Ball: An R package for detecting distribution difference and association in metric spaces

The rapid development of modern technology facilitates the appearance of numerous unprecedented complex data which do not satisfy the axioms of Euclidean geometry, while most of the statistical hypothesis tests are available in Euclidean or Hilbert spaces. To properly analyze the data of more complicated structures, efforts have been made to solve the fundamental test problems in more general spaces. In this paper, a publicly available R package Ball is provided to implement Ball statistical test procedures for K-sample distribution comparison and test of mutual independence in metric spaces, which extend the test procedures for two sample distribution comparison and test of independence. The tailormade algorithms as well as engineering techniques are employed on the Ball package to speed up computation to the best of our ability. Two real data analyses and several numerical studies have been performed and the results certify the powerfulness of Ball package in analyzing complex data, e.g., spherical data and symmetric positive matrix data

Ball: An R Package for Detecting Distribution Difference and Association in Metric Spaces

The rapid development of modern technology has created many complex datasets in non-linear spaces, while most of the statistical hypothesis tests are only available in Euclidean or Hilbert spaces. To properly analyze the data with more complicated structures, efforts have been made to solve the fundamental test problems in more general spaces (Lyons 2013; Pan, Tian, Wang, and Zhang 2018; Pan, Wang, Zhang, Zhu, and Zhu 2020). In this paper, we introduce a publicly available R package Ball for the comparison of multiple distributions and the test of mutual independence in metric spaces, which extends the test procedures for the equality of two distributions (Pan et al. 2018) and the independence of two random objects (Pan et al. 2020). The Ball package is computationally efficient since several novel algorithms as well as engineering techniques are employed in speeding up the ball test procedures. Two real data analyses and diverse numerical studies have been performed, and the results certify that the Ball package can detect various distribution differences and complicated dependencies in complex datasets, e.g., directional data and symmetric positive definite matrix data

Nonparametric statistical inference via metric distribution function in metric spaces

The distribution function is essential in statistical inference and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates a paradigm for statistical inference. However, existing distribution functions are defined in Euclidean spaces and are no longer convenient to use in rapidly evolving data objects of complex nature. It is imperative to develop the concept of the distribution function in a more general space to meet emerging needs. Note that the linearity allows us to use hypercubes to define the distribution function in a Euclidean space. Still, without the linearity in a metric space, we must work with the metric to investigate the probability measure. We introduce a class of metric distribution functions through the metric only. We overcome this challenging step by proving the correspondence theorem and the Glivenko-Cantelli theorem for metric distribution functions in metric spaces, laying the foundation for conducting rational statistical inference for metric space-valued data. Then, we develop a homogeneity test and a mutual independence test for non-Euclidean random objects and present comprehensive empirical evidence to support the performance of our proposed methods. Supplementary materials for this article are available online

Complete genome analysis of Bacillus velezensis TS5 and its potential as a probiotic strain in mice

IntroductionIn recent years, a large number of studies have shown that Bacillus velezensis has the potential as an animal feed additive, and its potential probiotic properties have been gradually explored.MethodsIn this study, Illumina NovaSeq PE150 and Oxford Nanopore ONT sequencing platforms were used to sequence the genome of Bacillus velezensis TS5, a fiber-degrading strain isolated from Tibetan sheep. To further investigate the potential of B. velezensis TS5 as a probiotic strain, in vivo experiments were conducted using 40 five-week-old male specific pathogen-free C57BL/6J mice. The mice were randomly divided into four groups: high fiber diet control group (H group), high fiber diet probiotics group (HT group), low fiber diet control group (L group), and low fiber diet probiotics group (LT group). The H and HT groups were fed high-fiber diet (30%), while the L and LT groups were fed low-fiber diet (5%). The total bacteria amount in the vegetative forms of B. velezensis TS5 per mouse in the HT and LT groups was 1 × 109 CFU per day, mice in the H and L groups were given the same volume of sterile physiological saline daily by gavage, and the experiment period lasted for 8 weeks.ResultsThe complete genome sequencing results of B. velezensis TS5 showed that it contained 3,929,788 nucleotides with a GC content of 46.50%. The strain encoded 3,873 genes that partially related to stress resistance, adhesion, and antioxidants, as well as the production of secondary metabolites, digestive enzymes, and other beneficial nutrients. The genes of this bacterium were mainly involved in carbohydrate metabolism, amino acid metabolism, vitamin and cofactor metabolism, biological process, and molecular function, as revealed by KEGG and GO databases. The results of mouse tests showed that B. velezensis TS5 could improve intestinal digestive enzyme activity, liver antioxidant capacity, small intestine morphology, and cecum microbiota structure in mice.ConclusionThese findings confirmed the probiotic effects of B. velezensis TS5 isolated from Tibetan sheep feces and provided the theoretical basis for the clinical application and development of new feed additives

Clinical analysis of decision implementation by a multidisciplinary team in cervical cancer cases in Ganzhou, China

ObjectiveIn this study, we evaluated the role of a multidisciplinary team (MDT) in clinical practice for cervical cancer by analyzing the development of a single-case multidisciplinary consultation for cervical cancer.MethodsPatients in MDT consultations for cervical cancer were retrospectively analyzed for clinical information, decision content of MDT discussion, implementation, and follow-up results.ResultsOf the 392 patients who met the inclusion criteria, 359 had a first episode, of which 284 were stage IA-IIA2 (79.11%) and 75 were stage IIB-IVB (20.89%). Of these 392, 33 had a recurrence (8.42%). A total of 416 cases were analyzed, and neoadjuvant chemotherapy with surgery was recommended in 43 cases, of which 40 cases were implemented, and 36 of the 40 achieved the expected outcome. Surgical treatment was recommended in 241 cases, of which 226 underwent surgery, and 215 of them achieved the expected outcome. Radiotherapy was recommended in 31 cases, of which 26 cases underwent it, and 22 of them achieved the expected efficacy. Concurrent chemoradiotherapy was recommended in 57 cases, of which 49 underwent it, and 39 of them achieved the expected efficacy. Other treatments were recommended in 44 cases, of which 23 cases were implemented, and 10 of them achieved the expected efficacy, with statistically significant differences compared with cases without implementation (P <0.05). MDT decisions were correlated with age; the younger the patients, the higher the implementation efficiency (P <0.05). The difference between MDT expectation in all implementation and partial implementation and age was statistically significant (P <0.05). No significant difference was found between age and MDT expectation in all not fully implemented decisions (P >0.05). Some decisions were not fully implemented due to economic status and fear of certain treatments of the patient.ConclusionThe MDT plays an important role in clinical practice such as clinical staging, treatment plan, and the complete treatment management of patients with cervical cancer, which can significantly improve the near-term treatment effect, whereas its effect on a long-term prognosis needs further clinical observation and active exploration