Constructing Precisely Computing Networks with Biophysical Spiking Neurons.

Science.gov (United States)

Schwemmer, Michael A; Fairhall, Adrienne L; Denéve, Sophie; Shea-Brown, Eric T

2015-07-15

While spike timing has been shown to carry detailed stimulus information at the sensory periphery, its possible role in network computation is less clear. Most models of computation by neural networks are based on population firing rates. In equivalent spiking implementations, firing is assumed to be random such that averaging across populations of neurons recovers the rate-based approach. Recently, however, Denéve and colleagues have suggested that the spiking behavior of neurons may be fundamental to how neuronal networks compute, with precise spike timing determined by each neuron's contribution to producing the desired output (Boerlin and Denéve, 2011; Boerlin et al., 2013). By postulating that each neuron fires to reduce the error in the network's output, it was demonstrated that linear computations can be performed by networks of integrate-and-fire neurons that communicate through instantaneous synapses. This left open, however, the possibility that realistic networks, with conductance-based neurons with subthreshold nonlinearity and the slower timescales of biophysical synapses, may not fit into this framework. Here, we show how the spike-based approach can be extended to biophysically plausible networks. We then show that our network reproduces a number of key features of cortical networks including irregular and Poisson-like spike times and a tight balance between excitation and inhibition. Lastly, we discuss how the behavior of our model scales with network size or with the number of neurons "recorded" from a larger computing network. These results significantly increase the biological plausibility of the spike-based approach to network computation. We derive a network of neurons with standard spike-generating currents and synapses with realistic timescales that computes based upon the principle that the precise timing of each spike is important for the computation. We then show that our network reproduces a number of key features of cortical networks

Noise-enhanced coding in phasic neuron spike trains.

Science.gov (United States)

Ly, Cheng; Doiron, Brent

2017-01-01

The stochastic nature of neuronal response has lead to conjectures about the impact of input fluctuations on the neural coding. For the most part, low pass membrane integration and spike threshold dynamics have been the primary features assumed in the transfer from synaptic input to output spiking. Phasic neurons are a common, but understudied, neuron class that are characterized by a subthreshold negative feedback that suppresses spike train responses to low frequency signals. Past work has shown that when a low frequency signal is accompanied by moderate intensity broadband noise, phasic neurons spike trains are well locked to the signal. We extend these results with a simple, reduced model of phasic activity that demonstrates that a non-Markovian spike train structure caused by the negative feedback produces a noise-enhanced coding. Further, this enhancement is sensitive to the timescales, as opposed to the intensity, of a driving signal. Reduced hazard function models show that noise-enhanced phasic codes are both novel and separate from classical stochastic resonance reported in non-phasic neurons. The general features of our theory suggest that noise-enhanced codes in excitable systems with subthreshold negative feedback are a particularly rich framework to study.

Real-time computing platform for spiking neurons (RT-spike).

Science.gov (United States)

Ros, Eduardo; Ortigosa, Eva M; Agís, Rodrigo; Carrillo, Richard; Arnold, Michael

2006-07-01

A computing platform is described for simulating arbitrary networks of spiking neurons in real time. A hybrid computing scheme is adopted that uses both software and hardware components to manage the tradeoff between flexibility and computational power; the neuron model is implemented in hardware and the network model and the learning are implemented in software. The incremental transition of the software components into hardware is supported. We focus on a spike response model (SRM) for a neuron where the synapses are modeled as input-driven conductances. The temporal dynamics of the synaptic integration process are modeled with a synaptic time constant that results in a gradual injection of charge. This type of model is computationally expensive and is not easily amenable to existing software-based event-driven approaches. As an alternative we have designed an efficient time-based computing architecture in hardware, where the different stages of the neuron model are processed in parallel. Further improvements occur by computing multiple neurons in parallel using multiple processing units. This design is tested using reconfigurable hardware and its scalability and performance evaluated. Our overall goal is to investigate biologically realistic models for the real-time control of robots operating within closed action-perception loops, and so we evaluate the performance of the system on simulating a model of the cerebellum where the emulation of the temporal dynamics of the synaptic integration process is important.

Decoding spikes in a spiking neuronal network

Energy Technology Data Exchange (ETDEWEB)

Feng Jianfeng [Department of Informatics, University of Sussex, Brighton BN1 9QH (United Kingdom); Ding, Mingzhou [Department of Mathematics, Florida Atlantic University, Boca Raton, FL 33431 (United States)

2004-06-04

We investigate how to reliably decode the input information from the output of a spiking neuronal network. A maximum likelihood estimator of the input signal, together with its Fisher information, is rigorously calculated. The advantage of the maximum likelihood estimation over the 'brute-force rate coding' estimate is clearly demonstrated. It is pointed out that the ergodic assumption in neuroscience, i.e. a temporal average is equivalent to an ensemble average, is in general not true. Averaging over an ensemble of neurons usually gives a biased estimate of the input information. A method on how to compensate for the bias is proposed. Reconstruction of dynamical input signals with a group of spiking neurons is extensively studied and our results show that less than a spike is sufficient to accurately decode dynamical inputs.

Decoding spikes in a spiking neuronal network

International Nuclear Information System (INIS)

Feng Jianfeng; Ding, Mingzhou

2004-01-01

We investigate how to reliably decode the input information from the output of a spiking neuronal network. A maximum likelihood estimator of the input signal, together with its Fisher information, is rigorously calculated. The advantage of the maximum likelihood estimation over the 'brute-force rate coding' estimate is clearly demonstrated. It is pointed out that the ergodic assumption in neuroscience, i.e. a temporal average is equivalent to an ensemble average, is in general not true. Averaging over an ensemble of neurons usually gives a biased estimate of the input information. A method on how to compensate for the bias is proposed. Reconstruction of dynamical input signals with a group of spiking neurons is extensively studied and our results show that less than a spike is sufficient to accurately decode dynamical inputs

Spiking Activity of a LIF Neuron in Distributed Delay Framework

Directory of Open Access Journals (Sweden)

Saket Kumar Choudhary

2016-06-01

Full Text Available Evolution of membrane potential and spiking activity for a single leaky integrate-and-fire (LIF neuron in distributed delay framework (DDF is investigated. DDF provides a mechanism to incorporate memory element in terms of delay (kernel function into a single neuron models. This investigation includes LIF neuron model with two different kinds of delay kernel functions, namely, gamma distributed delay kernel function and hypo-exponential distributed delay kernel function. Evolution of membrane potential for considered models is studied in terms of stationary state probability distribution (SPD. Stationary state probability distribution of membrane potential (SPDV for considered neuron models are found asymptotically similar which is Gaussian distributed. In order to investigate the effect of membrane potential delay, rate code scheme for neuronal information processing is applied. Firing rate and Fano-factor for considered neuron models are calculated and standard LIF model is used for comparative study. It is noticed that distributed delay increases the spiking activity of a neuron. Increase in spiking activity of neuron in DDF is larger for hypo-exponential distributed delay function than gamma distributed delay function. Moreover, in case of hypo-exponential delay function, a LIF neuron generates spikes with Fano-factor less than 1.

A model-based spike sorting algorithm for removing correlation artifacts in multi-neuron recordings.

Science.gov (United States)

Pillow, Jonathan W; Shlens, Jonathon; Chichilnisky, E J; Simoncelli, Eero P

2013-01-01

We examine the problem of estimating the spike trains of multiple neurons from voltage traces recorded on one or more extracellular electrodes. Traditional spike-sorting methods rely on thresholding or clustering of recorded signals to identify spikes. While these methods can detect a large fraction of the spikes from a recording, they generally fail to identify synchronous or near-synchronous spikes: cases in which multiple spikes overlap. Here we investigate the geometry of failures in traditional sorting algorithms, and document the prevalence of such errors in multi-electrode recordings from primate retina. We then develop a method for multi-neuron spike sorting using a model that explicitly accounts for the superposition of spike waveforms. We model the recorded voltage traces as a linear combination of spike waveforms plus a stochastic background component of correlated Gaussian noise. Combining this measurement model with a Bernoulli prior over binary spike trains yields a posterior distribution for spikes given the recorded data. We introduce a greedy algorithm to maximize this posterior that we call "binary pursuit". The algorithm allows modest variability in spike waveforms and recovers spike times with higher precision than the voltage sampling rate. This method substantially corrects cross-correlation artifacts that arise with conventional methods, and substantially outperforms clustering methods on both real and simulated data. Finally, we develop diagnostic tools that can be used to assess errors in spike sorting in the absence of ground truth.

Minimal time spiking in various ChR2-controlled neuron models.

Science.gov (United States)

Renault, Vincent; Thieullen, Michèle; Trélat, Emmanuel

2018-02-01

We use conductance based neuron models, and the mathematical modeling of optogenetics to define controlled neuron models and we address the minimal time control of these affine systems for the first spike from equilibrium. We apply tools of geometric optimal control theory to study singular extremals, and we implement a direct method to compute optimal controls. When the system is too large to theoretically investigate the existence of singular optimal controls, we observe numerically the optimal bang-bang controls.

Coherent and intermittent ensemble oscillations emerge from networks of irregular spiking neurons.

Science.gov (United States)

Hoseini, Mahmood S; Wessel, Ralf

2016-01-01

Local field potential (LFP) recordings from spatially distant cortical circuits reveal episodes of coherent gamma oscillations that are intermittent, and of variable peak frequency and duration. Concurrently, single neuron spiking remains largely irregular and of low rate. The underlying potential mechanisms of this emergent network activity have long been debated. Here we reproduce such intermittent ensemble oscillations in a model network, consisting of excitatory and inhibitory model neurons with the characteristics of regular-spiking (RS) pyramidal neurons, and fast-spiking (FS) and low-threshold spiking (LTS) interneurons. We find that fluctuations in the external inputs trigger reciprocally connected and irregularly spiking RS and FS neurons in episodes of ensemble oscillations, which are terminated by the recruitment of the LTS population with concurrent accumulation of inhibitory conductance in both RS and FS neurons. The model qualitatively reproduces experimentally observed phase drift, oscillation episode duration distributions, variation in the peak frequency, and the concurrent irregular single-neuron spiking at low rate. Furthermore, consistent with previous experimental studies using optogenetic manipulation, periodic activation of FS, but not RS, model neurons causes enhancement of gamma oscillations. In addition, increasing the coupling between two model networks from low to high reveals a transition from independent intermittent oscillations to coherent intermittent oscillations. In conclusion, the model network suggests biologically plausible mechanisms for the generation of episodes of coherent intermittent ensemble oscillations with irregular spiking neurons in cortical circuits. Copyright © 2016 the American Physiological Society.

Evoking prescribed spike times in stochastic neurons

Science.gov (United States)

Doose, Jens; Lindner, Benjamin

2017-09-01

Single cell stimulation in vivo is a powerful tool to investigate the properties of single neurons and their functionality in neural networks. We present a method to determine a cell-specific stimulus that reliably evokes a prescribed spike train with high temporal precision of action potentials. We test the performance of this stimulus in simulations for two different stochastic neuron models. For a broad range of parameters and a neuron firing with intermediate firing rates (20-40 Hz) the reliability in evoking the prescribed spike train is close to its theoretical maximum that is mainly determined by the level of intrinsic noise.

A memristive spiking neuron with firing rate coding

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Marina eIgnatov

2015-10-01

Full Text Available Perception, decisions, and sensations are all encoded into trains of action potentials in the brain. The relation between stimulus strength and all-or-nothing spiking of neurons is widely believed to be the basis of this coding. This initiated the development of spiking neuron models; one of today's most powerful conceptual tool for the analysis and emulation of neural dynamics. The success of electronic circuit models and their physical realization within silicon field-effect transistor circuits lead to elegant technical approaches. Recently, the spectrum of electronic devices for neural computing has been extended by memristive devices, mainly used to emulate static synaptic functionality. Their capabilities for emulations of neural activity were recently demonstrated using a memristive neuristor circuit, while a memristive neuron circuit has so far been elusive. Here, a spiking neuron model is experimentally realized in a compact circuit comprising memristive and memcapacitive devices based on the strongly correlated electron material vanadium dioxide (VO2 and on the chemical electromigration cell Ag/TiO2-x/Al. The circuit can emulate dynamical spiking patterns in response to an external stimulus including adaptation, which is at the heart of firing rate coding as first observed by E.D. Adrian in 1926.

Spiking neuron devices consisting of single-flux-quantum circuits

International Nuclear Information System (INIS)

Hirose, Tetsuya; Asai, Tetsuya; Amemiya, Yoshihito

2006-01-01

Single-flux-quantum (SFQ) circuits can be used for making spiking neuron devices, which are useful elements for constructing intelligent, brain-like computers. The device we propose is based on the leaky integrate-and-fire neuron (IFN) model and uses a SFQ pulse as an action signal or a spike of neurons. The operation of the neuron device is confirmed by computer simulator. It can operate with a short delay of 100 ps or less and is the highest-speed neuron device ever reported

Inherently stochastic spiking neurons for probabilistic neural computation

KAUST Repository

Al-Shedivat, Maruan

2015-04-01

Neuromorphic engineering aims to design hardware that efficiently mimics neural circuitry and provides the means for emulating and studying neural systems. In this paper, we propose a new memristor-based neuron circuit that uniquely complements the scope of neuron implementations and follows the stochastic spike response model (SRM), which plays a cornerstone role in spike-based probabilistic algorithms. We demonstrate that the switching of the memristor is akin to the stochastic firing of the SRM. Our analysis and simulations show that the proposed neuron circuit satisfies a neural computability condition that enables probabilistic neural sampling and spike-based Bayesian learning and inference. Our findings constitute an important step towards memristive, scalable and efficient stochastic neuromorphic platforms. © 2015 IEEE.

On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs.

Science.gov (United States)

Gerhard, Felipe; Deger, Moritz; Truccolo, Wilson

2017-02-01

Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a

The Effects of Guanfacine and Phenylephrine on a Spiking Neuron Model of Working Memory.

Science.gov (United States)

Duggins, Peter; Stewart, Terrence C; Choo, Xuan; Eliasmith, Chris

2017-01-01

We use a spiking neural network model of working memory (WM) capable of performing the spatial delayed response task (DRT) to investigate two drugs that affect WM: guanfacine (GFC) and phenylephrine (PHE). In this model, the loss of information over time results from changes in the spiking neural activity through recurrent connections. We reproduce the standard forgetting curve and then show that this curve changes in the presence of GFC and PHE, whose application is simulated by manipulating functional, neural, and biophysical properties of the model. In particular, applying GFC causes increased activity in neurons that are sensitive to the information currently being remembered, while applying PHE leads to decreased activity in these same neurons. Interestingly, these differential effects emerge from network-level interactions because GFC and PHE affect all neurons equally. We compare our model to both electrophysiological data from neurons in monkey dorsolateral prefrontal cortex and to behavioral evidence from monkeys performing the DRT. Copyright © 2016 Cognitive Science Society, Inc.

Channel noise effects on first spike latency of a stochastic Hodgkin-Huxley neuron

Science.gov (United States)

Maisel, Brenton; Lindenberg, Katja

2017-02-01

While it is widely accepted that information is encoded in neurons via action potentials or spikes, it is far less understood what specific features of spiking contain encoded information. Experimental evidence has suggested that the timing of the first spike may be an energy-efficient coding mechanism that contains more neural information than subsequent spikes. Therefore, the biophysical features of neurons that underlie response latency are of considerable interest. Here we examine the effects of channel noise on the first spike latency of a Hodgkin-Huxley neuron receiving random input from many other neurons. Because the principal feature of a Hodgkin-Huxley neuron is the stochastic opening and closing of channels, the fluctuations in the number of open channels lead to fluctuations in the membrane voltage and modify the timing of the first spike. Our results show that when a neuron has a larger number of channels, (i) the occurrence of the first spike is delayed and (ii) the variation in the first spike timing is greater. We also show that the mean, median, and interquartile range of first spike latency can be accurately predicted from a simple linear regression by knowing only the number of channels in the neuron and the rate at which presynaptic neurons fire, but the standard deviation (i.e., neuronal jitter) cannot be predicted using only this information. We then compare our results to another commonly used stochastic Hodgkin-Huxley model and show that the more commonly used model overstates the first spike latency but can predict the standard deviation of first spike latencies accurately. We end by suggesting a more suitable definition for the neuronal jitter based upon our simulations and comparison of the two models.

Computing with Spiking Neuron Networks

NARCIS (Netherlands)

H. Paugam-Moisy; S.M. Bohte (Sander); G. Rozenberg; T.H.W. Baeck (Thomas); J.N. Kok (Joost)

2012-01-01

htmlabstractAbstract Spiking Neuron Networks (SNNs) are often referred to as the 3rd gener- ation of neural networks. Highly inspired from natural computing in the brain and recent advances in neurosciences, they derive their strength and interest from an ac- curate modeling of synaptic interactions

Single-trial estimation of stimulus and spike-history effects on time-varying ensemble spiking activity of multiple neurons: a simulation study

International Nuclear Information System (INIS)

Shimazaki, Hideaki

2013-01-01

Neurons in cortical circuits exhibit coordinated spiking activity, and can produce correlated synchronous spikes during behavior and cognition. We recently developed a method for estimating the dynamics of correlated ensemble activity by combining a model of simultaneous neuronal interactions (e.g., a spin-glass model) with a state-space method (Shimazaki et al. 2012 PLoS Comput Biol 8 e1002385). This method allows us to estimate stimulus-evoked dynamics of neuronal interactions which is reproducible in repeated trials under identical experimental conditions. However, the method may not be suitable for detecting stimulus responses if the neuronal dynamics exhibits significant variability across trials. In addition, the previous model does not include effects of past spiking activity of the neurons on the current state of ensemble activity. In this study, we develop a parametric method for simultaneously estimating the stimulus and spike-history effects on the ensemble activity from single-trial data even if the neurons exhibit dynamics that is largely unrelated to these effects. For this goal, we model ensemble neuronal activity as a latent process and include the stimulus and spike-history effects as exogenous inputs to the latent process. We develop an expectation-maximization algorithm that simultaneously achieves estimation of the latent process, stimulus responses, and spike-history effects. The proposed method is useful to analyze an interaction of internal cortical states and sensory evoked activity

Predictive features of persistent activity emergence in regular spiking and intrinsic bursting model neurons.

Directory of Open Access Journals (Sweden)

Kyriaki Sidiropoulou

Full Text Available Proper functioning of working memory involves the expression of stimulus-selective persistent activity in pyramidal neurons of the prefrontal cortex (PFC, which refers to neural activity that persists for seconds beyond the end of the stimulus. The mechanisms which PFC pyramidal neurons use to discriminate between preferred vs. neutral inputs at the cellular level are largely unknown. Moreover, the presence of pyramidal cell subtypes with different firing patterns, such as regular spiking and intrinsic bursting, raises the question as to what their distinct role might be in persistent firing in the PFC. Here, we use a compartmental modeling approach to search for discriminatory features in the properties of incoming stimuli to a PFC pyramidal neuron and/or its response that signal which of these stimuli will result in persistent activity emergence. Furthermore, we use our modeling approach to study cell-type specific differences in persistent activity properties, via implementing a regular spiking (RS and an intrinsic bursting (IB model neuron. We identify synaptic location within the basal dendrites as a feature of stimulus selectivity. Specifically, persistent activity-inducing stimuli consist of activated synapses that are located more distally from the soma compared to non-inducing stimuli, in both model cells. In addition, the action potential (AP latency and the first few inter-spike-intervals of the neuronal response can be used to reliably detect inducing vs. non-inducing inputs, suggesting a potential mechanism by which downstream neurons can rapidly decode the upcoming emergence of persistent activity. While the two model neurons did not differ in the coding features of persistent activity emergence, the properties of persistent activity, such as the firing pattern and the duration of temporally-restricted persistent activity were distinct. Collectively, our results pinpoint to specific features of the neuronal response to a given

Emergent properties of interacting populations of spiking neurons.

Science.gov (United States)

Cardanobile, Stefano; Rotter, Stefan

2011-01-01

Dynamic neuronal networks are a key paradigm of increasing importance in brain research, concerned with the functional analysis of biological neuronal networks and, at the same time, with the synthesis of artificial brain-like systems. In this context, neuronal network models serve as mathematical tools to understand the function of brains, but they might as well develop into future tools for enhancing certain functions of our nervous system. Here, we present and discuss our recent achievements in developing multiplicative point processes into a viable mathematical framework for spiking network modeling. The perspective is that the dynamic behavior of these neuronal networks is faithfully reflected by a set of non-linear rate equations, describing all interactions on the population level. These equations are similar in structure to Lotka-Volterra equations, well known by their use in modeling predator-prey relations in population biology, but abundant applications to economic theory have also been described. We present a number of biologically relevant examples for spiking network function, which can be studied with the help of the aforementioned correspondence between spike trains and specific systems of non-linear coupled ordinary differential equations. We claim that, enabled by the use of multiplicative point processes, we can make essential contributions to a more thorough understanding of the dynamical properties of interacting neuronal populations.

A new supervised learning algorithm for spiking neurons.

Science.gov (United States)

Xu, Yan; Zeng, Xiaoqin; Zhong, Shuiming

2013-06-01

The purpose of supervised learning with temporal encoding for spiking neurons is to make the neurons emit a specific spike train encoded by the precise firing times of spikes. If only running time is considered, the supervised learning for a spiking neuron is equivalent to distinguishing the times of desired output spikes and the other time during the running process of the neuron through adjusting synaptic weights, which can be regarded as a classification problem. Based on this idea, this letter proposes a new supervised learning method for spiking neurons with temporal encoding; it first transforms the supervised learning into a classification problem and then solves the problem by using the perceptron learning rule. The experiment results show that the proposed method has higher learning accuracy and efficiency over the existing learning methods, so it is more powerful for solving complex and real-time problems.

Predicting Spike Occurrence and Neuronal Responsiveness from LFPs in Primary Somatosensory Cortex

Science.gov (United States)

Storchi, Riccardo; Zippo, Antonio G.; Caramenti, Gian Carlo; Valente, Maurizio; Biella, Gabriele E. M.

2012-01-01

Local Field Potentials (LFPs) integrate multiple neuronal events like synaptic inputs and intracellular potentials. LFP spatiotemporal features are particularly relevant in view of their applications both in research (e.g. for understanding brain rhythms, inter-areal neural communication and neronal coding) and in the clinics (e.g. for improving invasive Brain-Machine Interface devices). However the relation between LFPs and spikes is complex and not fully understood. As spikes represent the fundamental currency of neuronal communication this gap in knowledge strongly limits our comprehension of neuronal phenomena underlying LFPs. We investigated the LFP-spike relation during tactile stimulation in primary somatosensory (S-I) cortex in the rat. First we quantified how reliably LFPs and spikes code for a stimulus occurrence. Then we used the information obtained from our analyses to design a predictive model for spike occurrence based on LFP inputs. The model was endowed with a flexible meta-structure whose exact form, both in parameters and structure, was estimated by using a multi-objective optimization strategy. Our method provided a set of nonlinear simple equations that maximized the match between models and true neurons in terms of spike timings and Peri Stimulus Time Histograms. We found that both LFPs and spikes can code for stimulus occurrence with millisecond precision, showing, however, high variability. Spike patterns were predicted significantly above chance for 75% of the neurons analysed. Crucially, the level of prediction accuracy depended on the reliability in coding for the stimulus occurrence. The best predictions were obtained when both spikes and LFPs were highly responsive to the stimuli. Spike reliability is known to depend on neuron intrinsic properties (i.e. on channel noise) and on spontaneous local network fluctuations. Our results suggest that the latter, measured through the LFP response variability, play a dominant role. PMID:22586452

Spikes matter for phase-locked bursting in inhibitory neurons

Science.gov (United States)

Jalil, Sajiya; Belykh, Igor; Shilnikov, Andrey

2012-03-01

We show that inhibitory networks composed of two endogenously bursting neurons can robustly display several coexistent phase-locked states in addition to stable antiphase and in-phase bursting. This work complements and enhances our recent result [Jalil, Belykh, and Shilnikov, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.81.045201 81, 045201(R) (2010)] that fast reciprocal inhibition can synchronize bursting neurons due to spike interactions. We reveal the role of spikes in generating multiple phase-locked states and demonstrate that this multistability is generic by analyzing diverse models of bursting networks with various fast inhibitory synapses; the individual cell models include the reduced leech heart interneuron, the Sherman model for pancreatic beta cells, and the Purkinje neuron model.

Solving constraint satisfaction problems with networks of spiking neurons

Directory of Open Access Journals (Sweden)

Zeno eJonke

2016-03-01

Full Text Available Network of neurons in the brain apply – unlike processors in our current generation ofcomputer hardware – an event-based processing strategy, where short pulses (spikes areemitted sparsely by neurons to signal the occurrence of an event at a particular point intime. Such spike-based computations promise to be substantially more power-efficient thantraditional clocked processing schemes. However it turned out to be surprisingly difficult todesign networks of spiking neurons that can solve difficult computational problems on the levelof single spikes (rather than rates of spikes. We present here a new method for designingnetworks of spiking neurons via an energy function. Furthermore we show how the energyfunction of a network of stochastically firing neurons can be shaped in a quite transparentmanner by composing the networks of simple stereotypical network motifs. We show that thisdesign approach enables networks of spiking neurons to produce approximate solutions todifficult (NP-hard constraint satisfaction problems from the domains of planning/optimizationand verification/logical inference. The resulting networks employ noise as a computationalresource. Nevertheless the timing of spikes (rather than just spike rates plays an essential rolein their computations. Furthermore, networks of spiking neurons carry out for the Traveling Salesman Problem a more efficient stochastic search for good solutions compared with stochastic artificial neural networks (Boltzmann machines and Gibbs sampling.

The chronotron: a neuron that learns to fire temporally precise spike patterns.

Directory of Open Access Journals (Sweden)

Răzvan V Florian

Full Text Available In many cases, neurons process information carried by the precise timings of spikes. Here we show how neurons can learn to generate specific temporally precise output spikes in response to input patterns of spikes having precise timings, thus processing and memorizing information that is entirely temporally coded, both as input and as output. We introduce two new supervised learning rules for spiking neurons with temporal coding of information (chronotrons, one that provides high memory capacity (E-learning, and one that has a higher biological plausibility (I-learning. With I-learning, the neuron learns to fire the target spike trains through synaptic changes that are proportional to the synaptic currents at the timings of real and target output spikes. We study these learning rules in computer simulations where we train integrate-and-fire neurons. Both learning rules allow neurons to fire at the desired timings, with sub-millisecond precision. We show how chronotrons can learn to classify their inputs, by firing identical, temporally precise spike trains for different inputs belonging to the same class. When the input is noisy, the classification also leads to noise reduction. We compute lower bounds for the memory capacity of chronotrons and explore the influence of various parameters on chronotrons' performance. The chronotrons can model neurons that encode information in the time of the first spike relative to the onset of salient stimuli or neurons in oscillatory networks that encode information in the phases of spikes relative to the background oscillation. Our results show that firing one spike per cycle optimizes memory capacity in neurons encoding information in the phase of firing relative to a background rhythm.

Solving Constraint Satisfaction Problems with Networks of Spiking Neurons.

Science.gov (United States)

Jonke, Zeno; Habenschuss, Stefan; Maass, Wolfgang

2016-01-01

Network of neurons in the brain apply-unlike processors in our current generation of computer hardware-an event-based processing strategy, where short pulses (spikes) are emitted sparsely by neurons to signal the occurrence of an event at a particular point in time. Such spike-based computations promise to be substantially more power-efficient than traditional clocked processing schemes. However, it turns out to be surprisingly difficult to design networks of spiking neurons that can solve difficult computational problems on the level of single spikes, rather than rates of spikes. We present here a new method for designing networks of spiking neurons via an energy function. Furthermore, we show how the energy function of a network of stochastically firing neurons can be shaped in a transparent manner by composing the networks of simple stereotypical network motifs. We show that this design approach enables networks of spiking neurons to produce approximate solutions to difficult (NP-hard) constraint satisfaction problems from the domains of planning/optimization and verification/logical inference. The resulting networks employ noise as a computational resource. Nevertheless, the timing of spikes plays an essential role in their computations. Furthermore, networks of spiking neurons carry out for the Traveling Salesman Problem a more efficient stochastic search for good solutions compared with stochastic artificial neural networks (Boltzmann machines) and Gibbs sampling.

Emergent properties of interacting populations of spiking neurons

Directory of Open Access Journals (Sweden)

Stefano eCardanobile

2011-12-01

Full Text Available Dynamic neuronal networks are a key paradigm of increasing importance in brain research, concerned with the functional analysis of biological neuronal networks and, at the same time, with the synthesis of artificial brain-like systems. In this context, neuronal network models serve as mathematical tools to understand the function of brains, but they might as well develop into future tools for enhancing certain functions of our nervous system.Here, we discuss our recent achievements in developing multiplicative point processes into a viable mathematical framework for spiking network modeling. The perspective is that the dynamic behavior of these neuronal networks on the population level is faithfully reflected by a set of non-linear rate equations, describing all interactions on this level. These equations, in turn, are similar in structure to the Lotka-Volterra equations, well known by their use in modeling predator-prey relationships in population biology, but abundant applications to economic theory have also been described.We present a number of biologically relevant examples for spiking network function, which can be studied with the help of the aforementioned correspondence between spike trains and specific systems of non-linear coupled ordinary differential equations. We claim that, enabled by the use of multiplicative point processes, we can make essential contributions to a more thorough understanding of the dynamical properties of neural populations.

Stochastic optimal control of single neuron spike trains

DEFF Research Database (Denmark)

Iolov, Alexandre; Ditlevsen, Susanne; Longtin, Andrë

2014-01-01

stimulation of a neuron to achieve a target spike train under the physiological constraint to not damage tissue. Approach. We pose a stochastic optimal control problem to precisely specify the spike times in a leaky integrate-and-fire (LIF) model of a neuron with noise assumed to be of intrinsic or synaptic...... origin. In particular, we allow for the noise to be of arbitrary intensity. The optimal control problem is solved using dynamic programming when the controller has access to the voltage (closed-loop control), and using a maximum principle for the transition density when the controller only has access...... to the spike times (open-loop control). Main results. We have developed a stochastic optimal control algorithm to obtain precise spike times. It is applicable in both the supra-threshold and sub-threshold regimes, under open-loop and closed-loop conditions and with an arbitrary noise intensity; the accuracy...

Nicotine-Mediated ADP to Spike Transition: Double Spiking in Septal Neurons.

Science.gov (United States)

Kodirov, Sodikdjon A; Wehrmeister, Michael; Colom, Luis

2016-04-01

The majority of neurons in lateral septum (LS) are electrically silent at resting membrane potential. Nicotine transiently excites a subset of neurons and occasionally leads to long lasting bursting activity upon longer applications. We have observed simultaneous changes in frequencies and amplitudes of spontaneous action potentials (AP) in the presence of nicotine. During the prolonged exposure, nicotine increased numbers of spikes within a burst. One of the hallmarks of nicotine effects was the occurrences of double spikes (known also as bursting). Alignment of 51 spontaneous spikes, triggered upon continuous application of nicotine, revealed that the slope of after-depolarizing potential gradually increased (1.4 vs. 3 mV/ms) and neuron fired the second AP, termed as double spiking. A transition from a single AP to double spikes increased the amplitude of after-hyperpolarizing potential. The amplitude of the second (premature) AP was smaller compared to the first one, and this correlation persisted in regard to their duration (half-width). A similar bursting activity in the presence of nicotine, to our knowledge, has not been reported previously in the septal structure in general and in LS in particular.

Time Resolution Dependence of Information Measures for Spiking Neurons: Scaling and Universality

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James P Crutchfield

2015-08-01

Full Text Available The mutual information between stimulus and spike-train response is commonly used to monitor neural coding efficiency, but neuronal computation broadly conceived requires more refined and targeted information measures of input-output joint processes. A first step towards that larger goal is todevelop information measures for individual output processes, including information generation (entropy rate, stored information (statisticalcomplexity, predictable information (excess entropy, and active information accumulation (bound information rate. We calculate these for spike trains generated by a variety of noise-driven integrate-and-fire neurons as a function of time resolution and for alternating renewal processes. We show that their time-resolution dependence reveals coarse-grained structural properties of interspike interval statistics; e.g., $tau$-entropy rates that diverge less quickly than the firing rate indicate interspike interval correlations. We also find evidence that the excess entropy and regularized statistical complexity of different types of integrate-and-fire neurons are universal in the continuous-time limit in the sense that they do not depend on mechanism details. This suggests a surprising simplicity in the spike trains generated by these model neurons. Interestingly, neurons with gamma-distributed ISIs and neurons whose spike trains are alternating renewal processes do not fall into the same universality class. These results lead to two conclusions. First, the dependence of information measures on time resolution reveals mechanistic details about spike train generation. Second, information measures can be used as model selection tools for analyzing spike train processes.

Biophysical properties and computational modeling of calcium spikes in serotonergic neurons of the dorsal raphe nucleus.

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Tuckwell, Henry C

2013-06-01

Serotonergic neurons of the dorsal raphe nuclei, with their extensive innervation of nearly the whole brain have important modulatory effects on many cognitive and physiological processes. They play important roles in clinical depression and other psychiatric disorders. In order to quantify the effects of serotonergic transmission on target cells it is desirable to construct computational models and to this end these it is necessary to have details of the biophysical and spike properties of the serotonergic neurons. Here several basic properties are reviewed with data from several studies since the 1960s to the present. The quantities included are input resistance, resting membrane potential, membrane time constant, firing rate, spike duration, spike and afterhyperpolarization (AHP) amplitude, spike threshold, cell capacitance, soma and somadendritic areas. The action potentials of these cells are normally triggered by a combination of sodium and calcium currents which may result in autonomous pacemaker activity. We here analyse the mechanisms of high-threshold calcium spikes which have been demonstrated in these cells the presence of TTX (tetrodotoxin). The parameters for calcium dynamics required to give calcium spikes are quite different from those for regular spiking which suggests the involvement of restricted parts of the soma-dendritic surface as has been found, for example, in hippocampal neurons. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Spiking and bursting patterns of fractional-order Izhikevich model

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Teka, Wondimu W.; Upadhyay, Ranjit Kumar; Mondal, Argha

2018-03-01

Bursting and spiking oscillations play major roles in processing and transmitting information in the brain through cortical neurons that respond differently to the same signal. These oscillations display complex dynamics that might be produced by using neuronal models and varying many model parameters. Recent studies have shown that models with fractional order can produce several types of history-dependent neuronal activities without the adjustment of several parameters. We studied the fractional-order Izhikevich model and analyzed different kinds of oscillations that emerge from the fractional dynamics. The model produces a wide range of neuronal spike responses, including regular spiking, fast spiking, intrinsic bursting, mixed mode oscillations, regular bursting and chattering, by adjusting only the fractional order. Both the active and silent phase of the burst increase when the fractional-order model further deviates from the classical model. For smaller fractional order, the model produces memory dependent spiking activity after the pulse signal turned off. This special spiking activity and other properties of the fractional-order model are caused by the memory trace that emerges from the fractional-order dynamics and integrates all the past activities of the neuron. On the network level, the response of the neuronal network shifts from random to scale-free spiking. Our results suggest that the complex dynamics of spiking and bursting can be the result of the long-term dependence and interaction of intracellular and extracellular ionic currents.

Spiking irregularity and frequency modulate the behavioral report of single-neuron stimulation.

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Doron, Guy; von Heimendahl, Moritz; Schlattmann, Peter; Houweling, Arthur R; Brecht, Michael

2014-02-05

The action potential activity of single cortical neurons can evoke measurable sensory effects, but it is not known how spiking parameters and neuronal subtypes affect the evoked sensations. Here, we examined the effects of spike train irregularity, spike frequency, and spike number on the detectability of single-neuron stimulation in rat somatosensory cortex. For regular-spiking, putative excitatory neurons, detectability increased with spike train irregularity and decreasing spike frequencies but was not affected by spike number. Stimulation of single, fast-spiking, putative inhibitory neurons led to a larger sensory effect compared to regular-spiking neurons, and the effect size depended only on spike irregularity. An ideal-observer analysis suggests that, under our experimental conditions, rats were using integration windows of a few hundred milliseconds or more. Our data imply that the behaving animal is sensitive to single neurons' spikes and even to their temporal patterning. Copyright © 2014 Elsevier Inc. All rights reserved.

Inverse stochastic resonance in networks of spiking neurons.

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Uzuntarla, Muhammet; Barreto, Ernest; Torres, Joaquin J

2017-07-01

Inverse Stochastic Resonance (ISR) is a phenomenon in which the average spiking rate of a neuron exhibits a minimum with respect to noise. ISR has been studied in individual neurons, but here, we investigate ISR in scale-free networks, where the average spiking rate is calculated over the neuronal population. We use Hodgkin-Huxley model neurons with channel noise (i.e., stochastic gating variable dynamics), and the network connectivity is implemented via electrical or chemical connections (i.e., gap junctions or excitatory/inhibitory synapses). We find that the emergence of ISR depends on the interplay between each neuron's intrinsic dynamical structure, channel noise, and network inputs, where the latter in turn depend on network structure parameters. We observe that with weak gap junction or excitatory synaptic coupling, network heterogeneity and sparseness tend to favor the emergence of ISR. With inhibitory coupling, ISR is quite robust. We also identify dynamical mechanisms that underlie various features of this ISR behavior. Our results suggest possible ways of experimentally observing ISR in actual neuronal systems.

A spatially resolved network spike in model neuronal cultures reveals nucleation centers, circular traveling waves and drifting spiral waves.

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Paraskevov, A V; Zendrikov, D K

2017-03-23

We show that in model neuronal cultures, where the probability of interneuronal connection formation decreases exponentially with increasing distance between the neurons, there exists a small number of spatial nucleation centers of a network spike, from where the synchronous spiking activity starts propagating in the network typically in the form of circular traveling waves. The number of nucleation centers and their spatial locations are unique and unchanged for a given realization of neuronal network but are different for different networks. In contrast, if the probability of interneuronal connection formation is independent of the distance between neurons, then the nucleation centers do not arise and the synchronization of spiking activity during a network spike occurs spatially uniform throughout the network. Therefore one can conclude that spatial proximity of connections between neurons is important for the formation of nucleation centers. It is also shown that fluctuations of the spatial density of neurons at their random homogeneous distribution typical for the experiments in vitro do not determine the locations of the nucleation centers. The simulation results are qualitatively consistent with the experimental observations.

Span: spike pattern association neuron for learning spatio-temporal spike patterns.

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Mohemmed, Ammar; Schliebs, Stefan; Matsuda, Satoshi; Kasabov, Nikola

2012-08-01

Spiking Neural Networks (SNN) were shown to be suitable tools for the processing of spatio-temporal information. However, due to their inherent complexity, the formulation of efficient supervised learning algorithms for SNN is difficult and remains an important problem in the research area. This article presents SPAN - a spiking neuron that is able to learn associations of arbitrary spike trains in a supervised fashion allowing the processing of spatio-temporal information encoded in the precise timing of spikes. The idea of the proposed algorithm is to transform spike trains during the learning phase into analog signals so that common mathematical operations can be performed on them. Using this conversion, it is possible to apply the well-known Widrow-Hoff rule directly to the transformed spike trains in order to adjust the synaptic weights and to achieve a desired input/output spike behavior of the neuron. In the presented experimental analysis, the proposed learning algorithm is evaluated regarding its learning capabilities, its memory capacity, its robustness to noisy stimuli and its classification performance. Differences and similarities of SPAN regarding two related algorithms, ReSuMe and Chronotron, are discussed.

Clustering predicts memory performance in networks of spiking and non-spiking neurons

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Weiliang eChen

2011-03-01

Full Text Available The problem we address in this paper is that of finding effective and parsimonious patterns of connectivity in sparse associative memories. This problem must be addressed in real neuronal systems, so that results in artificial systems could throw light on real systems. We show that there are efficient patterns of connectivity and that these patterns are effective in models with either spiking or non-spiking neurons. This suggests that there may be some underlying general principles governing good connectivity in such networks. We also show that the clustering of the network, measured by Clustering Coefficient, has a strong linear correlation to the performance of associative memory. This result is important since a purely static measure of network connectivity appears to determine an important dynamic property of the network.

Superficial dorsal horn neurons with double spike activity in the rat.

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Rojas-Piloni, Gerardo; Dickenson, Anthony H; Condés-Lara, Miguel

2007-05-29

Superficial dorsal horn neurons promote the transfer of nociceptive information from the periphery to supraspinal structures. The membrane and discharge properties of spinal cord neurons can alter the reliability of peripheral signals. In this paper, we analyze the location and response properties of a particular class of dorsal horn neurons that exhibits double spike discharge with a very short interspike interval (2.01+/-0.11 ms). These neurons receive nociceptive C-fiber input and are located in laminae I-II. Double spikes are generated spontaneously or by depolarizing current injection (interval of 2.37+/-0.22). Cells presenting double spike (interval 2.28+/-0.11) increased the firing rate by electrical noxious stimulation, as well as, in the first minutes after carrageenan injection into their receptive field. Carrageenan is a polysaccharide soluble in water and it is used for producing an experimental model of semi-chronic pain. In the present study carrageenan also produces an increase in the interval between double spikes and then, reduced their occurrence after 5-10 min. The results suggest that double spikes are due to intrinsic membrane properties and that their frequency is related to C-fiber nociceptive activity. The present work shows evidence that double spikes in superficial spinal cord neurones are related to the nociceptive stimulation, and they are possibly part of an acute pain-control mechanism.

Stereopsis and 3D surface perception by spiking neurons in laminar cortical circuits: a method for converting neural rate models into spiking models.

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Cao, Yongqiang; Grossberg, Stephen

2012-02-01

A laminar cortical model of stereopsis and 3D surface perception is developed and simulated. The model shows how spiking neurons that interact in hierarchically organized laminar circuits of the visual cortex can generate analog properties of 3D visual percepts. The model describes how monocular and binocular oriented filtering interact with later stages of 3D boundary formation and surface filling-in in the LGN and cortical areas V1, V2, and V4. It proposes how interactions between layers 4, 3B, and 2/3 in V1 and V2 contribute to stereopsis, and how binocular and monocular information combine to form 3D boundary and surface representations. The model suggests how surface-to-boundary feedback from V2 thin stripes to pale stripes helps to explain how computationally complementary boundary and surface formation properties lead to a single consistent percept, eliminate redundant 3D boundaries, and trigger figure-ground perception. The model also shows how false binocular boundary matches may be eliminated by Gestalt grouping properties. In particular, the disparity filter, which helps to solve the correspondence problem by eliminating false matches, is realized using inhibitory interneurons as part of the perceptual grouping process by horizontal connections in layer 2/3 of cortical area V2. The 3D sLAMINART model simulates 3D surface percepts that are consciously seen in 18 psychophysical experiments. These percepts include contrast variations of dichoptic masking and the correspondence problem, the effect of interocular contrast differences on stereoacuity, Panum's limiting case, the Venetian blind illusion, stereopsis with polarity-reversed stereograms, da Vinci stereopsis, and perceptual closure. The model hereby illustrates a general method of unlumping rate-based models that use the membrane equations of neurophysiology into models that use spiking neurons, and which may be embodied in VLSI chips that use spiking neurons to minimize heat production. Copyright �

Spike Code Flow in Cultured Neuronal Networks.

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Tamura, Shinichi; Nishitani, Yoshi; Hosokawa, Chie; Miyoshi, Tomomitsu; Sawai, Hajime; Kamimura, Takuya; Yagi, Yasushi; Mizuno-Matsumoto, Yuko; Chen, Yen-Wei

2016-01-01

We observed spike trains produced by one-shot electrical stimulation with 8 × 8 multielectrodes in cultured neuronal networks. Each electrode accepted spikes from several neurons. We extracted the short codes from spike trains and obtained a code spectrum with a nominal time accuracy of 1%. We then constructed code flow maps as movies of the electrode array to observe the code flow of "1101" and "1011," which are typical pseudorandom sequence such as that we often encountered in a literature and our experiments. They seemed to flow from one electrode to the neighboring one and maintained their shape to some extent. To quantify the flow, we calculated the "maximum cross-correlations" among neighboring electrodes, to find the direction of maximum flow of the codes with lengths less than 8. Normalized maximum cross-correlations were almost constant irrespective of code. Furthermore, if the spike trains were shuffled in interval orders or in electrodes, they became significantly small. Thus, the analysis suggested that local codes of approximately constant shape propagated and conveyed information across the network. Hence, the codes can serve as visible and trackable marks of propagating spike waves as well as evaluating information flow in the neuronal network.

