We study the effective localization and forward stability of multinode Shepard operators for scattered data approximation. Although these operators are globally supported, the product structure of their inverse-distance weights yields a quantitatively controlled decay of the normalized weights, resulting in an effectively local numerical action. Using a geometric mean distance associated with each multinode subset, we derive explicit decay estimates for the normalized weights and algebraic bounds for the contribution of distant subsets. These results provide a rigorous basis for truncated implementations with controlled error. We also derive weighted approximation and stability estimates in terms of local Lebesgue functions, and develop a finite-precision analysis based on logarithmic weight evaluation, log-sum-exp normalization, and backward stable local Vandermonde solves. Under the stated assumptions, the fully computed operator is shown to be first-order forward stable. Numerical experiments confirm the effective localization mechanism, the practical sharpness of the stability bounds, and the accuracy of the truncated approximations.
This article investigates a queueing model relevant to telecommunication service infrastructures, where customer arrivals follow a phase-type (PH-type) distribution. Services are provided by a single server that processes customer requests in batches, constrained by a minimum ‘a’ and maximum ‘b’ batch size. The service time of each batch is heterogeneous, depending on the batch size, and is modeled using a PH-type distribution to accurately reflect real-world variability. The system is formulated as a Quasi-Birth-and-Death (QBD) process and analyzed using the matrix-analytic method (MAM) to derive the stationary joint distribution of the number of customers in the system and the phases of arrival and service processes. From an economic perspective, this model supports cost analysis by integrating performance measures such as queue lengths and server utilization. A metaheuristic soft optimization approach is employed to minimize operational costs, enabling efficient resource utilization. In the context of telecommunication networks, this framework can be applied to optimize batch processing in data transmission or call handling, leading to improved quality of service and reduced latency for end users.
We introduce VCKNet (Variable-sized Convolutional Kernel Network), an adaptive, modular, and lightweight Convolutional Neural Network (CNN) with three kernel-scale branches, channel attention, and dynamic fusion. These components recalibrate scale-aware features to reduce redundancy and support discriminative learning. The proposed architectural design preserves computational efficiency while maintaining a clear structural organization. Experiments on standard benchmarks and in-the-wild datasets show that VCKNet effectively captures multiscale structure, achieving performance competitive with that of deeper state-of-the-art models. Statistical analysis across repeated runs further confirms VCKNet’s stability. Computational cost and deployment efficiency analyses further support its suitability for resource-constrained and production-oriented scenarios where flexibility, stability, and conceptual clarity are essential.
We investigate stochastic bifurcations in the one-dimensional Gray–Scott model subjected to origin-preserving multiplicative noise. While the deterministic system is characterized by a rich bifurcation structure, including a codimension-2 Takens–Bogdanov point, we demonstrate how noise fundamentally reconfigures these transitions. Utilizing the stochastic parameterizing manifold (SPM) method, we derive reduced-order amplitude equations that capture the essential dynamics near critical points. Consistent with classical stochastic theory, we observe the σ2/2 threshold shift associated with the Wong–Zakai correction in the Itô interpretation. Our contribution lies in the systematic application and validation of this shift to the Gray–Scott bifurcation structure, quantifying how it leads to a robust noise-induced stabilization effect capable of suppressing deterministic oscillations and reinforcing the stability of the homogeneous steady state. Near the Takens–Bogdanov degeneracy, we derive explicit formulas for the effective parameter shifts, which quantify the noise-driven transition between distinct dynamical regimes. Furthermore, we analyze the dynamical role of the reference homogeneous state under origin-preserving multiplicative noise. The vanishing noise intensity at this state suggests a potential stabilization mechanism: linear stochastic analysis indicates that sufficiently strong noise can render the zero-amplitude state locally attracting. This points to the possibility of noise-induced pattern collapse, though rigorous characterization of the boundary behavior requires more refined analysis beyond the scope of the present work. Theoretical predictions, including explicit pullback attractor radii for random limit cycles, are numerically supported by reduced-amplitude tests, full stochastic partial differential equation (SPDE) projection comparisons, and representative spatiotemporal simulations within the parameter regimes considered. These results provide a quantitative framework for understanding and controlling pattern formation in noisy nonlinear systems.
