1. Input Variables

Time series clustering starts with the selection and preparation of the variables of interest. While the selection will necessarily be field- and concept-specific, there are a few conceptual and methodological issues that should be considered. Conceptually, we will need to make a choice of key variables that comprehensively capture the concept you would like to assess over time. Once the key variables are selected, we will need make sure that the variables are ready to be summarized using the time series features and that the format fits the chosen clustering procedure.

Variable Selection

The included variables should adequately capture the concept of interest and should be meaningful to the understanding of the time series. One of the advantages of feature-based clustering is that it is inherently adept at accommodating multi-variate concepts — a common aim in ESM research. In our illustration, we apply the clustering process to a recent set of studies that collected data on migration experiences. The data seek to capture the process of cultural adaptation and aims to identify diverging trajectories. Importantly for our illustration, the migration ESM research, also, exemplifies the real-world data issues that ESM data commonly face, including a multivariate conceptualization with event-specific missingness patterns.

For our illustration, we include 12 variables that were measured as part of the ESM surveys in all three studies and captured information about the participant’s interactions, as well as cognitive-, emotional-, and motivational self in relationship with the majority group (Kreienkamp et al., 2023).

Import the raw data

We begin by importing the raw data as well as the variable meta data. Both of these data files are available as part of our OSF repository. To ensure the privacy and confidentiality of the study participants, we took a number of steps to pre-process the data:

  • consistent naming
  • key variables only (participant privacy)
  • post-test variable pre-calculated
  • long format ESM data of all three studies combined (indicator variable: study)

This means that we import the minimal reproducible dataset of the key variables (dt_raw using the data/osf_mini.Rda file) as well as a Microsoft Excel sheet providing a range of supplementary information, including the survey questions and variable labels (var_meta using the data/osf_var_meta.xlsx file).

dt_raw <- readRDS(file="data/osf_mini.Rda")
var_meta <- readxl::read_excel("data/osf_var_meta.xlsx")

Variable Overview

To get an overview of the variables we display the variable names, labels, item descriptions, as well as the survey and analysis context (see Table 1).

Code
var_meta %>%
  transmute(
    "Variable Name" = name,
    "Label" = label,
    "Description" = description,
    "Type" = type,
    "Contact Specific" = recode(contact, `0`="", ` 1`="✔"),
    "ESM" = recode(esm, `0`="", ` 1`="✔"),
    "Post" = recode(post, `0`="", ` 1`="✔"),
    "Cluster" = recode(cluster, `0`="", ` 1`="✔"),
    "Validation" = recode(interpretation, `0`="", ` 1`="✔")
  ) %>%
  kbl(.,
      escape = FALSE,
      booktabs = TRUE,
      label = "var_overview",
      format = "html",
      align = c(rep("l", 4), rep("c", ncol(.)-4)),
      digits = 2,
      linesep = "",
      caption = "Variable Overview") %>%
  add_header_above(c(" " = 5, "Survey" = 2, "Analysis" = 2)) %>%
  kable_classic(
    full_width = FALSE,
    lightable_options = "hover",
    html_font = "Cambria"
  ) %>%
  scroll_box(width = "100%", height = "500px") %>%
  footnote(
    general = c('All ESM items used a continuous slider and were rescaled to a range of 0—100.')
  )
Table 1: Variable Overview
Survey
Analysis
Variable Name Label Description Type Contact Specific ESM Post Cluster Validation
PID Person ID participant ID id
TIDnum Measurement ID time ID id
TID Datetime date – daytime id
KeyNeedFulfillment Int: Need Fulfillment During your interaction with -NAME- your goal (-GOAL-) was fulfilled. needs
KeyNeedDueToPartner Int: Need Fulfillment Partner -NAME- helped fulfill your goal (-GOAL-) needs
InteractionContextAccidental Int: Accidental The interaction with -NAME- was accidental. cognition
InteractionContextvoluntary Int: Voluntary The interaction with -NAME- was voluntary. cognition
InteractionContextCooperative Int: Cooperative The interaction with -NAME- was cooperative. cognition
InteractionContextRepresentativeNL Int: Representative The interaction with -NAME- was representative of the Dutch. cognition
qualityOverall Int: Quality Overall, the interaction with -NAME- was: Unplesant --- Plesant cognition
qualityMeaning Int: Meaningful Overall, the interaction with -NAME- was: Superficial --- Meaningful cognition
DaytimeNeedFulfillment Need Fulfillment During this -morning/afternoon- your goal (-GOAL-) was fulfilled. needs
AttitudesDutch Outgroup Attitude At the moment, how favorably do you feel towards the Dutch. cognition
AttitudesPartner Int: Partner Attitude At the moment, how favorably do you feel towards -NAME- cognition
exWB Well-Being How do you feel right now? very sad --- very happy emotion
EvDayDiscr.post Post: Discrimination Mean of the Everyday Discrimination scale (past month) emotion
Note: All ESM items used a continuous slider and were rescaled to a range of 0—100.

