由于难以制备完全一致的文库，在单细胞RNA测序数据中经常观察到文库之间测序覆盖率的系统差异,这通常源于细胞cDNA捕获效率或PCR扩增效率的技术差异。
scaling normalization
标准化（normalization） 旨在消除这些差异，使它们不会干扰细胞之间表达谱的比较。 这确保了在细胞群体中观察到的任何异质性或差异表达都是由生物学差异而非技术差异造成的。 其中缩放标准化（scaling normalization） 是最简单和最常用的一类标准化策略。这涉及将每个细胞的总计数除以细胞特定的比例因子，通常称为”缩放因子(size factor)“。
假设 ：任何细胞特异性偏差（如捕获或扩增效率）都会通过缩放该细胞的预期平均计数来平等地影响所有基因。 每个细胞的缩放因子表示该细胞中相对偏差的估计值，因此将其计数除以缩放因子应消除该偏差。由此产生的”标准化表达式值”可用于下游分析，如聚类和降维。
Code #--- loading ---# sce.zeisel <- scRNAseq :: ZeiselBrainData ( ) library ( scater ) sce.zeisel <- aggregateAcrossFeatures ( sce.zeisel , id= sub ( "_loc[0-9]+$" , "" , rownames ( sce.zeisel ) ) )
#--- gene-annotation ---# library ( org.Mm.eg.db ) rowData ( sce.zeisel ) $ Ensembl <- mapIds ( org.Mm.eg.db , keys= rownames ( sce.zeisel ) , keytype= "SYMBOL" , column= "ENSEMBL" )
#--- quality-control ---# stats <- perCellQCMetrics ( sce.zeisel , subsets= list ( Mt= rowData ( sce.zeisel ) $ featureType == "mito" ) )
qc <- quickPerCellQC ( stats , percent_subsets= c ( "altexps_ERCC_percent" , "subsets_Mt_percent" ) )
sce.zeisel <- sce.zeisel [ ,! qc $ discard ]
Code sce.zeisel #> class: SingleCellExperiment #> dim: 19839 2816 #> metadata(0): #> assays(1): counts #> rownames(19839): 0610005C13Rik 0610007N19Rik ... Zzef1 Zzz3 #> rowData names(2): featureType Ensembl #> colnames(2816): 1772071015_C02 1772071017_G12 ... 1772063068_D01 #> 1772066098_A12 #> colData names(10): tissue group # ... level1class level2class #> reducedDimNames(0): #> mainExpName: endogenous #> altExpNames(2): ERCC repeat
文库大小标准化
文库大小标准化是执行缩放标准化的最简单策略。我们将文库大小定义为每个细胞所有基因的计数总和，假设其期望值与任何细胞特异性偏差成比例。然后，每个细胞的”文库缩放因子”与其文库大小成正比，其中定义了比例常数，使得所有细胞的平均缩放因子等于 1。 此定义可确保标准化表达式值与原始计数的比例相同，这对解释很有用，尤其是在处理转换后的数据时。
Code lib.sf.zeisel <- scuttle :: librarySizeFactors ( sce.zeisel ) summary ( lib.sf.zeisel ) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.1757 0.5680 0.8680 1.0000 1.2783 4.0839
在ZeiselBrainData中，细胞文库缩放因子在细胞之间相差多达 10 倍 Figure fig-histogram-log10sizefactor 。这是scRNA-seq数据覆盖率变异的典型特征。
Code hist ( log10 ( lib.sf.zeisel ) , xlab= "Log10[Size factor]" , col= 'grey80' )
反卷积标准化 Normalization by deconvolution
当样本之间存在任何不平衡的差异表达（DE）时，就会出现成分偏差。消除成分偏差可以使用 DESeq2 estimateSizeFactorsFromMatrix()或 edgeR calcNormFactors()执行标准化。
假设：细胞之间大多数基因并非差异表达，假设两个细胞之间大多数非 DE 基因的计数大小的任何系统性差异代表被用于计算去除系统性差异的适当缩放因子的偏差。
然而，由于低计数和零计数占主导地位，单细胞数据对于这些批量标准化方法来说可能是个问题。Pool-based size factors are then “deconvolved” into cell-based factors for normalization of each cell’s expression profile.基于 pool 的缩放因子”反卷积”为基于细胞的缩放因子，以标准化每个细胞的表达谱。
首先使用预聚类步骤quickCluster()
Code library ( scran ) set.seed ( 100 ) clust.zeisel <- quickCluster ( sce.zeisel ) table ( clust.zeisel ) #> clust.zeisel #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 #> 170 254 441 178 393 148 219 240 189 123 112 103 135 111
然后使用 scran calculateSumFactors()
Code deconv.sf.zeisel <- calculateSumFactors ( sce.zeisel , cluster= clust.zeisel ) summary ( deconv.sf.zeisel ) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.1186 0.4860 0.8314 1.0000 1.3209 4.5090
可以看到 Figure fig-deconvolution_vs_library 反卷积缩放因子表现出与文库缩放因子细胞特定类型的偏差。 这与细胞类型之间的强差异表达所引入的成分偏差的存在是一致的。 使用反卷积缩放因子可以调整这些偏差，以提高下游分析的标准化精度。
Normalization by spike-ins
RNA-seq常用的spike-in有 External RNA Controls Consortium mix (ERCCs)，spike-in RNA variants (SIRVs)和sequencing spike-ins (Sequins) 。
Spike-in normalization基于向每个细胞中添加相同数量的spike-in RNA 的假设。Spike-in transcripts覆盖率的系统性差异只能归因于细胞特异性偏差，如捕获效率或测序深度。 为了消除这些偏差，我们通过缩放”spike-in size factors “均衡细胞之间的 spike-in 覆盖率。
与之前的方法相比，Spike-in normalization 不需要对系统的生物学特性进行假设（即，缺乏许多DE基因）。 相反，它假设spike-in transcripts （i） 以恒定水平添加到每个细胞中，（ii） 以与内源性基因相同的相对方式对偏差做出反应。
实际上，如果对单个细胞的总RNA含量的差异感兴趣，并且必须在下游分析中保留，则应使用 spike-in normalization 。 对于给定的细胞，其内源性RNA总量的增加不会增加其spike-in size factor。 这确保了总RNA含量对整个群体表达的影响不会在缩放时被消除。 相比之下，上述其他标准化方法简单地将总RNA含量的任何变化解释为偏倚的一部分并将其消除。
Code library ( ensembldb ) sce.richard <- scRNAseq :: RichardTCellData ( ) sce.richard <- sce.richard [ ,sce.richard $ `single cell quality` == "OK" ] sce.richard #> class: SingleCellExperiment #> dim: 46603 528 #> metadata(0): #> assays(1): counts #> rownames(46603): ENSMUSG00000102693 ENSMUSG00000064842 ... #> ENSMUSG00000096730 ENSMUSG00000095742 #> rowData names(0): #> colnames(528): SLX-12611.N701_S502. SLX-12611.N702_S502. ... #> SLX-12612.i712_i522. SLX-12612.i714_i522. #> colData names(13): age individual ... stimulus time #> reducedDimNames(0): #> mainExpName: endogenous #> altExpNames(1): ERCC
使用computeSpikeFactors() librarySizeFactors()
Code sce.richard <- computeSpikeFactors ( sce.richard , "ERCC" ) summary ( sizeFactors ( sce.richard ) ) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.1247 0.4282 0.6274 1.0000 1.0699 23.3161 sce.richard $ sizeFactor [ 1 : 4 ] #> SLX-12611.N701_S502. SLX-12611.N702_S502. SLX-12611.N703_S502. #> 0.3772302 0.4580093 1.1991373 #> SLX-12611.N704_S502. #> 0.5944709
可以观察到每个处理条件下的 spike-in 缩放因子和反卷积缩放因子之间存在正相关关系（Figure fig-SpikeFactor_vs_DeconvFactor ）， 表明它们在测序深度和捕获效率方面捕获了类似的技术偏差。
还观察到，增加对 T 细胞受体的刺激 - 就亲和力或时间增加而言 - 导致相对于文库缩放因子的 spike-in 因子降低。 这与刺激过程中生物合成活性和总RNA含量的增加一致，这降低了每个文库中的相对 spike-in 覆盖率（从而降低了 spike-in 缩放因子），但增加了内源性基因的覆盖率（从而增加了文库缩放因子）。
这两组缩放因子之间的差异对下游分析有实际影响。 如果将 spike-in 缩放因子应用于计数，则未刺激细胞中的表达值将放大，而刺激细胞中的表达将缩小。 但是，如果使用反卷积缩放因子，则会出现相反的情况。 当我们在标准化策略之间切换时，这可能表现为不同条件之间 DE 的大小和方向的变化，如 Figure fig-fig-switch-between-normalization-strategies 所示
Code sce.richard.deconv <- logNormCounts ( sce.richard , size_factors= calculateSumFactors ( sce.richard ) ) sce.richard.spike <- logNormCounts ( sce.richard , size_factors= sizeFactors ( sce.richard ) ) gridExtra :: grid.arrange ( plotExpression ( sce.richard.deconv , x= "stimulus" ,
colour_by= "time" , features= "ENSMUSG00000092341" ) +
theme ( axis.text.x = element_text ( angle = 90 ) ) +
ggtitle ( "After deconvolution normalization" ) ,
plotExpression ( sce.richard.spike , x= "stimulus" ,
colour_by= "time" , features= "ENSMUSG00000092341" ) +
theme ( axis.text.x = element_text ( angle = 90 ) ) +
ggtitle ( "After spike-in normalization" ) ,
ncol= 2
)
标准化策略的选择取决于生物学假设。 在大多数情况下，总RNA含量的变化并不有趣，使用文库大小或反卷积因子标准化。 然而，如果总RNA的差异与感兴趣的生物学过程有关，例如细胞周期活性或T细胞活化，使用 spike-in 标准化将保留这些差异，以便生物组之间表达的任何变化都具有正确的符号。
spike-in transcripts 应该使用 spike-in size factors 标准化。 从内源性基因计数计算的缩放因子不应该spike-in transcripts ，因为前者捕获了后者没有的总 RNA 含量差异。 尝试使用基于内源性基因计数的缩放因子对spike-in计数进行标准化将导致过度标准化和不正确的定量。 因此，如果需要标准化spike-in数据，必须为spike-in transcripts计算一组单独的缩放因子，可以使用 modelGeneVarWithSpikes()
对数变换
The log-transformation is useful as differences in the log-values represent log-fold changes in expression. 这在基于欧几里得距离的下游分析中非常重要，其中包括多种形式的聚类和降维。 通过对数转换数据进行操作，我们确保这些程序是基于表达值的对数倍数变化测量细胞之间的距离。 对数转换可以促进具有强相对差异的基因的显现。
Code set.seed ( 100 ) clust.zeisel <- quickCluster ( sce.zeisel ) sce.zeisel <- computeSumFactors ( sce.zeisel , cluster= clust.zeisel , min.mean= 0.1 ) sce.zeisel $ sizeFactor #> [1] 1.5330163 1.5197806 2.3177092 2.3098243 1.6356501 1.9140228 2.3920849 #> [8] 1.7148351 1.7773327 1.8405697 1.3853361 2.2721463 2.7341116 1.6572794 #> [15] 2.4350214 3.0837875 1.9656279 2.7387063 2.3199978 1.3466584 1.6689281 #> [22] 1.1982640 1.7097079 1.3138173 3.3489395 2.9695867 2.6083104 1.2732532 #> [29] 1.8972124 2.6611017 3.4041656 1.4966486 2.0050764 1.1145625 2.0697233 #> [36] 1.7275731 1.2382277 1.5595997 2.1447774 1.7162959 2.6613901 1.4908977 #> [43] 1.6998759 1.2296894 1.6712818 0.9957191 1.0247037 1.9330533 1.3202147 #> [50] 1.3918146 1.0947499 1.0076070 0.6306301 0.9391774 1.9744421 1.2986612 #> [57] 1.7282730 1.9812199 2.1939957 1.9050923 1.0309859 1.1311469 3.2196183 #> [64] 1.9897407 1.1698584 1.5423988 2.9012917 2.5727057 1.2543136 1.3457439 #> [71] 1.9773897 1.0141278 1.9634541 3.6047891 3.1247672 1.5545336 1.5671957 #> [78] 2.8025919 1.6536579 1.3483879 1.9103567 1.8254057 1.0507183 0.8113664 #> [85] 1.1435887 1.4907576 1.3537895 1.6386828 2.3633390 1.5528725 1.4175381 #> [92] 2.5290150 1.7092174 1.6712773 2.8047605 1.0838338 1.4363547 0.8692671 #> [99] 1.9670167 1.1005335 2.0246962 1.4532231 2.1814908 1.9616708 0.6272988 #> [106] 0.9979319 0.8318206 1.4367589 1.5291424 3.6741494 1.3961974 1.9855423 #> [113] 2.5478784 1.6363302 0.9079047 1.2297099 1.1598110 1.6656445 1.7102919 #> [120] 1.4206852 1.2662669 1.0905115 2.8185136 2.0030667 1.5196415 1.7781672 #> [127] 0.9389815 0.5948236 2.1368286 0.9609240 1.2678778 1.0648258 2.3283010 #> [134] 1.6137400 1.9572214 0.8928580 1.2245865 2.7440866 0.5725257 0.7294713 #> [141] 1.1612172 1.2721188 0.9157980 0.8769774 1.0877930 1.3818578 1.1892912 #> [148] 1.0817491 1.5241187 1.3729887 1.7102339 2.0667730 1.6640898 1.0507156 #> [155] 0.8454547 0.7700251 0.9450501 0.6773467 1.9136837 1.2645070 2.1509118 #> [162] 2.5697851 2.5916841 3.4903858 3.6919619 2.6515232 1.7293947 2.3633059 #> [169] 2.5037744 3.4963656 2.9408237 2.4558110 2.3297240 4.4017711 2.5844353 #> [176] 1.5871295 2.3565178 1.8459824 2.1193997 2.5073216 2.7601100 1.2987744 #> [183] 1.5790883 1.4113102 1.4701675 2.2827587 0.8028364 1.3787878 0.9492620 #> [190] 0.6926455 0.9525613 1.2930658 1.1770449 1.1229564 1.2475542 2.0578707 #> [197] 1.1228340 1.6684490 0.9548474 0.5305375 0.5274671 1.0488002 0.7933984 #> [204] 0.4678283 0.6281701 0.6226001 0.6086995 0.6071521 0.6226950 0.5723453 #> [211] 0.9014781 1.1552337 0.9689474 0.5268485 0.6740200 0.6737290 0.7710886 #> [218] 1.6180252 0.4341768 0.9857983 0.7404861 0.7431644 0.8859762 0.7174846 #> [225] 0.7162020 0.8701763 1.3756729 0.8647946 0.5700038 0.9360704 1.2895164 #> [232] 1.1594801 1.2345250 1.0132500 0.4631851 0.8109412 0.6033283 0.8206932 #> [239] 0.4647301 1.5702412 0.9299049 0.9758857 0.5832573 0.5338430 0.9201596 #> [246] 0.8577819 0.9964547 0.9661969 0.9101791 0.5715371 0.6823990 1.0669941 #> [253] 0.6334253 0.5316475 0.6584934 0.5974557 0.7185425 0.7614784 0.7835897 #> [260] 0.5733475 0.6263241 0.6335817 0.9447329 0.7627304 0.8052265 