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Computation

Computation is a peer-reviewed journal of computational science and engineering published monthly online by MDPI.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High Visibility: indexed within Scopus, ESCI (Web of Science), CAPlus / SciFinder, Inspec, dblp, and other databases.
Journal Rank: JCR - Q2 (Mathematics, Interdisciplinary Applications) / CiteScore - Q1 (Applied Mathematics)
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 14.8 days after submission; acceptance to publication is undertaken in 5.6 days (median values for papers published in this journal in the second half of 2025).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Journal Cluster of Mathematics and Its Applications: AppliedMath, Axioms, Computation, Fractal and Fractional, Geometry, International Journal of Topology, Logics, Mathematics and Symmetry.

Impact Factor: 1.9 (2024); 5-Year Impact Factor: 1.9 (2024)

Imprint Information Journal Flyer Open Access ISSN: 2079-3197

Latest Articles

22 pages, 867 KB

Open AccessArticle

RankBridge: Privacy-Preserving Rank-Based Explanation Clustering for Heterogeneous Federated Phishing Detection

by Panhapiseth Lim, Priyanka Kumar, Richard Zanni and Timothy Lambdin

Computation 2026, 14(6), 137; https://doi.org/10.3390/computation14060137 (registering DOI) - 15 Jun 2026

Federated learning lets organizations train a shared model without pooling private data. The standard method, Federated Averaging, requires all participants to use the same input features, a condition that fails in cross-sector phishing detection, where banks analyze URL structure and hospitals analyze email [...] Read more.

Federated learning lets organizations train a shared model without pooling private data. The standard method, Federated Averaging, requires all participants to use the same input features, a condition that fails in cross-sector phishing detection, where banks analyze URL structure and hospitals analyze email content. We present RankBridge, a system that groups participants by comparing ranked lists of SHapley Additive exPlanations (SHAP) feature importance rather than model weights or gradients. Each participant trains a local LightGBM model, extracts the top-K features by SHAP importance, and sends a 60-byte ranked list of feature indices to a central server. The server applies rank correlation and Ward’s hierarchical clustering to identify similarly threatened organizations. RankBridge operates in two modes: ModelShare, where models are also shared within each discovered group for prediction ensembling, and RankOnly, where the server returns only a group label and each participant keeps their model private. Across 32 participants in five organization types, RankBridge (ModelShare) achieves F1

= 0.853

(AUC

= 0.926

) on synthetic data and F1

= 0.772

(AUC

= 0.812

) on real phishing data, and it is the only method to outperform isolated local training on both. On real heterogeneous data the standard baselines adapted to LightGBM, including Federated Averaging, retain a moderate thresholded F1 (≈0.73) but their ranking quality collapses to near-random (AUC

\approx 0.59

, PR-AUC

\approx 0.66

), whereas RankBridge sustains AUC

= 0.812

and PR-AUC

= 0.819

. RankBridge recovers the correct organizational groupings with Normalized Mutual Information (NMI)

= 0.973

. The rank-based grouping channel itself transmits 60 bytes per participant per round, roughly 10,000× less than a full model upload. Full article

(This article belongs to the Special Issue Selected Papers from the 57th International Carnahan Conference on Security Technology (the 57th Annual ICCST))

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24 pages, 782 KB

Open AccessArticle

Optimal Control and Cost-Effectiveness Analysis of Porosity-Driven Bone Remodeling Dynamics

by Moustafa El-Shahed, Kadi Alowais and Yousef Alnafisah

Computation 2026, 14(6), 136; https://doi.org/10.3390/computation14060136 - 12 Jun 2026

This paper develops an optimal control framework for a mechanical–structural model of bone remodeling that couples osteocytes, osteoblasts, and osteoclasts with bone density, incorporating porosity-dependent feedback mechanisms. To represent clinically relevant interventions, three bounded control functions are introduced: anabolic stimulation of osteoblast activity, [...] Read more.

This paper develops an optimal control framework for a mechanical–structural model of bone remodeling that couples osteocytes, osteoblasts, and osteoclasts with bone density, incorporating porosity-dependent feedback mechanisms. To represent clinically relevant interventions, three bounded control functions are introduced: anabolic stimulation of osteoblast activity, anti-resorptive suppression of osteoclast-mediated resorption, and structural modulation of porosity feedback. The controlled system is shown to be mathematically well-posed, and the necessary optimality conditions are derived via Pontryagin’s Maximum Principle, leading to explicit characterizations of the optimal controls. The resulting state–adjoint system is solved numerically using a forward–backward sweep method. Numerical results demonstrate that the optimal intervention effectively suppresses osteoclast activity and drives the system toward higher, more stable bone density levels than the uncontrolled dynamics. In particular, the anti-resorptive control consistently plays the dominant role in shaping the optimal strategy. A cost-effectiveness analysis based on ACER, ICER, and the efficient frontier shows that strategies involving anti-resorptive inhibition achieve the greatest therapeutic gains at moderate cost, while additional controls yield only marginal improvements. Sensitivity analysis further indicates that parameters associated with osteoclast dynamics and bone formation have the strongest influence on density-related outcomes. Full article

