Calculate lifetime sparseness according to Olsen et al. 2008

lifetime_sparseness(x, minodours = 0.75)

Arguments

x	matrix of odour data with one column per odour, 1 row per cell
minodours	Minimum number of odours required to compute valid score (see details)

Value

named numeric vector, one entry for each row (neuron) in x

Details

minodours is interpreted as fraction when <=1. If >1 it is assumed then there must be >= that many odour responses. Any cells that have been tested for fewer than than minodours will have a sparseness value of NA. Definition:

S = 1/(1-1/N)*( 1 - (sum(r/N)^2)/(sum(r^2/N)) )

where N is the number of odours and r is the analogue response intensity of the neuron to odour j minus baseline firing rate. Analogue response intensity was the mean spike rate (averaged across five sweeps) during the entire 500-ms odour stimulus period. Any values of rj < 0 were set to zero before computing lifetime sparseness (this was the only analysis in this study in which negative responses were zeroed). Responses to paraffin oil (solvent control) were not considered in the sparseness analysis. We computed the lifetime sparseness for each individual cell in our study for which we tested at least 12 of the odours in our set. We used the Mann--Whitney U test to assess the significance of sparseness differences.

Missing Values (NAs)

When there are missing values in x, they are omitted silently. NAs do not count towards the value of N, the number of responses /cell in the equation above.

References

Olsen S.R. and Wilson R.I. (2008). Lateral presynaptic inhibition mediates gain control in an olfactory circuit. Nature 452 (7190), 956--960. doi:10.1038/nature06864

Willmore B. and Tolhurst D.J.(2001). Characterizing the sparseness of neural codes. Network Comput. Neural Syst. 12, 255 (2001) doi:10.1080/net.12.3.255.270

Examples

spikes=CollectSpikesFromSweeps(
  system.file('igor','spikes','nm20120514c2',package='gphys'),
  subdir='BLOCKA')
od=OdourResponseFromSpikes(spikes,response=c(2200,2700),baseline=c(0,2000))
# NB we take mean response per odour since we must end up with one number
# per odour per cell
S=lifetime_sparseness(colMeans(od))
#> Warning: Zeroing 1 responses < 0
data.frame(odour=colnames(od), S=S)
#>    odour         S
#> 1    IAA 0.7138722
#> 2    cVA 0.7138722
#> 3    pro 0.7138722
#> 4    PAA 0.7138722
#> 5    4ol 0.7138722
#> 6    ctr 0.7138722
#> 7    vin 0.7138722
#> 8  ctr.1 0.7138722
#> 9    fly 0.7138722
#> 10   far 0.7138722
#> 11   oen 0.7138722
#> 12   pac 0.7138722
#> 13   aac 0.7138722

# check what happens with NAs
od2=od
od2[5,'cVA']=NA
lifetime_sparseness(colMeans(od2))
#> Warning: Zeroing 1 responses < 0
#> [1] 0.7545164

# compare with a sparse cell
spikes2=CollectSpikesFromSweeps(
  system.file('igor','spikes','nm20110914c4',package='gphys'),
  subdir='BLOCKI', sweeps=0:4)
od3=OdourResponseFromSpikes(spikes2,response=c(2200,2700),baseline=c(0,2000))
lifetime_sparseness(colMeans(od3))
#> Warning: Zeroing 4 responses < 0
#> [1] 0.9981043