0.7706259 #> [267] 0.6856238 0.7504869 0.8773453 0.6885880 1.0568634 0.3917429 1.2251737 #> [274] 0.8755311 0.7575448 0.8852126 0.5189990 0.8602191 0.4583515 0.3879638 #> [281] 0.5590731 1.0668200 0.7599856 0.6914372 0.7196741 0.8505898 1.3812232 #> [288] 1.3452989 0.9135613 0.9739585 1.3797249 2.1949168 2.4857605 1.8457511 #> [295] 2.2092759 4.1435115 1.1970007 2.9576143 1.7029819 1.6420352 2.5633888 #> [302] 1.4767779 2.8259132 1.6126512 2.9945293 1.6550794 2.4548934 2.4099312 #> [309] 1.3088486 1.9174640 3.3446696 1.9224331 1.4779425 0.9128779 2.0359754 #> [316] 2.7439796 1.4771812 2.3308218 1.7799427 2.0224509 2.1880150 3.1773360 #> [323] 0.8851925 0.9705332 1.6363540 2.9748171 3.1269373 3.4669377 1.6871591 #> [330] 2.2038589 2.7014019 1.7712089 1.9450240 1.2485032 1.3309646 2.2832857 #> [337] 1.6385040 1.2032255 1.9054603 1.3935487 1.3946249 2.2364203 1.1955069 #> [344] 1.2179445 1.2536955 1.0475863 1.6322312 2.1828373 1.7626096 1.0061896 #> [351] 1.2014554 1.5357725 0.9645444 1.1211442 1.0411483 1.6050370 2.7218458 #> [358] 0.6733965 0.4378360 0.4778743 0.6531542 0.6047653 1.4623700 0.6399014 #> [365] 1.4547163 1.2943950 0.8514705 0.5948366 0.6089371 1.1639215 1.0441309 #> [372] 1.2805472 0.4735388 0.9731095 1.0979021 1.0263722 1.0167818 0.8918727 #> [379] 0.7122539 1.3679107 1.5235087 0.6724249 1.0396070 2.4112723 1.2105126 #> [386] 1.5279857 1.6581576 0.6227837 0.5514674 0.7359139 1.2469293 1.0666827 #> [393] 0.5960312 1.5694254 0.7540834 1.0843334 0.7409505 1.1010909 0.5235231 #> [400] 0.5745306 0.7914525 0.7269037 1.0703832 1.0107087 0.6049607 0.9403788 #> [407] 1.0009131 0.6029252 0.6477509 0.6852968 0.5251828 0.4245346 0.4811482 #> [414] 0.8965592 0.4367785 1.0253395 1.6025913 0.4936238 0.6762127 1.3510103 #> [421] 1.1891784 1.0914293 0.7625631 0.8242901 1.3658258 0.7058226 0.7627094 #> [428] 1.3389957 1.2862766 0.6126421 0.6804102 0.8797511 2.3813272 0.7926611 #> [435] 1.4881881 1.0434350 0.6708035 1.1462024 1.5559427 1.5545401 1.0108777 #> [442] 0.7462698 0.6915743 0.9494440 0.6031972 0.6205379 0.4214221 1.1441965 #> [449] 0.8655398 0.8245929 1.9044939 0.8485801 0.6800323 0.7026683 0.5584465 #> [456] 0.5241432 0.5558936 0.6278175 1.1520379 0.5178296 1.1385848 1.0301602 #> [463] 0.7226877 0.5993044 0.4825436 0.5105344 0.8439236 0.5713371 2.1033578 #> [470] 2.3544387 3.1264613 0.8047828 1.5195378 1.3844148 1.7689273 1.4838110 #> [477] 0.6729402 0.5992327 0.6082110 2.0363420 1.0209233 1.1498635 1.1159846 #> [484] 1.8158598 0.7200269 1.0027084 1.1123197 0.7024021 0.9903908 0.9615554 #> [491] 0.9552009 1.1400174 1.5704352 0.8183878 3.0926387 2.4587651 1.4494763 #> [498] 1.2180325 1.4050475 1.3066058 1.5013131 1.9750311 1.3644021 1.4794974 #> [505] 2.4389298 2.2321682 1.3294620 1.3314245 1.9051281 2.0659105 1.2104720 #> [512] 0.8488917 1.0616241 1.5850674 1.8542774 0.9198832 0.8946121 1.7254407 #> [519] 1.0262563 1.4969745 0.8977452 0.5658717 0.7388280 0.7533931 0.6357109 #> [526] 0.4622575 0.6985520 0.5137994 0.6643873 0.5203546 0.5076352 0.5745068 #> [533] 0.7616415 0.5778672 0.8456912 0.3845223 0.8717655 0.8179566 0.8039451 #> [540] 0.4916569 0.9079307 1.4395769 0.6960558 0.9476552 0.7276457 0.6732644 #> [547] 1.0030072 1.0555326 1.4482241 1.0004559 2.6524889 3.8792994 1.1539016 #> [554] 2.1443062 1.9009690 3.3359895 1.3305623 3.2197262 1.0381801 1.4507614 #> [561] 1.5314977 2.0117943 2.1441972 2.1642644 1.1750233 1.0353364 1.4198693 #> [568] 1.1483711 1.3082480 1.1247142 1.2016734 0.9527688 1.9955224 2.2454369 #> [575] 1.3577371 1.6749821 1.0162314 1.4163645 1.2772393 1.0463877 1.3278312 #> [582] 0.7232718 1.3511497 1.2452307 1.2228272 0.9017718 1.1765293 0.8017050 #> [589] 0.9674600 1.1103725 1.1297938 0.8197256 1.0812791 1.7132373 1.1624210 #> [596] 1.2599556 1.5965877 1.7034614 1.4556641 1.5215966 0.8029330 0.9818501 #> [603] 2.2113942 1.4926664 0.9129868 1.2174291 1.6690306 1.8563100 1.8350925 #> [610] 1.4507951 1.8625066 1.7690421 0.9408636 1.4890231 0.7807303 1.0058283 #> [617] 1.1456073 1.5261179 1.5337394 1.4095891 0.8807919 1.8467518 1.0900318 #> [624] 0.9382351 1.0239823 1.5149546 1.4785130 1.5460960 0.9973684 0.9437285 #> [631] 0.5157146 0.8394680 0.5774733 0.4155600 1.1255522 0.8434126 0.9453405 #> [638] 0.5838220 0.6210658 1.1887829 0.6697891 0.5514818 0.5185334 0.6319382 #> [645] 0.8435973 0.6972803 1.3800695 1.5070860 0.8376889 0.7105544 0.8573945 #> [652] 0.7892364 0.8424190 1.5890703 0.8539142 0.5513256 1.0566437 1.0149963 #> [659] 0.6607940 0.7299950 0.8847720 0.9846624 1.2287996 0.7822108 1.2266836 #> [666] 1.0043474 0.8559562 1.0474038 1.0576028 0.9657859 1.3898346 1.1996680 #> [673] 1.0027953 0.9992063 1.0407104 1.0348848 1.3487158 1.6378601 0.7942841 #> [680] 0.7575124 0.8026522 1.0267446 0.9759880 0.5694754 0.7027845 0.6695126 #> [687] 1.0445579 1.0633528 0.9298840 1.0294389 1.0493784 0.8723287 0.7823291 #> [694] 2.3210899 1.1942687 