Poisson Spike Research Articles

Optimal configurations of spatial scale for grid cell firing under noise and uncertainty

We examined the accuracy with which the location of an agent moving within an environment could be decoded from the simulated firing of systems of grid cells. Grid cells were modelled with Poisson spiking dynamics and organized into multiple ‘modules’ of cells, with firing patterns of similar spatial scale within modules and a wide range of spatial scales across modules. The number of grid cells per module, the spatial scaling factor between modules and the size of the environment were varied. Errors in decoded location can take two forms: small errors of precision and larger errors resulting from ambiguity in decoding periodic firing patterns. With enough cells per module (e.g. eight modules of 100 cells each) grid systems are highly robust to ambiguity errors, even over ranges much larger than the largest grid scale (e.g. over a 500 m range when the maximum grid scale is 264 cm). Results did not depend strongly on the precise organization of scales across modules (geometric, co-prime or random). However, independent spatial noise across modules, which would occur if modules receive independent spatial inputs and might increase with spatial uncertainty, dramatically degrades the performance of the grid system. This effect of spatial uncertainty can be mitigated by uniform expansion of grid scales. Thus, in the realistic regimes simulated here, the optimal overall scale for a grid system represents a trade-off between minimizing spatial uncertainty (requiring large scales) and maximizing precision (requiring small scales). Within this view, the temporary expansion of grid scales observed in novel environments may be an optimal response to increased spatial uncertainty induced by the unfamiliarity of the available spatial cues.

Estimating the fraction of falsely detected spikes in high density microelectrode array recordings based on correlations

High-density microelectrode arrays (MEA) can measure neuronal activity in potentially thousands of units with a high spatial resolution [1]. However due to the small size of the preamplifers, noise artifacts can affect spike detection. Additionally, the MEA chip itself is not perfectly homogeneous and the electrical coupling between the electrodes and a neuron may be weak. Therefore, the characteristics of neuronal spikes and noise are inherently different in each recording channel, such that estimating an average performance of the spike detection would not be representative for individual recording channels. As we aim to observe slow changes in single neuron activity, it is crucial to know how much a change in electrical coupling could potentially affect the number of detected spikes. Here we estimate the quality of spike detection using correlations as an indicator to distinguish between neuronal activity and noise. First we use a threshold-based detection of putative spikes, with a deliberately low threshold to lower the number of undetected spikes. We estimate pairwise correlations between spike trains based on spike ranks rather than time in order to reduce the effects of nonstationarities in the recordings. We then assume that the frequency of spontaneous firing in the neurons is small compared to the evoked firing and check for each detected spike whether we can find correlated units which are active within a short interval around its spike time. For each unit, we compare the relative frequency of such correlated spikes to the frequency that would be obtained by doing the same analysis with a Poisson spike train. This yields a per unit estimate of the fraction of putatively falsely detected spikes and we validate the procedure using shuffled data and recordings of an empty MEA (see Figure ​Figure1.).1.). To investigate the dependency of this method on a specific network dynamics, we apply it to a few sample recordings of a hippocampal culture and a perinatal retina. It is possible to exclude spikes with a low amplitude after doing this analysis and this decreases the fraction of falsely detected spikes, but for the hippocampal cultures this leads to a loss of detected spikes in many units. Figure 1 Correlation-based estimate of the fraction of spikes corresponding to neuronal activity for a low detection threshold. Hippocampal culture, 15 min recording. A: Rasterplot of the activity. Dark colors correspond to highly correlated spikes. B: Fractions ...

Snow load models for probabilistic optimization of steel frames

Three probabilistic snow load models based on the Poisson spike process and the block maxima method are derived from the second moment probabilistic description of monthly extreme values of snow load. For comparison of the models, the upper tail asymptotic approximations of their cumulative probability distribution functions of yearly maxima are obtained. The performance of the models is checked by the probabilistic design and verification of representative portal frames of low-rise industrial buildings exposed to snow and wind loads using the first-order reliability method (FORM). The statistical parameters of monthly maxima of climatic loads related to measurements at six locations in Germany are employed. The considered snow load has a pattern of a seasonal occurrence of snowfall. The Poisson spike process model is then applied to the probabilistic optimization of safety factors for the standardized design of frames. A novel optimization of variable safety factors is proposed to differentiate design for frames with light to heavy weight roofs. It is shown that this differentiation significantly reduces scatter of the reliability level around the target value.

