Algorithms

9 pages, 354 KiB

Open AccessCommunication

Algorithm Providing Ordered Integer Sequences for Sampling with Replacement Confidence Intervals

by Lorentz Jäntschi

Algorithms 2025, 18(8), 459; https://doi.org/10.3390/a18080459 (registering DOI) - 24 Jul 2025

Sampling with replacement occurs when drawing without removing individuals from finite populations. It is a common distribution technique used in physics, biology, and medicine. It is used in state analysis of qubits, the physics of particle interactions, studies of genetic variation and variability, [...] Read more.

Sampling with replacement occurs when drawing without removing individuals from finite populations. It is a common distribution technique used in physics, biology, and medicine. It is used in state analysis of qubits, the physics of particle interactions, studies of genetic variation and variability, and analyzing the treatment effects from clinical trial analyses. When applied, sample statistics should be accompanied by confidence intervals. The major difficulty in expressing the confidence intervals in sampling with replacement consists of discreetness regarding the probability distribution. As a result, no mathematical formula can handle an optimum solution. Using a simple algorithm is proposed in order to obtain confidence intervals for sampling with replacement variables (x from m trials with replacement) and their proportion (

x / m

). A question-based discussion is presented. Traditional confidence intervals often require large sample sizes. Confidence intervals, constructed in a deterministic way provided by the proposed algorithm for sampling with replacement, allow constructing intervals without constraints. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

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34 pages, 1837 KiB

Open AccessArticle

A Predictive Method for Temperature Based on Ensemble EMD with Linear Regression

by Yujun Yang, Yimei Yang and Huijuan Liao

Algorithms 2025, 18(8), 458; https://doi.org/10.3390/a18080458 - 23 Jul 2025

Abstract

Temperature prediction plays a crucial role across various sectors, including agriculture and climate research. Understanding weather patterns, seasonal shifts, and climate dynamics heavily relies on accurate temperature forecasts. This paper presents an innovative hybrid method, EEMD-LR, that combines ensemble empirical mode decomposition (EEMD) [...] Read more.

Temperature prediction plays a crucial role across various sectors, including agriculture and climate research. Understanding weather patterns, seasonal shifts, and climate dynamics heavily relies on accurate temperature forecasts. This paper presents an innovative hybrid method, EEMD-LR, that combines ensemble empirical mode decomposition (EEMD) with linear regression (LR) for temperature prediction. EEMD is used to decompose temperature signals into stable sub-signals, enhancing their predictability. LR is then applied to forecast each sub-signal, and the resulting predictions are integrated to obtain the final temperature forecast. The proposed EEMD-LR model achieved RMSE, MAE, and R² values of 0.000027, 0.000021, and 1.000000, respectively, on the sine simulation time-series data used in this study. For actual temperature time-series data, the model achieved RMSE, MAE, and R² values of 0.713150, 0.512700, and 0.994749, respectively. The experimental results on these two datasets indicate that the EEMD-LR model demonstrates superior predictive performance compared to alternative methods. Full article

(This article belongs to the Section Algorithms for Multidisciplinary Applications)

27 pages, 705 KiB

Open AccessArticle

A Novel Wavelet Transform and Deep Learning-Based Algorithm for Low-Latency Internet Traffic Classification

by Ramazan Enisoglu and Veselin Rakocevic

Algorithms 2025, 18(8), 457; https://doi.org/10.3390/a18080457 - 23 Jul 2025

Abstract

Accurate and real-time classification of low-latency Internet traffic is critical for applications such as video conferencing, online gaming, financial trading, and autonomous systems, where millisecond-level delays can degrade user experience. Existing methods for low-latency traffic classification, reliant on raw temporal features or static [...] Read more.

