User:Nuri Purswani/NetworkReconstruction/Algorithms/Dynamical
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Summary of Operation
Robust dynamical network reconstruction. [references] - Necessary and sufficient conditions for biological network reconstruction are:
- bla
- bla
- bla
This method assumes that providing that the above have been met, we are able to recover the boolean network structure between observed nodes. In order to compute the "best boolean networks", a smallest distance measure approach was taken, but this proved to be misleading, as the best network is always the fully connected one. Instead, an approach employing BIC and AIC was taken to recover network structure.
Description
- Interest to measure input and partially measured output. problem of hidden variables.
- If we assume that the network is linear time invariant and the measurements are non noisy, it can be shown that classical system identification techniques are unable to solve the problem.
- A system's transfer function does not contain sufficient information about the network: because one transfer function can lead to several minimal realizations.
- Instead, use a dynamical structure function, which is an intermediate that captures information between the transfer function and the state space representation.
- dynamical structure functions encode information at the measurement level and some information about the hidden states.
This algorithm is proposing a new data acquisition protocol, whereby. If nothing is known about the network, experiments must be performed this way:
- For a network of p measured species, p experiments must be performed.
- Each experiment p must independently control a species i.
- Problems with direct system identification: A single transfer function can be consistent with state space realisations with different structures (reference).
- Dynamical structure functions. If we have a non linear system with y observed and z hidden states perturbed by a set of inputs u, assuming that we can linearise the system around an equilibrium point and that noise and the inputs do not move the states too far from this point, We can then partition the system as follows:
- [Derivation of dynamical structure function]
- This makes us obtain a dynamical structure function and a control structure function.
- With time series measurements, we obtain a matrix of transfer functions (in terms of s)
- With steady state measurements, we obtain Qo and Po, which correspond to the boolean structure of the system.