Search Results (125)

Some properties on large contractions in metric spaces are proven. In particular, such contractions are proven to be asymptotically regular. In addition, if the metric space is complete, then the sequences that they generate are bounded, Cauchy, and convergent to a unique fixed point. Also, cyclic large contractions are an area of focus. It is proven that, if subsets of the cyclic disposal are nonempty closed and they intersect, all the sequences are bounded and Cauchy, and they converge to a unique fixed point located in the intersection of such subsets if the metric space is complete. If the subsets have a pair-wise empty intersection, then the boundedness of such sequences is proven without the need to assume the boundedness of the subsets in the cyclic disposal. The convergence of the sequences to a unique limit cycle of best proximity points, with one per subset in the cyclic disposal, is proven provided that the metric space is complete and that one of such subsets is boundedly compact with a singleton best proximity set. For that property to hold, it is not assumed that the remaining best proximity points are necessarily singletons. It has also been proven that all the subsequences contained within each of the subsets are Cauchy and they converge to a unique best proximity point, even if the corresponding best proximity sets is not a singleton. Furthermore, the hypothesis that one of the best proximity sets between adjacent subsets is a singleton can be weakened for any particular cyclic large contraction. Later on, eventual perturbations of the cyclic large self-mappings in normed spaces are discussed. If the norm of the perturbation additive operator is small enough, it is proven that the perturbed cyclic self-mapping maintains the property of being a cyclic large contraction associated with the unperturbed nominal cyclic large contraction. The maximum upper-bound of the perturbed operator ensures that such a property is given in an explicit manner. Full article

This paper evaluates neural-network approaches for lithium-ion battery state-of-charge (SoC) estimation under a unified pipeline, fixed data partitions, and identical preprocessing. We study FNNs trained with Levenberg–Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG) across three hidden sizes (10, 20, 30) and three topologies: Fitting, Nonlinear Input–Output (Nonlinear I/O), and time-series NAR/NARX. Models are assessed using test MSE and RMSE, correlation (R), generalization gap, convergence indicators (final gradient, damping factor), wall time per epoch, and a relative compute-cost index. On the Fitting task, BR-Fitting-FNN with 20 neurons provides the best accuracy-efficiency balance, while LM-Fitting-FNN with 30 neurons reaches slightly lower error at a higher cost. For Nonlinear I/O, BR-Nonlinear I/O-FNN with 30 neurons achieves the lowest test MSE with clear evidence of effective weight shrinkage; LM-Nonlinear I/O-FNN with 20 neurons is a close alternative. In time-series settings, LM-NAR-FNN with 10 neurons attains the lowest test error and fastest epochs but shows a very negative gap that suggests test-split favorability; BR-NAR-FNN with 30 neurons is more costly yet consistently strong. For NARX, LM-NARX-FNN with 20 neurons yields the best test accuracy and robust convergence. Overall, BR delivers the most reliable accuracy–robustness trade-off as networks widen, LM often achieves the best raw accuracy with careful split validation, and SCG offers the lowest training cost when resources are limited. These results provide practical guidance for selecting SoC estimators to match accuracy targets, computing budgets, and deployment constraints in battery management systems. Full article

Current object detection methods deployed in closed-circuit television (CCTV) systems experience substantial performance degradation due to domain gaps between training datasets and real-world environments. At the same time, increasing privacy concerns and stricter personal data regulations limit the reuse or distribution of source-domain data, highlighting the need for source-free learning. To address these challenges, we propose a stable and effective source-free semi-supervised domain adaptation framework based on the Mean Teacher paradigm. The method integrates three key components: (1) pseudo-label fusion, which combines predictions from weakly and strongly augmented views to generate more reliable pseudo-labels; (2) static adversarial regularization (SAR), which replaces dynamic discriminator optimization with a frozen adversarial head to provide a stable domain-invariance constraint; and (3) a time-varying exponential weighting strategy that balances the contributions of labeled and unlabeled target data throughout training. We evaluate the method on four benchmark scenarios: Cityscapes, Foggy Cityscapes, Sim10k, and a real-world CCTV dataset. The experimental results demonstrate that the proposed method improves mAP@0.5 by an average of 7.2% over existing methods and achieves a 6.8% gain in a low-label setting with only 2% labeled target data. Under challenging domain shifts such as clear-to-foggy adaptation and synthetic-to-real transfer, our method yields an average improvement of 5.4%, confirming its effectiveness and practical relevance for real-world CCTV object detection under domain shift and privacy constraints. Full article

