Local Solution Research Articles

Mild solutions to fourth-order parabolic equations modeling thin film growth with time fractional derivative

In this article, we study initial-boundary problems for fourth-order nonlinear parabolic equations modeling thin film growth with Caputo-type time fractional derivative. By means of the theory of abstract fractional calculus and \(L^p-L^q\) estimates, we establish the existence and uniqueness of local mild solutions in the spaces \(C([0,T]; L^{\frac{\beta N}{2-\beta}}(\Omega))\) with \(1<\beta<2\). Moreover, the local solutions can be extended globally if the initial data is sufficiently small. For more information see https://ejde.math.txstate.edu/Volumes/2024/58/abstr.html

Application of SPNGO-VMD-SVM in rolling bearing fault diagnosis

Abstract Traditional bearing fault feature extraction and fault classification methods have low recognition accuracy and limited recognition capability in noisy environments. To address this problem, this paper proposes an improved northern eagle algorithm (SPNGO) to optimize the variational modal decomposition (VMD) and support vector machine (SVM) to achieve bearing fault diagnosis. Firstly, to overcome the disadvantages of NGO, such as easy fall into local optimal solutions and slow convergence speed, the Sine Cosine Strategy (SCA) and Position Optimisation Search Algorithm (POS) are introduced to optimize the NGO, and the superiority of the SPNGO algorithm is proved through the comparison of different algorithms. Then, SPNGO-VMD is used to adaptively decompose the vibration signals of faulty bearings and generate multiple modal components IMF. The effective IMF components are screened based on the craggy principle to reconstruct the signals. Finally, the reconstructed feature signals are input into SPNGO-SVM for fault classification and compared with other fault diagnosis models. The study results show that the fault diagnosis accuracy of SPNGO-VMD-SVM can reach 96.67%, which can effectively improve the accuracy of bearing fault diagnosis.

Method for robot kinematic parameters identification based on position and orientation data obtained with laser tracker.

How to quickly and accurately identify the kinematic parameter errors is an important prerequisite for robot accuracy compensation. The laser tracker is used to measure and identify the kinematic parameters of the robot. The influence of laser tracker layout in robot pose measurement is analyzed, and the evaluation function of laser tracker layout is constructed to determine the optimal layout position. Then, the mapping relationship between the position and orientation deviation of the robot end and the deviation of each kinematic parameter is established, and the kinematic parameter identification model integrating the position and orientation information is constructed. The identification model is compared to the identification model based on position information to clarify the intrinsic reason of high accuracy. Next, aiming at the problem that the genetic algorithm is easy to prematurely converge to the local optimal solution, a hybrid genetic algorithm is constructed by introducing the simplex method to determine the optimal calibration pose set of the robot. On this basis, the results of robot kinematics parameter identification based on position measurement data, pose measurement data, and optimal calibration pose set are compared and analyzed through experiments, which verifies the effectiveness of the robot kinematics parameter identification model based on pose measurement data and optimization strategy.

Reorganizing public value for city life in the Anthropocene

Public value and city governance are fundamental notions in contemporary settings, but, currently conceived, they are not fit for the challenges presented by the proposed new epoch of geological time—the Anthropocene. Walking through the locked-down streets or calle of Venice, we face the sudden emptiness that starkly reveals the impact of human activity on the city and its waterways. Reflecting on the walk, our starting point is to problematize how a city organizes and manages public value and what actually constitutes public value. In this, we develop a new definition, “New Public Value for the Anthropocene Epoch” (NPVA), which expands the notion of public value through the questions: “who” is it valuable to do things for, beyond humans and economic actors, building on a relational epistemology to incorporate the planet and its biosphere; and “what” is valuable to do, in order to ensure the inclusion of social, environmental, and cultural values alongside economic values. We conclude by arguing that NPVA is organized across scales in a manner that embeds global attentiveness toward local ecosystems solutions to drive the global response to the environmental crisis we all face.

A neurodynamic optimization approach to distributed nonconvex optimization based on an HP augmented Lagrangian function

This paper develops a neurodynamic model for distributed nonconvex-constrained optimization. In the distributed constrained optimization model, the objective function and inequality constraints do not need to be convex, and equality constraints do not need to be affine. A Hestenes–Powell augmented Lagrangian function for handling the nonconvexity is established, and a neurodynamic system is developed based on this. It is proved that it is stable at a local optimal solution of the optimization model. Two illustrative examples are provided to evaluate the enhanced stability and optimality of the developed neurodynamic systems.

