Search Results (1,807)

Classical enumeration of triangulations and angulations of convex polygons is governed by the Catalan and Fuss–Catalan families. In this paper, we introduce a Lucas-inspired symbolic encoding framework for a restricted subclass of triangulations, called Lucas-compatible triangulations. The purpose of the framework is not to replace classical Catalan enumeration, but to provide a complementary structural layer that records admissible local reductions through two canonical operations. Within this restricted setting, the geometric objects remain Catalan-based, whereas the associated encoding space satisfies a Fibonacci-type recurrence. We formalize the reduction model, define admissible Lucas words, and prove structural properties of the encoding map. We further present recursive generation algorithms, analyze their output-sensitive complexity, and compare the size of the encoding space with the size of the full triangulation space. In addition, we discuss geometric constraints, equivalence phenomena, and potential uses of the encoding in compact representation, constrained enumeration, and recursion-guided generation of polygon dissections. Computational experiments support the theoretical predictions and illustrate how the proposed encoding yields a compressed symbolic view of a restricted but mathematically meaningful class of dissections. Full article

Background: Intrathecal IgG synthesis is a well-established hallmark of multiple sclerosis (MS), yet the roles of other immunoglobulin isotypes remain under investigated. This study aimed to comprehensively profile immunoglobulin distributions in cerebrospinal fluid (CSF) and plasma from MS patients and neurological controls. Methods: Paired CSF and plasma samples from 23 MS patients and 20 neurological controls were analyzed using a multiplex Luminex-based immunoassay targeting IgG1–4, IgA, and IgM. The findings were validated using commercial ELISA kits and Western blot analysis. Results: Multiplex analysis revealed a selective intrathecal enrichment of IgA and IgM in MS CSF, with significantly higher levels compared to both matched plasma and control CSF. IgG1 was modestly elevated in MS CSF by ELISA but not by multiplex assay. Western blotting confirmed a robust elevation of IgA in MS CSF, providing qualitative support for intrathecal enrichment rather than definitive proof of synthesis. Conclusions: These findings uncover previously underappreciated selective enrichment of IgA and IgM in the MS CNS compartment, complementing, rather than replacing, the established IgG-centric paradigm. The results suggest alternative antibody-mediated mechanisms in MS and highlight the importance of assay selection in biomarker discovery, which suggests IgA as an emerging component of MS immunopathology. Full article

Quantitative forecasting and lifecycle pattern recognition of science and technology (S&T) innovation activities are essential for evidence-based technology management, yet modeling long-range dependencies in multivariate S&T time series while capturing cross-variate interactions remains a fundamental challenge. Existing Transformer-based forecasters suffer from quadratic complexity that limits effective lookback windows, while state space models typically process each variate independently, ignoring inter-variate coupling among technology fields. We propose MambaTech, a problem-specific hybrid architecture for patent innovation time series that explicitly decomposes intra-domain temporal dynamics from inter-domain technology interactions. The architecture fuses a Mamba-based selective state space branch for $O\left(n\right)$-complexity temporal modeling with a Transformer cross-attention branch for inter-variate association modeling, unified through a learnable domain-conditioned adaptive gating mechanism. An auxiliary classification head regularizes the shared representation by performing lifecycle stage recognition across technology domains. Evaluated on patent filing time series spanning eight CPC sections over 180 months (Harvard USPTO Patent Dataset, 4.5M records) and a 632-variate subclass setting, with additional cross-domain assessment on public benchmarks (Electricity, Traffic, Weather), MambaTech achieves one-step MAPEs of $3.71\%$ (coarse) and $6.24\%$ (fine), reducing errors by 31.4% over Transformer and 52.2% over ARIMA baselines (averaged over five random seeds). At a 12-step horizon, the degradation rate is only +0.48%/step versus +0.89% for the best competing method. The gating fusion yields a 12.8% improvement over naïve concatenation, and the lifecycle classification head attains a macro-F1 of $0.915$ across 632 technology domains, with statistically significant improvements under paired bootstrap and Diebold–Mariano tests. Ablation studies confirm the complementary branch contributions, and the learned cross-attention weights reveal technology association patterns consistent with known S&T innovation spillover theory and are validated against external co-classification networks. The originality of MambaTech lies in its task-specific hybridization and analytical framework for patent innovation time series, rather than in proposing a fundamentally new sequence modeling primitive. Full article

