Timothy D. Oleskiw, Wyeth Bair, Eric Shea-Brown, Nicolas Brunel
We compute the firing rate of a leaky integrate-and-fire (LIF) neuron with stochastic conductance-based inputs in the limit when synaptic decay times are much shorter than the membrane time constant. A comparison of our analytical results to numeric simulations is presented for a range of biophysically-realistic parameters.
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We derive analytical formulae for the firing rate of integrate-and-fire neurons endowed with realistic synaptic dynamics. In particular we include the possibility of multiple synaptic inputs as well as the effect of an absolute refractory period into the description.
Heterogeneity of firing rate statistics is known to have severe consequences on neural coding. Recent experimental recordings in weakly electric fish indicate that the distribution-width of superficial pyramidal cell firing rates (trial- and time-averaged) in the electrosensory lateral line lobe (ELL) depends on the stimulus, and also that network inputs can mediate changes in the firing rate distribution across the population. We previously developed theoretical methods to understand how two attributes (synaptic and intrinsic heterogeneity) interact and alter the firing rate distribution in a…
Two recent experimental observations pose a challenge to many cortical models. First, the activity in the auditory cortex is sparse, and firing rates can be described by a lognormal distribution. Second, the distribution of non-zero synaptic strengths between nearby cortical neurons can also be described by a lognormal distribution. Here we use a simple model of cortical activity to reconcile these observations. The model makes the experimentally testable prediction that synaptic efficacies onto a given cortical neuron are statistically correlated, i.e. it predicts that some neurons receive ma…
We investigate numerically the collective dynamical behavior of pulse-coupled non-leaky integrate-and-fire-neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for spontaneous firing for each neuron. We study network dynamics evolving from different sets of initial conditions in dependence on coupling strength and rewiring probability. Beside a homogeneous equilibrium state for low coupling strength, we observe different local patterns including cyclic waves, spiral waves, and turbulent-like patterns, which -- depending on netw…
We investigated the influence of efficacy of synaptic interaction on firing synchronization in excitatory neuronal networks. We found spike death phenomena, namely, the state of neurons transits from limit cycle to fixed point or transient state. The phenomena occur under the perturbation of excitatory synaptic interaction that has a high efficacy. We showed that the decrease of synaptic current results in spike death through depressing the feedback of sodium ionic current. In the networks with spike death property the degree of synchronization is lower and unsensitive to the heterogeneity of …
We studied the impact of a dynamical threshold on the f-I curve-the relationship between the input and the firing rate of a neuron-in the presence of background synaptic inputs. First, we found that, while the leaky integrate-and-fire model cannot reproduce the f-I curve of a cortical neuron, the leaky integrate-and-fire model with dynamical threshold can reproduce it very well. Second, we found that the dynamical threshold modulates the onset and the asymptotic behavior of the f-I curve. These results suggest that a cortical neuron has an adaptation mechanism and that the dynamical threshold …
The representation of the natural-density, heterogeneous connectivity of neuronal network models at relevant spatial scales remains a challenge for Computational Neuroscience and Neuromorphic Computing. In particular, the memory demands imposed by the vast number of synapses in brain-scale network simulations constitutes a major obstacle. Limiting the number resolution of synaptic weights appears to be a natural strategy to reduce memory and compute load. In this study, we investigate the effects of a limited synaptic-weight resolution on the dynamics of recurrent spiking neuronal networks res…
We examine the effects of stochastic input currents on the firing behavior of two excitable neurons coupled with fast excitatory synapses. In such cells (models), typified by the quadratic integrate and fire model, mutual synaptic coupling can cause sustained firing or oscillatory behavior which is necessarily antiphase. Additive Gaussian white noise can transiently terminate the oscillations, hence destroying the stable limit cycle. Further application of the noise may return the system to spiking activity. In a particular noise range, the transition times between the oscillating and the rest…
In timing-based neural codes, neurons have to emit action potentials at precise moments in time. We use a supervised learning paradigm to derive a synaptic update rule that optimizes via gradient ascent the likelihood of postsynaptic firing at one or several desired firing times. We find that the optimal strategy of up- and downregulating synaptic efficacies can be described by a two-phase learning window similar to that of Spike-Timing Dependent Plasticity (STDP). If the presynaptic spike arrives before the desired postsynaptic spike timing, our optimal learning rule predicts that the synapse…
We show that the stochastic Morris-Lecar neuron, in a neighborhood of its stable point, can be approximated by a two-dimensional Ornstein-Uhlenbeck (OU) modulation of a constant circular motion. The associated radial OU process is an example of a leaky integrate-and-fire (LIF) model prior to firing. A new model constructed from a radial OU process together with a simple firing mechanism based on detailed Morris-Lecar firing statistics reproduces the Morris-Lecar Interspike Interval (ISI) distribution, and has the computational advantages of a LIF. The result justifies the large amount of atten…
Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre-synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post-synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Our results are not limited to stimul…
Strong inhibitory input to neurons, which occurs in balanced states of neural networks, increases synaptic current fluctuations. This has led to the assumption that inhibition contributes to the high spike-firing irregularity observed in vivo. We used single compartment neuronal models with time-correlated (due to synaptic filtering) and state-dependent (due to reversal potentials) input to demonstrate that inhibitory input acts to decrease membrane potential fluctuations, a result that cannot be achieved with simplified neural input models. To clarify the effects on spike-firing regularity, w…
An Analytically Solvable Model of Firing Rate Heterogeneity in Balanced State Networks
针对皮层回路放电率分布缺乏数学可处理性的问题，基于 Gauss-Rice 神经元模型提出一种可精确计算放电率分布的平衡态皮层回路模型，支持多群体与多突触受体，为理解单神经元及突触特性对放电率分布的影响奠定基础。
Linear and non-linear integrate-and-fire neurons driven by synaptic shot noise with reversal potentials
本研究针对带反转电位的突触散粒噪声驱动的两类积分放电神经元模型，推导了指数分布电导下群体主方程的简化形式，结合解析与数值方法，为突触模型的比较研究提供支持。
Using a realistic model of activity dependent dynamical synapses and a standard integrate and fire neuron model we study, both analytically and numerically, the conditions in which a postsynaptic neuron efficiently detects temporal coincidences of spikes arriving at certain frequency from N different afferents. We extend a previous work that only considers synaptic depression as the most important mechanism in the transmission of information through synapses, to a more general situation including also synaptic facilitation. Our study shows that: 1) facilitation enhances the detection of correl…
Two elements of neural information processing have primarily been proposed: firing rate and spike timing of neurons. In the case of synaptic plasticity, although spike-timing-dependent plasticity (STDP) depending on presynaptic and postsynaptic spike times had been considered the most common rule, recent studies have shown the inhibitory nature of the brain in vivo for precise spike timing, which is key to the STDP. Thus, the importance of the firing frequency in synaptic plasticity in vivo has been recognized again. However, little is understood about how the frequency-dependent synaptic plas…
Neurons process information by transforming barrages of synaptic inputs into spiking activity. Synaptic inhibition suppresses the output firing activity of a neuron, and is commonly classified as having a subtractive or divisive effect on a neuron's output firing activity. Subtractive inhibition can narrow the range of inputs that evoke spiking activity by eliminating responses to non-preferred inputs. Divisive inhibition is a form of gain control: it modifies firing rates while preserving the range of inputs that evoke firing activity. Since these two "modes" of inhibition have distinct impac…
Artificial neural networks (ANNs) have been extensively used for the description of problems arising from biological systems and for constructing neuromorphic computing models. The third generation of ANNs, namely, spiking neural networks (SNNs), inspired by biological neurons enable a more realistic mimicry of the human brain. A large class of the problems from these domains is characterized by the necessity to deal with the combination of neurons, spikes and synapses via integrate-and-fire neuron models. Motivated by important applications of the integrate-and-fire of neurons in neuromorphic…
Quantifying information stored in synaptic connections rather than in firing activities of neural networks
本文提出了一种理论框架，用于量化神经网络突触连接分布中存储的信息，通过Hebbian网络和对数正态分布建模，揭示突触间协同作用及信息存储的双重性。
