Two-dimensional Variation Research Articles

Modeling the two-dimensional variations in EEG signals to analyze the impact of music on sleep states

Variations in music intensity and pitch can significantly impact sleep and alleviate insomnia through relaxing music. Traditional EEG analysis methods struggle with capturing temporal features and managing time-series data complexity. To address these challenges, we propose an improved Temporal Network model integrated with a Temporal Self-Attention (TSA) mechanism. This model enhances time-step feature capture in EEG signals, transforming one-dimensional EEG data into two-dimensional tensors to capture multi-scale temporal features. Experiments on the DEAP dataset demonstrate significant performance improvements, with 84.26% accuracy, 90.06% precision, and 97.82% recall, outperforming current models. Our model effectively analyzes the impact of relaxing music on different sleep stages, providing insights for improving sleep quality. Future work will optimize the model structure, incorporate additional deep learning techniques, and expand the scope to include multiple physiological signals, aiming to enhance the clinical value for sleep disorder diagnosis and personalized music therapy.

Salinity distribution in agricultural land by geophysical, hydrochemical and geostatistical approaches: a pilot area located in Qelabshowah–Belqas, East Nile Delta region, Egypt

The study area is situated in the Qelabshowah–Belqas region, known for its Quaternary deposits. This research aims to demonstrate the two-dimensional (2D) variation of subsurface layers and salinity distribution using geoelectrical data, hydrochemical analysis, and geostatistical analysis. DC resistivity measurements were taken at fifteen vertical electrical sounding (VES) survey points using a Schlumberger array (AB/2 = 100 m) along three profiles. In addition, an electrical resistivity tomography (ERT) survey was conducted with a dipole–dipole array across one profile. Seven surface water samples were collected in the area. From the 1D and 2D inversion of VES and ERT data sets, three-to-four geoelectric layers were identified, including unconsolidated surface deposits, saturated clayey sand, saturated sand, and a salt-rich layer. The 2D inversion of VES data revealed an ancient salt-rich layer deposited in swampy conditions over a conductive wet sand layer along profile one due to salt mineral infiltration and dissolution. The 2D inversion of ERT data showed accurate lateral geometric accuracy compared to the 2D inversion of VES data, highlighting geological features, such as caves in the second layer and a buried water canal on the ground surface. Surface water samples showed high salinity levels with sodium hazards, indicating an Na–Cl composition. Geoelectric and hydrochemical data sets were geostatistically analyzed using spherical variogram supported ordinary Kriging interpolation. The analysis indicated weak to moderate spatial dependency for true resistivity parameters, while sodium content (SC) and permeability index (PI) showed strong spatial correlation. The 2D spatial distribution resistivity maps based on the 1D inversion of VES data displayed a general decrease in resistivity with depth, likely due to clay minerals or moist soil in the second layer and saline irrigation water infiltration in the third layer. The 2D spatial distribution of SC and PI showed a high concentration zone, posing a potential risk to agricultural crops regardless of soil permeability. It is recommended to use these maps when cultivating plants that can tolerate high sodium levels during the reclamation process.

On simulating diffusional phase transformation in diffusion triple

Diffusion triple technique (stand-alone or composed diffusion multiples) is crucial for high-throughput construction of phase diagrams or extracting diffusion coefficients, taking advantage of the broad two-dimensional (2D) composition variations. However, currently there is a lack of methods available for simulating 2D diffusion accompanied by phase transformations inside diffusion triples. In the present work, we take a noticeable step forward by simulating diffusional phase transformation between the contacting interfaces, especially in the tri-junction of diffusion triple. The present method is an extension of the homogenization model (H. Larsson and L. Höglund, Calphad, 33 (2009) 495–501) to 2D simulations, allowing for disclosure of microstructure evolutions in diffusion triples. The practicability of the present method is demonstrated by comparing the simulation results with the experiment of a Fe-Cr-Ni diffusion triple (as a part of a multiple) from the literature.

