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In this article, we study eigenvalues λ\lambda and their associated eigenvectors xx of the adjacency matrices AA of balanced signed graphs. Balanced signed graphs were first introduced and studied by Harary to handle a problem in social psychology. Harary showed in 1953 that a signed graph is balanced if and only if its vertex set VV can be divided into two sets (either of which may be empty), XX and YY, so that each edge between the sets is negative and each within a set is positive. Based on this fundamental theorem for the balanced signed graphs, vertices of a balanced signed graph can be labeled in a way so that its adjacency matrix is well structured. Using this special structure, we find algebraically all eigenvalues and their associated eigenvectors of the adjacency matrix AA of a given balanced signed graph. We present in this study eigenpairs (λ,x)\left(\lambda ,x) of adjacency matrices of balanced signed graphs with some special structures.

Aiming at the naturalness and structural complexity of multivariate time series (MTS) data as well as the inability of existing algorithms to accurately identify clusters of high-dimensional time series data, the shape extraction multivariate time series clustering algorithm C-Shape under compactness constraints is proposed. Firstly, C-Shape performs largest triangle three buckets processing on the complex MTS to achieve the purpose of using fewer data while keeping the original shape unchanged. The raw data and the processed data are then selected to calculate the compactness between them to ensure the reduced spatial dimensionality is reasonable. Next, new cluster centers are obtained by using shape extraction while effectively preserving the shape integrity of the data, and the final cluster is formed by iteration. C-Shape can avoid the difficulty of grasping the low dimensional spatial dimensionality of the traditional down-sampling algorithm by fully taking into account the similarity between the shapes of the processed data and raw data. To validate its performance, C-Shape is tested with two classical and seven excellent time series clustering algorithms presented in recent years on the eight normal and four imbalanced MTS datasets with dimensions ranging from tens to thousands, respectively. Experimental results demonstrate all C-Shape clustering capabilities outperform those of the nine baseline algorithms, with an average improvement of 16.33% in Rand index and an average improvement of 69.71% in time performance. Thus C-Shape is an accurate and efficient multivariate time series clustering algorithm.

The existing low-rank graph representation algorithms fail to capture the global representation structure of data accurately, and cannot make full use of the valid information of data to guide the construction of the representation graph, then the constructed representation graph does not have a connected structure suitable for clustering. A smooth non-negative low-rank graph representation method for clustering (SNLRR) is proposed to solve these problems. To more accurately capture the global representation structure of data, SNLRR uses a logarithmic determinant function that is more consistent with the rank characteristics of the matrix to replace the kernel norm to estimate the rank function smoothly, which can effectively reduce the impact of larger singular values of the matrix on the rank estimation, balance the contribution of all singular values to the rank estimation, enhance the accuracy of the rank estimation, so as to more accurately capture the global representation structure of the data. The distance regularization term is also introduced to adaptively assign the optimal nearest neighbor learning representation matrix for each data point to capture the local representation structure of data. Besides, SNLRR applies rank constraint on the Laplace matrix of representation matrix so that the learned representation graph has the same number of connected components as the real number of clusters, that is, the resulting representation graph has a interconnected structure suitable for clustering. Experimental results on seven datasets with high dimensions and complex distribution, using eight comparison algorithms, show that the clustering performance of SNLRR algorithm is better than that of the eight comparison algorithms, with an average increase of 0.2073 in accuracy and 0.1758 in NMI. Therefore, SNLRR is a graph representation clustering algorithm that can effectively handle data with high dimensions and complex distribution.

Uveitis, a complex ocular disorder with numerous etiologies, can result from infection, autoimmune, and various physicochemical and mechanical injury factors. The treatment of this disease is difficult, and failure to receive timely and effective treatment can often lead to blindness. With the deepening of people's understanding of uveitis and its related mechanisms, various new sustained-release drug delivery systems for uveitis have been studied. However, due to the existence of various anatomical and physiological barriers in the eye, there are multiple obstacles to the sustained release treatment of uveitis. In this paper, the main research results in this field in recent years are reviewed, and the innovations and limitations of various new sustained-release drug delivery systems are discussed in order to provide new ideas for the sustained-release drug delivery treatment of uveitis in the future. These new sustained-release drug delivery systems will help to completely change the traditional treatment mode of uveitis with side effects and poor compliance in the future, bringing longer targeted sustained release and less toxic reactions.