(This article belongs to the Section Computational Biology)

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20 pages, 1663 KB

Open AccessArticle

Jacobi Elliptic Function Solutions for the Conformable Resonant Nonlinear Schrödinger Equation with Parabolic Nonlinearity

by Du’a Al-zaleq, Lewa’ Alzaleq and Suboh Alkhushayni

Computation 2026, 14(6), 135; https://doi.org/10.3390/computation14060135 - 11 Jun 2026

In this study, we utilize the

ϕ^{6}

-model expansion method to derive a diverse set of Jacobi elliptic function solutions for the conformable resonant Nonlinear Schrödinger Equation (NLSE) with parabolic law nonlinearity. As the modulus of the Jacobi elliptic functions approaches 1 [...] Read more.

In this study, we utilize the

ϕ^{6}

-model expansion method to derive a diverse set of Jacobi elliptic function solutions for the conformable resonant Nonlinear Schrödinger Equation (NLSE) with parabolic law nonlinearity. As the modulus of the Jacobi elliptic functions approaches 1 and 0, the solutions transform into hyperbolic and trigonometric functions, respectively. This methodology yields various exact traveling wave solutions, including kink solitons, singular solitons, periodic solutions, and singular periodic solutions. Notably, this work represents the first investigation into identifying Jacobi elliptic function solutions for the conformable resonant NLSE. These results enhance the understanding of the nonlinear dynamical properties intrinsic to the NLSE. We use graphical illustrations to highlight the dynamical features of the solutions. Moreover, our approach showcases versatility in addressing other nonlinear partial differential equations, offering insights applicable to nonlinear optics, fluid dynamics, and quantum physics. Full article

(This article belongs to the Section Computational Engineering)

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33 pages, 7237 KB

Open AccessArticle

Robust Passive Vibration Control of Monopile Offshore Wind Turbines Using a Single-Sided Vibro-Impact Nonlinear Energy Sink Under Wind-Wave-Seismic Loading

by Mulatijiang Maimaiti, Ge Yan, Qunyi Huang, Abudureyimujiang Aosimanjiang and Xiangyu Zhang

Computation 2026, 14(6), 134; https://doi.org/10.3390/computation14060134 - 7 Jun 2026

Monopile offshore wind turbines are vulnerable to excessive vibration under coupled wind, wave, and seismic loading because of their slender and flexible structural characteristics. This study investigates a single-sided vibro-impact nonlinear energy sink (SSVI NES) installed inside the nacelle of a 5 MW [...] Read more.

Monopile offshore wind turbines are vulnerable to excessive vibration under coupled wind, wave, and seismic loading because of their slender and flexible structural characteristics. This study investigates a single-sided vibro-impact nonlinear energy sink (SSVI NES) installed inside the nacelle of a 5 MW monopile offshore wind turbine. A reduced-order ten-degree-of-freedom dynamic model is established using the Euler-Lagrange formulation, and turbulent wind, irregular wave, and seismic inputs are generated using TurbSim, the Kaimal and JONSWAP spectra, the Morison equation, and 15 PEER ground-motion records. The proposed SSVI NES is compared with an optimized tuned mass damper (TMD) under nominal and frequency-detuned conditions. Under the nominal design condition, the optimized TMD and the representative SSVI NES reduce the RMS nacelle fore-aft displacement by approximately 55% and 50%, respectively, indicating that the SSVI NES provides near-benchmark vibration mitigation. Meanwhile, the maximum absorber stroke of the SSVI NES is reduced by approximately 40% compared with that of the optimized TMD, which is beneficial for nacelle-integrated implementation. Under frequency detuning, the response-reduction effectiveness of the TMD decreases from approximately 55% to 20%, whereas the SSVI NES retains approximately 80% of its nominal RMS-based control effectiveness. These quantified results show that the SSVI NES offers a balanced combination of competitive nominal response reduction, reduced absorber motion demand, and improved robustness against structural-frequency variations. The proposed device therefore provides a promising passive-control strategy for enhancing the serviceability and multi-hazard resilience of monopile offshore wind turbines. Full article

(This article belongs to the Section Computational Engineering)

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19 pages, 73674 KB

Open AccessArticle

Complex Dynamics and Bifurcations in a Discrete Switching Host–Parasitoid Model Under a Nonlinear Threshold Policy

by Yun Liu, Xijuan Liu and Lifeng Guo

Computation 2026, 14(6), 133; https://doi.org/10.3390/computation14060133 - 5 Jun 2026

In this study, we present a discrete switching host–parasitoid model that incorporates biological and chemical control interventions within the integrated pest management (IPM) measures. The coupling of multi-tactic control measures induces rich and complex dynamical behaviors in the proposed system. We begin by [...] Read more.