Quantitative 2D fruit shape analysis of a wide range of pear genetic resources toward shape design breeding

The shape of a fruit is one of the main characteristics of fruit morphology, and its quantitative description is crucial to improve fruit quality. However, the shape of a pear fruit is relatively complex, and difficult to describe comprehensively. This study aimed to quantitatively analyze the morphological diversity of 2D fruit shapes of 276 cultivars, covering 6 groups including Pyrus pyrifolia, Pyrus bretschneideri, Pyrus ussuriensis, Pyrus sinkiangensis, Pyrus communis and interspecific hybridization, and discover shape traits with high heritability. Through an automated image processing method, the fruit contour was first accurately extracted, and then geometrical parameters and Fourier descriptors of the pear fruit shape were obtained. Furthermore, principal components (PCs) of the Fourier descriptors were analyzed, and the broad-sense heritability (H2) of the PCs and standardized width (WSD) were estimated. After that, the pear shape stability was calculated, and cultivars were clustered by their shape characteristics. This paper mainly discusses the longitudinal section, as the cross-section variation among cultivars is small. For the longitudinal section, the results showed more than 95 % of the two-dimensional shape variation can be explained by only six principal components; WSD20, WSD30 and PC1 have high H2; the shape stability of western pear was the lowest; a new class of shape was found by clustering the shape traits. The results indicated that the proposed pipeline can provide an objective and comprehensive quantitative description of pear fruit shape for a wide range of cultivars, which is necessary to discover the key genes determining pear shape. This approach is also beneficial for research on pear breeding and germplasm resource management.

Quantitative Analysis of Fish Morphology Through Landmark and Outline-based Geometric Morphometrics with Free Software.

Morphology underpins key biological and evolutionary processes that remain elusive. This is in part due to the limitations in robustly and quantitatively analyzing shapes within and between groups in an unbiased and high-throughput manner. Geometric morphometrics (GM) has emerged as a widely employed technique for studying shape variation in biology and evolution. This study presents a comprehensive workflow for conducting geometric morphometric analysis of fish morphology. The step-by-step manual provides detailed instructions for using popular free software, such as the TPS series, MorphoJ, ImageJ, and R, to carry out generalized Procrustes analysis (GPA), principal component analysis (PCA), discriminant function analysis (DFA), canonical variate analysis (CVA), mean shape analysis, and thin plate spline analysis (TPS). The Momocs package in R is specifically utilized for in-depth analysis of fish outlines. In addition, selected functions from the dplyr package are used to assist in the analysis. The full process of fish outline analysis is covered, including extracting outline coordinates, converting and scaling data, defining landmarks, creating data objects, analyzing outline differences, and visualizing results. In conclusion, the current protocol compiles a detailed method for evaluating fish shape variation based on landmarks and outlines. As the field of GM continues to evolve and related software develops rapidly, the limitations associated with morphological analysis of fish are expected to decrease. Interoperable data formats and analytical methods may facilitate the sharing of morphological data and help resolve related scientific problems. The convenience of this protocol allows for fast and effective morphological analysis. Furthermore, this detailed protocol could be adapted to assess image-based differences across a broader range of species or to analyze morphological data of the same species from different origins. Key features • This protocol provides a comprehensive set of commonly used GM-analyzing methods and visualizing skills plus supporting information to help assess the appropriate analysis method • By incorporating both landmarks and outlines, this protocol facilitates a thorough analysis of two-dimensional shape variation in fish, covering a wide range of morphological features • The simplified workflow and detailed procedures make it accessible for non-experienced users to successfully complete the analysis while also providing valuable insights for experienced users Graphical overview Workflow for conducting geometric morphometrics analysis on fish. The steps include image acquisition as data sources, digitization of fish morphology using landmark-based methods, analysis of shape variation characteristics, and visualization of the results in relation to biological interpretation. Largemouth bass (Micropterus salmoides) is used as an example in the schematic representation.

Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System

In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor. By using fractional calculus theory and the Adomian numerical algorithm, special bifurcations, chaotic degradation, C0 and Spectral Entropy (SE) complexity under one-dimensional and two-dimensional parameter variations with different orders, parameters and initial memristor values of the system were studied. Meanwhile, in order to better utilize the applications of fractional-order memristor systems in communication and security, a misalignment projection synchronization scheme for fractional-order systems is proposed, which overcomes the shortcomings of constructing Lyapunov functions for fractional-order systems to prove stability and designing controllers for the Laplace transform matrix.

