Approximation Method Research Articles

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.

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.

Quantification and Sensitivity Analysis of the Model Uncertainty in the Projectile-Barrel Coupled Artillery Dynamics System Based on Random Matrix Theory

Simplifications in the engineering of artillery firing dynamics modeling introduce model uncertainty, which seriously affects the model’s predictive performance. To this end, a typical variable-section hollow cylindrical cantilever beam structure in artillery firing dynamics is investigated in this paper. The statistical approximation methods quantify parameter and model uncertainty separately, and their respective confidence intervals were calculated and compared. The results show that the traditional parameter uncertainty approach overestimates the parameter uncertainty ranges, and introducing the model uncertainty approach dramatically improves the model prediction performance. Additionally, a projectile-barrel coupled artillery dynamics model considering model uncertainty is established, and its effectiveness is validated through the actual launch experiments. The sensitivity of the dynamic responses to the system matrix, namely model uncertainty, is further analyzed. This paper provides theoretical references for the study of uncertainty in artillery launch dynamics and proposes effective methods to enhance the predictability of computational models for complex structural systems.

Advancing DFT predictions in Cu-chalcogenides with full-yet-shallow 3d-orbitals: Meta-GGA plus Hubbard-like U correction.

The technologically important Cu-chalcogenides, such as Cu2Se and CuInSe2, usually have relatively small band gaps. Achieving a reliable yet efficient description of the electronic properties has proven to be quite challenging for the popular exchange-correlation functionals of density functional theory, primarily due to the involvement of full-yet-shallow Cu-3d orbitals. In this study, we evaluate the applicability of several meta-generalized gradient approximation (GGA) functionals that have been recently developed. We find that the r2SCAN (regularized-restored strongly constrained and appropriately normed) functional significantly improves upon conventional local density approximation and GGA in terms of geometry and electronic band structure; however, there is still a notable discrepancy with experimental results due to the remaining delocalization error. This error is mitigated by combining r2SCAN with a Hubbard-like U correction applied to the Cu-3d orbitals. For predicting band gaps, both the TASK functional and the mBJ potential, when combined with the U correction, demonstrate similar accuracies with a mean absolute error of 0.17-0.19eV. This accuracy is lower than that achieved with the many-body Hedin's GW approximation method but more accurate than that of hybrid functionals. Moreover, the r2SCAN+U approach well reproduces the phonon dispersion in CuInSe2, revealing a neglected computational problem in previous reports. We conclude that the meta-GGA+U approach represents a significant advancement by striking a balance between reliability and computational effort, and further efforts are still required to describe the Cu-3d orbitals more accurately.

Minimasi Biaya Distribusi pada UMKM Keset Samian dengan Metode VAM dan Modi

Transportation methods are methods used to optimally manage the distribution of goods from suppliers to destinations. The method used is Vogel's Approximate Method (VAM) and Modified Distribution (MODI). This research aims to minimize distribution costs for Keset Samian MSMEs. Samian Doormat UMKM is a small and medium business engaged in the production of doormat crafts. The Samian Doors Umkm experiences problems in managing distribution costs efficiently which has a direct impact on business profits. This research uses primary and secondary data collection related to costs. distribution, demand, and production capacity. The data was analyzed using VAM to determine the initial optimal cost solution in allocating the distribution of doormat products. The results of the VAM method were further optimized using the MODI method to achieve minimal costs in the distribution of doormat products. The research results show that the VAM and MODI methods are able to reduce distribution costs significantly compared to the traditional methods currently used by the Samian Doormat MSMEs. Where from the initial cost of Rp. 4,250,000 to Rp. 2,843,500 which experienced a decrease in transportation costs of Rp. 1,406,500 or 33.09%. So the results of calculating transportation costs for UMKM Keset Samian are optimal and increase business profits.

Implementasi Vogel’s Approximation Method (VAM) dan Modified Distribution (Modi) untuk Minimasi Biaya Distribusi di PT Jimat Perkasa Farm

Efficient and effective distribution management is a key factor in the success of a company's operations. PT Jimat Perkasa Farm, which is engaged in the processing of seaweed waste for animal feed blends, faces significant challenges in minimizing distribution costs. This research aims to implement Vogel's Approximation Method (VAM) and Modified Distribution (MODI) to achieve an optimal solution in reducing distribution costs. The results show that the application of VAM as the initial solution and MODI as the optimal solution is able to produce significant distribution cost savings. The total distribution cost can be minimized from IDR 5,400,000 per month to IDR 5,275,000 per month, which shows a savings of IDR 125,000 / by 2.31% per month. This efficiency in distribution not only reduces operational costs but also improves the timeliness and reliability of delivery, which ultimately improves customer satisfaction and the company's competitiveness in the market

On weighted sum‐rate maximization of full‐duplex systems in presence of STAR‐RIS

AbstractReflecting intelligent surface (RIS) is one of the key enabling technologies for beyond fifth generation wireless networks to further improve coverage, spectral‐ and energy‐efficiency of wireless networks. Recently, a novel simultaneous transmission and reflection RIS (STAR‐RIS) technology is introduced which enables more degrees‐of‐freedom in simultaneously serving users in reflection and transmission regions of RIS. This paper investigates a STAR‐RIS assisted two‐user full‐duplex communication system, wherein multi‐antenna base station (BS) and single‐antenna users are subject to maximum power constraints. Firstly, weighted sum rates are computed for three well‐known STAR‐RIS protocols, e.g. energy splitting, mode selection, and time splitting. Then, for each of the cases, weighted sum rate optimization problem is investigated to find optimal resource allocations, i.e. base station's precoding and combining matrices, coefficients of STAR‐RIS, and power allocations. The optimization problem is transferred into multiple convex sub‐problems using equivalent weighted minimum mean‐square‐error forms. Also, by use of the successive convex approximation method, tunable parameters of the STAR‐RIS are optimized. Although the original problem is a non‐convex one, proposed iterative alternating technique achieves an acceptable sub‐optimal performance. Finally, performance of the system is analysed and compared to some baselines to highlight superiority of the STAR‐RIS compared to the conventional RIS schemes.