Firing-rate models capture essential response dynamics of LGN relay cells

Firing-rate models provide a practical tool for studying signal processing in the early visual system, permitting more thorough mathematical analysis than spike-based models. We show here that essential response properties of relay cells in the lateral geniculate nucleus (LGN) can be captured by surprisingly simple firing-rate models consisting of a low-pass filter and a nonlinear activation function. The starting point for our analysis are two spiking neuron models based on experimental data: a spike-response model fitted to data from macaque (Carandini et al. J. Vis., 20(14), 1-2011, 2007), and a model with conductance-based synapses and afterhyperpolarizing currents fitted to data from cat (Casti et al. J. Comput. Neurosci., 24(2), 235-252, 2008). We obtained the nonlinear activation function by stimulating the model neurons with stationary stochastic spike trains, while we characterized the linear filter by fitting a low-pass filter to responses to sinusoidally modulated stochastic spike trains. To account for the non-Poisson nature of retinal spike trains, we performed all analyses with spike trains with higher-order gamma statistics in addition to Poissonian spike trains. Interestingly, the properties of the low-pass filter depend only on the average input rate, but not on the modulation depth of sinusoidally modulated input. Thus, the response properties of our model are fully specified by just three parameters (low-frequency gain, cutoff frequency, and delay) for a given mean input rate and input regularity. This simple firing-rate model reproduces the response of spiking neurons to a step in input rate very well for Poissonian as well as for non-Poissonian input. We also found that the cutoff frequencies, and thus the filter time constants, of the rate-based model are unrelated to the membrane time constants of the underlying spiking models, in agreement with similar observations for simpler models.

Activity Propagation in a Network of Coincidence-Detecting Neurons

This paper presents a formal analytical description of activity propagation in a simple multilayer network of coincidence-detecting neuron models receiving and generating Poisson spike trains. Simulations are also presented. In feedforward networks of coincidence-detecting neurons, the average firing rate decreases layer by layer, until information disappears. To prevent this, the model assumes that all neurons exhibit self-sustained firing, at a preset rate, initiated by the recognition of local features of the stimulus. Such firing can be interpreted as a form of local short-term memory. Inhibitory feedback signals from higher layers are then included in the model to minimize the duration of sustained firing, while ensuring information propagation. The theory predicts the time-dependent firing probability in successive layers and can be used to fit experimental data. The analyzed multilayer neural network exhibits stochastic propagation of neural activity. Such propagation has interesting features, such as information delocalization, that could explain backward masking. Stochastic propagation is normally observed in simulations of networks of spiking neurons. One of the contributions of this paper is to offer a method for formalizing and quantifying such effects, albeit in a simplified system. The mathematical analysis produces expressions for latencies in successive layers in dependence of the number of inputs of a neuron, the level of sustained firing, and the onset time jitter in the first layer of the network. In this model, latencies are not caused by the neuronal integration time, but by the waiting time before a coincidence of input spikes occurs. Numerical evaluation indicates that the retinal jitter may make a major contribution to inter-layer visual latencies. This could be confirmed experimentally. An interesting feature of the model is its potential to describe, within a single framework, a number of apparently unrelated characteristics of visual information processing, such as latencies, backward masking, synchronization, and temporal pattern of post-stimulus histograms. Due to its simplicity, the model can easily be understood, refined, and extended. This work has its origins in the nineties, but modeling latencies and firing probabilities in realistic biological systems is still an unsolved problem.

Controlling uphill motion of an active Brownian particle driven by shot-noise energy pulses

We study self-propelled motion of an active Brownian particle moving in a periodic, ratchet-type potential and subject to energy support distributed in quantized portions according to a Poisson spiking process. The motor features of such a system are examined by analyzing its ability to perform work against additional external load. The control parameter of the system is a mean duration time between subsequent energy pulses. Our analysis indicates that directionality of the motion depends strongly on the correlation time between events of energy supply and can be adjusted to maintain optimal functionality of the motor.

