Algorithms

23 pages, 550 KB

Open AccessArticle

GRU Learning of Asymmetric Sequence Structure in Penney’s Game

by Huijuan Liao and Yanlong Sun

Algorithms 2026, 19(5), 374; https://doi.org/10.3390/a19050374 (registering DOI) - 10 May 2026

Alternation preference in random-sequence judgments has been linked to objective differences in pattern waiting times. The present study asks whether recurrent networks can learn such temporal asymmetries beyond single-pattern regularities and capture the more complex competitive structure of Penney’s game. To address this [...] Read more.

Alternation preference in random-sequence judgments has been linked to objective differences in pattern waiting times. The present study asks whether recurrent networks can learn such temporal asymmetries beyond single-pattern regularities and capture the more complex competitive structure of Penney’s game. To address this question, we adopt Penney’s game as a mathematically tractable testbed, in which competitive advantage is determined not by marginal sequence frequency but by the joint effect of self-overlap and cross-overlap structure. Based on Conway’s formula, we formulate two complementary tasks for gated recurrent units (GRUs): optimal counterstrategy prediction and win-probability estimation. Experimental results show that the GRU achieves strong performance on both tasks, recovering optimal or near-optimal second player responses and accurately estimating theoretical winning probabilities with good ranking consistency. These findings suggest that recurrent networks can learn structural regularities underlying asymmetric sequence competition, extending from single-pattern waiting-time effects to more complex competitive sequence settings. Full article

26 pages, 9861 KB

Open AccessArticle

Multiscale Model—Differential Evolutionary Algorithm for Inverse Solution of T-Wave Inversion in Electrocardiography

by Tengda Guo, Junjiang Zhu and Yunjie Li

Algorithms 2026, 19(5), 373; https://doi.org/10.3390/a19050373 (registering DOI) - 9 May 2026

Abstract

T-wave inversion (TWI) on an electrocardiogram (ECG) is a key indicator of myocardial ischemia, yet existing inverse ECG methods lack quantitative physiological parameter resolution. This study aims to propose a novel multiscale computational framework to inversely identify the ionic mechanisms underlying TWI. A [...] Read more.

T-wave inversion (TWI) on an electrocardiogram (ECG) is a key indicator of myocardial ischemia, yet existing inverse ECG methods lack quantitative physiological parameter resolution. This study aims to propose a novel multiscale computational framework to inversely identify the ionic mechanisms underlying TWI. A cell–tissue–torso cardiac electrophysiological model was integrated with a differential evolution (DE) algorithm. The forward model combined the Grandi atrial model and BPS2020 ventricular model, simulating action potential propagation via cellular automata and body surface ECGs via field point potentials. The inverse solution optimized 29 physiological parameters by minimizing the root-mean-square error between the simulated and clinical ECGs. The method was applied to 30 normal and 30 TWI cases to analyze the repolarization abnormalities. The study revealed that extracellular Ca²⁺ > 2.88 mmol/L and K⁺ < 3.4 mmol/L in ventricular myocytes (Endo, M, Epi) induce TWI. Quantitative analysis identified specific 95% confidence intervals for ionic imbalances in three scenarios: Case 1 (

V_{E p i} > V_{E n d o} > V_{M}

) with [Ca²⁺] 2.60–3.30 mmol/L and [K⁺] 1.9–4.7 mmol/L; Case 2 (

V_{M} > V_{E p i} > V_{E n d o}

) with [Ca²⁺] 2.36–3.68 mmol/L and [K⁺] 3.13–4.07 mmol/L; and Case 3 (

V_{E p i} > V_{M} > V_{E n d o}

) with [Ca²⁺] 2.67–3.91 mmol/L and [K⁺] 3.11–3.45 mmol/L. This approach enables cellular-scale mechanistic insights into TWI by quantifying ionic concentration changes. The framework supports the advancement of personalized cardiac diagnostics and drug development. Full article

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13 pages, 1647 KB

Open AccessArticle

Region-Based Algorithm for Switching Frequency Reduction in Predictive Control of Converter Supplied Electric Drives

by Manuel R. Arahal, Manuel G. Satué, Francisco Colodro and Alfredo P. Vega-Leal

Algorithms 2026, 19(5), 372; https://doi.org/10.3390/a19050372 (registering DOI) - 9 May 2026

Abstract

Switching losses make up for a notable portion of all losses in converter-supplied electric drives. Control algorithms such as Finite State Model Predictive Control (FSMPC) have tackled this issue in different ways; in particular incorporating a switching penalty to the cost function. This, [...] Read more.

