Scalar Method Research Articles

Unboundedness of the images of set-valued mappings having closed graphs: application to vector optimization

AbstractIn this paper, we propose criteria for unboundedness of the images of set-valued mappings having closed graphs in Euclidean spaces. We focus on mappings whose domains are non-closed or whose values are connected. These criteria allow us to see structural properties of solutions in vector optimization, where solution sets can be considered as the images of solution mappings associated to specific scalarization methods. In particular, we prove that if the domain of a certain solution mapping is non-closed, then the weak Pareto solution set is unbounded. Furthermore, for a quasi-convex problem, we demonstrate two criteria to ensure that if the weak Pareto solution set is disconnected then each connected component is unbounded.

Investigating Different Dynamic pHP1α States in Their KCl-Mediated Liquid-Liquid Phase Separation (LLPS) Using Solid-State NMR (SSNMR) and Molecular Dynamic (MD) Simulations.

Chromatin phase separation is dynamically regulated by many factors, such as post-translational modifications and effector proteins, and plays a critical role in genomic activities. The liquid-liquid phase separation (LLPS) of chromatin and/or effector proteins has been observed both in vitro and in vivo. However, the underlying mechanisms are largely unknown, and elucidating the physicochemical properties of the phase-separated complexes remains technically challenging. In this study, we detected dynamic, viscous, and intermediate components within the phosphorylated heterochromatin protein 1α (pHP1α) phase-separated system by using modified solid-state NMR (SSNMR) pulse sequences. The basis of these sequences relies on the different time scale of motion detected by heteronuclear Overhauser effect (hetNOE), scalar coupling-based, and dipolar coupling-based transfer schemes in NMR. In comparison to commonly utilized scalar coupling-based methods for studying the dynamic components in phase-separated systems, hetNOE offers more direct insight into molecular dynamics. NMR signals from the three different states in the protein gel were selectively excited and individually studied. Combined with molecular dynamics (MD) simulations, our findings indicate that at low KCl concentration (30 mM), the protein gel displays reduced molecular motion. Conversely, an increase in molecular motion was observed at a high KCl concentration (150 mM), which we attribute to the resultant intermolecular electrostatic interactions regulated by KCl.

A convergent stochastic scalar auxiliary variable method

A convergent stochastic scalar auxiliary variable method

A scalar method for measuring the reactive element in microwave and millimeter-wave bands

This paper introduces a novel scalar method to determine the value of reactive elements by only measuring the amplitude value of the reflection coefficient. The methodology is illustrated using a Smith Chart, integrating reactive elements in series or parallel with a standard resistance element, and deriving a corresponding equation. Simulation results closely align with theoretical predictions. This approach extends beyond reactive elements, applying universally to π/T-network circuits. It obviates the need for Vector Network Analyzers (VNA) in measurement, reduces equipment requirements, and holds substantial importance for measuring diverse types of reactive microwave elements.

Multiobjective optimization guided by image quality index for limited-angle CT image reconstruction.

Due to the incomplete projection data collected by limited-angle computed tomography (CT), severe artifacts are present in the reconstructed image. Classical regularization methods such as total variation (TV) minimization, ℓ0 minimization, are unable to suppress artifacts at the edges perfectly. Most existing regularization methods are single-objective optimization approaches, stemming from scalarization methods for multiobjective optimization problems (MOP). To further suppress the artifacts and effectively preserve the edge structures of the reconstructed image. This study presents a multiobjective optimization model incorporates both data fidelity term and ℓ0-norm of the image gradient as objective functions. It employs an iterative approach different from traditional scalarization methods, using the maximization of structural similarity (SSIM) values to guide optimization rather than minimizing the objective function.The iterative method involves two steps, firstly, simultaneous algebraic reconstruction technique (SART) optimizes the data fidelity term using SSIM and the Simulated Annealing (SA) algorithm for guidance. The degradation solution is accepted in the form of probability, and guided image filtering (GIF) is introduced to further preserve the image edge when the degradation solution is rejected. Secondly, the result from the first step is integrated into the second objective function as a constraint, we use ℓ0 minimization to optimize ℓ0-norm of the image gradient, and the SSIM, SA algorithm and GIF are introduced to guide optimization process by improving SSIM value like the first step. With visual inspection, the peak signal-to-noise ratio (PSNR), root mean square error (RMSE), and SSIM values indicate that our approach outperforms other traditional methods. The experiments demonstrate the effectiveness of our method and its superiority over other classical methods in artifact suppression and edge detail restoration.

