10X單細胞(10X空間轉(zhuǎn)錄組)通訊分析CellChat之多樣本通訊差異分析

hello庇配,各位好售睹,之前呢越锈,我們分享了Cellchat的文章內(nèi)容仗嗦,方法,以及單樣本分析案例甘凭,文章在10X單細胞(10X空間轉(zhuǎn)錄組)通訊分析之CellChat稀拐,這次我們來分享一下Cellchat分析多樣本通訊差異的分析過程。

Load the required libraries

library(CellChat)
library(patchwork)

Load CellChat object of each dataset and then merge together

cellchat.NL <- readRDS(url("https://ndownloader.figshare.com/files/25954199"))
cellchat.LS <- readRDS(url("https://ndownloader.figshare.com/files/25956518"))
object.list <- list(NL = cellchat.NL, LS = cellchat.LS)
cellchat <- mergeCellChat(object.list, add.names = names(object.list))

這個地方我看了一下丹弱,每個樣本都是單獨分析出來的結(jié)果德撬,其實對于細胞通訊一直有一個爭議,那就是先整合后再分析呢躲胳,還是單樣本分析完了進行比較蜓洪,不知道大家怎么看,Cellchat這里是建議分開做

Part I: Predict general principles of cell-cell communication

CellChat從全局出發(fā)坯苹,以預(yù)測細胞間通信的一般原理隆檀。 比較多種生物學(xué)條件之間的細胞間通訊時,它可以回答以下生物學(xué)問題:

  • 細胞通訊是否增強
  • 細胞通訊的相互聯(lián)系是否顯著改變
  • How the major sources and targets change from one condition to another
    這個地方很值得深入探討粹湃。

Compare the total number of interactions and interaction strength

首先是上述第一個問題恐仑,CellChat compares the the total number of interactions and interaction strength of the inferred cell-cell communication networks from different biological conditions.

gg1 <- compareInteractions(cellchat, show.legend = F, group = c(1,2))
gg2 <- compareInteractions(cellchat, show.legend = F, group = c(1,2), measure = "weight")
gg1 + gg2
圖片.png

Compare the number of interactions and interaction strength among different cell populations

To identify the interaction between which cell populations showing significant changes, CellChat compares the number of interactions and interaction strength among different cell populations.(配受體數(shù)量和通訊強度的差異)

看數(shù)量和強度變化

The differential number of interactions or interaction strength in the cell-cell communication network between two datasets can be visualized using circle plot, where red (or blue) colored edges represent increased (or decreased) signaling in the second dataset compared to the first one.(紅色加強,綠色降低

par(mfrow = c(1,2), xpd=TRUE)
netVisual_diffInteraction(cellchat, weight.scale = T)
netVisual_diffInteraction(cellchat, weight.scale = T, measure = "weight")

圖片.png

示例的數(shù)量差異變化很明顯为鳄。
熱圖展示

gg1 <- netVisual_heatmap(cellchat)
#> Do heatmap based on a merged object
gg2 <- netVisual_heatmap(cellchat, measure = "weight")
#> Do heatmap based on a merged object
gg1 + gg2
圖片.png

如果我們不止兩個樣本呢裳仆??
The differential network analysis only works for pairwise datasets. If there are more datasets for comparison, we can directly show the number of interactions or interaction strength between any two cell populations in each dataset.
為了更好地控制不同數(shù)據(jù)集上的推斷網(wǎng)絡(luò)的節(jié)點大小和邊緣權(quán)重孤钦,我們計算了每個單元格組的最大單元數(shù)以及所有數(shù)據(jù)集之間的最大交互數(shù)(或交互權(quán)重)鉴逞。

weight.max <- getMaxWeight(object.list, attribute = c("idents","count"))
par(mfrow = c(1,2), xpd=TRUE)
for (i in 1:length(object.list)) {
  netVisual_circle(object.list[[i]]@net$count, weight.scale = T, label.edge= F, edge.weight.max = weight.max[2], edge.width.max = 12, title.name = paste0("Number of interactions - ", names(object.list)[i]))
}

圖片.png

這種情況相對很少,因為即使多個樣本司训,我們也會兩兩比較构捡,總結(jié)出結(jié)果

Differential number of interactions or interaction strength among different cell types