Two-dimensional patterning of mesoscale fibers using acoustophoresis

The performance of functional composites can rely critically on the arrangement of secondary phases; for example, patterned networks of conductive particles can impart anisotropic thermal, electric or ionic conductivity while preserving flexibility in the matrix. We demonstrate the use of standing acoustic waves to generate periodic patterns of short fibers. We extend the range of possible patterns with the first demonstration of both rectangular grids and arrays of octagons interspersed with rectangles. These newly demonstrated patterns are rationalized using theoretical models of acoustic forces and torques on fibers that account for two-dimensional spatial variations arising from applied acoustic fields. The models enable simulations of fiber motion, which are used to (i) map out final fiber positions as a function of initial position and orientation, and (ii) corroborate experiments visualizing fiber motion and final patterns. This approach provides a fast and accurate way to predict emergent fiber patterns as a function of excitation modality and fiber length. The theory and experiments clearly indicate strong coupling between the length of the fibers and the spacing of the acoustic nodes. This coupling is used to estimate reductions in percolation thresholds associated with the ratio of fiber length and acoustic wavelength.

An Improved UAV Bi-SAR Imaging Algorithm with Two-Dimensional Spatial Variant Range Cell Migration Correction and Azimuth Non-Linear Phase Equalization

The transmitter and receiver of unmanned aerial vehicle (UAV) bistatic synthetic aperture radar (Bi-SAR) are respectively carried on different UAV platforms, which has the advantages of flexible movement and strong concealment, and has broad application prospects in remote sensing fields. However, the range cell migration (RCM) and azimuth non-linear phase (ANP) of UAV Bi-SAR are seriously spatially variant along the range and azimuth directions, while the UAV Bi-SAR has a short operating range, complex trajectory and wide azimuth beam. Aiming at the problem that the RCM and ANP of UAV Bi-SAR in spotlight mode are difficult to correct and equalize due to the severe two-dimensional (2D) spatial variation, an RCM correction (RCMC) and ANP equalization (ANPE) method based on Doppler domain blocking is proposed. First, the azimuth spatial variance of RCM is eliminated by Doppler blocking, and the range spatial variant RCMC is realized by RNCS. Second, by combining Doppler blocking with azimuth nonlinear chirp scaling (ANCS), this method can adapt to ANPE with larger width and more severe spatial variation. At last, the criteria of Doppler blocking are given in detail, and the effectiveness of the proposed method is verified by UAV Bi-SAR real data and computer simulation.

Development of two-dimensional temperature field solution method based on the stress–strain response of 316LN stainless steel at cryogenic temperatures

To better understand the tensile fracture behavior and temperature variation during the tension testing of the 316LN at cryogenic temperatures, a two-dimensional temperature field solution method is developed based on two-dimensional strain field measured by the digital image correlation technology combined with the Taylor Quinney coefficient model and the intrinsic model of strain-induced martensitic phase transformation. The method allows for visualization of the strain field and temperature variation of the 316LN austenitic stainless steel at cryogenic temperature. By numerical simulation, the localized temperature elevation of the 316LN is determined to be 13.3 K during the tensile test at 77 K, which is in good agreement with the experimental result of 10.2 K. This model reconstructed the two-dimensional temperature field variation throughout the entire tensile test, which is beneficial for facilitating the analysis of the mutual relation between the mechanical properties and microstructural evolution of the 316LN and other metastable austenitic stainless steels in cryogenic temperatures.

THz Imaging to Map the Lateral Microporosity Distribution in Carbonate Rocks

Terahertz (THz) spectroscopy is a nondestructive tool used in many industries to analyze materials, including measuring the water content and the distribution of water in biological samples. THz time-domain spectroscopy (THz-TDS) measures the dielectric and structural properties of a sample by probing it with an ultrafast THz pulse and measuring the change in amplitude and phase. In this study, we demonstrate the use of THz-TDS imaging to quickly map lateral (i.e., two-dimensional) variations in microporosity (ϕμ) using the THz attenuation due to water in the pores after clearing the large pores via centrifugation. Three carbonate rock plugs with differing ϕ and pore-size distributions were subsampled for this study. Three water saturation states were produced for each sample: saturated, centrifuged, and dry. At each saturation state, the sample is weighed and imaged using THz-TDS to spatially map and measure ϕμ. The results show that for each sample the ϕμ obtained using THz-TDS imaging is in excellent agreement with that obtained from both mass balance and MICP. In addition, the THz-TDS maps show significant differences in the spatial distribution of the microporosity for samples having similar composition. This method provides a means to measure ϕ and ϕμ while mapping the spatial distribution of ϕμ toward improved petrophysical characterization of carbonate reservoir rocks.

