Get trajectory sizes
Source:R/bayesian_graphical_clustering.R
get_trajectory_sizes_from_edge_sets.RdAuxiliary function for getting the largest paths in a graphical solution.
Usage
get_trajectory_sizes_from_edge_sets(
edge_sets = MotrpacRatTraining6moData::GRAPH_COMPONENTS$edge_sets,
min_size = 10
)Arguments
- edge_sets
A named list of string vectors. The name of an edge is
[node_id]---[node_id]edges with no analytes have a NULL set (a set of size zero, but are still represented), node ids are[timepoint]_F[x]_M[y]wherexandyrepresent the up/down state in each sex.GRAPH_COMPONENTS$edge_setsby default.- min_size
An integer specifying the minimal path size to be considered.
Value
NULL if no paths of size of at least min_size were found, otherwise
return a data frame that represents all paths of size min_size or greater,
ranked from the largest path to the smallest one.
Details
This is implemented using a dynamic programming approach where we iteratively add the data of the next edge.
When analyzing an edge (x,y) with a set of analytes s, we extend all trajectories that end with x using the new edge, but also all the trajectories that start with y.
At the end, because we examine all edges and all extensions we are guaranteed to have covered all full paths.
The min_size parameter is important, since we are interested in paths and edges with at least this number of analytes, then we know that if a current trajectory does not have at least min_size analytes, then since the set of any extension can only be the same or smaller then we can ignore such paths moving forward.
However, this parameter has to be considered with care, as specifying a number that is too high will result in no paths in the output.
See bayesian_graphical_clustering for more details about the graphical analysis.
Examples
if (FALSE) { # \dontrun{
### Example 1: Simulate data with a single cluster
zcolnames = c(
paste("female",c("1w","2w","4w","8w"),sep="_"),
paste("male",c("1w","2w","4w","8w"),sep="_")
)
zscores = matrix(rnorm(80000),ncol=8,dimnames = list(1:10000,zcolnames))