Within the framework of integral quadratic constraints, this paper conducts stability analysis for a class of networked control systems employing a novel semantic multi-packet parallel transmission mechanism. Such systems exhibit both aperiodic sampled-data and time-varying delay characteristics, and Lyapunov-based stability criteria are often overly conservative, making it difficult to fully characterize their time-varying dynamic behavior. To address this issue, a discrete-time feedback interconnection model suitable for the proposed semantic multi-packet parallel transmission strategy is first established via system discretization, laying a foundation for subsequent analysis. Furthermore, by fully exploiting the time-varying nature of delay parameters, stability conditions in the form of integral quadratic constraints are derived, which feature less conservatism than existing results. In addition, during theoretical derivation, the semantic error term is modeled as an extended operator, thereby ensuring the exponential stability of the system even in the presence of semantic error. Finally, numerical examples including automotive suspension systems and load frequency control of a single-area power system are provided, and simulation results verify the effectiveness and practicability of the proposed method.
This paper presents a novel adaptive fuzzy control approach for solving predefined-time synchronization problems in a class of chaotic systems. First, a new predefined-time stability criterion is introduced for general nonlinear systems. Based on this criterion, a novel sliding mode control surface is designed. To cope with system uncertainties and disturbances, the scheme combines fuzzy control with robust techniques, thereby enhancing the system’s adaptability and robustness. By constructing a well-defined Lyapunov function, it is rigorously proven that the synchronization error converges to zero within a predetermined time. Numerical simulations and comparisons with state-of-the-art algorithms demonstrate the significant effectiveness and superiority of this control approach.
This paper presents a hybrid model for medium- and long-term electricity demand forecasting, developed with the aim of achieving accurate forecasts on horizons ranging from a few weeks to several months. Univariate deep models show a significant drop in performance at higher time horizons and are unable to adequately model long-term nonlinearities and changes in electricity demand. To address these limitations, an approach is proposed that combines deterministic time-series decomposition, residual modeling using deep dilated convolutional networks (TitanResNet), and additional residual correction using the LightGBM model. In addition, the meta-model integrates two complementary components in order to achieve greater robustness and stability on long horizons.The proposed approach achieves strong long-horizon forecasting performance on the investigated dataset, especially on horizons from 720 to 2160 h, where MAPE≈4% and R2>0.95 under the adopted chronological protocol. By using climatological averages to generate future features, the framework preserves causality and remains applicable when true future meteorological measurements are unavailable. The results indicate that residual learning, deep convolutions, tree-based correction, and calibration-stage fusion provide a robust forecasting framework, while the broader generality of the approach requires validation on additional datasets.
This work investigates how toxin-mediated interactions and directed movements shape the emergence of coherent structures in plant–herbivore systems. The analysis focuses on a two-compartment model enclosing a toxin-dependent functional response and a cross-diffusion term that represents ecologically plausible herbivores’ movement towards, or away from, vegetation. Two distinct dynamical regimes arise depending on toxicity strength. Under weak toxicity, the system admits at most one biologically feasible coexistence equilibrium, which may lose stability through a Hopf bifurcation generating small-amplitude temporal oscillations. Under strong toxicity, the nonlinear functional response becomes non-monotonic, allowing for multiple coexistence equilibria and abrupt regime shifts. The influence of cross-diffusion on stability is also examined, identifying the conditions under which Turing instabilities and mixed spatiotemporal patterns occur. Near the corresponding bifurcation thresholds, Stuart-Landau amplitude equations are derived via weakly nonlinear analysis, providing a unified framework for the modulation of oscillatory, stationary, and combined Turing–Hopf modes. Numerical simulations corroborate the theoretical predictions, illustrating transitions from spatially uniform states to oscillations, spatial patterns, and mixed behavior. Overall, this manuscript highlights how chemical defences, nonlinear feedbacks, and movement strategies jointly determine the emergence, selection, and robustness of coherent structures in plant–herbivore systems.