1.1968942 1.0754281 1.0422050 1.1907227 1.1468923 #> [701] 1.1734709 1.0226293 1.2255000 1.1717891 1.0787814 1.5237716 1.5788753 #> [708] 0.7962111 1.5523182 1.0585643 1.4442415 0.9556174 1.3881071 0.9899135 #> [715] 0.9889097 1.1242205 0.8104387 0.5839989 1.0431384 0.8511014 1.5409678 #> [722] 1.6713461 1.2551406 1.2510039 1.2093598 1.7061547 1.5620917 1.6651808 #> [729] 1.7860971 2.1686661 1.6459519 0.8053885 0.8701435 1.6302618 1.3422038 #> [736] 0.6201912 1.0758632 1.1441367 0.8380599 1.4354914 0.7293117 0.7404872 #> [743] 1.7393011 1.5295749 0.6981503 0.7292310 1.2564434 0.8550340 1.1620488 #> [750] 1.2124820 1.3547105 0.6593134 0.8386717 1.3671924 1.2586046 0.9701293 #> [757] 0.9528374 0.7070263 1.0284216 1.6291636 0.7920776 1.1654820 0.8966922 #> [764] 0.9221471 1.3771352 1.3263169 1.1936213 0.6694114 0.8713434 0.9518539 #> [771] 1.3297144 1.0403798 1.3462559 0.9682087 1.0994306 1.4287400 1.3811720 #> [778] 1.1399155 1.1199272 1.0832702 1.0985103 0.9374391 0.7230505 1.1482673 #> [785] 1.4771534 0.7189566 1.0164999 0.8629676 1.4229433 1.3677170 1.0127181 #> [792] 0.6661480 0.9475485 0.9425252 1.2743182 0.7807289 1.0054663 0.7852705 #> [799] 0.9985101 1.3305539 0.9559742 1.1314823 1.1261450 0.9770246 0.9459067 #> [806] 1.1271177 0.7447718 0.7239790 0.7808820 0.7274916 1.0044975 1.0596408 #> [813] 0.9363497 0.7733938 0.9083720 0.8579631 0.8437680 1.1237174 1.3005203 #> [820] 1.0608592 1.0021539 1.2456155 0.8797666 1.4963513 1.5860060 1.3230046 #> [827] 1.1579637 1.1533193 1.1947518 1.1743405 1.4525032 0.8126317 1.0986917 #> [834] 1.0821845 1.1924374 0.8200512 1.0330796 0.9007668 1.3579798 1.1909936 #> [841] 0.9201088 1.2390036 1.1293947 0.8910967 1.0036202 1.2665897 1.1390892 #> [848] 0.9673425 1.1233957 1.0166612 1.1272967 1.1189713 1.1538260 1.2501878 #> [855] 1.2035419 1.1251572 1.1482353 1.0644329 1.3598861 1.2948352 1.8255984 #> [862] 1.0006174 1.5066844 0.6320842 1.3167285 1.3086036 1.1852624 1.0056703 #> [869] 1.4381378 0.7621736 1.6096472 1.3681211 1.0180159 3.0828898 1.3140623 #> [876] 1.7723159 1.7215711 1.2280052 3.2127049 2.5077800 3.5577716 1.2235574 #> [883] 2.1849213 2.5220094 1.5699280 2.1268483 2.7018646 1.6756284 1.7460522 #> [890] 1.7935177 1.9671034 2.1113685 1.2702823 1.6658309 1.4280144 2.4198907 #> [897] 1.7332639 1.6771589 2.4493191 1.2543158 1.5489605 1.7336579 2.4592755 #> [904] 1.1786342 1.8970813 1.4057113 1.4463945 1.9848746 2.1637914 2.5838883 #> [911] 1.0373312 1.2016134 0.9611963 1.6614755 1.7238247 1.3537720 1.3859257 #> [918] 1.5020704 1.9440916 1.6314686 1.2867411 1.7304632 1.7774690 1.6166150 #> [925] 1.8561194 1.3871096 1.1751649 1.7187642 1.9890042 2.0502580 1.7706663 #> [932] 1.5377562 1.5646640 1.8313302 1.5357102 1.9617975 1.8034478 2.3438346 #> [939] 2.8405541 1.6991792 2.5526685 2.3186579 1.6935992 2.3809601 2.0072786 #> [946] 2.9175344 4.1102784 2.3533319 2.9766518 2.1551046 3.1029336 2.2454765 #> [953] 2.9265314 2.5379153 1.6282346 3.2499909 2.8586721 2.9112074 3.6959168 #> [960] 3.2119981 2.6819271 3.0035974 3.2731946 2.7098342 2.9195059 2.4357352 #> [967] 3.1775101 2.3211472 2.3538824 3.4150464 3.5889787 3.5430131 2.4498071 #> [974] 2.6148833 3.3281905 3.1581968 2.1787535 4.5090433 3.5852797 3.0986577 #> [981] 1.9262503 3.2464307 3.1528499 2.7068641 2.2096617 2.9149225 3.6896458 #> [988] 2.1173741 3.0262407 1.7937082 2.8074005 1.8419479 2.0261148 2.3905322 #> [995] 2.8897796 2.3389254 1.5989613 2.0730476 2.2693057 2.5061578 1.5668474 #> [1002] 1.4114079 1.6035168 2.0031393 1.6725540 2.3660038 2.4311998 1.6220150 #> [1009] 2.2494320 2.0051703 2.1243174 2.3137332 1.6589288 3.4467558 1.5691870 #> [1016] 1.8953360 2.4556899 2.2539985 2.2632931 3.8048127 2.1062875 2.5598993 #> [1023] 2.2192511 2.6421708 1.7400770 1.5124711 1.5207794 2.5995934 2.3307619 #> [1030] 2.0934847 3.2544795 1.8926345 1.4927814 2.3655044 1.7459297 2.4425658 #> [1037] 1.5820139 2.2224054 1.3151016 1.4251559 3.1611684 2.2578275 2.0721744 #> [1044] 2.0793022 2.2152828 2.0429794 1.5929985 2.1745701 2.7086131 2.9550539 #> [1051] 1.7090408 2.1739534 2.4086475 1.9787019 2.1685043 1.4015268 1.6503744 #> [1058] 1.4254391 1.2530923 2.0696749 2.0167585 2.5186366 1.9865318 1.6596806 #> [1065] 1.6218729 3.6172797 2.3664484 1.8099254 1.1828798 1.5272390 2.0688849 #> [1072] 1.6155424 1.1114811 1.5785772 1.1878217 1.9366092 1.9448304 1.8256335 #> [1079] 1.6432771 1.7733448 1.3524660 1.3009940 1.5583433 1.5990498 1.1956981 #> [1086] 1.1246629 1.5628896 1.8918944 0.9587698 1.1277985 1.3429743 1.5713238 #> [1093] 1.4618784 1.1898080 0.9984213 1.0926962 1.0010741 1.0115749 0.9073197 #> [1100] 0.9599761 1.1998169 1.1254676 1.2467643 1.2205754 0.9219351 1.6349318 #> [1107] 1.1646507 1.4710606 1.3988183 1.4667866 0.9976346 1.0894299 1.1219767 #> [1114] 0.8450422 1.6812932 1.3645943 1.0716160 1.3410215 1.5903091 1.3101790 #> [1121] 1.1041573 1.1339439 2.0214663 0.9439803 