Study of the cumulative distribution of deviations in omega-Deltax plots for C. elegans

With outliers:
>> [desv_acum,omega_media]=omegadesv_acumuladas(desv,omega,1,7);

>> plot(log10(desv_acum),log10(omega_media),’.-‘)

We get exponent 1.

I reduce the probability, to let the outliers outside. In need to go to 0.7, and it is a disaster:

>> [desv_acum,omega_media]=omegadesv_acumuladas(desv,omega,.7,7);

>> plot(log10(desv_acum),log10(omega_media),’.-‘)

I remove the outliers:

>> buenas=omega<20 | desv<.2;
>> [desv_acum,omega_media]=omegadesv_acumuladas(desv(buenas),omega(buenas),1,7);

>> plot(log10(desv_acum),log10(omega_media),’.-‘)

It is very influentiated by the last bin, which only contains one point. I reduce the binning:

>> [desv_acum,omega_media]=omegadesv_acumuladas(desv(buenas),omega(buenas),1,5);

>> plot(log10(desv_acum),log10(omega_media),’.-‘)

Still not very good. I use a non-equispaced binning:

>> [desv_acum,omega_media]=omegadesv_acumuladas(desv(buenas),omega(buenas),1,[0 10 20 40 80]);

>> plot(log10(desv_acum),log10(omega_media),’.-‘)

Another binning:

>> [desv_acum,omega_media]=omegadesv_acumuladas(desv(buenas),omega(buenas),1,[0 5 10 20 40 80]);

>> plot(log10(desv_acum),log10(omega_media),’.-‘)

Essentially the same…

I do it with another binning, that keeps the same number of data in each bin (except perhaps for the last one, that may be not completely full).

>> [desv_acum,omega_media]=omegadesv_acumuladas_binningpornumero(desv(buenas),omega(buenas),1,50);

>> plot(log10(desv_acum),log10(omega_media),’.-‘)

Using the center-of-mass position of each neuron with the rest fixed in their real positions does not change these results:

>> clear
>> load datos_celegans_struct
>> [pos,omega_general,costes,x]=coste2pos_restofijas(todas.A*.05,todas.M*1.5+todas.S,todas.f,todas.pos_real,1);
>> desv=abs(pos-todas.pos_real);
>> omega=sum([todas.A*.05 todas.M*1.5+todas.S],2);
>> plot(desv,omega,’.’)

>> buenas=omega<20 | desv<.2;
>> [xi,b]=omegadesv2bestfittingexponent_exp(desv(buenas),omega(buenas))
xi =
5.4148
b =
0.1103

>> [desv_acum,omega_media]=omegadesv_acumuladas(desv(buenas),omega(buenas),1,[0 5 10 20 40 80]);

>> plot(log10(desv_acum),log10(omega_media),’.-‘)