BACKGROUND: Cheminformatics is a fascinating emerging subfield of chemical graph theory that studies quantitative structure-activity and property relationships of molecules and, in turn, uses these to predict the physical and chemical properties, which are extremely useful in drug discovery and optimization. Knowledge discovery can be put to use in pharmaceutical data matching to help in finding promising lead compounds.
METHODS: Topological descriptors are numerical quantities corresponding to the chemical structures that are used in the study of these phenomena.
RESULTS: This paper is concerned with developing the generalized analytical expression of topological descriptors for zeolite ACO structures with underlying degree and degree-sum parameters.
CONCLUSIONS: To demonstrate improved discrimination power between the topological descriptors, we have further modified Shannon\'s entropy approach and used it to calculate the entropy measures of zeolite ACO structures.

Disorders of consciousness are impaired states of consciousness caused by severe brain injuries. Previous resting-state functional magnetic resonance imaging studies have reported abnormal brain network properties at different topological scales in patients with disorders of consciousness by using graph theoretical analysis. However, it is still unclear how inter-regional directed propagation activities affect the topological organization of functional brain networks in patients with disorders of consciousness. To reveal the altered topological organization in patients with disorders of consciousness, we constructed whole-brain directed functional networks by combining functional connectivity analysis and time delay estimation. Then we performed graph theoretical analysis based on the directed functional brain networks at three topological scales, from the nodal scale, the resting-state network scale to the global scale. Finally, the canonical correlation analysis was used to determine the correlations between altered topological properties and clinical scores in patients with disorders of consciousness. At the nodal scale, we observed decreased in-degree and increased out-degree in the precuneus in patients with disorders of consciousness. At the resting-state network scale, the patients with disorders of consciousness showed reorganized motif patterns within the default mode network and between the default mode network and other resting-state networks. At the global scale, we found a lower global clustering coefficient in the patients with disorders of consciousness than in the controls. The results of the canonical correlation analysis showed that the abnormal degree and the disrupted motif were significantly correlated with the clinical scores of the patients with disorders of consciousness. Our findings showed that consciousness impairment can be revealed by abnormal directed connection patterns at multiple topological scales in the whole brain, and the disrupted directed connection patterns may serve as clinical biomarkers to assess the dysfunction of patients with disorders of consciousness.

The input-output (IO) network is the quantitative description of an IO-based economy in which nodes represent industries and edges connecting nodes represent the economic connection between industries. Robustness refers to the ability of tolerating perturbations that might affect the system\'s functional body. There is both practical and theoretical significance to explore the robustness of the IO network for economic development. In this paper, we probe the robustness of the Chinese IO network based on the relative entropy of the probability distribution of network parameters (node degree, strongest path betweenness, downstream closeness and upstream closeness) under random node or edge failure and intentional node or edge attack. It is found that the Chinese IO network shows relatively weak robustness when it is under intentional attack, but relatively strong robustness when it is under random failure. Our experiment also verifies the applicability and effectiveness of the relative entropy model in measuring the robustness of the IO network.

Numerous experiments have proved that microRNAs (miRNAs) could be used as diagnostic biomarkers for many complex diseases. Thus, it is conceivable that predicting the unobserved associations between miRNAs and diseases is extremely significant for the medical field. Here, based on heterogeneous networks built on the information of known miRNA-disease associations, miRNA function similarity, disease semantic similarity, and Gaussian interaction profile kernel similarity for miRNAs and diseases, we developed a computing model of biased random walk with restart on multilayer heterogeneous networks for miRNA-disease association prediction (BRWRMHMDA) through enforcing degree-based biased random walk with restart (BRWR). Assessment results reflected that an AUC of 0.8310 was gained in local leave-one-out cross-validation (LOOCV), which proved the calculation algorithm\'s good performance. Besides, we carried out BRWRMHMDA to prioritize candidate miRNAs for esophageal neoplasms based on HMDD v2.0. We further prioritize candidate miRNAs for breast neoplasms based on HMDD v1.0. The local LOOCV results and performance analysis of the case study all showed that the proposed model has good and stable performance.

Complex network is a powerful tool to discover important information from various types of big data. Although substantial studies have been conducted for the development of stock relation networks, correlation coefficient is dominantly used to measure the relationship between stock pairs. Information theory is much less discussed for this important topic, though mutual information is able to measure nonlinear pairwise relationship. In this work we propose to use part mutual information for developing stock networks. The path-consistency algorithm is used to filter out redundant relationships. Using the Australian stock market data, we develop four stock relation networks using different orders of part mutual information. Compared with the widely used planar maximally filtered graph (PMFG), we can generate networks with cliques of large size. In addition, the large cliques show consistency with the structure of industrial sectors. We also analyze the connectivity and degree distributions of the generated networks. Analysis results suggest that the proposed method is an effective approach to develop stock relation networks using information theory.