To simplify the complicated network and gain insights into the cell-cell communication at the cell type level, we can aggregate the cell-cell communication based on the defined cell groups. Here we categorize the cell populations into three cell types, and then re-merge the list of CellChat object.(細胞類型水平上分析

group.cellType <- c(rep("FIB", 4), rep("DC", 4), rep("TC", 4))
group.cellType <- factor(group.cellType, levels = c("FIB", "DC", "TC"))
object.list <- lapply(object.list, function(x) {mergeInteractions(x, group.cellType)})
cellchat <- mergeCellChat(object.list, add.names = names(object.list))
#> Merge the following slots: 'data.signaling','net', 'netP','meta', 'idents', 'var.features' , 'DB', and 'LR'.
weight.max <- getMaxWeight(object.list, slot.name = c("idents", "net", "net"), attribute = c("idents","count", "count.merged"))
par(mfrow = c(1,2), xpd=TRUE)
for (i in 1:length(object.list)) {
  netVisual_circle(object.list[[i]]@net$count.merged, weight.scale = T, label.edge= T, edge.weight.max = weight.max[3], edge.width.max = 12, title.name = paste0("Number of interactions - ", names(object.list)[i]))
}
圖片.png
par(mfrow = c(1,2), xpd=TRUE)
netVisual_diffInteraction(cellchat, weight.scale = T, measure = "count.merged", label.edge = T)
netVisual_diffInteraction(cellchat, weight.scale = T, measure = "weight.merged", label.edge = T)
圖片.png

Compare the major sources and targets in 2D space

比較二維空間中的傳出和傳入交互強度,可以輕松識別出具有不同數(shù)據(jù)集之間發(fā)送或接收信號的顯著變化的細胞群體壳猜。

num.link <- sapply(object.list, function(x) {rowSums(x@net$count) + colSums(x@net$count)-diag(x@net$count)})
weight.MinMax <- c(min(num.link), max(num.link)) # control the dot size in the different datasets
gg <- list()
for (i in 1:length(object.list)) {
  gg[[i]] <- netAnalysis_signalingRole_scatter(object.list[[i]], title = names(object.list)[i], weight.MinMax = weight.MinMax)
}
#> Signaling role analysis on the aggregated cell-cell communication network from all signaling pathways
#> Signaling role analysis on the aggregated cell-cell communication network from all signaling pathways
patchwork::wrap_plots(plots = gg)
圖片.png

Part II: Identify the conserved and context-specific signaling pathways

然后勾徽,CellChat可以基于它們在多種生物學(xué)條件下的細胞間通信網(wǎng)絡(luò),識別具有更大(或更少)差異的信號網(wǎng)絡(luò)统扳,信號組以及保守的和context-specific 的信號通路喘帚。

根據(jù)功能/結(jié)構(gòu)相似性畅姊,識別差異較大(或較小)的通訊網(wǎng)絡(luò)以及通訊group

CellChat performs joint manifold learning and classification of the inferred communication networks based on their functional and topological similarity. NB: Such analysis is applicable to more than two datasets.

Functional similarity: High degree of functional similarity indicates major senders and receivers are similar, and it can be interpreted as the two signaling pathways or two ligand-receptor pairs exhibit similar and/or redundant roles. NB: Functional similarity analysis is not applicable to multiple datsets with different cell type composition.(這個地方還是要注意一下吹由,我們來看一下功能相似性的定義)

圖片.png

我們重點要記住這個:d based on the overlap of communications

Structural similarity: A structural similarity was used to compare their signaling network structure, without considering the similarity of senders and receivers. NB: Structural similarity analysis is applicable to multiple datsets with the same cell type composition or the vastly different cell type composition.
這里要注意的是A structural similarity was used to compare their signaling network structure, without considering the similarity of senders and receivers, using a previously developed measure for structural topological differences算法在單樣本時候已經(jīng)分享過

Here we can run the manifold and classification learning analysis based on the functional similarity because the two datasets have the the same cell type composition.(這一部分單樣本已經(jīng)介紹過了)若未。

Identify signaling groups based on their functional similarity

cellchat <- computeNetSimilarityPairwise(cellchat, type = "functional")
#> Compute signaling network similarity for datasets 1 2
cellchat <- netEmbedding(cellchat, type = "functional")
#> Manifold learning of the signaling networks for datasets 1 2
cellchat <- netClustering(cellchat, type = "functional")
#> Classification learning of the signaling networks for datasets 1 2
# Visualization in 2D-space
netVisual_embeddingPairwise(cellchat, type = "functional", label.size = 3.5)
#> 2D visualization of signaling networks from datasets 1 2
圖片.png

