Related papers: Network Entropy measures applied to different syst…
The complexity of highly interconnected systems is rooted in the interwoven architecture defined by its connectivity structure. In this paper, we develop matrix energy of the underlying connectivity structure as a measure of topological…
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…
Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose…
A wide range of tasks in network analysis, such as clustering network populations or identifying anomalies in temporal graph streams, require a measure of the similarity between two graphs. To provide a meaningful data summary for…
Biological systems, from a cell to the human brain, are inherently complex. A powerful representation of such systems, described by an intricate web of relationships across multiple scales, is provided by complex networks. Recently, several…
Modeling and topological analysis of networks in biological and other complex systems, must venture beyond the limited consideration of very few network metrics like degree, betweenness or assortativity. A proper identification of…
Human dynamical social networks encode information and are highly adaptive. To characterize the information encoded in the fast dynamics of social interactions, here we introduce the entropy of dynamical social networks. By analysing a…
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…
Populations of heterogeneous cells play an important role in many biological systems. In this paper we consider systems where each cell can be modelled by an ordinary differential equation. To account for heterogeneity, parameter values are…
The network paradigm is increasingly used to describe the topology and dynamics of complex systems. Here we review the results of the topological analysis of protein structures as molecular networks describing their small-world character,…
For sensory networks, we determine the rate with which they acquire information about the changing external conditions. Comparing this rate with the thermodynamic entropy production that quantifies the cost of maintaining the network, we…
The two approaches to analyzing the large strain behavior of rubbery networks are phenomenologically, using strain energy functions drawn from continuum mechanics, and molecular models, which apply statistical mechanics to compute the…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…
Complex networks are a powerful modeling tool, allowing the study of countless real-world systems. They have been used in very different domains such as computer science, biology, sociology, management, etc. Authors have been trying to…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state…
In many biological processes heterogeneity within cell populations is an important issue. In this work we consider populations where the behavior of every single cell can be described by a system of ordinary differential equations.…
We introduce distance entropy as a measure of homogeneity in the distribution of path lengths between a given node and its neighbours in a complex network. Distance entropy defines a new centrality measure whose properties are investigated…