Attention-Deficit/Hyperactivity Disorder (ADHD) is a highly prevalent neurodevelopmental condition that is typically identified through behavioral assessments and subjective clinical reports. However, electroencephalography (EEG) offers a cost-effective and non-invasive alternative for capturing neural activity patterns closely associated with this disorder. Despite this potential, EEG-based ADHD classification remains challenged by overfitting, dependence on extensive preprocessing, and limited interpretability. Here, we propose a novel neural architecture that integrates transformer-based temporal attention with Gaussian mixture functional connectivity modeling and a cross-entropy loss regularized through $\alpha$-Rényi mutual information, termed T-GARNet. The multi-scale Gaussian kernel functional connectivity leverages parallel Gaussian kernels to identify complex spatial dependencies, which are further stabilized and regularized by the $\alpha$-Rényi term. This design enables direct modeling of long-range temporal dependencies from raw EEG while enhancing spatial interpretability and reducing feature redundancy. We evaluate T-GARNet on a publicly available ADHD EEG dataset using both leave-one-subject-out (LOSO) and stratified group k-fold cross-validation (SGKF-CV), where groups correspond to control and ADHD, and compare its performance against classical and modern state-of-the-art methods. Results show that T-GARNet achieves competitive or superior performance (82.10% accuracy), particularly under the more challenging SGKF-CV setting, while producing interpretable spatial attention patterns consistent with ADHD-related neurophysiological findings. These results underscore T-GARNet’s potential as a robust and explainable framework for objective EEG-based ADHD detection. Full article

This paper establishes a comprehensive framework for the hereditary transfer of categorical completeness and cocompleteness to categories of internal group objects in D-modules. We prove that while completeness of $\mathbf{Grp}\left(\mathbf{D}\text{-}\mathbf{Mod}\right)$ follows unconditionally from the completeness of the base category $\mathbf{D}\text{-}\mathbf{Mod}$, cocompleteness requires $\mathbf{D}\text{-}\mathbf{Mod}$ to be regular, cocomplete, and admit a free group functor left adjoint to the forgetful functor. Explicit constructions are provided for limits via componentwise operations and for colimits through coequalizers of relations induced by group axioms over free group objects. The theory reveals fundamental geometric obstructions: differentially constrained subcategories such as holonomic D-modules fail to be cocomplete due to characteristic variety constraints that prevent free group constructions. Applications demonstrate cocompleteness in topological D-module groups and D-module sheaves, while counterexamples in differential geometric groups exhibit necessary analytic constraints. Additional results include regularity inheritance under product-preserving free group functors, internal hom-object constructions in locally Cartesian closed settings yielding Tannaka-type dualities, and monadicity criteria for locally presentable base categories. This work unifies categorical algebra with differential geometric obstruction theory, resolving fundamental questions on exactness transfer while enabling new constructions in homotopical algebra and internal representation theory for D-modules. Full article

In this article, we develop a novel kernel-based estimation framework for functional regression models in the presence of missing responses, with particular emphasis on the Missing At Random (MAR) mechanism. The analysis is carried out in the setting of stationary and ergodic functional data, where we introduce apparently for the first time a local linear estimator of the regression operator. The principal theoretical contributions of the paper may be summarized as follows. First, we establish almost sure uniform rates of convergence for the proposed estimator, thereby quantifying its asymptotic accuracy in a strong sense. Second, we prove its asymptotic normality, which provides the foundation for distributional approximations and subsequent inference. Third, we derive explicit closed-form expressions for the associated asymptotic variance, yielding a precise characterization of the limiting law. These results are obtained under standard structural assumptions on the relevant functional classes and under mild regularity conditions on the underlying model, ensuring broad applicability of the theory. On the methodological side, the asymptotic analysis is exploited to construct pointwise confidence regions for the regression operator, thereby enabling valid statistical inference. Furthermore, a comprehensive set of simulation experiments is conducted, demonstrating that the proposed estimator exhibits superior finite-sample predictive performance when compared to existing procedures, while simultaneously retaining robustness in the presence of missingness governed by MAR mechanisms. Full article

