Reduced basis solvers for unfitted methods on parameterized domains

With the increased need for information exchanges, the communication part of stochastic nonlinear multiagent systems (MASs) suffers from the influence of limited communication resources, which brings challenges to the efficiency of the information exchange between agents. This paper investigates the synchronous self-triggered adaptive tracking control problem for stochastic nonlinear MASs. To begin with, a novel synchronous self-triggered mechanism is constructed based on nonlinear impulsive dynamics, which ensures simultaneous updates of agent states and adaptive laws without continuous monitoring. Besides, this mechanism ensures the consistency of triggering instants for the same-order states of multiple agents, thereby effectively avoiding the communication congestion problem caused by asynchronous triggering. Next, a new class of adaptive triggering update law is designed, which expands the feasible parameter domain and enhances system flexibility. In addition, a first-order filter is introduced into the controller design to address the discontinuity of virtual control signal caused by the triggering mechanism. Based on the Lyapunov stability theory, it is shown that the designed controller can ensure that all signals in the closed-loop system stay bounded in probability. Finally, a simulation example is conducted to further demonstrate the validity of the presented control method.

Daytime dysfunction and SUDEP risk: Exploring the role of sleep and heart rate variability in epilepsy.

Transverse shear deformation plays a non-negligible role in lightweight periodic-core structures and motivates the use of shear-corrected reduced-order plate and beam models. However, the shear correction factor ks is often treated as a constant despite its strong dependence on cross-sectional heterogeneity and geometry. This work quantifies the global sensitivity of ks in corrugated paperboard by combining an energy-consistent pixel-based identification of the effective shear stiffness GA)eff with a space-filling exploration of the parameter domain. Representative three-ply (single-wall) and five-ply (double-wall) configurations are generated directly in the pixel domain using sinusoidal fluting descriptions and non-overlapping liner bands. The effective shear stiffness is obtained from a heterogeneous shear-energy equivalence, where a normalized two-dimensional shear-stress shape function is computed from pixel-based sectional descriptors and integrated with spatially varying shear moduli. Latin Hypercube Sampling is employed to explore wide ranges of flute period, height, and thickness, liner thicknesses, and liner-flute shear-modulus contrasts. Global sensitivity is reported using unit-free normalized indices, including log-elasticities (based on the slope of lnks versus lnx) and partial rank correlation coefficients. The results demonstrate that flute geometry is the primary driver of ks variability, while material contrast significantly modulates shear-energy localization, particularly in double-wall boards with two distinct flutings. The proposed framework enables high-throughput shear correction assessment and supports robust parameterized reduced-order models for corrugated structures.

Phase transition in quantum mechanics is interpreted as an evolution, at the end of which, typically, a parameter-dependent and Hermitizable Hamiltonian H(g) loses its observability. In the language of mathematics, such a “quantum catastrophe” occurs at an exceptional point of order N (EPN). Although the Hamiltonian H(g) itself becomes unphysical in the limit of g→gEPN, it is shown that it can play the role of an unperturbed operator in an innovative perturbation-approximation analysis of the vicinity of the EPN singularity. As long as such an analysis is elementary at N≤3 and purely numerical at N≥5, we pick up N=4 and demonstrate that for an arbitrary quantum system, the specific (i.e., already sufficiently phenomenologically rich) EP4 degeneracy becomes accessible via a unitary evolution process. This process is shown realizable inside a parametric domain Dphysical, the boundaries of which are determined, near gEP4, non-numerically. Possible relevance of such a mathematical result in the context of non-Hermitian photonics is emphasized.

