In recent years， various semi-supervised self-training methods have made significant progress in solving image classification problems and have attracted widespread attention. However， even the state-of-the-art methods like FixMatch can suffer from training instability and extreme performance imbalance between classes due to the accumulation of pseudo-labeling errors. To address this issue， this paper introduces the concept of robust gamma divergence on top of the FixMatch method and proposes a semi-supervised self-training approach based on robust gamma divergence. In this method， we incorporate gamma divergence as a regularization term to the loss function of the training model to correct the mislabeled instances caused by error accumulation. Additionally， we conduct comparative experiments on artificially polluted simulated datasets and the CIFAR-10 dataset to demonstrate the superiority of the GammaFixMatch method in handling the problem of pseudo-label error accumulation.

Bayesian inference often faces challenges where the likelihood function is difficult to evaluate or lacks explicit expression， known as likelihood-free Bayesian problems， where posterior distributions can only be inferred indirectly through samples generated under specific parameters. Existing methods such as approximate Bayesian computation， synthetic likelihood， and Bayesian optimization focus on addressing these issues. This paper extends Miller et al.’s （2022） sequential neural ratio estimation method for likelihood-free Bayesian problems by transforming likelihood-to-evidence ratio estimation into a multi-class problem for efficient posterior estimation. We introduce a new calibration kernel-based ratio estimation method （CKRE）， to enhance the original method’s training efficiency and performance. The convergence of our proposed method is proven， and numerical experiments demonstrate its significant improvement in accurately estimating posterior distributions under limited sample generation conditions.

Consumer credit products have prevailed for a long time， allowing customers to spend first and pay later， stimulating customers to purchase products. Banks， financial service companies， and e-commerce platforms have all strategically laid out in this industry and provided corresponding online consumer credit services. To further stimulate consumption， companies will offer interest-free consumer credit services. We consider a firm that sells multiple substitutable products and provides interest-free consumer credit services and bears the service costs. We develop an MNL model and incorporate consumer responses to consumer credit services into the model， the firm’s objective is to make the optimal decisions of grace period for each product to maximize the total profit under linear and nonlinear credit service cost structures， respectively. The findings indicate that we can essentially transform the multiple products optimization problem into a single-variable root searching problem， which reduces the calculation complexity. The optimal grace period does not necessarily shrink with the increase of credit service cost and vice versa. Numerical analysis reveals that products with larger profit margins have longer optimal grace periods. We also compare the advantages and disadvantages of the two different credit options， namely， the uniform optimal grace periods for all products （Option 1） and the exclusive optimal grace period for each product （Option 2）. We find that the firm’s total profit from implementing Option 2 is always larger than that from implementing Option 1， especially when the firm’s ability to utilize the sales revenue is not strong， the profit improvement under Option 2 scheme is more significant.

The selection of divertor materials has always been one of the hot issues in the field of nuclear fusion. The experimental results in recent years show that using liquid lithium as plasma facing materials in divertor can not only effectively solve the problems faced by traditional solid materials， but also significantly improve the confinement property of plasma. However， the wettability of liquid lithium on the surface of most solid materials is not ideal. In view of this， the first-principles method was used to simulate and calculate the occupation and diffusion characteristics of lithium atoms on the surface of stainless steel， and the effects of nickel， tungsten， chromium and manganese were analyzed. The results show that the four alloying elements can significantly change the adsorption energy of lithium atoms on the （100） crystal plane. Around nickel and tungsten， the adsorption energy of lithium atom first increases and then decreases with the increase of distance， showing the effect of first attraction and then repulsion. However， around chromium and manganese， the adsorption energy decreases monotonously with the increase of distance， and it has a repulsive effect in the whole process. For nickel and tungsten， lithium atoms tend to diffuse in the direction close to alloy elements within a certain range， and move outward more easily beyond this range. For chromium and manganese， lithium atoms are always more likely to diffuse outward. The results of this paper are helpful to better understand the wetting and spreading characteristics of liquid lithium on the surface of stainless steel at the micro scale.