In this paper, we propose a shot noise-based leaky integrated and firing neuron model and provide a detailed analysis of the performance of this model compared to the traditional diffusion approximated model. In theoretical neuroscience, there are three general neuron models in the field: Compartmental neuron model is a conductance-based model, in which it views the biological neurons as a large circuit. The problem of this model comes from its structural complexity and the number of its free parameters; Leaky integrated and firing model is a more flexible model due to the special design calle…
Synapses change on multiple timescales, ranging from milliseconds to minutes, due to a combination of both short- and long-term plasticity. Here we develop an extension of the common Generalized Linear Model to infer both short- and long-term changes in the coupling between a pre- and post-synaptic neuron based on observed spiking activity. We model short-term synaptic plasticity using additive effects that depend on the presynaptic spike timing, and we model long-term changes in both synaptic weight and baseline firing rate using point process adaptive smoothing. Using simulations, we first s…
We propose a computational model of neuron, called firing cell (FC), properties of which cover such phenomena as attenuation of receptors for external stimuli, delay and decay of postsynaptic potentials, modification of internal weights due to propagation of postsynaptic potentials through the dendrite, modification of properties of the analog memory for each input due to a pattern of short-time synaptic potentiation or long-time synaptic potentiation (LTP), output-spike generation when the sum of all inputs exceeds a threshold, and refraction. The cell may take one of the three forms: excitat…
Firing rate distributions in plastic networks of spiking neurons
该研究扩展平均场理论，可同时处理突触权重异质性与连接数异质性的脉冲神经元网络，引入脉冲迹介导的可塑性机制，通过模拟验证了方程准确性，为理解可塑性对神经网络活动与结构的塑造提供了方法。
Recent experiments suggested that homeostatic regulation of synaptic balance leads the visual system to recover and maintain a regime of power-law avalanches. Here we study an excitatory/inhibitory (E/I) mean-field neuronal network that has a critical point with power-law avalanches and synaptic balance. When short term depression in inhibitory synapses and firing threshold adaptation are added, the system hovers around the critical point. This homeostatically self-organized quasi-critical (SOqC) dynamics generates E/I synaptic current cancellation in fast time scales, causing fluctuation-driv…
We consider a wide class of spiking neuron models, defined by rather general set of conditions typical for basic models like leaky integrate and fire, or binding neuron model. A neuron is fed with a point renewal process. A relation between the three probability density functions (pdf): (i) pdf of input interspike intervals, (ii) pdf of output interspike intervals of a neuron with instantaneous feedback and (iii) pdf for that same neuron without feedback is derived. This allows to calculate any of the three pdfs provided the another two are given. Similar relation between corresponding means a…
When a neuron fires and the resulting action potential travels down its axon toward other neurons' dendrites, the effect on each of those neurons is mediated by the weight of the synapse that separates it from the firing neuron. This weight, in turn, is affected by the postsynaptic neuron's response through a mechanism that is thought to underlie important processes such as learning and memory. Although of difficult quantification, cortical synaptic weights have been found to obey a long-tailed unimodal distribution peaking near the lowest values, thus confirming some of the predictive models …
Finite-state Markovian surrogates for long-time neuronal state distributions and firing rates
该研究构建有限状态马尔可夫代理模型，结合两种闭合方式，在LIF、EIF等神经元模型上实现无需逐尖峰模拟的长时间状态分布和放电率估计，性能良好。
Correlation-based Hebbian plasticity is thought to shape neuronal connectivity during development and learning, whereas homeostatic plasticity would stabilize network activity. Here we investigate another, new aspect of this dichotomy: Can Hebbian associative properties also emerge as a network effect from a plasticity rule based on homeostatic principles on the neuronal level? To address this question, we simulated a recurrent network of leaky integrate-and-fire neurons, in which excitatory connections are subject to a structural plasticity rule based on firing rate homeostasis. We show that …
The Nonlinear Noisy Leaky Integrate and Fire neuronal models are mathematical models that describe the activity of neural networks. These models have been studied at a microscopic level, using Stochastic Differential Equations, and at a mesoscopic/macroscopic level, through the mean field limits using Fokker-Planck type equations. The aim of this paper is to improve their understanding, using a numerical study of their particle systems. We analyse in depth the behaviour of the classical and physical solutions of the Stochastic Differential Equations and, we compare it with what is already know…
