Solution Of Problem Research Articles

Noise-Generating and Imaging Mechanism Inspired Implicit Regularization Learning Network for Low Dose CT Reconstrution.

Low-dose computed tomography (LDCT) helps to reduce radiation risks in CT scanning while maintaining image quality, which involves a consistent pursuit of lower incident rays and higher reconstruction performance. Although deep learning approaches have achieved encouraging success in LDCT reconstruction, most of them treat the task as a general inverse problem in either the image domain or the dual (sinogram and image) domains. Such frameworks have not considered the original noise generation of the projection data and suffer from limited performance improvement for the LDCT task. In this paper, we propose a novel reconstruction model based on noise-generating and imaging mechanism in full-domain, which fully considers the statistical properties of intrinsic noises in LDCT and prior information in sinogram and image domains. To solve the model, we propose an optimization algorithm based on the proximal gradient technique. Specifically, we derive the approximate solutions of the integer programming problem on the projection data theoretically. Instead of hand-crafting the sinogram and image regularizers, we propose to unroll the optimization algorithm to be a deep network. The network implicitly learns the proximal operators of sinogram and image regularizers with two deep neural networks, providing a more interpretable and effective reconstruction procedure. Numerical results demonstrate our proposed method improvements of > 2.9 dB in peak signal to noise ratio, > 1.4% promotion in structural similarity metric, and > 9 HU decrements in root mean square error over current state-of-the-art LDCT methods.

A solution for abstract decision problems based on maximum flow value

An abstract decision problem is an ordered pair where the first component is a nonempty and finite set of alternatives from which a society has to make a choice and the second component is an irreflexive relation on that set representing a dominance relation. A crucial problem is to find a reasonable solution that allows to select, for any given abstract decision problem, some of the alternatives. A variety of solutions have been proposed over the years. In this paper we propose a new solution, called maximum flow value set, that naturally stems from the work by Bubboloni and Gori (The flow network method, Social Choice and Welfare 51, pp.621-656, 2018) and that is based on the concept of maximum flow value in a digraph. We analyze its properties and its relation with other solutions such as the core, the admissible set, the uncovered set, the Copeland set and the generalized stable set. We also show that the maximum flow value set allows to define a new Condorcet social choice correspondence strictly related to the Copeland social choice correspondence and fulfilling lots of desirable properties.

Super-targeting of non-minimal WHEN systems

Energy conservation and emission reduction have become critical issues due to increasing environmental policy pressures and high energy prices. Work and heat exchange network (WHEN) synthesis is a promising approach to enhance the energy efficiency of energy-intensive processes. WHEN considering single-stage compression/expansion can be divided into two classes by structure complexity: minimal structure and non-minimal structure. The synthesis problem of minimal structure has been addressed in our previous work, where the global optimal solution can be guaranteed. In contrast, the compressors/expanders are not at the beginning or end of the streams' paths in the non-minimal structure and therefore the inlet/outlet temperatures are now variables of the problem. Instead of solving this complicated problem directly, we propose a super-targeting model to screen and scope the solution space for primal promising options before detailed structure design which can be designed using regular HEN synthesis methods. The super-target is estimated by regulating the thermodynamic paths of hot and cold streams where the objective function uses classical HEN super-target to evaluate the costs of the heat exchanger network. Benefiting from the unimodal nature of non-minimal WHEN super-targeting problems, we develop two deterministic algorithms: one relies on derivatives and one is derivative-free. Case studies show the efficiency of the proposed algorithm. The resulting TAC can be 23.1% lower than the literature report and the solution of super-targeting problems are proven to be globally optimal. The derivative optimization algorithm has been found to exhibit superior efficiency in solving problems of relatively large scale.

