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Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…
In this document, we introduce a notion of entropy for stochastic processes on marked rooted graphs. For this, we employ the framework of local weak limit theory for sparse marked graphs, also known as the objective method, due to…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
Recent research has explored the increasingly important role of social media by examining the dynamics of individual and group behavior, characterizing patterns of information diffusion, and identifying influential individuals. In this…
Intracranial aneurysms remain a major cause of neurological morbidity and mortality worldwide, where rupture risk is tightly coupled to local hemodynamics particularly wall shear stress and oscillatory shear index. Conventional…
Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality.…
This paper describes an entropy equation, but one that should be used for measuring energy and not information. In relation to the human brain therefore, both of these quantities can be used to represent the stored information. The human…
Identifying the status of individual network units is critical for understanding the mechanism of convolutional neural networks (CNNs). However, it is still challenging to reliably give a general indication of unit status, especially for…
The structure of the network can be described by motifs, which are subgraphs that often repeat themselves. In order to understand the structure of network motifs, it is of great importance to study subgraphs from the perspective of…
We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…
Contrastive learning on graphs aims at extracting distinguishable high-level representations of nodes. In this paper, we theoretically illustrate that the entropy of a dataset can be approximated by maximizing the lower bound of the mutual…
We introduce a novel method, called Dispersion Entropy for Graph Signals, $DE_G$, as a powerful tool for analysing the irregularity of signals defined on graphs. We demonstrate the effectiveness of $DE_G$ in detecting changes in the…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
Finding the correct encoding for a generic dynamical system's trajectory is a complicated task: the symbolic sequence needs to preserve the invariant properties from the system's trajectory. In theory, the solution to this problem is found…
Predictability of behavior has emerged an an important characteristic in many fields including biology, medicine, and marketing. Behavior can be recorded as a sequence of actions performed by an individual over a given time period. This…
Deep Graph Neural Networks struggle with oversmoothing. This paper introduces a novel, physics-inspired GNN model designed to mitigate this issue. Our approach integrates with existing GNN architectures, introducing an entropy-aware message…
Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments;…
We define a new quantitative measure for an arbitrary factorial language: the entropy of a random walk in the prefix tree associated with the language; we call it Markov entropy. We relate Markov entropy to the growth rate of the language…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…