In actinic keratosis (AK), clinical clearance after field-directed therapies does not necessarily correspond to histological resolution, resulting in subclinical persistence and risk of recurrence. To provide a practical, up-to-date framework for non-invasive monitoring of treatment response in AK, integrating clinical assessment and dermoscopy with high-resolution imaging techniques, reflectance confocal microscopy (RCM), line-field confocal optical coherence tomography (LC-OCT), and high-frequency ultrasound (HFUS), and to discuss emerging optical biomarkers based on Raman spectroscopy. For each modality, we summarize pre- and post-treatment imaging patterns, proposed response criteria, recommended follow-up timing, and correlations with clinical outcomes (including clearance and AKASI) and, when available, histological findings. The available evidence is derived from a limited number of observational studies, predominantly involving RCM and LC-OCT, whereas data on HFUS and Raman spectroscopy remain comparatively scarce. RCM and LC-OCT allow in vivo assessment of epidermal architectural normalization and reduction of intraepidermal keratinocyte atypia. HFUS captures quantitative trajectories of superficial dermal remodeling, including changes in the subepidermal low-echogenic band (SLEB) and dermal echogenicity after photodynamic therapy and other field treatments. Dermoscopy remains the first-line tool for routine follow-up but may fail to detect minimal subclinical persistence. Finally, we discuss the potential role of in vivo Raman spectroscopy for dynamic molecular endpoints and its possible integration with artificial intelligence-based analytical approaches. A standardized multimodal follow-up strategy improves the accuracy of treatment-response assessment compared with clinical evaluation alone. We propose a technique-specific checklist of minimal response criteria and a pragmatic temporal assessment scheme, and outline a research roadmap to support validation and clinical implementation of non-invasive imaging-guided monitoring in actinic keratosis.

In this paper we focus on the Cahn–Hilliard equation with dynamic boundary conditions, by adding two hyperbolic relaxation terms to the system. We verify that the energy of the total system is decreasing with time. By adding two stabilization terms, we have constructed a first-order temporal accuracy numerical scheme, which is linear and energy stable. Then we prove that the scheme is of first-order in time by the error estimates. At last we present comprehensive numerical results to validate the the temporal convergence and the energy stability of such scheme. Moreover, we present the differences of the numerical results with and without the hyperbolic terms, which show that the hyperbolic terms can help the total energy decreasing slowly.

Abstract Inspired by the Kadanoff transformation in the standard renormalization group theory, we propose a temporal renormalization scheme. A Boltzmann factor that explicitly depends on the renormalized timescale is constructed, permitting thermodynamic quantities to be evaluated self-consistently across different timescales. By applying the scheme to the long-time dynamics of supercooled liquids, we uncover critical-like behaviors of supercooled liquid with three characteristic renormalization timescales: At the first timescale s α , the system appears to be “thermodynamically frozen”, i.e., the energy fluctuation becomes temperature-independent throughout the supercooled regime. At the second timescale s β , the third-order moment of energy distribution reaches a maximum, and s β is nearly temperature-independent. At the third timescale s γ , the third-order moment of energy distribution passes through a minimum, and s γ diverges as a power law s γ ~| T - T c | -γ . The scaling relations may reveal an intrinsic behavior in supercooled liquids, highlighting their unique feature. The current findings also demonstrate that temporal renormalization provides a powerful lens for investigating the timescale-specific dynamics.

Length-based stock assessment methods are widely applied in data-limited fisheries, yet the effects of how length-frequency data are temporally grouped prior to analysis remain poorly examined. Temporal grouping is routinely used to increase sample size and approximate equilibrium conditions, but it may also alter the size structure presented to assessment models and bias inference. In this study, we evaluate how alternative temporal grouping schemes influence stock status inference within a single length-based framework, using the length-based spawning potential ratio (LBSPR) model as a diagnostic tool. Using a 30-year length-frequency dataset from a tropical purse seine fishery in the Northeast Atlantic as an illustrative case, we applied LBSPR under four practice-relevant temporal grouping schemes: full-period pooling, a broad regime-based scheme, decadal blocks, and five-year blocks. Life history parameters and model settings were held constant across schemes to isolate the effect of temporal grouping. A sensitivity analysis of biological parameters was conducted for the finest temporal scheme to contextualise robustness. Results show that temporal grouping alone can substantially alter the inferred status of the illustrative case. The fully pooled scheme produced an apparently favourable status signal, whereas finer temporal groupings revealed extended periods of inferred reproductive depletion, followed by a more recent recovery. Sensitivity analyses indicate that, while biological parameter uncertainty influences the magnitude of estimates, it does not overturn the dominant effect of temporal grouping on inferred status patterns. This study demonstrates that temporal grouping is not a neutral preprocessing step but a structural decision with the potential to conceal or reveal exploitation signals in length-based assessments. We argue that temporal grouping should be treated as an explicit sensitivity dimension in data-limited assessment workflows. By shifting attention from stock-specific outcomes to data-structuring choices, this work provides practical guidance for improving transparency and robustness in length-based stock status inference.

