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Volume 31
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Math. Comput. Appl., Volume 31, Issue 5 (October 2026) – 51 articles

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30 pages, 42050 KB  
Article
A 3D Memristive Hyperchaotic Map with Bounce-Escape Zigzag Scrambling for Color Image Encryption
by Muhammad Hayat, M. G. Abbas Malik and Zia Bashir
Math. Comput. Appl. 2026, 31(5), 218; https://doi.org/10.3390/mca31050218 - 9 Oct 2026
Abstract
As the need for secure image encryption grows, chaotic cryptography using hyperchaotic systems has attracted significant attention. This article proposes a novel three-dimensional (3D) memristive hyperchaotic map. We analyze the map using phase portraits, Lyapunov exponents, sensitivity analysis, the 0-1 test, Lyapunov dimension, [...] Read more.
As the need for secure image encryption grows, chaotic cryptography using hyperchaotic systems has attracted significant attention. This article proposes a novel three-dimensional (3D) memristive hyperchaotic map. We analyze the map using phase portraits, Lyapunov exponents, sensitivity analysis, the 0-1 test, Lyapunov dimension, bifurcation diagrams, and Kolmogorov–Sinai entropy. The map has two positive Lyapunov exponents, and the Kaplan–Yorke dimension equals three, confirming strong hyperchaotic dynamics across a wide parameter range. Based on this map, we introduce a new color image encryption scheme. It incorporates a key derived from both an external 256-bit secret key and the SHA-256 hash of the plaintext; a novel Bounce-Escape Zigzag (BEZ) scrambling algorithm with boundary-bouncing diagonal trajectories, variable-length diagonal traversals, and adaptive collision escape; dynamic DNA encoding; and chaotic XOR diffusion. Comprehensive security analysis on standard test images demonstrates near-ideal entropy values, NPCR and UACI close to the theoretical ideals, and correlation coefficients close to zero. The proposed scheme also shows strong robustness against differential, known-plaintext, and chosen-plaintext attacks, as well as cropping and noise corruption, with an effective key space of 2256. By integrating hyperchaotic dynamics, BEZ scrambling, and multi-layer DNA-XOR diffusion, the proposed method achieves superior performance. It is well-suited for secure image communication and storage applications. Full article
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27 pages, 1264 KB  
Article
Dictionary-Based Attention for Hyperedge Reweighting
by Li Wang, Jingyuan Yun, Jianbo Liu and Tianyu Zhu
Math. Comput. Appl. 2026, 31(5), 217; https://doi.org/10.3390/mca31050217 - 9 Oct 2026
Abstract
We introduce Dictionary-based Attention (DA), a label-free, support-preserving block that reweights existing vertex–hyperedge memberships using dictionary-code similarity. We evaluate local dictionaries with closed-form hypergraph learning (DA-HL) on visual data and a separate shared-dictionary variant with a static incidence network on citation data. Supplementary [...] Read more.
We introduce Dictionary-based Attention (DA), a label-free, support-preserving block that reweights existing vertex–hyperedge memberships using dictionary-code similarity. We evaluate local dictionaries with closed-form hypergraph learning (DA-HL) on visual data and a separate shared-dictionary variant with a static incidence network on citation data. Supplementary experiments under an explicitly reconstructed visual protocol cover nine dataset–generator combinations. Four DA-versus-uniform comparisons reach the 0.05 threshold after Holm correction; the three clustering settings show no mean advantage under the original stopping rule with an iteration cap of 200. In paired clustering runs extended to 5000 iterations, mean accuracy is practically stable between 4000 and 5000 iterations within a prespecified one-percentage-point margin, but weights, propagation operators, and some predictions continue to change. This does not establish convergence or equivalence to the original 12-iteration budget. In transductive citation experiments, test features participate in shared-dictionary fitting; the paired static-backbone results are negative on Cora, close to zero on Citeseer, and slightly positive on Pubmed, with only Pubmed meeting the multiplicity-corrected threshold. Additional controls separate injected-membership ranking from downstream classification and show sensitivity to weight mapping and member-specific assignment without identifying a unique gain mechanism. The evidence supports benefits in some tested visual configurations, rather than broad effectiveness across hypergraph learning. Full article
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33 pages, 1205 KB  
Review
A Critical Review of Fractional Operators, Control, and Machine Learning in Biomedical Models with Attention to Memory and Identifiability
by David Amilo and Mohamed Hafez
Math. Comput. Appl. 2026, 31(5), 216; https://doi.org/10.3390/mca31050216 - 8 Oct 2026
Abstract
Fractional operators are used in biomedical balance laws to encode memory. However, the order of the fractional operator used in these models is not the same as the memory recovered from the patients. This review maps one hundred scientific articles from the Scopus [...] Read more.
Fractional operators are used in biomedical balance laws to encode memory. However, the order of the fractional operator used in these models is not the same as the memory recovered from the patients. This review maps one hundred scientific articles from the Scopus and Web of Science databases from 2019 to 2026 in which fractional operators were used in biomedical applications. The articles are separated into three main communities: compartment fractional differential equations, fractional control, and tabular clinical machine learning. For each article, information regarding the fractional operator used, the biomedical plant it acted upon, the type of data used, whether the fractional order was identified, and whether a locked model would change the decision for the clinical application was collected. The results from well-posed Caputo systems, simulated glucose and intraocular-pressure controllers, and fractional physics-informed neural networks were standard results. New methodological pipelines that combined fractional operators with machine learning on public biomedical data tables yielded high area under the curve values and low pseudo-time residuals in predictions, but they have yet to prove whether they recover the fractional order from the biomedical subject’s biological clock. Clinical prediction using these models began only when there was a change in the locked model in an external cohort of biomedical subjects with a biological clock, not when the fractional model was plotted through the public biomedical data tables. Full article
(This article belongs to the Special Issue Celebrate the 30th Anniversary of Mathematical and Computational Applications (MCA))
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24 pages, 1112 KB  
Article
A Spectral Projected Gradient Algorithm for an Elliptic Inverse Coefficient Problem with a Robin Boundary Condition
by Murat A. Sultanov, Makhmud A. Sadybekov, Yerkebulan Nurlanuly and Bakytbek T. Sarsenov
Math. Comput. Appl. 2026, 31(5), 215; https://doi.org/10.3390/mca31050215 - 8 Oct 2026
Abstract
An inverse problem of recovering a lower-order coefficient in a second-order elliptic equation with a Robin boundary condition is considered. Uniqueness of the inverse problem solution is established. For the numerical solution of the inverse problem, a difference scheme is constructed by the [...] Read more.
An inverse problem of recovering a lower-order coefficient in a second-order elliptic equation with a Robin boundary condition is considered. Uniqueness of the inverse problem solution is established. For the numerical solution of the inverse problem, a difference scheme is constructed by the integro-interpolation method, and a discrete residual functional for the additional boundary data is introduced. A mesh-independent stability estimate is established for the discrete forward problem. The gradient of the functional is computed using the solution of an adjoint problem. To accelerate the iterative process, a spectral projected gradient method with a Barzilai–Borwein parameter and a nonmonotone line search is employed. Model boundary data are computed on a finer grid than the grid used to solve the inverse problem, and the stopping iteration is determined by the discrepancy principle, taking into account the error in the input data and the difference between the boundary values of the solutions computed on the two grids. The numerical experiments compare the proposed method with the fixed-step gradient method and investigate the effect of input-data errors on the recovery of a smooth coefficient and a coefficient defined by a continuous piecewise-linear function. The results demonstrate a substantial acceleration of the iterative process and the possibility of recovering the considered coefficients from perturbed model data. Full article
36 pages, 10912 KB  
Article
A Mixed-Variable Physics-Informed Neural Network for Direct and Converse Piezoelectricity in a Bimorph Cantilever
by Daniel González, Angel Higueros, Luke Shaw and Gabriel Barrientos
Math. Comput. Appl. 2026, 31(5), 214; https://doi.org/10.3390/mca31050214 - 8 Oct 2026
Abstract
In design applications, simulations enable rapid iterations and adjustments to device architecture, reducing the need for physical prototyping. The simulation of piezoelectric devices has traditionally relied on the Finite Element Method (FEM). Physics-Informed Neural Networks (PINNs) offer an alternative based on governing equations [...] Read more.
