Related papers: Volume entropy and information flow in a brain gra…
Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy…
Transfer entropy is a measure of the magnitude and the direction of information flow between jointly distributed stochastic processes. In recent years, its permutation analogues are considered in the literature to estimate the transfer…
Despite the numerous ways now available to quantify which parts or subsystems of a network are most important, there remains a lack of centrality measures that are related to the complexity of information flows and are derived directly from…
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…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
With the rapid expansion of graphs and networks and the growing magnitude of data from all areas of science, effective treatment and compression schemes of context-dependent data is extremely desirable. A particularly interesting direction…
We introduce the (private) entropy of a directed graph (in a new network coding sense) as well as a number of related concepts. We show that the entropy of a directed graph is identical to its guessing number and can be bounded from below…
New entropy measures have been recently introduced for the quantification of the complexity of networks. Most of these entropy measures apply to static networks or to dynamical processes defined on static complex networks. In this paper we…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…
Sleep stage classification is a widely discussed topic, due to its importance in the diagnosis of sleep disorders, e.g. insomnia. Analysis of the brain activity during sleep is necessary to gain further insight into the processing that…
We connect several notions relating the structural and dynamical properties of a graph. Among them are the topological entropy coming from the vertex shift, which is related to the spectral radius of the graph's adjacency matrix, the…
In this paper we revisit the concept of mobility entropy. Over time, the structure of spatial interactions among urban centres tends to become more complex and evolves from centralised models to more scattered origin and destination…
We introduce a graph-signal generalisation of Sample Entropy, denoted SampEn$_{G}$, to quantify irregularity of graph signals on a continuous state space, complementing existing methods on symbolic dynamics. Our approach replaces the…
The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world…
Among the normalized metrics on a graph, we show the existence and the uniqueness of an entropy-minimizing metric, and give explicit formulas for the minimal volume entropy and the metric realizing it.