## First results for the dynamics of C elegans

Eigenvectors and eigenvalues MUST be complex. Still, real solution for the voltage is possible (each eigenvector/value has another one which is complex conjugate. If the modulus of the coefficient of both is the same, the final linear combination is real).

With no membrane conductance:

>> V0=zeros(279,1);
>> solucion=matrizsistema2solucion(M,V0);
>> plot(solucion.autovalores,’.’)

This figure matches with Figure 8 of Mitya’s paper (y axis is imaginary part)

We see that there are positive eigenvalues. This has two consequences:
– Diverging voltage.
– Apparently some computations are not performed correctly. I get non-negligible imaginary parts in the voltages.

I see that I need about 30 in the membrane conductance to get all eigenvalues negative:

>> solucion=matrizsistema2solucion(M,V0);
>> plot(solucion.autovalores,’.’)

FIRST EXAMPLE: Excitation of neuron 1.

>> V0=zeros(279,1);
>> V0(1)=1;
>> solucion=matrizsistema2solucion(M,V0);
>> V=solucion2voltajes(solucion,0:.001:.5);
>> plot(V(1,:))

>> plot(V(2,:))

And so on…

SECOND EXAMPLE: Random excitation

>> V0=rand(279,1);
>> solucion=matrizsistema2solucion(M,V0);
>> V=solucion2voltajes(solucion,0:.001:.5);
>> imagesc(V)

What are those ‘rough’ zones?

>> plot(V(149,:))

What the…?

## Modelling reaction times with two overlapping processes

It turns out that the sum of normally distributed and exponentially distributed random numbers gives rise to Carpenter’s distribution:

>> t=.2+.02*randn(1,10000) + exprnd(.05,[1 10000]);
>> hist(t,30)

>> hist(1./t,30)

>> t_reaccion2histog_carpenter(t,20,’r.-‘);

## Model for reaction times with distractions

First, with all distractions having the same duration:

>> estimulo=generaestimulo(10000,[1 2]);
>> [t_reaccion,mom_despistes,t_reaccion_intrinseco]=estimulo2reaccion(estimulo,[.2 .03],[3 .2]);
>> hist(t_reaccion,30)

>> hist(1./t_reaccion,30)

>> t_reaccion2histog_carpenter(t_reaccion,20,’r.-‘);

The problem is that distractions produce a plateau which is not very natural. Let’s see a very clear case:

>> [t_reaccion,mom_despistes,t_reaccion_intrinseco]=estimulo2reaccion(estimulo,[.2 .03],[1 .2]);
>> hist(t_reaccion,30)

A more natural situation is that in which distractions have different durations: