Approximation Method Research Articles

Modified Successive Approximations Method for Solving Fuzzy Second Kind Fredholm Integral Equations with Separable Kernel

This paper presents an analysis, development, and application of a modified method of successive approximations to solve fuzzy second kind Fredholm integral equations with a separable kernel. The fuzziness in the equations is represented utilizing convex normalized triangular fuzzy numbers, which are based on a single and double parametric form of fuzzy numbers. In the single parametric form of the fuzzy number, a fuzzy equation converts to two crisp equations for the solution which increases the computational cost. Therefore, to reduce the computational cost and increase the solution's accuracy, the double parametric form of the fuzzy number will be used in this study. The feasibility of the proposed methods is illustrated through a numerical example. The results obtained using the presented approach demonstrate adequate agreement with relevant theoretical aspects.

Influences of modified Chaplygin dark fluid around a black hole

In this work, we study a static, spherically charged AdS black hole within a modified cosmological Chaplygin gas (MCG), adhering to the calorific equation of state, as a unified dark fluid model of dark energy and dark matter. We explore the influence of model parameters on several characteristics of the MCG-motivated charged AdS black hole (MCG-AdSBH), including the geodesic structure and some astrophysical phenomena such as null trajectories, shadow silhouettes, light deflection angles, and the determination of greybody bounds. We then discuss how the model parameters affect the Hawking temperature, remnant radius, and evaporation process of the MCG-AdSBH. Quasinormal modes are also investigated using the eikonal approximation method. Constraints on the MCG-AdSBH parameters are derived from EHT observations of M87* and Sgr A*, suggesting that MCG-AdSBH could be strong candidates for astrophysical black hole.

Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method

In this article, we construct and investigate a new fractional variational iteration technique which is named as AFVI method. After that, we formulate some IVPs corresponding to the fractional nonlinear evolution equations NLTFFWE, mNLTFFWE, TFmCHE and TFmDPE. The Caputo fractional order derivative has been used to fractionalize the considered NLEEs. Then, we solve the considered IVPs by applying the formulated AFVI method. Lastly, we check the accuracy of the attained AASs by making some graphical and numerical comparisons with their corresponding exact solutions and other existing equivalent AASs. The result of this article confirm that the efficiency, appropriateness and time spent capability of the newly constructed AFVI method are better than that of the other existing analogous fractional analytical approximation methods. Here, we apply the Maple 2021 programming software to obtain the AASs of the formulated IVPs and drawing the 3D graphs of the attained AASs. Finally, in this article we validate the applicability of the Caputo fractional order derivative to form a novel analytical approximation method as well as to fractionalize some essential NLEEs of Mathematical physics.

Approximation of sea surface velocity field by fitting surrogate two-dimensional flow to scattered measurements

In this paper, a rapid approximation method is introduced to estimate the sea surface velocity field based on scattered measurements. The method uses a simplified two-dimensional flow model as a surrogate model, which mimics the real submesoscale flow. The proposed approach treats the interpolation of the flow velocities as an optimization problem, aiming to fit the flow model to the scattered measurements. To ensure consistency between the simulated velocity field and the measured values, the boundary conditions in the numerical simulations are adjusted during the optimization process. Additionally, the relevance of quantity and quality of the scattered measurements is assessed, emphasizing the importance of the measurement locations within the domain as well as explaining how these measurements contribute to the accuracy and reliability of the sea surface velocity field approximation. The proposed methodology has been successfully tested in both synthetic and real-world scenarios, leveraging measurements obtained from Global Positioning System (GPS) drifters and high-frequency (HF) radar systems. The adaptability of this approach for different domains, measurement types and conditions implies that it is suitable for real-world submesoscale scenarios where only an approximation of the sea surface velocity field is sufficient.

Joint optimization of overbooking and seat allocation for high-speed railways considering stochastic demand

To mitigate empty seat loss caused by random passenger no-show behavior, this study extends seat allocation to joint optimization of overbooking and seat allocation for high-speed railways (HSR). Assuming that stochastic passenger demand follows a specific distribution and considering various constraints, including train capacity, demand, and denied boarding rate constraints, a nonlinear stochastic programming model for joint optimization of overbooking and seat allocation for HSR is constructed with the aim of maximizing railway expected revenue. To solve this optimization model, a multi-level optimization algorithm is designed. Based on the sampling averaging approximation method, demand scenarios and passenger no-show scenarios are generated and the optimization problem is decomposed, including the joint optimization of overbooking and seat allocation under a single demand scenario, and the ticket adjustment under other demand scenarios. For the former, it is further divided into two sub-problems according to the stochastic nature of passenger no-show behavior, which is optimized iteratively. Finally, the effectiveness of the proposed model and algorithm is evaluated through numerical studies. The results demonstrate that the proposed joint optimization method effectively addresses the randomness of passenger demand and no-show behavior, thereby improving HSR expected revenue and making up for the empty seat loss resulting from passenger no-show behavior.

Geotechnical engineering surveys and soil testing in the construction of buildings and structures

The article suggests a way to increase the efficiency of geotechnical engineering surveys through the rational use of fast approximate methods of soil testing (“express methods”). Such tests are recommended to be carried out in large volume and considered as a means of assessing the geotechnical structure of the site as a whole. In this paper, these issues are considered by the example of determining the bearing capacity of piles according to static sounding data and static tests of full-scale piles. A mathematical model for assessing the information content of the test complex based on the concepts of information theory is proposed. Calculations based on this model show that the informativeness of a large number of approximate tests may (due to the heterogeneity of the soil) exceed the informativeness of a small number of accurate tests.

Approximate Cross-Validated Mean Estimates for Bayesian Hierarchical Regression Models

We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). BHRMs are popular for modeling complex dependence structures (e.g., Gaussian processes and Gaussian Markov random fields) but can be computationally expensive to run. Cross-validation (CV) is, therefore, not a common practice to evaluate the predictive performance of BHRMs. Our method circumvents the need to rerun computationally costly estimation methods for each cross-validation fold and makes CV more feasible for large BHRMs. We shift the CV problem from probability-based sampling to a familiar and straightforward optimization problem by conditioning on the variance-covariance parameters. Our approximation applies to leave-one-out CV and leave-one-cluster-out CV, the latter of which is more appropriate for models with complex dependencies. In many cases, this produces estimates equivalent to full CV. We provide theoretical results, demonstrate the efficacy of our method on publicly available data and in simulations, and compare the model performance with several competing methods for CV approximation. Code and other supplementary materials available online.

Online Learning and Decision Making Under Generalized Linear Model with High-Dimensional Data

We propose a minimax concave penalized multiarmed bandit algorithm under the generalized linear model (G-MCP-Bandit) for decision-makers facing high-dimensional data in an online learning and decision-making environment. We demonstrate that in the data-rich regime, the G-MCP-Bandit algorithm attains the optimal cumulative regret in the sample size dimension and a tight bound in the covariate dimension and the significant covariate dimension. In the data-poor regime, the G-MCP-Bandit algorithm maintains a tight regret upper bound. In addition, we develop a local linear approximation method, the two-step weighted Lasso procedure, to identify the minimax concave penalty (MCP) estimator for the G-MCP-Bandit algorithm when samples are not independent and identically distributed. Under this procedure, the MCP estimator can match the oracle estimator with high probability and converge to the true parameters at the optimal convergence rate. Finally, through experiments based on both synthetic and real data sets, we show that the G-MCP-Bandit algorithm outperforms other benchmarking algorithms in terms of cumulative regret and that the benefits of the G-MCP-Bandit algorithm increase in the data’s sparsity level and the size of the decision set. This paper was accepted by J. George Shanthikumar, big data analytics. Funding: This work was supported by the National Natural Science Foundation of China (NSFC) [Grants W2441021, 72371172, 72342023, and 71929101] and the National Science Foundation (NSF) [Grant DMS 1820702]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.01557 .

Spatial heterogeneity of menstrual discriminatory practices against Nepalese women: A population-based study using the 2022 Demographic and Health Survey.