Background: Body image, physical self-concept and anxiety are closely intertwined aspects of psychological well-being among youth. The growing influence of social media and appearance-focused culture has intensified self-evaluation pressures, making it essential to understand whether physical activity fosters protective effects or, conversely, contributes to anxiety. Methods: The study examined the relationship between body appreciation, physical self-concept, self-esteem, and anxiety among 246 young adults aged 18–35 years (47.6% athletes, 52.4% non-athletes). Participants completed the Rosenberg Self-Esteem Scale (RSES), Body Appreciation Scale-2 (BAS-2), State-Trait Anxiety Inventory (STAI), and the short form of Physical Self-Description Questionnaire (PSDQ-S). Group differences were analyzed using the Mann–Whitney U and Kruskal–Wallis H tests, and associations were explored with Spearman’s correlations. Moderation analyses (PROCESS Model 1) tested whether physical activity buffered BMI-related effects, and structural equation modeling (SEM) evaluated direct and indirect pathways. Results: Athletes reported higher self-esteem and body appreciation and scored higher on all PSDQ-S subscales, alongside lower trait anxiety but higher state anxiety than non-athletes. Higher BMI predicted lower self-esteem, body appreciation, and less favorable self-perceptions. Physical activity moderated the BMI—self-esteem and BMI—body appreciation relationships, buffering negative effects among athletes. SEM showed that physical activity positively influenced physical self-concept and body appreciation, which in turn reduced trait anxiety. Gender differences were minimal. Conclusions: Regular sport participation supports psychological resilience by enhancing self-esteem and body appreciation while reducing anxiety. However, the findings also highlight the complexity of body–mind dynamics where individuals with strong body appreciation may still experience transient anxiety in evaluative contexts. Promoting body functionality, self-compassion, and positive physical self-concept in educational and sport settings may help prevent maladaptive behaviors and foster lasting mental well-being among youth. Full article

We present a head-to-head evaluation of the Improved Inexact–Newton–Smart (INS) algorithm against a primal–dual interior-point framework for large-scale nonlinear optimization. On extensive synthetic benchmarks, the interior-point method converges with roughly one-third fewer iterations and about one-half the computation time relative to INS, while attaining marginally higher accuracy and meeting all primary stopping conditions. By contrast, INS succeeds in fewer cases under default settings but benefits markedly from moderate regularization and step-length control; in tuned regimes, its iteration count and runtime decrease substantially, narrowing yet not closing the gap. A sensitivity study indicates that interior-point performance remains stable across parameter changes, whereas INS is more affected by step length and regularization choice. Collectively, the evidence positions the interior-point method as a reliable baseline and INS as a configurable alternative when problem structure favors adaptive regularization. Full article

We study compactness for the complex Green operator ${\mathsf{G}}_q$ associated with the Kohn Laplacian ${\square }_b$ on boundaries of pseudoconvex domains in Stein manifolds. Let $\Omega ⋐X$ be a bounded pseudoconvex domain in a Stein manifold X of complex dimension n with $C^1$ boundary. For $1\le q\le n-2$, we first prove a compactness theorem under weak potential-theoretic hypotheses: if $b\Omega$ satisfies weak $\left({\mathcal{P}}_q\right)$ and weak $\left({\mathcal{P}}_{n-1-q}\right)$, then ${\mathsf{G}}_q$ and ${\mathsf{G}}_{n-1-q}$ are compact on ${\mathsf{L}}_{p,q}^2\left(b\Omega \right)$. This extends known $C^{\infty }$ results in ${\mathbb{C}}^n$ to the minimal regularity $C^1$ and to the Stein setting. On locally convexifiable $C^1$ boundaries, we obtain a full characterization: compactness of ${\mathsf{G}}_q$ is equivalent to simultaneous compactness of ${\mathsf{G}}_q$ and ${\mathsf{G}}_{n-1-q}$, to compactness of the $\overline{\partial }$-Neumann operators ${\mathsf{N}}_q$ and ${\mathsf{N}}_{n-1-q}$ in the interior, to weak $\left({\mathcal{P}}_q\right)$ and $\left({\mathcal{P}}_{n-1-q}\right)$, and to the absence of (germs of) complex varieties of dimensions q and $n-1-q$ on $b\Omega$. A key ingredient is an annulus compactness transfer on ${\Omega }_{+}={\Omega }_2\setminus \overline{{\Omega }_1}$, which yields compactness of ${\mathsf{N}}_q^{{\Omega }_{+}}$ from weak $\left(\mathcal{P}\right)$ near each boundary component and allows us to build compact ${\overline{\partial }}_b$-solution operators via jump formulas. Consequences include the following: compact canonical solution operators for ${\overline{\partial }}_b$, compact resolvent for ${\square }_b$ on the orthogonal complement of its harmonic space (hence discrete spectrum and finite-dimensional harmonic forms), equivalence between compactness and standard compactness estimates, closed range and ${\mathsf{L}}^2$ Hodge decompositions, trace-class heat flow, stability under $C^1$ boundary perturbations, vanishing essential norms, Sobolev mapping (and gains under subellipticity), and compactness of Bergman-type commutators when $q=1$. Full article

