzylidene derivatives of nicotin and isonicotinamides crystal structures is determined and studied for their weak intermolecular interactions. The molecular structure is non-planar in general with the pyridine ring twisted with respect to the central hydrazone moiety. The crystal structures depict various intermolecular interactions, including N–H⋯O, C–H⋯O, N–H⋯N, and C–H⋯N hydrogen bonding along with weak C–H … π and π … π contacts. Further, Hirshfeld surface and 2D-fingerprint plot analysis confirm the role of intermolecular interactions in building the crystal packing in these derivatives. The PIXELC energy calculation shows that dispersion energy plays an essential role in stabilizing the crystal packing in all six derivatives.

Electric and magnetic dipole modes in high-resolution inelastic proton scattering at 0°

Inelastic proton scattering under extreme forward angles including $0^\circ$ and at energies of a few hundred MeV has been established as a new spectroscopic tool for the study of complete dipole strength distributions in nuclei. Such data allow an extraction of the electric dipole polarizability which provides important constraints parameters of the symmetry energy, which determine the neutron skin thickness and the equation of state (EOS) of neutron-rich matter. Also new insight into the much-debated nature of the pygmy dipole resonance (PDR) is obtained. Additionally, the isovector spin-M1 resonance can be studied in heavy nuclei, where only limited experimental information exists so far. Together with much improved results on the isoscalar spin-M1 strength distributions in $N = Z$ nuclei, these data shed new light on the phenomenon of quenching of the nuclear spin response. Using dispersion matching techniques, high energy resolution ($\Delta E/E \leq 10^{-4} \,\,$ full width at half maximum, FWHM) can be achieved in the experiments. In spherical-vibrational nuclei considerable fine structure is observed in the energy region of the isovector giant dipole resonance (IVGDR). A quantitative analysis of the fine structure with wavelet methods provides information on the role of different damping mechanisms contributing to the width of the IVGDR. Furthermore, level densities can be extracted from a fluctuation analysis at excitation energies well above neutron threshold, a region hardly accessible by other means. The combination of the gamma strength function (GSF) extracted from the E1 and M1 strength distributions with the independently derived level density permits novel tests of the Brink-Axel hypothesis underlying all calculations of statistical model reaction cross sections in astrophysical applications in the energy region of the PDR.

Quantitative analysis of super-resolved structures using ASAP.

Super resolution microscopy allows imaging of cellular structures with high throughput and detail. However, tools for the efficient and quantitative analysis of images generated are lacking. Here, we developed ASAP (Automated Structures Analysis Program) to enable rapid and automated detection, classification and quantification of super-resolved structures. We validate ASAP on ground truth data and demonstrate its broad applicability by analyzing images of nucleoporins, TORC1 complexes, endocytic vesicles and Bax pores.

2151-P: Quantification of Tissue Structure in Human and Mouse Islets

The pancreatic islet is a complex tissue consisting of multiple endocrine cell types, capillaries, and a peri-islet basement membrane. The 3D organization of cells, blood vessels, and basement membrane (BM), enhances islet function by (1) supporting beta cell electrochemical coupling and synchronization through gap junctions between adjacent cells and (2) providing access to nutrients and integrin-mediated signals for beta cell survival and function through contact with capillaries and BM. Though a quantitative understanding of islet structure is lacking, there is strong evidence linking islet structural changes to diabetes progression. Studies of these changes in islet structure will enhance understanding of diabetes-related losses in islet function and lead to the development of new therapeutics for diabetic and prediabetic patients. Here, we present a novel method for quantitative analysis of islet structure in terms of local cell-cell and cell-BM interactions at endocrine cell plasma membrane surfaces. The number and surface area of individual cell-cell and cell-BM interfaces are measured from high-resolution 3D confocal images of human and mouse islets immunolabeled for endocrine cell markers, epithelial cell plasma membranes, and BM. These measurements quantify both cellular interconnectivity and access to signals supporting beta cell survival and function. We report a baseline quantification of structure for healthy adult human and mouse islets. These data both provide a definitive answer to the ongoing debate regarding the differences in structure between human and mouse islets and set the stage for future quantification of islet structure in diabetes. Disclosure O.A. Creasey: None. D. Elnatan: None. J.B. Sneddon: Advisory Panel; Spouse/Partner; Akouos. Advisory Panel; Self; Encellin. Advisory Panel; Spouse/Partner; Encellin. Consultant; Self; Semma Therapeutics, Inc. Z.J. Gartner: Stock/Shareholder; Self; Provenance, Scribe Biosciences. Funding National Institutes of Health; National Science Foundation Graduate Research Fellowship Program; National Science Foundation; University of California, San Francisco Center for Cellular Construction; University of California, San Francisco Diabetes Research Center