A widely accepted view of computations in the brain relies on population coding, where the neural ensemble firing rate is modulated in a stable manner to transmit information and perform various cognitive tasks. At the same time, oscillatory neural activity is specifically modulated in frequency, coherence and power during cognitive performance. How the firing rate and oscillations interact remains a salient question. In this paper, we develop a theory for the interactions between oscillatory signals and the firing rate of neural populations based on activity of non-linear voltage-dependent NM…
We investigate the behavior of a model neuron that receives a biophysically-realistic noisy post-synaptic current based on uncorrelated spiking activity from a large number of afferents. We show that, with static synapses, such noise can give rise to inverse stochastic resonance (ISR) as a function of the presynaptic firing rate. We compare this to the case with dynamic synapses that feature short-term synaptic plasticity, and show that the interval of presynaptic firing rate over which ISR exists can be extended or diminished. We consider both short-term depression and facilitation. Interesti…
Our current understanding of neuroplasticity paints a picture of a complex interconnected system of dependent processes which shape cortical structure so as to produce an efficient information processing system. Indeed, the cooperation of these processes is associated with robust, stable, adaptable networks with characteristic features of activity and synaptic topology. However, combining the actions of these mechanisms in models has proven exceptionally difficult and to date no model has been able to do so without significant hand-tuning. Until such a model exists that can successfully combin…
Self-sustained activity in the brain is observed in the absence of external stimuli and contributes to signal propagation, neural coding, and dynamic stability. It also plays an important role in cognitive processes. In this work, by means of studying intracellular recordings from CA1 neurons in rats and results from numerical simulations, we demonstrate that self-sustained activity presents high variability of patterns, such as low neural firing rates and activity in the form of small-bursts in distinct neurons. In our numerical simulations, we consider random networks composed of coupled, ad…
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate-and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases with the strength of the synapses in the network and with the value to which the membrane potential is reset after a spike. Generalizing the model to include conductance-based synapses gives insight into the connection between the firing statistics and the high-conductance state observed experimentally in visual cort…
Space is represented in the mammalian brain by the activity of hippocampal place cells as well as in their spike-timing correlations. Here we propose a theory how this temporal code is transformed to spatial firing rate patterns via spike-timing-dependent synaptic plasticity. The resulting dynamics of synaptic weights resembles well-known pattern formation models in which a lateral inhibition mechanism gives rise to a Turing instability. We identify parameter regimes in which hexagonal firing patterns develop as they have been found in medial entorhinal cortex.
Firing patterns in the central nervous system often exhibit strong temporal irregularity and heterogeneity in their time averaged response properties. Previous studies suggested that these properties are outcome of an intrinsic chaotic dynamics. Indeed, simplified rate-based large neuronal networks with random synaptic connections are known to exhibit sharp transition from fixed point to chaotic dynamics when the synaptic gain is increased. However, the existence of a similar transition in neuronal circuit models with more realistic architectures and firing dynamics has not been established. I…
Leaky integrate-and-fire (LIF) models are mean-field limits, with a large number of neurons, used to describe neural networks. We consider inhomogeneous networks structured by a connec-tivity parameter (strengths of the synaptic weights) with the effect of processing the input current with different intensities. We first study the properties of the network activity depending on the distribution of synaptic weights and in particular its discrimination capacity. Then, we consider simple learning rules and determine the synaptic weight distribution it generates. We outline the role of noise as a …
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.