Switching losses make up for a notable portion of all losses in converter-supplied electric drives. Control algorithms such as Finite State Model Predictive Control (FSMPC) have tackled this issue in different ways; in particular incorporating a switching penalty to the cost function. This, however, results in an optimization problem with increased computational load, restricting the attainable sampling frequency for a given computing hardware. Recently, fast algorithms have been developed that reduce the computational load. However they cannot incorporate the switching penalty term. This paper explores a way around this problem for the particular case of stator current control of a five-phase induction motor. The proposal achieves fast computation even if a term for switching frequency reduction is present in the cost function. Experimental results show how stator current tracking performance is affected in both the torque producing plane and the harmonic subspace. Full article

(This article belongs to the Special Issue Advanced Predictive Control Algorithms for Electric Drives)

26 pages, 2747 KB

Open AccessArticle

Incremental Multi-Camera Extrinsic Calibration Method Based on PnP Integrating Weighted AprilTag Detections and Multi-View Triangulation

by Liliya A. Demidova and Vladimir E. Zhuravlev

Algorithms 2026, 19(5), 371; https://doi.org/10.3390/a19050371 - 8 May 2026

Abstract

Accurate extrinsic calibration of multi-camera systems is a central problem in three-dimensional computer vision, as errors in the relative positioning of sensors directly propagate into geometric distortions that critically degrade the quality of downstream applications. This paper proposes an incremental extrinsic camera parameter [...] Read more.

Accurate extrinsic calibration of multi-camera systems is a central problem in three-dimensional computer vision, as errors in the relative positioning of sensors directly propagate into geometric distortions that critically degrade the quality of downstream applications. This paper proposes an incremental extrinsic camera parameter initialization method that improves upon the baseline iterative registration algorithm based on the Perspective-n-Point (PnP) problem. Unlike board-based calibration frameworks, the proposed approach operates on individually placed markers with no prior knowledge of their mutual positions, enabling recalibration without dedicated calibration sessions. The accuracy improvement is achieved through the introduction of heuristic weighting of fiducial marker detections using AprilTags, as well as the application of a multi-view triangulation algorithm for dynamic refinement of marker spatial coordinates at each stage of scene expansion. Theoretical analysis demonstrates that the incorporation of these mechanisms does not increase the overall asymptotic computational complexity of the complete calibration cycle (including the global optimization stage), despite the higher computational cost of the initialization stage itself. Empirical validation of the method is performed on both synthetic datasets with known ground-truth camera parameters and real-world capture data through the evaluation of geometric errors and their comparison with the baseline method. Experimental results, supplemented by an ablation study, indicate that the proposed algorithm achieves statistically significant improvements on synthetic data in more than 80% of cases, while on real data it is on average 85% more accurate in terms of reprojection error. Full article

(This article belongs to the Special Issue Visual Attributes in Computer Vision Applications)

26 pages, 1305 KB

Open AccessArticle

Continuous-Variable Quantum Fourier Layer: Applications to Filtering and PDE Solving

by Paolo Marcandelli, Stefano Mariani, Martina Siena and Stefano Markidis

Algorithms 2026, 19(5), 370; https://doi.org/10.3390/a19050370 - 8 May 2026

Abstract

Fourier representations play a central role in operator learning for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT), particularly in its Cooley–Tukey decomposition, exhibits a structure that naturally matches continuous-variable quantum circuits. [...] Read more.

Fourier representations play a central role in operator learning for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT), particularly in its Cooley–Tukey decomposition, exhibits a structure that naturally matches continuous-variable quantum circuits. This correspondence establishes a direct structural isomorphism between the Cooley–Tukey butterfly network and Gaussian photonic gates, enabling the FFT to be realized as a native optical computation in continuous-variable quantum computing. Building on this observation, we introduce a continuous-variable Quantum Fourier Layer (CV–QFL) based on a bipartite Gaussian encoding and a Cooley–Tukey quantum Fourier transform, enabling exact two-dimensional spectral processing within a Gaussian photonic circuit. We test the CV–QFL on two representative tasks: spectral low-pass filtering and Fourier-domain integration of the heat equation. In both cases, the results match the classical reference to machine precision. More broadly, this work lays the foundation for continuous-variable approaches to quantum scientific computing and for the development of native spectral architectures in quantum machine learning. Full article

(This article belongs to the Section Analysis of Algorithms and Complexity Theory)

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22 pages, 1071 KB

Open AccessArticle

The Nonlinear Relationship Between Fasting Plasma Glucose, HbA1c, and Blood Pressure: A Cross-Sectional Analysis of 54,881 Adults from NHANES 1999–2023

by Mikhail Kolev, Irina Naskinova, Mariyan Milev, Hristo Kalinov, Gabriela Vasileva and Penko Mitev

Algorithms 2026, 19(5), 369; https://doi.org/10.3390/a19050369 - 7 May 2026

Abstract

The relationship between blood glucose levels and blood pressure is well established in clinical literature, yet its precise quantitative characterization, including nonlinear effects, threshold phenomena, and demographic modifiers, remains incompletely understood. In this study, we conducted a comprehensive cross-sectional analysis of the National [...] Read more.

