2,430 research outputs found
Singularity of Mean Curvature Flow of Lagrangian Submanifolds
In this article we study the tangent cones at first time singularity of a
Lagrangian mean curvature flow. If the initial compact submanifold is
Lagrangian and almost calibrated by Re\Omega in a Calabi-Yau n-fold (M,\Omega),
and T>0 is the first blow-up time of the mean curvature flow, then the tangent
cone of the mean curvature flow at a singular point (X,T) is a stationary
Lagrangian integer multiplicity current in R\sup 2n with volume density greater
than one at X. When n=2, the tangent cone consists of a finite union of more
than one 2-planes in R\sup 4 which are complex in a complex structure on R\sup
4
TROM: A Testing-based Method for Finding Transcriptomic Similarity of Biological Samples
Comparative transcriptomics has gained increasing popularity in genomic
research thanks to the development of high-throughput technologies including
microarray and next-generation RNA sequencing that have generated numerous
transcriptomic data. An important question is to understand the conservation
and differentiation of biological processes in different species. We propose a
testing-based method TROM (Transcriptome Overlap Measure) for comparing
transcriptomes within or between different species, and provide a different
perspective to interpret transcriptomic similarity in contrast to traditional
correlation analyses. Specifically, the TROM method focuses on identifying
associated genes that capture molecular characteristics of biological samples,
and subsequently comparing the biological samples by testing the overlap of
their associated genes. We use simulation and real data studies to demonstrate
that TROM is more powerful in identifying similar transcriptomes and more
robust to stochastic gene expression noise than Pearson and Spearman
correlations. We apply TROM to compare the developmental stages of six
Drosophila species, C. elegans, S. purpuratus, D. rerio and mouse liver, and
find interesting correspondence patterns that imply conserved gene expression
programs in the development of these species. The TROM method is available as
an R package on CRAN (http://cran.r-project.org/) with manuals and source codes
available at http://www.stat.ucla.edu/ jingyi.li/software-and-data/trom.html
A Bootstrap Lasso + Partial Ridge Method to Construct Confidence Intervals for Parameters in High-dimensional Sparse Linear Models
Constructing confidence intervals for the coefficients of high-dimensional
sparse linear models remains a challenge, mainly because of the complicated
limiting distributions of the widely used estimators, such as the lasso.
Several methods have been developed for constructing such intervals. Bootstrap
lasso+ols is notable for its technical simplicity, good interpretability, and
performance that is comparable with that of other more complicated methods.
However, bootstrap lasso+ols depends on the beta-min assumption, a theoretic
criterion that is often violated in practice. Thus, we introduce a new method,
called bootstrap lasso+partial ridge, to relax this assumption. Lasso+partial
ridge is a two-stage estimator. First, the lasso is used to select features.
Then, the partial ridge is used to refit the coefficients. Simulation results
show that bootstrap lasso+partial ridge outperforms bootstrap lasso+ols when
there exist small, but nonzero coefficients, a common situation that violates
the beta-min assumption. For such coefficients, the confidence intervals
constructed using bootstrap lasso+partial ridge have, on average, larger
coverage probabilities than those of bootstrap lasso+ols. Bootstrap
lasso+partial ridge also has, on average, shorter confidence interval
lengths than those of the de-sparsified lasso methods, regardless of whether
the linear models are misspecified. Additionally, we provide theoretical
guarantees for bootstrap lasso+partial ridge under appropriate conditions, and
implement it in the R package "HDCI.
Provincial government and regional development
This research uses a case study of Xinjiang to challenge China's reform by addressing the problems rooted in its partiality and regionalisation. The reform started in the field of political administration and toleration of decentralisation and marketisation in the economic sphere has generated economic prosperity in some regions. But economic reform was not necessarily accompanied by political transformation. Most characteristics of socialism have been retained, including political discretion and economic bailout. Both are regarded as major causes to economic weakness in some sectors and some provinces. The central argument for the continuation of the partial reform is decentralisation of decision-making to the local political state, enabling local government to give a "helping hand" in facilitating change. But the partiality of the reform drives local governments in those regions with political sensitivities to become a "political defender", holding back the progress of the reform there. Such unbalanced and unparalleled developments amongst the regions and institutions has create imbalances in provinces such as Xinjiang, challenging the success of China's reform overall. In politically sensitive regions, the Communist Party has retained an administrative stranglehold and development has stagnated, not only calling into question the sustainability the reforms but also potentially threatening China's unity and political stability. The thesis uses Xinjiang, which is politically very sensitive, because of its ethnicity and strategic resources, to argue this point
MSIQ: Joint Modeling of Multiple RNA-seq Samples for Accurate Isoform Quantification
Next-generation RNA sequencing (RNA-seq) technology has been widely used to
assess full-length RNA isoform abundance in a high-throughput manner. RNA-seq
data offer insight into gene expression levels and transcriptome structures,
enabling us to better understand the regulation of gene expression and
fundamental biological processes. Accurate isoform quantification from RNA-seq
data is challenging due to the information loss in sequencing experiments. A
recent accumulation of multiple RNA-seq data sets from the same tissue or cell
type provides new opportunities to improve the accuracy of isoform
quantification. However, existing statistical or computational methods for
multiple RNA-seq samples either pool the samples into one sample or assign
equal weights to the samples when estimating isoform abundance. These methods
ignore the possible heterogeneity in the quality of different samples and could
result in biased and unrobust estimates. In this article, we develop a method,
which we call "joint modeling of multiple RNA-seq samples for accurate isoform
quantification" (MSIQ), for more accurate and robust isoform quantification by
integrating multiple RNA-seq samples under a Bayesian framework. Our method
aims to (1) identify a consistent group of samples with homogeneous quality and
(2) improve isoform quantification accuracy by jointly modeling multiple
RNA-seq samples by allowing for higher weights on the consistent group. We show
that MSIQ provides a consistent estimator of isoform abundance, and we
demonstrate the accuracy and effectiveness of MSIQ compared with alternative
methods through simulation studies on D. melanogaster genes. We justify MSIQ's
advantages over existing approaches via application studies on real RNA-seq
data from human embryonic stem cells, brain tissues, and the HepG2 immortalized
cell line
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