In this study, we present a discrete switching host–parasitoid model that incorporates biological and chemical control interventions within the integrated pest management (IPM) measures. The coupling of multi-tactic control measures induces rich and complex dynamical behaviors in the proposed system. We begin by systematically characterizing the existence and stability of fixed points in the control subsystem. The analysis then proceeds to demonstrate how the system undergoes multiple bifurcation routes, including period-doubling, transcritical, and Neimark–Sacker bifurcations. Building on this theoretical foundation, extensive numerical simulations are conducted, not only corroborating our analytical predictions but also revealing emergent phenomena such as cascading period-doubling routes and chaotic regimes. Finally, high-resolution two-parameter stability diagrams are employed to identify the critical dynamical transition boundaries, and the corresponding ecological implications for practical pest management decision-making are elaborated in depth. Full article

(This article belongs to the Section Computational Biology)

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25 pages, 1222 KB

Open AccessArticle

Optimal Service Rate for M/M/1/DV Queues with Interrupted Vacations and Impatient Customers Using Particle Swarm Optimization

by Abdelhak Guendouzi and Fatimah A. Almulhim

Computation 2026, 14(6), 132; https://doi.org/10.3390/computation14060132 - 4 Jun 2026

This paper investigates an

M / M / 1

queueing system with differentiated vacations, threshold-based interruptions, and customer impatience in the form of balking and reneging. Using recursive analytical methods, we derive closed-form steady-state probabilities and key performance metrics, including average queue length [...] Read more.

This paper investigates an

M / M / 1

queueing system with differentiated vacations, threshold-based interruptions, and customer impatience in the form of balking and reneging. Using recursive analytical methods, we derive closed-form steady-state probabilities and key performance metrics, including average queue length and customer loss rates. To address the practical need for cost-efficient operation, we formulate an economic cost function and determine the optimal service rate using Particle Swarm Optimization (PSO). Numerical experiments conducted in R show that the optimal service rate ranges between 2.71 and 3.48 across different cost structures, achieving minimum expected total costs between 183.23 and 199.04. The results further reveal that the cost function is convex with a clear global minimum, and that earlier vacation interruptions (smaller

n_{1}

and

n_{2}

) significantly reduce both system congestion and customer loss. The proposed approach provides actionable insights for designing and managing service systems in domains such as healthcare, telecommunications, and cloud computing, where server availability is intermittent and customer patience is limited. Full article

(This article belongs to the Section Computational Engineering)

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27 pages, 3437 KB

Open AccessArticle

Numerically Stable Maclaurin Approximations for 3D Constant Turn Models in IMM Aircraft Tracking

by Yurii Kravchenko, Serhii Stavytskyi, Oleksandr Makhovych, Andriy Dudnik, Roman Dubik, Dmytro Obidin, Oleksandr Permiakov, Oleksandr Shapran, Yevhenii Makhno and Yevhen Rudenko

Computation 2026, 14(6), 131; https://doi.org/10.3390/computation14060131 - 3 Jun 2026

This paper considers a numerically stable discrete-time representation of the three-dimensional Constant Turn (CT) motion model within the Interacting Multiple Model (IMM) framework for radar tracking of maneuvering aerial targets. Classical discrete CT models used in Kalman-filter-based tracking contain singular expressions in the [...] Read more.

This paper considers a numerically stable discrete-time representation of the three-dimensional Constant Turn (CT) motion model within the Interacting Multiple Model (IMM) framework for radar tracking of maneuvering aerial targets. Classical discrete CT models used in Kalman-filter-based tracking contain singular expressions in the vicinity of zero and near-zero turn rates, which may degrade estimation accuracy and impair numerical robustness. To address this problem, a Maclaurin-series-based discretization of the three-dimensional CT model is developed, in which the state transition matrix and the process-noise-related matrices are approximated in polynomial form. Linear, quadratic, and cubic approximations are constructed and analyzed. The proposed CT model is integrated into a three-model IMM algorithm together with the Constant Velocity (CV) and Constant Acceleration (CA) models. The study includes both an internal comparison of Maclaurin approximations of different orders and an external comparison with the classical CT discretization and a Padé-based reference discretization. Numerical experiments are performed for representative three-dimensional maneuvering scenarios under radar measurement conditions. The obtained results show that the proposed discretization eliminates singular behavior near zero turn rate while preserving the tracking capability of the IMM estimator. The comparative analysis demonstrates that the quadratic Maclaurin approximation provides the most favorable trade-off between modeling accuracy, numerical stability, and computational cost. It yields tracking performance close to higher-order approximations and competitive with the Padé-based reference approach, while remaining simpler for practical implementation in real-time radar tracking systems. These results indicate that the proposed quadratic approximation is a suitable solution for maneuvering aerial target tracking in three-dimensional radar applications. Full article

(This article belongs to the Special Issue Moving Object Detection Using Computational Methods and Modeling)

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27 pages, 6132 KB

Open AccessArticle

Effect of Spraying Characteristics on Combustion of Red Liquor—Virtual Experiments Using CFD Simulation

by Barbara D. Weiß, Eva-Maria Wartha, Christian Jordan, Thomas Ladinek, Bahram Haddadi and Michael Harasek

Computation 2026, 14(6), 130; https://doi.org/10.3390/computation14060130 - 2 Jun 2026

Red liquor combustion is a crucial step in the chemical recovery process in the pulp and paper industry and has two main functions: recovering MgO and SO₂ from magnesium bisulfite spent liquor and generating steam as a heat source for further usage. [...] Read more.