Emergent dynamics of spiking neurons with fluctuating threshold

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Bhattacharjee, Anindita; Das, M. K.

2017-05-01

Role of fluctuating threshold on neuronal dynamics is investigated. The threshold function is assumed to follow a normal probability distribution. Standard deviation of inter-spike interval of the response is computed as an indicator of irregularity in spike emission. It has been observed that, the irregularity in spiking is more if the threshold variation is more. A significant change in modal characteristics of Inter Spike Intervals (ISI) is seen to occur as a function of fluctuation parameter. Investigation is further carried out for coupled system of neurons. Cooperative dynamics of coupled neurons are discussed in view of synchronization. Total and partial synchronization regimes are depicted with the help of contour plots of synchrony measure under various conditions. Results of this investigation may provide a basis for exploring the complexities of neural communication and brain functioning.

Colored noise and memory effects on formal spiking neuron models

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da Silva, L. A.; Vilela, R. D.

2015-06-01

Simplified neuronal models capture the essence of the electrical activity of a generic neuron, besides being more interesting from the computational point of view when compared to higher-dimensional models such as the Hodgkin-Huxley one. In this work, we propose a generalized resonate-and-fire model described by a generalized Langevin equation that takes into account memory effects and colored noise. We perform a comprehensive numerical analysis to study the dynamics and the point process statistics of the proposed model, highlighting interesting new features such as (i) nonmonotonic behavior (emergence of peak structures, enhanced by the choice of colored noise characteristic time scale) of the coefficient of variation (CV) as a function of memory characteristic time scale, (ii) colored noise-induced shift in the CV, and (iii) emergence and suppression of multimodality in the interspike interval (ISI) distribution due to memory-induced subthreshold oscillations. Moreover, in the noise-induced spike regime, we study how memory and colored noise affect the coherence resonance (CR) phenomenon. We found that for sufficiently long memory, not only is CR suppressed but also the minimum of the CV-versus-noise intensity curve that characterizes the presence of CR may be replaced by a maximum. The aforementioned features allow to interpret the interplay between memory and colored noise as an effective control mechanism to neuronal variability. Since both variability and nontrivial temporal patterns in the ISI distribution are ubiquitous in biological cells, we hope the present model can be useful in modeling real aspects of neurons.

Joint Probability-Based Neuronal Spike Train Classification

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Yan Chen

2009-01-01

Full Text Available Neuronal spike trains are used by the nervous system to encode and transmit information. Euclidean distance-based methods (EDBMs have been applied to quantify the similarity between temporally-discretized spike trains and model responses. In this study, using the same discretization procedure, we developed and applied a joint probability-based method (JPBM to classify individual spike trains of slowly adapting pulmonary stretch receptors (SARs. The activity of individual SARs was recorded in anaesthetized, paralysed adult male rabbits, which were artificially-ventilated at constant rate and one of three different volumes. Two-thirds of the responses to the 600 stimuli presented at each volume were used to construct three response models (one for each stimulus volume consisting of a series of time bins, each with spike probabilities. The remaining one-third of the responses where used as test responses to be classified into one of the three model responses. This was done by computing the joint probability of observing the same series of events (spikes or no spikes, dictated by the test response in a given model and determining which probability of the three was highest. The JPBM generally produced better classification accuracy than the EDBM, and both performed well above chance. Both methods were similarly affected by variations in discretization parameters, response epoch duration, and two different response alignment strategies. Increasing bin widths increased classification accuracy, which also improved with increased observation time, but primarily during periods of increasing lung inflation. Thus, the JPBM is a simple and effective method performing spike train classification.

Input-output relation and energy efficiency in the neuron with different spike threshold dynamics.

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Yi, Guo-Sheng; Wang, Jiang; Tsang, Kai-Ming; Wei, Xi-Le; Deng, Bin

2015-01-01

Neuron encodes and transmits information through generating sequences of output spikes, which is a high energy-consuming process. The spike is initiated when membrane depolarization reaches a threshold voltage. In many neurons, threshold is dynamic and depends on the rate of membrane depolarization (dV/dt) preceding a spike. Identifying the metabolic energy involved in neural coding and their relationship to threshold dynamic is critical to understanding neuronal function and evolution. Here, we use a modified Morris-Lecar model to investigate neuronal input-output property and energy efficiency associated with different spike threshold dynamics. We find that the neurons with dynamic threshold sensitive to dV/dt generate discontinuous frequency-current curve and type II phase response curve (PRC) through Hopf bifurcation, and weak noise could prohibit spiking when bifurcation just occurs. The threshold that is insensitive to dV/dt, instead, results in a continuous frequency-current curve, a type I PRC and a saddle-node on invariant circle bifurcation, and simultaneously weak noise cannot inhibit spiking. It is also shown that the bifurcation, frequency-current curve and PRC type associated with different threshold dynamics arise from the distinct subthreshold interactions of membrane currents. Further, we observe that the energy consumption of the neuron is related to its firing characteristics. The depolarization of spike threshold improves neuronal energy efficiency by reducing the overlap of Na(+) and K(+) currents during an action potential. The high energy efficiency is achieved at more depolarized spike threshold and high stimulus current. These results provide a fundamental biophysical connection that links spike threshold dynamics, input-output relation, energetics and spike initiation, which could contribute to uncover neural encoding mechanism.

A self-resetting spiking phase-change neuron

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Cobley, R. A.; Hayat, H.; Wright, C. D.

2018-05-01

Neuromorphic, or brain-inspired, computing applications of phase-change devices have to date concentrated primarily on the implementation of phase-change synapses. However, the so-called accumulation mode of operation inherent in phase-change materials and devices can also be used to mimic the integrative properties of a biological neuron. Here we demonstrate, using physical modelling of nanoscale devices and SPICE modelling of associated circuits, that a single phase-change memory cell integrated into a comparator type circuit can deliver a basic hardware mimic of an integrate-and-fire spiking neuron with self-resetting capabilities. Such phase-change neurons, in combination with phase-change synapses, can potentially open a new route for the realisation of all-phase-change neuromorphic computing.

A self-resetting spiking phase-change neuron.

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Cobley, R A; Hayat, H; Wright, C D

2018-05-11

Neuromorphic, or brain-inspired, computing applications of phase-change devices have to date concentrated primarily on the implementation of phase-change synapses. However, the so-called accumulation mode of operation inherent in phase-change materials and devices can also be used to mimic the integrative properties of a biological neuron. Here we demonstrate, using physical modelling of nanoscale devices and SPICE modelling of associated circuits, that a single phase-change memory cell integrated into a comparator type circuit can deliver a basic hardware mimic of an integrate-and-fire spiking neuron with self-resetting capabilities. Such phase-change neurons, in combination with phase-change synapses, can potentially open a new route for the realisation of all-phase-change neuromorphic computing.

Spike Code Flow in Cultured Neuronal Networks

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Shinichi Tamura

2016-01-01

Full Text Available We observed spike trains produced by one-shot electrical stimulation with 8 × 8 multielectrodes in cultured neuronal networks. Each electrode accepted spikes from several neurons. We extracted the short codes from spike trains and obtained a code spectrum with a nominal time accuracy of 1%. We then constructed code flow maps as movies of the electrode array to observe the code flow of “1101” and “1011,” which are typical pseudorandom sequence such as that we often encountered in a literature and our experiments. They seemed to flow from one electrode to the neighboring one and maintained their shape to some extent. To quantify the flow, we calculated the “maximum cross-correlations” among neighboring electrodes, to find the direction of maximum flow of the codes with lengths less than 8. Normalized maximum cross-correlations were almost constant irrespective of code. Furthermore, if the spike trains were shuffled in interval orders or in electrodes, they became significantly small. Thus, the analysis suggested that local codes of approximately constant shape propagated and conveyed information across the network. Hence, the codes can serve as visible and trackable marks of propagating spike waves as well as evaluating information flow in the neuronal network.

Inference of neuronal network spike dynamics and topology from calcium imaging data

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Henry eLütcke

2013-12-01

Full Text Available Two-photon calcium imaging enables functional analysis of neuronal circuits by inferring action potential (AP occurrence ('spike trains' from cellular fluorescence signals. It remains unclear how experimental parameters such as signal-to-noise ratio (SNR and acquisition rate affect spike inference and whether additional information about network structure can be extracted. Here we present a simulation framework for quantitatively assessing how well spike dynamics and network topology can be inferred from noisy calcium imaging data. For simulated AP-evoked calcium transients in neocortical pyramidal cells, we analyzed the quality of spike inference as a function of SNR and data acquisition rate using a recently introduced peeling algorithm. Given experimentally attainable values of SNR and acquisition rate, neural spike trains could be reconstructed accurately and with up to millisecond precision. We then applied statistical neuronal network models to explore how remaining uncertainties in spike inference affect estimates of network connectivity and topological features of network organization. We define the experimental conditions suitable for inferring whether the network has a scale-free structure and determine how well hub neurons can be identified. Our findings provide a benchmark for future calcium imaging studies that aim to reliably infer neuronal network properties.

A spiking neuron circuit based on a carbon nanotube transistor

International Nuclear Information System (INIS)

Chen, C-L; Kim, K; Truong, Q; Shen, A; Li, Z; Chen, Y

2012-01-01

A spiking neuron circuit based on a carbon nanotube (CNT) transistor is presented in this paper. The spiking neuron circuit has a crossbar architecture in which the transistor gates are connected to its row electrodes and the transistor sources are connected to its column electrodes. An electrochemical cell is incorporated in the gate of the transistor by sandwiching a hydrogen-doped poly(ethylene glycol)methyl ether (PEG) electrolyte between the CNT channel and the top gate electrode. An input spike applied to the gate triggers a dynamic drift of the hydrogen ions in the PEG electrolyte, resulting in a post-synaptic current (PSC) through the CNT channel. Spikes input into the rows trigger PSCs through multiple CNT transistors, and PSCs cumulate in the columns and integrate into a ‘soma’ circuit to trigger output spikes based on an integrate-and-fire mechanism. The spiking neuron circuit can potentially emulate biological neuron networks and their intelligent functions. (paper)

Modeling spiking behavior of neurons with time-dependent Poisson processes.

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Shinomoto, S; Tsubo, Y

2001-10-01

Three kinds of interval statistics, as represented by the coefficient of variation, the skewness coefficient, and the correlation coefficient of consecutive intervals, are evaluated for three kinds of time-dependent Poisson processes: pulse regulated, sinusoidally regulated, and doubly stochastic. Among these three processes, the sinusoidally regulated and doubly stochastic Poisson processes, in the case when the spike rate varies slowly compared with the mean interval between spikes, are found to be consistent with the three statistical coefficients exhibited by data recorded from neurons in the prefrontal cortex of monkeys.

Dynamical mean-field theory of noisy spiking neuron ensembles: Application to the Hodgkin-Huxley model

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Hasegawa, Hideo

2003-01-01

A dynamical mean-field approximation (DMA) previously proposed by the present author [H. Hasegawa, Phys. Rev E 67, 041903 (2003)] has been extended to ensembles described by a general noisy spiking neuron model. Ensembles of N-unit neurons, each of which is expressed by coupled K-dimensional differential equations (DEs), are assumed to be subject to spatially correlated white noises. The original KN-dimensional stochastic DEs have been replaced by K(K+2)-dimensional deterministic DEs expressed in terms of means and the second-order moments of local and global variables: the fourth-order contributions are taken into account by the Gaussian decoupling approximation. Our DMA has been applied to an ensemble of Hodgkin-Huxley (HH) neurons (K=4), for which effects of the noise, the coupling strength, and the ensemble size on the response to a single-spike input have been investigated. Numerical results calculated by the DMA theory are in good agreement with those obtained by direct simulations, although the former computation is about a thousand times faster than the latter for a typical HH neuron ensemble with N=100

Temporally coordinated spiking activity of human induced pluripotent stem cell-derived neurons co-cultured with astrocytes.

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Kayama, Tasuku; Suzuki, Ikuro; Odawara, Aoi; Sasaki, Takuya; Ikegaya, Yuji

2018-01-01

In culture conditions, human induced-pluripotent stem cells (hiPSC)-derived neurons form synaptic connections with other cells and establish neuronal networks, which are expected to be an in vitro model system for drug discovery screening and toxicity testing. While early studies demonstrated effects of co-culture of hiPSC-derived neurons with astroglial cells on survival and maturation of hiPSC-derived neurons, the population spiking patterns of such hiPSC-derived neurons have not been fully characterized. In this study, we analyzed temporal spiking patterns of hiPSC-derived neurons recorded by a multi-electrode array system. We discovered that specific sets of hiPSC-derived neurons co-cultured with astrocytes showed more frequent and highly coherent non-random synchronized spike trains and more dynamic changes in overall spike patterns over time. These temporally coordinated spiking patterns are physiological signs of organized circuits of hiPSC-derived neurons and suggest benefits of co-culture of hiPSC-derived neurons with astrocytes. Copyright © 2017 Elsevier Inc. All rights reserved.

Mirror Neurons Modeled Through Spike-Timing-Dependent Plasticity are Affected by Channelopathies Associated with Autism Spectrum Disorder.

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Antunes, Gabriela; Faria da Silva, Samuel F; Simoes de Souza, Fabio M

2018-06-01

Mirror neurons fire action potentials both when the agent performs a certain behavior and watches someone performing a similar action. Here, we present an original mirror neuron model based on the spike-timing-dependent plasticity (STDP) between two morpho-electrical models of neocortical pyramidal neurons. Both neurons fired spontaneously with basal firing rate that follows a Poisson distribution, and the STDP between them was modeled by the triplet algorithm. Our simulation results demonstrated that STDP is sufficient for the rise of mirror neuron function between the pairs of neocortical neurons. This is a proof of concept that pairs of neocortical neurons associating sensory inputs to motor outputs could operate like mirror neurons. In addition, we used the mirror neuron model to investigate whether channelopathies associated with autism spectrum disorder could impair the modeled mirror function. Our simulation results showed that impaired hyperpolarization-activated cationic currents (Ih) affected the mirror function between the pairs of neocortical neurons coupled by STDP.

A Cross-Correlated Delay Shift Supervised Learning Method for Spiking Neurons with Application to Interictal Spike Detection in Epilepsy.

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Guo, Lilin; Wang, Zhenzhong; Cabrerizo, Mercedes; Adjouadi, Malek

2017-05-01

This study introduces a novel learning algorithm for spiking neurons, called CCDS, which is able to learn and reproduce arbitrary spike patterns in a supervised fashion allowing the processing of spatiotemporal information encoded in the precise timing of spikes. Unlike the Remote Supervised Method (ReSuMe), synapse delays and axonal delays in CCDS are variants which are modulated together with weights during learning. The CCDS rule is both biologically plausible and computationally efficient. The properties of this learning rule are investigated extensively through experimental evaluations in terms of reliability, adaptive learning performance, generality to different neuron models, learning in the presence of noise, effects of its learning parameters and classification performance. Results presented show that the CCDS learning method achieves learning accuracy and learning speed comparable with ReSuMe, but improves classification accuracy when compared to both the Spike Pattern Association Neuron (SPAN) learning rule and the Tempotron learning rule. The merit of CCDS rule is further validated on a practical example involving the automated detection of interictal spikes in EEG records of patients with epilepsy. Results again show that with proper encoding, the CCDS rule achieves good recognition performance.

An online supervised learning method based on gradient descent for spiking neurons.

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Xu, Yan; Yang, Jing; Zhong, Shuiming

2017-09-01

The purpose of supervised learning with temporal encoding for spiking neurons is to make the neurons emit a specific spike train encoded by precise firing times of spikes. The gradient-descent-based (GDB) learning methods are widely used and verified in the current research. Although the existing GDB multi-spike learning (or spike sequence learning) methods have good performance, they work in an offline manner and still have some limitations. This paper proposes an online GDB spike sequence learning method for spiking neurons that is based on the online adjustment mechanism of real biological neuron synapses. The method constructs error function and calculates the adjustment of synaptic weights as soon as the neurons emit a spike during their running process. We analyze and synthesize desired and actual output spikes to select appropriate input spikes in the calculation of weight adjustment in this paper. The experimental results show that our method obviously improves learning performance compared with the offline learning manner and has certain advantage on learning accuracy compared with other learning methods. Stronger learning ability determines that the method has large pattern storage capacity. Copyright © 2017 Elsevier Ltd. All rights reserved.

Mapping cortical mesoscopic networks of single spiking cortical or sub-cortical neurons.

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Xiao, Dongsheng; Vanni, Matthieu P; Mitelut, Catalin C; Chan, Allen W; LeDue, Jeffrey M; Xie, Yicheng; Chen, Andrew Cn; Swindale, Nicholas V; Murphy, Timothy H

2017-02-04

Understanding the basis of brain function requires knowledge of cortical operations over wide-spatial scales, but also within the context of single neurons. In vivo, wide-field GCaMP imaging and sub-cortical/cortical cellular electrophysiology were used in mice to investigate relationships between spontaneous single neuron spiking and mesoscopic cortical activity. We make use of a rich set of cortical activity motifs that are present in spontaneous activity in anesthetized and awake animals. A mesoscale spike-triggered averaging procedure allowed the identification of motifs that are preferentially linked to individual spiking neurons by employing genetically targeted indicators of neuronal activity. Thalamic neurons predicted and reported specific cycles of wide-scale cortical inhibition/excitation. In contrast, spike-triggered maps derived from single cortical neurons yielded spatio-temporal maps expected for regional cortical consensus function. This approach can define network relationships between any point source of neuronal spiking and mesoscale cortical maps.

A Simple Deep Learning Method for Neuronal Spike Sorting

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Yang, Kai; Wu, Haifeng; Zeng, Yu

2017-10-01

Spike sorting is one of key technique to understand brain activity. With the development of modern electrophysiology technology, some recent multi-electrode technologies have been able to record the activity of thousands of neuronal spikes simultaneously. The spike sorting in this case will increase the computational complexity of conventional sorting algorithms. In this paper, we will focus spike sorting on how to reduce the complexity, and introduce a deep learning algorithm, principal component analysis network (PCANet) to spike sorting. The introduced method starts from a conventional model and establish a Toeplitz matrix. Through the column vectors in the matrix, we trains a PCANet, where some eigenvalue vectors of spikes could be extracted. Finally, support vector machine (SVM) is used to sort spikes. In experiments, we choose two groups of simulated data from public databases availably and compare this introduced method with conventional methods. The results indicate that the introduced method indeed has lower complexity with the same sorting errors as the conventional methods.

Contribution of LFP dynamics to single-neuron spiking variability in motor cortex during movement execution

Science.gov (United States)

Rule, Michael E.; Vargas-Irwin, Carlos; Donoghue, John P.; Truccolo, Wilson

2015-01-01

Understanding the sources of variability in single-neuron spiking responses is an important open problem for the theory of neural coding. This variability is thought to result primarily from spontaneous collective dynamics in neuronal networks. Here, we investigate how well collective dynamics reflected in motor cortex local field potentials (LFPs) can account for spiking variability during motor behavior. Neural activity was recorded via microelectrode arrays implanted in ventral and dorsal premotor and primary motor cortices of non-human primates performing naturalistic 3-D reaching and grasping actions. Point process models were used to quantify how well LFP features accounted for spiking variability not explained by the measured 3-D reach and grasp kinematics. LFP features included the instantaneous magnitude, phase and analytic-signal components of narrow band-pass filtered (δ,θ,α,β) LFPs, and analytic signal and amplitude envelope features in higher-frequency bands. Multiband LFP features predicted single-neuron spiking (1ms resolution) with substantial accuracy as assessed via ROC analysis. Notably, however, models including both LFP and kinematics features displayed marginal improvement over kinematics-only models. Furthermore, the small predictive information added by LFP features to kinematic models was redundant to information available in fast-timescale (spiking history. Overall, information in multiband LFP features, although predictive of single-neuron spiking during movement execution, was redundant to information available in movement parameters and spiking history. Our findings suggest that, during movement execution, collective dynamics reflected in motor cortex LFPs primarily relate to sensorimotor processes directly controlling movement output, adding little explanatory power to variability not accounted by movement parameters. PMID:26157365

Efficient computation in networks of spiking neurons: simulations and theory

International Nuclear Information System (INIS)

Natschlaeger, T.

1999-01-01

One of the most prominent features of biological neural systems is that individual neurons communicate via short electrical pulses, the so called action potentials or spikes. In this thesis we investigate possible mechanisms which can in principle explain how complex computations in spiking neural networks (SNN) can be performed very fast, i.e. within a few 10 milliseconds. Some of these models are based on the assumption that relevant information is encoded by the timing of individual spikes (temporal coding). We will also discuss a model which is based on a population code and still is able to perform fast complex computations. In their natural environment biological neural systems have to process signals with a rich temporal structure. Hence it is an interesting question how neural systems process time series. In this context we explore possible links between biophysical characteristics of single neurons (refractory behavior, connectivity, time course of postsynaptic potentials) and synapses (unreliability, dynamics) on the one hand and possible computations on times series on the other hand. Furthermore we describe a general model of computation that exploits dynamic synapses. This model provides a general framework for understanding how neural systems process time-varying signals. (author)

Racing to learn: statistical inference and learning in a single spiking neuron with adaptive kernels.

Science.gov (United States)

Afshar, Saeed; George, Libin; Tapson, Jonathan; van Schaik, André; Hamilton, Tara J

2014-01-01

This paper describes the Synapto-dendritic Kernel Adapting Neuron (SKAN), a simple spiking neuron model that performs statistical inference and unsupervised learning of spatiotemporal spike patterns. SKAN is the first proposed neuron model to investigate the effects of dynamic synapto-dendritic kernels and demonstrate their computational power even at the single neuron scale. The rule-set defining the neuron is simple: there are no complex mathematical operations such as normalization, exponentiation or even multiplication. The functionalities of SKAN emerge from the real-time interaction of simple additive and binary processes. Like a biological neuron, SKAN is robust to signal and parameter noise, and can utilize both in its operations. At the network scale neurons are locked in a race with each other with the fastest neuron to spike effectively "hiding" its learnt pattern from its neighbors. The robustness to noise, high speed, and simple building blocks not only make SKAN an interesting neuron model in computational neuroscience, but also make it ideal for implementation in digital and analog neuromorphic systems which is demonstrated through an implementation in a Field Programmable Gate Array (FPGA). Matlab, Python, and Verilog implementations of SKAN are available at: http://www.uws.edu.au/bioelectronics_neuroscience/bens/reproducible_research.

Spike timing rigidity is maintained in bursting neurons under pentobarbital-induced anesthetic conditions

Directory of Open Access Journals (Sweden)

Risako Kato

2016-11-01

Full Text Available Pentobarbital potentiates γ-aminobutyric acid (GABA-mediated inhibitory synaptic transmission by prolonging the open time of GABAA receptors. However, it is unknown how pentobarbital regulates cortical neuronal activities via local circuits in vivo. To examine this question, we performed extracellular unit recording in rat insular cortex under awake and anesthetic conditions. Not a few studies apply time-rescaling theorem to detect the features of repetitive spike firing. Similar to these methods, we define an average spike interval locally in time using random matrix theory (RMT, which enables us to compare different activity states on a universal scale. Neurons with high spontaneous firing frequency (> 5 Hz and bursting were classified as HFB neurons (n = 10, and those with low spontaneous firing frequency (< 10 Hz and without bursting were classified as non-HFB neurons (n = 48. Pentobarbital injection (30 mg/kg reduced firing frequency in all HFB neurons and in 78% of non-HFB neurons. RMT analysis demonstrated that pentobarbital increased in the number of neurons with repulsion in both HFB and non-HFB neurons, suggesting that there is a correlation between spikes within a short interspike interval. Under awake conditions, in 50% of HFB and 40% of non-HFB neurons, the decay phase of normalized histograms of spontaneous firing were fitted to an exponential function, which indicated that the first spike had no correlation with subsequent spikes. In contrast, under pentobarbital-induced anesthesia conditions, the number of non-HFB neurons that were fitted to an exponential function increased to 80%, but almost no change in HFB neurons was observed. These results suggest that under both awake and pentobarbital-induced anesthetized conditions, spike firing in HFB neurons is more robustly regulated by preceding spikes than by non-HFB neurons, which may reflect the GABAA receptor-mediated regulation of cortical activities. Whole-cell patch

Detection of bursts in neuronal spike trains by the mean inter-spike interval method

Institute of Scientific and Technical Information of China (English)

Lin Chen; Yong Deng; Weihua Luo; Zhen Wang; Shaoqun Zeng

2009-01-01

Bursts are electrical spikes firing with a high frequency, which are the most important property in synaptic plasticity and information processing in the central nervous system. However, bursts are difficult to identify because bursting activities or patterns vary with phys-iological conditions or external stimuli. In this paper, a simple method automatically to detect bursts in spike trains is described. This method auto-adaptively sets a parameter (mean inter-spike interval) according to intrinsic properties of the detected burst spike trains, without any arbitrary choices or any operator judgrnent. When the mean value of several successive inter-spike intervals is not larger than the parameter, a burst is identified. By this method, bursts can be automatically extracted from different bursting patterns of cultured neurons on multi-electrode arrays, as accurately as by visual inspection. Furthermore, significant changes of burst variables caused by electrical stimulus have been found in spontaneous activity of neuronal network. These suggest that the mean inter-spike interval method is robust for detecting changes in burst patterns and characteristics induced by environmental alterations.

Does spike-timing-dependent synaptic plasticity couple or decouple neurons firing in synchrony?

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Andreas eKnoblauch

2012-08-01

Full Text Available Spike synchronization is thought to have a constructive role for feature integration, attention, associativelearning, and the formation of bidirectionally connected Hebbian cell assemblies. By contrast, theoreticalstudies on spike-timing-dependent plasticity (STDP report an inherently decoupling influence of spikesynchronization on synaptic connections of coactivated neurons. For example, bidirectional synapticconnections as found in cortical areas could be reproduced only by assuming realistic models of STDP andrate coding. We resolve this conflict by theoretical analysis and simulation of various simple and realisticSTDP models that provide a more complete characterization of conditions when STDP leads to eithercoupling or decoupling of neurons firing in synchrony. In particular, we show that STDP consistentlycouples synchronized neurons if key model parameters are matched to physiological data: First, synapticpotentiation must be significantly stronger than synaptic depression for small (positive or negative timelags between presynaptic and postsynaptic spikes. Second, spike synchronization must be sufficientlyimprecise, for example, within a time window of 5-10msec instead of 1msec. Third, axonal propagationdelays should not be much larger than dendritic delays. Under these assumptions synchronized neuronswill be strongly coupled leading to a dominance of bidirectional synaptic connections even for simpleSTDP models and low mean firing rates at the level of spontaneous activity.

Reinforcement learning of targeted movement in a spiking neuronal model of motor cortex.

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George L Chadderdon

Full Text Available Sensorimotor control has traditionally been considered from a control theory perspective, without relation to neurobiology. In contrast, here we utilized a spiking-neuron model of motor cortex and trained it to perform a simple movement task, which consisted of rotating a single-joint "forearm" to a target. Learning was based on a reinforcement mechanism analogous to that of the dopamine system. This provided a global reward or punishment signal in response to decreasing or increasing distance from hand to target, respectively. Output was partially driven by Poisson motor babbling, creating stochastic movements that could then be shaped by learning. The virtual forearm consisted of a single segment rotated around an elbow joint, controlled by flexor and extensor muscles. The model consisted of 144 excitatory and 64 inhibitory event-based neurons, each with AMPA, NMDA, and GABA synapses. Proprioceptive cell input to this model encoded the 2 muscle lengths. Plasticity was only enabled in feedforward connections between input and output excitatory units, using spike-timing-dependent eligibility traces for synaptic credit or blame assignment. Learning resulted from a global 3-valued signal: reward (+1, no learning (0, or punishment (-1, corresponding to phasic increases, lack of change, or phasic decreases of dopaminergic cell firing, respectively. Successful learning only occurred when both reward and punishment were enabled. In this case, 5 target angles were learned successfully within 180 s of simulation time, with a median error of 8 degrees. Motor babbling allowed exploratory learning, but decreased the stability of the learned behavior, since the hand continued moving after reaching the target. Our model demonstrated that a global reinforcement signal, coupled with eligibility traces for synaptic plasticity, can train a spiking sensorimotor network to perform goal-directed motor behavior.

Reinforcement learning of targeted movement in a spiking neuronal model of motor cortex.

Science.gov (United States)

Chadderdon, George L; Neymotin, Samuel A; Kerr, Cliff C; Lytton, William W

2012-01-01

Sensorimotor control has traditionally been considered from a control theory perspective, without relation to neurobiology. In contrast, here we utilized a spiking-neuron model of motor cortex and trained it to perform a simple movement task, which consisted of rotating a single-joint "forearm" to a target. Learning was based on a reinforcement mechanism analogous to that of the dopamine system. This provided a global reward or punishment signal in response to decreasing or increasing distance from hand to target, respectively. Output was partially driven by Poisson motor babbling, creating stochastic movements that could then be shaped by learning. The virtual forearm consisted of a single segment rotated around an elbow joint, controlled by flexor and extensor muscles. The model consisted of 144 excitatory and 64 inhibitory event-based neurons, each with AMPA, NMDA, and GABA synapses. Proprioceptive cell input to this model encoded the 2 muscle lengths. Plasticity was only enabled in feedforward connections between input and output excitatory units, using spike-timing-dependent eligibility traces for synaptic credit or blame assignment. Learning resulted from a global 3-valued signal: reward (+1), no learning (0), or punishment (-1), corresponding to phasic increases, lack of change, or phasic decreases of dopaminergic cell firing, respectively. Successful learning only occurred when both reward and punishment were enabled. In this case, 5 target angles were learned successfully within 180 s of simulation time, with a median error of 8 degrees. Motor babbling allowed exploratory learning, but decreased the stability of the learned behavior, since the hand continued moving after reaching the target. Our model demonstrated that a global reinforcement signal, coupled with eligibility traces for synaptic plasticity, can train a spiking sensorimotor network to perform goal-directed motor behavior.

A reanalysis of "Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons".

Science.gov (United States)

Engelken, Rainer; Farkhooi, Farzad; Hansel, David; van Vreeswijk, Carl; Wolf, Fred

2016-01-01

Neuronal activity in the central nervous system varies strongly in time and across neuronal populations. It is a longstanding proposal that such fluctuations generically arise from chaotic network dynamics. Various theoretical studies predict that the rich dynamics of rate models operating in the chaotic regime can subserve circuit computation and learning. Neurons in the brain, however, communicate via spikes and it is a theoretical challenge to obtain similar rate fluctuations in networks of spiking neuron models. A recent study investigated spiking balanced networks of leaky integrate and fire (LIF) neurons and compared their dynamics to a matched rate network with identical topology, where single unit input-output functions were chosen from isolated LIF neurons receiving Gaussian white noise input. A mathematical analogy between the chaotic instability in networks of rate units and the spiking network dynamics was proposed. Here we revisit the behavior of the spiking LIF networks and these matched rate networks. We find expected hallmarks of a chaotic instability in the rate network: For supercritical coupling strength near the transition point, the autocorrelation time diverges. For subcritical coupling strengths, we observe critical slowing down in response to small external perturbations. In the spiking network, we found in contrast that the timescale of the autocorrelations is insensitive to the coupling strength and that rate deviations resulting from small input perturbations rapidly decay. The decay speed even accelerates for increasing coupling strength. In conclusion, our reanalysis demonstrates fundamental differences between the behavior of pulse-coupled spiking LIF networks and rate networks with matched topology and input-output function. In particular there is no indication of a corresponding chaotic instability in the spiking network.

Lateral Information Processing by Spiking Neurons: A Theoretical Model of the Neural Correlate of Consciousness

Directory of Open Access Journals (Sweden)

Marc Ebner

2011-01-01

Full Text Available Cognitive brain functions, for example, sensory perception, motor control and learning, are understood as computation by axonal-dendritic chemical synapses in networks of integrate-and-fire neurons. Cognitive brain functions may occur either consciously or nonconsciously (on “autopilot”. Conscious cognition is marked by gamma synchrony EEG, mediated largely by dendritic-dendritic gap junctions, sideways connections in input/integration layers. Gap-junction-connected neurons define a sub-network within a larger neural network. A theoretical model (the “conscious pilot” suggests that as gap junctions open and close, a gamma-synchronized subnetwork, or zone moves through the brain as an executive agent, converting nonconscious “auto-pilot” cognition to consciousness, and enhancing computation by coherent processing and collective integration. In this study we implemented sideways “gap junctions” in a single-layer artificial neural network to perform figure/ground separation. The set of neurons connected through gap junctions form a reconfigurable resistive grid or sub-network zone. In the model, outgoing spikes are temporally integrated and spatially averaged using the fixed resistive grid set up by neurons of similar function which are connected through gap-junctions. This spatial average, essentially a feedback signal from the neuron's output, determines whether particular gap junctions between neurons will open or close. Neurons connected through open gap junctions synchronize their output spikes. We have tested our gap-junction-defined sub-network in a one-layer neural network on artificial retinal inputs using real-world images. Our system is able to perform figure/ground separation where the laterally connected sub-network of neurons represents a perceived object. Even though we only show results for visual stimuli, our approach should generalize to other modalities. The system demonstrates a moving sub-network zone of

Spike propagation through the dorsal root ganglia in an unmyelinated sensory neuron: a modeling study.

Science.gov (United States)

Sundt, Danielle; Gamper, Nikita; Jaffe, David B

2015-12-01

Unmyelinated C-fibers are a major type of sensory neurons conveying pain information. Action potential conduction is regulated by the bifurcation (T-junction) of sensory neuron axons within the dorsal root ganglia (DRG). Understanding how C-fiber signaling is influenced by the morphology of the T-junction and the local expression of ion channels is important for understanding pain signaling. In this study we used biophysical computer modeling to investigate the influence of axon morphology within the DRG and various membrane conductances on the reliability of spike propagation. As expected, calculated input impedance and the amplitude of propagating action potentials were both lowest at the T-junction. Propagation reliability for single spikes was highly sensitive to the diameter of the stem axon and the density of voltage-gated Na(+) channels. A model containing only fast voltage-gated Na(+) and delayed-rectifier K(+) channels conducted trains of spikes up to frequencies of 110 Hz. The addition of slowly activating KCNQ channels (i.e., KV7 or M-channels) to the model reduced the following frequency to 30 Hz. Hyperpolarization produced by addition of a much slower conductance, such as a Ca(2+)-dependent K(+) current, was needed to reduce the following frequency to 6 Hz. Attenuation of driving force due to ion accumulation or hyperpolarization produced by a Na(+)-K(+) pump had no effect on following frequency but could influence the reliability of spike propagation mutually with the voltage shift generated by a Ca(2+)-dependent K(+) current. These simulations suggest how specific ion channels within the DRG may contribute toward therapeutic treatments for chronic pain. Copyright © 2015 the American Physiological Society.

Axonal propagation of simple and complex spikes in cerebellar Purkinje neurons.

Science.gov (United States)

Khaliq, Zayd M; Raman, Indira M

2005-01-12

In cerebellar Purkinje neurons, the reliability of propagation of high-frequency simple spikes and spikelets of complex spikes is likely to regulate inhibition of Purkinje target neurons. To test the extent to which a one-to-one correspondence exists between somatic and axonal spikes, we made dual somatic and axonal recordings from Purkinje neurons in mouse cerebellar slices. Somatic action potentials were recorded with a whole-cell pipette, and the corresponding axonal signals were recorded extracellularly with a loose-patch pipette. Propagation of spontaneous and evoked simple spikes was highly reliable. At somatic firing rates of approximately 200 spikes/sec, 375 Hz during somatic hyperpolarizations that silenced spontaneous firing to approximately 150 Hz during spontaneous activity. The probability of propagation of individual spikelets could be described quantitatively as a saturating function of spikelet amplitude, rate of rise, or preceding interspike interval. The results suggest that ion channels of Purkinje axons are adapted to produce extremely short refractory periods and that brief bursts of forward-propagating action potentials generated by complex spikes may contribute transiently to inhibition of postsynaptic neurons.

Error-backpropagation in temporally encoded networks of spiking neurons

NARCIS (Netherlands)

S.M. Bohte (Sander); J.A. La Poutré (Han); J.N. Kok (Joost)

2000-01-01

textabstractFor a network of spiking neurons that encodes information in the timing of individual spike-times, we derive a supervised learning rule, emph{SpikeProp, akin to traditional error-backpropagation and show how to overcome the discontinuities introduced by thresholding. With this algorithm,

A Computational Model to Investigate Astrocytic Glutamate Uptake Influence on Synaptic Transmission and Neuronal Spiking

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Sushmita Lakshmi Allam

2012-10-01

Full Text Available Over the past decades, our view of astrocytes has switched from passive support cells to active processing elements in the brain. The current view is that astrocytes shape neuronal communication and also play an important role in many neurodegenerative diseases. Despite the growing awareness of the importance of astrocytes, the exact mechanisms underlying neuron-astrocyte communication and the physiological consequences of astrocytic-neuronal interactions remain largely unclear. In this work, we define a modeling framework that will permit to address unanswered questions regarding the role of astrocytes. Our computational model of a detailed glutamatergic synapse facilitates the analysis of neural system responses to various stimuli and conditions that are otherwise difficult to obtain experimentally, in particular the readouts at the sub-cellular level. In this paper, we extend a detailed glutamatergic synaptic model, to include astrocytic glutamate transporters. We demonstrate how these glial transporters, responsible for the majority of glutamate uptake, modulate synaptic transmission mediated by ionotropic AMPA and NMDA receptors at glutamatergic synapses. Furthermore, we investigate how these local signaling effects at the synaptic level are translated into varying spatio-temporal patterns of neuron firing. Paired pulse stimulation results reveal that the effect of astrocytic glutamate uptake is more apparent when the input inter-spike interval is sufficiently long to allow the receptors to recover from desensitization. These results suggest an important functional role of astrocytes in spike timing dependent processes and demand further investigation of the molecular basis of certain neurological diseases specifically related to alterations in astrocytic glutamate uptake, such as epilepsy.

Synchronous spikes are necessary but not sufficient for a synchrony code in populations of spiking neurons.

Science.gov (United States)

Grewe, Jan; Kruscha, Alexandra; Lindner, Benjamin; Benda, Jan

2017-03-07

Synchronous activity in populations of neurons potentially encodes special stimulus features. Selective readout of either synchronous or asynchronous activity allows formation of two streams of information processing. Theoretical work predicts that such a synchrony code is a fundamental feature of populations of spiking neurons if they operate in specific noise and stimulus regimes. Here we experimentally test the theoretical predictions by quantifying and comparing neuronal response properties in tuberous and ampullary electroreceptor afferents of the weakly electric fish Apteronotus leptorhynchus These related systems show similar levels of synchronous activity, but only in the more irregularly firing tuberous afferents a synchrony code is established, whereas in the more regularly firing ampullary afferents it is not. The mere existence of synchronous activity is thus not sufficient for a synchrony code. Single-cell features such as the irregularity of spiking and the frequency dependence of the neuron's transfer function determine whether synchronous spikes possess a distinct meaning for the encoding of time-dependent signals.

Detecting dependencies between spike trains of pairs of neurons through copulas

DEFF Research Database (Denmark)

Sacerdote, Laura; Tamborrino, Massimiliano; Zucca, Cristina

2011-01-01

The dynamics of a neuron are influenced by the connections with the network where it lies. Recorded spike trains exhibit patterns due to the interactions between neurons. However, the structure of the network is not known. A challenging task is to investigate it from the analysis of simultaneously...... the two neurons. Furthermore, the method recognizes the presence of delays in the spike propagation....

Development of on-off spiking in superior paraolivary nucleus neurons of the mouse

Science.gov (United States)

Felix, Richard A.; Vonderschen, Katrin; Berrebi, Albert S.

2013-01-01

The superior paraolivary nucleus (SPON) is a prominent cell group in the auditory brain stem that has been increasingly implicated in representing temporal sound structure. Although SPON neurons selectively respond to acoustic signals important for sound periodicity, the underlying physiological specializations enabling these responses are poorly understood. We used in vitro and in vivo recordings to investigate how SPON neurons develop intrinsic cellular properties that make them well suited for encoding temporal sound features. In addition to their hallmark rebound spiking at the stimulus offset, SPON neurons were characterized by spiking patterns termed onset, adapting, and burst in response to depolarizing stimuli in vitro. Cells with burst spiking had some morphological differences compared with other SPON neurons and were localized to the dorsolateral region of the nucleus. Both membrane and spiking properties underwent strong developmental regulation, becoming more temporally precise with age for both onset and offset spiking. Single-unit recordings obtained in young mice demonstrated that SPON neurons respond with temporally precise onset spiking upon tone stimulation in vivo, in addition to the typical offset spiking. Taken together, the results of the present study demonstrate that SPON neurons develop sharp on-off spiking, which may confer sensitivity to sound amplitude modulations or abrupt sound transients. These findings are consistent with the proposed involvement of the SPON in the processing of temporal sound structure, relevant for encoding communication cues. PMID:23515791

Spiking, Bursting, and Population Dynamics in a Network of Growth Transform Neurons.

Science.gov (United States)

Gangopadhyay, Ahana; Chakrabartty, Shantanu

2017-04-27

This paper investigates the dynamical properties of a network of neurons, each of which implements an asynchronous mapping based on polynomial growth transforms. In the first part of this paper, we present a geometric approach for visualizing the dynamics of the network where each of the neurons traverses a trajectory in a dual optimization space, whereas the network itself traverses a trajectory in an equivalent primal optimization space. We show that as the network learns to solve basic classification tasks, different choices of primal-dual mapping produce unique but interpretable neural dynamics like noise shaping, spiking, and bursting. While the proposed framework is general enough, in this paper, we demonstrate its use for designing support vector machines (SVMs) that exhibit noise-shaping properties similar to those of ΣΔ modulators, and for designing SVMs that learn to encode information using spikes and bursts. It is demonstrated that the emergent switching, spiking, and burst dynamics produced by each neuron encodes its respective margin of separation from a classification hyperplane whose parameters are encoded by the network population dynamics. We believe that the proposed growth transform neuron model and the underlying geometric framework could serve as an important tool to connect well-established machine learning algorithms like SVMs to neuromorphic principles like spiking, bursting, population encoding, and noise shaping.

Versatile Networks of Simulated Spiking Neurons Displaying Winner-Take-All Behavior

Directory of Open Access Journals (Sweden)

Yanqing eChen

2013-03-01

Full Text Available We describe simulations of large-scale networks of excitatory and inhibitory spiking neurons that can generate dynamically stable winner-take-all (WTA behavior. The network connectivity is a variant of center-surround architecture that we call center-annular-surround (CAS. In this architecture each neuron is excited by nearby neighbors and inhibited by more distant neighbors in an annular-surround region. The neural units of these networks simulate conductance-based spiking neurons that interact via mechanisms susceptible to both short-term synaptic plasticity and STDP. We show that such CAS networks display robust WTA behavior unlike the center-surround networks and other control architectures that we have studied. We find that a large-scale network of spiking neurons with separate populations of excitatory and inhibitory neurons can give rise to smooth maps of sensory input. In addition, we show that a humanoid Brain-Based-Device (BBD under the control of a spiking WTA neural network can learn to reach to target positions in its visual field, thus demonstrating the acquisition of sensorimotor coordination.

Versatile networks of simulated spiking neurons displaying winner-take-all behavior.