Identify signaling groups based on structure similarity

cellchat <- computeNetSimilarityPairwise(cellchat, type = "structural")
#> Compute signaling network similarity for datasets 1 2
cellchat <- netEmbedding(cellchat, type = "structural")
#> Manifold learning of the signaling networks for datasets 1 2
cellchat <- netClustering(cellchat, type = "structural")
#> Classification learning of the signaling networks for datasets 1 2
# Visualization in 2D-space
netVisual_embeddingPairwise(cellchat, type = "structural", label.size = 3.5)
#> 2D visualization of signaling networks from datasets 1 2
圖片.png

Compute and visualize the pathway distance in the learned joint manifold

We can identify the signaling networks with larger (or less) difference based on their Euclidean distance in the shared two-dimensions space(我們可以在共享二維空間中基于它們的歐幾里得距離來識別具有較大(或較小)差異的信令網(wǎng)絡(luò)). Larger distance implies larger difference of the communication networks between two datasets in terms of either functional or structure similarity. NB: We only compute the distance of overlapped signaling pathways between two datasets. Those signaling pathways that are only identified in one dataset are not considered here. If there are more than three datasets, one can do pairwise comparisons by defining comparison in the function rankSimilarity.

rankSimilarity(cellchat, type = "functional")
#> Compute the distance of signaling networks between datasets 1 2
image.png

Identify and visualize the conserved and context-specific signaling pathways

By comparing the information flow/interaction strengh of each signaling pathway, we can identify signaling pathways, (i) turn off, (ii) decrease, (iii) turn on or (iv) increase, by change their information flow at one condition as compared to another condition.(這才是我們細胞通訊分析的重點倾鲫,高低開合四個方向

Compare the overall information flow of each signaling pathway

We can identify the conserved and context-specific signaling pathways by simply comparing the information flow for each signaling pathway(沒怎么變的通訊), which is defined by the sum of communication probability among all pairs of cell groups in the inferred network (i.e., the total weights in the network).

This bar graph can be plotted in a stacked mode or not. Significant signaling pathways were ranked based on differences in the overall information flow within the inferred networks between NL and LS skin. The top signaling pathways colored red are enriched in NL skin, and these colored green were enriched in the LS skin.

gg1 <- rankNet(cellchat, mode = "comparison", stacked = T, do.stat = TRUE)
gg2 <- rankNet(cellchat, mode = "comparison", stacked = F, do.stat = TRUE)
gg1 + gg2
image.png

Compare outgoing (or incoming) signaling associated with each cell population

The above analysis summarize the information from the outgoing and incoming signaling together. We can also compare the outgoing (or incoming) signaling pattern between two datasets, allowing to identify signaling pathways/ligand-receptors that exhibit different signaling patterns.

We can combine all the identified signaling pathways from different datasets and thus compare them side by side, including outgoing signaling, incoming signaling and overall signaling by aggregating outgoing and incoming signaling together. NB: rankNet also shows the comparison of overall signaling, but it does not show the signaling strength in specific cell populations.

library(ComplexHeatmap)
#> Loading required package: grid
#> ========================================
#> ComplexHeatmap version 2.7.1.1010
#> Bioconductor page: http://bioconductor.org/packages/ComplexHeatmap/
#> Github page: https://github.com/jokergoo/ComplexHeatmap
#> Documentation: http://jokergoo.github.io/ComplexHeatmap-reference
#> 
#> If you use it in published research, please cite:
#> Gu, Z. Complex heatmaps reveal patterns and correlations in multidimensional 
#>   genomic data. Bioinformatics 2016.
#> 
#> This message can be suppressed by:
#>   suppressPackageStartupMessages(library(ComplexHeatmap))
#> ========================================
i = 1
# combining all the identified signaling pathways from different datasets 
pathway.union <- union(object.list[[i]]@netP$pathways, object.list[[i+1]]@netP$pathways)
ht1 = netAnalysis_signalingRole_heatmap(object.list[[i]], pattern = "outgoing", signaling = pathway.union, title = names(object.list)[i], width = 5, height = 6)
ht2 = netAnalysis_signalingRole_heatmap(object.list[[i+1]], pattern = "outgoing", signaling = pathway.union, title = names(object.list)[i+1], width = 5, height = 6)
draw(ht1 + ht2, ht_gap = unit(0.5, "cm"))
image.png
ht1 = netAnalysis_signalingRole_heatmap(object.list[[i]], pattern = "incoming", signaling = pathway.union, title = names(object.list)[i], width = 5, height = 6, color.heatmap = "GnBu")
ht2 = netAnalysis_signalingRole_heatmap(object.list[[i+1]], pattern = "incoming", signaling = pathway.union, title = names(object.list)[i+1], width = 5, height = 6, color.heatmap = "GnBu")
draw(ht1 + ht2, ht_gap = unit(0.5, "cm"))

