Abstract A SimCLR-Enhanced Transformer, referred to as a Contrastive Temporal Transformer (CTT), is proposed for smooth and robust indoor trajectory estimation using visible light positioning (VLP). The framework combines contrastive pretraining to learn stable received
signal strength (RSS) embeddings with a Transformer-based temporal regressor to jointly optimize point-wise localization accuracy and trajectory smoothness. Experiments conducted in a controlled 5 m × 5 m × 3 m synthetic indoor environment modeled using visible light communication (VLC) channel characteristics achieve an RMSE of 0.046 m and a mean absolute error (MAE) of 0.037 m, while reducing trajectory jitter by more than 99% compared to GRU-based baselines. Robustness is evaluated under receiver orientation
perturbations and first-order multipath effects, demonstrating that the proposed method maintains smooth and stable trajectories under non-ideal channel conditions, albeit with increased localization error in the presence of strong multipath. These results indicate that
the CTT framework provides a promising foundation for practical VLP systems, subject to further validation using ray-traced and experimentally measured channels.

Recent advancements in smoothing techniques for quantile regression have addressed critical challenges in statistical inference, such as non-smooth objective functions and slow convergence rates. Building on this progress, we extend our work on the Generalized Sigmoidal Quantile Function–a novel smoothed quantile estimator based on an alternative formulation of the population quantile–to the regression setting, introducing the Generalized Sigmoidal Conditional Quantile Function. This new framework employs a smooth approximation of the absolute value function, enhancing both asymptotic properties and computational efficiency. We demonstrate that the Generalized Sigmoidal Conditional Quantile Function estimator belongs to the broad class of M-estimators. Additionally, we establish theoretical properties, conduct extensive simulation studies, and validate its practical utility through a real-world modeling example.

This paper presents a distributed smoothing neurodynamic approach for solving the L1-Lp minimization problem, with application to robust and collaborative multi-view three-dimensional (3D) space localization. To handle the non-Lipschitz continuity gradients, a smooth approximation technique is introduced, yielding a distributed neurodynamic model that integrates classical smoothing neural networks with multi-agents consensus theory. Theoretical analysis guarantees the global convergence of each agent’s state to the optimal solution. The stability and convergence of the proposed approaches are rigorously proved using Lyapunov theory. Numerical experiments on multi-view 3D space localization in the presence of measurement noise demonstrate the method’s effectiveness and practical value for distributed visual computing.

We introduce a novel Bayesian framework for estimating time-varying volatility by extending the Random Walk Stochastic Volatility (RWSV) model with Dynamic Shrinkage Processes (DSP) in log-variances. Unlike the classical Stochastic Volatility (SV) or GARCH-type models with restrictive parametric stationarity assumptions, our proposed Adaptive Stochastic Volatility (ASV) model provides smooth yet dynamically adaptive estimates of evolving volatility and its uncertainty. We further enhance the model by incorporating a nugget effect, allowing it to flexibly capture small-scale variability while preserving smoothness elsewhere. We derive the theoretical properties of the global-local shrinkage prior DSP. Simulation studies demonstrate that ASV is highly robust to misspecification, consistently recovering the latent volatility structure across a wide range of data-generating processes. Furthermore, ASV’s capacity to yield locally smooth and interpretable estimates facilitates a clearer understanding of the underlying patterns and trends in volatility. As an extension, we develop the Bayesian Trend Filter with ASV (BTF-ASV) which allows joint modeling of the mean and volatility with abrupt changes. Finally, our proposed models are applied to time series data from finance, econometrics, and environmental science, highlighting their flexibility and broad applicability.

Abstract Photoacoustic imaging (PAI) combines the optical absorption contrast of light with the high spatial resolution of ultrasound, yet its image reconstruction remains an ill-posed inverse problem due to acoustic attenuation and sparse measurements. To address this, we propose a Subspace Newton L0-Regularized (SNL0) reconstruction method for PAI based on sparse signal theory. Specifically, the algorithm reformulates the L0 minimization as a smooth approximation and iteratively solves it using a Newton-based subspace projection, achieving efficient convergence while maintaining sparsity. Compared with classical SPGL1 and Tikhonov regularizations under Gaussian noise, the proposed SNL0 method demonstrates superior noise suppression and edge preservation. Simulation results verify that SNL0 enhances structural sharpness and reconstruction accuracy, showing strong potential for sparse-sampling PAI applications.

