Regularized estimation of linear functionals of precision matrices for high-dimensional time series

This paper studies a Dantzig-selector type regularized estimator for linear functionals of high-dimensional linear processes. Explicit rates of convergence of the proposed estimator are obtained and they cover the broad regime from i.i.d. samples to long-range dependent time series and from sub-Gaussian innovations to those with mild polynomial moments. It is shown that the convergence rates depend on the degree of temporal dependence and the moment conditions of the underlying linear processes. The Dantzig-selector estimator is applied to the sparse Markowitz portfolio allocation and the optimal linear prediction for time series, in which the ratio consistency when compared with an oracle estimator is established. The effect of dependence and innovation moment conditions is further illustrated in the simulation study. Finally, the regularized estimator is applied to classify the cognitive states on a real fMRI dataset and to portfolio optimization on a financial dataset.Comment: 44 pages, 4 figure

Tuning Cell Fate on Self-assembled Structures

This dissertation presents novel biodegradable copolymers with dendritic architecture, classic polymers, and inorganic materials with controlled surface topography, stiffness, and surface energy for investigating cell-material interactions and targeting tissue engineering applications. Chapter I reviews the recent progress in bone and nerve regeneration, the key factors of materials influencing cell-material interaction, and self-assembled polymer structures. Chapter II presents a divergent method to synthesize biodegrable com-dendritic tri-block copolymers consisting of poly(ethylene glycol) and poly(L-lactide) or poly(e[epsilon]-caprolactone) and the MC3T3-E1 cell response to their spherulites. Chapter III presents the fabrication of deformable poly(e-caprolactone) honeycomb films prepared via a surfactant-free breath figure method in a water-miscible solvent and how the tunable topography regulates MC3T3-E1 cell functions. Chapter IV investigates the fabrication of photo-cured poly(e-caprolactone) triacrylate films with tunable pore size via breath figure method and how the pore size regulates MC3T3-E1 cell behavior. Chapter V invented a facile method to fabricate honeycomb films with submicron pores using monodisperse silica nanoparticle as template and studied the MC3T3-E1 cell functions on those honeycomb films. Chapter VI described a novel method to fabricate microgrooves with honeycomb patterns and investigated the MC3T3-E1 cell functions on this special topography. Chapter VII introduces a facile method to obtain controllable surface energy on poly(e-caprolactone) substrates via controlling the composition of edge-on and flat-on lamellae and how MC3T3-E1 cells behave on those substrates with different surface energy. Chapter VIII synthesizes biomimetic calcium carbonate concentric microgrooves with tunable width via self-assembly and studies the MC3T3-E1 cell response to those microgrooves. Chapter IX describes one method to fabricate controllable topographical features and mechanical properties on poly(e-caprolactone) substrates using uniaxial and biaxial stretching and how those substrates regulate MC3T3-E1 cell functions. Chapter X studies rat pheochromocytoma (PC12) response to the banded spherulites of poly(e-caprolactone) and polyhydroxybutyrate. Chapter XI presents the preparation of honeycomb-patterned copolymer films with tunable pore size and how the pore size regulates NPC cell attachment, proliferation, and differentiation

Physical characterization of the ecdysteroid and retinoid X receptor (UpEcR and UpRXR) in the fiddler crab Uca pugilator.

Ecdysteroid hormones regulate growth, metamorphic differentiation, vitellogenesis, and oogenesis in insects. In crustaceans, molt, limb regeneration, and reproduction are closely related to ecdysteroid titers. In the fiddler crab, Uca pugilator, limb regeneration is coordinated with the molt cycle. Both limb regeneration and molting correlate with the fluctuation of circulating ecdysteroid titers. The actions of ecdysteroids are mediated through a nuclear receptor (NR), the ecdysteroid receptor (EcR). EcR needs to dimerize with another nuclear receptor, the insect ultraspiracle (USP) protein, or its vertebrate homolog, retinoid X receptor (RXR), to form a functional receptor dimer. A functional EcR/USP(RXR) heterodimer regulates gene expression by binding to a specific DNA sequence in the promoter region, the ecdysteroid hormone responsive element (HRE), or EcRE. Both EcR and USP/RXR can exist as multiple forms with variant amino acid (aa) sequences, or isoforms. Most characterized insect EcRs and USPs have amino-terminal (N-terminal) variant isoforms. Studies in insects and vertebrates show that specific NR isoforms exhibit tissue and cell type specific expression, suggesting receptor isoform specific physiological function.Initial physical characterization of E. coli and in vitro synthesized UpEcR and UpRXR(-5+33) suggest that these crab receptors, just like insect EcR and USP/RXR, are able to heterodimerize. (Abstract shortened by UMI.)EcR and RXR gene homologs in U. pugilator ( UpEcR and UpRXR) have been previously cloned. Library screenings recovered cDNA clones containing a unique amino terminal open-reading frame (A/B domain) for each gene, most similar to insect EcR-B1 and USP1/RXR isoforms. Several UpRXR cDNA splicing variants, however, are found in coding regions that could potentially influence function. A five-aa insertion/deletion is located in the "T" box in the hinge region. Another 33-aa insertion/deletion is found inside the ligand-binding domain (LBD), between helix 1 and helix 3. All these UpRXR mRNA variants are expressed in regenerating limb buds, and the predominant mRNA isoform represents the UpRXR(-5+33) isoform