Influence of two-dimensional expiratory airflow variations on respiratory particle propagation during pronunciation of the fricative [f

Propagation of respiratory particles, potentially containing viable viruses, plays a significant role in the transmission of respiratory diseases (e.g., COVID-19) from infected people. Particles are produced in the upper respiratory system and exit the mouth during expiratory events such as sneezing, coughing, talking, and singing. The importance of considering speaking and singing as vectors of particle transmission has been recognized by researchers. Recently, in a companion paper, dynamics of expiratory flow during fricative utterances were explored, and significant variations of airflow jet trajectories were reported. This study focuses on respiratory particle propagation during fricative productions and the effect of airflow variations on particle transport and dispersion as a function of particle size. The commercial ANSYS-Fluent computational fluid dynamics (CFD) software was employed to quantify the fluid flow and particle dispersion from a two-dimensional mouth model of sustained fricative [f] utterance as well as a horizontal jet flow model. The fluid velocity field and particle distributions estimated from the mouth model were compared with those of the horizontal jet flow model. The significant effects of the airflow jet trajectory variations on the pattern of particle transport and dispersion during fricative utterances were studied. Distinct differences between the estimations of the horizontal jet model for particle propagation with those of the mouth model were observed. The importance of considering the vocal tract geometry and the failure of a horizontal jet model to properly estimate the expiratory airflow and respiratory particle propagation during the production of fricative utterances were emphasized.

Influence of geomechanics parameters on stress sensitivity in fractured reservoir

The complex fractures aggravate stress sensitivity and heterogeneity of the reservoir and seriously restrict effective development. Therefore, it is of great significance to study and quantitatively evaluate the stress sensitivity of the fractured reservoir. Taking the typical block of the Longmaxi shale reservoir in southern Sichuan as the engineering background, one uses the finite element method to develop a numerical model of a two-dimensional fracture closure variation subjected to the non-hydrostatic stress field. It explores the influence of different fracture occurrences and rock mechanical parameters on stress sensitivity. The theoretical model verifies the numerical simulation results to reveal the stress sensitivity mechanism of the fractured reservoir. The results show that the influence of the dip angle of fracture on the stress sensitivity depends on the anisotropy of applied in-situ stresses. The stronger stress sensitivity occurs in low-dip angles where the lateral pressure coefficient is less than 1. One defines the lateral pressure coefficient. On the contrary, the stronger stress sensitivity occurs in high-dip angles where the lateral pressure coefficient is more significant than 1. It is because the normal stress differences under different stress fields apply to the fracture. Under a given stress condition, the stress sensitivity of fracture negatively correlates with aspect ratio, elastic modulus, and Poisson’s ratio. Pressure maintenance may be more critical in a reservoir with a low aspect ratio and rich in soft minerals. The theoretical predicting model of fracture permeability under different conditions is established based on the linear elastic theory. The relative error between theoretically predicted results and numerical simulation ones is less than 10%, which verifies the accuracy of numerical simulation results. The fundamental reason for stress sensitivity in the fractured reservoir is the fracture geometry and mineral deformation change. The research results are of great significance for establishing the productivity equation considering the stress sensitivity, accurately evaluating the variation of reservoir seepage capacity, and formulating reasonable drainage and production system.

