Search Results (236)

Regulatory risk measurement under Basel III’s Fundamental Review of the Trading Book places Expected Shortfall (ES) at the center of market risk capital, yet the fourth-order Edgeworth expansion, still widely used for Value-at-Risk (VaR) and ES calculations, can produce negative densities in the tail regions where these measures concentrate, while saddlepoint approximations preserve positivity but face their own limits in heavy-tailed and sub-Gaussian settings. Whether either method delivers reliable tail estimates in the rare-disaster regimes documented in the empirical consumption-disaster literature therefore remains an open question. We address it by comparing the two approximations across 648 rare-disaster parameter combinations and five additional distributional families (Student-t, Hansen skewed-t, generalised error distribution (GED), two-sided jump mixture, and generalised hyperbolic), and by deriving a closed-form characterisation of the Edgeworth validity envelope. We establish three core findings. First, the validity envelope is bounded above by a sharp kurtosis ceiling at ${\gamma }_2=4$ and laterally by a non-monotone skewness boundary peaking at $|{\gamma }_1^{\ast ,\max }| \approx 0.685$ at ${\gamma }_2\approx 2.533$; $87.5\%$ of the rare-disaster grid falls outside it. Second, accuracy is threshold-dependent: Edgeworth dominates at moderate quantiles, saddlepoint at extreme quantiles, with negative-density regions inflating Edgeworth ES error from $6.20\%$ inside the envelope to $47.04\%$ outside it. Third, these results reconcile only when point probability, density validity, and integrated-tail accuracy are treated as distinct accuracy criteria. The findings have direct implications for ES-based regulatory capital in heavy-tailed regimes and motivate a regime-conditional rather than universal approximation choice. Full article

Accurate Unmanned Aerial Vehicle (UAV) position estimation is the cornerstone of urban low-altitude safety management systems. Time Difference of Arrival (TDOA) and Remote Identification (Remote ID) are widely used surveillance technologies with complementary characteristics. TDOA provides high-rate updates but suffers from geometry-induced horizontal–vertical anisotropy and multipath effects, while Remote ID supplies absolute state information yet struggles with intermittent sampling and packet loss. Existing fusion schemes typically address these issues in isolation: sequential filtering manages asynchrony but assumes Gaussian noise, robust estimators suppress outliers at the cost of discarding valid data, and coupled-filter architectures allow vertical anomalies to contaminate horizontal estimates through the Kalman gain cross-coupling. No prior framework jointly handles structural TDOA altitude jumps, stochastic Remote ID timing jitter, and the geometric anisotropy between estimation subspaces within a single coherent pipeline. To bridge this gap, we propose a Hybrid Conditional Kalman Filter (HCKF) framework comprising three integrated modules. First, a kinematics-based temporal alignment module maps asynchronous measurements onto a uniform timeline and predicts missing samples, resolving cross-modal time mismatches. Second, a measurement quality evaluation mechanism detects TDOA altitude steps via robust two-layer stratification and scores Remote ID timing irregularity through a confidence mapping, converting these anomalies into dynamic covariance adjustments and weight caps without discarding observations. Third, a Subspace-Decoupled Fusion strategy exploits the physical insight that TDOA horizontal precision derives from hyperbolic intersection geometry, whereas its vertical estimates suffer from weak observability due to near-coplanar ground-station deployment. By applying entropy-guided weighting in the horizontal plane and a conditional Remote ID-dominant rule in the vertical axis, this design prevents cross-dimensional error propagation. The framework was validated using three real-world flight missions at distinct altitudes (255 m, 345 m, and 440 m) totaling 13.51 km of flight distance, with RTK serving as ground truth. HCKF reduces the Root Mean Square Error by over 40% relative to single-source baselines (95% bootstrap confidence interval: [35.2%, 48.7%]), and paired Wilcoxon signed-rank tests confirm statistically significant improvement ($p<0.01$) over standard EKF, Covariance Intersection, and Iterative CI across all three tracks. Full article

