single null distribution for HYAA segemented cell tracking

One Cell ( Distance , Area, Spot ,Eccentricity Probability with y axis Correction )

Mehran, H Qin

11/26/2017 - Jan 16, 2018

library(gsubfn)

rm(list=ls())
debug = 0; 
DataTrap <- read.csv("data/DataSet_v6.csv",header=TRUE,stringsAsFactors = FALSE)

Take all the single cell traps

Data.trap.1Cell = DataTrap[ DataTrap$total_cells == 1, ]; 

calculathe the moving null distribution using single cell subset

moving_buffer = data.frame(matrix(data=NA, nrow = length(Data.trap.1Cell[,1]), ncol = 5));
names(moving_buffer) = c("d", "area", "d2spot", "eccent");

my_dist = function(x1, y1, x2, y2) {sqrt( (x1 - x2)^2 + (y1-y2)^2 ) }; 

#for( i in 2:length(Data.trap.1Cell[,1]) ){
for( i in 2:999 ){
  previous = Data.trap.1Cell[ i-1, ];
  current = Data.trap.1Cell [i,    ];
  
  #check image number
  if ( previous$Image_num[1] == current$Image_num[1] - 1 ) {
   # prevous and current segments are right next to each other in the time series
    if (debug > 0) { print(paste("calculate previous=", i-1, "current=",i )); }
    moving_buffer$d[i] = sqrt( (current$cell_X - previous$cell_X)^2 + (current$cell_Y - previous$cell_Y)^2 );
    moving_buffer$area[i]= abs(current$cell_area - previous$cell_area ); 
    moving_buffer$d2spot[i] = abs(current$cellsSpot_Dist - previous$cellsSpot_Dist );
    moving_buffer$eccent[i] = abs(current$eccentricity - previous$eccentricity );
  } else { if (debug > 1 ) { print(paste("skip previous=", i-1, "current=",i )); }
  }
}
    
summary(moving_buffer)

##        d               area            d2spot           eccent     
##  Min.   : 0.000   Min.   : 0.000   Min.   : 0.000   Min.   :0.000  
##  1st Qu.: 0.403   1st Qu.: 1.000   1st Qu.: 0.200   1st Qu.:0.017  
##  Median : 0.608   Median : 2.000   Median : 0.400   Median :0.040  
##  Mean   : 0.722   Mean   : 2.835   Mean   : 0.597   Mean   :0.060  
##  3rd Qu.: 0.854   3rd Qu.: 3.000   3rd Qu.: 0.730   3rd Qu.:0.078  
##  Max.   :14.403   Max.   :62.000   Max.   :19.500   Max.   :0.717  
##  NA's   :8917     NA's   :8917     NA's   :8917     NA's   :8917   
##     NA         
##  Mode:logical  
##  NA's:9655     
##                
##                
##                
##                
## 

hist( moving_buffer$d );

hist( moving_buffer$area )

hist( moving_buffer$d2spot )

hist( moving_buffer$eccent )

p-value calculations

p_dist = function(x, input_buffer) {
  input_buffer = input_buffer[ !is.na(input_buffer)];
  lower = input_buffer[ input_buffer < x]; lower = lower[!is.na(lower)];
  upper = input_buffer[input_buffer > x]; upper = upper[!is.na(upper)];
  
  LowerP =  (length(lower) / length(input_buffer))
  UpperP =  (length(upper) / length(input_buffer)) 
  
  return(list(LowerP,UpperP, mean(input_buffer, na.rm=T), sd(input_buffer, na.rm=T)))
}

 p_dist( 10, moving_buffer$d)   #  lower and upper bound of  distance  probability for  one cell 

## [[1]]
## [1] 0.998645
## 
## [[2]]
## [1] 0.001355014
## 
## [[3]]
## [1] 0.722106
## 
## [[4]]
## [1] 0.7843616

Probability Density Function & cumulative Distribution Funcion for area

 p_dist( 5, moving_buffer$area)

## [[1]]
## [1] 0.8292683
## 
## [[2]]
## [1] 0.1056911
## 
## [[3]]
## [1] 2.834688
## 
## [[4]]
## [1] 4.117974

Null distribution of cell distance from spot passed trap

p_dist(10, moving_buffer$d2spot)

## [[1]]
## [1] 0.998645
## 
## [[2]]
## [1] 0.001355014
## 
## [[3]]
## [1] 0.597019
## 
## [[4]]
## [1] 0.9887488

p_dist(5, moving_buffer$eccent)

## [[1]]
## [1] 1
## 
## [[2]]
## [1] 0
## 
## [[3]]
## [1] 0.06044309
## 
## [[4]]
## [1] 0.07491423

write.csv(moving_buffer, "data/moving_buffer.csv", quote = F, row.names = F)

Fit with gamma distribution

library(MASS)

x = moving_buffer$d; 
x[x==0] = 0.05; #zero should be adjusted to a small value. 
x = x[!is.na(x)];
 fitdistr(x, "log-normal");

##      meanlog        sdlog   
##   -0.57420032    0.69299129 
##  ( 0.02550936) ( 0.01803784)

x = moving_buffer$area; 
x[x==0] = 0.05; 
x = x[!is.na(x)];
 fitdistr(x, "log-normal");

##     meanlog       sdlog   
##   0.27596012   1.54133093 
##  (0.05673718) (0.04011924)

x = moving_buffer$d2spot; 
x[x==0] = 0.05; 
x = x[!is.na(x)];
 fitdistr(x, "log-normal");

##      meanlog        sdlog   
##   -1.05515338    1.09676306 
##  ( 0.04037241) ( 0.02854760)

x = moving_buffer$eccent; 
x[x==0] = 0.05; 
x = x[!is.na(x)];
 fitdistr(x, "log-normal");

##      meanlog        sdlog   
##   -3.35301141    1.17329016 
##  ( 0.04318941) ( 0.03053952)