Dynamic state estimation based on Poisson spike trains—towards a theory of optimal encoding

Neurons in the nervous system convey information to higher brain regions by the generation of spike trains. An important question in the field of computational neuroscience is how these sensory neurons encode environmental information in a way which may be simply analyzed by subsequent systems. Many aspects of the form and function of the nervous system have been understood using the concepts of optimal population coding. Most studies, however, have neglected the aspect of temporal coding. Here we address this shortcoming through a filtering theory of inhomogeneous Poisson processes. We derive exact relations for the minimal mean squared error of the optimal Bayesian filter and, by optimizing the encoder, obtain optimal codes for populations of neurons. We also show that a class of non-Markovian, smooth stimuli are amenable to the same treatment, and provide results for the filtering and prediction error which hold for a general class of stochastic processes. This sets a sound mathematical framework for a population coding theory that takes temporal aspects into account. It also formalizes a number of studies which discussed temporal aspects of coding using time-window paradigms, by stating them in terms of correlation times and firing rates. We propose that this kind of analysis allows for a systematic study of temporal coding and will bring further insights into the nature of the neural code.

Synchronization of an Excitatory Integrate-and-Fire Neural Network

In this paper, we study the influence of the coupling strength on the synchronization behavior of a population of leaky integrate-and-fire neurons that is self-excitatory with a population density approach. Each neuron of the population is assumed to be stochastically driven by an independent Poisson spike train and the synaptic interaction between neurons is modeled by a potential jump at the reception of an action potential. Neglecting the synaptic delay, we will establish that for a strong enough connectivity between neurons, the solution of the partial differential equation which describes the population density function must blow up in finite time. Furthermore, we will give a mathematical estimate on the average connection per neuron to ensure the occurrence of a burst. Interpreting the blow up of the solution as the presence of a Dirac mass in the firing rate of the population, we will relate the blow up of the solution to the occurrence of the synchronization of neurons. Fully stochastic simulations of a finite size network of leaky integrate-and-fire neurons are performed to illustrate our theoretical results.

A generative spike train model with time-structured higher order correlations

Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact the dynamics and function of neural ensembles remains an important open problem. Here we describe a new, generative model for correlated spike trains that can exhibit many of the features observed in data. Extending prior work in mathematical finance, this generalized thinning and shift (GTaS) model creates marginally Poisson spike trains with diverse temporal correlation structures. We give several examples which highlight the model's flexibility and utility. For instance, we use it to examine how a neural network responds to highly structured patterns of inputs. We then show that the GTaS model is analytically tractable, and derive cumulant densities of all orders in terms of model parameters. The GTaS framework can therefore be an important tool in the experimental and theoretical exploration of neural dynamics.

Stabilization of Memory States by Stochastic Facilitating Synapses

Bistability within a small neural circuit can arise through an appropriate strength of excitatory recurrent feedback. The stability of a state of neural activity, measured by the mean dwelling time before a noise-induced transition to another state, depends on the neural firing-rate curves, the net strength of excitatory feedback, the statistics of spike times, and increases exponentially with the number of equivalent neurons in the circuit. Here, we show that such stability is greatly enhanced by synaptic facilitation and reduced by synaptic depression. We take into account the alteration in times of synaptic vesicle release, by calculating distributions of inter-release intervals of a synapse, which differ from the distribution of its incoming interspike intervals when the synapse is dynamic. In particular, release intervals produced by a Poisson spike train have a coefficient of variation greater than one when synapses are probabilistic and facilitating, whereas the coefficient of variation is less than one when synapses are depressing. However, in spite of the increased variability in postsynaptic input produced by facilitating synapses, their dominant effect is reduced synaptic efficacy at low input rates compared to high rates, which increases the curvature of neural input-output functions, leading to wider regions of bistability in parameter space and enhanced lifetimes of memory states. Our results are based on analytic methods with approximate formulae and bolstered by simulations of both Poisson processes and of circuits of noisy spiking model neurons.