The global dynamics of a herringbone planetary gear system under stochastic excitations are analyzed, Specifically, excitation parameters following a normal distribution are generated via the Box-Muller transformation, while the Largest Lyapunov Exponent (LLE) and cell mapping spatial discretization are jointly applied to the system’s global analysis. The results show that periodic subdomains are intricately nested at the boundaries of the chaotic subdomain and with the higher-periodic enclosed by the lower-periodic in the parametric solution domain, quasi-periodic motion occurs in the sun gear speed range of [5200, 6000] r/min. In addition, lower periodic subdomains (e.g. P1 and P2) typically exhibit regular borders, increasing the damping ratio above 0.15 or reducing the backlash below 0.08 can weaken the vibration response, meanwhile, a P13 basin of attraction is validated at the [0, 0] state cell. Stochasticity induces chaos to erode periodic subdomains across their boundaries and with numerous scattered chaotic cells evolving into the P2 and P1 regions, enhancing the stochasticity of damping ratio or backlash significantly impairs high-speed vibration stability, and stochasticity acting on backlash more easily induces scattered chaotic cell distribution in the state space. These findings could help optimize the dynamic parameter design of gear systems and thereby mitigate their vibrations.

Abstract Wall shear stress (WSS) serves as a crucial link between the dynamics of blood flow and the biological mechanisms that underlie various cardiovascular diseases. This study investigates WSS fluctuations in a collapsible wavy channel using a two-dimensional (2D) fluid-structure interaction (FSI) model. A combination of immersed boundary-lattice Boltzmann and the generalized interpolation material point methods solves the nonlinear coupled equations. The effects of key parameters on WSS fluctuations, including Reynolds number, pulsatile flow period, and external pressures, are analyzed for two systems: one with a wall constraint and one without the constraint. The results show that decreasing the period of pulsatile flow and increasing external pressure contribute to increased local WSS fluctuations by destabilizing the system through a fluid symmetry-breaking mechanism. Across all investigated parameter domains, the unconstrained system demonstrates a significantly enhanced ability to minimize WSS fluctuations. Since the wavy channel represents a simplified model of a stented artery, the results obtained in this study can be used to guide and optimize the stent design. The two-dimensional simulation is chosen for its low computational cost and its ability to capture key mechanisms. Future research can extend to three-dimensional models for a more comprehensive analysis.

This paper introduces an innovative stochastic diffusion process with relation to a new formulation of the logistic curve and explores the use of simulated annealing to estimate by maximum likelihood the process parameters. At first, the principal characteristics of the process are determined, notably the probability density and mean functions. Next, the parameter estimation is done by the maximum likelihood technique with the use of discrete sampling. For this purpose, the simulated annealing method is applied after bounding the parameters domain by a step-by-step approach. Finally, in order to justify this approach, we enclose the results obtained by different simulation examples, and we give an application related to an example of a microorganism growth.

ABSTRACT In response of the recurrent bifurcation and chaotic phenomena observed in second‐order inverters, this study proposes an improved exponential reaching law sliding mode control strategy, predicated on the principles of sliding mode control and its requisite reaching conditions. A discrete iterative model is formulated utilizing stroboscopic mapping theory, and the intricate dynamic evolution patterns of the inverter are meticulously examined through various analytical tools, including bifurcation diagrams, folding diagrams and spectral diagrams. Furthermore, leveraging the fast‐scale stability theorem, the research investigates the stable operational domain of the system's control parameters. To validate the enhanced performance of the proposed method, numerical simulation experiments were carried out under the traditional exponential reaching law. These simulations encompassed bifurcation analyses of the control parameters and , as well as the circuit parameters , and , along with rapid stability verification. A comparative analysis was also performed against the improved method. The results demonstrate that the system is more prone to chaotic behavior under the traditional exponential reaching law, with a relatively narrow parameter stability region. In contrast, the improved exponential reaching law significantly expands the stable parameter range, enhancing overall system robustness. Furthermore, to mitigate instability caused by parameter perturbations, an extended delayed feedback chaos control strategy was integrated into the improved exponential sliding mode controlled second‐order inverter. Numerical simulations confirmed the feasibility and effectiveness of this chaos control approach. The findings provide valuable insights for the optimized design, dynamic tuning, and reliable steady‐state operation of second‐order inverters.