We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our treatment, we can determine self-consistently both the firing rates and the firing correlations, without being restricted to specific neuron models. Here, we solve the analytically derived mean-field equations numerically for integrate-and-fire neurons. Several known key properties of orientation selective cortical neurons emerge naturally from the descript…
Heterogeneity of neural attributes has recently gained a lot of attention and is increasing recognized as a crucial feature in neural processing. Despite its importance, this physiological feature has traditionally been neglected in theoretical studies of cortical neural networks. Thus, there is still a lot unknown about the consequences of cellular and circuit heterogeneity in spiking neural networks. In particular, combining network or synaptic heterogeneity and intrinsic heterogeneity has yet to be considered systematically despite the fact that both are known to exist and likely have signi…
We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky integrate-and-fire neurons, driven by excitatory input from an external population. The high connectivity permits a mean-field description in which synaptic currents can be treated as Gaussian noise, the mean and autocorrelation function of which are calculated self-consistently from the firing statistics of single model neurons. Within this description, we find that th…
ILIF: Temporal Inhibitory Leaky Integrate-and-Fire Neuron for Overactivation in Spiking Neural Networks
针对 SNN 替代梯度宽度 gamma 导致的过度激活与梯度消失困境，提出受生物抑制机制启发的 ILIF 神经元，通过互联抑制单元降低发放率并保持梯度传播，从而提升能效、训练稳定性与准确率。
Working memory (WM) has been intensively used to enable the temporary storing of information for processing purposes, playing an important role in the execution of various cognitive tasks. Recent studies have shown that information in WM is not only maintained through persistent recurrent activity but also can be stored in activity-silent states such as in short-term synaptic plasticity (STSP). Motivated by important applications of the STSP mechanisms in WM, the main focus of the present work is on the analysis of the effects of random inputs on a leaky integrate-and-fire (LIF) synaptic condu…
Most neurons in the primary visual cortex initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. The functional consequences of adaptation are unclear. Typically a reduction of firing rate would reduce single neuron accuracy as less spikes are available for decoding, but it has been suggested that on the population level, adaptation increases coding accuracy. This question requires careful analysis as adaptation not only changes the firing rates of neurons, but also the neural variability and correlations between neurons, which affect coding ac…
We consider a cerebellar ring network for the optokinetic response (OKR), and investigate the effect of diverse recoding of granule (GR) cells on OKR by varying the connection probability $p_c$ from Golgi to GR cells. For an optimal value of $p_c^*~(=0.06)$, individual GR cells exhibit diverse spiking patterns which are in-phase, anti-phase, or complex out-of-phase with respect to their population-averaged firing activity. Then, these diversely-recoded signals via parallel fibers (PFs) from GR cells are effectively depressed by the error-teaching signals via climbing fibers from the inferior o…
Low-dimensional firing-rate dynamics for populations of renewal-type spiking neurons
本文通过不应期密度方程的特征模态展开，为更新型脉冲神经元群体推导了能捕捉脉冲同步效应的低维放电率模型，并建立了特征值与脉冲间隔分布拉普拉斯变换的简单关系。
A recurrent loop consisting of a single neuron is considered which is influenced by a chemical excitatory delayed synaptic feedback. We show the response of the system is dependent to the duration of the activity of the synapse which is determined by the deactivation time constant of the synapse. We show that loops with slow synapses, those which the effect of the synaptic activation remains for time constants comparable to the period of firing, show more predictable results where the effect of the fast synapses is tightly dependent on the loop delay time. The results are compared to those of …
The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission unachievable. In addition, as a result of the enormous number of required measurements, the estimated network parameters would differ from the original ones. Here we present a versatile experimental technique, which enables the study of recurrent neural networks activity while being capable of dictating the network connectivity and synaptic strengths. This m…
Starting from a spectral expansion of the Fokker-Plank equation for the membrane potential density in a network of spiking neurons, a low-dimensional dynamics of the collective firing rate is derived. As a result a $n$-order ordinary differential equation for the network activity can be worked out by taking into account the slowest $n$ modes of the expansion. The resulting low-dimensional dynamics naturally takes into account the strength of the synaptic couplings under the hypothesis of a not too fast changing membrane potential density. By considering only the two slowest modes, the firing r…
In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of the neural activity, as expected, but it can also promote neural reactivation. In particular, for globally coupled systems, the number of firing neurons monotonically reduces upon increasing the strength of inhibition (neurons' death). However, the random pruning of the connections is able to reverse the action of inhibition, i.e. in a sparse network a sufficiently strong synaptic strength can surprisingly promote, ra…
