Search Results (269)

As a critical carbon offset mechanism, China’s Certified Emission Reduction (CCER) plays a pivotal role in achieving the “dual carbon” targets. With the relaunch of its trading market, refining the CCER valuation framework has become imperative. This study develops a multidimensional CCER valuation methodology based on both the income and market approaches. Under the income approach, two probabilistic models—discrete and continuous emission distribution frameworks—are proposed to quantify CCER value. Under the market approach, a Geometric Brownian Motion (GBM) model and a Long Short-Term Memory (LSTM) neural network model are constructed to capture nonlinear temporal dynamics in CCER pricing. Through a systematic comparative analysis of the outputs and methodologies of these models, this study identifies optimal pricing strategies to enhance CCER valuation. Results reveal significant disparities among models in predictive accuracy, computational efficiency, and adaptability to market dynamics. Each model exhibits distinct strengths and limitations, necessitating scenario-specific selection based on data availability, application context, and timeliness requirements to strike a balance between precision and efficiency. These findings offer both theoretical and practical insights to support the development of the CCER market. Full article

This paper focuses on the Caputo-Hadamard fractional uncertain differential equations (CH-FUDEs) governed by Liu processes, which combine the Caputo–Hadamard fractional derivative with uncertain differential equations to describe dynamic systems involving memory characteristics and uncertain information. Within the framework of uncertain theory, this Liu process serves as the counterpart to Brownian motion. We establish some new Bihari type fractional inequalities that are easy to apply in practice and can be considered as a more general tool in some situations. As applications of those inequalities, we establish the well-posedness of a proposed class of equations under specified non-Lipschitz conditions. Building upon this result, we establish the notions of stability in distribution and stability in measure solutions to CH-FUDEs, deriving sufficient conditions to ensure these stability properties. Finally, the theoretical findings are verified through two numerical examples. Full article

In PAC spectroscopy, hyperfine interactions of a radioactive probe nucleus with its surroundings are measured, providing information about the local atomic structure and dynamics at the probe site. In the so-called fast reorientation time regime for fluctuating nuclear quadrupole interactions (NQIs), the PAC signal is an exponentially decaying function, with decay constant λ depending on both the hyperfine interaction and dynamics. For a molecular system in solution, dynamics may originate from Brownian molecular tumbling (rotational diffusion) with rotational correlation time τ_c and from local dynamics at the probe site, occurring at a characteristic time scale τ_loc. The τ_c and the τ_loc cannot be discriminated in a single PAC spectrum; however, assuming that they scale differently with viscosity and temperature, a series of experiments in which these parameters are varied may allow for discrimination of τ_c and the τ_loc. Three models are presented for the effect of dynamics on the PAC signal: (1) the Stokes–Einstein–Debye model with linear scaling of λ with viscosity ξ; (2) a more general model presenting a power law scaling of λ with (ξ/ξ₀)ⁿ; and (3) a model that includes rotational and local dynamics leading to an expression for λ that scales with ξ/(ξ + c), where c is a constant that depends on temperature, molecular volume, and τ_loc. These models may serve as different approaches to analyze PAC data and their dependence on temperature and solvent viscosity in the fast reorientation time regime, and they can be applied to design experiments for optimal discrimination of global rotational diffusion and local dynamics at the probe site. Full article

Cascade reservoir optimization faces significant challenges due to multi-dimensional, non-convex, and nonlinear characteristics with coupled constraints. As reservoir numbers increase, computational complexity escalates dramatically, limiting conventional optimization methods’ effectiveness. This paper proposes HHONMPA, a hybrid algorithm combining Harris Hawks Optimization (HHO) with Marine Predators Algorithm (MPA). The method uses SPM chaotic mapping for population initialization to enhance diversity and integrates both algorithms’ predatory behaviors. During exploration, it employs Brownian motion and improved Lévy flight strategies for global search, while exploitation uses enhanced HHO for local optimization. A novel Dual-Period Oscillation Attenuation Strategy dynamically adjusts parameters to balance exploration-exploitation. Performance validation using CEC2017 benchmark functions shows HHONMPA significantly outperforms the original HHO and MPA in solution accuracy and convergence speed, confirmed through statistical testing. Engineering validation applies the algorithm to the Lower Jinsha River—Three Gorges four-reservoir system, conducting experiments across various hydrological scenarios. Results demonstrate substantial improvements in search accuracy and convergence efficiency compared to existing methods. HHONMPA effectively addresses large-scale cascade reservoir optimization challenges, offering promising prospects for water resource management and hydropower scheduling applications. Full article