image.png

功能差異的熱圖展示還是很直觀的

ht1 = netAnalysis_signalingRole_heatmap(object.list[[i]], pattern = "all", signaling = pathway.union, title = names(object.list)[i], width = 5, height = 6, color.heatmap = "OrRd")
ht2 = netAnalysis_signalingRole_heatmap(object.list[[i+1]], pattern = "all", signaling = pathway.union, title = names(object.list)[i+1], width = 5, height = 6, color.heatmap = "OrRd")
draw(ht1 + ht2, ht_gap = unit(0.5, "cm"))
image.png

Part III: Identify the upgulated and down-regulated signaling ligand-receptor pairs(上調(diào)和下調(diào)的信號通路粗合,一般我們需要關(guān)注上調(diào)的,但是下調(diào)的也非常重要

We can compare the communication probabilities mediated by ligand-receptor pairs from some cell groups to other cell groups. This can be done by setting comparison in the function netVisual_bubble.

netVisual_bubble(cellchat, sources.use = 4, targets.use = c(5:11),  comparison = c(1, 2), angle.x = 45)
#> Comparing communications on a merged object
image.png

Moreover, we can identify the upgulated (increased) and down-regulated (decreased) signaling ligand-receptor pairs in one dataset compared to the other dataset. This can be done by specifying max.dataset and min.dataset in the function netVisual_bubble. The increased signaling means these signaling have higher communication probability (strength) in one dataset compared to the other dataset.

gg1 <- netVisual_bubble(cellchat, sources.use = 4, targets.use = c(5:11),  comparison = c(1, 2), max.dataset = 2, title.name = "Increased signaling in LS", angle.x = 45, remove.isolate = T)
#> Comparing communications on a merged object
gg2 <- netVisual_bubble(cellchat, sources.use = 4, targets.use = c(5:11),  comparison = c(1, 2), max.dataset = 1, title.name = "Decreased signaling in LS", angle.x = 45, remove.isolate = T)
#> Comparing communications on a merged object
gg1 + gg2
image.png

NB: The ligand-receptor pairs shown in the bubble plot can be accessed via signaling.LSIncreased = gg1$data.

The above method for identifying the upgulated and down-regulated signaling is perfomed by comparing the communication probability between two datasets for each L-R pair and each pair of cell groups. Alternative, we can identify the upgulated and down-regulated signaling ligand-receptor pairs based on the differential gene expression analysis. Specifically, we perform differential expression analysis between two biological conditions (i.e., NL and LS) for each cell group, and then obtain the upgulated and down-regulated signaling based on the fold change of ligands in the sender cells and receptors in the receiver cells. Such analysis can be done as follows.

# define a positive dataset, i.e., the dataset with positive fold change against the other dataset
pos.dataset = "LS"
# define a char name used for storing the results of differential expression analysis
features.name = pos.dataset
# perform differential expression analysis
cellchat <- identifyOverExpressedGenes(cellchat, group.dataset = "datasets", pos.dataset = pos.dataset, features.name = features.name, only.pos = FALSE, thresh.pc = 0.1, thresh.fc = 0.1, thresh.p = 1)
#> Use the joint cell labels from the merged CellChat object
# map the results of differential expression analysis onto the inferred cell-cell communications to easily manage/subset the ligand-receptor pairs of interest
net <- netMappingDEG(cellchat, features.name = features.name)
# extract the ligand-receptor pairs with upregulated ligands in LS
net.up <- subsetCommunication(cellchat, net = net, datasets = "LS",ligand.logFC = 0.2, receptor.logFC = NULL)
# extract the ligand-receptor pairs with upregulated ligands and upregulated recetptors in NL, i.e.,downregulated in LS
net.down <- subsetCommunication(cellchat, net = net, datasets = "NL",ligand.logFC = -0.1, receptor.logFC = -0.1)

