Category: 7. Maths

Dataset and experimental setup

A dataset was constructed from multi-dimensional temporal features extracted from flame videos, comprising 7,445 samples spanning four damage sizes: 5 cm (n = 1,489), 10 cm (n = 1,902), 15 cm…

Digit twin model

The DT consisted of four main components: physical space, twin model space, data space, and data interaction space, as illustrated in Fig.  1. Initially, a physical space was established, comprising components such as feed…

This section outlines the in-depth methodology used to meet the research gaps outlined earlier. Drawing on the findings of the literature review, our suggested methodology combines drone inspection with ground-based robotic cleaning to create an…

Application of DR-PINNs to Poisson Equation

Widely used in fields such as electrostatics, heat conduction, and fluid dynamics, the Poisson equation serves as a fundamental model for describing steady-state distributions influenced by spatially…

Real data construction

We used longitudinal data from the Korean Genome and Epidemiology Study (KoGES), a large cohort study primarily designed to identify gene-environment interactions and their effects on common chronic diseases¹². With the…

To derive the real and imaginary components of the given CGL Eq. (1). Suppose the following traveling wave transformation:

Smart cities enhance the quality of life of its residents, and promote transparent management of public resources, including financial assets, natural resources, and infrastructure. Successful smart city initiatives rely on three core components…

We illustrate the overall architecture of P-Mamba in Fig. 3. The P-Mamba network, designed for automatically segmenting the left ventricle in echocardiograms, leverages the Mixture of Experts framework. The DWT-based PMD block suppresses…

Experimental setup

Training setup

All models were trained using a single NVIDIA RTX 3090 GPU with 24 GB of memory. The Garment-Body Integration module was trained for approximately 150 epochs and a batch size of 16, which took around 32 h in…

This section presents detailed numerical experiments on a range of ordinary differential equations, including the Logistic growth model, the Lotka-Volterra model, damped harmonic oscillators, a multiscale model for p53 activation, the Lorenz…