arXiv subjects

Matteo di Volo

Publications and source records attributed to Matteo di Volo.

16 recordsLinked to original sources

arXiv2025

Synaptic shot-noise triggers fast and slow global oscillations in balanced neural networks

Neural dynamics is determined by the transmission of discrete synaptic pulses (synaptic shot-noise) among neurons. However, the neural responses are usually obtained within the diffusion approximation modeling synaptic inputs as continuous Gaussian noise. Here, we present a rigorous mean-field theory that encompasses synaptic shot-noise for sparse balanced inhibitory neural networks driven by an excitatory drive. Our theory predicts new dynamical regimes, in agreement with numerical simulations, which are not captured by the classical diffusion approximation. Notably, these regimes feature self-sustained global oscillations emerging at low connectivity (in-degree) via either continuous or hysteretic transitions and characterized by irregular neural activity, as expected for balanced dynamics. For sufficiently weak (strong) excitatory drive (inhibitory feedback) the transition line displays a peculiar re-entrant shape revealing the existence of global oscillations at low and high in-degrees, separated by an asynchronous regime at intermediate levels of connectivity. The mechanisms leading to the emergence of these global oscillations are distinct: drift-driven at high connectivity and cluster activation at low connectivity. The frequency of these two kinds of global oscillations can be varied from slow (around 1 Hz) to fast (around 100 Hz), without altering their microscopic and macroscopic features, by adjusting the excitatory drive and the synaptic inhibition strength in a prescribed way. Furthermore, the cluster-activated oscillations at low in-degrees could correspond to the gamma rhythms reported in mammalian cortex and hippocampus and attributed to ensembles of inhibitory neurons sharing few synaptic connections [G. Buzsaki and X.-J. Wang, Annual Review of Neuroscience 35, 203 (2012)].

cond-mat.dis-nn↗

arXiv2023

Discrete synaptic events induce global oscillations in balanced neural networks

Neural dynamics is triggered by discrete synaptic inputs of finite amplitude. However, the neural response is usually obtained within the diffusion approximation (DA) representing the synaptic inputs as Gaussian noise. We derive a mean-field formalism encompassing synaptic shot-noise for sparse balanced networks of spiking neurons. For low (high) external drives (synaptic strengths) irregular global oscillations emerge via continuous and hysteretic transitions, correctly predicted by our approach, but not from the DA. These oscillations display frequencies in biologically relevant bands.

q-bio.NC↗

arXiv2023

A new generation of reduction methods for networks of neurons with complex dynamic phenotypes

Collective dynamics of spiking networks of neurons has been of central interest to both computation neuroscience and network science. Over the past years a new generation of neural population models based on exact reductions (ER) of spiking networks have been developed. However, most of these efforts have been limited to networks of neurons with simple dynamics (e.g. the quadratic integrate and fire models). Here, we present an extension of ER to conductance-based networks of two-dimensional Izhikevich neuron models. We employ an adiabatic approximation, which allows us to analytically solve the continuity equation describing the evolution of the state of the neural population and thus to reduce model dimensionality. We validate our results by showing that the reduced mean-field description we derived can qualitatively and quantitatively describe the macroscopic behaviour of populations of two-dimensional QIF neurons with different electrophysiological profiles (regular firing, adapting, resonator and type III excitable). Most notably, we apply this technique to develop an ER for networks of neurons with bursting dynamics.

q-bio.NC↗

arXiv2021

Order symmetry breaking and broad distribution of events in spiking neural networks with continuous membrane potential

We introduce an exactly integrable version of the well-known leaky integrate-and-fire (LIF) model, with continuous membrane potential at the spiking event, the c-LIF. We investigate the dynamical regimes of a fully connected network of excitatory c-LIF neurons in the presence of short-term synaptic plasticity. By varying the coupling strength among neurons, we show that a complex chaotic dynamics arises, characterized by scale free avalanches. The origin of this phenomenon in the c-LIF can be related to the order symmetry breaking in neurons spike-times, which corresponds to the onset of a broad activity distribution. Our analysis uncovers a general mechanism through which networks of simple neurons can be attracted to a complex basin in the phase space.

q-bio.NC↗

arXiv2021

A reduction methodology for fluctuation driven population dynamics

Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions, due to the divergence of all the moments (cumulants). We have solved this problem by introducing a `pseudo-cumulants' expansion. This allows us to develop a reduction methodology for heterogeneous spiking neural networks subject to extrinsinc and endogenous noise sources, thus generalizing the mean-field formulation introduced in [E. Montbrió et al., Phys. Rev. X 5, 021028 (2015)].