Nexus among artificial intelligence implementation, healthcare social innovation, and green image of hospitals’ operations management in Egypt

The aim of this paper is to decipher and investigate the relationship between artificial intelligence implementation (AII), healthcare social innovation (HSI) and hospitals’ green image (HGI) in an Egyptian emerging market. An interdisciplinary research with a mixed-methods approach was conducted to add bricks, conceptually and empirically, that fill a literature gap between using this evolving AI-technology and sustaining socially-innovative medical operations and supply-chain management (OSCM) practices in a dynamic green healthcare industry. After scanning the relevant transdisciplinary literature, the authors developed and tested a conceptual model through analysing data collected from 116 quantitative questionnaires answered by healthcare managers/leaders in 46 Egyptian hospitals. After applying structural equation modeling using SmartPLS-v4, the results illustrated that AII has a positive significant impact on HSI, which has a positive significant influence on HGI. Furthermore, AII-HGI relationship can be fully-mediated significantly by HSI, which confirms the significant role of AI-powered technology in reinforcing socially-innovative medical OSCM processes to sustain an environmental-friendly image of Egyptian hospitals. Based on these quantitative findings and qualitative fruitful interviews with healthcare leaders and technology experts, this article used a comprehensive approach to contribute to AI-enhanced healthcare OSCM literature in interdependent ways. It encapsulated the benefits and obstacles of using AI-driven socially-innovative green medical OSCM practices in emerging healthcare markets similar to Egypt. Moreover, it proposed a balanced scorecard map for communicating and evaluating socially-responsible ecofriendly OSCM strategy of AI-powered hospitals. As for the practical implications, the medical operations and supply-chain managers of similar emerging healthcare markets can benefit from the exemplars highlighted throughout this paper on how their hospitals can invest in AI-based healthcare processes/services, which can provide creative and scientific solutions for social, educational, environmental and economic problems within their countries. Thus, reflecting on the social implications, these digitally-transformed hospitals can contribute innovatively to the social wellbeing of their communities and promote their green image among their supply-chain stakeholders.

Flow modeling and structural characterization in fungal pellets

Fungal pellets are hierarchical systems that can be found in an ample variety of applications. Modeling transport phenomena in this type of systems is a challenging but necessary task to provide knowledge-based processes that improve the outcome of their biotechnological applications. In this work, an upscaled model for total mass and momentum transport in fungal pellets is implemented and analyzed, using elements of the volume averaging and adjoint homogenization methods departing from the governing equations at the microscale in the intracellular and extracellular phases. The biomass is assumed to be composed of a non-Newtonian fluid and the organelles impervious to momentum transport are modeled as a rigid solid phase. The upscaled equations contain effective-medium coefficients, which are predicted from the solution of adjoint closure problems in a three-dimensional periodic domains representative of the microstructure. The construction of these domains was performed for Laccaria trichodermophora based on observations of actual biological structures. The upscaled model was validated with direct numerical simulations in homogeneous portions of the pellets core. It is shown that no significant differences are observed when the dolipores are open or closed to fluid flow. By comparing the predictions of the average velocity in the extracellular phase resulting from the upscaled model with those from the classical Darcy equation (i.e., assuming that the biomass is a solid phase) the contribution of the intracellular fluid phase was evidenced. This work sets the foundations for further studies dedicated to transport phenomena in this type of systems.

Convex Combination Search Algorithm: A Novel Metaheuristic Optimization Algorithm for Solving Global Optimization and Engineering Design Problems

In this paper, a novel metaheuristic optimization algorithm (MHOA) called convex combination search (CCS) is proposed as a solution to global optimization problems and engineering design problems. CCS is based on a combination of rules that depend upon the concept of the linear convex combination. These rules are mathematically modeled to guarantee the variety of solutions at the initialization stage and achieve equilibrium between exploitation, exploration capabilities at the generation stage, the algorithm’s convergence, and robustness. A detailed mathematical model of the algorithm is offered. As an advantage for the CCS algorithm, it requires just two parameters which are the population size and the number of generations for determining the global optimal solution of any optimization problem. The effectiveness of the suggested algorithm is investigated on 17 unconstrained multimodal test functions, and 7 constrained benchmark problems having different characteristics. In addition, five engineering design challenges are resolved to confirm the robustness and dependability of CCS in resolving engineering applications. The efficiency and competitiveness of the proposed algorithm were illustrated in comparison with other methods. A statistical analysis of the results has been carried out to illustrate the competitiveness and power effectiveness of the proposed algorithm. Finally, the sensitivity of the CCS parameters is presented to show the sensitivities of these parameters to the performance of the proposed algorithm.

