We have developed a statistical method named IsoDOT to assess differential isoform expression (DIE) and differential isoform usage (DIU) using RNA-seq data. Here isoform usage refers to relative isoform expression given the total expression of the co
rresponding gene. IsoDOT performs two tasks that cannot be accomplished by existing methods: to test DIE/DIU with respect to a continuous covariate, and to test DIE/DIU for one case versus one control. The latter task is not an uncommon situation in practice, e.g., comparing paternal and maternal allele of one individual or comparing tumor and normal sample of one cancer patient. Simulation studies demonstrate the high sensitivity and specificity of IsoDOT. We apply IsoDOT to study the effects of haloperidol treatment on mouse transcriptome and identify a group of genes whose isoform usages respond to haloperidol treatment.
We performed a Chandra X-ray study of three giant H II regions (GHRs), NGC 5461, NGC 5462, and NGC 5471, in the spiral galaxy M101. The X-ray spectra of the three GHRs all contain a prominent thermal component with a temperature of ~0.2 keV. In NGC 5
461, the spatial distribution of the soft (< 1.5 keV) X-ray emission is generally in agreement with the extent of H1105, the most luminous H II region therein, but extends beyond its southern boundary, which could be attributed to outflows from the star cloud between H1105 and H1098. In NGC 5462, the X-ray emission is displaced from the H II regions and a ridge of blue stars; the H-alpha filaments extending from the ridge of star cloud to the diffuse X-rays suggest that hot gas outflows have occurred. The X-rays from NGC 5471 are concentrated at the B-knot, a hypernova remnant candidate. Assuming a Sedov-Taylor evolution, the derived explosion energy, on the order of 10^52 ergs, is consistent with a hypernova origin. In addition, a bright source in the field of NGC 5462 has been identified as a background AGN, instead of a black hole X-ray binary in M101.
Quantum phase transition in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudo-spin transformation method and the trace map method. The exact solutions are presented, the fidelity, the nearest-neighbor ps
eudo-spin entanglement, spin and pseudo-spin correlation functions are then calculated. At the critical point, the fidelity and its susceptibility change substantially, the gap of pseudo-spin concurrence is observed, which scales as $1/N$ (N is system size). The spin correlation functions show smooth behavior around the critical point. In the period-two chain, the pseudo-spin correlation functions exhibit a oscillating behavior, which is absent in the unform chain. The divergent correlation length at the critical point is demonstrated in the general trend for both cases.
The two parameter Poisson-Dirichlet distribution $PD(alpha,theta)$ is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingmans Poisson-Dirichlet distribution. The two parameter Dirichlet process $Pi_
{alpha,theta, u_0}$ is the law of a pure atomic random measure with masses following the two parameter Poisson-Dirichlet distribution. In this article we focus on the construction and the properties of the infinite dimensional symmetric diffusion processes with respective symmetric measures $PD(alpha,theta)$ and $Pi_{alpha,theta, u_0}$. The methods used come from the theory of Dirichlet forms.