In continuous attractor neural networks (CANNs), spatially continuous information such as orientation, head direction, and spatial location is represented by Gaussian-like tuning curves that can be displaced continuously in the space of the preferred stimuli of the neurons. We investigate how short-term synaptic depression (STD) can reshape the intrinsic dynamics of the CANN model and its responses to a single static input. In particular, CANNs with STD can support various complex firing patterns and chaotic behaviors. These chaotic behaviors have the potential to encode various stimuli in the…
The background activity of a cortical neural network is modeled by a homogeneous integrate-and-fire network with unreliable inhibitory synapses. Numerical and analytical calculations show that the network relaxes into a stationary state of high attention. The majority of the neurons has a membrane potential just below the threshold; as a consequence the network can react immediately - on the time scale of synaptic transmission- on external pulses. The neurons fire with a low rate and with a broad distribution of interspike intervals. Firing events of the total network are correlated over short…
We analyze a large system of heterogeneous quadratic integrate-and-fire (QIF) neurons with time delayed, all-to-all synaptic coupling. The model is exactly reduced to a system of firing rate equations that is exploited to investigate the existence, stability and bifurcations of fully synchronous, partially synchronous, and incoherent states. In conjunction with this analysis we perform extensive numerical simulations of the original network of QIF neurons, and determine the relation between the macroscopic and microscopic states for partially synchronous states. The results are summarized in t…
Spike correlations between neurons are ubiquitous in the cortex, but their role is at present not understood. Here we describe the firing response of a leaky integrate-and-fire neuron (LIF) when it receives a temporarily correlated input generated by presynaptic correlated neuronal populations. Input correlations are characterized in terms of the firing rates, Fano factors, correlation coefficients and correlation timescale of the neurons driving the target neuron. We show that the sum of the presynaptic spike trains cannot be well described by a Poisson process. Solutions of the output firing…
An analytical description of the response properties of simple but realistic neuron models in the presence of noise is still lacking. We determine completely up to the second order the firing statistics of a single and a pair of leaky integrate-and-fire neurons (LIFs) receiving some common slowly filtered white noise. In particular, the auto- and cross-correlation functions of the output spike trains of pairs of cells are obtained from an improvement of the adiabatic approximation introduced in \cite{Mor+04}. These two functions define the firing variability and firing synchronization between …
This paper proposes a neuronal circuitry layout and synaptic plasticity principles that allow the (pyramidal) neuron to act as a "combinatorial switch". Namely, the neuron learns to be more prone to generate spikes given those combinations of firing input neurons for which a previous spiking of the neuron had been followed by a positive global reward signal. The reward signal may be mediated by certain modulatory hormones or neurotransmitters, e.g., the dopamine. More generally, a trial-and-error learning paradigm is suggested in which a global reward signal triggers long-term enhancement or w…
Synaptic delay induced macroscopic dynamics of the large-scale network of Izhikevich neurons
本研究构建含突触延迟的大规模Izhikevich神经元网络模型，通过Ott-Antonsen理论约简为平均场系统，分析了突触延迟等因素对宏观动力学的调控作用，揭示了环面分岔介导双频群体簇放电的机制，为脑功能研究提供了理论参考。
Maintaining the ability to fire sparsely is crucial for information encoding in neural networks. Additionally, spiking homeostasis is vital for spiking neural networks with changing numbers of weights and neurons. We discuss a range of network stabilisation approaches, inspired by homeostatic synaptic plasticity mechanisms reported in the brain. These include weight scaling, and weight change as a function of the network's spiking activity. We tested normalisation of the sum of weights for all neurons, and by neuron type. We examined how this approach affects firing rate and performance on clu…
We 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 $f_I$ and their connectivity level to investigate the cooperation between hub features and inhibition. We show that, depending on $f_I$, highly connected inhibitory nodes strongly drive the synchronization properties of the overall network through d…
There is consensus in the current literature that stable states of asynchronous irregular spiking activity require (i) large networks of 10 000 or more neurons and (ii) external background activity or pacemaker neurons. Yet already in 1963, Griffith showed that networks of simple threshold elements can be persistently active at intermediate rates. Here, we extend Griffith's work and demonstrate that sparse networks of integrate-and-fire neurons assume stable states of self-sustained asynchronous and irregular firing without external input or pacemaker neurons. These states can be robustly indu…
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