Using molecular dynamics simulations, we explore the impact of correlated monomer activity and star topology on the structure and dynamics of active polymers. Unlike uncorrelated active Brownian particle (ABP) stars, correlated activity induces a rather steep stretching of the star polymer at intermediate activity levels. This stretching is characterized by transitions between distinct, metastable states defined by the coordinated movement of the arms, leading to novel collective dynamics. The behavior is consistent with experimental observations of active oligomers, highlighting the critical role of activity correlations for the understanding and modeling of active polymers. Full article

This study investigates the valuation of defaultable corporate bonds using a two-factor model of Markov-modulated stochastic volatility with double exponential jumps (2FMMSVDEJ). This model captures long- and short-term SV and asymmetrical jumps in the underlying asset value. Concurrently, the firm’s debt dynamics are governed by a Markov-modulated GBM (MMGBM) model to reflect state transitions. A dynamic measure change technique is employed to determine the pricing kernel, and the resulting credit spreads and default probabilities are analyzed. Full article

This paper investigates the existence of square-mean S-asymptotically $(\omega ,c)$-periodic solutions for a class of neutral impulsive stochastic differential equations driven by fractional Brownian motion, addressing the challenge of modeling long-range dependencies, delayed feedback, and abrupt changes in systems like biological networks or mechanical oscillators. By employing semigroup theory to derive mild solution representations and the Banach contraction principle, we establish sufficient conditions–such as Lipschitz continuity of nonlinear terms and growth bounds on the resolvent operator—that guarantee the uniqueness and existence of such solutions in the space ${\mathcal{S}AP}_{\omega ,c}([0,\infty ),L^2(\Omega ,\mathbb{H}))$. The important results demonstrate that under these assumptions, the mild solution exhibits square-mean S-asymptotic $(\omega ,c)$-periodicity, enabling robust asymptotic analysis beyond classical periodicity. We illustrate these findings with examples, such as a neutral stochastic heat equation with impulses, revealing stability thresholds and decay rates and highlighting the framework’s utility in predicting long-term dynamics. These outcomes advance stochastic analysis by unifying neutral, impulsive, and fractional noise effects, with potential applications in control theory and engineering. Full article

We first investigate the dynamical behavior of an active Brownian particle influenced by a viscoelastic memory effect characterized by a power-law kernel, under the effects of thermal and active noises. We then analyze the dynamics of an active Brownian particle confined in a harmonic trap in the presence of the same noise sources. To derive the Fokker–Planck equation for the joint probability density of the active particle, we obtain analytical solutions for the joint probability density and its moments using double Fourier transforms in the limits $t\ll \tau$, $t\gg \tau$, and $\tau =0$. As a result, the mean squared displacement of an active Brownian particle driven by thermal noise exhibits a super-diffusive scaling of $t^{2h+1}$ in the short-time regime ($t\ll \tau$). In contrast, for a particle in a harmonic trap driven by active noise, the mean squared velocity scales linearly with $t$ when $\tau =0$. Moreover, the higher-order moments of an active Brownian particle in a harmonic trap with thermal noise scale with $t^{4h+2}$ in the long-time limit ($t\gg \tau$) and for $\tau =0$, consistent with our analytical results. Full article

Recent denoising methods based on diffusion models typically formulate the task as a conditional generation process initialized from a standard Gaussian distribution. However, such stochastic initialization often leads to redundant sampling steps and unstable results due to the neglect of structured noise characteristics. To address these limitations, we propose a novel framework that directly bridges the probabilistic distributions of noisy and clean images while jointly modeling structured noise. We introduce Dual-diffusion Brownian Bridge Coupled Sampling (DBBCS) the first framework to incorporate Brownian bridge diffusion into image denoising. DBBCS synchronously models the distributions of clean images and structural noise via two coupled diffusion processes. Unlike conventional diffusion models, our method starts sampling directly from noisy observations and jointly optimizes image reconstruction and noise estimation through a coupled posterior sampling scheme. This allows for dynamic refinement of intermediate states by adaptively updating the sampling gradients using residual feedback from both image and noise paths. Specifically, DBBCS employs two parallel Brownian bridge models to learn the distributions of clean images and noise. During inference, their respective residual processes regulate each other to progressively enhance both denoising and noise estimation. A consistency constraint is enforced among the estimated noise, the reconstructed image, and the original noisy input to ensure stable and physically coherent results. Extensive experiments on standard benchmarks demonstrate that DBBCS achieves superior performance in both visual fidelity and quantitative metrics, offering a robust and efficient solution to image denoising. Full article

