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Ciba, Manuel, Robert Bestel, Christoph Nick, Guilherme Ferraz de Arruda, Thomas Peron, Comin César Henrique, Luciano da Fontoura Costa, Francisco Aparecido Rodrigues, and Christiane Thielemann. "Comparison of Different Spike Train Synchrony Measures Regarding Their Robustness to Erroneous Data From Bicuculline-Induced Epileptiform Activity." Neural Computation 32, no. 5 (May 2020): 887–911. http://dx.doi.org/10.1162/neco_a_01277.
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As synchronized activity is associated with basic brain functions and pathological states, spike train synchrony has become an important measure to analyze experimental neuronal data. Many measures of spike train synchrony have been proposed, but there is no gold standard allowing for comparison of results from different experiments. This work aims to provide guidance on which synchrony measure is best suited to quantify the effect of epileptiform-inducing substances (e.g., bicuculline, BIC) in in vitro neuronal spike train data. Spike train data from recordings are likely to suffer from erroneous spike detection, such as missed spikes (false negative) or noise (false positive). Therefore, different timescale-dependent (cross-correlation, mutual information, spike time tiling coefficient) and timescale-independent (Spike-contrast, phase synchronization (PS), A-SPIKE-synchronization, A-ISI-distance, ARI-SPIKE-distance) synchrony measures were compared in terms of their robustness to erroneous spike trains. For this purpose, erroneous spike trains were generated by randomly adding (false positive) or deleting (false negative) spikes (in silico manipulated data) from experimental data. In addition, experimental data were analyzed using different spike detection threshold factors in order to confirm the robustness of the synchrony measures. All experimental data were recorded from cortical neuronal networks on microelectrode array chips, which show epileptiform activity induced by the substance BIC. As a result of the in silico manipulated data, Spike-contrast was the only measure that was robust to false-negative as well as false-positive spikes. Analyzing the experimental data set revealed that all measures were able to capture the effect of BIC in a statistically significant way, with Spike-contrast showing the highest statistical significance even at low spike detection thresholds. In summary, we suggest using Spike-contrast to complement established synchrony measures because it is timescale independent and robust to erroneous spike trains.
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Kreuz, Thomas, Daniel Chicharro, Conor Houghton, Ralph G. Andrzejak, and Florian Mormann. "Monitoring spike train synchrony." Journal of Neurophysiology 109, no. 5 (March 1, 2013): 1457–72. http://dx.doi.org/10.1152/jn.00873.2012.
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Recently, the SPIKE-distance has been proposed as a parameter-free and timescale-independent measure of spike train synchrony. This measure is time resolved since it relies on instantaneous estimates of spike train dissimilarity. However, its original definition led to spuriously high instantaneous values for eventlike firing patterns. Here we present a substantial improvement of this measure that eliminates this shortcoming. The reliability gained allows us to track changes in instantaneous clustering, i.e., time-localized patterns of (dis)similarity among multiple spike trains. Additional new features include selective and triggered temporal averaging as well as the instantaneous comparison of spike train groups. In a second step, a causal SPIKE-distance is defined such that the instantaneous values of dissimilarity rely on past information only so that time-resolved spike train synchrony can be estimated in real time. We demonstrate that these methods are capable of extracting valuable information from field data by monitoring the synchrony between neuronal spike trains during an epileptic seizure. Finally, the applicability of both the regular and the real-time SPIKE-distance to continuous data is illustrated on model electroencephalographic (EEG) recordings.
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Kreuz, Thomas, Mario Mulansky, and Nebojsa Bozanic. "SPIKY: a graphical user interface for monitoring spike train synchrony." Journal of Neurophysiology 113, no. 9 (May 2015): 3432–45. http://dx.doi.org/10.1152/jn.00848.2014.
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Techniques for recording large-scale neuronal spiking activity are developing very fast. This leads to an increasing demand for algorithms capable of analyzing large amounts of experimental spike train data. One of the most crucial and demanding tasks is the identification of similarity patterns with a very high temporal resolution and across different spatial scales. To address this task, in recent years three time-resolved measures of spike train synchrony have been proposed, the ISI-distance, the SPIKE-distance, and event synchronization. The Matlab source codes for calculating and visualizing these measures have been made publicly available. However, due to the many different possible representations of the results the use of these codes is rather complicated and their application requires some basic knowledge of Matlab. Thus it became desirable to provide a more user-friendly and interactive interface. Here we address this need and present SPIKY, a graphical user interface that facilitates the application of time-resolved measures of spike train synchrony to both simulated and real data. SPIKY includes implementations of the ISI-distance, the SPIKE-distance, and the SPIKE-synchronization (an improved and simplified extension of event synchronization) that have been optimized with respect to computation speed and memory demand. It also comprises a spike train generator and an event detector that makes it capable of analyzing continuous data. Finally, the SPIKY package includes additional complementary programs aimed at the analysis of large numbers of datasets and the estimation of significance levels.