In this paper, we investigate discrete regularity estimates for a broad class of temporal numerical schemes for parabolic stochastic evolution equations. We provide a characterization of discrete stochastic maximal ell ^p-regularity in terms of its continuous counterpart, thereby establishing a unified framework that yields numerous new discrete regularity results. Moreover, as a consequence of the continuous-time theory, we establish several important properties of discrete stochastic maximal regularity such as extrapolation in the exponent p and with respect to a power weight. Furthermore, employing the H^infty -functional calculus, we derive a powerful discrete maximal estimate in the trace space norm D_A(1-frac{1}{p},p) for p in [2,infty ).

A Temporal Broadening-Aware Pulse Width Adaptation Scheme for ISI Mitigation and Energy Efficiency in THz Communication

Securing the reintegration of outlier nodes in dynamic UAV networks is challenging. This challenge arises from the lack of time-sensitive access control in existing key management schemes. We propose the Salted Temporal Key scheme (STK), which combines blockchain-based dynamic key management with temporal validation. This work addresses the absence of a time-sensitive admission policy by coupling reintegration cost to a UAV’s verifiable disconnection time: short-term outliers reintegrate quickly, while long-duration, high-risk outliers face increasing barriers. STK binds reintegration difficulty to the block-broadcast interval τ, making reintegration a computational challenge proportional to the number of missed consensus cycles. Experiments on swarms with 50–100 nodes show that STK efficiently manages reintegration latency, providing scalable and adaptable security for decentralized UAV networks. The results demonstrate that by adjusting τ, operators can isolate UAVs with excessive delays and ensure reliable swarm communication. STK offers a flexible, non-interactive solution, significantly enhancing security and scalability for UAV swarm reintegration in diverse environments.

Diffusion on curved surfaces deviates from the flat case due to geometrical corrections in the evolution of its moments, such as the geodesic mean square displacement. Moreover, anomalous diffusion is widely used to model transport in disordered, confined, or crowded environments and can be described by a temporal subordination scheme, leading to a time-fractional diffusion equation. In this work, we analyze the dynamics of time subordinated anomalous diffusion on curved surfaces. By using a generalized Taylor expansion with fractional derivatives in the Caputo sense, we express the moments as a temporal power series and show that the anomalous exponent couples with curvature terms, leading to a competition between geometric and anomalous effects. This coupling indicates a mechanism through which curvature modulates anomalous transport.

This paper considers a parabolic equation involving the Caputo fractional time derivative of order $\gamma\in(0,1)$ and the spectral fractional power, of order $s\in(0,1)$, of a symmetric second order elliptic operator $L$. By using the Caffarelli–Silvestre extension, the original problem is converted to a quasi-stationary elliptic problem on a semi-infinite cylinder in one more spatial dimension and with a dynamic boundary condition. Based on the solution representation with the Mittag–Leffler function and the eigenpairs of the elliptic operator $L$, some new regularity results are derived. For the temporal semi-discrete scheme using the Alikhanov difference approximation, stability and convergence are established. Furthermore, the first-degree tensor product finite element method is adopted for the spatial discretization to obtain a fully discrete scheme, and an error estimate is derived. Finally, an efficient algorithm based on a generalized eigenvalue problem is applied to solve the matrix system of the full discretization. Numerical examples are provided to verify the theoretical results.

