1,721,006 research outputs found
Biologically Realistic Mean-Field Models of Conductance-Based Networks of Spiking Neurons with Adaptation
No full textAccurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas
Microscopic mechanism for self-organized quasiperiodicity in random networks of nonlinear oscillators
No full textSelf-organized quasiperiodicity is one of the most puzzling dynamical phases observed in systems of nonlinear 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 quasiperiodicity, and we showhowcomplex 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
Synchronization and long-time memory in neural networks with inhibitory hubs and synaptic plasticity
No full textWe 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 fI and their connectivity level to investigate the cooperation between hub features and inhibition. We show that, depending on fI, 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
Average synaptic activity and neural networks topology: a global inverse problem
No full textThe 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
State-dependent mean-field formalism to model different activity states in conductance-based networks of spiking neurons
No full textMore interest has been shown in recent years to large-scale spiking simulations of cerebral neuronal networks, coming both from the presence of high-performance computers and increasing details in experimental observations. In this context it is important to understand how population dynamics are generated by the designed parameters of the networks, which is the question addressed by mean-field theories. Despite analytic solutions for the mean-field dynamics already being proposed for current-based neurons (CUBA), a complete analytic description has not been achieved yet for more realistic neural properties, such as conductance-based (COBA) network of adaptive exponential neurons (AdEx). Here, we propose a principled approach to map a COBA on a CUBA. Such an approach provides a state-dependent approximation capable of reliably predicting the firing-rate properties of an AdEx neuron with noninstantaneous COBA integration. We also applied our theory to population dynamics, predicting the dynamical properties of the network in very different regimes, such as asynchronous irregular and synchronous irregular (slow oscillations). This result shows that a state-dependent approximation can be successfully introduced to take into account the subtle effects of COBA integration and to deal with a theory capable of correctly predicting the activity in regimes of alternating states like slow oscillations
Chaos and Correlated Avalanches in Excitatory Neural Networks with Synaptic Plasticity
No full textA 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 quasisynchronous 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 period doubling transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaotic phase with avalanches exhibits a spontaneous emergence of persistent 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
Heterogeneous mean field for neural networks with short-term plasticity
No full textWe 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 use of a heterogeneous mean-field formulation of the model that is able to reproduce dynamical phases characterized by the presence of quasisynchronous 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
Dynamics, synchronization and inverse problem in mean field neural networks with synaptic plasticity
No full textThis thesis regards the dynamics of neural ensembles, investigated through mathematical models. When the parameters defining the dynamics of single elements are inhomogeneous, i.e. disorder is present in the system, the model taken under consideration is able to reproduce a wide range of dynamical phases, typically observed in experiments. After describing the dynamical regimes of the model, it is proposed an heterogeneous mean–field approach to neural dynamics on random networks, that explicitly preserves the disorder on the parameters of the system at growing network sizes, and leads to a set of self-consistent equations. Within this approach, an effective description of microscopic and large scale temporal signals is provided. The mean field equations provide a clear analytical picture of the dynamics and can be applied in presence of disorder on network structure or on other parameters of the model. A great advantage of the mean field model is the possibility to formulate and solve a global inverse problem of reconstructing the in-degree distribution of the network from the knowledge of the average activity field detected from a finite size sample. Furthermore, the method applies in presence of inhibitory neurons, reconstructing also the fraction of inhibitory neurons from the knowledge of the only global activity field. The method is very general and applies to a large class of dynamical models on dense random networks
Dynamics, synchronization and inverse problem in mean field neural networks with synaptic plasticity
No full textThis thesis regards the dynamics of neural ensembles, investigated through mathematical models. When the parameters defining the dynamics of single elements are inhomogeneous, i.e. disorder is present in the system, the model taken under consideration is able to reproduce a wide range of dynamical phases, typically observed in experiments. After describing the dynamical regimes of the model, it is proposed an heterogeneous mean–field approach to neural dynamics on random networks, that explicitly preserves the disorder on the parameters of the system at growing network sizes, and leads to a set of self-consistent equations. Within this approach, an effective description of microscopic and large scale temporal signals is provided. The mean field equations provide a clear analytical picture of the dynamics and can be applied in presence of disorder on network structure or on other parameters of the model. A great advantage of the mean field model is the possibility to formulate and solve a global inverse problem of reconstructing the in-degree distribution of the network from the knowledge of the average activity field detected from a finite size sample. Furthermore, the method applies in presence of inhibitory neurons, reconstructing also the fraction of inhibitory neurons from the knowledge of the only global activity field. The method is very general and applies to a large class of dynamical models on dense random networks
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