In design applications, simulations enable rapid iterations and adjustments to device architecture, reducing the need for physical prototyping. The simulation of piezoelectric devices has traditionally relied on the Finite Element Method (FEM). Physics-Informed Neural Networks (PINNs) offer an alternative based on governing equations without requiring labeled solution data. This study develops a mixed PINN architecture for the static direct and converse piezoelectric responses of a polyvinylidene fluoride (PVDF) bimorph cantilever. The network predicts two mechanical displacements, electric potential, three stress components, and two electric-displacement components. The methodology integrates the piezoelectric governing equations into a first-order loss formulation. The models are evaluated against coupled FEM solutions. For the converse effect, the relative L2 errors in horizontal displacement, vertical displacement, and electric potential are 0.107, 0.150, and 0.045, respectively. For the direct effect, they are 0.117, 0.153, and 0.067. The mixed configurations give lower displacement errors than the tested networks predicting only displacement and electric potential. However, they also use hard traction enforcement in the direct problem and mechanical gradient routing in the converse problem, so the improvement cannot be attributed to the additional outputs alone. Discrepancies between independently predicted stresses and those reconstructed from displacement and potential derivatives from the PINN reveal incomplete physical consistency. These results support approximate displacement and potential prediction while identifying constitutive consistency as a remaining limitation. Full article
(This article belongs to the Special Issue Advances in Computational and Applied Mechanics (SACAM))
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33 pages, 4038 KB  
Article
CARE-Net: Causality-Aware Self-Supervised Learning with Anatomy-Constrained Attention for Robust Pneumonia Classification
by Omobayo Ayokunle Esan and Temidayo Oluwafunke Otunniyi
Math. Comput. Appl. 2026, 31(5), 213; https://doi.org/10.3390/mca31050213 - 6 Oct 2026
Viewed by 31
Abstract
Deep learning methods for pneumonia detection from chest X-ray images have achieved promising results; however, their reliability is limited by scarce labelled data, susceptibility to spurious correlations, poor cross-domain generalisation, and inadequate interpretability. This study proposes CARE-Net, a unified framework integrating radiology-aware Self-Supervised [...] Read more.
Deep learning methods for pneumonia detection from chest X-ray images have achieved promising results; however, their reliability is limited by scarce labelled data, susceptibility to spurious correlations, poor cross-domain generalisation, and inadequate interpretability. This study proposes CARE-Net, a unified framework integrating radiology-aware Self-Supervised Learning (SSL), Causality-Aware Training (CAT), and Anatomy-Constrained Causality-Aware Attention (ACCA). Radiology-aware SSL learns robust representations from labelled and unlabelled chest X-ray images, while the Invariant Pneumonia Feature Loss (IPFL) reduces dependence on environment-specific information. ACCA further constrains model attention toward anatomically relevant lung regions to improve explanation alignment. Experimental evaluation on the RSNA and Chest X-ray Pneumonia datasets demonstrated strong classification performance. On the Chest X-ray Pneumonia dataset, CARE-Net achieved a mean accuracy of 97.9 ± 0.7%, precision of 97.2 ± 0.8%, recall of 97.6 ± 0.7%, F1-score of 97.8 ± 0.6%, and AUC of 0.978 ± 0.005. On RSNA, it achieved an accuracy of 95.6 ± 0.6%, an AUC of 0.972 ± 0.004, and an F1-score of 0.957 ± 0.005. The framework reduced performance variability by over 50%, improved robustness under distribution shift, and achieved lung-region IoU of 0.47 versus 0.32 for Grad-CAM. These findings demonstrate the potential of integrating SSL, causality-aware training, and anatomy-constrained attention for robust and interpretable pneumonia classification. Full article
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33 pages, 2125 KB  
Article
Classification-Guided Specialized Regression for Non-Invasive Blood Glucose Estimation: A Synthetic E-Nose Benchmark Study
by Ehab H. El-shazly, Mazen Ferihy, Yazan Dia El Din, Omar Elfeky, Ahmed Khalifa and Sameh Sherif
Math. Comput. Appl. 2026, 31(5), 212; https://doi.org/10.3390/mca31050212 - 3 Oct 2026
Viewed by 189
Abstract
Accurate non-invasive blood glucose level (BGL) prediction remains challenging, motivating the development of machine learning approaches that can account for heterogeneity in physiological measurements. Electronic nose (E-Nose) systems provide a promising non-invasive sensing modality by capturing volatile organic compound patterns in exhaled breath. [...] Read more.
Accurate non-invasive blood glucose level (BGL) prediction remains challenging, motivating the development of machine learning approaches that can account for heterogeneity in physiological measurements. Electronic nose (E-Nose) systems provide a promising non-invasive sensing modality by capturing volatile organic compound patterns in exhaled breath. However, conventional approaches typically employ a single global regression model across the full glycemic range, despite substantial differences between diabetic and non-diabetic BGL distributions. This study investigates whether classification-guided specialization can improve BGL regression by explicitly modeling these clinically distinct subpopulations and quantifying the extent to which imperfect routing limits the resulting performance. We develop a two-stage framework in which each E-Nose sample is first classified as diabetic or non-diabetic using a stacking classifier comprising Random Forest, XGBoost, and LightGBM with logistic regression as the meta-learner, and is then routed to a class-specific stacking regressor trained on the corresponding BGL distribution. To evaluate this architecture, the study utilizes a CTGAN-generated computational benchmark comprising 14,512 total observations synthesized from 1452 empirical breath measurements collected across 58 original human participants; these 14,512 observations do not represent independent clinical subjects. Under observation-level stratified five-fold cross-validation (not participant-disjoint), the routing classifier achieved 94.98% accuracy. The classification-guided framework reduced mean absolute error (MAE) from 25.21 mg/dL for a global stacking baseline to 24.87 mg/dL and improved the ±20% accuracy criterion from 84.95% to 88.29%. An oracle-routing analysis, using the true class labels for routing, achieved an MAE of 20.64 mg/dL and showed that the 5.02% routing error accounted for 21.08% of the total prediction error, demonstrating that routing reliability represents a major limitation on the attainable performance of specialized regression. A probabilistic soft-routing strategy was further evaluated to reduce sensitivity to hard routing decisions near the diabetic/non-diabetic boundary. Conformalized quantile regression provided distribution-free predictive uncertainty quantification, achieving 85.4% empirical coverage for a 90% nominal target, while SHAP analysis provided feature-level interpretation of the routing and regression models. Overall, the findings provide computational evidence that classification-guided specialization can improve BGL prediction over global regression on the evaluated synthetic E-Nose benchmark, while the routing-error analysis identifies a measurable performance gap attributable to imperfect subpopulation assignment. Given the synthetic nature of the benchmark, the derivation from 58 original human participants, and the absence of metadata on unmeasured clinical confounders (e.g., medication, diet, and alcohol), these findings represent preliminary computational evidence rather than clinical diagnostic validation. Full article
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25 pages, 658 KB  
Article
The Calibrated d’Alembert Cost on Positive Paths: Convexity Under Step Evaluation
by Sebastian Pardo-Guerra and Jonathan Washburn
Math. Comput. Appl. 2026, 31(5), 211; https://doi.org/10.3390/mca31050211 - 3 Oct 2026
Viewed by 79
Abstract
A calibrated solution of d’Alembert’s equation gives the cost K(v)=coshv−1. Under the explicit postulate that this cost is evaluated at log-velocity, we study the resulting free action on positive paths. Geometric interpolation makes the [...] Read more.