직립방파제의 케이슨 활동에 대한 확률과정에 기반한 시간의존 신뢰성 설계법 개발

직립 케이슨 방파제에 대한 기존의 성능설계법은 임의의 시간 동안의 평균활동량을 산정하지만 허용활동량을 최초로 초과하는 사건의 발생확률(최초통과확률)은 계산하지 못한다. 설계자는 구조물이 최초로 피해를 입을 확률에 대한 정보를 구조물의 설계 단계뿐 아니라 관리 및 운영에서도 필요로 한다. 따라서 본 연구에서는 케이슨 활동의 최초통과확률을 산정하기 위해 확률과정에 기반한 시간의존 신뢰성 설계법을 개발하였다. 방파제의 활동을 일으키는 폭풍파는 발생 시간과 강도의 임의성의 특징이 있기 때문에 Poisson spike process를 사용하여 케이슨 활동을 정식화할 수 있다. 여기서 방파제의 활동을 일으키는 폭풍파의 발생률은 활동량분포함수와 폭풍파의 평균발생률로 표현된다. 성능설계법으로 모의된 이들은 설계변수들의 다변량 회귀함수로 나타내진다. 결과적으로 활동량분포함수와 폭풍파의 평균발생률은 유의파고, 케이슨 폭, 수심의 함수로 표현되어 케이슨 활동에 대한 최초통과확률을 손쉽게 산정할 수 있다. Although the existing performance-based design method for the vertical breakwater evaluates an average sliding distance during an arbitrary time, it does not calculate the probability of the first occurrence of an event exceeding an allowable sliding distance(i.e. the first-passage probability). Designers need information about the probability that the structure is damaged for the first time for not only design but also maintenance and operation of the structure. Therefore, in this study, a time-dependent reliability design method based on a stochastic process is developed to evaluate the first-passage probability of caisson sliding. Caisson sliding can be formulated by the Poisson spike process because both occurrence time and intensity of severe waves causing caisson sliding are random processes. The occurrence rate of severe waves is expressed as a function of the distribution function of sliding distance and mean occurrence rate of severe waves. These values simulated by a performance-based design method are expressed as multivariate regression functions of design variables. As a result, because the distribution function of sliding distance and the mean occurrence rate of severe waves are expressed as functions of significant wave height, caisson width, and water depth, the first-passage probability of caisson sliding can be easily evaluated.

A Homeostatic Model of Neuronal Firing Governed by Feedback Signals from the Extracellular Matrix

Molecules of the extracellular matrix (ECM) can modulate the efficacy of synaptic transmission and neuronal excitability. These mechanisms are crucial for the homeostatic regulation of neuronal firing over extended timescales. In this study, we introduce a simple mathematical model of neuronal spiking balanced by the influence of the ECM. We consider a neuron receiving random synaptic input in the form of Poisson spike trains and the ECM, which is modeled by a phenomenological variable involved in two feedback mechanisms. One feedback mechanism scales the values of the input synaptic conductance to compensate for changes in firing rate. The second feedback accounts for slow fluctuations of the excitation threshold and depends on the ECM concentration. We show that the ECM-mediated feedback acts as a robust mechanism to provide a homeostatic adjustment of the average firing rate. Interestingly, the activation of feedback mechanisms may lead to a bistability in which two different stable levels of average firing rates can coexist in a spiking network. We discuss the mechanisms of the bistability and how they may be related to memory function.