The relationship between blood glucose levels and blood pressure is well established in clinical literature, yet its precise quantitative characterization, including nonlinear effects, threshold phenomena, and demographic modifiers, remains incompletely understood. In this study, we conducted a comprehensive cross-sectional analysis of the National Health and Nutrition Examination Survey (NHANES) spanning 11 survey cycles (1999–2023), comprising 54,881 adult participants with at least one glycemic marker and standardized blood pressure measurements. Of these, 26,981 had valid fasting plasma glucose (FPG) measurements, and 49,327 had valid glycated hemoglobin (HbA1c) measurements. We employed restricted cubic splines (RCS), generalized additive models (GAMs), and segmented regression to characterize the dose–response relationship between glycemic markers and both systolic (SBP) and diastolic blood pressure (DBP). A 10 mg/dL increase in FPG was associated with a 0.32 mmHg increase in SBP (95% CI: 0.26–0.38, p < 0.001) after adjusting for age, sex, and body mass index (BMI). Nonlinearity was statistically significant for all exposure–outcome combinations (p < 10⁻⁷ for Wald tests). Segmented regression identified a FPG breakpoint at 122.1 mg/dL (95% CI: 119.5–125.6), below which SBP increased at 0.39 mmHg per mg/dL and above which the association was essentially flat. Stratified analyses revealed that the glucose–BP association was strongest in females (β = 0.048 per mg/dL) compared with males (β = 0.021), and in prediabetic individuals (β = 0.065) compared with those with established diabetes (β = 0.014). In the statistical mediation decomposition, body mass index accounted for 23.5% of the total FPG–SBP association. A significant FPG × BMI interaction (p < 0.001) indicated that the glucose–BP relationship is modulated by adiposity. These findings provide a large-scale population-level analysis of the glucose–blood pressure dose–response relationship and identify potential thresholds warranting further investigation for integrated cardiometabolic risk management (95% bootstrap CI: 19.3–28.9%; 1000 resamples); given the cross-sectional design and BMI’s plausible role as a shared upstream determinant of glucose and blood pressure, this proportion is reported as a confounding decomposition rather than as evidence of causal mediation. Insulin resistance (HOMA-IR) and C-reactive protein did not contribute significantly as additional decomposition pathways. Full article

(This article belongs to the Special Issue Advanced Algorithms for Biomedical Data Analysis)

23 pages, 607 KB

Open AccessArticle

Stroke Rehabilitation in Virtual Reality Through Enhanced Plantar Pressure Detection Using Sensor Resolution and Adaptive Thresholding

by Audrey Rah and Yuhua Chen

Algorithms 2026, 19(5), 368; https://doi.org/10.3390/a19050368 - 6 May 2026

Abstract

Early-stage stroke rehabilitation increasingly incorporates virtual reality (VR) systems to provide interactive motor training and positive reinforcement. However, the minimal voluntary plantar pressure activations generated during early recovery are often below the detection limits of conventional pressure-sensing platforms, restricting timely feedback. This study [...] Read more.

Early-stage stroke rehabilitation increasingly incorporates virtual reality (VR) systems to provide interactive motor training and positive reinforcement. However, the minimal voluntary plantar pressure activations generated during early recovery are often below the detection limits of conventional pressure-sensing platforms, restricting timely feedback. This study quantitatively evaluates the detectability of low-amplitude plantar micro-intent signals under varying sensor resolution and adaptive threshold conditions. Publicly available plantar pressure recordings from the PhysioNet Center for Verification and Evaluation of Stroke (CVES) database were used as physiological baseline signals. Micro-intent was modeled as short-duration half-sine pressure pulses with systematically varied amplitudes and integrated into low-load baseline segments. Sensor resolution was represented through controlled noise modeling to emulate low-, medium-, and high-resolution sensing scenarios. A sliding-window adaptive threshold detector was evaluated across multiple amplitudes and sensitivity stages. The detection probability, false positive rate, and minimum detectable amplitude (defined as ≥80% detection probability) were quantified. The results show that detection probability increases with signal amplitude and shifts toward lower amplitudes with improved sensor resolution and more sensitive threshold configurations. Higher-resolution sensing reduced the minimum detectable amplitude, while adaptive thresholding enabled earlier detection of weak plantar activations without substantial increases in false positives. These findings provide quantitative design guidance for pressure-sensing VR rehabilitation systems targeting early-stage motor recovery. Full article

(This article belongs to the Special Issue Advanced Algorithms for Biomedical Data Analysis)