A Methodology to Optimize PMSM Driven Solar Water Pumps Using a Hybrid MPPT Approach in Partially Shaded Conditions

Solar water pumps are crucial for farmers, significantly reducing energy costs and providing independence from conventional fuels. Their adoption is further incentivized by government subsidies, making them a practical choice that aligns with sustainable agricultural practices. However, the cost of the required solar panels for the chosen power makes it essential to optimize solar water pumping systems (SWPS) for economic viability. This study enhances the efficiency and reliability of permanent magnet synchronous motor (PMSM)-driven SWPS in rural areas using hybrid maximum power point tracking (MPPT) algorithms and voltage-to-frequency (V/f) control strategy. It investigates the sensorless scalar control method for PMSM-based water pumps and evaluates various MPPT algorithms, including grey wolf optimization (GWO), particle swarm optimization (PSO), perturb and observe (PO), and incremental conductance (INC), along with hybrid combinations. The study, conducted using MATLAB Simulink, assesses these algorithms on convergence time, MPPT accuracy, torque ripple, and system efficiency under different partial shading conditions. Findings reveal that INC-GWO excels, providing higher accuracy, faster convergence, and reduced steady-state oscillations, thus boosting system efficiency. The V/f control strategy simplifies control mechanisms and enhances performance. Considering system non-idealities and maximum duty cycle limitations, PMSM-based SWPS achieve superior efficiency and stability, making them viable for off-grid water pumping applications.

Green Scalar Function Method for Analyzing Dielectric Media

In this work we present a formalism based on scalar Green’s functions to deal with electromagnetic scattering problems. Although the formulations of the Mie theory and Born approximations in terms of electromagnetic scattering are well known and relevant, they have certain disadvantages: complexity, computational time, few symmetries, etc. Therefore, the study with scalar Green’s functions allows dealing with these problems with greater simplicity and efficiency. However, the information provided by the vector formulation is sacrificed. Nevertheless, different cases of electromagnetic scattering of dielectric media with different dimensions, geometries and refractive indices will be presented. Thus, we will be able to verify the capacity of this scalar method in predicting light-scattering problems.

Analysis and numerical simulation of a generalized compressible Cahn–Hilliard–Navier–Stokes model with friction effects

We propose a new generalized compressible diphasic Navier–Stokes Cahn–Hilliard model that we name G-NSCH. This new G-NSCH model takes into account important properties of diphasic compressible fluids such as possible non-matching densities and contrast in mechanical properties (viscosity, friction) between the two phases of the fluid. The model also comprises a term to account for possible exchange of mass between the two phases. Our G-NSCH system is derived rigorously and satisfies basic mechanics of fluids and thermodynamics of particles. Under some simplifying assumptions, we prove the existence of global weak solutions. We also propose a structure preserving numerical scheme based on the scalar auxiliary variable method to simulate our system and present some numerical simulations validating the properties of the numerical scheme and illustrating the solutions of the G-NSCH model.

Center Conditions for Nilpotent Singularities in the Plane Using Invariant Solutions

Recalling that at any regular point we always have a unique particular solution curve passing through it. In this work it is constructed such particular solution curve not passing through the nilpotent singularity but as close as we want to the singularity. By product the existence of such particular curve allows to use it to determine necessary conditions to have a center for nilpotent singularities in the plane. Several involve methods to solve the center problem are known all based in the existence of a change of variables and a scaling transformation of time bringing any differential system with a nilpotent center into a time-reversible system. Here we present a new algebraic method based on the existence of such particular solution curve not passing through the singular point and the involution associated to the nilpotent system with a center. The algebraic method needs the computation of this particular curve up to certain order, which can be done with the help of an algebraic manipulator. Finally a new algebraic method is derived computing the vanishing of a unique function which really gives a scalar method for computing the necessary conditions.