cond-mat.stat-mech↗

arXiv2020

Optimal responsiveness and collective oscillations emerging from the heterogeneity of inhibitory neurons

The brain is characterized by a strong heterogeneity of inhibitory neurons. We report that spiking neural networks display a resonance to the heterogeneity of inhibitory neurons, with optimal input/output responsiveness occurring for levels of heterogeneity similar to that found experimentally in cerebral cortex. A heterogeneous mean-field model predicts such optimal responsiveness. Moreover, we show that new dynamical regimes emerge from heterogeneity that were not present in the equivalent homogeneous system, such as sparsely synchronous collective oscillations.

q-bio.NC↗

arXiv2019

Cholinergic switch between two types of slow waves in cerebral cortex

Sleep slow waves are known to participate in memory consolidation, yet slow waves occurring under anesthesia present no positive effects on memory. Here, we shed light onto this paradox, based on a combination of extracellular recordings in vivo, in vitro, and computational models. We find two types of slow waves, based on analyzing the temporal patterns of successive slow-wave events. The first type is consistently observed in natural slow-wave sleep, while the second is shown to be ubiquitous under anesthesia. Network models of spiking neurons predict that the two slow wave types emerge due to a different gain on inhibitory vs excitatory cells and that different levels of spike-frequency adaptation in excitatory cells can account for dynamical distinctions between the two types. This prediction was tested in vitro by varying adaptation strength using an agonist of acetylcholine receptors, which demonstrated a neuromodulatory switch between the two types of slow waves. Finally, we show that the first type of slow-wave dynamics is more sensitive to external stimuli, which can explain how slow waves in sleep and anesthesia differentially affect memory consolidation, as well as provide a link between slow-wave dynamics and memory diseases.

q-bio.NC↗

arXiv2019

Inferring network structure and local dynamics from neuronal patterns with quenched disorder

An inverse procedure is proposed and tested which aims at recovering the a priori unknown functional and structural information from global signals of living brains activity. To this end we consider a Leaky-Integrate and Fire (LIF) model with short term plasticity neurons, coupled via a directed network. Neurons are assigned a specific current value, which is heterogenous across the sample, and sets the firing regime in which the neuron is operating in. The aim of the method is to recover the distribution of incoming network degrees, as well as the distribution of the assigned currents, from global field measurements. The proposed approach to the inverse problem implements the reductionist Heterogenous Mean-Field approximation. This amounts in turn to organizing the neurons in different classes, depending on their associated degree and current. When tested again synthetic data, the method returns accurate estimates of the sought distributions, while managing to reproduce and interpolate almost exactly the time series of the supplied global field. Finally, we also applied the proposed technique to longitudinal wide-field fluorescence microscopy data of cortical functionality in groups of awake Thy1-GCaMP6f mice. Mice are induced a photothrombotic stroke in the primary motor cortex and their recovery monitored in time. An all-to-all LIF model which accommodates for currents heterogeneity allows to adequately explain the recorded patterns of activation. Altered distributions in neuron excitability are in particular detected, compatible with the phenomenon of hyperexcitability in the penumbra region after stroke.

cond-mat.dis-nn↗

arXiv2019

Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons

Oscillations are a hallmark of neural population activity in various brain regions with a spectrum covering a wide range of frequencies. Within this spectrum gamma oscillations have received particular attention due to their ubiquitous nature and to their correlation with higher brain functions. Recently, it has been reported that gamma oscillations in the hippocampus of behaving rodents are segregated in two distinct frequency bands: slow and fast. These two gamma rhythms correspond to dfferent states of the network, but their origin has been not yet clarified. Here, we show theoretically and numerically that a single inhibitory population can give rise to coexisting slow and fast gamma rhythms corresponding to collective oscillations of a balanced spiking network. The slow and fast gamma rhythms are generated via two different mechanisms: the fast one being driven by the coordinated tonic neural firing and the slow one by endogenous fluctuations due to irregular neural activity. We show that almost instantaneous stimulations can switch the collective gamma oscillations from slow to fast and vice versa. Furthermore, to make a closer contact with the experimental observations, we consider the modulation of the gamma rhythms induced by a slower (theta) rhythm driving the network dynamics. In this context, depending on the strength of the forcing, we observe phase-amplitude and phase-phase coupling between the fast and slow gamma oscillations and the theta forcing. Phase-phase coupling reveals different theta-phases preferences for the two coexisting gamma rhythms.

q-bio.NC↗

arXiv2018

Transition from asynchronous to oscillatory dynamics in balanced spiking networks with instantaneous synapses

