Alessandro Torcini (CY Cergy Paris Université)

Next Generation Neural Mass Models

I will first give a brief overview of the next generation neural mass models, which represent a complete new perspective for the development of exact mean field models of heterogenous spiking neural networks [1]. Then I will report recent results on the application of this formalism to reproduce relevant phenomena in neuroscience ranging from cross-frequency coupling [2] to theta-nested gamma oscillations [3], from slow and fast gamma oscillations [4] to synaptic-based working memory [5]. I will finally show how these neural masses can be extended to capture fluctuations driven phenomena induced by dynamical sources of disorder, naturally present in brain circuits, such as background noise and current fluctuations due to the sparsness in the connections [6-8].

References
[1] Complete classification of the macroscopic behavior of a heterogeneous network of theta neurons, TB Luke, E Barreto, P So, Neural computation 25 (12), 3207-3234 1482013 (2013); Derivation of a neural field model from a network of theta neurons, CR Laing, Physical Review E 90 (1), 010901 (2014); Montbrió, Ernest, Diego Pazó, Alex Roxin. “Macroscopic description for networks of spiking neurons.” Physical Review X 5.2 (2015): 021028.
[2] A.Ceni, S. Olmi, AT, D. Angulo Garcia, “Cross frequency coupling in next generation inhibitory neural mass models”, Chaos , 30, 053121 (2020)
[3] M. Segneri, H.Bi, S. Olmi, AT, “Theta-nested gamma oscillations in next generation neural mass models”, Frontiers in Computational Neuroscience , 14:47 (2020)
[4] H. Bi, M. Segneri, M. di Volo, AT, “Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons”, Physical Review Research ,2, 013042 (2020)
[5] H. Taher, AT, S. Olmi, “Exact neural mass model for synaptic-based working memory”, PLOS Computational Biology , 16(12): e1008533 (2020)
[6] M. di Volo, AT, “Transition from asynchronous to oscillatory dynamics in balanced spiking networks with instantaneous synapses”, Phys. Rev. Lett. 121 , 128301 (2018)
[7] D. Goldobin, M diVolo, AT, “A reduction methodology for fluctuation driven population dynamics”, Physical Review Letters 127,038301 (2021)
[8] M. di Volo, M. Segneri, D. Goldobin, A. Politi, AT, “Coherent oscillations in balanced neural networks driven by endogenous fluctuations”, Chaos 32, 023120 (2022)

Léonie Canet (Université Grenoble Alpes)

Kardar-Parisi-Zhang universality in  exciton-polariton condensates

Since the seminal paper by Kardar, Parisi and Zhang (KPZ) in 1986 on kinetic roughening of classical growing interfaces, the KPZ equation has arisen as a fundamental model in statistical physics for non-equilibrium scaling phenomena and phase transitions. Unexpectedly, it still unfolds new branching, such as a connection with the phase dynamics of open quantum systems displaying macroscopic spontaneous coherence.

In this talk, I will first give an overview of the realm of the KPZ equation. I will then focus on exciton-polaritons. These are hybrid quasi-particles emerging in semiconductor optical cavities from the strong coupling between electronic excitations in a quantum well and cavity photons. They behave collectively as a quantum fluid, featuring a Bose-Einstein condensation, which is genuinely out-of-equilibrium  because of its driven-dissipative nature. I will explore the connection between the exciton-polariton condensate and the KPZ universality, and show that it extends well beyond the mere KPZ critical exponents. I will present results from both numerical simulations and a recent experiment.

Q. Fontaine et al, Nature 608, 687 (2022)
K. Deligiannis, D. Squizzato, A. Minguzzi, LC, EPL 132, 67004 (2021)
D. Squizzato, LC, A. Minguzzi, PRB 97, 195453 (2018)

Ada Altieri (Labo MSC, U. Paris Cité)

Evidence of glassy phases and aging dynamics in large interacting ecosystems

Many complex systems in Nature, from metabolic networks to ecosystems, appear to be poised at the edge of stability, hence displaying enormous responses to external perturbations. This marginal stability condition is often the consequence of the complex underlying interaction network, which can induce large-scale collective dynamics, and therefore critical behavior.

I will address some crucial questions, which are grabbing attention in the last few years in theoretical ecology, by focusing on the generalised Lotka-Volterra model with many randomly interacting species and finite demographic noise. Using techniques rooted in spin glasses and random matrix theory, I will unveil a very rich structure in the organisation of the equilibria and relate slow relaxation of the correlation functions to aging dynamics and glassy-like behavior [1]. I will then discuss possible extensions to non-logistic growth functions in the species abundance dynamics [2-3], which turn out to be of great interest to capture positive feedback mechanisms, notably in the case of weak and strong Allee effects [2].

[1] A. Altieri, F. Roy, C. Cammarota, G. Biroli, Phys. Rev. Lett. 126, 258301 (2021);                                      
[2] A. Altieri, G. Biroli, SciPost Physics 12, 013 (2022);
[3] I. Hatton, O. Mazzarisi, A. Altieri & M. Smerlak, submitted (2022).

Gleb Oshanin (LPTMC, Paris)

Spectral density of an individual trajectory of a Gaussian stochastic process

In this talk I will focus on the behavior of a particular random (non-local) functional - the spectral density S(f,T) (with f being the frequency and T - the observation time) of an individual random trajectory of a stochastic Gaussian process. I will first recall the textbook definition based on the covariance function of the process, and show on several examples how diverse its functional form can be depending on the spread of a process. Then, I will specify the limitations of the standard definition and will go beyond it by considering the “noise-to-signal” ratio - the ratio of the standard deviation of S(f,T) and its mean value. Next, I will prove a simple but crucial double-sided inequality obeyed by the noise-to-signal ratio for any Gaussian process, any f and any T, and eventually will derive the full probability density function of S(f,T) in most general conditions. Lastly, for several Gaussian processes I will discuss the behavior of the frequency-frequency correlations of such random variables and will demonstrate that they may be used as a robust property permitting to distinguish between normal and anomalous diffusion.

A Squarcini, E Marinari, G Oshanin, L Peliti, and L Rondoni, Noise-to-signal ratio of single-trajectory spectral densities in centered Gaussian processes, Journal of Physics A: Mathematical and Theoretical 55, 405001 (2022).
A Squarcini, E Marinari, G Oshanin, L Peliti, and L Rondoni, Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes, New Journal of Physics 24, 093031 (2022).