Potential Discontinuities Research Articles

A critical evaluation of regression discontinuity studies in school effectiveness research

ABSTRACT School start regulations allocate children born immediately either side of a given date to different life paths: those slightly older starting school a full year earlier. School effectiveness literature exploits this to estimate causal effects described as ‘the absolute effect of schooling’ or ‘the effect of an additional year's schooling’, using the logic of regression discontinuity (RD). This paper examines the causal arguments and assumptions underpinning RD, noting particularly the importance of the causal description. It highlights concerns with describing causes in terms of school effectiveness including failure to consider the alternative treatment pathway; presence of other post-allocation causal factors and potential discontinuities at allocation. The paper notes that these can be overcome by using wider causal descriptions but at the expense of no longer identifying school effectiveness.

A detailed quartz and feldspar luminescence chronology for the Khonako II loess section (Southern Tajikistan)

Parts of Central Asia have been dominated by high dust flux since the start of the Quaternary. The resulting loess-palaeosol deposits are important archives for landscape and climate changes, but there is a lack of chronological data for the subaerial deposits of Southern Tajikistan. Our study presents a high-resolution luminescence chronology for the Khonako II section in the Khovaling region. Thirty-seven samples were collected from the first ∼8 m of the section, corresponding to the Holocene soil and the upper part of the Loess 1 (L1) unit. We applied quartz OSL dating to the coarse-silt fraction (40–63 μm) and polymineral pIRIR200,290 dating to the very fine sand fraction (63–90 μm). The polymineral pIRIR200,290 signal has satisfactory characteristics. The quartz dose response curve displays a non-single exponential growth above ∼100 Gy, thus, the De values were estimated by fitting a single exponential function plus linear component to the dose response data. To assess the pIRIR200,290 residual dose at deposition, we used the offset between our quartz and polymineral chronologies from Khonako II and equivalent doses measured on modern dust samples from Tajikistan and Uzbekistan. The resulting 9.2 ± 0.4 Gy dose was then subtracted from the pIRIR200,290 doses for final age calculation. The quartz OSL and pIRIR ages are then generally consistent. The obtained high-resolution luminescence chronology shows that the upper part of the L1 unit accumulated during the end of marine isotope stage (MIS) 3 and through MIS 2 (39–20 ka). The average dust accumulation rates (DAR) increased from ∼31 cm ka−1 to 41 cm ka−1 between MIS 3 and MIS 2. The DAR reached a peak of ∼71 cm ka−1 at 21 ka. A hiatus of ∼7–9 ka was then identified between the end of the last glacial maximum (LGM) and the beginning of the Holocene, and the average DAR decreased during the Holocene. Our results indicate a continuous high dust flux in the Khovaling plateau over the last 39 ka, but reworking processes and potential deflation events mark the LGM-Holocene transition. High-resolution luminescence dating studies in Tajikistan are therefore important to detect potential discontinuities in the sequences and provide an independent timescale for interpreting the climate proxies and calculating dust accumulation rates.

Fracture Analysis of Planar Cracks in 3D Thermal Piezoelectric Semiconductors

The study of piezoelectric semiconductor (PSC) materials and devices is experiencing rapid growth, giving rise to a burgeoning research domain known as piezotronics. Understanding the fracture behavior of PSC materials is essential for designing robust devices and ensuring their long-term functionality. A planar crack of arbitrary shape in the isotropic plane of a three-dimensional (3D) transversely isotropic thermal PSC body subjected to combined thermal-electrical-mechanical loadings is studied via the extended displacement discontinuity (EDD) boundary integral equation method. Under the framework of linearized basic equations and one-way thermal coupling, the hypersingular boundary integral equations with the volume integrals containing the temperature and carrier concentration are obtained and expressed by the EDDs which include displacement, electric potential, carrier concentration and temperature discontinuities across the crack surfaces and are the basic variables in analyzing crack problems. Based on the finite part of hypersingular integrals, the EDDs near the crack border are proved to have the classical behavior of O(r). Furthermore, the asymptotic solutions of extended stresses including the stress, electric displacement, current density and heat flux at the crack front are presented and display classical singular behavior of O(1/r). The extended stress intensity factors are defined and given in terms of EDDs. A 3D numerical model of a penny-shaped crack in the thermal PSC cylinder is established and used to verify the presented formulae.