Weakly Supervised Underwater Object Real-time Detection Based on High-resolution Attention Class Activation Mapping and Category Hierarchy

Recently, deep learning-based underwater object detection technology has achieved remarkable success. However, the accuracy and completeness of dataset instance annotation are crucial for its success. The quality of underwater images is low, severe objects clustering, and occlusion, acquiring object's annotations demands substantial time and labor costs, while mis annotation and missed annotation can also degrade model performance and limit their application in practical scenarios. To address this issue, this paper presents a novel weakly supervised underwater object real-time detection method, which is divided into two subtasks: weakly supervised object localization and real-time object detection. In the weakly supervised object localization task, we design a novel category hierarchy structure network that integrates the high-resolution attention-class activation mapping algorithm to obtain high-quality object class activation maps, weaken background interference, and obtain more complete object regions. The parameterized spatial loss module is devised to enable the model to escape from local optimal solutions, thus accurately and efficiently obtaining object pseudo-detection annotation boxes. For the real-time object detection task, the single-stage detector YOLOv7 is selected as the basic detection model, and an object perception loss function is designed based on the class activation map to jointly supervise the training process. A method for filtering noisy pseudo-supervision information is proposed to enhance the pseudo-supervision information involved in training. Ablation experiments and multi-method comparison experiments were conducted on the URPC and RUOD datasets, and the results verify the effectiveness of the proposed strategy, and our model exhibits significant advantages in detection performance and detection efficiency compared to current mainstream and advanced models.

Dual-space distribution metric-based evolutionary algorithm for multimodal multi-objective optimization

Multimodal multi-objective optimization problems (MMOPs) are characterized by having multiple global or local Pareto solution sets. In most of multimodal multi-objective evolutionary algorithms, the distribution of population in objective space and decision space cannot be taken into account, simultaneously. In this paper, an innovative evolutionary algorithm based on dual-space distribution metric for multimodal multi-objective optimization (DsDMEA) is designed to solve this problem. Specifically, the two enhanced performance metrics are coupled together as a single dual-space distribution metric (DsDM) serving as the criterion for environmental selection. DsDMEA explores solutions on Pareto front and Pareto solutions sets that are not associated with the reference point, which show limited contributions to the distribution in dual spaces. Then DsDMEA removes any bi-noncontributing solutions using DsDM during environmental selection until the population size is met. This achieves a balance between the distribution of solutions and convergence in decision space. At the same time, this paper introduces a novel fitness computation method, enabling the precise localization of local Pareto fronts within the population. Finally, eight state-of-the-art multimodal multi-objective evolutionary algorithms are adopted to make a comparison on two types of benchmark to verify the performance of the DsDMEA. The experimental results demonstrated the DsDMEA effectiveness in solving MMOPs with local problems and traditional MMOPs.

Existence Results for A Nonlinear Degenerate Parabolic Equation involving -Laplacian Type Diffusion Process

In this study, a nonlinear degenerate parabolic equation is used to describe a nonlinear -Laplacian equation process that arises in many areas of science and engineering in mechanics, quantum physics, and chemical design. This work has the objective of proving the existence of the local weak solution of a nonlinear p(x)-Laplacian equation by the compactness theorem. The uniformly local characteristics of the solutions for the gradients by estimating the regularization problem and using the Moser iterative techniques. Moreover, some properties of the local solutions depend on uniformly bounded situations and the -norm to the gradient is considered.

Local smooth solutions to the Euler-Poisson equations for semiconductor in vacuum

In this paper, we study the initial-boundary value problem to the Euler-Poisson equations for semiconductors, which involves the vacuum for the electronic density, a challenging case because of its degeneracy and singularity. The main issue is to investigate the local well-posedness of smooth solutions to the isentropic system with an adiabatic exponent γ>1, a degenerate hyperbolic-elliptic system on the free boundary. By setting the system to the Lagrangian coordinates, we reduce it to the quasi-linear wave equation coupling the Poisson equations, where the initial degeneracy can be explicitly expressed by the function ρ0γ−1 of the initial density ρ0, which equals to the distance function near boundaries. By applying the Hardy inequality and weighted Sobolev spaces depending on the distance function, we can overcome the degeneracy and singularity of the system caused by the vacuum, and we technically establish some crucial priori estimates and then prove the existence and uniqueness of the local smooth solution. This is the first result on the smooth solution to the Euler-Poisson equations for semiconductors in vacuum.