Cell assembly detection with frequent item set mining

Hebb (1949) suggested cell assemblies as the building blocks of information processing in the brain. The member neurons are assumed to show correlated activity. Advances in multi-electrode technology providing simultaneous recordings from 100 or more neurons increased chances to identify such ensembles considerably. We present a data mining method that detects assemblies in massively parallel spike data both reliably and efficiently. Gerstein et al. [1] developed an accretion approach to detect joint spiking patterns in parallel spike trains. Starting from single neurons, it iteratively accretes neurons into sequences as long as another neuron shows significantly correlated activity (χ2 test) with the accreted neurons (represented by their coincident spikes). However, accretion suffers from several drawbacks: it works on sequences instead of sets, thus incurring high costs from redundant detections (memory consumption, speed), and it may miss assemblies, since it needs a significantly correlated pair to start from and limits the branching factor to two sequences. We present and test an alternative approach based on frequent item set mining (FIM) that amends these drawbacks and is also conceptually neater. FIM was originally developed for market basket analysis and aims at finding sets of products that are frequently bought together. Conceptually this is the same as finding neurons that (frequently) fire together. FIM algorithms efficiently count joint spiking events that exceed a given minimal support (occurrence frequency) by eliminating all redundancy. Found patterns may be assessed statistically by taking the maximum p-value over all one-neuron-against-rest tests, for which we compared χ2, Yates-corrected χ2, G-statistic and Fisher's exact test. In addition, subset conditions may be considered to reduce false positives. We examined (a) no subset conditions, (b) weak subset conditions (existence of a stepwise significant sequence as in accretion), and (c) strong subset conditions (all possible sequences must be stepwise significant). Note that (b) with χ2 is very similar to accretion, except that accretion executes only one test one-neuron-against-rest for the full set (which is fixed by the sequence followed). Due to accretion's redundant search this is effectively the same as taking the minimum of the p-values. We generated data sets of 1s duration with 1ms resolution (i.e., 1000 time bins) and 100 independent Poisson spike trains with stationary and non-stationary rate profiles (sinusoidal or phasic-tonic, [2]). False positive (FP) tests: we counted the reported assemblies per size and number of joint spiking events (averaged over 1000 data sets). Not surprisingly, more FPs are found for higher average firing rate (37.75Hz vs. 18.875Hz) and non-stationary processes. However, they rarely exceed size 3 and 3 coincidences. FPs are lowest for strong subset requirements and depended only marginally on the used statistics. False negative (FN) tests: we injected synchronous spiking events (2-7 coincidences) of a small assembly (3-7 neurons) and counted how often this group or a superset was detected (in 1000 data sets). FNs occur mostly for 2 coincidence and 3 neurons, rarely for 3 coincidences and here only for higher firing rates and small assembly sizes. FNs are considerably more and have larger sizes and more coincidences, the stricter the subset condition. The percentage of true positive patterns with excess neurons (usually one) increases with the number of injected coincidences. Since no redundant search is carried out, FIM is much faster than accretion and does not require reducing the results to unique sets. In summary, FIM without subset requirements, even without any statistical test, leads to essentially the same results as with subset requirements and as accretion. However, FIM uses a neater test concept (worst p-value of all one-neuron-against-rest tests) and eliminates all redundancy from the search. Introducing subset conditions reduces FPs, but increases FNs. We recommend to use FIM without subset conditions and a minimum support of 3, which reduces the number of excess neurons in the true positives. Since FIM is fast and reliable, it will allow us to apply it in a time resolved manner to detect the dynamics assembly processing [3].

A novel, jitter-based method for detecting and measuring spike synchrony and quantifying temporal firing precision

BackgroundPrecise spike synchrony, at the millisecond or even sub-millisecond time scale, has been reported in different brain areas, but its neurobiological meaning and its underlying mechanisms remain unknown or controversial. Studying these questions is complicated by the lack of a validated, well-normalized and robust index for quantifying synchrony. Previously used measures of synchrony are often improperly normalized and thereby are not comparable between different experimental conditions, are sensitive to variations in firing rate or to the firing rate differential between the two neurons, and/or rely on untenable assumptions of firing rate stationarity and Poisson statistics. I describe here a novel measure, the Jitter-Based Synchrony Index (JBSI), that overcomes these issues.Results and discussionThe JBSI method is based on the introduction of virtual spike jitter. While previous implementations of the jitter method used it only to detect synchrony, the JBSI method also quantifies synchrony. Previous implementations of the jitter method used computationally intensive Monte Carlo simulations to generate surrogate spike trains, whereas the JBSI is computed analytically. The JBSI method does not assume any specific firing model, and does not require that the spike trains be locked to a repeating external stimulus. The JBSI can assume values from 1 (maximal possible synchrony) to −1 (minimal possible synchrony) and is therefore properly normalized. Using simulated Poisson spike trains with introduced controlled spike coincidences, I demonstrate that the JBSI is a linear measure of the spike coincidence rate, is independent of the mean firing frequency or the firing frequency differential between the two neurons, and is not sensitive to co-modulations in the firing rates of the two neurons. In contrast, several commonly used synchrony indices fail under one or more of these scenarios. I also demonstrate how the JBSI can be used to estimate the spike timing precision in the system.ConclusionsThe JBSI is a conceptually simple and computationally efficient method that can be used to compute the statistical significance of firing synchrony, to quantify synchrony as a well-normalized index, and to estimate the degree of temporal precision in the system.