A comparative study of different algorithms and scalarization techniques for constructing the Pareto front of multiobjective optimization problems

This paper presents an analysis and comparison of various algorithms applied to different scalarization methods for multiobjective optimization problems (MOPs). At first, some theoretical results are provided on the relation between (weakly) efficient solutions of an MOP and optimal solutions of the related numerical method. Moreover, we consider some deficiencies in different scalarization approaches given in the literature and try to fill some gaps in these works. Hence, by considering appropriate limitations, we provide sufficient conditions for (ε-)properly efficient and (ε-)efficient solutions of an MOP via scalarization techniques. Then, an algorithm for approximating the Pareto front of MOPs is presented. The main purpose of this algorithm is to generate efficient points on the Pareto front with a uniform distribution. One advantage of this algorithm, compared to some other algorithms, is that in each iteration of the algorithm, more than one efficient point located on the Pareto border can be generated. The new algorithm is implemented by applying the modified Pascoletti–Serafini, the unified direction, and the modified normal boundary intersection scalarization techniques, and then the procedures are considered on different test problems including (non-)convex and discrete Pareto fronts. The capability of the numerical method is shown by comparing the results with the algorithms in the literature. To compare the algorithms, measures of coverage and spacing metric indicators are used.

Intrinsic second-order magnon thermal Hall effect

In this paper, we study the intrinsic contribution of nonlinear magnon thermal Hall Effect. We derive the intrinsic second-order thermal Hall conductivity of magnon by the thermal scalar potential method and the thermal vector potential method. We find that the intrinsic second-order magnon thermal Hall conductivity is related to the thermal Berry-connection polarizability. We apply our theory to the monolayer ferromagnetic Hexagonal lattice, and we find that the second-order magnon thermal Hall conductivity can be controlled by changing Dzyaloshinskii–Moriya strength and applying strain.

On Necessary Optimality Conditions for Sets of Points in Multiobjective Optimization

Taking inspiration from what is commonly done in single-objective optimization, most local algorithms proposed for multiobjective optimization extend the classical iterative scalar methods and produce sequences of points able to converge to single efficient points. Recently, a growing number of local algorithms that build sequences of sets has been devised, following the real nature of multiobjective optimization, where the aim is that of approximating the efficient set. This calls for a new analysis of the necessary optimality conditions for multiobjective optimization. We explore conditions for sets of points that share the same features of the necessary optimality conditions for single-objective optimization. On the one hand, from a theoretical point of view, these conditions define properties that are necessarily satisfied by the (weakly) efficient set. On the other hand, from an algorithmic point of view, any set that does not satisfy the proposed conditions can be easily improved by using first-order information on some objective functions. We analyse both the unconstrained and the constrained case, giving some examples.

The Weighted p-Norm Weight Set Decomposition for Multiobjective Discrete Optimization Problems

Many solution algorithms for multiobjective optimization problems are based on scalarization methods that transform the multiobjective problem into a scalar-valued optimization problem. In this article, we study the theory of weighted p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p$$\\end{document}-norm scalarizations. These methods minimize the distance induced by a weighted p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p$$\\end{document}-norm between the image of a feasible solution and a given reference point. We provide a comprehensive theory of the set of eligible weights and, in particular, analyze the topological structure of the normalized weight set. This set is composed of connected subsets, called weight set components which are in a one-to-one relation with the set of optimal images of the corresponding weighted p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p$$\\end{document}-norm scalarization. Our work generalizes and complements existing results for the weighted sum and the weighted Tchebycheff scalarization and provides new insights into the structure of the set of all Pareto optimal solutions.