# now add a cluster with a strong signal and rerun
zscores[1:500,1:4] = zscores[1:500,1:4] + 5
# run the clustering solution wrapper
clustering_sol = bayesian_graphical_clustering(zscores)
# extract the top full trajectories in the data
# these should be the clusters with at least 10 features
min_cluster_size=10
get_trajectory_sizes_from_edge_sets(clustering_sol$edge_sets,
min_size = min_cluster_size)
# extract the edges of the top two full trajectories
# this step "cleans" the edge sets by removing edges of trajectories with very few features
top2traj_edge_sets = filter_edge_sets_by_trajectories(
clustering_sol$edge_sets,
topk = 2,
min_path_size = 10
)
# examine the new edge set sizes, excluded edges should have zero size
sapply(top2traj_edge_sets,length)
} # }
### Example 2: Use published data
get_trajectory_sizes_from_edge_sets()
#> X1 X2 X3 X4 X5 X6
#> 18 0w 1w_F-1_M1 2w_F-1_M0 4w_F-1_M0 8w_F-1_M0 1459
#> 146 0w 1w_F0_M1 2w_F0_M1 4w_F0_M1 8w_F1_M1 1112
#> 190 0w 1w_F1_M1 2w_F1_M1 4w_F1_M1 8w_F1_M1 1078
#> 122 0w 1w_F0_M0 2w_F0_M0 4w_F0_M0 8w_F1_M1 987
#> 66 0w 1w_F0_M0 2w_F0_M0 4w_F0_M0 8w_F-1_M-1 946
#> 139 0w 1w_F0_M1 2w_F0_M1 4w_F0_M1 8w_F0_M1 824
#> 1 0w 1w_F-1_M-1 2w_F-1_M-1 4w_F-1_M-1 8w_F-1_M-1 718
#> 36 0w 1w_F-1_M0 2w_F-1_M0 4w_F-1_M0 8w_F0_M1 698
#> 106 0w 1w_F0_M0 2w_F0_M0 4w_F0_M0 8w_F0_M1 594
#> 82 0w 1w_F0_M0 2w_F0_M0 4w_F0_M0 8w_F0_M-1 578
#> 52 0w 1w_F0_M-1 2w_F0_M-1 4w_F0_M-1 8w_F0_M-1 478
#> 74 0w 1w_F0_M1 2w_F0_M1 4w_F0_M0 8w_F-1_M0 476
#> 14 0w 1w_F-1_M0 2w_F-1_M0 4w_F-1_M0 8w_F-1_M-1 460
#> 184 0w 1w_F0_M1 2w_F0_M1 4w_F1_M1 8w_F1_M1 423
#> 173 0w 1w_F1_M0 2w_F1_M0 4w_F1_M0 8w_F1_M1 403
#> 112 0w 1w_F0_M-1 2w_F0_M-1 4w_F0_M0 8w_F1_M0 396
#> 158 0w 1w_F1_M0 2w_F1_M0 4w_F1_M0 8w_F0_M0 396
#> 159 0w 1w_F1_M0 2w_F1_M1 4w_F1_M0 8w_F0_M0 384
#> 167 0w 1w_F1_M-1 2w_F1_M0 4w_F1_M0 8w_F1_M0 340
#> 144 0w 1w_F0_M0 2w_F0_M0 4w_F0_M1 8w_F1_M1 330
#> 99 0w 1w_F1_M0 2w_F1_M0 4w_F0_M0 8w_F0_M0 327
#> 34 0w 1w_F-1_M0 2w_F-1_M0 4w_F-1_M0 8w_F0_M0 322
#> 136 0w 1w_F0_M0 2w_F0_M0 4w_F0_M1 8w_F0_M1 303
#> 90 0w 1w_F-1_M0 2w_F-1_M0 4w_F0_M0 8w_F0_M0 282
#> 5 0w 1w_F0_M-1 2w_F0_M-1 4w_F-1_M-1 8w_F-1_M-1 278
