Search Results (264)

We investigate dynamic weighted fractional information-theoretic measures for linear stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/2,1)$. Motivated by recent constructions of fractional Deng entropy and building upon explicit Gaussian solutions and closed-form fractional moments derived in previous work, we establish fully analytical expressions for the Shannon entropy, Rényi entropy, Tsallis entropy, extropy, and a continuous weighted fractional entropy $\mathbb{E}\left[X_t^p(-log{p}_{X_t}\left(X_t\right))\right]$ for $p\ge 0$, expressed directly in terms of known fractional moments without density estimation. All derived measures share a universal asymptotic scaling law growing as $Hlogt$, establishing a precise quantitative link between long-memory effects and information dynamics. The weighted fractional entropy further reveals remarkable structural properties as a function of the weighting order p, exposing a dual role of long memory on the system’s informational content. As a concrete application, we characterize anomalous diffusion in aging soft materials through an explicit critical time linking maximal uncertainty to the memory exponent H and the macroscopic aging rate. All results are validated through extensive Monte-Carlo simulations, demonstrating excellent agreement with the closed-form expressions across a wide range of Hurst exponents H and weighting orders p. Full article

Although the sharing of data is an important part of multicenter biomedical AI, direct data sharing is hindered by privacy laws, institutional data silos, and restrained trust and cooperation between institutions. While federated learning offers an opportunity for collaborative model training without centralizing patient data, many current methods rely on the same fixed levels of privacy protection on all clients, every layer of the model, each round, and each modality, resulting in suboptimal privacy–utility–latency trade-offs. In this study, we introduce Adaptive Trust-Aware Encrypted Federated Artificial Intelligence with Blockchain Auditability (ATEB-AI) for biomedical signal and medical image analysis. ATEB-AI is an adaptive CKKS encryption, trust-aware aggregation, and permissioned blockchain-based audit logging combination. The proposed framework was tested on four public benchmarks, namely, MIT-BIH, CHB-MIT, BraTS, and NIH ChestXray. ATEB-AI had the highest overall performance out of all compared federated methods and remained near the centralized training benchmark at up to 99.0% of the reference centralized training performance. It reduced membership-inference success from 0.71 to 0.24 (−66.2%), inversion leakage from 0.64 to 0.27 (−57.8%), and poisoning-related utility loss from 0.18 to 0.07 (−61.1%). Round latency was 1.90× FedAvg, compared with 2.85× for HE-FL (−33.3%) and 3.50× for BC-FL (−45.7%). The key contribution of this study is a single biomedical federated learning framework in which privacy, client trust, reliability, and auditability are unified, instead of being disjointed components. The results obtained with the proposed model prove the feasibility of co-optimizing confidentiality, robustness, efficiency, and governance in a single deployable multicenter medical AI pipeline. Full article

A reinforcement-learning-based wall-modeled large-eddy simulation (RL-WMLES) framework is proposed to improve the physical consistency of near-wall turbulence predictions. In this approach, a reinforcement learning agent is coupled with the WMLES solver to dynamically adjust a compensating stress term, with the objective of enforcing agreement between the LES solution and the law of the wall. The agent is trained using the proximal policy optimization (PPO) algorithm, where the state is defined as the discrepancy between the near-wall LES velocity and the wall-model prediction, and the action corresponds to modifying a parameterized support viscosity distribution. The proposed method is implemented within a high-performance CFD solver and trained on turbulent channel flow. Numerical results demonstrate that the trained agent effectively reduces the log-layer mismatch and significantly improves the accuracy of near-wall velocity predictions. Furthermore, the RL-WMLES framework exhibits a degree of generalization capability: the trained agent performs robustly with varying levels of numerical dissipation and Reynolds numbers. By introducing a simple interpolation strategy, the same agent can be successfully applied to configurations with different matching locations. Overall, the RL-WMLES framework provides a flexible and data-driven approach for enforcing physical constraints in turbulence modeling. The method shows strong potential for extension to more complex flows. Full article

