Heavy paths and cycles in weighted graphs

A weighted graph is a graph in which each edge e is assigned a non-negative\ud number $w(e)$, called the weight of $e$. In this paper, some theorems on the\ud existence of long paths and cycles in unweighted graphs are generalized to heavy\ud paths and cycles in weighted graphs

Modeling the AgInSbTe Memristor

The AgInSbTe memristor shows gradual resistance tuning characteristics, which makes it a potential candidate to emulate biological plastic synapses. The working mechanism of the device is complex, and both intrinsic charge-trapping mechanism and extrinsic electrochemical metallization effect are confirmed in the AgInSbTe memristor. Mathematical model of the AgInSbTe memristor has not been given before. We propose the flux-voltage controlled memristor model. With piecewise linear approximation technique, we deliver the flux-voltage controlled memristor model of the AgInSbTe memristor based on the experiment data. Our model fits the data well. The flux-voltage controlled memristor model and the piecewise linear approximation method are also suitable for modeling other kinds of memristor devices based on experiment data