Search Results (8)

We develop a design-conditional limit theory for kernel estimators of conditional U-functionals based on locally stationary functional random fields observed at irregular random locations and under incomplete response observation. The covariates take values in a separable Hilbert space, the responses are allowed to take values in a general Polish space, and the target is indexed by a class of symmetric kernels of a fixed order. Functional localization is induced by single-index semi-metrics, while spatial localization is performed on the rescaled observation domain. Missing responses are incorporated through a complete-case construction under a Missing At Random condition and a uniform-positivity assumption. The resulting estimator is a ratio of spatially weighted U-statistics with random tuplewise observation indicators. The asymptotic analysis must account simultaneously for four sources of complexity: dependence within the spatial field, nonstationarity across an expanding domain, concentration in an infinite-dimensional covariate space, and the random thinning generated by missing responses. Conditioning on the sampling locations removes the randomness of the spatial design weights but does not eliminate dependence among the observations. We therefore derive a design-conditional projection decomposition adapted to the triangular-array structure of the model. The leading component is represented by a spatially dependent complete-case empirical process, whereas the higher-order canonical terms are controlled uniformly over the response kernels, functional-target points, single-index directions, and rescaled spatial locations. The proofs combine stationary tangent-field approximations for locally stationary random fields, large-block–small-block decompositions, coupling arguments under spatial absolute regularity, small-ball probability estimates, and entropy bounds for the joint indexing class. These arguments yield a uniform stochastic expansion in which the empirical fluctuation, the spatial–functional smoothing bias, and the local-stationarity approximation error appear as distinct contributions. In particular, the local-stationarity remainder has no counterpart in the strictly stationary theory and quantifies the cost of replacing the observed nonstationary field with its stationary tangent approximation. Under the MAR and positivity conditions, complete-case sampling reduces the effective local information and modifies the covariance structure, but it does not change the formal order of the uniform-convergence rate. Under strengthened moment, mixing, entropy, and negligibility conditions, we establish weak convergence of the normalized conditional U-process in the corresponding supremum-norm function space to a tight centered Gaussian process. The limiting covariance is determined by the complete-case first-order projection and consequently retains the effect of the observation propensity and the spatial dependence structure. We also introduce a complete-case leave-tuple-out spatial prediction criterion for bandwidth selection and prove oracle optimality over admissible bandwidth families. The general theory applies to conditional rank association, discrimination probabilities, set-indexed conditional distribution functionals, and related pairwise statistical-learning criteria. Simulation experiments and applications to spatial environmental and epidemiological data illustrate the finite-sample implications of the theory and the stabilizing role of single-index localization. Viewed through the lens of data-driven science, the framework addresses a fundamental asymmetry between the information carried by irregular, locally heterogeneous functional covariates and the selectively observed response tuples. By combining design conditioning, complete-case normalization, tangent-field localization, and single-index dimension reduction, the proposed approach resolves this inferential asymmetry at the level of the model by matching estimation and uncertainty quantification to the information actually available locally, without imposing artificial stationarity or complete-data symmetry. Full article

The Picasso triggerfish Rhinecanthus aculeatus is common in Indo-Pacific coral reefs, yet quantitative data on intraspecific morphological variation and developmental stability of its caudal peduncle spines remain limited, especially in the South China Sea, where reef degradation has been extensively documented in the literature. To address this, we examined 31 individuals from the Yongle Islands (Xisha Islands) using traditional morphometrics, truss distances, and angular cosine parameters for body shape, and developed a multi-level fluctuating asymmetry (FA) framework to dissect asymmetry in the caudal spine complex. Eye diameter showed strong negative allometry and low FA (FA5_pct = 1.56% ± 1.57%), supporting its suitability as a reference trait. Angular cosine values captured body shape variation more sensitively (mean CV = 14.78%) than traditional ratios (7.10%) or truss ratios (6.66%). Principal component analysis revealed continuous morphological dispersion without discrete clustering. Total spine FA5_abs was 2.13 ± 1.75, per-row difference FA5_abs was 3.10 ± 3.30, and within-row standard deviation FA5_abs was 0.59 ± 0.44. Per-row absolute differences declined numerically from anterior to posterior rows, although this trend was not statistically significant (Jonckheere–Terpstra test, p = 0.0955). A significant negative partial correlation between eye FA and total spine FA (partial ρ = −0.498, p = 0.0048; FDR-adjusted p = 0.0397) emerged after controlling for standard length, which we tentatively interpret as possible evidence of inter-organ developmental compensation. These findings document substantial developmental instability in the caudal spine complex of R. aculeatus from the Xisha Islands and illustrate the utility of multi-level FA analysis for functionally partitioned structures. Full article

