相关论文: Control of neural field equations with step-functi…

We consider a data-driven formulation of the classical discrete-time stochastic control problem. Our approach exploits the natural structure of many such problems, in which significant portions of the system are uncontrolled. Employing the…

The theory of Balanced Neural Networks is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. Roughly speaking, it entails that typical neurons receive many excitatory and inhibitory…

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…

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…

We present a method for representing the closed-loop dynamics of piecewise affine (PWA) systems with bounded additive disturbances and neural network-based controllers as mixed-integer (MI) linear constraints. We show that such…

Recent advances in experimental techniques enable the simultaneous recording of activity from thousands of neurons in the brain, presenting both an opportunity and a challenge: to build meaningful, scalable models of large neural…

The computational capabilities of a neural network are widely assumed to be determined by its static architecture. Here we challenge this view by establishing that a fixed neural structure can operate in fundamentally different…

We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…

Recent whole brain imaging experiments on $\textit{C. elegans}$ has revealed that the neural population dynamics encode motor commands and stereotyped transitions between behaviors on low dimensional manifolds. Efforts to characterize the…

We study neural field equations, which are prototypical models of large-scale cortical activity, subject to random data. We view this spatially-extended, nonlocal evolution equation as a Cauchy problem on abstract Banach spaces, with…

We study a chain of non-linear, interacting spins driven by a static and a time-dependent magnetic field. The aim is to identify the conditions for the locally and temporally controlled spin switching. Analytical and full numerical…

Some biological systems operate at the critical point between stability and instability and this requires a fine-tuning of parameters. We bring together two examples from the literature that illustrate this: neural integration in the…

This paper investigates recurrence properties of dynamical systems under the restriction that control is available only through inputs and outputs. We introduce the concept of ``coarse non-wandering'', a generalization of the classical…

Understanding the activity of large populations of neurons is difficult due to the combinatorial complexity of possible cell-cell interactions. To reduce the complexity, coarse-graining had been previously applied to experimental neural…

This paper introduces a framework for quantitative characterization of the controllability of time-varying linear systems (or networks) in terms of input novelty. The motivation for such an approach comes from the study of biophysical…

Neural populations exhibit complex recurrent structures that drive behavior, while continuously receiving and integrating external inputs from sensory stimuli, upstream regions, and neurostimulation. However, neural populations are often…

Spatiotemporal patterns such as traveling waves are frequently observed in recordings of neural activity. The mechanisms underlying the generation of such patterns are largely unknown. Previous studies have investigated the existence and…

We investigate stability analysis and controller design of unknown continuous-time systems under state-feedback with aperiodic sampling, using only noisy data but no model knowledge. We first derive a novel data-dependent parametrization of…

Creating a quantitative theory for the cortex presents challenges and raises questions. What are the significant scales--micro, meso, or macroscopic? What are the interactions--pairwise, higher order, or mean-field? And what control…

Brain aging synthesis is a critical task with broad applications in clinical and computational neuroscience. The ability to predict the future structural evolution of a subject's brain from an earlier MRI scan provides valuable insights…