A calibrated solution of d’Alembert’s equation gives the cost K(v)=coshv−1. Under the explicit postulate that this cost is evaluated at log-velocity, we study the resulting free action on positive paths. Geometric interpolation makes the action strongly convex, and Jensen’s inequality gives its unique fixed-endpoint minimizer. An exact Bregman identity converts excess action into a trajectory-error bound. The purpose is quantitative rather than formal: because the minimum action is available in closed form, the excess action of any computed path is itself computable and returns a rigorous bound on that path’s error. We determine the optimal global velocity-gap constant at fixed endpoints and its sharper small-perturbation limit. Sine and tent competitors separate velocity-gap sharpness from equality in the trajectory inequality. Reproducible numerical examples illustrate these estimates and their use as error certificates. A separate scalar-mechanics interpretation yields the Newtonian limit and a cosh-dual Hamiltonian distinct from the special-relativistic Hamiltonian. For the native oscillator, an explicit mixed-harmonic perturbation resolves the degenerate conjugate-time case. Full article
38 pages, 1497 KB  
Article
A Hybrid Block–Pseudospectral Scheme for Spatiotemporal Pattern Formation in Phase-Field Models: The Allen–Cahn and Cahn–Hilliard Equations
by Sixolile Baqiwe, Yusuf Olatunji Tijani and Shina Daniel Oloniiju
Math. Comput. Appl. 2026, 31(5), 210; https://doi.org/10.3390/mca31050210 - 2 Oct 2026
Viewed by 83
Abstract
This study introduces a hybrid numerical scheme for analysing spatiotemporal pattern formation in phase-field models, specifically the Allen–Cahn (AC) and the Cahn–Hilliard (CH) equations. These equations are important parabolic partial differential equations (PDEs) that arise in many interesting scientific problems. However, their strong [...] Read more.
This study introduces a hybrid numerical scheme for analysing spatiotemporal pattern formation in phase-field models, specifically the Allen–Cahn (AC) and the Cahn–Hilliard (CH) equations. These equations are important parabolic partial differential equations (PDEs) that arise in many interesting scientific problems. However, their strong nonlinearity makes finding analytical solutions practically impossible, while traditional numerical methods often suffer from instability. To address this challenge, this study proposes a robust hybrid block–pseudospectral method (HB–PSM) that integrates the off-step hybrid block method (HBM) for temporal integration, Chebyshev pseudospectral for spatial discretisation, and the quasilinearisation method (QLM) to handle nonlinearity. The primary aim is to develop a high-order, energy-stable numerical solver that accurately captures spatiotemporal patterns in both 1D and 2D configurations at reasonable computational cost. Through extensive numerical experimentation, the findings demonstrate that the HB–PSM is a competitive method for solving gradient flow systems, and it can be applied more broadly across many fields to solve a broader class of complex, multidimensional partial differential equations. Full article
(This article belongs to the Section Natural Sciences)
33 pages, 1257 KB  
Article
Integrating Absorbing Markov Chains and Multi-Issue Bankruptcy Problems with Cross-Claims for Resource Allocation Under Production Uncertainty
by Rick Acosta-Vega, Samuel Alvarez-Cayón and Manuel J. Campuzano
Math. Comput. Appl. 2026, 31(5), 209; https://doi.org/10.3390/mca31050209 - 2 Oct 2026
Viewed by 104
Abstract
Production systems may generate resource scarcity as products progress through production stages that are subject to deterioration, reprocessing, or failure. This study builds upon the integration of absorbing Markov chains with Multi-Issue Bankruptcy Problems with Cross-Claims (MI-MIBC) and develops a method for deriving [...] Read more.
Production systems may generate resource scarcity as products progress through production stages that are subject to deterioration, reprocessing, or failure. This study builds upon the integration of absorbing Markov chains with Multi-Issue Bankruptcy Problems with Cross-Claims (MI-MIBC) and develops a method for deriving a multi-resource estate based on the fundamental matrix of a Markov chain and state-specific multi-resource requirements. This method defines a multi-resource allocation problem with connected claims. The resulting MI-MIBC is addressed using Constrained Proportional Awards (CPA), Constrained Equal Awards (CEA), and Constrained Sequential Priority (CSP) rules. This method is illustrated with the postharvest system of Colombian plantains, which consists of money, labor, transportation, and packing resources. The three rules produce different allocation patterns when scarcity is identical. The cross-claims structure may also leave a residual estate even when claims remain unmet. This method interlinks stochastic production systems with multi-resource allocation and derives the estate from the stochastic production model rather than specifying it independently at the allocation stage. Full article
(This article belongs to the Topic Mathematical, Computational and Data-Driven Methods in Mechanics, Engineering and Applied Sciences)
36 pages, 3790 KB  
Article
Strongly Nonlinear Responses in Coupled Duffing Oscillators: Homotopy-Enriched Multiple Scales and Branch-Resolved Continuation Benchmarking
by Hussain Al-Qahtani
Math. Comput. Appl. 2026, 31(5), 208; https://doi.org/10.3390/mca31050208 - 2 Oct 2026
Viewed by 67
Abstract
First-order classical multiple scales (MMS) linearizes frequency detuning and discards a quadratic correction that grows away from resonance. Homotopy-enriched multiple scales (EMMS) uses the forcing-frequency carrier and retains the full squared-frequency mismatch. We derive coupled modulation equations and explicit stability Jacobians for a [...] Read more.
First-order classical multiple scales (MMS) linearizes frequency detuning and discards a quadratic correction that grows away from resonance. Homotopy-enriched multiple scales (EMMS) uses the forcing-frequency carrier and retains the full squared-frequency mismatch. We derive coupled modulation equations and explicit stability Jacobians for a two-degree-of-freedom Duffing system with a general cubic modal tensor, and compare its algebraic responses with AUTO2000 periodic-orbit continuation. The principal benchmark is a large-detuning stress test. On the 107 reference cells matched by both methods, the median amplitude errors are 1.28% for EMMS and 10.89% for classical MMS. EMMS matches 186 of 201 reference cells, and classical MMS 107. The lower-fold frequency errors are 0.011% and 0.503%, respectively; the EMMS and reference lower-fold frequencies both round to 1.108. Both methods recover a separate weak small-detuning control. Shooting of the full equations of motion shows that the maximum sampled peak–fundamental difference increases from 3.55% to 4.28% with forcing. Classical MMS predicts both secondary-lobe stability boundaries more closely, while EMMS predicts the interval width more closely. The symmetric coupling sweep tests consistency because the direct coupling cubic term cancels from the first modal equation; an asymmetric benchmark exercises the additional odd tensor coefficients. Full article
(This article belongs to the Section Engineering)
17 pages, 731 KB  
Article
Some Salient Features of a (31)-Dimensional Nonlinear Integro-Differential Evolution Equation: Lie Symmetries, Traveling Waves and Conservation Laws+
by Yanga Gaxela, Abdullahi Rashid Adem, Ben Muatjetjeja, Sivenathi Oscar Mbusi, Ahmed H. Arnous and Anjan Biswas
Math. Comput. Appl. 2026, 31(5), 207; https://doi.org/10.3390/mca31050207 - 1 Oct 2026
Viewed by 244
Abstract
A generalized (3+1)-dimensional Hirota-type nonlinear wave equation is investigated by combining Lie point symmetry analysis, invariant reductions, exact traveling-wave construction, and the direct multiplier method. A potential formulation is introduced under an explicit decay condition that makes the [...] Read more.
