I am new user of netlogo. I have a system of reactions (converted to Ordinary Differential Equations), which can be solved using Matlab. I want to develop the same model in netlogo (for comparison with matlab results). I have the confusion regarding time/tick because netlogo uses "ticks" for increment in time, whereas Matlab uses time in seconds. How to convert my matlab sec to number of ticks? Can anyone help me in writing the code. The model is :
A + B ---> C (with rate constant k1 = 1e-6)
2A+ C ---> D (with rate constant k2 = 3e-7)
A + E ---> F (with rate constant k3 = 2e-5)
Initial values are A = B = C = 500, D = E = F = 10
Initial time t=0 sec and final time t=6 sec
I have a general comment first, NetLogo is intended for agent-based modelling. ABM has multiple entities with different characteristics interacting in some way. ABM is not really an appropriate methodology for solving ODEs. If your goal is to simply build your model in something other than Matlab for comparison rather than specifically requiring NetLogo, I can recommend Vensim as more appropriate. Having said that, you can build the model you want in NetLogo, it is just very awkward.
NetLogo handles time discretely rather than continuously. You can have any number of ticks per second (I would suggest 10 and then final time is 60 ticks). You will need to convert your equations into a discrete form, so your rates would be something like k1-discrete = k1 / 10. You may have precision problems with very small numbers.
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I have been working on this all day but I haven't figured it out yet. So I thought I may as well ask on here and see if someone can help.
The problem is as follow:
----------
F(input)(t) --> | | --> F(output)(t)
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Given a sample with a known length, density, and spring constant (or young's modulus), find the 'output' force against time when a known variable force is applied at the 'input'.
My current solution can already discretise the sample into finite elements, however I am struggling to figure out how the force should transmit given that the change in transmission speed in the material changes itself with respect to the force (using equation c = sqrt(force*area/density)).
If someone could point me to a solution or any other helpful resources, it would be highly appreciated.
A method for applying damping to the system would also be helpful but I should be able to figure out that part myself. (losses to the environment via sound or internal heating)
I will remodel the porbem in the following way:
___ ___
F_input(t) --> |___|--/\/\/\/\/\/\/\/\--|___|
At time t=0 the system is in equilibrium, the distance between the two objects is L, the mass of the left one (object 1) is m1 and the mass of the right one (object 2) is m2.
___ ___
F_input(t) --> |<-x->|___|--/\/\/\/\/\/-|<-y->|___|
During the application of the force F_input(t), at time t > 0, denote by x the oriented distance of the position of object 1 from its original position at time t=0. Similarly, at time t > 0, denote by y the oriented distance of the position of object 2 from its original position at time t=0 (see the diagram above). Then the system is subject to the following system of ordinary differential equations:
x'' = -(k/m1) * x + (k/m2) * y + F_input(t)/m2
y'' = (k/m2) * x - (k/m2) * y
When you solve it, you get the change of x and y with time, i.e. you get two functions x = x(t), y = y(t). Then, the output force is
F_output(t) = m2 * y''(t)
The problem isn't well defined at all. For starters for F_out to exist, there must be some constraint it must obey. Otherwise, the system will have more unknowns than equations.
The discretization will lead you to a system like
M*xpp = -K*x + F
with m=ρ*A*Δx and k=E*A/Δx
But to solve this system with n equations, you either need to know F_in and F_out, or prescribe the motion of one of the nodes, like x_n = 0, which would lead to xpp_n = 0
As far as damping, usually, you employ proportional damping, with a damping matrix proportional to the stiffness matrix D = α*K multiplied by the vector of speeds.
I'm attempting to model fMRI data so I can check the efficacy of an experimental design. I have been following a couple of tutorials and have a question.
I first need to model the BOLD response by convolving a stimulus input time series with a canonical haemodynamic response function (HRF). The first tutorial I checked said that one can make an HRF that is of any amplitude as long as the 'shape' of the HRF is correct so they created the following HRF in matlab:
hrf = [ 0 0 1 5 8 9.2 9 7 4 2 0 -1 -1 -0.8 -0.7 -0.5 -0.3 -0.1 0 ]
And then convolved the HRF with the stimulus by just using 'conv' so:
hrf_convolved_with_stim_time_series = conv(input,hrf);
This is very straight forward but I want my model to eventually be as accurate as possible so I checked a more advanced tutorial and they did the following. First they created a vector of 20 timepoints then used the 'gampdf' function to create the HRF.
t = 1:1:20; % MEASUREMENTS
h = gampdf(t,6) + -.5*gampdf(t,10); % HRF MODEL
h = h/max(h); % SCALE HRF TO HAVE MAX AMPLITUDE OF 1
Is there a benefit to doing it this way over the simpler one? I suppose I have 3 specific questions.
The 'gampdf' help page is super short and only says the '6' and '10' in each function call represents 'A' which is a 'shape' parameter. What does this mean? It gives no other information. Why is it 6 in the first call and 10 in the second?
This question is directly related to the above one. This code is written for a situation where there is a TR = 1 and the stimulus is very short (like 1s). In my situation my TR = 2 and my stimulus is quite long (12s). I tried to adapt the above code to make a working HRF for my situation by doing the following:
t = 1:2:40; % 2s timestep with the 40 to try to equate total time to above
h = gampdf(t,6) + -.5*gampdf(t,10); % HRF MODEL
h = h/max(h); % SCALE HRF TO HAVE MAX AMPLITUDE OF 1
Because I have no idea what the 'gampdf' parameters mean (or what that line does, in all actuality) I'm not sure this gives me what I'm looking for. I essentially get out 20 values where 1-14 have SOME numeric value in them but 15-20 are all 0. I'm assuming there will be a response during the entire 12s stimulus period (first 6 TRs so values 1-6) with the appropriate rectification which could be the rest of the values but I'm not sure.