This study examined the efficacy of a 12-week school-based program combining proprioceptive and plyometric training to enhance static and dynamic balance in children and adolescents with visual impairment. A total of 33 students were randomly assigned to either an experimental group (EG; n = 18), receiving a one-weekly session of integrative training alongside regular physical education, or a control group (CG; n = 15), following only the standard curriculum. Balance outcomes were assessed at baseline (T0) and post intervention (T1) using stabilometric measures under visual deprivation (eyes closed) and BOT-2 (Bruininks-Oseretsky Test of Motor Proficiency, Second Edition) balance subtests. The EG demonstrated statistically significant reductions in ellipse surface area (p = 0.002, d = −1.29), center of pressure displacement (p < 0.001, d = −1.67), and sway velocity (p = 0.015, d = −1.06), indicating improved postural stability when vision was unavailable. BOT-2 Test 4 showed significant intra-group improvement (p = 0.006, d = 1.37), while BOT-2 Test 3 and between-group comparisons revealed medium-to-large effect sizes, though not always statistically significant. These findings suggest that augmenting somatosensory input through proprioceptive and plyometric training may partially compensate for visual deficits and improve postural control in individuals with visual impairments. This improvement likely reflects the activation of compensatory mechanisms that enhance proprioceptive and vestibular contributions to balance maintenance. Importantly, meaningful improvements occurred with just one weekly session, making this an accessible and scalable intervention for inclusive school settings. Full article

Compaction quality control in earthworks and pavements still relies mainly on density-based acceptance referenced to laboratory Proctor tests, which are costly, time-consuming, and spatially sparse. Lightweight dynamic cone penetrometer (LDCP) provides rapid indices, such as $q_{d0}$ and $q_{d1}$, yet acceptance thresholds commonly depend on ad hoc, site-specific calibrations. This study develops and validates a supervised machine learning framework that estimates $q_{d0}$, $q_{d1}$, and $Z_c$ directly from readily available soil descriptors (gradation, plasticity/activity, moisture/state variables, and GTR class) using a multi-campaign dataset of $n=360$ observations. While the framework does not remove the need for the standard soil characterization performed during design (e.g., W, ${\gamma }_{d,\mathrm{field}}$, and $R{C}_{\mathrm{SPC}}$), it reduces reliance on additional LDCP calibration campaigns to obtain device-specific reference curves. Models compared under a unified pipeline include regularized linear baselines, support vector regression, Random Forest, XGBoost, and a compact multilayer perceptron (MLP). The evaluation used a fixed 80/20 train–test split with 5-fold cross-validation on the training set and multiple error metrics ($R^2$, RMSE, MAE, and MAPE). Interpretability combined SHAP with permutation importance, 1D partial dependence (PDP), and accumulated local effects (ALE); calibration diagnostics and split-conformal prediction intervals connected the predictions to QA/QC decisions. A naïve GTR-average baseline was added for reference. Computation was lightweight. On the test set, the MLP attained the best accuracy for $q_{d1}$ ($R^2=0.794$, RMSE $=5.866$), with XGBoost close behind ($R^2=0.773$, RMSE $=6.155$). Paired bootstrap contrasts with Holm correction indicated that the MLP–XGBoost difference was not statistically significant. Explanations consistently highlighted density- and moisture-related variables (${\gamma }_{d,\mathrm{field}}$, $R{C}_{\mathrm{SPC}}$, and W) as dominant, with gradation/plasticity contributing second-order adjustments; these attributions are model-based and associational rather than causal. The results support interpretable, computationally efficient surrogates of LDCP indices that can complement density-based acceptance and enable risk-aware QA/QC via conformal prediction intervals. Full article