Since the signaling genes in the net.up and net.down might be complex with multi-subunits, we can do further deconvolution to obtain the individual signaling genes.

gene.up <- extractGeneSubsetFromPair(net.up, cellchat)
gene.down <- extractGeneSubsetFromPair(net.down, cellchat)

We then visualize the upgulated and down-regulated signaling ligand-receptor pairs using bubble plot or chord diagram.

pairLR.use.up = net.up[, "interaction_name", drop = F]
gg1 <- netVisual_bubble(cellchat, pairLR.use = pairLR.use.up, sources.use = 4, targets.use = c(5:11), comparison = c(1, 2),  angle.x = 90, remove.isolate = T,title.name = paste0("Up-regulated signaling in ", names(object.list)[2]))
#> Comparing communications on a merged object
pairLR.use.down = net.down[, "interaction_name", drop = F]
gg2 <- netVisual_bubble(cellchat, pairLR.use = pairLR.use.down, sources.use = 4, targets.use = c(5:11), comparison = c(1, 2),  angle.x = 90, remove.isolate = T,title.name = paste0("Down-regulated signaling in ", names(object.list)[2]))
#> Comparing communications on a merged object
gg1 + gg2
image.png

Visualize the upgulated and down-regulated signaling ligand-receptor pairs using Chord diagram

# Chord diagram
par(mfrow = c(1,2), xpd=TRUE)
netVisual_chord_gene(object.list[[2]], sources.use = 4, targets.use = c(5:11), slot.name = 'net', net = net.up, lab.cex = 0.8, small.gap = 3.5, title.name = paste0("Up-regulated signaling in ", names(object.list)[2]))
#> Note: The first link end is drawn out of sector 'MIF'.
netVisual_chord_gene(object.list[[1]], sources.use = 4, targets.use = c(5:11), slot.name = 'net', net = net.down, lab.cex = 0.8, small.gap = 3.5, title.name = paste0("Down-regulated signaling in ", names(object.list)[2]))
image.png

Part IV: Visually compare cell-cell communication using Hierarchy plot, Circle plot or Chord diagram(一些個性化的展示了

Similar to the CellChat analysis of individual dataset, we can visualize the cell-cell communication network using Hierarchy plot, Circle plot or Chord diagram.

Edge color/weight, node color/size/shape: In all visualization plots, edge colors are consistent with the sources as sender, and edge weights are proportional to the interaction strength. Thicker edge line indicates a stronger signal. In the Hierarchy plot and Circle plot, circle sizes are proportional to the number of cells in each cell group. In the hierarchy plot, solid and open circles represent source and target, respectively. In the Chord diagram, the inner thinner bar colors represent the targets that receive signal from the corresponding outer bar. The inner bar size is proportional to the signal strength received by the targets. Such inner bar is helpful for interpreting the complex chord diagram. Note that there exist some inner bars without any chord for some cell groups, please just igore it because this is an issue that has not been addressed by circlize package.

pathways.show <- c("CXCL") 
weight.max <- getMaxWeight(object.list, slot.name = c("netP"), attribute = pathways.show) # control the edge weights across different datasets
par(mfrow = c(1,2), xpd=TRUE)
for (i in 1:length(object.list)) {
  netVisual_aggregate(object.list[[i]], signaling = pathways.show, layout = "circle", edge.weight.max = weight.max[1], edge.width.max = 10, signaling.name = paste(pathways.show, names(object.list)[i]))
}
image.png
pathways.show <- c("CXCL") 
par(mfrow = c(1,2), xpd=TRUE)
ht <- list()
for (i in 1:length(object.list)) {
  ht[[i]] <- netVisual_heatmap(object.list[[i]], signaling = pathways.show, color.heatmap = "Reds",title.name = paste(pathways.show, "signaling ",names(object.list)[i]))
}
#> Do heatmap based on a single object 
#> 
#> Do heatmap based on a single object
ComplexHeatmap::draw(ht[[1]] + ht[[2]], ht_gap = unit(0.5, "cm"))
image.png
# Chord diagram
pathways.show <- c("CXCL") 
par(mfrow = c(1,2), xpd=TRUE)
for (i in 1:length(object.list)) {
  netVisual_aggregate(object.list[[i]], signaling = pathways.show, layout = "chord", signaling.name = paste(pathways.show, names(object.list)[i]))
}
#> Note: The first link end is drawn out of sector 'Inflam. FIB'.
image.png

For the chord diagram, CellChat has an independent function netVisual_chord_cell to flexibly visualize the signaling network by adjusting different parameters in the circlize package. For example, we can define a named char vector group to create multiple-group chord diagram, e.g., grouping cell clusters into different cell types.

