MBI Videos

Videos by Workshop 1: Mathematical Challenges in Neural Network Dynamics

  • Wilson's Rivalry Networks and Derived Patterns
    Marty Golubitsky
    Wilson's Rivalry Networks and Derived Patterns...
  • Neural field model of binocular rivalry waves in primary visual cortex
    Paul Bressloff
    Neural fields model the large-scale dynamics of spatially structured cortical networks in terms of continuum integro-differential equations, whose associated integral kernels represent the spatial distribution of neuronal synaptic connections. The advantage of a continuum rather than a discrete representation of spatially structured networks is that various techniques from...
  • Balanced cortical microcircuitry for maintaining short-term memory
    Sukbin Lim
    Persistent neural activity in the absence of a stimulus has been identified as a neural correlate of working memory, but how such activity is maintained by neocortical circuits remains unknown. Here we show that the inhibitory and excitatory microcircuitry of neocortical memory-storing regions is sufficient to implement a corrective feedback mechanism that enables persiste...
  • Emergent dynamics in a model of visual cortex
    Lai-Sang Young
    I will report on recent work which proposes that the network dynamics of the mammalian visual cortex are neither homogeneous nor synchronous but highly structured and strongly shaped by temporally localized barrages of excitatory and inhibitory firing we call `multiple-firing events' (MFEs). Our proposal is based on careful study of a network of spiking neurons built ...
  • Finite-size effects in neural networks
    Carson Chow
    The dynamics of neural networks have traditionally been analyzed for small systems or in the infinite size mean field limit. While both of these approaches have made great strides in understanding these systems, large but finite-sized networks have not been explored as much analytically. Here, I will show how the dynamical behavior of finite-sized systems can be inferred b...
  • Wandering bumps in stochastic neural fields
    Bard Ermentrout
    We study the effects of noise on stationary pulse solutions (bumps) in spatially extended neural fields. The dynamics of a neural field is described by an integrodifferential equation whose integral term characterizes synaptic interactions between neurons in different spatial locations of the network. Translationally symmetric neural fields support a continuum of stationar...
  • Detecting the many roles of inhibition in shaping sensory processing
    Daniel Butts
    Inhibition is a component of nearly every neural system, and increasingly prevalent component in theoretical network models. However, its role in sensory processing is often difficult to directly measure and/or infer. Using a nonlinear modeling framework that can infer the presence and stimulus tuning of inhibition using extracellular and intracellular recordings, I will b...
  • Capturing effective neuronal dynamics in random networks with complex topologies
    Duane Nykamp
    We introduce a random network model in which one can prescribe the frequency of second order edge motifs. We derive effective equations for the activity of spiking neuron models coupled via such networks. A key consequence of the motif-induced edge correlations is that one cannot derive closed equations for average activity of the nodes (the average firing rate neurons) bu...
  • Balanced spiking networks can implement dynamical systems with predictive coding
    Sophie Deneve
    Neural networks can integrate sensory information and generate continuously varying outputs, even though individual neurons communicate only with spikes---all-or-none events. Here we show how this can be done efficiently if spikes communicate "prediction errors" between neurons. We focus on the implementation of linear dynamical systems and derive a spiking netwo...

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