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Through the last years, different strategies to enhance synchronization in complex networks have been proposed. In this Letter, we show that the synchronization in a small-world network of attractively coupled non-identical neurons is…

In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is of paramount importance but still challenging. Considering that these interactions may…

Transformer-based Language Models have become ubiquitous in Natural Language Processing (NLP) due to their impressive performance on various tasks. However, expensive training as well as inference remains a significant impediment to their…

Control of complex processes is a major goal of network analyses. Most approaches to control nonlinearly coupled systems require the network topology and/or network dynamics. Unfortunately, neither the full set of participating nodes nor…

Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…

Understanding what makes high-dimensional data learnable is a fundamental question in machine learning. On the one hand, it is believed that the success of deep learning lies in its ability to build a hierarchy of representations that…

Graphical modelling techniques based on sparse selection have been applied to infer complex networks in many fields, including biology and medicine, engineering, finance, and social sciences. One structural feature of some of the networks…

Structure entails function and thus a structural description of the brain will help to understand its function and may provide insights into many properties of brain systems, from their robustness and recovery from damage, to their dynamics…

This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…

This paper describes a hierarchical learning strategy for generating sparse representations of multivariate datasets. The hierarchy arises from approximation spaces considered at successively finer scales. A detailed analysis of stability,…

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…

We consider continuous time Hopfield-like recurrent networks as dynamical models for gene regulation and neural networks. We are interested in networks that contain n high-degree nodes preferably connected to a large number of Ns weakly…

Through the success of deep learning in various domains, artificial neural networks are currently among the most used artificial intelligence methods. Taking inspiration from the network properties of biological neural networks (e.g.…

Coordinated human behaviour takes place within a diverse range of social organisational structures, which can be thought of as power structures with "managers" who influence "subordinates". A change in policy in one part of the organisation…

Dynamics and function of neuronal networks are determined by their synaptic connectivity. Current experimental methods to analyze synaptic network structure on the cellular level, however, cover only small fractions of functional neuronal…

One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity and how information processing occurs in the neural circuits. At the cellular and molecular level, mechanisms of signal…

In this article, we present a method to reconstruct the topology of a partially observed radial network of linear dynamical systems with bi-directional interactions. Our approach exploits the structure of the inverse power spectral density…

Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…

Hopfield models, originally developed to study memory retrieval in neural networks, have become versatile tools for modeling diverse biological systems in which function emerges from collective dynamics. In this review, we provide a…

The organization of the connectivity between mammalian cortical areas has become a major subject of study, because of its important role in scaffolding the macroscopic aspects of animal behavior and intelligence. In this study we present a…