We present a general method for calculating the mean span dimension of various branched and ringed polymers under the assumption of Gaussian chain statistics. The method allows a routine construction of an integral expression of the mean span dimension based on three base functions, determined for a connector, an arm and a loop, respectively. Applications of our method are shown to a variety of polymer architectures including star, two-branch-point, comb and various cyclic chains (eight-shaped, Θ-shaped and several semicyclic chains). Comparing the mean span dimension with other commonly used molecular size parametersthe radius of gyration and the hydrodynamic radius, it is found that both the mean span dimension and the hydrodynamic radius shrink less than does the radius of gyration when comparing averaged sizes of a branched chain with its linear analogue. Finally, possible use of the mean span dimension in size exclusion chromatography (SEC) experiments is discussed.

For the existing medical image edge detection algorithm image reconstruction accuracy is not high, the fitness of optimization coefficient is low, resulting in the detection results of low information recall, poor smoothness and low detection accuracy, we proposes an edge detection algorithm of cancer image based on deep learning. Firstly, the three-dimensional surface structure reconstruction model of cancer image was constructed. Secondly, the edge contour feature extraction method was used to extract the fine-grained features of cancer cells in the cancer image. Finally, the multi-dimensional pixel feature distributed recombination model of cancer image was constructed, and the fine-grained feature segmentation method was adopted to realize regional fusion and information recombination, and the ultra-fine particle feature was extracted. The adaptive optimization of edge detection was realized by combining with deep learning algorithm. The adaptive optimization in the process of edge detection was realized by combining with the deep learning algorithm. The experimental results show that the three-dimensional reconstruction accuracy of the proposed algorithm is about 95%, the fitness of the optimization coefficient is high, the algorithm has a strong edge information detection ability, and the output result smoothness and the accuracy of edge feature detection are high, which can effectively realize the detection of cancer image edge.

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