Bazilevič mappings are considered very important in the theory of geometric mappings because they provide a way to generalize and study the properties of important classes of univalent mappings. Their importance is not only in the deepening of the theory, but also in the practical means of modeling phenomena in applied science and engineering, physics, and differential equations. This paper, in this sense, provides a new subclass of bi-Bazilevič mappings with the use of advanced analytical methods, Chebyshev polynomials on one side, and a Miller–Ross-type Poisson distribution on the other side. The Poisson distribution is considered one of the most important models of probability distributions with a large scope of application in the various sciences. The main components of this study are the definition and the study of this new class of functions, in which the initial Taylor–Maclaurin coefficients, in particular, $q_2$ and $q_3$, are determined and estimated for mappings in this subclass. Also, the classical Fekete–Szegö problem is solved and the first-order limits of this important functional are obtained with respect to the newly introduced bi-Bazilevič mappings. The outcomes contribute to expanding both the theoretical and practical aspects of this type of mapping. Full article

Phospholipid fatty acid incorporation and remodeling are central processes through which immune cells adapt their membranes during activation. Macrophages are known to integrate oxidized fatty acids into phospholipids, yet the principles governing this distribution remain incompletely defined. Hydroxyeicosatetraenoic acids (HETEs) are abundant products generated during inflammation, and their integration into membrane phospholipids may influence signaling, trafficking, and membrane organization. Although individual HETE isomers differ in biosynthesis and function, it is not known whether macrophages handle them differently. Here, we address how 5-, 12-, and 15-HETE are incorporated into murine peritoneal macrophage phospholipids during inflammatory stimulation. We show that each isomer exhibits a distinctive phospholipid-class distribution, with 12-HETE preferentially entering choline phospholipids (PC), 15-HETE enriching phosphatidylinositol (PI), and 5-HETE distributing more broadly across PC, PI and ethanolamine phospholipids (PE). All three isomers are incorporated predominantly at the sn-2 position and showed similar molecular species distribution within each class, with diacyl PC, PE plasmalogens, and PI(18:0/HETE) serving as dominant acceptors. RAW264.7 cells reproduce these patterns. In ether phospholipid-deficient RAW.108 cells, incorporation into ether species is lost but compensated by increased routing into diacyl PC and PE, while PI incorporation remains unchanged. Collectively, these findings reveal that phospholipid class, not simple availability, determines where HETEs are incorporated. This distribution is preserved across macrophage cell types and remains intact even when ether phospholipids are absent, indicating that class specific pathways, rather than lipid subclass composition, primarily determine HETE incorporation. Full article

Four-edge type low-density parity-check (FET-LDPC) codes, as an important subclass of multi-edge type LDPC codes, offer greater design flexibility and performance potential due to their heterogeneous edge type structure. However, their multi-dimensional degree distribution significantly increases the complexity of optimization. This paper proposes a joint optimization framework for FET-LDPC codes leveraging the symmetric decoding structure inherent in their dual-branch architecture. The main contributions are as follows. First, an improved decoding model is established to analyze the mutual information transmission among the four edge types during iterative decoding, where the symmetry between the accumulator (ACC) and single parity-check (SPC) branches facilitates balanced information exchange. Second, a full-dimensional extrinsic information transfer (FEXIT) chart suitable for FET-LDPC codes is constructed, capturing the mutual information flow across branches. Third, a collaborative optimization model is designed by integrating the FEXIT chart with multi-constraint linear programming (LP) to perform asymmetric optimization for different edge types. The simulation results show that the proposed method achieves significant performance improvement over unoptimized codes in additive white Gaussian noise (AWGN) channels, particularly at a bit error rate (BER) of 10⁻⁶. Full article