In this paper, we present a general framework for constructively proving the existence of stationary localized solutions, spatially periodic solutions, and branches of spatially periodic solutions in the 1D Thomas model. Specifically, we develop the necessary analysis to compute explicit upper bounds required in a Newton–Kantorovich approach. Given an approximate solution ū, this approach relies on establishing that a well-chosen fixed point map is contracting on a neighborhood ū. For this matter, we construct an approximate inverse of the linearization around ū, and establish sufficient conditions under which the contraction is achieved. This provides a framework for which computer-assisted analysis can be applied to verify the existence and local uniqueness of solutions in a vicinity of ū, and control the linearization around ū. Furthermore, as the Thomas model has a non-polynomial nonlinearity, we will need to use different techniques to handle it during our analysis. Our contributions are to provide a partial answer to how one can approach rigorously verifying results in the Thomas model, to adapt and combine previously developed techniques to apply to the Thomas model, and to perform the computer-assisted analysis to obtain such results. The code to perform the rigorous proofs is available on Github at Blanco (2026).
Metapopulation models are powerful tools for capturing the spatio-temporal spread of infectious diseases. Models that explicitly account for traveler origins and destinations, such as Lagrangian metapopulation models, enable a detailed representation of mobility and traveling subpopulations. However, in densely connected networks, tracking these subpopulations leads to quadratic growth in system size with the number of spatial patches. While specific approaches reducing the effort of traveler state estimation have been proposed, these approaches are either model-specific or heuristic. Here, we introduce a Runge-Kutta (RK) stage-aligned computation of traveler states that leverages the precomputed intermediate stage values of explicit RK methods under the assumption of localized homogeneous mixing. We prove that the resulting numerical solution is identical to that of the standard Lagrangian formulation when solved with the corresponding RK method. For compartments without inflows, we further show that the exact same results can be obtained using a simple algebraic scaling based on the initial traveler share. When embedded in a recently proposed metapopulation framework that combines local dynamics with discrete mobility, the stage-aligned approach eliminates the need for heuristic traveler approximations. In contrast to the standard Lagrangian formulation, the resulting method enables efficient simulations by reducing the global ODE system to linear scaling in the number of patches, while the remaining quadratic interactions are handled through highly efficient algebraic updates. Numerical experiments confirm the theoretical results, demonstrating optimal convergence order. Benchmarks on fully connected networks with up to 1025 patches, 1024 local travel connections, and six age groups achieve speedups of up to 76 and 50 for first- and fourth-order Runge-Kutta methods, respectively.
Deoxysphingolipids (dSLs) are atypical sphingolipids that accumulate in several pathological settings, yet their impact on hematologic malignancies is poorly understood. Here, we investigate the pathways and mechanisms of deoxysphinganine (dSA) cytotoxicity in lymphoma cells and its potential as a therapeutic agent. dSA exhibited markedly greater cytotoxicity than canonical sphingoid bases in lymphoma cell lines, yet induced only cytostatic effects in normal human T cells, indicating a therapeutically exploitable window. Inhibition of ceramide synthase blocked the generation of deoxy(dihydro)ceramides, prevented mitochondrial depolarization, caspase activation, ER stress, and DNA damage, establishing CerS-dependent deoxysphingolipids as essential mediators of dSA-induced death. Mechanistically, dSA engaged a mitochondrial apoptotic pathway, with DNA damage occurring downstream of mitochondrial permeabilization and caspase activation, while PERK-driven ER stress occurred in parallel and was dispensable for cytotoxicity. Subtype-specific engagement of ER stress and DNA damage further suggests that dSL signaling is shaped by lineage context. The differential sensitivity between malignant lymphoid cells and normal T cells, together with the central role of CerS-derived deoxy(dihydro)ceramides, highlights deoxysphingolipid metabolism as a druggable vulnerability in lymphoma. These findings support further exploration of dSA-based strategies and targeted modulation of dSL synthesis as a novel therapeutic avenue for non-solid hematologic malignancies.
We investigate a spatially extended prey–predator system in which the prey population growth is subject to an additive Allee effect, while the predator is modelled as a generalist species whose growth is sustained by both prey consumption and intrinsic density-dependent reproduction governed by a modified Beverton–Holt mechanism reflecting sexual reproduction limitation and alternative food support. The trophic interaction is described through a Beddington–DeAngelis functional response. We investigate the stability of spatially homogeneous steady states and derive conditions for the Turing instability and Turing–Hopf interaction. Weakly nonlinear analysis near the Turing threshold yields amplitude equations that predict stationary pattern transitions among hexagonal, mixed hexagon–stripe, and stripe states. Numerical simulations reveal a rich variety of stationary and nonstationary structures, including hot spots, cold spots, labyrinths, spirals, concentric travelling waves (circles), target patterns, and spatiotemporal chaos. Spatiotemporal chaos is confirmed through four complementary diagnostic approaches, including spatial snapshots, temporal series analysis, max–min bifurcation diagrams, and largest Lyapunov exponent computation. The Allee effect and alternative food availability strongly influence persistence, extinction risk, and spatial self-organisation, while certain oscillatory states are found to evolve around a virtual (“ghost”) attractor rather than the spatially homogeneous positive steady state. These findings provide new ecological insights into how dispersal, low-density prey limitation, and alternative food resources interact to regulate spatial pattern formation, species persistence, the long–term resilience, and the stability or instability of ecological systems.