[Objective] In order to explore the impact of uranium on algae growth and photosynthesis, and to screen new ecological risk assessment indicators for uranium pollution in water bodies based on photosynthesis. [Methods] This experiment used different concentrations of uranium (0, 0.5, 1, 5, 10, 20 mg/ L U6+ ) to treat two types of microalgae, chlorella (Chlorella vulgaris) and Huanglong chlorella, from different environments. The relative growth rate, photosynthetic oxygen release rate, chlorophyll content, and chlorophyll fluorescence kinetic parameters were measured on the 3rd, 5th, 7th, 10th, and 14th days after treatment. [Results] (1) Low concentration uranium (0.5 mg/L) treatment significantly promoted the growth and photosynthetic efficiency of the two types of microalgae, where the relative growth rate, photosynthetic oxygen release rate, maximum photochemical quantum yield (Fv/Fm) of photosystem Ⅱ, actual photochemical quantum yield Y (Ⅱ), and relative electron transfer rate (rETR) of the two microalgae were significantly higher than the control. However, high concentration uranium treatment (5 -20 mg/L) significantly inhibited the growth and photosynthesis of the two types of chlorella. (2) Huanglong chlorella was more sensitive to uranium treatment than chlorella, and its growth and photosynthesis were significantly inhibited at 1mg/L, and it could be used as an bioindicator for monitoring of uranium pollution in water bodies. (3) Regression analysis showed that under different concentrations of uranium treatment, the response speed of chlorophyll fluorescence parameters Y (Ⅱ) and rETR was faster than the changes in relative growth rate, photosynthetic oxygen release rate, chlorophyll content, and Fv/Fm, which could be used as sensitive indicators for ecological risk assessment of uranium pollution in water bodies. [Conclusion] Uranium exhibits a concentration effect on the growth and photosynthesis of chlorella, where low concentrations promote growth while high concentrations inhibit growth. Huanglong chlorella is more sensitive to uranium pollution. Therefore, the combination of Huanglong chlorella and chlorophyll fluorescence kinetic parameters Y (Ⅱ) and rETR can be applied for the ecological risk assessment of uranium pollution in water bodies.

Background and aim: Spontaneous rupture of hepatocellular carcinoma (HCC) is a life-threatening complication, and patients who experience it are formally assigned to stage T4 in the TNM system, while many clinicians informally assign them to stage C in the more widely used Barcelona Clinic Liver Cancer (BCLC) system. The present study explored whether these re-staging practices are appropriate for HCC patients who suffer tumor rupture. Methods: We retrospectively reviewed the records of 1952 HCC patients who underwent hepatic resection at our hospital between January 2017 and June 2021. We compared recurrence-free and overall survival between 143 patients who had BCLC stage A or B disease at the time of spontaneous rupture and 449 patients who had BCLC stage C disease without rupture. Results: Overall survival rate was significantly higher among the 143 patients (1, 3, 5-year survival rate was 80.3%, 60.4%, 51.4%) with rupture than among the 449 (1, 3, 5-year survival rate was 69.5%, 41.5%, 32.4%) with BCLC stage C disease (hazard ratio 1.65, 95% confidence interval 1.29 to 2.12). The two groups had similar recurrence-free survival (hazard ratio 1.19, 95% confidence interval 0.92 to 1.53), but most patients with rupture were able to receive interventional and potentially curative treatments after recurrence, whereas most patients in BCLC stage C received interventional or supportive care. Similar results were obtained after propensity score matching. Conclusion: HCC patients who experience spontaneous rupture tumor while in BCLC stage A or B have better prognosis than patients in BCLC stage C without rupture. Our results suggest that HCC patients who suffer rupture in BCLC stage A or B should not be assigned to BCLC stage C.