STUDY OF GEOMETRIC UNSHARPNESS PHENOMENON IN WELDED PLATES USING INDUSTRIAL RADIOGRAPHY METHOD

The purpose of this document is to elucidate the methodology employed in analyzing the impact of unsharpness resulting from an X-ray generator on the assessment of steel welded joints. The presence of unsharpness significantly affects the accuracy of welded joint inspections conducted through industrial radiographic techniques, distorting actual measurements of potential discontinuities within the weld. To address this issue, a series of welded joint testing specimens were fabricated using a Shielded Metal Arc Welding (SMAW) process. Each specimen was intentionally designed to contain simulated discontinuities whose dimensions adhered to the acceptance or rejection criteria outlined in the API 1104 standard. Subsequently, radiographic testing was conducted on each specimen, and the dimensions of the simulated discontinuities captured on the radiographic films were measured using the "ISee!" software, as recommended by the ASTM E1165 standard. Upon comparison of the actual and theoretical measurements, it was observed that the maximum unsharpness along the X-axis was recorded in specimens featuring elongated slag inclusions (ESI), with a value of 0.1948 mm. Conversely, the maximum unsharpness along the Y-axis was attributed to individual porosities (P), with a recorded value of 0.1041 mm.

Smoothing Splines for Discontinuous Signals

Smoothing splines are twice differentiable by construction, so they cannot capture potential discontinuities in the underlying signal. In this work, we consider a special case of the weak rod model of Blake and Zisserman that allows for discontinuities penalizing their number by a linear term. The corresponding estimates are cubic smoothing splines with discontinuities (CSSD) which serve as representations of piecewise smooth signals and facilitate exploratory data analysis. However, computing the estimates requires solving a non-convex optimization problem. So far, efficient and exact solvers exist only for a discrete approximation based on equidistantly sampled data. In this work, we propose an efficient solver for the continuous minimization problem with non-equidistantly sampled data. Its worst case complexity is quadratic in the number of data points, and if the number of detected discontinuities scales linearly with the signal length, we observe linear growth in runtime. This efficient algorithm allows to use cross-validation for automatic selection of the hyperparameters within a reasonable time frame on standard hardware. We provide a reference implementation and supplementary material. We demonstrate the applicability of the approach for the aforementioned tasks using both simulated and real data. Supplementary materials for this article are available online.

The apparent effusivity method for normalized thermal contrast evaluation in infrared thermographic testing

Thermographic nondestructive testing is used for the detection of near-surface discontinuities in materials, where indications of potential defects or discontinuities are detected and evaluated by their thermal contrast. The key requirements for successful thermographic data processing include managing non-uniform heating and identifying nominal areas. Advanced methods often rely on numerical simulation, which can be challenging and time-consuming. This study suggests a new simple method of thermal contrast calculation for flash-pulse thermography. It is based on the analysis of the inverse apparent effusivity. It includes an automated indication of the sound (defect-free) area and the creation of an artificial reference sequence, which is based on a temperature profile of the sound area and the non-uniform heating map. Derivative analysis of the smoothed contrast data is applied to improve detectability and Contrast/Noise Ratio (CNR). An experimental comparison of the proposed method with other known methods is presented. In the presented example, it allowed detection of 23 defects with an average CNR of 6.13 dB, against the traditional differential absolute contrast method, which detected only 13 defects with an average CNR of 0.53 dB. Thus, high detectability and high CNR values provided by the proposed method are demonstrated.

Estimation of Daily Seamless PM2.5 Concentrations with Climate Feature in Hubei Province, China

The urgent necessity for precise and uninterrupted PM2.5 datasets of high spatial–temporal resolution is underscored by the significant influence of PM2.5 on weather, climate, and human health. This study leverages the AOD reconstruction method to compensate for missing values in the MAIAC AOD throughout Hubei Province. The reconstructed AOD dataset, exhibiting an R2/RMSE of 0.76/0.18, compared to AERONET AOD, was subsequently used for PM2.5 estimation. Our research breaks from traditional methodologies that solely depend on latitude and longitude information. Instead, it emphasizes the use of climate feature as an input for estimating PM2.5 concentrations. This strategic approach prevents potential spatial discontinuities triggered by geolocation information (latitude and longitude), thus ensuring the precision of the PM2.5 estimation (sample/spatial CV R2 = 0.91/0.88). Moreover, we proposed a method for identifying the absolute feature importance of machine-learning models. Contrasted with the relative feature-importance property typical of machine-learning models (a minor difference in the order of top three between geolocation-based and climate-feature-based models, and the slight difference in the top three: 0.08%/0.17%), our method provides a more comprehensive explanation of the absolute significance of features to the model (maintaining the same order and a larger difference in the top three: 0.99%/0.72%). Crucially, our findings demonstrated that AOD reconstruction can mitigate the overestimation of annual mean PM2.5 concentrations (ranging from 0.52 to 9.28 µg/m3). In addition, the seamless PM2.5 dataset contributes to reducing the bias in exposure risk assessment (ranging from −0.11 to 9.81 µg/m3).