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Brown, Emery N., Riccardo Barbieri, Valérie Ventura, Robert E. Kass, and Loren M. Frank. "The Time-Rescaling Theorem and Its Application to Neural Spike Train Data Analysis." Neural Computation 14, no. 2 (February 1, 2002): 325–46. http://dx.doi.org/10.1162/08997660252741149.
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Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model's validity prior to using it to make inferences about a particular neural system. Assessing goodness-of-fit is a challenging problem for point process neural spike train models, especially for histogram-based models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The time-rescaling theorem is a well-known result in probability theory, which states that any point process with an integrable conditional intensity function may be transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodness-of-fit tests for both parametric and histogram-based point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers, inhomogeneous Poisson, inhomogeneous gamma, and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity. To help make the logic behind the time-rescaling theorem more accessible to researchers in neuroscience, we present a proof using only elementary probability theory arguments.We also show how the theorem may be used to simulate a general point process model of a spike train. Our paradigm makes it possible to compare parametric and histogram-based neural spike train models directly. These results suggest that the time-rescaling theorem can be a valuable tool for neural spike train data analysis.
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Koyama, Shinsuke, and Robert E. Kass. "Spike Train Probability Models for Stimulus-Driven Leaky Integrate-and-Fire Neurons." Neural Computation 20, no. 7 (July 2008): 1776–95. http://dx.doi.org/10.1162/neco.2008.06-07-540.
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Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spike train data in important ways, but they are not very easy to apply to the analysis of spike train data. Instead, statistical methods based on point process models of spike trains provide a wide range of data-analytical techniques. Two simplified point process models have been introduced in the literature: the time-rescaled renewal process (TRRP) and the multiplicative inhomogeneous Markov interval (m-IMI) model. In this letter we investigate the extent to which the TRRP and m-IMI models are able to fit spike trains produced by stimulus-driven leaky integrate-and-fire (LIF) neurons. With a constant stimulus, the LIF spike train is a renewal process, and the m-IMI and TRRP models will describe accurately the LIF spike train variability. With a time-varying stimulus, the probability of spiking under all three of these models depends on both the experimental clock time relative to the stimulus and the time since the previous spike, but it does so differently for the LIF, m-IMI, and TRRP models. We assessed the distance between the LIF model and each of the two empirical models in the presence of a time-varying stimulus. We found that while lack of fit of a Poisson model to LIF spike train data can be evident even in small samples, the m-IMI and TRRP models tend to fit well, and much larger samples are required before there is statistical evidence of lack of fit of the m-IMI or TRRP models. We also found that when the mean of the stimulus varies across time, the m-IMI model provides a better fit to the LIF data than the TRRP, and when the variance of the stimulus varies across time, the TRRP provides the better fit.
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Houghton, Conor, and Kamal Sen. "A New Multineuron Spike Train Metric." Neural Computation 20, no. 6 (June 2008): 1495–511. http://dx.doi.org/10.1162/neco.2007.10-06-350.
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The Victor-Purpura spike train metric has recently been extended to a family of multineuron metrics and used to analyze spike trains recorded simultaneously from pairs of proximate neurons. The metric is one of the two metrics commonly used for quantifying the distance between two spike trains; the other is the van Rossum metric. Here, we suggest an extension of the van Rossum metric to a multineuron metric. We believe this gives a metric that is both natural and easy to calculate. Both types of multineuron metric are applied to simulated data and are compared.
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Vargas-Irwin, Carlos E., David M. Brandman, Jonas B. Zimmermann, John P. Donoghue, and Michael J. Black. "Spike Train SIMilarity Space (SSIMS): A Framework for Single Neuron and Ensemble Data Analysis." Neural Computation 27, no. 1 (January 2015): 1–31. http://dx.doi.org/10.1162/neco_a_00684.
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Increased emphasis on circuit level activity in the brain makes it necessary to have methods to visualize and evaluate large-scale ensemble activity beyond that revealed by raster-histograms or pairwise correlations. We present a method to evaluate the relative similarity of neural spiking patterns by combining spike train distance metrics with dimensionality reduction. Spike train distance metrics provide an estimate of similarity between activity patterns at multiple temporal resolutions. Vectors of pair-wise distances are used to represent the intrinsic relationships between multiple activity patterns at the level of single units or neuronal ensembles. Dimensionality reduction is then used to project the data into concise representations suitable for clustering analysis as well as exploratory visualization. Algorithm performance and robustness are evaluated using multielectrode ensemble activity data recorded in behaving primates. We demonstrate how spike train SIMilarity space (SSIMS) analysis captures the relationship between goal directions for an eight-directional reaching task and successfully segregates grasp types in a 3D grasping task in the absence of kinematic information. The algorithm enables exploration of virtually any type of neural spiking (time series) data, providing similarity-based clustering of neural activity states with minimal assumptions about potential information encoding models.