Variable Preparation

the important variables have been selected, the data needs to be prepared for the analysis steps. Importantly, this not only means validating and cleaning the data (e.g., re-coding, removing duplicate or unwanted measurements) but also making the time-series comparable. Two important steps are making the time-frames and response scales comparable across participants — for example, by choosing a time frame that is common to most participants and standardizing the participants’ responses (Liao, 2005).

Data Availability

In our illustration data set, the studies differed substantially in the maximum length of participation (\(max(t_{S1})\) = 63, \(max(t_{S2})\) = 69, \(max(t_{S3})\) = 155). To make the three studies comparable in participation and time frames, we iteratively removed all measurement occasions and participants that had more than 45% missingness. This procedure is in line with the general recommendation for data that might still need to rely on imputations for later model testing (Madley-Dowd et al., 2019).

Study 1

For the Study 1 we first assess the data availability pattern. We do this visually by representing participants as rows and measurement occasions as columns:

Study 1: Data Availability
t_1 t_2 t_3 t_4 t_5 t_6 t_7 t_8 t_9 t_10 t_11 t_12 t_13 t_14 t_15 t_16 t_17 t_18 t_19 t_20 t_21 t_22 t_23 t_24 t_25 t_26 t_27 t_28 t_29 t_30 t_31 t_32 t_33 t_34 t_35 t_36 t_37 t_38 t_39 t_40 t_41 t_42 t_43 t_44 t_45 t_46 t_47 t_48 t_49 t_50 t_51 t_52 t_53 t_54 t_55 t_56 t_57 t_58 t_59 t_60 t_61 t_62 t_63
PP_1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1
PP_2 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_3 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0
PP_4 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0
PP_5 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
PP_6 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_7 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_8 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_9 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_10 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_12 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_13 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1
PP_14 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_15 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1
PP_17 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_18 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_19 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
PP_21 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_22 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
PP_23 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1

We then run the cleanM function, where sequentially remove the row or column with the most missing data until only rows and columns remain that have less than 45% missingness.

source("scripts/cleanM.R")
dtS1RedInfo <- cleanM(M = as.data.frame(dtS1Availability), c = 55)
1: Row PP_20 had a completion rate of 3.17% and was removed.
2: Row PP_22 had a completion rate of 4.76% and was removed.
3: Column t_1 had a completion rate of 23.81% and was removed.
4: Column t_2 had a completion rate of 52.38% and was removed.
5: All row- and column means are over 55%. The final matrix has 21 rows and 61 columns.

With the adjusted dataset we again visualize the data availability.

PIDout <- gsub("PP_", "", dtS1RedInfo$rowNamesOut) %>% as.numeric
TIDout <- gsub("t_", "", dtS1RedInfo$colNamesOut) %>% as.numeric
TIDInRed <- gsub("t_", "", dtS1RedInfo$colNamesIn) %>% as.numeric
TIDIn <- seq(min(TIDInRed), max(TIDInRed), 1)

dtS1Red <- dt_raw %>%
  filter(study == "S1") %>%
  filter(
    !PID %in% PIDout,
    TIDnum %in% TIDIn
  ) %>% 
  mutate(TIDnum = TIDnum - min(TIDnum))
rm(PIDout, TIDout, TIDInRed, TIDIn)

# change glitch where survey was sent too early
dtS1Red$TIDnum[dtS1Red$PID == 7 & as.character(dtS1Red$created) == "2018-05-18 11:46:40"] <- 10
dtS1Red$TID[dtS1Red$PID == 7 & as.character(dtS1Red$created) == "2018-05-18 11:46:40"] <- "2018-05-18 Morning"

dtS1AvailabilityRedKbl <- dtS1RedInfo$reducedMatrix
dtS1AvailabilityRedKbl[1:ncol(dtS1AvailabilityRedKbl)] <- lapply(dtS1AvailabilityRedKbl[1:ncol(dtS1AvailabilityRedKbl)], function(x) {
    cell_spec(x,
              bold = FALSE,
              color = "white",
              background = ifelse(x == 1, "green", "red")
              )
})
kbl(
  dtS1AvailabilityRedKbl,
  format = "html",
  escape = FALSE,
  align = "c",
  booktabs = TRUE,
  caption = "Study 1: Final Data Availability" # complete caption for main document
) %>%
  kable_classic(
    full_width = FALSE,
    lightable_options = "hover",
    html_font = "Cambria"
  ) %>%
  scroll_box(width = "100%", height = "500px")
Study 1: Final Data Availability
t_3 t_4 t_5 t_6 t_7 t_8 t_9 t_10 t_11 t_12 t_13 t_14 t_15 t_16 t_17 t_18 t_19 t_20 t_21 t_22 t_23 t_24 t_25 t_26 t_27 t_28 t_29 t_30 t_31 t_32 t_33 t_34 t_35 t_36 t_37 t_38 t_39 t_40 t_41 t_42 t_43 t_44 t_45 t_46 t_47 t_48 t_49 t_50 t_51 t_52 t_53 t_54 t_55 t_56 t_57 t_58 t_59 t_60 t_61 t_62 t_63
PP_1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1
PP_2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_3 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0
PP_4 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0
PP_5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
PP_6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_7 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_8 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_9 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_10 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_13 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1
PP_14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_15 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1
PP_17 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_18 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_21 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
PP_23 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1

Study 2

For Study 2 we follow the same procedure, where we first visualize the original data availability:

Study 2: Data Availability
t_1 t_2 t_3 t_4 t_5 t_6 t_7 t_8 t_9 t_10 t_11 t_12 t_13 t_14 t_15 t_16 t_17 t_18 t_19 t_20 t_21 t_22 t_23 t_24 t_25 t_26 t_27 t_28 t_29 t_30 t_31 t_32 t_33 t_34 t_35 t_36 t_37 t_38 t_39 t_40 t_41 t_42 t_43 t_44 t_45 t_46 t_47 t_48 t_49 t_50 t_51 t_52 t_53 t_54 t_55 t_56 t_57 t_58 t_59 t_60 t_61 t_62 t_63 t_64 t_65 t_66 t_67 t_68 t_69
PP_1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0
PP_2 0 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0
PP_3 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0
PP_4 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0
PP_5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0
PP_6 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0
PP_7 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0
PP_8 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 0
PP_9 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0
PP_10 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0
PP_11 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
PP_12 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0
PP_13 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
PP_14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1
PP_15 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0
PP_16 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0
PP_17 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
PP_18 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0
PP_19 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
PP_20 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0
PP_21 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0
PP_22 0 0 0 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0
PP_23 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0
PP_24 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0
PP_25 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0
PP_26 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
PP_27 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0
PP_28 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0
PP_29 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
PP_30 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0
PP_31 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
PP_32 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0
PP_33 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
PP_34 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0
PP_35 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0
PP_36 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
PP_37 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0
PP_38 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1