The Empirical Bayes Classification Rules for Mixtures of Discrete and Continuous Variables

Let us consider a general population π. Each object belonging to the population π is characterized by a pair of correlated random vectors (X, Y ). Both X and Y may be mixtures of discrete and continuous random variables. It will be assumed that our population π consists of k groups π₁,….,πk, which depend on the value of the random vector Y. A certain object, which is an element of one of the k groups π₁, …, πk, has to be classified into the correct group. The knowledge of the value of the random vector Y would permit its correct classification, but the observation of this vector is difficult or dangerous and we must assign the individual on the basis of the observation of the random vector X . The classification procedure is based on randomized decision function δ* which minimizes the risk function i.e. Bayes decision function. We give also two empirical Bayes classification rules i.e. decision functions based on the sample from population π and having property that their risks converge to Bayes risk when the sample size increases.     

Missing Data and the Mixtures of Discrete and Continuous Random Variables

In many practical applications we deal with a problem of estimation of a density function of a vector x some components of which are discrete, while the remaining ones are continuous. Among many models that can be used in this case the most useful are the location model and the kernel model. The problem arises when the observed data contain missing values i.e. on some individuals some of the variables have not been observed with no particular pattern of missingness. An application of the EM algorithm will allow us to estimate the parameters of the location model from incomplete data. The method is described in Section 2. In Section 3 some suggestions how to deal with incompleteness when the kernel model is used are made. Finally, Section 4 contains an example.     

Two-Group Classification when Both Groups are Mixtures of Normals

In this paper we consider a two-group discriminant analysis problem where each group is a mixture of two subgroups. Based upon data from a clinical study of alcohol involvement and diseases, simulation experiments were performed for three different configurations of means and covariance matrices. Expected actual non-error rates are estimated for the linear, quadratic, and kernel discriminant functions for sample sizes 30, 50, 75, 100, 150 and 200. A conclusion of the article is that the kernel discriminant function performs as well as or better than quadratic discriminant function. However, the linear discriminant function was clearly inferior to either the quadratic or kernel discriminant functions.     

Model for Heterogeneous Random Networks Using Continuous Latent Variables and an Application to a Tree–Fungus Network

Summary The mixture model is a method of choice for modeling heterogeneous random graphs, because it contains most of the known structures of heterogeneity: hubs, hierarchical structures, or community structure. One of the weaknesses of mixture models on random graphs is that, at the present time, there is no computationally feasible estimation method that is completely satisfying from a theoretical point of view. Moreover, mixture models assume that each vertex pertains to one group, so there is no place for vertices being at intermediate positions. The model proposed in this article is a grade of membership model for heterogeneous random graphs, which assumes that each vertex is a mixture of extremal hypothetical vertices. The connectivity properties of each vertex are deduced from those of the extreme vertices. In this new model, the vector of weights of each vertex are fixed continuous parameters. A model with a vector of parameters for each vertex is tractable because the number of observations is proportional to the square of the number of vertices of the network. The estimation of the parameters is given by the maximum likelihood procedure. The model is used to elucidate some of the processes shaping the heterogeneous structure of a well‐resolved network of host/parasite interactions.     

Application of Logistic Regression and Logistic Discrimination in Medical Decision Making

The logit linear model has been shown to be very useful for investigations in many fields of biology and medicine. One kind of application of this model is that of logistic discriminant analysis. To conquer some theoretical disadvantages of logistic discriminant analysis and Fisher's linear discriminant analysis too, it has been recommended to augment their model equations with appropriate interaction terms. The present paper discusses experiences with epidemiologic data going this way.     

Random mutant generation and its utility in uncovering structural and functional features of cytochromeb inSaccharomyces cerevisiae

The generation of random mutations in the mitochondrial cytochromeb gene ofSaccharomyces cerevisiae has been used as a most fruitful means of identifying subregions that play a key role in thebc ₁ complex mechanism, best explained by the protonmotive Q cycle originally proposed by Peter Mitchell. Selection for center i and center o inhibitor resistance mutants, in particular, has yielded much information. The combined approaches of genetics and structural predictions have led to a two-dimensional folding model for cytochromeb that is most compatible with current knowledge of the protonmotive Q cycle. A three-dimensional model is emerging from studies of distant reversions of deficient mutants. Finally, interactions between cytochromeb and the other subunits of thebc ₁ complex, such as the iron-sulfur protein, can be affected by a single amino acid change.     

A Stochastic Process and Generalized Distributions for the Study of Oviposition Evolution of a Parasite

This paper considers a generalized birth process {X^m(t), t > 0} and presents a new stochastic model for the number of eggs laid by a parasite on a host. Also, given an underlying distribution for the number of visits between parasites and a host, this distribution is generalized by the distribution of the number of eggs per visit laid on the host. If a certain number of eggs are already present on the host, a parasite such as a Japanese weevil, may avoid oviposition in subsequent visits (see JANARDAN (1980)) to the same host. A class of generalized distributions are presented to model such situations. The case of a single egg laying parasite and a Poisson distribution for the number of visits of the parasite to the same host yields a distribution of particular interest. In order to develop this model, certain lemmas are derived. Finally a characteristic property of this stochastic model is presented.     