Quantitative analysis of local fine structure on diffusion of point defects in passive film on Ti

The diffusion of point defects in passivation determines all physico-electrochemical processes in materials corrosion and protection. In this study, a multiscale quantitative methodology was developed to reveal the diffusivity of oxygen vacancies on titanium surface (～5.0 nm thickness) in 1.0 M H2SO4 solution based on X-ray absorption fine structure (XAFS), combining with electrochemical impedance spectroscopy (EIS) and Mott-Schottky. EIS equivalent circuit exhibits that the high electronic field across passive film is 1.06 × 106 V cm–1. Mott-Schottky space charge capacitance indicates n-type semiconducting film with the donor density of ～1021 cm–3. Three important structure parameters have been firstly proposed from XAFS theoretical calculation at Ti K-edge to quantitatively describe the point defects transport between metal/film/solution interfaces. The half-jump distance equals half Ti–Ti distance subtly changing with oxidation potentials. The coordination coefficient is defined as the probability of activation jump from Ti–O coordination. And the Debye-Waller factor of structure disorder is related to the donor density of Mott-Schottky. Overall, the diffusivity of oxygen vacancies is in the range of (1.84–4.71) × 10–17 cm2 s–1 under the electric field, which determines the interfacial equilibrium of passivation and dissolution during potentiodynamic polarization. And the activation energy for motion has a minimum of 0.89 eV at 1.5 V. This multiscale quantitative methodology predicts well the potential dependent steady-state in the corrosive system.

Modern tendencies of functioning of nongovernmental pension funds in the system of obligatory pension insurance

This article summarizes and systematizes key trends in the development of non-state pension funds (NPFs) in the exercise of the functions of trust management of pension savings of citizens for the period from 2005 to 2017. The participation of non-state pension funds in the compulsory pension insurance system has led to their emergence as the largest insurer, so starting from 2016, the NPF, as a large institutional investor, began to concentrate more than half of all pension savings funds transferred to management. A quantitative analysis of the institutional structure of the Russian system of trust management of the pension system means allows determining the main directions of its transformation; there is a clear tendency to a reduction: the total number of NPFs operating in the OPS system. The article defines the strategy of investing APFs in various classes of assets during the study period, it has been revealed that of the total amount of invested pension savings in corporate securities, 2/3 of them fall on NPF investments. Over the last analyzed period, there has been a sharp increase in the investment of pension savings of NPFs in government securities, which is largely due to the tightening of regulatory requirements for the risk level of portfolio investment. Important areas of research are evaluating the effectiveness of the functioning of APFs in the system of compulsory pension insurance from the position of comparing the accumulated return on the NPF portfolio with accumulated inflation for the period analyzed, and also according to the criterion of actually accumulated investment income with indexed income on inflation.

Quantitative structural analysis of trabecular alveolar bone in the mandible by multidetector computed tomography: Differences according to tooth presence and type