The class of tier-based strictly 2-local (TSL2) languages has been shown to be useful in modeling patterns across different linguistic domains. This paper discusses the learnability of the intersection closure of the TSL2 languages, multi-TSL2 (MTSL2). I present two learning algorithms, one that learns a relevant subclass of MTSL in polynomial time, and one that learns MTSL proper but requires potentially exponential time. Both algorithms generalize across tree-based and string-based data representations. I show that each algorithm correctly learns its target class from a limited sample of positive data, and discuss the tradeoffs between the two. The success of these algorithms delivers a key learning result for subregular linguistics, and demonstrates the utility of subregular language classes in developing a unified learning theory that spans different linguistic domains. Full article

The theory of analytic functions remains a fundamental area of geometric function theory, with particular emphasis on coefficient problems, differential subordinations, and determinant estimates. Motivated by recent developments in fractional calculus and quantum calculus, this paper introduces two new subclasses of normalized analytic functions by employing the subordination principle in combination with the q-derivative operator and the q-Sălăgeăn differential operator within the framework of quantum calculus. The inclusion of fractional and q-calculus techniques provides a more flexible and generalized approach to classical problems in complex analysis, enabling deeper structural insights into analytic function classes. Using the subordination framework, we derive coefficient relations for the proposed subclasses. Furthermore, we establish sharp upper bounds for the Fekete–Szegö functional $|a_3-\delta a_2^2|$ and for the second Hankel determinant $H_{2,2}\left(f\right)=a_2{a}_4-a_3^2$. The obtained results extend and unify several known works in the literature and demonstrate how the interaction between fractional calculus, quantum operators, and subordination theory can be effectively used in geometric function theory. Finally, the presented approach opens the door for further investigations involving higher-order Hankel determinants, other subclasses of analytic functions, and potential extensions involving special functions and fractional operators. Full article

River ice products from optical satellites are still dominated by binary ice–water or ice–snow discrimination, leaving within-ice spectral heterogeneity largely unresolved. This study benchmarks how far river ice can be subclassified from multispectral reflectance alone on the Tibetan Plateau using Landsat 5/7, Landsat 8/9, and Sentinel-2 surface-reflectance imagery. We compiled 356 winter scenes acquired between 2000 and 2024 across eight Tibetan Plateau basins, delineated river ice using NDSI and RDRI, and extracted 24,674 pixel-level spectra. To define reproducible subclasses, we applied K-means clustering guided by the Silhouette Coefficient, Davies–Bouldin index, Calinski–Harabasz index, and Gap Statistic. Combined with stratified visual interpretation, this approach consistently supported four optical spectral subclasses: thin-snow-covered ice, thick ice cover, thin ice, and frazil ice. Within-sensor classification accuracy remained extremely high (overall accuracy ≥ 0.948; kappa ≥ 0.929), with the Backpropagation Neural Network (BPNN) and tree ensembles performing best. Crucially, evaluating the optimal BPNN architecture revealed exceptional multi-dimensional generalizability: a Leave-One-Basin-Out spatial cross-validation yielded a stable average OA > 99% with an average Kappa > 0.98, while a unified multi-sensor model achieved a robust OA of 90.14% and a Kappa of 0.86. The most stable discriminative cues were visible-band brightness, reflectance turnover near ~0.7 μm, and shortwave-infrared sensitivity to effective thickness and surface wetness. These results provide a sensor-aware benchmark for practical optical river ice spectral subclassification and clarify which multispectral bands most strongly constrain subclass separability. Full article

In the evolving landscape of next-generation wireless networks, ensuring seamless mobility and high-quality service delivery for millions of devices and end users in dynamic scenarios, where the speed of a wireless device keeps changing with time, is important. The mobility, seamless and continuous connectivity, and ultra-dense deployment of wireless networks pose a significant challenge. Seamless and successful transition of a wireless device from point A to point B in variable-speed scenarios is one of the major challenges in future networks. This paper presents a novel Deep Q-Network (DQN)-based reinforcement learning (RL) framework integrated with Software-Defined Networking (SDN) for intelligent mobility management in hybrid 5G cellular networks consisting of macro and small base stations. The proposed system architecture utilizes a SDN controller to receive real-time user measurement reports, including Reference Signal Received Power (RSRP), Signal-to-Interference Noise Ratio (SINR), and user velocity, thereby classifying user mobility into distinct subclasses and dynamically determining optimal handover parameters. Leveraging the DQN’s capability to learn adaptive strategies, the model enables seamless transitions between macro and small cells based on mobility profiles, thereby enhancing Quality of Service (QoS) metrics such as latency, throughput, and handover efficiency. Simulation results demonstrate consistent performance improvements over baseline and existing models in ultra-dense network environments, with handover success rates 10–15% higher across SINR and different speed scenarios, while maintaining a packet failure rate of 9% across different speed scenarios, allowing more users to transition during various environmental changes seamlessly. Our proposed model is compared with our previous work and Learning-based Intelligent Mobility Management (LIM2) models. Specifically, our previous work focused on adaptive handover management primarily for high-speed train scenarios using a learning-assisted approach tailored to fixed high-mobility scenarios, with a limitation to single mobility conditions. This work contributes to the field of merging SDN’s centralized control with the predictive power of RL, paving the way for more resilient and responsive mobile networks in high-mobility scenarios. The proposed approach incorporates subclass-based mobility action abstraction, joint optimization of TTT and hysteresis margin, and dynamic target cell selection using global network information available at the SDN controller. Full article