This paper proposes a current model predictive control strategy for the permanent magnet synchronous motor (PMSM) based on a novel sliding mode observer to reduce the cost of PMSM and ensure good tracking performance. A super twisting sliding mode observer (STSMO) is designed to address the issues of high-frequency chattering and noise sensitivity caused by the large positive gain of traditional SMO. The discontinuous effect of the traditional SMO switching function is introduced into the derivative of the control rate, and a smooth estimate of the back electromotive force (EMF) is obtained through integration. Replace the sign function with a sigmoid function with smooth continuity to further reduce the chattering effect. To enhance the dynamic performance of the PMSM current loop, a finite control set model predictive control (FCS-MPC) strategy is employed in place of the conventional PI controller. Within each sampling period, all possible switching states are evaluated, and the optimal one is selected and directly applied to the inverter. Additionally, a dual-vector model predictive current control (DVMPCC) method is adopted to reduce current ripple. This approach synthesizes a voltage vector with arbitrary magnitude and direction by combining two voltage vectors within each sampling period. Numerical results demonstrate that the proposed sensorless PMSM predictive current control method achieves high accuracy in speed estimation and excellent dynamic response performance.

Rtglm: Unifying estimation of the time-varying reproduction number, Rt, under the Generalised Linear and Additive Models.

The input parameters of an optimization problem are often affected by uncertainties. Chance constraints are one way to model stochastic uncertainties in the constraints. Typically, solution algorithms for chance-constrained problems require convex functions or discrete distributions. Here, we go one step further and allow non-convexities and continuous distributions. We propose a gradient-based approach to approximately solve joint chance-constrained models. We approximate the original problem by smoothing indicator functions. The smoothed chance constraints are relaxed by penalizing their violation in the objective function. The approximation problem is solved with the Continuous Stochastic Gradient method that is an enhanced version of the stochastic gradient descent and has recently been introduced in the literature. We present a convergence theory for the smoothing and penalty approximations. Under very mild assumptions, our approach is applicable to a wide range of problems. We illustrate its computational efficiency on difficult practical problems in gas networks. The numerical experiments demonstrate that the approach quickly finds nearly feasible solutions for joint chance-constrained problems with non-convex constraint functions and continuous distributions, even for realistically-sized instances.

Local Smoothing Estimates for Schrödinger Equations in Modulation Spaces

Smoothness estimation for Whittle–Matérn processes on closed Riemannian manifolds

The partial linear model is a very important class of semiparametric model in applied quantitative sciences. This article considers the estimation of a partial linear model with a discontinuous unknown non parametric function. We embed the jump-preserving techniques in the profiled local linear kernel smoothing method, then propose an adaptive jump-preserving profiled local linear estimation procedure to estimate the parametric coefficients and non parametric function. This method can automatically accommodate possible jumps of the non parametric function without knowing the number and locations of jump points. The resulting estimators can preserve the jumps well and also give smooth estimates of the continuity part. The asymptotical properties of the resulting estimators are demonstrated under some mild conditions. Several numerical simulations are conducted to evaluate the finite sample performance of the proposed methodologies.

This paper presents an adaptive fixed-time fault-tolerant control scheme for nonstrict-feedback nonlinear systems subject to actuator faults, input saturation, and external disturbances. Radial basis function neural networks approximate unknown nonlinear functions within the system. To address the complexity typically associated with the traditional backstepping design, command filtering is introduced, significantly simplifying the control development process. An error compensation technique is further incorporated to reduce the impact of filtering-induced errors on system performance. To effectively handle input saturation, a smooth non-affine approximation is utilized to represent the saturation behavior. The proposed controller is developed using Lyapunov-based analysis and backstepping design, ensuring both transient and steady-state tracking objectives are met. A funnel constraint mechanism is integrated to maintain the tracking error within predefined performance bounds. Theoretical analysis confirms the fixed-time stability of the closed-loop system, and simulation examples are provided to demonstrate the effectiveness and feasibility of the proposed approach.

Abstract The goal of this note is to prove that every real-valued Lipschitz function on a Banach space can be pointwise approximated on a given $$\sigma $$ σ -compact set by smooth cylindrical functions whose asymptotic Lipschitz constants are controlled. This result has applications in the study of metric Sobolev and BV spaces: it implies that smooth cylindrical functions are dense in energy in these kinds of functional spaces defined over any weighted Banach space.

