Mean field approximation of two coupled populations of excitable units

The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the inter-ensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains where the stationary state is stable, the scenarios for the onset and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical inter-population couplings.Comment: 5 figure

Short Conduction Delays Cause Inhibition Rather than Excitation to Favor Synchrony in Hybrid Neuronal Networks of the Entorhinal Cortex

How stable synchrony in neuronal networks is sustained in the presence of conduction delays is an open question. The Dynamic Clamp was used to measure phase resetting curves (PRCs) for entorhinal cortical cells, and then to construct networks of two such neurons. PRCs were in general Type I (all advances or all delays) or weakly type II with a small region at early phases with the opposite type of resetting. We used previously developed theoretical methods based on PRCs under the assumption of pulsatile coupling to predict the delays that synchronize these hybrid circuits. For excitatory coupling, synchrony was predicted and observed only with no delay and for delays greater than half a network period that cause each neuron to receive an input late in its firing cycle and almost immediately fire an action potential. Synchronization for these long delays was surprisingly tight and robust to the noise and heterogeneity inherent in a biological system. In contrast to excitatory coupling, inhibitory coupling led to antiphase for no delay, very short delays and delays close to a network period, but to near-synchrony for a wide range of relatively short delays. PRC-based methods show that conduction delays can stabilize synchrony in several ways, including neutralizing a discontinuity introduced by strong inhibition, favoring synchrony in the case of noisy bistability, and avoiding an initial destabilizing region of a weakly type II PRC. PRCs can identify optimal conduction delays favoring synchronization at a given frequency, and also predict robustness to noise and heterogeneity

Delay dynamics of neuromorphic optoelectronic nanoscale resonators: Perspectives and applications

With the recent exponential growth of applications using artificial intelligence (AI), the development of efficient and ultrafast brain-like (neuromorphic) systems is crucial for future information and communication technologies. While the implementation of AI systems using computer algorithms of neural networks is emerging rapidly, scientists are just taking the very first steps in the development of the hardware elements of an artificial brain, specifically neuromorphic microchips. In this review article, we present the current state of the art of neuromorphic photonic circuits based on solid-state optoelectronic oscillators formed by nanoscale double barrier quantum well resonant tunneling diodes. We address, both experimentally and theoretically, the key dynamic properties of recently developed artificial solid-state neuron microchips with delayed perturbations and describe their role in the study of neural activity and regenerative memory. This review covers our recent research work on excitable and delay dynamic characteristics of both single and autaptic (delayed) artificial neurons including all-or-none response, spike-based data encoding, storage, signal regeneration and signal healing. Furthermore, the neural responses of these neuromorphic microchips display all the signatures of extended spatio-temporal localized structures (LSs) of light, which are reviewed here in detail. By taking advantage of the dissipative nature of LSs, we demonstrate potential applications in optical data reconfiguration and clock and timing at high-speeds and with short transients. The results reviewed in this article are a key enabler for the development of high-performance optoelectronic devices in future high-speed brain-inspired optical memories and neuromorphic computing. (C) 2017 Author(s).Fundacao para a Ciencia e a Tecnologia (FCT) [UID/Multi/00631/2013]European Structural and Investment Funds (FEEI) through the Competitiveness and Internationalization Operational Program - COMPETE 2020National Funds through FCT [ALG-01-0145-FEDER-016432/POCI-01-0145-FEDER-016432]European Commission under the project iBROW [645369]project COMBINA [TEC2015-65212-C3-3-PAEI/FEDER UE]Ramon y Cajal fellowshipinfo:eu-repo/semantics/publishedVersio

Causally Investigating Cortical Dynamics and Signal Processing by Targeting Natural System Attractors With Precisely Timed (Electrical) Stimulation

