Commit 3b010651 authored by SOLIMAN Sylvain's avatar SOLIMAN Sylvain
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Starting M8 MODAL

parent 455e0f5f
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# Let us start by looking again at the Prey-Predator model
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load(library:examples/lotka_volterra/LVi.bc).
```
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list_model.
```
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### SSA means Stochastic Simulation Algorithm (from Gillespie)
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```
numerical_simulation(method: ssa).
plot.
```
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### SPN is a Stochastic Petri Net, i.e., SSA without time
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```
numerical_simulation(method: spn).
plot.
```
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### SBN is a Stochastic Boolean Net, i.e., a stochastic boolean simulation
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```
numerical_simulation(method: sbn).
plot.
```
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---
Now let us look at different ways to approach PAC learning for this model.
First, the biocham command: `pac_learning(Model, #Initial_states, Time_horizon)`
it will read the file `Model` and generate `#Initial_states` random initial states from which it will run simulations for `Time_horizon`.
You can add options for the simulation, notably: `boolean_simulation: yes` to go from default `ssa` to `sbn` method,
and `cnf_clause_size: 2` to change the size of the disjuncts considered from the default `3`.
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## Question 1
Compare the results of trying to learn a model from traces of the above `library:examples/lotka_volterra/LVi.bc` model in the 3 following conditions:
1. A single boolean simulation of length 50
2. 25 boolean simulations of length 2
3. 50 stochastic simulations of length 1
Explain what you observe
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## Question 2
In the output, the `h` corresponds to Valiant's precision parameter. What we know (see François' slides) is that with $L(h, s)$ samples we have probability higher than $1 - h^{-1}$ to find our approximation, and its total amount of false negatives has measure $< h^{-1}$
How did we turn this into an estimate of the number of samples needed for a given $h$?
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## Question 3
Why do we have to provide a `cnf_clause_size` to learn CNF formulae of size less than `K`?
What does it represent "biologically"?
Could we have used the DNF learning algorithm here? why?
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Let us now consider a bigger model coming from L. Mendoza (Biosystems 2006), and made Boolean by the same author with Remy et al. (Dynamical Roles and Functionality of Feedback Circuits, Springer 2006).
![Th Lymphocite differentiation](RemyEtAl06.png)
The model is about the control and differentiation of Th (lymphocite) cells.
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```
load(library:examples/Th_lymphocytes/lympho.bc).
list_model.
```
%% Output
STAT4,TBet -> IFNg.
/ STAT4 -< IFNg.
/ TBet -< IFNg.
GATA3 / STAT1 -> IL4.
/ GATA3 -< IL4.
STAT1 -< IL4.
IFNg / SOCS1 -> IFNgR.
/ IFNg -< IFNgR.
SOCS1 -< IFNgR.
IL4 / SOCS1 -> IL4R.
/ IL4 -< IL4R.
SOCS1 -< IL4R.
IL12 / STAT6 -> IL12R.
/ IL12 -< IL12R.
STAT6 -< IL12R.
IFNgR -> STAT1.
/ IFNgR -< STAT1.
IL4R -> STAT6.
/ IL4R -< STAT6.
IL12R / GATA3 -> STAT4.
/ IL12R -< STAT4.
GATA3 -< STAT4.
STAT1 -> SOCS1.
TBet -> SOCS1.
/ STAT1,TBet -< SOCS1.
STAT6 / TBet -> GATA3.
STAT1 / GATA3 -> TBet.
TBet / GATA3 -> TBet.
GATA3 -< TBet.
/ STAT1,TBet -< TBet.
/ STAT6 -< GATA3.
TBet -< GATA3.
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