Search Results (170)

Time series data are fundamental for analyzing temporal dynamics and patterns, enabling researchers and practitioners to model, forecast, and support decision-making across a wide range of domains, such as finance, climate science, environmental studies, and signal processing. In the context of high-dimensional time series, the Vector Autoregressive model (VAR) is widely used, wherein each variable is modeled as a linear combination of lagged values of all variables in the system. However, the traditional VAR framework relies on the assumption of stationarity, which states that the autoregressive coefficients remain constant over time. Unfortunately, this assumption often fails in practice, especially in systems subject to structural breaks or evolving temporal dynamics. The Time-Varying Vector Autoregressive (TV-VAR) model has been developed to address this limitation, allowing model parameters to vary over time and thereby offering greater flexibility in capturing non-stationary behavior. In this study, we propose an enhanced modeling approach for the TV-VAR framework by incorporating minimization solvers in generalized additive models and one-sided kernel smoothing techniques. The effectiveness of the proposed methodology is assessed using simulations based on non-homogeneous Markov chains, accompanied by a detailed discussion of its advantages and limitations. Finally, we illustrate the practical utility of our approach using an application to real-world financial data. Full article

Introduction: Federated Learning (FL) is a distributed machine learning paradigm where a global model is collaboratively trained across multiple decentralized clients without exchanging raw data. This is especially important in sensor networks and edge intelligence, where data privacy, bandwidth constraints, and data locality are paramount. Traditional FL methods like FedAvg struggle with highly heterogeneous (non-IID) client data, which is common in these settings. Background: Traditional FL aggregation methods, such as FedAvg, weigh client updates primarily by dataset size, potentially overlooking the informativeness or diversity of each client’s contribution. These limitations are especially pronounced in sensor networks and IoT environments, where clients may hold sparse, unbalanced, or single-modality data. Methods: We propose FedEmerge, an entropy-guided aggregation approach that adjusts each client’s impact on the global model based on the information entropy of its local data distribution. This formulation introduces a principled way to quantify and reward data diversity, enabling an emergent collective learning dynamic in which globally informative updates drive convergence. Unlike existing methods that weigh updates by sample count or heuristics, FedEmerge prioritizes clients with more representative, high-entropy data. The FedEmerge algorithm is presented with full mathematical detail, and we prove its convergence under the Polyak–Łojasiewicz (PL) condition. Results: Theoretical analysis shows that FedEmerge achieves linear convergence to the optimal model under standard assumptions (smoothness and PL condition), similar to centralized gradient descent. Empirically, FedEmerge improves global model accuracy and convergence speed on highly skewed non-IID benchmarks, and it reduces performance disparities among clients compared to FedAvg. Evaluations on CIFAR-10 (non-IID), Federated EMNIST, and Shakespeare datasets confirm its effectiveness in practical edge-learning settings. Conclusions: This entropy-guided federated strategy demonstrates that weighting client updates by data diversity enhances learning outcomes in heterogeneous networks. The approach preserves privacy like standard FL and adds minimal computation overhead, making it a practical solution for real-world federated systems. Full article

Purpose: Many individuals with stroke partake in rehabilitation to improve their movements. Rehabilitation operates on the assumption that individuals with stroke can use visual feedback from their movements or visual cues from a therapist to improve their movements through practice. However, this type of visuomotor learning can be impaired after stroke. It is unclear whether and how learning impairments relate to impairments in movement. Here, we examined the relationship between learning and movement impairments after stroke. Methods: We recruited adults with first-time unilateral stroke and controls matched for overall age and sex. The participants performed a visuomotor learning task in a Kinarm exoskeleton robot. The task assessed how they adapted their reaching movements to a systematic visual disturbance that altered the relationship between the observed and actual motion of their hand. Learning was quantified as the extent to which the participants adapted their movements to the visual disturbance. A separate visually-guided reaching task was used to assess the straightness, direction, smoothness, and duration of their movements. The relationships between visuomotor adaptation and movement were analyzed using Spearman’s correlations. Control data were used to identify impairments in visuomotor adaptation and movement. The independence of these impairments was examined using Fisher’s exact tests. Results: Impairments in visuomotor adaptation (46.3%) and movement (73.2%) were common in participants with stroke (n = 41). We observed weak–moderate correlations between continuous measures of adaptation and movement performance (rho range: −0.44–0.58). Adaptation and movement impairments, identified using the range of performance in the control participants, were statistically independent (all p > 0.05). Conclusions: Movement impairments accounted for 34% of the variance in visuomotor adaptation at best. Our findings suggest that factors other than movement impairments may influence visuomotor adaptation after stroke. Full article