#> 110 0w 1w_F-1_M0 2w_F-1_M0 4w_F0_M0 8w_F1_M0 266
#> 57 0w 1w_F0_M-1 2w_F0_M-1 4w_F0_M-1 8w_F0_M0 264
#> 168 0w 1w_F1_M0 2w_F1_M0 4w_F1_M0 8w_F1_M0 251
#> 31 0w 1w_F-1_M-1 2w_F-1_M-1 4w_F-1_M0 8w_F0_M0 250
#> 189 0w 1w_F1_M0 2w_F1_M1 4w_F1_M1 8w_F1_M1 230
#> 76 0w 1w_F1_M0 2w_F1_M0 4w_F0_M0 8w_F-1_M0 223
#> 49 0w 1w_F0_M0 2w_F0_M0 4w_F0_M-1 8w_F-1_M-1 209
#> 6 0w 1w_F0_M0 2w_F0_M0 4w_F-1_M-1 8w_F-1_M-1 208
#> 97 0w 1w_F0_M1 2w_F0_M1 4w_F0_M0 8w_F0_M0 197
#> 43 0w 1w_F-1_M1 2w_F-1_M1 4w_F-1_M1 8w_F-1_M1 196
#> 182 0w 1w_F0_M0 2w_F0_M0 4w_F1_M1 8w_F1_M1 191
#> 187 0w 1w_F1_M0 2w_F1_M0 4w_F1_M1 8w_F1_M1 190
#> 131 0w 1w_F1_M1 2w_F0_M1 4w_F0_M1 8w_F0_M0 185
#> 140 0w 1w_F1_M1 2w_F0_M1 4w_F0_M1 8w_F0_M1 185
#> 130 0w 1w_F0_M1 2w_F0_M1 4w_F0_M1 8w_F0_M0 177
#> 155 0w 1w_F1_M0 2w_F1_M0 4w_F1_M0 8w_F0_M-1 176
#> 177 0w 1w_F1_M1 2w_F1_M1 4w_F1_M1 8w_F0_M0 176
#> 32 0w 1w_F-1_M0 2w_F-1_M-1 4w_F-1_M0 8w_F0_M0 173
#> 16 0w 1w_F0_M0 2w_F0_M0 4w_F-1_M0 8w_F-1_M-1 171
#> 126 0w 1w_F0_M1 2w_F0_M1 4w_F0_M1 8w_F-1_M0 159
#> 166 0w 1w_F0_M-1 2w_F1_M0 4w_F1_M0 8w_F1_M0 159
#> 170 0w 1w_F0_M0 2w_F0_M0 4w_F1_M0 8w_F1_M1 157
#> 4 0w 1w_F-1_M0 2w_F-1_M0 4w_F-1_M-1 8w_F-1_M-1 152
#> 87 0w 1w_F-1_M-1 2w_F-1_M-1 4w_F0_M0 8w_F0_M0 152
#> 101 0w 1w_F1_M1 2w_F1_M1 4w_F0_M0 8w_F0_M0 151
#> 154 0w 1w_F1_M-1 2w_F1_M-1 4w_F1_M0 8w_F0_M-1 151
#> 25 0w 1w_F-1_M0 2w_F-1_M0 4w_F-1_M0 8w_F-1_M1 149
#> 88 0w 1w_F-1_M0 2w_F-1_M-1 4w_F0_M0 8w_F0_M0 148
#> 64 0w 1w_F-1_M0 2w_F-1_M0 4w_F0_M0 8w_F-1_M-1 146
#> 72 0w 1w_F1_M0 2w_F0_M0 4w_F0_M0 8w_F-1_M0 143
#> 100 0w 1w_F1_M0 2w_F1_M1 4w_F0_M0 8w_F0_M0 143
#> 17 0w 1w_F-1_M0 2w_F-1_M0 4w_F-1_M0 8w_F-1_M0 141
#> 44 0w 1w_F-1_M0 2w_F-1_M0 4w_F-1_M1 8w_F0_M1 138
#> 12 0w 1w_F-1_M-1 2w_F-1_M-1 4w_F-1_M-1 8w_F0_M0 136
#> 165 0w 1w_F1_M-1 2w_F1_M-1 4w_F1_M0 8w_F1_M0 132
#> 21 0w 1w_F-1_M1 2w_F-1_M1 4w_F-1_M0 8w_F-1_M0 128
#> 85 0w 1w_F0_M1 2w_F0_M1 4w_F0_M0 8w_F0_M-1 122
#> 188 0w 1w_F0_M1 2w_F1_M1 4w_F1_M1 8w_F1_M1 120
#> 53 0w 1w_F0_M0 2w_F0_M0 4w_F0_M-1 8w_F0_M-1 116
#> 7 0w 1w_F-1_M-1 2w_F-1_M-1 4w_F-1_M-1 8w_F-1_M0 113
