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A major challenge in neuroscience is posed by the need for relating the emerging dynamical features of brain activity with the underlying modular structure of neural connections, hierarchically organized throughout several scales. The…
Adaptive behavior, cognition and emotion are the result of a bewildering variety of brain spatiotemporal activity patterns. An important problem in neuroscience is to understand the mechanism by which the human brain's 100 billion neurons…
Activity in neocortex exhibits a range of behaviors, from irregular to temporally precise, and from weakly to strongly correlated. So far there has been no single theoretical framework that could explain all these behaviors, leaving open…
We investigate numerically the collective dynamical behavior of pulse-coupled non-leaky integrate-and-fire-neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for…
Bump attractors are wandering localised patterns observed in in vivo experiments of spatially-extended neurobiological networks. They are important for the brain's navigational system and specific memory tasks. A bump attractor is…
Adaptive behavior requires the brain to transition between distinct contexts while maintaining representations of prior experience. The ability to reconfigure neural representations without erasing previously acquired knowledge is central…
Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes -- flexibility and selection -- must…
Time-varying networks are fast emerging in a wide range of scientific and business disciplines. Most existing dynamic network models are limited to a single-subject and discrete-time setting. In this article, we propose a mixed-effect…
Recently it has been found that different physical systems driven by identical random noise behave exactly identical after a long time. It is also suggested that this is an outcome of finite precision in numerical experiments. Here we show…
It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent…
We consider the self-attention model - an interacting particle system on the unit sphere, which serves as a toy model for Transformers, the deep neural network architecture behind the recent successes of large language models. We prove the…
We use linear stability analysis and hybrid lattice Boltzmann simulations to study the dynamical behaviour of an active nematic confined in a channel made of viscoelastic material. We find that the quiescent, ordered active nematic is…
Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust,…
Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…
Network remodeling, or adaptation, in the presence of periodically driven forcings has hereto remained largely unexplored, despite the fact that a broad class of biological transport networks, e.g. animal vasculature, depends on periodic…
Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) and neuroscience. Prior theoretical work has focused on RNNs with additive interactions. However, gating - i.e. multiplicative -…
Coherent oscillatory activity can arise spontaneously as a result of increased coupling in a system of excitable and passive cells, each being quiescent in isolation. This can potentially explain the appearance of spontaneous rhythmic…
This paper studies subtypes of restricted, repetitive and stereotypical behaviors (RRBs) in adolescent males with autism spectrum disorder (ASD) from the viewpoint of the dynamics of brain functional connectivities (FCs). Data from the…
Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous…
We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…