Magnetic nanoparticles (MNPs) perturb magnetic field homogeneity, influencing transverse relaxation and the full width at half maximum (FWHM) of nuclear magnetic resonance (NMR) spectra. In Nuclear Magnetic Resonance (NMR), this appears as decay of the free induction decay (FID) signal, whose relaxation rate determines spectral FWHM. In D₂O containing MNPs, both nanoparticles and solvent molecules undergo Brownian motion and diffusion. Under a vertical main field ($B_0$), MNPs respond to their magnetization behavior, evolving toward a dynamic steady state in which the time-averaged distribution of local field fluctuations remains stable. The resulting spatial magnetic field can thus characterize field homogeneity. Within this framework, Monte Carlo simulations of spatial field distributions approximate the dynamic environment experienced by nuclear spins. NMR experiments confirm that increasing MNP concentration and particle size significantly broadens FWHM, while stronger $B_0$ enhances sensitivity to MNP-induced inhomogeneities. Full article

Unmanned aerial vehicle (UAV) flight trajectories in complex environments are often affected by multiple uncertainties, making accurate prediction challenging. To address this issue, this study proposes a probabilistic four-dimensional (4D) trajectory prediction model based on Brownian bridge motion. The UAV’s flight from mission start to endpoint is modeled as a Brownian bridge stochastic process with endpoint constraints, where the mean function sequence is constructed from path planning results and UAV performance parameters. To incorporate operational feasibility, the concept of the spatiotemporal reachable domain from time geography is introduced to dynamically constrain reachable positions, while a truncated Brownian bridge distribution is used to model probabilistic positions in three-dimensional space. A simulation platform in a realistic 3D geographical environment is developed to validate the model. Case studies show that the proposed method achieves dynamic probabilistic trajectory prediction under mission constraints with strong adaptability and practicality. The results provide theoretical support and technical reference for trajectory planning, conflict detection, and flight risk assessment in the pre-tactical phase. Full article

We consider first-order impulses for impulsive stochastic differential equations driven by fractional Brownian motion (fBm) with Hurst parameter $H\in ({\displaystyle \frac{1}{2}},1)$ involving a nonlinear $\varphi$-Laplacian operator. The system incorporates both state and derivative impulses at fixed time instants. First, we establish the existence of at least one mild solution under appropriate conditions in terms of nonlinearities, impulses, and diffusion coefficients. We achieve this by applying a nonlinear alternative of the Leray–Schauder fixed-point theorem in a generalized Banach space setting. The topological structure of the solution set is established, showing that the set of all solutions is compact, closed, and convex in the function space considered. Our results extend existing impulsive differential equation frameworks to include fractional stochastic perturbations (via fBm) and general $\varphi$-Laplacian dynamics, which have not been addressed previously in tandem. These contributions provide a new existence framework for impulsive systems with memory and hereditary properties, modeled in stochastic environments with long-range dependence. Full article

Wetland loss and human activities are forcing migratory waterbirds to rely on alternative habitats such as croplands, yet their adaptive habitat use across contrasting landscape contexts remains unclear. The Bar-headed Goose (Anser indicus) is a key indicator species in the wetland ecosystems of the Yunnan–Guizhou Plateau. Comparing differences in its wintering habitat selection and utilization is of great significance for understanding its ecological adaptation mechanisms and formulating regional wetland conservation strategies. In this study, we compared the diurnal habitat use during the wintering period of Bar-headed Geese at three wetlands (Nianhu, Caohai, and Napahai) representing distinct landscape contexts. We used GPS satellite tracking and dynamic Brownian bridge movement modeling, combined with random forest analysis of environmental variables, to quantify diurnal habitat use and selection at each site. Our results revealed significant regional differences in habitat use. In the agriculture-dominated wetlands (Nianhu and Caohai), geese primarily utilized cropland and marsh habitats (Nianhu: cropland 45.88% ± 30.70%, marsh 42.55% ± 33.17%; Caohai: cropland 62.33% ± 12.16%, marsh 28.61% ± 13.62%). In contrast, at Napahai, which is dominated by natural habitats, geese primarily used grassland (65.92% ± 20.01%) and marsh (26.85% ± 21.88%), with minimal use of cropland (4.21% ± 7.00%). Diurnal habitat selection was influenced by multiple environmental factors, with distinct regional differences identified through random forest modeling. In Nianhu, key factors included distance to supplemental feeding site, distance to grassland, distance to woodland, and distance to open water. In Caohai, distance to grassland, distance to nocturnal roost site, distance to settlement, and distance to open water were significant drivers. In Napahai, distance to nocturnal roost site, distance to open water, and distance to marsh were the most influential (all with p < 0.01), reflecting flexible behavioral responses. Based on these findings, we recommend region-specific conservation management strategies. Specifically, supplemental feeding at Nianhu should be strictly regulated. Agricultural planning in farming areas should account for the habitat needs of wintering waterbirds. Grassland and marsh habitats at Napahai should also be more effectively protected. Full article

