# Theses

## Open Theses (Applications encouraged):

## Next Generation Neural Mass Models

## A major goal of neuroscience, statistical physics and nonlinear dynamics is to understand how brain functions arise from the collective dynamics of cortical circuits. Often reported collective phenomena include oscillations, synchronous dynamics or more general rhythms, characteristic of various neural circuits [1]. Oscillations of neural activity are ubiquitous in the brain in many frequency bands and it has been argued that they play a functional role in cortical processing [2]. In particular, the mechanisms underlying the coupling between neural oscillations at different timescales have recently received much attention from experimentalists and theoreticians [3]. The most studied example of this phenomenon, usually termed cross-frequency coupling (CFC), concerns the coupling between θ and γ oscillatory activity in the rodent hippocampus [4]. Furthermore, CFC appears to be implicated in cognitive operations: multi-item representation, long-distance communication, and stimulus parsing [3].

## It has been recently suggested that simple neural architectures involving few excitatory and inhibitory populations are able to reproduce the mechanisms underlying CFC [5]. These and other evidences suggest that information is encoded in the population response and hence can be captured via macroscopic measures of the network activity [6]. The collective behavior is particularly relevant given that current brain measurement techniques, such as EEG or fMRI, provide data averaged over the activity of a large number of neurons. So far the analysis of spiking neural circuits has been mainly addressed through numerical simulations, with limitations in the maximal affordable number of neurons due to the available numerical resources. Alternatively, researchers have formulated effective mean-field representation of the neural dynamics at the level of populations, in terms of neural mass models [7]. However an extremely powerful exact method recently developed, is the Ott-Antonsen (OA) Ansatz [8], which allows us to rewrite the dynamics of fully-coupled networks of phase oscillators in terms of few collective variables in the thermodynamic limit. Only recently, a few studies, published in statistical physics journals, revealed the possibility, by applying and extending the OA Ansatz, to derive exact neural field models starting from microscopic spiking neural circuits [9,10]. This novel exact reduction methodology (ERM) allows to reproduce the collective evolution of a population of spiking Θ-neurons [11] with a few collective variables representing the firing rate and the mean membrane potential of the neuronal populations [10] or their level of synchronization [9].

## These results are particularly relevant for the neuroscience community, since the Θ-neuron is a paradigmatic model employed, for example, for the study of working memory and for the reproduction of θ-γ coupled rhythms emerging in the auditory cortex [12]. However, these theoretical results have not been yet applied to address relevant issues in neuroscience.

[1] G. Buzsaki, Rhythms of the Brain (Oxford University Press, USA, 2006), 1st ed., ISBN 0195301064.

[2] T. Womelsdorf et al., Science 316, 1609 (2007); X.-J. Wang, Physiological reviews 90, 1195 (2010).

[3] A. Hyafil, A.-L. Giraud, L. Fontolan, and B. Gutkin, Trends in neurosciences 38, 725 (2015).

[4] J. E. Lisman and O. Jensen, Neuron 77, 1002 (2013).

[5] L. Fontolan, M. Krupa, A. Hyafil, and B. Gutkin, The Journal of Mathematical Neuroscience 3, 1 (2013).

[6] B. B. Averbeck, P. E. Latham, and A. Pouget, Nature Reviews Neuroscience 7, 358 (2006).

[7] G. Deco, V. K. Jirsa, P. A. Robinson, M. Breakspear, and K. Friston, PLoS Comput Biol 4, e1000092 (2008); J. Touboul, F. Wendling, P. Chauvel, O. Faugeras, Neural computation, 23(12), 3232-86 (2011).

[8] E. Ott and T. M. Antonsen, Chaos, 18, 037113 (2008).

[9] D. Pazó and E. Montbrió, Phys. Rev. X 4, 011009 (2014); P. So, T. B. Luke, and E. Barreto,Physica D 267, 16 (2014); C. R. Laing, Phys. Rev. E 90, 010901 (2014).

[10] E. Montbrió, D. Pazó, and A. Roxin, Phys. Rev. X 5, 021028 (2015).