Rockfall records for hazard assessments commonly present rockfall volume–cumulative frequency curves based on observations of rockfall occurrences that are noticed at or in the vicinity of infrastructure. These curves are in log–log scale, where the curves for larger volumes are fitted to a power law (linear fit in the log–log plot). The slope of this linear fit in log–log plots has been qualitatively attributed to rock mass characteristics (lithology, rock mass quality, discontinuities); however, there are not many direct insights that greenfield sites (new sites or areas with scarce to no data) could adopt for an order-of-magnitude estimation of rockfall hazard. This paper collects data from the literature, past and current, and presents details of these rockfall volume–cumulative frequency curves for different lithologies and rock mass qualities. Importantly, recent databases on rockfall frequency and volumes as obtained through change detection are utilized, which can provide more detailed and less biased rockfall occurrence data. Full article

We propose an interactive approach to teaching Coulomb’s law and electrostatics in general, rooted in two complementary pedagogical methodologies: hyper-constructivism (H-C) and neo-realism. Unlike standard constructivism, our hyper-constructivist approach treats students’ prior ideas—even if incomplete or inconsistent—as essential “submerged logs” that teachers may use to guide students across the cognitive lake, toward the correct understanding. We implement a triadic model of cognitive didactics, balancing amusement (the ludic “hook”), formal teaching, and deepening scientific inquiry. Here, we present a hyper-constructivist path on electrostatics—Coulomb’s and Gauss’s laws. Through a sequential path of experiments involving plastic rods, “trained” aluminum cans, Volta’s electrophorus, and “Christmas” ornaments, we demonstrate how students can spontaneously formulate problems and bridge the gap between intuitive observations and complex effects of electrical polarization, going beyond the scholastic Coulomb’s law, via numerical modeling. The proposed interactive approach is rooted in phenomena-based learning and leverages discrepant events—surprising physical phenomena that challenge prior intuitions—as “ludic hooks” to trigger spontaneous inquiry and conceptual reconstruction. The main goal of our strategies is to trigger and develop young students’ interest in physics, which in many European countries is low. This method not only facilitates the acquisition of physical laws but also fosters “intellectual inquisitiveness” and social competencies, proving that well-rooted knowledge emerges from a synthesis of tangible experience and advanced scientific modeling. Our contribution constitutes a complex pedagogical proposal, iteratively developed and implemented in diverse didactical environments over several years. This paper presents a pedagogical proposal developed and refined through more than twenty years of educational practice. For teachers interested in implementing hyper-constructivist instruction, we provide a detailed teaching pathway on electrostatics, with didactical explanations and pedagogical notes. Full article

