Biology subjects

Torcini, A.

Publications and source records attributed to Torcini, A..

At least 19 recordsLinked to original sources

bioRxiv2026

Slow relaxation oscillations in multi-scale adaptive next generation neural masses

We have studied the emergence of slow relaxation oscillations in next generation neural mass models with spike frequency adaptation. Relaxation oscillations connect low firing state (Down state) to high firing state (Up state) via the slow adaptation. In the examined cases, the orbit relaxes towards the Up State via a sequence of collective damped oscillations (peaks of activity), thus revealing population bursting dynamics. The slower is the adaptation time scale the higher is the complexity (number of peaks) displayed by the relaxation oscillations. In particular, a chaos-induced spike-adding mechanism regulates the increase in the number of peaks. In analogy to what found in the Hidmarsh-Rose neuron model, two different types of chaotic behaviors have been identified: Population Spiking and Population Bursting Chaos. The increase of the adaptation strength leads to shorter (longer) Up (Down) state durations somehow mimicking the effect of charbachol in in vitro experiments, where spontaneous slow waves are observed. Indeed, the scenario depicted in [1], where an increase of the concentration of carbachol induces a transition from anesthesia-like to sleep-like dynamics is consistent with our results based on the variation of the adaptation strength. HighlightsO_LISpike Frequency Adaptation (SFA) promotes the emergence of Slow Relaxation Oscillations C_LIO_LISpike-adding mechanisms, controlled by SFA, lead to Relaxation Oscillations of increasing complexity C_LIO_LITwo types of chaotic behaviours: Population Spiking and Population Bursting Chaos C_LIO_LISFA regulates Up and Down States durations and their correlation C_LI

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bioRxiv2026

A detailed investigation of Shared Variance Component Analysis as a tool to characterize neural dimensionality

BackgroundThe relevance of spontaneous activity has been unlocked thanks to recent large scale recordings that revealed, via Shared Variance Component Analysis (SVCA), the high-dimensional nature of the ongoing activity. A fundamental problem is how the dimension modifies when more neurons are included in the analysis. Contradictory results have been reported on this subject based on SVCA and Principal Component Analysis (PCA). New MethodWe investigate pro et contra of SVCA and PCA for the identification of reliable responses encoding underlying state variables. We focus on common features of the spectra of the reliable variances (RVs) and on their dimensionality. The analysis is demonstrated on previously published Ca2+ data from the visual and the dorsal cortex in head fixed mice during spontaneous behavior. ResultsRVs grow proportionally to the number N of neurons and show a power-law decay k- with the k-th SVC dimension over a range bounded by a maximal dimension kc, initially diverging as N 1/ and then saturating at sufficiently large N. The reliable dimensionality, estimated with different methodologies, also shows a clear saturation to an asymptotic value for large N. Furthermore, its value decreases when becomes larger, as demonstrated by employing experimental data as well as theoretical predictions. ConclusionWe have shown that SVCA is an extremely effective tool to extract reliable features from the neural signals, and that the exponent represents a biomarker able to reveal the level of correlation of the neurons as well as the dimensionality of the reliable space. HighlightsO_LIAdvantages and drawbacks of Shared Variance Component Analysis to extract reliable signals from neural data C_LIO_LIComparison of different methods to estimate reliable neural dimensionality associated to spontaneous activity C_LIO_LIAnalytical expressions of embedding dimensionality for power-law decaying reliable variances C_LIO_LIBounded growth of the dimensionality with the number of neurons C_LI

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bioRxiv2025

A theory for self-sustained balanced states in absence of strong external currents