#> 86 0w 1w_F1_M0 2w_F1_M0 4w_F0_M0 8w_F0_M-1 113
#> 83 0w 1w_F1_M0 2w_F0_M0 4w_F0_M0 8w_F0_M-1 112
#> 38 0w 1w_F0_M0 2w_F0_M0 4w_F-1_M0 8w_F0_M1 110
#> 102 0w 1w_F-1_M0 2w_F-1_M0 4w_F0_M0 8w_F0_M1 109
#> 103 0w 1w_F0_M-1 2w_F0_M-1 4w_F0_M0 8w_F0_M1 108
#> 54 0w 1w_F1_M-1 2w_F1_M-1 4w_F0_M-1 8w_F0_M-1 106
#> 2 0w 1w_F-1_M0 2w_F-1_M-1 4w_F-1_M-1 8w_F-1_M-1 105
#> 124 0w 1w_F1_M0 2w_F1_M0 4w_F0_M0 8w_F1_M1 104
#> 9 0w 1w_F0_M-1 2w_F0_M-1 4w_F-1_M-1 8w_F-1_M0 100
#> 24 0w 1w_F0_M1 2w_F0_M1 4w_F-1_M0 8w_F-1_M0 97
#> 51 0w 1w_F-1_M-1 2w_F-1_M-1 4w_F0_M-1 8w_F0_M-1 96
#> 142 0w 1w_F1_M1 2w_F1_M1 4w_F0_M1 8w_F0_M1 92
#> 11 0w 1w_F-1_M-1 2w_F-1_M-1 4w_F-1_M-1 8w_F0_M-1 88
#> 109 0w 1w_F-1_M0 2w_F-1_M-1 4w_F0_M0 8w_F1_M0 86
#> 125 0w 1w_F-1_M0 2w_F-1_M1 4w_F0_M1 8w_F-1_M0 86
#> 48 0w 1w_F0_M-1 2w_F0_M-1 4w_F0_M-1 8w_F-1_M-1 85
#> 134 0w 1w_F-1_M0 2w_F-1_M0 4w_F0_M1 8w_F0_M1 84
#> 186 0w 1w_F1_M1 2w_F0_M1 4w_F1_M1 8w_F1_M1 84
#> 28 0w 1w_F-1_M1 2w_F-1_M1 4w_F-1_M0 8w_F-1_M1 83
#> 133 0w 1w_F1_M1 2w_F1_M1 4w_F0_M1 8w_F0_M0 83
#> 20 0w 1w_F0_M1 2w_F-1_M0 4w_F-1_M0 8w_F-1_M0 82
#> 50 0w 1w_F1_M-1 2w_F1_M-1 4w_F0_M-1 8w_F-1_M-1 81
#> 92 0w 1w_F0_M-1 2w_F0_M-1 4w_F0_M0 8w_F0_M0 81
#> 40 0w 1w_F-1_M1 2w_F-1_M1 4w_F-1_M1 8w_F-1_M0 80
#> 56 0w 1w_F-1_M-1 2w_F-1_M-1 4w_F0_M-1 8w_F0_M0 79
#> 150 0w 1w_F1_M-1 2w_F1_M-1 4w_F1_M-1 8w_F1_M0 76
#> 181 0w 1w_F1_M1 2w_F1_M1 4w_F1_M1 8w_F1_M0 75
#> 143 0w 1w_F-1_M0 2w_F-1_M0 4w_F0_M1 8w_F1_M1 74
#> 69 0w 1w_F0_M1 2w_F-1_M0 4w_F0_M0 8w_F-1_M0 72
#> 157 0w 1w_F1_M-1 2w_F1_M0 4w_F1_M0 8w_F0_M0 71
#> 81 0w 1w_F0_M-1 2w_F0_M-1 4w_F0_M0 8w_F0_M-1 70
#> 22 0w 1w_F0_M0 2w_F0_M0 4w_F-1_M0 8w_F-1_M0 68
#> 10 0w 1w_F0_M0 2w_F0_M0 4w_F-1_M-1 8w_F-1_M0 66
#> 29 0w 1w_F-1_M-1 2w_F-1_M-1 4w_F-1_M0 8w_F0_M-1 66
#> 116 0w 1w_F0_M0 2w_F0_M0 4w_F0_M0 8w_F1_M0 65
#> 164 0w 1w_F1_M0 2w_F0_M0 4w_F1_M0 8w_F1_M0 64
#> 148 0w 1w_F1_M-1 2w_F1_M-1 4w_F1_M-1 8w_F1_M-1 63
#> 163 0w 1w_F0_M0 2w_F0_M0 4w_F1_M0 8w_F1_M0 63
#> 62 0w 1w_F0_M-1 2w_F0_M-1 4w_F0_M-1 8w_F1_M0 61
#> 95 0w 1w_F1_M0 2w_F0_M0 4w_F0_M0 8w_F0_M0 57
#> 160 0w 1w_F1_M1 2w_F1_M1 4w_F1_M0 8w_F0_M0 57
