arXiv subjects

Nan Lin

Publications and source records attributed to Nan Lin.

25 records · Page 2Linked to original sources

arXiv2015

Testing SgrA$^*$ with the spectrum of its accretion structure

SgrA$^*$ is the supermassive black hole candidate at the center of the Galaxy and an ideal laboratory to test general relativity. Following previous work by other authors, we use the Polish doughnut model to describe an optically thin and constant angular momentum ion torus in hydrodynamical equilibrium and model the accretion structure around SgrA$^*$. The radiation mechanisms are bremsstrahlung, synchrotron emission, and inverse Compton scattering. We compute the spectrum as seen by a distant observer in Kerr and non-Kerr spacetimes and we study how an accurate measurement can constrain possible deviations form the Kerr solution. As in the case of emission from a thin accretion disk, we find a substantial degeneracy between the determination of the spin and of possible deviations from the Kerr geometry, even when the parameters of the ion torus are fixed. This means that this technique cannot independently test the nature of SgrA$^*$ even in the presence of good data and with the systematics under control. However, it might do it in combination with other measurements (black hole shadow, radio pulsar, etc.).

gr-qc↗

arXiv2014

Methods for Joint Imaging and RNA-seq Data Analysis

Emerging integrative analysis of genomic and anatomical imaging data which has not been well developed, provides invaluable information for the holistic discovery of the genomic structure of disease and has the potential to open a new avenue for discovering novel disease susceptibility genes which cannot be identified if they are analyzed separately. A key issue to the success of imaging and genomic data analysis is how to reduce their dimensions. Most previous methods for imaging information extraction and RNA-seq data reduction do not explore imaging spatial information and often ignore gene expression variation at genomic positional level. To overcome these limitations, we extend functional principle component analysis from one dimension to two dimension (2DFPCA) for representing imaging data and develop a multiple functional linear model (MFLM) in which functional principal scores of images are taken as multiple quantitative traits and RNA-seq profile across a gene is taken as a function predictor for assessing the association of gene expression with images. The developed method has been applied to image and RNA-seq data of ovarian cancer and KIRC studies. We identified 24 and 84 genes whose expressions were associated with imaging variations in ovarian cancer and KIRC studies, respectively. Our results showed that many significantly associated genes with images were not differentially expressed, but revealed their morphological and metabolic functions. The results also demonstrated that the peaks of the estimated regression coefficient function in the MFLM often allowed the discovery of splicing sites and multiple isoform of gene expressions.

q-bio.GN↗

arXiv2014

Functional Principal Component Analysis and Randomized Sparse Clustering Algorithm for Medical Image Analysis

Due to advances in sensors, growing large and complex medical image data have the ability to visualize the pathological change in the cellular or even the molecular level or anatomical changes in tissues and organs. As a consequence, the medical images have the potential to enhance diagnosis of disease, prediction of clinical outcomes, characterization of disease progression, management of health care and development of treatments, but also pose great methodological and computational challenges for representation and selection of features in image cluster analysis. To address these challenges, we first extend one dimensional functional principal component analysis to the two dimensional functional principle component analyses (2DFPCA) to fully capture space variation of image signals. Image signals contain a large number of redundant and irrelevant features which provide no additional or no useful information for cluster analysis. Widely used methods for removing redundant and irrelevant features are sparse clustering algorithms using a lasso-type penalty to select the features. However, the accuracy of clustering using a lasso-type penalty depends on how to select penalty parameters and a threshold for selecting features. In practice, they are difficult to determine. Recently, randomized algorithms have received a great deal of attention in big data analysis. This paper presents a randomized algorithm for accurate feature selection in image cluster analysis. The proposed method is applied to ovarian and kidney cancer histology image data from the TCGA database. The results demonstrate that the randomized feature selection method coupled with functional principal component analysis substantially outperforms the current sparse clustering algorithms in image cluster analysis.

stat.ML↗

arXiv2012

Two-particle response in Cluster Dynamical Mean-Field Theory: Formalism and application to the Raman Response of High-temperature Superconductors

A method is presented for the unbiased numerical computation of two-particle response functions of correlated electron materials via a solution of the dynamical mean-field equations in the presence of a perturbing field. The power of the method is demonstrated via a computation of the Raman $B_{1g}$ and $B_{2g}$ scattering intensities of the two dimensional Hubbard model, in parameter regimes believed to be relevant to high-temperature superconductivity. The theory reproduces the `two-magnon' peak characteristic of the Raman intensity of the insulating parent compounds of high-$T_c$ copper oxide superconductors and shows how it evolves to a quasiparticle response as carriers are added. The method can be applied in any situation where a solution of the equilibrium dynamical mean-field equations is feasible.

cond-mat.str-el↗

arXiv2011

Dynamical Mean-Field Theory for Quantum Chemistry

The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to molecules, i.e., finite systems with a discrete energy spectrum. The application to small clusters of hydrogen atoms yields ground state energies which are competitive with leading quantum chemical approaches at intermediate and large interatomic distances as well as good approximations to the excitation spectrum.

cond-mat.str-el↗

arXiv2010

Physics of the Pseudogap in 8-site Cluster Dynamical Mean Field Theory: photoemission, Raman scattering, in-plane and c-axis conductivity

Cluster dynamical mean field and maximum entropy analytical continuation methods are used to obtain theoretical estimates for the many-body density of states, electron self-energy, in-plane and c-axis optical conductivity and the $B_{1g}$ and $B_{2g}$ Raman scattering spectra of the two dimensional square lattice Hubbard model at intermediate interaction strengths and carrier concentrations near half filling. The calculations are based on an 8-site cluster approximation which gives access to both the zone-diagonal and zone-face portions of the Fermi surface. At low dopings the zone-face regions exhibit a 'pseudogap', a suppression of the many-body density of states for energies near the Fermi surface. The pseudogap magnitude is largest near half filling and decreases smoothly with doping, but as temperature is increased the gap fills in rather than closes. The calculated response functions bear a strong qualitative resemblance to data taken in the pseudogap regime of high-$T_c$ cuprates, strongly suggesting that the intermediate coupling Hubbard model accounts for much of the exotic behavior observed in high-$T_c$ materials.

cond-mat.str-el↗

arXiv2009

Optical conductivity in cluster dynamical mean field theory: formalism and application to high temperature superconductors

The optical conductivity of the one-band Hubbard model is calculated using the 'Dynamical Cluster Approximation' implementation of dynamical mean field theory for parameters appropriate to high temperature copper-oxide superconductors. The calculation includes vertex corrections and the result demonstrates their importance. At densities of one electron per site, an insulating state is found with gap value and above-gap absorption consistent with measurements. As carriers are added the above gap conductivity rapidly weakens and a three component structure emerges, with a low frequency 'Drude' peak, a mid-infrared absorption, and a remnant of the insulating gap. The mid-infrared feature obtained at intermediate dopings is shown to arise from a pseudogap structure in the density of states. On further doping the conductivity evolves to the Drude peak plus weakly frequency dependent tail structure expected for less strongly correlated metals.

cond-mat.str-el↗