We present several terms and definitions related to the local analysis of dynamical systems. Multiple terms for one and the same thing that were found in literature are put together to provide a “dictionary” of terms and to avoid potential confusion due to misleading definitions. Additionally, some important concepts which are necessary to analyze a dynamical system are briefly discussed and a ...

In this paper the convergence behavior of the population based incremental learning algorithm (PBIL) is analyzed using discrete dynamical systems. A discrete dynamical system is associated with the PBIL algorithm. We demonstrate that the behavior of the PBIL algorithm follows the iterates of the discrete dynamical system for a long time when the parameter Α is near zero. We show that all the po...

In this paper the convergence behavior of the Population Based Incremental Learning algorithm (PBIL) is analyzed using discrete dynamical systems. A discrete dynamical system is associated with the PBIL algorithm. We demonstrate that the behavior of the PBIL algorithm follows the iterates of the discrete dynamical system for a long time when the parameter α is near zero. We show that all the po...

On account of their role played in the fundamental biological rhythms and by considering their potential use in information processing, the dynamical properties of an artificial neural network are particularly interesting to investigate. In order to reduce the degree of complexity of this work, we have considered in this paper a fully connected neural network of two discrete neurons. We have pr...

We report subnanometer, high-bandwidth measurements of the out-of-plane (vertical) motion of atoms in freestanding graphene using scanning tunneling microscopy. By tracking the vertical position over a long time period, a 1000-fold increase in the ability to measure space-time dynamics of atomically thin membranes is achieved over the current state-of-the-art imaging technologies. We observe th...