Search Results (304)

The simulation of modern wireless communication circuits remains challenging because of the coexistence of nonlinear behavior, heterogeneous subsystems, and widely separated time scales. This review presents a structured overview of advanced numerical methods for solving multitime partial differential–algebraic equations (MPDAEs) arising in circuit-level modeling of RF and microwave systems. Compared with previous survey papers, the main contribution of this work is to organize the literature according to the underlying numerical strategy, distinguishing purely time-domain, hybrid time–frequency, multidimensional frequency-domain, and circuit-block partitioning approaches. The reviewed methods show that multitime formulations can deliver substantial computational gains over conventional simulation techniques, particularly for multirate and multiscale circuits. Time-domain techniques are generally more robust for strongly nonlinear regimes, whereas frequency-domain and hybrid methods are often more efficient when the waveform can be represented with a limited number of harmonics. Circuit-block partitioning further improves efficiency by exploiting active and latent variables, but the computational complexity of MPDAE methods increases rapidly with the number of time scales, and their applicability becomes more limited for aperiodic or highly general multirate excitations. Overall, this review highlights both the strengths and the practical limitations of current MPDAE-based numerical approaches and identifies open challenges for future research. Full article

Individual tree modeling (ITM) is an effective system for thinned stands, especially in teak (Tectona grandis Linn F.) plantations, allowing the estimation of individual-tree-specific variables. Heartwood diameter and volume have high added value and can be estimated in living trees. Therefore, we developed an ITM system for clonal teak stands capable of projecting technical intervention ages and quantifying heartwood production throughout the rotation in the Eastern Brazilian Amazon. The system included equations for total tree height, site index, and taper of both stem and heartwood, with volumes obtained by integrating the respective taper equations. Future diameters and heights were projected using models based on the algebraic difference approach (ADA) and the generalized algebraic difference approach (GADA). Ages of technical intervention were defined by the maximum mean annual increment in volume with bark. The Lundqvist-Korf-ADA base model was the most accurate in estimating future trees’ diameters and heights. The inclusion of the number of trees as a covariate to represent thinning had a significant and positive impact on variable projections. Optimal technical rotations ranged from 17.1 to 21.3 years, considering volume with bark. An increase in the proportion of heartwood was observed, reaching 78% of the diameter and 53% of the volume at rotation ages. The modeling system developed in the present study enables the estimation of technical rotation ages and the quantification of heartwood production throughout the rotation, which provides reliable information for silvicultural planning and decision-making in the management of clonal teak stands. Full article

This paper develops a direct analytical framework for synchronizing and controlling fractional-order octonion-valued fuzzy bidirectional associative memory neural networks (FOOVFBAMNNs). Octonion algebra is neither commutative nor associative, which limits the application of standard analytical tools. To address this challenge, we first propose a generalized Cauchy–Schwarz inequality tailored to the octonionic domain, which operates directly without relying on system decomposition. This inequality lays the groundwork for a Lyapunov-based stability analysis that retains the system’s inherent geometric structure to avoid decomposition into real-valued components. Based on this framework, we derive concise 2-norm inequality criteria, which are sufficient to guarantee Mittag-Leffler synchronization of the proposed model. We also employ a Particle Swarm Optimization (PSO) algorithm to systematically optimize the flexible parameters in the generalized inequality, enhancing the practical performance of the synchronization scheme. To validate the effectiveness of the proposed method, we apply it to a multi-domain image restoration task. Numerical experiments verify the performance of our method. In terms of Peak Signal-to-Noise Ratio (PSNR), the octonion-valued network with PSO-tuned parameters achieves better results than its non-optimized counterpart as well as models constructed in complex or quaternion domains. Full article

Econometric estimation of panel data models by feasible generalized least squares (FGLS) provides an example of how conceptually simple problems may run into computational bottlenecks. I address the main computational tasks of FGLS within the R system for statistical computing, comparing different tools from the point of view of computational efficiency. I concentrate on estimating two models: the popular “random effects” with two error components and the less restrictive “general GLS” specification, which does not fit into the standard computational framework usually employed for the former. I compare the standard solution (partial time demeaning) with two alternative strategies, based respectively on algebraic properties and on object-oriented programming. I show how, while naive implementations become infeasible with large datasets, both list operators and object-oriented matrix routines available in the R environment make the problem tractable for most practically relevant sample sizes on any machine. I conclude by briefly discussing the parallelization of critical tasks. Full article

We review the structure of pseudoscalar mesons within an algebraic model formulated in the light-front framework. The approach provides a unified description of leading-twist parton distribution amplitudes, light-front wave functions, generalized parton distributions, parton distribution functions, elastic electromagnetic form factors, charge radii, and impact-parameter space distributions, all obtained from the same underlying Bethe–Salpeter wave-function representation. The analysis covers light mesons $(\pi ,K)$, the mixed $\eta$–${\eta }^{\prime }$ system, heavy–light states $(D,D_s,B,B_s,B_c)$, and heavy quarkonia $({\eta }_c,{\eta }_b)$, thereby enabling a systematic study of quark-mass effects, flavor-symmetry breaking, and the transition from emergent hadronic mass to heavy-quark dynamics. Where available, results are compared with experimental measurements, functional methods such as lattice-QCD calculations and Dyson–Schwinger Equation formalism, and other phenomenological approaches. The algebraic model thus offers a transparent, symmetry-preserving, and analytically tractable framework for connecting the longitudinal, transverse-momentum, and spatial structure of pseudoscalar mesons across all quark-mass regimes. Full article

Accurate design and performance assessment of solar thermal domestic hot water systems coupled with a heat pump auxiliary typically requires transient simulation, as the system’s behavior depends on multiple interactions among collector characteristics, storage stratification, control logic, weather, and draw-off timing. Monthly methods such as the f-chart are useful for first-pass estimates, but they do not resolve stratification, thermostat operation, or demand timing, and they may become inaccurate for stratified thermostat-controlled systems. Direct comparisons of locally inspectable symbolic and black-box surrogate families for this system class remain limited. A 10,982-case development dataset was generated from minute-resolved annual MATLAB simulations, parameterized by collector area, optical efficiency, and first- and second-order loss coefficients. Three surrogate families were benchmarked under a unified protocol, random forest-assisted shape-constrained symbolic regression (SR), feed-forward artificial neural network (ANN) models, and Automatic Learning of Algebraic Models for Optimization (ALAMO), with the f-chart used as a monthly reference method. The targets were the 12 monthly solar fractions under the direct solar heat definition and the corresponding annual mean solar fraction, evaluated on the same independent 991-case test set. SR achieved the lowest average error (mean absolute percentage error, MAPE = 0.82%; root mean square error, RMSE = 0.006), followed by the ANN (MAPE = 2.07%, RMSE = 0.028) and ALAMO (MAPE = 3.67%, RMSE = 0.060), with Nash–Sutcliffe efficiency (NSE) values above 0.98 for all models. Evaluation times were 0.0026–0.124 s per target, compared with about 1000 s for one full-year simulation. These results define the study as a common protocol benchmark within the studied simulator-defined envelope. SR gives the strongest accuracy with local symbolic inspectability, the ANN remains the flexible retrainable option, and ALAMO provides compact algebraic evaluation with the shortest learned model runtime. Full article

Carbon monoxide (CO) is a colorless, odorless byproduct of incomplete combustion that binds to hemoglobin to form carboxyhemoglobin (COHb), impairing oxygen delivery and causing systemic hypoxia. Two widely used models for estimating CO toxicity are the Coburn–Forster–Kane (CFK) equation, which incorporates physiological and anthropometric parameters, and the workload-based MIL-STD-1472 model, developed in the late 1960s and 1970s. Both have been applied extensively in military armored motor vehicle (AMV) operations, firefighting, and mining. This study evaluates the predictive performance of these models during field trials involving AMV crews conducting live-fire exercises. Ambient CO concentrations were continuously monitored, and serial blood samples were obtained for COHb determination. Individual physiological and anthropometric data were used to generate CFK-based predictions, while the MIL-STD-1472 estimates were derived using the activity level equivalent (ALE) values, which were developed to allow for mathematical alignment between the two models. Measured COHb levels showed strong agreement with predictions from both the CFK and MIL-STD-1472 equations. An ALE analysis indicated that the actual physical workload during AMV operations was substantially lower than the activity level (AL = 4) originally recommended in MIL-STD-1472. In addition, algebraic rearrangement of the MIL-STD-1472 equation enabled the estimation of COHb recovery time following cessation of exposure. This study provides a field-based evaluation of two established models for predicting carboxyhemoglobin formation. Measurements obtained during live armored motor vehicle operations demonstrate that both the CFK and MIL-STD-1472 equations accurately estimate COHb under conditions of near-ambient oxygen tension and minimal CO₂ accumulation. Importantly, MIL-STD-1472 predictions using moderate ALE values were more consistent with the observed COHb values, suggesting that the commonly applied activity level (AL = 4) may overestimate CO exposure risk in comparable operational environments. Full article

This paper develops a geometric framework for analyzing the ideal structure of the bipolar semigroup $B=\{(-a,b)\mid a,b\in {\mathbb{R}}_0^{+}\}$ under coordinate-wise addition. Subsets of B are interpreted as planar regions, allowing ideals to be described in terms of boundary behavior. In particular, we prove that the complement of a simply connected region is an ideal of the commutative additive semigroup $(B,+)$ if and only if its boundary contains no strictly decreasing segment. This provides a direct and visually verifiable criterion for ideality, linking algebraic structure to geometric shape. Each ideal can be written as a union of translates of the form $z+B$, with minimal generating sets determined by boundary structure. Potential applications to modeling bipolar system states, including cybersecurity contexts, are also discussed. These results uncover an intrinsic symmetry between algebraic closure and geometric monotonicity, offering a new perspective on semigroup ideals through spatial structure. In contrast to our previous work on the semiring $(B,+,·)$, where ideals necessarily exhibit symmetry with respect to the line $y=-x$, we show that removing the multiplicative operation leads to a fundamentally different geometric behavior: ideals in the semigroup $(B,+)$ no longer possess symmetric shapes. This demonstrates that the multiplicative structure is the key mechanism enforcing geometric symmetry. Full article

Dynamic Movement Primitives (DMPs) are widely used for learning and generalizing robot skills. However, standard quaternion DMPs, when modeling orientation trajectories, constrain only the final orientation and cannot freely specify the final angular velocity. This limitation restricts its application to dynamic tasks requiring precise boundary conditions, such as hitting or throwing. Although existing improved methods achieve velocity generalization to some extent, they often struggle to balance trajectory shape preservation with dynamic smoothness, frequently causing significant deviation from demonstrations or abrupt acceleration discontinuities. In this paper, we propose a novel robot skill generalization method that enables controllable final angular velocity for quaternion DMPs. Specifically, we construct a dynamic goal system driven by a quintic polynomial in Lie algebra space, analytically planning the target orientation’s evolution based on given multi-order boundary constraints. This mechanism not only achieves precise control over the final angular velocity but also inherently guarantees global C² continuous dynamics across primitive segments. Comparative simulations and real-world robot hitting experiments demonstrate that, compared to existing approaches, our proposed method effectively satisfies dynamic boundary constraints while exhibiting superior shape preservation, minimal trajectory deviation, and higher smoothness, thereby significantly improving skill generalization performance in complex dynamic tasks. Full article

Water utilities frequently perform pipeline-emptying operations for maintenance, repair, and operational management. This process involves transient flow conditions with entrapped air. It must be carefully controlled, as the expansion of air pockets can generate sub-atmospheric pressures that may lead to pipeline collapse. The mathematical modelling of emptying processes with air valves has been extensively studied in recent years; however, such approaches typically rely on complex algebraic–differential equation systems. This study advances understanding of this phenomenon by proposing a novel procedure that uses a machine learning model to approximate system behaviour while avoiding fully coupled hydraulic formulations. An experimental facility consisting of a pipeline with an internal diameter of 0.042 m and a total length of 4.6 m was used, in conjunction with a complete regulation valve manoeuvre. The system was first calibrated using experimental data and subsequently employed in Monte Carlo simulations to generate a dataset for training the machine learning model. The results demonstrate that a Rational Quadratic Gaussian Process Regression model can accurately predict the minimum sub-atmospheric pressure, achieving a coefficient of determination greater than 0.999 during validation and testing. The proposed framework is presented as a proof-of-concept and has been validated only for the specific case study analysed. While the results highlight its potential to support planning for emptying operations under varying air-admission conditions and air-pocket sizes, further validation is required before generalising to real-world water distribution systems. For practical implementation, the model must be appropriately trained for each specific installation. Full article

This paper studies capacity planning for a wind–hydrogen integrated energy system under scenario-based uncertainty in wind generation, hydrogen demand, and electricity prices. The model is formulated as a two-stage stochastic program in which first-stage investment decisions are selected before uncertainty is realized and second-stage hourly operation is optimized for each representative scenario. The main methodological difficulty is that part of the first-stage hydrogen-storage investment cost may be available only through a non-analytical evaluator, such as supplier quotation logic, simulation software, or a data-driven estimator, while the operational recourse model remains linear. To address this setting, a hybrid heuristic–Benders framework, denoted as GSOA-Benders, is developed by coupling the General-Soldiers Optimization Algorithm for derivative-free first-stage search with Benders cuts generated from linear programming subproblems. The framework is not presented as a replacement for commercial solvers on explicit convex or mixed-integer models; rather, it is intended for cases where exact algebraic reformulation of the first-stage cost is unreliable or unavailable. In the black-box case study with 500 scenarios, the method converges in 35.86 s and obtains an investment plan expressed as $\mathbf{x}=[1,0.53,23.23,0]$, corresponding to wind-farm construction, a 0.53 MW electrolyzer, a 23.23 MWh hydrogen tank, and no fuel-cell investment. Additional discussion is provided on stability-gap interpretation, benchmark limitations, component lifetime assumptions, hydrogen losses, and environmental extensions. Full article

This study develops an effective numerical method for addressing the time-fractional gas dynamics equation formulated with the Caputo time-fractional derivative. Novel basis functions are utilized, formulated as particular generalized Fibonacci polynomials contingent on a free parameter. This family generalizes the second kind of Chebyshev family. For the proposed polynomials, we establish basic analytical properties, including closed-form series expansion, inverse relation, moment and linearization formulas, and operational matrices for both integer-order and Caputo fractional derivatives. Using these tools, the fractional model, together with its underlying conditions, can be transformed into a finite system of nonlinear algebraic equations via a collocation strategy. Using Newton’s iterative method, the resulting system can be treated. A full convergence analysis of the double generalized Chebyshev expansion is provided. We demonstrate the accuracy and reliability of the presented method through several numerical simulations. Comparisons with existing numerical methods show that this approach achieves higher accuracy and faster execution. Full article

Artificial intelligence is typically formulated as an information-processing system composed of artificial neurons, where computation is understood as recursive operations connecting inputs and outputs. However, real neural systems are materially embodied and continuously reconfigured by metabolic and physical processes, suggesting that computation cannot be reduced to fixed causal structures. In this paper, we propose a theoretical framework that captures the interplay between informational and material processes as the interaction between two computational schemes: a vertical scheme, representing fixed cause–effect relations, and a horizontal scheme, representing transformations between such relations. We show that the vertical scheme corresponds to Bayesian inference, which updates probability distributions over a fixed hypothesis space, and is consistent with the free-energy minimization principle. In contrast, the horizontal scheme is formalized as inverse Bayesian inference, which modifies the hypothesis space itself by updating likelihood structures based on experienced data. We further demonstrate that the interplay between these schemes can be expressed algebraically as a process of continuously gluing Boolean algebras. This construction yields a non-distributive orthomodular lattice, i.e., quantum logic, without invoking Hilbert space formalism. In this view, quantum logic emerges not as a static logical system but as a structural consequence of dynamically reconfiguring causal contexts. This framework provides a unified perspective in which inference is understood not only as optimization within a fixed model but also as a process that generates and transforms the model itself. It offers a formal basis for describing open-ended computation and suggests a connection to approaches such as unconventional computing and Natural Born Intelligence, where computational structures evolve through interaction with material processes. Unlike existing approaches, this framework derives quantum-logic-like structure from the continual reconfiguration of causal contexts rather than from Hilbert-space assumptions or optimization within a fixed hypothesis space. Full article

In this paper, we investigate the application of the relative entropy framework for safety assessments of steel elements with structural defects at the micro- and macro-scales. Mathematical theories developed by Bhattacharyya and by Kullback and Leibler (K-L) have been used for this purpose. This approach uses both expectations and variations, similar to the First-Order Reliability Method (FORM), but is extended to include 3rd- and 4th-order central probabilistic moments. It is necessary to use a hybrid computational technique that combines the Finite Element Method (FEM) software ABAQUS CAE 2017 with the implemented Gurson–Tvergaard–Needleman (GTN) damage model and the computer algebra system MAPLE. The iterative generalized stochastic perturbation technique has been used to determine the probabilistic moments of structural response, to utilize the Weighted Least Squares Method to approximate the structural response function, and to determine uncertainty in the stress, strain, and displacement state functions. This approach is based on relative entropy because of its universality. There is no need to assume a type of distribution of the state functions, in contrast to FORM, where a Gaussian distribution is required. This paper verifies whether relative entropy can serve as an alternative to FORM for determining reliability. The yield surface of the porous material with a random values of the void volume fraction f are also presented. Full article

Recursive constructions derived from finite projective geometries generate scalable families of resolvable block designs exhibiting strong algebraic regularity and intrinsic symmetry. In this work, we investigate the structural optimization of recursion depth in such constructions and demonstrate that the combinatorial growth of recursive chains is governed by a quadratic scaling law originating from the asymptotic expansion of Gaussian binomial coefficients. We show that the resulting exponent is strictly concave, which guarantees the existence and uniqueness of an optimal recursion depth. This optimum occurs at the midpoint of the projective dimension and reflects the dual symmetry of the lattice of projective subspaces. To analyze this behavior, we introduce a normalized objective function that compares recursion depths and reveals a unique maximum corresponding to the midpoint of the projective dimension. Theoretical analysis is supported by exact enumeration and asymptotic validation, confirming that the optimal depth is robust to lower-order perturbations and remains invariant under the natural duality of projective geometry. The proposed framework establishes a direct connection between symmetry properties of discrete geometric structures and optimality in nonlinear discrete systems. These results provide a unified perspective on recursive design constructions, revealing that symmetry not only governs combinatorial structure but also induces a mathematically inevitable optimal configuration. The approach opens new directions for studying symmetry-induced optimality in combinatorial geometry, discrete optimization, and related nonlinear mathematical models. Full article