60,771 research outputs found
A Direct Estimation of High Dimensional Stationary Vector Autoregressions
The vector autoregressive (VAR) model is a powerful tool in modeling complex
time series and has been exploited in many fields. However, fitting high
dimensional VAR model poses some unique challenges: On one hand, the
dimensionality, caused by modeling a large number of time series and higher
order autoregressive processes, is usually much higher than the time series
length; On the other hand, the temporal dependence structure in the VAR model
gives rise to extra theoretical challenges. In high dimensions, one popular
approach is to assume the transition matrix is sparse and fit the VAR model
using the "least squares" method with a lasso-type penalty. In this manuscript,
we propose an alternative way in estimating the VAR model. The main idea is,
via exploiting the temporal dependence structure, to formulate the estimating
problem into a linear program. There is instant advantage for the proposed
approach over the lasso-type estimators: The estimation equation can be
decomposed into multiple sub-equations and accordingly can be efficiently
solved in a parallel fashion. In addition, our method brings new theoretical
insights into the VAR model analysis. So far the theoretical results developed
in high dimensions (e.g., Song and Bickel (2011) and Kock and Callot (2012))
mainly pose assumptions on the design matrix of the formulated regression
problems. Such conditions are indirect about the transition matrices and not
transparent. In contrast, our results show that the operator norm of the
transition matrices plays an important role in estimation accuracy. We provide
explicit rates of convergence for both estimation and prediction. In addition,
we provide thorough experiments on both synthetic and real-world equity data to
show that there are empirical advantages of our method over the lasso-type
estimators in both parameter estimation and forecasting.Comment: 36 pages, 3 figur
Characterisation of microRNAs in the heart
MicroRNAs (miRNAs) are endogenous, non-coding RNA species that regulate gene
expression at the post-transcriptional level. Recent studies have shown that miRNAs are
important for cardiac hypertrophy and heart failure, and are critical determinants of
tissue metabolism.
To investigate the role(s) of miRNAs in the insulin resistant heart, left ventricular
biopsies were collected from patients with normal ventricular function with or without
type 2 diabetes, and patients with left ventricular dysfunction (LVD). Using TaqMan
based reverse transcriptase PCR, quantitative expression levels of 155 mature miRNAs
in normal and diabetic hearts were determined. Five miRNAs were significantly
upregulated in the diabetic human heart. Among these, miR-223 was upregulated in
both diabetic heart and patients with LVD. Adenoviral-mediated overexpression of
miR-223 increased baseline glucose uptake in cardiac myocytes in vitro with an effect
size similar to that observed for insulin stimulation. This increase was associated with
increase in Glut4 protein expression but independent of PI3K/Akt signalling and AMPK
activity. In contrast to findings in other cells, in cardiac myocytes miR-223 did not
downregulate protein levels of Mef2c or Igf1r, and an unexpected increase in NfIa
protein was observed, where all three genes are miR-223 targets in immune cells.
Systemic inhibition of miR-223 in vivo decreased blood glucose level 48 hours after
administration and increased Glut4 protein level in the skeletal muscle, however Glut4
levels were decreased in the heart. Cardiac-specific transgenic mice overexpressing
miR-223 showed no detectable changes in Glut4 protein level and cardiac insulin
signalling at baseline.
Collectively, these data characterise the expression of miRNAs in the human heart,demonstrate that miRNAs regulate gene targets in a cell/tissue type specific manner,
they can unexpectedly increase protein expression in cardiac myocytes, and miR-223
regulates cardiac glucose metabolism through a non-canonical pathway, which may
have implications for future investigations and treatment of insulin resistance
Fine gradings of complex simple Lie algebras and Finite Root Systems
A -grading on a complex semisimple Lie algebra , where is a finite
abelian group, is called quasi-good if each homogeneous component is
1-dimensional and 0 is not in the support of the grading.
Analogous to classical root systems, we define a finite root system to be
some subset of a finite symplectic abelian group satisfying certain axioms.
There always corresponds to a semisimple Lie algebra together with a
quasi-good grading on it. Thus one can construct nice basis of by means
of finite root systems.
We classify finite maximal abelian subgroups in \Aut(L) for complex
simple Lie algebras such that the grading induced by the action of on
is quasi-good, and show that the set of roots of in is always a
finite root system. There are five series of such finite maximal abelian
subgroups, which occur only if is a classical simple Lie algebra
- …