Accurate and real-time classification of low-latency Internet traffic is critical for applications such as video conferencing, online gaming, financial trading, and autonomous systems, where millisecond-level delays can degrade user experience. Existing methods for low-latency traffic classification, reliant on raw temporal features or static statistical analyses, fail to capture dynamic frequency patterns inherent to real-time applications. These limitations hinder accurate resource allocation in heterogeneous networks. This paper proposes a novel framework integrating wavelet transform (WT) and artificial neural networks (ANNs) to address this gap. Unlike prior works, we systematically apply WT to commonly used temporal features—such as throughput, slope, ratio, and moving averages—transforming them into frequency-domain representations. This approach reveals hidden multi-scale patterns in low-latency traffic, akin to structured noise in signal processing, which traditional time-domain analyses often overlook. These wavelet-enhanced features train a multilayer perceptron (MLP) ANN, enabling dual-domain (time–frequency) analysis. We evaluate our approach on a dataset comprising FTP, video streaming, and low-latency traffic, including mixed scenarios with up to four concurrent traffic types. Experiments demonstrate 99.56% accuracy in distinguishing low-latency traffic (e.g., video conferencing) from FTP and streaming, outperforming k-NN, CNNs, and LSTMs. Notably, our method eliminates reliance on deep packet inspection (DPI), offering ISPs a privacy-preserving and scalable solution for prioritizing time-sensitive traffic. In mixed-traffic scenarios, the model achieves 74.2–92.8% accuracy, offering ISPs a scalable solution for prioritizing time-sensitive traffic without deep packet inspection. By bridging signal processing and deep learning, this work advances efficient bandwidth allocation and enables Internet Service Providers to prioritize time-sensitive flows without deep packet inspection, improving quality of service in heterogeneous network environments. Full article

(This article belongs to the Section Algorithms for Multidisciplinary Applications)

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25 pages, 760 KiB

Open AccessArticle

Scheduling the Exchange of Context Information for Time-Triggered Adaptive Systems

by Daniel Onwuchekwa, Omar Hekal and Roman Obermaisser

Algorithms 2025, 18(8), 456; https://doi.org/10.3390/a18080456 - 22 Jul 2025

Abstract

This paper presents a novel metascheduling algorithm to enhance communication efficiency in off-chip time-triggered multi-processor system-on-chip (MPSoC) platforms, particularly for safety-critical applications in aerospace and automotive domains. Time-triggered communication standards such as time-sensitive networking (TSN) and TTEthernet effectively enable deterministic and reliable communication [...] Read more.

This paper presents a novel metascheduling algorithm to enhance communication efficiency in off-chip time-triggered multi-processor system-on-chip (MPSoC) platforms, particularly for safety-critical applications in aerospace and automotive domains. Time-triggered communication standards such as time-sensitive networking (TSN) and TTEthernet effectively enable deterministic and reliable communication across distributed systems, including MPSoC-based platforms connected via Ethernet. However, their dependence on static resource allocation limits adaptability under dynamic operating conditions. To address this challenge, we propose an offline metascheduling framework that generates multiple precomputed schedules corresponding to different context events. The proposed algorithm introduces a selective communication strategy that synchronizes context information exchange with key decision points, thereby minimizing unnecessary communication while maintaining global consistency and system determinism. By leveraging knowledge of context event patterns, our method facilitates coordinated schedule transitions and significantly reduces communication overhead. Experimental results show that our approach outperforms conventional scheduling techniques, achieving a communication overhead reduction ranging from 9.89 to 32.98 times compared to a two-time-unit periodic sampling strategy. This work provides a practical and certifiable solution for introducing adaptability into Ethernet-based time-triggered MPSoC systems without compromising the predictability essential for safety certification. Full article

(This article belongs to the Special Issue Bio-Inspired Algorithms: 2nd Edition)

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26 pages, 654 KiB

Open AccessArticle

Entropy-Regularized Federated Optimization for Non-IID Data

by Koffka Khan

Algorithms 2025, 18(8), 455; https://doi.org/10.3390/a18080455 - 22 Jul 2025

Abstract

Federated learning (FL) struggles under non-IID client data when local models drift toward conflicting optima, impairing global convergence and performance. We introduce entropy-regularized federated optimization (ERFO), a lightweight client-side modification that augments each local objective with a Shannon entropy penalty on the per-parameter [...] Read more.