We investigate the arrow of time problem in the context of gravitational collapse of radiating stars in higher dimensions for both neutral and charged matter. The interior spacetime is described by a shear-free, isotropic spherically symmetric metric filled with a dissipative fluid. The exterior spacetime of the radiating star is taken as the higher dimensional Vaidya metric. We establish that the arrow of time, measured by the epoch function, is opposite to the thermodynamic arrow of time for all dimensions in such spacetimes. The physical consequences of our results are considered. Our results conform with previous studies on shear-free spherical collapse, which suggests avoidance of the naked singularity as the end state results in a wrong arrow of time, indicating a fundamental problem with the local application of the epoch functions to test the Weyl curvature hypothesis, which we have demonstrated in the context of shear-free, pressure-isotropic subclass of radiating spherical collapse for dimension four and beyond. Full article

Background: Inflammatory signaling and oxidative stress machinery are interconnected and play roles in apoptosis, proliferation, redox state control, and the progression of many diseases, including cancer. The marine environment harbors a wealth of organisms that produce a wide variety of bioactive molecules with significant biological activities. Over the last decade, the advent of AI-driven approaches has enhanced the study and analysis of peptides, helping to reduce costly and time-consuming conventional laboratory testing, validation, and synthetic procedures. Methods: In this study, we predicted the antioxidative and anti-inflammatory activities of peptides isolated from proteomic data obtained from circulating cells and humoral components of the sea cucumber defense system using a bioinformatic workflow based on different artificial intelligence tools. Results: We identified 40 top-ranked peptides with antioxidative and anti-inflammatory activity and a sub-class of eight peptides shared by FreD domains. Molecular docking and molecular dynamics simulations showed that they have active binding sites for different key molecules involved in inflammatory and oxidative processes. Conclusions: The results showed that the peptides highlighted by our analysis workflow can be identified as potential molecules used as therapeutic strategies for diseases by targeting both inflammatory and oxidative processes. Full article

In this paper, a new class of special polynomials, called the Sheffer-type general-$\lambda$-matrix polynomials, is introduced within the framework of the monomiality principle. This family is obtained by combining the structure of Sheffer sequences with the theory of general-$\lambda$ matrix polynomials, which leads to a unified formulation encompassing several polynomial families. Fundamental properties of the proposed polynomials are established, including their generating function, explicit series representation, summation formulas, quasi-monomial structure, differential relations, and determinant representation. The proposed framework addresses an important problem in the theory of special functions: the systematic construction of matrix-valued polynomial families that simultaneously generalize both classical scalar polynomials and existing matrix polynomial hierarchies. Such a unified structure is of broad significance, with applications in quantum mechanics (wave function expansions), mathematical physics (matrix differential equations and spectral problems), approximation theory, and the study of special functions in the matrix domain. Several hybrid forms of the proposed family are derived through appropriate choices of the defining functions, which yield polynomial subclasses related to classical families such as Hermite, Laguerre, Bessel, and Poisson–Charlier polynomials. These subclasses illustrate how the proposed framework provides a systematic approach for constructing and studying generalized polynomial structures. In each case, the matrix parameter L introduces a new layer of structural richness not present in the scalar setting, enabling the modelling of phenomena governed by matrix-valued spectral data. Furthermore, a numerical and graphical investigation of selected hybrid forms is carried out using Mathematica (version 14.3, 2025; Wolfram Research, Inc.). Surface plots, distributions of complex zeros, and real-zero patterns are presented for different parameter values, highlighting the influence of the parameters on the behavior and structural characteristics of the polynomials. Full article