Science.gov (United States)

Chen, Yanqing; McKinstry, Jeffrey L; Edelman, Gerald M

2013-01-01

We describe simulations of large-scale networks of excitatory and inhibitory spiking neurons that can generate dynamically stable winner-take-all (WTA) behavior. The network connectivity is a variant of center-surround architecture that we call center-annular-surround (CAS). In this architecture each neuron is excited by nearby neighbors and inhibited by more distant neighbors in an annular-surround region. The neural units of these networks simulate conductance-based spiking neurons that interact via mechanisms susceptible to both short-term synaptic plasticity and STDP. We show that such CAS networks display robust WTA behavior unlike the center-surround networks and other control architectures that we have studied. We find that a large-scale network of spiking neurons with separate populations of excitatory and inhibitory neurons can give rise to smooth maps of sensory input. In addition, we show that a humanoid brain-based-device (BBD) under the control of a spiking WTA neural network can learn to reach to target positions in its visual field, thus demonstrating the acquisition of sensorimotor coordination.

A unified framework for spiking and gap-junction interactions in distributed neuronal network simulations

Directory of Open Access Journals (Sweden)

Jan eHahne

2015-09-01

Full Text Available Contemporary simulators for networks of point and few-compartment model neurons come with a plethora of ready-to-use neuron and synapse models and support complex network topologies. Recent technological advancements have broadened the spectrum of application further to the efficient simulation of brain-scale networks on supercomputers. In distributed network simulations the amount of spike data that accrues per millisecond and process is typically low, such that a common optimization strategy is to communicate spikes at relatively long intervals, where the upper limit is given by the shortest synaptic transmission delay in the network. This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions. Here, we present a numerical algorithm based on a waveform-relaxation technique which allows for network simulations with gap junctions in a way that is compatible with the delayed communication strategy. Using a reference implementation in the NEST simulator, we demonstrate that the algorithm and the required data structures can be smoothly integrated with existing code such that they complement the infrastructure for spiking connections. To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy...

How adaptation shapes spike rate oscillations in recurrent neuronal networks

Directory of Open Access Journals (Sweden)

Moritz eAugustin

2013-02-01

Full Text Available Neural mass signals from in-vivo recordings often show oscillations with frequencies ranging from <1 Hz to 100 Hz. Fast rhythmic activity in the beta and gamma range can be generated by network based mechanisms such as recurrent synaptic excitation-inhibition loops. Slower oscillations might instead depend on neuronal adaptation currents whose timescales range from tens of milliseconds to seconds. Here we investigate how the dynamics of such adaptation currents contribute to spike rate oscillations and resonance properties in recurrent networks of excitatory and inhibitory neurons. Based on a network of sparsely coupled spiking model neurons with two types of adaptation current and conductance based synapses with heterogeneous strengths and delays we use a mean-field approach to analyze oscillatory network activity. For constant external input, we find that spike-triggered adaptation currents provide a mechanism to generate slow oscillations over a wide range of adaptation timescales as long as recurrent synaptic excitation is sufficiently strong. Faster rhythms occur when recurrent inhibition is slower than excitation and oscillation frequency increases with the strength of inhibition. Adaptation facilitates such network based oscillations for fast synaptic inhibition and leads to decreased frequencies. For oscillatory external input, adaptation currents amplify a narrow band of frequencies and cause phase advances for low frequencies in addition to phase delays at higher frequencies. Our results therefore identify the different key roles of neuronal adaptation dynamics for rhythmogenesis and selective signal propagation in recurrent networks.

Note on the coefficient of variations of neuronal spike trains.

Science.gov (United States)

Lengler, Johannes; Steger, Angelika

2017-08-01

It is known that many neurons in the brain show spike trains with a coefficient of variation (CV) of the interspike times of approximately 1, thus resembling the properties of Poisson spike trains. Computational studies have been able to reproduce this phenomenon. However, the underlying models were too complex to be examined analytically. In this paper, we offer a simple model that shows the same effect but is accessible to an analytic treatment. The model is a random walk model with a reflecting barrier; we give explicit formulas for the CV in the regime of excess inhibition. We also analyze the effect of probabilistic synapses in our model and show that it resembles previous findings that were obtained by simulation.

Spiking Regularity and Coherence in Complex Hodgkin–Huxley Neuron Networks

International Nuclear Information System (INIS)

Zhi-Qiang, Sun; Ping, Xie; Wei, Li; Peng-Ye, Wang

2010-01-01

We study the effects of the strength of coupling between neurons on the spiking regularity and coherence in a complex network with randomly connected Hodgkin–Huxley neurons driven by colored noise. It is found that for the given topology realization and colored noise correlation time, there exists an optimal strength of coupling, at which the spiking regularity of the network reaches the best level. Moreover, when the temporal regularity reaches the best level, the spatial coherence of the system has already increased to a relatively high level. In addition, for the given number of neurons and noise correlation time, the values of average regularity and spatial coherence at the optimal strength of coupling are nearly independent of the topology realization. Furthermore, there exists an optimal value of colored noise correlation time at which the spiking regularity can reach its best level. These results may be helpful for understanding of the real neuron world. (cross-disciplinary physics and related areas of science and technology)

Deep Learning with Dynamic Spiking Neurons and Fixed Feedback Weights.

Science.gov (United States)

Samadi, Arash; Lillicrap, Timothy P; Tweed, Douglas B

2017-03-01

Recent work in computer science has shown the power of deep learning driven by the backpropagation algorithm in networks of artificial neurons. But real neurons in the brain are different from most of these artificial ones in at least three crucial ways: they emit spikes rather than graded outputs, their inputs and outputs are related dynamically rather than by piecewise-smooth functions, and they have no known way to coordinate arrays of synapses in separate forward and feedback pathways so that they change simultaneously and identically, as they do in backpropagation. Given these differences, it is unlikely that current deep learning algorithms can operate in the brain, but we that show these problems can be solved by two simple devices: learning rules can approximate dynamic input-output relations with piecewise-smooth functions, and a variation on the feedback alignment algorithm can train deep networks without having to coordinate forward and feedback synapses. Our results also show that deep spiking networks learn much better if each neuron computes an intracellular teaching signal that reflects that cell's nonlinearity. With this mechanism, networks of spiking neurons show useful learning in synapses at least nine layers upstream from the output cells and perform well compared to other spiking networks in the literature on the MNIST digit recognition task.

Memory-induced resonancelike suppression of spike generation in a resonate-and-fire neuron model

Science.gov (United States)

Mankin, Romi; Paekivi, Sander

2018-01-01

The behavior of a stochastic resonate-and-fire neuron model based on a reduction of a fractional noise-driven generalized Langevin equation (GLE) with a power-law memory kernel is considered. The effect of temporally correlated random activity of synaptic inputs, which arise from other neurons forming local and distant networks, is modeled as an additive fractional Gaussian noise in the GLE. Using a first-passage-time formulation, in certain system parameter domains exact expressions for the output interspike interval (ISI) density and for the survival probability (the probability that a spike is not generated) are derived and their dependence on input parameters, especially on the memory exponent, is analyzed. In the case of external white noise, it is shown that at intermediate values of the memory exponent the survival probability is significantly enhanced in comparison with the cases of strong and weak memory, which causes a resonancelike suppression of the probability of spike generation as a function of the memory exponent. Moreover, an examination of the dependence of multimodality in the ISI distribution on input parameters shows that there exists a critical memory exponent αc≈0.402 , which marks a dynamical transition in the behavior of the system. That phenomenon is illustrated by a phase diagram describing the emergence of three qualitatively different structures of the ISI distribution. Similarities and differences between the behavior of the model at internal and external noises are also discussed.

Supervised learning with decision margins in pools of spiking neurons.

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Le Mouel, Charlotte; Harris, Kenneth D; Yger, Pierre

2014-10-01

Learning to categorise sensory inputs by generalising from a few examples whose category is precisely known is a crucial step for the brain to produce appropriate behavioural responses. At the neuronal level, this may be performed by adaptation of synaptic weights under the influence of a training signal, in order to group spiking patterns impinging on the neuron. Here we describe a framework that allows spiking neurons to perform such "supervised learning", using principles similar to the Support Vector Machine, a well-established and robust classifier. Using a hinge-loss error function, we show that requesting a margin similar to that of the SVM improves performance on linearly non-separable problems. Moreover, we show that using pools of neurons to discriminate categories can also increase the performance by sharing the load among neurons.

How many neurons can we see with current spike sorting algorithms?

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Pedreira, Carlos; Martinez, Juan; Ison, Matias J; Quian Quiroga, Rodrigo

2012-10-15

Recent studies highlighted the disagreement between the typical number of neurons observed with extracellular recordings and the ones to be expected based on anatomical and physiological considerations. This disagreement has been mainly attributed to the presence of sparsely firing neurons. However, it is also possible that this is due to limitations of the spike sorting algorithms used to process the data. To address this issue, we used realistic simulations of extracellular recordings and found a relatively poor spike sorting performance for simulations containing a large number of neurons. In fact, the number of correctly identified neurons for single-channel recordings showed an asymptotic behavior saturating at about 8-10 units, when up to 20 units were present in the data. This performance was significantly poorer for neurons with low firing rates, as these units were twice more likely to be missed than the ones with high firing rates in simulations containing many neurons. These results uncover one of the main reasons for the relatively low number of neurons found in extracellular recording and also stress the importance of further developments of spike sorting algorithms. Copyright © 2012 Elsevier B.V. All rights reserved.

Implementing Signature Neural Networks with Spiking Neurons.

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Carrillo-Medina, José Luis; Latorre, Roberto

2016-01-01

Spiking Neural Networks constitute the most promising approach to develop realistic Artificial Neural Networks (ANNs). Unlike traditional firing rate-based paradigms, information coding in spiking models is based on the precise timing of individual spikes. It has been demonstrated that spiking ANNs can be successfully and efficiently applied to multiple realistic problems solvable with traditional strategies (e.g., data classification or pattern recognition). In recent years, major breakthroughs in neuroscience research have discovered new relevant computational principles in different living neural systems. Could ANNs benefit from some of these recent findings providing novel elements of inspiration? This is an intriguing question for the research community and the development of spiking ANNs including novel bio-inspired information coding and processing strategies is gaining attention. From this perspective, in this work, we adapt the core concepts of the recently proposed Signature Neural Network paradigm-i.e., neural signatures to identify each unit in the network, local information contextualization during the processing, and multicoding strategies for information propagation regarding the origin and the content of the data-to be employed in a spiking neural network. To the best of our knowledge, none of these mechanisms have been used yet in the context of ANNs of spiking neurons. This paper provides a proof-of-concept for their applicability in such networks. Computer simulations show that a simple network model like the discussed here exhibits complex self-organizing properties. The combination of multiple simultaneous encoding schemes allows the network to generate coexisting spatio-temporal patterns of activity encoding information in different spatio-temporal spaces. As a function of the network and/or intra-unit parameters shaping the corresponding encoding modality, different forms of competition among the evoked patterns can emerge even in the absence

Spectral components of cytosolic [Ca2+] spiking in neurons

DEFF Research Database (Denmark)

Kardos, J; Szilágyi, N; Juhász, G

1998-01-01

. Delayed complex responses of large [Ca2+]c spiking observed in cells from a different set of cultures were synthesized by a set of frequencies within the range 0.018-0.117 Hz. Differential frequency patterns are suggested as characteristics of the [Ca2+]c spiking responses of neurons under different...

Modulation of the spike activity of neocortex neurons during a conditioned reflex.

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Storozhuk, V M; Sanzharovskii, A V; Sachenko, V V; Busel, B I

2000-01-01

Experiments were conducted on cats to study the effects of iontophoretic application of glutamate and a number of modulators on the spike activity of neurons in the sensorimotor cortex during a conditioned reflex. These studies showed that glutamate, as well as exerting a direct influence on neuron spike activity, also had a delayed facilitatory action lasting 10-20 min after iontophoresis was finished. Adrenomimetics were found to have a double modulatory effect on intracortical glutamate connections: inhibitory and facilitatory effects were mediated by beta1 and beta2 adrenoceptors respectively. Although dopamine, like glutamate, facilitated neuron spike activity during the period of application, the simultaneous facilitatory actions of glutamate and L-DOPA were accompanied by occlusion of spike activity, and simultaneous application of glutamate and haloperidol suppressed spike activity associated with the conditioned reflex response. Facilitation thus appears to show a significant level of dependence on metabotropic glutamate receptors which, like dopamine receptors, are linked to the intracellular medium via Gi proteins.

Spike Pattern Structure Influences Synaptic Efficacy Variability Under STDP and Synaptic Homeostasis. I: Spike Generating Models on Converging Motifs

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Zedong eBi

2016-02-01

Full Text Available In neural systems, synaptic plasticity is usually driven by spike trains. Due to the inherent noises of neurons and synapses as well as the randomness of connection details, spike trains typically exhibit variability such as spatial randomness and temporal stochasticity, resulting in variability of synaptic changes under plasticity, which we call efficacy variability. How the variability of spike trains influences the efficacy variability of synapses remains unclear. In this paper, we try to understand this influence under pair-wise additive spike-timing dependent plasticity (STDP when the mean strength of plastic synapses into a neuron is bounded (synaptic homeostasis. Specifically, we systematically study, analytically and numerically, how four aspects of statistical features, i.e. synchronous firing, burstiness/regularity, heterogeneity of rates and heterogeneity of cross-correlations, as well as their interactions influence the efficacy variability in converging motifs (simple networks in which one neuron receives from many other neurons. Neurons (including the post-synaptic neuron in a converging motif generate spikes according to statistical models with tunable parameters. In this way, we can explicitly control the statistics of the spike patterns, and investigate their influence onto the efficacy variability, without worrying about the feedback from synaptic changes onto the dynamics of the post-synaptic neuron. We separate efficacy variability into two parts: the drift part (DriftV induced by the heterogeneity of change rates of different synapses, and the diffusion part (DiffV induced by weight diffusion caused by stochasticity of spike trains. Our main findings are: (1 synchronous firing and burstiness tend to increase DiffV, (2 heterogeneity of rates induces DriftV when potentiation and depression in STDP are not balanced, and (3 heterogeneity of cross-correlations induces DriftV together with heterogeneity of rates. We anticipate our

Communication through resonance in spiking neuronal networks.

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Hahn, Gerald; Bujan, Alejandro F; Frégnac, Yves; Aertsen, Ad; Kumar, Arvind

2014-08-01

The cortex processes stimuli through a distributed network of specialized brain areas. This processing requires mechanisms that can route neuronal activity across weakly connected cortical regions. Routing models proposed thus far are either limited to propagation of spiking activity across strongly connected networks or require distinct mechanisms that create local oscillations and establish their coherence between distant cortical areas. Here, we propose a novel mechanism which explains how synchronous spiking activity propagates across weakly connected brain areas supported by oscillations. In our model, oscillatory activity unleashes network resonance that amplifies feeble synchronous signals and promotes their propagation along weak connections ("communication through resonance"). The emergence of coherent oscillations is a natural consequence of synchronous activity propagation and therefore the assumption of different mechanisms that create oscillations and provide coherence is not necessary. Moreover, the phase-locking of oscillations is a side effect of communication rather than its requirement. Finally, we show how the state of ongoing activity could affect the communication through resonance and propose that modulations of the ongoing activity state could influence information processing in distributed cortical networks.

A Neuron Model Based Ultralow Current Sensor System for Bioapplications

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A. K. M. Arifuzzman

2016-01-01

Full Text Available An ultralow current sensor system based on the Izhikevich neuron model is presented in this paper. The Izhikevich neuron model has been used for its superior computational efficiency and greater biological plausibility over other well-known neuron spiking models. Of the many biological neuron spiking features, regular spiking, chattering, and neostriatal spiny projection spiking have been reproduced by adjusting the parameters associated with the model at hand. This paper also presents a modified interpretation of the regular spiking feature in which the firing pattern is similar to that of the regular spiking but with improved dynamic range offering. The sensor current ranges between 2 pA and 8 nA and exhibits linearity in the range of 0.9665 to 0.9989 for different spiking features. The efficacy of the sensor system in detecting low amount of current along with its high linearity attribute makes it very suitable for biomedical applications.

Spiking sychronization regulated by noise in three types of Hodgkin—Huxley neuronal networks

International Nuclear Information System (INIS)

Zhang Zheng-Zhen; Zeng Shang-You; Tang Wen-Yan; Hu Jin-Lin; Zeng Shao-Wen; Ning Wei-Lian; Qiu Yi; Wu Hui-Si

2012-01-01

In this paper, we study spiking synchronization in three different types of Hodgkin—Huxley neuronal networks, which are the small-world, regular, and random neuronal networks. All the neurons are subjected to subthreshold stimulus and external noise. It is found that in each of all the neuronal networks there is an optimal strength of noise to induce the maximal spiking synchronization. We further demonstrate that in each of the neuronal networks there is a range of synaptic conductance to induce the effect that an optimal strength of noise maximizes the spiking synchronization. Only when the magnitude of the synaptic conductance is moderate, will the effect be considerable. However, if the synaptic conductance is small or large, the effect vanishes. As the connections between neurons increase, the synaptic conductance to maximize the effect decreases. Therefore, we show quantitatively that the noise-induced maximal synchronization in the Hodgkin—Huxley neuronal network is a general effect, regardless of the specific type of neuronal network

Neuronal spike sorting based on radial basis function neural networks

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Taghavi Kani M

2011-02-01

Full Text Available "nBackground: Studying the behavior of a society of neurons, extracting the communication mechanisms of brain with other tissues, finding treatment for some nervous system diseases and designing neuroprosthetic devices, require an algorithm to sort neuralspikes automatically. However, sorting neural spikes is a challenging task because of the low signal to noise ratio (SNR of the spikes. The main purpose of this study was to design an automatic algorithm for classifying neuronal spikes that are emitted from a specific region of the nervous system."n "nMethods: The spike sorting process usually consists of three stages: detection, feature extraction and sorting. We initially used signal statistics to detect neural spikes. Then, we chose a limited number of typical spikes as features and finally used them to train a radial basis function (RBF neural network to sort the spikes. In most spike sorting devices, these signals are not linearly discriminative. In order to solve this problem, the aforesaid RBF neural network was used."n "nResults: After the learning process, our proposed algorithm classified any arbitrary spike. The obtained results showed that even though the proposed Radial Basis Spike Sorter (RBSS reached to the same error as the previous methods, however, the computational costs were much lower compared to other algorithms. Moreover, the competitive points of the proposed algorithm were its good speed and low computational complexity."n "nConclusion: Regarding the results of this study, the proposed algorithm seems to serve the purpose of procedures that require real-time processing and spike sorting.

Model-based analysis and control of a network of basal ganglia spiking neurons in the normal and Parkinsonian states

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Liu, Jianbo; Khalil, Hassan K.; Oweiss, Karim G.

2011-08-01

Controlling the spatiotemporal firing pattern of an intricately connected network of neurons through microstimulation is highly desirable in many applications. We investigated in this paper the feasibility of using a model-based approach to the analysis and control of a basal ganglia (BG) network model of Hodgkin-Huxley (HH) spiking neurons through microstimulation. Detailed analysis of this network model suggests that it can reproduce the experimentally observed characteristics of BG neurons under a normal and a pathological Parkinsonian state. A simplified neuronal firing rate model, identified from the detailed HH network model, is shown to capture the essential network dynamics. Mathematical analysis of the simplified model reveals the presence of a systematic relationship between the network's structure and its dynamic response to spatiotemporally patterned microstimulation. We show that both the network synaptic organization and the local mechanism of microstimulation can impose tight constraints on the possible spatiotemporal firing patterns that can be generated by the microstimulated network, which may hinder the effectiveness of microstimulation to achieve a desired objective under certain conditions. Finally, we demonstrate that the feedback control design aided by the mathematical analysis of the simplified model is indeed effective in driving the BG network in the normal and Parskinsonian states to follow a prescribed spatiotemporal firing pattern. We further show that the rhythmic/oscillatory patterns that characterize a dopamine-depleted BG network can be suppressed as a direct consequence of controlling the spatiotemporal pattern of a subpopulation of the output Globus Pallidus internalis (GPi) neurons in the network. This work may provide plausible explanations for the mechanisms underlying the therapeutic effects of deep brain stimulation (DBS) in Parkinson's disease and pave the way towards a model-based, network level analysis and closed

Training Spiking Neural Models Using Artificial Bee Colony

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Vazquez, Roberto A.; Garro, Beatriz A.

2015-01-01

Spiking neurons are models designed to simulate, in a realistic manner, the behavior of biological neurons. Recently, it has been proven that this type of neurons can be applied to solve pattern recognition problems with great efficiency. However, the lack of learning strategies for training these models do not allow to use them in several pattern recognition problems. On the other hand, several bioinspired algorithms have been proposed in the last years for solving a broad range of optimization problems, including those related to the field of artificial neural networks (ANNs). Artificial bee colony (ABC) is a novel algorithm based on the behavior of bees in the task of exploring their environment to find a food source. In this paper, we describe how the ABC algorithm can be used as a learning strategy to train a spiking neuron aiming to solve pattern recognition problems. Finally, the proposed approach is tested on several pattern recognition problems. It is important to remark that to realize the powerfulness of this type of model only one neuron will be used. In addition, we analyze how the performance of these models is improved using this kind of learning strategy. PMID:25709644

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size.

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Schwalger, Tilo; Deger, Moritz; Gerstner, Wulfram

2017-04-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50-2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

Impact of morphometry, myelinization and synaptic current strength on spike conduction in human and cat spiral ganglion neurons.

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Frank Rattay

Full Text Available Our knowledge about the neural code in the auditory nerve is based to a large extent on experiments on cats. Several anatomical differences between auditory neurons in human and cat are expected to lead to functional differences in speed and safety of spike conduction.Confocal microscopy was used to systematically evaluate peripheral and central process diameters, commonness of myelination and morphology of spiral ganglion neurons (SGNs along the cochlea of three human and three cats. Based on these morphometric data, model analysis reveales that spike conduction in SGNs is characterized by four phases: a postsynaptic delay, constant velocity in the peripheral process, a presomatic delay and constant velocity in the central process. The majority of SGNs are type I, connecting the inner hair cells with the brainstem. In contrast to those of humans, type I neurons of the cat are entirely myelinated. Biophysical model evaluation showed delayed and weak spikes in the human soma region as a consequence of a lack of myelin. The simulated spike conduction times are in accordance with normal interwave latencies from auditory brainstem response recordings from man and cat. Simulated 400 pA postsynaptic currents from inner hair cell ribbon synapses were 15 times above threshold. They enforced quick and synchronous spiking. Both of these properties were not present in type II cells as they receive fewer and much weaker (∼26 pA synaptic stimuli.Wasting synaptic energy boosts spike initiation, which guarantees the rapid transmission of temporal fine structure of auditory signals. However, a lack of myelin in the soma regions of human type I neurons causes a large delay in spike conduction in comparison with cat neurons. The absent myelin, in combination with a longer peripheral process, causes quantitative differences of temporal parameters in the electrically stimulated human cochlea compared to the cat cochlea.

Impact of Morphometry, Myelinization and Synaptic Current Strength on Spike Conduction in Human and Cat Spiral Ganglion Neurons

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Rattay, Frank; Potrusil, Thomas; Wenger, Cornelia; Wise, Andrew K.; Glueckert, Rudolf; Schrott-Fischer, Anneliese

2013-01-01

Background Our knowledge about the neural code in the auditory nerve is based to a large extent on experiments on cats. Several anatomical differences between auditory neurons in human and cat are expected to lead to functional differences in speed and safety of spike conduction. Methodology/Principal Findings Confocal microscopy was used to systematically evaluate peripheral and central process diameters, commonness of myelination and morphology of spiral ganglion neurons (SGNs) along the cochlea of three human and three cats. Based on these morphometric data, model analysis reveales that spike conduction in SGNs is characterized by four phases: a postsynaptic delay, constant velocity in the peripheral process, a presomatic delay and constant velocity in the central process. The majority of SGNs are type I, connecting the inner hair cells with the brainstem. In contrast to those of humans, type I neurons of the cat are entirely myelinated. Biophysical model evaluation showed delayed and weak spikes in the human soma region as a consequence of a lack of myelin. The simulated spike conduction times are in accordance with normal interwave latencies from auditory brainstem response recordings from man and cat. Simulated 400 pA postsynaptic currents from inner hair cell ribbon synapses were 15 times above threshold. They enforced quick and synchronous spiking. Both of these properties were not present in type II cells as they receive fewer and much weaker (∼26 pA) synaptic stimuli. Conclusions/Significance Wasting synaptic energy boosts spike initiation, which guarantees the rapid transmission of temporal fine structure of auditory signals. However, a lack of myelin in the soma regions of human type I neurons causes a large delay in spike conduction in comparison with cat neurons. The absent myelin, in combination with a longer peripheral process, causes quantitative differences of temporal parameters in the electrically stimulated human cochlea compared to the cat

Inherently stochastic spiking neurons for probabilistic neural computation

KAUST Repository

Al-Shedivat, Maruan; Naous, Rawan; Neftci, Emre; Cauwenberghs, Gert; Salama, Khaled N.

2015-01-01

. Our analysis and simulations show that the proposed neuron circuit satisfies a neural computability condition that enables probabilistic neural sampling and spike-based Bayesian learning and inference. Our findings constitute an important step towards

Upregulation of transmitter release probability improves a conversion of synaptic analogue signals into neuronal digital spikes

Science.gov (United States)

2012-01-01

Action potentials at the neurons and graded signals at the synapses are primary codes in the brain. In terms of their functional interaction, the studies were focused on the influence of presynaptic spike patterns on synaptic activities. How the synapse dynamics quantitatively regulates the encoding of postsynaptic digital spikes remains unclear. We investigated this question at unitary glutamatergic synapses on cortical GABAergic neurons, especially the quantitative influences of release probability on synapse dynamics and neuronal encoding. Glutamate release probability and synaptic strength are proportionally upregulated by presynaptic sequential spikes. The upregulation of release probability and the efficiency of probability-driven synaptic facilitation are strengthened by elevating presynaptic spike frequency and Ca2+. The upregulation of release probability improves spike capacity and timing precision at postsynaptic neuron. These results suggest that the upregulation of presynaptic glutamate release facilitates a conversion of synaptic analogue signals into digital spikes in postsynaptic neurons, i.e., a functional compatibility between presynaptic and postsynaptic partners. PMID:22852823

On the number of preganglionic neurones driving human postganglionic sympathetic neurones: a comparison of modelling and empirical data

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Vaughan G Macefield

2011-12-01

Full Text Available Postganglionic sympathetic axons in awake healthy human subjects, regardless of their identity as muscle vasoconstrictor, cutaneous vasoconstrictor or sudomotor neurones, discharge with a low firing probability (~30%, generate low firing rates (~0.5 Hz and typically fire only once per cardiac interval. The purpose of the present study was to use modelling of spike trains in an attempt to define the number of preganglionic neurones that drive an individual postganglionic neurone. Artificial spike trains were generated in 1-3 preganglionic neurones converging onto a single postganglionic neurone. Each preganglionic input fired with a mean interval distribution of either 1000, 1500, 2000, 2500 or 3000 ms and the standard deviation varied between 0.5, 1.0 and 2.0 x the mean interval; the discharge frequency of each preganglionic neurone exhibited positive skewness and kurtosis. Of the 45 patterns examined, the mean discharge properties of the postganglionic neurone could only be explained by it being driven by, on average, two preganglionic neurones firing with a mean interspike interval of 2500 ms and SD of 5000 ms. The mean firing rate resulting from this pattern was 0.22 Hz, comparable to that of spontaneously active muscle vasoconstrictor neurones in healthy subjects (0.40 Hz. Likewise, the distribution of the number of spikes per cardiac interval was similar between the modelled and actual data: 0 spikes (69.5 vs 66.6 %, 1 spike (25.6 vs 21.2 %, 2 spikes (4.3 vs 6.4 %, 3 spikes (0.5 vs 1.7 % and 4 spikes (0.1 vs 0.7 %. Although some features of the firing patterns could be explained by the postganglionic neurone being driven by a single preganglionic neurone, none of the emulated firing patterns generated by the firing of three preganglionic neurones matched the discharge of the real neurones. These modelling data indicate that, on average, human postganglionic sympathetic neurones are driven by two preganglionic inputs.

Spiking Neural P Systems with Communication on Request.

Science.gov (United States)

Pan, Linqiang; Păun, Gheorghe; Zhang, Gexiang; Neri, Ferrante

2017-12-01

Spiking Neural [Formula: see text] Systems are Neural System models characterized by the fact that each neuron mimics a biological cell and the communication between neurons is based on spikes. In the Spiking Neural [Formula: see text] systems investigated so far, the application of evolution rules depends on the contents of a neuron (checked by means of a regular expression). In these [Formula: see text] systems, a specified number of spikes are consumed and a specified number of spikes are produced, and then sent to each of the neurons linked by a synapse to the evolving neuron. [Formula: see text]In the present work, a novel communication strategy among neurons of Spiking Neural [Formula: see text] Systems is proposed. In the resulting models, called Spiking Neural [Formula: see text] Systems with Communication on Request, the spikes are requested from neighboring neurons, depending on the contents of the neuron (still checked by means of a regular expression). Unlike the traditional Spiking Neural [Formula: see text] systems, no spikes are consumed or created: the spikes are only moved along synapses and replicated (when two or more neurons request the contents of the same neuron). [Formula: see text]The Spiking Neural [Formula: see text] Systems with Communication on Request are proved to be computationally universal, that is, equivalent with Turing machines as long as two types of spikes are used. Following this work, further research questions are listed to be open problems.

Spike Neural Models Part II: Abstract Neural Models

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Johnson, Melissa G.

2018-02-01

Full Text Available Neurons are complex cells that require a lot of time and resources to model completely. In spiking neural networks (SNN though, not all that complexity is required. Therefore simple, abstract models are often used. These models save time, use less computer resources, and are easier to understand. This tutorial presents two such models: Izhikevich's model, which is biologically realistic in the resulting spike trains but not in the parameters, and the Leaky Integrate and Fire (LIF model which is not biologically realistic but does quickly and easily integrate input to produce spikes. Izhikevich's model is based on Hodgkin-Huxley's model but simplified such that it uses only two differentiation equations and four parameters to produce various realistic spike patterns. LIF is based on a standard electrical circuit and contains one equation. Either of these two models, or any of the many other models in literature can be used in a SNN. Choosing a neural model is an important task that depends on the goal of the research and the resources available. Once a model is chosen, network decisions such as connectivity, delay, and sparseness, need to be made. Understanding neural models and how they are incorporated into the network is the first step in creating a SNN.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

Science.gov (United States)

Gerstner, Wulfram

2017-01-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50–2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations. PMID:28422957

SPAN: spike pattern association neuron for learning spatio-temporal sequences

OpenAIRE

Mohemmed, A; Schliebs, S; Matsuda, S; Kasabov, N

2012-01-01

Spiking Neural Networks (SNN) were shown to be suitable tools for the processing of spatio-temporal information. However, due to their inherent complexity, the formulation of efficient supervised learning algorithms for SNN is difficult and remains an important problem in the research area. This article presents SPAN — a spiking neuron that is able to learn associations of arbitrary spike trains in a supervised fashion allowing the processing of spatio-temporal information encoded in the prec...

Statistical properties of superimposed stationary spike trains.

Science.gov (United States)

Deger, Moritz; Helias, Moritz; Boucsein, Clemens; Rotter, Stefan

2012-06-01

The Poisson process is an often employed model for the activity of neuronal populations. It is known, though, that superpositions of realistic, non- Poisson spike trains are not in general Poisson processes, not even for large numbers of superimposed processes. Here we construct superimposed spike trains from intracellular in vivo recordings from rat neocortex neurons and compare their statistics to specific point process models. The constructed superimposed spike trains reveal strong deviations from the Poisson model. We find that superpositions of model spike trains that take the effective refractoriness of the neurons into account yield a much better description. A minimal model of this kind is the Poisson process with dead-time (PPD). For this process, and for superpositions thereof, we obtain analytical expressions for some second-order statistical quantities-like the count variability, inter-spike interval (ISI) variability and ISI correlations-and demonstrate the match with the in vivo data. We conclude that effective refractoriness is the key property that shapes the statistical properties of the superposition spike trains. We present new, efficient algorithms to generate superpositions of PPDs and of gamma processes that can be used to provide more realistic background input in simulations of networks of spiking neurons. Using these generators, we show in simulations that neurons which receive superimposed spike trains as input are highly sensitive for the statistical effects induced by neuronal refractoriness.

Spike neural models (part I: The Hodgkin-Huxley model

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Johnson, Melissa G.

2017-05-01

Full Text Available Artificial neural networks, or ANNs, have grown a lot since their inception back in the 1940s. But no matter the changes, one of the most important components of neural networks is still the node, which represents the neuron. Within spiking neural networks, the node is especially important because it contains the functions and properties of neurons that are necessary for their network. One important aspect of neurons is the ionic flow which produces action potentials, or spikes. Forces of diffusion and electrostatic pressure work together with the physical properties of the cell to move ions around changing the cell membrane potential which ultimately produces the action potential. This tutorial reviews the Hodkgin-Huxley model and shows how it simulates the ionic flow of the giant squid axon via four differential equations. The model is implemented in Matlab using Euler's Method to approximate the differential equations. By using Euler's method, an extra parameter is created, the time step. This new parameter needs to be carefully considered or the results of the node may be impaired.

Reinforcement learning using a continuous time actor-critic framework with spiking neurons.

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Nicolas Frémaux

2013-04-01

Full Text Available Animals repeat rewarded behaviors, but the physiological basis of reward-based learning has only been partially elucidated. On one hand, experimental evidence shows that the neuromodulator dopamine carries information about rewards and affects synaptic plasticity. On the other hand, the theory of reinforcement learning provides a framework for reward-based learning. Recent models of reward-modulated spike-timing-dependent plasticity have made first steps towards bridging the gap between the two approaches, but faced two problems. First, reinforcement learning is typically formulated in a discrete framework, ill-adapted to the description of natural situations. Second, biologically plausible models of reward-modulated spike-timing-dependent plasticity require precise calculation of the reward prediction error, yet it remains to be shown how this can be computed by neurons. Here we propose a solution to these problems by extending the continuous temporal difference (TD learning of Doya (2000 to the case of spiking neurons in an actor-critic network operating in continuous time, and with continuous state and action representations. In our model, the critic learns to predict expected future rewards in real time. Its activity, together with actual rewards, conditions the delivery of a neuromodulatory TD signal to itself and to the actor, which is responsible for action choice. In simulations, we show that such an architecture can solve a Morris water-maze-like navigation task, in a number of trials consistent with reported animal performance. We also use our model to solve the acrobot and the cartpole problems, two complex motor control tasks. Our model provides a plausible way of computing reward prediction error in the brain. Moreover, the analytically derived learning rule is consistent with experimental evidence for dopamine-modulated spike-timing-dependent plasticity.

First-spike latency in Hodgkin's three classes of neurons.

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Wang, Hengtong; Chen, Yueling; Chen, Yong

2013-07-07

We study the first-spike latency (FSL) in Hodgkin's three classes of neurons with the Morris-Lecar neuron model. It is found that all the three classes of neurons can encode an external stimulus into FSLs. With DC inputs, the FSLs of all of the neurons decrease with input intensity. With input current decreased to the threshold, class 1 neurons show an arbitrary long FSL whereas class 2 and 3 neurons exhibit the short-limit FSLs. When the input current is sinusoidal, the amplitude, frequency and initial phase can be encoded by all the three classes of neurons. The FSLs of all of the neurons decrease with the input amplitude and frequency. When the input frequency is too high, all of the neurons respond with infinite FSLs. When the initial phase increases, the FSL decreases and then jumps to a maximal value and finally decreases linearly. With changes in the input parameters, the FSLs of the class 1 and 2 neurons exhibit similar properties. However, the FSL of the class 3 neurons became slightly longer and only produces responses for a narrow range of initial phase if input frequencies are low. Moreover, our results also show that the FSL and firing rate responses are mutually independent processes and that neurons can encode an external stimulus into different FSLs and firing rates simultaneously. This finding is consistent with the current theory of dual or multiple complementary coding mechanisms. Copyright © 2013 Elsevier Ltd. All rights reserved.

Reconstruction of neuronal input through modeling single-neuron dynamics and computations

International Nuclear Information System (INIS)

Qin, Qing; Wang, Jiang; Yu, Haitao; Deng, Bin; Chan, Wai-lok

2016-01-01

Mathematical models provide a mathematical description of neuron activity, which can better understand and quantify neural computations and corresponding biophysical mechanisms evoked by stimulus. In this paper, based on the output spike train evoked by the acupuncture mechanical stimulus, we present two different levels of models to describe the input-output system to achieve the reconstruction of neuronal input. The reconstruction process is divided into two steps: First, considering the neuronal spiking event as a Gamma stochastic process. The scale parameter and the shape parameter of Gamma process are, respectively, defined as two spiking characteristics, which are estimated by a state-space method. Then, leaky integrate-and-fire (LIF) model is used to mimic the response system and the estimated spiking characteristics are transformed into two temporal input parameters of LIF model, through two conversion formulas. We test this reconstruction method by three different groups of simulation data. All three groups of estimates reconstruct input parameters with fairly high accuracy. We then use this reconstruction method to estimate the non-measurable acupuncture input parameters. Results show that under three different frequencies of acupuncture stimulus conditions, estimated input parameters have an obvious difference. The higher the frequency of the acupuncture stimulus is, the higher the accuracy of reconstruction is.

Reconstruction of neuronal input through modeling single-neuron dynamics and computations

Energy Technology Data Exchange (ETDEWEB)

Qin, Qing; Wang, Jiang; Yu, Haitao; Deng, Bin, E-mail: dengbin@tju.edu.cn; Chan, Wai-lok [School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072 (China)

2016-06-15

Mathematical models provide a mathematical description of neuron activity, which can better understand and quantify neural computations and corresponding biophysical mechanisms evoked by stimulus. In this paper, based on the output spike train evoked by the acupuncture mechanical stimulus, we present two different levels of models to describe the input-output system to achieve the reconstruction of neuronal input. The reconstruction process is divided into two steps: First, considering the neuronal spiking event as a Gamma stochastic process. The scale parameter and the shape parameter of Gamma process are, respectively, defined as two spiking characteristics, which are estimated by a state-space method. Then, leaky integrate-and-fire (LIF) model is used to mimic the response system and the estimated spiking characteristics are transformed into two temporal input parameters of LIF model, through two conversion formulas. We test this reconstruction method by three different groups of simulation data. All three groups of estimates reconstruct input parameters with fairly high accuracy. We then use this reconstruction method to estimate the non-measurable acupuncture input parameters. Results show that under three different frequencies of acupuncture stimulus conditions, estimated input parameters have an obvious difference. The higher the frequency of the acupuncture stimulus is, the higher the accuracy of reconstruction is.

Transmitter modulation of spike-evoked calcium transients in arousal related neurons

DEFF Research Database (Denmark)

Kohlmeier, Kristi Anne; Leonard, Christopher S

2006-01-01

Nitric oxide synthase (NOS)-containing cholinergic neurons in the laterodorsal tegmentum (LDT) influence behavioral and motivational states through their projections to the thalamus, ventral tegmental area and a brainstem 'rapid eye movement (REM)-induction' site. Action potential-evoked intracel......Nitric oxide synthase (NOS)-containing cholinergic neurons in the laterodorsal tegmentum (LDT) influence behavioral and motivational states through their projections to the thalamus, ventral tegmental area and a brainstem 'rapid eye movement (REM)-induction' site. Action potential......-evoked intracellular calcium transients dampen excitability and stimulate NO production in these neurons. In this study, we investigated the action of several arousal-related neurotransmitters and the role of specific calcium channels in these LDT Ca(2+)-transients by simultaneous whole-cell recording and calcium...... of cholinergic LDT neurons and that inhibition of spike-evoked Ca(2+)-transients is a common action of neurotransmitters that also activate GIRK channels in these neurons. Because spike-evoked calcium influx dampens excitability, our findings suggest that these 'inhibitory' transmitters could boost firing rate...

Sequentially switching cell assemblies in random inhibitory networks of spiking neurons in the striatum.

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Ponzi, Adam; Wickens, Jeff

2010-04-28

The striatum is composed of GABAergic medium spiny neurons with inhibitory collaterals forming a sparse random asymmetric network and receiving an excitatory glutamatergic cortical projection. Because the inhibitory collaterals are sparse and weak, their role in striatal network dynamics is puzzling. However, here we show by simulation of a striatal inhibitory network model composed of spiking neurons that cells form assemblies that fire in sequential coherent episodes and display complex identity-temporal spiking patterns even when cortical excitation is simply constant or fluctuating noisily. Strongly correlated large-scale firing rate fluctuations on slow behaviorally relevant timescales of hundreds of milliseconds are shown by members of the same assembly whereas members of different assemblies show strong negative correlation, and we show how randomly connected spiking networks can generate this activity. Cells display highly irregular spiking with high coefficients of variation, broadly distributed low firing rates, and interspike interval distributions that are consistent with exponentially tailed power laws. Although firing rates vary coherently on slow timescales, precise spiking synchronization is absent in general. Our model only requires the minimal but striatally realistic assumptions of sparse to intermediate random connectivity, weak inhibitory synapses, and sufficient cortical excitation so that some cells are depolarized above the firing threshold during up states. Our results are in good qualitative agreement with experimental studies, consistent with recently determined striatal anatomy and physiology, and support a new view of endogenously generated metastable state switching dynamics of the striatal network underlying its information processing operations.

Stochastic resonance of ensemble neurons for transient spike trains: Wavelet analysis

International Nuclear Information System (INIS)

Hasegawa, Hideo

2002-01-01

By using the wavelet transformation (WT), I have analyzed the response of an ensemble of N (=1, 10, 100, and 500) Hodgkin-Huxley neurons to transient M-pulse spike trains (M=1 to 3) with independent Gaussian noises. The cross correlation between the input and output signals is expressed in terms of the WT expansion coefficients. The signal-to-noise ratio (SNR) is evaluated by using the denoising method within the WT, by which the noise contribution is extracted from the output signals. Although the response of a single (N=1) neuron to subthreshold transient signals with noises is quite unreliable, the transmission fidelity assessed by the cross correlation and SNR is shown to be much improved by increasing the value of N: a population of neurons plays an indispensable role in the stochastic resonance (SR) for transient spike inputs. It is also shown that in a large-scale ensemble, the transmission fidelity for suprathreshold transient spikes is not significantly degraded by a weak noise which is responsible to SR for subthreshold inputs

Weak noise in neurons may powerfully inhibit the generation of repetitive spiking but not its propagation.

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Henry C Tuckwell

2010-05-01

Full Text Available Many neurons have epochs in which they fire action potentials in an approximately periodic fashion. To see what effects noise of relatively small amplitude has on such repetitive activity we recently examined the response of the Hodgkin-Huxley (HH space-clamped system to such noise as the mean and variance of the applied current vary, near the bifurcation to periodic firing. This article is concerned with a more realistic neuron model which includes spatial extent. Employing the Hodgkin-Huxley partial differential equation system, the deterministic component of the input current is restricted to a small segment whereas the stochastic component extends over a region which may or may not overlap the deterministic component. For mean values below, near and above the critical values for repetitive spiking, the effects of weak noise of increasing strength is ascertained by simulation. As in the point model, small amplitude noise near the critical value dampens the spiking activity and leads to a minimum as noise level increases. This was the case for both additive noise and conductance-based noise. Uniform noise along the whole neuron is only marginally more effective in silencing the cell than noise which occurs near the region of excitation. In fact it is found that if signal and noise overlap in spatial extent, then weak noise may inhibit spiking. If, however, signal and noise are applied on disjoint intervals, then the noise has no effect on the spiking activity, no matter how large its region of application, though the trajectories are naturally altered slightly by noise. Such effects could not be discerned in a point model and are important for real neuron behavior. Interference with the spike train does nevertheless occur when the noise amplitude is larger, even when noise and signal do not overlap, being due to the instigation of secondary noise-induced wave phenomena rather than switching the system from one attractor (firing regularly to

Integrated workflows for spiking neuronal network simulations

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Ján eAntolík

2013-12-01

Full Text Available The increasing availability of computational resources is enabling more detailed, realistic modelling in computational neuroscience, resulting in a shift towards more heterogeneous models of neuronal circuits, and employment of complex experimental protocols. This poses a challenge for existing tool chains, as the set of tools involved in a typical modeller's workflow is expanding concomitantly, with growing complexity in the metadata flowing between them. For many parts of the workflow, a range of tools is available; however, numerous areas lack dedicated tools, while integration of existing tools is limited. This forces modellers to either handle the workflow manually, leading to errors, or to write substantial amounts of code to automate parts of the workflow, in both cases reducing their productivity.To address these issues, we have developed Mozaik: a workflow system for spiking neuronal network simulations written in Python. Mozaik integrates model, experiment and stimulation specification, simulation execution, data storage, data analysis and visualisation into a single automated workflow, ensuring that all relevant metadata are available to all workflow components. It is based on several existing tools, including PyNN, Neo and Matplotlib. It offers a declarative way to specify models and recording configurations using hierarchically organised configuration files. Mozaik automatically records all data together with all relevant metadata about the experimental context, allowing automation of the analysis and visualisation stages. Mozaik has a modular architecture, and the existing modules are designed to be extensible with minimal programming effort. Mozaik increases the productivity of running virtual experiments on highly structured neuronal networks by automating the entire experimental cycle, while increasing the reliability of modelling studies by relieving the user from manual handling of the flow of metadata between the individual

Impacts of clustering on noise-induced spiking regularity in the excitatory neuronal networks of subnetworks.

