Relating Lurie's problem, Hopfield's network and Alzheimer's disease

  • R. F. Pinheiro Sant'anna University Center
  • D. Colón University of São Paulo
  • L. L. R. Reinoso University of São Paulo
Keywords: Lurie's problem, Hopfield's networks, Alzheimer's disease, H∞ Control, u-Analysis, DK-iteration


Alzheimer's disease is a degenerative brain disorder that affects millions of people around the world and still without cure. A very common application of Hopfield neural networks is to simulate a human memory as well as to evaluate problems of degeneration and memory loss. On the other hand, from the control area, one has Lurie's problem, which emerged in the 1940s and which still does not have a general solution. However many works and results came in an attempt to solve it. In this paper, the Hopfield's network is shown as a particular case of Lurie's problem, then one of the consequences of Alzheimer's disease, memory failure, is modeled using Hopfield's networks and nally a recent result of Lurie's problem is applied to the computationally modeled disease to correct the problem of memory loss. The correction is made using a controller via DK-iteration. Simulations are performed to validate the computational model of the disease and to demonstrate the effectiveness of the application of the recent Lurie's problem theorem. Therefore, in addition to the results presented, this work aims at encouraging the researches in the area, so that in the future, better diagnostic and treatment conditions will be achieved.