Related papers: Modeling sequential cognitive states via populatio…
Networks of interacting nodes connected by edges arise in almost every branch of scientific enquiry. The connectivity structure of the network can force the existence of invariant subspaces, which would not arise in generic dynamical…
Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient…
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…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
Consider an unknown nonlinear dynamical system that is known to be dissipative. The objective of this paper is to learn a neural dynamical model that approximates this system, while preserving the dissipativity property in the model. In…
In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Monte Carlo method for the simulation of the microscopic system,…
We propose a simple (12 parameter) hybrid dynamic model that simultaneously captures the continuous-valued dynamics of three human cognitive states-trust, perceived risk, and mental workload-as well as discrete transitions in reliance on…
In this paper we developed a hierarchical network model, called Hierarchical Prediction Network (HPNet), to understand how spatiotemporal memories might be learned and encoded in the recurrent circuits in the visual cortical hierarchy for…
This paper studies a dynamical system that models the free recall dynamics of working memory. This model is a modular neural network with n modules, named hypercolumns, and each module consists of m minicolumns. Under mild conditions on the…
This review provides a dynamical systems perspective on psychiatric symptoms and disease, and discusses its potential implications for diagnosis, prognosis, and treatment. After a brief introduction into the theory of dynamical systems, we…
Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…
Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…
Empirical estimates of the dimensionality of neural population activity are often much lower than the population size. Similar phenomena are also observed in trained and designed neural network models. These experimental and computational…
An open question in systems and computational neuroscience is how neural circuits accumulate evidence towards a decision. Fitting models of decision-making theory to neural activity helps answer this question, but current approaches limit…
In recent years, the interdisciplinary research between information science and neuroscience has been a hotspot. In this paper, based on recent biological findings, we proposed a new model to mimic visual information processing, motor…
Short-term memory is essential for cognitive processing, yet our understanding of its neural mechanisms remains unclear. Neuroscience has long focused on how sequential activity patterns, where neurons fire one after another within large…
The principled design and discovery of biologically- and physically-informed models of neuronal dynamics has been advancing since the mid-twentieth century. Recent developments in artificial intelligence (AI) have accelerated this progress.…
The stability of heteroclinic cycles may be obtained from the value of the local stability index along each connection of the cycle. We establish a way of calculating the local stability index for quasi-simple cycles: cycles whose…
Recording simultaneous activity of hundreds of neurons is now possible. Existing methods can model such population activity, but do not directly reveal the computations used by the brain. We present a fully unsupervised method that models…
Understanding the dynamics of large-scale brain models remains a central challenge due to the inherent complexity of these systems. In this work, we explore the emergence of complex spatiotemporal patterns in a large scale-brain model…