Statistical Methods for High Dimensional Count and Compositional Data With Applications to Microbiome Studies

Next generation sequencing (NGS) technologies make the studies of microbiomes in very large-scale possible without cultivation in vitro. One approach to sequencing-based microbiome studies is to sequence specific genes (often the 16S rRNA gene) to produce a profile of diversity of bacterial taxa. Alternatively, the NGS-based sequencing strategy, also called shotgun metagenomics, provides further insights at the molecular level, such as species/strain quantification, gene function analysis and association studies. Such studies generate large-scale high-dimensional count and compositional data, which are the focus of this dissertation. In microbiome studies, the taxa composition is often estimated based on the sparse counts of sequencing reads in order to account for the large variability in the total number of reads. The first part of this thesis deals with the problem of estimating the bacterial composition based on sparse count data, where a penalized likelihood of a multinomial model is proposed to estimate the composition by regularizing the nuclear norm of the compositional matrix. Under the assumption that the observed composition is approximately low rank, a nearly optimal theoretical upper bound of the estimation error under the Kullback-Leibler divergence and the Frobenius norm is obtained. Simulation studies demonstrate that the penalized likelihood-based estimator outperforms the commonly used naive estimator in term of the estimation error of the composition matrix and various bacterial diversity measures. An analysis of a microbiome dataset is used to illustrate the methods. Understanding the dependence structure among microbial taxa within a community, including co-occurrence and co-exclusion relationships between microbial taxa, is another important problem in microbiome research. However, the compositional nature of the data complicates the investigation of the dependency structure since there are no known multivariate distributions that are flexible enough to model such a dependency. The second part of the thesis develops a composition-adjusted thresholding (COAT) method to estimate the sparse covariance matrix of the latent log-basis components. The method is based on a decomposition of the variation matrix into a rank-2 component and a sparse component. The resulting procedure can be viewed as thresholding the sample centered log-ratio covariance matrix and hence is scalable to large covariance matrice estimations based on compositional data. The issue of the identifiability problem of the covariance parameters is rigorously characterized. In addition, rate of convergence under the spectral norm is derived and the procedure is shown to have theoretical guarantee on support recovery under certain assumptions. In the application to gut microbiome data, the COAT method leads to more stable and biologically more interpretable results when comparing the dependence structures of lean and obese microbiomes. The third part of the thesis considers the two-sample testing problem for high-dimensional compositional data and formulates a testable hypothesis of compositional equivalence for the means of two latent log-basis vectors. A test for such a compositional equivalence through the centered log-ratio transformation of the compositions is proposed and is shown have an asymptotic extreme value of type 1 distribution under the null. The power of the test against sparse alternatives is derived. Simulations demonstrate that the proposed tests can be significantly more powerful than existing tests that are applied to the raw and log-transformed compositional data. The usefulness of the proposed tests is illustrated by applications to test for differences in gut microbiome composition between lean and obese individuals and changes of gut microbiome between different time points during treatment in Crohn\u27s disease patients

Generalized quantization condition in topological insulator

The topological magnetoelectric effect (TME) is the fundamental quantization effect for topological insulators in units of the fine structure constant $\alpha$. In [Phys. Rev. Lett. 105, 166803(2010)], a topological quantization condition of the TME is given under orthogonal incidence of the optical beam, in which the wave length of the light or the thickness of the TI film must be tuned to some commensurate values. This fine tuning is difficult to realize experimentally. In this article, we give manifestly $SL(2,\mathbb{Z})$ covariant expressions for Kerr and Faraday angles at oblique incidence at a topological insulator thick film. We obtain a generalized quantization condition independent of material details, and propose a more easily realizable optical experiment, in which only the incidence angle is tuned, to directly measure the topological quantization associated with the TME.Comment: 3 figure