Differing from previous work on ionospheric models only using a relative method, in this paper, stereoscopic ionospheric models are innovatively constructed utilizing both relative and absolute automatic plasma perturbations. Firstly, ionospheric perturbations are globally searched from electron density data measured for 10 years by Swarm-A/C satellites via automatic detection software. In total, 621,999 Swarm-A perturbations and 630,668 Swarm-C ones are obtained, respectively. Then, the variation for each perturbation is calculated in two ways: via the relative method and absolute method. To check possible discrepancy between ionospheric models under these two different calculations, seasonal ionospheric models have been globally established using relative and absolute perturbations for both satellites. The results show that both kinds of models for each satellite can comprehensively reveal the main ionospheric structures, like EIA, WSA/MSNA, the mid-latitude trough and the auroral anomaly zone. Relatively, the EIA always shows its significance in equinox under calculation methods due to strong ionospheric irregularities caused by seasonal variation, but it is more obvious under the absolute method than relative one because of its higher background density. Comparatively, the auroral anomaly zone is predominantly filled with relatively large perturbations and is particularly conspicuous, especially in winter, due to its low background density. By contrast, mid-latitude structures, such as WSA/MSNA and mid-latitude trough, are comparatively affected less under these dual methods. At the same time, the interhemispheric asymmetry of EIA phenomena, as well as latitudinal WN4/3, is also significantly distinguished by seasonal ionospheric models. The occurrence probabilities of perturbations as a function of various variation magnitudes are also examined and the results demonstrate that the percentages of all variation segments vary widely with seasonal changes but this uneven fluctuation is more pronounced in summer under relative calculation and in winter under absolute calculation. Small fluctuations with relative variation ΔVr < 10% or absolute ΔVa < 10⁴ m⁻³ always demonstrate significance in each group of seasonal perturbations while their percentage changes in different ways, decreasing in the order of summer, equinox and winter under the relative method and increasing under the absolute method. The measurements performed by Swarm-A/C demonstrate excellent consistency during the period considered. Full article

Under the framework of the Paris Agreement, carbon trading has emerged as a pivotal market-based instrument for achieving carbon neutrality. Following years of pilot programs, China has taken a critical step toward establishing a unified national carbon market. Consequently, accurate carbon price forecasting is essential for constructing a stable and effective carbon pricing mechanism. However, the 2017 reform of the EU Emissions Trading System (EU ETS) significantly altered the carbon price formation mechanism, exacerbating price volatility and uncertainty. This shift further underscores the urgent need for research into high-precision carbon price forecasting.Existing deep learning models struggle to simultaneously capture short-term high-frequency fluctuations and long-term evolutionary trends within complex carbon market data, a limitation that compromises their prediction accuracy and stability. To address these challenges, this paper proposes a Transformer-based carbon price forecasting model that incorporates an sLSTM structure. By enhancing sequence memory and state update mechanisms, this model effectively improves the capability to model both short-term volatility characteristics and long-term evolutionary patterns of carbon prices. In the data preprocessing phase, Variational Mode Decomposition (VMD) is employed to perform multi-scale decomposition of carbon price sequences, effectively mitigating the issue of overlapping fluctuations across different time scales. Furthermore, the Whale Optimization Algorithm (WOA) is utilized to optimize the number of decomposition modes and the penalty factor, thereby resolving the parameter sensitivity issues inherent in modal decomposition. Experimental results on real-world carbon price datasets demonstrate that the model achieves an average coefficient of determination ($R^2$) of 0.9862 and a Mean Absolute Percentage Error (MAPE) of only 0.5607%. These findings indicate that the proposed method possesses significant advantages in characterizing the complex dynamic features of time series, thereby effectively enhancing prediction accuracy.The proposed model can serve as a supportive tool for carbon-market risk monitoring and policy evaluation by identifying abnormal fluctuations and mitigating market inefficiencies caused by information asymmetry. This enhances the stability and predictability of carbon price signals as incentives for emissions reduction, enabling firms to plan abatement pathways and low-carbon investments, and strengthening the sustainable role of carbon markets in achieving carbon neutrality. Full article

Against the backdrop of the rapid growth in the scale of the prepared food market, safety issues have gradually become prominent. Establishing a traceability system has become crucial to safeguarding consumer rights and promoting the sustainable development of the industry, with traceability information sharing serving as the core link. However, affected by differences in interest demands and information asymmetry between manufacturers and retailers in the prepared food supply chain, there are obstacles to traceability information sharing. To explore the coordination mechanism of traceability information-sharing behavior in the prepared food supply chain under different decision-making models and its impact on profit distribution, this paper constructs a two-level supply chain model including manufacturers and retailers, comprehensively considers the online–offline dual-channel sales model, and distinguishes four scenarios: centralized decision-making, decentralized decision-making, retailer-led cost-sharing contract decision-making, and manufacturer-led cost-sharing contract decision-making. Using a differential game model, the equilibrium results under different decision-making models are discussed. The validity of the model is verified through fitting with empirical analysis and numerical example analysis. The research results show the following: (1) The centralized decision-making model has the best effect on increasing the market share of the prepared food supply chain, and although the cost-sharing contract model can improve it, there is still a gap. (2) The centralized decision-making model is not the one with the maximum profit, and manufacturer-led cost-sharing decision-making basically achieves Pareto optimality. The main reasons are the insufficient incentive mechanism, high coordination costs, and uneven profit distribution in centralized decision-making. (3) The impact of manufacturers’ offline channel traceability information-sharing behavior on profits is more significant than that of online channels. (4) In a market environment with information asymmetry, the impact of goodwill on the profits of prepared foods is more prominent. This research provides a theoretical basis for the management of the prepared food supply chain, helps optimize the traceability information-sharing mechanism and profit distribution plan, and promotes the healthy development of the industry. (5) When the coefficient measuring the intensity of traceability information sharing’s impact on product quality across manufacturers’ online and offline channels increases, only under the retailer-led model does product quality and goodwill exhibit a fluctuating trend of “rising from the bottom to the second place and then falling back to the bottom,” while the profits of all subjects increase simultaneously. (6) As the system attenuation coefficient increases, the evolution of product quality and goodwill under different cooperation models shows significant differences; in terms of profits, the profits of manufacturers’ online channels increase over time, while those of other subjects decrease. (7) When the discount rate rises, the manufacturer-led model presents distinct characteristics: both the ranking and absolute value of product quality decline synchronously, the ranking of goodwill falls, but its absolute value rises against the trend, the evolution of product quality and goodwill shows obvious model heterogeneity, and the profits of all subjects generally decrease. Full article

Sabots are vital to the successful launch of hypervelocity projectiles (HVPs), supporting and protecting the projectile’s flight body within the barrel. After the projectile exits the muzzle, aerodynamic forces induce relative motion between the sabot and the flight body, termed ‘sabot discard’. During this process, there are complex aerodynamic interactions between the sabot and flight body. These interactions impact the flight body’s flight stability and accuracy. This research focuses on an HVP with a two-segment sabot at Mach 7.2, employing the unstructured overset grid method and three-degree-of-freedom model to investigate the impact of the angle of attack (AOA) on the discard. At the AOA = 0 Deg, the sabot segments’ movement is symmetric, causing fluctuations in the flight body’s drag. However, at AOAs $\ne$ 0 Deg, the sabot segments’ movement becomes asymmetric. The upper sabot segment accelerates while the lower one decelerates, causing significant fluctuations in drag and lift, and prolonged disturbance. As the AOA increases, both asymmetry and disturbances intensify. Notably, at the AOA = 8 Deg, the absolute value of the discard angle difference between the upper and lower sabot segments reaches 45 Deg. Considering the AOA’s impact, it is advisable to maintain the AOA for HVP sabot discard in the range of [−2, 2] Deg. Full article

Three FA indices showed correlations with age and magnitude of traits, but not in general. Significant correlations between magnitude of traits and their FA were more pronounced in AFA (12 traits) than in RFA (10 traits) in all age classes except yearlings. For the tray tine form (curvature), FA significantly correlated with its magnitude in young, middle-aged and ripe stags, which indicates that the trait is a reliable indicator of asymmetry. Significant differences in AFA among age classes were found in four traits (weight of dry antlers, volume of antlers, distal circumference of beams and total length of crown tines). By RFA, a significant difference among age classes was only found for the distal circumference of beams. Thus, AFA is a more vulnerable condition index. Contrary to other research findings, developmental instability was more pronounced in older age classes. In yearlings, no significant FA dependence on the trait of antler size was detected, but in certain traits, an asymmetry detected at an early age remains visible later as well, although in stags grown under relatively optimal (especially trophic) environment conditions, developmental instability was present anyway. This proposes two hypotheses for further research: Competition may be manifested even under controlled conditions, which might jeopardize the developmental stability of certain individuals, or some traits will show developmental instability regardless of relatively good environmental conditions. Full article

Work is needed to better understand the control of knee movement and knee health. Specifically, work is needed to further understand knee muscle force control variability and complexity and how it is organized on both sides of the body. The purpose of this study was to explore side-to-side comparisons of magnitude- and complexity-based measures of knee muscle force control to support future interpretations of complexity-based analyses and clinical reasoning in knee injury control. Participants (male/female n = 11/5) performed constant-force isometric efforts at 50% maximal effort. Force variability was quantified during the constant-force efforts using a coefficient of variation (CV%) and force complexity using approximate entropy (ApEn) and detrended fluctuation analysis (DFA) α. Outcomes were right/left and dominant/nondominant group-level and individual-level comparisons. A limb-symmetry index was calculated for each variable and clinically significant absolute asymmetry was defined (>15%). The only significant side-to-side difference was for right/left DFA α (p = 0.00; d = 1.12). Maximum absolute asymmetries were (right/left, dominant/nondominant): CV 18.2%, 18.0%; ApEn 34.5%, 32.3%; DFA α 4.9%, 5.0%. Different side-to-side comparisons yield different findings. Consideration for how side-to-side comparisons are performed (right/left, dominant/nondominant) is required. Because a significant difference existed for complexity but not variability, this indicates that both complexity-based and magnitude-based measures should be used when studying knee muscle force control. Full article