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22 pages, 3966 KB

Open AccessArticle

Prediction of Percutaneous Coronary Intervention from Clinical and ECG Data Using Machine Learning: A Retrospective Single-Center Observational Study

by Zhadyra Alimbayeva, Chingiz Alimbayev, Kassymbek Ozhikenov, Kairat Karibayev, Aiman Ozhikenova, Ussen Shylmyrza and Dilfuza Akhmedova

Algorithms 2026, 19(5), 367; https://doi.org/10.3390/a19050367 - 6 May 2026

Abstract

The aim of this study was to evaluate the feasibility of predicting percutaneous coronary intervention (PCI) based on clinical, laboratory, and electrocardiographic data available at various stages of hospitalization. A retrospective single-center study was conducted, including 137 patients with suspected coronary artery disease. [...] Read more.

The aim of this study was to evaluate the feasibility of predicting percutaneous coronary intervention (PCI) based on clinical, laboratory, and electrocardiographic data available at various stages of hospitalization. A retrospective single-center study was conducted, including 137 patients with suspected coronary artery disease. The fact that PCI was performed during the current hospitalization was considered as the endpoint. Taking into account the temporary availability of data, three sets of signs were formed: basic (SAFE), including indicators available at admission; clinical (CLINICAL); and extended (EXTENDED), supplemented with glycemic parameters. Logistic regression, random forest, and gradient boosting were used to build the models. The assessment was carried out using repeated stratified cross-validation (5 × 10). The main metrics were ROC-AUC, PR-AUC, accuracy and F1-measure. The models demonstrated moderate predictive ability. The basic model (SAFE) showed a ROC-AUC of 0.734 ± 0.092, while the best results were achieved using an extended model based on a random forest (ROC-AUC 0.755 ± 0.079). The addition of glycemic parameters provided a moderate improvement in prediction quality. In the logistic regression, the most significant predictor was the presence of type 2 diabetes mellitus (OR = 7.36; p < 0.001). The results indicate the potential for using non-invasive data to assess the likelihood of PCI in the early stages of hospitalization. However, the models show moderate accuracy and require further validation on larger and more independent samples. Full article

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25 pages, 5829 KB

Open AccessArticle

Chainguard: A Blockchain-Based Aid Distribution System with Mobile Application and System Architecture Design

by Enes Rayman, Serra Öğütcen, Okan Yaman and Yusuf Murat Erten

Algorithms 2026, 19(5), 366; https://doi.org/10.3390/a19050366 - 5 May 2026

Abstract

Natural disasters are devastating occurrences that have a major influence on the well-being of numerous individuals on a global scale. The primary goal of this study is to facilitate the rapid, transparent, and safe delivery of various aid such as food and clothing [...] Read more.

Natural disasters are devastating occurrences that have a major influence on the well-being of numerous individuals on a global scale. The primary goal of this study is to facilitate the rapid, transparent, and safe delivery of various aid such as food and clothing to people in disaster areas. For this purpose, a system has been established using blockchain technology in cooperation with institutions and humanitarian organizations. This system is designed to be accountable and reliable; it will supervise all processes from the source of aid materials to their distribution while protecting the personal information of disaster victims. The assistance process is improved using Smart Contracts in order to provide fast, effective, and coordinated assistance. Unlike existing humanitarian frameworks that rely on permissionless networks such as Bitcoin or Ethereum, this study proposes Hyperledger Fabric to ensure beneficiary privacy and eliminate per-transaction fees for end-users, thereby offering a more sustainable economic model for high-frequency aid distribution compared to public blockchains. The proposed system (Chainguard) addresses the ’efficiency gap’ in the current literature JSON Web Token (JWT)-based authentication layer. The results showed that Chainguard achieves a stable throughput of ~180 TPS with an end-to-end latency of less than 1.5 s, outperforming traditional heavy-cryptography models in terms of scalability and resource efficiency during real-time disaster response. Full article

(This article belongs to the Special Issue Blockchain and Big Data Analytics: AI-Driven Data Science)

26 pages, 2255 KB

Open AccessArticle

Distribution Network Planning Considering Harmonics Based on a Parallel Genetic Algorithm Using Message Passing Interface

by Vincent Roberge and Mohammed Tarbouchi

Algorithms 2026, 19(5), 365; https://doi.org/10.3390/a19050365 - 5 May 2026

Abstract

This paper presents a parallel genetic algorithm (GA) for the planning of power distribution networks considering harmonics. Power distribution systems are generally operated in a radial configuration, supplemented by tie switches that enable network reconfiguration during unexpected outages or planned maintenance. They can [...] Read more.