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Li, Huiyan; Sun, Xiaojuan; Xiao, Jinghua

2015-01-01

In this paper, we investigate how clustering factors influent spiking regularity of the neuronal network of subnetworks. In order to do so, we fix the averaged coupling probability and the averaged coupling strength, and take the cluster number M, the ratio of intra-connection probability and inter-connection probability R, the ratio of intra-coupling strength and inter-coupling strength S as controlled parameters. With the obtained simulation results, we find that spiking regularity of the neuronal networks has little variations with changing of R and S when M is fixed. However, cluster number M could reduce the spiking regularity to low level when the uniform neuronal network's spiking regularity is at high level. Combined the obtained results, we can see that clustering factors have little influences on the spiking regularity when the entire energy is fixed, which could be controlled by the averaged coupling strength and the averaged connection probability.

Extraction of Inter-Aural Time Differences Using a Spiking Neuron Network Model of the Medial Superior Olive

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Jörg Encke

2018-03-01

Full Text Available The mammalian auditory system is able to extract temporal and spectral features from sound signals at the two ears. One important cue for localization of low-frequency sound sources in the horizontal plane are inter-aural time differences (ITDs which are first analyzed in the medial superior olive (MSO in the brainstem. Neural recordings of ITD tuning curves at various stages along the auditory pathway suggest that ITDs in the mammalian brainstem are not represented in form of a Jeffress-type place code. An alternative is the hemispheric opponent-channel code, according to which ITDs are encoded as the difference in the responses of the MSO nuclei in the two hemispheres. In this study, we present a physiologically-plausible, spiking neuron network model of the mammalian MSO circuit and apply two different methods of extracting ITDs from arbitrary sound signals. The network model is driven by a functional model of the auditory periphery and physiological models of the cochlear nucleus and the MSO. Using a linear opponent-channel decoder, we show that the network is able to detect changes in ITD with a precision down to 10 μs and that the sensitivity of the decoder depends on the slope of the ITD-rate functions. A second approach uses an artificial neuronal network to predict ITDs directly from the spiking output of the MSO and ANF model. Using this predictor, we show that the MSO-network is able to reliably encode static and time-dependent ITDs over a large frequency range, also for complex signals like speech.

Code-specific learning rules improve action selection by populations of spiking neurons.

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Friedrich, Johannes; Urbanczik, Robert; Senn, Walter

2014-08-01

Population coding is widely regarded as a key mechanism for achieving reliable behavioral decisions. We previously introduced reinforcement learning for population-based decision making by spiking neurons. Here we generalize population reinforcement learning to spike-based plasticity rules that take account of the postsynaptic neural code. We consider spike/no-spike, spike count and spike latency codes. The multi-valued and continuous-valued features in the postsynaptic code allow for a generalization of binary decision making to multi-valued decision making and continuous-valued action selection. We show that code-specific learning rules speed up learning both for the discrete classification and the continuous regression tasks. The suggested learning rules also speed up with increasing population size as opposed to standard reinforcement learning rules. Continuous action selection is further shown to explain realistic learning speeds in the Morris water maze. Finally, we introduce the concept of action perturbation as opposed to the classical weight- or node-perturbation as an exploration mechanism underlying reinforcement learning. Exploration in the action space greatly increases the speed of learning as compared to exploration in the neuron or weight space.

Reconstructing stimuli from the spike-times of leaky integrate and fire neurons

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Sebastian eGerwinn

2011-02-01

Full Text Available Reconstructing stimuli from the spike-trains of neurons is an important approach for understanding the neural code. One of the difficulties associated with this task is that signals which are varying continuously in time are encoded into sequences of discrete events or spikes. An important problem is to determine how much information about the continuously varying stimulus can be extracted from the time-points at which spikes were observed, especially if these time-points are subject to some sort of randomness. For the special case of spike trains generated by leaky integrate and fire neurons, noise can be introduced by allowing variations in the threshold every time a spike is released. A simple decoding algorithm previously derived for the noiseless case can be extended to the stochastic case, but turns out to be biased. Here, we review a solution to this problem, by presenting a simple yet efficient algorithm which greatly reduces the bias, and therefore leads to better decoding performance in the stochastic case.

Biophysical Insights into How Spike Threshold Depends on the Rate of Membrane Potential Depolarization in Type I and Type II Neurons.

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Guo-Sheng Yi

Full Text Available Dynamic spike threshold plays a critical role in neuronal input-output relations. In many neurons, the threshold potential depends on the rate of membrane potential depolarization (dV/dt preceding a spike. There are two basic classes of neural excitability, i.e., Type I and Type II, according to input-output properties. Although the dynamical and biophysical basis of their spike initiation has been established, the spike threshold dynamic for each cell type has not been well described. Here, we use a biophysical model to investigate how spike threshold depends on dV/dt in two types of neuron. It is observed that Type II spike threshold is more depolarized and more sensitive to dV/dt than Type I. With phase plane analysis, we show that each threshold dynamic arises from the different separatrix and K+ current kinetics. By analyzing subthreshold properties of membrane currents, we find the activation of hyperpolarizing current prior to spike initiation is a major factor that regulates the threshold dynamics. The outward K+ current in Type I neuron does not activate at the perithresholds, which makes its spike threshold insensitive to dV/dt. The Type II K+ current activates prior to spike initiation and there is a large net hyperpolarizing current at the perithresholds, which results in a depolarized threshold as well as a pronounced threshold dynamic. These predictions are further attested in several other functionally equivalent cases of neural excitability. Our study provides a fundamental description about how intrinsic biophysical properties contribute to the threshold dynamics in Type I and Type II neurons, which could decipher their significant functions in neural coding.

Fractal characterization of acupuncture-induced spike trains of rat WDR neurons

International Nuclear Information System (INIS)

Chen, Yingyuan; Guo, Yi; Wang, Jiang; Hong, Shouhai; Wei, Xile; Yu, Haitao; Deng, Bin

2015-01-01

Highlights: •Fractal analysis is a valuable tool for measuring MA-induced neural activities. •In course of the experiments, the spike trains display different fractal properties. •The fractal properties reflect the long-term modulation of MA on WDR neurons. •The results may explain the long-lasting effects induced by acupuncture. -- Abstract: The experimental and the clinical studies have showed manual acupuncture (MA) could evoke multiple responses in various neural regions. Characterising the neuronal activities in these regions may provide more deep insights into acupuncture mechanisms. This paper used fractal analysis to investigate MA-induced spike trains of Wide Dynamic Range (WDR) neurons in rat spinal dorsal horn, an important relay station and integral component in processing acupuncture information. Allan factor and Fano factor were utilized to test whether the spike trains were fractal, and Allan factor were used to evaluate the scaling exponents and Hurst exponents. It was found that these two fractal exponents before and during MA were different significantly. During MA, the scaling exponents of WDR neurons were regulated in a small range, indicating a special fractal pattern. The neuronal activities were long-range correlated over multiple time scales. The scaling exponents during and after MA were similar, suggesting that the long-range correlations not only displayed during MA, but also extended to after withdrawing the needle. Our results showed that fractal analysis is a useful tool for measuring acupuncture effects. MA could modulate neuronal activities of which the fractal properties change as time proceeding. This evolution of fractal dynamics in course of MA experiments may explain at the level of neuron why the effect of MA observed in experiment and in clinic are complex, time-evolutionary, long-range even lasting for some time after stimulation

Spiking neural network for recognizing spatiotemporal sequences of spikes

International Nuclear Information System (INIS)

Jin, Dezhe Z.

2004-01-01

Sensory neurons in many brain areas spike with precise timing to stimuli with temporal structures, and encode temporally complex stimuli into spatiotemporal spikes. How the downstream neurons read out such neural code is an important unsolved problem. In this paper, we describe a decoding scheme using a spiking recurrent neural network. The network consists of excitatory neurons that form a synfire chain, and two globally inhibitory interneurons of different types that provide delayed feedforward and fast feedback inhibition, respectively. The network signals recognition of a specific spatiotemporal sequence when the last excitatory neuron down the synfire chain spikes, which happens if and only if that sequence was present in the input spike stream. The recognition scheme is invariant to variations in the intervals between input spikes within some range. The computation of the network can be mapped into that of a finite state machine. Our network provides a simple way to decode spatiotemporal spikes with diverse types of neurons

Neuronal spike-train responses in the presence of threshold noise.

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Coombes, S; Thul, R; Laudanski, J; Palmer, A R; Sumner, C J

2011-03-01

The variability of neuronal firing has been an intense topic of study for many years. From a modelling perspective it has often been studied in conductance based spiking models with the use of additive or multiplicative noise terms to represent channel fluctuations or the stochastic nature of neurotransmitter release. Here we propose an alternative approach using a simple leaky integrate-and-fire model with a noisy threshold. Initially, we develop a mathematical treatment of the neuronal response to periodic forcing using tools from linear response theory and use this to highlight how a noisy threshold can enhance downstream signal reconstruction. We further develop a more general framework for understanding the responses to large amplitude forcing based on a calculation of first passage times. This is ideally suited to understanding stochastic mode-locking, for which we numerically determine the Arnol'd tongue structure. An examination of data from regularly firing stellate neurons within the ventral cochlear nucleus, responding to sinusoidally amplitude modulated pure tones, shows tongue structures consistent with these predictions and highlights that stochastic, as opposed to deterministic, mode-locking is utilised at the level of the single stellate cell to faithfully encode periodic stimuli.

DL-ReSuMe: A Delay Learning-Based Remote Supervised Method for Spiking Neurons.

Science.gov (United States)

Taherkhani, Aboozar; Belatreche, Ammar; Li, Yuhua; Maguire, Liam P

2015-12-01

Recent research has shown the potential capability of spiking neural networks (SNNs) to model complex information processing in the brain. There is biological evidence to prove the use of the precise timing of spikes for information coding. However, the exact learning mechanism in which the neuron is trained to fire at precise times remains an open problem. The majority of the existing learning methods for SNNs are based on weight adjustment. However, there is also biological evidence that the synaptic delay is not constant. In this paper, a learning method for spiking neurons, called delay learning remote supervised method (DL-ReSuMe), is proposed to merge the delay shift approach and ReSuMe-based weight adjustment to enhance the learning performance. DL-ReSuMe uses more biologically plausible properties, such as delay learning, and needs less weight adjustment than ReSuMe. Simulation results have shown that the proposed DL-ReSuMe approach achieves learning accuracy and learning speed improvements compared with ReSuMe.

Energy consumption in Hodgkin–Huxley type fast spiking neuron model exposed to an external electric field

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K. Usha

2016-09-01

Full Text Available This paper evaluates the change in metabolic energy required to maintain the signalling activity of neurons in the presence of an external electric field. We have analysed the Hodgkin–Huxley type conductance based fast spiking neuron model as electrical circuit by changing the frequency and amplitude of the applied electric field. The study has shown that, the presence of electric field increases the membrane potential, electrical energy supply and metabolic energy consumption. As the amplitude of applied electric field increases by keeping a constant frequency, the membrane potential increases and consequently the electrical energy supply and metabolic energy consumption increases. On increasing the frequency of the applied field, the peak value of membrane potential after depolarization gradually decreases as a result electrical energy supply decreases which results in a lower rate of hydrolysis of ATP molecules.

Fluctuations and information filtering in coupled populations of spiking neurons with adaptation.

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Deger, Moritz; Schwalger, Tilo; Naud, Richard; Gerstner, Wulfram

2014-12-01

Finite-sized populations of spiking elements are fundamental to brain function but also are used in many areas of physics. Here we present a theory of the dynamics of finite-sized populations of spiking units, based on a quasirenewal description of neurons with adaptation. We derive an integral equation with colored noise that governs the stochastic dynamics of the population activity in response to time-dependent stimulation and calculate the spectral density in the asynchronous state. We show that systems of coupled populations with adaptation can generate a frequency band in which sensory information is preferentially encoded. The theory is applicable to fully as well as randomly connected networks and to leaky integrate-and-fire as well as to generalized spiking neurons with adaptation on multiple time scales.

An FPGA Platform for Real-Time Simulation of Spiking Neuronal Networks.

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Pani, Danilo; Meloni, Paolo; Tuveri, Giuseppe; Palumbo, Francesca; Massobrio, Paolo; Raffo, Luigi

2017-01-01

In the last years, the idea to dynamically interface biological neurons with artificial ones has become more and more urgent. The reason is essentially due to the design of innovative neuroprostheses where biological cell assemblies of the brain can be substituted by artificial ones. For closed-loop experiments with biological neuronal networks interfaced with in silico modeled networks, several technological challenges need to be faced, from the low-level interfacing between the living tissue and the computational model to the implementation of the latter in a suitable form for real-time processing. Field programmable gate arrays (FPGAs) can improve flexibility when simple neuronal models are required, obtaining good accuracy, real-time performance, and the possibility to create a hybrid system without any custom hardware, just programming the hardware to achieve the required functionality. In this paper, this possibility is explored presenting a modular and efficient FPGA design of an in silico spiking neural network exploiting the Izhikevich model. The proposed system, prototypically implemented on a Xilinx Virtex 6 device, is able to simulate a fully connected network counting up to 1,440 neurons, in real-time, at a sampling rate of 10 kHz, which is reasonable for small to medium scale extra-cellular closed-loop experiments.

A complex-valued firing-rate model that approximates the dynamics of spiking networks.

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Evan S Schaffer

2013-10-01

Full Text Available Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons.

A complex-valued firing-rate model that approximates the dynamics of spiking networks.

Science.gov (United States)

Schaffer, Evan S; Ostojic, Srdjan; Abbott, L F

2013-10-01

Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons.

Thalamic neuron models encode stimulus information by burst-size modulation

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Daniel Henry Elijah

2015-09-01

Full Text Available Thalamic neurons have been long assumed to fire in tonic mode during perceptive states, and in burst mode during sleep and unconsciousness. However, recent evidence suggests that bursts may also be relevant in the encoding of sensory information. Here we explore the neural code of such thalamic bursts. In order to assess whether the burst code is generic or whether it depends on the detailed properties of each bursting neuron, we analyzed two neuron models incorporating different levels of biological detail. One of the models contained no information of the biophysical processes entailed in spike generation, and described neuron activity at a phenomenological level. The second model represented the evolution of the individual ionic conductances involved in spiking and bursting, and required a large number of parameters. We analyzed the models' input selectivity using reverse correlation methods and information theory. We found that n-spike bursts from both models transmit information by modulating their spike count in response to changes to instantaneous input features, such as slope, phase, amplitude, etc. The stimulus feature that is most efficiently encoded by bursts, however, need not coincide with one of such classical features. We therefore searched for the optimal feature among all those that could be expressed as a linear transformation of the time-dependent input current. We found that bursting neurons transmitted 6 times more information about such more general features. The relevant events in the stimulus were located in a time window spanning ~100 ms before and ~20 ms after burst onset. Most importantly, the neural code employed by the simple and the biologically realistic models was largely the same, implying that the simple thalamic neuron model contains the essential ingredients that account for the computational properties of the thalamic burst code. Thus, our results suggest the n-spike burst code is a general property of

Thalamic neuron models encode stimulus information by burst-size modulation.

Science.gov (United States)

Elijah, Daniel H; Samengo, Inés; Montemurro, Marcelo A

2015-01-01

Thalamic neurons have been long assumed to fire in tonic mode during perceptive states, and in burst mode during sleep and unconsciousness. However, recent evidence suggests that bursts may also be relevant in the encoding of sensory information. Here, we explore the neural code of such thalamic bursts. In order to assess whether the burst code is generic or whether it depends on the detailed properties of each bursting neuron, we analyzed two neuron models incorporating different levels of biological detail. One of the models contained no information of the biophysical processes entailed in spike generation, and described neuron activity at a phenomenological level. The second model represented the evolution of the individual ionic conductances involved in spiking and bursting, and required a large number of parameters. We analyzed the models' input selectivity using reverse correlation methods and information theory. We found that n-spike bursts from both models transmit information by modulating their spike count in response to changes to instantaneous input features, such as slope, phase, amplitude, etc. The stimulus feature that is most efficiently encoded by bursts, however, need not coincide with one of such classical features. We therefore searched for the optimal feature among all those that could be expressed as a linear transformation of the time-dependent input current. We found that bursting neurons transmitted 6 times more information about such more general features. The relevant events in the stimulus were located in a time window spanning ~100 ms before and ~20 ms after burst onset. Most importantly, the neural code employed by the simple and the biologically realistic models was largely the same, implying that the simple thalamic neuron model contains the essential ingredients that account for the computational properties of the thalamic burst code. Thus, our results suggest the n-spike burst code is a general property of thalamic neurons.

Pulsed neural networks consisting of single-flux-quantum spiking neurons

International Nuclear Information System (INIS)

Hirose, T.; Asai, T.; Amemiya, Y.

2007-01-01

An inhibitory pulsed neural network was developed for brain-like information processing, by using single-flux-quantum (SFQ) circuits. It consists of spiking neuron devices that are coupled to each other through all-to-all inhibitory connections. The network selects neural activity. The operation of the neural network was confirmed by computer simulation. SFQ neuron devices can imitate the operation of the inhibition phenomenon of neural networks

Generalized activity equations for spiking neural network dynamics

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Michael A Buice

2013-11-01

Full Text Available Much progress has been made in uncovering the computational capabilities of spiking neural networks. However, spiking neurons will always be more expensive to simulate compared to rate neurons because of the inherent disparity in time scales - the spike duration time is much shorter than the inter-spike time, which is much shorter than any learning time scale. In numerical analysis, this is a classic stiff problem. Spiking neurons are also much more difficult to study analytically. One possible approach to making spiking networks more tractable is to augment mean field activity models with some information about spiking correlations. For example, such a generalized activity model could carry information about spiking rates and correlations between spikes self-consistently. Here, we will show how this can be accomplished by constructing a complete formal probabilistic description of the network and then expanding around a small parameter such as the inverse of the number of neurons in the network. The mean field theory of the system gives a rate-like description. The first order terms in the perturbation expansion keep track of covariances.

Spike-based population coding and working memory.

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Martin Boerlin

2011-02-01

Full Text Available Compelling behavioral evidence suggests that humans can make optimal decisions despite the uncertainty inherent in perceptual or motor tasks. A key question in neuroscience is how populations of spiking neurons can implement such probabilistic computations. In this article, we develop a comprehensive framework for optimal, spike-based sensory integration and working memory in a dynamic environment. We propose that probability distributions are inferred spike-per-spike in recurrently connected networks of integrate-and-fire neurons. As a result, these networks can combine sensory cues optimally, track the state of a time-varying stimulus and memorize accumulated evidence over periods much longer than the time constant of single neurons. Importantly, we propose that population responses and persistent working memory states represent entire probability distributions and not only single stimulus values. These memories are reflected by sustained, asynchronous patterns of activity which make relevant information available to downstream neurons within their short time window of integration. Model neurons act as predictive encoders, only firing spikes which account for new information that has not yet been signaled. Thus, spike times signal deterministically a prediction error, contrary to rate codes in which spike times are considered to be random samples of an underlying firing rate. As a consequence of this coding scheme, a multitude of spike patterns can reliably encode the same information. This results in weakly correlated, Poisson-like spike trains that are sensitive to initial conditions but robust to even high levels of external neural noise. This spike train variability reproduces the one observed in cortical sensory spike trains, but cannot be equated to noise. On the contrary, it is a consequence of optimal spike-based inference. In contrast, we show that rate-based models perform poorly when implemented with stochastically spiking neurons.

One-dimensional map-based neuron model: A logistic modification

International Nuclear Information System (INIS)

Mesbah, Samineh; Moghtadaei, Motahareh; Hashemi Golpayegani, Mohammad Reza; Towhidkhah, Farzad

2014-01-01

A one-dimensional map is proposed for modeling some of the neuronal activities, including different spiking and bursting behaviors. The model is obtained by applying some modifications on the well-known Logistic map and is named the Modified and Confined Logistic (MCL) model. Map-based neuron models are known as phenomenological models and recently, they are widely applied in modeling tasks due to their computational efficacy. Most of discrete map-based models involve two variables representing the slow-fast prototype. There are also some one-dimensional maps, which can replicate some of the neuronal activities. However, the existence of four bifurcation parameters in the MCL model gives rise to reproduction of spiking behavior with control over the frequency of the spikes, and imitation of chaotic and regular bursting responses concurrently. It is also shown that the proposed model has the potential to reproduce more realistic bursting activity by adding a second variable. Moreover the MCL model is able to replicate considerable number of experimentally observed neuronal responses introduced in Izhikevich (2004) [23]. Some analytical and numerical analyses of the MCL model dynamics are presented to explain the emersion of complex dynamics from this one-dimensional map

Linear stability analysis of retrieval state in associative memory neural networks of spiking neurons

International Nuclear Information System (INIS)

Yoshioka, Masahiko

2002-01-01

We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatiotemporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatiotemporal patterns, we assume the spike-timing-dependent synaptic plasticity with the asymmetric time window. Analysis for periodic solution of retrieval state reveals that if the area of the negative part of the time window is equivalent to the positive part, then crosstalk among encoded patterns vanishes. Phase transition due to the loss of the stability of periodic solution is observed when we assume fast α function for direct interaction among neurons. In order to evaluate the critical point of this phase transition, we employ Floquet theory in which the stability problem of the infinite number of spiking neurons interacting with α function is reduced to the eigenvalue problem with the finite size of matrix. Numerical integration of the single-body dynamics yields the explicit value of the matrix, which enables us to determine the critical point of the phase transition with a high degree of precision

Arcuate hypothalamic AgRP and putative POMC neurons show opposite changes in spiking across multiple timescales

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Mandelblat-Cerf, Yael; Ramesh, Rohan N; Burgess, Christian R; Patella, Paola; Yang, Zongfang; Lowell, Bradford B; Andermann, Mark L

2015-01-01

Agouti-related-peptide (AgRP) neurons—interoceptive neurons in the arcuate nucleus of the hypothalamus (ARC)—are both necessary and sufficient for driving feeding behavior. To better understand the functional roles of AgRP neurons, we performed optetrode electrophysiological recordings from AgRP neurons in awake, behaving AgRP-IRES-Cre mice. In free-feeding mice, we observed a fivefold increase in AgRP neuron firing with mounting caloric deficit in afternoon vs morning recordings. In food-restricted mice, as food became available, AgRP neuron firing dropped, yet remained elevated as compared to firing in sated mice. The rapid drop in spiking activity of AgRP neurons at meal onset may reflect a termination of the drive to find food, while residual, persistent spiking may reflect a sustained drive to consume food. Moreover, nearby neurons inhibited by AgRP neuron photostimulation, likely including satiety-promoting pro-opiomelanocortin (POMC) neurons, demonstrated opposite changes in spiking. Finally, firing of ARC neurons was also rapidly modulated within seconds of individual licks for liquid food. These findings suggest novel roles for antagonistic AgRP and POMC neurons in the regulation of feeding behaviors across multiple timescales. DOI: http://dx.doi.org/10.7554/eLife.07122.001 PMID:26159614

Spiking neurons in a hierarchical self-organizing map model can learn to develop spatial and temporal properties of entorhinal grid cells and hippocampal place cells.

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Praveen K Pilly

Full Text Available Medial entorhinal grid cells and hippocampal place cells provide neural correlates of spatial representation in the brain. A place cell typically fires whenever an animal is present in one or more spatial regions, or places, of an environment. A grid cell typically fires in multiple spatial regions that form a regular hexagonal grid structure extending throughout the environment. Different grid and place cells prefer spatially offset regions, with their firing fields increasing in size along the dorsoventral axes of the medial entorhinal cortex and hippocampus. The spacing between neighboring fields for a grid cell also increases along the dorsoventral axis. This article presents a neural model whose spiking neurons operate in a hierarchy of self-organizing maps, each obeying the same laws. This spiking GridPlaceMap model simulates how grid cells and place cells may develop. It responds to realistic rat navigational trajectories by learning grid cells with hexagonal grid firing fields of multiple spatial scales and place cells with one or more firing fields that match neurophysiological data about these cells and their development in juvenile rats. The place cells represent much larger spaces than the grid cells, which enable them to support navigational behaviors. Both self-organizing maps amplify and learn to categorize the most frequent and energetic co-occurrences of their inputs. The current results build upon a previous rate-based model of grid and place cell learning, and thus illustrate a general method for converting rate-based adaptive neural models, without the loss of any of their analog properties, into models whose cells obey spiking dynamics. New properties of the spiking GridPlaceMap model include the appearance of theta band modulation. The spiking model also opens a path for implementation in brain-emulating nanochips comprised of networks of noisy spiking neurons with multiple-level adaptive weights for controlling autonomous

Dynamics of Competition between Subnetworks of Spiking Neuronal Networks in the Balanced State

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Lagzi, Fereshteh; Rotter, Stefan

2015-01-01

We explore and analyze the nonlinear switching dynamics of neuronal networks with non-homogeneous connectivity. The general significance of such transient dynamics for brain function is unclear; however, for instance decision-making processes in perception and cognition have been implicated with it. The network under study here is comprised of three subnetworks of either excitatory or inhibitory leaky integrate-and-fire neurons, of which two are of the same type. The synaptic weights are arranged to establish and maintain a balance between excitation and inhibition in case of a constant external drive. Each subnetwork is randomly connected, where all neurons belonging to a particular population have the same in-degree and the same out-degree. Neurons in different subnetworks are also randomly connected with the same probability; however, depending on the type of the pre-synaptic neuron, the synaptic weight is scaled by a factor. We observed that for a certain range of the “within” versus “between” connection weights (bifurcation parameter), the network activation spontaneously switches between the two sub-networks of the same type. This kind of dynamics has been termed “winnerless competition”, which also has a random component here. In our model, this phenomenon is well described by a set of coupled stochastic differential equations of Lotka-Volterra type that imply a competition between the subnetworks. The associated mean-field model shows the same dynamical behavior as observed in simulations of large networks comprising thousands of spiking neurons. The deterministic phase portrait is characterized by two attractors and a saddle node, its stochastic component is essentially given by the multiplicative inherent noise of the system. We find that the dwell time distribution of the active states is exponential, indicating that the noise drives the system randomly from one attractor to the other. A similar model for a larger number of populations might

Dynamics of Competition between Subnetworks of Spiking Neuronal Networks in the Balanced State.

Science.gov (United States)

Lagzi, Fereshteh; Rotter, Stefan

2015-01-01

We explore and analyze the nonlinear switching dynamics of neuronal networks with non-homogeneous connectivity. The general significance of such transient dynamics for brain function is unclear; however, for instance decision-making processes in perception and cognition have been implicated with it. The network under study here is comprised of three subnetworks of either excitatory or inhibitory leaky integrate-and-fire neurons, of which two are of the same type. The synaptic weights are arranged to establish and maintain a balance between excitation and inhibition in case of a constant external drive. Each subnetwork is randomly connected, where all neurons belonging to a particular population have the same in-degree and the same out-degree. Neurons in different subnetworks are also randomly connected with the same probability; however, depending on the type of the pre-synaptic neuron, the synaptic weight is scaled by a factor. We observed that for a certain range of the "within" versus "between" connection weights (bifurcation parameter), the network activation spontaneously switches between the two sub-networks of the same type. This kind of dynamics has been termed "winnerless competition", which also has a random component here. In our model, this phenomenon is well described by a set of coupled stochastic differential equations of Lotka-Volterra type that imply a competition between the subnetworks. The associated mean-field model shows the same dynamical behavior as observed in simulations of large networks comprising thousands of spiking neurons. The deterministic phase portrait is characterized by two attractors and a saddle node, its stochastic component is essentially given by the multiplicative inherent noise of the system. We find that the dwell time distribution of the active states is exponential, indicating that the noise drives the system randomly from one attractor to the other. A similar model for a larger number of populations might suggest a

Deep Spiking Networks

NARCIS (Netherlands)

O'Connor, P.; Welling, M.

2016-01-01

We introduce an algorithm to do backpropagation on a spiking network. Our network is "spiking" in the sense that our neurons accumulate their activation into a potential over time, and only send out a signal (a "spike") when this potential crosses a threshold and the neuron is reset. Neurons only

Adaptive coupling optimized spiking coherence and synchronization in Newman-Watts neuronal networks.

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Gong, Yubing; Xu, Bo; Wu, Ya'nan

2013-09-01

In this paper, we have numerically studied the effect of adaptive coupling on the temporal coherence and synchronization of spiking activity in Newman-Watts Hodgkin-Huxley neuronal networks. It is found that random shortcuts can enhance the spiking synchronization more rapidly when the increment speed of adaptive coupling is increased and can optimize the temporal coherence of spikes only when the increment speed of adaptive coupling is appropriate. It is also found that adaptive coupling strength can enhance the synchronization of spikes and can optimize the temporal coherence of spikes when random shortcuts are appropriate. These results show that adaptive coupling has a big influence on random shortcuts related spiking activity and can enhance and optimize the temporal coherence and synchronization of spiking activity of the network. These findings can help better understand the roles of adaptive coupling for improving the information processing and transmission in neural systems.

A Reward-Maximizing Spiking Neuron as a Bounded Rational Decision Maker.

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Leibfried, Felix; Braun, Daniel A

2015-08-01

Rate distortion theory describes how to communicate relevant information most efficiently over a channel with limited capacity. One of the many applications of rate distortion theory is bounded rational decision making, where decision makers are modeled as information channels that transform sensory input into motor output under the constraint that their channel capacity is limited. Such a bounded rational decision maker can be thought to optimize an objective function that trades off the decision maker's utility or cumulative reward against the information processing cost measured by the mutual information between sensory input and motor output. In this study, we interpret a spiking neuron as a bounded rational decision maker that aims to maximize its expected reward under the computational constraint that the mutual information between the neuron's input and output is upper bounded. This abstract computational constraint translates into a penalization of the deviation between the neuron's instantaneous and average firing behavior. We derive a synaptic weight update rule for such a rate distortion optimizing neuron and show in simulations that the neuron efficiently extracts reward-relevant information from the input by trading off its synaptic strengths against the collected reward.

Noise and Synchronization Analysis of the Cold-Receptor Neuronal Network Model

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Ying Du

2014-01-01

Full Text Available This paper analyzes the dynamics of the cold receptor neural network model. First, it examines noise effects on neuronal stimulus in the model. From ISI plots, it is shown that there are considerable differences between purely deterministic simulations and noisy ones. The ISI-distance is used to measure the noise effects on spike trains quantitatively. It is found that spike trains observed in neural models can be more strongly affected by noise for different temperatures in some aspects; meanwhile, spike train has greater variability with the noise intensity increasing. The synchronization of neuronal network with different connectivity patterns is also studied. It is shown that chaotic and high period patterns are more difficult to get complete synchronization than the situation in single spike and low period patterns. The neuronal network will exhibit various patterns of firing synchronization by varying some key parameters such as the coupling strength. Different types of firing synchronization are diagnosed by a correlation coefficient and the ISI-distance method. The simulations show that the synchronization status of neurons is related to the network connectivity patterns.

Mechanisms of Winner-Take-All and Group Selection in Neuronal Spiking Networks.

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Chen, Yanqing

2017-01-01

A major function of central nervous systems is to discriminate different categories or types of sensory input. Neuronal networks accomplish such tasks by learning different sensory maps at several stages of neural hierarchy, such that different neurons fire selectively to reflect different internal or external patterns and states. The exact mechanisms of such map formation processes in the brain are not completely understood. Here we study the mechanism by which a simple recurrent/reentrant neuronal network accomplish group selection and discrimination to different inputs in order to generate sensory maps. We describe the conditions and mechanism of transition from a rhythmic epileptic state (in which all neurons fire synchronized and indiscriminately to any input) to a winner-take-all state in which only a subset of neurons fire for a specific input. We prove an analytic condition under which a stable bump solution and a winner-take-all state can emerge from the local recurrent excitation-inhibition interactions in a three-layer spiking network with distinct excitatory and inhibitory populations, and demonstrate the importance of surround inhibitory connection topology on the stability of dynamic patterns in spiking neural network.

Spike-Timing of Orbitofrontal Neurons Is Synchronized With Breathing.

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Kőszeghy, Áron; Lasztóczi, Bálint; Forro, Thomas; Klausberger, Thomas

2018-01-01

The orbitofrontal cortex (OFC) has been implicated in a multiplicity of complex brain functions, including representations of expected outcome properties, post-decision confidence, momentary food-reward values, complex flavors and odors. As breathing rhythm has an influence on odor processing at primary olfactory areas, we tested the hypothesis that it may also influence neuronal activity in the OFC, a prefrontal area involved also in higher order processing of odors. We recorded spike timing of orbitofrontal neurons as well as local field potentials (LFPs) in awake, head-fixed mice, together with the breathing rhythm. We observed that a large majority of orbitofrontal neurons showed robust phase-coupling to breathing during immobility and running. The phase coupling of action potentials to breathing was significantly stronger in orbitofrontal neurons compared to cells in the medial prefrontal cortex. The characteristic synchronization of orbitofrontal neurons with breathing might provide a temporal framework for multi-variable processing of olfactory, gustatory and reward-value relationships.

Spike-Timing of Orbitofrontal Neurons Is Synchronized With Breathing

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Áron Kőszeghy

2018-04-01

Full Text Available The orbitofrontal cortex (OFC has been implicated in a multiplicity of complex brain functions, including representations of expected outcome properties, post-decision confidence, momentary food-reward values, complex flavors and odors. As breathing rhythm has an influence on odor processing at primary olfactory areas, we tested the hypothesis that it may also influence neuronal activity in the OFC, a prefrontal area involved also in higher order processing of odors. We recorded spike timing of orbitofrontal neurons as well as local field potentials (LFPs in awake, head-fixed mice, together with the breathing rhythm. We observed that a large majority of orbitofrontal neurons showed robust phase-coupling to breathing during immobility and running. The phase coupling of action potentials to breathing was significantly stronger in orbitofrontal neurons compared to cells in the medial prefrontal cortex. The characteristic synchronization of orbitofrontal neurons with breathing might provide a temporal framework for multi-variable processing of olfactory, gustatory and reward-value relationships.

Auto- and Crosscorrelograms for the Spike Response of Leaky Integrate-and-Fire Neurons with Slow Synapses

International Nuclear Information System (INIS)

Moreno-Bote, Ruben; Parga, Nestor

2006-01-01

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 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 previously by Moreno-Bote and Parga [Phys. Rev. Lett. 92, 028102 (2004)]. These two functions define the firing variability and firing synchronization between neurons, and are of much importance for understanding neuron communication

A Frank mixture copula family for modeling higher-order correlations of neural spike counts

International Nuclear Information System (INIS)

Onken, Arno; Obermayer, Klaus

2009-01-01

In order to evaluate the importance of higher-order correlations in neural spike count codes, flexible statistical models of dependent multivariate spike counts are required. Copula families, parametric multivariate distributions that represent dependencies, can be applied to construct such models. We introduce the Frank mixture family as a new copula family that has separate parameters for all pairwise and higher-order correlations. In contrast to the Farlie-Gumbel-Morgenstern copula family that shares this property, the Frank mixture copula can model strong correlations. We apply spike count models based on the Frank mixture copula to data generated by a network of leaky integrate-and-fire neurons and compare the goodness of fit to distributions based on the Farlie-Gumbel-Morgenstern family. Finally, we evaluate the importance of using proper single neuron spike count distributions on the Shannon information. We find notable deviations in the entropy that increase with decreasing firing rates. Moreover, we find that the Frank mixture family increases the log likelihood of the fit significantly compared to the Farlie-Gumbel-Morgenstern family. This shows that the Frank mixture copula is a useful tool to assess the importance of higher-order correlations in spike count codes.

Decoding spatiotemporal spike sequences via the finite state automata dynamics of spiking neural networks

International Nuclear Information System (INIS)

Jin, Dezhe Z

2008-01-01

Temporally complex stimuli are encoded into spatiotemporal spike sequences of neurons in many sensory areas. Here, we describe how downstream neurons with dendritic bistable plateau potentials can be connected to decode such spike sequences. Driven by feedforward inputs from the sensory neurons and controlled by feedforward inhibition and lateral excitation, the neurons transit between UP and DOWN states of the membrane potentials. The neurons spike only in the UP states. A decoding neuron spikes at the end of an input to signal the recognition of specific spike sequences. The transition dynamics is equivalent to that of a finite state automaton. A connection rule for the networks guarantees that any finite state automaton can be mapped into the transition dynamics, demonstrating the equivalence in computational power between the networks and finite state automata. The decoding mechanism is capable of recognizing an arbitrary number of spatiotemporal spike sequences, and is insensitive to the variations of the spike timings in the sequences

A Communication Theoretical Modeling of Axonal Propagation in Hippocampal Pyramidal Neurons.

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Ramezani, Hamideh; Akan, Ozgur B

2017-06-01

Understanding the fundamentals of communication among neurons, known as neuro-spike communication, leads to reach bio-inspired nanoscale communication paradigms. In this paper, we focus on a part of neuro-spike communication, known as axonal transmission, and propose a realistic model for it. The shape of the spike during axonal transmission varies according to previously applied stimulations to the neuron, and these variations affect the amount of information communicated between neurons. Hence, to reach an accurate model for neuro-spike communication, the memory of axon and its effect on the axonal transmission should be considered, which are not studied in the existing literature. In this paper, we extract the important factors on the memory of axon and define memory states based on these factors. We also describe the transition among these states and the properties of axonal transmission in each of them. Finally, we demonstrate that the proposed model can follow changes in the axonal functionality properly by simulating the proposed model and reporting the root mean square error between simulation results and experimental data.

Detection of M-Sequences from Spike Sequence in Neuronal Networks

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Yoshi Nishitani

2012-01-01

Full Text Available In circuit theory, it is well known that a linear feedback shift register (LFSR circuit generates pseudorandom bit sequences (PRBS, including an M-sequence with the maximum period of length. In this study, we tried to detect M-sequences known as a pseudorandom sequence generated by the LFSR circuit from time series patterns of stimulated action potentials. Stimulated action potentials were recorded from dissociated cultures of hippocampal neurons grown on a multielectrode array. We could find several M-sequences from a 3-stage LFSR circuit (M3. These results show the possibility of assembling LFSR circuits or its equivalent ones in a neuronal network. However, since the M3 pattern was composed of only four spike intervals, the possibility of an accidental detection was not zero. Then, we detected M-sequences from random spike sequences which were not generated from an LFSR circuit and compare the result with the number of M-sequences from the originally observed raster data. As a result, a significant difference was confirmed: a greater number of “0–1” reversed the 3-stage M-sequences occurred than would have accidentally be detected. This result suggests that some LFSR equivalent circuits are assembled in neuronal networks.

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses.

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Gabriel Koch Ocker

2015-08-01

Full Text Available The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses.

Science.gov (United States)

Ocker, Gabriel Koch; Litwin-Kumar, Ashok; Doiron, Brent

2015-08-01

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

Synchronization in a non-uniform network of excitatory spiking neurons

Science.gov (United States)

Echeveste, Rodrigo; Gros, Claudius

Spontaneous synchronization of pulse coupled elements is ubiquitous in nature and seems to be of vital importance for life. Networks of pacemaker cells in the heart, extended populations of southeast asian fireflies, and neuronal oscillations in cortical networks, are examples of this. In the present work, a rich repertoire of dynamical states with different degrees of synchronization are found in a network of excitatory-only spiking neurons connected in a non-uniform fashion. In particular, uncorrelated and partially correlated states are found without the need for inhibitory neurons or external currents. The phase transitions between these states, as well the robustness, stability, and response of the network to external stimulus are studied.

A Markovian event-based framework for stochastic spiking neural networks.

Science.gov (United States)

Touboul, Jonathan D; Faugeras, Olivier D

2011-11-01

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks.

Simulating large-scale spiking neuronal networks with NEST

OpenAIRE

Schücker, Jannis; Eppler, Jochen Martin

2014-01-01

The Neural Simulation Tool NEST [1, www.nest-simulator.org] is the simulator for spiking neural networkmodels of the HBP that focuses on the dynamics, size and structure of neural systems rather than on theexact morphology of individual neurons. Its simulation kernel is written in C++ and it runs on computinghardware ranging from simple laptops to clusters and supercomputers with thousands of processor cores.The development of NEST is coordinated by the NEST Initiative [www.nest-initiative.or...

Delay selection by spike-timing-dependent plasticity in recurrent networks of spiking neurons receiving oscillatory inputs.

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Robert R Kerr

Full Text Available Learning rules, such as spike-timing-dependent plasticity (STDP, change the structure of networks of neurons based on the firing activity. A network level understanding of these mechanisms can help infer how the brain learns patterns and processes information. Previous studies have shown that STDP selectively potentiates feed-forward connections that have specific axonal delays, and that this underlies behavioral functions such as sound localization in the auditory brainstem of the barn owl. In this study, we investigate how STDP leads to the selective potentiation of recurrent connections with different axonal and dendritic delays during oscillatory activity. We develop analytical models of learning with additive STDP in recurrent networks driven by oscillatory inputs, and support the results using simulations with leaky integrate-and-fire neurons. Our results show selective potentiation of connections with specific axonal delays, which depended on the input frequency. In addition, we demonstrate how this can lead to a network becoming selective in the amplitude of its oscillatory response to this frequency. We extend this model of axonal delay selection within a single recurrent network in two ways. First, we show the selective potentiation of connections with a range of both axonal and dendritic delays. Second, we show axonal delay selection between multiple groups receiving out-of-phase, oscillatory inputs. We discuss the application of these models to the formation and activation of neuronal ensembles or cell assemblies in the cortex, and also to missing fundamental pitch perception in the auditory brainstem.

Training spiking neural networks to associate spatio-temporal input-output spike patterns

OpenAIRE

Mohemmed, A; Schliebs, S; Matsuda, S; Kasabov, N

2013-01-01

In a previous work (Mohemmed et al., Method for training a spiking neuron to associate input–output spike trains) [1] we have proposed a supervised learning algorithm based on temporal coding to train a spiking neuron to associate input spatiotemporal spike patterns to desired output spike patterns. The algorithm is based on the conversion of spike trains into analogue signals and the application of the Widrow–Hoff learning rule. In this paper we present a mathematical formulation of the prop...

Power-law inter-spike interval distributions infer a conditional maximization of entropy in cortical neurons.