Cayley graphs sit at the intersection of algebra, geometry, and theoretical computer science. Their spectra encode fine structural information about both the underlying group and the graph itself. Building on classical work of Alon–Milman, Dodziuk, Margulis, Lubotzky–Phillips–Sarnak, and many others, we develop a unified representation-theoretic framework that yields several new results. We establish a monotonicity principle showing that the algebraic connectivity never decreases when generators are added. We provide closed-form spectra for canonical 3-regular dihedral Cayley graphs, with exact spectral gaps. We prove a quantitative obstruction demonstrating that bounded-degree Cayley graphs of groups with growing abelian quotients cannot form expander families. In addition, we present two universal comparison theorems: one for quotients and one for direct products of groups. We also derive explicit eigenvalue formulas for class-sum-generating sets together with a Hoffman-type second-moment bound for all Cayley graphs. We also establish an exact relation between the Laplacian spectra of a Cayley graph and its complement, giving a closed-form expression for the complementary spectral gap. These results give new tools for deciding when a given family of Cayley graphs can or cannot expand, sharpening and extending several classical criteria. Full article

This work establishes definitive conditions for the inheritance of categorical completeness and cocompleteness by categories of internal group objects. We prove that while the completeness of $\mathbf{Grp}\left(\mathcal{C}\right)$ follows unconditionally from the completeness of the base category $\mathcal{C}$, cocompleteness requires $\mathcal{C}$ to be regular, cocomplete, and admit a free group functor left adjoint to the forgetful functor. Explicit limit and colimit constructions are provided, with colimits realized via coequalizers of relations induced by group axioms over free group objects. Applications demonstrate cocompleteness in topological groups, ordered groups, and group sheaves, while Lie groups serve as counterexamples revealing necessary analytic constraints—particularly the impossibility of equipping free groups on non-discrete manifolds with smooth structures. Further results include the inheritance of regularity when the free group functor preserves finite products, the existence of internal hom-objects in locally Cartesian closed settings, monadicity for locally presentable $\mathcal{C}$, and homotopical extensions where model structures on $\mathbf{Grp}\left(\mathcal{M}\right)$ reflect those of $\mathcal{M}$. This framework unifies classical category theory with geometric obstruction theory, resolving fundamental questions on exactness transfer and enabling new constructions in homotopical algebra and internal representation theory. Full article

We develop a rigorous algebraic–analytic framework for multidual complex numbers ${\mathbb{DC}}_n$ within the setting of Clifford analysis and establish a comprehensive theory of hyperholomorphic multidual complex-valued functions. Our main contributions are (i) a fully coupled multidual Cauchy–Riemann system derived from the Dirac operator, yielding precise differentiability criteria; (ii) generalized conjugation laws and the associated norms that clarify metric and geometric structure; and (iii) explicit operator and kernel constructions—including generalized Cauchy kernels and Borel–Pompeiu-type formulas—that produce new representation theorems and regularity results. We further provide matrix–exponential and functional calculus representations tailored to ${\mathbb{DC}}_n$, which unify algebraic and analytic viewpoints and facilitate computation. The theory is illustrated through a portfolio of examples (polynomials, rational maps on invertible sets, exponentials, and compositions) and a solvable multidual boundary value problem. Connections to applications are made explicit via higher-order automatic differentiation (using nilpotent infinitesimals) and links to kinematics and screw theory, highlighting how multidual analysis expands classical holomorphic paradigms to richer, nilpotent-augmented coordinate systems. Our results refine and extend prior work on dual/multidual numbers and situate multidual hyperholomorphicity within modern Clifford analysis. We close with a concise summary of notation and a set of concrete open problems to guide further development. Full article

Mastering client-side Web programming is essential for the development of responsive and interactive Web applications. To support novice students’ self-study, in this paper, we propose a novel exercise format called the phrase fill-in-blank problem (PFP) in the Web Programming Learning Assistant System (WPLAS). A PFP instance presents a source code with blanked phrases (a set of elements) and corresponding Web page screenshots. Then, it requests the user to fill in the blanks, and the answers are automatically evaluated through string matching with predefined correct answers. By increasing blanks, PFP can come close to writing a code from scratch. To facilitate scalable and context-aware question creation, we implemented the PFP instance generation algorithm in Python using regular expressions. This approach targets meaningful code segments in HTML, CSS, and JavaScript that reflect the interactive behavior of front-end development. For evaluations, we generated 10 PFP instances for basic Web programming topics and 5 instances for video games and assigned them to students at Okayama University, Japan, and the State Polytechnic of Malang, Indonesia. Their solution results show that most students could solve them correctly, indicating the effectiveness and accessibility of the generated instances. In addition, we investigated the ability of generative AI, specifically ChatGPT, to solve the PFP instances. The results show 86.7% accuracy for basic-topic PFP instances. Although it still cannot fully find answers, we must monitor progress carefully. In future work, we will enhance PFP in WPLAS to handle non-unique answers by improving answer validation for flexible recognition of equivalent responses. Full article