Liquid lithium （Li） has a wide range of applications in nuclear fusion test devices， but the slip characteristics of liquid Li on the surface of solid materials have not been fully studied. In this paper， the Couette flow of liquid Li in α-iron （Fe） nanochannels was simulated by the molecular dynamics method， and the effect of triangular roughness units on the slip characteristics of liquid Li on the α-Fe （100） surface was analyzed. The results show that the influence of the angle on both sides of the triangle on the slip length is not significant， but there is a critical angle， when the angle on both sides of the triangle exceeds the critical value， the liquid Li will form a microscale vortex on the front side of the triangle， which significantly increases the flow resistance， and then causes a sudden and large decrease in the slip length， the critical angle and the height show a downward trend. The height of the triangles has a more pronounced impact on slip length， and a similar critical height exists. Vortices only form when the height exceeds this critical value， regardless of changes to the angles. Temperature has a certain influence on these parameters. As temperature rises， both the critical angle and critical height decrease.

Inspired by the natural bifurcation structure such as leaf veins， this paper uses numerical simulation to study the convective heat transfer of the basic unit of the bifurcated microchannel heat sink. On the basis of fixing the parameters of the first-stage-channel， changing the width of the second-stage-channel of the bifurcated structure， and analyzing the temperature field and flow field in the channel in detail， the pressure drop， convective heat transfer coefficient and comprehensive heat transfer evaluation coefficient from the inlet to the second-stage were obtained. The results show that the bifurcation structure can enhance the fluid disturbance， interrupt and form a new fluid boundary layer， strengthen the heat transfer and make the temperature distribution more uniform. Within 1 mm of the inlet of the second-stage-channel diameter， the inlet effect of internal flow is more influential， and the comprehensive heat transfer evaluation coefficient reaches its maximum when the ratio of hydraulic diameter after bifurcation to that before bifurcation is 0.54. When the ratio of hydraulic diameter bifurcation is 0.80， the comprehensive heat transfer evaluation coefficient reaches its maximum outside the second-stage-channel above 1 mm. The research can be used as a reference and guidance for the optimal design of bifurcated microchannel heat sinks.

Based on density functional theory， the geometric optimization of thioglycolic acid molecules was performed at the B3LYP/6-311G（d，p） level， and the first 20 excited states of the molecules were calculated at the CAM-B3LYP/TZVP theoretical level. Firstly， the ground state information of the molecules was calculated and obtained. The results showed that when the center wavenumber of infrared spectrum number was less than 1 856 cm^-1， the main vibrational mode of the molecules was bending vibration； when the center wavenumber of infrared spectrum number was greater than 1 856 cm^-1， the main vibrational mode of the molecules was stretching vibration. Secondly， the first 20 excited states of the molecules were calculated， and four electronic state transitions with high transition probabilities （oscillator strength 0.05） were selected， and ultraviolet-visible spectra were plotted. Finally， the excitation types of these four transitions are determined by orbital pair transitions. the excitation type of S0→S13 was charge transfer excitation； the excitation types of S0→S10 and S0→S11 were charge transfer excitation； the excitation type of S0→S20 was localized excitation. Studying thioglycolic acid， which is harmful to humans， can provide theoretical support for experimental research and provide a theoretical basis for subsequent research on its degradation.

Taking Haidai region as the study area， this paper analyzes the elevation， slope， slope direction， river system， and other geographical factors of 9 448 residential settlement sites in Pre-Qin Period （600-2.1 ka BP）， and explores the relationship between the spatial-temporal distribution of the sites and geographical environment， by collecting the residential settlement sites of Pre-Qin Period extensively and establishing a database of the region， combining with SRTM DEM data， and using ArcGIS 10.7. Results show that： 1） The development of human settlements in the Haidai Region during the Pre-Qin Period went through a historical process of elevation from high to low， terrain from mountainous to flat， spatial distribution from small to large， then decreasing and continuing to increase. 2） The spatial distribution characteristics of archaeological sites in different periods are basically consistent. Archaeological sites mainly distributed in the elevation range of 0-150 m above sea level， with the range of 0-50 m being the most concentrated and inclined towards undulating slopes of 2°-15°. The range from flat land to slopes within 15° is the most concentrated， and archaeological sites are concentrated in the slope direction range of flat land （-1°） and southeast to southwest （112.5°-247.5°）. 3）The daily human activity radius of Haidai Region in Pre-Qin Period is about 3-4 km， and the residential settlement sites are closely connected with the river. Overall， the geographical environment has a close influence on the distribution and changes of site locations across different periods， also reflecting that the spatial cognition and utilization of the geographical environment by the predecessors in the Haidai Region during the Pre-Qin Period were already at a relatively high level.

Fire poses the greatest threat to the cultural heritage of timber buildings. The fire risk assessment of ancient buildings in the Palace Museum， the world’s largest remaining ancient palace complex， aids in the management， protection， and fire prevention efforts of the heritage site. This study constructed a dataset of fire risk factors， taking into account the hazard of causal factors， the sensitivity of disaster-bearing bodies， and loss control lability， reflecting the temporal and spatial characteristics of the Palace Museum’s ancient buildings. Utilizing the entropy-weighted TOPSIS algorithm， a fire risk index calculation model was developed to determine the relative fire risk among ancient buildings. This assessment was performed using the monthly spatio-temporal factor data of the Palace Museum from 2014 to 2019. The findings reveal that the comprehensive fire risk index of the Palace Museum ranges from 0.23 to 0.58， with the central axis area exhibiting the highest fire risk， especially in July and August. Hazard and sensitivity indices are higher in the central axis， northwestern， and northeastern zones， whereas the control index is higher in the central and southern parts of the central axis area as well as in the northwestern and northeastern zones. These areas are thus more susceptible to fire hazards， more impacted by fire disturbances， and possess a stronger response and coping capacity post-disturbance. In conjunction with GIS， the comprehensive time-series fire risk map of individual ancient buildings in the Palace Museum offers valuable insights for relevant departments to develop fire management plans and allocate resources for ancient buildings.

As socioeconomic development progresses， the interaction between climatic hazards and socioeconomic conditions amplifies substantial economic losses at varying scales. This study focuses on the characteristics and economic impacts of compound drought-heatwave events in China from 1984 to 2021. Using a standardized methodology， we developed a drought intensity-loss ratio model to isolate the influence of socioeconomic development on drought-related economic losses， providing a scientific basis for loss estimation and regional disaster prevention strategies. The results indicate that 1984 to 1990 was a period of high drought frequency， with the primary drought centers located in Southwest China， the central Huang-Huai region， and the upper Yangtze River， where economic losses were particularly significant. While raw economic losses increased over time， losses adjusted for population and economic growth showed a declining trend， closely aligning with the spatiotemporal distribution of droughts. Population growth and economic development are identified as the main drivers of the significant increase in China’s drought-related economic losses. The standardization approach effectively reveals the actual impacts of drought events. Based on these findings， this study constructed a drought intensity-loss ratio model to better characterize the relationship between natural drought variability and economic losses， offering a robust framework for accurately assessing drought impacts and supporting disaster mitigation strategies.

Sustainable development science satellite-1 （SDGSAT-1） is the first earth science satellite of the Chinese Academy of Sciences. It was successfully launched on November 5， 2021， aiming to achieve the global sustainable development goals and provide data for the study of interaction between humans and nature. Due to the poor penetration of visible light through cloud， many optical satellite remote sensing images are inevitably disturbed by cloud. Therefore， cloud mask production is an important processing step in optical remote sensing processing system. However， SDGSAT-1 multispectral images lack the short-wave infrared band required by the traditional cloud mask production algorithm， so the traditional cloud mask production algorithm is difficult to apply. Therefore， this paper proposes a cloud mask production method for SDGSAT-1 multispectral images based on fuzzy C-means （FCM） algorithm. The method selects the four spectral features of brightness， NDWI， NDVI， and HOT as input features. On this basis， the Mahalanobis distance is introduced， the results of K-means algorithm are used as the initial clustering center， and finally FCM algorithm is executed to obtain the final cloud mask. In the paper， the published SDGSAT-1 multispectral images are used to verify the performance of the proposed method and to compare it with other methods. The experimental results show that the average accuracy of the proposed method is 95.33%， which is higher than those of other methods.

As a green ecological barrier in northern China， changes in the ecological environment of Hulunbuir steppe have a profound impact on both the regional ecological balance and， to some extent， the broader ecological equilibrium of the entire country. Based on the long-term MOD13Q1 vegetation index dataset and meteorological data， this study developed a dynamically adaptable vegetation cover index， gsNDVI， which is sensitive to the active vegetation season. The vegetation change trend and future development of the Hulunbuir typical steppe from 2000 to 2022 were analyzed using the Theil-Sen regression， the Mann-Kendall method， and the Hurst exponent. Additionally， partial correlation analysis was employed to investigate the impact of climate factors on vegetation change. The results show that the multi-year average gsNDVI value for the study area is 0.39， with a spatial distribution characterized by higher values in the northeast and lower values in the southwest. Overall， the mean gsNDVI value exhibits a slow growth trend， though periodic fluctuations are observed. Vegetation coverage has increased in most areas， though noticeable degradation is evident in urban areas. The partial correlation analysis results indicate that precipitation is the primary factor influencing vegetation cover change in the study area， with grasslands being the most sensitive to changes in precipitation. Furthermore， based on the combined results of trend analysis and the Hurst exponent， the vegetation trend in certain areas of Hulunbuir is expected to reverse in the future， which may pose significant challenges to ecological and environmental protection in the region.

In federated learning， Byzantine nodes can carefully manipulate the model updates of clients. As a result， the central model accuracy decreases or fails to converge after aggregation. The number of communication rounds also increases. Without trusted reference gradients， the central model can not be properly aggregated solely from updates provided by untrustworthy clients. In this paper， we introduce a trusted reference and we regard it as a shadow model. To overcome this challenge， we propose a novel Byzantine robust federated aggregation method. The central server collects the shadow dataset in advance and trains a model called the shadow model. The central server compares the update direction between the client model and the trusted shadow model. Accordingly， the central server computes malicious score and marks the malicious clients. Then， the central model deletes or prunes the updates from the malicious clients. Finally， the central model aggregates the corrected gradients to ensure good convergence and maintain accuracy. The proposed method has been evaluated on a variety of model architectures and real datasets. The results show that the proposed method can effectively defend against six different Byzantine node attacks on three datasets.

Multimodal models show great potential in tasks such as generating language， video， and musical scores. However， they still face problems such as emotional consistency and professional guidance for background music generation tasks oriented toward rich melodic elements. In this paper， we propose multidimensional interaction guidance and temporal scaling encoding to generate music vector representations with multidimensional interaction properties by embedding emotion labels， rhythmic density， and rhythmic intensity into music expression compound words. We design the background music transformer （BMT）， a model for generating film and television soundtracks with rhythmic and harmonic correspondence between video and music， and provide a corresponding unpaired data-driven network training method for the model. We propose a “creator-audience” dual-view evaluation strategy to evaluate the interactivity and soundtrack effect of the model in a more comprehensive way. The experimental results show that the BMT model improves the objective evaluation index by 20.6%， and the model inference efficiency increases from 0.125 to 14.370， and also has obvious advantages in subjective evaluation index.