Federated learning (FL) struggles under non-IID client data when local models drift toward conflicting optima, impairing global convergence and performance. We introduce entropy-regularized federated optimization (ERFO), a lightweight client-side modification that augments each local objective with a Shannon entropy penalty on the per-parameter update distribution. ERFO requires no additional communication, adds a single-scalar hyperparameter

λ

, and integrates seamlessly into any FedAvg-style training loop. We derive a closed-form gradient for the entropy regularizer and provide convergence guarantees: under

μ

-strong convexity and L-smoothness, ERFO achieves the same

O (1 / T)

(or linear) rates as FedAvg (with only

O (λ)

bias for fixed

λ

and exact convergence when

λ_{t} \to 0

); in the non-convex case, we prove stationary-point convergence at

O (1 / T)

. Empirically, on five-client non-IID splits of the UNSW-NB15 intrusion-detection dataset, ERFO yields a +1.6 pp gain in accuracy and +0.008 in macro-F1 over FedAvg with markedly smoother dynamics. On a three-of-five split of PneumoniaMNIST, a fixed

λ

matches or exceeds FedAvg, FedProx, and SCAFFOLD—achieving 90.3% accuracy and 0.878 macro-F1—while preserving rapid, stable learning. ERFO’s gradient-only design is model-agnostic, making it broadly applicable across tasks. Full article

(This article belongs to the Special Issue Advances in Parallel and Distributed AI Computing)

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24 pages, 5200 KiB

Open AccessArticle

DRFAN: A Lightweight Hybrid Attention Network for High-Fidelity Image Super-Resolution in Visual Inspection Applications

by Ze-Long Li, Bai Jiang, Liang Xu, Zhe Lu, Zi-Teng Wang, Bin Liu, Si-Ye Jia, Hong-Dan Liu and Bing Li

Algorithms 2025, 18(8), 454; https://doi.org/10.3390/a18080454 - 22 Jul 2025

Abstract

Single-image super-resolution (SISR) plays a critical role in enhancing visual quality for real-world applications, including industrial inspection and embedded vision systems. While deep learning-based approaches have made significant progress in SR, existing lightweight SR models often fail to accurately reconstruct high-frequency textures, especially [...] Read more.

Single-image super-resolution (SISR) plays a critical role in enhancing visual quality for real-world applications, including industrial inspection and embedded vision systems. While deep learning-based approaches have made significant progress in SR, existing lightweight SR models often fail to accurately reconstruct high-frequency textures, especially under complex degradation scenarios, resulting in blurry edges and structural artifacts. To address this challenge, we propose a Dense Residual Fused Attention Network (DRFAN), a novel lightweight hybrid architecture designed to enhance high-frequency texture recovery in challenging degradation conditions. Moreover, by coupling convolutional layers and attention mechanisms through gated interaction modules, the DRFAN enhances local details and global dependencies with linear computational complexity, enabling the efficient utilization of multi-level spatial information while effectively alleviating the loss of high-frequency texture details. To evaluate its effectiveness, we conducted ×4 super-resolution experiments on five public benchmarks. The DRFAN achieves the best performance among all compared lightweight models. Visual comparisons show that the DRFAN restores more accurate geometric structures, with up to +1.2 dB/+0.0281 SSIM gain over SwinIR-S on Urban100 samples. Additionally, on a domain-specific rice grain dataset, the DRFAN outperforms SwinIR-S by +0.19 dB in PSNR and +0.0015 in SSIM, restoring clearer textures and grain boundaries essential for industrial quality inspection. The proposed method provides a compelling balance between model complexity and image reconstruction fidelity, making it well-suited for deployment in resource-constrained visual systems and industrial applications. Full article