Red liquor combustion is a crucial step in the chemical recovery process in the pulp and paper industry and has two main functions: recovering MgO and SO₂ from magnesium bisulfite spent liquor and generating steam as a heat source for further usage. This research aims to analyze how different red liquor spraying characteristics affect combustion time, guiding recommendations for optimal spraying characteristics to achieve faster combustion using computational fluid dynamics (CFD). Red liquor combustion is simulated in the open-source environment OpenFOAM^®, employing Eulerian–Lagrangian coupling simulations, treating red liquor droplets as Lagrangian particles. One-step devolatilization and combustion kinetics are derived from performed non-isothermal thermogravimetric analyses (TGA) and implemented into the model. An industrial red liquor combustion vessel served as a reference case. Through virtual experiments, we explore the impact of spray angle (15° and 30°), droplet size (2 mm and 3 mm), and spray type (fullcone vs. hollowcone) on combustion time. The performed simulations indicate that the combustion time can be reduced by approximately 30% by reducing the characteristic particle diameter from 3 mm to 2 mm. Furthermore, hollowcone spraying revealed faster combustion times than fullcone spraying. The fastest combustion time was achieved with a characteristic particle size of 2 mm, a spraying angle of 30°, and using a hollowcone spray type. Full article

(This article belongs to the Section Computational Engineering)

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31 pages, 5198 KB

Open AccessArticle

From Instability to Pest Eradication: Linear Harvesting in a Modified Holling–Tanner System

by Aladeen Al Basheer

Computation 2026, 14(6), 129; https://doi.org/10.3390/computation14060129 - 2 Jun 2026

This study analyzes a modified Holling–Tanner predator–prey system with linear harvesting and supplementary food for the predator. The framework examines how harvesting interacts with predation and external resources to determine system dynamics. We derive explicit conditions for the existence and stability of all [...] Read more.

This study analyzes a modified Holling–Tanner predator–prey system with linear harvesting and supplementary food for the predator. The framework examines how harvesting interacts with predation and external resources to determine system dynamics. We derive explicit conditions for the existence and stability of all equilibria and identify a critical predation threshold separating stable coexistence from oscillatory dynamics. Harvesting acts as a control parameter that can suppress oscillations, eliminate interior equilibria, and drive the system toward a prey-free state. We establish sufficient conditions for pest eradication by linking harvesting intensity, predation rate, and the loss of coexistence equilibria. Local bifurcation analysis reveals Hopf and saddle–node bifurcations, marking transitions between steady states and periodic oscillations. For the spatially extended system, diffusion-driven instability is investigated, and conditions for Turing pattern formation are derived from the modified equilibrium structure. Numerical simulations support the analytical results and illustrate transitions between dynamical regimes under varying harvesting levels. The results provide explicit parameter thresholds governing stabilization, oscillation, and eradication in predator–prey systems with external resource support. Full article

(This article belongs to the Section Computational Biology)

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14 pages, 568 KB

Open AccessArticle

Signal Statistical Mechanics

by Peter D. Morley

Computation 2026, 14(6), 128; https://doi.org/10.3390/computation14060128 - 2 Jun 2026

We are interested in determining the physics bound for the detection of signals in modern digital radio frequency (RF) hardware. Classical signal theory (Kalman filters) requires that the signal-to-noise power ratio (SNR)

> 10

, but this is not the physics bound. Instead, [...] Read more.

We are interested in determining the physics bound for the detection of signals in modern digital radio frequency (RF) hardware. Classical signal theory (Kalman filters) requires that the signal-to-noise power ratio (SNR)

> 10

, but this is not the physics bound. Instead, the physics bound is much more complicated. Because an important application is radar, we ask whether, in a time interval of 1

μ

s, a signal is present within the noise of the receiver baseband. For radar, this would be the pulse return reflection. For our analysis, we use the Keysight Technologies UXR_25 oscilloscope as the RF receiver that has an analogue-to-digital converter (ADC) chip of 256 billion samples per second. In 1

μ

s, then, 256 thousand voltage samples are taken. We want to determine if a signal is present using the 256 thousand voltage samples using random matrix theory (RMT). The answer for this particular ADC is that we can detect any signals with SNR >−20 dB, a thousand-fold increase from SNR > 10. This paper gives the physics bound of signal detection. Full article

(This article belongs to the Section Computational Engineering)

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28 pages, 3621 KB

Open AccessArticle

Evaluating Pre-Trained Transformer-Based Models for Political Sentiment Analysis on Social Media

by María Patricia Tzili Cruz, Salvador Contreras Hernández, José Martín Espínola Sánchez, Raúl Hernández Medina, Alma Alejandra Luna Gómez and Adriana Marlene Pacheco Orozco

Computation 2026, 14(6), 127; https://doi.org/10.3390/computation14060127 - 31 May 2026

Sentiment analysis has broad applications in social media networks due to the high volume of user activity on diverse topics such as political debates. Transformer-based neural networks are among the technologies that achieve significant results in text classification. This study evaluates twelve pre-trained [...] Read more.

