title: Average synaptic activity and neural networks topology: a global inverse problem.
abstract: The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal signals are crucial for brain functioning. They strongly depend on the topology of the network and on the fluctuations of the connectivity. We propose a heterogeneous mean-field approach to neural dynamics on random networks, that explicitly preserves the disorder in the topology at growing network sizes, and leads to a set of self-consistent equations. Within this approach, we provide an effective description of microscopic and large scale temporal signals in a leaky integrate-and-fire model with short term plasticity, where quasi-synchronous events arise. Our equations provide a clear analytical picture of the dynamics, evidencing the contributions of both periodic (locked) and aperiodic (unlocked) neurons to the measurable average signal. In particular, we formulate and solve a global inverse problem of reconstructing the in-degree distribution from the knowledge of the average activity field. Our method is very general and applies to a large class of dynamical models on dense random networks.
authors.affiliation: 1] Dipartimento di Fisica e Scienza della Terra, Università di Parma, via G.P. Usberti, 7/A - 43124, Parma, Italy [2] INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A - 43124, Parma, Italy.
authors.forename: Raffaella
authors.initials: R
authors.lastname: Burioni
authors.affiliation: 1] Dipartimento di Fisica e Scienza della Terra, Università di Parma, via G.P. Usberti, 7/A - 43124, Parma, Italy [2] INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A - 43124, Parma, Italy.
authors.forename: Mario
authors.initials: M
authors.lastname: Casartelli
authors.affiliation: 1] Dipartimento di Fisica e Scienza della Terra, Università di Parma, via G.P. Usberti, 7/A - 43124, Parma, Italy [2] Centro Interdipartimentale per lo Studio delle Dinamiche Complesse, via Sansone, 1 - 50019 Sesto Fiorentino, Italy [3] INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A - 43124, Parma, Italy.
authors.forename: Matteo
authors.initials: M
authors.lastname: di Volo
authors.affiliation: 1] Dipartimento di Fisica, Università di Firenze, via Sansone, 1 - 50019 Sesto Fiorentino, Italy [2] Istituto dei Sistemi Complessi, CNR, via Madonna del Piano 10 - 50019 Sesto Fiorentino, Italy [3] INFN Sez. Firenze, via Sansone, 1 -50019 Sesto Fiorentino, Italy [4] Centro Interdipartimentale per lo Studio delle Dinamiche Complesse, via Sansone, 1 - 50019 Sesto Fiorentino, Italy.
authors.forename: Roberto
authors.initials: R
authors.lastname: Livi
authors.affiliation: 1] S3, CNR Istituto di Nanoscienze, Via Campi, 213A - 41125 Modena, Italy [2] Dipartimento di Fisica e Scienza della Terra, Università di Parma, via G.P. Usberti, 7/A - 43124, Parma, Italy.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Vezzani
mesh_terms: D000818:Animals; D003198:Computer Simulation; D006801:Humans; D008564:Membrane Potentials / Q000502:physiology; D008959:Models, Neurological; D009010:Monte Carlo Method; D009415:Nerve Net; D009474:Neurons / Q000502:physiology*; D009435:Synaptic Transmission