Metal accumulation in cacao (Theobroma cacao L.) cultivation represents an important agronomic and food-safety concern, particularly in acidic tropical soils where cadmium (Cd) and other trace metals can become bioavailable and translocate to plant tissues. Green magnetic nanomaterials offer a potential strategy for reducing metal mobility in agricultural substrates, but their performance depends on surface chemistry, dose, and plant genotype. In this study, we synthesized and evaluated MCRES, defined here as a maghemite–Citrus reticulata extract system, a biofunctionalized γ-Fe₂O₃-based nanosystem prepared by coupling iron oxide nanoparticles (NPs) with a 3% (w/v) Citrus reticulata peel extract. The objective was to determine whether citrus-mediated biofunctionalization could produce a scalable magnetic nanoamendment capable of modifying Cd and naturally occurring Ni partitioning in cacao seedlings. MCRES was recovered magnetically and dried, yielding 8.44 g of product from 10 g of precursor. Rietveld analysis performed in X ray diffractograms confirmed phase-pure cubic γ-Fe₂O₃ with a lattice parameter of 0.8332 nm, a crystallite size of 11.3(1) nm, and satisfactory refinement quality (χ² ≈ 1.34). Transmission electron microscope images showed quasi-spherical NPs with a log-normal size distribution centered at 7.5 nm. Magnetic measurements showed superparamagnetic-like behavior at 300 K, high saturation magnetization values of 62 emu g⁻¹ at 300 K and 71 emu g⁻¹ at 5 K, and elevated effective anisotropy values obtained from the Law of Approach to Saturation fitting. MCRES was applied at 0, 1, 2, 4, and 6 g pot⁻¹ to cacao seedlings containing Cd-amended Ultisol with naturally occurring Ni. Plant responses were genotype and dose dependent: TSH-1188 genotype showed limited dose sensitivity for most biometric variables, whereas ICS-95 genotype showed significant dose effects, with maximum growth at the 2 g pot⁻¹ treatment. Metal-partitioning results indicated that Cd remained comparatively mobile toward shoots, whereas Ni was preferentially retained in roots. In TSH-1188 genotype, the Ni translocation factor decreased from 3.07 in the control to 0.85–1.00 at higher MCRES doses. Compared with previous work on non-biofunctionalized nanomaghemite, these results suggest that citrus-mediated biofunctionalization produces a distinct Cd/Ni partitioning response. Overall, MCRES is recommended as a promising nursery-scale green nanoamendment for reducing metal mobility in cacao cultivation, but its agronomic use should be optimized according to genotype and dose. Future work should include side-by-side comparisons with unfunctionalized γ-Fe₂O₃, Citrus reticulata extract alone, and non-contaminated controls under field conditions to validate its long-term effectiveness and environmental safety. Full article

This study tackles the middle atmosphere phenomenon known as Mesospheric Inversion Layers (MILs). Reinterpreting Envisat’s GOMOS instrument limb-sounding temperature profiles which we compared to the MSIS-2.0 climatological model, we studied 340,000 resolute temperature profiles, detecting 44,000 (13%) MILs in this dataset. We have shown that MILs are a worldwide phenomenon, concentrated around the tropics and in the Winter Hemisphere’s mid-latitude region (between $30\%$ and $50\%$ of profiles are MILs in those areas). MILs follow a correlation law ($R^2=0.5$ on pure data, $R^2=0.97$ on binned-mean data) between the log-amplitude of its peak and its altitude. Median altitudes are about 70 km worldwide, but the median amplitude reached by equatorial MILs is typically higher (14.5 K compared to the others at 12.5 K). Lastly, equatorial MILs (but not mid-latitude MILs) are correlated with high-difference estimated tide temperature gradient contributions. Results suggest that the MIL is a common phenomenon with statistically consistent characteristics. Seasonal occurrence hinted that there is probably a class of MILs favoured by planetary waves at the edge of the polar vortex, while the equatorial type of inversions seems to occur when the atmospheric tide model flattens the temperature gradient around 70 km. Full article

Electrolytic-plasma hardening of steel components requires reliable non-contact temperature monitoring, but traditional pyrometry is complicated by the variable emissivity of steel and the intense radiation of the plasma envelope. This work presents an approach that repurposes a compact multispectral AS7341 sensor into a virtual temperature sensor based on physically grounded spectral feature engineering and regularized machine learning. The use of logarithmic ratios of the near-infrared channel (940 nm) to the visible channels suppresses the plasma contribution and linearizes Wien’s radiation law. On a controlled dataset of 20 cycles, this increases the Pearson correlation with the peak temperature from r = 0.498 (raw NIR channel) to r = 0.781 for the log(NIR/Clear) feature. Current is identified as a confounding variable; normalizing the NIR/Clear ratio by the cycle-averaged current (r = 0.761) ensures correct signal interpretation under varying process conditions. Two narrow channels–NIR (940 nm) and F8 (680 nm)–provide accuracy equivalent to the broadband Clear channel (r = 0.778 vs. 0.781), thus simplifying hardware implementation. Ridge regression using three weakly correlated features (log(NIR/Clear), cycle duration, and initial temperature) achieves a mean absolute error of 91.4 °C under leave-one-out cross-validation (LOOCV) and 85.5 °C on an independent current-group test (R² = 0.536). Independent verification by scanning electron microscopy and Vickers microhardness on 30KhGSA steel confirms reliable separation of the three thermal regimes: underheating (<800 °C, 280–320 HV), optimal quenching (800–900 °C, 620–680 HV, fine-needle martensite), and overheating (>900 °C, 540–590 HV). The proposed set of spectral features provides a physically justified basis for a low-cost industrial temperature sensor for electrolytic-plasma processing. Full article

We propose a microphysical completion for the scalar sector of dilatonic gravity by identifying the dilaton with the coarse-grained stiffness mode of a constrained complex tension field defined on a discrete relational network. Under a controlled ordered-regime coarse-graining, the real projection of the tension scales as $\Phi (\Theta )={\Phi }_{0}cos\Theta$, so the Planck mass varies with the phase angle $\Theta$ and the Einstein-frame canonical scalar becomes $\phi \propto ln[\Phi (\Theta )/{\Phi }_0]$. This logarithmic structure emerges naturally from the Weyl map and provides the correct canonical variable for vacuum models inspired by the Logarithmic Schrödinger Equation (LogSE). We outline how this scalar–tensor interface can satisfy Solar-System constraints through environmental locking and discuss avenues for laboratory and astrophysical tests based on stiffness–coherence coupling. This paper does not introduce a new scalar–tensor EFT class as such; rather, it provides a controlled microphysical origin for a specific scalar stiffness law, $\Phi (\Theta )\propto cos\Theta$, and for the resulting logarithmic Einstein-frame canonical structure. Full article

Digital elevation models (DEMs) are key fundamental inputs in hydrological modelling, yet the influence of spatial resolution on basin delineation and process representation remains insufficiently understood, particularly in small catchments. This study investigates the influence of DEM resolution on topographic characterization and hydrological response in a small agroforestry basin in central Portugal. Three DEMs with resolutions of 5 m, 10 m, and 30 m were generated from contour data and satellite sources and processed using the TOPAZ-based TopAGNPS delineation framework. The sensitivity of basin structure to delineation parameters—critical source area (CSA) and minimum source channel length (MSCL)—was assessed, and the resulting configurations were used as inputs to the AnnAGNPS model. Results show that DEM resolution strongly influences the representation of hydrological cells and stream reaches. Increasing resolution from 30 m to 5 m leads to a nearly doubling of average cell slope and increases reach slope by more than four times, with corresponding changes in drainage network density and connectivity. Log-linear relationships were identified between slope and contributing area, as well as between slope and reach length, consistent with established geomorphic scaling laws. Hydrological simulations further indicate that resolution-dependent delineation significantly influences runoff, erosion, and peak discharge estimates, with finer resolutions increasing sensitivity to parametrization. Among land-cover scenarios, desertified conditions generate substantially higher runoff and peak flows compared to naturalized and forested conditions. Overall, the findings demonstrate that DEM resolution, together with preprocessing and delineation choices, exerts a critical control on hydrological model outputs. These effects are particularly pronounced in low-relief, human-influenced catchments, where coarse-resolution DEMs may lead to systematic underestimation of hydrological responses. The study highlights the need for resolution-aware modelling strategies and careful parametrization to improve the reliability and transferability of hydrological simulations. Full article

