Network topology estimation through synchronization: A case study on quantum dot CNN

The reconstruction of the links among coupled dynamical systems can be handled in many ways. One of them is through synchronization, building a system composed by a "mirror" network and by evolution equations for the links of interest, in such a way that the two networks will synchronize if and only if the links are correctly estimated. A procedure based on this idea to estimate the topology of a network of interacting objects when the state variables are known is already present in literature, and here it is extended to systems ruled by implicit differential equations, to better suit some actual cases arising, in particular, in electric and electronic systems. The developed method is applied to a case of practical interest: the test of connections in a nanoscale device, introduced in the literature as "quantum dot cellular neural network", which can be easily produced in a self-assembled way. The whole iter has some steps sensitive to errors which can lead to a final device where the links among the "dots" are different from the desired ones. Our interest is in applying the method to detect such bad links.