Fine-Grained Few-Shot Classification (FG-FSC) in remote sensing has become a critical task, as the scarcity of high-quality annotated data severely restricts the performance of deep learning models in fine-grained classification. Although Contrastive Language-Image Pre-Training (CLIP) exhibits strong generalization ability in few-shot learning, it fails to generate discriminative text and image features when adapted to remote sensing tasks. In this paper, a framework is proposed to adapt CLIP to remote sensing FG-FSC from both visual and text aspects. First, we introduce a Distribution-AWare Adapter (DAWA) that adaptively fuses instance-level visual knowledge from few-shot samples with distribution-aware representations derived from Gaussian Discriminant Analysis based on the original CLIP zero-shot knowledge, leading to stable visual feature representations under various few-shot settings. A hybrid loss function that incorporates transductive and contrastive regularization is employed to further prevent overfitting and improve the discriminability of features. Furthermore, we generate category-level fine-grained text captions, optimizing the image–text alignment when extremely few training images are available. Experiments on multiple remote sensing and natural image datasets verify that the proposed framework achieves state-of-the-art few-shot fine-grained classification performance with a modest training cost, providing a practical solution for few-shot remote sensing image analysis. Full article

High-precision identification of acoustic convergence zones (CZs) and acoustic shadow zones (SZs) is a core prerequisite for deep-sea sonar performance prediction and long-range underwater target detection. However, in data-scarce marine environments, traditional acoustic identification methods suffer from high environmental sensitivity and significant computational costs, while pure data-driven deep learning methods face dilemmas such as a lack of physical consistency and poor generalization on small samples. To address these issues, a three-level cascaded recognition framework based on physics-prior-augmented deep learning is proposed in this paper, enabling accurate segmentation of CZs and intelligent classification of sound field types under data-scarce scenarios. In this framework, physical acoustic principles are incorporated exclusively as priors through a training dataset generated by a Gaussian beam acoustic propagation code (Bellhop) and through hand-crafted geometric features derived post hoc from the initial segmentation outputs. Taking a typical deep-sea area in the Northwest Pacific Ocean as the research object, a hybrid dataset comprising 5000 simulated transmission loss images and 500 simulated images from a geographically distinct sea area is constructed. The sound field is categorized into four types: strong convergence, usable convergence, weak convergence, and shadow zone. In the first stage, the ResNet-34 backbone is improved by integrating deformable convolution and a global statistical feature module, which, combined with a joint loss function, achieves high-precision pixel-level segmentation of CZs and SZs, with the regional gray contrast reaching 86.9%. In the second stage, a customized dual-channel VGG16 architecture is designed to fuse the extracted geometric priors and visual features, achieving a sound field classification accuracy of 89.91%. In the third stage, a hybrid data augmentation technique combining Mixup and convolutional autoencoder is adopted alongside a transfer learning strategy to mitigate the data scarcity under cross-domain conditions, boosting the small-sample classification accuracy to 84.45%. The experimental results demonstrate that the models in each stage of the proposed framework significantly outperform traditional methods and baseline networks. This study provides a novel methodology and technical support for intelligent sound field identification in data-scarce marine environments. Finally, the core contributions and current limitations are summarized, and future research directions, such as constructing a dynamic hydrological parameter feedback mechanism and identifying three-dimensional complex sound fields, are prospected. Full article