Bi-directional astrocytic regulation of neuronal activity within a network

The concept of a tripartite synapse holds that astrocytes can affect both the pre- and post-synaptic compartments through the Ca2+-dependent release of gliotransmitters. Because astrocytic Ca2+ transients usually last for a few seconds, we assumed that astrocytic regulation of synaptic transmission may also occur on the scale of seconds. Here, we considered the basic physiological functions of tripartite synapses and investigated astrocytic regulation at the level of neural network activity. The firing dynamics of individual neurons in a spontaneous firing network was described by the Hodgkin–Huxley model. The neurons received excitatory synaptic input driven by the Poisson spike train with variable frequency. The mean field concentration of the released neurotransmitter was used to describe the presynaptic dynamics. The amplitudes of the excitatory postsynaptic currents (PSCs) obeyed the gamma distribution law. In our model, astrocytes depressed the presynaptic release and enhanced the PSCs. As a result, low frequency synaptic input was suppressed while high frequency input was amplified. The analysis of the neuron spiking frequency as an indicator of network activity revealed that tripartite synaptic transmission dramatically changed the local network operation compared to bipartite synapses. Specifically, the astrocytes supported homeostatic regulation of the network activity by increasing or decreasing firing of the neurons. Thus, the astrocyte activation may modulate a transition of neural network into bistable regime of activity with two stable firing levels and spontaneous transitions between them.

How spurious correlations affect a correlation-based measure of spike timing reliability

The spike timing reliability of a neuron can be assessed via measuring the similarity of spike trains obtained in trials with repeated presentations of the same stimulus. Using a correlation-based measure of spike timing reliability we show that spurious correlations between independent Poisson spike trains can lead to a systematic misinterpretation to an extent that scales with the neural spike rate. Therefore, a correction is essential before comparing neurons with distinctly different spike rates. Such a comparison may, for instance, guide the choice of stimulus selective sensory neurons that are pooled for optimal stimulus reconstruction. We propose straightforward methods to abstract from these spurious correlations and demonstrate effects in an application to recorded spike trains of a retinal ganglion cell population.

Statistical properties of superimposed stationary spike trains

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.

Robustness of STDP-induced memory to perturbations of presynaptic activity: a simulation study

Memory is believed to be stored in the patterns of synaptic connections, which have to be plastic in order to allow for learning new memories, but also stable to retain previously learned patterns (plasticity vs. stability). Previous work has shown that the so-called “additive” STDP rule leads to memory retention times, which are orders of magnitudes longer than achievable with a “multiplicative” rule [1]. Here we investigate a related consequence of STDP in model neurons for memory retention, namely the extent to which transient perturbations in presynaptic activity (mimicking paroxysmal activity) may affect previously learned memories. We simulate a conductance-based one-compartment spiking model neuron with (“additive” and “multiplicative”) STDP learning rules for the excitatory (but not the inhibitory) synapses. Presynaptic activity is modeled via Poisson spike trains. We first let the distribution of synaptic weights converge to a steady-state. Then, the effects of transient changes in excitatory presynaptic activity are characterized in terms of the cross-correlation of the subsequent time-dependent synaptic weight patterns relative to a reference time just before the perturbation. We find that even after moderate and short transients (10 to 15 Hz, < 1 min), a neuron may completely remain silent due to synaptic learning within the transient period, where strong synapses become weak. If a neuron does not remain silent, both magnitude and duration of the perturbation determine the scale of memory destruction, which was generally more severe for the multiplicative rule. As abnormal activity in epilepsy may be due to the changes of GABAergic functions, we also studied the effect of an increased GABAergic reversal potential reported in epilepsy. Surprisingly, increased reversal potentials (less inhibition) can benefit the robustness of memory as studied here. Our results demonstrate that in model neurons without other homeostatic mechanisms, paroxysmal activity could easily override memories. This suggests that pathological brain states may be even more disruptive than previously thought when learning mechanisms are also taken into account.