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Yasuhiro Tsubo

Full Text Available The brain is considered to use a relatively small amount of energy for its efficient information processing. Under a severe restriction on the energy consumption, the maximization of mutual information (MMI, which is adequate for designing artificial processing machines, may not suit for the brain. The MMI attempts to send information as accurate as possible and this usually requires a sufficient energy supply for establishing clearly discretized communication bands. Here, we derive an alternative hypothesis for neural code from the neuronal activities recorded juxtacellularly in the sensorimotor cortex of behaving rats. Our hypothesis states that in vivo cortical neurons maximize the entropy of neuronal firing under two constraints, one limiting the energy consumption (as assumed previously and one restricting the uncertainty in output spike sequences at given firing rate. Thus, the conditional maximization of firing-rate entropy (CMFE solves a tradeoff between the energy cost and noise in neuronal response. In short, the CMFE sends a rich variety of information through broader communication bands (i.e., widely distributed firing rates at the cost of accuracy. We demonstrate that the CMFE is reflected in the long-tailed, typically power law, distributions of inter-spike intervals obtained for the majority of recorded neurons. In other words, the power-law tails are more consistent with the CMFE rather than the MMI. Thus, we propose the mathematical principle by which cortical neurons may represent information about synaptic input into their output spike trains.

Stochastic Variational Learning in Recurrent Spiking Networks

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Danilo eJimenez Rezende

2014-04-01

Full Text Available The ability to learn and perform statistical inference with biologically plausible recurrent network of spiking neurons is an important step towards understanding perception and reasoning. Here we derive and investigate a new learning rule for recurrent spiking networks with hidden neurons, combining principles from variational learning and reinforcement learning. Our network defines a generative model over spike train histories and the derived learning rule has the form of a local Spike Timing Dependent Plasticity rule modulated by global factors (neuromodulators conveying information about ``novelty on a statistically rigorous ground.Simulations show that our model is able to learn bothstationary and non-stationary patterns of spike trains.We also propose one experiment that could potentially be performed with animals in order to test the dynamics of the predicted novelty signal.

Stochastic variational learning in recurrent spiking networks.

Science.gov (United States)

Jimenez Rezende, Danilo; Gerstner, Wulfram

2014-01-01

The ability to learn and perform statistical inference with biologically plausible recurrent networks of spiking neurons is an important step toward understanding perception and reasoning. Here we derive and investigate a new learning rule for recurrent spiking networks with hidden neurons, combining principles from variational learning and reinforcement learning. Our network defines a generative model over spike train histories and the derived learning rule has the form of a local Spike Timing Dependent Plasticity rule modulated by global factors (neuromodulators) conveying information about "novelty" on a statistically rigorous ground. Simulations show that our model is able to learn both stationary and non-stationary patterns of spike trains. We also propose one experiment that could potentially be performed with animals in order to test the dynamics of the predicted novelty signal.

Variable Action Potential Backpropagation during Tonic Firing and Low-Threshold Spike Bursts in Thalamocortical But Not Thalamic Reticular Nucleus Neurons.

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Connelly, William M; Crunelli, Vincenzo; Errington, Adam C

2017-05-24

Backpropagating action potentials (bAPs) are indispensable in dendritic signaling. Conflicting Ca 2+ -imaging data and an absence of dendritic recording data means that the extent of backpropagation in thalamocortical (TC) and thalamic reticular nucleus (TRN) neurons remains unknown. Because TRN neurons signal electrically through dendrodendritic gap junctions and possibly via chemical dendritic GABAergic synapses, as well as classical axonal GABA release, this lack of knowledge is problematic. To address this issue, we made two-photon targeted patch-clamp recordings from rat TC and TRN neuron dendrites to measure bAPs directly. These recordings reveal that "tonic"' and low-threshold-spike (LTS) "burst" APs in both cell types are always recorded first at the soma before backpropagating into the dendrites while undergoing substantial distance-dependent dendritic amplitude attenuation. In TC neurons, bAP attenuation strength varies according to firing mode. During LTS bursts, somatic AP half-width increases progressively with increasing spike number, allowing late-burst spikes to propagate more efficiently into the dendritic tree compared with spikes occurring at burst onset. Tonic spikes have similar somatic half-widths to late burst spikes and undergo similar dendritic attenuation. In contrast, in TRN neurons, AP properties are unchanged between LTS bursts and tonic firing and, as a result, distance-dependent dendritic attenuation remains consistent across different firing modes. Therefore, unlike LTS-associated global electrical and calcium signals, the spatial influence of bAP signaling in TC and TRN neurons is more restricted, with potentially important behavioral-state-dependent consequences for synaptic integration and plasticity in thalamic neurons. SIGNIFICANCE STATEMENT In most neurons, action potentials (APs) initiate in the axosomatic region and propagate into the dendritic tree to provide a retrograde signal that conveys information about the level of

Real-time cerebellar neuroprosthetic system based on a spiking neural network model of motor learning.

Science.gov (United States)

Xu, Tao; Xiao, Na; Zhai, Xiaolong; Kwan Chan, Pak; Tin, Chung

2018-02-01

Damage to the brain, as a result of various medical conditions, impacts the everyday life of patients and there is still no complete cure to neurological disorders. Neuroprostheses that can functionally replace the damaged neural circuit have recently emerged as a possible solution to these problems. Here we describe the development of a real-time cerebellar neuroprosthetic system to substitute neural function in cerebellar circuitry for learning delay eyeblink conditioning (DEC). The system was empowered by a biologically realistic spiking neural network (SNN) model of the cerebellar neural circuit, which considers the neuronal population and anatomical connectivity of the network. The model simulated synaptic plasticity critical for learning DEC. This SNN model was carefully implemented on a field programmable gate array (FPGA) platform for real-time simulation. This hardware system was interfaced in in vivo experiments with anesthetized rats and it used neural spikes recorded online from the animal to learn and trigger conditioned eyeblink in the animal during training. This rat-FPGA hybrid system was able to process neuronal spikes in real-time with an embedded cerebellum model of ~10 000 neurons and reproduce learning of DEC with different inter-stimulus intervals. Our results validated that the system performance is physiologically relevant at both the neural (firing pattern) and behavioral (eyeblink pattern) levels. This integrated system provides the sufficient computation power for mimicking the cerebellar circuit in real-time. The system interacts with the biological system naturally at the spike level and can be generalized for including other neural components (neuron types and plasticity) and neural functions for potential neuroprosthetic applications.

The local field potential reflects surplus spike synchrony

DEFF Research Database (Denmark)

Denker, Michael; Roux, Sébastien; Lindén, Henrik

2011-01-01

While oscillations of the local field potential (LFP) are commonly attributed to the synchronization of neuronal firing rate on the same time scale, their relationship to coincident spiking in the millisecond range is unknown. Here, we present experimental evidence to reconcile the notions...... of synchrony at the level of spiking and at the mesoscopic scale. We demonstrate that only in time intervals of significant spike synchrony that cannot be explained on the basis of firing rates, coincident spikes are better phase locked to the LFP than predicted by the locking of the individual spikes....... This effect is enhanced in periods of large LFP amplitudes. A quantitative model explains the LFP dynamics by the orchestrated spiking activity in neuronal groups that contribute the observed surplus synchrony. From the correlation analysis, we infer that neurons participate in different constellations...

Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process

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Konno, Hidetoshi; Tamura, Yoshiyasu

2018-01-01

In neural spike counting experiments, it is known that there are two main features: (i) the counting number has a fractional power-law growth with time and (ii) the waiting time (i.e., the inter-spike-interval) distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs) is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii) can be modeled by the method of SSPPs. Namely, the first one (i) associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP).

Spike-timing computation properties of a feed-forward neural network model

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Drew Benjamin Sinha

2014-01-01

Full Text Available Brain function is characterized by dynamical interactions among networks of neurons. These interactions are mediated by network topology at many scales ranging from microcircuits to brain areas. Understanding how networks operate can be aided by understanding how the transformation of inputs depends upon network connectivity patterns, e.g. serial and parallel pathways. To tractably determine how single synapses or groups of synapses in such pathways shape transformations, we modeled feed-forward networks of 7-22 neurons in which synaptic strength changed according to a spike-timing dependent plasticity rule. We investigated how activity varied when dynamics were perturbed by an activity-dependent electrical stimulation protocol (spike-triggered stimulation; STS in networks of different topologies and background input correlations. STS can successfully reorganize functional brain networks in vivo, but with a variability in effectiveness that may derive partially from the underlying network topology. In a simulated network with a single disynaptic pathway driven by uncorrelated background activity, structured spike-timing relationships between polysynaptically connected neurons were not observed. When background activity was correlated or parallel disynaptic pathways were added, however, robust polysynaptic spike timing relationships were observed, and application of STS yielded predictable changes in synaptic strengths and spike-timing relationships. These observations suggest that precise input-related or topologically induced temporal relationships in network activity are necessary for polysynaptic signal propagation. Such constraints for polysynaptic computation suggest potential roles for higher-order topological structure in network organization, such as maintaining polysynaptic correlation in the face of relatively weak synapses.

Spike rate and spike timing contributions to coding taste quality information in rat periphery

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Vernon eLawhern

2011-05-01

Full Text Available There is emerging evidence that individual sensory neurons in the rodent brain rely on temporal features of the discharge pattern to code differences in taste quality information. In contrast, in-vestigations of individual sensory neurons in the periphery have focused on analysis of spike rate and mostly disregarded spike timing as a taste quality coding mechanism. The purpose of this work was to determine the contribution of spike timing to taste quality coding by rat geniculate ganglion neurons using computational methods that have been applied successfully in other sys-tems. We recorded the discharge patterns of narrowly-tuned and broadly-tuned neurons in the rat geniculate ganglion to representatives of the five basic taste qualities. We used mutual in-formation to determine significant responses and the van Rossum metric to characterize their temporal features. While our findings show that spike timing contributes a significant part of the message, spike rate contributes the largest portion of the message relayed by afferent neurons from rat fungiform taste buds to the brain. Thus, spike rate and spike timing together are more effective than spike rate alone in coding stimulus quality information to a single basic taste in the periphery for both narrowly-tuned specialist and broadly-tuned generalist neurons.

Consensus-Based Sorting of Neuronal Spike Waveforms.

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Fournier, Julien; Mueller, Christian M; Shein-Idelson, Mark; Hemberger, Mike; Laurent, Gilles

2016-01-01

Optimizing spike-sorting algorithms is difficult because sorted clusters can rarely be checked against independently obtained "ground truth" data. In most spike-sorting algorithms in use today, the optimality of a clustering solution is assessed relative to some assumption on the distribution of the spike shapes associated with a particular single unit (e.g., Gaussianity) and by visual inspection of the clustering solution followed by manual validation. When the spatiotemporal waveforms of spikes from different cells overlap, the decision as to whether two spikes should be assigned to the same source can be quite subjective, if it is not based on reliable quantitative measures. We propose a new approach, whereby spike clusters are identified from the most consensual partition across an ensemble of clustering solutions. Using the variability of the clustering solutions across successive iterations of the same clustering algorithm (template matching based on K-means clusters), we estimate the probability of spikes being clustered together and identify groups of spikes that are not statistically distinguishable from one another. Thus, we identify spikes that are most likely to be clustered together and therefore correspond to consistent spike clusters. This method has the potential advantage that it does not rely on any model of the spike shapes. It also provides estimates of the proportion of misclassified spikes for each of the identified clusters. We tested our algorithm on several datasets for which there exists a ground truth (simultaneous intracellular data), and show that it performs close to the optimum reached by a support vector machine trained on the ground truth. We also show that the estimated rate of misclassification matches the proportion of misclassified spikes measured from the ground truth data.

A network of spiking neurons that can represent interval timing: mean field analysis.

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Gavornik, Jeffrey P; Shouval, Harel Z

2011-04-01

Despite the vital importance of our ability to accurately process and encode temporal information, the underlying neural mechanisms are largely unknown. We have previously described a theoretical framework that explains how temporal representations, similar to those reported in the visual cortex, can form in locally recurrent cortical networks as a function of reward modulated synaptic plasticity. This framework allows networks of both linear and spiking neurons to learn the temporal interval between a stimulus and paired reward signal presented during training. Here we use a mean field approach to analyze the dynamics of non-linear stochastic spiking neurons in a network trained to encode specific time intervals. This analysis explains how recurrent excitatory feedback allows a network structure to encode temporal representations.

The Second Spiking Threshold: Dynamics of Laminar Network Spiking in the Visual Cortex

DEFF Research Database (Denmark)

Forsberg, Lars E.; Bonde, Lars H.; Harvey, Michael A.

2016-01-01

and moving visual stimuli from the spontaneous ongoing spiking state, in all layers and zones of areas 17 and 18 indicating that the second threshold is a property of the network. Spontaneous and evoked spiking, thus can easily be distinguished. In addition, the trajectories of spontaneous ongoing states......Most neurons have a threshold separating the silent non-spiking state and the state of producing temporal sequences of spikes. But neurons in vivo also have a second threshold, found recently in granular layer neurons of the primary visual cortex, separating spontaneous ongoing spiking from...... visually evoked spiking driven by sharp transients. Here we examine whether this second threshold exists outside the granular layer and examine details of transitions between spiking states in ferrets exposed to moving objects. We found the second threshold, separating spiking states evoked by stationary...

Simple cortical and thalamic neuron models for digital arithmetic circuit implementation

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Takuya eNanami

2016-05-01

Full Text Available Trade-off between reproducibility of neuronal activities and computational efficiency is one ofcrucial subjects in computational neuroscience and neuromorphic engineering. A wide variety ofneuronal models have been studied from different viewpoints. The digital spiking silicon neuron(DSSN model is a qualitative model that focuses on efficient implementation by digital arithmeticcircuits. We expanded the DSSN model and found appropriate parameter sets with which itreproduces the dynamical behaviors of the ionic-conductance models of four classes of corticaland thalamic neurons. We first developed a 4-variable model by reducing the number of variablesin the ionic-conductance models and elucidated its mathematical structures using bifurcationanalysis. Then, expanded DSSN models were constructed that reproduce these mathematicalstructures and capture the characteristic behavior of each neuron class. We confirmed thatstatistics of the neuronal spike sequences are similar in the DSSN and the ionic-conductancemodels. Computational cost of the DSSN model is larger than that of the recent sophisticatedIntegrate-and-Fire-based models, but smaller than the ionic-conductance models. This modelis intended to provide another meeting point for above trade-off that satisfies the demand forlarge-scale neuronal network simulation with closer-to-biology models.

Spike-threshold adaptation predicted by membrane potential dynamics in vivo.

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Bertrand Fontaine

2014-04-01

Full Text Available Neurons encode information in sequences of spikes, which are triggered when their membrane potential crosses a threshold. In vivo, the spiking threshold displays large variability suggesting that threshold dynamics have a profound influence on how the combined input of a neuron is encoded in the spiking. Threshold variability could be explained by adaptation to the membrane potential. However, it could also be the case that most threshold variability reflects noise and processes other than threshold adaptation. Here, we investigated threshold variation in auditory neurons responses recorded in vivo in barn owls. We found that spike threshold is quantitatively predicted by a model in which the threshold adapts, tracking the membrane potential at a short timescale. As a result, in these neurons, slow voltage fluctuations do not contribute to spiking because they are filtered by threshold adaptation. More importantly, these neurons can only respond to input spikes arriving together on a millisecond timescale. These results demonstrate that fast adaptation to the membrane potential captures spike threshold variability in vivo.

Surfing a spike wave down the ventral stream.

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VanRullen, Rufin; Thorpe, Simon J

2002-10-01

Numerous theories of neural processing, often motivated by experimental observations, have explored the computational properties of neural codes based on the absolute or relative timing of spikes in spike trains. Spiking neuron models and theories however, as well as their experimental counterparts, have generally been limited to the simulation or observation of isolated neurons, isolated spike trains, or reduced neural populations. Such theories would therefore seem inappropriate to capture the properties of a neural code relying on temporal spike patterns distributed across large neuronal populations. Here we report a range of computer simulations and theoretical considerations that were designed to explore the possibilities of one such code and its relevance for visual processing. In a unified framework where the relation between stimulus saliency and spike relative timing plays the central role, we describe how the ventral stream of the visual system could process natural input scenes and extract meaningful information, both rapidly and reliably. The first wave of spikes generated in the retina in response to a visual stimulation carries information explicitly in its spatio-temporal structure: the most salient information is represented by the first spikes over the population. This spike wave, propagating through a hierarchy of visual areas, is regenerated at each processing stage, where its temporal structure can be modified by (i). the selectivity of the cortical neurons, (ii). lateral interactions and (iii). top-down attentional influences from higher order cortical areas. The resulting model could account for the remarkable efficiency and rapidity of processing observed in the primate visual system.

ViSAPy: a Python tool for biophysics-based generation of virtual spiking activity for evaluation of spike-sorting algorithms.

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Hagen, Espen; Ness, Torbjørn V; Khosrowshahi, Amir; Sørensen, Christina; Fyhn, Marianne; Hafting, Torkel; Franke, Felix; Einevoll, Gaute T

2015-04-30

New, silicon-based multielectrodes comprising hundreds or more electrode contacts offer the possibility to record spike trains from thousands of neurons simultaneously. This potential cannot be realized unless accurate, reliable automated methods for spike sorting are developed, in turn requiring benchmarking data sets with known ground-truth spike times. We here present a general simulation tool for computing benchmarking data for evaluation of spike-sorting algorithms entitled ViSAPy (Virtual Spiking Activity in Python). The tool is based on a well-established biophysical forward-modeling scheme and is implemented as a Python package built on top of the neuronal simulator NEURON and the Python tool LFPy. ViSAPy allows for arbitrary combinations of multicompartmental neuron models and geometries of recording multielectrodes. Three example benchmarking data sets are generated, i.e., tetrode and polytrode data mimicking in vivo cortical recordings and microelectrode array (MEA) recordings of in vitro activity in salamander retinas. The synthesized example benchmarking data mimics salient features of typical experimental recordings, for example, spike waveforms depending on interspike interval. ViSAPy goes beyond existing methods as it includes biologically realistic model noise, synaptic activation by recurrent spiking networks, finite-sized electrode contacts, and allows for inhomogeneous electrical conductivities. ViSAPy is optimized to allow for generation of long time series of benchmarking data, spanning minutes of biological time, by parallel execution on multi-core computers. ViSAPy is an open-ended tool as it can be generalized to produce benchmarking data or arbitrary recording-electrode geometries and with various levels of complexity. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.

Asynchronous Rate Chaos in Spiking Neuronal Circuits.

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Omri Harish

2015-07-01

Full Text Available The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results.

Asynchronous Rate Chaos in Spiking Neuronal Circuits

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Harish, Omri; Hansel, David

2015-01-01

The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI) spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results. PMID:26230679

Human Brain Networks: Spiking Neuron Models, Multistability, Synchronization, Thermodynamics, Maximum Entropy Production, and Anesthetic Cascade Mechanisms

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Wassim M. Haddad

2014-07-01

Full Text Available Advances in neuroscience have been closely linked to mathematical modeling beginning with the integrate-and-fire model of Lapicque and proceeding through the modeling of the action potential by Hodgkin and Huxley to the current era. The fundamental building block of the central nervous system, the neuron, may be thought of as a dynamic element that is “excitable”, and can generate a pulse or spike whenever the electrochemical potential across the cell membrane of the neuron exceeds a threshold. A key application of nonlinear dynamical systems theory to the neurosciences is to study phenomena of the central nervous system that exhibit nearly discontinuous transitions between macroscopic states. A very challenging and clinically important problem exhibiting this phenomenon is the induction of general anesthesia. In any specific patient, the transition from consciousness to unconsciousness as the concentration of anesthetic drugs increases is very sharp, resembling a thermodynamic phase transition. This paper focuses on multistability theory for continuous and discontinuous dynamical systems having a set of multiple isolated equilibria and/or a continuum of equilibria. Multistability is the property whereby the solutions of a dynamical system can alternate between two or more mutually exclusive Lyapunov stable and convergent equilibrium states under asymptotically slowly changing inputs or system parameters. In this paper, we extend the theory of multistability to continuous, discontinuous, and stochastic nonlinear dynamical systems. In particular, Lyapunov-based tests for multistability and synchronization of dynamical systems with continuously differentiable and absolutely continuous flows are established. The results are then applied to excitatory and inhibitory biological neuronal networks to explain the underlying mechanism of action for anesthesia and consciousness from a multistable dynamical system perspective, thereby providing a

Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process

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Hidetoshi Konno

2018-01-01

Full Text Available In neural spike counting experiments, it is known that there are two main features: (i the counting number has a fractional power-law growth with time and (ii the waiting time (i.e., the inter-spike-interval distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii can be modeled by the method of SSPPs. Namely, the first one (i associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP.

Introduction to spiking neural networks: Information processing, learning and applications.

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Ponulak, Filip; Kasinski, Andrzej

2011-01-01

The concept that neural information is encoded in the firing rate of neurons has been the dominant paradigm in neurobiology for many years. This paradigm has also been adopted by the theory of artificial neural networks. Recent physiological experiments demonstrate, however, that in many parts of the nervous system, neural code is founded on the timing of individual action potentials. This finding has given rise to the emergence of a new class of neural models, called spiking neural networks. In this paper we summarize basic properties of spiking neurons and spiking networks. Our focus is, specifically, on models of spike-based information coding, synaptic plasticity and learning. We also survey real-life applications of spiking models. The paper is meant to be an introduction to spiking neural networks for scientists from various disciplines interested in spike-based neural processing.

Real-time cerebellar neuroprosthetic system based on a spiking neural network model of motor learning

Science.gov (United States)

Xu, Tao; Xiao, Na; Zhai, Xiaolong; Chan, Pak Kwan; Tin, Chung

2018-02-01

Objective. Damage to the brain, as a result of various medical conditions, impacts the everyday life of patients and there is still no complete cure to neurological disorders. Neuroprostheses that can functionally replace the damaged neural circuit have recently emerged as a possible solution to these problems. Here we describe the development of a real-time cerebellar neuroprosthetic system to substitute neural function in cerebellar circuitry for learning delay eyeblink conditioning (DEC). Approach. The system was empowered by a biologically realistic spiking neural network (SNN) model of the cerebellar neural circuit, which considers the neuronal population and anatomical connectivity of the network. The model simulated synaptic plasticity critical for learning DEC. This SNN model was carefully implemented on a field programmable gate array (FPGA) platform for real-time simulation. This hardware system was interfaced in in vivo experiments with anesthetized rats and it used neural spikes recorded online from the animal to learn and trigger conditioned eyeblink in the animal during training. Main results. This rat-FPGA hybrid system was able to process neuronal spikes in real-time with an embedded cerebellum model of ~10 000 neurons and reproduce learning of DEC with different inter-stimulus intervals. Our results validated that the system performance is physiologically relevant at both the neural (firing pattern) and behavioral (eyeblink pattern) levels. Significance. This integrated system provides the sufficient computation power for mimicking the cerebellar circuit in real-time. The system interacts with the biological system naturally at the spike level and can be generalized for including other neural components (neuron types and plasticity) and neural functions for potential neuroprosthetic applications.

Symbol manipulation and rule learning in spiking neuronal networks.

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Fernando, Chrisantha

2011-04-21

It has been claimed that the productivity, systematicity and compositionality of human language and thought necessitate the existence of a physical symbol system (PSS) in the brain. Recent discoveries about temporal coding suggest a novel type of neuronal implementation of a physical symbol system. Furthermore, learning classifier systems provide a plausible algorithmic basis by which symbol re-write rules could be trained to undertake behaviors exhibiting systematicity and compositionality, using a kind of natural selection of re-write rules in the brain, We show how the core operation of a learning classifier system, namely, the replication with variation of symbol re-write rules, can be implemented using spike-time dependent plasticity based supervised learning. As a whole, the aim of this paper is to integrate an algorithmic and an implementation level description of a neuronal symbol system capable of sustaining systematic and compositional behaviors. Previously proposed neuronal implementations of symbolic representations are compared with this new proposal. Copyright © 2011 Elsevier Ltd. All rights reserved.

Analytical Calculation of Mutual Information between Weakly Coupled Poisson-Spiking Neurons in Models of Dynamically Gated Communication.

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Cannon, Jonathan

2017-01-01

Mutual information is a commonly used measure of communication between neurons, but little theory exists describing the relationship between mutual information and the parameters of the underlying neuronal interaction. Such a theory could help us understand how specific physiological changes affect the capacity of neurons to synaptically communicate, and, in particular, they could help us characterize the mechanisms by which neuronal dynamics gate the flow of information in the brain. Here we study a pair of linear-nonlinear-Poisson neurons coupled by a weak synapse. We derive an analytical expression describing the mutual information between their spike trains in terms of synapse strength, neuronal activation function, the time course of postsynaptic currents, and the time course of the background input received by the two neurons. This expression allows mutual information calculations that would otherwise be computationally intractable. We use this expression to analytically explore the interaction of excitation, information transmission, and the convexity of the activation function. Then, using this expression to quantify mutual information in simulations, we illustrate the information-gating effects of neural oscillations and oscillatory coherence, which may either increase or decrease the mutual information across the synapse depending on parameters. Finally, we show analytically that our results can quantitatively describe the selection of one information pathway over another when multiple sending neurons project weakly to a single receiving neuron.

Computational modeling of seizure dynamics using coupled neuronal networks: factors shaping epileptiform activity.

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Sebastien Naze

2015-05-01

Full Text Available Epileptic seizure dynamics span multiple scales in space and time. Understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. Mathematical models have been developed to reproduce seizure dynamics across scales ranging from the single neuron to the neural population. In this study, we develop a network model of spiking neurons and systematically investigate the conditions, under which the network displays the emergent dynamic behaviors known from the Epileptor, which is a well-investigated abstract model of epileptic neural activity. This approach allows us to study the biophysical parameters and variables leading to epileptiform discharges at cellular and network levels. Our network model is composed of two neuronal populations, characterized by fast excitatory bursting neurons and regular spiking inhibitory neurons, embedded in a common extracellular environment represented by a slow variable. By systematically analyzing the parameter landscape offered by the simulation framework, we reproduce typical sequences of neural activity observed during status epilepticus. We find that exogenous fluctuations from extracellular environment and electro-tonic couplings play a major role in the progression of the seizure, which supports previous studies and further validates our model. We also investigate the influence of chemical synaptic coupling in the generation of spontaneous seizure-like events. Our results argue towards a temporal shift of typical spike waves with fast discharges as synaptic strengths are varied. We demonstrate that spike waves, including interictal spikes, are generated primarily by inhibitory neurons, whereas fast discharges during the wave part are due to excitatory neurons. Simulated traces are compared with in vivo experimental data from rodents at different stages of the disorder. We draw the conclusion

Impact of sub and supra-threshold adaptation currents in networks of spiking neurons.

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Colliaux, David; Yger, Pierre; Kaneko, Kunihiko

2015-12-01

Neuronal adaptation is the intrinsic capacity of the brain to change, by various mechanisms, its dynamical responses as a function of the context. Such a phenomena, widely observed in vivo and in vitro, is known to be crucial in homeostatic regulation of the activity and gain control. The effects of adaptation have already been studied at the single-cell level, resulting from either voltage or calcium gated channels both activated by the spiking activity and modulating the dynamical responses of the neurons. In this study, by disentangling those effects into a linear (sub-threshold) and a non-linear (supra-threshold) part, we focus on the the functional role of those two distinct components of adaptation onto the neuronal activity at various scales, starting from single-cell responses up to recurrent networks dynamics, and under stationary or non-stationary stimulations. The effects of slow currents on collective dynamics, like modulation of population oscillation and reliability of spike patterns, is quantified for various types of adaptation in sparse recurrent networks.

Extracting functionally feedforward networks from a population of spiking neurons.

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Vincent, Kathleen; Tauskela, Joseph S; Thivierge, Jean-Philippe

2012-01-01

Neuronal avalanches are a ubiquitous form of activity characterized by spontaneous bursts whose size distribution follows a power-law. Recent theoretical models have replicated power-law avalanches by assuming the presence of functionally feedforward connections (FFCs) in the underlying dynamics of the system. Accordingly, avalanches are generated by a feedforward chain of activation that persists despite being embedded in a larger, massively recurrent circuit. However, it is unclear to what extent networks of living neurons that exhibit power-law avalanches rely on FFCs. Here, we employed a computational approach to reconstruct the functional connectivity of cultured cortical neurons plated on multielectrode arrays (MEAs) and investigated whether pharmacologically induced alterations in avalanche dynamics are accompanied by changes in FFCs. This approach begins by extracting a functional network of directed links between pairs of neurons, and then evaluates the strength of FFCs using Schur decomposition. In a first step, we examined the ability of this approach to extract FFCs from simulated spiking neurons. The strength of FFCs obtained in strictly feedforward networks diminished monotonically as links were gradually rewired at random. Next, we estimated the FFCs of spontaneously active cortical neuron cultures in the presence of either a control medium, a GABA(A) receptor antagonist (PTX), or an AMPA receptor antagonist combined with an NMDA receptor antagonist (APV/DNQX). The distribution of avalanche sizes in these cultures was modulated by this pharmacology, with a shallower power-law under PTX (due to the prominence of larger avalanches) and a steeper power-law under APV/DNQX (due to avalanches recruiting fewer neurons) relative to control cultures. The strength of FFCs increased in networks after application of PTX, consistent with an amplification of feedforward activity during avalanches. Conversely, FFCs decreased after application of APV

The design of a new spiking neuron using dual work function silicon nanowire transistors

International Nuclear Information System (INIS)

Bindal, Ahmet; Hamedi-Hagh, Sotoudeh

2007-01-01

A new spike neuron cell is designed using vertically grown, undoped silicon nanowire transistors. This study presents an entire design cycle from designing and optimizing vertical nanowire transistors for minimal power dissipation to realizing a neuron cell and measuring its dynamic power consumption, performance and layout area. The design cycle starts with determining individual metal gate work functions for NMOS and PMOS transistors as a function of wire radius to produce a 300 mV threshold voltage. The wire radius and effective channel length are subsequently varied to find a common body geometry for both transistors that yields smaller than 1 pA OFF current while producing maximum drive currents. A spike neuron cell is subsequently built using these transistors to measure its transient performance, power dissipation and layout area. Post-layout simulation results indicate that the neuron consumes 0.397 μW to generate a +1 V and 1.12 μW to generate a -1 V output pulse for a fan-out of five synapses at 500 MHz; the power dissipation increases by approximately 3 nW for each additional synapse at the output for generating either pulse. The neuron circuit occupies approximately 0.27 μm 2

Motif statistics and spike correlations in neuronal networks

International Nuclear Information System (INIS)

Hu, Yu; Shea-Brown, Eric; Trousdale, James; Josić, Krešimir

2013-01-01

Motifs are patterns of subgraphs of complex networks. We studied the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells in a recurrent network of integrate and fire neurons. For a range of network architectures, we find that the pairwise correlation coefficients, averaged across the network, can be closely approximated using only three statistics of network connectivity. These are the overall network connection probability and the frequencies of two second order motifs: diverging motifs, in which one cell provides input to two others, and chain motifs, in which two cells are connected via a third intermediary cell. Specifically, the prevalence of diverging and chain motifs tends to increase correlation. Our method is based on linear response theory, which enables us to express spiking statistics using linear algebra, and a resumming technique, which extrapolates from second order motifs to predict the overall effect of coupling on network correlation. Our motif-based results seek to isolate the effect of network architecture perturbatively from a known network state. (paper)

Timed Synaptic Inhibition Shapes NMDA Spikes, Influencing Local Dendritic Processing and Global I/O Properties of Cortical Neurons

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Michael Doron

2017-11-01

Full Text Available The NMDA spike is a long-lasting nonlinear phenomenon initiated locally in the dendritic branches of a variety of cortical neurons. It plays a key role in synaptic plasticity and in single-neuron computations. Combining dynamic system theory and computational approaches, we now explore how the timing of synaptic inhibition affects the NMDA spike and its associated membrane current. When impinging on its early phase, individual inhibitory synapses strongly, but transiently, dampen the NMDA spike; later inhibition prematurely terminates it. A single inhibitory synapse reduces the NMDA-mediated Ca2+ current, a key player in plasticity, by up to 45%. NMDA spikes in distal dendritic branches/spines are longer-lasting and more resilient to inhibition, enhancing synaptic plasticity at these branches. We conclude that NMDA spikes are highly sensitive to dendritic inhibition; sparse weak inhibition can finely tune synaptic plasticity both locally at the dendritic branch level and globally at the level of the neuron’s output.

Spike-timing-based computation in sound localization.

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Dan F M Goodman

2010-11-01

Full Text Available Spike timing is precise in the auditory system and it has been argued that it conveys information about auditory stimuli, in particular about the location of a sound source. However, beyond simple time differences, the way in which neurons might extract this information is unclear and the potential computational advantages are unknown. The computational difficulty of this task for an animal is to locate the source of an unexpected sound from two monaural signals that are highly dependent on the unknown source signal. In neuron models consisting of spectro-temporal filtering and spiking nonlinearity, we found that the binaural structure induced by spatialized sounds is mapped to synchrony patterns that depend on source location rather than on source signal. Location-specific synchrony patterns would then result in the activation of location-specific assemblies of postsynaptic neurons. We designed a spiking neuron model which exploited this principle to locate a variety of sound sources in a virtual acoustic environment using measured human head-related transfer functions. The model was able to accurately estimate the location of previously unknown sounds in both azimuth and elevation (including front/back discrimination in a known acoustic environment. We found that multiple representations of different acoustic environments could coexist as sets of overlapping neural assemblies which could be associated with spatial locations by Hebbian learning. The model demonstrates the computational relevance of relative spike timing to extract spatial information about sources independently of the source signal.

STD-dependent and independent encoding of input irregularity as spike rate in a computational model of a cerebellar nucleus neuron

NARCIS (Netherlands)

J. Luthman (Johannes); F.E. Hoebeek (Freek); R. Maex (Reinoud); N. Davey (Neil); R. Adams (Rod); C.I. de Zeeuw (Chris); V. Steuber (Volker)

2011-01-01

textabstractNeurons in the cerebellar nuclei (CN) receive inhibitory inputs from Purkinje cells in the cerebellar cortex and provide the major output from the cerebellum, but their computational function is not well understood. It has recently been shown that the spike activity of Purkinje cells is

Comparing Realistic Subthalamic Nucleus Neuron Models

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Njap, Felix; Claussen, Jens C.; Moser, Andreas; Hofmann, Ulrich G.

2011-06-01

The mechanism of action of clinically effective electrical high frequency stimulation is still under debate. However, recent evidence points at the specific activation of GABA-ergic ion channels. Using a computational approach, we analyze temporal properties of the spike trains emitted by biologically realistic neurons of the subthalamic nucleus (STN) as a function of GABA-ergic synaptic input conductances. Our contribution is based on a model proposed by Rubin and Terman and exhibits a wide variety of different firing patterns, silent, low spiking, moderate spiking and intense spiking activity. We observed that most of the cells in our network turn to silent mode when we increase the GABAA input conductance above the threshold of 3.75 mS/cm2. On the other hand, insignificant changes in firing activity are observed when the input conductance is low or close to zero. We thus reproduce Rubin's model with vanishing synaptic conductances. To quantitatively compare spike trains from the original model with the modified model at different conductance levels, we apply four different (dis)similarity measures between them. We observe that Mahalanobis distance, Victor-Purpura metric, and Interspike Interval distribution are sensitive to different firing regimes, whereas Mutual Information seems undiscriminative for these functional changes.

Temporal Information Processing and Stability Analysis of the MHSN Neuron Model in DDF

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Saket Kumar Choudhary

2016-12-01

Full Text Available Implementation of a neuron like information processing structure at hardware level is a burning research problem. In this article, we analyze the modified hybrid spiking neuron model (the MHSN model in distributed delay framework (DDF for hardware level implementation point of view. We investigate its temporal information processing capability in term of inter-spike-interval (ISI distribution. We also perform the stability analysis of the MHSN model, in which, we compute nullclines, steady state solution, eigenvalues corresponding the MHSN model. During phase plane analysis, we notice that the MHSN model generates limit cycle oscillations which is an important phenomenon in many biological processes. Qualitative behavior of these limit cycle does not changes due to the variation in applied input stimulus, however, delay effect the spiking activity and duration of cycle get altered.

Interplay between Graph Topology and Correlations of Third Order in Spiking Neuronal Networks.

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Stojan Jovanović

2016-06-01

Full Text Available The study of processes evolving on networks has recently become a very popular research field, not only because of the rich mathematical theory that underpins it, but also because of its many possible applications, a number of them in the field of biology. Indeed, molecular signaling pathways, gene regulation, predator-prey interactions and the communication between neurons in the brain can be seen as examples of networks with complex dynamics. The properties of such dynamics depend largely on the topology of the underlying network graph. In this work, we want to answer the following question: Knowing network connectivity, what can be said about the level of third-order correlations that will characterize the network dynamics? We consider a linear point process as a model for pulse-coded, or spiking activity in a neuronal network. Using recent results from theory of such processes, we study third-order correlations between spike trains in such a system and explain which features of the network graph (i.e. which topological motifs are responsible for their emergence. Comparing two different models of network topology-random networks of Erdős-Rényi type and networks with highly interconnected hubs-we find that, in random networks, the average measure of third-order correlations does not depend on the local connectivity properties, but rather on global parameters, such as the connection probability. This, however, ceases to be the case in networks with a geometric out-degree distribution, where topological specificities have a strong impact on average correlations.

Interplay between Graph Topology and Correlations of Third Order in Spiking Neuronal Networks.

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Jovanović, Stojan; Rotter, Stefan

2016-06-01

The study of processes evolving on networks has recently become a very popular research field, not only because of the rich mathematical theory that underpins it, but also because of its many possible applications, a number of them in the field of biology. Indeed, molecular signaling pathways, gene regulation, predator-prey interactions and the communication between neurons in the brain can be seen as examples of networks with complex dynamics. The properties of such dynamics depend largely on the topology of the underlying network graph. In this work, we want to answer the following question: Knowing network connectivity, what can be said about the level of third-order correlations that will characterize the network dynamics? We consider a linear point process as a model for pulse-coded, or spiking activity in a neuronal network. Using recent results from theory of such processes, we study third-order correlations between spike trains in such a system and explain which features of the network graph (i.e. which topological motifs) are responsible for their emergence. Comparing two different models of network topology-random networks of Erdős-Rényi type and networks with highly interconnected hubs-we find that, in random networks, the average measure of third-order correlations does not depend on the local connectivity properties, but rather on global parameters, such as the connection probability. This, however, ceases to be the case in networks with a geometric out-degree distribution, where topological specificities have a strong impact on average correlations.

Multineuronal Spike Sequences Repeat with Millisecond Precision

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Koki eMatsumoto

2013-06-01

Full Text Available Cortical microcircuits are nonrandomly wired by neurons. As a natural consequence, spikes emitted by microcircuits are also nonrandomly patterned in time and space. One of the prominent spike organizations is a repetition of fixed patterns of spike series across multiple neurons. However, several questions remain unsolved, including how precisely spike sequences repeat, how the sequences are spatially organized, how many neurons participate in sequences, and how different sequences are functionally linked. To address these questions, we monitored spontaneous spikes of hippocampal CA3 neurons ex vivo using a high-speed functional multineuron calcium imaging technique that allowed us to monitor spikes with millisecond resolution and to record the location of spiking and nonspiking neurons. Multineuronal spike sequences were overrepresented in spontaneous activity compared to the statistical chance level. Approximately 75% of neurons participated in at least one sequence during our observation period. The participants were sparsely dispersed and did not show specific spatial organization. The number of sequences relative to the chance level decreased when larger time frames were used to detect sequences. Thus, sequences were precise at the millisecond level. Sequences often shared common spikes with other sequences; parts of sequences were subsequently relayed by following sequences, generating complex chains of multiple sequences.

Goal-Directed Decision Making with Spiking Neurons.

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Friedrich, Johannes; Lengyel, Máté

2016-02-03

Behavioral and neuroscientific data on reward-based decision making point to a fundamental distinction between habitual and goal-directed action selection. The formation of habits, which requires simple updating of cached values, has been studied in great detail, and the reward prediction error theory of dopamine function has enjoyed prominent success in accounting for its neural bases. In contrast, the neural circuit mechanisms of goal-directed decision making, requiring extended iterative computations to estimate values online, are still unknown. Here we present a spiking neural network that provably solves the difficult online value estimation problem underlying goal-directed decision making in a near-optimal way and reproduces behavioral as well as neurophysiological experimental data on tasks ranging from simple binary choice to sequential decision making. Our model uses local plasticity rules to learn the synaptic weights of a simple neural network to achieve optimal performance and solves one-step decision-making tasks, commonly considered in neuroeconomics, as well as more challenging sequential decision-making tasks within 1 s. These decision times, and their parametric dependence on task parameters, as well as the final choice probabilities match behavioral data, whereas the evolution of neural activities in the network closely mimics neural responses recorded in frontal cortices during the execution of such tasks. Our theory provides a principled framework to understand the neural underpinning of goal-directed decision making and makes novel predictions for sequential decision-making tasks with multiple rewards. Goal-directed actions requiring prospective planning pervade decision making, but their circuit-level mechanisms remain elusive. We show how a model circuit of biologically realistic spiking neurons can solve this computationally challenging problem in a novel way. The synaptic weights of our network can be learned using local plasticity rules

Segmental Bayesian estimation of gap-junctional and inhibitory conductance of inferior olive neurons from spike trains with complicated dynamics

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Huu eHoang

2015-05-01

Full Text Available The inverse problem for estimating model parameters from brain spike data is an ill-posed problem because of a huge mismatch in the system complexity between the model and the brain as well as its non-stationary dynamics, and needs a stochastic approach that finds the most likely solution among many possible solutions. In the present study, we developed a segmental Bayesian method to estimate the two parameters of interest, the gap-junctional (gc and inhibitory conductance (gi from inferior olive spike data. Feature vectors were estimated for the spike data in a segment-wise fashion to compensate for the non-stationary firing dynamics. Hierarchical Bayesian estimation was conducted to estimate the gc and gi for every spike segment using a forward model constructed in the principal component analysis (PCA space of the feature vectors, and to merge the segmental estimates into single estimates for every neuron. The segmental Bayesian estimation gave smaller fitting errors than the conventional Bayesian inference, which finds the estimates once across the entire spike data, or the minimum error method, which directly finds the closest match in the PCA space. The segmental Bayesian inference has the potential to overcome the problem of non-stationary dynamics and resolve the ill-posedness of the inverse problem because of the mismatch between the model and the brain under the constraints based, and it is a useful tool to evaluate parameters of interest for neuroscience from experimental spike train data.

Phasic spike patterning in rat supraoptic neurones in vivo and in vitro

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Sabatier, Nancy; Brown, Colin H; Ludwig, Mike; Leng, Gareth

2004-01-01

In vivo, most vasopressin cells of the hypothalamic supraoptic nucleus fire action potentials in a ‘phasic’ pattern when the systemic osmotic pressure is elevated, while most oxytocin cells fire continuously. The phasic firing pattern is believed to arise as a consequence of intrinsic activity-dependent changes in membrane potential, and these have been extensively studied in vitro. Here we analysed the discharge patterning of supraoptic nucleus neurones in vivo, to infer the characteristics of the post-spike sequence of hyperpolarization and depolarization from the observed spike patterning. We then compared patterning in phasic cells in vivo and in vitro, and we found systematic differences in the interspike interval distributions, and in other statistical parameters that characterized activity patterns within bursts. Analysis of hazard functions (probability of spike initiation as a function of time since the preceding spike) revealed that phasic firing in vitro appears consistent with a regenerative process arising from a relatively slow, late depolarizing afterpotential that approaches or exceeds spike threshold. By contrast, in vivo activity appears to be dominated by stochastic rather than deterministic mechanisms, and appears consistent with a relatively early and fast depolarizing afterpotential that modulates the probability that random synaptic input exceeds spike threshold. Despite superficial similarities in the phasic firing patterns observed in vivo and in vitro, there are thus fundamental differences in the underlying mechanisms. PMID:15146047

Perceptron learning rule derived from spike-frequency adaptation and spike-time-dependent plasticity.