An adaptive time stepping scheme for rate-independent systems with nonconvex energy

Abstract We investigate a local incremental stationary scheme for the numerical solution of rate-independent systems. Such systems are characterized by a (possibly) nonconvex energy and a dissipation potential, which is positively homogeneous of degree one. Due to the nonconvexity of the energy, the system does in general not admit a time-continuous solution. In order to resolve these potential discontinuities, the algorithm produces a sequence of state variables and physical time points as functions of a curve parameter. The main novelty of our approach in comparison to existing methods is an adaptive choice of the step size for the update of the curve parameter, depending on a prescribed tolerance for the residua in the energy-dissipation balance, and in a complementarity relation concerning the so-called local stability condition. It is proven that, for tolerance tending to zero, the piecewise affine approximations generated by the algorithm converge (weakly) to a so-called parametrized balanced viscosity solution. Numerical experiments illustrate the theoretical findings, and show that an adaptive choice of the step size indeed pays off as they lead to a significant increase of the step size during sticking and in viscous jumps.

Relationship between fissility, composition, rock fabric and reservoir properties in Vaca Muerta Formation (Neuquén Basin, Argentina): from outcrop to subsurface core data

The fissility is the ability of some rocks to split along relatively smooth surfaces parallel to the bedding. This property observed mostly in fine-grained rocks is particularly expressed in outcrops, where rocks are subjected to weathering processes. Most authors associate the fissility to the abundance of clay minerals and their orientation parallel to the bedding. The horizontal fabric can be promoted by depositional conditions such as sediment composition, quantity of total organic carbon content (TOC) and depositional mechanisms, giving rise to a primary fissility. Alternatively, the alignment of platy minerals can be linked to the burial history of the rock, by processes such as mechanical compaction or secondary mineral growth, resulting in a secondary fissility. The present study aims to identify the main controls of fissility development at the micro- and macroscopic scale in rocks of the Vaca Muerta Formation exposed in the Cerro Mulichinco area and in a 121-meter-long core extracted from a well within the Neuquén Basin. In outcrops, fissility is related to fine-grained laminated facies with low carbonate content, revealing the strong control exerted by lithology. The TOC measurements allow establishing a positive correlation between organic matter content and fissility intensity. Moreover, the analysis of the transgressive-regressive cycles shows that fissility is higher around the maximum flooding surfaces. Regarding their mechanical characteristics, the different interfaces observed in core are classified into first and second-order, the last one including fissility planes. Some of these interfaces evolve from potential (partially open) to effective (totally open) discontinuities in response to changes of stress conditions during the core extraction and due to the stress relaxation through time: weeks (T1), months (T2) and years (T3) after extraction. The time evolution of the effective core discontinuities points out rock intervals that are variably broken and core segments that remain intact. The Drying Alcohol Discontinuities (DAD) methodology reveals potential discontinuities within apparently intact core segments. By using this technique, a 4-class index is established as a proxy for fissility degree. When integrated with geological, petrophysical and geomechanical data, this index enables characterizing the main mechanisms controlling rock fissility that express through discontinuities promoting the loss of competence of a rock. Consequently, this mechanical property is considered to influence the efficiency of hydraulic fracture in shale reservoir completion.