This study investigates the robustness of Frenet–Serret curvature ($\kappa$) and torsion ($\tau$) estimates derived from noisy discretely-sampled three-dimensional space curves, with emphasis on the comparative performance of cubic spline and cubic Hermite interpolation methods. Accurate estimation of these geometric invariants is essential for reliable analysis of curves arising in signal processing and shape reconstruction; yet, the higher-order derivatives required for their computation exhibit pronounced sensitivity to measurement noise. We examine curves constructed through a Hilbert transform-based parameterization of the form $\mathrm{r}\left(t\right)=\left(X\left(t\right),A\left(t\right)sin\varphi \left(t\right),g\left(t\right)\right),$ where discrete samples are contaminated with additive white Gaussian noise at varying signal-to-noise ratios. Reconstruction is performed using cubic spline interpolation, which ensures global $C^2$ continuity, as well as cubic Hermite spline interpolation, which provides $C^1$ continuity with local tangent control. Frenet frame computations are then applied via regularized finite difference schemes. To characterize noise amplification theoretically, we derive the Curvature Stability Index (CSI) and Torsion Stability Index (TSI) as first-order variance bounds under the delta method. While these indices formalize the derivative-order dependence of noise sensitivity, Monte Carlo simulations reveal that empirical variance exceeds theoretical predictions by factors of ${10}^4$ to ${10}^6$, indicating dominance of nonlinear error propagation. Nevertheless, the indices establish that torsion instability arises fundamentally from third-order derivative structure rather than ground-truth magnitude. Numerical experiments across three geometric regimes constant-invariant helices, variable-curvature helices, and planar curves with identically zero torsion demonstrate that the ratio of the torsion root mean square error to curvature root mean square error consistently ranges from $6.5$ to $9.8$. This disparity persists even in the degenerate planar case, where $\tau \equiv 0$ analytically, confirming that torsion sensitivity is an intrinsic property of the Frenet–Serret formulation. Across all configurations, cubic spline reconstruction yields lower Monte Carlo mean RMSE and reduced empirical variance compared to Hermite spline, providing superior stability for derivative-based invariant estimation. Full article

Continuous-variable quantum communication (CVQC) operates under finite-resolution inference (finite data windows, calibration uncertainty, and estimator tolerances) and hardware control/readout limits that can be exploited by structured and adversarial disturbances. We study a feedback-inspired phase-space modulation strategy for implementation-layer resilience under DoS-like receiver-observable stress (e.g., fluctuation inflation, phase reference destabilization, or interface non-idealities), rather than proposing a protocol-level security proof. We propose a phase-first framework in which the defender selects a phase-space rotation angle $\theta$ (and, in principle, a squeezing parameter r) to minimize a receiver-observable centered second-moment degradation proxy, emphasizing containment rather than disturbance inversion. Because platforms expose different native observables, we evaluate phase-first modulation using two complementary tracks: (i) in theory/simulation, we monitor basis-dependent quadrature variance and covariance-derived summaries formed from mean-subtracted second moments so that $\Delta E_{\mathrm{cov}}$ reflects covariance inflation rather than coherent displacement; (ii) in the X8_01 hardware workflow, the readout is Fock sampling; thus, we use the shot-to-shot standard deviation ${\sigma }_N\left(\theta \right):=\sqrt{\widehat{Var}\left(N\left(\theta \right)\right)}$, where $N\left(\theta \right)$ denotes the shot-level detected count random variable at fixed $\theta$. In the reported hardware workflow, this shot-level count is formed by aggregating the returned Fock counts prior to postprocessing. We emphasize that ${\sigma }_N\left(\theta \right)$ is not claimed to estimate $Tr\left(V\right)$; it is an implementation-layer variability proxy aligned with the available readout. Our experimental validation is restricted to phase-only control instantiated as offline phase selection via one-dimensional grid search over $\theta$. Across numerical simulations and hardware phase-angle scans on Xanadu’s X8_01 photonic quantum processor, we find that static operating points can be brittle under strong DoS-like stress, whereas optimized phase selection can materially reduce a receiver-observed degradation proxy even without real-time feedback. Since $Tr\left(V\right)$ is invariant under pure rotations for phase-independent additive noise and ideal photon-number probabilities are invariant under a terminal Fock-basis phase gate, any observed $\theta$-dependence is interpreted operationally as evidence of a phase-dependent effective disturbance/measurement channel at the receiver interface. Simulation-only analyses indicate additional upside when squeezing is available, motivating future extensions incorporating higher-rate re-optimization, feedback-assisted architectures, and extended Gaussian control when available. Full article