We study the stability of Weak Rescaled Pure Greedy Algorithms for convex optimization, WRPGA(co), in general Banach spaces. We obtain the convergence rates of WRPGA(co) with noise and errors under a weaker assumption for the modulus of smoothness of the objective function. The results show that the rate is almost the same as that of WRPGA(co) without noise and errors, which is optimal and independent of the spatial dimension. This makes WRPGA(co) more practically applicable and scalable for high-dimensional data. Furthermore, we apply WRPGA(co) with errors to the problem of m-term approximation and derive the optimal convergence rate. This indicates the flexibility of WRPGA(co) and its wide utility across machine learning and signal processing. Our numerical experiments verify the stability of WRPGA(co). Thus, WRPGA(co) is a desirable choice for practical implementation. Full article

Pipe–soil interaction encompasses the study of stress distributions and deformation mechanisms occurring between buried pipelines and their surrounding soil. Understanding the mechanical behavior of this coupled system is essential for the analysis of deformation patterns and failure modes in buried pipelines, thereby providing critical guidance for construction design and risk assessment protocols. Traditional analytical approaches have relied on classical mechanics theories and experimental methodologies; however, these approaches often incorporate excessive simplifications and assumptions that inadequately represent the complex properties of both soil and pipeline structures. Numerical simulation methodologies have emerged as viable alternatives for investigating pipe–soil interaction. Among these numerical approaches, Smoothed Particle Hydrodynamics (SPH)—an advanced Lagrangian meshless particle method—offers distinct advantages in modeling complex behaviors, including free surfaces, deformable boundaries, and large deformation scenarios that characterize pipe–soil interaction. This research establishes a pipe–soil interaction model for buried pipelines utilizing the SPH method, incorporating elastic–plastic constitutive relationships to represent soil behavior. The investigation examines lateral interaction mechanisms, vertical interaction responses in sandy soils, and the parametric influence of various soil properties on pipe–soil interaction characteristics. This study contributes insights into the application of meshfree numerical simulation techniques for pipe–soil interaction analysis, offering both engineering utility and theoretical advancement for pipeline infrastructure design and safety assessment. Full article

In this paper, we propose a novel alternating direction method of multipliers based on acceleration technique involving two symmetrical inertial terms for a class of nonconvex optimization problems with a two-block structure. To address the nonconvex subproblem, we introduce a proximal term to reduce the difficulty of solving this subproblem. For the smooth subproblem, we employ a gradient descent method on the augmented Lagrangian function, which significantly reduces the computational complexity. Under appropriate assumptions, we prove subsequential convergence of the algorithm. Moreover, when the generated sequence is bounded and the auxiliary function satisfies Kurdyka–Łojasiewicz property, we establish global convergence of the algorithm. Finally, effectiveness and superior performance of the proposed algorithm are validated through numerical experiments in signal processing and smoothly clipped absolute deviation penalty problems. Full article

Achieving high-order accuracy in finite difference/spectral methods for space-time fractional differential equations often relies on very restrictive and usually unrealistic smoothness assumptions in the spatial and/or temporal domains. For spatial discretization, spectral methods using smooth basis functions are commonly employed. However, spatial–fractional derivatives pose challenges, as they often lack guaranteed spatial smoothness, requiring non-smooth basis functions. In the temporal domain, finite difference schemes on uniformly graded meshes are commonly employed; however, achieving accuracy remains challenging for non-smooth solutions. In this paper, an efficient algorithm is adopted to improve the accuracy of finite difference/Pertrov–Galerkin spectral schemes for a time-space fractional reaction–diffusion equation, with a hyper-singular integral fractional Laplacian and non-smooth solutions in both time and space domains. The Pertrov–Galerkin spectral method is adapted using non-smooth generalized basis functions to discretize the spatial variable, and the L1 scheme on a non-uniform graded mesh is used to approximate the Caputo fractional derivative. The unconditional stability and convergence are established. The rate of convergence is $O\left(N^{\mu -\gamma }+K^{-min\{\rho \beta ,2-\beta \}}\right),$ achieved without requiring additional regularity assumptions on the solution. Finally, numerical results are provided to validate our theoretical findings. Full article