Floral symmetry (corolla symmetry) has important biological significance in plant genetics and evolution. However, it is often multi-dimensional and difficult to quantify. Here, we constructed a multi-dimensional data matrix [X Y Z] by extracting three qualitative variables with binary properties (X: corolla regularity of interval and coplanarity; Y: petal regularity of shape and size; Z: petal local regularity of curling and wrinkle) from different dimensions of petals (overall to individual, and then to the local): all petals (corolla), individual petals, and local areas of petals. To quantitatively express the degree of Malus corolla symmetry, these variables were then combined with weight assignments (X: 22 > Y: 21 > Z: 20) based on their contributions to the corolla symmetry and the algorithm rule of converting binary to decimal values, which facilitated the unification of qualitative and quantitative analyses. Our results revealed significant reduction in degrees of Malus corolla symmetry along the direction of local to overall. Species showed higher degree of corolla symmetry than cultivars; however, taxa with stronger corolla symmetry might not necessarily be species. These findings provide new insights into the circumscription of Malus controversial species. The matrix model should be reference for future evaluation of angiosperm flower symmetry (lack of corolla fusion).

BACKGROUND: Phenotypic diversity of floral organs plays an important role in plant systematic taxonomy and genetic variation studies. Previous research have focused on the direction of variation but disregarded its degree. Phenotypic variation (including directions and degrees) of 17 floral traits from wild to cultivated crabapples were explored by comparing their distributions and deviations in three different dimensions: floral organ number, size, and the shape.
RESULTS: Except for petal number, petal length / petal width, and sepal length / sepal width, the analyzed floral traits of cultivated crabapples all showed downward distributed box bodies in box plot analysis and left deviations of fitted curves in frequency distribution function analysis when compared to the wild, which revealed consistent variation directions of petaloid conversion (pistils or stamens → petals), size miniaturization (large → small), and shape narrowness (petal shape: circular → elliptic; sepal shape: triangular → lanceolate). However, only seven floral traits exhibited significant differences in box plot analysis, while all of the traits in frequency distribution function analysis were obviously offset. The variation degrees were quantitatively characterized by sizing traits > shaping traits > numbering traits and by horizontal dimensions > radial dimensions.
CONCLUSIONS: Frequency distribution function analysis was more sensitive than the box plot analysis, which constructed a theoretical basis for Malus flower type breeding and would provide a new quantitative method for future evaluation of floral variation among different groups of angiosperms at large.

The aim of the present study was to investigate the potential changes in the choroidal thickness (CT) after surgical implantation of collamer lens (ICL) and to determine whether the variations in CT were associated with the degree of myopia. In the study, 98 eyes from 98 myopia patients were divided into two groups according to the degree of myopia: High myopia and super-high myopia. All eyes were measured using the swept-source optical coherence tomography (SS-OCT) technique. CT and CT variations were also recorded. The foveal CT increased significantly in high-myopia patients at 2 h after surgery and 3 months after surgery; the same tendency was observed in the inner nasal CT and outer nasal CT at the same time-points. In patients with super-high myopia, the subfoveal CT increased significantly at 2 h and 3 months after surgery compared with the pre-operative values. No statistically significant differences were obtained in any of the nine different choroidal regions evaluated at post-operative week 1 and post-operative month one. Furthermore, the increase in the subfoveal CT in the super-myopia group was significantly higher than that in the high-myopia group at 2 h and at 3 months after ICL. The results of the present study indicated that the CT significantly increased 2 h after the surgery and then reached a peak at 3 months, particularly in the subfoveal and nasal areas. A higher degree of myopia was associated with greater subfoveal choroidal changes.

Autophagy is a ubiquitous catabolic process by which damaged or harmful intracellular components are delivered to the lysosomes for self-digestion and recycling. It is critical in cancer treatment. Therapy-induced autophagy predominantly acts as a pro-survival mechanism, but progressive autophagy can lead to non-apoptotic cell death, also known as autophagic cell death. Plants or herbs contain various natural compounds that are widely used in the treatment of many types of malignancies. Emerging evidence indicates that phytochemicals targeting the autophagic pathway are promising agents for cancer treatment. However, these compounds play different roles in autophagy. In this review, we discussed the role of autophagy in cancer development and therapy, and focussed on elucidating the anti-cancer activities of autophagic modulators, especially phytochemicals. Notably, we described a novel premise that the dynamic role of phytochemicals should be evaluated in regulation of autophagy in cancer.

A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.