In this paper, the author introduces new methods to construct Archimedean copulas. The generator of each copula fulfills the sufficient conditions as regards the boundary and being continuous, decreasing, and convex. Each inverse generator also fulfills the necessary conditions as regards the boundary conditions, marginal uniformity, and 2-increasing properties. Although these copulas satisfy these conditions, they have some limitations. They do not cover the entire dependency spectrum, ranging from perfect negative dependency to perfect positive dependency, passing through the state of independence. Both copulas exhibit positive dependency and upper tail dependency, but neither has lower tail dependency. The product copula is present for each of them. For each copula, the author discusses the derivation, the properties, whether it has a singular part or not, the Kendall tau measure for dependency, and the upper and lower tail dependency. The article shows figures for depicting the joint CDF, and joint PDF for each copula. For each copula, inference is supported by real data analysis using the inference function for margins (IFM) for estimation. The new copulas, Attia-1 and Attia-2 inherent both the limitations and the advantages of the classical Archimedean copulas as discussed in the introduction. The two new copulas and the Gumbel copula exhibit similarity for modelling weak positive association and upper tail dependence. However, both new copulas can add new substantial contributions to the field of copula theory. The new copula, Attia-1 has a domain (0,1], while Attia-2 copula has a domain [-1,1]-{0}. The Attia-1 copula allows the dependency parameter exploration near the zero adding finer control of the weak positive association and extreme upper tail co-occurrences. Attia-2 copula allows the dependency parameter exploration near the zero and negative dependency parameter adding finer control over the weak positive association and the extreme upper tail co-occurrence. The Gumbel copula also model the weak positive association and upper tail dependency but has a parameter domain that is bounded below by 1. So the new copulas extend the domain of modelling weak positive association and upper tail dependency that are encountered in many medical and financial datasets where the variables are mostly independent but extreme values can co-occur. This enhances the flexibility of Archimedean copula. The Attia-2 copula can be generalized by replacing the (2) in the exponent by a free parameter to partially decouple the global dependency from the tail dependency. This also adds more flexibility to the Archimedean copula.

This study aims to evaluate and compare cardiac autonomic function, specifically through heart rate variability (HRV), between individuals with bronchiectasis and their age- and gender-matched healthy counterparts. This study employed a case-control design, involving 60 participants diagnosed with bronchiectasis (cases) and a control group of healthy individuals matched by age and gender. HRV data was collected over a five-minute interval, focusing on frequency domain parameters including total power, very low frequency (VLF), low frequency (LF), high frequency (HF), and the LF/HF ratio. The bronchiectasis group exhibited a significantly elevated LF/HF ratio, indicating a shift in cardiac sympathovagal balance, relative to the control group (2.25 ± 0.39 vs. 2.05 ± 0.38; p = 0.006). Additionally, marked differences were found in specific frequency domain parameters: LF (2.33 ± 0.55 vs. 2.55 ± 0.46; p = 0.021) and HF (2.06 ± 0.75 vs. 2.5 ± 0.56; p = 0.001). The results suggest a notable disturbance in cardiac autonomic regulation among individuals with bronchiectasis, compared to healthy individuals.

In this paper, the author utilizes the frailty model to construct a parametric new Archimedean copula, Attia-3 copula. This copula depends on the transformed Median Based Unit Rayleigh (MBUR) distribution to an unbounded distribution defined on the interval from zero to infinity. In the paper, the joint PDF and CDF of the copula are derived for two bivariate distributions. The singularity of the copula is explained. The generator and inverse generator of the new copula are explored to depict the decreasing and convex nature of the generator. The Kendall tau measure of dependency is derived. Inference Function for Margin (IFM) is explored and utilized in real data analysis. The novelty of Attia-3 copula is that it is constructed using the frailty models that account for unobserved heterogeneity in the time to event data serving as a multiplicative element on the hazard rate. Attia-3 copula which is based on frailty model and cox proportional hazard model can only model positive dependency. The domain of the dependency parameter is (0,1]. The Kendall tau coefficient is (1-0.8 θ), where θ is the dependency parameter. It can model upper and lower tail dependency, λU=2-2θ and λL= 2-2θ . The upper and the lower tail coefficients are decreasing function in the parameter. The Kendall tau is also a decreasing function in the parameter. For a copula to model simultaneously upper and lower tail dependency with a single parameter without switching families or using mixture is very attractive for applications such as medical complications due to simultaneous deteriorations in organs, insurances losses as joint small-moderate losses, and environmental risks in the form of joint droughts are stronger than floods. The limitation of the Attia-3 is modelling only positive dependency and lack of singular part which denotes that the probability mass is concentrated along the diagonal signifying strong concurrences and permitting modelling ties that the continuous part fights to model. There is no product copula for this copula.