Detection and localization of multiple rate changes in Poisson spike trains

In statistical spike train analysis, stochastic point process models usually assume stationarity, in particular that the underlying spike train shows a constant firing rate (e.g. [1]). However, such models can lead to misinterpretation of the associated tests if the assumption of rate stationarity is not met (e.g. [2]). Therefore, the analysis of nonstationary data requires that rate changes can be located as precisely as possible. However, present statistical methods focus on rejecting the null hypothesis of stationarity without explicitly locating the change point(s) (e.g. [3]). We propose a test for stationarity of a given spike train that can also be used to estimate the change points in the firing rate. Assuming a Poisson process with piecewise constant firing rate, we propose a Step-Filter-Test (SFT) which can work simultaneously in different time scales, accounting for the high variety of firing patterns in experimental spike trains. Formally, we compare the numbers N1=N1(t,h) and N2=N2(t,h) of spikes in the time intervals (t-h,t] and (h,t+h]. By varying t within a fine time lattice and simultaneously varying the interval length h, we obtain a multivariate statistic D(h,t):=(N1-N2)/√(N1+N2), for which we prove asymptotic multivariate normality under homogeneity. From this a practical, graphical device to spot changes of the firing rate is constructed. Our graphical representation of D(h,t) (Figure ​(Figure1A)1A) visualizes the changes in the firing rate. For the statistical test, a threshold K is chosen such that under homogeneity, |D(h,t)|<K holds for all investigated h and t with probability 0.95. This threshold can indicate potential change points in order to estimate the inhomogeneous rate profile (Figure ​(Figure1B).1B). The SFT is applied to a sample data set of spontaneous single unit activity recorded from the substantia nigra of anesthetized mice. In this data set, multiple rate changes are identified which agree closely with visual inspection. In contrast to approaches choosing one fixed kernel width [4], our method has advantages in the flexibility of h. Figure 1 Graphical representation of the step filter test (SFT) that detects rate changes in Poisson spike trains. A. Curves indicate values of D(h,t) as a function of time t for different window sizes h (in different colors). B. Rate histogram (grey) of the corresponding ...

Active exploration is important for reinforcement learning of interval timing

Timing of initiating action is often critical for performance of voluntary behaviors. Appropriate times for initiating voluntary actions are considered to be acquired by reinforcement learning. In this learning process, exploration in the time domain is essential. The basal ganglia have been implicated in the initiation of voluntary movements. Recently, we proposed a biologically plausible mechanism for probabilistic timing of action initiation in the basal ganglia, and by computer simulations of the spiking neural network model we demonstrated the probabilistic nature of the action initiation of the model which supports active exploration in the range of several seconds [1]. For further characterization of the probabilistic timing mechanism, we tested the simplified version of the model in numerical simulations of the interval generation task in which subjects are required to initiate an action after a specific period that follows a instruction stimulus. The simplified model is a leaky-integrator, which integrates incoming spikes and once the “membrane potential” reaches a threshold it generates an output. In each trial, a time point at which the model begins the input-integration is determined probabilistically based on the probability distribution which depends on the product of intrinsic “prior” probability distribution and a time course of total external inputs. The resultant distributions of output times resembled those of the spiking neural network model. We compared this active exploration model with the passive exploration model that is a similar leaky-integrator model but the input-integration begins at the instruction stimulus is presented. The input consisted of 5000 homogeneous Poisson spike trains of the same mean rate, and was fixed across trials in a session. The learning rule is as follows: a synapse that contributes to the generation of a desired output is strengthened while a synapse that contributes to the generation of an inappropriate output is weakened. In numerical simulations, as the mean rate of the input and/or the time interval between the appearance of the instruction stimulus and the target time progressively increased, the performance of the passive exploration model decreased dramatically. On the contrary, the active exploration model exhibits relatively stable performance in the same ranges of parameters. Heuristically, this drop in the learning performance in the passive model arises as a result of increasing conflicts on weight update of a synapse in proportion to increasing chances that a synapse could contribute both of desired and inappropriate outputs at different times. Because the passive model explores in a way that an output time is progressively increasing toward the target time by decreasing weights of synapses relevant to the generation of inappropriate outputs, the passive model tends to experience intensive decreases in weight of a synapse which should contribute to the desired output. However, the active exploration model explores much wider range of time than the passive one, and thus tends to avoid intensive deceases in strength of specific synapses. These results indicate the importance of the probabilistic timing of action initiation for reinforcement learning of interval timing.