The synergistic impact of market and technology orientations on sustainable innovation performance: evidence from manufacturing firms

PurposeThe purpose of this study is to identify groups of manufacturing firms having different combinations of strategic orientation (market and technology orientations) and compare the viable groups for differences in their sustainable innovation (SI) performance.Design/methodology/approachA sample of 373 Italian manufacturing firms is clustered (using non-hierarchical cluster analysis) based on their combinations of market orientation (MO) and technology orientation (TO). Subsequently, the one-way between-groups analysis of variance (ANOVA) with post-hoc tests is conducted to detect how the resulting groups differ in their SI performance.FindingsThe synergistic co-alignment of TO with both dimensions of MO (i.e. responsive and proactive) can help firms enhance their performance regarding SI. Amongst the groups of manufacturing firms identified in the context of this research, ‘future-oriented entrepreneurs’ appear to represent the strongest combination of MO with TO, leading them to achieve higher levels of SI performance.Research limitations/implicationsThis study, by referring to a survey-based empirical study of manufacturing firms in Italy, extends the literature by arguing that higher levels of balanced TO–MO results in greater SI performance. To confirm and extend the results of this work, future research should assess the examined combinations of orientations in other contexts, and with respect to other performance variables (e.g. sustainable entrepreneurship).Practical implicationsBy recognizing the real value of foresight practices, manufacturing firms should be equipped with organizational capabilities that enable them to systematically predict potential discontinuities, explore the future and simultaneously maximize their innovation and technology capacity. The findings of this research provide insights to managers on how to invest in resources linked to different configurations of MO and TO so that they can lead to the improvement of sustainability-oriented innovation performance.Originality/valueThis work represents a first attempt to explore the viable combinations of MO (including responsive and proactive dimensions) with TO in the manufacturing context, and to investigate how these combinations contribute to different levels of SI performance.

Employee income, premium pricing, and high deductible health plan enrollment

ABSTRACT Employer health plan premiums are often subsidized at different levels according to enrollee income. When enrollees cross an income threshold, they lose some of the income-based subsidy resulting in higher premium prices for their plan choices. We use these discontinuous subsidy reductions, which induce relative price changes across plans, to assess the relationship between premium price and plan choice for workers in a large, national firm. We segmented individuals by income into $100 bins surrounding a $40,000 subsidy threshold and $200 bins surrounding a $110,000 subsidy threshold. We plotted these bins to visualize potential discontinuities and then estimated regression models that fit linear trends to the binned data at each subsidy threshold. Higher income workers were more likely to enrol in high deductible health plans (HDHPs) when those plans became relatively cheaper compared to traditional plans (estimate = −0.057, standard error = 0.027; p-value = 0.02). In contrast, lower income workers were less likely to enrol in a HDHP when the relative price fell (estimate = 0.065, standard error = 0.029, p-value = 0.03). Our findings indicate that responses to relative price distortions between insurance plan options differ by income and that benefit design should account for such heterogeneity.

Improving receiver function imaging with high-resolution Radon transform

SUMMARY The receiver function (RF) method is one of the most widely used passive seismic approaches for imaging subsurface structures from shallow sedimentary basins to the deep Earth’s interior. RF is typically computed with a deconvolution operation that enables separating structural response from source–time function embedded in teleseismic wavefields. However, seismic recordings of temporary arrays are often contaminated with strong random noise and even amplitude bias due to poor installation conditions. Both factors can cause instability to deconvolution and severely degrade the accuracy, thereby the imaging quality, of the RF method. This underscores the importance of effective denoising algorithms in RF processing. In this study, we explore the application of high-resolution Radon transform (RT) to improve the conventional RF imaging workflow. Contrary to the commonly implemented post-processing (i.e. after deconvolution) noise suppression schemes, we introduce the RT to data pre-processing (i.e. before deconvolution). This method seeks a sparse representation of teleseismic wavefields in the τ–p domain by iteratively solving a least-squares minimization problem with the conjugate gradient algorithm. Synthetic test with a 2-D step-Moho model shows that non-linear phase arrivals including incoherent noise and diffraction energy are effectively removed in resulting RFs, with the signal-to-noise ratio increased by as much as ∼8 dB. Real data experiments using the Hi-CLIMB network in the Tibetan Plateau demonstrate the superior performance of the proposed workflow in regularizing the wavefield and improving the coherence of converted phases across the recording array. Consequently, imaging results of common conversion point stacking using a single and a group of teleseismic events both recover subtle converted phases from the Moho and potential lithospheric discontinuities that are otherwise obscured by noise arising from the conventional processing workflow. This study highlights the necessity of wavefield regularization in the RF method and calls for improved data processing techniques in array-based seismic imaging.