Soft set theory constitutes a logically rigorous and algebraically expressive formalism for representing systems permeated by ambiguity, epistemic uncertainty, and parameter-dependent variability. In this context, the present study introduces the soft union–star product, a novel binary operation defined on soft sets whose parameter do-mains are endowed with an intrinsic group-theoretic structure. Formulated within a strictly axiomatic framework, the operation is proven to exhibit full compatibility with generalized formulations of soft subsethood and soft equality. A comprehensive algebraic analysis is conducted to establish its core structural invariants, including closure, associativity, commutativity, and idempotency. Moreover, the operation’s behavior is rigorously characterized in relation to the identity and absorbing elements, as well as its interaction with the null and absolute soft sets. The findings confirm that the soft union–star product satisfies all algebraic conditions imposed by group-parameterized domains, thereby generating a robust and internally coherent algebraic structure over the universe of soft sets. Beyond its foundational significance, the operation meaningfully enriches the operational landscape of soft set theory and provides a formal platform for advancing a generalized soft group theory. Its structural compatibility with key relational constructs—particularly generalized soft equalities and inclusion hierarchies—underscores its potential utility in diverse application domains, including algebraic abstraction, uncertainty-sensitive classification, and multi-criteria decision-making. As such, this work contributes not only a substantive theoretical advancement but also a mathematically principled pathway for practical deployment in uncertainty-aware systems.

Abstract Offshore wind farm monitoring data faces challenges such as large data volumes, susceptibility to tampering, information leakage, and malicious attacks during transmission and storage. To address these issues, a lightweight encryption method is proposed. Firstly, to overcome the limitations of discontinuous parameter intervals and chaotic degradation in existing chaotic systems, a modular chaotic method is proposed to construct a two-dimensional discrete chaotic system(2D-DCS). This approach facilitates the dynamic adjustment of the Lyapunov exponent, effectively preventing chaotic degradation within continuous parameter domains. Next, chaotic sequences generated by the 2D-DCS are used for dynamic DNA encoding of the data to produce nucleotide sequences, which are then processed using extended DNA operation rules (from 4 to 8) to further enhance the data's diffusion. Finally, simulation experiments and security tests are conducted to validate the proposed method. The results show that the encrypted data achieves an average information entropy of 7.9993. Moreover, compared to some existing chaotic encryption algorithms, the proposed method reduces encryption/decryption delays by 38%-52%, fully meeting the real-time transmission and security requirements of offshore wind farm monitoring data.

In this work, a novel framework is proposed which includes Hjorth parameters as features from time and time-frequency domain (Multi-Domain) and attention-enhanced temporal modeling, to classify epileptic seizure stages, namely normal, inter-ictal, and ictal. Three different approaches are compared, i.e. Hjorth parameters in time domain, time-frequency domain, and multi-domain. In time-frequency domain, Hjorth parameters are derived from the wavelet coefficients obtained using Discrete Wavelet Transform (DWT). The extracted features are then fed to a 1D Convolutional Neural Network (CNN), Bidirectional Long Short-Term Memory (BiLSTM), and attention mechanism. The performance of the proposed framework is evaluated on Bonn EEG dataset using different performance evaluation metrics namely precision, recall, F1-score, and accuracy. The binary, three-class, and five-class seizure classification are examined using the proposed framework. The validation of the model is performed through the 10-fold cross-validation with sample level partitioning. Experimental findings show that the proposed framework with multi-domain features has given outstanding performance with 98.40, 98.00, and 85.40% test classification accuracy for binary, three-class, and five-class discrimination, respectively.

