An Effective Meshless Approach for Inverse Cauchy Problems in 2D and 3D Electroelastic Piezoelectric Structures

In the past decade,notable progress has been achieved in the development of the generalized finite difference method(GFDM).The underlying principle of GFDM involves dividing the domain into multiple sub-domains.Within each sub-domain,explicit formulas for the necessary partial derivatives of the partial differential equations(PDEs)can be obtained through the application of Taylor series expansion and moving-least square approximation methods.Consequently,the method generates a sparse coefficient matrix,exhibiting a banded structure,making it highly advantageous for large-scale engineering computations.In this study,we present the application of the GFDM to numerically solve inverse Cauchy problems in two-and three-dimensional piezoelectric structures.Through our preliminary numerical experiments,we demonstrate that the proposed GFDMapproach shows great promise for accurately simulating coupled electroelastic equations in inverse problems,even with 3%errors added to the input data.

Inverse Spectral Problem for Sturm-Liouville Operator with Boundary and Jump Conditions Dependent on the Spectral Parameter

In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.

A Non-parametric Gradient-Based Shape Optimization Approach for Solving Inverse Problems in Directed Self-Assemblyof Block Copolymers

We consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts.Specifically,we model polymer selfassembly using the self-consistent field theory and derive,in a non-parametric setting,the sensitivity of the dissimilarity between the desired and the actual morphologies to arbitrary perturbations in the guiding pattern shape.The sensitivity is then used for the optimization of the confining pattern shapes such that the dissimilarity between the desired and the actual morphologies is minimized.The efficiency and robustness of the proposed gradient-based algorithm are demonstrated in a number of examples related to templating vertical interconnect accesses(VIA).

Incorporating Lasso Regression to Physics-Informed Neural Network for Inverse PDE Problem

Partial Differential Equation(PDE)is among the most fundamental tools employed to model dynamic systems.Existing PDE modeling methods are typically derived from established knowledge and known phenomena,which are time-consuming and labor-intensive.Recently,discovering governing PDEs from collected actual data via Physics Informed Neural Networks(PINNs)provides a more efficient way to analyze fresh dynamic systems and establish PEDmodels.This study proposes Sequentially Threshold Least Squares-Lasso(STLasso),a module constructed by incorporating Lasso regression into the Sequentially Threshold Least Squares(STLS)algorithm,which can complete sparse regression of PDE coefficients with the constraints of l0 norm.It further introduces PINN-STLasso,a physics informed neural network combined with Lasso sparse regression,able to find underlying PDEs from data with reduced data requirements and better interpretability.In addition,this research conducts experiments on canonical inverse PDE problems and compares the results to several recent methods.The results demonstrated that the proposed PINN-STLasso outperforms other methods,achieving lower error rates even with less data.

An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method

This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications.

An Algorithm for the Inverse Problem of Matrix Processing: DNA Chains, Their Distance Matrices and Reconstructing

We continue to consider one of the cybernetic methods in biology related to the study of DNA chains. Exactly, we are considering the problem of reconstructing the distance matrix for DNA chains. Such a matrix is formed on the basis of any of the possible algorithms for determining the distances between DNA chains, as well as any specific object of study. At the same time, for example, the practical programming results show that on an average modern computer, it takes about a day to build such a 30 × 30 matrix for mnDNAs using the Needleman-Wunsch algorithm;therefore, for such a 300 × 300 matrix, about 3 months of continuous computer operation is expected. Thus, even for a relatively small number of species, calculating the distance matrix on conventional computers is hardly feasible and the supercomputers are usually not available. Therefore, we started publishing our variants of the algorithms for calculating the distance between two DNA chains, then we publish algorithms for restoring partially filled matrices, i.e., the inverse problem of matrix processing. Previously, we used the method of branches and boundaries, but in this paper we propose to use another new algorithm for restoring the distance matrix for DNA chains. Our recent work has shown that even greater improvement in the quality of the algorithm can often be achieved without improving the auxiliary heuristics of the branches and boundaries method. Thus, we are improving the algorithms that formulate the greedy function of this method only. .

Association of preschool children behavior and emotional problems with the parenting behavior of both parents