Recurrent neural networks with balanced excitation and inhibition exhibit irregular asynchronous dynamics, which is fundamental for cortical computations. Classical balance mechanisms require strong external inputs to sustain finite firing rates, raising concerns about their biological plausibility. Here, we investigate an alternative mechanism based on short-term synaptic depression (STD) acting on excitatory-excitatory synapses, which dynamically balances the network activity without the need of external inputs. By employing accurate numerical simulations and theoretical investigations we characterize the dynamics of a massively coupled network made up of N rate-neuron models. Depending on the synaptic strength J0, the network exhibits two distinct regimes: at sufficiently small J0, it converges to a homogeneous fixed point, while for sufficiently large J0, it exhibits Rate Chaos. For finite networks, we observe several different routes to chaos depending on the network realization. The width of the transition region separating the homogeneous stable solution from Rate Chaos appears to shrink for increasing N and eventually to vanish in the thermodynamic limit (N [->] {infty}). The characterization of the Rate Chaos regime performed by employing Dynamical Mean Field (DMF) approaches allow us on one side to confirm that this novel balancing mechanism is able to sustain finite irregular activity even in the thermodynamic limit, and on the other side to reveal that the balancing occurs via dynamic cancellation of the input correlations generated by the massive coupling. Our findings show that STD provides an intrinsic self-regulating mechanism for balanced networks, sustaining irregular yet stable activity without the need of biologically unrealistic inputs. This work extends the balanced network paradigm, offering insights into how cortical circuits could maintain robust dynamics via synaptic adaptation. Author summaryThe human brain is constantly active. This ongoing activity is not random but follows complex patterns that emerge from the interactions between billions of neurons. Understanding how these patterns arise is a fundamental question in neuroscience. One influential idea is that the brain maintains a delicate balance between excitatory and inhibitory signals, preventing runaway activity while allowing rich, flexible dynamics. However, classic theories for this balance mechanism often require strong external inputs to sustain realistic firing rates, which may not agree with biological observations. In this work, we propose an alternative mechanism based on a biological process called short-term synaptic depression. This process weakens excitatory-excitatory connections when neurons fire too fast, acting as a natural self-regulating mechanism. Using mathematical analysis and computer simulations, we show that this mechanism can maintain stable irregular activity, similar to that observed in the cortex, without the need of external inputs. Furthermore, we identify several different paths that our model follows to pass from stable activity to chaotic dynamics, somehow resembling the complex scenarios observed in the brain. Our findings suggest that internal synaptic adaptation may play a key role in shaping neural activity, offering new perspectives on how the brain organizes its complex dynamics.

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bioRxiv2025

Is the cortical dynamics ergodic? A numerical study in partially symmetric networks of spiking neurons

Cortical activity in-vivo displays relaxational time scales much longer than the membrane time constant of the neurons or the deactivation time of ionotropic synaptic conductances. The mechanisms responsible for such slow dynamics are not understood. Here, we show that slow dynamics naturally and robustly emerges in dynamically-balanced networks of spiking neurons. This requires only partial symmetry in the synaptic connectivity, a feature of local cortical networks observed in experiments. The symmetry generates an effective, excitatory self-coupling of the neurons that leads to long-lived fluctuations in the network activity, without destroying the dynamical balance. When the excitatory self-coupling is suitably strong, the same mechanism leads to multiple equilibrium states of the network dynamics. Our results reveal a novel dynamical regime of the collective activity in spiking networks, where the memory of the initial state persists for very long times and ergodicity is broken.

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bioRxiv2024

Emergence and long-term maintenance of modularity in plastic networks of spiking neurons