Accurate S-wave velocity models are essential for revealing near-surface characterization. Conventional wave-equation surface-wave dispersion inversion (WD) and full waveform inversion (FWI) face challenges related to non-differentiability in dispersion curve extraction and sensitivity to the inaccurate initial model. This work introduces a novel wave-equation surface-wave dispersion spectrum inversion (SWD) strategy, which addresses these limitations by implementing a smooth gradient approximation between the dispersion spectrum and the misfit function through the $SoftMax$ method. We utilize the dispersion spectrum information to improve the inversion accuracy. The gradient is derived using the chain rule and the adjoint state method. SWD achieves accurate and stable S-wave velocity inversion results. The convexity of the skeletonized misfit function mitigates the cycle-skipping problem common in FWI. The SWD offers high lateral resolution without requiring a layered assumption, compared to 1D dispersion inversion. Synthetic data tests show that SWD reduces dependence on poor or inaccurate initial models, and two real land seismic examples further demonstrate its reliability in reconstructing near-surface S-wave velocity models.

Abstract For any given set , we discuss a fractal frequency‐localized version of the local smoothing estimates for the half‐wave propagator with times in . A conjecture is formulated in terms of a quantity involving the Assouad spectrum of and the Legendre transform. We validate the conjecture for radial functions. We also prove a similar result for fractal‐time and square function bounds, for arbitrary functions and general time sets. We formulate a conjecture for generalizations.

This paper presents a numerical approach for solving intuitionistic fuzzy parabolic partial differential equations (IFPPDEs) using the explicit cubic spline method. Intuitionistic fuzzy systems, which extend classical fuzzy sets by incorporating a degree of non-membership, provide a more flexible framework for modelling uncertainty in real-world phenomena. The initial and boundary conditions of the intuitionistic fuzzy parabolic partial differential equation are considered intuitionistic triangular fuzzy numbers. The proposed cubic spline-based scheme ensures smooth and accurate approximations of the solution while maintaining stability and convergence properties. A discretization strategy is developed to transform the IFPPDE into a solvable system, and an iterative algorithm is introduced to handle the intuitionistic fuzzy parameters effectively. The efficiency and accuracy of the method are demonstrated through numerical experiments, comparing the results with the exact solution. The findings suggest that the cubic spline method provides good accuracy and computational efficiency, making it a promising tool for solving intuitionistic fuzzy parabolic partial differential problems in various scientific and engineering applications.

Dynamical systems have inspired and explained several accelerated algorithms for a wide range of optimization problems. But due to the lack of smoothness and convexity of the objective functions in many real world applications, we cannot directly apply these accelerated algorithms in these situations. This paper proposes to apply a smoothing approximation approach to address non-smooth, non-convex machine learning optimization problems. Our work is motivated by the following goal: developing a direct method for finding critical points of objective functions of machine learning problems where functions are known to be non-smooth and non-convex. To achieve these goals, we establish the convergence of an alternative algorithm for smooth functions without convexity that supplements some recent results of Attouch et al.

Abstract We consider a CMC hypersurface with an isolated singular point at which the tangent cone is regular, and such that, in a neighbourhood of said point, the hypersurface is the boundary of a Caccioppoli set that minimises the standard prescribed-mean-curvature functional. We prove that in a ball centred at the singularity there exists a sequence of smooth CMC hypersurfaces, with the same prescribed mean curvature, that converge to the given one. Moreover, these hypersurfaces arise as boundaries of minimisers. In ambient dimension 8 the condition on the cone is redundant. (When the mean curvature vanishes identically, the result is the well-known Hardt–Simon approximation theorem.

Effectiveness of Xuanbai Shengmai Decoction, a compound Chinese herbal medicine, on disease progress and viral RNA shedding in COVID-19 patients: A retrospective study of medical chart in China.

This work investigates the relationship between the smoothness measure and the function norm in the space , where modified symmetric difference based on the Ditzian-Totik function are employed to assess the behavior of functions within centered subintervals. The focus is on the weighted smoothness measure of order used to derive both local and global estimates of the function. The weighted smoothness measure can be bound in terms of a series involving , which represents the optimal approximation of the function by polynomials. The following estimate incorporates the effects of the weight, partial smoothness, and derivative behavior into a precise quantitative expression linking approximation properties with smoothness analysis. The results contribute to a deeper understanding of the interplay between function smoothness and behavior in approximation function spaces, and they open pathways to accurate numerical applications.