A generalized (3+1)-dimensional Hirota-type nonlinear wave equation is investigated by combining Lie point symmetry analysis, invariant reductions, exact traveling-wave construction, and the direct multiplier method. A potential formulation is introduced under an explicit decay condition that makes the nonlocal term well defined. The admitted point symmetries are re-derived from the prolonged invariance criterion, and several symmetry reductions are obtained, including mixed translations, a transverse shear, scaling, and a general traveling-wave phase. The reduced traveling-wave equation admits an affine Riccati representation with hyperbolic, trigonometric, rational, and Bernoulli-type branches under explicit parameter restrictions. The corresponding 3D, 2D, and density visualizations are retained to illustrate the resulting wave profiles. Zeroth-order multipliers are then used to construct local conserved vectors in divergence form. The analysis provides a verified symmetry and conservation-law framework for the proposed higher-dimensional Hirota-type extension and supplies exact solutions that can be used as analytical benchmarks. The transverse-variable reductions and the zeroth-order multiplier family are derived specifically for the present (3+1)-dimensional potential equation, while the Riccati functional forms are used as standard representations rather than claimed as new special functions. Full article
24 pages, 5925 KB  
Article
Fractional-Order Soft-Voting Ensemble Framework for Cohort-Level Gallstone Risk Prediction
by David Amilo, Khadijeh Sadri, Mohamed Hafez and Yakup Yildirim
Math. Comput. Appl. 2026, 31(5), 206; https://doi.org/10.3390/mca31050206 - 1 Oct 2026
Viewed by 138
Abstract
This study proposes a hybrid framework for predicting gallstone presence versus absence in the UCI clinical cohort by coupling a soft-voting ensemble (Neural Network, Random Forest, and Bagging) with a doubly-pruned seven-state Caputo system. The classifiers are trained on the top-10 features selected [...] Read more.
This study proposes a hybrid framework for predicting gallstone presence versus absence in the UCI clinical cohort by coupling a soft-voting ensemble (Neural Network, Random Forest, and Bagging) with a doubly-pruned seven-state Caputo system. The classifiers are trained on the top-10 features selected by minimum-redundancy maximum-relevance (MRMR), and the ensemble probability is injected as an external forcing of the seven leading markers. On a frozen held-out test set (N=79) the ensemble attains AUC 0.7558, a modest increment over the best single learner (neural network, AUC 0.7500) and over equal-weight voting (AUC 0.7545). Identification of the Caputo system on the order-statistic axis of the top MRMR marker (coronary artery disease), not Age, reconstructs the cohort-level marker curves with training-weighted MSE 1.65×10−4. Existence and uniqueness of solutions are proved; positivity and an a priori bound hold only under sign restrictions that the identified couplings do not satisfy. A prototype graphical interface for exploratory use is provided; it is not a clinically validated tool. All reconstructed trajectories are cohort-level snapshots on a cross-sectional pseudo-time axis and are not individual longitudinal histories. Full article
(This article belongs to the Special Issue Celebrate the 30th Anniversary of Mathematical and Computational Applications (MCA))
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26 pages, 3928 KB  
Article
Numerical Assessment of the Thermal and Ventilation Performance of an Earth–Air Heat Exchanger Coupled with a Solar Chimney for Passive Conditioning of Dwellings in a Warm–Humid Climate
by Belisario Morales-Morales, Carlos E. Torres-Aguilar, Karla M. Aguilar-Castro and Edgar V. Macias-Melo
Math. Comput. Appl. 2026, 31(5), 205; https://doi.org/10.3390/mca31050205 - 30 Sep 2026
Viewed by 260
Abstract
Passive cooling strategies are essential to curbing the growing air-conditioning demand of dwellings in warm–humid regions. This work presents a Computational Fluid Dynamics (CFD) study, carried out with the open-source code OpenFOAM, of a passive system that couples an earth–air heat exchanger (EAHE) [...] Read more.
Passive cooling strategies are essential to curbing the growing air-conditioning demand of dwellings in warm–humid regions. This work presents a Computational Fluid Dynamics (CFD) study, carried out with the open-source code OpenFOAM, of a passive system that couples an earth–air heat exchanger (EAHE) with a solar chimney (SC) serving a room-representative cavity, i.e., the coupled EAHE–SC device is analyzed together with the room it conditions. The methodology was built progressively: (i) a transient conduction sub-model (laplacianFoam) characterized the thermal inertia of the soil around the buried duct; (ii) a parametric study of eight coupling geometries identified the best relative position of the EAHE and the SC; (iii) three configurations—the complete system, the EAHE + cavity system, and the bare cavity—were solved under identical numerical conditions with the buoyancy-driven solvers of OpenFOAM and the k–ε turbulence model with the Boussinesq approximation; and (iv) the complete system was evaluated for a representative hot and a representative cold design day through a section-based post-processing of the ventilation and thermal-energy indicators. Over the four-day period simulated, the soil behaved as a stable thermal reservoir with no depletion. At the design condition, the complete system reached a mean cavity temperature of 33.2 °C, 8.32 air changes per hour (ACH) and 67.0 W of thermal power removed from the cavity, against 34.4 °C, 2.01 ACH and 4.56 W for the bare cavity; coupling the chimney raised ventilation by 94.8% and 313.9% relative to the EAHE-only and bare-cavity cases, respectively. The design-day comparison showed a marked climate-dependent response: on the hot day the EAHE dominated (air cooled by 5.75 °C, 2.51 ACH), whereas on the cold day the exchanger remained nearly neutral (+0.19 °C) and ventilation dropped to 0.69 ACH, lowering the cavity temperature to 24.1 °C. The results indicate a complementary, mutually reinforcing behavior—the coupled system removes more heat and renews more air than either device does on its own—for the design conditions analyzed. Full article
(This article belongs to the Special Issue Advances in Computational and Applied Mechanics (SACAM))
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20 pages, 3757 KB  
Article
Numerical Integration of FGM Beam Vibration Equations Using a Discrete Variational Approach with Algebraic Constraints
by Xianyu Xu and Yuanyuan Wang
Math. Comput. Appl. 2026, 31(5), 204; https://doi.org/10.3390/mca31050204 - 25 Sep 2026
Viewed by 168
Abstract
This paper develops a constrained differential-quadrature/discrete-variational framework for vibration analysis of functionally graded beams. Spatial derivatives are discretized on a Chebyshev–Lobatto grid, while time integration is constructed from Lagrange interpolation and Gauss–Legendre quadrature. Boundary conditions are retained as algebraic constraints and enforced with [...] Read more.
This paper develops a constrained differential-quadrature/discrete-variational framework for vibration analysis of functionally graded beams. Spatial derivatives are discretized on a Chebyshev–Lobatto grid, while time integration is constructed from Lagrange interpolation and Gauss–Legendre quadrature. Boundary conditions are retained as algebraic constraints and enforced with Lagrange multipliers, leading to the semi-discrete operator K=k1I+kf2A(4)−k2A(2). For the default two-node formulation, the DVM keeps position-level constraint residuals near machine precision and suppresses cumulative position- and velocity-level drift relative to the RK4 comparison, while acceleration-level residuals remain of comparable order. The DVM response remains bounded in simulations up to 10,000 s. An empirical time-step scan is stable through h=0.30 and unstable at h=0.35 for the tested problem. Temporal convergence against an exact-in-time solution of the same constrained semi-discrete system is essentially second order, and pairwise self-convergence gives the same result. Spatial refinement from 5 to 11 Chebyshev–Lobatto nodes reduces the L∞ displacement error from 4.01×10−3 to 8.26×10−10, consistent with spectral-type DQM convergence. Additional sensitivity studies confirm that the principal conclusions are robust to algebraic-solver initialization, stopping tolerance, and several boundary-condition choices within the tested parameter range. Full article
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20 pages, 1317 KB  
Article
A Right-Sided Cl(0,2)-Valued Linear Canonical Stockwell Transform: Rigorous Formulation and Chirp-Adaptive Computation
by Yi-Qiao Xu and Bing-Zhao Li
Math. Comput. Appl. 2026, 31(5), 203; https://doi.org/10.3390/mca31050203 - 24 Sep 2026
Viewed by 134
Abstract
Quadratic phase disperses the spectrum of chirped multicomponent data and can defeat the ordinary Stockwell analysis. We formulate a right-sided Cl(0,2)-valued linear canonical Stockwell transform (CLCST) on a positive real Hilbert space, using standard Clifford conjugation, a real scalar window, and an invariant [...] Read more.