#> 117 0w 1w_F0_M-1 2w_F1_M0 4w_F0_M0 8w_F1_M0 56
#> 55 0w 1w_F1_M0 2w_F1_M0 4w_F0_M-1 8w_F0_M-1 55
#> 59 0w 1w_F1_M-1 2w_F1_M-1 4w_F0_M-1 8w_F0_M0 54
#> 60 0w 1w_F1_M0 2w_F1_M0 4w_F0_M-1 8w_F0_M0 54
#> 178 0w 1w_F0_M1 2w_F0_M1 4w_F1_M1 8w_F0_M1 54
#> 15 0w 1w_F0_M0 2w_F-1_M0 4w_F-1_M0 8w_F-1_M-1 53
#> 93 0w 1w_F-1_M-1 2w_F0_M0 4w_F0_M0 8w_F0_M0 51
#> 104 0w 1w_F-1_M0 2w_F0_M0 4w_F0_M0 8w_F0_M1 51
#> 179 0w 1w_F1_M1 2w_F1_M1 4w_F1_M1 8w_F0_M1 51
#> 3 0w 1w_F0_M-1 2w_F-1_M-1 4w_F-1_M-1 8w_F-1_M-1 50
#> 65 0w 1w_F0_M0 2w_F-1_M0 4w_F0_M0 8w_F-1_M-1 50
#> 94 0w 1w_F-1_M0 2w_F0_M0 4w_F0_M0 8w_F0_M0 49
#> 8 0w 1w_F-1_M0 2w_F-1_M0 4w_F-1_M-1 8w_F-1_M0 48
#> 107 0w 1w_F0_M1 2w_F0_M1 4w_F0_M0 8w_F0_M1 48
#> 105 0w 1w_F0_M-1 2w_F0_M0 4w_F0_M0 8w_F0_M1 47
#> 132 0w 1w_F0_M1 2w_F1_M1 4w_F0_M1 8w_F0_M0 47
#> 39 0w 1w_F0_M1 2w_F0_M1 4w_F-1_M0 8w_F0_M1 46
#> 120 0w 1w_F1_M1 2w_F1_M1 4w_F0_M0 8w_F1_M0 46
#> 135 0w 1w_F-1_M1 2w_F-1_M1 4w_F0_M1 8w_F0_M1 46
#> 169 0w 1w_F1_M1 2w_F1_M1 4w_F1_M0 8w_F1_M0 46
#> 171 0w 1w_F1_M0 2w_F0_M0 4w_F1_M0 8w_F1_M1 46
#> 156 0w 1w_F1_M-1 2w_F1_M-1 4w_F1_M0 8w_F0_M0 45
#> 26 0w 1w_F-1_M1 2w_F-1_M0 4w_F-1_M0 8w_F-1_M1 44
#> 61 0w 1w_F0_M-1 2w_F0_M-1 4w_F0_M-1 8w_F0_M1 43
#> 58 0w 1w_F1_M0 2w_F0_M0 4w_F0_M-1 8w_F0_M0 42
#> 121 0w 1w_F-1_M0 2w_F-1_M0 4w_F0_M0 8w_F1_M1 42
#> 137 0w 1w_F1_M0 2w_F0_M0 4w_F0_M1 8w_F0_M1 42
#> 70 0w 1w_F0_M0 2w_F0_M0 4w_F0_M0 8w_F-1_M0 41
#> 162 0w 1w_F0_M-1 2w_F0_M-1 4w_F1_M0 8w_F1_M0 41
#> 30 0w 1w_F-1_M-1 2w_F-1_M0 4w_F-1_M0 8w_F0_M-1 40
#> 27 0w 1w_F0_M0 2w_F-1_M0 4w_F-1_M0 8w_F-1_M1 39
#> 13 0w 1w_F0_M-1 2w_F0_M-1 4w_F-1_M-1 8w_F0_M0 38
#> 78 0w 1w_F0_M0 2w_F-1_M0 4w_F0_M0 8w_F-1_M1 38
#> 84 0w 1w_F0_M0 2w_F0_M1 4w_F0_M0 8w_F0_M-1 38
#> 175 0w 1w_F0_M1 2w_F0_M1 4w_F1_M1 8w_F0_M0 38
#> 123 0w 1w_F0_M1 2w_F0_M1 4w_F0_M0 8w_F1_M1 37
#> 180 0w 1w_F1_M0 2w_F0_M0 4w_F1_M1 8w_F1_M0 37
#> 79 0w 1w_F0_M1 2w_F-1_M1 4w_F0_M0 8w_F-1_M1 35
#> 152 0w 1w_F0_M0 2w_F0_M0 4w_F1_M0 8w_F0_M-1 35
#> 141 0w 1w_F1_M0 2w_F1_M0 4w_F0_M1 8w_F0_M1 34
#> 176 0w 1w_F1_M1 2w_F0_M1 4w_F1_M1 8w_F0_M0 34
#> 183 0w 1w_F0_M0 2w_F0_M1 4w_F1_M1 8w_F1_M1 34