1.1267065 1.2143603 1.3196209 #> [1128] 1.7350399 1.0944809 1.2603603 1.6680055 1.2302154 1.1709295 1.1705211 #> [1135] 1.4053441 1.0205349 1.0776672 1.1106556 1.7998767 1.1041277 1.4733491 #> [1142] 0.8847309 1.1548478 1.1672925 1.3634149 1.2986403 0.9983065 1.2258095 #> [1149] 1.2805782 1.5274471 0.7835923 1.2384986 1.2630262 0.9830290 1.1584144 #> [1156] 0.7730562 1.4204987 1.1875031 1.1608277 1.0293036 1.1550926 1.2404073 #> [1163] 1.1350604 1.1697781 1.0396657 1.5029071 1.1045276 1.0470572 0.9916286 #> [1170] 1.1516204 1.0732875 0.9635962 0.9855650 0.9665151 1.2677482 1.4508596 #> [1177] 0.9103599 1.1965157 0.9681111 0.9153152 1.0101716 1.1456105 1.1097732 #> [1184] 1.0952213 1.1588938 1.5651955 1.0969937 1.2885726 1.2306014 1.1777239 #> [1191] 1.1280920 1.4509668 1.2481868 1.5404296 1.1049026 0.9944161 1.1210815 #> [1198] 1.2180880 1.9729227 1.3250372 1.2836482 1.9568878 1.4861531 1.6709074 #> [1205] 1.5925817 1.5295277 1.4978853 1.4373888 1.6601385 2.0293235 1.5452102 #> [1212] 1.6272004 1.9352393 1.5222468 1.6257843 1.7911349 2.3830577 1.5763894 #> [1219] 2.6126999 2.1933588 2.0929171 2.2011629 1.9352697 2.2955444 2.8861865 #> [1226] 2.9552345 2.2613133 2.6639325 2.1523901 2.8057533 2.1340534 2.6258171 #> [1233] 2.2999139 2.0940000 1.7328389 2.3555786 2.1806384 3.1185515 1.9701430 #> [1240] 1.4621855 2.3269978 2.1435613 2.0391143 2.4242183 1.6568129 1.6558294 #> [1247] 1.9366905 2.3090787 1.5365381 1.4884115 1.4678630 1.5559647 1.8403051 #> [1254] 1.8473467 1.8153408 1.3129040 2.2613158 1.9670988 1.4154392 1.2908701 #> [1261] 1.2258223 1.2372617 1.3849682 1.3818803 1.2538744 1.1849972 1.7617029 #> [1268] 1.7325100 1.2804203 1.2099329 1.5433375 1.5288363 1.1548616 1.3522775 #> [1275] 1.1011602 1.0240457 1.1777433 1.5095902 1.2662287 1.3481304 1.1775619 #> [1282] 2.1898014 2.4356150 1.1462779 1.3011903 1.9175148 1.3330944 1.0293250 #> [1289] 2.6867689 1.6482486 1.4650174 1.2926335 1.4375425 1.2441105 1.2041385 #> [1296] 1.5829333 1.0643759 1.6027268 1.2599680 1.3493846 1.4224224 1.8318894 #> [1303] 1.8551248 1.3857349 1.5089324 1.7910394 1.4537953 1.3186464 1.2702681 #> [1310] 1.6567580 2.2368272 1.3609936 1.2797122 1.7588604 2.4624490 1.0951129 #> [1317] 1.1250763 2.1508337 1.3056081 1.4719237 1.6373696 1.1926972 1.6467304 #> [1324] 1.1967850 1.5288154 1.6994916 1.3078353 1.7071282 1.6307058 2.0945353 #> [1331] 1.5813155 1.5353813 1.8369776 1.7642609 1.7056686 1.9938155 2.0873159 #> [1338] 1.6829740 1.9125649 1.7720332 1.7746976 2.1561757 0.9653558 0.8088880 #> [1345] 0.7360886 0.7395960 0.8940323 0.8418392 0.7201133 0.8511230 0.6913129 #> [1352] 1.0219706 0.8689029 0.5181278 0.5277838 0.7245848 0.7611660 0.5324247 #> [1359] 0.5993920 0.6236139 0.8848116 0.4192274 0.6806630 0.4080807 0.4779475 #> [1366] 0.5140040 0.5022263 0.6443545 0.4157305 0.8687701 0.6591495 0.6843288 #> [1373] 0.8852431 0.8858092 0.6953236 0.7255371 1.1914329 0.8731844 0.7849798 #> [1380] 0.9953081 0.8090009 0.5402882 0.7815379 0.8058473 0.6582348 0.4962809 #> [1387] 0.4988824 0.4257798 0.4619465 0.4085881 0.6462098 0.4914837 0.7554860 #> [1394] 0.7472177 0.6999301 0.5638754 0.7454765 0.6815110 0.8310953 1.0195647 #> [1401] 0.8101851 0.8538987 0.8873966 0.6731303 0.4953527 0.5952867 0.9476776 #> [1408] 0.4686318 0.3857080 0.7851322 0.5354460 0.5764285 0.8763402 0.8132314 #> [1415] 0.5523675 0.3511134 0.5050648 0.6796039 0.5155442 0.5050880 0.7463906 #> [1422] 0.7251611 1.3526618 1.1272332 0.8016495 0.6826865 0.7056803 1.1026667 #> [1429] 0.9247235 0.8851372 0.6534319 0.5801436 0.3893488 0.6114579 0.6167070 #> [1436] 0.6754668 0.8245834 0.8139450 0.7979698 1.4157208 0.5218744 0.7386448 #> [1443] 0.6870876 0.6051782 0.5921110 0.5777571 1.0435589 1.0533465 1.0530631 #> [1450] 0.7953334 1.4565100 0.9747399 0.7527319 0.6604109 0.3542887 1.0911197 #> [1457] 0.7901656 0.7943126 0.8144576 0.5169447 0.8539651 0.6932919 0.4599519 #> [1464] 0.6951089 0.8977796 1.0130326 0.6157421 0.5384808 0.6876578 0.5375342 #> [1471] 0.7455276 0.8498052 0.7537698 1.1119474 0.6651347 0.6489344 0.6998483 #> [1478] 0.6939484 1.0282467 1.2867972 0.9544156 2.0118871 0.5616915 0.4157957 #> [1485] 0.5825153 0.7750856 0.8931690 0.6664378 0.4879787 0.7262067 0.8454136 #> [1492] 0.6892062 0.7478006 0.8640789 0.4766958 0.6664301 0.6480702 0.7858980 #> [1499] 0.8760208 0.9575838 0.9994447 0.9722927 1.0810623 0.7575799 0.6467193 #> [1506] 0.9780209 0.9740309 1.1716945 1.0786408 0.9943956 0.5061224 0.4524044 #> [1513] 0.5057673 0.4740530 1.0331030 0.5196038 0.7348322 1.1206846 0.6920994 #> [1520] 1.1621855 0.7272086 0.8346632 0.9121902 0.8432456 1.1183990 0.7884524 #> [1527] 1.3201840 1.5013425 1.0728153 1.1875924 0.9295014 0.7498272 0.7591448 #> [1534] 0.5599025 0.5372163 0.9804927 0.7498926 0.5820417 0.4903905 0.7116135 #> [1541] 1.0077901 1.1531920 0.8787868 0.8846637 0.9911535 0.9352925 0.5836973 #> [1548] 0.7704072 0.9842912 