Search Results (869)

We develop a Laurent-series framework for the analytical characterization of singularities in any three-step frozen-Jacobian iterative operator parametrized by $(\lambda ,\alpha ,\beta )$ (where $\lambda$ controls the predictor step and $(\alpha ,\beta )$ are the weight-function coefficients) and apply it to the fifth-order Newton–Jarratt–Newton (NJN) method. Three principal results are established. First, any operator with a quadratic weight function ($\beta \ne 0$) possesses a pole of order $m=d(d+1)+1$ at every simple critical point of f, where d is the asymptotic polynomial degree, independently of $\lambda$ and $\alpha$; when $\beta =0$ the order reduces to $m=d+1$, recovering the classical Jarratt-class result. Second, for each fixed $\lambda$ there exists a unique parameter pair $({\alpha }^{*}\left(\lambda \right),{\beta }^{*}\left(\lambda \right))$ that minimises the Laurent residue $|a_{-1}|$ subject to fifth-order convergence; for the NJN ($\lambda =2/3$) the explicit solution ${\alpha }^{*}=\frac{1}{4}$, ${\beta }^{*}=\frac{3}{8}$ provides the first analytical justification for these design values. Third, the Laurent Validity Radius ${\rho }_L={inf}_{z_s\in S\setminus \left\{z_c\right\}}|z_c-z_s|$ is the exact boundary of the domain in which the single-pole representation is valid; starting points satisfying $|z_0-z_c|\ll |\kappa |$ experience pole-dominated first-iterate growth $|G\left(z_0\right){|\sim |\kappa |}^m{\delta }^{-m}\to +\infty$. All results are validated on five test functions (including polynomial,transcendental, meromorphic, and non-symmetric cases) and all three, quantities can be computed from $f\left(z_c\right)$, $f^{\prime }\left(z_c\right)$, $f^{\prime \prime }\left(z_c\right)$ alone. Full article

We develop a tensor-based dynamical framework for monetary flows in multi-sector, multi-agent economies and quantify the information destroyed when the monetary state is reduced to a scalar aggregate. The state is a third-order tensor encoding capital flows across sectors, agent classes, and time; deviations from equilibrium obey a tensor-indexed Langevin (multivariate Ornstein–Uhlenbeck) equation with a coupling operator and channel-specific friction rates. Using standard Lyapunov theory, we assemble a stability and convergence framework for the induced vectorized system, with a bound stated so as to remain valid for the non-normal system matrices generated by asymmetric economic coupling, and characterize the stochastically forced case in the mean-square sense. Shannon entropy, Kullback–Leibler divergence, and sector–agent mutual information measure the structural information discarded by scalar aggregation. We then study a stylized, heuristically calibrated $3\times 3$ economy subject to a shock inspired by the 2007–2009 crisis; we emphasize at the outset that the figures reported below are properties of that calibration and are not empirical estimates. In this scenario Finance absorbs an 18.9% peak capital loss while Manufacturing and Services suffer 5.8% and 3.9% secondary drops, against an aggregate contraction of only 8.6%; the Kullback–Leibler divergence of the sector–agent flow distribution recovers systematically later than the aggregate signal, a lag that is positive in 96.6% of a 1000-draw Monte Carlo ensemble, although its magnitude is calibration-dependent. Under a symmetric exit rule, a deficit-targeted stimulus restores equilibrium substantially faster than a share-weighted uniform stimulus in 100% of the ensemble while spending strictly less—its realized expenditure saturates below the uniform budget because it self-terminates as deficits close—and attains integrated disequilibrium within 18% of the exact linear-quadratic optimum at equal control effort while requiring no knowledge of the system matrix. The ordinal conclusions—aggregation masks the epicenter, structure lags the aggregate, and deficit targeting dominates uniformity—are robust across a wide neighborhood of the calibration, and identify the disaggregated state as the object that stabilization policy needs and that scalar aggregation destroys. Full article

Although coronary CT angiography (CCTA) is widely utilized for diagnosing coronary artery disease (CAD), automated CCTA image segmentation is frequently hindered by sparse annotations, pseudo-label noise, and under-delineated fine branches. To mitigate these issues, we present PCDW-Net, a semi-supervised segmentation framework that couples perturbation consistency with discrepancy-aware weighting for enhanced label-scarce performance. Utilizing Adaptive Multi-scale Attention Fusion Network (AMAF-Net) as the backbone within a teacher-student architecture, the network applies diverse perturbations to unlabeled samples, leveraging a consistency loss to promote feature invariance. Simultaneously, a pixel-level discrepancy-aware weighting scheme serves to suppress erroneous pseudo-labels. Evaluated on the public ASOCA and private CTA40 datasets using 10% and 20% annotated fractions, the model was evaluated using Dice similarity coefficient (DSC) and Average Symmetric Surface Distance (ASSD). Under the 20% labeling constraint, PCDW-Net yielded a DSC of 85.36% on ASOCA and 83.48% on CTA40, superior to both Mean Teacher (MT) and Mutual Consistency Network+ (MC-Net+). Ablation studies confirmed the efficacy of each module. Overall, the framework effectively leverages unlabeled volumetric data to yield precise vessel boundary delineations. Full article

Reliable electric load forecasting is an important engineering problem for power-system planning, grid stability, and mission-critical energy management. This paper presents a symmetry-aware simulation and modeling framework for medium-range electric load forecasting under noisy and uncertain operating conditions. The proposed approach combines a Multi-Model Partitioning Filter (MMPF) with Nonlinear Autoregressive Exogenous (NARX) submodels, while two adaptive optimization strategies, genetic algorithm-based resource allocation (GARA) and Particle Swarm Optimization (PSO), are used to optimize the contribution weights of the parallel predictors. The modeling process uses real commercial power-system data and evaluates the forecasting framework over April–September 2025. To simulate realistic engineering disturbances, correlated symmetric Gaussian noise is injected into the testing phase under moderate and heavy noise scenarios. The cyclic symmetry of temporal variables, such as hours and months, is preserved through unit-circle encoding, while the symmetry and asymmetry of residual error symmetric distributions are examined through scatter plot analysis. As for the context of forecasting residuals as diagnostic signals, it is important to transfer symmetry properties that can be used to evaluate the behavior of optimized predictors, along with the cyclic encoding of inputs. This means that by implementing residual-symmetry analysis, the conclusion that GARA and PSO produce concentrated, balanced, and biased errors under moderate noise and heavily correlated noise conditions can be achieved. Finally, our results show that both GARA and PSO improve the robustness of the hybrid MMPF-NARX model, but PSO consistently achieves lower MAPE values, smoother convergence, and lower computational burden. The optimal configuration is obtained with nine NARX submodels, beyond which additional model complexity offers no meaningful performance gain. Overall, the study shows that symmetry-aware modeling, adaptive optimization, and noise-based simulation can support more reliable forecasting in modern power-system engineering applications. Full article

Multi-threshold image segmentation is a common technique in computer vision and image analysis. However, segmentation quality suffers greatly as the number of thresholds increases, particularly for color image segmentation tasks. To address this challenge, this paper proposes a modified reptile search algorithm (MRSA) based on Otsu and Kapur objective functions. Firstly, an RSA algorithm is developed by combining an adaptive weight factor and elite-guided learning to improve segmentation performance. Secondly, an RGB channel symmetric cooperation mechanism is introduced to exchange information among color channels. Thirdly, a repair mechanism is designed to maintain the structural symmetry of solutions throughout the optimization process. We conduct extensive experiments on the BSD500 benchmark color images under different threshold levels and compare MRSA with an improved bald eagle search algorithm (IBES), enhanced Giza pyramids construction algorithm (GGPC), multi-mechanism artificial lemming algorithm (MALA), and RSA. The experimental results demonstrate that the proposed MRSA algorithm achieves superior segmentation performance in terms of objective function values, region covering, peak signal-to-noise ratio, structural similarity index measure, and feature similarity index, and it exhibits excellent results even at high threshold levels. Full article