Generational Views On Cars and Public Transportation

In an America where cars reign supreme, it may be a surprise to learn that some people dislike driving. Cars have long represented the American dream and our cultural values of individualism and freedom; for some, they are a social status symbol representative of wealth or personality (Griffith and Marion 2020, 310). In this research project, we set out to explore how older and younger people in our community perceive cars and public transportation in order to try to determine if this cultural value, and the role that cars play in America\u27s cultural heritage, are changing

A Review of Thermal Analysis on Novel Roofing Systems

In this paper, we reviewed three types of novel roofing systems which can reduce building thermal loads: cool roof, green roof, and phase change material (PCM) roof. Cool roofs are designed to keep the roof cool by reflecting the incident solar radiation away from the building and radiating the stored heat away at night. Green roof, also called eco-roof, covered by vegetation, utilizes the thermal insulation provided by the soil and evapo-transpiration to keep the roof cool under the sun. PCM roofs employ phase change material with high latent heat of fusion in the roofs. PCM roofs are able to absorb large amount of heat at demand peak when PCM changes its phase, so that the heat from outdoor is stored in the PCM rather than flows into indoor space. The effort in the paper has compared the key parameters of each of the systems, thermal analysis methodologies, and the energy savings due to each of them with reference cases, in addition, we provide a comprehensive thermal analysis methods applied in novel roof systems and a guide to design proper novel roofing system for a give climate and building types

Sequential Dexterity: Chaining Dexterous Policies for Long-Horizon Manipulation

Many real-world manipulation tasks consist of a series of subtasks that are significantly different from one another. Such long-horizon, complex tasks highlight the potential of dexterous hands, which possess adaptability and versatility, capable of seamlessly transitioning between different modes of functionality without the need for re-grasping or external tools. However, the challenges arise due to the high-dimensional action space of dexterous hand and complex compositional dynamics of the long-horizon tasks. We present Sequential Dexterity, a general system based on reinforcement learning (RL) that chains multiple dexterous policies for achieving long-horizon task goals. The core of the system is a transition feasibility function that progressively finetunes the sub-policies for enhancing chaining success rate, while also enables autonomous policy-switching for recovery from failures and bypassing redundant stages. Despite being trained only in simulation with a few task objects, our system demonstrates generalization capability to novel object shapes and is able to zero-shot transfer to a real-world robot equipped with a dexterous hand. More details and video results could be found at https://sequential-dexterity.github.ioComment: CoRL 202

Multifunctional targeting micelle nanocarriers with both imaging and therapeutic potential for bladder cancer.

BackgroundWe previously developed a bladder cancer-specific ligand (PLZ4) that can specifically bind to both human and dog bladder cancer cells in vitro and in vivo. We have also developed a micelle nanocarrier drug-delivery system. Here, we assessed whether the targeting micelles decorated with PLZ4 on the surface could specifically target dog bladder cancer cells.Materials and methodsMicelle-building monomers (ie, telodendrimers) were synthesized through conjugation of polyethylene glycol with a cholic acid cluster at one end and PLZ4 at the other, which then self-assembled in an aqueous solution to form micelles. Dog bladder cancer cell lines were used for in vitro and in vivo drug delivery studies.ResultsCompared to nontargeting micelles, targeting PLZ4 micelles (23.2 ± 8.1 nm in diameter) loaded with the imaging agent DiD and the chemotherapeutic drug paclitaxel or daunorubicin were more efficient in targeted drug delivery and more effective in cell killing in vitro. PLZ4 facilitated the uptake of micelles together with the cargo load into the target cells. We also developed an orthotopic invasive dog bladder cancer xenograft model in mice. In vivo studies with this model showed the targeting micelles were more efficient in targeted drug delivery than the free dye (14.3×; P < 0.01) and nontargeting micelles (1.5×; P < 0.05).ConclusionTargeting micelles decorated with PLZ4 can selectively target dog bladder cancer cells and potentially be developed as imaging and therapeutic agents in a clinical setting. Preclinical studies of targeting micelles can be performed in dogs with spontaneous bladder cancer before proceeding with studies using human patients