The high-order exponential semi-implicit scalar auxiliary variable approach for the general nonlocal Cahn-Hilliard equation

The nonlocal Cahn-Hilliard equation with nonlocal diffusion operator is more suitable for the simulation of microstructure phase transition than the local Cahn-Hilliard equation. In this paper, based on the exponential semi-implicit scalar auxiliary variable method, the highly efficient and accurate schemes (in time) with unconditional energy stability for solving the nonlocal Cahn-Hilliard equation are proposed. On the one hand, we have demonstrated the unconditional energy stability and mass conservation for the nonlocal Cahn-Hilliard equation with its high-order numerical schemes in the continuous and discrete level carefully and rigorously. On the other hand, in order to reduce the calculation and storage cost in numerical simulation, we use the fast solver based on fast Fourier transform and conjugate gradient approach for spatial discretization. Some numerical simulations involving the Gaussian kernel are presented and show the stability, accuracy, efficiency and unconditional energy stability of the proposed schemes.

Applying motion compensation to offshore wind lidar reconstructed wind measurements

Floating lidar systems present an effective and advantageous solution for offshore wind speed measurements, providing wind speed and direction data at multiple heights with easy deployment to provide widespread wind information around an area. One of the causes of apprehension, however, concerns buoy motion which induces overestimations of turbulence intensity and potentially imprecise measurements of horizontal wind speed. This research aims to reduce this uncertainty by applying motion compensation to three wind field reconstruction techniques (scalar, vector, and hybrid) to assess the amelioration on horizontal wind speed and turbulence intensity; especially how motion compensation can improve scalar and hybrid outputs. A three-month dataset of a floating lidar system (FLS) was compared to a nearby fixed lidar. The results demonstrate that motion compensation provides an improvement for horizontal wind speed measurement but inflates the overestimation of turbulence intensity from the floating lidar system. Though scalar reconstruction measurements provide slightly more accurate data compared to hybrid reconstructed measurements, motion compensation helps limit the bias disparity; ergo, applying motion compensation reduces the differences in bias for scalar and hybrid reconstructed measurements. This study results in two conclusions. Basic motion compensation provides a notable amelioration for horizontal wind speed FLS measurements, yet further research must be conducted to find a suitable method to improve turbulence intensity. Additionally, the scalar reconstruction method still slightly outperforms hybrid reconstruction in offshore measurement results, but motion compensation aids in limiting the differences between the two.

Employing a Convolutional Neural Network to Classify Sleep Stages from EEG Signals Using Feature Reduction Techniques

One of the most essential components of human life is sleep. One of the first steps in spotting abnormalities connected to sleep is classifying sleep stages. Based on the kind and frequency of signals obtained during a polysomnography test, sleep phases can be separated into groups. Accurate classification of sleep stages from electroencephalogram (EEG) signals plays a crucial role in sleep disorder diagnosis and treatment. This study proposes a novel approach that combines feature selection techniques with convolutional neural networks (CNNs) to enhance the classification performance of sleep stages using EEG signals. Firstly, a comprehensive feature selection process was employed to extract discriminative features from raw EEG data, aiming to reduce dimensionality and enhance the efficiency of subsequent classification using mutual information (MI) and analysis of variance (ANOVA) after splitting the dataset into two sets—the training set (70%) and testing set (30%)—then processing it using the standard scalar method. Subsequently, a 1D-CNN architecture was designed to automatically learn hierarchical representations of the selected features, capturing complex patterns indicative of different sleep stages. The proposed method was evaluated on a publicly available EDF-Sleep dataset, demonstrating superior performance compared to traditional approaches. The results highlight the effectiveness of integrating feature selection with CNNs in improving the accuracy and reliability of sleep stage classification from EEG signals, which reached 99.84% with MI-50. This approach not only contributes to advancing the field of sleep disorder diagnosis, but also holds promise for developing more efficient and robust clinical decision support systems.

