A Scalable Framework for Learning the Geometry-Dependent Solution Operators of Partial Differential Equations

Mathematics, Information Science, Computer Science, Artificial Intelligence,
partial differential equations   geometric mapping   neural operator   artificial intelligence   computational efficiency  

Introduction In recent years, solving partial differential equations (PDEs) using numerical methods has played a significant role in various fields such as engineering and medicine. These methods have shown remarkable effectiveness in applications like topology and design optimization as well as clinical prognostication. However, the high computati...

Migrant Resettlement by Evolutionary Multiobjective Optimization

Mathematics, Engineering, Information Science, Computer Science, Artificial Intelligence,
migrant resettlement   multiobjective optimization   evolutionary algorithms   greedy algorithm   submodular optimization   humanitarianism   employment rate  

A Research Report on a New Framework for Solving Migrant Resettlement Using Multiobjective Evolutionary Optimization Against the backdrop of accelerated globalization and evolving socio-economic conditions, migration has become an undeniable global trend. From the perspective of humanitarian relief or the sustainable development of a globalized eco...

New Results on Finite-Time Stability and Instability Theorems for Stochastic Nonlinear Time-Varying Systems

Mathematics, Engineering, Information Science, Electronic Information, Computer Science,
stochastic systems   nonlinear dynamics   finite-time stability   stability theorems   nonlinear systems   time-varying systems   Lyapunov method  

New Results on Finite-Time Stability and Instability Theorems for Stochastic Nonlinear Time-Varying Systems 1. Research Background and Significance Stability theory is a central topic in systems theory and engineering applications, serving as the fundamental consideration in system analysis and synthesis. In stability theory, the two most commonly ...

Comparative Numerical Analysis of Astigmatism Tolerance in Bifocal, Extended Depth-of-Focus, and Trifocal Intraocular Lenses

Mathematics, Physics, Optics, Medicine, Ophthalmology, Medical Imaging,
bifocal intraocular lenses   astigmatism tolerance   extended depth of focus   trifocal lenses   visual function   full-wave analysis   postoperative prediction  

Numerical Analysis Enhances Postoperative Visual Assessment and Optimization for Multifocal Intraocular Lenses (IOLs) Introduction and Research Background One of the main goals of cataract surgery is to achieve spectacle-free vision for patients. However, this goal is limited by two major challenges: loss of accommodative function and postoperative...

Event-Triggered Fuzzy Adaptive Stabilization of Parabolic PDE–ODE Systems

Mathematics, Engineering, Electrical Engineering, Information Science, Automation, Artificial Intelligence,
Event-Triggered Control   Fuzzy Logic Systems   Parabolic PDE-ODE Systems   Stabilization Control   Adaptive Backstepping  

Scientific Report: On “Event-Triggered Fuzzy Adaptive Stabilization of Parabolic PDE–ODE Systems” Research Background and Significance In modern engineering systems, such as flexible manipulators, heat transfer devices, and reactor controllers, many complex systems must be modeled using partial differential equations (PDEs). Due to their unique rea...

Optimal Control of Stochastic Markovian Jump Systems with Wiener and Poisson Noises: Two Reinforcement Learning Approaches

Mathematics, Engineering, Information Science, Computer Science, Artificial Intelligence,
Stochastic Markovian Jump Systems   Wiener Noise   Poisson Noise   Reinforcement Learning   Optimal Control   Policy Iteration Algorithm   Numerical Verification  

Optimal Control of Stochastic Markovian Jump Systems with Wiener and Poisson Noises: Two Reinforcement Learning Approaches Academic Context In modern control theory, optimal control is a crucial research field, aiming to design an optimal control strategy under various constraints for dynamic systems to minimize a given cost function. For stochasti...

Toward Optimal Disease Surveillance with Graph-Based Active Learning

Mathematics, Information Science, Medicine, Environmental and Public Health,
disease surveillance   active learning   network dynamics   epidemiology   public health  

Toward Optimal Disease Surveillance with Graph-Based Active Learning Academic Background With the acceleration of globalization, the speed and scope of infectious disease transmission have significantly increased. How to effectively monitor and control the spread of infectious diseases has become a critical issue in public health. Traditional disea...

Basis Restricted Elastic Shape Analysis Framework for Surfaces

Mathematics, Physics, Mechanics, Information Science, Computer Science, Artificial Intelligence,
Elastic Shape Analysis   Surface Meshes   Geometric Deep Learning   Riemannian Shape Metrics   Human Body Analysis   Shape Registration   Random Shape Generation  

# Basis Restricted Elastic Shape Analysis on the Space of Unregistered Surfaces ## Introduction Analyzing three-dimensional (3D) surfaces has become increasingly important in computer vision, driven by the emergence of high-accuracy 3D scanning devices. These devices have significantly increased the availability of 3D data, enabling applications in...

An Adaptive and Robust Method for Multi-Trait Analysis of Genome-Wide Association Studies Using Summary Statistics

Mathematics, Life Sciences, Genetics,
Multi-Trait Analysis   Genome-Wide Association Studies   Summary Statistics   Computational Efficiency   Mathematical Methods   Brain Imaging Phenotypes   Genetic Variants  

Adaptive Robust Method for Multi-trait Genome-wide Association Studies Abstract: Genome-wide association studies (GWAS) over the past decade have identified thousands of genetic variants associated with human traits or diseases. However, the heritability of many traits remains largely unexplained. Traditional single-trait analysis methods are overl...

Bayesian Tensor Modeling for Image-Based Classification of Alzheimer's Disease

Mathematics, Information Science, Computer Science, Artificial Intelligence, Medicine, Neurology, Medical Imaging,
Alzheimer's disease   Bayesian tensor modeling   logistic regression   support vector machines   neuroimaging analysis  

Image Classification Based on Bayesian Tensor Modeling for Alzheimer’s Disease Introduction Neuroimaging research is a crucial component of contemporary neuroscience, significantly enhancing our understanding of brain structure and function. Through these non-invasive visualization techniques, researchers can more accurately predict the risk of cer...