0.5173397 0.7483261 0.6875950 0.7003904 0.6603721 #> [1555] 0.9271906 0.8890525 0.8237133 1.0163698 0.7594113 0.8121115 1.8198729 #> [1562] 1.5357705 1.4372282 1.1031280 1.4122130 1.4315779 0.5258931 0.7706262 #> [1569] 1.1256164 0.7207678 0.6988243 0.9473092 1.0896225 0.8260061 1.0386023 #> [1576] 1.0883189 0.8270599 1.2671909 1.2386844 0.8748349 0.7354412 0.8954159 #> [1583] 1.0184482 0.9516339 0.5583479 0.7213641 0.5284113 0.7222739 0.9048404 #> [1590] 1.1282593 0.7072499 1.1016535 0.8228369 0.8260160 1.0442151 1.0603454 #> [1597] 1.4668654 0.5109011 0.7216269 0.9712953 0.7816815 0.7073726 0.7631673 #> [1604] 0.8179849 1.0443102 1.1122032 0.9762749 0.9876565 1.0763955 1.1560530 #> [1611] 1.3384748 1.0235572 1.8922754 0.7630282 1.0254020 0.9757036 1.0700090 #> [1618] 0.9273128 0.8395983 1.6392733 1.1058986 1.0561444 1.6337118 1.1186396 #> [1625] 1.1033191 1.0773524 1.8263244 1.0720210 0.2911117 1.4373436 2.4195393 #> [1632] 1.1868709 1.1548829 1.1193327 0.9695513 0.8022943 1.4923693 0.6637413 #> [1639] 0.8657324 0.7816868 0.9331310 1.0757870 0.3087072 0.5545849 0.7911884 #> [1646] 0.2912017 0.4413287 0.4047777 0.6865842 0.5965641 0.7073914 0.7083717 #> [1653] 0.3257121 1.2267367 0.6991645 0.5003331 0.8299406 0.3446821 0.5119481 #> [1660] 0.5460494 0.2527538 0.4980215 0.4793745 0.2390909 0.3063718 0.4780652 #> [1667] 0.3468704 0.5647756 0.5799160 0.5893349 0.6044347 1.3318968 0.9223936 #> [1674] 1.2632257 0.7151569 2.6353804 0.7606637 1.8600487 1.1594456 0.6990555 #> [1681] 1.6322244 1.3488994 0.9838737 0.8176246 1.3078982 0.6608375 0.7223215 #> [1688] 0.3654063 0.4976277 1.4405905 0.4484513 0.3619810 0.4646215 0.4863196 #> [1695] 1.2628293 0.5747780 0.4311496 0.2570045 0.4763998 0.3423045 0.4986576 #> [1702] 0.1546115 0.2697218 0.5260067 0.6210552 0.7320022 0.4053707 0.8925925 #> [1709] 0.3613431 0.4455241 0.5134008 0.5013095 0.7802967 0.5268212 0.4259175 #> [1716] 0.5576820 0.5975482 0.6011044 0.4973374 0.6116289 0.5054736 0.6192072 #> [1723] 0.5090478 0.5040769 0.9446011 0.8500495 0.7489095 1.0614800 0.9406836 #> [1730] 0.5362001 1.2385027 0.6798513 0.9918448 0.7279280 1.2816965 0.5902391 #> [1737] 0.6925330 1.3994519 1.4933212 0.5377329 0.5222376 0.9718772 1.0824840 #> [1744] 0.7592822 0.7301152 0.9433451 1.2412503 0.7270139 1.3509821 0.6900271 #> [1751] 0.7968342 0.6603002 0.6260857 0.7887641 0.4948665 0.2780412 0.4749624 #> [1758] 0.2508551 0.2982464 0.5804526 0.5625477 0.4066206 0.3046059 1.2253597 #> [1765] 0.5559651 1.0457118 0.7994551 1.3440013 0.9961839 1.0020388 0.5385029 #> [1772] 0.4674314 0.2616294 1.2105138 0.4524819 0.4542351 0.7310676 0.3612578 #> [1779] 0.5081622 1.3882393 0.6318721 1.1520620 0.4122325 0.4936302 0.5325540 #> [1786] 0.7512715 0.8029994 0.2939272 0.4044326 0.3023137 0.6919864 0.5412266 #> [1793] 0.4034261 0.4581508 0.4952783 0.4792820 0.4240549 0.8795449 0.5198946 #> [1800] 0.4498185 0.5944958 0.4160601 0.3616347 0.3784102 0.3879226 0.3668270 #> [1807] 1.0689319 1.3530525 0.6672569 0.5111265 0.5264421 0.4894098 0.5567643 #> [1814] 0.2635722 0.3272222 0.3113549 0.5795473 0.4884843 0.4827135 0.3070431 #> [1821] 0.9622414 0.5902189 0.6219537 0.6331766 0.8796945 1.2701423 0.4621150 #> [1828] 0.9693789 0.6863603 0.6258230 0.8449143 0.5873824 0.4005487 0.6199068 #> [1835] 0.4487902 0.6253062 1.0200908 0.6048290 0.6988500 0.4610389 0.5833347 #> [1842] 0.4438454 0.5928337 0.6236207 0.3883815 0.4677255 0.7084155 0.6521611 #> [1849] 0.9264167 0.4070021 0.6480348 0.4951042 0.5818162 0.7867157 0.8303511 #> [1856] 1.6285373 0.9733055 0.4491801 0.6612826 0.7431446 0.8665191 1.0213992 #> [1863] 0.6069557 0.3885037 0.4760245 1.0309520 0.8372552 0.4635037 0.9721007 #> [1870] 0.6847242 0.6361946 0.8837353 1.0921986 0.6098380 0.7902345 0.5383318 #> [1877] 0.6446980 0.6979953 0.4196233 0.4186904 0.5651838 0.6617430 0.9302860 #> [1884] 1.3169632 0.3282824 0.7170733 0.3670739 1.1899200 0.8499313 0.4306886 #> [1891] 1.0785692 0.3151203 0.9345436 0.3390976 0.4965932 0.7961058 0.5706065 #> [1898] 0.9187941 0.6891014 0.6175564 0.4079581 0.5464646 0.5065788 0.4263459 #> [1905] 0.7463988 0.8718825 0.6509877 0.3511409 0.6414118 0.4304407 0.6245323 #> [1912] 1.1339294 0.5335999 0.5186633 0.4438136 0.8019067 0.7675673 0.8483450 #> [1919] 0.4729379 0.6527594 1.4672563 0.4399404 0.7208876 0.5294233 0.4094581 #> [1926] 0.4735922 0.4548688 0.4020252 0.7721232 1.2558609 0.9267072 0.3825402 #> [1933] 0.3652230 0.6269795 0.5641959 0.3452133 0.3928226 0.5161994 0.5512446 #> [1940] 1.2338821 0.4638423 0.6066752 0.4170909 0.4008721 0.3863312 0.4013191 #> [1947] 0.4314811 0.5463247 0.2633923 0.5228119 0.3740951 0.5126126 0.2331486 #> [1954] 0.3341242 0.5404200 0.5565543 0.4295936 0.3216725 0.3776489 0.3458137 #> [1961] 0.4720188 0.9240084 0.4047615 0.3622011 0.3279143 0.3480292 0.3304065 #> [1968] 0.2750190 0.3014467 0.2532567 0.3186137 0.3720056 0.2676346 0.3386728 #> [1975] 0.8753460 0.4061477 0.2842846 0.2254836 0.2466870 0.3155173 0.2961903 #> [1982] 0.2077289 0.3759241 0.5354238 0.2358507 0.1619807 0.2463813 0.2550037 #> [1989] 0.3074768 0.2060943 1.2579911 0.5932873 0.2796345 0.6500187 0.3506551 #> [1996] 0.2246158 0.1818966 0.2958629 0.2100690 0.3157083 0.3969760 0.2999422 #> [2003] 0.2524608 0.2492081 0.4075342 0.2901719 0.3393726 0.2919893 0.4092746 #> [2010] 0.3311639 0.9415432 0.5072848 0.4190125 0.8574011 0.8270439 0.6843318 #> [2017] 0.3047039 0.5351327 0.4691358 1.4074926 0.6081978 0.9656880 0.5153933 #> [2024] 0.2886532 0.4834876 0.4066724 0.5219218 0.3703168 0.6791694 0.3931903 #> [2031] 0.4994441 0.4253156 0.3679932 0.4097774 0.4179452 0.2894216 0.5097507 #> [2038] 0.5931507 0.5676834 0.7037546 0.2954604 0.2847767 0.3139241 0.3591782 #> [2045] 0.3700514 0.9419805 0.7679279 0.2259706 0.4971050 0.3131396 0.3293400 #> [2052] 0.3808412 0.2294010 0.1977593 0.8789923 0.2780995 0.3868216 0.3911774 #> [2059] 0.2481172 0.2466739 0.9591529 0.3056657 0.3637453 0.4350124 0.2336056 #> [2066] 0.3284589 0.3031779 0.3497253 0.4812900 0.3005270 0.8063567 0.3654640 #> [2073] 0.5679070 0.3869461 0.3959355 0.3226061 0.4479985 0.2083477 0.4123446 #> [2080] 0.5967332 0.4176557 0.5093769 0.3934224 0.2115775 0.3988500 0.8746273 #> [2087] 0.5769037 0.4123359 0.4613252 0.2722316 0.6972135 0.4670983 0.4429698 #> [2094] 0.4172959 0.2290493 0.4804406 1.2509093 0.2829198 0.6633743 0.2747363 #> [2101] 0.3945378 0.6453250 2.2959056 0.2933780 0.3144920 0.2634070 0.3239291 #> [2108] 0.4957374 0.3576186 0.3340109 0.4471038 0.2717489 0.4690844 0.3923683 #> [2115] 0.3090569 0.3193750 0.2333399 0.2937070 0.2948800 0.2677876 0.2313617 #> [2122] 0.6364412 0.5024070 0.1866584 0.5150607 0.2498373 0.3155827 0.4471219 #> [2129] 0.1719359 0.1943005 0.2017262 0.2724710 0.3285416 0.2203443 0.4159256 #> [2136] 0.4196351 0.2301003 0.8317642 0.1338864 0.1784346 0.3839533 0.1397454 #> [2143] 0.2540023 0.7262252 0.3108532 0.1605738 0.2991070 0.2730480 0.3271999 #> [2150] 0.2298224 0.5798367 0.3024647 0.3824327 0.2500173 0.4085065 0.8480274 #> [2157] 0.3818955 0.3110832 0.2026175 0.3847243 0.5596895 0.1854043 0.5090915 #> [2164] 0.4966700 0.8310243 0.5501934 0.3872394 0.9628184 0.2816797 0.5340677 #> [2171] 0.4059914 0.2793635 0.6304969 0.2974488 0.2511299 0.4299391 0.3209973 #> [2178] 0.2715077 0.1515817 0.3384499 0.2957582 0.3293122 0.4347742 0.6477881 #> [2185] 0.6636268 0.4349038 0.5353818 0.1986231 1.0138863 0.2782783 0.5025696 #> [2192] 0.3104328 0.2549752 0.3385694 0.2775399 0.8166846 0.4498288 0.3661325 #> [2199] 0.6063422 0.3580387 1.0382955 0.2486334 0.4660297 0.1481857 0.3151760 #> [2206] 0.3767768 0.4134927 0.2009403 0.4981774 0.3357615 0.3598718 0.5601545 #> [2213] 0.3867702 0.3060634 0.5329099 0.1845309 0.3754400 0.3582437 0.2772678 #> [2220] 0.4136815 0.2030331 0.2827223 0.3595073 0.4857523 0.3467909 0.2293891 #> [2227] 0.4945056 0.7539187 0.2400091 0.3723597 0.2805319 0.3196303 0.2151282 #> [2234] 0.6126489 0.6455950 0.3773039 0.3692933 0.3902774 0.4636191 0.7661175 #> [2241] 0.3994208 0.2919770 0.3183749 0.4447788 0.7668559 0.2314136 0.4925914 #> [2248] 0.8124874 0.5521009 0.7189629 0.6602622 0.3649289 0.3033085 0.4429471 #> [2255] 2.9277190 0.7993884 0.3379693 0.4835457 0.5822415 0.6902686 0.4580242 #> [2262] 0.6096529 0.2828681 0.1937415 0.5634228 0.3315439 0.5217990 0.4119918 #> [2269] 0.3020709 0.5700104 0.4266720 0.3314343 1.1201103 0.2701472 0.5245469 #> [2276] 0.5538259 0.7162064 0.5766364 0.9441206 0.9247033 0.4112339 0.4201593 #> [2283] 0.9371560 0.4992336 0.5466830 0.4592743 0.5227295 0.3018594 0.3394750 #> [2290] 1.3477624 0.2928928 0.4578168 0.8878936 1.1410114 0.2542868 0.3372272 #> [2297] 0.4563875 0.4314396 0.9105045 0.3313652 0.4494479 0.3000139 0.3000866 #> [2304] 0.6235051 0.4122679 0.6833321 0.4980124 0.3459037 0.3981625 0.3952567 #> [2311] 0.5233365 0.5129183 0.4572469 0.7279957 0.4945273 0.6624391 0.4022587 #> [2318] 0.5395278 0.4356956 0.3579911 0.6630037 0.5816756 0.4685089 0.6823472 #> [2325] 0.5819805 0.9311662 1.0488614 0.9318283 1.6292467 0.6981743 0.6648595 #> [2332] 0.6775941 0.4268293 0.7494903 0.4835852 0.5718912 0.5373147 1.1607007 #> [2339] 0.8066709 0.4653635 0.7013220 0.6249051 0.6914545 0.4605551 0.4919683 #> [2346] 0.7217936 0.6287437 0.6008857 0.8595073 0.5698717 0.3781724 0.5098608 #> [2353] 0.5411919 0.5091915 0.3423090 1.0074896 1.0925127 1.1869311 0.4208647 #> [2360] 0.4163492 0.8215561 1.0279051 0.7166196 0.7263878 0.8528227 0.4053844 #> [2367] 1.2948969 1.0070887 0.5895896 0.9230134 0.4969995 0.4520987 1.4509265 #> [2374] 0.5578303 0.6051646 0.5151992 0.5648480 0.5538298 0.4801829 0.8573574 #> [2381] 0.8398927 0.7227336 0.7580617 0.5260110 0.5380821 0.7589127 0.5825038 #> [2388] 0.5006498 0.4111484 0.4824041 0.6079369 0.7113848 0.6180898 0.5761356 #> [2395] 0.5884400 0.6096206 0.4108353 0.3304339 1.0062956 0.2076443 