Generalized Bernoulli process and fractional Poisson process

We propose a generalized Bernoulli process that can approximate the fractional Poisson process. A Bernoulli process is a sequence of independent binary random variables, and the binomial distribution concerns the behavior of the sum of the variables in a Bernoulli process. Recently, a generalized Bernoulli process (GBP-I) was developed in which binary random variables are correlated with its covariance function obeying a power law. In this paper, we propose a different generalized Bernoulli process (GBP-II) that can possess long-memory property as the GBP-I but has a different limiting behavior. We show that the sum of the variables in the GBP-I can serve as an over-dispersed binomial model when long-memory presents, whereas the GBP-II can be considered as a discrete-time counterpart of the fractional Poisson process. Considering that the binomial distribution approximates the Poisson distribution under certain conditions, the connection we found between the GBP-II and the fractional Poisson process is thought of as its counterpart under long-range dependence. Data analysis with the unemployment rate shows that under long-range dependence, the GBPs fit the data better than a Markov chain

A finite-state stationary process with long-range dependence and fractional multinomial distribution

We propose a discrete-time, finite-state stationary process that can possess long-range dependence. Among the interesting features of this process is that each state can have different long-term dependency, i.e., the indicator sequence can have different Hurst index for different states. Also, inter-arrival time for each state follows heavy tail distribution, with different states showing different tail behavior. A possible application of this process is to model over-dispersed multinomial distribution. In particular, we define fractional multinomial distribution from our model

The role of Toc receptor interactions in controlling protein import into chloroplasts

Nuclear-encoded chloroplast proteins are synthesized as precursors in the cytosol with N-terminal cleavable transit peptides. The post translational import of proteins into chloroplasts occurs first through the outer membrane via the Toc complex (Translocon of Outer membrane of Chloroplast). The high fidelity of the protein import process is maintained by the specific recognition of the transit peptide of nucleus-encoded proteins by the coordinate activities of two homologous GTPase Toc receptors, Toc34 and Toc159. Structural and biochemical studies suggest that dimerization of the Toc receptors functions as a component of the mechanism to control access of preproteins to the membrane translocation channel of the translocon chloroplast envelope. I show that specific mutations that disrupt receptor dimerization in vitro reduce the rate of protein import in transgenic Arabidopsis compared to the wild type receptor. The mutations do not affect the GTPase activities of the receptors. Interestingly, these mutations do not disrupt initial preprotein binding at the receptors, but they reduce the efficiency of the transition from preprotein binding to membrane translocation. These data indicate that dimerization of receptors has a direct role in protein import, and support a hypothesis in which conformational changes that initiate membrane translocation of chloroplast preproteins is part of the molecular mechanism of GTP-regulated protein import

Clustering Noise-Included Data by Controlling Decision Errors

Cluster analysis is an unsupervised learning technique for partitioning objects into several clusters. Assuming that noisy objects are included, we propose a soft clustering method which assigns objects that are significantly different from noise into one of the specified number of clusters by controlling decision errors through multiple testing. The parameters of the Gaussian mixture model are estimated from the EM algorithm. Using the estimated probability density function, we formulated a multiple hypothesis testing for the clustering problem, and the positive false discovery rate (pFDR) is calculated as our decision error. The proposed procedure classifies objects into significant data or noise simultaneously according to the specified target pFDR level. When applied to real and artificial data sets, it was able to control the target pFDR reasonably well, offering a satisfactory clustering performance.X110sciescopu