B. Cessac, H. Rostro, J. C. Vasquez, T. Viéville
We introduce a mathematical framework where the statistics of spikes trains, produced by neural networks evolving under synaptic plasticity, can be analysed.
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In an all-to-all network of integrate-fire oscillators in which there is a disorder in the intrinsic firing rates of the neurons, we show that through spike timing-dependent plasticity the links which have the faster oscillators as presynaptic, tend to be strengthened while the links originated from the slow spiking neurons are weakened. The emergent effective flow of directed connections, introduces the faster neurons as the more influent elements in the network and facilitates synchronization by decreasing the synaptic cost for onset of synchronization.
Models of learning typically focus on synaptic plasticity. However, learning is the result of both synaptic and myelin plasticity. Specifically, synaptic changes often co-occur and interact with myelin changes, leading to complex dynamic interactions between these processes. Here, we investigate the implications of these interactions for the coupling behavior of a system of Kuramoto oscillators. To that end, we construct a fully connected, one-dimensional ring network of phase oscillators whose coupling strength (reflecting synaptic strength) as well as conduction velocity (reflecting myelinat…
We explore both analytically and numerically an ensemble of coupled phase-oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time-delay (due to finite signal-propagation speeds) and network plasticity (via dynamic coupling constants) inspired by the Hebbian learning rule in neuroscience. When time-delay and learning effects combine, novel synchronization phenomena are observed. We investigate the formation of spatio-temporal patterns in both one- and two-dimensional oscillator lattices with periodic boundary conditions and comment…
A 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 quasi-synchronous 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 doubling-period transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaot…
Generalized Wilson-Cowan model with short term synaptic plasticity
本文提出了一种考虑短时突触可塑性的广义威尔逊-科温模型，通过绝热消除快速变量简化了兴奋性与抑制性神经元的耦合相互作用，并在适当极限下收敛到基准模型，识别了可用资源群体的极限环振荡。
Synaptic bundle theory for spike-driven sensor-motor system: More than eight independent synaptic bundles collapse reward-STDP learning
该研究提出通过调节突触束数量来解决尖峰驱动传感器-运动系统中学习崩溃的问题，揭示了突触束数量与学习成功和失败之间的定量关系。
This work introduces a methodology for studying synchronization in adaptive networks with heterogeneous plasticity (adaptation) rules. As a paradigmatic model, we consider a network of adaptively coupled phase oscillators with distance-dependent adaptations. For this system, we extend the master stability function approach to adaptive networks with heterogeneous adaptation. Our method allows for separating the contributions of network structure, local node dynamics, and heterogeneous adaptation in determining synchronization. Utilizing our proposed methodology, we explain mechanisms leading to…
Large networks of spiking neurons show abrupt changes in their collective dynamics resembling phase transitions studied in statistical physics. An example of this phenomenon is the transition from irregular, noise-driven dynamics to regular, self-sustained behavior observed in networks of integrate-and-fire neurons as the interaction strength between the neurons increases. In this work we show how a network of spiking neurons is able to self-organize towards a critical state for which the range of possible inter-spike-intervals (dynamic range) is maximized. Self-organization occurs via synapti…
Neuronal avalanches measured in vitro and in vivo in different cortical networks consistently exhibit power law behaviour for the size and duration distributions with exponents typical for a mean field self-organized branching process. These exponents are also recovered in neuronal network simulations implementing various neuronal dynamics on different network topologies. They can therefore be considered a very robust feature of spontaneous neuronal activity. Interestingly, this scaling behaviour is also observed on regular lattices in finite dimensions, which raises the question about the ori…
The small-world property in the context of complex networks implies structural benefits to the processes taking place within a network, such as optimal information transmission and robustness. In this paper, we study a model network of integrate-and-fire neurons that are subject to activity-dependent synaptic plasticity. We find the learning rule that gives rise to a small-world structure when the collective dynamics of the system reaches a critical state which is characterised by power-law distributions of activity clusters. Moreover, by analysing the motif profile of the networks, we observe…
We examine the hypothesis, that short-term synaptic plasticity (STSP) may generate self-organized motor patterns. We simulated sphere-shaped autonomous robots, within the LPZRobots simulation package, containing three weights moving along orthogonal internal rods. The position of a weight is controlled by a single neuron receiving excitatory input from the sensor, measuring its actual position, and inhibitory inputs from the other two neurons. The inhibitory connections are transiently plastic, following physiologically inspired STSP-rules. We find that a wide palette of motion patterns are ge…
Neurons regulate the distribution of signaling components across an extended tree-like cellular structure using both local and global feedback control. This is hypothesized to allow homeostatic control of the electrical activity of a neuron and at the same time enable normalization of distribution of inputs received from other cells. The performance and robustness of these mechanisms are poorly understood, and are subject to nonlinearities, making their analysis difficult. Firstly, we formally show that global homeostasis of electrical activity and local activity-dependent degradation can coex…
Reservoir Computing (RC) is an appealing approach in Machine Learning that combines the high computational capabilities of Recurrent Neural Networks with a fast and easy training method. Likewise, successful implementation of neuro-inspired plasticity rules into RC artificial networks has boosted the performance of the original models. In this manuscript, we analyze the role that plasticity rules play on the changes that lead to a better performance of RC. To this end, we implement synaptic and non-synaptic plasticity rules in a paradigmatic example of RC model: the Echo State Network. Testing…
Coherence resonance (CR), stochastic synchronization (SS), and spike-timing-dependent plasticity (STDP) are ubiquitous dynamical processes in biological neural networks. Whether there exists an optimal network and STDP configuration at which CR and SS are both pronounced is a fundamental question of interest that is still elusive. We expect such a configuration to enable the brain to make synergistic and optimal use of these phenomena to process information efficiently. This paper considers a small-world network of excitable Hodgkin-Huxley neurons driven by channel noise and STDP with an asymm…
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