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D'Souza, Prashanth; Liu, Shih-Chii; Hahnloser, Richard H R

2010-03-09

It is widely believed that sensory and motor processing in the brain is based on simple computational primitives rooted in cellular and synaptic physiology. However, many gaps remain in our understanding of the connections between neural computations and biophysical properties of neurons. Here, we show that synaptic spike-time-dependent plasticity (STDP) combined with spike-frequency adaptation (SFA) in a single neuron together approximate the well-known perceptron learning rule. Our calculations and integrate-and-fire simulations reveal that delayed inputs to a neuron endowed with STDP and SFA precisely instruct neural responses to earlier arriving inputs. We demonstrate this mechanism on a developmental example of auditory map formation guided by visual inputs, as observed in the external nucleus of the inferior colliculus (ICX) of barn owls. The interplay of SFA and STDP in model ICX neurons precisely transfers the tuning curve from the visual modality onto the auditory modality, demonstrating a useful computation for multimodal and sensory-guided processing.

Effect of the sub-threshold periodic current forcing on the regularity and the synchronization of neuronal spiking activity

International Nuclear Information System (INIS)

Ozer, Mahmut; Uzuntarla, Muhammet; Agaoglu, Sukriye Nihal

2006-01-01

We first investigate the amplitude effect of the subthreshold periodic forcing on the regularity of the spiking events by using the coefficient of variation of interspike intervals. We show that the resonance effect in the coefficient of variation, which is dependent on the driving frequency for larger membrane patch sizes, disappears when the amplitude of the subthreshold forcing is decreased. Then, we demonstrate that the timings of the spiking events of a noisy and periodically driven neuron concentrate on a specific phase of the stimulus. We also show that increasing the intensity of the noise causes the phase probability density of the spiking events to get smaller values, and eliminates differences in the phase locking behavior of the neuron for different patch sizes

A reconfigurable on-line learning spiking neuromorphic processor comprising 256 neurons and 128K synapses.

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Qiao, Ning; Mostafa, Hesham; Corradi, Federico; Osswald, Marc; Stefanini, Fabio; Sumislawska, Dora; Indiveri, Giacomo

2015-01-01

Implementing compact, low-power artificial neural processing systems with real-time on-line learning abilities is still an open challenge. In this paper we present a full-custom mixed-signal VLSI device with neuromorphic learning circuits that emulate the biophysics of real spiking neurons and dynamic synapses for exploring the properties of computational neuroscience models and for building brain-inspired computing systems. The proposed architecture allows the on-chip configuration of a wide range of network connectivities, including recurrent and deep networks, with short-term and long-term plasticity. The device comprises 128 K analog synapse and 256 neuron circuits with biologically plausible dynamics and bi-stable spike-based plasticity mechanisms that endow it with on-line learning abilities. In addition to the analog circuits, the device comprises also asynchronous digital logic circuits for setting different synapse and neuron properties as well as different network configurations. This prototype device, fabricated using a 180 nm 1P6M CMOS process, occupies an area of 51.4 mm(2), and consumes approximately 4 mW for typical experiments, for example involving attractor networks. Here we describe the details of the overall architecture and of the individual circuits and present experimental results that showcase its potential. By supporting a wide range of cortical-like computational modules comprising plasticity mechanisms, this device will enable the realization of intelligent autonomous systems with on-line learning capabilities.

Biophysical Neural Spiking, Bursting, and Excitability Dynamics in Reconfigurable Analog VLSI.

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Yu, T; Sejnowski, T J; Cauwenberghs, G

2011-10-01

We study a range of neural dynamics under variations in biophysical parameters underlying extended Morris-Lecar and Hodgkin-Huxley models in three gating variables. The extended models are implemented in NeuroDyn, a four neuron, twelve synapse continuous-time analog VLSI programmable neural emulation platform with generalized channel kinetics and biophysical membrane dynamics. The dynamics exhibit a wide range of time scales extending beyond 100 ms neglected in typical silicon models of tonic spiking neurons. Circuit simulations and measurements show transition from tonic spiking to tonic bursting dynamics through variation of a single conductance parameter governing calcium recovery. We similarly demonstrate transition from graded to all-or-none neural excitability in the onset of spiking dynamics through the variation of channel kinetic parameters governing the speed of potassium activation. Other combinations of variations in conductance and channel kinetic parameters give rise to phasic spiking and spike frequency adaptation dynamics. The NeuroDyn chip consumes 1.29 mW and occupies 3 mm × 3 mm in 0.5 μm CMOS, supporting emerging developments in neuromorphic silicon-neuron interfaces.

Operant conditioning of synaptic and spiking activity patterns in single hippocampal neurons.

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Ishikawa, Daisuke; Matsumoto, Nobuyoshi; Sakaguchi, Tetsuya; Matsuki, Norio; Ikegaya, Yuji

2014-04-02

Learning is a process of plastic adaptation through which a neural circuit generates a more preferable outcome; however, at a microscopic level, little is known about how synaptic activity is patterned into a desired configuration. Here, we report that animals can generate a specific form of synaptic activity in a given neuron in the hippocampus. In awake, head-restricted mice, we applied electrical stimulation to the lateral hypothalamus, a reward-associated brain region, when whole-cell patch-clamped CA1 neurons exhibited spontaneous synaptic activity that met preset criteria. Within 15 min, the mice learned to generate frequently the excitatory synaptic input pattern that satisfied the criteria. This reinforcement learning of synaptic activity was not observed for inhibitory input patterns. When a burst unit activity pattern was conditioned in paired and nonpaired paradigms, the frequency of burst-spiking events increased and decreased, respectively. The burst reinforcement occurred in the conditioned neuron but not in other adjacent neurons; however, ripple field oscillations were concomitantly reinforced. Neural conditioning depended on activation of NMDA receptors and dopamine D1 receptors. Acutely stressed mice and depression model mice that were subjected to forced swimming failed to exhibit the neural conditioning. This learning deficit was rescued by repetitive treatment with fluoxetine, an antidepressant. Therefore, internally motivated animals are capable of routing an ongoing action potential series into a specific neural pathway of the hippocampal network.

Predictive coding of dynamical variables in balanced spiking networks.

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Boerlin, Martin; Machens, Christian K; Denève, Sophie

2013-01-01

Two observations about the cortex have puzzled neuroscientists for a long time. First, neural responses are highly variable. Second, the level of excitation and inhibition received by each neuron is tightly balanced at all times. Here, we demonstrate that both properties are necessary consequences of neural networks that represent information efficiently in their spikes. We illustrate this insight with spiking networks that represent dynamical variables. Our approach is based on two assumptions: We assume that information about dynamical variables can be read out linearly from neural spike trains, and we assume that neurons only fire a spike if that improves the representation of the dynamical variables. Based on these assumptions, we derive a network of leaky integrate-and-fire neurons that is able to implement arbitrary linear dynamical systems. We show that the membrane voltage of the neurons is equivalent to a prediction error about a common population-level signal. Among other things, our approach allows us to construct an integrator network of spiking neurons that is robust against many perturbations. Most importantly, neural variability in our networks cannot be equated to noise. Despite exhibiting the same single unit properties as widely used population code models (e.g. tuning curves, Poisson distributed spike trains), balanced networks are orders of magnitudes more reliable. Our approach suggests that spikes do matter when considering how the brain computes, and that the reliability of cortical representations could have been strongly underestimated.

A unified approach to linking experimental, statistical and computational analysis of spike train data.

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Liang Meng

Full Text Available A fundamental issue in neuroscience is how to identify the multiple biophysical mechanisms through which neurons generate observed patterns of spiking activity. In previous work, we proposed a method for linking observed patterns of spiking activity to specific biophysical mechanisms based on a state space modeling framework and a sequential Monte Carlo, or particle filter, estimation algorithm. We have shown, in simulation, that this approach is able to identify a space of simple biophysical models that were consistent with observed spiking data (and included the model that generated the data, but have yet to demonstrate the application of the method to identify realistic currents from real spike train data. Here, we apply the particle filter to spiking data recorded from rat layer V cortical neurons, and correctly identify the dynamics of an slow, intrinsic current. The underlying intrinsic current is successfully identified in four distinct neurons, even though the cells exhibit two distinct classes of spiking activity: regular spiking and bursting. This approach--linking statistical, computational, and experimental neuroscience--provides an effective technique to constrain detailed biophysical models to specific mechanisms consistent with observed spike train data.

The role of dendritic non-linearities in single neuron computation

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Boris Gutkin

2014-05-01

Full Text Available Experiment has demonstrated that summation of excitatory post-synaptic protientials (EPSPs in dendrites is non-linear. The sum of multiple EPSPs can be larger than their arithmetic sum, a superlinear summation due to the opening of voltage-gated channels and similar to somatic spiking. The so-called dendritic spike. The sum of multiple of EPSPs can also be smaller than their arithmetic sum, because the synaptic current necessarily saturates at some point. While these observations are well-explained by biophysical models the impact of dendritic spikes on computation remains a matter of debate. One reason is that dendritic spikes may fail to make the neuron spike; similarly, dendritic saturations are sometime presented as a glitch which should be corrected by dendritic spikes. We will provide solid arguments against this claim and show that dendritic saturations as well as dendritic spikes enhance single neuron computation, even when they cannot directly make the neuron fire. To explore the computational impact of dendritic spikes and saturations, we are using a binary neuron model in conjunction with Boolean algebra. We demonstrate using these tools that a single dendritic non-linearity, either spiking or saturating, combined with somatic non-linearity, enables a neuron to compute linearly non-separable Boolean functions (lnBfs. These functions are impossible to compute when summation is linear and the exclusive OR is a famous example of lnBfs. Importantly, the implementation of these functions does not require the dendritic non-linearity to make the neuron spike. Next, We show that reduced and realistic biophysical models of the neuron are capable of computing lnBfs. Within these models and contrary to the binary model, the dendritic and somatic non-linearity are tightly coupled. Yet we show that these neuron models are capable of linearly non-separable computations.

Automatic spike sorting using tuning information.

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Ventura, Valérie

2009-09-01

Current spike sorting methods focus on clustering neurons' characteristic spike waveforms. The resulting spike-sorted data are typically used to estimate how covariates of interest modulate the firing rates of neurons. However, when these covariates do modulate the firing rates, they provide information about spikes' identities, which thus far have been ignored for the purpose of spike sorting. This letter describes a novel approach to spike sorting, which incorporates both waveform information and tuning information obtained from the modulation of firing rates. Because it efficiently uses all the available information, this spike sorter yields lower spike misclassification rates than traditional automatic spike sorters. This theoretical result is verified empirically on several examples. The proposed method does not require additional assumptions; only its implementation is different. It essentially consists of performing spike sorting and tuning estimation simultaneously rather than sequentially, as is currently done. We used an expectation-maximization maximum likelihood algorithm to implement the new spike sorter. We present the general form of this algorithm and provide a detailed implementable version under the assumptions that neurons are independent and spike according to Poisson processes. Finally, we uncover a systematic flaw of spike sorting based on waveform information only.

Spiking Neural Networks with Unsupervised Learning Based on STDP Using Resistive Synaptic Devices and Analog CMOS Neuron Circuit.

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Kwon, Min-Woo; Baek, Myung-Hyun; Hwang, Sungmin; Kim, Sungjun; Park, Byung-Gook

2018-09-01

We designed the CMOS analog integrate and fire (I&F) neuron circuit can drive resistive synaptic device. The neuron circuit consists of a current mirror for spatial integration, a capacitor for temporal integration, asymmetric negative and positive pulse generation part, a refractory part, and finally a back-propagation pulse generation part for learning of the synaptic devices. The resistive synaptic devices were fabricated using HfOx switching layer by atomic layer deposition (ALD). The resistive synaptic device had gradual set and reset characteristics and the conductance was adjusted by spike-timing-dependent-plasticity (STDP) learning rule. We carried out circuit simulation of synaptic device and CMOS neuron circuit. And we have developed an unsupervised spiking neural networks (SNNs) for 5 × 5 pattern recognition and classification using the neuron circuit and synaptic devices. The hardware-based SNNs can autonomously and efficiently control the weight updates of the synapses between neurons, without the aid of software calculations.

Spike and burst coding in thalamocortical relay cells.

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Fleur Zeldenrust

2018-02-01

Full Text Available Mammalian thalamocortical relay (TCR neurons switch their firing activity between a tonic spiking and a bursting regime. In a combined experimental and computational study, we investigated the features in the input signal that single spikes and bursts in the output spike train represent and how this code is influenced by the membrane voltage state of the neuron. Identical frozen Gaussian noise current traces were injected into TCR neurons in rat brain slices as well as in a validated three-compartment TCR model cell. The resulting membrane voltage traces and spike trains were analyzed by calculating the coherence and impedance. Reverse correlation techniques gave the Event-Triggered Average (ETA and the Event-Triggered Covariance (ETC. This demonstrated that the feature selectivity started relatively long before the events (up to 300 ms and showed a clear distinction between spikes (selective for fluctuations and bursts (selective for integration. The model cell was fine-tuned to mimic the frozen noise initiated spike and burst responses to within experimental accuracy, especially for the mixed mode regimes. The information content carried by the various types of events in the signal as well as by the whole signal was calculated. Bursts phase-lock to and transfer information at lower frequencies than single spikes. On depolarization the neuron transits smoothly from the predominantly bursting regime to a spiking regime, in which it is more sensitive to high-frequency fluctuations. The model was then used to elucidate properties that could not be assessed experimentally, in particular the role of two important subthreshold voltage-dependent currents: the low threshold activated calcium current (IT and the cyclic nucleotide modulated h current (Ih. The ETAs of those currents and their underlying activation/inactivation states not only explained the state dependence of the firing regime but also the long-lasting concerted dynamic action of the two

Noisy Spiking in Visual Area V2 of Amblyopic Monkeys.

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Wang, Ye; Zhang, Bin; Tao, Xiaofeng; Wensveen, Janice M; Smith, Earl L; Chino, Yuzo M

2017-01-25

being noisy by perceptual and modeling studies, the exact nature or origin of this elevated perceptual noise is not known. We show that elevated and noisy spontaneous activity and contrast-dependent noisy spiking (spiking irregularity and trial-to-trial fluctuations in spiking) in neurons of visual area V2 could limit the visual performance of amblyopic primates. Moreover, we discovered that the noisy spiking is linked to a high level of binocular suppression in visual cortex during development. Copyright © 2017 the authors 0270-6474/17/370922-14$15.00/0.

Hue opponency: chromatic valence functions, individual differences, cortical winner-take-all opponent modeling, and the relationship between spikes and sensitivity.

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Billock, Vincent A

2018-04-01

Neural spike rate data are more restricted in range than related psychophysical data. For example, several studies suggest a compressive (roughly cube root) nonlinear relationship between wavelength-opponent spike rates in primate midbrain and color appearance in humans, two rather widely separated domains. This presents an opportunity to partially bridge a chasm between these two domains and to probe the putative nonlinearity with other psychophysical data. Here neural wavelength-opponent data are used to create cortical competition models for hue opponency. This effort led to creation of useful models of spiking neuron winner-take-all (WTA) competition and MAX selection. When fed with actual primate data, the spiking WTA models generate reasonable wavelength-opponent spike rate behaviors. An average psychophysical observer for red-green and blue-yellow opponency is curated from eight applicable studies in the refereed and dissertation literatures, with cancellation data roughly every 10 nm in 18 subjects for yellow-blue opponency and 15 subjects for red-green opponency. A direct mapping between spiking neurons with broadband wavelength sensitivity and human psychophysical luminance yields a power law exponent of 0.27, similar to the cube root nonlinearity. Similarly, direct mapping between the WTA model opponent spike rates and psychophysical opponent data suggests power law relationships with exponents between 0.24 and 0.41.

Computational modeling of spiking neural network with learning rules from STDP and intrinsic plasticity

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Li, Xiumin; Wang, Wei; Xue, Fangzheng; Song, Yongduan

2018-02-01

Recently there has been continuously increasing interest in building up computational models of spiking neural networks (SNN), such as the Liquid State Machine (LSM). The biologically inspired self-organized neural networks with neural plasticity can enhance the capability of computational performance, with the characteristic features of dynamical memory and recurrent connection cycles which distinguish them from the more widely used feedforward neural networks. Despite a variety of computational models for brain-like learning and information processing have been proposed, the modeling of self-organized neural networks with multi-neural plasticity is still an important open challenge. The main difficulties lie in the interplay among different forms of neural plasticity rules and understanding how structures and dynamics of neural networks shape the computational performance. In this paper, we propose a novel approach to develop the models of LSM with a biologically inspired self-organizing network based on two neural plasticity learning rules. The connectivity among excitatory neurons is adapted by spike-timing-dependent plasticity (STDP) learning; meanwhile, the degrees of neuronal excitability are regulated to maintain a moderate average activity level by another learning rule: intrinsic plasticity (IP). Our study shows that LSM with STDP+IP performs better than LSM with a random SNN or SNN obtained by STDP alone. The noticeable improvement with the proposed method is due to the better reflected competition among different neurons in the developed SNN model, as well as the more effectively encoded and processed relevant dynamic information with its learning and self-organizing mechanism. This result gives insights to the optimization of computational models of spiking neural networks with neural plasticity.

The Second Spiking Threshold: Dynamics of Laminar Network Spiking in the Visual Cortex

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Forsberg, Lars E.; Bonde, Lars H.; Harvey, Michael A.; Roland, Per E.

2016-01-01

Most neurons have a threshold separating the silent non-spiking state and the state of producing temporal sequences of spikes. But neurons in vivo also have a second threshold, found recently in granular layer neurons of the primary visual cortex, separating spontaneous ongoing spiking from visually evoked spiking driven by sharp transients. Here we examine whether this second threshold exists outside the granular layer and examine details of transitions between spiking states in ferrets exposed to moving objects. We found the second threshold, separating spiking states evoked by stationary and moving visual stimuli from the spontaneous ongoing spiking state, in all layers and zones of areas 17 and 18 indicating that the second threshold is a property of the network. Spontaneous and evoked spiking, thus can easily be distinguished. In addition, the trajectories of spontaneous ongoing states were slow, frequently changing direction. In single trials, sharp as well as smooth and slow transients transform the trajectories to be outward directed, fast and crossing the threshold to become evoked. Although the speeds of the evolution of the evoked states differ, the same domain of the state space is explored indicating uniformity of the evoked states. All evoked states return to the spontaneous evoked spiking state as in a typical mono-stable dynamical system. In single trials, neither the original spiking rates, nor the temporal evolution in state space could distinguish simple visual scenes. PMID:27582693

Serial Spike Time Correlations Affect Probability Distribution of Joint Spike Events.

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Shahi, Mina; van Vreeswijk, Carl; Pipa, Gordon

2016-01-01

Detecting the existence of temporally coordinated spiking activity, and its role in information processing in the cortex, has remained a major challenge for neuroscience research. Different methods and approaches have been suggested to test whether the observed synchronized events are significantly different from those expected by chance. To analyze the simultaneous spike trains for precise spike correlation, these methods typically model the spike trains as a Poisson process implying that the generation of each spike is independent of all the other spikes. However, studies have shown that neural spike trains exhibit dependence among spike sequences, such as the absolute and relative refractory periods which govern the spike probability of the oncoming action potential based on the time of the last spike, or the bursting behavior, which is characterized by short epochs of rapid action potentials, followed by longer episodes of silence. Here we investigate non-renewal processes with the inter-spike interval distribution model that incorporates spike-history dependence of individual neurons. For that, we use the Monte Carlo method to estimate the full shape of the coincidence count distribution and to generate false positives for coincidence detection. The results show that compared to the distributions based on homogeneous Poisson processes, and also non-Poisson processes, the width of the distribution of joint spike events changes. Non-renewal processes can lead to both heavy tailed or narrow coincidence distribution. We conclude that small differences in the exact autostructure of the point process can cause large differences in the width of a coincidence distribution. Therefore, manipulations of the autostructure for the estimation of significance of joint spike events seem to be inadequate.

On the sample complexity of learning for networks of spiking neurons with nonlinear synaptic interactions.

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Schmitt, Michael

2004-09-01

We study networks of spiking neurons that use the timing of pulses to encode information. Nonlinear interactions model the spatial groupings of synapses on the neural dendrites and describe the computations performed at local branches. Within a theoretical framework of learning we analyze the question of how many training examples these networks must receive to be able to generalize well. Bounds for this sample complexity of learning can be obtained in terms of a combinatorial parameter known as the pseudodimension. This dimension characterizes the computational richness of a neural network and is given in terms of the number of network parameters. Two types of feedforward architectures are considered: constant-depth networks and networks of unconstrained depth. We derive asymptotically tight bounds for each of these network types. Constant depth networks are shown to have an almost linear pseudodimension, whereas the pseudodimension of general networks is quadratic. Networks of spiking neurons that use temporal coding are becoming increasingly more important in practical tasks such as computer vision, speech recognition, and motor control. The question of how well these networks generalize from a given set of training examples is a central issue for their successful application as adaptive systems. The results show that, although coding and computation in these networks is quite different and in many cases more powerful, their generalization capabilities are at least as good as those of traditional neural network models.

Timing intervals using population synchrony and spike timing dependent plasticity

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Wei Xu

2016-12-01

Full Text Available We present a computational model by which ensembles of regularly spiking neurons can encode different time intervals through synchronous firing. We show that a neuron responding to a large population of convergent inputs has the potential to learn to produce an appropriately-timed output via spike-time dependent plasticity. We explain why temporal variability of this population synchrony increases with increasing time intervals. We also show that the scalar property of timing and its violation at short intervals can be explained by the spike-wise accumulation of jitter in the inter-spike intervals of timing neurons. We explore how the challenge of encoding longer time intervals can be overcome and conclude that this may involve a switch to a different population of neurons with lower firing rate, with the added effect of producing an earlier bias in response. Experimental data on human timing performance show features in agreement with the model’s output.

Precise-spike-driven synaptic plasticity: learning hetero-association of spatiotemporal spike patterns.

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Qiang Yu

Full Text Available A new learning rule (Precise-Spike-Driven (PSD Synaptic Plasticity is proposed for processing and memorizing spatiotemporal patterns. PSD is a supervised learning rule that is analytically derived from the traditional Widrow-Hoff rule and can be used to train neurons to associate an input spatiotemporal spike pattern with a desired spike train. Synaptic adaptation is driven by the error between the desired and the actual output spikes, with positive errors causing long-term potentiation and negative errors causing long-term depression. The amount of modification is proportional to an eligibility trace that is triggered by afferent spikes. The PSD rule is both computationally efficient and biologically plausible. The properties of this learning rule are investigated extensively through experimental simulations, including its learning performance, its generality to different neuron models, its robustness against noisy conditions, its memory capacity, and the effects of its learning parameters. Experimental results show that the PSD rule is capable of spatiotemporal pattern classification, and can even outperform a well studied benchmark algorithm with the proposed relative confidence criterion. The PSD rule is further validated on a practical example of an optical character recognition problem. The results again show that it can achieve a good recognition performance with a proper encoding. Finally, a detailed discussion is provided about the PSD rule and several related algorithms including tempotron, SPAN, Chronotron and ReSuMe.

Precise-spike-driven synaptic plasticity: learning hetero-association of spatiotemporal spike patterns.

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Yu, Qiang; Tang, Huajin; Tan, Kay Chen; Li, Haizhou

2013-01-01

A new learning rule (Precise-Spike-Driven (PSD) Synaptic Plasticity) is proposed for processing and memorizing spatiotemporal patterns. PSD is a supervised learning rule that is analytically derived from the traditional Widrow-Hoff rule and can be used to train neurons to associate an input spatiotemporal spike pattern with a desired spike train. Synaptic adaptation is driven by the error between the desired and the actual output spikes, with positive errors causing long-term potentiation and negative errors causing long-term depression. The amount of modification is proportional to an eligibility trace that is triggered by afferent spikes. The PSD rule is both computationally efficient and biologically plausible. The properties of this learning rule are investigated extensively through experimental simulations, including its learning performance, its generality to different neuron models, its robustness against noisy conditions, its memory capacity, and the effects of its learning parameters. Experimental results show that the PSD rule is capable of spatiotemporal pattern classification, and can even outperform a well studied benchmark algorithm with the proposed relative confidence criterion. The PSD rule is further validated on a practical example of an optical character recognition problem. The results again show that it can achieve a good recognition performance with a proper encoding. Finally, a detailed discussion is provided about the PSD rule and several related algorithms including tempotron, SPAN, Chronotron and ReSuMe.

Modeling task-specific neuronal ensembles improves decoding of grasp

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Smith, Ryan J.; Soares, Alcimar B.; Rouse, Adam G.; Schieber, Marc H.; Thakor, Nitish V.

2018-06-01

Objective. Dexterous movement involves the activation and coordination of networks of neuronal populations across multiple cortical regions. Attempts to model firing of individual neurons commonly treat the firing rate as directly modulating with motor behavior. However, motor behavior may additionally be associated with modulations in the activity and functional connectivity of neurons in a broader ensemble. Accounting for variations in neural ensemble connectivity may provide additional information about the behavior being performed. Approach. In this study, we examined neural ensemble activity in primary motor cortex (M1) and premotor cortex (PM) of two male rhesus monkeys during performance of a center-out reach, grasp and manipulate task. We constructed point process encoding models of neuronal firing that incorporated task-specific variations in the baseline firing rate as well as variations in functional connectivity with the neural ensemble. Models were evaluated both in terms of their encoding capabilities and their ability to properly classify the grasp being performed. Main results. Task-specific ensemble models correctly predicted the performed grasp with over 95% accuracy and were shown to outperform models of neuronal activity that assume only a variable baseline firing rate. Task-specific ensemble models exhibited superior decoding performance in 82% of units in both monkeys (p  <  0.01). Inclusion of ensemble activity also broadly improved the ability of models to describe observed spiking. Encoding performance of task-specific ensemble models, measured by spike timing predictability, improved upon baseline models in 62% of units. Significance. These results suggest that additional discriminative information about motor behavior found in the variations in functional connectivity of neuronal ensembles located in motor-related cortical regions is relevant to decode complex tasks such as grasping objects, and may serve the basis for more

Directional spike propagation in a recurrent network: dynamical firewall as anisotropic recurrent inhibition.

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Samura, Toshikazu; Hayashi, Hatsuo

2012-09-01

It has been demonstrated that theta rhythm propagates along the septotemporal axis of the hippocampal CA1 of the rat running on a track, and it has been suggested that directional spike propagation in the hippocampal CA3 is reflected in CA1. In this paper, we show that directional spike propagation occurs in a recurrent network model in which neurons are connected locally and connection weights are modified through STDP. The recurrent network model consists of excitatory and inhibitory neurons, which are intrinsic bursting and fast spiking neurons developed by Izhikevich, respectively. The maximum length of connections from excitatory neurons is shorter in the horizontal direction than the vertical direction. Connections from inhibitory neurons have the same maximum length in both directions, and the maximum length of inhibitory connections is the same as that of excitatory connections in the vertical direction. When connection weights between excitatory neurons (E→E) were modified through STDP and those from excitatory neurons to inhibitory neurons (E→I) were constant, spikes propagated in the vertical direction as expected from the network structure. However, when E→I connection weights were modified through STDP, as well as E→E connection weights, spikes propagated in the horizontal direction against the above expectation. This paradoxical propagation was produced by strengthened E→I connections which shifted the timing of inhibition forward. When E→I connections are enhanced, the direction of effective inhibition changes from horizontal to vertical, as if a gate for spike propagation is opened in the horizontal direction and firewalls come out in the vertical direction. These results suggest that the advance of timing of inhibition caused by potentiation of E→I connections is influential in network activity and is an important element in determining the direction of spike propagation. Copyright © 2012 Elsevier Ltd. All rights reserved.

A Model of Electrically Stimulated Auditory Nerve Fiber Responses with Peripheral and Central Sites of Spike Generation

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Joshi, Suyash Narendra; Dau, Torsten; Epp, Bastian

2017-01-01

. A single ANF is modeled as a network of two exponential integrateand-fire point-neuron models, referred to as peripheral and central axons of the ANF. The peripheral axon is excited by the cathodic charge, inhibited by the anodic charge, and exhibits longer spike latencies than the central axon......A computational model of cat auditory nerve fiber (ANF) responses to electrical stimulation is presented. The model assumes that (1) there exist at least two sites of spike generation along the ANF and (2) both an anodic (positive) and a cathodic (negative) charge in isolation can evoke a spike......; the central axon is excited by the anodic charge, inhibited by the cathodic charge, and exhibits shorter spike latencies than the peripheral axon. The model also includes subthreshold and suprathreshold adaptive feedback loops which continuously modify the membrane potential and can account for effects...

A Re-configurable On-line Learning Spiking Neuromorphic Processor comprising 256 neurons and 128K synapses

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Ning eQiao

2015-04-01

Full Text Available Implementing compact, low-power artificial neural processing systems with real-time on-line learning abilities is still an open challenge. In this paper we present a full-custom mixed-signal VLSI device with neuromorphic learning circuits that emulate the biophysics of real spiking neurons and dynamic synapses for exploring the properties of computational neuroscience models and for building brain-inspired computing systems. The proposed architecture allows the on-chip configuration of a wide range of network connectivities, including recurrent and deep networks with short-term and long-term plasticity. The device comprises 128 K analog synapse and 256 neuron circuits with biologically plausible dynamics and bi-stable spike-based plasticity mechanisms that endow it with on-line learning abilities. In addition to the analog circuits, the device comprises also asynchronous digital logic circuits for setting different synapse and neuron properties as well as different network configurations. This prototype device, fabricated using a 180 nm 1P6M CMOS process, occupies an area of 51.4 mm 2 , and consumes approximately 4 mW for typical experiments, for example involving attractor networks. Here we describe the details of the overall architecture and of the individual circuits and present experimental results that showcase its potential. By supporting a wide range of cortical-like computational modules comprising plasticity mechanisms, this device will enable the realization of intelligent autonomous systems with on-line learning capabilities.

Detection of bursts in extracellular spike trains using hidden semi-Markov point process models.

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Tokdar, Surya; Xi, Peiyi; Kelly, Ryan C; Kass, Robert E

2010-08-01

Neurons in vitro and in vivo have epochs of bursting or "up state" activity during which firing rates are dramatically elevated. Various methods of detecting bursts in extracellular spike trains have appeared in the literature, the most widely used apparently being Poisson Surprise (PS). A natural description of the phenomenon assumes (1) there are two hidden states, which we label "burst" and "non-burst," (2) the neuron evolves stochastically, switching at random between these two states, and (3) within each state the spike train follows a time-homogeneous point process. If in (2) the transitions from non-burst to burst and burst to non-burst states are memoryless, this becomes a hidden Markov model (HMM). For HMMs, the state transitions follow exponential distributions, and are highly irregular. Because observed bursting may in some cases be fairly regular-exhibiting inter-burst intervals with small variation-we relaxed this assumption. When more general probability distributions are used to describe the state transitions the two-state point process model becomes a hidden semi-Markov model (HSMM). We developed an efficient Bayesian computational scheme to fit HSMMs to spike train data. Numerical simulations indicate the method can perform well, sometimes yielding very different results than those based on PS.

Forskolin suppresses delayed-rectifier K+ currents and enhances spike frequency-dependent adaptation of sympathetic neurons.

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Angel-Chavez, Luis I; Acosta-Gómez, Eduardo I; Morales-Avalos, Mario; Castro, Elena; Cruzblanca, Humberto

2015-01-01

In signal transduction research natural or synthetic molecules are commonly used to target a great variety of signaling proteins. For instance, forskolin, a diterpene activator of adenylate cyclase, has been widely used in cellular preparations to increase the intracellular cAMP level. However, it has been shown that forskolin directly inhibits some cloned K+ channels, which in excitable cells set up the resting membrane potential, the shape of action potential and regulate repetitive firing. Despite the growing evidence indicating that K+ channels are blocked by forskolin, there are no studies yet assessing the impact of this mechanism of action on neuron excitability and firing patterns. In sympathetic neurons, we find that forskolin and its derivative 1,9-Dideoxyforskolin, reversibly suppress the delayed rectifier K+ current (IKV). Besides, forskolin reduced the spike afterhyperpolarization and enhanced the spike frequency-dependent adaptation. Given that IKV is mostly generated by Kv2.1 channels, HEK-293 cells were transfected with cDNA encoding for the Kv2.1 α subunit, to characterize the mechanism of forskolin action. Both drugs reversible suppressed the Kv2.1-mediated K+ currents. Forskolin inhibited Kv2.1 currents and IKV with an IC50 of ~32 μM and ~24 µM, respectively. Besides, the drug induced an apparent current inactivation and slowed-down current deactivation. We suggest that forskolin reduces the excitability of sympathetic neurons by enhancing the spike frequency-dependent adaptation, partially through a direct block of their native Kv2.1 channels.

SpikeTemp: An Enhanced Rank-Order-Based Learning Approach for Spiking Neural Networks With Adaptive Structure.

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Wang, Jinling; Belatreche, Ammar; Maguire, Liam P; McGinnity, Thomas Martin

2017-01-01

This paper presents an enhanced rank-order-based learning algorithm, called SpikeTemp, for spiking neural networks (SNNs) with a dynamically adaptive structure. The trained feed-forward SNN consists of two layers of spiking neurons: 1) an encoding layer which temporally encodes real-valued features into spatio-temporal spike patterns and 2) an output layer of dynamically grown neurons which perform spatio-temporal classification. Both Gaussian receptive fields and square cosine population encoding schemes are employed to encode real-valued features into spatio-temporal spike patterns. Unlike the rank-order-based learning approach, SpikeTemp uses the precise times of the incoming spikes for adjusting the synaptic weights such that early spikes result in a large weight change and late spikes lead to a smaller weight change. This removes the need to rank all the incoming spikes and, thus, reduces the computational cost of SpikeTemp. The proposed SpikeTemp algorithm is demonstrated on several benchmark data sets and on an image recognition task. The results show that SpikeTemp can achieve better classification performance and is much faster than the existing rank-order-based learning approach. In addition, the number of output neurons is much smaller when the square cosine encoding scheme is employed. Furthermore, SpikeTemp is benchmarked against a selection of existing machine learning algorithms, and the results demonstrate the ability of SpikeTemp to classify different data sets after just one presentation of the training samples with comparable classification performance.

Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights

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Wilten eNicola

2016-02-01

Full Text Available A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF. The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks

Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights.

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Nicola, Wilten; Tripp, Bryan; Scott, Matthew

2016-01-01

A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks.

Point process modeling and estimation: Advances in the analysis of dynamic neural spiking data

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Deng, Xinyi

2016-08-01

A common interest of scientists in many fields is to understand the relationship between the dynamics of a physical system and the occurrences of discrete events within such physical system. Seismologists study the connection between mechanical vibrations of the Earth and the occurrences of earthquakes so that future earthquakes can be better predicted. Astrophysicists study the association between the oscillating energy of celestial regions and the emission of photons to learn the Universe's various objects and their interactions. Neuroscientists study the link between behavior and the millisecond-timescale spike patterns of neurons to understand higher brain functions. Such relationships can often be formulated within the framework of state-space models with point process observations. The basic idea is that the dynamics of the physical systems are driven by the dynamics of some stochastic state variables and the discrete events we observe in an interval are noisy observations with distributions determined by the state variables. This thesis proposes several new methodological developments that advance the framework of state-space models with point process observations at the intersection of statistics and neuroscience. In particular, we develop new methods 1) to characterize the rhythmic spiking activity using history-dependent structure, 2) to model population spike activity using marked point process models, 3) to allow for real-time decision making, and 4) to take into account the need for dimensionality reduction for high-dimensional state and observation processes. We applied these methods to a novel problem of tracking rhythmic dynamics in the spiking of neurons in the subthalamic nucleus of Parkinson's patients with the goal of optimizing placement of deep brain stimulation electrodes. We developed a decoding algorithm that can make decision in real-time (for example, to stimulate the neurons or not) based on various sources of information present in

Recurrently connected and localized neuronal communities initiate coordinated spontaneous activity in neuronal networks

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Amin, Hayder; Maccione, Alessandro; Nieus, Thierry

2017-01-01

Developing neuronal systems intrinsically generate coordinated spontaneous activity that propagates by involving a large number of synchronously firing neurons. In vivo, waves of spikes transiently characterize the activity of developing brain circuits and are fundamental for activity-dependent circuit formation. In vitro, coordinated spontaneous spiking activity, or network bursts (NBs), interleaved within periods of asynchronous spikes emerge during the development of 2D and 3D neuronal cultures. Several studies have investigated this type of activity and its dynamics, but how a neuronal system generates these coordinated events remains unclear. Here, we investigate at a cellular level the generation of network bursts in spontaneously active neuronal cultures by exploiting high-resolution multielectrode array recordings and computational network modelling. Our analysis reveals that NBs are generated in specialized regions of the network (functional neuronal communities) that feature neuronal links with high cross-correlation peak values, sub-millisecond lags and that share very similar structural connectivity motifs providing recurrent interactions. We show that the particular properties of these local structures enable locally amplifying spontaneous asynchronous spikes and that this mechanism can lead to the initiation of NBs. Through the analysis of simulated and experimental data, we also show that AMPA currents drive the coordinated activity, while NMDA and GABA currents are only involved in shaping the dynamics of NBs. Overall, our results suggest that the presence of functional neuronal communities with recurrent local connections allows a neuronal system to generate spontaneous coordinated spiking activity events. As suggested by the rules used for implementing our computational model, such functional communities might naturally emerge during network development by following simple constraints on distance-based connectivity. PMID:28749937

Recurrently connected and localized neuronal communities initiate coordinated spontaneous activity in neuronal networks.

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Davide Lonardoni

2017-07-01

Full Text Available Developing neuronal systems intrinsically generate coordinated spontaneous activity that propagates by involving a large number of synchronously firing neurons. In vivo, waves of spikes transiently characterize the activity of developing brain circuits and are fundamental for activity-dependent circuit formation. In vitro, coordinated spontaneous spiking activity, or network bursts (NBs, interleaved within periods of asynchronous spikes emerge during the development of 2D and 3D neuronal cultures. Several studies have investigated this type of activity and its dynamics, but how a neuronal system generates these coordinated events remains unclear. Here, we investigate at a cellular level the generation of network bursts in spontaneously active neuronal cultures by exploiting high-resolution multielectrode array recordings and computational network modelling. Our analysis reveals that NBs are generated in specialized regions of the network (functional neuronal communities that feature neuronal links with high cross-correlation peak values, sub-millisecond lags and that share very similar structural connectivity motifs providing recurrent interactions. We show that the particular properties of these local structures enable locally amplifying spontaneous asynchronous spikes and that this mechanism can lead to the initiation of NBs. Through the analysis of simulated and experimental data, we also show that AMPA currents drive the coordinated activity, while NMDA and GABA currents are only involved in shaping the dynamics of NBs. Overall, our results suggest that the presence of functional neuronal communities with recurrent local connections allows a neuronal system to generate spontaneous coordinated spiking activity events. As suggested by the rules used for implementing our computational model, such functional communities might naturally emerge during network development by following simple constraints on distance-based connectivity.

Application of cross-correlated delay shift rule in spiking neural networks for interictal spike detection.

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Lilin Guo; Zhenzhong Wang; Cabrerizo, Mercedes; Adjouadi, Malek

2016-08-01

This study proposes a Cross-Correlated Delay Shift (CCDS) supervised learning rule to train neurons with associated spatiotemporal patterns to classify spike patterns. The objective of this study was to evaluate the feasibility of using the CCDS rule to automate the detection of interictal spikes in electroencephalogram (EEG) data on patients with epilepsy. Encoding is the initial yet essential step for spiking neurons to process EEG patterns. A new encoding method is utilized to convert the EEG signal into spike patterns. The simulation results show that the proposed algorithm identified 69 spikes out of 82 spikes, or 84% detection rate, which is quite high considering the subtleties of interictal spikes and the tediousness of monitoring long EEG records. This CCDS rule is also benchmarked by ReSuMe on the same task.

Six types of multistability in a neuronal model based on slow calcium current.

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Tatiana Malashchenko

Full Text Available BACKGROUND: Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified. METHODOLOGY/PRINCIPAL FINDINGS: Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1 bursting and silence, 2 tonic spiking and silence, 3 tonic spiking and subthreshold oscillations, 4 bursting and subthreshold oscillations, 5 bursting, subthreshold oscillations and silence, and 6 bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate. CONCLUSIONS: We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability.

SpikingLab: modelling agents controlled by Spiking Neural Networks in Netlogo.

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Jimenez-Romero, Cristian; Johnson, Jeffrey

2017-01-01

The scientific interest attracted by Spiking Neural Networks (SNN) has lead to the development of tools for the simulation and study of neuronal dynamics ranging from phenomenological models to the more sophisticated and biologically accurate Hodgkin-and-Huxley-based and multi-compartmental models. However, despite the multiple features offered by neural modelling tools, their integration with environments for the simulation of robots and agents can be challenging and time consuming. The implementation of artificial neural circuits to control robots generally involves the following tasks: (1) understanding the simulation tools, (2) creating the neural circuit in the neural simulator, (3) linking the simulated neural circuit with the environment of the agent and (4) programming the appropriate interface in the robot or agent to use the neural controller. The accomplishment of the above-mentioned tasks can be challenging, especially for undergraduate students or novice researchers. This paper presents an alternative tool which facilitates the simulation of simple SNN circuits using the multi-agent simulation and the programming environment Netlogo (educational software that simplifies the study and experimentation of complex systems). The engine proposed and implemented in Netlogo for the simulation of a functional model of SNN is a simplification of integrate and fire (I&F) models. The characteristics of the engine (including neuronal dynamics, STDP learning and synaptic delay) are demonstrated through the implementation of an agent representing an artificial insect controlled by a simple neural circuit. The setup of the experiment and its outcomes are described in this work.

Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

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Rodrigo Cofré

2018-01-01

Full Text Available The spiking activity of neuronal networks follows laws that are not time-reversal symmetric; the notion of pre-synaptic and post-synaptic neurons, stimulus correlations and noise correlations have a clear time order. Therefore, a biologically realistic statistical model for the spiking activity should be able to capture some degree of time irreversibility. We use the thermodynamic formalism to build a framework in the context maximum entropy models to quantify the degree of time irreversibility, providing an explicit formula for the information entropy production of the inferred maximum entropy Markov chain. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.

Improved SpikeProp for Using Particle Swarm Optimization

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Falah Y. H. Ahmed

2013-01-01

Full Text Available A spiking neurons network encodes information in the timing of individual spike times. A novel supervised learning rule for SpikeProp is derived to overcome the discontinuities introduced by the spiking thresholding. This algorithm is based on an error-backpropagation learning rule suited for supervised learning of spiking neurons that use exact spike time coding. The SpikeProp is able to demonstrate the spiking neurons that can perform complex nonlinear classification in fast temporal coding. This study proposes enhancements of SpikeProp learning algorithm for supervised training of spiking networks which can deal with complex patterns. The proposed methods include the SpikeProp particle swarm optimization (PSO and angle driven dependency learning rate. These methods are presented to SpikeProp network for multilayer learning enhancement and weights optimization. Input and output patterns are encoded as spike trains of precisely timed spikes, and the network learns to transform the input trains into target output trains. With these enhancements, our proposed methods outperformed other conventional neural network architectures.

A COMPUTATIONAL MODEL OF MOTOR NEURON DEGENERATION

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Le Masson, Gwendal; Przedborski, Serge; Abbott, L.F.

2014-01-01

SUMMARY To explore the link between bioenergetics and motor neuron degeneration, we used a computational model in which detailed morphology and ion conductance are paired with intracellular ATP production and consumption. We found that reduced ATP availability increases the metabolic cost of a single action potential and disrupts K+/Na+ homeostasis, resulting in a chronic depolarization. The magnitude of the ATP shortage at which this ionic instability occurs depends on the morphology and intrinsic conductance characteristic of the neuron. If ATP shortage is confined to the distal part of the axon, the ensuing local ionic instability eventually spreads to the whole neuron and involves fasciculation-like spiking events. A shortage of ATP also causes a rise in intracellular calcium. Our modeling work supports the notion that mitochondrial dysfunction can account for salient features of the paralytic disorder amyotrophic lateral sclerosis, including motor neuron hyperexcitability, fasciculation, and differential vulnerability of motor neuron subpopulations. PMID:25088365

A computational model of motor neuron degeneration.

