Divisible Statistics and Their Partial Sum Processes: Asymptotic Properties and Applications

Divisible statistics have been widely used in many areas of statistical analysis. For example, Pearson's Chi-square statistic and the log-likelihood ratio statistic are frequently used in goodness of fit (GOF) and categorical analysis; the maximum likelihood (ML) estimators of the Shannon's and Simpson's diversity indices are often used as measure of diversity; and the spectral statistic plays a key role in the theory of large number of rare events. In the classical multinomial model, where the number of disjoint events N and their probabilities are all fixed, limit distributions of many divisible statistics have gradually been established. However, most of the results are based on the asymptotic equivalence of these statistics to Pearson's Chi-square statistic and the known limit distribution of the latter. In fact, with deeper analysis, one can conclude that the key point is not the asymptotic behavior of the Chi-square statistic, but that of the normalized frequencies. Based on the asymptotic normality of the normalized frequencies in the classical model, a unified approach to the limit theorems of more general divisible statistics can be established, of which the case of the Chi-square statistic is simply a natural corollary. In many applications, however, the classical multinomial model is not appropriate, and an extension to new models becomes necessary. This new type of model, called "non-classical" multinomial models, considers the case when N increases and the {Pni} change as sample size n increases. As we will see, in these non-classical models, both the asymptotic normality of the normalized frequencies and the asymptotic equivalence of many divisible statistics to the Chi-square statistic are lost, and the limit theorems established in classical model are no longer valid in non-classical models. The extension to non-classical models not only met the demands of many real world applications, but also opened a new research area in statistical analysis, which has not been thoroughly investigated so far. Although some results on the limit distributions of the divisible statistics in non-classical models have been acquired, e.g., Holst (1972); Morris (1975); Ivchenko and Levin (1976); Ivchenko and Medvedev (1979), they are far from complete. Though not yet attracting much attention by many applied statisticians, another advanced approach, introduced by Khmaladze (1984), makes use of modern martingale theory to establish functional limit theorems of the partial sum processes of divisible statistics successfully. In the main part of this thesis, we show that this martingale approach can be extended to more general situations where both Gaussian and Poissonian frequencies exist, and further discuss the properties and applications of the limiting processes, especially in constructing distribution-free statistics. The last part of the thesis is about the statistical analysis of large number of rare events (LNRE), which is an important class of non-classical multinomial models and presented in numerous applications. In LNRE models, most of the frequencies are very small and it is not immediately clear how consistent and reliable inference can be achieved. Based on the definitions and key concepts firstly introduced by Khmaladze (1988), we discuss a particular model with the context of diversity of questionnaires. The advanced statistical techniques such as large deviation, contiguity and Edgeworth expansion used in establishing limit theorems underpin the potential of LNRE theory to become a fruitful research area in future

Aqua­bis­(methacrylato-κO)bis(pyridine-κN)copper(II)

In the crystal structure of the title complex, [Cu(C4H5O2)2(C5H5N)2(H2O)], the CuII cation is located on a twofold rotation axis and coordinated by two methyl­acrylate anions, two pyridine ligands and one water mol­ecule in a distorted square-pyramidal geometry. The coordinated water mol­ecule is also located on the twofold axis. In the crystal structure O—H⋯O hydrogen bonds link the mol­ecules, forming chains along the c axis

Design and Implementation of Campus Competition Information Sharing Platform Based on Android

At present, the market share of the Android system in the smartphone operating system has reached 90%. In view of the limitations of the existing sharing platform for campus competition information, a campus APP, which integrates competition and activity information release, information sharing and interrogative interaction, is put forward. In this paper, the overall architecture design, function module design, database design and RESTful API design are carried out. The Java language and MVP pattern are used by Android part. Python language, RESTful architecture and ORM technology are used at the backend to realize the information of publishing competition information, the list of competition information, the information of search competition and the management of competition information. The platform is running on the North Campus of Guizhou University, the current operation situation is well

RNA-seq liver transcriptome analysis reveals an activated MHC-I pathway and an inhibited MHC-II pathway at the early stage of vaccine immunization in zebrafish