Menstrual discrimination hampers progress toward Sustainable Development Goals. Examining the spatial heterogeneity of menstrual discriminatory practices may present an opportunity for targeted interventions. Here we evaluate geographical disparities in menstrual-related restrictions and assess their association with socio-economic and demographic factors. We used data from the 2022 Nepal Demographic and Health Survey which included 13,065 women aged 15-49 who reported menstruating within the past year. We explored the spatial heterogeneity of menstrual restriction outcomes using the standard Gaussian kernel density approximation method and the spatial scan statistic. The Poisson regression model with robust standard errors was used to assess the association between the different forms of menstrual restriction and the socio-economic, and demographic factors. Overall, the prevalence of women who reported any form of menstrual restriction was 84.8% and was subject to geographical variations ranging from 79.0% in Bagmati to 95.6% in Sudurpashchim. Religious restrictions were the most prevalent (79.8%) followed by household-level restrictions (39.5%) and then Chhaupadi (6.2%). Geographical variations were more prominent for women experiencing Chhaupadi (primary geographical cluster: relative risk = 7.4, p<0.001). Strikingly, women who reside in households led by female household heads were less likely to report experiencing household-level restriction during menstruation (Adjusted prevalence ratio (aPR) = 0.89, [95%CI: 0.84-0.94], p<0.001) whilst those residing in wealthy households were less likely to report experiencing Chhaupadi (aPR = 0.26, [95%CI: 0.17-0.39], p<0.001; among the richest). Our study demonstrated marked geographical micro-variations in menstrual discriminatory practices in Nepal. Policymakers should implement preventive behavioral interventions in the most vulnerable geographic areas to effectively and efficiently reduce the overall prevalence of menstrual discrimination. It is crucial to prioritize the designing and testing of targeted interventions to determine their effectiveness against Chhaupadi in these high-prevalence settings. Additionally, empowering women appears to be a promising strategy for combating menstrual discrimination within the household.

Effect of Dielectric Properties of Cochlea on Electrode Insertion Guidance Based on Impedance Variation

The cochlear neuromodulator provides substantial auditory perception to those with impaired hearing. The accurate insertion of electrodes into the cochlea is an important factor, as misplaced may lead to further damage. The impedance measurement may be used as a marker of the electrode insertion guidance. It is feasible to investigate the impact of the dielectric properties of the cochlea tissue layers on the electrode insertion guidance using sophisticated bio-computational methods that are impractical or impossible to perform in cochlear implant (CI) patients. Although previous modeling approaches of the cochlea argued that the capacitive impact of the tissue layer can be neglected using the quasi-static (QS) approximation method, it is widely accepted that tissue acts as a frequency filter. Thus, the QS method may not always be appropriate due to short-duration pulses. This study aimed to investigate the impact of the frequency-dependent dielectric properties of the cochlea tissue layers on the impedance variation by following a systematic approach. The volume conductor model of the cochlea layers was developed, the dielectric properties of each tissue layer were attained, and the cochlea neuromodulator settings were applied to obtain the results based on both QS and transient solution (TS) methods. The results based on the QS and TS methods were compared to define to what extent these parameters affect the outcome. It was suggested that the capacitive impact of the cochlea layers should be considered after a certain frequency level.

Reduced order modelling method for electromagnetic analysis of electrical machines

AbstractThis paper presents a workflow to create a reduced order model for the electromagnetic analysis of electrical machines over its operating range so that the stator forces can be exported for mechanical analysis. A permanent magnet synchronous motor developed within the EDISON (Electric Drivetrain Integration by Simulation and OptimizatioN) project is used as a model to validate the workflow. The response surface model approximation method is used to generate the reduced order model, which is then validated by comparing with the results from finite element analyses.

Adaptive state-feedback control for nonlinear systems with input delay and state constraints

This paper investigates the adaptive tracking control for more general nonlinear systems that encompass input delay, state constraints, and parameter uncertainty. Firstly, the parametric nonlinearities of the system are addressed by adaptive control and parameter separation technique. By integrating the Pade approximation method with the barrier Lyapunov function in a unified framework, the uncertainties arising from input delay and state constraints are effectively tackled. Then, an adaptive state-feedback control strategy is constructed based on the backstepping design procedure and rigorous stability analysis. It is verified that all the signals in the closed-loop system are uniformly ultimately bounded, the tracking error of the system converges to a compact set of the origin, and the system state constraints are never violated. Finally, the designed controller is applied to a single-link robot system to demonstrate the effectiveness of the proposed control strategy.

