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

Enhancement in Interfacial Adhesion of Ti/Polyetheretherketone by Electrophoretic Deposition of Graphene Oxide

This is the peer reviewed version of the following article: Pan, L., Lv, Y., Nipon, R., Wang, Y., Duan, L., Hu, J., ... & Shi, Y. (2019). Enhancement in Interfacial Adhesion of Ti/Polyetheretherketone by Electrophoretic Deposition of Graphene Oxide. Polymer Composites, 40(S2), E1243-E1251, which has been published in final form at https://doi.org/10.1002/pc.24955. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.This article discusses about the significance of graphene oxide (GO) deposition on the surface of a titanium plate by electrophoretic deposition (EPD) method to improve the adhesive strength of Ti/polyetheretherketone (PEEK) interfacial adhesive. Firstly, the anodic EPD method was applied to a water dispersion solution of GO, and then the morphology and the properties of titanium plate surface were characterized by scanning electron microscopy and contact angle measurements before and after GO deposition. Furthermore, the changes in the properties of GO after heating at 390°C were characterized by Raman and Fourier transform infrared spectroscopies. According to the results of single lap tensile shear test, the adhesion strength of Ti/PEEK interface after the anodization and deposition of GO was 34.94 MPa, an increase of 29.2% compared with 27.04 MPa of sample with only anodization. Also, the adhesion strengths were 58.1 and 76.5% higher compared with the samples of only GO deposited (22.1 MPa) and pure titanium (19.8 MPa), respectively

Identification of Key Aroma Compounds in Fig Extract through Sensomics Approach

In this study, headspace solid phase microextraction-gas chromatography-mass spectrometry (HS-SPME-GC-MS) and gas chromatography-olfactory (GC-O) were applied to identify and analyze the volatile aroma compounds of the ethanol extract of figs. Its key characteristic flavor compounds were analyzed by odor activity (OAV) and aroma recombination and omission tests. The results showed that a total of 40 volatile aroma components were identified, of which 18 compounds, such as isobutyrate, γ-butyl lactone, aromatic camphor, nonaldehyde, vanillin and furfural, were important aroma components in the fig extract (OAV > 1). The aroma recombination experiments showed that the sensory properties of the recombined samples, which had typical aroma characteristics such as fruity, sweet, baked and burnt sweet with slight sour, ointment-like and milky, were similar to those of the fig extract. Furthermore, the aroma omission experiments identified gamma-hexanoate, ethyl palmitate, phenmethanol, aromatic camphor, vanillin, benzaldehyde, 4-hydroxy-2,5-dimethyl-3 (2H)-furan, 5-hydroxymyfuran, and methyl cyclopentanolone as key characteristic flavor compounds of the fig extract. The findings of this study provide a theoretical basis for the development and quality control of fig characteristic flavorings