In this paper, we introduce the type II exponentiated half logistic-odd log-logistic-G power series class of distributions for modeling symmetric, skewed and heavy-tailed data with diverse hazard rate shapes. The proposed class of distributions is obtained by compounding the generalized family of distributions involving the type II exponentiated half logistic-G and odd log-logistic-G families with a discrete power series distribution. Various statistical properties of the proposed class of distributions, including moments, survival and hazard rate functions, order statistics, probability weighted moments, and Rényi entropy are derived. The model parameters are estimated using different estimation methods, and their performance is evaluated through Monte Carlo simulation studies. Finally, the flexibility and applicability of the proposed class of distributions are illustrated using real data sets. The results demonstrate that the proposed model provides a better fit than several existing competing models. Full article

Conventional hip exoskeletons typically employ multiple actuators to provide effective assistance to the corresponding joint, leading to an increase in the weight of the exoskeleton. Underactuated designs reduce the number of actuators, thereby lowering system weight and cost. However, existing single-motor underactuated hip exoskeletons still face challenges in achieving precise assistance and accommodating non-walking movements such as free sitting. In this work, we propose an underactuated hip exoskeleton with a series elastic actuator (SEA) and two independent cables for walking assistance. The incorporation of the SEA contributes to system safety and precise assistive force control. Furthermore, the proposed differential cable structure enables free sitting movement and allows for non-strictly symmetric hip motion. In experiments, with a target assistive force of 300 N, the proposed actuator achieves a peak force-tracking accuracy of 98.01% in walking tests, and the hip exoskeleton reduces peak muscle activation by up to 23.62% during walking. Full article

Symmetric electromagnetic sensing architectures induce representation-space decompositions that organize how measured fields respond to rotations, reflections, and programmable configurations. This paper develops a symmetry-resolved framework for analyzing how local parameter sensitivity is distributed across irreducible sectors and how this distribution changes under tensor lifting. Character-weighted Reynolds projectors decompose the derivatives of first-, second-, and fourth-order observables into orthogonal isotypic components, whose relative weights are quantified through normalized entropy, effective-sector occupancy, and dominant-sector concentration. The formulation distinguishes algebraic sector accessibility, determined by induced representations and tensor-product fusion, from the sensitivity profile realized by a specific physical observation model. The framework is validated using a narrowband far-field electromagnetic model of a two-ring $C_4$-symmetric receiving array and is further examined through matched cyclic and dihedral array ensembles. The results reveal a robust redistribution of sensitivity under tensor lifting in the tested cyclic architectures, while the dihedral configurations exhibit a different, order-dependent behavior associated with their richer representation structure. These findings do not imply a universal increase in information or estimation performance; rather, they show that tensorization reorganizes the symmetry channels through which local sensitivity is expressed. The proposed framework provides a diagnostic tool for comparing and designing symmetry-aware antenna arrays, metasurfaces, reconfigurable intelligent surfaces, and related programmable sensing architectures. Full article

Ensuring information integrity requires not only reducing decoding errors but also reducing the probability that corrupted data are accepted as valid. This research presents a hybrid integrity protection system that incorporates seeded universal hash verification, algebraic manipulation detection (AMD), and a binary Reed–Muller outer code. Transmission over the binary symmetric channel $\mathrm{B}\mathrm{S}\mathrm{C}\left(p\right)$, outer encoding using $\mathrm{R}\mathrm{M}(r, m)$, bounded-distance decoding, an ${\epsilon }_{\mathrm{A}\mathrm{M}\mathrm{D}}$-secure AMD layer, and a seeded 2-universal hash family with $\mathcal{l}$-bit output define the model used in the analysis. Under explicitly stated freshness and conditional-independence assumptions, the system-level undetected error probability is upper-bounded by the residual decoder-miscorrection probability multiplied by the AMD acceptance bound and the seeded universal hash collision bound. A conservative alternative is also provided for settings in which the required conditional independence cannot be guaranteed. In this context, an explicit upper bound for the undetected error probability is derived. The outcome makes clear the different functions of outer coding and post-decoding verification and results in a direct dependency on the parameters r, m, p, and l. Finite-length Monte Carlo validation for a concrete instantiation based on RM(2, 5) complements the theoretical study and verifies that the hybrid construction offers a lower empirical undetected error probability compared to the comparable outer-only, AMD-only, and hash-only variations. The study does not propose new coding or verification primitives. Its contribution is a finite-length layered acceptance model and a Reed–Muller-specific undetected error analysis that incorporates the code weight distribution and bounded-distance decoding regions. The resulting spectrum-based bound distinguishes decoder miscorrection from the broader event of exceeding the guaranteed correction radius and is evaluated together with post-decoding verification and redundancy overhead. The model’s formal manipulation detection and collision guarantees are provided by AMD and universal hash layers, while Reed–Muller code parameters and their standard distance formulas are conventional. Full article