Accurate modeling of irradiance scintillation is important for evaluating underwater wireless optical communication (UWOC) systems operating in oceanic turbulence. Existing studies have mainly focused on weak oceanic turbulence conditions, while irradiance scintillation modeling under arbitrary oceanic turbulence strength remains insufficiently developed. In this work, the Gaussian beam is adopted as the representative model of practical laser beams, whereas the plane-wave and spherical-wave cases are introduced as limiting cases to support the derivation and theoretical completeness of the Gaussian-beam formulation. A unified theoretical framework is developed based on the general oceanic turbulence optical power spectrum (OTOPS). Building upon previously reported weak-turbulence results, the scintillation index (SI) under saturated strong turbulence is first derived using asymptotic theory. Then, within the extended Rytov approximation, an effective-scale treatment is introduced to characterize the contributions of large- and small-scale eddies to irradiance fluctuations. By connecting the weak- and saturated-turbulence limits through asymptotic matching, a closed-form SI expression valid over a wide range of oceanic turbulence strengths is obtained. Numerical results show that the proposed model agrees well with the corresponding boundary cases and reproduces the characteristic “bump” behavior of oceanic turbulence, while highlighting the influence of ocean-specific cutoff spatial frequencies on the predicted scintillation peaks. These results provide a physically consistent analytical framework for UWOC channel modeling and performance evaluation under arbitrary oceanic turbulence strength. Full article

The Expectation-Maximisation (EM) algorithm is widely used for maximum likelihood estimation in incomplete data problems such as mixture modelling, but it often converges slowly, particularly when mixture components overlap substantially. This study presents a comprehensive empirical evaluation of simple EM acceleration schemes for Gaussian mixture models, comparing linear (STEM), quadratic (SQUAREM), and greedy (line search, golden section) methods across 240 simulated mixture configurations spanning three dimensionalities, four component counts, five overlap levels, and four sample sizes. A key contribution is the first systematic comparison of the three acceleration parameter estimates (${\alpha }_1$, ${\alpha }_2$, ${\alpha }_3$) in the mixture modelling context: we show that only ${\alpha }_3$, which is derived as the geometric mean estimate of ${\alpha }_1$ and ${\alpha }_2$, provides genuine acceleration, while ${\alpha }_1$ and ${\alpha }_2$ consistently increase iteration counts by 50–110% relative to ${\alpha }_3$, effectively acting as deceleration. With ${\alpha }_3$, SQUAREM reduces iterations by up to 48% with negligible computational overhead, while greedy methods achieve similar iteration reductions but at 50–110% greater wall-clock time due to repeated log-likelihood evaluations. Crucially, acceleration does not degrade parameter estimation quality under any tested combination of initialisation, overlap, dimensionality, or number of components. We further examine the interaction between acceleration and initialisation, finding that k-means benefits most from acceleration (up to 50% time savings), while the REBMIX (Rough-Enhanced-Bayes MIXture estimation) algorithm benefits least as it already starts near the optimum. Among REBMIX configurations, histogram preprocessing with the outliers mode traversing strategy offers the best trade-off between quality and computational cost. The findings are validated on a real-world Backblaze hard drive failure dataset, confirming the practical utility of EM acceleration. All methods are implemented in the free and open-source R package rebmix, accompanied by full source code. Full article