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Romero, Richard, and Tai Sing Lee. "Spike train analysis for single trial data." Neurocomputing 44-46 (June 2002): 597–603. http://dx.doi.org/10.1016/s0925-2312(02)00446-0.
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Haslinger, Robert, Kristina Lisa Klinkner, and Cosma Rohilla Shalizi. "The Computational Structure of Spike Trains." Neural Computation 22, no. 1 (January 2010): 121–57. http://dx.doi.org/10.1162/neco.2009.12-07-678.
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Neurons perform computations, and convey the results of those computations through the statistical structure of their output spike trains. Here we present a practical method, grounded in the information-theoretic analysis of prediction, for inferring a minimal representation of that structure and for characterizing its complexity. Starting from spike trains, our approach finds their causal state models (CSMs), the minimal hidden Markov models or stochastic automata capable of generating statistically identical time series. We then use these CSMs to objectively quantify both the generalizable structure and the idiosyncratic randomness of the spike train. Specifically, we show that the expected algorithmic information content (the information needed to describe the spike train exactly) can be split into three parts describing (1) the time-invariant structure (complexity) of the minimal spike-generating process, which describes the spike train statistically; (2) the randomness (internal entropy rate) of the minimal spike-generating process; and (3) a residual pure noise term not described by the minimal spike-generating process. We use CSMs to approximate each of these quantities. The CSMs are inferred nonparametrically from the data, making only mild regularity assumptions, via the causal state splitting reconstruction algorithm. The methods presented here complement more traditional spike train analyses by describing not only spiking probability and spike train entropy, but also the complexity of a spike train's structure. We demonstrate our approach using both simulated spike trains and experimental data recorded in rat barrel cortex during vibrissa stimulation.
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Brasselet, Romain, Roland S. Johansson, and Angelo Arleo. "Quantifying Neurotransmission Reliability Through Metrics-Based Information Analysis." Neural Computation 23, no. 4 (April 2011): 852–81. http://dx.doi.org/10.1162/neco_a_00099.
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We set forth an information-theoretical measure to quantify neurotransmission reliability while taking into full account the metrical properties of the spike train space. This parametric information analysis relies on similarity measures induced by the metrical relations between neural responses as spikes flow in. Thus, in order to assess the entropy, the conditional entropy, and the overall information transfer, this method does not require any a priori decoding algorithm to partition the space into equivalence classes. It therefore allows the optimal parameters of a class of distances to be determined with respect to information transmission. To validate the proposed information-theoretical approach, we study precise temporal decoding of human somatosensory signals recorded using microneurography experiments. For this analysis, we employ a similarity measure based on the Victor-Purpura spike train metrics. We show that with appropriate parameters of this distance, the relative spike times of the mechanoreceptors’ responses convey enough information to perform optimal discrimination—defined as maximum metrical information and zero conditional entropy—of 81 distinct stimuli within 40 ms of the first afferent spike. The proposed information-theoretical measure proves to be a suitable generalization of Shannon mutual information in order to consider the metrics of temporal codes explicitly. It allows neurotransmission reliability to be assessed in the presence of large spike train spaces (e.g., neural population codes) with high temporal precision.
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Du, Ying, Rubin Wang, and Jingyi Qu. "Noise and Synchronization Analysis of the Cold-Receptor Neuronal Network Model." Discrete Dynamics in Nature and Society 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/173894.
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This paper analyzes the dynamics of the cold receptor neural network model. First, it examines noise effects on neuronal stimulus in the model. FromISIplots, it is shown that there are considerable differences between purely deterministic simulations and noisy ones. TheISI-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 theISI-distance method. The simulations show that the synchronization status of neurons is related to the network connectivity patterns.
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Belisle, Patrick, Lawrence Joseph, Brenda MacGibbon, David B. Wolfson, and Roxane du Berger. "Change-Point Analysis of Neuron Spike Train Data." Biometrics 54, no. 1 (March 1998): 113. http://dx.doi.org/10.2307/2534000.
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Wu, Wei, Nicholas G. Hatsopoulos, and Anuj Srivastava. "Analysis of spike train data: Discussion of results." Electronic Journal of Statistics 8, no. 2 (2014): 1808–10. http://dx.doi.org/10.1214/14-ejs865rej.