Sentiment analysis has broad applications in social media networks due to the high volume of user activity on diverse topics such as political debates. Transformer-based neural networks are among the technologies that achieve significant results in text classification. This study evaluates twelve pre-trained transformer-based models through fine-tuning for sentiment classification of Spanish-language political texts from the social media network X. Some of these models were originally created in Spanish, while others are multilingual models that include Spanish. The twelve models were trained to specialize in sentiment classification on political topics, using the same training and testing parameters, in order to compare them under equal conditions during fine-tuning. Good results were obtained with the precision, recall, and F1-score metrics mainly in multilingual models but also in some models originally created in Spanish. The study includes the detailed results of the evaluation in training and testing for the three metrics employed. Full article

(This article belongs to the Special Issue Sentiment-Driven Modelling in Business, Economics, and Social Sciences)

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25 pages, 4665 KB

Open AccessArticle

A Spatial Analog of the Compass Rose Constructed Using Galois Fields

by Ibragim Suleimenov and Akhat Bakirov

Computation 2026, 14(6), 126; https://doi.org/10.3390/computation14060126 - 29 May 2026

This paper proposes a spatial analog of the compass rose, constructed using finite fields and the discrete logarithm operation. The basic idea is to match the geometric elements of regular and semiregular polyhedra with elements of Galois fields (GF), which allows for the [...] Read more.

This paper proposes a spatial analog of the compass rose, constructed using finite fields and the discrete logarithm operation. The basic idea is to match the geometric elements of regular and semiregular polyhedra with elements of Galois fields (GF), which allows for the introduction of discrete spherical coordinates defined in algebraic form. The icosahedron is considered as a basic example. It is shown that using the icosahedron faces and the GF(41) field results in a 20-directed spatial structure that can be interpreted through discrete analogs of polar and azimuthal coordinates. Next, a variant based on the icosahedron edges and the GF(31) field is investigated, in which the number of directions increases to 30 while maintaining the regularity of the construction. A further generalization to the case of a truncated icosahedron, associated with the GF(181) field, is also considered, demonstrating the possibility of increasing the angular resolution without abandoning the algebraic organization of the set of directions. The obtained results demonstrate that the spatial rose of compass points can be represented as a finite system of directions with an explicit internal structure, convenient for coding, enumeration, and algorithmic processing. The proposed approach is of interest for problems of discrete description of rotations, construction of finite coordinate systems, and development of sectoral control algorithms, including those applicable to UAVs and their groups. The proposed formalism may also be considered as a sector-level coding layer for command-and-control architectures in which it is sufficient to identify a spatial sector rather than reconstruct full continuous coordinates. Full article

(This article belongs to the Section Computational Engineering)

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91 pages, 6222 KB

Open AccessReview

A Comprehensive Survey and Guide to Multimodal Large Language Models in Vision–Language Tasks

by Chia Xin Liang, Pu Tian, Caitlyn Heqi Yin, Yao Yua, An-Hou Wei, Ming Li, Xinyuan Song, Tianyang Wang, Ziqian Bi, Ming Liu, Riyang Bao and Pengbin Feng

Computation 2026, 14(6), 125; https://doi.org/10.3390/computation14060125 - 29 May 2026

This survey provides a comprehensive guide to Multimodal Large Language Models (MLLMs) with a focus on vision–language tasks, including image captioning, visual question answering, cross-modal retrieval, visual grounding, multi-image reasoning, long-video understanding, and embodied AI. We examine architectures, training pipelines, and practical applications, [...] Read more.

This survey provides a comprehensive guide to Multimodal Large Language Models (MLLMs) with a focus on vision–language tasks, including image captioning, visual question answering, cross-modal retrieval, visual grounding, multi-image reasoning, long-video understanding, and embodied AI. We examine architectures, training pipelines, and practical applications, covering visual encoders, language model backbones, connector modules, contrastive pre-training, instruction tuning, and preference alignment. We also foreground first-principles constraints—information bottlenecks, data-processing limits, and statistical co-occurrence bias—that shape architecture, robustness, and evaluation. This survey centers on vision–language systems and does not cover audio-only models or code-generation tools without visual inputs. Through task-level analysis and system-level case studies, we examine prominent MLLM implementations while addressing key challenges in scalability, memory, energy use, inference cost, robustness, and cross-modal learning. We present a unified taxonomy of the MLLM design space, a comparative overview of representative models and evaluation benchmarks, and a discussion of open problems. Concluding with ethical considerations and responsible AI development, this survey offers theoretical frameworks and practical insights for researchers, practitioners, and students working at the intersection of natural language processing and computer vision. Full article

