Related papers: Information and Topology in Attractor Neural Netwo…
Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally…
We study network properties of networks evolving in time based on optimal transport principles. These evolve from a structure covering uniformly a continuous space towards an optimal design in terms of optimal transport theory. At…
Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches,…
The mutual information, I, of the three-state neural network can be obtained exactly for the mean-field architecture, as a function of three macroscopic parameters: the overlap, the neural activity and the {\em activity-overlap}, i.e. the…
We examine numerically the storage capacity and the behaviour near saturation of an attractor neural network consisting of bistable elements with an adjustable coupling strength, the Bistable Gradient Network (BGN). For strong coupling, we…
We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered…
Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the…
In this work we propose a computational scheme inspired by the workings of human cognition. We embed some fundamental aspects of the human cognitive system into this scheme in order to obtain a minimization of computational resources and…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
Let $N$ local decision makers in a sensor network communicate with their neighbors to reach a decision \emph{consensus}. Communication is local, among neighboring sensors only, through noiseless or noisy links. We study the design of the…
Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant topological signals across distinct systems. In geometry and…
A recurrent neural network model storing multiple spatial maps, or ``charts'', is analyzed. A network of this type has been suggested as a model for the origin of place cells in the hippocampus of rodents. The extremely diluted and fully…
We introduce a flexible setup allowing for a neural network to learn both its size and topology during the course of a standard gradient-based training. The resulting network has the structure of a graph tailored to the particular learning…
In this work we evaluate the excitation and measurement patterns (EMP) for networks with tree topology. We investigate guidelines for the selection of the minimal EMPs, i.e. those with the least number of excited and measured nodes…
Community structure discovery in complex networks is a quite challenging problem spanning many applications in various disciplines such as biology, social network and physics. Emerging from various approaches numerous algorithms have been…
Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…
In this article, we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a new node, having randomly assigned coordinates in a $1 \times 1$…
We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive…
A framework integrating information theory and network science is proposed, giving rise to a potentially new area. By incorporating and integrating concepts such as complexity, coding, topological projections and network dynamics, the…
The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…