Quadratic phase disperses the spectrum of chirped multicomponent data and can defeat the ordinary Stockwell analysis. We formulate a right-sided Cl(0,2)-valued linear canonical Stockwell transform (CLCST) on a positive real Hilbert space, using standard Clifford conjugation, a real scalar window, and an invariant multiplication order. Since Cl(0,2) is isomorphic to the quaternion algebra, the construction is algebraically a one-sided quaternion transform; its contribution over existing quaternion Stockwell and quaternion linear canonical Stockwell formulations is not a larger algebra but a rigorously ordered chirp–Clifford Stockwell transform (CST)–dechirp factorization, direct unit-integral-window reconstruction, and a reproducible fast Fourier transform (FFT) realization for chirp estimation. We correct the canonical output-phase ordering and specify the discrete correlation kernel and sign-preserving zero-frequency regularization. A nonsymmetric-window stress test verifies these conventions independently. The theory establishes pointwise boundedness, covariance, reconstruction, and a collapsed-energy identity. Experiments on noisy synthetic fields, a four-component signal, a Shepp–Logan phantom, and measured Hubble image content with an injected phase aberration quantify concentration, resolution, and computational cost. The results delimit rather than conceal the method’s scope: it targets a global quadratic phase in Cl(0,2), while orientation sweeps, zero-mean windows, locally varying chirps, and higher-dimensional Clifford algebras require additional machinery. Full article
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26 pages, 1343 KB  
Article
Fixed-Time Adaptive Stabilization of Underactuated Euler–Lagrange Systems with Certified Internal Dynamics
by Okaile Rodney Marumo, Mavuna Sebapalo and Tshepo Gobonamang
Math. Comput. Appl. 2026, 31(5), 202; https://doi.org/10.3390/mca31050202 - 24 Sep 2026
Viewed by 142
Abstract
This paper addresses the fixed-time adaptive stabilization problem for a class of underactuated mechanical systems governed by Euler–Lagrange dynamics with matched parametric uncertainty. Unlike conventional adaptive schemes that guarantee only asymptotic convergence and usually assume stable internal dynamics, we develop a framework that [...] Read more.
This paper addresses the fixed-time adaptive stabilization problem for a class of underactuated mechanical systems governed by Euler–Lagrange dynamics with matched parametric uncertainty. Unlike conventional adaptive schemes that guarantee only asymptotic convergence and usually assume stable internal dynamics, we develop a framework that (i) drives the actuated coordinates and the parameter-adaptive sliding manifold to the origin in a fixed time whose upper bound is independent of the initial condition, and (ii) supplies an explicit Lyapunov certificate for the zero dynamics induced by underactuation, thereby removing the minimum-phase assumption. The controller couples partial feedback linearization with a recursive fixed-time backstepping design and an online σ-modified adaptation law that preserves the structural properties of Euler–Lagrange systems. A composite Lyapunov function handles the coupled actuated/unactuated dynamics and yields a differential inequality of the form V˙≤−αVp−βVq with 0<p<1 and q>1, which certifies fixed-time reaching on the actuated channel. A separate internal-dynamics certificate establishes uniform boundedness of the unactuated coordinate throughout the fixed-time reaching phase and its asymptotic convergence once the actuated manifold is reached, so all closed-loop signals are globally bounded and the full state converges to the origin under matched uncertainty. Numerical studies on the translational oscillator with rotational actuator (TORA) and the cart–pole show the initial-condition-independent settling of the actuated channel and quantify the advantage over an asymptotic adaptive baseline. Full article
(This article belongs to the Section Engineering)
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32 pages, 1193 KB  
Article
Stochastic Analysis and Stability of Diabetic Population Dynamics
by Jawaria, Guo Min, Jorge E. Macías-Díaz, Muhammad Waqas Yasin, Nauman Ahmed and Luis E. Ayala-Hernández
Math. Comput. Appl. 2026, 31(5), 201; https://doi.org/10.3390/mca31050201 - 22 Sep 2026
Viewed by 216
Abstract
Modeling diabetic illness with random perturbations is the goal of this work. The proposed model consists of three classes: the pre-diabetic population, the diabetic population with complications, and the diabetic population without complications. We examined the suggested problem to determine at least one [...] Read more.
Modeling diabetic illness with random perturbations is the goal of this work. The proposed model consists of three classes: the pre-diabetic population, the diabetic population with complications, and the diabetic population without complications. We examined the suggested problem to determine at least one unique solution within the positive feasible region. The stationary distribution of this model was also explored, and the non-negative C2-Lyapunov function was used to create an adequate condition for the persistence of one stationary ergodic distribution. For this model, the existence and uniqueness of the solution were also established. Additionally, the stochastic non-standard finite difference (NSFD) scheme was developed for the model. The consistency and stability of the scheme were analyzed, showing that it is consistent and stable in the mean-square sense. The underlying system admits a unique endemic equilibrium point. Finally, a test problem was studied by using a numerical technique, varying the noise levels, and maintaining the same parameter values. The outcomes for each stated class were numerically simulated in order to validate our proposed approach. Full article
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29 pages, 3938 KB  
Perspective
Physics by Design: Additive Manufacturing for Reproducible Science
by Daniel N. Wilke
Math. Comput. Appl. 2026, 31(5), 200; https://doi.org/10.3390/mca31050200 - 22 Sep 2026
Viewed by 245
Abstract
Additive manufacturing (AM) is usually framed as a production technology. We argue that it is more importantly a scientific instrument: the bundle of (script, STL, slicer profile, feedstock specification, printer family) can be made FAIR-aligned when archived with persistent identifiers, metadata, hashes, licences, [...] Read more.
Additive manufacturing (AM) is usually framed as a production technology. We argue that it is more importantly a scientific instrument: the bundle of (script, STL, slicer profile, feedstock specification, printer family) can be made FAIR-aligned when archived with persistent identifiers, metadata, hashes, licences, and process records, and AM makes the design variables held constant in a sweep explicit and the residual drift in secondary variables measurable. We make the position concrete with four sweeps from computational and applied mechanics: a Schoenhardt twist sweep for non-convex granular particles, a shell-thickness sweep for the principal scalar moment of inertia at fixed outer geometry and total mass, a triply-periodic-minimal-surface (TPMS)-derived bulk-porosity sweep, and an iso-porosity strut-lattice family of five topologies, accompanied by an illustrative photograph of specimens printed on a desktop MSLA vat-photopolymerisation machine. A held–target–track matrix names, for every sweep, the variables held, the target, and the secondary quantities that drift as a side-effect and must be tracked. A one-dimensional toy fin model with closed-cell porosity maps a porosity sweep to a predicted temperature signal; a true TPMS heat sink additionally requires flow conditions and the (Sv(ϕ),hconv(ϕ),keff(ϕ),(ρc)eff(ϕ),Pwet(ϕ)) characterisation. A three-process protocol (FDM, vat photopolymerisation, laser powder-bed fusion) specifies the proposed reporting requirements. Full article
(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics (AfriComp7))
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58 pages, 1452 KB  
Article
Spatial Conflict-Aware Multi-Objective Scheduling for Parallel Construction Tasks with Coupled Fatigue Dynamics
by Ting Wang, Xuefeng Ding and Bangguo Liu
Math. Comput. Appl. 2026, 31(5), 199; https://doi.org/10.3390/mca31050199 - 21 Sep 2026
Viewed by 185
Abstract
Parallel operations by multiple trades on constrained workfaces pit safety against schedule. Static schedulers, scalar fatigue models, and standard evolutionary algorithms all struggle to reconcile the two. Simulation tackles the Parallel Task Matching Problem (PTMP). A Spatial Conflict Graph quantifies workspace interference, with [...] Read more.
