Trees with the most subtrees -- an algorithmic approach

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in applications. The number of subtrees in the extremal cases constitute sequences which are of interest to number theorists. The structures which maximize or minimize the number of subtrees among general trees, binary trees and trees with a given maximum degree have been identified previously. Most recently, results of this nature are generalized to trees with a given degree sequence. In this note, we characterize the trees which maximize the number of subtrees among trees of a given order and degree sequence. Instead of using theoretical arguments, we take an algorithmic approach that explicitly describes the process of achieving an extremal tree from any random tree. The result also leads to some interesting questions and provides insight on finding the trees close to extremal and their numbers of subtrees.Comment: 12 pages, 7 figures; Journal of combinatorics, 201

Effect of mesenchymal stem cell transplantation on behavior and structural changes in myelin in experimental rat autoimmune encephalomyelitis

Purpose: To investigate the effect of bone marrow mesenchymal stem cell (BM-MSC) transplantation on behavior and structural changes in myelin of experimental autoimmune encephalomyelitis (EAE) in rats.Methods: Wistar rats were randomly assigned to normal control, EAE, placebo injection treatment, and MSCs treatment. EAE, placebo injection treatment and MSCs treatment groups were further divided into six groups, i.e., 1-day, 3-day, 7-day, 14-day, 21-day, and 28-day post-onset. Changes in the diseasestatus of the rats and structural changes in myelin at different time points were assessed with silver staining.Results: Behavioral changes peaked between 13 to 17 days post-immunization (71.90 % incidence), while disease symptoms peaked between 3 and 5 days after onset, were sustained for about 7 days, and then eased gradually thereafter. The highest therapeutic scores and the entire course of the disease in EAE and placebo treatment groups were not significantly different (p > 0.05). However, in MSC treatment group, these parameters were significantly lower than in the above two groups (p < 0.05). In EAE and placebo treatment groups, myelin sheath lesions were obvious from day 3 to 7 but on day 14, the number of myelin sheath fragments decreased significantly. Recovery at different time points was also better than those in EAE and placebo treatment groups.Conclusion: MSC transplantation shortens the course of EAE, and also reduces its severity. Thus, it has some prospects for use in the management of EAE.Keywords: Bone marrow mesenchymal stem cells, Autoimmune encephalomyelitis, Transplantation, Myeli

A Bridge Between Two Worlds: a Cultural Interpretation of Dragonwings

Living in the dual worlds of his life as a Chinese American and in places such as Chinatown, Laurence Yep felt that he was culturally alienated and that he did not have a culture of his own. With the driving wish to find out about Chinese culture―his culture, he finished his best known novel Dragonwings after six years of research on Chinese culture. Based on the true story of Fung Joe Guey, a Chinese American who built and flew an airplane in the Oakland hills in 1909, Dragonwings tells the story of Moon Shadow, who comes to San Francisco to join his unknown father, Windrider, who cherishes the dream of flying. To pursue the dream, Moon Shadow and his father have to move out of Chinatown. After enduring a sea of misunderstanding, cruelty and poverty, Windrider finally realizes his flying dream with the support and aid of his beloved son and his fellowmen, as well as his American friends. Trying to show the process from misinterpretation and misunderstanding to mutual understanding and the possibilities of cultural exchange and cultural fusion between two different cultures, we will discuss how the Chinese culture is rediscovered by a Chinese American and how cultural misunderstanding leads to an unbalanced world and how tolerance and understanding restore the world into a harmonious one. This paper attempts to demonstrate, through the analysis of Dragonwings, the author’s exploration of Chinese culture, cultural exchange and human nature transcending cultural differences. Key words: Dragonwings, Laurence Yep, cultural exchange Abstrait: En vivant dans le monde dual de sa vie comme Américain chinois et aux endroits comme la Cité chinoise, Laurence Yep trouve qu’il était aliéné culturellement et qu’il n’avait pas de culture de sa ville. Avec l’espoir violent à découvrir la culture chinoise----sa culture, il a achevé son roman bien connu Dragon-ailes après une recherche de six années sur la culture chinoise. Basé sur l’histoire vraie de Fung Joe Guey , un Américain Chinois qui a fabriqué et manié un avion dans les Montagnes Oakland en 1909, Dragon-ailes raconte le conte de Ombre de lune, qui vient à San Francisco pour rejoindre son père inconnu , Windrider, qui a le rêve de voler .Poursuivant le rêve, Ombre Lunaire et son père sont obligés de bouger de la Cité chinoise. Après avoir enduré une mer d’incompréhension , de cruauté et de pauvreté, Windrider a finalement réalizé son rêve de voler avec l’aide de son fils et ses compagnons, ainsi que ses amis américains. Essayant de montrer le processus de malinterprétation et de incompréhension à compréhension mutuelle et les possibilités d’échange et de fusion culturels entre deux cultures différentes, nous discuterons comment la culture chinoise est redécouverte par un Américian chinois et comment l’incompréhension culturelle conduit à un monde inégal et comment la tolérance et la compréhension reconstruisent le monde à celui d’harmonique. Ce papier tente de démontrer , à travers l’analyse de Dragon-ailes , l’exploration de l’auteur de la culture chinoise , de l’échange culturel et des différences transcendantes naturelles de la nature humaine. Mots clefs: Dragon-ailes, Laurence Yep, échange culture