(This article belongs to the Special Issue Applied Large Language Models for Science, Engineering, and Mathematics: Reasoning, Reliability and Efficient Systems)

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27 pages, 2024 KB

Open AccessArticle

Complex-Order Gold Rush Optimizer Algorithm

by Sixuan Chen, Xiaobo Wu, Tao Wang, Hongli Ma, Xiang Li and Lisheng Yin

Computation 2026, 14(6), 124; https://doi.org/10.3390/computation14060124 - 27 May 2026

This study proposes an enhanced variant of the gold rush optimizer (GRO) algorithm, termed the complex-order gold rush optimizer (CoGRO) algorithm, to address two inherent theoretical limitations of the original GRO. First, GRO employs a random initialization strategy that lacks ergodicity and uniform [...] Read more.

This study proposes an enhanced variant of the gold rush optimizer (GRO) algorithm, termed the complex-order gold rush optimizer (CoGRO) algorithm, to address two inherent theoretical limitations of the original GRO. First, GRO employs a random initialization strategy that lacks ergodicity and uniform coverage, leading to insufficient population diversity and a higher risk of premature convergence. Second, its position update mechanism relies solely on current-time information without incorporating historical search experience, which restricts the algorithm’s ability to model long-term dependencies and escape local optima in complex multimodal landscapes. To overcome these deficiencies, we introduce a chaotic LCS1 initialization to enhance population diversity through improved ergodic coverage, and we embed a complex-order derivative mechanism into the migration and collaboration updates to provide infinite memory capability. A comprehensive sensitivity analysis is conducted to examine the influence of control parameters on CoGRO’s performance, leading to the identification of an optimal parameter configuration. The effectiveness of the proposed algorithm is evaluated using the CEC2022 benchmark suite through ablation studies and comparative analyses with state-of-the-art algorithms. Experimental results on the CEC2022 benchmark suite comprising 12 test functions demonstrate that CoGRO significantly outperforms the original GRO, achieving an average solution accuracy improvement of 0.84% and an average standard deviation reduction of 67.6 across all 12 functions, with particularly notable improvements on hybrid and composition functions. Wilcoxon signed-rank tests confirm the statistical significance of these improvements (

p < 0.05

). These results confirm the feasibility and effectiveness of CoGRO as an improved optimization method for complex engineering problems. Full article

(This article belongs to the Topic Fractional Calculus: Theory and Applications, 2nd Edition)

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32 pages, 1705 KB

Open AccessArticle

From Interfaces to Networks: Energetic Control of Specificity in Bacterial Two-Component Systems

by Eduardo M. Martin, Alma L. Guerrero-Barrera, F. Javier Avelar-Gonzalez, Rogelio Salinas-Gutierrez and Mario Jacques

Computation 2026, 14(6), 123; https://doi.org/10.3390/computation14060123 - 25 May 2026

Bacterial two-component systems (TCSs) mediate environmental sensing and adaptive responses through signal transduction between histidine kinases (HKs) and response regulators (RRs), thereby regulating biochemical processes essential for survival and, in pathogenic species, infection. How signaling specificity and insulation are maintained in organisms encoding [...] Read more.

Bacterial two-component systems (TCSs) mediate environmental sensing and adaptive responses through signal transduction between histidine kinases (HKs) and response regulators (RRs), thereby regulating biochemical processes essential for survival and, in pathogenic species, infection. How signaling specificity and insulation are maintained in organisms encoding multiple paralogous two-component systems remains an open question. Here, we investigate specificity in the Actinobacillus pleuropneumoniae TCS signaling network using an integrated computational framework that combines coevolutionary analysis, structural modeling, molecular dynamics simulations, and free-energy calculations. We show that cognate HK-RR recognition is established locally through clusters of coevolving interface residues, termed the orthologue interface specificity core (OISC), which mediate symmetric molecular recognition at individual interaction interfaces. However, interface-level recognition alone is insufficient to explain signaling fidelity across the network. Instead, system-wide specificity and pathway insulation emerge in this network from asymmetric energetic discrimination among cognate and non-cognate interactions across the ensemble of paralogous interfaces. Graded free-energy profiles reveal that broadly compatible interfaces can coexist with robust signaling insulation, reconciling interface promiscuity with stable network organization. Together, these findings support a two-tiered model for the TCS network analyzed here, in which symmetric interface constraints enable cognate recognition, while asymmetric network-level energetics govern signaling specificity. This framework may extend to other paralogous TCS networks. Full article

(This article belongs to the Section Computational Biology)

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17 pages, 5706 KB

Open AccessArticle

Investigation of Decomposition Techniques for Characterizing Complex Vortex Structures in MVG-Controlled Boundary Layer

by Mai Al Shaaban, Joey Takei, Annamaria Palmiero, Leya Dereje, Sam Panitch, Caixia Chen, Yong Yang and Yonghua Yan

Computation 2026, 14(6), 122; https://doi.org/10.3390/computation14060122 - 25 May 2026

Accurate characterization of coherent vortex structures in high-speed turbulent boundary layers presents a persistent challenge due to the flow’s high dimensionality and nonlinear dynamics. This study investigates an optimized decomposition framework that integrates modal decomposition techniques with a novel vortex identification strategy to [...] Read more.