Parallel operations by multiple trades on constrained workfaces pit safety against schedule. Static schedulers, scalar fatigue models, and standard evolutionary algorithms all struggle to reconcile the two. Simulation tackles the Parallel Task Matching Problem (PTMP). A Spatial Conflict Graph quantifies workspace interference, with edge weights combining a 3D Jaccard overlap and a process-coupling coefficient. The Cross-Task Fatigue Transfer Model (CTFTM) governs whole-body, localized, and cognitive fatigue. Task-specific accumulation, recovery, and crosstalk parameters in this coupled ODE system capture fatigue carryover across heterogeneous activities. Minimizing schedule delay and OHS risk then follows from a bi-objective model under spatial-conflict, fatigue, skill, crew-size, and precedence constraints. An NSGA-III extension uses integer worker–task encoding, a Conflict Repair Operator that modifies fewer than 7% of genes and removes penalty calibration, and TOPSIS-based Pareto selection. Hybrid re-scheduling pairs persistent event triggers with structural state updates and a periodic trigger. The test campaign used three parallel tasks, eight heterogeneous workers, five ablative baselines, four empirical sensitivity analyses, and a design-level threshold assessment. Standalone calibration produced comparable, trade-off-dependent multi-objective performance for NSGA-III, NSGA-II, and MOEA/D; NSGA-III with conflict repair was retained for the full dynamic experiments. Over-threshold-fatigue workers fell from 5.789 to 0.020 relative to the scalar-fatigue baseline. Fatigue-efficiency index (FEI) improved by 43.5% relative to the scalar-fatigue baseline, alongside robust real-time disruption handling. Taken together, these results establish a simulation-based foundation for intelligent, safety-aware workforce scheduling. Full article
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46 pages, 6937 KB  
Article
Transient Pressure Redistribution and Hydraulic-Junction Localization in Ring Gas Pipelines: Analytical Modeling and Numerical Verification
by Ibrahim M. Hasanov and Ilgar G. Aliyev
Math. Comput. Appl. 2026, 31(5), 198; https://doi.org/10.3390/mca31050198 - 21 Sep 2026
Viewed by 155
Abstract
Transient pressure redistribution in ring gas pipelines is governed by both withdrawal intensity and spatial configuration, which determine circumferential flow redistribution and the location of the hydraulic junction. This study develops an analytical framework for transient pressure dynamics and hydraulic-junction localization in ring [...] Read more.
Transient pressure redistribution in ring gas pipelines is governed by both withdrawal intensity and spatial configuration, which determine circumferential flow redistribution and the location of the hydraulic junction. This study develops an analytical framework for transient pressure dynamics and hydraulic-junction localization in ring pipelines with multiple discrete withdrawals. A closed-form Fourier-series solution is derived and numerically verified against an independently implemented finite-difference model, demonstrating close analytical–numerical agreement. The hydraulic-junction coordinate is identified from the transient pressure-extremum condition, while a dimensionless localization factor is introduced to characterize its position relative to the geometric midpoint. Two contrasting ring configurations reveal distinct behaviors: For the investigated 30 km configuration, the hydraulic junction remains localized near the geometric midpoint under the considered proportional-withdrawal scenarios. In the second, increasing withdrawal loading causes progressive upstream migration toward a withdrawal-controlled limiting location. A steady balanced flow-reversal criterion provides a physical interpretation of the limiting junction position without being extended to globally unbalanced transient states. The results further show that efficient distributed withdrawal requires consideration of both pressure retention and hydraulic-junction behavior. The proposed framework provides a mathematically interpretable basis for assessing transient hydraulic states and withdrawal strategies in ring gas pipelines. Full article
(This article belongs to the Section Engineering)
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24 pages, 917 KB  
Article
Numerical Simulation of Hyperbolic Problems with Interface Discontinuities via Multi-Resolution Collocation Method
by Nadeem Haider, Muhammad Asif, Naveed Ullah, Muhammad Adil, Zeeshan Ali and Ioan-Lucian Popa
Math. Comput. Appl. 2026, 31(5), 197; https://doi.org/10.3390/mca31050197 - 21 Sep 2026
Viewed by 203
Abstract
Hyperbolic interface problems are widely applied to model wave propagation and shock transmission across discontinuous media, such as acoustic waves in layered materials, seismic waves in the Earth’s crust, and stress or electromagnetic waves in composite structures. This study introduces a novel computational [...] Read more.
Hyperbolic interface problems are widely applied to model wave propagation and shock transmission across discontinuous media, such as acoustic waves in layered materials, seismic waves in the Earth’s crust, and stress or electromagnetic waves in composite structures. This study introduces a novel computational framework for hyperbolic interface problems, specifically designed to unify and extend the treatment of regular interfaces within partial differential equations. The proposed hybrid approach combined Haar wavelet-based spatial discretization with finite difference schemes for temporal integration. By employing truncated Haar series to approximate spatial derivatives and leveraging finite difference techniques for time evolution, the method delivers accurate solutions for both linear and nonlinear systems regardless of whether the governing coefficients are constant or spatially variable. In addressing linear problems, the resulting algebraic equations are solved efficiently using Gaussian elimination. For nonlinear formulations, the method incorporates a quasi-Newton linearization strategy, effectively transforming the system into a linear one. Extensive validation is performed through a suite of benchmark problems, with performance assessed via metrics including maximum absolute errors (MAEs), root mean square errors (RMSEs), and convergence behavior as a function of collocation point (CP) density. Numerical experiments highlight the method’s superior stability and accuracy, particularly in scenarios marked by discontinuities or sharp gradients in the solution. The approach proves especially effective in bridging inconsistencies between boundary and initial conditions, offering a robust alternative to existing techniques. Theoretical soundness, strong convergence properties, and comprehensive numerical validation collectively underscore the method’s reliability and adaptability across a broad spectrum of applications. Full article
(This article belongs to the Special Issue Celebrate the 30th Anniversary of Mathematical and Computational Applications (MCA))
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37 pages, 4522 KB  
Review
From Pixels to Volumes: Generative AI in 3D Medical Imaging
by Chanumolu Kiran Kumar, Maheswara Kishore Kumar, Venkataramana Gurrala, Appalaraju Grandhi, Rajendra Babu Chikkala and Surapaneni Phani Praveen
Math. Comput. Appl. 2026, 31(5), 196; https://doi.org/10.3390/mca31050196 - 20 Sep 2026
Viewed by 698
Abstract
With the advent of generative AI, medical imaging has been revolutionized, allowing for unprecedented capabilities in data generation, volumetric reconstruction, and clinical decision support. Although significant advances have been achieved in two-dimensional modalities, extending them to three-dimensional medical imaging, such as Magnetic Resonance [...] Read more.
