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 gain insight of the 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 related to stimulus-locked transient oscillations followed by a steady-state activity in the β-γ band, thus resembling what is 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 γ power increases with the number of loaded items, as reported in many experiments, while θ and β power reveal non monotonic behaviours. In particular, β and γ rhythms are crucially sustained by the inhibitory activity, while the θ rhythm is controlled by excitatory synapses.

We study the synchronization and stability of power grids within the Kuramoto phase oscillator model with inertia with a bimodal frequency distribution representing the generators and the loads. The Kuramoto model describes the dynamics of the ac voltage phase, and allows for a comprehensive understanding of fundamental network properties capturing the essential dynamical features of a power grid on coarse scales. We identify critical nodes through solitary frequency deviations and Lyapunov vectors corresponding to unstable Lyapunov exponents. To cure dangerous deviations from synchronization we propose time-delayed feedback control, which is an efficient control concept in nonlinear dynamic systems. Different control strategies are tested and compared with respect to the minimum number of controlled nodes required to achieve synchronization and Lyapunov stability. As a proof of principle, this fast-acting control method is demonstrated for different networks (the German and the Italian power transmission grid), operating points, configurations, and models. In particular an extended version of the Kuramoto model with inertia is considered, that includes the voltage dynamics, thus taking into account the interplay of amplitude and phase typical of the electrodynamical behavior of a machine.

A synaptic theory of Working Memory (WM) has been developed in the last decade to overcome several drawbacks related to the persistent spiking paradigm. Memory items are maintained in the synaptic facilitation and refreshed thanks to Population Bursts (PBs) promoted by synaptic depression. We have developed a neural mass model able to reproduce exactly the dynamics of heterogeneous spiking neural networks with short-term synaptic plasticity. This neural mass model gives access not only to the population firing rate, but also to the mean membrane potential. The latter is correlated to the Local Field Potentials and to electroencephalographic signals, usually measured during WM tasks to characterize the brain dynamics. The model is able to mimic several operations required by WM : memory loading, memory maintenance, competition of memory items and multi-item memory juggling. Memory access and loading is associated to self-sustained oscillations in the β-γ band and to transient evoked responses in the δ band, analougously to what observed in the prefrontal cortex of monkeys during object recognition tasks. More items can be stored in the WM by considering neural architectures composed by multiple excitatory populations and a common inhibitory pool. The items can be loaded and maintained at the same time: they are represented as trains of PBs with the same period, but delivered at evenly shifted phases. A memory competition is observable already by loading only two items. Depending on the stimulation features we can observe three different outcomes: maintenance of the first or second loaded item or their juggling in the memory. As reported in many experiments, the γ power increases with the number of loaded items. The power in the α-β instead shows a non monotonic behaviour. Finally, we report an expression for the maximal capacity adapted to the present model and architecture. Author summaryWorking Memory (WM) is the ability to temporary store and manipulate stimuli representations that are no longer available to the senses. WM can be represented in terms of spiking neural networks with synaptic facilitation and depression. Here, we present a neural mass model able to reproduce exactly the macroscopic dynamics of the network in terms of few collective variables. Memory items are transiently held as traces in the short-term synaptic facilitation. Memory refreshment is achieved thanks to bursts of neuronal activity controlled by synaptic depression. Memory operations are joined to June 24, 2020 1/36 sustained or transient oscillations emerging in different frequency bands, in accordance with experimental results. We show that memory maintenance of several items can be achieved thanks to periodic trains of bursts delivered by different excitatory populations at preferential phases. This model can represent the first building block for the realization of more realistic multi-layer architectures. IntroductionWorking memory (WM) is the ability to keep recently accessed information, available for manipulation: it is fundam...

Dynamics underlying epileptic seizures span multiple scales in space and time, therefore, understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. In this view, mathematical models have been developed, ranging from single neuron to neural population. In this study, we consider a neural mass model able to exactly reproduce the dynamics of heterogeneous spiking neural networks. We combine mathematical modeling with structural information from non invasive brain imaging, thus building large-scale brain network models to explore emergent dynamics and test the clinical hypothesis. We provide a comprehensive study on the effect of external drives on neuronal networks exhibiting multistability, in order to investigate the role played by the neuroanatomical connectivity matrices in shaping the emergent dynamics. In particular, we systematically investigate the conditions under which the network displays a transition from a low activity regime to a high activity state, which we identify with a seizure-like event. This approach allows us to study the biophysical parameters and variables leading to multiple recruitment events at the network level. We further exploit topological network measures in order to explain the differences and the analogies among the subjects and their brain regions, in showing recruitment events at different parameter values. We demonstrate, along with the example of diffusion-weighted magnetic resonance imaging (dMRI) connectomes of 20 healthy subjects and 15 epileptic patients, that individual variations in structural connectivity, when linked with mathematical dynamic models, have the capacity to explain changes in spatiotemporal organization of brain dynamics, as observed in network-based brain disorders. In particular, for epileptic patients, by means of the integration of the clinical hypotheses on the epileptogenic zone (EZ), i.e., the local network where highly synchronous seizures originate, we have identified the sequence of recruitment events and discussed their links with the topological properties of the specific connectomes. The predictions made on the basis of the implemented set of exact mean-field equations turn out to be in line with the clinical pre-surgical evaluation on recruited secondary networks.