Accurate prediction of tool wear plays a vital role in improving machining quality in intelligent manufacturing. However, traditional Gaussian Process Regression (GPR) models are constrained by linear assumptions, while conventional filtering algorithms struggle in noisy environments with low signal-to-noise ratios. To address these challenges, this paper presents an innovative tool wear prediction method that integrates a nonlinear mean function and a multi-kernel function-optimized GPR model combined with an LSTM-enhanced particle filter algorithm. The approach incorporates the LSTM network into the state transition model, utilizing its strong time-series feature extraction capabilities to dynamically adjust particle weight distributions, significantly enhancing the accuracy of state estimation. Experimental results demonstrate that the proposed method reduces the mean absolute error (MAE) by 47.6% and improves the signal-to-noise ratio by 15.4% compared to traditional filtering approaches. By incorporating a nonlinear mean function based on machining parameters, the method effectively models the coupling relationships between cutting depth, spindle speed, feed rate, and wear, leading to a 31.09% reduction in MAE and a 42.61% reduction in RMSE compared to traditional linear models. The kernel function design employs a composite strategy using a Gaussian kernel and a 5/2 Matern kernel, achieving a balanced approach that captures both data smoothness and abrupt changes. This results in a 58.7% reduction in MAE and a 64.5% reduction in RMSE. This study successfully tackles key challenges in tool wear monitoring, such as noise suppression, nonlinear modeling, and non-stationary data handling, providing an efficient and stable solution for tool condition monitoring in complex manufacturing environments. Full article

In this paper, we consider the nonlinear elliptic equation $-\Delta u+V\left(x\right)u=g\left(x\right)u^{{\displaystyle \frac{n+2}{n-2}}-\epsilon }$ in a bounded, smooth domain $\Omega$ in ${\mathbb{R}}^n$, under zero Neumann boundary conditions, where $n\ge 4$, $\epsilon$ is a small positive parameter, and V and g are non-constant smooth positive functions on $\overline{\Omega }$. Under certain flatness conditions on the function g, we provide a complete description of the single interior blow-up scenario for solutions that weakly converge to zero. We also construct interior multipeaked solutions, both with isolated and clustered bubbles. The proofs of our results rely on a refined asymptotic expansion of the gradient of the corresponding functional. Furthermore, no assumption regarding the symmetry of the domain is required. Full article

In this paper, developed in the context of the Clean Sky 2 project SIENA (Scalability Investigation of hybrid-Electric concepts for Next-generation Aircraft), an extensive analysis is carried out to identify and accelerate the development of innovative propulsion technologies and architectures that can be scaled across five aircraft categories, from small General Aviation airplanes to long-range airliners. The assessed propulsive architectures consider various components such as batteries and fuel cells to provide electricity as well as electric motors and jet engines to provide thrust, combined to find feasible aircraft architectures that satisfy certification constraints and deliver the required performance. The results provide a comprehensive analysis of the impact of key technology performance indicators on aircraft performance. They also highlight technology switching points as well as the potential for scaling up technologies from smaller to larger aircraft based on different hypotheses and assumptions concerning the upcoming technological advancements of components crucial for the decarbonization of aviation. Given the considered scenarios, the common denominator of the obtained results is hydrogen as the main energy source. The presented work shows that for the underlying models and technology assumptions, hydrogen can be efficiently used by fuel cells for propulsive and system power for smaller aircraft (General Aviation, commuter and regional), typically driven by propellers. For short- to long-range jet aircraft, direct combustion of hydrogen combined with a fuel cell to power the on-board subsystems appears favorable. The results are obtained for two different temporal scenarios, 2030 and 2050, and are assessed using Payload-Range Energy Efficiency as the key performance indicator. Naturally, introducing such innovative architectures will face a lack of applicable regulation, which could hamper a smooth entry into service. These regulatory gaps are assessed, detailing the level of maturity in current regulations for the different technologies and aircraft categories. Full article