Soft representation of the square-well and square-shoulder potentials to be used in Brownian and molecular dynamics simulations

The discrete hard-sphere (HS), square-well (SW), and square-shoulder (SS) potentials have become the battle horse of molecular and complex fluids because they contain the basic elements to describe the thermodynamic, structural, and transport properties of both types of fluids. The mathematical simplicity of these discrete potentials allows us to obtain some analytical results despite the nature and complexity of the modeled systems. However, the divergent forces arising at the potential discontinuities may lead to severe issues when discrete potentials are used in computer simulations with uniform time steps. One of the few routes to avoid these technical problems is to replace the discrete potentials with continuous and differentiable forms built under strict physical criteria to capture the correct phenomenology. The match of the second virial coefficient between the discrete and the soft potentials has recently been successfully used to construct a continuous representation that mimics some physical properties of HSs (Báez et al 2018 J. Chem. Phys. 149 164907). In this paper, we report an extension of this idea to construct soft representations of the discrete SW and SS potentials. We assess the accuracy of the resulting soft potential by studying structural and thermodynamic properties of the modeled systems by using extensive Brownian and molecular dynamics computer simulations. Besides, Monte Carlo results for the original discrete potentials are used as benchmark. We have also implemented the discrete interaction models and their soft counterparts within the integral equations theory of liquids, finding that the most widely used approximations predict almost identical results for both potentials.

The Grand Strategic Thought of Colin S. Gray

Colin S. Gray distinguished himself from other scholars in the field of strategic studies with his belief that grand strategy is indispensable, complex, and inherently agential. This article identifies key themes, continuities, conceptual relationships, and potential discontinuities from his decades of grand strategic thought. Gray’s statement that “all strategy is grand strategy” remains highly relevant today, emphasizing the importance of agential context in military environments—a point often neglected in strategic practice.

Burst Overlap Coregistration for Sentinel-1 TOPS DInSAR Ice Velocity Measurements

The application of Sentinel-1 interferometry to ice velocity measurements has until recently been limited by the significant horizontal scene motion associated with ice flow, which causes phase discontinuities (and associated unwrapping problems) at burst boundaries in Terrain Observation by Progressive Scans (TOPS) interferograms. Coregistering with a multiyear averaged external velocity mosaic based on offset-tracking can account for the bulk of the ice motion, but residual discontinuities sometimes remain, for example, due to seasonal variations in the ice velocity, or due to error sources such as azimuth shifts caused by ionospheric propagation. The presented method extends the external velocity coregistration with a local, spatially varying, coregistration in the burst overlap regions. This is based on the extended spectral diversity principle, which can only be applied in the overlap regions, but offers superior accuracy and resolution compared with traditional coregistration methods. The method considerably reduces phase discontinuities at burst boundaries, and potential new phase discontinuities at the overlap region edges are suppressed by an azimuth tapering of the applied coregistration shifts. An example scene is presented, and the phase discontinuities before and after application of the method are evaluated. The method is seen to remove phase discontinuities, with no adverse effects.

Free Vibration Analysis of Laminated Composite Double-Plate Structure System with Elastic Constraints Based on Improved Fourier Series Method

An analytical model of laminated composite double-plate system (LCDPS) is established, which efficiently analyzes the common 3D plate structure in engineering applications. The proposed model combines the first-order shear deformation theory (FSDT) and the classical delamination theory, and then the LCDPS’s vibration characteristics are investigated. In the process of analysis, the improved Fourier series method (IFSM) is used to describe the displacement admissible function of the LCDPS, which can remove the potential discontinuities at the boundaries. Five sets of artificial springs are introduced to simulate the elastic boundary constraints, and the restraints of the Winkler elastic layer can be adjustable. The improved Fourier series is substituted into the governing equations and boundary conditions; then, applying the Rayleigh–Ritz method, we take all the series expansion coefficients as the generalized coordinates. After that, a set of standard linear algebraic equations was obtained. On this basis, the natural frequency and mode shapes of the LCDPS can be obtained by solving the standard eigenvalue problem. By the discussion of numerical examples and the comparison with those of the reports in the literature, the convergence and the reliability of the present approach are validated. Finally, the parametric investigations of the free vibration with complex boundary conditions are carried out, including the influence of boundary conditions, lamination scheme, plate geometric parameters, and elastic coefficient between two plates.