With the advent of generative AI, medical imaging has been revolutionized, allowing for unprecedented capabilities in data generation, volumetric reconstruction, and clinical decision support. Although significant advances have been achieved in two-dimensional modalities, extending them to three-dimensional medical imaging, such as Magnetic Resonance Imaging (MRI), Computed Tomography (CT), and Positron Emission Tomography (PET), remains a developing frontier with new technical and clinical challenges. This survey offers a thorough, systematic exploration of generative AI approaches uniquely applicable to 3D medical imaging, including voxel-based generative models, implicit neural representations, and latent diffusion models. The literature is organized in three orthogonal axes: imaging modality (MRI, CT, and PET), model architecture (GAN, VAE, diffusion, and NeRF), and clinical application (augmentation, reconstruction, surgical planning, and anomaly detection). We provide detailed taxonomy tables for each axis, including landmark papers, strengths, limitations, key techniques, and benchmark performance. We also address evaluation protocols, ethical issues related to synthetic data, and open research challenges. We analyzed more than 50 representative works and found that latent diffusion models have firmly established themselves as the standard for high-fidelity 3D synthesis and that implicit neural 3D representations are best for reconstructing 3D scenes from sparse views with limited memory. It does not, however, mean that they perform better across all modalities and tasks, as they have significantly greater requirements in terms of computational and memory load, sampling time, and training data compared to alternatives like diffusion-based methods (which account for about 44% of the surveyed landmark architectures. Finally, we propose a clinical, ethical, and technically sound blueprint for the use of generative AI in volumetric medical imaging. Full article
(This article belongs to the Special Issue Artificial Intelligence, Machine Learning, and Deep Learning: Innovations and Real-World Applications)
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21 pages, 418 KB  
Article
Stochastic Mutation Semigroups: From Deterministic Collapse to Probabilistic Evolutionary Dynamics
by Marshal I. Sampson, Christiana F. Igiri, Reny George and Julie S. George
Math. Comput. Appl. 2026, 31(5), 195; https://doi.org/10.3390/mca31050195 - 19 Sep 2026
Viewed by 240
Abstract
The deterministic framework of mutation semigroups provides algebraic conditions for evolutionary collapse, but real mutation processes are inherently stochastic. This paper develops a comprehensive theory of stochastic mutation semigroups, where elementary mutations occur with empirically measured probabilities. A stochastic mutation semigroup is introduced [...] Read more.
The deterministic framework of mutation semigroups provides algebraic conditions for evolutionary collapse, but real mutation processes are inherently stochastic. This paper develops a comprehensive theory of stochastic mutation semigroups, where elementary mutations occur with empirically measured probabilities. A stochastic mutation semigroup is introduced as a Markov chain on the transformation semigroup generated by elementary mutation operators. We prove a stochastic transitivity threshold theorem under a positivity condition on the probability of rank reduction, correcting a logical gap in previous formulations, and we characterize collapse via the spectral properties of the associated Markov chain. Using HIV-1 sequence data from public databases and empirical mutation rates reported in the literature, the framework is illustrated through conceptual examples. Complete pseudocode is provided for the probabilistic pair-graph algorithm, along with convergence criteria and numerical examples demonstrating performance. The framework is further extended to infinite state spaces via topological semigroup theory and to time-varying mutation rates through dynamic L∗-classes. These results bridge the gap between abstract semigroup theory and evolutionary biology, offering a theoretical foundation for understanding stochastic mutation dynamics. Full article
(This article belongs to the Topic Machine Learning, Optimization, and Computational Methods in Biomedical Informatics)
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26 pages, 10233 KB  
Article
Terrain-Aware Head Gesture Recognition for Turret Control Using Helmet-Mounted IMUs and Vehicle Vibration Fusion
by Lonwabo Rooibaard, Dithoto Modungwa, Malusi Sibiya and Thanyani Pandelani
Math. Comput. Appl. 2026, 31(5), 194; https://doi.org/10.3390/mca31050194 - 18 Sep 2026
Viewed by 289
Abstract
Head gesture-based control using inertial measurement units (IMUs) provides an intuitive alternative to conventional human–machine interfaces for mobile and vehicle-mounted systems. However, gesture recognition reliability degrades significantly under terrain-induced vibration and mechanically dynamic operating conditions. This study investigates terrain-aware head gesture recognition through [...] Read more.
Head gesture-based control using inertial measurement units (IMUs) provides an intuitive alternative to conventional human–machine interfaces for mobile and vehicle-mounted systems. However, gesture recognition reliability degrades significantly under terrain-induced vibration and mechanically dynamic operating conditions. This study investigates terrain-aware head gesture recognition through the integration of helmet-mounted IMU measurements and vehicle vibration sensing to improve discrimination between intentional gestures and non-intentional motion artefacts. Vehicle vibration data were collected from a patrol vehicle traversing the Ndumo Border Patrol route, characterised by variable terrain roughness and dynamic excitation profiles. Triaxial seat-rack acceleration data were acquired at 10 kHz, anti-alias filtered and down sampled to 100 Hz before being integrated with IMU-derived head motion measurements using both vibration-aware data augmentation and early sensor fusion strategies. FFT-based spectral processing and classification using a lightweight fully connected neural network (FCNN) were implemented using the Edge Impulse framework. Experimental evaluation was performed using temporally independent training and testing segments to reduce overlap leakage and ensure realistic generalisation assessment. Results demonstrate that terrain-informed sensing substantially improves operational robustness under mobile conditions. The early-fusion approach achieved 98.45% independent-test accuracy under float32 inference and maintained 90.02% accuracy after int8 quantization, corresponding to an accuracy reduction of 8.43 percentage points. In comparison, the Clean IMU and vibration-augmented models exhibited reductions of 20.13 and 27.02 percentage points, respectively, demonstrating greater sensitivity to quantization. The evaluated models also exhibited low inference latency and compact memory requirements, supporting their suitability for real-time edge implementation. These findings demonstrate that treating terrain vibration as contextual information, rather than solely as environmental noise, can improve the quantization robustness and deployment characteristics of IMU-based gesture-recognition systems intended for mechanically dynamic platforms. Full article
(This article belongs to the Topic Machine Learning, Optimization, and Computational Methods in Biomedical Informatics)
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35 pages, 2897 KB  
Article
Numerical Spectral Correspondence Between a Non-Autonomous Quadratic Map and the Riemann Zeros: An Exploratory Study
by Liang Wang
Math. Comput. Appl. 2026, 31(5), 193; https://doi.org/10.3390/mca31050193 - 17 Sep 2026
Viewed by 205
Abstract
This study examines a non-autonomous quadratic map driven by a logarithmic cooling schedule (μn∼1/ln2n, a phenomenological ansatz), building on our recent published result that the logistic map’s symbolic dynamics at its band-merging point is [...] Read more.