Background: The emergence of SARS-CoV-2 variants necessitates the development of effective adjuvants to enhance subunit vaccine immunogenicity. Safe adjuvants are essential to enhance the immunogenicity of SARS-CoV-2 receptor-binding domain (RBD) subunit vaccines. Traditional Chinese medicine polysaccharides are attractive candidates due to their immunomodulatory properties. Methods: Female BALB/c mice (6–8 weeks) were immunized on days 0, 7, and 21 with an RBD protein (20 μg) alone or formulated with Poria cocos polysaccharide fraction PCP-I or PCP-II (200 μg), Isatis indigotica polysaccharide, or aluminum adjuvant; PBS served as a control. RBD-specific total IgG and subclasses were quantified by ELISA on day 7 after the third immunization. Neutralizing antibody titers were measured by a pseudovirus assay on days 14, 28, and 56 after the first immunization. Splenic CD19⁺ B cells were analyzed by flow cytometry, and antigen-stimulated IFN-γ and IL-4 spot-forming cells were quantified by ELISpot. Results: PCP-II significantly increased RBD-specific total IgG and IgG1 compared with RBD alone and other formulations, whereas IgG2a and IgG2b remained unchanged. Both PCP-I and PCP-II increased neutralizing titers versus RBD alone, and PCP-II showed an earlier and sustained increase in neutralizing responses through day 56. PCP-II showed a non-significant increase in splenic CD19⁺ B cell frequency. PCP-I and PCP-II markedly increased IFN-γ-secreting splenocytes without increasing IL-4, indicating enhanced antigen-specific cellular responses. Conclusion: In this comparative evaluation of traditional Chinese medicine polysaccharide candidates in a SARS-CoV-2 RBD subunit vaccine model, PCP-II showed the most prominent adjuvant activity. PCP-II enhanced antigen-specific humoral immunogenicity, improved neutralizing antibody responses, and was associated with increased IFN-γ-related cellular responses, supporting its potential as a candidate polysaccharide adjuvant for protein subunit vaccines. Full article

We present a high-precision joint gravitational-lensing and kinematic analysis of nine massive galaxy clusters from the CLASH and CLASH-VLT surveys to test chameleon screening gravity and its $f\left(R\right)$ sub-class at Mpc scales. We investigate the dependence on the assumed parametrization of the total cluster mass profile by adopting three models, namely Navarro–Frenk–White (NFW), Burkert, and Hernquist. When cuspy models (NFW or Hernquist) are assumed in the general chameleon framework, the combined constraints from the nine clusters are fully consistent with General Relativity (GR), excluding large regions of the modified-gravity parameter space (the coupling constant $\mathcal{Q}$ and the background chameleon field ${\varphi }_{\infty }$), providing one of the tightest bounds on general chameleon models with clusters to date. In contrast, adopting a Burkert profile—disfavored by lensing data—leads to a mild (∼2σ) departure from the GR expectation in joint analysis. When considering the $f\left(R\right)$ sub-case, we obtain a bound on the background scalaron field of $|f_R| \lesssim 2-5 \times {10}^{-5}$ (95% C.L.) for NFW and Hernquist models, in agreement with current constraints at cosmological scales, and an apparent deviation from standard gravity of ${log}_{10}|f_R|=-4.7\pm 1.2$ for the Burkert case. We investigate the impact of systematics in the kinematical analysis, showing that the tension is mitigated when clusters exhibiting clear dynamical disturbance are excluded from the sample. Our results show that galaxy clusters provide competitive tests of screened modified gravity at mega-parsec scales, while highlighting the critical role of accurate mass modeling and dynamical-state assessment. The upcoming generation of wide-field lensing surveys and spectroscopic follow-up programs will enable similar analyses on substantially larger samples, offering the prospect of tightening cluster-based constraints on gravity and the dark sector. Full article