## Metric for different values of alfa and beta

18 Feb 09

m=mapametrica(todas.A,todas.M,todas.S,todas.f,todas.pos_real,10.^(-3:1:3),10.^(-3:1:3),2,1000);
>> imagesc(-3:3,-3:3,log10(m))
>> xlabel(‘log10(beta)’)
>> ylabel(‘log10(alfa)’)

19 Feb 09

Assuming quadratic cost and independent neurons, the increment of cost when interchanging the deviations of two neurons is

DeltaW=(omega1-omega2)(Deltax2^2-Deltax1^2). This is used in efectoperms.m.

For a ideal simple system, this works fine:

>> A=zeros(100);
>> B=rand(100,2);
>> f=[0 0];
>> pos=rand(100,1);
>> [Deltacostes_perm,Deltacostes_perm_teor]=efectoperms(A,B,f,pos,2,[]);

When alfa is small, also works great for elegans:

>> alfa=0.0001; beta=10;
>> [Deltacostes_perm,Deltacostes_perm_teor]=efectoperms(todas.A*alfa,todas.M*beta+todas.S,todas.f,todas.pos_real,2,[]);

Good agreement for alfa and beta of the pnas:

>> alfa=0.05; beta=1.5;
[Deltacostes_perm,Deltacostes_perm_teor]=efectoperms(todas.A*alfa,todas.M*beta+todas.S,todas.f,todas.pos_real,2,[]);

For alfa=10, fuzzier but reasonable:

>> alfa=10; beta=10;
>> [Deltacostes_perm,Deltacostes_perm_teor]=efectoperms(todas.A*alfa,todas.M*beta+todas.S,todas.f,todas.pos_real,2,[]);

We try permutations of multiple neurons:

n_neur=[2 3 5 10 20 50];
for c=1:6
subplot(2,3,c)
[Deltacostes_perm,Deltacostes_perm_teor]=efectoperms_multiples(A,B,f,pos,2,n_neur(c),1000,[]);
End

n_neur=[2 3 5 10 20 50];
alfa=.00001; beta=10;
for c=1:6
subplot(2,3,c)
[Deltacostes_perm,Deltacostes_perm_teor]=efectoperms_multiples(todas.A*alfa,todas.M*beta+todas.S,todas.f,todas.pos_real,2,n_neur(c),1000,[]);
End

n_neur=[2 3 5 10 20 50];
alfa=.05; beta=1.5;
for c=1:6
subplot(2,3,c)
[Deltacostes_perm,Deltacostes_perm_teor]=efectoperms_multiples(todas.A*alfa,todas.M*beta+todas.S,todas.f,todas.pos_real,2,n_neur(c),1000,[]);
end

For big alfas and large number of permutations, there is a shift:

n_neur=[2 3 5 10 20 50];
alfa=10; beta=10;
for c=1:6
subplot(2,3,c)
[Deltacostes_perm,Deltacostes_perm_teor]=efectoperms_multiples(todas.A*alfa,todas.M*beta+todas.S,todas.f,todas.pos_real,2,n_neur(c),1000,[]);
end

With permutations as in the metric:

>> [Deltacostes_perm,Deltacostes_perm_teor]=efectoperms_completas(A,B,f,pos,2,1000,[]);

>> alfa=.05; beta=1.5;
>> [Deltacostes_perm,Deltacostes_perm_teor]=efectoperms_completas(todas.A*alfa,todas.M*beta+todas.S,todas.f,todas.pos_real,2,1000,[]);

>> alfa=10; beta=10;
>> [Deltacostes_perm,Deltacostes_perm_teor]=efectoperms_completas(todas.A*alfa,todas.M*beta+todas.S,todas.f,todas.pos_real,2,1000,[]);

Study of the effect neuron-by-neuron

[Deltacostes_perm,Deltacostes_perm_teor]=efectoperms_neuraneur(A,B,f,pos,2,1000,[]);

alfa=10; beta=10;
>> [m,Deltacostes_perm,Deltacostes_perm_teor]=efectoperms_neuraneur(todas.A*alfa,todas.M*beta+todas.S,todas.f,todas.pos_real,2,10000,[]);

Oh, AVAL and AVAR!

Oh, it’s the opposite: AVAL and AVAR are not producing the shift, their effect is actually against the shift, as we see when removing them from the calculation:

>> [m,Deltacostes_perm,Deltacostes_perm_teor]=efectoperms_completas(todas.A*alfa,todas.M*beta+todas.S,todas.f,todas.pos_real,2,1000,[],[54 55]);