Surface functionalization of magnetic nanoparticles, commonly used for their biocompatibility in biomedical applications, plays a critical role in optimizing iron oxide nanoparticles (IONPs) for magnetic hyperthermia (MH), a promising modality in cancer therapy. In this study, we provide the first comprehensive comparison of hyperbranched dendron coatings versus linear dicarboxylate ligands on IONPs, revealing their contrasting impacts on heating efficiency under varying magnetic field amplitudes (H). Dendron-coated IONPs outperform dicarboxylate-coated ones at low fields (H < 25 kA/m) due to reduced dipolar interactions and enhanced Brownian relaxation. Conversely, dicarboxylate coatings excel at high fields (H > 25 kA/m) by enabling magnetically aligned chains, which amplify hysteresis losses. Our work also introduces an approach to dynamically modulate the heating efficiency of IONPs by applying a static DC magnetic field (H_DC) in conjunction with the alternating magnetic field (AMF). We observed a coating-dependent response to H_DC in the parallel configuration (H_DC aligned with AMF), the specific absorption rate (SAR) increased by ~620 W/g_Fe for cubes and ~370 W/g_Fe for spheres at high AMF amplitudes (H > 30 kA/m) for dicarboxylate-coated IONPs. This enhancement arises from magnetically aligned chains (visualized via Transmission Electron Microscopy), which amplify extrinsic anisotropy and hysteresis losses; in contrast, for dendron-coated IONPs, their SAR values decreased under H_DC (up to ~665 W/g_Fe reduction for cubes in the perpendicular configuration), as the thick dendron shell prevents close interparticle contact, suppressing chain formation and fanning rotation modes. These findings underscore the significance of surface functionalization in enhancing the therapeutic efficacy of magnetic nanoparticles. Full article

This study introduces and evaluates stochastic models to describe Bitcoin price dynamics at different time scales, using daily data from January 2019 to December 2024 and intraday data from 20 January 2025. In the daily analysis, models based on are introduced to capture long memory, paired with both constant-volatility (CONST) and stochastic-volatility specifications via the Cox–Ingersoll–Ross (CIR) process. The novel family of models is based on Generalized Ornstein–Uhlenbeck processes with a fluctuating exponential trend (GOU-FE), which are modified to account for multiplicative fBm noise. Traditional Geometric Brownian Motion processes (GFBM) with either constant or stochastic volatilities are employed as benchmarks for comparative analysis, bringing the total number of evaluated models to four: GFBM-CONST, GFBM-CIR, GOUFE-CONST, and GOUFE-CIR models. Estimation by numerical optimization and evaluation through error metrics, information criteria (AIC, BIC, and EDC), and 95% Expected Shortfall (ES₉₅) indicated better fit for the stochastic-volatility models (GOUFE-CIR and GFBM-CIR) and the lowest tail-risk for GOUFE-CIR, although residual analysis revealed heteroscedasticity and non-normality. For intraday data, Exponential, Weibull, and Generalized Gamma Autoregressive Conditional Duration (ACD) models, with adjustments for intraday patterns, were applied to model the time between transactions. Results showed that the ACD models effectively capture duration clustering, with the Generalized Gamma version exhibiting superior fit according to the Cox–Snell residual-based analysis and other metrics (AIC, BIC, and mean-squared error). Overall, this work advances the modeling of Bitcoin prices by rigorously applying and comparing stochastic frameworks across temporal scales, highlighting the critical roles of long memory, stochastic volatility, and intraday dynamics in understanding the behavior of this digital asset. Full article