Characterization of E-Benson proper efficient solutions of vector optimization problems with variable ordering structures in linear spaces

Characterization of E-Benson proper efficient solutions of vector optimization problems with variable ordering structures in linear spaces

A general formulation of reweighted least squares fitting

We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when the solution is sought in any finite-dimensional vector space; secondly, to provide a general strategy to iteratively update the weights according to the approximation error and apply it to the spline fitting problem. In the experiments, we provide numerical examples for the case of polynomials and splines spaces. Subsequently, we evaluate the performance of our fitting scheme for spline curve and surface approximation, including adaptive spline constructions.

Procrustes problem for the inverse eigenvalue problem of normal (skew) J-Hamiltonian matrices and normal J-symplectic matrices

ABSTRACT A square complex matrix A is called (skew) J-Hamiltonian if AJ is (skew) Hermitian where J is a real normal matrix such that J 2 = − I , where I is the identity matrix. In this paper, we solve the Procrustes problem to find normal (skew) J-Hamiltonian solutions for the inverse eigenvalue problem. In addition, a similar problem is investigated for normal J-symplectic matrices.

Closed-Loop Subspace Predictive Control of Gyroscope

Control moment gyroscope (CMG) is used in many applications, especially related to spacecraft navigation. Hence, the trajectory tracking problem of the CMG control is important and worth researching. To address this problem, a closed-loop subspace predictive control (CSPC) of the gyroscope is presented in this paper. The proposed control technique constructs an auxiliary variable based on the known controller information. The constructed auxiliary variable assists to handle the inherent correlation between control inputs and noises in the closed-loop system. Additionally, an unbiased prediction of the system output is obtained to calculate the optimal control input. The theoretical analysis of the recursive feasibility and stability of the proposed control technique is also provided. Ultimately, the effectiveness of the proposed control technique is verified on a real-time experimental platform of the CMG. The experimental results demonstrate the improved trajectory tracking and predictive performance of the proposed control technique. Overall, this paper provides a solution for the trajectory tracking problem of the CMG control.

Recent advances in employing the Laplace homotopy analysis method to nonlinear fractional models for evolution equations and heat-typed problems

This study stems from the growing need for effective mathematical tools to tackle nonlinear fractional evolution equations, which find wide applications in physics and engineering. Traditional methods often struggle to provide exact closed-form solutions for such equations, leading to the development of novel approaches. In this context, the combination of the homotopy analysis method with the Laplace transform presents a promising avenue for obtaining exact solutions to these complex equations. By exploring this hybrid approach, the study aims to address the existing challenges in solving nonlinear fractional models and provide a reliable method for obtaining closed-form solutions. In this way, this study focuses on rendering the coupling between the homotopy analysis approach and the Laplace transform in the search for exact closed-form solutions for the class of fractional evolution and heat-typed equations. In fact, this class of equations features some interesting nonlinear Caputo fractional partial differential equations that model dissimilar physical processes in physics and engineering. A generalized recurrent scheme is derived, which is applicable to all the members of the governing class, and further analyzed the application of this very scheme on some test fractional initial-value problems of much concern. Eventually, the method has been found to be advantageous, with various advantages, including convergence to available exact solutions. Thus, of the advantage of the current study is innovative combination of mathematical methods, the applicability of these methods to a special class of fractional equations, the development of a generalized scheme, the successful solution of prototype problems, and the practical advantages of the method.

Nonlinear optimal control for triangular tethered multi-satellite formations

Triangular satellite constellations are created by three satellites which are linked through tethers. Such formations serve distributed observation space missions or the creation of high-density satellite communication networks over high-frequency bands. In a tethered multi-satellite system consisting of three-satellites in triangular formation the associated dynamic model exhibits strong nonlinearities. Stabilization and precise positioning of the multi-satellite constellation is a nontrivial task and the solution of the associated nonlinear control problem is an elaborated procedure. In this article a novel nonlinear optimal control method is applied to the above-noted model the tethered multi-satellite system in triangular formation. First, the state-space model of the triangular tethered multi-satellite formation undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the tethered satellites a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of setpoints under moderate variations of the control inputs and a minimum dispersion of energy when changing the position of the satellites in their triangular tethered formation.

