Efficient computation of extreme eigenvalues of large-scale linear Hermitian eigenproblems can be achieved by preconditioned conjugate gradient (PCG) methods. In this paper, we study PCG methods for computing extreme eigenvalues of nonlinear Hermitian eigenproblems of the form T (λ)v = 0 that admit a nonlinear variational principle. We investigate some theoretical properties of a basic CG metho...

Polycomb group (PcG) proteins participate in the maintenance of transcriptionally repressed state of genes relevant to cell differentiation. Here, we show anterior homeotic transformations of the axial skeleton of YY1(+/-) mice. We find that the penetrance of some of these alterations was reduced in mice that are deficient in the class II PcG gene Ring1/Ring1A, indicating a genetic interaction ...

TrxG and PcG complexes play key roles in the epigenetic regulation of development through H3K4me3 and H3K27me3 modification at specific sites throughout the human genome, but how these sites are selected is poorly understood. We find that in pluripotent cells, clustered CpG-islands at genes predict occupancy of H3K4me3 and H3K27me3, and these "bivalent" chromatin domains precisely span the boun...

Polycomb group (PcG) proteins are important epigenetic regulators, yet the underlying targeting mechanism in mammals is still poorly understood. We have developed a computational approach to predict genome-wide PcG target genes in mouse embryonic stem cells. We use TF binding and motif information as predictors and apply the Bayesian Additive Regression Trees (BART) model for classification. Ou...

This paper is concerned with a synthesis study of the fast Fourier transform (FFT), the short-time Fourier transform (STFT), the Wigner distribution (WD) and the wavelet transform (WT) in analysing the phonocardiogram signal (PCG). It is shown that these transforms provide enough features of the PCG signals that will help clinics to obtain qualitative and quantitative measurements of the time-f...

The molecular mechanisms underlying the formation of neurons with defined neurotransmitters are not well understood. In this study, we demonstrate that the PcG-like genes in Caenorhabditis elegans, sop-2 and sor-3, regulate the formation of dopaminergic and serotonergic neurons and several other neuronal properties. sor-3 encodes a novel protein containing an MBT repeat, a domain that contains ...

Drosophila Polycomb group response elements (PRE) silence neighboring genes, but silencing can be blocked by one copy of the Su(Hw) insulator element. We show here that Polycomb group (PcG) proteins can spread from a PRE in the flanking chromatin region and that PRE blocking depends on a physical barrier established by the insulator to PcG protein spreading. On the other hand, PRE-mediated sile...

A graph G = (V,E) with a vertex set V and an edge set E is called a pairwise compatibility graph (PCG, for short) if there are a tree T whose leaf set is V , a non-negative edge weight w in T , and two non-negative reals dmin ≤ dmax such that G has an edge uv ∈ E if and only if the distance between u and v in the weighted tree (T,w) is in the interval [dmin, dmax]. PCG is a new graph class moti...

As one of the most important mathematics-physics equations, heat equation has been widely used in engineering area and computing science research. Large-scale heat problems are difficult to solve due to computational intractability. The parallelization of heat equation is available to improve the simulation model efficiency. In order to solve the three-dimensional heat problems more rapidly, th...

By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an e...