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Abstract This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell’s equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad applications, such as antenna synthesis and design, medical imaging, and pollution source tracing. We introduce new imaging functions and a computational algorithm to determine the number of point sources, their locations, and associated moment vectors, even when these vectors have notably different magnitudes. The number of sources and locations are estimated using significant peaks of the imaging functions, and the moment vectors are computed via explicitly simple formulas. The theoretical analysis and stability of the imaging functions are investigated, where the main challenge lies in analyzing the behavior of the dot products between the columns of the imaginary part of the Green’s tensor and the unknown moment vectors. Additionally, we extend our method to reconstruct small-volume sources using an asymptotic expansion of their radiated electric field. We provide numerical examples in three dimensions to demonstrate the performance of our method. 

This paper proposes a novel intelligent human activity recognition (HAR) framework based on a new design of Federated Split Learning (FSL) with Differential Privacy (DP) over edge networks. Our FSL-DP framework leverages both accelerometer and gyroscope data, achieving significant improvements in HAR accuracy. The evaluation includes a detailed comparison between traditional Federated Learning (FL) and our FSL framework, showing that the FSL framework outperforms FL models in both accuracy and loss metrics. Additionally, we examine the privacy-performance trade-off under different data settings in the DP mechanism, highlighting the balance between privacy guarantees and model accuracy. The results also indicate that our FSL framework achieves faster communication times per training round compared to traditional FL, further emphasizing its efficiency and effectiveness. This work provides valuable insight and a novel framework which was tested on a real-life dataset. 

This paper presents a novel approach for classifying electrocardiogram (ECG) signals in healthcare applications using federated learning and stacked convolutional neural networks (CNNs). Our innovative technique leverages the distributed nature of federated learning to collaboratively train a high-performance model while preserving data privacy on local devices. We propose a stacked CNN architecture tailored for ECG data, effectively extracting discriminative features across different temporal scales. The evaluation confirms the strength of our approach, culminating in a final model accuracy of 98.6% after 100 communication rounds, significantly exceeding baseline performance. This promising result paves the way for accurate and privacy-preserving ECG classification in diverse healthcare settings, potentially leading to improved diagnosis and patient monitoring. 

This paper presents a numerical method for solving the inverse problem of reconstructing the shape of periodic structures from scattering data. This inverse problem is motivated by applications in the nondestructive evaluation of photonic crystals. The numerical method belongs to the class of sampling methods that aim to construct an imaging function for the shape of the periodic structure using scattering data. By extending the results of Nguyen, Stahl, and Truong [Inverse Problems, 39:065013, 2023], we studied a simple imaging function that uses half the data required by the numerical method in the cited paper. Additionally, this imaging function is fast, simple to implement, and very robust against noise in the data. Both isotropic and anisotropic cases were investigated, and numerical examples were presented to demonstrate the performance of the numerical method. 

Abstract This paper is concerned with the inverse problem of determining the shape of penetrable periodic scatterers from scattered field data. We propose a sampling method with a novel indicator function for solving this inverse problem. This indicator function is very simple to implement and robust against noise in the data. The resolution and stability analysis of the indicator function is analyzed. Our numerical study shows that the proposed sampling method is more stable than the factorization method and more efficient than the direct or orthogonality sampling method in reconstructing periodic scatterers. 

This paper is concerned with the numerical solution to the direct and inverse electromagnetic scattering problem for bi-anisotropic periodic structures. The direct problem can be reformulated as an integro-di erential equation. We study the existence and uniqueness of solution to the latter equation and analyze a spectral Galerkin method to solve it. This spectral method is based on a periodization technique which allows us to avoid the evaluation of the quasiperiodic Green's tensor and to use the fast Fourier transform in the numerical implementation of the method. For the inverse problem, we study the orthogonality sampling method to reconstruct the periodic structures from scattering data generated by only two incident fields. The sampling method is fast, simple to implement, regularization free, and very robust against noise in the data. Numerical examples for both direct and inverse problems are presented to examine the efficiency of the numerical solvers.