Approximation Approach Research Articles

Collaborative deployment of multiple reinforcement methods for network‐loss reduction in distribution system with seasonal loads

AbstractThe integration of seasonal loads, such as cereal baking and aquatic‐product processing loads, often leads to significant voltage deviations and severe peak loads of the distribution system during specific periods, resulting in increased network losses. Traditional approaches for reducing network losses are becoming less effective and cost‐efficient due to the spatiotemporally uneven distribution characteristics of seasonal loads. To address this issue, this study proposes an optimisation model that collaboratively integrates mobile energy storage, switching capacitors, and tie lines to minimise annual network losses in special planning scenarios affected by seasonal loads. The deployment strategies of multiple reinforcement methods are thoroughly analysed, greatly enhancing the explainability and feasibility of the collaborative deployment model. Then, the proposed model is reformulated to a mixed‐integer linear programming model using the inscribed regular dodecagon approximation approach, thereby making it trackable for state‐of‐the‐art solvers. To illustrate the effectiveness of the model, case studies are conducted on a unique 55‐bus distribution system located in East China, which contains feeders with substantial seasonal variation aquaculture loads and with general loads. The effectiveness of multiple reinforcement methods is thoroughly analysed through detailed numerical results. Furthermore, a sensitivity analysis of the investment budget is conducted.

A new quasi-finite-rank approximation of compression operators on [formula omitted] with applications to sampled-data and time-delay systems: Piecewise linear kernel approximation approach

This paper provides a new quasi-finite-rank approximation (QFRA) of infinite-rank compression operators defined on the Banach space L∞[0,H), which are associated with tractable representations of infinite-dimensional systems such as time-delay and sampled-data systems. We first formulate the QFRA by an optimization problem with a matrix-valued parameter X to minimize the associated error in terms of the L∞[0,H)-induced norm. To facilitate solving the optimization problem, we next employ the piecewise linear kernel approximation (PLKA) technique, by which the optimization problem is then converted to a linear programming (LP) problem. The solution of the LP problem is shown to converge to the optimal solution of the original QFRA with the order of 1/M, where M is the PLKA parameter. The PLKA-based QFRA is shown to lead to practical methods of the stability analysis for time-delay systems and the L1 optimal controller synthesis for sampled-data systems. Finally, the overall arguments developed in this paper are demonstrated through some numerical and experimental studies.

Uniform exponential stability approximations of semi‐discretization schemes for two hybrid systems

The uniform exponential stabilities (UESs) of two hybrid control systems comprised of a wave equation and a second‐order ordinary differential equation are investigated in this study. Linear feedback law and local viscosity are considered, as are nonlinear feedback law and internal anti‐damping. The hybrid system is first reduced to a first‐order port‐Hamiltonian system with dynamical boundary conditions, and the resulting system is discretized using the average central‐difference scheme. Second, the UES of the discrete system is obtained without prior knowledge of the exponential stability of the continuous system. The frequency domain characterization of UES for a family of contractive semigroups and the discrete multiplier approach are used to validate the main conclusions. Finally, the Trotter–Kato theorem is used to perform a convergence study on the numerical approximation approach. Most notably, the exponential stability of the continuous system is derived by the convergence of energy and UES, which is a novel approach to studying the exponential stability of some complex systems. Numerical simulation is used to validate the effectiveness of the numerical approximating strategy.

An Approximate Bayesian Computation Approach for Embryonic Astrocyte Migration Model Reduction.

During embryonic development of the retina of the eye, astrocytes, a type of glial cell, migrate over the retinal surface and form a dynamic mesh. This mesh then serves as scaffolding for blood vessels to form the retinal vasculature network that supplies oxygen and nutrients to the inner portion of the retina. Astrocyte spreading proceeds in a radially symmetric manner over the retinal surface. Additionally, astrocytes mature from astrocyte precursor cells (APCs) to immature perinatal astrocytes (IPAs) during this embryonic stage. We extend a previously-developed continuum model that describes tension-driven migration and oxygen and growth factor influenced proliferation and differentiation. Comparing numerical simulations to experimental data, we identify model equation components that can be removed via model reduction using approximate Bayesian computation (ABC). Our results verify experimental studies indicating that the choroid oxygen supply plays a negligible role in promoting differentiation of APCs into IPAs and in promoting IPA proliferation, and the hyaloid artery oxygen supply and APC apoptosis play negligible roles in astrocyte spreading and differentiation.

Addressing the implementation challenge of risk prediction model due to missing risk factors: The submodel approximation approach.

Clinical prediction models have been widely acknowledged as informative tools providing evidence-based support for clinical decision making. However, prediction models are often underused in clinical practice due to many reasons including missing information upon real-time risk calculation in electronic health records (EHR) system. Existing literature to address this challenge focuses on statistical comparison of various approaches while overlooking the feasibility of their implementation in EHR. In this article, we propose a novel and feasible submodel approach to address this challenge for prediction models developed using the model approximation (also termed "preconditioning") method. The proposed submodel coefficients are equivalent to the corresponding original prediction model coefficients plus a correction factor. Comprehensive simulations were conducted to assess the performance of the proposed method and compared with the existing "one-step-sweep" approach as well as the imputation approach. In general, the simulation results show the preconditioning-based submodel approach is robust to various heterogeneity scenarios and is comparable to the imputation-based approach, while the "one-step-sweep" approach is less robust under certain heterogeneity scenarios. The proposed method was applied to facilitate real-time implementation of a prediction model to identify emergency department patients with acute heart failure who can be safely discharged home.

Start-off MHD electrokinetic Couette flow in an annulus: A Riemann-sum approximation approach

Start-off MHD electrokinetic Couette flow in an annulus: A Riemann-sum approximation approach

A DFT investigation of Li substitution in CsCaY3 (Y[dbnd]F, Cl, Br) having admirable optoelectronic characteristics as a viable candidate for photocatalytic water splitting

In this study we investigated pristine and Li substituted Cs1-xLixCaY3 (YF, Cl, Br) lead free halide perovskite with different concentrations x = 0, 0.11, 0.33, 0.55, 0.77, and 1 using CASTEP under Density functional theory (DFT) has been employed under Perdew Burke Ernzerhof generalized gradient approximation (GGA-PBE) and Ultrasoft pseudo potential (USSP) approaches. Understudy pristine materials have a cubic phase Pm3 m space group. At the same time, doped compositions show a tetragonal phase structure except those in which Li completely swaps out Cs, so both end materials own a cubic nature. Li introduced at the Cs site is more effective than Ca because additional gamma points formed, influencing the electronic formation of pristine CsCaF3, CsCaCl3, and CsCaBr3 minimized band gap from 6.299 to 4.152 eV, 5.261–3.613 eV and 4.338–2.752 eV respectively. All compositions are thermodynamically stable, as suggested by the negative values of the formation energy. For all compositions, the Fermi level resides near the valence band which confirms the p-type behavior of the semiconductors. All of the materials retain the indirect bandgap. The total/partial/elemental density of states calculated has been approximated to provide a full picture of the band structure. Although elastic constants for all compounds, whether cubic or tetragonal, are used to predict mechanical parameters such as bulk modulus, shear modulus, young modulus, Poisson ratio, and Pugh's ratio, materials were first developed to support born stability criteria. From all of the compositions Cs1-xLixCaF3 for x = (0.11, 0.55, 0.77, and 1) and Cs0.23Li0.77CaCl3 are found to be mechanically unstable. All other combinations are stable, whether cubic or tetragonal. We evaluated and contrasted many optical properties like absorption spectra, refractive index, dielectric function, reflectivity, and energy loss function of pristine CsCaY3 (YF, Cl, Br) in comparison with Li substitution concentrations. For both pristine and Li substituted CsCaY3 (YF, Cl, Br) the overall water splitting was explored. All the compositions can be used for hydrogen evolution reaction (HER), oxygen evolution reaction (OER), and overall water splitting reactions but Cs0.23Li0.77CaBr3 is a good catalyst among all. It is proposed that the aforementioned materials have a bandgap range suitable for solar cell applications in addition to being lead-free for environmentally conscious applications in photocatalytic activity.

Quaternion-Aware Low-Rank Prior for Blind Color Image Deblurring

Blind image deblurring is a critical and challenging task in the field of imaging science due to its severe ill-posedness. Appropriate prior information and regularizations are normally introduced to alleviate this problem. Inspired by the fact that the matrix representing a natural image is intrinsically low-rank or approximately low-rank, we employ the low-rank matrix approximation (LRMA) approach for tackling blind image deblurring problems with unknown kernels. When applied to color image restoration tasks, making use of the quaternion representation in the hypercomplex domain enables us to better illustrate the inner relationships among color channels and thus more accurately characterize color image structure. Following this idea, we develop a novel model for color image blind deblurring by implementing the quaternion representation to the LRMA method. This proposed model facilitates better results for blur kernel estimation through preserving the sharper color intermediate latent image, which is first implemented for addressing the blind color image deblurring problem. Extensive numerical experiments demonstrate that our proposed quaternion-aware low-rank prior model greatly improves the performance when compared with the conventional low-rank based scheme and outperforms some of the state-of-the-art methods in terms of some criteria and visual quality.