Electrical stimulation is a promising tool for interacting with neuronal dynamics to identify neural mechanisms that underlie cognitive function. Since effects of a single short stimulation pulse typically vary greatly and depend on the current network state, many experimental paradigms have rather resorted to continuous or periodic stimulation in order to establish and maintain a desired effect. However, such an approach explicitly leads to forced and “unnatural” brain activity. Further, continuous stimulation can make it hard to parse the recorded activity and separate neural signal from stimulation artifacts. In this study we propose an alternate strategy: by monitoring a system in realtime, we use the existing preferred states or attractors of the network and apply short and precise pulses in order to switch between those states. When pushed into one of its attractors, one can use the natural tendency of the system to remain in such a state to prolong the effect of a stimulation pulse, opening a larger window of opportunity to observe the consequences on cognitive processing. To elaborate on this idea, we consider flexible information routing in the visual cortex as a prototypical example. When processing a stimulus, neural populations in the visual cortex have been found to engage in synchronized gamma activity. In this context, selective signal routing is achieved by changing the relative phase between oscillatory activity in sending and receiving populations (communication through coherence, CTC). In order to explore how perturbations interact with CTC, we investigate a network of interneuronal gamma (ING) oscillators composed of integrate-and-fire neurons exhibiting similar synchronization and signal routing phenomena. We develop a closed-loop stimulation paradigm based on the phase-response characteristics of the network and demonstrate its ability to establish desired synchronization states. By measuring information content throughout the model, we evaluate the effect of signal contamination caused by the stimulation in relation to the magnitude of the injected pulses and intrinsic noise in the system. Finally, we demonstrate that, up to a critical noise level, precisely timed perturbations can be used to artificially induce the effect of attention by selectively routing visual signals to higher cortical areas

Oscillations and neuronal synchronization in epilepsy: an approach based on oscillation theory and statistical mechanics.

openIn questo lavoro si propone di studiare i processi di sincronizzazione neuronale dal punto di vista dei sistemi dinamici, in particolare, della teoria delle oscillazioni. Si può dimostrare che esistono oscillazioni macroscopiche nel sistema talamocorticale dei topi epilettici. Questo fatto permette di modellare gli attacchi epilettici come processi di sincronizzazione di uno o due oscillatori auto-sostenuti, i cui parametri vengono ricavati dalle funzioni di risposta di fase ottenute sperimentalmente. Si osservano anche le cosiddette lingue di Arnold e i plateau di sincronizzazione, caratteristici della risposta di fase dei processi con un ciclo limite. Inoltre, utilizzando metodi della fisica statistica e la teoria di informazione, si ricava un rapporto fra la sincronizzazione e la quantità di informazione contenuta nelle rette funzionali del cervello. Si osserva che questa quantità di informazione è massima a livelli intermedi di sincronizzazione, in stati normali di veglia, e molto più bassa durante gli attacchi epiletticiIn this work we propose to study the neuronal synchronization processes from the point of view of the dynamical systems, in particular of the oscillations theory. It can be demonstrated that there are macroscopic oscillations in the thalamocortical network in epileptic rats. So we are able to model the epileptic seizures as synchronization processes of one or two self-sustained oscillator, whose parameters are extracted from the phase response functions obtained experimentally. We observe also the Arnold tongues and the synchronization plateau that are typical pf the phase response processes with a limit cycle. Moreover, using statistical physics and information theory methods, we obtain a relation between synchronization and quantity of information contained in the brain functional lines. This quantity of information has a peak at intermediate synchronization levels, as in conscious awareness states, and it is lower during epileptic seizures

Regenerative memory in time-delayed neuromorphic photonic resonators

We investigate a photonic regenerative memory based upon a neuromorphic oscillator with a delayed self-feedback (autaptic) connection. We disclose the existence of a unique temporal response characteristic of localized structures enabling an ideal support for bits in an optical buffer memory for storage and reshaping of data information. We link our experimental implementation, based upon a nanoscale nonlinear resonant tunneling diode driving a laser, to the paradigm of neuronal activity, the FitzHugh-Nagumo model with delayed feedback. This proof-of-concept photonic regenerative memory might constitute a building block for a new class of neuron-inspired photonic memories that can handle high bit-rate optical signals

Multistability and metastability: understanding dynamic coordination in the brain

Multistable coordination dynamics exists at many levels, from multifunctional neural circuits in vertebrates and invertebrates to large-scale neural circuitry in humans. Moreover, multistability spans (at least) the domains of action and perception, and has been found to place constraints upon, even dictating the nature of, intentional change and the skill-learning process. This paper reviews some of the key evidence for multistability in the aforementioned areas, and illustrates how it has been measured, modelled and theoretically understood. It then suggests how multistability—when combined with essential aspects of coordination dynamics such as instability, transitions and (especially) metastability—provides a platform for understanding coupling and the creative dynamics of complex goal-directed systems, including the brain and the brain–behaviour relation