We study finite-horizon first-passage time and boundary non-crossing probabilities for Gaussian martingales, viewed as continuous local martingales obtained by running Brownian motion on a deterministic variance clock associated with deterministic volatility. Our aim is to quantify how the associated survival probability changes when the variance clock is perturbed. Using a deterministic time change representation, we reduce the problem to a Brownian boundary-crossing problem with a transformed horizon and a transformed boundary. This allows us to combine time change arguments with recent differentiability results for boundary-crossing probabilities. Under suitable regularity assumptions, we derive a first-order sensitivity formula with respect to the variance clock. The derivative splits naturally into two components: one produced by the deformation of the transformed boundary and one produced by the variation of the terminal transformed horizon. Several explicit examples are provided, including affine barriers and nonlinear deterministic clocks. These examples show in particular that, for nonconstant boundaries, redistributing variance over calendar time can change the finite-horizon survival probability even when the terminal variance is kept fixed. Full article

In this paper, we study the Ricci-harmonic flow under the assumption that the scalar curvature is bounded. First, we establish a time-derivative bound for solutions to the heat equation along the flow. Based on this estimate, we derive a short-time distance-distortion estimate and prove the existence of suitable cutoff functions. Using these results, we obtain Gaussian-type upper and lower bounds for the heat kernel along the Ricci-harmonic flow. Our results generalize the previous work of Bamler–Zhang on Ricci flow to the Ricci-harmonic flow setting, and can be used to study the regularity theory of Ricci-harmonic flow. Full article

In this paper, we establish the large deviation principle for the supremum of partial sums of a sequence of non-independent and non-identically distributed random variables. Let $\{X_n:n\ge 1\}$ be a sequence of random variables with the same negative mean, and denote $S_n={\sum }_{i=1}^n{X}_i$, $S_0=0$, and assume that the limit $\mathsf{\Lambda }\left(\theta \right)={lim}_{n\to \infty }{\displaystyle \frac{1}{n}}{\mathsf{\Lambda }}_n\left(\theta \right)$ of the logarithmic moment generating functions ${\mathsf{\Lambda }}_n\left(\theta \right)=logE\left[e^{\theta S_n}\right]$ exists and is essentially smooth and lower semi-continuous. We prove that the sequence $\left\{{\displaystyle \frac{1}{l}}{sup}_{n\ge 0}{S}_n:l\ge 1\right\}$ satisfies the large deviation principle on $\mathbb{R}$ and provide the exact form of its rate function. As a consequence, we obtain the large deviation principle for the supremum of sums formed by combining independent and identically distributed components with correlated components. As applications, we analyze the first-order autoregressive process and the Poisson–Gaussian mixture case and derive exact expressions for the corresponding rate functions and asymptotic estimates for the decay of tail probabilities. Full article

To evaluate the coupled deformation of existing shield tunnels induced by multi-segment excavations with isolation piles, this study develops an integrated analytical framework combining a Kerr three-parameter foundation-plate model with a three-dimensional image-source solution. A closed-form expression for the soil displacement field is first derived by incorporating layered soil conditions, staged excavation, and associated spatial effects. The soil–pile interaction of isolation piles is then modeled using the Kerr foundation, and the flexural response is obtained through variational formulation and finite-difference discretization. These responses are sequentially propagated through the excavation stages, enabling the superposition of multi-pit effects on the final retaining-wall deformation. The image-source method and a volume-equivalent transformation are further used to convert wall deformation into an additional stress field acting on the tunnel, which is ultimately coupled with a tunnel–soil deformation–coordination model to compute horizontal tunnel displacements. This unified workflow establishes a continuous mechanical transfer chain—from excavation-induced soil loss to isolation-pile bending and finally tunnel deformation. Parametric analyses show that lateral displacement of the retaining structure is jointly governed by wall bending and pit-bottom uplift, producing a right-skewed “S-shaped” profile. The bending-moment peak shifts toward earlier-excavated zones, indicating a memory effect of excavation sequencing. Two engineering cases verify that the proposed method accurately reproduces the magnitude and depth of measured wall deflections, while predicted tunnel displacements show a near-Gaussian pattern with high accuracy near the peak. The analytical framework provides a robust theoretical basis for optimizing pit segmentation and excavation sequencing adjacent to shield tunnels. Full article

This paper proposes a machine-learning-assisted framework for modal sensitivity analysis of systems with viscoelastic damping elements, including both classical and fractional rheological models. Surrogate models are trained to approximate natural frequencies over a prescribed parameter space using two sampling strategies (Grid and Latin Hypercube) and two regression approaches: multi-layer perceptron (MLP) and Gaussian process regression (GPR). Sensitivities are obtained from the surrogates by finite differences and complemented by model-interpretability measures, namely permutation feature importance (PFI) and Shapley Additive Explanations (SHAP). The surrogate-based results are compared with analytically obtained sensitivities. Local first- and second-order sensitivities of natural frequencies are derived analytically using the direct differentiation method (DDM) for a nonlinear eigenvalue problem formulated in the Laplace domain and further transformed into dimensionless sensitivity measures. The methodology is demonstrated for a single-degree-of-freedom oscillator with classical and fractional Kelvin damper models and a two-story frame equipped with a fractional Kelvin damper. The results show very good agreement between analytical and surrogate-based sensitivities. Feature-importance rankings obtained by PFI and SHAP are consistent with the dimensionless sensitivities and capture changes in parameter influence under varying damping levels. Dispersion studies indicate only minor ranking variations. Full article

M-ary frequency-shift keying (MFSK) is employed for several applications, including Internet-of-Things (IoT) and sensor-based communications. Previous studies have demonstrated that coherent detection of well-designed nonorthogonal MFSK signals outperforms orthogonal MFSK. This paper optimizes the error performance of nonorthogonal MFSK signals when the receiver uses a simple coherent detector on a symbol-by-symbol basis. First, we derive the theoretical conditions on the frequency separations to produce M symbol waveforms with negative crosscorrelation. Second, assuming equispaced frequencies, we analytically determine the optimum modulation index that maximizes the minimum distance among the symbol waveforms. Third, assuming non-equispaced frequencies, we optimize both nonorthogonal 4FSK and 8FSK signal sets. The optimized signal waveforms reduce the symbol error probability with respect to the current-best MFSK schemes existing in the literature, at the price of a bandwidth increase. For additive white Gaussian noise (AWGN) channels, an accurate expression for the symbol error probability of nonorthogonal 4FSK is also proposed. Full article

Therapist shortages make home-based rehabilitation an essential component of post-stroke care, yet patients often exhibit reduced adherence when functional gains are difficult to quantify and interpret. This study presents a cloud-enabled assessment framework centered on a dynamic reaching task for upper-limb rehabilitation in individuals with mild stroke. The proposed system combines wearable sensing and Internet of Things (IoT) connectivity to stream kinematic data to the cloud for near real-time analysis, and integrates a force-feedback rehabilitation robot to deliver motion guidance during training. The pipeline proceeds in three stages. First, smoothness-related kinematic descriptors are extracted and fed into a deep multi-class classifier to discriminate the affected side (left, right, or healthy). Second, movement quality is modeled using a Gaussian Mixture Model (GMM) trained on IoT-acquired trajectories to quantify performance via probabilistic similarity. Third, a calibrated scoring function transforms GMM log-likelihood into a normalized 0–1 quality index, producing visual reports that support interpretable feedback for patients and therapists. The framework is validated using motion data collected from stroke patients at Taipei Veterans General Hospital. Experimental results demonstrate that the neural network multi-classifier achieved an F1-score of 0.95. Incorporating robot-derived interaction signals further improved classification performance by approximately 5%. For movement quality assessment, the derived scores showed a significant positive correlation (Pearson correlation = 0.632, p = 0.02) with therapist-defined gold reference standards for right-affected patients. Additionally, integrating robot force-feedback signals and AIoT-enabled dynamic streams improved score accuracy by 8% and score responsiveness by 10%. These quantitative outcomes substantiate the efficacy of combining IoT-driven sensing and robot-assisted training for objective, interpretable, and remotely deployable motor assessment. Full article