Hybrid Bee Colony Algorithm with Whale Algorithm

In this research paper, two hybrid algorithms of Meta-Heuristic algorithms, both of which are inspired by nature, are presented: the Bee- settlement Amendment algorithm (BCO) and the Whale Amendment Algorithm (WOA). The Bee settlement Amendment algorithm is an amendment algorithm founded on swarm intelligence modeling attitude. It is one of the techniques of synthetic information that focuses on studying the grouping conduct of decentralized systems, which are represented by groups of modest elements that react locally simultaneously and with the surrounding perimeter. One of the methods that distinguishes it is the method of exploration. As for the Whale Amendment Algorithm, whom represents the friendly conduct of the hump-back whale. It is based on the fancy net fishing design. One of the advantages of this algorithm depends on the poise between screening and utilization and avoidance of falling into local solutions. A hybridization process was carried out between the two algorithms, and the new algorithm was named (ABCWOA), and the whole algorithm was used to 16 rising -measurement Amendment assignment with diverse frequencies between (100, 200, 500, and 1000). The outcomes of the proposition algorithm showed access to optimality solutions by achieving the minimum value (f_min). For most assignment, the outcomes of this algorithm were disparity with the search algorithms.

An Efficient Gradient Based Modified Cuckoo Search Optimization with Dynamic Levy Flight (MCSO-DLF) Algorithm for Breast Cancer Detection

Purpose of Study: This study evaluates the Gradient-Based Dynamic Levy Flight Cuckoo Search Optimization (MCSO-DLF) for breast cancer detection and compares it to six established optimization algorithms. The goal is to determine if MCSO-DLF offers higher accuracy and computational efficiency for optimizing diagnostic models. Methodology: The study compares MCSO-DLF with PSO, GA, ACO, SA, DE, and ABC using the Breast Cancer Wisconsin dataset. The algorithms are evaluated based on accuracy, convergence speed, and efficiency. MCSO-DLF uses dynamic Levy flight and gradient-based optimization to improve solution quality. Main Findings: MCSO-DLF achieved the highest accuracy (0.9912) and fastest computation time (65.94 seconds), outperforming all other algorithms. This demonstrates its effective balance between exploration and local solution refinement. Implications: MCSO-DLF significantly improves accuracy and speed, offering potential advancements in breast cancer detection systems, leading to better patient outcomes and more efficient healthcare. Novelty of Study: This study introduces MCSO-DLF as a novel hybrid optimization method that combines gradient-based optimization with dynamic Levy flight, outperforming traditional algorithms in complex medical diagnostics.

An Efficient Gradient Based Modified Cuckoo Search Optimization with Dynamic Levy Flight (MCSO-DLF) Algorithm for Breast Cancer Detection

Purpose of Study: This study evaluates the Gradient-Based Dynamic Levy Flight Cuckoo Search Optimization (MCSO-DLF) for breast cancer detection and compares it to six established optimization algorithms. The goal is to determine if MCSO-DLF offers higher accuracy and computational efficiency for optimizing diagnostic models. Methodology: The study compares MCSO-DLF with PSO, GA, ACO, SA, DE, and ABC using the Breast Cancer Wisconsin dataset. The algorithms are evaluated based on accuracy, convergence speed, and efficiency. MCSO-DLF uses dynamic Levy flight and gradient-based optimization to improve solution quality. Main Findings: MCSO-DLF achieved the highest accuracy (0.9912) and fastest computation time (65.94 seconds), outperforming all other algorithms. This demonstrates its effective balance between exploration and local solution refinement. Implications: MCSO-DLF significantly improves accuracy and speed, offering potential advancements in breast cancer detection systems, leading to better patient outcomes and more efficient healthcare. Novelty of Study: This study introduces MCSO-DLF as a novel hybrid optimization method that combines gradient-based optimization with dynamic Levy flight, outperforming traditional algorithms in complex medical diagnostics.