For the problem of large joint angular velocity and high input in the trajectory planning and control of robots, an explicit-time trajectory tracking for a state-constraint continuum free-floating space robot with smooth joint-path and low input is proposed. Employing the piecewise constant curvature (PCC) assumption as the modeling foundation for the continuum space robot and utilizing modified Rodriguez parameters (MRPs) to describe attitude errors, a pose error feedback kinematic model for the continuum space robot is established. Based on the Lagrangian method, a dynamic model for the continuum space robot is developed. Explicit time theory and pose feedback methods are employed for the trajectory planning of the continuum space robot. Using explicit time theory and sliding mode control, tracking control for the planned joint trajectory is conducted. The Lyapunov theory is utilized to demonstrate the convergence of the system tracking error within the explicit time. Finally, the combination of trajectory planning and tracking control enhances the control performance of the continuum space robot. Simulation results validate the effectiveness of the proposed methods. Full article

The agglomeration railway networks form the backbone of modern urban transport systems, providing safe and reliable access from home to work or school for thousands of residents of agglomeration districts. This article examines the possibilities and directions of development for the agglomeration railway of the city of Poznań, providing a comparative analysis of this system with the networks of the cities of Szczecin and Gdańsk. Each rail system was described and presented in terms of its most important features. The collected data were then collected in tabular form and based on them, a comparison was made using two methods: AHP and COPRAS. Both methods, although with different strengths, indicated the unquestionable advantage of the agglomeration railway in Gdańsk for the adopted assumptions. The Poznań network obtained the weakest result in light of the assumptions. The analysis showed aspects of passenger transport, the improvement of which is crucial for the development of public transport in Poznań, e.g., too low frequency of trains, the need to increase passengers’ awareness of the possibilities of using rail transport, or the need to create stops ensuring a smooth possibility of changing to another means of transport. Full article

In this paper, a completely smooth lower-order penalty method for solving a second-order cone mixed complementarity problem (SOCMCP) is studied. Four distinct types of smoothing functions are taken into account. According to this method, SOCMCP is approximated by asymptotically completely smooth lower-order penalty equations (CSLOPEs), which includes penalty and smoothing parameters. Under mild assumptions, the main results show that as the penalty parameter approaches positive infinity and the smooth parameter monotonically decreases to zero, the solution sequence of asymptotic CSLOPEs converges exponentially to the solution of SOCMCP. An algorithm based on this approach is developed, and numerical experiments demonstrate its feasibility. The performance profile of four specific smooth functions is given. The final results show that the numerical performance of CSLOPEs is better than that of a smooth-like lower-order penalty method. Full article

In this study, we analyze the convergence rate of Adagrad with momentum for non-convex optimization problems. We establish the first dimension-independent convergence rate under the $(L_0,L_1)$-smoothness assumption, which is a generalization of the standard L-smoothness. We show the $\mathcal{O}\left(\sqrt{1/T}\right)$ convergence rate under bounded noise in stochastic gradients, where the bound can scale with the current optimality gap and gradient norm. Full article

Distributed frameworks for statistical estimation and inference have become a critical toolkit for analyzing massive data efficiently. In this paper, we present distributed estimation for high-dimensional quantile regression with ${\mathsf{\ell }}_0$ constraint using iterative hard thresholding (IHT). We propose a communication-efficient distributed estimator which is linearly convergent to the true parameter up to the statistical precision of the model, despite the fact that the check loss minimization problem with an ${\mathsf{\ell }}_0$ constraint is neither strongly smooth nor convex. The distributed estimator we develop can achieve the same convergence rate as the estimator based on the whole data set under suitable assumptions. In our simulations, we illustrate the convergence of the estimators under different settings and also demonstrate the accuracy of nonzero parameter identification. Full article