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31 pages, 7723 KiB

Open AccessArticle

A Hybrid CNN–GRU–LSTM Algorithm with SHAP-Based Interpretability for EEG-Based ADHD Diagnosis

by Makbal Baibulova, Murat Aitimov, Roza Burganova, Lazzat Abdykerimova, Umida Sabirova, Zhanat Seitakhmetova, Gulsiya Uvaliyeva, Maksym Orynbassar, Aislu Kassekeyeva and Murizah Kassim

Algorithms 2025, 18(8), 453; https://doi.org/10.3390/a18080453 - 22 Jul 2025

Abstract

This study proposes an interpretable hybrid deep learning framework for classifying attention deficit hyperactivity disorder (ADHD) using EEG signals recorded during cognitively demanding tasks. The core architecture integrates convolutional neural networks (CNNs), gated recurrent units (GRUs), and long short-term memory (LSTM) layers to [...] Read more.

This study proposes an interpretable hybrid deep learning framework for classifying attention deficit hyperactivity disorder (ADHD) using EEG signals recorded during cognitively demanding tasks. The core architecture integrates convolutional neural networks (CNNs), gated recurrent units (GRUs), and long short-term memory (LSTM) layers to jointly capture spatial and temporal dynamics. In addition to the final hybrid architecture, the CNN–GRU–LSTM model alone demonstrates excellent accuracy (99.63%) with minimal variance, making it a strong baseline for clinical applications. To evaluate the role of global attention mechanisms, transformer encoder models with two and three attention blocks, along with a spatiotemporal transformer employing 2D positional encoding, are benchmarked. A hybrid CNN–RNN–transformer model is introduced, combining convolutional, recurrent, and transformer-based modules into a unified architecture. To enhance interpretability, SHapley Additive exPlanations (SHAP) are employed to identify key EEG channels contributing to classification outcomes. Experimental evaluation using stratified five-fold cross-validation demonstrates that the proposed hybrid model achieves superior performance, with average accuracy exceeding 99.98%, F1-scores above 0.9999, and near-perfect AUC and Matthews correlation coefficients. In contrast, transformer-only models, despite high training accuracy, exhibit reduced generalization. SHAP-based analysis confirms the hybrid model’s clinical relevance. This work advances the development of transparent and reliable EEG-based tools for pediatric ADHD screening. Full article

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27 pages, 532 KiB

Open AccessArticle

Bayesian Binary Search

by Vikash Singh, Matthew Khanzadeh, Vincent Davis, Harrison Rush, Emanuele Rossi, Jesse Shrader and Pietro Lio’

Algorithms 2025, 18(8), 452; https://doi.org/10.3390/a18080452 - 22 Jul 2025

Abstract

We present Bayesian Binary Search (BBS), a novel framework that bridges statistical learning theory/probabilistic machine learning and binary search. BBS utilizes probabilistic methods to learn the underlying probability density of the search space. This learned distribution then informs a modified bisection strategy, where [...] Read more.

We present Bayesian Binary Search (BBS), a novel framework that bridges statistical learning theory/probabilistic machine learning and binary search. BBS utilizes probabilistic methods to learn the underlying probability density of the search space. This learned distribution then informs a modified bisection strategy, where the split point is determined by probability density rather than the conventional midpoint. This learning process for search space density estimation can be achieved through various supervised probabilistic machine learning techniques (e.g., Gaussian Process Regression, Bayesian Neural Networks, and Quantile Regression) or unsupervised statistical learning algorithms (e.g., Gaussian Mixture Models, Kernel Density Estimation (KDE), and Maximum Likelihood Estimation (MLE)). Our results demonstrate substantial efficiency improvements using BBS on both synthetic data with diverse distributions and in a real-world scenario involving Bitcoin Lightning Network channel balance probing (3–6% efficiency gain), where BBS is currently in production. Full article

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Algorithms, Volume 18, Issue 8 (August 2025) – 8 articles

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