Stochastic Processes (SPs) appear in a wide field, such as ecology, biology, chemistry, and computer science. In transport dynamics, deviations from Brownian motion leading to anomalous diffusion are found, including transport mechanisms, cellular organization, signaling, and more. For various reasons, identifying anomalous diffusion is still challenging; for example, (i) a system can have different physical processes running simultaneously, (ii) the analysis of the mean-squared displacements (MSDs) of the diffusing particles is used to distinguish between normal diffusion and anomalous diffusion. However, MSD calculations are not very informative because different models can yield curves with the same scaling exponent. Recently, proposals have suggested several new approaches. The majority of these are based on the machine learning revolution. This paper is based on machine learning algorithms known as the convolutional neural network (CNN) to classify SPs. To do this, we generated the dataset from published paper codes for 12 SPs. We use a pre-trained model, the ResNet-50, to automatically classify the dataset. Accuracy of 99\% has been achieved by running the ResNet-50 model on the dataset. We also show the comparison of the Resnet18 and GoogleNet models with the ResNet-50 model. The ResNet-50 model outperforms these models in terms of classification accuracy.

In this paper, we are concerned with the numerical solution for the two-dimensional time fractional Fokker-Planck equation with tempered fractional derivative of order α. Although some of its variants are considered in many recent numerical analysis papers, there are still some significant differences. Here we first provide the regularity estimates of the solution. And then a modified L1 scheme inspired by the middle rectangle quadrature formula on graded meshes is employed to compensate for the singularity of the solution at t → 0 + , while the five-point difference scheme is used in space. Stability and convergence are proved in the sence of L ∞ norm, then a sharp error estimate O(τ min{2−α,rα} ) is derived on graded meshes. Furthermore, unlike the bounds proved in the previous works, the constant multipliers in our analysis do not blow up as the Caputo fractional derivative α approaches the classical value of 1. Finally, we perform the numerical experiments to verify the effectiveness and convergence order of the presented algorithms.

Rapid development and urbanization processes have had significant effects, including the shaping of sustainability practices focused on the urban level. Chinese cities have begun to pay attention to their rivers, and a large number of waterfront linear parks have been built in the riverside areas, so that the public can easily enjoy their landscape and entertainment functions. The purpose of this study is to demonstrate how the urban issue is commonly associated with environmental, economic, and social development, and how it is from there that solutions to the crisis we are currently facing can be found and implemented. The rationale of this study Changsha landscape continues to maintain its core traditions by preserving their landscape design safe and current through the use of innovation that is strategically implemented to its physical through online infrastructure. The benefits and challenges facing the listing system in practice should be made clearer by analyzing the background, the used criteria, the accountable agencies, and the protective mechanisms. To comprehend the design, the attributes, and the current state of these structures, this study conducted a literature review using the systematic literature review (SLR) and a survey has been done. These findings will be useful in defining the objectives for future lists of historic buildings in Changsha, and when combined with research on previous lists, they may be significant in understanding the prospects for modern heritage conservation in Changsha City.

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