RegExplainer: Generating Explanations for Graph Neural Networks in Regression Task

Graph regression is a fundamental task and has received increasing attention in a wide range of graph learning tasks. However, the inference process is often not interpretable. Most existing explanation techniques are limited to understanding GNN behaviors in classification tasks. In this work, we seek an explanation to interpret the graph regression models (XAIG-R). We show that existing methods overlook the distribution shifting and continuously ordered decision boundary, which hinders them away from being applied in the regression tasks. To address these challenges, we propose a novel objective based on the information bottleneck theory and introduce a new mix-up framework, which could support various GNNs in a model-agnostic manner. We further present a contrastive learning strategy to tackle the continuously ordered labels in regression task. To empirically verify the effectiveness of the proposed method, we introduce three benchmark datasets and a real-life dataset for evaluation. Extensive experiments show the effectiveness of the proposed method in interpreting GNN models in regression tasks

2,2′-[(4,6-Dinitro-1,3-phenyl­ene)dioxy]diacetic acid hemihydrate

The skeletons of both independent mol­ecules of the carboxylic acid hemihydrate, C10H8N2O10·0.5H2O, are approximately planar [maximum deviations 0.642 (3) and 0.468 (1) Å]. The deviations arise from the twisting of the nitro groups with respect to the aromatic rings [dihedral angles = 3.24 (2) and 27.01 (1), and 7.87 (1) and 16.37 (2)° in the two molecules]. The crystal structure features inter­molecular O—H⋯O hydrogen bonds, which the link the dicarboxylic acid and water mol­ecules into a supra­molecular layer network

Suan Zao Ren Tang

Insomnia is a serious worldwide health problem that is often comorbid with anxiety. The purpose of the present study was to evaluate the efficacy of a Chinese formula containing Suan Zao Ren Tang (SZRT) and Zhi Zi Chi Tang (ZZCT; SZR-ZZC) for improving sleep quality and anxiety states with four indices of Polysomnography (PSG), the Insomnia Severity Index (ISI), the Pittsburgh Sleep Quality Index (PSQI), and the Self Rating Anxiety Scale (SAS). Methods. A randomized, parallel-controlled trial compared SZR-ZZC to lorazepam tablet in insomniacs with anxiety. Patients were randomized to the SZR-ZZC treatment group (n=60) and the lorazepam tablet treatment group (n=59). Results. SZR-ZZC significantly improved scores on all four treatment indices. Compared with lorazepam, treatment with SZR-ZZC resulted in a significant reduction in the ISI (P=0.029), the PSQI (P=0.017), and wake after sleep onset (WASO; P=0.008) scores and improved sleep architecture (P=0.000–0.003) after a 4-week treatment period. Only one subject in the SZR-ZZC group experienced adverse side effects. Conclusion. Treatment with SZR-ZZC for 4 weeks appears to be a relatively safe and effective complementary therapeutic option when aiming to improve sleep quality and anxiety in insomniacs with anxiety

Effects of losses in the hybrid atom-light interferometer

Enhanced Raman scattering can be obtained by injecting a seeded light field which is correlated with the initially prepared collective atomic excitation. This Raman amplification process can be used to realize atom-light hybrid interferometer. We numerically calculate the phase sensitivities and the signal-to-noise ratios of this interferometer with the method of homodyne detection and intensity detection, and give their differences between this two methods. In the presence of loss of light field and atomic decoherence the measure precision will be reduced which can be explained by the break of the intermode decorrelation conditions of output modesComment: 9 pages, 7 figure