November 23, 2015
In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.
Similar papers 1
December 9, 2013
Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place. However, this mechanism is non-local, in the sense that it requires knowledge of the whole graph in order for the graph to be updated. Instead, if preferential attachment and realistic networks occur in physical systems, these features need...
August 21, 2019
We provide an introduction to a very specific toy model of memristive networks, for which an exact differential equation for the internal memory which contains the Kirchhoff laws is known. In particular, we highlight how the circuit topology enters the dynamics via an analysis of directed graph. We try to highlight in particular the connection between the asymptotic states of memristors and the Ising model, and the relation to the dynamics and statics of disordered systems.
November 9, 2020
Stochastic network-dynamics are typically assumed to be memory-less. Involving prolonged dwells interrupted by instantaneous transitions between nodes such Markov networks stand as a coarse-graining paradigm for chemical reactions, gene expression, molecular machines, spreading of diseases, protein dynamics, diffusion in energy landscapes, epigenetics and many others. However, as soon as transitions cease to be negligibly short, as often observed in experiments, the dynamics ...
April 5, 2013
We show that memristive networks-namely networks of resistors with memory-can efficiently solve shortest-path optimization problems. Indeed, the presence of memory (time non-locality) promotes self organization of the network into the shortest possible path(s). We introduce a network entropy function to characterize the self-organized evolution, show the solution of the shortest-path problem and demonstrate the healing property of the solution path. Finally, we provide an alg...
August 30, 2016
Networks with memristive elements (resistors with memory) are being explored for a variety of applications ranging from unconventional computing to models of the brain. However, analytical results that highlight the role of the graph connectivity on the memory dynamics are still a few, thus limiting our understanding of these important dynamical systems. In this paper, we derive an exact matrix equation of motion that takes into account all the network constraints of a purely...
February 25, 2024
Networks with memristive devices are a potential basis for the next generation of computing devices. They are also an important model system for basic science, from modeling nanoscale conductivity to providing insight into the information-processing of neurons. The resistance in a memristive device depends on the history of the applied bias and thus displays a type of memory. The interplay of this memory with the dynamic properties of the network can give rise to new behavior...
February 4, 2021
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into account the natural information geometry of probability distributions. We apply this framework to the Gibbs distribution of random graphs obtained with constraints on the node connectivity. The information geometry for this graph ensemble is ca...
December 3, 2007
The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree heterogeneity and correlations affect the diffusion entropy rate. In addition, the entropy rate is used to characterize complex networks from the real world. Our results point out how to design optimal diffusion processes that maximize the...
December 31, 2023
At the intersection of computation and cognitive science, graph theory is utilized as a formalized description of complex relationships and structures. Traditional graph models are often static, lacking dynamic and autonomous behavioral patterns. They rely on algorithms with a global view, significantly differing from biological neural networks, in which, to simulate information storage and retrieval processes, the limitations of centralized algorithms must be overcome. This ...
November 10, 2018
This paper mainly discusses the diffusion on complex networks with time-varying couplings. We propose a model to describe the adaptive diffusion process of local topological and dynamical information, and find that the Barabasi-Albert scale-free network (BA network) is beneficial to the diffusion and leads nodes to arrive at a larger state value than other networks do. The ability of diffusion for a node is related to its own degree. Specifically, nodes with smaller degrees a...