This study examines a non-autonomous quadratic map driven by a logarithmic cooling schedule (μn∼1/ln2n, a phenomenological ansatz), building on our recent published result that the logistic map’s symbolic dynamics at its band-merging point is isomorphic to the prime sieve. From its trajectories, we construct an empirical, non-normal, dissipative transfer matrix and compares its complex eigenphases to the non-trivial Riemann zeros after calibrating a few free parameters against the same low-order zeros—an in-sample numerical correspondence, not an independent prediction. We quantify this gap directly: fitting on the first M∈{50,70,80} zeros and evaluating on the rest gives a held-out MSE one to two orders of magnitude larger than the training error, with the fitted coupling drifting across M but remaining comparatively stable across ten random seeds at fixed M=70 (CV ≈4.7%). At low order (N≲20), an unselected re-computation shows a qualitative rank correlation (ρ=0.56, p=0.010) with, but no significant joint co-location (p=0.099) of, a residual feature reported in recent ion-trap quantum simulations of the same zeros. At larger N (N≥1000), the model matches a globally rescaled GUE surrogate’s mean counting-function trend better once conjugate eigenphases are restored, though this partly follows from the construction’s own symmetry; a separate, standard unfolded local-statistics test shows the model’s own eigenphase spacings do not match GUE, unlike the true zeros. These are numerical observations on a heuristic model, not a proof or Hilbert–Pólya-type operator construction; a dedicated table tabulates the epistemic status of every main claim. Full article
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18 pages, 367 KB  
Article
First-Order Multipliers, Noether Symmetries and Variational Reduction of the Hunter–Saxton Equation
by Molahlehi Charles Kakuli
Math. Comput. Appl. 2026, 31(5), 192; https://doi.org/10.3390/mca31050192 - 17 Sep 2026
Viewed by 184
Abstract
We revisit the Hunter–Saxton equation through its classical first-order Lagrangian. The determining system for all first-order multipliers is reduced to one linear equation in two variables. Its solutions include both point-symmetry characteristics and genuinely generalised variational characteristics; in the analytic category, the remaining [...] Read more.
We revisit the Hunter–Saxton equation through its classical first-order Lagrangian. The determining system for all first-order multipliers is reduced to one linear equation in two variables. Its solutions include both point-symmetry characteristics and genuinely generalised variational characteristics; in the analytic category, the remaining freedom is locally parameterised by two arbitrary analytic functions. Every member of the known infinite-dimensional point-symmetry ideal is shown to preserve the action up to a total divergence and produces an arbitrary-function family of conserved currents, whereas one finite point symmetry is excluded from the Noether point-symmetry algebra of the Lagrangian. We also correct an omission in the previously reported associations between finite currents and Lie point symmetries. For the scaling symmetry, the radial component of an associated current vanishes identically after transformation. Alignment and multiplier criteria explain this degeneracy and show when it is a property of the conservation-law class. Thus association guarantees invariance of the transformed component, but not that the component retains differential content. Reducing the Lagrangian instead recovers the known similarity equations and their first integrals for two representative symmetries. In the scaling reduction, the reduced Noether symmetry is induced by a commuting member of the infinite-dimensional ideal. Full article
(This article belongs to the Topic Mathematical, Computational and Data-Driven Methods in Mechanics, Engineering and Applied Sciences)
25 pages, 709 KB  
Article
Evaluation of a Subclass Kp,r = ∫xp(1 + x2)rdx of the Binomial Integral
by Iickho Song, So Ryoung Park and Lismer Andres Caceres-Najarro
Math. Comput. Appl. 2026, 31(5), 191; https://doi.org/10.3390/mca31050191 - 16 Sep 2026
Viewed by 185
Abstract
Employing the fundamental techniques of substitution, or change of variables, and integration by parts, the discussion in this paper focuses on obtaining explicit formulas for the integral Kp,r=∫xp1+x2rdx for [...] Read more.
Employing the fundamental techniques of substitution, or change of variables, and integration by parts, the discussion in this paper focuses on obtaining explicit formulas for the integral Kp,r=∫xp1+x2rdx for p∈Z and r∈12Z. As the case where r is a non-negative integer is rather simple and obvious, we concentrate mainly on the cases where r is a negative integer or an odd multiple of 12 except when consideration of other cases is appropriate. Full article
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24 pages, 7109 KB  
Article
DAVis-Net: A Dual-Attention Deep Supervision Framework for Reliable Retinal OCT Image Classification with Integrated Explainability and Uncertainty Quantification
by Varun Kaza, Padmini Chattu, Chanumolu Kiran Kumar, Thandava Krishna Sai Pandraju and Uddagiri Sirisha
Math. Comput. Appl. 2026, 31(5), 190; https://doi.org/10.3390/mca31050190 - 16 Sep 2026
Viewed by 350
Abstract
Classification accuracy in retinal optical coherence tomography (OCT) alone does not establish whether a model is reliable or whether to refer to a specialist. To address this, we propose DAVis-Net, a VGG16-based architecture that is equipped with two Convolutional Block Attention Modules (CBAMs), [...] Read more.
Classification accuracy in retinal optical coherence tomography (OCT) alone does not establish whether a model is reliable or whether to refer to a specialist. To address this, we propose DAVis-Net, a VGG16-based architecture that is equipped with two Convolutional Block Attention Modules (CBAMs), an auxiliary deep-supervision head, and an integrated reliability framework that includes Monte Carlo Dropout uncertainty estimation, model calibration, split conformal prediction, and quantitative multi-method attribution analysis. DAVis-Net has achieved a cross-validated accuracy of 98.02% ± 0.12% on the four classes of OCT (CNV, DME, DRUSEN, NORMAL), statistically significantly higher than the VGG16 baseline in a matched-fold paired comparison (accuracy: p = 0.023; macro-F1: p = 0.004), with the highest gain on the hardest class (DRUSEN F1 +4.57 pp). Joint correlation analysis showed strong redundancy between predictive entropy and conformal set size (r = 0.67–0.78) across all classes, and a near zero linear correlation between both of these and a geometric proxy for spatial attention placement (|r| < 0.08), suggesting that, as captured by this central-region localization proxy, distributional uncertainty and spatial attention placement may reflect largely distinct reliability dimensions. A composite Trust/Refer triage rule achieved an accuracy of 99.76% on the 73.9% of cases it retained. All reported figures are internal estimates derived from a single dataset at the image-level, and multi-center validation is still required. The results show that the multi-dimensional reliability assessment is a more informative characterization of a medical image classifier than accuracy alone. Full article
(This article belongs to the Special Issue Artificial Intelligence, Machine Learning, and Deep Learning: Innovations and Real-World Applications)
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24 pages, 1204 KB  
Article
Quiescent Optical Solitons for Cubic–Quintic Nonlinear Schrödinger’s Equation with Intensity-Dependent Dispersion and Weak Nonlocality
by Hanaa A. Eldidamony, Ahmed H. Arnous, Yakup Yildirim, Muhammad Amin S. Murad and Anjan Biswas
Math. Comput. Appl. 2026, 31(5), 189; https://doi.org/10.3390/mca31050189 - 15 Sep 2026
Viewed by 238
Abstract
This study examined quiescent optical structures in a cubic–quintic nonlinear Schrödinger model that combines intensity-dependent dispersion with a weakly nonlocal intensity-curvature response. A real phase–amplitude reduction establishes the compatibility conditions for stationary localized profiles. The enhanced direct algebraic method then produces regular bright [...] Read more.
This study examined quiescent optical structures in a cubic–quintic nonlinear Schrödinger model that combines intensity-dependent dispersion with a weakly nonlocal intensity-curvature response. A real phase–amplitude reduction establishes the compatibility conditions for stationary localized profiles. The enhanced direct algebraic method then produces regular bright and dark states, singular hyperbolic states, and Jacobi and Weierstrass elliptic families. Spatially shifted formulas are identified as translated representatives rather than new orbit types. Each family is validated through the auxiliary equation, the stationary residual, explicit reality and nondegeneracy restrictions, and an independent first-integral formulation. The quintic response changes the dominant balance and the admissible coefficient manifolds relative to the corresponding Kerr-only setting. Parameter continuations illustrate distinct roles of cubic, quintic, dispersive, and weakly nonlocal effects without implying unconstrained one-parameter dynamics. For a representative regular bright state, refined Chebyshev collocation locates no persistent unstable eigenvalue and direct Fourier propagation under simultaneous amplitude and phase perturbations remains bounded. The numerical conclusion is restricted to the tested branch and finite propagation interval. Full article
(This article belongs to the Special Issue Celebrate the 30th Anniversary of Mathematical and Computational Applications (MCA))
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