Physics – Data Analysis – Statistics and Probability
Scientific paper
2009-02-23
Physics
Data Analysis, Statistics and Probability
7 figures, submitted to IEEE Trans. on Circuits and Systems 1 (TCAS1) in Sep 2009
Scientific paper
In this paper, we present and analyse two Hopfield-like nonlinear networks, in continuous-time and discrete-time respectively. The proposed network is based on an autonomous linear system with a symmetric weight matrix, which is designed to be unstable, and a nonlinear function stabilizing the whole network thanks to a manipulated state variable called``ultimate SIR''. This variable is observed to be equal to the traditional Signal-to-Interference Ratio (SIR) definition in telecommunications engineering. The underlying linear system of the proposed continuous-time network is $\dot{{\mathbf x}} = {\mathbf B} {\mathbf x}$ where {\bf B} is a real symmetric matrix whose diagonal elements are fixed to a constant. The nonlinear function, on the other hand, is based on the defined system variables called ``SIR''s. We also show that the ``SIR''s of all the states converge to a constant value, called ``system-specific Ultimate SIR''; which is equal to $\frac{r}{\lambda_{max}}$ where $r$ is the diagonal element of matrix ${\bf B}$ and $\lambda_{max}$ is the maximum (positive) eigenvalue of diagonally-zero matrix $({\bf B} - r{\bf I})$, where ${\bf I}$ denotes the identity matrix. The same result is obtained in its discrete-time version as well. Computer simulations for binary associative memory design problem show the effectiveness of the proposed network as compared to the traditional Hopfield Networks.
No associations
LandOfFree
Ultimate "SIR" in Autonomous Linear Networks with Symmetric Weight Matrices, and Its Use to Stabilize the Network - A Hopfield-like network does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Ultimate "SIR" in Autonomous Linear Networks with Symmetric Weight Matrices, and Its Use to Stabilize the Network - A Hopfield-like network, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ultimate "SIR" in Autonomous Linear Networks with Symmetric Weight Matrices, and Its Use to Stabilize the Network - A Hopfield-like network will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-583988