# Chord diagram
group.cellType <- c(rep("FIB", 4), rep("DC", 4), rep("TC", 4)) # grouping cell clusters into fibroblast, DC and TC cells
names(group.cellType) <- levels(object.list[[1]]@idents)
pathways.show <- c("CXCL") 
par(mfrow = c(1,2), xpd=TRUE)
for (i in 1:length(object.list)) {
  netVisual_chord_cell(object.list[[i]], signaling = pathways.show, group = group.cellType, title.name = paste0(pathways.show, " signaling network - ", names(object.list)[i]))
}
#> Plot the aggregated cell-cell communication network at the signaling pathway level
#> Plot the aggregated cell-cell communication network at the signaling pathway level
#> Note: The first link end is drawn out of sector 'Inflam. FIB'.
image.png

Using chord diagram, CellChat provides two functions netVisual_chord_cell and netVisual_chord_gene for visualizing cell-cell communication with different purposes and different levels. netVisual_chord_cell is used for visualizing the cell-cell communication between different cell groups (where each sector in the chord diagram is a cell group), and netVisual_chord_gene is used for visualizing the cell-cell communication mediated by mutiple ligand-receptors or signaling pathways (where each sector in the chord diagram is a ligand, receptor or signaling pathway.)

par(mfrow = c(1, 2), xpd=TRUE)
# compare all the interactions sending from Inflam.FIB to DC cells
for (i in 1:length(object.list)) {
  netVisual_chord_gene(object.list[[i]], sources.use = 4, targets.use = c(5:8), lab.cex = 0.5, title.name = paste0("Signaling from Inflam.FIB - ", names(object.list)[i]))
}
image.png

# compare all the interactions sending from fibroblast to inflamatory immune cells
par(mfrow = c(1, 2), xpd=TRUE)
for (i in 1:length(object.list)) {
  netVisual_chord_gene(object.list[[i]], sources.use = c(1,2, 3, 4), targets.use = c(8,10),  title.name = paste0("Signaling received by Inflam.DC and .TC - ", names(object.list)[i]), legend.pos.x = 10)
}
image.png
# show all the significant signaling pathways from fibroblast to immune cells
par(mfrow = c(1, 2), xpd=TRUE)
for (i in 1:length(object.list)) {
  netVisual_chord_gene(object.list[[i]], sources.use = c(1,2,3,4), targets.use = c(5:11),slot.name = "netP", title.name = paste0("Signaling pathways sending from fibroblast - ", names(object.list)[i]), legend.pos.x = 10)
}
#> Note: The second link end is drawn out of sector ' '.
#> Note: The first link end is drawn out of sector 'MIF'.
#> Note: The second link end is drawn out of sector ' '.
#> Note: The first link end is drawn out of sector 'CXCL '.
image.png

NB: Please ignore the note when generating the plot such as “Note: The first link end is drawn out of sector ‘MIF’.”. If the gene names are overlapped, you can adjust the argument small.gap by decreasing the value.

Part V: Compare the signaling gene expression distribution between different datasets(簡單的展示

We can plot the gene expression distribution of signaling genes related to L-R pairs or signaling pathway using a Seurat wrapper function plotGeneExpression.

cellchat@meta$datasets = factor(cellchat@meta$datasets, levels = c("NL", "LS")) # set factor level
plotGeneExpression(cellchat, signaling = "CXCL", split.by = "datasets", colors.ggplot = T)
#> The default behaviour of split.by has changed.
#> Separate violin plots are now plotted side-by-side.
#> To restore the old behaviour of a single split violin,
#> set split.plot = TRUE.
#>       
#> This message will be shown once per session.
#> Scale for 'y' is already present. Adding another scale for 'y', which will
#> replace the existing scale.
#> Scale for 'y' is already present. Adding another scale for 'y', which will
#> replace the existing scale.
#> Scale for 'y' is already present. Adding another scale for 'y', which will
#> replace the existing scale.
image.png

相當(dāng)不錯乌昔,大家多多嘗試分析

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