BACKGROUND: Zebrafish (Danio rerio) is a prominent vertebrate model of human development and pathogenic disease and has recently been utilized to study teleost immune responses to infectious agents threatening the aquaculture industry. In this work, to clarify the host immune mechanisms underlying the protective effects of a putative vaccine and improve its immunogenicity in the future efforts, high-throughput RNA sequencing technology was used to investigate the immunization-related gene expression patterns of zebrafish immunized with Edwardsiella tarda live attenuated vaccine. RESULTS: Average reads of 18.13 million and 14.27 million were obtained from livers of zebrafish immunized with phosphate buffered saline (mock) and E. tarda vaccine (WED), respectively. The reads were annotated with the Ensembl zebrafish database before differential expressed genes sequencing (DESeq) comparative analysis, which identified 4565 significantly differentially expressed genes (2186 up-regulated and 2379 down-regulated in WED; p<0.05). Among those, functional classifications were found in the Gene Ontology database for 3891 and in the Kyoto Encyclopedia of Genes and Genomes database for 3467. Several pathways involved in acute phase response, complement activation, immune/defense response, and antigen processing and presentation were remarkably affected at the early stage of WED immunization. Further qPCR analysis confirmed that the genes encoding the factors involved in major histocompatibility complex (MHC)-I processing pathway were up-regulated, while those involved in MHC-II pathway were down-regulated. CONCLUSION: These data provided insights into the molecular mechanisms underlying zebrafish immune response to WED immunization and might aid future studies to develop a highly immunogenic vaccine against gram-negative bacteria in teleosts

LmbU, a Cluster-Situated Regulator for Lincomycin, Consists of a DNA-Binding Domain, an Auto-Inhibitory Domain, and Forms Homodimer

Few studies were reported about the regulatory mechanism of lincomycin biosynthesis since it was found in 1962. Although we have proved that a cluster-situated regulator (CSR) LmbU (GenBank Accession No. ABX00623.1) positively modulates lincomycin biosynthesis in Streptomyces lincolnensis NRRL 2936, the molecular mechanism of LmbU regulation is still unclear. In this study, we demonstrated that LmbU binds to the target lmbAp by a central DNA-binding domain (DBD), which interacts with the binding sites through the helix-turn-helix (HTH) motif. N-terminal of LmbU includes an auto-inhibitory domain (AID), inhibiting the DNA-binding activity of LmbU. Without the AID, LmbU variant can bind to its own promoter. Interestingly, compared to other LmbU homologs, the homologs within the biosynthetic gene clusters (BGCs) of known antibiotics generally contain N-terminal AIDs, which offer them the abilities to play complex regulatory functions. In addition, cysteine 12 (C12) has been proved to be mainly responsible for LmbU homodimer formation in vitro. In conclusion, LmbU homologs naturally exist in hundreds of actinomycetes, and belong to a new regulatory family, LmbU family. The present study reveals the DBD, AID and dimerization of LmbU, and sheds new light on the regulatory mechanism of LmbU and its homologs

Innate Host Response in Primary Human Hepatocytes with Hepatitis C Virus Infection

The interaction between hepatitis C virus (HCV) and innate antiviral defense systems in primary human hepatocytes is not well understood. The objective of this study is to examine how primary human hepatocytes response to HCV infection.An infectious HCV isolate JFH1 was used to infect isolated primary human hepatocytes. HCV RNA or NS5A protein in the cells was detected by real-time PCR or immunofluorescence staining respectively. Apoptosis was examined with flow cytometry. Mechanisms of HCV-induced IFN-β expression and apoptosis were determined.Primary human hepatocytes were susceptible to JFH1 virus and released infectious virus. IFN-α inhibited viral RNA replication in the cells. IFN-β and interferon-stimulated genes were induced in the cells during acute infection. HCV infection induced apoptosis of primary human hepatocytes through the TRAIL-mediated pathway. Silencing RIG-I expression in primary human hepatocytes inhibited IFN-β and TRAIL expression and blocked apoptosis of the cells, which facilitated viral RNA replication in the cells. Moreover, HCV NS34A protein inhibited viral induced IFN-β expression in primary human hepatocytes.Innate host response is intact in HCV-infected primary human hepatocytes. RIG-I plays a key role in the induction of IFN and TRAIL by viruses and apoptosis of primary human hepatocytes via activation of the TRAIL-mediated pathway. HCV NS34A protein appears to be capable of disrupting the innate antiviral host responses in primary human hepatocytes. Our study provides a novel mechanism by which primary human hepatocytes respond to natural HCV infection

Acute hematologic toxicity prediction using dosimetric and radiomics features in patients with cervical cancer: does the treatment regimen matter?

