Let $G$ be a connected graph with the usual shortest-path metric $d$. The graph $G$ is $\delta$-hyperbolic provided for any vertices $x,y,u,v$ in it, the two larger of the three sums $d(u,v)+d(x,y),d(u,x)+d(v,y)$ and $d(u,y)+d(v,x)$ differ by at most $2\delta.$ The graph $G$ is $k$-chordal provided it has no induced cycle of length greater than $k.$ Brinkmann, Koolen and Moulton find that every $3$-chordal graph is $1$-hyperbolic and that graph is not $\frac{1}{2}$-hyperbolic if and only if it contains one of two special graphs as an isometric subgraph. For every $k\geq 4,$ we show that a $k$-chordal graph must be $\frac{\lfloor\frac{k}{2}\rfloor}{2}$-hyperbolic and there does exist a $k$-chordal graph which is not $\frac{\lfloor \frac{k-2}{2}\rfloor}{2}$-hyperbolic. Moreover, we prove that a $5$-chordal graph is $\frac{1}{2}$-hyperbolic if and only if it does not contain any of a list of five special graphs as an isometric subgraph.

Understanding the relationship between exogenous melatonin and water deficit stress is crucial for achieving high yields and alleviating the effects of water deficit stress on soybean (Glycine max (L.) Merrill) plants in agriculture. This study investigated the effects of exogenous melatonin on soybean photosynthetic capacity under water deficit stress induced by polyethylene glycol (PEG) 6000. We conducted a potting experiment in 2018 using the soybean (Glycine max L. Merrill) cultivar Suinong 26. We identified the impacts of a concentration of PEG 6000 simulating drought (15%, w/v) and an appropriate melatonin concentration (100 μmol/L) on the growth of soybean seedlings and flowering stages in a preliminary test. We applied exogenous melatonin by foliar spraying and root application to determine the effects on leaf photosynthesis during water deficit stress. Our results indicated that 15% PEG 6000 had an obvious inhibitory effect on the growth of soybean seedlings and flowering stages, causing oxidative stress and damage due to reactive oxygen species (ROS) (H2O2 and O2·-) accumulation and potentially reducing air exchange parameters and photosystem II (PSII) efficiency. The application of exogenous melatonin significantly relieved the inhibitory effects of PEG 6000 stress on seedlings and flowering growth, and gas exchange parameters, potentially improved PSII efficiency, improved the leaf area index (LAI) and the accumulation of dry matter, slowed down oxidative stress and damage to leaves by increasing the activity of antioxidant enzymes (SOD, POD, and CAT), reduced the content of malondialdehyde (MDA), and ultimately improved soybean yield. Overall, the results of this study demonstrated that application of exogenous melatonin at the seedlings and flowering stages of soybean is effective in alleviating plant damage caused by water deficit stress and improving the drought resistance of soybean plants. In addition, the results showed that application of exogenous melatonin by root is superior to foliar spraying.

No abstract

No abstract

BackgroundHepatocellular carcinoma (HCC) is the sixth most common cancer in the world and the third leading cause of cancer-related death. Although the diagnostic scheme of HCC is currently undergoing refinement, the prognosis of HCC is still not satisfactory. In addition to certain factors, such as tumor size and number and vascular invasion displayed on traditional imaging, some histopathological features and gene expression parameters are also important for the prognosis of HCC patients. However, most parameters are based on postoperative pathological examinations, which cannot help with preoperative decision-making. As a new field, radiomics extracts high-throughput imaging data from different types of images to build models and predict clinical outcomes noninvasively before surgery, rendering it a powerful aid for making personalized treatment decisions preoperatively.ObjectiveThis study reviewed the workflow of radiomics and the research progress on magnetic resonance imaging (MRI) radiomics in the diagnosis and treatment of HCC.MethodsA literature review was conducted by searching PubMed for search of relevant peer-reviewed articles published from May 2017 to June 2021.The search keywords included HCC, MRI, radiomics, deep learning, artificial intelligence, machine learning, neural network, texture analysis, diagnosis, histopathology, microvascular invasion, surgical resection, radiofrequency, recurrence, relapse, transarterial chemoembolization, targeted therapy, immunotherapy, therapeutic response, and prognosis.ResultsRadiomics features on MRI can be used as biomarkers to determine the differential diagnosis, histological grade, microvascular invasion status, gene expression status, local and systemic therapeutic responses, and prognosis of HCC patients.ConclusionRadiomics is a promising new imaging method. MRI radiomics has high application value in the diagnosis and treatment of HCC.

No abstract

No abstract

Abstract. Consider a social network where each person holds an opinion represented by a numerical value. Whenever a member of the social network is given a chance, the member updates his/her opinion according to a certain convex combination of the opinions of all network members. The influence digraph of the network has network members as vertices, and there is an arc from a vertex v to a vertex u if and only if, in the opinion update formula for v, the coefficient of u's opinion is positive. The sink vertices in the influence digraph correspond to those stubborn people who never change their opinions. Assuming network members update their opinions one by one according to a given sequence, this note provides a description of the resulting opinion dynamics when every vertex can reach some sink vertex in the influence digraph.