We report a transition from asynchronous to oscillatory behaviour in balanced inhibitory networks for class I and II neurons with instantaneous synapses. Collective oscillations emerge for sufficiently connected networks. Their origin is understood in terms of a recently developed mean-field model, whose stable solution is a focus. Microscopic irregular firings, due to balance, trigger sustained oscillations by exciting the relaxation dynamics towards the macroscopic focus. The same mechanism induces in balanced excitatory-inhibitory networks quasi-periodic collective oscillations.

cond-mat.dis-nn↗

arXiv2018

State equation from the spectral structure of human brain activity

Neural electromagnetic (EM) signals recorded non-invasively from individual human subjects vary in complexity and magnitude. Nonetheless, variation in neural activity has been difficult to quantify and interpret, due to complex, broad-band features in the frequency domain. Studying signals recorded with magnetoencephalography (MEG) from healthy young adult subjects while in resting and active states, a systematic framework inspired by thermodynamics is applied to neural EM signals. Despite considerable inter-subject variation in terms of spectral entropy and energy across time epochs, data support the existence of a robust and linear relationship defining an effective state equation, with higher energy and lower entropy in the resting state compared to active, consistently across subjects. Mechanisms underlying the emergence of relationships between empirically measured effective state functions are further investigated using a model network of coupled oscillators, suggesting an interplay between noise and coupling strength can account for coherent variation of empirically observed quantities. Taken together, the results show macroscopic neural observables follow a robust, non-trivial conservation rule for energy modulation and information generation.

q-bio.NC↗

arXiv2017

Chaos and correlated avalanches in excitatory neural networks with synaptic plasticity

A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram exhibits two transitions from quasi-synchronous and asynchronous regimes to the nontrivial, collective, bursty regime with avalanches. In the homogeneous case without disorder, the system synchronizes and the bursty behavior is reflected into a doubling-period transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaotic phase with avalanches exhibits a spontaneous emergence of time correlations and enhanced Kolmogorov complexity. Our analysis reveals a mechanism for the generation of irregular avalanches that emerges from the combination of disorder and deterministic underlying chaotic dynamics.

cond-mat.dis-nn↗

arXiv2017

Synchronization and long-time memory in neural networks with inhibitory hubs and synaptic plasticity

We investigate the dynamical role of inhibitory and highly connected nodes (hub) in synchronization and input processing of leaky-integrate-and-fire neural networks with short term synaptic plasticity. We take advantage of a heterogeneous mean-field approximation to encode the role of network structure and we tune the fraction of inhibitory neurons $f_I$ and their connectivity level to investigate the cooperation between hub features and inhibition. We show that, depending on $f_I$, highly connected inhibitory nodes strongly drive the synchronization properties of the overall network through dynamical transitions from synchronous to asynchronous regimes. Furthermore, a metastable regime with long memory of external inputs emerges for a specific fraction of hub inhibitory neurons, underlining the role of inhibition and connectivity also for input processing in neural networks.

cond-mat.dis-nn↗

arXiv2014

A microscopic mechanism for self-organized quasi periodicity in random networks of non linear oscillators

Self-organized quasi periodicity is one of the most puzzling dynamical phases observed in systems of non linear coupled oscillators. The single dynamical units are not locked to the periodic mean field they produce, but they still feature a coherent behavior, through an unexplained complex form of correlation. We consider a class of leaky integrate-and-fire oscillators on random sparse and massive networks with dynamical synapses, featuring self-organized quasi periodicity, and we show how complex collective oscillations arise from constructive interference of microscopic dynamics. In particular, we find a simple quantitative relationship between two relevant microscopic dynamical time scales and the macroscopic time scale of the global signal. We show that the proposed relation is a general property of collective oscillations, common to all the partially synchronous dynamical phases analyzed. We argue that an analogous mechanism could be at the origin of similar network dynamics.

cond-mat.dis-nn↗

arXiv2014

Heterogeneous Mean Field for neural networks with short term plasticity

We report about the main dynamical features of a model of leaky-integrate-and fire excitatory neurons with short term plasticity defined on random massive networks. We investigate the dynamics by a Heterogeneous Mean-Field formulation of the model, that is able to reproduce dynamical phases characterized by the presence of quasi-synchronous events. This formulation allows one to solve also the inverse problem of reconstructing the in-degree distribution for different network topologies from the knowledge of the global activity field. We study the robustness of this inversion procedure, by providing numerical evidence that the in-degree distribution can be recovered also in the presence of noise and disorder in the external currents. Finally, we discuss the validity of the heterogeneous mean-field approach for sparse networks, with a sufficiently large average in-degree.

cond-mat.dis-nn↗

arXiv2014

Average synaptic activity and neural networks topology: a global inverse problem

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.

cond-mat.dis-nn↗