const-ae

#' @param p,q two orthonormal matrices of size `N x M`  (i.e., `t(p) %*% p == diag(nrow=N)`) 
#'   that each represent an `M` dimensional subspace in the `N` dimensional gene space.
#'
#' @return the tangent vector to go from point `p` to `q` on the Grassmann manifold
#'   represented as an `N x M` dimensional matrix.
grassmann_log <- function(p, q){
  n <- nrow(p)
  k <- ncol(p)
  z <- t(q) %*% p
  At <- t(q) - z %*% t(p)

const-ae

-- Search for supplementary figures and properly resolve links to them
-- Important. You need to flag the refstepcounter commands in LATEX. 
-- Please include the following in your preamble
--     % Help with pandoc conversion
--     \newcommand{\arabic}[1]{__||supfiganchor:display||__}
--     \newcommand{\refstepcounter}[1]{__||supfiganchor:increment||__}


-- Bail if we are converting to LaTeX.
if FORMAT:match('latex') then

const-ae

-- Based on https://github.com/openjournals/inara/blob/f47cfd4e87d5d1afda9db353966b5102f9c941f2/data/filters/resolve-references.lua
-- Bail if we are converting to LaTeX.
if FORMAT:match('latex') then
  return {}
end

local nequations = 0
local equation_labels = {}

const-ae

#' Combine two SummarizedExperiments / SingleCellExperiments with partially overlapping
#' genes into one
#' 
#' Note: This ignores all but the first assay
#' Can handle column sparse and standard matrices
cbind_se <- function(se1, se2, assay_fill = 0, colData_fill = NA, rowData_fill = NA, post_fix = c("_1", "_2")){
  stopifnot(length(post_fix) == 2)
  # Merge assays based on rowNames
  if( (is.null(rownames(se1)) || is.null(rownames(se2))) && nrow(se1) != nrow(se2)){
    stop("To cbind SummarizedExperiments either rownames are needed or the ",

const-ae

df <- data.frame(Circulatory=c(32,26,19,16,14,13,11,11),
                 Mental=c(11,11,18,24,23,24,26,23),
                 Musculoskeletal=c(17,18,13,16,12,18,20,26),
                 Cancer=c(10,15,15,14,16,16,14,14))

rownames(df) <- seq(1975,2010,by=5)

df

library(ggplot2)