The modular and hierarchical organization of the brain is believed to support the coexistence of segregated (specialization) and integrated (binding) information processes. A relevant question is yet to understand how such architecture naturally emerges and is sustained over time, given the plastic nature of the brains wiring. Following evidences that the sensory cortices organize into assemblies under selective stimuli, it has been shown that stable neuronal assemblies can emerge due to targeted stimulation, embedding various forms of synaptic plasticity in presence of homeostatic and/or control mechanisms. Here, we show that simple spike-timing-dependent plasticity (STDP) rules, based only on pre- and post-synaptic spike times, can also lead to the stable encoding of memories in the absence of any control mechanism. We develop a model of spiking neurons, trained by stimuli targeting different sub-populations. The model satisfies some biologically plausible features: (i) it contains excitatory and inhibitory neurons with Hebbian and anti-Hebbian STDP; (ii) neither the neuronal activity nor the synaptic weights are frozen after the learning phase. Instead, the neurons are allowed to fire spontaneously while synaptic plasticity remains active. We find that only the combination of two inhibitory STDP sub-populations allows for the formation of stable modules in the network, with each sub-population playing a distinctive role. The Hebbian sub-population controls for the firing activity, while the anti-Hebbian neurons promote pattern selectivity. After the learning phase, the network settles into an asynchronous irregular resting-state. This post-learning activity is associated with spontaneous memory recalls which turn out to be fundamental for the long-term consolidation of the learned memories. Due to its simplicity, the introduced model can represent a test-bed for further investigations on the role played by STDP on memory storing and maintenance. Author summaryOne of the most remarkable qualities of the brain is its capacity to learn and adapt. How the learning process imprints and maintains memories, by shaping the architecture of connectivity among neurons in a constantly changing and dynamic environment, is a major question of neuroscience. Here, we explore the idea that the segregation of inputs received by a neural network, with inputs targeting distinct populations, is a key factor for shaping the architecture of the network. We find that the presence of inhibitory neurons is necessary for the emergence and the long-term maintenance of modularity in spiking neural networks with plasticity. In particular, we show that two different inhibitory sub-populations, one subject to Hebbian and the other to anti-Hebbian plasticity, are required to promote the formation of feedback and feed-forward inhibition circuits controlling memory consolidation. On one side, these inhibitory circuits favour long-term memory consolidation by inducing spontaneous memory recalls in the asynchronous irregular resting phase. On another side, the number of inhibitory neurons control the maximal memory capacity of the considered model.

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bioRxiv2024

Chaotic synchronization in adaptive networks of pulse-coupled oscillators

Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a robust irregular macroscopic dynamics. The resulting, strongly synchronized, regime is sustained by a homeostatic mechanism induced by the shape of the phase-response curve combined with adaptive coupling strength, included to account for energy dissipated by the pulse emission. The proposed setup mimicks a neural network composed of excitatory and inhibitory neurons.

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bioRxiv2024

Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks

A regime of coexistence of asynchronous and clustered dynamics is analyzed for globally coupled homogeneous and heterogeneous inhibitory networks of quadratic integrate-and-fire (QIF) neurons subject to Gaussian noise. The analysis is based on accurate extensive simulations and complemented by a mean-field description in terms of low-dimensional next generation neural mass models for heterogeneously distributed synaptic couplings. The asynchronous regime is observable at low noise and becomes unstable via a sub-critical Hopf bifurcation at sufficiently large noise. This gives rise to a coexistence region between the asynchronous and the clustered regime. The clustered phase is characterized by population bursts in the{gamma} -range (30-120 Hz), where neurons are split in two equally populated clusters firing in alternation. This clustering behaviour is quite peculiar: despite the global activity being essentially periodic, single neurons display switching between the two clusters due to heterogeneity and/or noise.

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bioRxiv2023

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 strenghts) 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.

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bioRxiv2023

A robust balancing mechanism for spiking neural networks

Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, in absence of strong external currents. The mechanism exploits the plasticity of excitatory-excitatory synapses induced by short-term depression. A simple self-consistent analysis accompanied by direct simulations shows the emergence and stability of a balanced asynchronous state in the thermodynamic limit. This regime is essentially fluctuation driven and characterized by highly irregular spiking dynamics of all neurons.

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bioRxiv2023

Inhibitory neurons control the consolidation of neural assemblies via adaptation to selective stimuli

Brain circuits display modular architecture at different scales of organization. Such neural assemblies are typically associated to functional specialization but the mechanisms leading to their emergence and consolidation still remain elusive. In this paper we investigate the role of inhibition in structuring new neural assemblies driven by the entrainment to various inputs. In particular, we focus on the role of partially synchronized dynamics for the creation and maintenance of structural modules in neural circuits by considering a network of excitatory and inhibitory{theta} -neurons with plastic Hebbian synapses. The learning process consists of an entrainment to temporally alternating stimuli that are applied to separate regions of the network. This entrainment leads to the emergence of modular structures. Contrary to common practice in artificial neural networks - where the acquired weights are typically frozen after the learning session - we allow for synaptic adaptation even after the learning phase. We find that the presence of inhibitory neurons in the network is crucial for the emergence and the post-learning consolidation of the modular structures. Indeed networks made of purely excitatory neurons or of neurons not respecting Dales principle are unable to form or maintain the modular architecture induced by the entrained stimuli. We also demonstrate that the number of inhibitory neurons in the network is directly related to the maximal number of neural assemblies that can be consolidated, supporting the idea that inhibition has a direct impact on the memory capacity of the neural network.

