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Among his most attributed quotes: "Use the sport, don't let the sport use you,'' and "Never give up on a kid. Community Rules apply to all content you upload or otherwise submit to this site. Known for his speed, defense and power, Burks enjoyed an year career with five teams, including the Indians and two turns with the Boston Red Sox. Urbas grew up in Collinwood and played football at St. Joseph High School and Grove City. His Big Ten long jump record of
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Here, we develop a network method, CoCoNet, to facilitate the identification of trait-relevant tissues or cell types. In particular, CoCoNet relies on a covariance regression network model to express gene-level effect measurements for the given GWAS trait as a function of the tissue-specific co-expression adjacency matrix. With a composite likelihood-based inference algorithm, CoCoNet is scalable to tens of thousands of genes.
We validate the performance of CoCoNet through extensive simulations. In the real data applications, we show how CoCoNet can help identify specific glial cell types relevant for neurological disorders and identify disease-targeted colon tissues as relevant for autoimmune diseases.
Identifying trait-relevant tissues or cell types is important for understanding disease etiology. Several computational methods have been recently developed to integrate omics studies with genome-wide association studies GWASs in order to infer trait-relevant tissues or cell types. However, these previous methods have thus far ignored an important biological feature of gene expression data; that is, genes are interconnected with each other and are co-regulated together.
Such gene co-expression pattern occurs in a tissue specific or cell type specific fashion and may contain invaluable information for inferring trait-tissue relevance. Here, we develop a network model to take advantage of the tissue-specific or cell type specific gene co-expression patterns inferred from bulk RNA sequencing or single cell RNA sequencing studies into GWASs.
We illustrate the benefits of our method in identifying trait-relevant tissues or cell types through simulations and applications to real data sets.
PLoS Genet 16 4 : e This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The CoCoNet method is implemented as an R package, which, together with all processed data and scripts to reproduce the results in the paper, are freely available at www.
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. Characterizing the biological functions of these identified associations requires the identification of trait-relevant tissues, as the SNP effects on most traits likely act in a tissue-specific fashion [ 2 , 3 ].
For example, it is well recognized that brain-specific SNP effects underlie many brain related diseases such as psychiatric disorders [ 4 — 7 ]. For most complex traits, however, their trait-relevant tissues are often obscure. As a result, identifying trait-relevant tissues from GWAS becomes an important first step towards understanding disease etiology and the genetic basis of phenotypic variation [ 8 — 15 ]. These RNAseq studies produce accurate gene expression measurements both at a genome-wide scale and in a tissue specific or cell type specific fashion.
More recently, various scRNAseq studies are being performed to collect cell type specific gene expression measurements on tens of thousands of cells from various tissues and organs [ 17 ]. Such tissue specific and cell type specific expression measurements collected from bulk RNAseq and scRNAseq provide valuable information for inferring disease relevant tissue types.
Indeed, methods have been developed to identify genes that are specifically expressed in a particular tissue or cell type to construct tissue specific or cell type specific annotations at the gene level, which are further integrated into GWASs to infer disease-relevant tissues or cell types[ 18 , 19 ]. However, these previous methods have ignored an important biological feature of gene expression data; that is, genes are interconnected with each other and are co-regulated together.
Such gene co-expression patterns occur in a tissue specific or cell type specific fashion [ 8 ]. Certain gene co-expression sub-networks have been shown to contain valuable information for predicting gene-level association effect measurements on diseases in GWASs [ 8 , 20 — 22 ]. In addition, genes with high network connectivity are enriched for heritability of common diseases and disease related traits [ 23 ]. Indeed, one key hypothesis in the recent omnigenic model states that tissue-specific gene networks underlie the etiology of various common diseases [ 24 ].
Therefore, it is important to develop statistical methods that can take advantage of tissue-specific topological connections contained in tissue specific gene co-expression networks to facilitate the inference of disease tissue relevance.
Here, we make such a first attempt to integrate GWAS data with gene co-expression patterns obtained from gene expression studies, through developing a statistical method for the inference of trait-relevant tissues. To do so, for a given trait, we treat the gene-level association statistics obtained from GWAS as the outcome variable and treat the tissue-specific adjacency matrices inferred from gene expression studies as input matrices.
We examine one tissue at a time and model the gene-level association statistics as a function of the tissue-specific adjacency matrix. Afterwards, we identify trait-relevant tissues through likelihood-based inference. To accompany our model, we also develop a composite likelihood-based algorithm, which is computationally efficient and ensures result robustness in the presence of substantial noise in the estimated tissue-specific gene adjacency matrices. We demonstrate the effectiveness of our method through simulations.