Accurate characterization of coherent vortex structures in high-speed turbulent boundary layers presents a persistent challenge due to the flow’s high dimensionality and nonlinear dynamics. This study investigates an optimized decomposition framework that integrates modal decomposition techniques with a novel vortex identification strategy to extract dynamically significant features. The numerical solution from a previously conducted high-fidelity simulation of MVG-controlled supersonic flow serves as the testbed. Principal Component Decomposition and Non-negative Matrix Factorization are applied across multiple flow variables to evaluate their effectiveness in isolating coherent structures. The results show that, across the velocity-based cases, 3–4 modes capture 70% of the TKE with MSE about 0.1, while the Liutex case requires 14 modes but achieves a lower MSE of about 0.04. Overall, using the same number of modes yields similar reconstruction performance across all cases. The influence of various normalization and rescaling methods on decomposition performance is also examined. Optimization is guided by two primary criteria: the interpretability of spatial modes and MSE in reconstructing vortex structures. By employing low-rank matrix representations, this optimization study aims to enhance interpretability and reduce computational costs. This approach establishes a mathematically rigorous and efficient platform for analyzing vortex dynamics, achieving significant dimensionality reduction while preserving key features of turbulent transport. Full article

(This article belongs to the Special Issue Advances in Computational Methods for Fluid Flow—2nd Edition)

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25 pages, 1047 KB

Open AccessArticle

ADL-KG: Diacritic-Aware Knowledge Graph Prompting for Arabic LLM Question Answering

by Narimene Ayat, Fouzi Harrag, Nassir Harrag and Khaled Shaalan

Computation 2026, 14(6), 121; https://doi.org/10.3390/computation14060121 - 24 May 2026

Arabic’s complex morphological system and the optional use of short vowels (tashkīl) introduce substantial lexical ambiguity, posing significant challenges for Large Language Models (LLMs). While diacritics enhance linguistic precision, LLMs trained predominantly on undiacritized corpora often exhibit performance degradation when processing fully diacritized [...] Read more.

Arabic’s complex morphological system and the optional use of short vowels (tashkīl) introduce substantial lexical ambiguity, posing significant challenges for Large Language Models (LLMs). While diacritics enhance linguistic precision, LLMs trained predominantly on undiacritized corpora often exhibit performance degradation when processing fully diacritized inputs due to representation shifts and tokenization inconsistencies. To address this limitation, we propose the Arabic Diacritic Lexical Knowledge Graph (ADL-KG), a structured framework that links diacritized and undiacritized forms through integrated lexical, morphological, and semantic knowledge. Building upon this resource, we introduce Diacritic-Aware Knowledge Graph Prompting (DA-KGP), a prompt augmentation strategy that injects explicit linguistic features into LLM inputs to facilitate robust interpretation of diacritized Arabic text. The framework is evaluated on the Arabic Reading Comprehension Dataset under zero-shot and few-shot question answering across AraGPT2-base, BLOOMZ-560M, SILMA-v1, and LLaMA 3.1-8B. Performance is assessed using Exact Match, BLEU, ROUGE-1, and BERTScore-F1. Experimental results show that fully diacritized prompts significantly degrade baseline performance, whereas DA-KGP consistently mitigates this effect by improving semantic alignment across diverse architectures. For AraGPT2-base, KG augmentation improves average BERTScore-F1 by +5.96 points. SILMA-v1 achieves the strongest lexical improvements, reaching 21.57 BLEU and 81.31% BERTScore-F1 in the KG-enhanced two-shot configuration. LLaMA 3.1-8B achieves the highest overall semantic performance with 82.54% BERTScore-F1 under KG-enhanced prompting, while BLOOMZ-560M also demonstrates statistically significant semantic gains through structured augmentation. These findings demonstrate that morphologically informed prompting and structured lexical grounding provide an effective and parameter-efficient strategy for improving the robustness and semantic fidelity of Arabic LLMs under fully diacritized input conditions. Full article

(This article belongs to the Special Issue Recent Advances on Computational Linguistics and Natural Language Processing)

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23 pages, 9171 KB

Open AccessArticle

Optimal Placement of Seismic-Resistant Systems in Frame Structures Using Weighted Special Relativity Search Algorithm

by Vahid Goodarzimehr, Farnaz Salajegheh and Ghanshyam Tejani

Computation 2026, 14(6), 120; https://doi.org/10.3390/computation14060120 - 23 May 2026

Developing seismic-resistant systems for steel frames presents a significant challenge in structural engineering, requiring sophisticated computational methods to achieve effective and precise outcomes. This study focuses on enhancing the Special Relativity Search (SRS) algorithm by redefining the mass (m) parameter, a critical element [...] Read more.