Ameliorated Fick’s law algorithm based multi-threshold medical image segmentation

Medical image segmentation is a critical and demanding step in medical image processing, which provides a solid foundation for subsequent medical image data extraction and analysis. Multi-threshold image segmentation, one of the most commonly used and specialized image segmentation techniques, limits its application to medical images because it requires demanding computational performance and is difficult to produce satisfactory segmentation results. To overcome the above problems, an ameliorated Fick's law algorithm (MsFLA) for multi-threshold image segmentation is developed in this paper. First, an optimized sine–cosine strategy is introduced to extend the molecular diffusion process to alleviate the problem of easily falling into local optima, thus improving the convergence accuracy of the Fick's law algorithm (FLA). Secondly, the introduction of local minimal value avoidance enriches the individual molecular information and enhances the local search ability, thus improving computational accuracy. In addition, the optimal neighborhood learning strategy is added to ensure a more careful and reasonable reliance on the optimal solution, thus reducing the chance of convergence of a local solution. The efficient optimization capability of MsFLA is comprehensively validated by comparing MsFLA with the original FLA and other algorithms in 23 classical benchmark functions. Finally, MsFLA is applied to image segmentation of grayscale images of COVID-19 and brain and color images of Lung and Colon cancer histopathology by using Cross entropy to validate its segmentation capability. The experimental results show that the MsFLA obtains the best segmentation results in three medical image cases compared to other comparison algorithms, which indicates that MsFLA can effectively solve the multi-threshold medical image segmentation problem.Graphical abstract

Could deep-sea mining sustain sustainability? The international seabed authority and the UN 2030 agenda

Madureira et al. (2023)published a timely article about the role of deep-sea mining in sustainable development – UN Agenda 2030. We take the opportunity to join the discussion initiated by the authors and highlight the known challenges in deep-sea mining discussions using rich, empirical social and natural science literature. Our premise is the following: sustainable development depends on careful assessment of pressing, known issues that need attention. Local problems require context-specific, local solutions to make propositions about the future and sustainability unambiguous and workable. Meaningful discussions on sustainability in relation to ocean and terrestrial mining depend on engagement with a broad body of literature, from anthropology to human geography, policy and governance research, among others. In sum, we hope to contribute to a more comprehensive interdisciplinary discussion on the contested topic of deep-sea mining and its role in sustainability.

Robotic navigation with deep reinforcement learning in transthoracic echocardiography

Abstract Purpose The search for heart components in robotic transthoracic echocardiography is a time-consuming process. This paper proposes an optimized robotic navigation system for heart components using deep reinforcement learning to achieve an efficient and effective search technique for heart components. Method The proposed method introduces (i) an optimized search behavior generation algorithm that avoids multiple local solutions and searches for the optimal solution and (ii) an optimized path generation algorithm that minimizes the search path, thereby realizing short search times. Results The mitral valve search with the proposed method reaches the optimal solution with a probability of 74.4%, the mitral valve confidence loss rate when the local solution stops is 16.3% on average, and the inspection time with the generated path is 48.6 s on average, which is 56.6% of the time cost of the conventional method. Conclusion The results indicate that the proposed method improves the search efficiency, and the optimal location can be searched in many cases with the proposed method, and the loss rate of the confidence in the mitral valve was low even when a local solution rather than the optimal solution was reached. It is suggested that the proposed method enables accurate and quick robotic navigation to find heart components.

SPLHRNMTF: robust orthogonal non-negative matrix tri-factorization with self-paced learning and dual hypergraph regularization for predicting miRNA-disease associations

MicroRNAs (miRNAs) have been demonstrated to be closely related to human diseases. Studying the potential associations between miRNAs and diseases contributes to our understanding of disease pathogenic mechanisms. As traditional biological experiments are costly and time-consuming, computational models can be considered as effective complementary tools. In this study, we propose a novel model of robust orthogonal non-negative matrix tri-factorization (NMTF) with self-paced learning and dual hypergraph regularization, named SPLHRNMTF, to predict miRNA-disease associations. More specifically, SPLHRNMTF first uses a non-linear fusion method to obtain miRNA and disease comprehensive similarity. Subsequently, the improved miRNA-disease association matrix is reformulated based on weighted k-nearest neighbor profiles to correct false-negative associations. In addition, we utilize L2,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_{2,1}$$\\end{document} norm to replace Frobenius norm to calculate residual error, alleviating the impact of noise and outliers on prediction performance. Then, we integrate self-paced learning into NMTF to alleviate the model from falling into bad local optimal solutions by gradually including samples from easy to complex. Finally, hypergraph regularization is introduced to capture high-order complex relations from hypergraphs related to miRNAs and diseases. In 5-fold cross-validation five times experiments, SPLHRNMTF obtains higher average AUC values than other baseline models. Moreover, the case studies on breast neoplasms and lung neoplasms further demonstrate the accuracy of SPLHRNMTF. Meanwhile, the potential associations discovered are of biological significance.