BackgroundAcute hematologic toxicity (HT) is a prevalent adverse tissue reaction observed in cervical cancer patients undergoing chemoradiotherapy (CRT), which may lead to various negative effects such as compromised therapeutic efficacy and prolonged treatment duration. Accurate prediction of HT occurrence prior to CRT remains challenging.MethodsA discovery dataset comprising 478 continuous cervical cancer patients (140 HT patients) and a validation dataset consisting of 205 patients (52 HT patients) were retrospectively enrolled. Both datasets were categorized into the CRT group and radiotherapy (RT)-alone group based on the treatment regimen, i.e., whether chemotherapy was administered within the focused RT duration. Radiomics features were derived by contouring three regions of interest (ROIs)—bone marrow (BM), femoral head (FH), and clinical target volume (CTV)—on the treatment planning CT images before RT. A comprehensive model combining the radiomics features as well as the demographic, clinical, and dosimetric features was constructed to classify patients exhibiting acute HT symptoms in the CRT group, RT group, and combination group. Furthermore, the time-to-event analysis of the discriminative ROI was performed on all patients with acute HT to understand the HT temporal progression.ResultsAmong three ROIs, BM exhibited the best performance in classifying acute HT, which was verified across all patient groups in both discovery and validation datasets. Among different patient groups in the discovery dataset, acute HT was more precisely predicted in the CRT group [area under the curve (AUC) = 0.779, 95% CI: 0.657–0.874] than that in the RT-alone (AUC = 0.686, 95% CI: 0.529–0.817) or combination group (AUC = 0.748, 95% CI: 0.655–0.827). The predictive results in the validation dataset similarly coincided with those in the discovery dataset: CRT group (AUC = 0.802, 95% CI: 0.669–0.914), RT-alone group (AUC = 0.737, 95% CI: 0.612–0.862), and combination group (AUC = 0.793, 95% CI: 0.713–0.874). In addition, distinct feature sets were adopted for different patient groups. Moreover, the predicted HT risk of BM was also indicative of the HT temporal progression.ConclusionsHT prediction in cervical patients is dependent on both the treatment regimen and ROI selection, and BM is closely related to the occurrence and progression of HT, especially for CRT patients

Distinct biogeographic patterns for archaea, bacteria, and fungi along the vegetation gradient at the continental scale in Eastern China

© The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in mSystems 2 (2017): e00174-16, doi:10.1128/mSystems.00174-16.The natural forest ecosystem in Eastern China, from tropical forest to boreal forest, has declined due to cropland development during the last 300 years, yet little is known about the historical biogeographic patterns and driving processes for the major domains of microorganisms along this continental-scale natural vegetation gradient. We predicted the biogeographic patterns of soil archaeal, bacterial, and fungal communities across 110 natural forest sites along a transect across four vegetation zones in Eastern China. The distance decay relationships demonstrated the distinct biogeographic patterns of archaeal, bacterial, and fungal communities. While historical processes mainly influenced bacterial community variations, spatially autocorrelated environmental variables mainly influenced the fungal community. Archaea did not display a distance decay pattern along the vegetation gradient. Bacterial community diversity and structure were correlated with the ratio of acid oxalate-soluble Fe to free Fe oxides (Feo/Fed ratio). Fungal community diversity and structure were influenced by dissolved organic carbon (DOC) and free aluminum (Ald), respectively. The role of these environmental variables was confirmed by the correlations between dominant operational taxonomic units (OTUs) and edaphic variables. However, most of the dominant OTUs were not correlated with the major driving variables for the entire communities. These results demonstrate that soil archaea, bacteria, and fungi have different biogeographic patterns and driving processes along this continental-scale natural vegetation gradient, implying different community assembly mechanisms and ecological functions for archaea, bacteria, and fungi in soil ecosystems.This research was financially supported by the National Natural Science Foundation of China (grant number 41520104001), the 111 Project, and the Fundamental Research Funds for the Central Universities

Characterization of a Species-Specific Insulinase-Like Protease in Cryptosporidium parvum

Cryptosporidium parvum is an intracellular protozoan that can cause severe diarrhea in humans and various mammals. Results of a comparative genomic analysis indicated that genes encoding two C. parvum-specific insulinase-like proteases (INS19 and INS20), cgd6_5510 and cgd6_5520, are lost in many Cryptosporidium species. In this study, we provided evidence indicating that cgd6_5510 and cgd6_5520 are fragments of a full gene (cgd6_5520-5510) encoding one insulinase-like protease (INS20-19) that is similar in structure to classic insulinases. We expressed cgd6_5510 in Escherichia coli for antiserum preparation and found the protein (INS19) that was partially degraded. A ~180 kDa protein of INS20-19 was specifically recognized by the polyclonal anti-INS19 antiserum in sporozoite lysate. We observed that INS20-19 is likely a protein with high expression in the apical region of sporozoites, and neutralization of the protein led to a partial reduction of parasite load in HCT-8 and MDBK cell cultures at 24 h. Taken together, our findings support the involvement of INS20-19 in the invasion or early developmental process of C. parvum