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bioRxiv2022

Hippocampal gamma oscillations form complex ensembles modulated by behavior and learning

The hippocampus and the entorhinal cortex display a rich oscillatory activity, believed to support neural information processing in key cognitive functions1. In the hippocampal region CA1, a "slow gamma" rhythm (30-80 Hz) generated in CA3 would support memory retrieval whereas a "medium gamma" rhythm (60-120 Hz) generated in the entorhinal cortex would support memory encoding2,3. However, descriptions involving discrete gamma sub-bands can only partially account for the haphazard diversity of oscillatory behaviors observed in individual recordings during spatial navigation behavior. Here, we stress that transient gamma oscillatory episodes at any frequency or phase relative to the ongoing theta (4-12 Hz) rhythm can be recorded at any layer within CA1. Eventually, the commonly reported averages are dominated by a minority of very strong power events overshadowing gamma heterogeneity. Nevertheless, we show that such gamma diversity can be naturally explained by a simple mechanistic model, and that behavior-related information (position within a maze) can be decoded from most individual gamma events, despite their low power and erratic-like nature. Our results indicate that behavior specifically shapes ensembles of irregular hippocampal gamma oscillations, in a way which evolves with learning, depends on the hippocampal layer and is hard to reconcile with the hypothesis of rigid, narrowly tuned gamma sub-bands. Beyond randomness, the pervasive gamma diversity may thus reflect complexity at the "fringe-of-synchrony"4 likely functional but invisible to classic average-based analyses.

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bioRxiv2022

Population spiking and bursting in next generation neural masses with spike-frequency adaptation

Spike-frequency adaptation (SFA) is a fundamental neuronal mechanism taking into account the fatigue due to spike emissions and the consequent reduction of the firing activity. We have studied the effect of this adaptation mechanism on the macroscopic dynamics of excitatory and inhibitory networks of quadratic integrate-and-fire (QIF) neurons coupled via exponentially decaying post-synaptic potentials. In particular, we have studied the population activities by employing an exact mean field reduction, which gives rise to next generation neural mass models. This low-dimensional reduction allows for the derivation of bifurcation diagrams and the identification of the possible macroscopic regimes emerging both in a single and in two identically coupled neural masses. In single popukations SFA favours the emergence of population bursts in excitatory networks, while it hinders tonic population spiking for inhibitory ones. The symmetric coupling of two neural masses, in absence of adaptation, leads to the emergence of macroscopic solutions with broken symmetry : namely, chimera-like solutions in the inhibitory case and anti-phase population spikes in the excitatory one. The addition of SFA leads to new collective dynamical regimes exhibiting cross-frequency coupling (CFC) among the fast synaptic time scale and the slow adaptation one, ranging from anti-phase slow-fast nested oscillations to symmetric and asymmetric bursting phenomena. The analysis of these CFC rhythms in the{theta} -{gamma} range has revealed that a reduction of SFA leads to an increase of the{theta} frequency joined to a decrease of the{gamma} one. This is analogous to what reported experimentally for the hippocampus and the olfactory cortex of rodents under cholinergic modulation, that is known to reduce SFA.

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bioRxiv2021

Coherent oscillations in balanced neural networks driven by endogenous fluctuations

We present a detailed analysis of the dynamical regimes observed in a balanced network of identical Quadratic Integrate-and-Fire (QIF) neurons with a sparse connectivity for homogeneous and heterogeneous in-degree distribution. Depending on the parameter values, either an asynchronous regime or periodic oscillations spontaneously emerge. Numerical simulations are compared with a mean field model based on a self-consistent Fokker-Planck equation (FPE). The FPE reproduces quite well the asynchronous dynamics in the homogeneous case by either assuming a Poissonian or renewal distribution for the incoming spike trains. An exact self consistent solution for the mean firing rate obtained in the limit of infinite in-degree allows identifying balanced regimes that can be either mean- or fluctuation-driven. A low-dimensional reduction of the FPE in terms of circular cumulants is also considered. Two cumulants suffice to reproduce the transition scenario observed in the network. The emergence of periodic collective oscillations is well captured both in the homogeneous and heterogeneous set-ups by the mean field models upon tuning either the connectivity, or the input DC current. In the heterogeneous situation we analyze also the role of structural heterogeneity.