ANALYSIS OF OPTIMAL PORTFOLIO ON FINITE AND SMALL-TIME HORIZONS FOR A STOCHASTIC VOLATILITY MODEL WITH MULTIPLE CORRELATED ASSETS

In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by [Formula: see text]-dimensional Brownian motions. At first, we derive a Hamilton–Jacobi–Bellman equation including the correlations among the standard Brownian motions. We use an approximation method for the optimization of portfolios. With such approximation, the value function is analyzed using the first-order terms of expansion of the utility function in the powers of time to the horizon. The error of this approximation is controlled using the second-order terms of expansion of the utility function. It is also shown that the one-dimensional version of this analysis corresponds to a known result in the literature. We also generate a close-to-optimal portfolio near the time to horizon using the first-order approximation of the utility function. It is shown that the error is controlled by the square of the time to the horizon. Finally, we provide an approximation scheme to the value function for all times and generate a close-to-optimal portfolio.

Large-Scale Low-Rank Gaussian Process Prediction with Support Points

Low-rank approximation is a popular strategy to tackle the “big n problem” associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified. Predictive processes simplify the problem by inducing basis functions with a covariance function and a set of knots. The existing literature suggests certain practical implementations of knot selection and covariance estimation; however, theoretical foundations explaining the influence of these two factors on predictive processes are lacking. In this article, the asymptotic prediction performance of the predictive process and Gaussian process predictions are derived and the impacts of the selected knots and estimated covariance are studied. The use of support points as knots, which best represent data locations, is advocated. Extensive simulation studies demonstrate the superiority of support points and verify our theoretical results. Real data of precipitation and ozone are used as examples, and the efficiency of our method over other widely used low-rank approximation methods is verified. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Approximate reasoning based on the preference implication

In fuzzy logic, most of the implication operators are based on generalizations of the classical, material implication. That is, these implications are defined as the disjunction of the negated value of the first argument and the value of the second argument, while the underlying disjunction operators are associative triangular conorms. In our study, we concentrate on how a class of implication operators, called the preference implication operators, can be used in approximate reasoning. Using this implication operator family, we present a novel, Modus Ponens-like approximate reasoning method, in which we have two premises: (1) a statement and (2) a preference implication with an antecedent of this statement. Here, we show how the continuous logical value of the consequent of the preference implication can be derived from the continuous logical values of the premises. We point out that this novel approximate reasoning method is strongly connected with the so-called aggregative operator, which is a representable uninorm. Next, we also present a threshold value-based generalization of the Modus Ponens syllogism and demonstrate that the Modus Tollens syllogism can be generalized in the same way. Lastly, we provide an illustrative example.

Enhanced Subspace Iteration Technique for Probabilistic Modal Analysis of Statically Indeterminate Structures

In structural stochastic dynamic analysis, the consideration of the randomness in the physical parameters of the structure necessitates the establishment of numerous stochastic finite element models and the subsequent computation of their corresponding vibration modes. When the complete analysis is applied to calculate the vibration modes for each sample of the stochastic finite element model, a substantial computational expense is incurred. To enhance computational efficiency, this work presents an extended subspace iteration method aimed at rapidly determining the vibration modal parameters of statically indeterminate structures. The essence of this proposed method revolves around efficiently constructing reduced basis vectors during the subspace iteration process, utilizing flexibility disassembly perturbation and the Krylov subspace. This extended subspace iteration method proves particularly advantageous for the modal analysis of finite element models that incorporate a multitude of random variables. The proposed modal random analysis method has been validated using both a truss structure and a beam structure. The results demonstrate that the proposed method achieves substantial savings in computational time. Specifically, for the truss structure, the calculation time of the proposed method is approximately 1.2% and 65% of that required by the comprehensive analysis method and the combined approximation method, respectively. For the beam structure, on average, the computational time of the proposed method is roughly 2.1% of a full analysis and approximately 48.2% of the Ritz vector method’s time requirement. Compared to existing stochastic modal analysis algorithms, the proposed method offers improved computational accuracy and efficiency, particularly in scenarios involving high-discreteness random analyses.

Is Half a Century-Based Suturing Pattern Worth the Upgrade? Evaluating a Novel Suturing Technique: Knot Less is More.