An Efficient Integral Approach for Kinematic Reliability Sensitivity Analysis of Industrial Robots

Abstract Assessment of the reliability and reliability sensitivity of positioning accuracy for industrial robots subject to aleatoric and epistemic uncertainties registers a challenging task. This study proposes a new optimized moment-based method for kinematic reliability analysis and its sensitivity analysis, which incorporates the sparse grid (SPGR) technique and the saddlepoint approximation (SPA) method. To start with, the positioning accuracy reliability and its sensitivity models of industrial robots are established via computational optimization techniques and kinematic criteria. The kinematic accuracy reliability and its sensitivity are then calculated. Specifically, the sparse grid technique is adopted to approach the positioning error statistical moments and moment sensitivities. On this basis, positioning accuracy reliability bounds and reliability sensitivity bounds are obtained by the saddlepoint approximation method and optimization techniques. Finally, two practical examples are implemented to demonstrate the proficiency of the currently proposed method against Monte Carlo simulation (MCS) results. The results show that the currently proposed method exhibits superior computational accuracy and efficiency in kinematic reliability and its sensitivity analyses for industrial robots.

Hydroelastic responses of a multi-modular very large floating structure on a flexible bottom with lateral stress in a two-layer fluid

Based on the small-amplitude water wave theory, an analytical investigation is performed for the interaction between incident waves and a multi-modular very large floating structure (VLFS) in a two-layer fluid with a flexible seabed. A vertical porous flexible plate is fixed in the center of each floating plate to suppress the hydroelastic response. A key innovation is the modeling of both the VLFSs and the seabed as thin elastic plates with the lateral stress. The analytical expressions for dispersion relationships and vertical eigenfunctions are exactly derived in the water regions with a flexible seabed. The series solution of the velocity potential is obtained through the combination of inner product and the least squares approximation method. The study uniquely illustrates the impact of lateral stress and flexible seabeds on wave propagation, revealing that at low frequencies, waves in both open water and plate-covered regions with a flexible seabed exhibit the similar propagation characteristics. At higher frequencies, however, the propagation characteristics of the waves in the open water regions remain unaffected by the presence of a flexible seabed. The lateral stress has significant effects on the roots of dispersion relationships and the hydroelastic responses. The influences of other physical parameters of the fluid and structures are also displayed graphically. The results demonstrate that the increasing number of modules and extending the vertical plates effectively suppress hydroelastic responses and reduce wave transmission. The porous barriers can reduce the stress on the vertical plates and weaken the effect of barriers for suppressing hydroelastic response.

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.

A general valuation framework for rough stochastic local volatility models and applications

Rough volatility models are a new class of stochastic volatility models that have been shown to provide a consistently good fit to implied volatility smiles of SPX options. They are continuous-time stochastic volatility models, whose volatility process is driven by a fractional Brownian motion with the corresponding Hurst parameter less than a half. Albeit the empirical success, the valuation of derivative securities under rough volatility models is challenging. The reason is that it is neither a semi-martingale nor a Markov process. This paper proposes a novel valuation framework for rough stochastic local volatility (RSLV) models. In particular, we introduce the perturbed stochastic local volatility (PSLV) model as the semi-martingale approximation for the RSLV model and establish its existence, uniqueness, Markovian representation and convergence. Then we propose a fast continuous-time Markov chain (CTMC) approximation algorithm to the PSLV model and establish its convergence. Numerical experiments demonstrate the convergence of our approximation method to the true prices, and also the remarkable accuracy and efficiency of the method in pricing European, barrier and American options. Comparing with existing literature, a significant reduction in the CPU time to arrive at the same level of accuracy is observed.

Statistical Properties of SIS Processes with Heterogeneous Nodal Recovery Rates in Networks

The modeling and analysis of epidemic processes in networks have attracted much attention over the past few decades. A major underlying assumption is that the recovery process and infection process are homogeneous, allowing the associated theoretical studies to be conducted in a convenient manner. However, the recovery and infection processes usually exhibit heterogeneous rates in the real world, which makes it difficult to characterize the general relations between the dynamics and the underlying network structure. In this work, we focus on the susceptible–infected–susceptible (SIS) epidemic process with heterogeneous recovery rates in a finite-size complete graph. Specifically, we study the metastable-state statistical properties of SIS epidemic dynamics with two different nodal recovery rates in complete graphs. We propose approximate solutions to the metastable-state expectation and the variance in the number of infected nodes within the framework of the mean-field approximation method. We also derive several upper and lower bounds of the steady-state probability that a node is in the infected state. We verify the proposed approximate solutions of the mean and variance via simulations. This work provides insights into the fluctuations in the statistical properties of epidemic processes with complex dynamical behaviors in networks.