Comparative sequence analysis reveals an intricate network among REST, CREB and miRNA in mediating neuronal gene expression

BACKGROUND: Two distinct classes of regulators have been implicated in regulating neuronal gene expression and mediating neuronal identity: transcription factors such as REST/NRSF (RE1 silencing transcription factor) and CREB (cAMP response element-binding protein), and microRNAs (miRNAs). How these two classes of regulators act together to mediate neuronal gene expression is unclear. RESULTS: Using comparative sequence analysis, here we report the identification of 895 sites (NRSE) as the putative targets of REST. A set of the identified NRSE sites is present in the vicinity of the miRNA genes that are specifically expressed in brain-related tissues, suggesting the transcriptional regulation of these miRNAs by REST. We have further identified target genes of these miRNAs, and discovered that REST and its cofactor complex are targets of multiple brain-related miRNAs including miR-124a, miR-9 and miR-132. Given the role of both REST and miRNA as repressors, these findings point to a double-negative feedback loop between REST and the miRNAs in stabilizing and maintaining neuronal gene expression. Additionally, we find that the brain-related miRNA genes are highly enriched with evolutionarily conserved cAMP response elements (CRE) in their regulatory regions, implicating the role of CREB in the positive regulation of these miRNAs. CONCLUSION: The expression of neuronal genes and neuronal identity are controlled by multiple factors, including transcriptional regulation through REST and post-transcriptional modification by several brain-related miRNAs. We demonstrate that these different levels of regulation are coordinated through extensive feedbacks, and propose a network among REST, CREB proteins and the brain-related miRNAs as a robust program for mediating neuronal gene expression

The ensemble photometric variability of over 10510^5 quasars in the Dark Energy Camera Legacy Survey and the Sloan Digital Sky Survey

We present the ensemble variability analysis results of quasars using the Dark Energy Camera Legacy Survey (DECaLS) and the Sloan Digital Sky Survey (SDSS) quasar catalogs. Our dataset includes 119,305 quasars with redshifts up to 4.89. Combining the two datasets provides a 15-year baseline and permits analysis of the long timescale variability. Adopting a power-law form for the variability structure function, $V=A(t/1yr)^{\gamma}$, we use the multi-dimensional parametric fitting to explore the relationships between the quasar variability amplitude and a wide variety of quasar properties, including redshift (positive), bolometric luminosity (negative), rest-frame wavelength (negative), and black hole mass (uncertain). We also find that $\gamma$ can be also expressed as a function of redshift (negative), bolometric luminosity (positive), rest-frame wavelength (positive), and black hole mass (positive). Tests of the fitting significance with the bootstrap method show that, even with such a large quasar sample, some correlations are marginally significant. The typical value of $\gamma$ for the entire dataset is $\gtrsim 0.25$, consistent with the results in previous studies on both the quasar ensemble variability and the structure function. A significantly negative correlation between the variability amplitude and the Eddington ratio is found, which may be explained as an effect of accretion disk instability.Comment: 13 pages, 8 figures, 4 tables, accepted for publication in Ap

Central limit theorems for high dimensional dependent data

Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles, simple convex sets and sparsely convex sets. We investigate the quantitative effect of temporal dependence on the rates of convergence to a Gaussian random vector over three different dependency frameworks ($\alpha$-mixing, $m$-dependent, and physical dependence measure). In particular, we establish new error bounds under the $\alpha$-mixing framework and derive faster rate over existing results under the physical dependence measure. To implement the proposed results in practical statistical inference problems, we also derive a data-driven parametric bootstrap procedure based on a kernel estimator for the long-run covariance matrices. We apply the unified Gaussian and bootstrap approximation results to test mean vectors with combined $\ell^2$ and $\ell^\infty$ type statistics, change point detection, and construction of confidence regions for covariance and precision matrices, all for time series data