The aesthetic outcomes of wise pattern-based breast reduction and mastopexy procedures are significantly influenced by the final scar quality, which is directly impacted by the suturing technique. Over the past century literature on suture placement has remained limited, with little advancement in tissue approximation methods. The success of conventional suturing depends on the surgeon's skills and expertise and the selection of suture material. Proper deep placement of absorbable sutures is essential to reduce risks; in fact, incorrect placement can lead to complications such as poor scar quality and negative psychological effects on the patient, and occasionally more severe issues like delayed wound healing. Our experience with a running suturing technique for wise pattern-based mammoplasty indicates that reducing the number of knots can lead to a better overall experience for both the patient and the surgeon. This technique may improve aesthetic results, decrease complications, and streamline the surgical process.Level of Evidence IV This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .

Application of Digital Technology for Oil and Gas Fields

The paper investigates the problem of isothermal filtration using an approximate method for solving the theory of partial differential equations. The mathematical model under consideration is nonlinear and does not lend itself to analytical methods of solution. The results obtained indicate the need for wide application in the development of oil and gas fields in the Republic of Kazakhstan. In particular, the results of the study make it possible to solve the problems of adapting mathematical models and evaluating changes in technological indicators, which are necessary attributes in the digital technology ""Information System for the Analysis of oil and Gas Field Development"" (ISAR). Many problems and mathematical problems of filtration theory arose while working on specific oil and gas fields in the western region of the Republic of Kazakhstan. The above approximate solution methods have found applications not only in filtration theory, but also in other problems (geophysics, ecology, etc.)"

A comprehensive study of beam modal functions in the free vibration analysis of cylindrical shells: Critical examination on the applicability to the clamped-free boundary condition

Over the past few decades, approximate methods that can provide solutions of sufficient accuracy have received considerable attention in the free vibration analysis of cylindrical shells, where a great deal of studies adopted the beam modal functions as the trial functions for the axial mode shapes of cylindrical shells. Nevertheless, most studies were restricted to the application of single term beam modal function and failed to simulate elastic boundary conditions of cylindrical shells, while the accuracy of the corresponding methods has recently sparked significant controversy, especially for cylindrical shells under the clamped-free boundary condition. This paper presents a comparative study of three forms of beam modal functions in the free vibration analysis of cylindrical shells, one of which is proposed for the first time to simulate elastic boundary conditions of cylindrical shells. A unified model is developed using the general Rayleigh–Ritz method, incorporating the breathing modes with circumferential orders being zero, and four types of commonly used thin shell theories, namely the Donnell, Reissner, Love, and Sanders theories. From both perspectives of natural frequencies and mode shapes, numerical results are validated by comparison with those existing in the literature and those calculated from the finite element method (FEM). The results not only clarify the distinction of different forms of beam modal functions used in the Rayleigh-Ritz method, but also provide explanations for the controversy raised in recent studies. Furthermore, the unified formulations can be extended to vibration analysis of various forms of shell structures, and can also be helpful to the vibration analysis of beams and plates with elastic boundary conditions.

Evaluation method of carbon-fiber-reinforced polymer material anti-radiation performance based on synergistic effect model

Aiming at the high computational costs of the current multi-source X-ray radiation numerical simulations, a multi-source X-ray evaluation method based on a synergistic effect model is studied. First, based on the advantage of the low computational cost of single-source X-ray radiation numerical simulations, a hierarchical Gaussian process model is used to construct a superimposed single-source numerical simulation data fusion model. Second, by constructing composite correlation functions, the data fusion ability of the Gaussian process model is improved. The unknown parameters in the data fusion evaluation model are solved with the help of the Markov chain Monte Carlo method and a nonlinear optimization algorithm. Based on the obtained sampling values of the unknown parameters, an approximate solution method for the estimated value of the superimposed single-source X-ray radiation numerical simulations with unknown input conditions is given. Then a synergistic effect model is constructed based on the established linear regression surrogate model. The synergistic evaluation of multi-source X-ray radiation tests based on single-source X-ray radiation numerical simulation superimposed test data is studied. Finally, carbon-fiber-reinforced polymer experiments show the proposed method in better than existing Kriging methods, for prediction of multi-source X-ray radiation data.