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Register a new userNoise-induced network bursts and coherence in a calcium-mediated neural network
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Noise-induced population bursting has been widely identified to play important roles in the information process. We constructed a mathematical model for a random and sparse neural network where bursting can be induced from the resting state by the global stochastic stimulus. Importantly, the noise-induced bursting dynamics of this network are mediated by calcium conductance. We use two spectral measures to evaluate the network coherence in the context of network bursts, the spike trains of all neurons and the individual bursts of all neurons. Our results show that the coherence of the network is optimized by an optimal level of stochastic stimulus, which is known as coherence resonance (CR). We also demonstrate that the interplay of calcium conductance and noise intensity can modify the degree of CR.
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We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of many individual subsystems linked by a network of interactions. As a specific example of the general theory, a model of neural network, introduced to describe the electrical activity of the cerebral cortex, is analyzed in detail: on the basis of this analysis we propose a novel definition of neuronal cascade, a physiological phenomenon of primary importance. We derive extreme value laws for the statistics of these cascades, both from the point of view of exceedances (that satisfy critical scaling theory) and of block maxima.
A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically unfeasible even in dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct approximations to network structural connectivities from network activity monitored through calcium fluorescence imaging. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time-series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the effective network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (e.g., bursting or non-bursting). We thus demonstrate how conditioning with respect to the global mean activity improves the performance of our method. [...] Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good reconstruction of the network clustering coefficient, allowing to discriminate between weakly or strongly clustered topologies, whereas on the other hand an approach based on cross-correlations would invariantly detect artificially high levels of clustering. Finally, we present the applicability of our method to real recordings of in vitro cortical cultures. We demonstrate that these networks are characterized by an elevated level of clustering compared to a random graph (although not extreme) and by a markedly non-local connectivity.
Learning latent features from time series data is an important problem in both machine learning and brain function. One approach, called Slow Feature Analysis (SFA), leverages the slowness of many salient features relative to the rapidly varying input signals. Furthermore, when trained on naturalistic stimuli, SFA reproduces interesting properties of cells in the primary visual cortex and hippocampus, suggesting that the brain uses temporal slowness as a computational principle for learning latent features. However, despite the potential relevance of SFA for modeling brain function, there is currently no SFA algorithm with a biologically plausible neural network implementation, by which we mean an algorithm operates in the online setting and can be mapped onto a neural network with local synaptic updates. In this work, starting from an SFA objective, we derive an SFA algorithm, called Bio-SFA, with a biologically plausible neural network implementation. We validate Bio-SFA on naturalistic stimuli.
The theory of communication through coherence (CTC) proposes that brain oscillations reflect changes in the excitability of neurons, and therefore the successful communication between two oscillating neural populations depends not only on the strength of the signal emitted but also on the relative phases between them. More precisely, effective communication occurs when the emitting and receiving populations are properly phase locked so the inputs sent by the emitting population arrive at the phases of maximal excitability of the receiving population. To study this setting, we consider a population rate model consisting of excitatory and inhibitory cells modelling the receiving population, and we perturb it with a time-dependent periodic function modelling the input from the emitting population. We consider the stroboscopic map for this system and compute numerically the fixed and periodic points of this map and their bifurcations as the amplitude and the frequency of the perturbation are varied. From the bifurcation diagram, we identify the phase-locked states as well as different regions of bistability. We explore carefully the dynamics emphasizing its implications for the CTC theory. In particular, we study how the input gain depends on the timing between the input and the inhibitory action of the receiving population. Our results show that naturally an optimal phase locking for CTC emerges, and provide a mechanism by which the receiving population can implement selective communication. Moreover, the presence of bistable regions, suggests a mechanism by which different communication regimes between brain areas can be established without changing the structure of the network
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