[11] G. Ermentrout and N. Kopell, SIAM Journal on Applied Mathematics 46, 233 (1986).

[12] M. Dipoppa and B. S. Gutkin, PNAS 110, 12828 (2013); M. Krupa, S. Gielen, and B. Gutkin, J. Comput. Neurosci. 37, 357 (2014).

Publications on this research topic:

Taher, Halgurd, Alessandro Torcini, and Simona Olmi. "Exact neural mass model for synaptic-based working memory." PLoS Computational Biology 16, no. 12 (2020): e1008533.

Ceni, Andrea, Simona Olmi, Alessandro Torcini, and David Angulo-Garcia. "Cross frequency coupling in next generation inhibitory neural mass models." Chaos: An Interdisciplinary Journal of Nonlinear Science 30, no. 5 (2020): 053121.

Segneri, Marco, Hongjie Bi, Simona Olmi, and Alessandro Torcini. "Theta-nested gamma oscillations in next generation neural mass models." Frontiers in computational neuroscience 14 (2020): 47.

## Ongoing Theses:

MSc thesis of Arturo Mariani, entitled "Latency correction in neuronal spike trains with overlapping global events", Academic course in Physics at the University of Florence

MSc thesis of Federico Senocrate, entitled "Latency correction in neuronal data", Academic course in Physics at the University of Florence

## Past Theses:

(September 2022 - April 2023) MSc Luca Governini (Academic course in Physics at the University of Firenze, thesis discussed on 20/04/23 - Mark 110/110). Thesis entitled "Propagation Patterns in Coupled Neural Mass Models with Short Term Synaptic Plasticity".

(March-September 2021) MSc thesis of Alberto Ferrara, entitled " Theory and modeling of whisking rhythm generation in the brainstem", Academic course in Physics at the University of Trieste (A.A. 2020/2021)

(October 2018-December 2021) PhD thesis of Halgurd Taher, entitled "Next Generation Neural Mass Models: working memory, all-brain modelling and multi-timescale phenomena", Inria Sophia Antipolis Research Center and École Doctorale des sciences fondamentales et appliquées, Université de la Côte d'Azur

(February-April 2019) BSc thesis of Luca Governini, entitled "Exact Macroscopic Models of Interacting Neural Populations ", Academic course in Physics at the University of Firenze

(2015-2018) PhD thesis of Eero Satuvuori, entitled "Spike train distances and neuronal coding", European Joint Degree at the University of Firenze and the Vrije Universiteit Amsterdam (VUA), Netherlands

(2015-2018) PhD thesis of Irene Malvestio, entitled "Detection of directional interactions between neurons from spike trains", European Joint Degree at the University of Firenze and the University Pompeu Fabra Barcelona, Spain

(September-April, 2017) Msc thesis in Applied Mathematics of Andrea Ceni, entitled "Exact macroscopic models of interacting neural populations", Department of Mathematics, University of Firenze (Italy)

(2013-2015) PhD thesis of Nebojsa Bozanic (Marie-Curie Fellow), entitled "Measures of Spike Train Synchrony" , Corso di Dottorato in Dinamica Nonlineare e Sistemi Complessi -- XXVIII cycle - University of Firenze

(2013-2015) PhD thesis of David Angulo Garcia (Marie-Curie Fellow), entitled "Biological Relevance of Spiking Neural networks", Corso di Dottorato in Dinamica Nonlineare e Sistemi Complessi-- XXVIII cycle - University of Firenze

(2010-2012) PhD thesis of Simona Olmi, entitled "Collective Dynamics in Complex neural networks", Corso di Dottorato in Dinamica Nonlineare e Sistemi Complessi -- XXV cycle - University of Firenze

(2010) Laurea Breve (BSc) thesis of Iacopo Di Pietro, entitled "Collective solutions in neural networks", Academic course in Physics at the University of Firenze

(2008-2009) - MSc thesis of Simona Olmi, entitled "Dynamics of diluted pulse coupled excitatory networks", Academic course in Physics at the University of Firenze

(2004-2005) - MSc thesis of Stefano Luccioli, entitled "Dynamics of realistic single neuron models", Academic course in Physics at the University of Firenze