We study the discrete-time amplitude-constrained additive white Gaussian noise (AWGN) channel from the perspective of near-optimal input distributions in the high-SNR, or equivalently large-amplitude, regime. While it is known that the capacity-achieving input is discrete with finitely many mass points, the precise scaling of its support size as a function of the amplitude constraint remains an open problem. In this work, we instead consider the minimal support size required to achieve capacity up to an $\epsilon$-gap. We introduce the quantity $K_{\epsilon }\left(A\right)$, defined as the smallest support size among discrete inputs supported on $[-A,A]$ that achieves mutual information within $\epsilon$ of capacity. We show that this relaxed formulation is significantly more tractable and admits sharp characterizations in several vanishing-gap regimes. In particular, for polynomially decaying gaps, $\epsilon =A^{-\beta }$ with $\beta \ge 1$, we establish that $K_{\epsilon }\left(A\right)=\Theta \left(A\sqrt{logA}\right)$ as $A\to \infty$. For exponentially small gaps, we obtain bounds of order between $A\sqrt{logA}$ and $A^{3/2}$. Our approach combines approximation-theoretic bounds for Gaussian mixtures with information-theoretic control of entropy via ${\chi }^2$-divergence, together with a wrapping argument that relates the problem to approximating the uniform distribution on a circle. Beyond the technical results, our framework provides a conceptual explanation for the variety of scaling laws observed in prior numerical studies, suggesting that these may correspond to different regimes of $\epsilon$-optimality rather than intrinsic properties of the exact optimizer. Full article

We study functions satisfying the composition law $F\left(xy\right)+F(x/y)=P\left(F\right(x),F(y\left)\right)$ with a symmetric polynomial combiner P. We prove that symmetry together with a quadratic degree bound on P forces a composition law of d’Alembert type. We establish a degree mismatch exclusion criterion showing that symmetric polynomial combiners with $degP(u,v)\ge 3$ do not admit nonconstant continuous solutions, provided the leading term does not cancel (Theorem 1). For continuous nonconstant functions $F:{\mathbb{R}}_{>0}\to \mathbb{R}$ with $F\left(1\right)=0$ satisfying the composition law with a symmetric polynomial P of degree at most two, the combiner is necessarily of the form $P(u,v)=2u+2v+cuv$, $c\in \mathbb{R}$ (Theorem 3). The equation reduces in logarithmic coordinates to the classical d’Alembert functional equation. For $c\ne 0$, one obtains hyperbolic or trigonometric branches, while $c=0$ yields the squared-logarithm family. Under the cost-function assumptions $F\ge 0$ and convexity, only the hyperbolic branch with $c>0$ remains. A unit log-curvature calibration selects the canonical value $c=2$, which yields the canonical reciprocal cost $F\left(x\right)=\frac{1}{2}(x+x^{-1})-1$. For $c\ne 0$, the result extends to ${\mathbb{R}}_{>0}^n$: every solution depends only on a single linear combination of coordinate logarithms; for $c=0$, the solution is a general quadratic form ${\sum }_{i,j}{a}_{ij}ln{x}_{i}ln{x}_j$. In either case, nontrivial coordinate-wise separable costs are excluded. Full article

This paper develops a rigorous inferential framework for a class of Gaussian stochastic processes driven by white noise with constant drift, whose temporal evolution is governed by a Caputo fractional derivative of order ${\displaystyle \alpha \in (1/2,1)}$. The model belongs to the family of fractional Volterra processes, where memory is generated by the dynamics themselves rather than by correlated noise. We derive explicit analytical expressions for the mean, variance, and covariance structure of the solution, thereby characterizing in a precise manner how the fractional order ${\displaystyle \alpha }$ governs both variance growth and the strength of temporal dependence. In particular, the process exhibits correlated increments and a power-law variance scaling of order ${\displaystyle t^{2\alpha -1}}$, highlighting the dual role of ${\displaystyle \alpha }$ as a regularity and memory parameter. Building on this structural analysis, we address the statistical problem of estimating the parameter vector ${\displaystyle (\mu ,\sigma ,\alpha )}$ from discrete-time observations. Two complementary procedures are proposed for the estimation of the fractional order: a variance-growth method based on log–log regression of empirical variances, and a wavelet-based estimator exploiting multi-scale scaling properties of the process. For the drift and diffusion parameters ${\displaystyle (\mu ,\sigma )}$, we construct explicit Gaussian pseudo-maximum likelihood estimators derived from the Volterra covariance structure of the increment process. We establish unbiasedness, ${\displaystyle L^2}$-convergence, strong consistency, and asymptotic normality for all estimators. Furthermore, we derive Berry–Esseen type bounds that quantify the rate of convergence toward the Gaussian law, providing sharp distributional approximations in a genuinely fractional and non-Markovian setting. A Monte Carlo study is carried out, using high-resolution Volterra discretizations, large-scale simulation budgets, covariance-structured linear algebra, and multi-scale diagnostic tools. The numerical experiments confirm the theoretical convergence rates, demonstrate the finite-sample reliability of the estimators, and illustrate the sensitivity of the process dynamics to the fractional order ${\displaystyle \alpha }$: smaller values of ${\displaystyle \alpha }$ produce stronger memory effects and higher variability, while values closer to one lead to smoother and more stable trajectories. The proposed methodology unifies statistical inference for long-memory Gaussian processes with fractional differential stochastic dynamics, offering a coherent analytical and computational framework applicable in areas such as quantitative finance, anomalous diffusion in physics, hydrology, and engineering systems with hereditary effects. Full article