Multi-objective reinforcement learning based on nonlinear scalarization and long-short-term optimization

PurposeMany practical control problems require achieving multiple objectives, and these objectives often conflict with each other. The existing multi-objective evolutionary reinforcement learning algorithms cannot achieve good search results when solving such problems. It is necessary to design a new multi-objective evolutionary reinforcement learning algorithm with a stronger searchability.Design/methodology/approachThe multi-objective reinforcement learning algorithm proposed in this paper is based on the evolutionary computation framework. In each generation, this study uses the long-short-term selection method to select parent policies. The long-term selection is based on the improvement of policy along the predefined optimization direction in the previous generation. The short-term selection uses a prediction model to predict the optimization direction that may have the greatest improvement on overall population performance. In the evolutionary stage, the penalty-based nonlinear scalarization method is used to scalarize the multi-dimensional advantage functions, and the nonlinear multi-objective policy gradient is designed to optimize the parent policies along the predefined directions.FindingsThe penalty-based nonlinear scalarization method can force policies to improve along the predefined optimization directions. The long-short-term optimization method can alleviate the exploration-exploitation problem, enabling the algorithm to explore unknown regions while ensuring that potential policies are fully optimized. The combination of these designs can effectively improve the performance of the final population.Originality/valueA multi-objective evolutionary reinforcement learning algorithm with stronger searchability has been proposed. This algorithm can find a Pareto policy set with better convergence, diversity and density.

Scalar auxiliary variable pressure-correction method for natural convection problems⋆

In this article, we present first-order standard pressure-correction and second-order rotational pressure-correction algorithms using an exponential scalar auxiliary variable (SAV) approach for the natural convection problems. The SAV pressure-correction method is linear and decoupled with explicit treatment of nonlinear terms, so it only needs to solve a sequence of Poisson equations for velocity and pressure at each time step. Furthermore, we proved the first- and second-order algorithms are unconditionally stable and established error estimates of the velocity, temperature and pressure approximation for the first-order algorithms without any restriction on the time step. Finally, some numerical experiments are provided to support the theoretical analysis and to show the performances of our proposed algorithms.

Efficient invariant-preserving scheme for the [formula omitted]-coupled nonlinear Schrödinger equations

The N-coupled nonlinear Schrödinger equations are reformulated into an expanded form by using a scalar auxiliary variable method, and then a scheme preserving exactly original mass and energy conservation laws is proposed based on discretizing the expanded form. The scheme is efficient as it consists of decoupled linear systems with constant coefficients, along with a nonlinear algebraic equation that can be solved with negligible computational cost. Some numerical experiments are carried out to demonstrate the behavior of wave solutions, the accuracy of solution and the preservation of physical invariants.

A comparative cost assessment of coalescing epidemic control strategies in heterogeneous social-contact networks

The outcome of an epidemic is contingent upon the mitigating control strategies deployed by policymakers. The deployment of control strategies is constrained by the cost of economic, social, and technological factors, which often depend on regional conditions. Our model facilitates a comparative assessment of costs between two interconnected subpopulations within a heterogeneous social-contact network, which may deploy either aligned or divergent control strategies, as is frequently the case for neighboring countries. Depending on their respective asymmetric resources, each subpopulation can deploy a contact confinement strategy, a vaccination strategy, or a hybrid of both. The multi-objective goal of minimizing both the epidemic burden and the economic cost from policy implementation and productivity losses is compounded using a scaled scalarization method. Due to the inter-dependence of policy outcomes, the optimal strategy is derived from the Nash equilibrium in a 2-player compounded pay-off matrix of the total cost. Our network-based model implements a probabilistic Susceptible-Exposed-Infectious-Recovered-Dead dynamics. It also includes the effects of ego-network support and waning immunity modulated by re-exposure to viral contaminants (‘SEIRSD’). Robust outcomes of repeated network simulations with COVID-19 parameters are examined. Our method aims to equip policymakers in a negotiation process with a comparative cost matrix for divergent mitigation policies and to identify the optimal Nash-based strategy profile.