The increasing integration of solar power requires highly accurate intra‐hour solar irradiance forecasts. This study aims to significantly improve intra‐hour solar irradiance forecasts by developing and evaluating a blending approach that integrates distinct forecast sources. Our methodology involves extending the horizon of an All‐sky imager (ASI) data‐driven transformer‐based model up to 1 h ahead. The outputs of this ASI model are blended with a Heliosat‐3‐based satellite forecast and a persistence forecast via linear regression as well as with distinct advanced machine learning algorithms. We assess the hybrid system's performance across varying sky conditions and analyze the impact of temporal aggregation schemes and the effective spatial coverage of a single ASI installation. Results demonstrate that this integrated multisource hybrid approach provides substantial benefits by reducing the overall root mean squared error and mean absolute error over the standalone satellite forecast by 13.6% and 17.0%, respectively. This is attributed to the complementary strengths of the individual models: ASI excels under dynamic conditions, satellite offers broader spatial coverage, and persistence provides a robust baseline for the immediate future. Furthermore, the strong generalization capability of the ASI model is shown through its effective performance across climatically distinct sites (training in southern Spain and validation in northern Germany).

Atmospheric pollution causes millions of excess deaths annually, with particulate matter (PM) being a major concern. While research has traditionally focused on PM10 and PM2.5, ultrafine particles (UFPs, diameter < 100 nm) have emerged as a critical human health risk due to their ability to penetrate deeply into the respiratory system, transmigrate into the bloodstream and induce systemic health impacts. The total particle number concentration (PNC) serves as a proxy measure for UFP prevalence, as UFPs dominate particle number counts despite contributing minimally to total particle mass. This study presents the first global datasets of PNCs and UFPs at 1 km resolution over land by combining ground station measurements with machine learning. We developed an XGBoost model to predict annual PNC levels from 2010–2019, integrating diverse environmental and anthropogenic variables available at the global scale. Our model achieves an R2 of ≥0.9 and a mean relative error of about 30% for polluted urban areas, based on comparison with test datasets, and its performance was evaluated by including spatial and temporal cross-validation schemes. We find that global annual mean PNCs near the Earth’s surface vary between a few thousand per cm3 in pristine environments up to more than 40,000 per cm3 in some urban centres and that UFPs contribute about 91% to PNCs. The model incorporates a conformal prediction framework to provide reliable coverage intervals, making local-to-global PNC and UFP data available and supporting exposure assessments and health impact studies.

This research aims to present a comprehensive investigation of the self-organization of two-dimensional patterns composed of numerous dots and lines using numerical techniques, specifically focusing on the Gray–Scott (GS) model, a well-established framework for studying reaction–diffusion systems. The staggered grid finite volume approach is utilized and the Crank–Nicholson method (θ=12⋅) is used for time discretization in our simulations, as it is known to yield a reliable and accurate solution. The present study involves an investigation into the stability of the temporal semi-discrete numerical scheme, along with a comprehensive analysis of the errors through the utilization of standard solutions that demonstrate second-order convergence in both temporal and spatial domains. The utilization of pattern formulations proves to be extremely useful in the analysis of the interaction between diffusion and reactions. This is accomplished by solving the coupled partial differential system using finite difference techniques, which serve to enhance accuracy while simultaneously preserving the stability of the system. To further examine the system’s behavior, the finite volume methodology (FVM) was utilized to examine the dynamics of the GS model. The assessment of stability is performed on fixed points, wherein analytical solutions are compared to computational techniques such as the Alternate Direction Implicit methodology and the FVM. Furthermore, we employ the FVM in spatial discretization and the Crank–Nicolson scheme in temporal discretization to solve the GS model. This study represents a novel application of two distinct methodologies to analyze error co-variances and system efficiency in a particular system. The utilization of these approaches in combination is unprecedented in the existing literature and aligns with our current comprehension of the subject matter. The results demonstrate the accuracy and reliability of the proposed numerical schemes, highlighting their potential applicability to a wide range of reaction–diffusion systems. The findings of this research have significant implications for several disciplines, including material science, chemical engineering, and biophysics, where self-organization patterns are essential to the creation of innovative materials, novel devices, and biological systems. The results of our research provide vital insight into the fundamental mechanics of pattern formation. In addition, these discoveries have the potential to be utilized in the advancement and enhancement of a wide variety of technologies and applications.