Whether the fecal metabolome differs according to intensive low-density lipoprotein cholesterol (LDL-C) target achievement among statin-treated patients is unclear. In this cross-sectional study, 124 statin-treated adults with chronic disease were stratified by fasting LDL-C into a target-achieved group (< 70 mg/dL, n = 52) and a target-not-achieved group (≥ 70 mg/dL, n = 72). Stool samples were profiled by untargeted ultra-high-performance liquid chromatography-tandem mass spectrometry, and multivariable models adjusted for age, sex, chronic kidney disease, and angiotensin-converting enzyme inhibitor/angiotensin receptor blocker use were used to identify metabolites independently associated with target achievement. Statin dose, treatment duration and glucose-lowering therapy were also compared between the groups. Paired 16S rRNA gene sequencing data available for a subset (n = 86) were used for integrative correlation and network analyses. Partial least-squares discriminant analysis showed separation between the two groups. Eight annotated metabolites-glutamine, glutamate, phenylalanine, N-acetyl-L-phenylalanine, L-methionine, N-acetyl-L-methionine, lysine, and N-methyl-D-aspartic acid, predominantly amino acids and their derivatives-were present at lower fecal levels in participants who achieved the LDL-C target. Metabolite set enrichment analysis implicated amino acid and nitrogen metabolism, and multiomics network analysis identified an Anaerotruncus-centered amino acid module with high degree centrality. In conclusion, LDL-C target achievement under statin therapy was associated with a coherent "low fecal amino acid" signature and an Anaerotruncus-linked microbe-metabolite hub. These findings suggest that intestinal nutrient handling and gut microbial amino acid metabolism may contribute to variability in LDL-C response, and they warrant prospective mechanistic evaluation.
Metabolic dysfunction-associated liver disease (MASLD) arises from the accumulation of triglycerides within the liver. MASLD can advance to metabolic dysfunction-associated steatohepatitis (MASH), cirrhosis, and hepatocellular carcinoma. Monoacylglycerol acyltransferase 2 (MOGAT2) is essential for triglyceride synthesis and plays a significant role in regulating lipid metabolism. Here, we demonstrate the ability of a new human MOGAT 2 inhibitor, VB-85387, to inhibit the development of MASLD/MASH and further define its effects on the key metabolic pathways that progress MASH development. MASLD/MASH was induced using a methionine, choline-deficient diet (LMCD) or by streptozotocin treatment combined with high fat diet feeding (STAM-HFD). VB-85387 significantly mitigated the severity of MASLD and reduced signs of MASH in mice subjected to these two distinct diets. VB-85387-treated mice exhibited decreased fibrosis, evidenced by reduced hepatic triglyceride concentrations, hydroxyproline levels, and collagen deposition. NAS scores were consistently lower in VB-85387-treated mice across both models. VB-85387-treated mice showed induced PPARα signaling and reduced SREBP transcription, demonstrating a likely role for VB-85387 in regulating lipogenesis and fatty acid β-oxidation. STAM-HFD treated mice showed lower NF-κBp65 activation, which was associated with lower TNFα expression. IL-1β and IFNβ levels were also both reduced, suggesting VB-85387 can reduce pro-inflammatory pattern recognition receptor signaling. In addition, treatment suppressed IL-4/IL-6-dependent JAK activation. Overall, VB-85387 inhibited MASLD development by reducing liver triglyceride levels, fibrosis, and meta-inflammatory signaling. VB-85387 was as effective or superior to the MOGAT2 inhibitor phase I clinical trial drug BMS-963272 in reducing MASLD and fibrosis. VB-85387 has considerable potential for developing therapeutics targeting MASLD/MASH.
