# Advanced theoretical approaches to collective network phenomena (Helias, Farkhooi)

Abstract

Collective phenomena are the heart of many dynamical properties of neuronal networks: neuronal avalanches at critical states, global oscillations, activity waves in the local field potential, correlated activity between pairs of cells in massively parallel recordings. Yet, they arise only from the concerted Interaction of many elements and are hence inherently challenging to describe and understand mathematically. Systems of similar complexity as neuronal networks have with big success been investigated in other fields of science, such as many particle physics, field theory, theory of disordered systems. Also mathematical statistics has developed powerful tools to describe stochastic processes that often form the core of neuronal network models.

We here compose a workshop of speakers who have applied methods from mathematics and statistical physics to foster our understanding of such collective states, for example using large deviation techniques, theory of disordered systems, martingales, field theory, the renormalization group and methods for many particle systems and critical phenomena. The workshop aims to reflect on and discuss the current state of these endeavors. in particular we want to point out strengths, weaknesses, and domains of application of the respective approaches, highlight recent trends and pinpoint the experimental phenomena that challenge existing theoretical models.

Recent years witnessed increased understanding of weakly correlated, stationary and oscillatory states by help of conventional perturbative methods and mean-field theory. But only rather recently, network activity has been formulated in** t**he language of statistical field theory and path Integrals [reviewed in e.g. Chow & Buice 2015, Hertz, Sollich, Roudl 2016], opening up new routes to apply powerful methods from statistical physics, field theory, and mathematics to the dynamics of neuronal networks. in particular, these tools provide means to describe neural activity beyond the population Ievel and allow Interpretations of the heterogeneity across neurons in massively parallel spike data that can nowadays be obtained by multi-electrode recordings. We now need a phase of active knowledge transfer to make maximal use of these analogies to foster progress in computational neuroscience on the challenging problem of the Interaction between large numbers of neurons.

### Schedule

Tue, Sept 12, 2017 | |

13:00 | Moritz Helias, Farzad Farkhooi, David Dahmen, Forschungszentrum Jülich, Jülich and TU Berlin, GermanyOpening remarks |

13:20 | Nicolas Brunel, University of Chicago, USAThe strong coupling limit in networks of spiking neurons with conductance-based synaptic inputs |

14:10 | John Hertz, NorditaThe Fate of False Balanced States |

15:00 | Coffee Break |

15:30 | Andrea Crisanti, University of Rome, Rome, ItalyField Theoretical Approach to Multi-Population Neuronal Networks |

16:20 | Merav Stern, Washington University, USAFootprints of learning: When mice and models of random neural networks perform a change detection task |

17:10 | Bruno Cessac, INRIA Gibbs distribution: from neural network dynamics to spike train statistics estimation |

17:30 | General discussion |

Wed, Sept 13, 2017 | |

9:00 | Alex D. Reyes, NYU, USAScaling of synaptic strength with network size: effects on Excitatory/Inhibitory balance and network dynamics |

9:45 | Viola Priesemann, MPI DS, Göttingen, Germany Inferring Network Dynamics and Topology under Spatial Subsampling |

10:30 | Coffee break |

11:00 | Wilhelm Stannat, TU Berlin, Berlin, GermanyA new approach to the derivation of mean-field theories of cortical networks with stochastic analysis |

11:45 | Barbara Bravi, Ecole Polytechnique Fédérale Lausanne, SwitzerlandExtended Plefka Expansion for Stochastic Dynamics |

12:30 | OrganizersClosing remarks on the workshop |