Solving Time of Least Square Systems in Sigma-Pi Unit Networks

Nombre de pages: 7International audienceThe solving of least square systems is a useful operation in neurocomputational modeling of learning, pattern matching, and pattern recognition. In these last two cases, the solution must be obtained on-line, thus the time required to solve a system in a plausible neural architecture is critical. This paper presents a recurrent network of Sigma-Pi neurons, whose solving time increases at most like the logarithm of the system size, and of its condition number, which provides plausible computation times for biological systems

How does bond percolation happen in coloured networks?

Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial transformations that include a phase transition in the connectivity, and in some special cases, multiple phase transitions. Here we establish a generic analytic theory that describes how structure and sizes of all connected components in the network are affected by simple and colour-dependant bond percolations. This theory predicts all locations where the phase transitions take place, existence of wide critical windows that do not vanish in the thermodynamic limit, and a peculiar phenomenon of colour switching that occurs in small connected components. These results may be used to design percolation-like processes with desired properties, optimise network response to percolation, and detect subtle signals that provide an early warning of a network collapse