This paper presents a parallel genetic algorithm (GA) for the planning of power distribution networks considering harmonics. Power distribution systems are generally operated in a radial configuration, supplemented by tie switches that enable network reconfiguration during unexpected outages or planned maintenance. They can also include distributed generators (DGs), capacitor banks (CBs), and soft open points (SOPs) to lower distribution losses and improve the voltage profile. Some of the loads and DG units may be nonlinear, generating harmonic currents in the system, polluting the power, and increasing losses. This paper makes use of a parallel GA to find an optimized configuration, optimized location, and sizing of DGs, CBs, and SOPs to lower real power distribution losses while considering harmonics and the physical constraints of the network. The proposed algorithm uses a solution encoding based on the minimum spanning tree to guarantee the radial topology of candidate solutions. It uses the backward–forward power flow method to compute the fundamental voltages and a decoupled harmonic power flow for the harmonic components. The algorithm is parallelized on a small computer cluster using the Message Passing Interface (MPI) to reduce its execution time. The proposed solver is validated on distribution systems ranging from 16 to 880 buses. The results show that simultaneously optimizing the topology, the DGs, the CBs, and the SOPs results in reducing power losses by 37% to 93%, improving the overall efficiency of the distribution system. The parallelization using MPI allows for a 90.9× speedup on a 96-core cluster. Full article

(This article belongs to the Special Issue Swarm Intelligence and Evolutionary Algorithms for Real World Applications (3rd Edition))

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23 pages, 1016 KB

Open AccessArticle

QuantFT-VL: Harmonizing Quantization and LoRA for Efficient Mobile Vision–Language Model Fine-Tuning

by Fangyuan Jin, Hui Lin, Lu Zhang and Yiwei Chen

Algorithms 2026, 19(5), 364; https://doi.org/10.3390/a19050364 - 4 May 2026

Abstract

Vision–language models (VLMs) are increasingly deployed in resource-constrained environments, yet efficient fine-tuning remains challenging because post-training quantization often degrades the effectiveness of low-rank adaptation. This paper revisits that mismatch in the context of MobileVLM1.7B and presents QuantFT-VL, a novel initialization strategy following the [...] Read more.

Vision–language models (VLMs) are increasingly deployed in resource-constrained environments, yet efficient fine-tuning remains challenging because post-training quantization often degrades the effectiveness of low-rank adaptation. This paper revisits that mismatch in the context of MobileVLM1.7B and presents QuantFT-VL, a novel initialization strategy following the quantization phase to seamlessly align with the LoRA technique. The key idea is to initialize LoRA using a low-rank approximation of the quantization residual instead of the default zero-initialization used in QLoRA-style pipelines. After quantizing a pretrained weight matrix W into Q, we compute the residual W − Q and use truncated singular value decomposition to initialize the LoRA factors (A and B) so that the starting adapted weight Q + AB^T better matches the full-precision model. This residual-aware initialization reduces the discrepancy introduced by quantization and leads to faster and more stable optimization. Experiments on six standard VLM benchmarks show that QuantFT-VL consistently improves over QLoRA and recovers performance close to or better than full-precision LoRA in the best setting. On two RTX 3090 GPUs, QuantFT-VL improves the average benchmark score by 3.27 percentage points over QLoRA while preserving the memory and speed advantages of quantized fine-tuning. Full article

41 pages, 1967 KB

Open AccessArticle

A Reproducible Benchmarking Methodology for Machine Learning Hardware: Performance–Energy Trade-Offs from GPUs to Apple Silicon

by Oscar H. Sierra-Herrera, Mario Eduardo González Niño, Edwin Francis Cárdenas Correa, Jersson X. Leon-Medina and Francesc Pozo

Algorithms 2026, 19(5), 363; https://doi.org/10.3390/a19050363 - 4 May 2026

Abstract

While hardware selection is widely recognized as a key factor in machine learning performance, systematic and reproducible evaluation across heterogeneous and accessible platforms remains limited, particularly when jointly considering execution time, energy consumption, stability, and cost-efficiency. This work presents a unified and fully [...] Read more.