#> 19 0w 1w_F0_M0 2w_F-1_M0 4w_F-1_M0 8w_F-1_M0 33
#> 111 0w 1w_F0_M0 2w_F-1_M0 4w_F0_M0 8w_F1_M0 33
#> 68 0w 1w_F-1_M0 2w_F-1_M0 4w_F0_M0 8w_F-1_M0 31
#> 80 0w 1w_F-1_M0 2w_F-1_M0 4w_F0_M0 8w_F0_M-1 31
#> 47 0w 1w_F0_M-1 2w_F-1_M-1 4w_F0_M-1 8w_F-1_M-1 29
#> 63 0w 1w_F0_M-1 2w_F1_M-1 4w_F0_M-1 8w_F1_M0 29
#> 75 0w 1w_F0_M0 2w_F1_M0 4w_F0_M0 8w_F-1_M0 29
#> 153 0w 1w_F1_M0 2w_F0_M0 4w_F1_M0 8w_F0_M-1 29
#> 33 0w 1w_F-1_M-1 2w_F-1_M0 4w_F-1_M0 8w_F0_M0 28
#> 98 0w 1w_F0_M-1 2w_F1_M0 4w_F0_M0 8w_F0_M0 28
#> 119 0w 1w_F1_M0 2w_F1_M1 4w_F0_M0 8w_F1_M0 28
#> 128 0w 1w_F-1_M0 2w_F-1_M0 4w_F0_M1 8w_F0_M0 28
#> 138 0w 1w_F0_M0 2w_F0_M1 4w_F0_M1 8w_F0_M1 28
#> 37 0w 1w_F0_M0 2w_F-1_M0 4w_F-1_M0 8w_F0_M1 27
#> 114 0w 1w_F-1_M0 2w_F0_M0 4w_F0_M0 8w_F1_M0 27
#> 149 0w 1w_F0_M-1 2w_F0_M-1 4w_F1_M-1 8w_F1_M0 27
#> 185 0w 1w_F1_M0 2w_F0_M1 4w_F1_M1 8w_F1_M1 27
#> 41 0w 1w_F0_M1 2w_F-1_M1 4w_F-1_M1 8w_F-1_M0 26
#> 45 0w 1w_F0_M1 2w_F-1_M1 4w_F-1_M1 8w_F0_M1 26
#> 129 0w 1w_F-1_M0 2w_F0_M1 4w_F0_M1 8w_F0_M0 26
#> 161 0w 1w_F1_M0 2w_F1_M0 4w_F1_M0 8w_F1_M-1 26
#> 71 0w 1w_F0_M1 2w_F0_M0 4w_F0_M0 8w_F-1_M0 25
#> 115 0w 1w_F0_M-1 2w_F0_M0 4w_F0_M0 8w_F1_M0 25
#> 147 0w 1w_F1_M-1 2w_F1_M-1 4w_F1_M-1 8w_F0_M-1 25
#> 23 0w 1w_F-1_M1 2w_F0_M1 4w_F-1_M0 8w_F-1_M0 24
#> 127 0w 1w_F-1_M1 2w_F-1_M1 4w_F0_M1 8w_F-1_M1 24
#> 145 0w 1w_F0_M0 2w_F0_M1 4w_F0_M1 8w_F1_M1 24
#> 174 0w 1w_F1_M0 2w_F1_M1 4w_F1_M0 8w_F1_M1 24
#> 113 0w 1w_F0_M0 2w_F0_M-1 4w_F0_M0 8w_F1_M0 23
#> 151 0w 1w_F1_M0 2w_F1_M0 4w_F1_M-1 8w_F1_M0 23
#> 46 0w 1w_F0_M1 2w_F0_M1 4w_F-1_M1 8w_F0_M1 22
#> 35 0w 1w_F-1_M-1 2w_F-1_M0 4w_F-1_M0 8w_F0_M1 21
#> 96 0w 1w_F1_M1 2w_F0_M0 4w_F0_M0 8w_F0_M0 21
#> 172 0w 1w_F0_M0 2w_F1_M0 4w_F1_M0 8w_F1_M1 21
#> 108 0w 1w_F1_M0 2w_F1_M0 4w_F0_M0 8w_F0_M1 20
#> 118 0w 1w_F1_M0 2w_F1_M0 4w_F0_M0 8w_F1_M0 18
#> 42 0w 1w_F0_M1 2w_F0_M1 4w_F-1_M1 8w_F-1_M0 17
#> 73 0w 1w_F0_M0 2w_F0_M1 4w_F0_M0 8w_F-1_M0 17
#> 91 0w 1w_F-1_M0 2w_F0_M-1 4w_F0_M0 8w_F0_M0 17
#> 67 0w 1w_F0_M1 2w_F0_M1 4w_F0_M0 8w_F-1_M-1 14
#> 89 0w 1w_F0_M-1 2w_F-1_M-1 4w_F0_M0 8w_F0_M0 13
#> 77 0w 1w_F1_M0 2w_F1_M1 4w_F0_M0 8w_F-1_M0 11