Abstract This paper introduces a high-order nonuniform finite difference scheme for the time-fractional Swift-Hohenberg equation, leveraging a nonuniform fractional BDF2 formula. The scheme’s unique solvability is established via the Brouwer theorem. By exploiting the discrete gradient structure of the fractional BDF2 formula, the energy stability of the difference scheme is theoretically derived. Numerical experiments validate the scheme’s accuracy and confirm the consistency between the discrete energy dissipation behavior and theoretical predictions.

Abstract We investigate a fully discrete scheme for a space-dependent variable-order fractional diffusion equation in the flowing media, which can be derived by introducing a velocity field to continuous time random walk model with waiting time obeying a spatially dependent power-law distribution. We provide regularity estimates for the solution under some regularity assumptions on the variable-order αx and the velocity field v. A temporal semidiscrete scheme generated by the backward Euler convolution quadrature method is proposed, and an Oτ convergence rate is obtained by some skillful error analyses. Then, the fully discrete scheme is built by using finite element method to approximate the spatial operator, and an optimal spatial error estimate is obtained by introducing some discrete operators, i.e., the convergence order can well match the order of optimal spatial regularity of the solution. Finally, various numerical examples are presented to validate our theoretical results.

Based on the spatial compact finite difference (SCFD) method, an improved high-order temporal accuracy scheme for high-dimensional time-fractional diffusion equations (TFDEs) is presented in this work. Combining the temporal piecewise quadratic interpolation and the high-dimensional SCFD method, the proposed numerical method is described. In order to establish the stability and convergence analysis, we introduce a norm ||·||H˜1, which is rigorously proved equivalent to the standard H1-norm. Considering that the coefficients of high-order numerical schemes are not entirely positive, we introduce an appropriate parameter to transform the numerical scheme into an equivalent form with positive coefficients. Based on the equivalent form, we prove that the temporal and spatial convergence orders are (3−γ) and 4 by applying the convergence of geometric progression. The proposed scheme ensures that the theoretical convergence accuracy at each time step is of order (3−γ) without requiring any additional processing techniques. Ultimately, the convergence of the proposed high-order accurate scheme is verified through numerical experiments involving (non-)linear high-dimensional TFDEs.

Hourly calibration algorithm for Fengyun-2G quantitative precipitation estimates using spatial random forest and improved temporal disaggregation scheme

Cell types implement multiple coding schemes in distinct prefrontal cortex areas during goal-directed behavior.

In this paper, we develop a peridynamic computational framework to analyze thermomechanical interactions in fractured thin films subjected to ultrashort-pulsed laser excitation, employing nonlocal discrete material point discretization to eliminate mesh dependency artifacts. The generalized Cattaneo–Fourier thermal flux formulation uncovers contrasting dynamic responses: hyperbolic heat propagation (FT=0) generates intensified temperature localization and elevates transient crack-tip stress concentrations relative to classical Fourier diffusion (FT=1). A GSSSS (Generalized Single Step Single Solve) i-Integration temporal scheme achieves oscillation-free numerical solutions across picosecond-level laser–matter interactions, effectively resolving steep thermal fronts through adaptive stabilization. These findings underscore hyperbolic conduction’s essential influence on stress-mediated fracture evolution during ultrafast laser processing, providing critical guidelines for thermal management in micro-/nano-electromechanical systems.

A collision-based hybrid method for the discrete ordinates approximation of the multigroup neutron transport equation is developed for time-dependent problems. This expands upon previous multigroup work by extending the method to two spatial dimensions using a second-order temporal discretization scheme, and optimizes the energy group coarsening approach. For the collision-based hybrid method, the neutron transport equation is split into two equations at each time step. The first equation includes the uncollided terms of the neutron transport equation, the external and boundary sources, which can be solved in one iteration. The second equation is comprised of the collision terms, where the number of iterations is dependent on the number of collisions. To minimize the required time for convergence, the collided equation uses low-fidelity energy and angular grids. To limit the discretization error from the coarser grid structures, the uncollided equation uses high-fidelity energy and angular grids. The solutions from the uncollided and collided transport equations are combined to estimate the flux at each time step. This hybrid method is shown to be a better solution in terms of both convergence time and accuracy when compared to traditional monolithic coarsening schemes. In two time-dependent problems, the hybrid method is shown to use up to 50% less convergence time than an equivalent monolithic coarsening scheme. It is able to achieve this while remaining more accurate in most low-fidelity model comparisons.

A semi-implicit second-order temporal scheme for solving the pressure head-based form of Richards' and advection-dispersion equations