While hardware selection is widely recognized as a key factor in machine learning performance, systematic and reproducible evaluation across heterogeneous and accessible platforms remains limited, particularly when jointly considering execution time, energy consumption, stability, and cost-efficiency. This work presents a unified and fully reproducible benchmarking framework for supervised learning, designed to enable controlled and comparable evaluation across diverse hardware environments. The proposed methodology enforces consistent training pipelines, fixed hyperparameter configurations, and repeated executions to ensure statistical reliability, while incorporating performance metrics such as execution time, power consumption, and energy usage, as well as performance-per-dollar. The framework is validated on a representative set of platforms, including CUDA-enabled GPUs, Apple Silicon (CPU/GPU), x86 processors, ARM-based embedded systems, and cloud-based environments, using convolutional, recurrent (RNN, LSTM, BiLSTM), and tree-based (XGBoost) models. The results reveal that hardware efficiency is strongly model-dependent. GPUs provide the highest computational performance and stability for parallel workloads, whereas Apple Silicon achieves superior energy efficiency with competitive execution times, particularly for recurrent architectures. The batch size analysis shows that performance can vary significantly depending on workload configuration, especially on CPU-based platforms, while epoch-based evaluation confirms that the measured performance reflects steady-state behavior rather than initialization overhead. In contrast, conventional CPUs and embedded systems exhibit significant scalability limitations for deep learning training, although they remain competitive for tree-based methods such as XGBoost, which demonstrates near hardware-independent predictive performance. These findings highlight the limitations of generalized hardware selection criteria and emphasize the need for model-aware and hardware-aware benchmarking. The proposed framework offers a practical and extensible foundation for reproducible, hardware-aware evaluation of machine learning systems, supporting informed decision-making in research, deployment, and cost-constrained scenarios. Full article

(This article belongs to the Collection Feature Papers in Algorithms for Multidisciplinary Applications)

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30 pages, 6363 KB

Open AccessArticle

Multiple String Pattern Matching Algorithm Using Multi-Character Inverted Lists

by Chouvalit Khancome

Algorithms 2026, 19(5), 362; https://doi.org/10.3390/a19050362 - 4 May 2026

Abstract

Multiple string matching is a fundamental operation in real-time analytics, cybersecurity, bioinformatics, and large-scale information retrieval. Nevertheless, existing approaches continue to face inherent trade-offs among preprocessing efficiency, verification overhead, and support for dynamic pattern updates, particularly in large and continuously evolving environments. This [...] Read more.

Multiple string matching is a fundamental operation in real-time analytics, cybersecurity, bioinformatics, and large-scale information retrieval. Nevertheless, existing approaches continue to face inherent trade-offs among preprocessing efficiency, verification overhead, and support for dynamic pattern updates, particularly in large and continuously evolving environments. This paper presents MMIVL, a high-performance algorithm founded on the multi-character inverted list (m-CIVL), a unified and inherently dynamic indexing framework for pattern management. By integrating positional information, termination semantics, and pattern associations within a single structure, m-CIVL enables direct matching without requiring a separate verification stage. MMIVL achieves a preprocessing complexity of O(|P|/s), a search complexity of O(|T| + n_occ), and an update complexity of O(|p|/s), where s denotes the segment length. Extensive experiments on synthetic and real-world datasets demonstrate that MMIVL consistently outperforms representative baselines, with especially strong gains in large-scale scenarios, while maintaining stable performance and favorable memory efficiency. Overall, these results establish m-CIVL as an effective, scalable, and practically viable solution that unifies efficient preprocessing, high-throughput searching, and dynamic update capability for modern multiple string-matching applications. Full article

(This article belongs to the Special Issue Algorithmic Innovations: Bridging Theoretical Foundations and Practical Applications (2nd Edition))

35 pages, 3775 KB

Open AccessArticle

Bayesian Optimization for Categorical and Mixed Variables Using a Multinomial Logit Surrogate

by Muhammad Amir Saeed and Antonio Candelieri

Algorithms 2026, 19(5), 361; https://doi.org/10.3390/a19050361 - 4 May 2026

Abstract

Bayesian optimization (BO) is a widely used framework for optimizing expensive black-box functions. Most BO methods rely on Gaussian process (GP) surrogates, which perform well in continuous domains but encounter difficulties when decision variables include categorical or mixed discrete–continuous components. In particular, GP-based [...] Read more.

Bayesian optimization (BO) is a widely used framework for optimizing expensive black-box functions. Most BO methods rely on Gaussian process (GP) surrogates, which perform well in continuous domains but encounter difficulties when decision variables include categorical or mixed discrete–continuous components. In particular, GP-based approaches typically require ad hoc numerical encodings of categorical variables that may fail to capture the structure of discrete decision spaces. In this work, we propose MNL-BO (Multinomial Logit Bayesian Optimization), a preference-based Bayesian optimization framework that replaces the GP surrogate with a multinomial logit (MNL) model trained from pairwise preference comparisons. The resulting surrogate provides a natural and interpretable representation of categorical alternatives while allowing continuous, discrete, and categorical variables to be handled within a unified optimization framework. The predictive utility estimates and uncertainty indicators generated by the MNL model are employed to formulate acquisition functions that reconcile exploration with exploitation. The proposed methodology is evaluated on three progressively complex optimization challenges: a purely categorical benchmark, a combinatorial Traveling Salesman problem, and a constrained mixed-variable engineering design problem concerning material selection in pressure vessel optimization. Multi-run tests provide consistent advantages over random search and exhibit stable convergence behavior across diverse random initializations. In addition to heuristic baselines such as local search and classical metaheuristics, we also compare against tree-based Bayesian optimization baselines inspired by the Sequential Model-based Algorithm Configuration (SMAC) framework. The results indicate that the proposed MNL-BO method achieves competitive performance under comparable evaluation budgets while providing an interpretable probabilistic surrogate for categorical decision spaces. These findings suggest that preference-based surrogate modeling provides a practical and flexible alternative for Bayesian optimization in categorical and mixed-variable optimization problems. Full article