The study examines center-of-pressure dynamics in the anteroposterior direction (CoPx). It is assumed that CoPx dynamics involve two dynamical processes during quiet stance. The first process describes fast postural corrections around the given equilibrium. The second process describes slowly changing equilibrium point which is assumed to be controlled by higher nervous system. We proposed a novel system of coupled stochastic differential equations, double Ornstein-Uhlenbeck process (dOU), where two processes are described in terms of two Ornstein-Uhlenbeck processes (OU). Specifically, the equilibrium point of the fast postural correction OU process is controlled by the slowly evolving equilibrium point OU process. We derived closed forms of correlation and the power spectral density (PSD) functions of the processes. We conducted experiments with three repetitions from eight healthy subjects at four different sensory conditions on rigid and compliant surfaces. We optimized four model parameters in frequency domain by comparing averaged PSD estimates of experimental data and analytical PSD functions at each sensory combination. We found that mean reversion rate λ of the first OU governing postural reflexes around a given equilibrium, was significantly higher on the rigid surface. Consequently, the dynamics of postural sway on rigid surface were predominantly captured by a single OU. Contrarily, on compliant surface, λ approached the second OU's mean reversion rate, κ, and we observed a significant increase in its volatility, [Formula: see text]. Findings suggest that two-level CoPx dynamics become more pronounced under the compliant surface. We showed that dOU is capable of capturing bounded diffusive characteristics of CoPx dynamics.

Vaginal hyaluronic acid (HA) filler is a minimally invasive option primarily aimed at functional improvement (sexual function and pelvic muscle performance), with aesthetic effects considered secondary. The procedure aims to address changes in the female genitalia that may occur due to aging, childbirth, or other factors. This review aims to provide a detailed overview of the techniques involved, anatomical considerations, safety profiles, and clinical outcomes associated with vaginal filler injections. In this study, 42 women (24 premenopausal, 18 postmenopausal) underwent posterior vaginal wall augmentation using cross-linked hyaluronic acid, volume ranging from 3-5 cc (e.p.t.q.® Lidocaine S 300 and e.p.t.q.® eve X, JETEMA Co., Ltd. Korea), which has an expected reabsorption period of approximately 9-12months. Outcomes were assessed at baseline, 6, and 12months. Female sexual function was evaluated using the Female Sexual Function Index (FSFI), which measures six domains: desire, arousal, lubrication, orgasm, satisfaction, and pain. Pelvic floor muscle strength and function were objectively assessed using the Peritron perineometer, which records resting pressure, peak pressure, average pressure, and contraction duration. All 42 participants completed the 12month follow-up, with improvements in every FSFI domain and Peritron parameter observed at 6months and maintained through 12months. Participant satisfaction increased from 71% at 6months to 81% at 12months, and no participants reported dissatisfaction at any time point. This study demonstrates the potential of vaginal filler treatment to positively impact female sexual well-being. Both subjective reports of satisfaction and objective physiological measures indicate improvements following the procedure. This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .

Quantitative appreciation of electronic substituent effects is beneficial across the chemical sciences, from reaction kinetics and catalysis to functional materials design and enzymatic processes. While Hammett parameters (σ constants) constitute the most widely invoked paradigm, their determination for structurally complex functional groups is often impractical by traditional empirical means. Herein, we demonstrate that the reversible one-step, 2-e− reduction of linearly functionalized 1,1′,3,3′-tetraethoxycarbonyl-6,6′-biazulene provides a simple electrochemical readout of effective Hammett constants. By design, the values obtained align closely with the conventional σp descriptors pertaining to benzenoid systems. This approach not only helps reevaluate previously reported Hammett values but also quantifies the role of intramolecular hydrogen bonding (e.g., CCreated by potrace 1.16, written by Peter Selinger 2001-2019]]>O⋯H–S) and enables determining effective σ constants (σeff) for “designer” functional groups, such as –SAuPPh3 and –NCCr(CO)5. Moreover, the long-range net electron donor/acceptor influence of the substituents –S−, –SAuPPh3, –SH, –SCH2CH2CO2CH2CH3, and –NCCr(CO)5 on the [(–NC)Cr(CO)5] 13C NMR reporter across the 6,6′-biazulenic π-linker was unveiled through inverse-linear δ(13COtrans) vs. δ(13CN) and δ(13COcis) vs. δ(13CN) correlations. The π-communication along the molecular axis of the 6,6′-biazulenic scaffold was further confirmed via Reflection-Absorption Infrared (RAIR) spectroscopic analysis of [(OC)5Cr(η1-2-isocyano-2′-mercapto-1,1′,3,3′-tetraethoxycarbonyl-6,6′-biazulene)] self-assembled on the Au(111) surface. By uniting redox tunability with rigorous linear free-energy correlations, this work offers both a versatile molecular platform and a straightforward electrochemical strategy for expanding and refining the Hammett parameter domain.

Electrical discharge machining (EDM) is widely used for machining hard and difficult-to-cut materials; however, the complex and nonlinear nature of the process makes the accurate prediction of key performance indicators challenging, particularly when only limited experimental data are available. In this study, a combined Taguchi design and Gaussian process regression (GPR) modeling framework is proposed to predict the surface roughness (Ra), material removal rate (MRR), and overcut (OC) in die-sinking EDM. An L18 Taguchi orthogonal array was employed to efficiently design experiments involving discharge current, pulse duration, and electrode material. GPR models with an automatic relevance determination (ARD) radial basis function kernel were developed to capture nonlinear relationships and varying parameter relevance. Model performance was evaluated using strict leave-one-out cross-validation (LOOCV). The developed GPR models achieved low prediction errors, with RMSE (MAE) values of 0.54 µm (0.41 µm) for Ra, 1.56 mm3/min (1.21 mm3/min) for MRR, and 0.0065 mm (0.0055 mm) for OC, corresponding to approximately 9.8%, 5.4%, and 5.9% of the respective response ranges. These results confirm stable and reliable predictive accuracy within the investigated parameter domain. Based on the validated surrogate models, multi-objective optimization was performed to identify Pareto-optimal process conditions, revealing graphite electrodes as the dominant choice within the feasible operating region. The proposed approach demonstrates that accurate and robust prediction of EDM performance can be achieved even with compact experimental datasets, providing a practical tool for process analysis and optimization.

Many engineering applications rely on numerical methods to simulate complex physical systems, which often entail prohibitive computational costs. Additionally, problems involving parametrized domains require the generation of a computational mesh for each configuration, which is an expensive and error-prone process. Surrogates based on proper orthogonal decomposition can alleviate this burden providing rapid predictions of partial differential equations (PDEs) solutions, but they rely on explicit geometric parametrizations and shared reference meshes, requirements rarely satisfied in practice. In this paper, we present a machine-learning-based workflow for predicting PDEs solutions and derived quantities in the context of geometric parametrization, without explicit knowledge of the geometric parameters or a common discretization of the geometries. The workflow is composed of two encoding blocks that independently encode the geometries and the associated outputs, and a mapping block that learns the relationship between the two encodings. The main contribution of this work is the introduction of a regularization method for INR-based encoders, designed to preserve the structure of the encoded spaces in the learned latent space. The workflow was tested on two problems. The prediction of one-dimensional signals (radial and thrust force) on a vertical axis turbine blade with varying thickness and curvature, and the prediction of the two-dimensional pressure coefficient fields associated with geometric variations of the Royal Aircraft Establishment airfoil 2822 (RAE2822). The experimental results demonstrate that the proposed regularization substantially enhances the overall predictive accuracy, reducing the prediction error of unseen configurations by one order of magnitude compared to more standard approaches.