This paper employs Physics-Informed Neural Networks (PINNs) for the reconstruction and modelling of mean velocity profiles in fully developed turbulent channel flow over a high friction Reynolds number ($R{e}_{\tau }$). The network is trained with a high-fidelity Direct Numerical Simulation (DNS) dataset from channel flows, for $R{e}_{\tau }=395$–4186, and can extrapolate up to $R{e}_{\tau }$ = 10,049. The model predicts the mean velocity in terms of the inner-law variables, $u^{+}$, across Reynolds numbers using the inputs $\eta =y^{+}/R{e}_{\tau }$ and $R{e}_{\tau }$. A key novelty is the simultaneous optimisation of the network weights alongside two fundamental turbulence parameters, i.e., the von Kármán constant ($\kappa$) and the van Driest damping constant ($A^{+}$), allowing the PINN to autonomously calibrate the near-wall damping and log-law scaling directly from the physics-augmented loss function. The model performance is evaluated using profile-based metrics ($R^2$, mean square and absolute error) and integrated quantities (${\overline{V}}^{+}$, $R{e}_b$, and the skin-friction coefficient $C_f$), with comparisons against DNS-integrated friction values and classical theoretical values. The resulting hybrid framework offers a promising foundation for real-time digital twins and the acceleration of Computational Fluid Dynamics (CFD) solvers in canonical wall-bounded flows. By establishing a physically grounded connection between sparse data and structural constraints, these models enable accurate extrapolation into high Reynolds number regimes where the computational costs of traditional high-fidelity simulations are otherwise prohibitive. Full article

Canopy gaps are important footprints in understanding the forests’ disturbance regime and regeneration process, yet there is a need to employ multiple metrics along the gradient of time for a deeper understanding of the dynamics. In this study, aerial laser scanning-derived canopy gap data of three protected forests in the Carpathian Mountains, stratified by location and forest types, were examined at temporal and spatial scales. Multiple features were examined, such as gap size structure, gap area proportion, gap geometry, and the relationship between gap geometry and size and gap formation. The results indicated that the gap size frequency has a heavy-tailed right-skewed distribution and mostly maintains the same proportion across time, even after the reduction in gap numbers. Meanwhile, the probability distribution of the gap sizes is not exclusive to the power law; it also follows log-normal and exponential distributions. Gap counts and gap percentages decreased over time, but with the increasing size of gaps. Gap shape complexity was moderate around 2.0, but tended to have a complex shape as the gap size increased. The temporal gap dynamics were characterized by four gap types: recovered or closed gaps, persistent gaps, expanded gaps, or new openings, with the balance influenced by the severity of disturbance. These findings underscore the importance of collective gap metrics across temporal and spatial scales in elucidating gap dynamics of unmanaged forests. Full article