27 pages, 10852 KB

Open AccessArticle

Optimization of Gabor Filters Based on Quaternions for Image Preprocessing in the Automated Detection of Bemisia tabaci in Yellow Traps

by Ramiro Esquivel-Felix, Mireya Moreno-Lucio, Celina Lizeth Castañeda-Miranda, Héctor Alonso Guerrero-Osuna, Rodrigo Castañeda-Miranda, Carlos A. Olvera-Olvera, Ma. del Rosario Martínez-Blanco and Luis Octavio Solís-Sánchez

Algorithms 2026, 19(5), 360; https://doi.org/10.3390/a19050360 - 4 May 2026

Abstract

In precision agriculture, identifying pests such as the whitefly (Bemisia tabaci) is a significant challenge, as precise knowledge of these insects is essential for developing effective Integrated Pest Management (IPM) strategies. Automated daily monitoring within IPM programs optimizes the diagnostic registration [...] Read more.

In precision agriculture, identifying pests such as the whitefly (Bemisia tabaci) is a significant challenge, as precise knowledge of these insects is essential for developing effective Integrated Pest Management (IPM) strategies. Automated daily monitoring within IPM programs optimizes the diagnostic registration stage by reducing logistical expenses and manual errors, enabling early pest treatment interventions and providing quantitative data for informed decision-making. In this study, an image bank was processed using a Quaternionic Gabor Filter (QGF) algorithmto highlight textural features through hypercomplex correlation. The highlighted objects were then processed by a YOLOv8 pretrained model to identify Bemisia tabaci. Experimental results demonstrate that this combination achieves a precision of 0.868 and an mAP@0.5 of 0.950, while a PSNR of 34.10 dB ensures the structural integrity of the enhanced images. Although the total execution time averages 2.3 s per image due to preprocessing complexity, the GPU inference time of 10.3 ms confirms the potential for high-speed detection. This approach significantly enhanced the morphological features of Bemisia tabaci, increasing the robustness of the detection model and narrowing down processing conditions for yellow trap samples to strengthen precision in the semi-arid regions of Zacatecas, Mexico. Full article

(This article belongs to the Special Issue Advances in Computer Vision: Emerging Trends and Applications)

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25 pages, 605 KB

Open AccessArticle

Eigenvalue Bounds for Symmetric, Multiple Saddle-Point Matrices with SPD Preconditioners

by Luca Bergamaschi and Michele Bergamaschi

Algorithms 2026, 19(5), 359; https://doi.org/10.3390/a19050359 - 4 May 2026

Abstract

We derive the eigenvalue bounds for symmetric block-tridiagonal multiple saddle-point systems preconditioned with the symmetric positive definite (SPD) preconditioner proposed by J. Pearson and A. Potschka in 2024 and further studied by L. Bergamaschi and coauthors, and for double saddle-point problems with inexact [...] Read more.

We derive the eigenvalue bounds for symmetric block-tridiagonal multiple saddle-point systems preconditioned with the symmetric positive definite (SPD) preconditioner proposed by J. Pearson and A. Potschka in 2024 and further studied by L. Bergamaschi and coauthors, and for double saddle-point problems with inexact Schur complement matrices. The analysis applies to an arbitrary number of blocks. We validate the proposed estimates with both synthetic and realistic test problems, and show the good performance of the proposed preconditioner under the condition that the Schur complements are accurately approximated. Full article

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

29 pages, 3934 KB

Open AccessArticle

Explainability as a Structural Property: An Empirical Analysis of Rashomon Sets and Pareto Fronts

by Roberto Stevens Porto Solano, Antonio Berlanga de Jesús, José M. Molina López Berlanga and Yair Rivera Julio

Algorithms 2026, 19(5), 358; https://doi.org/10.3390/a19050358 - 4 May 2026

Abstract

While most current work on interpretable models has centered on post hoc explainability of individual predictive models, the structure of the hypothesis space from which such models are drawn has been largely neglected. This paper proposes a contrasting perspective in which explainability is [...] Read more.