We apply our method for an in-depth analysis of four autoimmune diseases and four neurological disorders, through integrating the corresponding GWASs with bulk RNAseq data from 38 tissues and single cell RNAseq data from 10 cell types. In this section, we provide a simplified version of the covariance regression network model, which is used in most analyses in the present study. The general version of the covariance regression network model is described in the next section.
Here, we aim to leverage tissue-specific gene co-expression networks to infer trait relevant tissues through integrating GWAS and gene expression studies. To do so, we perform gene-centric analysis and focus on a common set of m genes that are measured in both GWAS and gene expression studies.
We also obtain tissue-specific gene expression measurements from gene expression studies on multiple tissues. For each tissue in turn, we construct an m by m gene-gene adjacency matrix to represent the co-expression network. Such adjacency matrix is constructed based on gene expression measurements, paired with prior gene-gene interaction information obtained from external data sources more details in the following subsections.
We reason that, in the trait-relevant tissue, if two genes share similar functionality, then these two genes will likely have similar effects on the trait of interest. In contrast, in the trait irrelevant tissue, two genes sharing similar functionality would not be strongly predictive of their effect measurement similarity on the trait of interest.
Therefore, the prediction ability of the adjacency matrix A on the gene-level effect measurement y i would be an effective indication on whether the examined tissue is relevant to trait or not. To capture such intuition, we use the Covariance Regression Network Model [ 26 ] to model the relationship between A and y.
In the simplified version, we consider. We also define , which represents the relative signal strength of gene co-expression pattern on gene-level effect measurements y. An extension of the model is shown in the next section. The above model can be fitted through a standard maximum likelihood inference procedure. However, parameter estimation through the standard maximum likelihood inference procedure is computationally inefficient as it scales cubically with the number of genes m.
To enable scalable computation, we consider the composite likelihood approach for inference [ 27 ]. Specifically, instead of working on the joint likelihood specified in Eq 1 , we consider pairs of genes one at a time.
For each pair of genes i and j , we consider the pair-wise likelihood as 2 where BN denotes a bivariate normal distribution. With the model specified in Eq 2 , we can obtain the corresponding log composite likelihood as: 3. We use the Nelder-Mead method implemented in the optim function in R to obtain the composite likelihood estimates that maximizes the above composite likelihood.
Our inference algorithm scales only quadratically with the number of genes, and, with a small K , can analyze each trait-tissue pair with 10, genes in a few minutes. Besides scalable computation, we note that the composite likelihood-based inference algorithm also ensures result robustness with respect to model mis-specifications.
Specifically, instead of making the strong assumption that the m -vector of y jointly follows a multivariate Gaussian distribution, our composite likelihood only needs to make a much weaker assumption that each pair y i , y j follows a bivariate normal distribution. As a result, the composite likelihood-based algorithm can be robust to various model misspecifications, relieving a potential concern in real data applications, where the tissue specific adjacency matrices may be estimated with a substantial estimation noise.
We refer to the above model as the simplified version of the Co mposite likelihood-based Co variance regression Net work model, or CoCoNet. With the composite likelihood inference algorithm, we examine one tissue at a time and obtain the maximum composite likelihood. Afterwards, we rank the tissues based on the maximum composite likelihood and select the tissue with the highest likelihood as the most trait-relevant tissue.
Because of the composite likelihood approach, CoCoNet is computationally efficient and can analyze each trait-tissue pair in real data in minutes S1 Table. In the previous section, we have only focused on the simple case of.
Here, we consider its natural extension. To do so, we denote as the k- th power of A , for any integer k.
It can be easily shown that a ij k is the number of k -paths linking from gene i to gene j in the co-expression network, where k -paths are any paths of length k. Intuitively, captures the gene-level effect measurement correlation due to direct connections among genes, while captures the gene-level effect measurement correlation due to indirect connections among genes i.
In the above model, the number of covariance matrices used, K , is treated as a fixed parameter. In the real data applications, we explored a few different choices of K in the range between one and four.
The lower BIC in models with small K is presumably because the direct connections described in A contain most information for predicting the correlation among gene-level effect measurements. We note, however, that our CoCoNet model and software implementation are general: it applies to any pre-specified K and can also perform model selection to determine the optimal choice of K.