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Le Masson, Gwendal; Przedborski, Serge; Abbott, L F

2014-08-20

To explore the link between bioenergetics and motor neuron degeneration, we used a computational model in which detailed morphology and ion conductance are paired with intracellular ATP production and consumption. We found that reduced ATP availability increases the metabolic cost of a single action potential and disrupts K+/Na+ homeostasis, resulting in a chronic depolarization. The magnitude of the ATP shortage at which this ionic instability occurs depends on the morphology and intrinsic conductance characteristic of the neuron. If ATP shortage is confined to the distal part of the axon, the ensuing local ionic instability eventually spreads to the whole neuron and involves fasciculation-like spiking events. A shortage of ATP also causes a rise in intracellular calcium. Our modeling work supports the notion that mitochondrial dysfunction can account for salient features of the paralytic disorder amyotrophic lateral sclerosis, including motor neuron hyperexcitability, fasciculation, and differential vulnerability of motor neuron subpopulations. Copyright © 2014 Elsevier Inc. All rights reserved.

Computer Modelling of Functional Aspects of Noise in Endogenously Oscillating Neurons

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Huber, M. T.; Dewald, M.; Voigt, K.; Braun, H. A.; Moss, F.

1998-03-01

Membrane potential oscillations are a widespread feature of neuronal activity. When such oscillations operate close to the spike-triggering threshold, noise can become an essential property of spike-generation. According to that, we developed a minimal Hodgkin-Huxley-type computer model which includes a noise term. This model accounts for experimental data from quite different cells ranging from mammalian cortical neurons to fish electroreceptors. With slight modifications of the parameters, the model's behavior can be tuned to bursting activity, which additionally allows it to mimick temperature encoding in peripheral cold receptors including transitions to apparently chaotic dynamics as indicated by methods for the detection of unstable periodic orbits. Under all conditions, cooperative effects between noise and nonlinear dynamics can be shown which, beyond stochastic resonance, might be of functional significance for stimulus encoding and neuromodulation.

A phase plane analysis of neuron-astrocyte interactions.

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Amiri, Mahmood; Montaseri, Ghazal; Bahrami, Fariba

2013-08-01

Intensive experimental studies have shown that astrocytes are active partners in modulation of synaptic transmission. In the present research, we study neuron-astrocyte signaling using a biologically inspired model of one neuron synapsing one astrocyte. In this model, the firing dynamics of the neuron is described by the Morris-Lecar model and the Ca(2+) dynamics of a single astrocyte explained by a functional model introduced by Postnov and colleagues. Using the coupled neuron-astrocyte model and based on the results of the phase plane analyses, it is demonstrated that the astrocyte is able to activate the silent neuron or change the neuron spiking frequency through bidirectional communication. This suggests that astrocyte feedback signaling is capable of modulating spike transmission frequency by changing neuron spiking frequency. This effect is described by a saddle-node on invariant circle bifurcation in the coupled neuron-astrocyte model. In this way, our results suggest that the neuron-astrocyte crosstalk has a fundamental role in producing diverse neuronal activities and therefore enhances the information processing capabilities of the brain. Crown Copyright © 2013. Published by Elsevier Ltd. All rights reserved.

Chimera-like states in a neuronal network model of the cat brain

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Santos, M. S.; Szezech, J. D.; Borges, F. S.; Iarosz, K. C.; Caldas, I. L.; Batista, A. M.; Viana, R. L.; Kurths, J.

2017-08-01

Neuronal systems have been modeled by complex networks in different description levels. Recently, it has been verified that networks can simultaneously exhibit one coherent and other incoherent domain, known as chimera states. In this work, we study the existence of chimera states in a network considering the connectivity matrix based on the cat cerebral cortex. The cerebral cortex of the cat can be separated in 65 cortical areas organised into the four cognitive regions: visual, auditory, somatosensory-motor and frontolimbic. We consider a network where the local dynamics is given by the Hindmarsh-Rose model. The Hindmarsh-Rose equations are a well known model of neuronal activity that has been considered to simulate membrane potential in neuron. Here, we analyse under which conditions chimera states are present, as well as the affects induced by intensity of coupling on them. We observe the existence of chimera states in that incoherent structure can be composed of desynchronised spikes or desynchronised bursts. Moreover, we find that chimera states with desynchronised bursts are more robust to neuronal noise than with desynchronised spikes.

Cerebellar Nuclear Neurons Use Time and Rate Coding to Transmit Purkinje Neuron Pauses.

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Sudhakar, Shyam Kumar; Torben-Nielsen, Benjamin; De Schutter, Erik

2015-12-01

Neurons of the cerebellar nuclei convey the final output of the cerebellum to their targets in various parts of the brain. Within the cerebellum their direct upstream connections originate from inhibitory Purkinje neurons. Purkinje neurons have a complex firing pattern of regular spikes interrupted by intermittent pauses of variable length. How can the cerebellar nucleus process this complex input pattern? In this modeling study, we investigate different forms of Purkinje neuron simple spike pause synchrony and its influence on candidate coding strategies in the cerebellar nuclei. That is, we investigate how different alignments of synchronous pauses in synthetic Purkinje neuron spike trains affect either time-locking or rate-changes in the downstream nuclei. We find that Purkinje neuron synchrony is mainly represented by changes in the firing rate of cerebellar nuclei neurons. Pause beginning synchronization produced a unique effect on nuclei neuron firing, while the effect of pause ending and pause overlapping synchronization could not be distinguished from each other. Pause beginning synchronization produced better time-locking of nuclear neurons for short length pauses. We also characterize the effect of pause length and spike jitter on the nuclear neuron firing. Additionally, we find that the rate of rebound responses in nuclear neurons after a synchronous pause is controlled by the firing rate of Purkinje neurons preceding it.

Cerebellar Nuclear Neurons Use Time and Rate Coding to Transmit Purkinje Neuron Pauses

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Sudhakar, Shyam Kumar; Torben-Nielsen, Benjamin; De Schutter, Erik

2015-01-01

Neurons of the cerebellar nuclei convey the final output of the cerebellum to their targets in various parts of the brain. Within the cerebellum their direct upstream connections originate from inhibitory Purkinje neurons. Purkinje neurons have a complex firing pattern of regular spikes interrupted by intermittent pauses of variable length. How can the cerebellar nucleus process this complex input pattern? In this modeling study, we investigate different forms of Purkinje neuron simple spike pause synchrony and its influence on candidate coding strategies in the cerebellar nuclei. That is, we investigate how different alignments of synchronous pauses in synthetic Purkinje neuron spike trains affect either time-locking or rate-changes in the downstream nuclei. We find that Purkinje neuron synchrony is mainly represented by changes in the firing rate of cerebellar nuclei neurons. Pause beginning synchronization produced a unique effect on nuclei neuron firing, while the effect of pause ending and pause overlapping synchronization could not be distinguished from each other. Pause beginning synchronization produced better time-locking of nuclear neurons for short length pauses. We also characterize the effect of pause length and spike jitter on the nuclear neuron firing. Additionally, we find that the rate of rebound responses in nuclear neurons after a synchronous pause is controlled by the firing rate of Purkinje neurons preceding it. PMID:26630202

Stress-Induced Impairment of a Working Memory Task: Role of Spiking Rate and Spiking History Predicted Discharge

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Devilbiss, David M.; Jenison, Rick L.; Berridge, Craig W.

2012-01-01

Stress, pervasive in society, contributes to over half of all work place accidents a year and over time can contribute to a variety of psychiatric disorders including depression, schizophrenia, and post-traumatic stress disorder. Stress impairs higher cognitive processes, dependent on the prefrontal cortex (PFC) and that involve maintenance and integration of information over extended periods, including working memory and attention. Substantial evidence has demonstrated a relationship between patterns of PFC neuron spiking activity (action-potential discharge) and components of delayed-response tasks used to probe PFC-dependent cognitive function in rats and monkeys. During delay periods of these tasks, persistent spiking activity is posited to be essential for the maintenance of information for working memory and attention. However, the degree to which stress-induced impairment in PFC-dependent cognition involves changes in task-related spiking rates or the ability for PFC neurons to retain information over time remains unknown. In the current study, spiking activity was recorded from the medial PFC of rats performing a delayed-response task of working memory during acute noise stress (93 db). Spike history-predicted discharge (SHPD) for PFC neurons was quantified as a measure of the degree to which ongoing neuronal discharge can be predicted by past spiking activity and reflects the degree to which past information is retained by these neurons over time. We found that PFC neuron discharge is predicted by their past spiking patterns for nearly one second. Acute stress impaired SHPD, selectively during delay intervals of the task, and simultaneously impaired task performance. Despite the reduction in delay-related SHPD, stress increased delay-related spiking rates. These findings suggest that neural codes utilizing SHPD within PFC networks likely reflects an additional important neurophysiological mechanism for maintenance of past information over time. Stress

Forskolin suppresses delayed-rectifier K+ currents and enhances spike frequency-dependent adaptation of sympathetic neurons.

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Luis I Angel-Chavez

Full Text Available In signal transduction research natural or synthetic molecules are commonly used to target a great variety of signaling proteins. For instance, forskolin, a diterpene activator of adenylate cyclase, has been widely used in cellular preparations to increase the intracellular cAMP level. However, it has been shown that forskolin directly inhibits some cloned K+ channels, which in excitable cells set up the resting membrane potential, the shape of action potential and regulate repetitive firing. Despite the growing evidence indicating that K+ channels are blocked by forskolin, there are no studies yet assessing the impact of this mechanism of action on neuron excitability and firing patterns. In sympathetic neurons, we find that forskolin and its derivative 1,9-Dideoxyforskolin, reversibly suppress the delayed rectifier K+ current (IKV. Besides, forskolin reduced the spike afterhyperpolarization and enhanced the spike frequency-dependent adaptation. Given that IKV is mostly generated by Kv2.1 channels, HEK-293 cells were transfected with cDNA encoding for the Kv2.1 α subunit, to characterize the mechanism of forskolin action. Both drugs reversible suppressed the Kv2.1-mediated K+ currents. Forskolin inhibited Kv2.1 currents and IKV with an IC50 of ~32 μM and ~24 µM, respectively. Besides, the drug induced an apparent current inactivation and slowed-down current deactivation. We suggest that forskolin reduces the excitability of sympathetic neurons by enhancing the spike frequency-dependent adaptation, partially through a direct block of their native Kv2.1 channels.

Effects of Spike Anticipation on the Spiking Dynamics of Neural Networks

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Daniel ede Santos-Sierra

2015-11-01

Full Text Available Synchronization is one of the central phenomena involved in information processing in living systems. It is known that the nervous system requires the coordinated activity of both local and distant neural populations. Such an interplay allows to merge different information modalities in a whole processing supporting high-level mental skills as understanding, memory, abstraction, etc. Though the biological processes underlying synchronization in the brain are not fully understood there have been reported a variety of mechanisms supporting different types of synchronization both at theoretical and experimental level. One of the more intriguing of these phenomena is the anticipating synchronization, which has been recently reported in a pair of unidirectionally coupled artificial neurons under simple conditions cite{Pyragas}, where the slave neuron is able to anticipate in time the behaviour of the master one. In this paper we explore the effect of spike anticipation over the information processing performed by a neural network at functional and structural level. We show that the introduction of intermediary neurons in the network enhances spike anticipation and analyse how these variations in spike anticipation can significantly change the firing regime of the neural network according to its functional and structural properties. In addition we show that the interspike interval (ISI, one of the main features of the neural response associated to the information coding, can be closely related to spike anticipation by each spike, and how synaptic plasticity can be modulated through that relationship. This study has been performed through numerical simulation of a coupled system of Hindmarsh-Rose neurons.

Effects of Spike Anticipation on the Spiking Dynamics of Neural Networks.

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de Santos-Sierra, Daniel; Sanchez-Jimenez, Abel; Garcia-Vellisca, Mariano A; Navas, Adrian; Villacorta-Atienza, Jose A

2015-01-01

Synchronization is one of the central phenomena involved in information processing in living systems. It is known that the nervous system requires the coordinated activity of both local and distant neural populations. Such an interplay allows to merge different information modalities in a whole processing supporting high-level mental skills as understanding, memory, abstraction, etc. Though, the biological processes underlying synchronization in the brain are not fully understood there have been reported a variety of mechanisms supporting different types of synchronization both at theoretical and experimental level. One of the more intriguing of these phenomena is the anticipating synchronization, which has been recently reported in a pair of unidirectionally coupled artificial neurons under simple conditions (Pyragiene and Pyragas, 2013), where the slave neuron is able to anticipate in time the behavior of the master one. In this paper, we explore the effect of spike anticipation over the information processing performed by a neural network at functional and structural level. We show that the introduction of intermediary neurons in the network enhances spike anticipation and analyse how these variations in spike anticipation can significantly change the firing regime of the neural network according to its functional and structural properties. In addition we show that the interspike interval (ISI), one of the main features of the neural response associated with the information coding, can be closely related to spike anticipation by each spike, and how synaptic plasticity can be modulated through that relationship. This study has been performed through numerical simulation of a coupled system of Hindmarsh-Rose neurons.

A Framework for the Comparative Assessment of Neuronal Spike Sorting Algorithms towards More Accurate Off-Line and On-Line Microelectrode Arrays Data Analysis.

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Regalia, Giulia; Coelli, Stefania; Biffi, Emilia; Ferrigno, Giancarlo; Pedrocchi, Alessandra

2016-01-01

Neuronal spike sorting algorithms are designed to retrieve neuronal network activity on a single-cell level from extracellular multiunit recordings with Microelectrode Arrays (MEAs). In typical analysis of MEA data, one spike sorting algorithm is applied indiscriminately to all electrode signals. However, this approach neglects the dependency of algorithms' performances on the neuronal signals properties at each channel, which require data-centric methods. Moreover, sorting is commonly performed off-line, which is time and memory consuming and prevents researchers from having an immediate glance at ongoing experiments. The aim of this work is to provide a versatile framework to support the evaluation and comparison of different spike classification algorithms suitable for both off-line and on-line analysis. We incorporated different spike sorting "building blocks" into a Matlab-based software, including 4 feature extraction methods, 3 feature clustering methods, and 1 template matching classifier. The framework was validated by applying different algorithms on simulated and real signals from neuronal cultures coupled to MEAs. Moreover, the system has been proven effective in running on-line analysis on a standard desktop computer, after the selection of the most suitable sorting methods. This work provides a useful and versatile instrument for a supported comparison of different options for spike sorting towards more accurate off-line and on-line MEA data analysis.

Fast computation with spikes in a recurrent neural network

International Nuclear Information System (INIS)

Jin, Dezhe Z.; Seung, H. Sebastian

2002-01-01

Neural networks with recurrent connections are sometimes regarded as too slow at computation to serve as models of the brain. Here we analytically study a counterexample, a network consisting of N integrate-and-fire neurons with self excitation, all-to-all inhibition, instantaneous synaptic coupling, and constant external driving inputs. When the inhibition and/or excitation are large enough, the network performs a winner-take-all computation for all possible external inputs and initial states of the network. The computation is done very quickly: As soon as the winner spikes once, the computation is completed since no other neurons will spike. For some initial states, the winner is the first neuron to spike, and the computation is done at the first spike of the network. In general, there are M potential winners, corresponding to the top M external inputs. When the external inputs are close in magnitude, M tends to be larger. If M>1, the selection of the actual winner is strongly influenced by the initial states. If a special relation between the excitation and inhibition is satisfied, the network always selects the neuron with the maximum external input as the winner

Inferring oscillatory modulation in neural spike trains.

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Arai, Kensuke; Kass, Robert E

2017-10-01

Oscillations are observed at various frequency bands in continuous-valued neural recordings like the electroencephalogram (EEG) and local field potential (LFP) in bulk brain matter, and analysis of spike-field coherence reveals that spiking of single neurons often occurs at certain phases of the global oscillation. Oscillatory modulation has been examined in relation to continuous-valued oscillatory signals, and independently from the spike train alone, but behavior or stimulus triggered firing-rate modulation, spiking sparseness, presence of slow modulation not locked to stimuli and irregular oscillations with large variability in oscillatory periods, present challenges to searching for temporal structures present in the spike train. In order to study oscillatory modulation in real data collected under a variety of experimental conditions, we describe a flexible point-process framework we call the Latent Oscillatory Spike Train (LOST) model to decompose the instantaneous firing rate in biologically and behaviorally relevant factors: spiking refractoriness, event-locked firing rate non-stationarity, and trial-to-trial variability accounted for by baseline offset and a stochastic oscillatory modulation. We also extend the LOST model to accommodate changes in the modulatory structure over the duration of the experiment, and thereby discover trial-to-trial variability in the spike-field coherence of a rat primary motor cortical neuron to the LFP theta rhythm. Because LOST incorporates a latent stochastic auto-regressive term, LOST is able to detect oscillations when the firing rate is low, the modulation is weak, and when the modulating oscillation has a broad spectral peak.

Model-based decoding, information estimation, and change-point detection techniques for multineuron spike trains.

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Pillow, Jonathan W; Ahmadian, Yashar; Paninski, Liam

2011-01-01

One of the central problems in systems neuroscience is to understand how neural spike trains convey sensory information. Decoding methods, which provide an explicit means for reading out the information contained in neural spike responses, offer a powerful set of tools for studying the neural coding problem. Here we develop several decoding methods based on point-process neural encoding models, or forward models that predict spike responses to stimuli. These models have concave log-likelihood functions, which allow efficient maximum-likelihood model fitting and stimulus decoding. We present several applications of the encoding model framework to the problem of decoding stimulus information from population spike responses: (1) a tractable algorithm for computing the maximum a posteriori (MAP) estimate of the stimulus, the most probable stimulus to have generated an observed single- or multiple-neuron spike train response, given some prior distribution over the stimulus; (2) a gaussian approximation to the posterior stimulus distribution that can be used to quantify the fidelity with which various stimulus features are encoded; (3) an efficient method for estimating the mutual information between the stimulus and the spike trains emitted by a neural population; and (4) a framework for the detection of change-point times (the time at which the stimulus undergoes a change in mean or variance) by marginalizing over the posterior stimulus distribution. We provide several examples illustrating the performance of these estimators with simulated and real neural data.

Spiking neural P systems with multiple channels.

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Peng, Hong; Yang, Jinyu; Wang, Jun; Wang, Tao; Sun, Zhang; Song, Xiaoxiao; Luo, Xiaohui; Huang, Xiangnian

2017-11-01

Spiking neural P systems (SNP systems, in short) are a class of distributed parallel computing systems inspired from the neurophysiological behavior of biological spiking neurons. In this paper, we investigate a new variant of SNP systems in which each neuron has one or more synaptic channels, called spiking neural P systems with multiple channels (SNP-MC systems, in short). The spiking rules with channel label are introduced to handle the firing mechanism of neurons, where the channel labels indicate synaptic channels of transmitting the generated spikes. The computation power of SNP-MC systems is investigated. Specifically, we prove that SNP-MC systems are Turing universal as both number generating and number accepting devices. Copyright © 2017 Elsevier Ltd. All rights reserved.

Integration of Continuous-Time Dynamics in a Spiking Neural Network Simulator

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Jan Hahne

2017-05-01

Full Text Available Contemporary modeling approaches to the dynamics of neural networks include two important classes of models: biologically grounded spiking neuron models and functionally inspired rate-based units. We present a unified simulation framework that supports the combination of the two for multi-scale modeling, enables the quantitative validation of mean-field approaches by spiking network simulations, and provides an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes. While most spiking simulations rely on the communication of discrete events, rate models require time-continuous interactions between neurons. Exploiting the conceptual similarity to the inclusion of gap junctions in spiking network simulations, we arrive at a reference implementation of instantaneous and delayed interactions between rate-based models in a spiking network simulator. The separation of rate dynamics from the general connection and communication infrastructure ensures flexibility of the framework. In addition to the standard implementation we present an iterative approach based on waveform-relaxation techniques to reduce communication and increase performance for large-scale simulations of rate-based models with instantaneous interactions. Finally we demonstrate the broad applicability of the framework by considering various examples from the literature, ranging from random networks to neural-field models. The study provides the prerequisite for interactions between rate-based and spiking models in a joint simulation.

Integration of Continuous-Time Dynamics in a Spiking Neural Network Simulator.

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Hahne, Jan; Dahmen, David; Schuecker, Jannis; Frommer, Andreas; Bolten, Matthias; Helias, Moritz; Diesmann, Markus

2017-01-01

Contemporary modeling approaches to the dynamics of neural networks include two important classes of models: biologically grounded spiking neuron models and functionally inspired rate-based units. We present a unified simulation framework that supports the combination of the two for multi-scale modeling, enables the quantitative validation of mean-field approaches by spiking network simulations, and provides an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes. While most spiking simulations rely on the communication of discrete events, rate models require time-continuous interactions between neurons. Exploiting the conceptual similarity to the inclusion of gap junctions in spiking network simulations, we arrive at a reference implementation of instantaneous and delayed interactions between rate-based models in a spiking network simulator. The separation of rate dynamics from the general connection and communication infrastructure ensures flexibility of the framework. In addition to the standard implementation we present an iterative approach based on waveform-relaxation techniques to reduce communication and increase performance for large-scale simulations of rate-based models with instantaneous interactions. Finally we demonstrate the broad applicability of the framework by considering various examples from the literature, ranging from random networks to neural-field models. The study provides the prerequisite for interactions between rate-based and spiking models in a joint simulation.

Hyperbolic Plykin attractor can exist in neuron models

DEFF Research Database (Denmark)

Belykh, V.; Belykh, I.; Mosekilde, Erik

2005-01-01

Strange hyperbolic attractors are hard to find in real physical systems. This paper provides the first example of a realistic system, a canonical three-dimensional (3D) model of bursting neurons, that is likely to have a strange hyperbolic attractor. Using a geometrical approach to the study...... of the neuron model, we derive a flow-defined Poincare map giving ail accurate account of the system's dynamics. In a parameter region where the neuron system undergoes bifurcations causing transitions between tonic spiking and bursting, this two-dimensional map becomes a map of a disk with several periodic...... holes. A particular case is the map of a disk with three holes, matching the Plykin example of a planar hyperbolic attractor. The corresponding attractor of the 3D neuron model appears to be hyperbolic (this property is not verified in the present paper) and arises as a result of a two-loop (secondary...

Multistability in a neuron model with extracellular potassium dynamics

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Wu, Xing-Xing; Shuai, J. W.

2012-06-01

Experiments show a primary role of extracellular potassium concentrations in neuronal hyperexcitability and in the generation of epileptiform bursting and depolarization blocks without synaptic mechanisms. We adopt a physiologically relevant hippocampal CA1 neuron model in a zero-calcium condition to better understand the function of extracellular potassium in neuronal seizurelike activities. The model neuron is surrounded by interstitial space in which potassium ions are able to accumulate. Potassium currents, Na+-K+ pumps, glial buffering, and ion diffusion are regulatory mechanisms of extracellular potassium. We also consider a reduced model with a fixed potassium concentration. The bifurcation structure and spiking frequency of the two models are studied. We show that, besides hyperexcitability and bursting pattern modulation, the potassium dynamics can induce not only bistability but also tristability of different firing patterns. Our results reveal the emergence of the complex behavior of multistability due to the dynamical [K+]o modulation on neuronal activities.

A Scalable Weight-Free Learning Algorithm for Regulatory Control of Cell Activity in Spiking Neuronal Networks.

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Zhang, Xu; Foderaro, Greg; Henriquez, Craig; Ferrari, Silvia

2018-03-01

Recent developments in neural stimulation and recording technologies are providing scientists with the ability of recording and controlling the activity of individual neurons in vitro or in vivo, with very high spatial and temporal resolution. Tools such as optogenetics, for example, are having a significant impact in the neuroscience field by delivering optical firing control with the precision and spatiotemporal resolution required for investigating information processing and plasticity in biological brains. While a number of training algorithms have been developed to date for spiking neural network (SNN) models of biological neuronal circuits, exiting methods rely on learning rules that adjust the synaptic strengths (or weights) directly, in order to obtain the desired network-level (or functional-level) performance. As such, they are not applicable to modifying plasticity in biological neuronal circuits, in which synaptic strengths only change as a result of pre- and post-synaptic neuron firings or biological mechanisms beyond our control. This paper presents a weight-free training algorithm that relies solely on adjusting the spatiotemporal delivery of neuron firings in order to optimize the network performance. The proposed weight-free algorithm does not require any knowledge of the SNN model or its plasticity mechanisms. As a result, this training approach is potentially realizable in vitro or in vivo via neural stimulation and recording technologies, such as optogenetics and multielectrode arrays, and could be utilized to control plasticity at multiple scales of biological neuronal circuits. The approach is demonstrated by training SNNs with hundreds of units to control a virtual insect navigating in an unknown environment.

Hardware implementation of stochastic spiking neural networks.

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Rosselló, Josep L; Canals, Vincent; Morro, Antoni; Oliver, Antoni

2012-08-01

Spiking Neural Networks, the last generation of Artificial Neural Networks, are characterized by its bio-inspired nature and by a higher computational capacity with respect to other neural models. In real biological neurons, stochastic processes represent an important mechanism of neural behavior and are responsible of its special arithmetic capabilities. In this work we present a simple hardware implementation of spiking neurons that considers this probabilistic nature. The advantage of the proposed implementation is that it is fully digital and therefore can be massively implemented in Field Programmable Gate Arrays. The high computational capabilities of the proposed model are demonstrated by the study of both feed-forward and recurrent networks that are able to implement high-speed signal filtering and to solve complex systems of linear equations.

Artificial neuron operations and spike-timing-dependent plasticity using memristive devices for brain-inspired computing

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Marukame, Takao; Nishi, Yoshifumi; Yasuda, Shin-ichi; Tanamoto, Tetsufumi

2018-04-01

The use of memristive devices for creating artificial neurons is promising for brain-inspired computing from the viewpoints of computation architecture and learning protocol. We present an energy-efficient multiplier accumulator based on a memristive array architecture incorporating both analog and digital circuitries. The analog circuitry is used to full advantage for neural networks, as demonstrated by the spike-timing-dependent plasticity (STDP) in fabricated AlO x /TiO x -based metal-oxide memristive devices. STDP protocols for controlling periodic analog resistance with long-range stability were experimentally verified using a variety of voltage amplitudes and spike timings.

Memory effects on a resonate-and-fire neuron model subjected to Ornstein-Uhlenbeck noise

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Paekivi, S.; Mankin, R.; Rekker, A.

2017-10-01

We consider a generalized Langevin equation with an exponentially decaying memory kernel as a model for the firing process of a resonate-and-fire neuron. The effect of temporally correlated random neuronal input is modeled as Ornstein-Uhlenbeck noise. In the noise-induced spiking regime of the neuron, we derive exact analytical formulas for the dependence of some statistical characteristics of the output spike train, such as the probability distribution of the interspike intervals (ISIs) and the survival probability, on the parameters of the input stimulus. Particularly, on the basis of these exact expressions, we have established sufficient conditions for the occurrence of memory-time-induced transitions between unimodal and multimodal structures of the ISI density and a critical damping coefficient which marks a dynamical transition in the behavior of the system.

Spike Pattern Structure Influences Synaptic Efficacy Variability Under STDP and Synaptic Homeostasis. II: Spike Shuffling Methods on LIF Networks

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Zedong Bi

2016-08-01

Full Text Available Synapses may undergo variable changes during plasticity because of the variability of spike patterns such as temporal stochasticity and spatial randomness. Here, we call the variability of synaptic weight changes during plasticity to be efficacy variability. In this paper, we investigate how four aspects of spike pattern statistics (i.e., synchronous firing, burstiness/regularity, heterogeneity of rates and heterogeneity of cross-correlations influence the efficacy variability under pair-wise additive spike-timing dependent plasticity (STDP and synaptic homeostasis (the mean strength of plastic synapses into a neuron is bounded, by implementing spike shuffling methods onto spike patterns self-organized by a network of excitatory and inhibitory leaky integrate-and-fire (LIF neurons. With the increase of the decay time scale of the inhibitory synaptic currents, the LIF network undergoes a transition from asynchronous state to weak synchronous state and then to synchronous bursting state. We first shuffle these spike patterns using a variety of methods, each designed to evidently change a specific pattern statistics; and then investigate the change of efficacy variability of the synapses under STDP and synaptic homeostasis, when the neurons in the network fire according to the spike patterns before and after being treated by a shuffling method. In this way, we can understand how the change of pattern statistics may cause the change of efficacy variability. Our results are consistent with those of our previous study which implements spike-generating models on converging motifs. We also find that burstiness/regularity is important to determine the efficacy variability under asynchronous states, while heterogeneity of cross-correlations is the main factor to cause efficacy variability when the network moves into synchronous bursting states (the states observed in epilepsy.

Distributed Bayesian Computation and Self-Organized Learning in Sheets of Spiking Neurons with Local Lateral Inhibition.

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Johannes Bill

Full Text Available During the last decade, Bayesian probability theory has emerged as a framework in cognitive science and neuroscience for describing perception, reasoning and learning of mammals. However, our understanding of how probabilistic computations could be organized in the brain, and how the observed connectivity structure of cortical microcircuits supports these calculations, is rudimentary at best. In this study, we investigate statistical inference and self-organized learning in a spatially extended spiking network model, that accommodates both local competitive and large-scale associative aspects of neural information processing, under a unified Bayesian account. Specifically, we show how the spiking dynamics of a recurrent network with lateral excitation and local inhibition in response to distributed spiking input, can be understood as sampling from a variational posterior distribution of a well-defined implicit probabilistic model. This interpretation further permits a rigorous analytical treatment of experience-dependent plasticity on the network level. Using machine learning theory, we derive update rules for neuron and synapse parameters which equate with Hebbian synaptic and homeostatic intrinsic plasticity rules in a neural implementation. In computer simulations, we demonstrate that the interplay of these plasticity rules leads to the emergence of probabilistic local experts that form distributed assemblies of similarly tuned cells communicating through lateral excitatory connections. The resulting sparse distributed spike code of a well-adapted network carries compressed information on salient input features combined with prior experience on correlations among them. Our theory predicts that the emergence of such efficient representations benefits from network architectures in which the range of local inhibition matches the spatial extent of pyramidal cells that share common afferent input.

Distributed Bayesian Computation and Self-Organized Learning in Sheets of Spiking Neurons with Local Lateral Inhibition

Science.gov (United States)

Bill, Johannes; Buesing, Lars; Habenschuss, Stefan; Nessler, Bernhard; Maass, Wolfgang; Legenstein, Robert

2015-01-01

During the last decade, Bayesian probability theory has emerged as a framework in cognitive science and neuroscience for describing perception, reasoning and learning of mammals. However, our understanding of how probabilistic computations could be organized in the brain, and how the observed connectivity structure of cortical microcircuits supports these calculations, is rudimentary at best. In this study, we investigate statistical inference and self-organized learning in a spatially extended spiking network model, that accommodates both local competitive and large-scale associative aspects of neural information processing, under a unified Bayesian account. Specifically, we show how the spiking dynamics of a recurrent network with lateral excitation and local inhibition in response to distributed spiking input, can be understood as sampling from a variational posterior distribution of a well-defined implicit probabilistic model. This interpretation further permits a rigorous analytical treatment of experience-dependent plasticity on the network level. Using machine learning theory, we derive update rules for neuron and synapse parameters which equate with Hebbian synaptic and homeostatic intrinsic plasticity rules in a neural implementation. In computer simulations, we demonstrate that the interplay of these plasticity rules leads to the emergence of probabilistic local experts that form distributed assemblies of similarly tuned cells communicating through lateral excitatory connections. The resulting sparse distributed spike code of a well-adapted network carries compressed information on salient input features combined with prior experience on correlations among them. Our theory predicts that the emergence of such efficient representations benefits from network architectures in which the range of local inhibition matches the spatial extent of pyramidal cells that share common afferent input. PMID:26284370

Spike Timing Matters in Novel Neuronal Code Involved in Vibrotactile Frequency Perception.

Science.gov (United States)

Birznieks, Ingvars; Vickery, Richard M

2017-05-22

Skin vibrations sensed by tactile receptors contribute significantly to the perception of object properties during tactile exploration [1-4] and to sensorimotor control during object manipulation [5]. Sustained low-frequency skin vibration (perception of frequency is still unknown. Measures based on mean spike rates of neurons in the primary somatosensory cortex are sufficient to explain performance in some frequency discrimination tasks [7-11]; however, there is emerging evidence that stimuli can be distinguished based also on temporal features of neural activity [12, 13]. Our study's advance is to demonstrate that temporal features are fundamental for vibrotactile frequency perception. Pulsatile mechanical stimuli were used to elicit specified temporal spike train patterns in tactile afferents, and subsequently psychophysical methods were employed to characterize human frequency perception. Remarkably, the most salient temporal feature determining vibrotactile frequency was not the underlying periodicity but, rather, the duration of the silent gap between successive bursts of neural activity. This burst gap code for frequency represents a previously unknown form of neural coding in the tactile sensory system, which parallels auditory pitch perception mechanisms based on purely temporal information where longer inter-pulse intervals receive higher perceptual weights than short intervals [14]. Our study also demonstrates that human perception of stimuli can be determined exclusively by temporal features of spike trains independent of the mean spike rate and without contribution from population response factors. Copyright © 2017 Elsevier Ltd. All rights reserved.

Neural Spike Train Synchronisation Indices: Definitions, Interpretations and Applications.

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Halliday, D M; Rosenberg, J R

2017-04-24

A comparison of previously defined spike train syncrhonization indices is undertaken within a stochastic point process framework. The second order cumulant density (covariance density) is shown to be common to all the indices. Simulation studies were used to investigate the sampling variability of a single index based on the second order cumulant. The simulations used a paired motoneurone model and a paired regular spiking cortical neurone model. The sampling variability of spike trains generated under identical conditions from the paired motoneurone model varied from 50% { 160% of the estimated value. On theoretical grounds, and on the basis of simulated data a rate dependence is present in all synchronization indices. The application of coherence and pooled coherence estimates to the issue of synchronization indices is considered. This alternative frequency domain approach allows an arbitrary number of spike train pairs to be evaluated for statistically significant differences, and combined into a single population measure. The pooled coherence framework allows pooled time domain measures to be derived, application of this to the simulated data is illustrated. Data from the cortical neurone model is generated over a wide range of firing rates (1 - 250 spikes/sec). The pooled coherence framework correctly characterizes the sampling variability as not significant over this wide operating range. The broader applicability of this approach to multi electrode array data is briefly discussed.

Temporal sequence learning in winner-take-all networks of spiking neurons demonstrated in a brain-based device.

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McKinstry, Jeffrey L; Edelman, Gerald M

2013-01-01

Animal behavior often involves a temporally ordered sequence of actions learned from experience. Here we describe simulations of interconnected networks of spiking neurons that learn to generate patterns of activity in correct temporal order. The simulation consists of large-scale networks of thousands of excitatory and inhibitory neurons that exhibit short-term synaptic plasticity and spike-timing dependent synaptic plasticity. The neural architecture within each area is arranged to evoke winner-take-all (WTA) patterns of neural activity that persist for tens of milliseconds. In order to generate and switch between consecutive firing patterns in correct temporal order, a reentrant exchange of signals between these areas was necessary. To demonstrate the capacity of this arrangement, we used the simulation to train a brain-based device responding to visual input by autonomously generating temporal sequences of motor actions.

Distribution of orientation selectivity in recurrent networks of spiking neurons with different random topologies.

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Sadeh, Sadra; Rotter, Stefan

2014-01-01

Neurons in the primary visual cortex are more or less selective for the orientation of a light bar used for stimulation. A broad distribution of individual grades of orientation selectivity has in fact been reported in all species. A possible reason for emergence of broad distributions is the recurrent network within which the stimulus is being processed. Here we compute the distribution of orientation selectivity in randomly connected model networks that are equipped with different spatial patterns of connectivity. We show that, for a wide variety of connectivity patterns, a linear theory based on firing rates accurately approximates the outcome of direct numerical simulations of networks of spiking neurons. Distance dependent connectivity in networks with a more biologically realistic structure does not compromise our linear analysis, as long as the linearized dynamics, and hence the uniform asynchronous irregular activity state, remain stable. We conclude that linear mechanisms of stimulus processing are indeed responsible for the emergence of orientation selectivity and its distribution in recurrent networks with functionally heterogeneous synaptic connectivity.

Dynamic Control of Synchronous Activity in Networks of Spiking Neurons.

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Axel Hutt

Full Text Available Oscillatory brain activity is believed to play a central role in neural coding. Accumulating evidence shows that features of these oscillations are highly dynamic: power, frequency and phase fluctuate alongside changes in behavior and task demands. The role and mechanism supporting this variability is however poorly understood. We here analyze a network of recurrently connected spiking neurons with time delay displaying stable synchronous dynamics. Using mean-field and stability analyses, we investigate the influence of dynamic inputs on the frequency of firing rate oscillations. We show that afferent noise, mimicking inputs to the neurons, causes smoothing of the system's response function, displacing equilibria and altering the stability of oscillatory states. Our analysis further shows that these noise-induced changes cause a shift of the peak frequency of synchronous oscillations that scales with input intensity, leading the network towards critical states. We lastly discuss the extension of these principles to periodic stimulation, in which externally applied driving signals can trigger analogous phenomena. Our results reveal one possible mechanism involved in shaping oscillatory activity in the brain and associated control principles.

Dynamic Control of Synchronous Activity in Networks of Spiking Neurons.

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Hutt, Axel; Mierau, Andreas; Lefebvre, Jérémie

Oscillatory brain activity is believed to play a central role in neural coding. Accumulating evidence shows that features of these oscillations are highly dynamic: power, frequency and phase fluctuate alongside changes in behavior and task demands. The role and mechanism supporting this variability is however poorly understood. We here analyze a network of recurrently connected spiking neurons with time delay displaying stable synchronous dynamics. Using mean-field and stability analyses, we investigate the influence of dynamic inputs on the frequency of firing rate oscillations. We show that afferent noise, mimicking inputs to the neurons, causes smoothing of the system's response function, displacing equilibria and altering the stability of oscillatory states. Our analysis further shows that these noise-induced changes cause a shift of the peak frequency of synchronous oscillations that scales with input intensity, leading the network towards critical states. We lastly discuss the extension of these principles to periodic stimulation, in which externally applied driving signals can trigger analogous phenomena. Our results reveal one possible mechanism involved in shaping oscillatory activity in the brain and associated control principles.

Interspike interval correlation in a stochastic exponential integrate-and-fire model with subthreshold and spike-triggered adaptation.

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Shiau, LieJune; Schwalger, Tilo; Lindner, Benjamin

2015-06-01

We study the spike statistics of an adaptive exponential integrate-and-fire neuron stimulated by white Gaussian current noise. We derive analytical approximations for the coefficient of variation and the serial correlation coefficient of the interspike interval assuming that the neuron operates in the mean-driven tonic firing regime and that the stochastic input is weak. Our result for the serial correlation coefficient has the form of a geometric sequence and is confirmed by the comparison to numerical simulations. The theory predicts various patterns of interval correlations (positive or negative at lag one, monotonically decreasing or oscillating) depending on the strength of the spike-triggered and subthreshold components of the adaptation current. In particular, for pure subthreshold adaptation we find strong positive ISI correlations that are usually ascribed to positive correlations in the input current. Our results i) provide an alternative explanation for interspike-interval correlations observed in vivo, ii) may be useful in fitting point neuron models to experimental data, and iii) may be instrumental in exploring the role of adaptation currents for signal detection and signal transmission in single neurons.

Coincidence Detection Using Spiking Neurons with Application to Face Recognition

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Fadhlan Kamaruzaman

2015-01-01

Full Text Available We elucidate the practical implementation of Spiking Neural Network (SNN as local ensembles of classifiers. Synaptic time constant τs is used as learning parameter in representing the variations learned from a set of training data at classifier level. This classifier uses coincidence detection (CD strategy trained in supervised manner using a novel supervised learning method called τs Prediction which adjusts the precise timing of output spikes towards the desired spike timing through iterative adaptation of τs. This paper also discusses the approximation of spike timing in Spike Response Model (SRM for the purpose of coincidence detection. This process significantly speeds up the whole process of learning and classification. Performance evaluations with face datasets such as AR, FERET, JAFFE, and CK+ datasets show that the proposed method delivers better face classification performance than the network trained with Supervised Synaptic-Time Dependent Plasticity (STDP. We also found that the proposed method delivers better classification accuracy than k nearest neighbor, ensembles of kNN, and Support Vector Machines. Evaluation on several types of spike codings also reveals that latency coding delivers the best result for face classification as well as for classification of other multivariate datasets.

Efficient transmission of subthreshold signals in complex networks of spiking neurons.

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Torres, Joaquin J; Elices, Irene; Marro, J

2015-01-01

We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances--that naturally balances the network with excitatory and inhibitory synapses--and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios, including spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it could also occur in actual neural systems as recent psycho-physical experiments suggest.

Efficient transmission of subthreshold signals in complex networks of spiking neurons.

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Joaquin J Torres

Full Text Available We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances--that naturally balances the network with excitatory and inhibitory synapses--and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios, including spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it could also occur in actual neural systems as recent psycho-physical experiments suggest.

Bifurcation software in Matlab with applications in neuronal modeling.

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Govaerts, Willy; Sautois, Bart

2005-02-01

Many biological phenomena, notably in neuroscience, can be modeled by dynamical systems. We describe a recent improvement of a Matlab software package for dynamical systems with applications to modeling single neurons and all-to-all connected networks of neurons. The new software features consist of an object-oriented approach to bifurcation computations and the partial inclusion of C-code to speed up the computation. As an application, we study the origin of the spiking behaviour of neurons when the equilibrium state is destabilized by an incoming current. We show that Class II behaviour, i.e. firing with a finite frequency, is possible even if the destabilization occurs through a saddle-node bifurcation. Furthermore, we show that synchronization of an all-to-all connected network of such neurons with only excitatory connections is also possible in this case.

How pattern formation in ring networks of excitatory and inhibitory spiking neurons depends on the input current regime.

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Kriener, Birgit; Helias, Moritz; Rotter, Stefan; Diesmann, Markus; Einevoll, Gaute T

2013-01-01

Pattern formation, i.e., the generation of an inhomogeneous spatial activity distribution in a dynamical system with translation invariant structure, is a well-studied phenomenon in neuronal network dynamics, specifically in neural field models. These are population models to describe the spatio-temporal dynamics of large groups of neurons in terms of macroscopic variables such as population firing rates. Though neural field models are often deduced from and equipped with biophysically meaningful properties, a direct mapping to simulations of individual spiking neuron populations is rarely considered. Neurons have a distinct identity defined by their action on their postsynaptic targets. In its simplest form they act either excitatorily or inhibitorily. When the distribution of neuron identities is assumed to be periodic, pattern formation can be observed, given the coupling strength is supracritical, i.e., larger than a critical weight. We find that this critical weight is strongly dependent on the characteristics of the neuronal input, i.e., depends on whether neurons are mean- or fluctuation driven, and different limits in linearizing the full non-linear system apply in order to assess stability. In particular, if neurons are mean-driven, the linearization has a very simple form and becomes independent of both the fixed point firing rate and the variance of the input current, while in the very strongly fluctuation-driven regime the fixed point rate, as well as the input mean and variance are important parameters in the determination of the critical weight. We demonstrate that interestingly even in "intermediate" regimes, when the system is technically fluctuation-driven, the simple linearization neglecting the variance of the input can yield the better prediction of the critical coupling strength. We moreover analyze the effects of structural randomness by rewiring individual synapses or redistributing weights, as well as coarse-graining on the formation of

Simulating synchronization in neuronal networks

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Fink, Christian G.

2016-06-01

We discuss several techniques used in simulating neuronal networks by exploring how a network's connectivity structure affects its propensity for synchronous spiking. Network connectivity is generated using the Watts-Strogatz small-world algorithm, and two key measures of network structure are described. These measures quantify structural characteristics that influence collective neuronal spiking, which is simulated using the leaky integrate-and-fire model. Simulations show that adding a small number of random connections to an otherwise lattice-like connectivity structure leads to a dramatic increase in neuronal synchronization.

