Related papers: Dynamical mean-field theory for a highly heterogen…

This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…

We present a unified field-theoretic framework for the dynamics of activity and connectivity in interacting neuronal systems. Building upon previous works, where a field approach to activity--connectivity dynamics, formation of collective…

This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…

Although static networks have been extensively studied in machine learning, data mining, and AI communities for many decades, the study of dynamic networks has recently taken center stage due to the prominence of social media and its…

Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive…

Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…

If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…

Network science has become an essential interdisciplinary tool for understanding complex biological systems. However, because these systems undergo continuous, often stimulus-driven changes in both structure and function, traditional static…

We investigate the emergence of synchronization in a network of coupled chaotic macroeconomic systems. Each node represents an economy characterized by three key variables savings, gross domestic product (GDP), and foreign capital inflows.…

Collective cell migration plays a crucial role in numerous biological processes, including tumour growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This…

Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…

The constituents of a complex system exchange information to function properly. Their signalling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange…

Biological systems represent time from microseconds to years. An important gap in our knowledge concerns the mechanisms for encoding time intervals of hundreds of milliseconds to minutes that matter for tasks like navigation, communication,…

Despite the knowledge that social, economical, and ecological networks are often of a small-world nature with inter-nodal distance growing even slower than logarithmically with system size, we often assume theoretical systems to be outside…

Neural networks rely on learning synaptic weights. However, this overlooks other neural parameters that can also be learned and may be utilized by the brain. One such parameter is the delay: the brain exhibits complex temporal dynamics with…

We use the annealed formulation of complex networks to study the dynamical behavior of disease spreading on both static and adaptive networked systems. This unifying approach relies on the annealed adjacency matrix, representing one network…

Phase transitions are crucial in shaping the collective dynamics of a broad spectrum of natural systems across disciplines. Here, we report two distinct heterogeneous nucleation facilitating single-step and multi-step phase transitions to…

We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic…

Decoding stimuli or behaviour from recorded neural activity is a common approach to interrogate brain function in research, and an essential part of brain-computer and brain-machine interfaces. Reliable decoding even from small neural…

We present a rigorous mathematical framework for analyzing dynamics of a broad class of Boolean network models. We use this framework to provide the first formal proof of many of the standard critical transition results in Boolean network…