Bayesian Analysis of Multifidelity Computer Models With Local Features and Nonnested Experimental Designs: Application to the WRF Model

ABSTRACT Motivated by a multi-fidelity Weather Research and Forecasting (WRF) climate model application where the available simulations are not generated based on hierarchically nested experimental design, we develop a new co-kriging procedure called augmented Bayesian treed co-kriging. The proposed procedure extends the scope of co-kriging in two major ways. We introduce a binary treed partition latent process in the multifidelity setting to account for nonstationary and potential discontinuities in the model outputs at different fidelity levels. Moreover, we introduce an efficient imputation mechanism which allows the practical implementation of co-kriging when the experimental design is nonhierarchically nested by enabling the specification of semiconjugate priors. Our imputation strategy allows the design of an efficient reversible jump Markov chain Monte Carlo implementation that involves collapsed blocks and direct simulation from conditional distributions. We develop the Monte Carlo recursive emulator which provides a Monte Carlo proxy for the full predictive distribution of the model output at each fidelity level, in a computationally feasible manner. The performance of our method is demonstrated on benchmark examples and used for the analysis of a large-scale climate modeling application which involves the WRF model.

How do energy systems model and scenario studies explicitly represent socio-economic, political and technological disruption and discontinuity? Implications for policy and practitioners

Scenarios may be qualitative or quantitative, the latter of which can be developed using energy systems models. This study explores how different energy systems models and scenarios explicitly represent and assess potential disruptions and discontinuities. The focus is on futures studies and forward-looking scenario and modelling exercises. We apply definitions of ‘emergent’ (uncoordinated) and ‘purposive’ (coordinated) disruption to a systematic review on how energy systems models and scenarios have been used to capture disruption and discontinuity. We first conducted a review of reviews of energy models and scenarios to provide an overview of their common classifications. Additional searches then sought studies which use different types of models and scenarios to explore disruption and discontinuity. We analyse a subset of 30 of these modelling or scenario studies in which authors self-identify and represent disruption or discontinuity, finding that the most frequently used methods were qualitative, exploratory foresight scenarios or agent-based models. We conclude that policy makers could prepare more effectively for social, economic and political disruption by integrating multidisciplinary insights from social and political sciences, engineering and economics through a broader range of methods: exploratory, foresight scenarios, simulation and agent-based models and repurposed energy systems optimisation models.

In-plane vibration characteristics of isotropic plate with elastic edge restraints

It has been well-established that in-plane vibration modes in structures occur at high frequencies. Hence, it is important from the perspective of design consideration to analyse the dynamic behaviour of built up structures subjected to high frequency excitation. In light of the above, the present analysis has been undertaken for analysis of in-plane free vibration characteristics of isotropic rectangular plates using single Fourier series solution for the in-plane plate displacements. The Fourier series representation has been supplemented with auxiliary functions, so chosen, as to remove any potential discontinuities associated with Fourier series function defined over the entire x-y plane. Rayleigh-Ritz procedure has been applied to determine the in-plane natural frequencies of the plate and generation of natural modes. The demonstrated numerical examples provide an excellent accuracy and convergence of resulting solutions and bring out the effects of variation of boundary conditions on the in-plane vibration characteristics.

A discontinuous Galerkin method for the simulation of compressible gas-gas and gas-water two-medium flows

In this paper, we develop a new discontinuous Galerkin method for the simulation of shocks and interfaces in compressible gas-gas and gas-water two-medium flows by solving the γ-based model. The spatial discretization is carefully designed to possess the following features: discrete conservation in terms of the total mass, total momentum and total energy; high-order accuracy and consistency for smooth flows; free of oscillations at an isolated material interface. In order to handle potential discontinuities arising in the simulation, a nonlinear limiter based on the weighted essentially non-oscillatory (WENO) strategy is employed to suppress numerical oscillations and to preserve high order of accuracy in regions of smooth flows. The WENO reconstruction is imposed on suitably selected quantities, rather than the conserved ones. In case for discontinuities with large pressure ratio, low density and dramatic change of material property where unphysical variables may be encountered, a posteriori solution correction on the subcell level is locally adopted to enhance the robustness. A series of typical test cases for both one- and two-dimensional problems are provided to demonstrate the performance of the proposed method.