Developing seismic-resistant systems for steel frames presents a significant challenge in structural engineering, requiring sophisticated computational methods to achieve effective and precise outcomes. This study focuses on enhancing the Special Relativity Search (SRS) algorithm by redefining the mass (m) parameter, a critical element affecting its convergence characteristics. Traditionally, the SRS algorithm treated m as a fixed unit value. However, detailed analysis indicates that dynamically modifying m can substantially improve the algorithm’s ability to solve complex optimization problems. To address this, a novel weighted equation for m is proposed, leading to improved convergence rates and greater accuracy in solutions. The refined Weighted Special Relativity Search (WSRS) algorithm is then applied to optimize the placement of seismic-resistant systems in steel frames. Comparative evaluations demonstrate that the WSRS algorithm outperforms its predecessor, delivering enhanced precision and computational efficiency. This research contributes to the advancement of algorithmic techniques and the optimization of seismic-resistant structural designs. Full article

(This article belongs to the Section Computational Engineering)

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25 pages, 1819 KB

Open AccessArticle

AI-Driven Thermodynamic Evaluation of Beta-Type Stirling Engine Using CFD Simulation and Numerical Calculations

by Amir H. Shahriari, Majid Monajjemi and Fatemeh Mollaamin

Computation 2026, 14(6), 119; https://doi.org/10.3390/computation14060119 - 22 May 2026

This study presents an AI-assisted thermodynamic and computational fluid dynamics (CFD) evaluation of a β-type Stirling engine to improve its thermal efficiency and indicated power output. The engine performance was investigated using Restricted Dimensions Thermodynamics (RDT), the Schmidt thermodynamic model, and three-dimensional CFD [...] Read more.

This study presents an AI-assisted thermodynamic and computational fluid dynamics (CFD) evaluation of a β-type Stirling engine to improve its thermal efficiency and indicated power output. The engine performance was investigated using Restricted Dimensions Thermodynamics (RDT), the Schmidt thermodynamic model, and three-dimensional CFD simulations under various operating and geometric conditions. Key parameters including rotational speed, phase angle, piston diameter, displacer stroke, porosity, and charged pressure were systematically analyzed to determine their influence on engine behavior. A feed-forward artificial neural network (ANN) trained using the Levenberg–Marquardt optimization algorithm was integrated with CFD-generated datasets to predict engine performance and accelerate the optimization process. The AI-assisted optimization was coupled with the Variable Step-size Simplified Conjugate Gradient Method (VSCGM) to identify near-optimal operating conditions while reducing computational cost. Simulation results demonstrated that the optimization process improved the indicated power from 180.33 W to 185.44 W and increased thermal efficiency from 10.32% to 11.54%. The results also showed close agreement between predicted and experimental pressure–temperature profiles, confirming the reliability of the proposed methodology. Furthermore, CFD analyses revealed that increasing piston diameter and optimizing porosity enhanced heat transfer and pressure distribution within the engine chambers, resulting in improved thermodynamic performance. The proposed AI-driven framework provides a reliable and computationally efficient approach for the design and optimization of advanced β-type Stirling engines operating under realistic thermal conditions. Full article

(This article belongs to the Section Computational Engineering)

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22 pages, 4406 KB

Open AccessArticle

Numerical Investigation on Cathode Gas Diffusion Layer with Conical Frustum Grooves for Enhancing Performance of Proton Exchange Membrane Fuel Cell

by Wei Zuo, Xiongwei Yao, Yimin Li and Qingqing Li

Computation 2026, 14(6), 118; https://doi.org/10.3390/computation14060118 - 22 May 2026

To address performance limitations in proton exchange membrane fuel cells (PEMFCs), this work proposes and numerically investigates a cathode gas diffusion layer (GDL) with conical frustum grooves. A systematic comparison is performed across three GDL configurations: a baseline structure without grooves, a design [...] Read more.

To address performance limitations in proton exchange membrane fuel cells (PEMFCs), this work proposes and numerically investigates a cathode gas diffusion layer (GDL) with conical frustum grooves. A systematic comparison is performed across three GDL configurations: a baseline structure without grooves, a design with cylindrical grooves, and the proposed conical frustum grooves. The results demonstrate that the conical frustum grooves effectively enhance liquid water removal, oxygen mass transport, membrane current density, and peak power density. This improvement arises as the grooves expand transport pathways for both liquid water and oxygen, facilitating more robust electrochemical reactions. A parametric analysis is further conducted to evaluate the effects of groove spacing, depth, top radius, and bottom radius. Reduced groove spacing, together with increased groove depth, top radius, and bottom radius, consistently improves water management and oxygen delivery. However, membrane current density and power density do not vary monotonically with groove depth and bottom radius. The optimal values for these two parameters are identified as 0.3 mm and 0.5 mm, respectively. Full article

(This article belongs to the Special Issue Computational Modelling of Transport Phenomena in Advanced Energy Systems)

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