BACKGROUND Parental behaviors are key in shaping children’s psychological and behavioral development,crucial for early identification and prevention of mental health issues,reducing psychological trauma in childhood.AIM To investigate the relationship between parenting behaviors and behavioral and emotional issues in preschool children.METHODS From October 2017 to May 2018,7 kindergartens in Ma’anshan City were selected to conduct a parent self-filled questionnaire-Health Development Survey of Preschool Children.Children’s Strength and Difficulties Questionnaire(Parent Version)was applied to measures the children’s behavioral and emotional performance.Parenting behavior was evaluated using the Parental Behavior Inventory.Binomial logistic regression model was used to analyze the association between the detection rate of preschool children’s behavior and emotional problems and their parenting behaviors.RESULTS High level of parental support/participation was negatively correlated with conduct problems,abnormal hyperactivity,abnormal total difficulty scores and abnormal prosocial behavior problems.High level of maternal support/participation was negatively correlated with abnormal emotional symptoms and abnormal peer interaction in children.High level of parental hostility/coercion was positively correlated with abnormal emotional symptoms,abnormal conduct problems,abnormal hyperactivity,abnormal peer interaction,and abnormal total difficulty scores in children(all P<0.05).Moreover,paternal parenting behaviors had similarly effects on behavior and emotional problems of preschool children compared with maternal parenting behaviors(all P>0.05),after calculating ratio of odds ratio values.CONCLUSION Our study found that parenting behaviors are associated with behavioral and emotional issues in preschool children.Overall,the more supportive or involved the parents are,the fewer behavioral and emotional problems the children experience;conversely,the more hostile or controlling the parents are,the more behavioral and emotional problems the children face.Moreover,the impact of fathers’parenting behaviors on preschool children’s behavior and emotions is no less significant than that of mothers’parenting behaviors.

A Note on the Inverse Connected p-Median Problem on Block Graphs

Recently, the inverse connected p-median problem on block graphs G(V,E,w) under various cost functions, say rectilinear norm, Chebyshev norm, and bottleneck Hamming distance. Their contributions include finding a necessary and sufficient condition for the connected p-median problem on block graphs, developing algorithms and showing that these problems can be solved in O(n log n) time, where n is the number of vertices in the underlying block graph. Using similar technique, we show that some results are incorrect by a counter-example. Then we redefine some notations, reprove Theorem 1 and redescribe Theorem 2, Theorem 3 and Theorem 4.

Riemann–Hilbert problem for the defocusing Lakshmanan–Porsezian–Daniel equation with fully asymmetric nonzero boundary conditions

The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.

Inverse Electromagnetic Scattering by a Penetrable Chiral Object

We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering problem by the variational method. We focus on a uniqueness result for the inverse scattering problem that is under what conditions an obstacle can be identified by the knowledge of the electric far-field pattern corresponding to all time-harmonic incident planes waves with a fixed wave number. To this end, we establish a chiral mixed reciprocity relation that connects the electric far-field pattern of a spherical wave with the scattered field of a plane wave.

Fuzzy-Inverse-Model-Based Networked Tracking Control Frameworks of Time-Varying Signals

Dear Editor,Tracking control in networked environment is a very challenging problem due to the contradiction of rapid response to the time-varying signal and the inevitable delay introduced by networks. This letter has proposed several fuzzy-inverse-model-based network tracking control frameworks which are helpful in handling the system with nonlinear dynamics and uncertainties.

Enhancing Critical Path Problem in Neutrosophic Environment Using Python

In the real world,one of the most common problems in project management is the unpredictability of resources and timelines.An efficient way to resolve uncertainty problems and overcome such obstacles is through an extended fuzzy approach,often known as neutrosophic logic.Our rigorous proposed model has led to the creation of an advanced technique for computing the triangular single-valued neutrosophic number.This innovative approach evaluates the inherent uncertainty in project durations of the planning phase,which enhances the potential significance of the decision-making process in the project.Our proposed method,for the first time in the neutrosophic set literature,not only solves existing problems but also introduces a new set of problems not yet explored in previous research.A comparative study using Python programming was conducted to examine the effectiveness of responsive and adaptive planning,as well as their differences from other existing models such as the classical critical path problem and the fuzzy critical path problem.The study highlights the use of neutrosophic logic in handling complex projects by illustrating an innovative dynamic programming framework that is robust and flexible,according to the derived results,and sets the stage for future discussions on its scalability and application across different industries.

A Comparative Study of Metaheuristic Optimization Algorithms for Solving Real-World Engineering Design Problems

Real-world engineering design problems with complex objective functions under some constraints are relatively difficult problems to solve.Such design problems are widely experienced in many engineering fields,such as industry,automotive,construction,machinery,and interdisciplinary research.However,there are established optimization techniques that have shown effectiveness in addressing these types of issues.This research paper gives a comparative study of the implementation of seventeen new metaheuristic methods in order to optimize twelve distinct engineering design issues.The algorithms used in the study are listed as:transient search optimization(TSO),equilibrium optimizer(EO),grey wolf optimizer(GWO),moth-flame optimization(MFO),whale optimization algorithm(WOA),slimemould algorithm(SMA),harris hawks optimization(HHO),chimp optimization algorithm(COA),coot optimization algorithm(COOT),multi-verse optimization(MVO),arithmetic optimization algorithm(AOA),aquila optimizer(AO),sine cosine algorithm(SCA),smell agent optimization(SAO),and seagull optimization algorithm(SOA),pelican optimization algorithm(POA),and coati optimization algorithm(CA).As far as we know,there is no comparative analysis of recent and popular methods against the concrete conditions of real-world engineering problems.Hence,a remarkable research guideline is presented in the study for researchersworking in the fields of engineering and artificial intelligence,especiallywhen applying the optimization methods that have emerged recently.Future research can rely on this work for a literature search on comparisons of metaheuristic optimization methods in real-world problems under similar conditions.