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bioRxiv2021

Asynchronous and coherent dynamics in balanced excitatory-inhibitory populations

Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex. However, we will show that the E-I balance can be at the origin of other regimes observable in the brain. The analysis is performed by combining extensive simulations of sparse E-I networks composed of N spiking neurons with analytical investigations of low dimensional neural mass models. The bifurcation diagrams, derived for the neural mass model, allow to classify the possible asynchronous and coherent behaviours emerging in balanced E-I networks with structural heterogeneity for any finite in-degree K. In the limit N >> K >> 1 both supra and sub-threshold balanced asynchronous regimes can be observed in our system. Due to the heterogeneity the asynchronous states are characterized by the splitting of the neurons in three groups: silent, fluctuation and mean driven. These features are consistent with experimental observations reported for heterogeneous neural circuits. The coherent rhythms observed in our system can range from periodic and quasi-periodic collective oscillations (COs) to coherent chaos. These rhythms are characterized by regular or irregular temporal fluctuations joined to spatial coherence somehow similar to coherent fluctuations observed in the cortex over multiple spatial scales. The COs can emerge due to two different mechanisms. A first mechanism similar to the pyramidal-interneuron gamma (PING) one, usually invoked for the emergence of{gamma} -oscillations. The second mechanism is intimately related to the presence of current fluctuations, which sustain COs characterized by an essentially simultaneous bursting of the two populations. We observe period-doubling cascades involving the PING-like COs finally leading to the appearance of coherent chaos. Fluctuation driven COs are usually observable in our system as quasi-periodic collective motions characterized by two incommensurate frequencies. However, for sufficiently strong current fluctuations we report a novel mechanism of frequency locking among collective rhythms promoted by these intrinsic fluctuations. Our analysis suggest that despite PING-like or fluctuation driven COS are observable for any finite in-degree K, in the limit N >> K >> 1 these solutions finally result in two coexisting balanced regimes: an asynchronous and a fully synchronized one.

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bioRxiv2021

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 fluctuations, thus obtaining an unified mean-field formulation encompassing quenched and dynamical disorder sources.

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bioRxiv2020

Exact neural mass model for synaptic-based working memory

A synaptic theory of Working Memory (WM) has been developed in the last decade as a possible alternative to the persistent spiking paradigm. In this context, we have developed a neural mass model able to reproduce exactly the dynamics of heterogeneous spiking neural networks encompassing realistic cellular mechanisms for short-term synaptic plasticity. This population model reproduces the macroscopic dynamics of the network in terms of the firing rate and the mean membrane potential. The latter quantity allows us to get insigth on Local Field Potential and electroencephalographic signals measured during WM tasks to characterize the brain activity. More specifically synaptic facilitation and depression integrate each other to efficiently mimic WM operations via either synaptic reactivation or persistent activity. Memory access and loading are associated to stimulus-locked transient oscillations followed by a steady-state activity in the {beta}-{gamma} band, thus resembling what observed in the cortex during vibrotactile stimuli in humans and object recognition in monkeys. Memory juggling and competition emerge already by loading only two items. However more items can be stored in WM by considering neural architectures composed of multiple excitatory populations and a common inhibitory pool. Memory capacity depends strongly on the presentation rate of the items and it maximizes for an optimal frequency range. In particular we provide an analytic expression for the maximal memory capacity. Furthermore, the mean membrane potential turns out to be a suitable proxy to measure the memory load, analogously to event driven potentials in experiments on humans. Finally we show that the{gamma} power increases with the number of loaded items, as reported in many experiments, while{theta} and {beta} power reveal non monotonic behaviours. In particular, {beta} and{gamma} rhytms are crucially sustained by the inhibitory activity, while the{theta} rhythm is controlled by excitatory synapses. Author summaryWorking Memory (WM) is the ability to temporarily store and manipulate stimuli representations that are no longer available to the senses. We have developed an innovative coarse-grained population model able to mimic several operations associated to WM. The novelty of the model consists in reproducing exactly the dynamics of spiking neural networks with realistic synaptic plasticity composed of hundreds of thousands neurons in terms of a few macroscopic variables. These variables give access to experimentally measurable quantities such as local field potentials and electroencephalografic signals. Memory operations are joined to sustained or transient oscillations emerging in different frequency bands, in accordance with experimental results for primate and humans performing WM tasks. We have designed an architecture composed of many excitatory populations and a common inhibitory pool able to store and retain several memory items. The capacity of our multi-item architecture is around 3-5 items, a value corresponding to the WM capacities measured in many experiments. Furthermore, the maximal capacity is achievable only for presentation rates within an optimal frequency range. Finally, we have defined a measure of the memory load analogous to the event-related potentials employed to test humans WM capacity during visual memory tasks.