Background and objectiveThere is a lack of quantitative measures of the quality of alveolar trabecular bone, an important factor in implantology. This study aimed to develop a method of objectively assessing the quality of trabecular bone by means of image processing and structural analysis of multidetector computed tomography images and to establish differences between tooth types and tooth presence/absence. Materials and methodsWe analysed 20 patients who underwent multidetector computed tomography to evaluate mandibular bone and tooth positioning. Image analysis included automatic segmentation of the mandible, obtainment of sections perpendicular to the dental arch, and structural analysis of the trabecular bone in each section. We calculated the ratio between the volume of bone and the total volume of the section, the thickness, the trabecular number, and the mean attenuation in Hounsfield units. We analysed the differences among different tooth types (incisors, canines, premolars, and molars) and between present and absent teeth. ResultsWe found statistically significant differences between different tooth types and between sections in which teeth were present or absent. Incisors had a greater ratio of trabecular bone; the ratio of trabecular bone progressively decreased from the incisors to the canines, premolars, and molars. The ratio of trabecular bone was greater in sections in which teeth were absent than in those in which teeth were present. ConclusionsThe method allows to quantify the structural properties of alveolar bone from multidetector computed tomography images. Our results provide an objective picture of the bone substrate that can be useful for planning and following up dental implant procedures.

Real-Time 3D High-Resolution Microscopy of Human Cells on the International Space Station.

Here we report the successful first operation of FLUMIAS-DEA, a miniaturized high-resolution 3D fluorescence microscope on the International Space Station (ISS) by imaging two scientific samples in a temperature-constant system, one sample with fixed cells and one sample with living human cells. The FLUMIAS-DEA microscope combines features of a high-resolution 3D fluorescence microscope based on structured illumination microscope (SIM) technology with hardware designs to meet the requirements of a space instrument. We successfully demonstrated that the FLUMIAS technology was able to acquire, transmit, and store high-resolution 3D fluorescence images from fixed and living cells, allowing quantitative and dynamic analysis of subcellular structures, e.g., the cytoskeleton. The capability of real-time analysis methods on ISS will dramatically extend our knowledge about the dynamics of cellular reactions and adaptations to the space environment, which is not only an option, but a requirement of evidence-based medical risk assessment, monitoring and countermeasure development for exploration class missions.

A deep learning approach to the structural analysis of proteins.

Deep learning (DL) algorithms hold great promise for applications in the field of computational biophysics. In fact, the vast amount of available molecular structures, as well as their notable complexity, constitutes an ideal context in which DL-based approaches can be profitably employed. To express the full potential of these techniques, though, it is a prerequisite to express the information contained in a molecule’s atomic positions and distances in a set of input quantities that the network can process. Many of the molecular descriptors devised so far are effective and manageable for relatively small structures, but become complex and cumbersome for larger ones. Furthermore, most of them are defined locally, a feature that could represent a limit for those applications where global properties are of interest. Here, we build a DL architecture capable of predicting non-trivial and intrinsically global quantities, that is, the eigenvalues of a protein’s lowest-energy fluctuation modes. This application represents a first, relatively simple test bed for the development of a neural network approach to the quantitative analysis of protein structures, and demonstrates unexpected use in the identification of mechanically relevant regions of the molecule.

Probabilistic analysis of two-dimensional vector random processes on the phase plane

Introduction: The models of vector random processes are characterized by a variety of practical applications and, at the same time, by the complexity of studying the detailed probabilistic structure. Such features often lead to considering only separate components of vector functions, forcing the shift to scalar process analysis. All this significantly reduces the overall information content of the research, increasing the relevance of the search for promising approaches to probabilistic analysis of vector processes. Purpose: To present vector random processes in a phase space of states, and to apply the general theory of level crossings of random functions to the study of probabilistic structure of phase trajectories. Results: We have identified the characteristic features of displaying random processes on a phase plane, and introduced numerical characteristics for the description and analysis of probabilistic behavior of sample functions. A probabilistic analysis has been performed for the characteristics of the «level crossing» type for vector processes with various definitions of the areas of acceptable values. We used the typical models of two-dimensional Gaussian processes and «signal plus noise» models to demonstrate how the probabilistic structure of the phase trajectories depends on the given threshold levels, major distribution parameters and spectral-correlation properties of the studied processes. Practical relevance : The article contributes to the research information content and its visualization in the analysis of probabilistic behavior of vector random processes. It combines general methods of phase space of vector processes, methods of phase plane in the analysis of scalar processes and the theory of level crossings of random functions. The classical approaches to the visual description of phase trajectories are supplemented by the methods of quantitative analysis of detailed probabilistic structure of random functions.