PP-wave reflection coefficient for vertically cracked media: Single set of aligned cracks

The main goal is to analyze the influence of cracks on the azimuthal variations of amplitude. We restrict our investigation to a single set of vertical, circular, and flat cavities aligned along a horizontal axis. Such cracks are embedded in either transversely isotropic background with a vertical symmetry axis (VTI) or isotropic surroundings. We employ the effective medium theory to obtain either orthotropic or VTI homogenised medium, respectively. To consider the amplitudes, we focus on a Vavrycuk-Psencik approximation of the PP-wave reflection coefficient. We assume that cracks are situated in one of the halfspaces only.Azimuthal variations depend on the background stiffnesses, incidence angle, and crack density parameter. Upon analytical analysis, we indicate which factors (such as background’s saturation) cause the reflection coefficient to have maximum absolute value in the direction parallel or perpendicular to cracks. We discuss the irregular cases, where such extreme values appear in the other than the aforementioned directions.Due to the support of numerical simulations, we propose graphic patterns of two-dimensional amplitude variations with azimuth. The patterns consist of a series of shapes that change with the increasing value of the crack density parameter. Schemes appear to differ depending on the incidence angle and the saturation. Finally, we extract these shapes that are characteristic of gas-bearing rocks. They may be treated as gas indicators. We support the findings and verify our patterns using real values of stiffnesses extracted from the sedimentary rocks’ samples.

A Modified NLCS Algorithm for High-Speed Bistatic Forward-Looking SAR Focusing with Spaceborne Illuminator

The coupling and spatial variation of range and azimuth parameters is the biggest challenge for bistatic forward-looking SAR (BFSAR) imaging. In contrast with the monostatic SAR and translational invariant bistatic SAR (TI-BSAR), the range cell migration (RCM), and Doppler parameters of high-speed bistatic forward-looking SAR (HS-BFSAR) have two-dimensional spatial variation characteristics, which makes it difficult to obtain SAR images with satisfactory global focusing. Firstly, based on the configuration of the spaceborne illuminator and high-speed forward-looking receiving platform, the accurate range-Doppler domain expression of the echo signal is derived in this paper. Secondly, using this analytical expression, a range nonlinear chirp scaling (NLCS) is proposed to equalize the RCM and equivalent range frequency modulation (FM) rate so that they can be uniformly processed in the two-dimensional frequency domain. Next, in the azimuth processing, the proposed method decomposes the Doppler contribution of the transmitter and receiver, respectively. Then, an azimuth NLCS is used to eliminate the spatial variation of the azimuth FM rate. Finally, a range-dependent azimuth filter is constructed to achieve azimuth compression. Simulation results validate the efficiency and effectiveness of the proposed algorithm.

Phase-regularized and displacement-regularized compressed sensing for fast magnetic resonance elastography.

Liver magnetic resonance elastography (MRE) is a noninvasive stiffness measurement technique that captures the tissue displacement in the phase of the signal. To limit the scanning time to a single breath-hold, liver MRE usually involves advanced readout techniques such as simultaneous multislice (SMS) or multishot methods. Furthermore, all these readout techniques require additional in-plane acceleration using either parallel imaging capabilities, such as sensitivity encoding (SENSE), or -space undersampling, such as compressed sensing (CS). However, these methods apply a single regularization function on the complex image. This study aims to design and evaluate methods that use separate regularization on the magnitude and phase of MRE to exploit their distinct spatiotemporal characteristics. Specifically, we introduce two compressed sensing methods. The first method, termed phase-regularized compressed sensing (PRCS), applies a two-dimensional total variation (TV) prior to the magnitude and two-dimensional wavelet regularization to the phase. The second method, termed displacement-regularized compressed sensing (DRCS), exploits the spatiotemporal redundancy using 3D total variation on the magnitude. Additionally, DRCS includes a displacement fitting function to apply wavelet regularization to the displacement phasor. Both DRCS and PRCS were evaluated with different levels of compression factors in three datasets: an in silico abdomen dataset, an in vitro tissue-mimicking phantom, and an in vivo liver dataset. The reconstructed images were compared with the full sampled reconstruction, zero-filling reconstruction, wavelet-regularized compressed sensing, and a low rank plus sparse reconstruction. The metrics used for quantitative evaluation were the structural similarity index (SSIM) of magnitude (M-SSIM), displacement (D-SSIM), and shear modulus (S-SSIM), and mean shear modulus. Results from highly undersampled in silico and in vitro datasets demonstrate that the DRCS method provides higher reconstruction quality than the conventional compressed sensing method for a wide range of stiffness values. Notably, DRCS provides 24% and 22% increase in D-SSIM compared with CS for the in silico and in vitro datasets, respectively. Comparison with liver stiffness measured from full sampled data and highly undersampled data (CR=4) demonstrates that the DRCS method provided the strongest correlation ( =0.95), second-lowest mean bias (-0.18 kPa, lowest for CS with -0.16 kPa), and lowest coefficient of variation (CV=3.6%). Our results demonstrate the potential of using DRCS to improve the reconstruction quality of accelerated MRE.

