The airfoil is prone to flow separation under low Reynolds number flow conditions, which leads to a sharp deterioration of aerodynamic performance of micro aircraft. This paper proposes a bionic separation flow airfoil design concept, which turns to fix the separation point through the leading edge sharpening structure and induce stable vortices, combined with the rear edge arc airfoil surface to promote flow reattachment and vortex stability. Numerical simulation results show that This bionic airfoil can effectively suppress flow separation over a wide Angle of attack (8°-16°), significantly increase lift coefficient, significantly improve stall characteristics, and extend the efficient operating range by about twice compared to traditional airfoils. Parameter analysis reveals the influence of key geometric parameters such as the leading edge tip Angle and the installation position of the arc wing on aerodynamic performance.

Within clinical research and healthcare decision-making, stochastic modeling methods are becoming increasingly more necessary due to the complexity of predicting the results of clinical processes, disease progression, and analyzing the effectiveness of various treatments. Markov chain models in particular present a good mix of accuracy and simplicity for modeling healthcare outcomes. This study presents a detailed overview of the theoretical foundations of Markov chain models while also discussing their application in patient risk stratification, clinical decision-making, and cost-effectiveness analysis of treatments. Both the advantages and disadvantages of Markov chain models like the memoryless assumption, data requirements needed, and state complexity particularly in healthcare contexts, are examined. Possible future directions for Markov chain modeling, namely hybrid modeling approaches and Markov decision processes (MDPs), are assessed to compare their ability to improve predictive accuracy and influence healthcare policies with regular Markov chain models. Combined all the elements, this study offers clinical researchers and policymakers a comprehensive reference on the strengths and weaknesses of Markov chain modeling specifically in healthcare applications.

This paper investigates the existence and properties of solutions to a class of stationary fractional mean-field games. The system is coupled with a Hamilton Jacobi Bellman equation with a fractional Laplace operator and a steady fractional Fokker Planck equation describing the agent distribution. Compared to traditional second order diffusion models, the fractional dynamics considered in this paper better characterize stochastic processes with anomalous diffusion properties. The authors explore the normality, uniqueness, and asymptotic behavior of the agent distribution density of the system solutions under different nonlocal diffusion orderss∈(1/2,1). Using the variational method or fixed-point theory, it is proven that the stationary system possesses classical or weak solutions under specific monotonicity or growth conditions of the coupled terms. Furthermore, the paper analyzes the impact of the nonlocality of the fractional operator on the game equilibrium state. The results not only generalize classical mean-field game theory but also provide theoretical support for the application of nonlocal diffusion models in economics and social sciences.

This paper investigates the existence and regularity theory of steady fractional diffusion equations with first-order convection terms in the whole spaceRn. Specifically, within the framework of the Bessel potential spaceLαp(Rn), we analyze the interaction between the nonlocal operator(-Δ)sand the divergence-type drift termdiv(b(x)m). The main challenges of this study lie in the regularity competition between the fractional diffusion operator and the first-order derivative drift term, and the analytical challenges arising from the lack of compact embedding properties in unbounded regions. The fractional Fokker-Planck equation is an important generalization of the classical Fokker-Planck equation combined with fractional calculus and is a core mathematical model for describing anomalous diffusion and non-Markovian stochastic processes. The classical Fokker-Planck equation mainly characterizes normal diffusion behaviors such as Brownian motion and is suitable for transport processes that are local, memoryless, and obey Gaussian distributions. However, a large number of practical systems (such as diffusion in complex media, movement of biological cells, financial price fluctuations, relaxation in amorphous materials, etc.) exhibit long-range memory, non-local interactions, heavy-tailed distributions, and anomalous diffusion characteristics that deviate from Fick's law, which are difficult to accurately describe using integer-order differential models.

With the explosive growth of multimedia data, the preservation of privacy in multimodal data has become a key research challenge. The traditional desensitization approach for a single data modality often fails to consider hidden privacy correlations between multiple data modalities, resulting in either information leakage or serious data utility loss. In this paper, we propose a joint multimodal desensitization framework to deal with face-related sensitive information in multimodal data. By utilizing Large Language Models (LLM) and YOLO World, we can accurately identify sensitive facial regions in multimodal data. We propose a customized face-swapping approach based on Stable Diffusion and IP Adapter to achieve visual anonymity, coupled with a Variational Autoencoder (VAE) to process text reconstruction. In addition, CLIP-based constraints are used to ensure the semantic consistency of multimodal data. The experimental results show that the proposed approach can reduce the Re-ID rate to 2.1% with high data utility.

A two-dimensional MPM model of unsaturated two-phase hydro-mechanical coupling was established to address the restart problem of retrogressive loess landslides under irrigation infiltration conditions, with zoning parameters for the disturbed zone and stable zone as well as periodic irrigation conditions set. The results show that the pore pressure in the disturbed zone responds more rapidly, forming a continuous high pore pressure zone from 0.5 s to 25 s, with the first displacement penetration and shear localization occurring at 155 s and 162 s respectively; concentrated deformation reoccurs at the new rear edge and the landslide restarts at 625 s, 700 s and 900 s. The model well reveals the chain mechanism of "sliding-disturbance-seepage-resliding".

Constraint satisfaction problems usually exhibit a distinct satisfiability transition phenomenon under stochastic models, and an exact phase transition threshold has been strictly proven to exist especially in the RB model. Aiming at the difficulty in solving hard instances of the random binary model with growing domains (RB) near the phase transition region, this paper proposes a guided decimation algorithm based on asynchronous belief propagation with gradual perturbation (P-BP). On the basis of the asynchronous BP-guided decimation framework, the algorithm introduces a linear annealing perturbation mechanism, which enables the variable-to-constraint messages to transit smoothly from deterministic update to the style of Gibbs sampling. Meanwhile, in the late stage of decimation, the variable fixing strategy is changed from greedy selection to direct sampling from the marginal distribution, supplemented by an automatic restart strategy with a maximum of 3 restarts. These improvements retain the asynchronous update, damping factor and A/B/C edge processing rules of the original algorithm, while significantly enhancing the stochastic exploration capability and effectively alleviating the problems of message oscillation, local convergence and error propagation of fixed variables in the phase transition region. Research shows that the combination of gradual perturbation with late-stage probabilistic sampling and a restart mechanism provides an effective way to enhance the robustness of belief propagation-based algorithms for stochastic constraint satisfaction problems.

With the extensive application of power electronics technology in the fields of new energy and information communication, the existing core material loss models can hardly meet the requirements of practical applications. This paper deeply analyzes the loss of magnetic components through mathematical modeling, providing theoretical support for the design of high-performance magnetic components. The study finds that the change of magnetic flux density in the excitation waveform can be characterized by only a small number of time series points. Combined with the idea of Fast Fourier Transform, a few key features can be identified for waveform classification. The morphological features of the magnetic flux density time series are extracted by principal component analysis, and then the random forest model is used to realize the effective identification of waveform categories. The validity of the model is verified on the given test set, which well reflects the rationality and effectiveness of the model.

The hidden flaws in the tunnel lines of the highways are hard to determine since their signals are small, overlapping and susceptible to environmental noise. Based on this study, a nondestructive testing system with multiple sources is offered to combine ground penetrating radar, infrared thermography and ultrasonic testing to intelligently detect and classify tunnel lining defects as graded. A common workflow is created, such as sensor alignment, signal preprocessing, feature construction, feature-level fusion and decision-level classification. Specimens of concrete with embedded voids, cracks and layer separation were prepared and repeated scanning was performed under both laboratory and semi-field conditions. Detection accuracy of 93.84 +1.27% was recorded with fused model which is 8.61 percentage points higher than the highest performing single source model. On four level defect grading, the proposed method had a macro-F1 of 0.912 +0.018 and minimized the confusion between neighboring severity classes. The findings indicate that multi-source fusion has the potential to offer consistent localization, accurate grading and greater robustness compared to the individual sensing techniques and can be used as a viable foundation of detailed assessment of tunnel lining.

Large language models perform exceptionally well in mathematical reasoning tasks, generating reasoning chains spontaneously upon receiving result prompts. However, the differences in quality between these spontaneous reasoning chains and those guided by structured process constraints remain unquantified systematically. This study selects 240 mathematical problems from GSM8K and MATH, using the self-consistency sampling strategy to invoke the large language model three times for each problem with the temperature parameter set to 0.7. The final answer is determined through majority voting. An evaluation index is designed to quantify the number of formulas and step markers in the reasoning chains and the stability of multiple generations is measured. The results show that process constraints increase the process quality score of the reasoning chains by 0.14 to 0.20, and the answer accuracy is close on GSM8K, but differs by 11% on MATH. The consistency rates are both 0.95 on GSM8K and 0.94 and 0.90 on MATH respectively. In complex problem types, the improvement in process quality brought by process constraints is greater, but the stability decline is more significant. An inherent trade-off between quality of the process and accuracy of the answer is present, and it provides empirical evidence of enhancing timely approaches in future research.