0.7126168 #> [2402] 0.2868410 0.4117384 0.5164422 0.1999613 0.2800385 0.3983793 0.2423988 #> [2409] 0.2047528 0.3138491 0.1856415 0.2019871 0.2160289 0.5216748 0.2650189 #> [2416] 0.1815483 0.3252232 0.4613807 0.3179969 0.3499368 0.3387076 0.5509831 #> [2423] 0.5447549 0.5403906 0.2255327 0.4068846 0.5249015 0.7672507 0.5872768 #> [2430] 0.4700469 0.3788719 0.5980767 0.3393054 0.3179006 0.3939546 0.2473771 #> [2437] 0.4752199 0.9412012 0.6952965 0.9912573 0.2714045 0.5694427 0.5864496 #> [2444] 0.3094394 0.4944054 0.3155485 0.3455518 0.3554037 0.5485801 0.5637233 #> [2451] 0.4860388 0.2941673 0.4500015 0.5535388 0.4134069 0.5583496 0.3925462 #> [2458] 0.6925893 0.2146080 0.2919583 0.3828987 0.6884410 0.2043576 0.1740035 #> [2465] 0.8680209 0.5759633 0.5072931 0.3471606 0.2658161 0.1824395 0.2273628 #> [2472] 0.1988667 0.4574221 0.1870769 0.3260304 0.1892063 0.6966907 0.4882125 #> [2479] 0.3836444 0.3655271 0.8164587 0.1830506 0.4550484 0.3004721 0.1185658 #> [2486] 0.2324333 0.2761192 0.3982234 0.2981836 0.2894114 0.3013962 1.2012092 #> [2493] 2.4725929 0.2901326 1.3766797 0.8620510 0.7236363 0.3114939 0.2307754 #> [2500] 0.2964688 0.4624136 0.2566711 0.3369860 0.3344777 0.3385442 0.3110918 #> [2507] 0.2121480 0.3003881 0.3082711 0.1843243 0.2401711 0.2688840 0.6385495 #> [2514] 0.4021759 0.2307940 0.2002314 0.7760884 1.3485700 0.3981584 0.5813856 #> [2521] 0.6078029 0.4205376 0.3958241 0.5679613 0.8133076 0.3369549 0.5572460 #> [2528] 0.6409976 0.3086102 0.2310904 0.2240608 0.3373634 0.3666926 0.1860829 #> [2535] 0.4811159 0.6227676 0.5039504 1.1841169 0.4018291 0.3482626 0.2413254 #> [2542] 0.1886398 0.4188107 0.6475609 0.4388209 0.2319748 0.1757912 0.5143676 #> [2549] 0.3538551 0.5567272 0.2479046 0.4571197 0.2070337 0.6267536 1.5893273 #> [2556] 0.4874952 0.5411368 0.5180651 0.6037162 0.2355265 0.3266229 0.2505072 #> [2563] 0.6339140 0.5596668 0.2068564 0.5287665 0.1938271 0.3635211 0.8005122 #> [2570] 0.3309513 0.2659026 0.5608869 0.4150862 0.3516087 0.5060428 0.3293715 #> [2577] 0.6637494 0.2331143 0.1826957 0.1968636 0.1637478 0.2548292 0.6935695 #> [2584] 0.1953248 0.6001239 0.3155270 0.2194079 0.1509978 0.2424578 0.2317265 #> [2591] 0.3243732 0.3288374 0.3622562 0.4452402 0.3183281 0.4216950 0.1768032 #> [2598] 0.3157800 0.2748601 0.5669095 0.9538581 0.5007944 0.4112026 0.5419732 #> [2605] 0.6708303 0.6817836 0.4972728 0.6271715 0.6885709 0.9341907 0.4167574 #> [2612] 0.4030011 0.2834534 0.5366840 0.9934301 0.3218117 0.3638974 0.4195645 #> [2619] 0.3931779 0.3283593 0.2515434 0.6684912 0.6318029 0.4022234 0.3903859 #> [2626] 0.5421202 0.6625022 0.4305596 0.4180285 0.9524911 0.2082381 0.5283789 #> [2633] 0.2513484 0.2997781 0.3134889 0.1816127 0.2429556 0.1890579 0.3247658 #> [2640] 0.3495208 0.3928180 0.3489503 0.3210952 0.3394099 0.8585630 0.2678618 #> [2647] 0.3162043 0.3524275 0.2394644 0.2584395 0.1701799 0.1727409 0.1746249 #> [2654] 0.5730624 0.2941838 0.1690575 0.1961935 0.1811626 0.2282455 0.9045508 #> [2661] 0.2262194 0.2580276 0.3782178 0.3156207 0.2507244 0.5832143 0.4912288 #> [2668] 0.6757900 0.4318327 0.3006227 0.5691340 0.2621215 1.1200184 0.5515888 #> [2675] 0.2766747 0.2434754 0.2698712 0.2126860 0.4631313 0.4056000 0.3867958 #> [2682] 0.2933197 0.2022617 0.1403880 0.1864157 0.2643433 0.3698243 0.2434626 #> [2689] 0.2570670 0.3292387 0.3079758 0.4487707 0.3206108 0.1554492 0.5621817 #> [2696] 0.1436284 0.1983419 0.5880159 0.1528923 0.3530707 0.1982939 0.1982902 #> [2703] 0.2355622 0.1704211 0.1321239 0.7986746 0.3184677 0.3170377 0.3721524 #> [2710] 0.5657967 0.3462929 0.2806170 0.4475955 0.4365709 0.4158947 0.4067549 #> [2717] 0.8617303 0.7601747 0.4912575 0.4485458 0.5991391 0.3486318 0.4730358 #> [2724] 0.4817742 0.9689694 0.4695508 0.3312377 0.2784567 0.4334092 0.1992452 #> [2731] 0.2712010 0.3559502 0.4257551 0.1648501 0.4851980 0.1513140 0.2839699 #> [2738] 0.3914359 0.1545951 0.3119780 0.2559816 0.2391704 0.1906621 0.8227662 #> [2745] 0.7486176 0.2896909 0.2195900 0.5043748 1.4110073 0.2810749 2.7340267 #> [2752] 1.0720169 0.3855015 0.7354700 0.3715817 0.5594359 0.7873926 0.2737729 #> [2759] 0.5171470 0.3687170 0.3427423 0.9178332 1.3096429 0.2934791 0.2381196 #> [2766] 0.1809482 0.2742789 0.5026276 0.5193515 0.3637623 0.1679808 0.2061580 #> [2773] 0.2759568 0.2351670 0.1623629 0.2997975 0.3583705 0.2096810 0.2258624 #> [2780] 0.2863432 0.5146719 0.3257726 0.2219938 0.4469241 0.4304666 0.2596782 #> [2787] 0.3801490 0.2746723 0.4018288 0.2800701 0.8713919 0.1779662 0.3158951 #> [2794] 0.4396445 0.6759492 0.2994991 0.2292734 0.2183087 0.2350233 0.4970463 #> [2801] 0.3038212 0.4411677 0.2437759 0.1977158 0.5185834 0.3921943 0.4381089 #> [2808] 0.2139585 0.2736933 0.4645330 0.4127345 0.4987151 0.3383534 0.3614454 #> [2815] 0.3042653 0.1925791 sce.zeisel <- logNormCounts ( sce.zeisel ) assayNames ( sce.zeisel ) #> [1] "counts" "logcounts"