Systems biology approach for mutational and site-specific structural investigation of DNA repair genes for xeroderma pigmentosum

Xeroderma pigmentosum (XP) is a rare genetic skin disorder caused due to the extreme sensitivity for ultraviolet (UV) radiations. On its exposure, DNA acquires damages leading to skin and often neurological abnormalities. The DNA repair implicated in fixing UV-induced damages is NER and mutations in genes involved in NER and TLS form the basis of XP. The analyses of such mutations are vital for understanding XP and involved cancer genetics to facilitate the identification of crucial biomarkers and anticancer therapeutics. We detected the deleterious nsSNPs and examined them at structure-level by altering the structure, estimating secondary structure, solvent accessibility and performing site specific analysis. Crucial phosphorylation sites were also identified for their role in the disorder. These mutational and structural analyses offer valuable insight to the fundamental association of genetic mutations with phenotypic variations in XP and will assist experimental biologists to evaluate the mutations and their impact on genome.     

The function and structural influence of selective relaxed constraint at functional intracellular loop3 of 5-HT1A serotonin-1 receptor family

Serotonin (5-HT) and its receptors have been involved in critical signal transduction mechanism and deregulation implicated in mood-related disorders. 5-HT activities are mediated through a family of transmembrane spanning serotonin receptors. Both within the family and species, 5-HT receptor protein sequence diversity and 7-transmembrane structural homogeneity have long been intriguing. In this study, we have analyzed the codon site constraint in 5-HT1 subclass receptors from 13 orthologous mammalian mRNA coding sequence. Further, the study was extended to computationally investigate the impact of non-synonymous sites with respect to function and structural significance through sequence homology algorithm and molecular dynamics simulation (MDS). Codon sites with significant posterior probability were observed in 5-HT_1A, 5‐HT_1B and 5-HT_1D receptor indicating variations in site constraint within the 5‐HT1 sub-class genes. In 5-HT_1A receptor, seven sites were detected at the functional intracellular loop₃ (ICL₃) with higher substitution rate through Codeml program. Sequence homology algorithm identifies that these sites were functionally tolerant within the mammals representing a selectively relaxed constraint at this domain. On the other hand, the root mean square deviation (rmsd) values from MDS suggest differences in structural conformation of ICL₃ models among the species. Specifically, the human ICL₃ model fluctuation was comparatively more stable than other species. Hence, we argue that these sites may have varying influence in G-proteins coupling and activation of effectors systems through downstream interacting accessory proteins of cell among the species. However, further experimental studies are required to elucidate the precise role and the seeming difference of these sites in 5-HT receptors between species.     

Construction of miRNA-mRNA network for the identification of key biological markers and their associated pathways in IgA nephropathy by employing the integrated bioinformatics analysis

BackgroundAbout half-century ago, Immunoglobulin A nephropathy (IgAN) was discovered as a complicated disease with frequent clinical symptoms. Until now, exact mechanism underlying the pathogenesis of IgAN is poorly known. Therefore, current study was aimed to understand the molecular mechanism of IgAN by identifying the key miRNAs and their targeted hub genes. The key miRNAs might contribute to the diagnosis and therapy of IgAN, and could turn out to be a new star in the field of IgAN.MethodsThe microarray datasets were downloaded from Gene Expresssion Omnibus (GEO) database and analyzed using R package (LIMMA) in order to obtain differential expressed genes (DEGs). Then, the hub genes were identified using cytoHubba plugin of cytoscpae tool and other bioinformatics approaches including protein-protein interaction (PPI) network analysis, module analysis, and miRNA-hub gene network construction was also performed.ResultsA total of 348 DEGs were identified, of which 107 were upregulated genes and 241 were downregulated genes. Subsequently, the 12 overlapped genes were predicted from cytoHubba, and considered as hub genes. Moreover, a network among miRNA-hub genes was created to explore the correlation between the hub genes and their targeted miRNAs. Network construction ultimately lead to the identification of nine gene named FN1, EGR1, FOS, JUN, SERPINE1, MMP2, ATF3, MYC, and IL1B and one novel key miRNA namely, has-miR-144-3p as biomarker for diagnosis and therapy of IgAN.ConclusionThis study updates the information and yield a new perspective in context of understanding the pathogenesis and development of IgAN. In future, key miRNAs might be capable of improving the personalized detection and therapies for IgAN. In vivo and in vitro investigation of miRNAs and pathway interaction is essential to delineate the specific roles of the novel miRNAs, which may help to further reveal the mechanisms underlying IgAN.