Low-Rank Adaptation (LoRA) is a representative parameter-efficient fine-tuning method that reduces computational and memory costs without modifying the model architecture. Standard LoRA initializes matrix A from a symmetric distribution, such as Gaussian or Kaiming initialization, and matrix B to zero. Although this provides a statistically neutral starting point, it ignores the influence of task-specific input features on initialization. We propose Gamma-Moment Equalization Initialization (GME-Init), a data-aware asymmetric LoRA initialization method based on output-moment calibration. Using a small calibration set, GME-Init estimates the variance and skewness of target-layer outputs and adjusts the layer-wise initialization scale and asymmetry of LoRA weights, improving their statistical alignment with task-specific skewed representations. GME-Init operates only during initialization and does not change the LoRA architecture, trainable parameter count, training budget, or inference cost. We evaluate it on a GLUE subset with RoBERTa-base, integrate it with AdaLoRA and DoRA, and test it on VRSBench-VQA, VRSBench-Caption, and UCM-Caption using Qwen2.5-VL-3B-Instruct. Results show that GME-Init serves as a simple plug-in PEFT initialization module with no additional inference cost and that it consistently improves standard LoRA and selected LoRA-style methods across the evaluated text understanding and multimodal tasks. Full article

This paper proposes a systematic permutation-based construction method for multi-rate quasi-cyclic low-density parity-check (QC-LDPC) codes. We first present a graph-theoretic framework in which any regular QC-LDPC code can be normalized to a canonical base matrix that is uniquely determined by a permutation $\pi$. This normalization reduces the complex code design to a single combinatorial optimization problem over the symmetric group. Based on this normalization, we analyze the cycle structure of the lifted Tanner graph and derive necessary and sufficient conditions for 4-cycle elimination in terms of the permutation difference function. We develop two complementary algorithms: a simulated annealing algorithm that searches for permutations that minimize a weighted sum of 4-cycles and 6-cycles, and a progressive column-ordering algorithm that ensures every prefix subgraph maintains high girth. This approach yields a nested family of rate-compatible codes. Simulation results show that the constructed codes outperform the 5G-LDPC codes. The nested base matrix structure facilitates seamless rate switching, which makes the proposed code family well suited for adaptive transmission systems in future wireless networks. Full article

This paper establishes new Fejér and Hermite–Hadamard-type inequalities for functions of two variables whose mixed second-order partial derivatives satisfy coordinated GA-convexity or coordinated GA-quasi-convexity on a rectangle in the positive quadrant. Our main results are formulated for non-negative continuous weight functions that are not necessarily symmetric with respect to the geometric means of the interval endpoints, thereby extending the classical framework to genuinely asymmetric weights. However, to obtain explicit and sharp integral bounds in certain cases, we also employ a technical lemma that assumes a special symmetric setting where the weight function is symmetric on each coordinate with respect to $\sqrt{h_1{h}_2}$ and $\sqrt{k_1{k}_2}$. We clearly distinguish which theorems hold for general asymmetric weights and which depend on this symmetry condition. Our findings unify and extend numerous previously known results for both symmetric and non-symmetric weight functions. Full article

We study the finite-volume nearest-neighbor energy generated by the symmetric reciprocal-ratio penalty and its logarithmic representation as a gradient model with potential $V\left(t\right)=\cosh t-1$. We separate general convex structure from formulas specific to this hyperbolic potential. For an oriented nearest-neighbor energy, the gradient form gives a weighted-Laplacian Hessian, while a global lower-curvature bound $W^{″}\ge \kappa >0$ yields strong convexity after removal of the constant mode, spectral-gap coercivity, unique minimizers on fixed-mean slices, unique minimizing edge representatives in fixed-flux sectors, and quadratic stability gaps. On coordinate-constant twisted tori, strict convexity already forces affine minimizers and gives the exact energy density ${\sum }_{i}W\left(a_i\right)$. What is specific to the reciprocal-ratio model is the elementary hyperbolic form $W^{\prime }=\sinh$, $W^{″}=\cosh$: the sector equation becomes $\delta \sinh \omega =0$, the cycle calculation is explicit, and the twisted energy density is ${\sum }_i(\cosh a_i-1)$. For boxes and discrete tori in ${\mathbb{Z}}^d$, explicit spectral gaps yield, in $d=3$, an $o\left(L\right)$ sufficient condition for the normalized logarithmic field to vanish in averaged $L^2$. Our analysis is carried out in finite volume on fixed graphs with prescribed boundary, mean, or flux data. At positive temperature, we formulate the corresponding height Gibbs measures on mean-fixed slices within each flux sector and describe explicitly how they transform under a change in sector representative. Full article

In this paper, we investigate densely defined Toeplitz composition operators $T_u{C}_{\phi }$ on the Fock space ${\mathcal{F}}^2$. We completely characterize the $J_{\lambda }$-complex symmetry of such operators and derive necessary and sufficient conditions for normality. We further establish full criteria for self-adjointness and construct an explicit example showing that an operator may be $J_{\lambda }$-complex symmetric without being normal. To extend the theory beyond fixed radial–trigonometric expansions, we combine the Gaussian-weighted Mellin transform with Adaptive Fourier Decomposition (AFD) and establish the unified AFD-Mellin Symmetry Criterion, which generalizes these symmetry characterizations to adaptive rational basis systems. Full article

Piezoelectric flexure micro-positioning stages are essential micromotion actuators for micro-assembly, atomic force microscopy and nano-manufacturing, but intrinsic hysteresis nonlinearity of piezoelectric stacks distorts the linear voltage-to-displacement mapping and induces significant micro-positioning errors. Conventional hysteresis compensation based on offline-calibrated Krasnosel’skii-Pokrovskii (KP) models cannot adapt to time-varying excitation, whereas state-of-the-art adaptive KP control requires auxiliary dynamic equations and imposes high computational overhead on miniature real-time controllers. To address these limitations, this paper develops a single-degree-of-freedom micromotion positioning device equipped with symmetric two-stage displacement amplification mechanisms and straight circular flexure hinges. ANSYS finite element simulations validate the mechanical stiffness, structural safety and linear amplification characteristic of the micro-positioning stage, achieving a maximum output stroke of 95.95 μm. A discretized KP hysteresis model is constructed to accurately capture the asymmetric rate-dependent hysteresis of piezoelectric stacks. On this basis, a lightweight adaptive inverse control framework is proposed, which realizes online tuning of KP weights through gradient descent iteration only relying on real-time position feedback, eliminating static pre-calibration and extra dynamic correction links. Tracking experiments under 0.1–2 Hz sinusoidal waveforms and 3–7 V variable-amplitude sinusoidal waveforms are implemented. Experimental results show that the proposed approach reduces the root-mean-square error (RMSE) by 7.41–85.65% and the mean absolute percentage error (MAPE) by 7.56–87.81% compared with uncompensated open-loop micromotion control. The combined micro-flexure mechanical design and adaptive hysteresis compensation strategy greatly improves positioning accuracy and anti-interference capacity, offering a low-computation technical route for high-performance micro-positioning systems. Full article