Final question. The other code does not 'scale' the HRF to have an amplitude of 1. Will that matter, ultimately?
The canonical HRF you choose is dependent upon where in the brain the BOLD signal is coming from. It would be inappropriate to choose just any HRF. Your best source of a model is going to come from a lit review. I've linked a paper discussing the merits of multiple HRF models. The methods section brings up some salient points.
I have a dataset with 274 samples (9 months) of the daily energy (Watts.hour) used on a residential household. I'm not sure if i'm applying the lpc function correctly.
My code is the following:
filename='9-months.csv';
energy = csvread(filename);
C=zeros(5,1);
counter=0;
N=3;
for n=274:-1:31
w2=energy(1:n-1,1);
a=lpc(w2,N);
energy_estimated=0;
for X = 1:N
energy_estimated = energy_estimated + (-a(X+1)*energy(n-X));
end
w_real=energy(n);
error2=abs(w_real-energy_estimated);
counter=counter+1;
C(counter,1)=error2;
end
mean_error=round(mean(C));
Being "n" the sample on analysis, I will use the energy array's values, from 1 to n-1, to calculate the lpc coefficientes (with N=3).
After that, it will apply the calculated coefficients on the "for" cycle presented, in order to calculate the estimated energy.
Finally, error2 outputs the error between the real energy and estimated value.
On the example presented ( http://www.mathworks.com/help/signal/ref/lpc.html ) some filters are used. Do I need to apply any filter to it? Is my methodology correct?
Thank you very much in advance!
The lpc seems to be used correctly, but there are a few other things about your code. I am adressign the part at he "for n" :
for n=31:274 %for me it would seem more logically to go forward in time
w2=energy(1:n-1,1);
a=lpc(w2,N);
energy_estimate=filter([0 -a(2:end)],1,w2);
energy_estimate=energy_estimate(end);
estimates(n)=energy_estimate;
end
error=energy(31:274)-estimates(31:274)';
meanerror=mean(error); %you dont really round mean errors
filter is exactly what you are trying to do with the X=1:N loop. but this will perform the calculation for the entire w2 vector. If you just want the last value take the (end) command as well.
Now there is no reason to calculate the error for every single value and then add them to a vector you can do that faster after the calculation.
Now if your trying to estimate future values with a lpc it could work like that, but you are implying that every value is only dependend on the last 3 values. Have you tried something like a polynominal approach? i would think that this would be closer to reality.
I'm trying to simulate an optical network algorithm in MATLAB for a homework project. Most of it is already done, but I have an issue with the diagrams I'm getting.
In the simulation I'm generating exponential traffic, however, for low lambda values (0.1) I'm getting very high packet drop rates (99%). I wrote a sample here which is very close to the testbench I'm running on my simulator.
% Run the simulation 10 times, with different lambda values
l = [1 2 3 4 5 6 7 8 9 10];
for i=l(1):l(end)
X = rand();
% In the 'real' simulation the following line defines the time
% when the next packet generation event will occur. Suppose that
% i is the current time
t_poiss = i + ceil((-log(X)/(i/10)));
distr(i)=t_poiss;
end
figure, plot(distr)
axis square
grid on;
title('Exponential test:')
The resulting image is
The diagram I'm getting in this sample is IDENTICAL to the diagram I'm getting for the drop rate/λ. So I would like to ask if I'm doing something wrong or if I miss something? Is this the right thing to expect?
So the problem is coming from might be a numerical problem. Since you are generating a random number for X, the number might be incredibly small - say, close to zero. If you have a number close to zero numerically, log(X) is going to be HUGE. So your calculation of t_poiss will be huge. I would suggest doing something like X = rand() + 1 to make sure that X is never close to zero.
I am new to HMM but I have gone through enough literature. I am working on a project in which I will be predicting rainfall using atmospheric parameters.
I have four observable characteristics of the atmosphere (humidity, temperature, wind, sea level height) for 10 years. I have also rainfall amount data with me.
As per I can understand, for each day a weather state will be specified on the basis of the spatial rainfall. So here goes the question. Lets suppose I have data for 100 days.
Rainfall = { 1,2,3,4... 100}. So if I want to generate weather states what should I do?
Lets suppose
temperature = { 30 to 45, some kind of distribution }
humidity = { 25 to 80 }
wind = { 60 to 100 }
sea level height = { 35 to 90 }
How to find
P(X_0) Initial parameter,
P(X_t|X_t-1) state transition matrix,
P(Y_t|X_t) dependence of observation on state
Do I need some clustering for generating states?
I am coding it in MATLAB.
You can come with your example or any source which can explain the procedure to implement in program.
An HMM has a discrete number of states, so your first step will be to define your states. Once you have well-defined states, come up with a numbering scheme for your states and write a function that can accept the data for a given time period, and output the state number that corresponds to that state.
Once you have a function (let's call it get_state) that maps data to a state number, you can create your state transition matrix as follows:
T = zeros(num_states);
for day = 2:num_days
s1 = get_state(data(day-1));
s2 = get_state(data(day));
T(s1,s2) = T(s1,s2) + 1;
end
The i,j-th element of the matrix T now gives you the transition counts from state i to j. You can turn this into transition probabilities as follows:
M = bsxfun(#rdivide,T+1,sum(T+1,2));
The dependence of the observation on the state is harder. You will have to figure out how you want to turn the observed data into a probability density function or probability mass function. You can have mutliple observed distributions from a single state instead of combining temperature, humidity, etc., into a single observation.
This is obviously not a full implementation, but hopefully it is enough to give you a starting point.