Generation of genetic codes with 2-adic codon algebra and adaptive dynamics

This is a brief review on modeling genetic codes with the aid of 2-adic dynamical systems. In this model amino acids are encoded by the attractors of such dynamical systems. Each genetic code is coupled to the special class of 2-adic dynamics. We consider the discrete dynamical systems, These are the iterations of a function F:Z2→Z2, where Z2 is the ring of 2-adic numbers (2-adic tree). A genetic code is characterized by the set of attractors of a function belonging to the code generating functional class. The main mathematical problem is to reduce degeneration of dynamic representation and select the optimal generating function. Here optimality can be treated in many ways. One possibility is to consider the Lipschitz functions playing the crucial role in general theory of iterations. Then we minimize the Lip-constant. The main issue is to find the proper biological interpretation of code-functions. One can speculate that the evolution of the genetic codes can be described in information space of the nucleotide-strings endowed with ultrametric (treelike) geometry. A code-function is a fitness function; the solutions of the genetic code optimization problem are attractors of the code-function. We illustrate this approach by generation of the standard nuclear and (vertebrate) mitochondrial genetics codes.

Informed Adaptive Sensing.

For many inverse problems, the data on which the solution is based is acquired sequentially. We present an approach to the solution of such inverse problems where a sensor can be directed (or otherwise reconfigured on the fly) to acquire a particular measurement. An example problem is magnetic resonance image reconstruction. We use an estimate of mutual information derived from an empirical conditional distribution provided by a generative model to guide our measurement acquisition given measurements acquired so far. The conditionally generated data is a set of samples which are representative of the plausible solutions that satisfy the acquired measurements. We present experiments on toy and real world data sets. We focus on image data but we demonstrate that the method is applicable to a broader class of problems. We also show how a learned model such as a deep neural network can be leveraged to allow generalisation to unseen data. Our informed adaptive sensing method outperforms random sampling, variance based sampling, sparsity based methods, and compressed sensing.

Homogenization of non-Darcy flow in porous media containing spheroidal impervious inclusions

The aim of the present study is to determine the nonlinear filtration law of a porous medium containing spheroidal impervious inclusions through a homogenization framework. At the local scale, it is assumed that the fluid flow through the porous solid surrounding the inclusions obeys the Forchheimer equation. The macroscopic law is derived in the field of nonlinear variational approach applied to some representative cell, namely a porous spheroid containing a single centered spheroidal inclusion confocal to the outer. Both a static and kinematical approach are developed to bound the overall filtration properties of the heterogeneous solid. Appropriate trial fields are considered to determine closed-form estimates and are obtained from the solution of a linear problem replacing the Forchheimer law in the porous solid at the microscopic scale by the Darcy law. The analytic estimates are calculated through some approximations and lead to accurate solutions of the nonlinear problems. Finally, the analytic models are compared with FFT solutions in the case of a regular array of spheroidal impervious inclusions.

Subdifferential calculus and ideal solutions for set optimization problems

Subdifferential calculus and ideal solutions for set optimization problems

A novel anode with improved electrochemical performance based on cobalt squarate for lithium-ion batteries

Organics matter squaric acid with small molecules and multiple active sites are of great potential to obtain a high theoretical specific capacity. However, square acids are easily dissolved in the electrolyte, causing it to exhibit characteristics of low capacity and poor cycling performance. Metal ions are introduced to create metal–organic frameworks (MOFs), which is one of the efficient solutions for the aforementioned problems. MOFs based on π-d systems can improve stabilities and inhibit the dissolution of organic ligands. Meanwhile, different metal ions can modify its electrochemical properties, especially those with redox activity, which can significantly improve the capacity and stability of the MOFs. In this paper, the M−SQ (M = Co, Ni, Mn) based on square acid was synthesized, compare to Ni-SQ and Mn-SQ, Co-SQ with multiple redox-active centers shown greater reversible capacity and cycle stability, which has 1242.2 mA h g−1 at 0.1 A g−1, it is present an excellent capacity, and Co-SQ also has good rate capacity, when current density added to 2 A g−1, it has 807.9 mA h g−1. Meanwhile, Co-SQ showing an outstanding long cycle life with 481.8 mA h g−1 after 700 cycles at 1 A g−1. In addition, Co-SQ with a porous structure has a higher capacity than Co-SQ-NaOH with rod-like structure. Further, the Li+ storage advantage of the porous structure Co-SQ was revealed by kinetic studies. The strategy though tunable active sites of metals and carbonyl is great potential for obtaining high-performance energy storage materials.

Physics-informed neural network for diffusive wave model

The diffusive wave model (DWM), a nonlinear second-order simplified form of the shallow water equation, has been widely used in hydraulic, hydrologic and irrigation engineering. Solving the forward problem of the DWM can be utilized to predict evolution in water levels and discharge. Solving its inverse problem allows for the identification of crucial parameters (such as Manning's coefficient, rainfall intensity, etc.) based on observations. This paper applies the physics-informed neural network (PINN) with novel improvements to solve the DWM for both forward and inverse problems. In the forward problem, compared to traditional numerical methods, PINN can predict the evolution at any location. In the inverse problem, PINN provides a simple and efficient solution process. In order to overcome the gradient explosion in the training process caused by the characteristics of the DWM, the stop-gradient technique was adopted to train the neural network. To improve the estimation of DWM parameters, the concept of time division was developed, and a new network structure was then proposed. To verify the effectiveness of PINN and its improved algorithm for DWM, seven examples were simulated. The PINN solutions for forward problems were compared with the results obtained by classical numerical methods, while the correct rainfall pattern was learnt for the inverse problem.

Highly accurate wavelet solution for the two-dimensional Bratu's problem

A modified wavelet interpolation Galerkin method (WIGM) with improved flexibility of nodal distribution is formulated and utilized to solve the Bratu's problem. Such a method treats the nonlinear term as an independent function and directly approximates it through the proposed wavelet interpolation, resulting in a low-cost discretization of the Bratu's equation with exponential nonlinearity. An efficient implementation of Newton's method to find the lower and upper branches of solution as well as the turning point is then presented. Numerical results demonstrate that the present WIGM can accurately estimate both two solution branches and turning point for the Bratu's problem. Compared with many other existing methods, the proposed WIGM also offers marked superiority in terms of accuracy when using the same node distribution. Moreover, a convergent solution to the resulting nonlinear discrete system obtained by the WIGM can be observed in a few iterations even when the initial guess significantly deviates from the exact solution. Finally, a highly accurate approximation of both two-branched solutions and the turning point for the two-dimensional Bratu's problem is obtained by the proposed WIGM.

A mid-range approximation method assisted by trust region strategy for aerodynamic shape optimization

This paper presents an efficient solution for high-fidelity large-scale aerodynamic shape optimization problems based on several developments in the mid-range approximation method within a trust region optimization framework. The mid-range approximation method is an iterative optimization technique that utilizes mid-range approximations to replace the physical experiments or simulations during the optimization based on the selected trust region strategy. It could transform the original optimization problem into a sequence of approximate sub-optimization problems. In this work, an improved trust region strategy is proposed to contain more optimization states with a flexible and controllable performance to suit different types of problems. A metamodel assembly technique and its gradient-enhanced version are developed to further relax the requirements of computational costs in the mid-range approximation method. Its performance is discussed through a detailed comparison of metamodel performance using a mathematical benchmark case named Vanderplaats scalable beam. The wing only of the Common Research Model is offered to the proposed method for aerodynamic shape optimization. The optimization has 1 design objective, 232 design variables, and 135 design constraints. With all constraints satisfied, the optimized configuration has a 4.85% improvement in wing drag performance. The shock region is greatly reduced and the wing pressure distribution is smooth and nearly parallel. These results show that the proposed method could achieve the design goal successfully within a reasonable computational cost for large-scale problems.