Empirical comparison of time series models and tensor product penalised splines for modelling spatial dependence in plant breeding field trials.

Plant breeding field trials are typically arranged as a row by column rectangular lattice. They have been widely analysed using linear mixed models in which low order autoregressive integrated moving average (ARIMA) time series models, and the subclass of separable lattice processes, are used to account for two-dimensional spatial dependence between the plot errors. A separable first order autoregressive model has been shown to be particularly useful in the analysis of plant breeding trials. Recently, tensor product penalised splines (TPS) have been proposed to model two-dimensional smooth variation in field trial data. This represents a non-stochastic smoothing approach which is in contrast to the autoregressive (AR) approach which models a stochastic covariance structure between the lattice of errors. This paper compares the AR and TPS methods empirically for a large set of early generation plant breeding trials. Here, the fitted models include information on genetic relatedness among the entries being evaluated. This provides a more relevant framework for comparison than the assumption of independent genetic effects. Judged by Akaike Information Criteria (AIC), the AR models were a better fit than the TPS model for more than 80% of trials. In the cases where the TPS model provided a better fit it did so by only a small amount whereas the AR models made a substantial improvement across a range of trials. When the AR and TPS models differ, there can be marked differences in the ranking of genotypes between the two methods of analysis based on their predicted genetic effects. Using the best fitting model for a trial as the benchmark, the rate of mis-classification of entries for selection was greater for the TPS model than the AR models. This has important practical implications for breeder selection decisions.

Two-dimensional variations of the coda Q in Northern Morocco and their interpretation

Two-dimensional variations of the coda Q in Northern Morocco and their interpretation

Effect of thermal environment on the asymmetric vibration of temperature-dependent two-dimensional functionally graded annular plate by Chebyshev polynomials

In the present paper, an accurate numerical technique is employed to analyze the effect of two-dimensional temperature variation on the free asymmetric vibrations of functionally graded (FG) annular plates using the first-order shear deformation theory. The temperature-dependent mechanical properties of the plate material are graded along the thickness and radial directions. The governing differential equations for asymmetric motion are derived from Hamilton’s principle and the exact solution for the two-dimensional heat conduction equation is obtained using the separation of variables method considering thermal boundary conditions. The Chebyshev collocation technique is adopted to compute the numerical values of fundamental frequency for different boundary conditions. The impact of volume fraction index, heterogeneity parameter, density parameter, nodal lines, radii ratio, and thermal boundary conditions on the frequencies of the plate is investigated. An excellent agreement between the results obtained by the present approach and other methods available in the literature validated the authors’ model and technique. Three-dimensional normalized mode shapes with different nodal lines are illustrated for the specified plates.

Deformed WZW models and Hodge theory. Part I

We investigate a relationship between a particular class of two-dimensional integrable non-linear σ-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the λ-deformed G/G model and show that a special class of solutions to its equations of motion precisely describes a one-parameter variation of Hodge structures. We find that this special class is obtained by identifying the group-valued field of the σ-model with the Weil operator of the Hodge structure. In this way, the study of strings on classifying spaces of Hodge structures suggests an interesting connection between the broad field of integrable models and the mathematical study of period mappings.

Time Period of Thermal-Induced Vibration of Skew Plate with Two-Dimensional Circular Thickness

In this study, two-dimensional circular thickness effects on time period of skew plate made with nonhomogeneous material properties are computed in variable temperature environment. Clamped C , simply supported S , and free-edge F conditions are the various combinations considered in this work. One-dimensional circular density and two-dimensional parabolic temperature variation on the plate are considered due to the nonhomogeneous nature of the material and variable temperature environment. Rayleigh–Ritz method is used to compute the time period for the first two modes of vibration. A convergence study of frequency modes of skew plate on various edge conditions has also been performed. The present work has been compared with the frequency modes of parallelogram and rectangle plate on various edge conditions. The objective of the study is to present a numerical data of time period as well as to show how one can control the frequencies of plate by taking an appropriate variation in plate parameters.