Inverse design of mechanical metamaterial achieving a prescribedconstitutive curve

Besides exhibiting excellent capabilities such as energy absorption,phase-transforming metamaterials offer a vast design space for achieving nonlinear constitutive relations.This is facilitated by switching between different patterns under deformation.However,the related inverse design problem is quite challenging,due to the lack of appropriate mathematical formulation and the convergence issue in the post-buckling analysis of intermediate designs.In this work,periodic unit cells are explicitly described by the moving morphable voids method and effectively analyzed by eliminating the degrees of freedom in void regions.Furthermore,by exploring the Pareto frontiers between error and cost,an inverse design formulation is proposed for unit cells.This formulation aims to achieve a prescribed constitutive curve and is validated through numerical examples and experimental results.The design approach presented here can be extended to the inverse design of other types of mechanical metamaterials with prescribed nonlinear effective properties.

Triple reverse order law for the Drazin inverse

In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.

Uncertainty quantification of inverse analysis for geomaterials using probabilistic programming

Uncertainty is an essentially challenging for safe construction and long-term stability of geotechnical engineering.The inverse analysis is commonly utilized to determine the physico-mechanical parameters.However,conventional inverse analysis cannot deal with uncertainty in geotechnical and geological systems.In this study,a framework was developed to evaluate and quantify uncertainty in inverse analysis based on the reduced-order model(ROM)and probabilistic programming.The ROM was utilized to capture the mechanical and deformation properties of surrounding rock mass in geomechanical problems.Probabilistic programming was employed to evaluate uncertainty during construction in geotechnical engineering.A circular tunnel was then used to illustrate the proposed framework using analytical and numerical solution.The results show that the geomechanical parameters and associated uncertainty can be properly obtained and the proposed framework can capture the mechanical behaviors under uncertainty.Then,a slope case was employed to demonstrate the performance of the developed framework.The results prove that the proposed framework provides a scientific,feasible,and effective tool to characterize the properties and physical mechanism of geomaterials under uncertainty in geotechnical engineering problems.

Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems

This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.

Linking 24-h Movement Behavior Guidelines to Cognitive Difficulties,Internalizing and Externalizing Problems in Preterm Youth

Background:Given the heightened risk of developmental challenges associated with preterm birth,it is crucial to explore interventions that may ameliorate potential adverse outcomes.This study aimed to examine whether meeting the 24-h movement behavior(24-HMB)guidelines,which include recommendations on physical activity(PA),screen time(ST),and sleep(SL),is related to indicators of cognitive difficulties,internalizing problems(e.g.,depression and anxiety),and externalizing problems(e.g.,difficulties in making friends and arguing)in a sample of preterm youth(children and adolescents born preterm).Methods:In this cross-sectional study,data from 3410 preterm youth(aged 6 to 17 years)were included for data analyses.Multivariable logistic regression was used to investigate associations between meeting the 24-HMB guidelines and the above-mentioned health outcomes,while controlling for sociodemographic and health-related factors.Results:The prevalence of meeting 24-HMB guidelines varied across independent and integrated components of the 24-HMB guidelines.Meeting the ST guideline alone(p<0.05)and integrated guidelines(i.e.,ST+SL and ST+SL+PA)were associated with fewer cognitive difficulties and reduced internalizing and externalizing problems(p<0.05).Specifically,meeting the SL guideline alone and integrated guidelines(i.e.,SL+ST)were associated with lower odds of depression and anxiety(p<0.01).Additionally,meeting independent,and integrated(PA and/or ST)guidelines were associated with less pronounced difficulties in making friends and arguing(p<0.05).Meeting 24-HMB guidelines in an isolated and integrated manner are linked to better cognitive performance and fewer internalizing and externalizing problems in preterm youth.Conclusion:Results suggest that advocating for the implementation of the 24-HMB guidelines may reduce cognitive challenges and behavioral issues,which is of high relevance for improving public health.Future longitudinal studies in preterm youth should investigate how modifying specific 24-HMB behaviors,especially ST,influence cognitive difficulties,internalizing and externalizing problems in this vulnerable population.

Sequential Inverse Optimal Control of Discrete-Time Systems

This paper presents a novel sequential inverse optimal control(SIOC)method for discrete-time systems,which calculates the unknown weight vectors of the cost function in real time using the input and output of an optimally controlled discrete-time system.The proposed method overcomes the limitations of previous approaches by eliminating the need for the invertible Jacobian assumption.It calculates the possible-solution spaces and their intersections sequentially until the dimension of the intersection space decreases to one.The remaining one-dimensional vector of the possible-solution space’s intersection represents the SIOC solution.The paper presents clear conditions for convergence and addresses the issue of noisy data by clarifying the conditions for the singular values of the matrices that relate to the possible-solution space.The effectiveness of the proposed method is demonstrated through simulation results.

Optimal Shape Factor and Fictitious Radius in the MQ-RBF:Solving Ill-Posed Laplacian Problems

To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).