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bioRxiv2020

Theta-nested gamma oscillations in next generation neural mass models

Theta-nested gamma oscillations have been reported in many areas of the brain and are believed to represent a fundamental mechanism to transfer information across spatial and temporal scales. In a series of recent experiments in vitro it has been possible to replicate with an optogenetic theta frequency stimulation several features of cross-frequency coupling (CFC) among theta and gamma rhythms observed in behaving animals. In order to reproduce the main findings of these experiments we have considered a new class of neural mass models able to reproduce exactly the macroscopic dynamics of spiking neural networks. In this framework, we have examined two set-ups able to support collective gamma oscillations: namely, the pyramidal interneuronal network gamma (PING) and the interneuronal network gamma (ING). In both set-ups we observe the emergence of theta-nested gamma oscillations by driving the system with a sinusoidal theta-forcing in proximity of a Hopf bifurcation. These mixed rhythms display always phase amplitude coupling. However two different types of nested oscillations can be identified: one characterized by a perfect phase locking between theta and gamma rhythms, corresponding to an overall periodic behaviour; another one where the locking is imperfect and the dynamics is quasi-periodic or even chaotic. From our analysis it emerges that the locked states are more frequent in the ING set-up. In agreement with the experiments, we find theta-nested gamma oscillations for forcing frequencies in the range [1:10] Hz, whose amplitudes grow proportionally to the forcing one and which are clearly modulated by the theta phase. Furthermore, analogously to the experiments, the gamma power and the frequency of the gamma-power peak increase with the forcing amplitude. At variance with experimental findings, the gamma-power peak does not shift to higher frequencies by increasing the theta frequency. This effect can be obtained, in or model, only by incrementing, at the same time, also the noise or the forcing amplitude. On the basis of our analysis both the PING and ING mechanisms give rise to theta-nested gamma oscillations with almost identical features.

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bioRxiv2019

Quantitative and qualitative analysis of asynchronous neural activity

The activity of a sparse network of leaky integrate-and-fire neurons is carefully revisited with reference to a regime of a bona-fide asynchronous dynamics. The study is preceded by a finite-size scaling analysis, carried out to identify a setup where collective synchronization is negligible. The comparison between quenched and annealed networks reveals the emergence of substantial differences when the coupling strength is increased, via a scenario somehow reminiscent of a phase transition. For sufficiently strong synaptic coupling, quenched networks exhibit a highly bursting neural activity, well reproduced by a self-consistent approach, based on the assumption that the input synaptic current is the superposition of independent renewal processes. The distribution of interspike intervals turns out to be relatively long-tailed; a crucial feature required for the self-sustainment of the bursting activity in a regime where neurons operate on average (much) below threshold. A semi-quantitative analogy with Ornstein-Uhlenbeck processes helps validating this interpretation. Finally, an alternative explanation in terms of Poisson processes is offered under the additional assumption of mutual correlations among excitatory and inhibitory spikes.

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