A Retrospective Approximation Approach for Smooth Stochastic Optimization

Stochastic Gradient (SG) is the de facto iterative technique to solve stochastic optimization (SO) problems with a smooth (nonconvex) objective f and a stochastic first-order oracle. SG’s attractiveness is due in part to its simplicity of executing a single step along the negative subsampled gradient direction to update the incumbent iterate. In this paper, we question SG’s choice of executing a single step as opposed to multiple steps between subsample updates. Our investigation leads naturally to generalizing SG into Retrospective Approximation (RA), where, during each iteration, a “deterministic solver” executes possibly multiple steps on a subsampled deterministic problem and stops when further solving is deemed unnecessary from the standpoint of statistical efficiency. RA thus formalizes what is appealing for implementation—during each iteration, “plug in” a solver—for example, L-BFGS line search or Newton-CG—as is, and solve only to the extent necessary. We develop a complete theory using relative error of the observed gradients as the principal object, demonstrating that almost sure and L1 consistency of RA are preserved under especially weak conditions when sample sizes are increased at appropriate rates. We also characterize the iteration and oracle complexity (for linear and sublinear solvers) of RA and identify a practical termination criterion leading to optimal complexity rates. To subsume nonconvex f, we present a certain “random central limit theorem” that incorporates the effect of curvature across all first-order critical points, demonstrating that the asymptotic behavior is described by a certain mixture of normals. The message from our numerical experiments is that the ability of RA to incorporate existing second-order deterministic solvers in a strategic manner might be important from the standpoint of dispensing with hyper-parameter tuning. Funding: R. Pasupathy received financial support from the Office of Naval Research [Grants N000141712295 and 13000991]. R. Bollapragada received financial support from the Lawrence Livermore National Laboratory and the National Science Foundation [Grant NSF DMS 2324643].

A new high-precision numerical method for solving the HIV infection model of CD4(+) cells

This paper proposes a new method called the “Special Neural Network” to solve the HIV infection model of CD4(+) cells using a novel approximation approach. Unlike traditional methods that involve constructing loss functions and performing inverse matrix operations, our method discretizes the differential equations at configuration points, combines them, and transforms the system into a set of nonlinear equations. Parameters in the neural network are then iteratively solved using optimization to obtain an approximate solution. Additionally, when using the neural network as an approximate solution to the differential equations, we provide a form that satisfies the initial conditions through construction, eliminating the need to handle initial conditions during the solving process and thus streamlining the method. Finally, by comparing with other numerical methods using two sets of models and parameters, the Special Neural Network achieves high precision results and further demonstrates the advantages of our approach.

Venus Magnetotail Long-Term Sensing Using Solar Sails

Propellantless propulsion systems, such as the well-known photonic solar sails that provide thrust by exploiting the solar radiation pressure, theoretically allow for extremely complex space missions that require a high value of velocity variation to be carried out. Such challenging space missions typically need the application of continuous thrust for a very long period of time, compared to the classic operational life of a space vehicle equipped with a more conventional propulsion system as, for example, an electric thruster. In this context, an interesting application of this propellantless thruster consists of using the solar sail-induced acceleration to artificially precess the apse line of a planetocentric elliptic orbit. This specific mission application was thoroughly investigated about twenty years ago in the context of the GeoSail Technology Reference Study, which analyzed the potential use of a spacecraft equipped with a small solar sail to perform an in situ study of the Earth’s upper magnetosphere. Taking inspiration from the GeoSail concept, this study analyzes the performance of a solar sail-based spacecraft in (artificially) precessing the apse line of a high elliptic orbit around Venus with the aim of exploring the planet’s induced magnetotail. In particular, during flight, the solar sail orientation is assumed to be Sun-facing, and the required thruster’s performance is evaluated as a function of the elliptic orbit’s characteristics by using both a simplified mathematical model of the spacecraft’s planetocentric dynamics and an approximate analytical approach. Numerical results show that a medium–low-performance sail is able to artificially precess the apse line of a Venus-centered orbit in order to ensure the long-term sensing of the planet’s induced magnetotail.

Design of a reverse logistics network for medical waste considering location and routing decisions

Medical waste generated in healthcare facilities is categorized as hazardous due to its infectious, toxic, or radioactive properties, posing substantial risks to human health and the environment. This research proposes a bi-objective Mixed-Integer Linear Programming model for designing reverse logistics networks that enable both economical and safe medical waste management. Said model determines optimal quantity, depot locations, and routes for transporting waste from its generating points (hospitals) to the treatment and disposal sites (depots).This research addresses a bi-objective location routing problem, with multiple depots, time windows, capacity constraints, and variated waste types, across a multi-period horizon. It is innovative because no previous works have successfully dealt with such a combination of pragmatic features. The Location Routing Problem is an already well-known NP-Hard problem, with the additional aforementioned features further adding to its complexity. Thus, a genetic algorithm to solve large-sized realistic instances within reasonable computing times had been developed.Numerical experiments considered 20 random instances contrasting exact and approximate solution approaches. Also, a medical waste collection case study of a public hospital network in Atlántico Department, Colombia, delivering a Pareto frontier solution set, was introduced. The results demonstrated the efficacy of the proposed genetic algorithm in successfully addressing small instances of the problem, delivering outcomes comparable to the Mixed-Integer Linear Programming model. Furthermore, it yields good-quality solutions in a reduced computational time for larger instances deemed unfeasible for the Mixed-Integer Linear Programming model.This article contributes to both scientific literature and practitioners by presenting a decision-making tool designed to address the medical waste reverse logistics challenge under realistic scenarios. It approaches the issue from a bi-objective standpoint, jointly considering economic factors and biomedical safety. Additionally, the article introduces realistic and pertinent assumptions that have not been explored in previous literature.

Statistical prediction for nonlinear failure function of linear loads: application to plate buckling in ship structure

AbstractThis study presents a practical method for calculating the probability of exceedance (PoE) of the nonlinear failure function of the linear loads randomly fluctuating in irregular waves. In general, obtaining the exact PoE of such nonlinear quantities requires sophisticated computational method that are not well-suited for practical design. In contrast, the author in a previous study proposed a practical formula of the PoE distribution for von Mises stresses by asymptotic approximation, which can be applied when the criterion surface is ellipsoid in the stochastic variable space. Following this, the present study shows a method for calculating the PoE for a more general function of which the isosurface is expressed as a combination of ellipsoids. As a specific example of its application, this paper takes the limit state of the plates in ship structures specified in the common structural rules (CSR) and presents the calculation procedure of direct numerical integration as well as asymptotic approximation approaches. Calculation of the 1/1000 maximum expected value of the evaluation function of plates in short-term sea states using 700 actual plates in a ship structure confirms that the proposed method, which does not require integration, is in good agreement with rigorous methods using numerical integration.

Approximating problems in abstract argumentation with graph convolutional networks

In this article, we present a novel approximation approach for abstract argumentation using a customized Graph Convolutional Network (GCN) architecture and a tailored training method. Our approach demonstrates promising results in approximating abstract argumentation tasks across various semantics, setting a new state of the art for performance on certain tasks. We provide a detailed analysis of approximation and runtime performance and propose a new scheme for evaluation. By advancing the state of the art for approximating the acceptability status of abstract arguments, we make theoretical and empirical advances in understanding the limits and opportunities for approximation in this field. Our approach shows potential for creating both general purpose and task-specific approximators and offers insights into the performance differences across benchmarks and semantics.

The Processing Spatial Data for Statistical Modeling and Visualization Case study: INLA model for COVID-19 in Alabama, USA

This research emphasizes the visualization of spatial data for statistical modelling and analysis of the relative risk associated with the COVID-19 pandemic in Alabama, USA. We used Bayesian analysis and the Integrated Nested Laplace Approximation (INLA) approach on data ranging from March 11, 2020, to December 31, 2022, which included observed COVID-19 cases, the population for each of the Alabama counties, and a Geographical map of the state. The geographical distribution of COVID-19’s relative risk was determined using various spatial statistical techniques, indicating high-risk locations. The study used Besag-York-Mollié (BYM) models to assess the posterior relative risk of COVID-19, and it found a statistically significant average decrease in COVID-19 case rates across the 67 counties evaluated. These findings have practical implications for evidence-based policymaking in pandemic prevention, mitigation, and preparation.

Beyond Traditional Perovskites: Xenon's Influence on the Vibrational and Electronic Properties of K4Xe3O12

AbstractThe perovskite structure is one of the most fascinating configurations existing in nature, with its physical and chemical properties heavily influenced by the nature and oxidation states of cations, stoichiometry, and crystalline structure. Layered perovskite material K4Xe3O12, an interesting member of this family, possesses energetic properties that require detailed investigation. To establish the governing principles and quantify the observed behaviors, a detailed computational investigation is conducted into the electronic, vibrational, structural, and optical characteristics of K4Xe3O12, utilizing Density Functional Theory (DFT) calculations. The calculated elastic constants adhere to Born's criteria, affirming the mechanical stability of trigonal K4Xe3O12, with a bulk modulus (Bo) of ≈53.93 GPa. This low compressibility is intricately tied to its robust perovskite structure, featuring XeO6 octahedra sandwiched between XeO3 molecules. Precise determination of the valence‐conduction bandgap is crucial for understanding potential connections to the photodecomposition phenomenon. Using the Tran‐Blaha‐modified Becke‐Johnson (TB‐mB) potential alongside traditional generalized gradient approximation (GGA) approach, a bandgap of ≈1.32 eV is determined. Rapid fluctuations in optical properties also suggest a propensity for photodecomposition in the visible spectrum. The study provides critical insights into perovskite materials, especially those containing noble gas atoms, unveiling unique chemical and physical properties that open up new avenues for versatile applications across various fields.

A hybrid intersection control strategy for CAVs under fluctuating traffic demands: A value approximation approach

Confronted with growing and fluctuating traffic demands, urban transportation system has been encountering mounting challenges in traffic congestion, especially at intersections. With enhanced traffic control precision enabled by the emerging Connected and Automated Vehicle (CAV) technologies, this study proposes a hybrid control strategy for connected and automated traffic at urban intersections, which enables the integration of diverse control schemes to harness their strengths and mitigate their weaknesses. With rolling horizon strategy, a nonlinear optimization model is developed to determine the optimal traffic control plans considering both current status and forthcoming vehicle arrivals. Vehicle delays are elaborately characterized without relying on any empirical assumptions. The original model is converted to a Mixed Integer Programming with Quadratic Constraints (MIP-QC) by employing appropriate linearization techniques, which could be solved by commercial solvers. For the acquisition of instant and reliable solutions, a multilayer feedforward network-based approximate algorithm is developed, referred as Value Approximation Control (VAC) algorithm. Theoretical derivation is provided to validate the capability of VAC algorithm in the precise approximations of the value function in the traffic plan optimization problem, and ultimately enabling to acquire global optimal solutions via specific network design and training techniques. Numerical experiments on both artificial and researcher-collected datasets demonstrate that our proposed VAC algorithm achieves performance nearly equivalent to the mathematical model. Significantly, it outperforms current state-of-art traffic control methods in terms of both intersection throughput and average vehicle delay. Moreover, sensitivity analysis reveals the robustness of the VAC algorithm against inaccuracy in vehicle arrival information, and the stable performance even in the presence of significant disturbances.

Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds

In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints. We investigate the convergence of the method, which is based on a stochastic approximation approach with random stopping combined with an iterative procedure for updating Lagrange multipliers. The algorithm is applied to a multi-shape optimization problem with geometric constraints and demonstrated numerically.

Distributed adaptive event‐triggered consensus of switched nonlinear multi‐agent systems with state and input delays

SummaryIn this article, for switched nonlinear time‐delay multi‐agent systems (MASs) under directed graphs, an adaptive event‐triggered (ET) consensus problem is investigated. Each agent's switching signal is allowed to be arbitrary and asynchronous. To save communication resources, an adaptive ET consensus strategy is designed. In addition, the Pade approximation approach is introduced to transform the system into an input delay‐free system. A Lyapunov–Krasovskii functional is employed to analyze the effect of time‐varying delays on system stability. It is proved that the consensus errors of switched NMASs are bounded, and the Zeno behavior does not exist. Finally, the presented strategy's effectiveness is verified by simulation results.

Stochastic and robust truck-and-drone routing problems with deadlines: A Benders decomposition approach

Time-definite delivery service requires efficient and punctual delivery within specified deadlines. Enhancing the service level of delivery in last-mile logistics prompted the application of a truck-and-drone cooperative system. However, the inherent uncertainty in travel time contributes to frequent service delays. To address this challenge, our study addresses the stochastic and robust truck-and-drone routing problems with deadlines, aiming to minimize service delay risk under uncertainty. We leverage the sample average approximation (SAA) and robust optimization (RO) approaches to handle uncertainty in scenarios involving both big and small datasets. Benders decomposition (BD) algorithms are developed to solve the SAA and RO truck-and-drone routing problems efficiently. Numerical experiments showcase the algorithms’ effectiveness and reveal interesting insights. These findings suggest the importance of tailoring the approach to data availability for optimizing truck-and-drone delivery under uncertainty. Furthermore, the proposed model formulations and algorithms are generalized to address truck-and-drone routing problems under more complex scenarios, such as that with uncertainty of service time, or with nonlinear objective functions.