While most current work on interpretable models has centered on post hoc explainability of individual predictive models, the structure of the hypothesis space from which such models are drawn has been largely neglected. This paper proposes a contrasting perspective in which explainability is treated not as an attribute of a single solution but as a structural property of the model space. By combining Rashomon set analysis with Pareto-based performance–model complexity trade-offs, we formulate a computational framework for identifying near-optimal and structurally simple models. A performance–model complexity trade-off landscape is constructed by systematically generating models under controlled complexity bounds and extracting Pareto-optimal solutions. The results show that explainability can emerge as a regional property of hypothesis spaces in which multiple interpretable models achieve competitive predictive performance. This perspective supports the identification of robust and auditable predictive solutions and complements traditional explainability approaches centered on isolated models. Cross-dataset replication on Wine (UCI) and Vehicle (UCI) confirms the generalizability of these findings. Full article

(This article belongs to the Special Issue Explainable AI: Advances in Interpretability Algorithms and Applications)

44 pages, 14806 KB

Open AccessArticle

An Agricultural Product Price Prediction Model Based on Quadratic Clustering Decomposition and TOC-Optimized Deep Learning

by Fengkai Ye, Ruoqian Li, Danping Wang and Mengyang Li

Algorithms 2026, 19(5), 357; https://doi.org/10.3390/a19050357 - 3 May 2026

Abstract

Accurate forecasting of agricultural product prices is crucial for informed decision-making in agricultural markets; however, such time series are inherently characterized by non-stationarity, multi-scale dynamics, and substantial noise, posing significant challenges to conventional methods. To overcome these limitations, this study proposes a novel [...] Read more.

Accurate forecasting of agricultural product prices is crucial for informed decision-making in agricultural markets; however, such time series are inherently characterized by non-stationarity, multi-scale dynamics, and substantial noise, posing significant challenges to conventional methods. To overcome these limitations, this study proposes a novel hybrid framework, termed TOC-CNN-BiLSTM-SA, built upon a “quadratic decomposition–clustering–optimization” paradigm. Specifically, a composite CEEMDAN–K-means++–VMD approach is first employed to hierarchically decompose the raw price series via coarse decomposition, feature clustering, and refined decomposition, enabling effective noise suppression and multi-scale feature extraction. Subsequently, a deep learning architecture integrating Convolutional Neural Networks (CNNs), Bidirectional Long Short-Term Memory networks (BiLSTM), and a self-attention mechanism is developed, where CNN captures local patterns, BiLSTM models bidirectional temporal dependencies, and the attention mechanism enhances global feature representation. Furthermore, the Tornado Optimizer with Coriolis force (TOC) is introduced to adaptively tune key hyperparameters, thereby improving model robustness and generalization capability. Empirical results based on wheat price data from Henan Province, China, demonstrate that the proposed model achieves outstanding predictive performance, with RMSE, MAE, MAPE, and R² values of 4.425, 3.9372, 0.16%, and 99.97%, respectively, significantly outperforming existing benchmark models. These research indicate that the proposed framework effectively captures complex price dynamics and offers a reliable and practical solution for agricultural price forecasting. Full article

33 pages, 11937 KB

Open AccessArticle

Trajectory-Based Behavioral Analytics for Blockchain Systems

by Francisco Javier Moreno Arboleda, Luzarait Cañas Quintero and Georgia Garani

Algorithms 2026, 19(5), 356; https://doi.org/10.3390/a19050356 - 2 May 2026

Abstract

Blockchain systems generate massive volumes of transactional data, yet most existing analytical approaches rely on query-based retrieval mechanisms that treat transactions as isolated records. In this paper, a trajectory-based framework for blockchain analysis is introduced where user activity is modeled as temporally ordered [...] Read more.

Blockchain systems generate massive volumes of transactional data, yet most existing analytical approaches rely on query-based retrieval mechanisms that treat transactions as isolated records. In this paper, a trajectory-based framework for blockchain analysis is introduced where user activity is modeled as temporally ordered behavioral patterns. Four types of blockchain trajectories are formally defined: miner reward trajectories, sender value-and-fee trajectories, receiver value trajectories, and sender–receiver interaction trajectories. Unlike traditional query frameworks, trajectories are treated as first-class analytical objects, explicitly constructed and returned as outputs, thereby enabling structured temporal reasoning over blockchain behavior. To demonstrate the practicality of the approach, the proposed trajectory functions are implemented in Python 3.12 and experiments are conducted using real data from the Ethereum blockchain. Compared with conventional query-based approaches that return isolated transactions, the experimental results show that the proposed trajectory-based framework enables a more systematic identification of temporal behavioral patterns, including persistent miner dominance, recurrent zero-value interactions, sender–receiver role reversals and sender dominance by sending the highest values across several periods. The results show that trajectory-based modeling provides a systematic lens for uncovering temporal and structural regularities that are not readily observable through conventional query techniques. This work establishes a formal foundation for behavioral blockchain analytics and opens new research directions in centralization measurement, predictive modeling, and trajectory similarity analysis. Full article

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