Competition model for aperiodic stochastic resonance in a Fitzhugh-Nagumo model of cardiac sensory neurons.

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Kember, G C; Fenton, G A; Armour, J A; Kalyaniwalla, N

2001-04-01

Regional cardiac control depends upon feedback of the status of the heart from afferent neurons responding to chemical and mechanical stimuli as transduced by an array of sensory neurites. Emerging experimental evidence shows that neural control in the heart may be partially exerted using subthreshold inputs that are amplified by noisy mechanical fluctuations. This amplification is known as aperiodic stochastic resonance (ASR). Neural control in the noisy, subthreshold regime is difficult to see since there is a near absence of any correlation between input and the output, the latter being the average firing (spiking) rate of the neuron. This lack of correlation is unresolved by traditional energy models of ASR since these models are unsuitable for identifying "cause and effect" between such inputs and outputs. In this paper, the "competition between averages" model is used to determine what portion of a noisy, subthreshold input is responsible, on average, for the output of sensory neurons as represented by the Fitzhugh-Nagumo equations. A physiologically relevant conclusion of this analysis is that a nearly constant amount of input is responsible for a spike, on average, and this amount is approximately independent of the firing rate. Hence, correlation measures are generally reduced as the firing rate is lowered even though neural control under this model is actually unaffected.

Transformation-invariant visual representations in self-organizing spiking neural networks.

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Evans, Benjamin D; Stringer, Simon M

2012-01-01

The ventral visual pathway achieves object and face recognition by building transformation-invariant representations from elementary visual features. In previous computer simulation studies with rate-coded neural networks, the development of transformation-invariant representations has been demonstrated using either of two biologically plausible learning mechanisms, Trace learning and Continuous Transformation (CT) learning. However, it has not previously been investigated how transformation-invariant representations may be learned in a more biologically accurate spiking neural network. A key issue is how the synaptic connection strengths in such a spiking network might self-organize through Spike-Time Dependent Plasticity (STDP) where the change in synaptic strength is dependent on the relative times of the spikes emitted by the presynaptic and postsynaptic neurons rather than simply correlated activity driving changes in synaptic efficacy. Here we present simulations with conductance-based integrate-and-fire (IF) neurons using a STDP learning rule to address these gaps in our understanding. It is demonstrated that with the appropriate selection of model parameters and training regime, the spiking network model can utilize either Trace-like or CT-like learning mechanisms to achieve transform-invariant representations.

Transform-invariant visual representations in self-organizing spiking neural networks

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Benjamin eEvans

2012-07-01

Full Text Available The ventral visual pathway achieves object and face recognition by building transform-invariant representations from elementary visual features. In previous computer simulation studies with rate-coded neural networks, the development of transform invariant representations has been demonstrated using either of two biologically plausible learning mechanisms, Trace learning and Continuous Transformation (CT learning. However, it has not previously been investigated how transform invariant representations may be learned in a more biologically accurate spiking neural network. A key issue is how the synaptic connection strengths in such a spiking network might self-organize through Spike-Time Dependent Plasticity (STDP where the change in synaptic strength is dependent on the relative times of the spikes emitted by the pre- and postsynaptic neurons rather than simply correlated activity driving changes in synaptic efficacy. Here we present simulations with conductance-based integrate-and-fire (IF neurons using a STDP learning rule to address these gaps in our understanding. It is demonstrated that with the appropriate selection of model pa- rameters and training regime, the spiking network model can utilize either Trace-like or CT-like learning mechanisms to achieve transform-invariant representations.

Event-Driven Contrastive Divergence for Spiking Neuromorphic Systems

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Emre eNeftci

2014-01-01

Full Text Available Restricted Boltzmann Machines (RBMs and Deep Belief Networks have been demonstrated to perform efficiently in variety of applications, such as dimensionality reduction, feature learning, and classification. Their implementation on neuromorphic hardware platforms emulating large-scale networks of spiking neurons can have significant advantages from the perspectives of scalability, power dissipation and real-time interfacing with the environment. However the traditional RBM architecture and the commonly used training algorithm known as Contrastive Divergence (CD are based on discrete updates and exact arithmetics which do not directly map onto a dynamical neural substrate. Here, we present an event-driven variation of CD to train a RBM constructed with Integrate & Fire (I&F neurons, that is constrained by the limitations of existing and near future neuromorphic hardware platforms. Our strategy is based on neural sampling, which allows us to synthesize a spiking neural network that samples from a target Boltzmann distribution. The reverberating activity of the network replaces the discrete steps of the CD algorithm, while Spike Time Dependent Plasticity (STDP carries out the weight updates in an online, asynchronous fashion.We demonstrate our approach by training an RBM composed of leaky I&F neurons with STDP synapses to learn a generative model of the MNIST hand-written digit dataset, and by testing it in recognition, generation and cue integration tasks. Our results contribute to a machine learning-driven approach for synthesizing networks of spiking neurons capable of carrying out practical, high-level functionality.

Event-driven contrastive divergence for spiking neuromorphic systems.

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Neftci, Emre; Das, Srinjoy; Pedroni, Bruno; Kreutz-Delgado, Kenneth; Cauwenberghs, Gert

2013-01-01

Restricted Boltzmann Machines (RBMs) and Deep Belief Networks have been demonstrated to perform efficiently in a variety of applications, such as dimensionality reduction, feature learning, and classification. Their implementation on neuromorphic hardware platforms emulating large-scale networks of spiking neurons can have significant advantages from the perspectives of scalability, power dissipation and real-time interfacing with the environment. However, the traditional RBM architecture and the commonly used training algorithm known as Contrastive Divergence (CD) are based on discrete updates and exact arithmetics which do not directly map onto a dynamical neural substrate. Here, we present an event-driven variation of CD to train a RBM constructed with Integrate & Fire (I&F) neurons, that is constrained by the limitations of existing and near future neuromorphic hardware platforms. Our strategy is based on neural sampling, which allows us to synthesize a spiking neural network that samples from a target Boltzmann distribution. The recurrent activity of the network replaces the discrete steps of the CD algorithm, while Spike Time Dependent Plasticity (STDP) carries out the weight updates in an online, asynchronous fashion. We demonstrate our approach by training an RBM composed of leaky I&F neurons with STDP synapses to learn a generative model of the MNIST hand-written digit dataset, and by testing it in recognition, generation and cue integration tasks. Our results contribute to a machine learning-driven approach for synthesizing networks of spiking neurons capable of carrying out practical, high-level functionality.

Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns

International Nuclear Information System (INIS)

Gu Hua-Guang; Chen Sheng-Gen; Li Yu-Ye

2015-01-01

We investigated the synchronization dynamics of a coupled neuronal system composed of two identical Chay model neurons. The Chay model showed coexisting period-1 and period-2 bursting patterns as a parameter and initial values are varied. We simulated multiple periodic and chaotic bursting patterns with non-(NS), burst phase (BS), spike phase (SS), complete (CS), and lag synchronization states. When the coexisting behavior is near period-2 bursting, the transitions of synchronization states of the coupled system follows very complex transitions that begins with transitions between BS and SS, moves to transitions between CS and SS, and to CS. Most initial values lead to the CS state of period-2 bursting while only a few lead to the CS state of period-1 bursting. When the coexisting behavior is near period-1 bursting, the transitions begin with NS, move to transitions between SS and BS, to transitions between SS and CS, and then to CS. Most initial values lead to the CS state of period-1 bursting but a few lead to the CS state of period-2 bursting. The BS was identified as chaos synchronization. The patterns for NS and transitions between BS and SS are insensitive to initial values. The patterns for transitions between CS and SS and the CS state are sensitive to them. The number of spikes per burst of non-CS bursting increases with increasing coupling strength. These results not only reveal the initial value- and parameter-dependent synchronization transitions of coupled systems with coexisting behaviors, but also facilitate interpretation of various bursting patterns and synchronization transitions generated in the nervous system with weak coupling strength. (paper)

Differential Activation of Fast-Spiking and Regular-Firing Neuron Populations During Movement and Reward in the Dorsal Medial Frontal Cortex

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Insel, Nathan; Barnes, Carol A.

2015-01-01

The medial prefrontal cortex is thought to be important for guiding behavior according to an animal's expectations. Efforts to decode the region have focused not only on the question of what information it computes, but also how distinct circuit components become engaged during behavior. We find that the activity of regular-firing, putative projection neurons contains rich information about behavioral context and firing fields cluster around reward sites, while activity among putative inhibitory and fast-spiking neurons is most associated with movement and accompanying sensory stimulation. These dissociations were observed even between adjacent neurons with apparently reciprocal, inhibitory–excitatory connections. A smaller population of projection neurons with burst-firing patterns did not show clustered firing fields around rewards; these neurons, although heterogeneous, were generally less selective for behavioral context than regular-firing cells. The data suggest a network that tracks an animal's behavioral situation while, at the same time, regulating excitation levels to emphasize high valued positions. In this scenario, the function of fast-spiking inhibitory neurons is to constrain network output relative to incoming sensory flow. This scheme could serve as a bridge between abstract sensorimotor information and single-dimensional codes for value, providing a neural framework to generate expectations from behavioral state. PMID:24700585

Multiplicative multifractal modeling and discrimination of human neuronal activity

International Nuclear Information System (INIS)

Zheng Yi; Gao Jianbo; Sanchez, Justin C.; Principe, Jose C.; Okun, Michael S.

2005-01-01

Understanding neuronal firing patterns is one of the most important problems in theoretical neuroscience. It is also very important for clinical neurosurgery. In this Letter, we introduce a computational procedure to examine whether neuronal firing recordings could be characterized by cascade multiplicative multifractals. By analyzing raw recording data as well as generated spike train data from 3 patients collected in two brain areas, the globus pallidus externa (GPe) and the globus pallidus interna (GPi), we show that the neural firings are consistent with a multifractal process over certain time scale range (t 1 ,t 2 ), where t 1 is argued to be not smaller than the mean inter-spike-interval of neuronal firings, while t 2 may be related to the time that neuronal signals propagate in the major neural branching structures pertinent to GPi and GPe. The generalized dimension spectrum D q effectively differentiates the two brain areas, both intra- and inter-patients. For distinguishing between GPe and GPi, it is further shown that the cascade model is more effective than the methods recently examined by Schiff et al. as well as the Fano factor analysis. Therefore, the methodology may be useful in developing computer aided tools to help clinicians perform precision neurosurgery in the operating room

Motor control by precisely timed spike patterns

DEFF Research Database (Denmark)

Srivastava, Kyle H; Holmes, Caroline M; Vellema, Michiel

2017-01-01

whether the information in spike timing actually plays a role in brain function. By examining the activity of individual motor units (the muscle fibers innervated by a single motor neuron) and manipulating patterns of activation of these neurons, we provide both correlative and causal evidence......A fundamental problem in neuroscience is understanding how sequences of action potentials ("spikes") encode information about sensory signals and motor outputs. Although traditional theories assume that this information is conveyed by the total number of spikes fired within a specified time...... interval (spike rate), recent studies have shown that additional information is carried by the millisecond-scale timing patterns of action potentials (spike timing). However, it is unknown whether or how subtle differences in spike timing drive differences in perception or behavior, leaving it unclear...

SuperSpike: Supervised Learning in Multilayer Spiking Neural Networks.

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Zenke, Friedemann; Ganguli, Surya

2018-04-13

A vast majority of computation in the brain is performed by spiking neural networks. Despite the ubiquity of such spiking, we currently lack an understanding of how biological spiking neural circuits learn and compute in vivo, as well as how we can instantiate such capabilities in artificial spiking circuits in silico. Here we revisit the problem of supervised learning in temporally coding multilayer spiking neural networks. First, by using a surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based three-factor learning rule capable of training multilayer networks of deterministic integrate-and-fire neurons to perform nonlinear computations on spatiotemporal spike patterns. Second, inspired by recent results on feedback alignment, we compare the performance of our learning rule under different credit assignment strategies for propagating output errors to hidden units. Specifically, we test uniform, symmetric, and random feedback, finding that simpler tasks can be solved with any type of feedback, while more complex tasks require symmetric feedback. In summary, our results open the door to obtaining a better scientific understanding of learning and computation in spiking neural networks by advancing our ability to train them to solve nonlinear problems involving transformations between different spatiotemporal spike time patterns.

On the Universality and Non-Universality of Spiking Neural P Systems With Rules on Synapses.

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Song, Tao; Xu, Jinbang; Pan, Linqiang

2015-12-01

Spiking neural P systems with rules on synapses are a new variant of spiking neural P systems. In the systems, the neuron contains only spikes, while the spiking/forgetting rules are moved on the synapses. It was obtained that such system with 30 neurons (using extended spiking rules) or with 39 neurons (using standard spiking rules) is Turing universal. In this work, this number is improved to 6. Specifically, we construct a Turing universal spiking neural P system with rules on synapses having 6 neurons, which can generate any set of Turing computable natural numbers. As well, it is obtained that spiking neural P system with rules on synapses having less than two neurons are not Turing universal: i) such systems having one neuron can characterize the family of finite sets of natural numbers; ii) the family of sets of numbers generated by the systems having two neurons is included in the family of semi-linear sets of natural numbers.

A spiking network model of cerebellar Purkinje cells and molecular layer interneurons exhibiting irregular firing

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William eLennon

2014-12-01

Full Text Available While the anatomy of the cerebellar microcircuit is well studied, how it implements cerebellar function is not understood. A number of models have been proposed to describe this mechanism but few emphasize the role of the vast network Purkinje cells (PKJs form with the molecular layer interneurons (MLIs – the stellate and basket cells. We propose a model of the MLI-PKJ network composed of simple spiking neurons incorporating the major anatomical and physiological features. In computer simulations, the model reproduces the irregular firing patterns observed in PKJs and MLIs in vitro and a shift toward faster, more regular firing patterns when inhibitory synaptic currents are blocked. In the model, the time between PKJ spikes is shown to be proportional to the amount of feedforward inhibition from an MLI on average. The two key elements of the model are: (1 spontaneously active PKJs and MLIs due to an endogenous depolarizing current, and (2 adherence to known anatomical connectivity along a parasagittal strip of cerebellar cortex. We propose this model to extend previous spiking network models of the cerebellum and for further computational investigation into the role of irregular firing and MLIs in cerebellar learning and function.

Simple networks for spike-timing-based computation, with application to olfactory processing.

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Brody, Carlos D; Hopfield, J J

2003-03-06

Spike synchronization across neurons can be selective for the situation where neurons are driven at similar firing rates, a "many are equal" computation. This can be achieved in the absence of synaptic interactions between neurons, through phase locking to a common underlying oscillatory potential. Based on this principle, we instantiate an algorithm for robust odor recognition into a model network of spiking neurons whose main features are taken from known properties of biological olfactory systems. Here, recognition of odors is signaled by spike synchronization of specific subsets of "mitral cells." This synchronization is highly odor selective and invariant to a wide range of odor concentrations. It is also robust to the presence of strong distractor odors, thus allowing odor segmentation within complex olfactory scenes. Information about odors is encoded in both the identity of glomeruli activated above threshold (1 bit of information per glomerulus) and in the analog degree of activation of the glomeruli (approximately 3 bits per glomerulus).

Striatal fast-spiking interneurons: from firing patterns to postsynaptic impact

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Andreas eKlaus

2011-07-01

Full Text Available In the striatal microcircuit, fast-spiking (FS interneurons have an important role in mediating inhibition onto neighboring medium spiny (MS projection neurons. In this study, we combined computational modeling with in vitro and in vivo electrophysiological measurements to investigate FS cells in terms of their discharge properties and their synaptic efficacies onto MS neurons. In vivo firing of striatal FS interneurons is characterized by a high firing variability. It is not known, however, if this variability results from the input that FS cells receive, or if it is promoted by the stuttering spike behavior of these neurons. Both our model and measurements in vitro show that FS neurons that exhibit random stuttering discharge in response to steady depolarization, do not show the typical stuttering behavior when they receive fluctuating input. Importantly, our model predicts that electrically coupled FS cells show substantial spike synchronization only when they are in the stuttering regime. Therefore, together with the lack of synchronized firing of striatal FS interneurons that has been reported in vivo, these results suggest that neighboring FS neurons are not in the stuttering regime simultaneously and that in vivo FS firing variability is more likely determined by the input fluctuations. Furthermore, the variability in FS firing is translated to variability in the postsynaptic amplitudes in MS neurons due to the strong synaptic depression of the FS-to-MS synapse. Our results support the idea that these synapses operate over a wide range from strongly depressed to almost fully recovered. The strong inhibitory effects that FS cells can impose on their postsynaptic targets, and the fact that the FS-to-MS synapse model showed substantial depression over extended periods of time might indicate the importance of cooperative effects of multiple presynaptic FS interneurons and the precise orchestration of their activity.

A supervised learning rule for classification of spatiotemporal spike patterns.

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Lilin Guo; Zhenzhong Wang; Adjouadi, Malek

2016-08-01

This study introduces a novel supervised algorithm for spiking neurons that take into consideration synapse delays and axonal delays associated with weights. It can be utilized for both classification and association and uses several biologically influenced properties, such as axonal and synaptic delays. This algorithm also takes into consideration spike-timing-dependent plasticity as in Remote Supervised Method (ReSuMe). This paper focuses on the classification aspect alone. Spiked neurons trained according to this proposed learning rule are capable of classifying different categories by the associated sequences of precisely timed spikes. Simulation results have shown that the proposed learning method greatly improves classification accuracy when compared to the Spike Pattern Association Neuron (SPAN) and the Tempotron learning rule.

Coding and decoding with adapting neurons: a population approach to the peri-stimulus time histogram.

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Naud, Richard; Gerstner, Wulfram

2012-01-01

The response of a neuron to a time-dependent stimulus, as measured in a Peri-Stimulus-Time-Histogram (PSTH), exhibits an intricate temporal structure that reflects potential temporal coding principles. Here we analyze the encoding and decoding of PSTHs for spiking neurons with arbitrary refractoriness and adaptation. As a modeling framework, we use the spike response model, also known as the generalized linear neuron model. Because of refractoriness, the effect of the most recent spike on the spiking probability a few milliseconds later is very strong. The influence of the last spike needs therefore to be described with high precision, while the rest of the neuronal spiking history merely introduces an average self-inhibition or adaptation that depends on the expected number of past spikes but not on the exact spike timings. Based on these insights, we derive a 'quasi-renewal equation' which is shown to yield an excellent description of the firing rate of adapting neurons. We explore the domain of validity of the quasi-renewal equation and compare it with other rate equations for populations of spiking neurons. The problem of decoding the stimulus from the population response (or PSTH) is addressed analogously. We find that for small levels of activity and weak adaptation, a simple accumulator of the past activity is sufficient to decode the original input, but when refractory effects become large decoding becomes a non-linear function of the past activity. The results presented here can be applied to the mean-field analysis of coupled neuron networks, but also to arbitrary point processes with negative self-interaction.

Transitions to Synchrony in Coupled Bursting Neurons

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Dhamala, Mukeshwar; Jirsa, Viktor K.; Ding, Mingzhou

2004-01-01

Certain cells in the brain, for example, thalamic neurons during sleep, show spike-burst activity. We study such spike-burst neural activity and the transitions to a synchronized state using a model of coupled bursting neurons. In an electrically coupled network, we show that the increase of coupling strength increases incoherence first and then induces two different transitions to synchronized states, one associated with bursts and the other with spikes. These sequential transitions to synchronized states are determined by the zero crossings of the maximum transverse Lyapunov exponents. These results suggest that synchronization of spike-burst activity is a multi-time-scale phenomenon and burst synchrony is a precursor to spike synchrony.

Transitions to synchrony in coupled bursting neurons

International Nuclear Information System (INIS)

Dhamala, Mukeshwar; Jirsa, Viktor K.; Ding Mingzhou

2004-01-01

Certain cells in the brain, for example, thalamic neurons during sleep, show spike-burst activity. We study such spike-burst neural activity and the transitions to a synchronized state using a model of coupled bursting neurons. In an electrically coupled network, we show that the increase of coupling strength increases incoherence first and then induces two different transitions to synchronized states, one associated with bursts and the other with spikes. These sequential transitions to synchronized states are determined by the zero crossings of the maximum transverse Lyapunov exponents. These results suggest that synchronization of spike-burst activity is a multi-time-scale phenomenon and burst synchrony is a precursor to spike synchrony

Coherence resonance in globally coupled neuronal networks with different neuron numbers

International Nuclear Information System (INIS)

Ning Wei-Lian; Zhang Zheng-Zhen; Zeng Shang-You; Luo Xiao-Shu; Hu Jin-Lin; Zeng Shao-Wen; Qiu Yi; Wu Hui-Si

2012-01-01

Because a brain consists of tremendous neuronal networks with different neuron numbers ranging from tens to tens of thousands, we study the coherence resonance due to ion channel noises in globally coupled neuronal networks with different neuron numbers. We confirm that for all neuronal networks with different neuron numbers there exist the array enhanced coherence resonance and the optimal synaptic conductance to cause the maximal spiking coherence. Furthermoremore, the enhancement effects of coupling on spiking coherence and on optimal synaptic conductance are almost the same, regardless of the neuron numbers in the neuronal networks. Therefore for all the neuronal networks with different neuron numbers in the brain, relative weak synaptic conductance (0.1 mS/cm 2 ) is sufficient to induce the maximal spiking coherence and the best sub-threshold signal encoding. (interdisciplinary physics and related areas of science and technology)

Population density models of integrate-and-fire neurons with jumps: well-posedness.

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Dumont, Grégory; Henry, Jacques

2013-09-01

In this paper we study the well-posedness of different models of population of leaky integrate-and-fire neurons with a population density approach. The synaptic interaction between neurons is modeled by a potential jump at the reception of a spike. We study populations that are self excitatory or self inhibitory. We distinguish the cases where this interaction is instantaneous from the one where there is a repartition of conduction delays. In the case of a bounded density of delays both excitatory and inhibitory population models are shown to be well-posed. But without conduction delay the solution of the model of self excitatory neurons may blow up. We analyze the different behaviours of the model with jumps compared to its diffusion approximation.

Impact of spike train autostructure on probability distribution of joint spike events.

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Pipa, Gordon; Grün, Sonja; van Vreeswijk, Carl

2013-05-01

The discussion whether temporally coordinated spiking activity really exists and whether it is relevant has been heated over the past few years. To investigate this issue, several approaches have been taken to determine whether synchronized events occur significantly above chance, that is, whether they occur more often than expected if the neurons fire independently. Most investigations ignore or destroy the autostructure of the spiking activity of individual cells or assume Poissonian spiking as a model. Such methods that ignore the autostructure can significantly bias the coincidence statistics. Here, we study the influence of the autostructure on the probability distribution of coincident spiking events between tuples of mutually independent non-Poisson renewal processes. In particular, we consider two types of renewal processes that were suggested as appropriate models of experimental spike trains: a gamma and a log-normal process. For a gamma process, we characterize the shape of the distribution analytically with the Fano factor (FFc). In addition, we perform Monte Carlo estimations to derive the full shape of the distribution and the probability for false positives if a different process type is assumed as was actually present. We also determine how manipulations of such spike trains, here dithering, used for the generation of surrogate data change the distribution of coincident events and influence the significance estimation. We find, first, that the width of the coincidence count distribution and its FFc depend critically and in a nontrivial way on the detailed properties of the structure of the spike trains as characterized by the coefficient of variation CV. Second, the dependence of the FFc on the CV is complex and mostly nonmonotonic. Third, spike dithering, even if as small as a fraction of the interspike interval, can falsify the inference on coordinated firing.

Gradient Learning in Spiking Neural Networks by Dynamic Perturbation of Conductances

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Fiete, Ila R.; Seung, H. Sebastian

2006-01-01

We present a method of estimating the gradient of an objective function with respect to the synaptic weights of a spiking neural network. The method works by measuring the fluctuations in the objective function in response to dynamic perturbation of the membrane conductances of the neurons. It is compatible with recurrent networks of conductance-based model neurons with dynamic synapses. The method can be interpreted as a biologically plausible synaptic learning rule, if the dynamic perturbations are generated by a special class of 'empiric' synapses driven by random spike trains from an external source

Phase-locking of bursting neuronal firing to dominant LFP frequency components.

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Constantinou, Maria; Elijah, Daniel H; Squirrell, Daniel; Gigg, John; Montemurro, Marcelo A

2015-10-01

Neuronal firing in the hippocampal formation relative to the phase of local field potentials (LFP) has a key role in memory processing and spatial navigation. Firing can be in either tonic or burst mode. Although bursting neurons are common in the hippocampal formation, the characteristics of their locking to LFP phase are not completely understood. We investigated phase-locking properties of bursting neurons using simulations generated by a dual compartmental model of a pyramidal neuron adapted to match the bursting activity in the subiculum of a rat. The model was driven with stochastic input signals containing a power spectral profile consistent with physiologically relevant frequencies observed in LFP. The single spikes and spike bursts fired by the model were locked to a preferred phase of the predominant frequency band where there was a peak in the power of the driving signal. Moreover, the preferred phase of locking shifted with increasing burst size, providing evidence that LFP phase can be encoded by burst size. We also provide initial support for the model results by analysing example data of spontaneous LFP and spiking activity recorded from the subiculum of a single urethane-anaesthetised rat. Subicular neurons fired single spikes, two-spike bursts and larger bursts that locked to a preferred phase of either dominant slow oscillations or theta rhythms within the LFP, according to the model prediction. Both power-modulated phase-locking and gradual shift in the preferred phase of locking as a function of burst size suggest that neurons can use bursts to encode timing information contained in LFP phase into a spike-count code. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

Visually Evoked Spiking Evolves While Spontaneous Ongoing Dynamics Persist

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Huys, Raoul; Jirsa, Viktor K.; Darokhan, Ziauddin; Valentiniene, Sonata; Roland, Per E.

2016-01-01

Neurons in the primary visual cortex spontaneously spike even when there are no visual stimuli. It is unknown whether the spiking evoked by visual stimuli is just a modification of the spontaneous ongoing cortical spiking dynamics or whether the spontaneous spiking state disappears and is replaced by evoked spiking. This study of laminar recordings of spontaneous spiking and visually evoked spiking of neurons in the ferret primary visual cortex shows that the spiking dynamics does not change: the spontaneous spiking as well as evoked spiking is controlled by a stable and persisting fixed point attractor. Its existence guarantees that evoked spiking return to the spontaneous state. However, the spontaneous ongoing spiking state and the visual evoked spiking states are qualitatively different and are separated by a threshold (separatrix). The functional advantage of this organization is that it avoids the need for a system reorganization following visual stimulation, and impedes the transition of spontaneous spiking to evoked spiking and the propagation of spontaneous spiking from layer 4 to layers 2–3. PMID:26778982

Fast and Efficient Asynchronous Neural Computation with Adapting Spiking Neural Networks

NARCIS (Netherlands)

D. Zambrano (Davide); S.M. Bohte (Sander)

2016-01-01

textabstractBiological neurons communicate with a sparing exchange of pulses - spikes. It is an open question how real spiking neurons produce the kind of powerful neural computation that is possible with deep artificial neural networks, using only so very few spikes to communicate. Building on

Enhanced polychronisation in a spiking network with metaplasticity

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Mira eGuise

2015-02-01

Full Text Available Computational models of metaplasticity have usually focused on the modeling of single synapses (Shouval et al., 2002. In this paper we study the effect of metaplasticity on network behavior. Our guiding assumption is that the primary purpose of metaplasticity is to regulate synaptic plasticity, by increasing it when input is low and decreasing it when input is high. For our experiments we adopt a model of metaplasticity that demonstrably has this effect for a single synapse; our primary interest is in how metaplasticity thus defined affects network-level phenomena. We focus on a network-level phenomenon called polychronicity, that has a potential role in representation and memory. A network with polychronicity has the ability to produce non-synchronous but precisely timed sequences of neural firing events that can arise from strongly connected groups of neurons called polychronous neural groups (Izhikevich et al., 2004; Izhikevich, 2006a. Polychronous groups (PNGs develop readily when spiking networks are exposed to repeated spatio-temporal stimuli under the influence of spike-timing-dependent plasticity (STDP, but are sensitive to changes in synaptic weight distribution. We use a technique we have recently developed called Response Fingerprinting to show that PNGs formed in the presence of metaplasticity are significantly larger than those with no metaplasticity. A potential mechanism for this enhancement is proposed that links an inherent property of integrator type neurons called spike latency to an increase in the tolerance of PNG neurons to jitter in their inputs.

Bayesian Inference and Online Learning in Poisson Neuronal Networks.

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Huang, Yanping; Rao, Rajesh P N

2016-08-01

Motivated by the growing evidence for Bayesian computation in the brain, we show how a two-layer recurrent network of Poisson neurons can perform both approximate Bayesian inference and learning for any hidden Markov model. The lower-layer sensory neurons receive noisy measurements of hidden world states. The higher-layer neurons infer a posterior distribution over world states via Bayesian inference from inputs generated by sensory neurons. We demonstrate how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carlo methods such as particle filtering. Each spike in a higher-layer neuron represents a sample of a particular hidden world state. The spiking activity across the neural population approximates the posterior distribution over hidden states. In this model, variability in spiking is regarded not as a nuisance but as an integral feature that provides the variability necessary for sampling during inference. We demonstrate how the network can learn the likelihood model, as well as the transition probabilities underlying the dynamics, using a Hebbian learning rule. We present results illustrating the ability of the network to perform inference and learning for arbitrary hidden Markov models.

Statistical characteristics of climbing fiber spikes necessary for efficient cerebellar learning.

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Kuroda, S; Yamamoto, K; Miyamoto, H; Doya, K; Kawat, M

2001-03-01

Mean firing rates (MFRs), with analogue values, have thus far been used as information carriers of neurons in most brain theories of learning. However, the neurons transmit the signal by spikes, which are discrete events. The climbing fibers (CFs), which are known to be essential for cerebellar motor learning, fire at the ultra-low firing rates (around 1 Hz), and it is not yet understood theoretically how high-frequency information can be conveyed and how learning of smooth and fast movements can be achieved. Here we address whether cerebellar learning can be achieved by CF spikes instead of conventional MFR in an eye movement task, such as the ocular following response (OFR), and an arm movement task. There are two major afferents into cerebellar Purkinje cells: parallel fiber (PF) and CF, and the synaptic weights between PFs and Purkinje cells have been shown to be modulated by the stimulation of both types of fiber. The modulation of the synaptic weights is regulated by the cerebellar synaptic plasticity. In this study we simulated cerebellar learning using CF signals as spikes instead of conventional MFR. To generate the spikes we used the following four spike generation models: (1) a Poisson model in which the spike interval probability follows a Poisson distribution, (2) a gamma model in which the spike interval probability follows the gamma distribution, (3) a max model in which a spike is generated when a synaptic input reaches maximum, and (4) a threshold model in which a spike is generated when the input crosses a certain small threshold. We found that, in an OFR task with a constant visual velocity, learning was successful with stochastic models, such as Poisson and gamma models, but not in the deterministic models, such as max and threshold models. In an OFR with a stepwise velocity change and an arm movement task, learning could be achieved only in the Poisson model. In addition, for efficient cerebellar learning, the distribution of CF spike

A compound memristive synapse model for statistical learning through STDP in spiking neural networks

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Johannes eBill

2014-12-01

Full Text Available Memristors have recently emerged as promising circuit elements to mimic the function of biological synapses in neuromorphic computing. The fabrication of reliable nanoscale memristive synapses, that feature continuous conductance changes based on the timing of pre- and postsynaptic spikes, has however turned out to be challenging. In this article, we propose an alternative approach, the compound memristive synapse, that circumvents this problem by the use of memristors with binary memristive states. A compound memristive synapse employs multiple bistable memristors in parallel to jointly form one synapse, thereby providing a spectrum of synaptic efficacies. We investigate the computational implications of synaptic plasticity in the compound synapse by integrating the recently observed phenomenon of stochastic filament formation into an abstract model of stochastic switching. Using this abstract model, we first show how standard pulsing schemes give rise to spike-timing dependent plasticity (STDP with a stabilizing weight dependence in compound synapses. In a next step, we study unsupervised learning with compound synapses in networks of spiking neurons organized in a winner-take-all architecture. Our theoretical analysis reveals that compound-synapse STDP implements generalized Expectation-Maximization in the spiking network. Specifically, the emergent synapse configuration represents the most salient features of the input distribution in a Mixture-of-Gaussians generative model. Furthermore, the network’s spike response to spiking input streams approximates a well-defined Bayesian posterior distribution. We show in computer simulations how such networks learn to represent high-dimensional distributions over images of handwritten digits with high fidelity even in presence of substantial device variations and under severe noise conditions. Therefore, the compound memristive synapse may provide a synaptic design principle for future neuromorphic

A compound memristive synapse model for statistical learning through STDP in spiking neural networks.

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Bill, Johannes; Legenstein, Robert

2014-01-01

Memristors have recently emerged as promising circuit elements to mimic the function of biological synapses in neuromorphic computing. The fabrication of reliable nanoscale memristive synapses, that feature continuous conductance changes based on the timing of pre- and postsynaptic spikes, has however turned out to be challenging. In this article, we propose an alternative approach, the compound memristive synapse, that circumvents this problem by the use of memristors with binary memristive states. A compound memristive synapse employs multiple bistable memristors in parallel to jointly form one synapse, thereby providing a spectrum of synaptic efficacies. We investigate the computational implications of synaptic plasticity in the compound synapse by integrating the recently observed phenomenon of stochastic filament formation into an abstract model of stochastic switching. Using this abstract model, we first show how standard pulsing schemes give rise to spike-timing dependent plasticity (STDP) with a stabilizing weight dependence in compound synapses. In a next step, we study unsupervised learning with compound synapses in networks of spiking neurons organized in a winner-take-all architecture. Our theoretical analysis reveals that compound-synapse STDP implements generalized Expectation-Maximization in the spiking network. Specifically, the emergent synapse configuration represents the most salient features of the input distribution in a Mixture-of-Gaussians generative model. Furthermore, the network's spike response to spiking input streams approximates a well-defined Bayesian posterior distribution. We show in computer simulations how such networks learn to represent high-dimensional distributions over images of handwritten digits with high fidelity even in presence of substantial device variations and under severe noise conditions. Therefore, the compound memristive synapse may provide a synaptic design principle for future neuromorphic architectures.

An Overview of Bayesian Methods for Neural Spike Train Analysis

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Zhe Chen

2013-01-01

Full Text Available Neural spike train analysis is an important task in computational neuroscience which aims to understand neural mechanisms and gain insights into neural circuits. With the advancement of multielectrode recording and imaging technologies, it has become increasingly demanding to develop statistical tools for analyzing large neuronal ensemble spike activity. Here we present a tutorial overview of Bayesian methods and their representative applications in neural spike train analysis, at both single neuron and population levels. On the theoretical side, we focus on various approximate Bayesian inference techniques as applied to latent state and parameter estimation. On the application side, the topics include spike sorting, tuning curve estimation, neural encoding and decoding, deconvolution of spike trains from calcium imaging signals, and inference of neuronal functional connectivity and synchrony. Some research challenges and opportunities for neural spike train analysis are discussed.

Dynamics and spike trains statistics in conductance-based integrate-and-fire neural networks with chemical and electric synapses

International Nuclear Information System (INIS)

Cofré, Rodrigo; Cessac, Bruno

2013-01-01

We investigate the effect of electric synapses (gap junctions) on collective neuronal dynamics and spike statistics in a conductance-based integrate-and-fire neural network, driven by Brownian noise, where conductances depend upon spike history. We compute explicitly the time evolution operator and show that, given the spike-history of the network and the membrane potentials at a given time, the further dynamical evolution can be written in a closed form. We show that spike train statistics is described by a Gibbs distribution whose potential can be approximated with an explicit formula, when the noise is weak. This potential form encompasses existing models for spike trains statistics analysis such as maximum entropy models or generalized linear models (GLM). We also discuss the different types of correlations: those induced by a shared stimulus and those induced by neurons interactions

A codimension-2 bifurcation controlling endogenous bursting activity and pulse-triggered responses of a neuron model.

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Barnett, William H; Cymbalyuk, Gennady S

2014-01-01

The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals-the duration of the burst and the duration of latency to spiking-are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of

Correlations decrease with propagation of spiking activity in the mouse barrel cortex

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Gayathri Nattar Ranganathan

2011-05-01

Full Text Available Propagation of suprathreshold spiking activity through neuronal populations is important for the function of the central nervous system. Neural correlations have an impact on cortical function particularly on the signaling of information and propagation of spiking activity. Therefore we measured the change in correlations as suprathreshold spiking activity propagated between recurrent neuronal networks of the mammalian cerebral cortex. Using optical methods we recorded spiking activity from large samples of neurons from two neural populations simultaneously. The results indicate that correlations decreased as spiking activity propagated from layer 4 to layer 2/3 in the rodent barrel cortex.

Bursts generate a non-reducible spike-pattern code

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Hugo G Eyherabide

2009-05-01

Full Text Available On the single-neuron level, precisely timed spikes can either constitute firing-rate codes or spike-pattern codes that utilize the relative timing between consecutive spikes. There has been little experimental support for the hypothesis that such temporal patterns contribute substantially to information transmission. Using grasshopper auditory receptors as a model system, we show that correlations between spikes can be used to represent behaviorally relevant stimuli. The correlations reflect the inner structure of the spike train: a succession of burst-like patterns. We demonstrate that bursts with different spike counts encode different stimulus features, such that about 20% of the transmitted information corresponds to discriminating between different features, and the remaining 80% is used to allocate these features in time. In this spike-pattern code, the "what" and the "when" of the stimuli are encoded in the duration of each burst and the time of burst onset, respectively. Given the ubiquity of burst firing, we expect similar findings also for other neural systems.

Application of unfolding transformation in the random matrix theory to analyze in vivo neuronal spike firing during awake and anesthetized conditions

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Risako Kato

2018-03-01

Full Text Available General anesthetics decrease the frequency and density of spike firing. This effect makes it difficult to detect spike regularity. To overcome this problem, we developed a method utilizing the unfolding transformation which analyzes the energy level statistics in the random matrix theory. We regarded the energy axis as time axis of neuron spike and analyzed the time series of cortical neural firing in vivo. Unfolding transformation detected regularities of neural firing while changes in firing densities were associated with pentobarbital. We found that unfolding transformation enables us to compare firing regularity between awake and anesthetic conditions on a universal scale. Keywords: Unfolding transformation, Spike-timing, Regularity

SPICODYN: A Toolbox for the Analysis of Neuronal Network Dynamics and Connectivity from Multi-Site Spike Signal Recordings.

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Pastore, Vito Paolo; Godjoski, Aleksandar; Martinoia, Sergio; Massobrio, Paolo

2018-01-01

We implemented an automated and efficient open-source software for the analysis of multi-site neuronal spike signals. The software package, named SPICODYN, has been developed as a standalone windows GUI application, using C# programming language with Microsoft Visual Studio based on .NET framework 4.5 development environment. Accepted input data formats are HDF5, level 5 MAT and text files, containing recorded or generated time series spike signals data. SPICODYN processes such electrophysiological signals focusing on: spiking and bursting dynamics and functional-effective connectivity analysis. In particular, for inferring network connectivity, a new implementation of the transfer entropy method is presented dealing with multiple time delays (temporal extension) and with multiple binary patterns (high order extension). SPICODYN is specifically tailored to process data coming from different Multi-Electrode Arrays setups, guarantying, in those specific cases, automated processing. The optimized implementation of the Delayed Transfer Entropy and the High-Order Transfer Entropy algorithms, allows performing accurate and rapid analysis on multiple spike trains from thousands of electrodes.

Spatiotemporal Dynamics and Reliable Computations in Recurrent Spiking Neural Networks

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Pyle, Ryan; Rosenbaum, Robert

2017-01-01

Randomly connected networks of excitatory and inhibitory spiking neurons provide a parsimonious model of neural variability, but are notoriously unreliable for performing computations. We show that this difficulty is overcome by incorporating the well-documented dependence of connection probability on distance. Spatially extended spiking networks exhibit symmetry-breaking bifurcations and generate spatiotemporal patterns that can be trained to perform dynamical computations under a reservoir computing framework.

Spatiotemporal Dynamics and Reliable Computations in Recurrent Spiking Neural Networks.

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Pyle, Ryan; Rosenbaum, Robert

2017-01-06

Randomly connected networks of excitatory and inhibitory spiking neurons provide a parsimonious model of neural variability, but are notoriously unreliable for performing computations. We show that this difficulty is overcome by incorporating the well-documented dependence of connection probability on distance. Spatially extended spiking networks exhibit symmetry-breaking bifurcations and generate spatiotemporal patterns that can be trained to perform dynamical computations under a reservoir computing framework.

Mouse neuroblastoma cell-based model and the effect of epileptic events on calcium oscillations and neural spikes

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Kim, Suhwan; Jung, Unsang; Baek, Juyoung; Lee, Sangwon; Jung, Woonggyu; Kim, Jeehyun; Kang, Shinwon

2013-01-01

Recently, mouse neuroblastoma cells have been considered as an attractive model for the study of human neurological and prion diseases, and they have been intensively used as a model system in different areas. For example, the differentiation of neuro2a (N2A) cells, receptor-mediated ion current, and glutamate-induced physiological responses have been actively investigated with these cells. These mouse neuroblastoma N2A cells are of interest because they grow faster than other cells of neural origin and have a number of other advantages. The calcium oscillations and neural spikes of mouse neuroblastoma N2A cells in epileptic conditions are evaluated. Based on our observations of neural spikes in these cells with our proposed imaging modality, we reported that they can be an important model in epileptic activity studies. We concluded that mouse neuroblastoma N2A cells produce epileptic spikes in vitro in the same way as those produced by neurons or astrocytes. This evidence suggests that increased levels of neurotransmitter release due to the enhancement of free calcium from 4-aminopyridine causes the mouse neuroblastoma N2A cells to produce epileptic spikes and calcium oscillations.

The role of degree distribution in shaping the dynamics in networks of sparsely connected spiking neurons

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Alex eRoxin

2011-03-01

Full Text Available Neuronal network models often assume a fixed probability of connectionbetween neurons. This assumption leads to random networks withbinomial in-degree and out-degree distributions which are relatively narrow. Here I study the effect of broaddegree distributions on network dynamics by interpolating between abinomial and a truncated powerlaw distribution for the in-degree andout-degree independently. This is done both for an inhibitory network(I network as well as for the recurrent excitatory connections in anetwork of excitatory and inhibitory neurons (EI network. In bothcases increasing the width of the in-degree distribution affects theglobal state of the network by driving transitions betweenasynchronous behavior and oscillations. This effect is reproduced ina simplified rate model which includes the heterogeneity in neuronalinput due to the in-degree of cells. On the other hand, broadeningthe out-degree distribution is shown to increase the fraction ofcommon inputs to pairs of neurons. This leads to increases in theamplitude of the cross-correlation (CC of synaptic currents. In thecase of the I network, despite strong oscillatory CCs in the currents, CCs of the membrane potential are low due to filtering and reset effects, leading to very weak CCs of the spikecount. In the asynchronous regime ofthe EI network, broadening the out-degree increases the amplitude ofCCs in the recurrent excitatory currents, while CC of the totalcurrent is essentially unaffected as are pairwise spikingcorrelations. This is due to a dynamic balance between excitatoryand inhibitory synaptic currents. In the oscillatory regime, changesin the out-degree can have a large effect on spiking correlations andeven on the qualitative dynamical state of the network.

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks

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Yu, Haitao; Guo, Xinmeng; Wang, Jiang, E-mail: jiangwang@tju.edu.cn; Deng, Bin; Wei, Xile [School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072 (China)

2014-09-01

The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks.

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks

International Nuclear Information System (INIS)

Yu, Haitao; Guo, Xinmeng; Wang, Jiang; Deng, Bin; Wei, Xile

2014-01-01

The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks