As a major disturbance to forest ecosystems, wildfires pose a serious threat to the ecological environment. Monitoring post-fire vegetation recovery is critical to quantifying the effects of wildfire on ecosystems and conducting forest resource management. Most previous studies have analyzed short-term (less than five years) post-fire recovery and limited the driving factors to temperature and precipitation. The lack of long-term and multi-faceted observational analyses has limited our understanding of the long-term effects of fire on vegetation recovery. This study utilized multi-source remote sensing data for a long time series analysis of post-fire vegetation recovery in China based on Google Earth Engine (GEE) cloud computing platform. Normalized Difference Vegetation Index (NDVI), Enhanced Vegetation Index (EVI), Normalized Burn Ratio (NBR), and Normalized Difference Moisture Index (NDMI) were selected to quantify the low, moderate, and high severity of burned areas. Ridge Regression Model (RRM) was used to analyze the relationship between 15 driving factors and the vegetation regeneration process. The results show that it took at least 7–10 years for the vegetation index to recover to the pre-fire level after a forest fire. The recovery rate of high severity combustion areas was the fastest within the first two years. From the results of Ridge Regression, it came out that the overall fitting degree of the model with NDVI as the dependent variable was superior than that with EVI. The four variables of temperature, precipitation, soil temperature, and soil moisture were able to explain the change in more detail in vegetation indices. Our study enriches the research cases of global forest fires and vegetation recovery, provides a scientific basis for the sustainable development of forest ecosystems in China, and provides insight into environmental issues and resource management.

We extend the differentiated product model, first developed by Bowley (1924), by relaxing the assumption that each firm produces only one differentiated product. By doing so, we are able to analyze the potential for collusive market segmentation in a two-stage decision framework, first in product space and second in output. We find that when firms cannot coordinate on output, the required discount factor that supports collusive market segmentation is strictly decreasing in product substitutability and is greater than partial output and full collusion. Overall we find that output collusion alone is easier to sustain than collusive product market segmentation

We propose the Weak Rescaled Pure Super Greedy Algorithm (WRPSGA) for approximation with respect to a dictionary $\mathcal{D}$ in Hilbert space. The WRPSGA is simpler than some popular greedy algorithms. We show that the convergence rate of the RPSGA on the closure of the convex hull of the $\mu$-coherent dictionary $\mathcal{D}$ is optimal. Then, we design the Rescaled Pure Super Greedy Learning Algorithm (RPSGLA) for kernel-based supervised learning. We prove that the convergence rate of the RPSGLA can be arbitrarily close to the best rate $O\left(m^{-1}\right)$ under some mild assumptions.

This study focused on improving the clustering performance of hyperspectral imaging (HSI) by employing the Generalized Orthogonal Matching Pursuit (GOMP) algorithm for feature extraction. Hyperspectral remote sensing imaging technology, which is crucial in various fields like environmental monitoring and agriculture, faces challenges due to its high dimensionality and complexity. Supervised learning methods require extensive data and computational resources, while clustering, an unsupervised method, offers a more efficient alternative. This research presents a novel approach using GOMP to enhance clustering performance in HSI. The GOMP algorithm iteratively selects multiple dictionary elements for sparse representation, which makes it well-suited for handling complex HSI data. The proposed method was tested on two publicly available HSI datasets and evaluated in comparison with other methods to demonstrate its effectiveness in enhancing clustering performance.

We first study the error performances of the Vector Weak Rescaled Pure Greedy Algorithm for simultaneous approximation with respect to a dictionary $\mathcal{D}$ in a Hilbert space. We show that the convergence rate of the Vector Weak Rescaled Pure Greedy Algorithm on ${\mathcal{A}}_1\left(\mathcal{D}\right)$ and the closure of the convex hull of the dictionary $\mathcal{D}$ is optimal. The Vector Weak Rescaled Pure Greedy Algorithm has some advantages. It has a weaker convergence condition and a better convergence rate than the Vector Weak Pure Greedy Algorithm and is simpler than the Vector Weak Orthogonal Greedy Algorithm. Then, we design a Vector Weak Rescaled Pure Greedy Algorithm in a uniformly smooth Banach space setting. We obtain the convergence properties and error bound of the Vector Weak Rescaled Pure Greedy Algorithm in this case. The results show that the convergence rate of the VWRPGA on ${\mathcal{A}}_1\left(\mathcal{D}\right)$ is sharp. Similarly, the Vector Weak Rescaled Pure Greedy Algorithm is simpler than the Vector Weak Chebyshev Greedy Algorithm and the Vector Weak Relaxed Greedy Algorithm.