Tuning parameters of deep neural network training algorithms pays off: a computational study

AbstractThe paper aims to investigate the impact of the optimization algorithms on the training of deep neural networks with an eye to the interaction between the optimizer and the generalization performance. In particular, we aim to analyze the behavior of state-of-the-art optimization algorithms in relationship to their hyperparameters setting to detect robustness with respect to the choice of a certain starting point in ending on different local solutions. We conduct extensive computational experiments using nine open-source optimization algorithms to train deep Convolutional Neural Network architectures on an image multi-class classification task. Precisely, we consider several architectures by changing the number of layers and neurons per layer, to evaluate the impact of different width and depth structures on the computational optimization performance. We show that the optimizers often return different local solutions and highlight the strong correlation between the quality of the solution found and the generalization capability of the trained network. We also discuss the role of hyperparameters tuning and show how a tuned hyperparameters setting can be re-used for the same task on different problems achieving better efficiency and generalization performance than a default setting.

Constricting Gaps: Protocol development, implementation challenges and lessons learned for the reality map of unmet needs for Palliative Care Interventions in advanced cancer patients study in Romania and Switzerland

BackgroundPatients with advanced cancer experience many symptoms and needs requiring a Palliative Care Intervention (PCI). Identifying gaps between needs for PCIs and experienced delivery may improve health care, furthermore the association of gaps with quality indicators (QI). The multicentre Romanian (RO)-Swiss (CH) reality map study implemented a novel protocol based on needs concepts and culturally adapted quality indicators (QI). MethodsAn interactive mapping guide measuring unmet needs for PCIs monthly over six months, patient characteristics (cognition, EAPC basic data set, Cofactors) and QI (Inappropriate Anticancer Treatment, High Symptom Burden [IPOS, EQ5D], Repeated ER Admissions, Aggressive End-of-Life Care, and Quality of Death-and-Dying) were developed, applying swiss standards for quality assurance. A composite endpoint (QI, cofactors) was planned. Finally, local solutions responding to gaps were piloted. ResultsFrom 308 patients (RO: 262, CH: 46, age 62j [mean], 74 % ECOG PS 1&2, 81 % current anticancer treatment) baseline and first follow-up data revealed main gaps (symptom management, spiritual needs, family support), country differences (e.g. illness understanding, spiritual needs) and a significant association of the number of gaps with depression. Later data become less, and data quality on QI variable, revealing gaps in research conduct competences, resources, and applicability of over-sophisticated quality assurance tools. Nevertheless, the unmet needs data promoted local initiatives, 81 patients participated in feasibility studies. Finally, the joint experience stimulated academic developments and national integration of palliative care into oncology. ConclusionsPairing motivation and enthusiasm with more modest aims, feasibility testing of all outcomes and investment in research competences may disperse gaps.

On the local existence and blow-up solutions to a quasi-linear bi-hyperbolic equation with dynamic boundary conditions

This note aims to study the existence of the local solutions and derive a blow-up result for a quasi-linear bi-hyperbolic equation with dynamic boundary conditions. We use the maximal monotone operator theory to demonstrate the solution’s local well-posedness, and a concavity method to establish the blow-up result.

An Exponential Map-based Whale Optimization Algorithm (Exp-WOA) for Optimization

This research work offers three variations of the Whale Optimization Algorithm (WOA) based on exponential chaotic maps, namely Logistic-Exponential-Logistic WOA (LEL-WOA), Logistic-Exponential-Sinusoidal WOA (LES-WOA), and Logistic-Exponential-Tent WOA (LET-WOA). The WOA with an exponential chaos-based mechanism is developed in this study to overcome the poor rate of convergence of the WOA and to prevent getting caught in local optimal solutions while dealing with the challenges. An exponential chaotic mechanism was employed in this research to initialize the agents and control the parameters of the exploration and exploitation phases of WOA. The proposed methodologies (Exp-WOA) are evaluated using twenty-three widely recognized test functions. The results demonstrate that the given solutions can enhance the performance of WOA by achieving optimal (minimum) values. The findings also indicate that LEL-WOA and LES-WOA exhibit faster convergence than WOA.