Related papers: General representation of collective neural dynami…
Mammalian functional architecture flexibly adapts, transitioning from integration where information is distributed across the cortex, to segregation where information is focal in densely connected communities of brain regions. This…
Seizure activity is a ubiquitous and pernicious pathophysiology that, in principle, should yield to mathematical treatments of (neuronal) ensemble dynamics - and therefore interventions on stochastic chaos. A seizure can be characterised as…
Cognitive diagnosis is a fundamental issue in intelligent education, which aims to discover the proficiency level of students on specific knowledge concepts. Existing approaches usually mine linear interactions of student exercising process…
A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…
The recent theoretical and experimental studies have revealed many details of signal propagation in nervous systems. In this paper an attempt is made to unify various mathematical models which describe the signal propagation in nerve…
In this work, we present a mathematical model for cyclic and sequential patterns of brain activity, combining heteroclinic dynamics with discrete neural-field models. We first show that spatial-discrete neural-field equations with…
In Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional…
Objective. Modelling is an important way to study the working mechanism of brain. While the characterization and understanding of brain are still inadequate. This study tried to build a model of brain from the perspective of thermodynamics…
This chapter sheds light on the synaptic organization of the brain from the perspective of computational neuroscience. It provides an introductory overview on how to account for empirical data in mathematical models, implement such models…
A central challenge in the computational modeling of neural dynamics is the trade-off between accuracy and simplicity. At the level of individual neurons, nonlinear dynamics are both experimentally established and essential for neuronal…
In this note, variational Monte Carlo method based on neural quantum states for spin systems is reviewed. Using a neural network as the wave function allows for a more generalized expression of various types of interactions, including…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
The fundamental, powerful process of computation in the brain has been widely misunderstood. The paper [1] associates the general failure to build intelligent thinking machines with current reductionist principles of temporal coding and…
Recurrent neural networks (RNNs) trained on compositional tasks can exhibit functional modularity, in which neurons can be clustered by activity similarity and participation in shared computational subtasks. Unlike brains, these RNNs do not…
This technical note introduces parametric dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow…
The analyses presented herein demonstrate that neuronal electrical activity can be consistently interpreted as a manifestation of murburn redox-mediated electronic dynamics rather than as a process fundamentally driven by transmembrane…
This paper proposes a theory for understanding perceptual learning processes within the general framework of laws of nature. Neural networks are regarded as systems whose connections are Lagrangian variables, namely functions depending on…
The static synaptic connectivity of neuronal circuits stands in direct contrast to the dynamics of their function. As in changing community interactions, different neurons can participate actively in various combinations to effect behaviors…
Foundation models have shown remarkable success in fitting biological visual systems; however, their black-box nature inherently limits their utility for understanding brain function. Here, we peek inside a SOTA foundation model of neural…
We present a numerical framework for solving neural field equations on surfaces using Radial Basis Function (RBF) interpolation and quadrature. Neural field models describe the evolution of macroscopic brain activity, but modeling studies…