Research Background and Problem Introduction Nonlinear wave systems are core research topics in fields such as physics, optics, and condensed matter physics. However, real-world nonlinear wave systems are often subject to random noise interference, which can significantly alter the behavior of waves, such as soliton propagation, wave turbulence for...
In today’s era of information explosion, decision-makers are faced with a vast amount of information, not all of which is relevant to their decisions. To better make optimal decisions in data-rich environments, the Rational Inattention (RI) model has been introduced into the field of economics. The core idea of this model is that decision-makers ne...
Research Report on Identifying New Classes of Financial Price Jumps Using Wavelets Academic Background Price jumps in financial markets refer to significant price fluctuations occurring within an extremely short period, typically caused by exogenous factors (such as sudden news) or endogenous factors (internal market feedback mechanisms). Distingui...
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...
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 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 ...
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...
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 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 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...