For example, CoCoNet or some simple extension of it may be directly used in gene expression studies for predicting disease status using gene network information e. In all these cases, it is possible that higher order terms may help improve prediction or inference accuracy. We performed simulations to examine the effectiveness of our method. To do so, we first randomly selected 10 tissues and 1, genes from the genotype-tissue expression GTEx study. We then used these gene expression data to construct tissue-specific gene adjacency matrices, with which we further simulated gene level effects sizes as outcomes.
Specifically, for each tissue in turn, we first categorized the selected 1, genes into non-overlapping gene clusters using the k -means clustering algorithm. The number of clusters for each tissue was determined based on BIC and ranged from 10 to 15 across tissues.
Based on the gene clusters, we constructed the tissue-specific gene adjacency matrix as a block diagonal matrix: two genes are adjacent to each other if both belong to the same inferred cluster and are not adjacent to each other otherwise.
Note that we constructed the gene adjacency matrices in a simpler way in the simulations than in the real data details of how gene adjacency matrices are constructed in the real data are provided in the following section , to ensure that the covariance matrices are positive definite in the simulations so that we can easily simulate outcome variables from multivariate normal distributions.
Next, we denoted one of the 10 tissues as the trait-relevant tissue and used its tissue-specific adjacency matrix to simulate our outcome variables. Afterwards, we fit data using the 10 tissues one at a time to identify the trait-relevant tissue. We examined three main simulation scenarios, each consisting of multiple parameter settings.
We performed simulation replicates for each parameter setting. We computed power as the percent of replicates where the true trait relevant tissue is correctly identified.
The first simulation scenario is based on our model and assumes that we can directly observe the gene adjacency matrices for all tissues. Here, in each simulation replicate, we randomly designated one tissue out of the 10 tissues to be the trait-relevant tissue. We simulated the outcome variables through a multivariate normal distribution with mean zero and covariance matrix as , where A is the adjacency matrix from the designated trait-relevant tissue.
In the simulations, we set and varied in the range of 0 to 0. In each replicate, we applied our model to examine one tissue at a time, treated the tissue-specific adjacency matrices as observed, and selected among the 10 tissues the one with the highest log likelihood equivalently the lowest BIC as the trait-relevant tissue.
The simulation scenario II is similar to scenario I, except that we were unable to observe the true adjacency matrices. Instead, we were able to observe only a noisy version of the adjacency matrices.
Specifically, we simulated the data using the true tissue-specific adjacency matrix as done in scenario I. However, when we fitted data, we were only provided with the observed tissue-specific adjacency matrices that were a noisy version of the truth. To generate these observed adjacency matrices, for each tissue in turn, we randomly converted a proportion p of the adjacent gene pairs in the true adjacency matrix to be nonadjacent, and randomly converted a proportion q of nonadjacent gene pairs in the true adjacency matrix to be adjacent.
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This increase has been well received by the colleges and should help retention. Brief reports from the Office of the Provost units which were not requested to submit individual annual reports to the chancellor are included in Appendix A. FY , 13 and 14 Implementation Plan: Gathered data to report on completion of the first three-year implementation plan. Report presented by the chancellor in Fall
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What books do WaSP members refer to when we run into issues or questions? Which ones do we recommend to friends and colleagues, whether they be seasoned design and development veterans or total newbies? Read on to find out. Note: Recommendations are made and reviews are written by individual WaSP members. Their views may not necessarily represent the view of the Web Standards Project as a whole. Some books were written or contributed to by WaSP members. And not just a technical reference — this book will help you successfully argue the benefits of Web standards to every boss or client that questions or doubts its merits. Back when I was at AOL, we gave copies out to all developers, and to senior management, and what a difference it made! When I find developers that are struggling to make the transition to standards-compliant coding, I sit them down and hand them this book. In the last few years, books on CSS have crowded the book shelves as designers clamored to better understand how to use the mighty tool that blew away tables.
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After shining her light for 98 years, Patricia Peck Tiebout died while sleeping at home in Princeton, in the early morning of May 9, Family members, neighbors and longtime friends recall her warmth, kindness, and beautiful smile, all of which she had until the very end, all of which she brought into this world on March 25, , when she was born in Dobbs Ferry, NY, to parents Edwin D. Being of a generation that grew up during the Depression and World War II, Patty learned the values of sharing, frugality, pitching in, and being grateful. Through her cherished years of child-raising, Patty was an active member of The Hastings Literature Club.
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