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Tomas, P., and L. Sousa. "Statistical Analysis of a Spike Train Distance in Poisson Models." IEEE Signal Processing Letters 15 (2008): 357–60. http://dx.doi.org/10.1109/lsp.2008.919994.
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Itskov, Vladimir, Carina Curto, and Kenneth D. Harris. "Valuations for Spike Train Prediction." Neural Computation 20, no. 3 (March 2008): 644–67. http://dx.doi.org/10.1162/neco.2007.3179.
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The ultimate product of an electrophysiology experiment is often a decision on which biological hypothesis or model best explains the observed data. We outline a paradigm designed for comparison of different models, which we refer to as spike train prediction. A key ingredient of this paradigm is a prediction quality valuation that estimates how close a predicted conditional intensity function is to an actual observed spike train. Although a valuation based on log likelihood (L) is most natural, it has various complications in this context. We propose that a quadratic valuation (Q) can be used as an alternative to L. Q shares some important theoretical properties with L, including consistency, and the two valuations perform similarly on simulated and experimental data. Moreover, Q is more robust than L, and optimization with Q can dramatically improve computational efficiency. We illustrate the utility of Q for comparing models of peer prediction, where it can be computed directly from cross-correlograms. Although Q does not have a straightforward probabilistic interpretation, Q is essentially given by Euclidean distance.
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Park, Il Memming, Sohan Seth, Murali Rao, and José C. Príncipe. "Strictly Positive-Definite Spike Train Kernels for Point-Process Divergences." Neural Computation 24, no. 8 (August 2012): 2223–50. http://dx.doi.org/10.1162/neco_a_00309.
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Exploratory tools that are sensitive to arbitrary statistical variations in spike train observations open up the possibility of novel neuroscientific discoveries. Developing such tools, however, is difficult due to the lack of Euclidean structure of the spike train space, and an experimenter usually prefers simpler tools that capture only limited statistical features of the spike train, such as mean spike count or mean firing rate. We explore strictly positive-definite kernels on the space of spike trains to offer both a structural representation of this space and a platform for developing statistical measures that explore features beyond count or rate. We apply these kernels to construct measures of divergence between two point processes and use them for hypothesis testing, that is, to observe if two sets of spike trains originate from the same underlying probability law. Although there exist positive-definite spike train kernels in the literature, we establish that these kernels are not strictly definite and thus do not induce measures of divergence. We discuss the properties of both of these existing nonstrict kernels and the novel strict kernels in terms of their computational complexity, choice of free parameters, and performance on both synthetic and real data through kernel principal component analysis and hypothesis testing.
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Natschläger, Thomas, and Wolfgang Maass. "Computing the Optimally Fitted Spike Train for a Synapse." Neural Computation 13, no. 11 (November 1, 2001): 2477–94. http://dx.doi.org/10.1162/089976601753195987.
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Experimental data have shown that synapses are heterogeneous: different synapses respond with different sequences of amplitudes of postsynaptic responses to the same spike train. Neither the role of synaptic dynamics itself nor the role of the heterogeneity of synaptic dynamics for computations in neural circuits is well understood. We present in this article two computational methods that make it feasible to compute for a given synapse with known synaptic parameters the spike train that is optimally fitted to the synapse in a certain sense. With the help of these methods, one can compute, for example, the temporal pattern of a spike train (with a given number of spikes) that produces the largest sum of postsynaptic responses for a specific synapse. Several other applications are also discussed. To our surprise, we find that most of these optimally fitted spike trains match common firing patterns of specific types of neurons that are discussed in the literature. Hence, our analysis provides a possible functional explanation for the experimentally observed regularity in the combination of specific types of synapses with specific types of neurons in neural circuits.
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Grün, Sonja. "Data-Driven Significance Estimation for Precise Spike Correlation." Journal of Neurophysiology 101, no. 3 (March 2009): 1126–40. http://dx.doi.org/10.1152/jn.00093.2008.
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The mechanisms underlying neuronal coding and, in particular, the role of temporal spike coordination are hotly debated. However, this debate is often confounded by an implicit discussion about the use of appropriate analysis methods. To avoid incorrect interpretation of data, the analysis of simultaneous spike trains for precise spike correlation needs to be properly adjusted to the features of the experimental spike trains. In particular, nonstationarity of the firing of individual neurons in time or across trials, a spike train structure deviating from Poisson, or a co-occurrence of such features in parallel spike trains are potent generators of false positives. Problems can be avoided by including these features in the null hypothesis of the significance test. In this context, the use of surrogate data becomes increasingly important, because the complexity of the data typically prevents analytical solutions. This review provides an overview of the potential obstacles in the correlation analysis of parallel spike data and possible routes to overcome them. The discussion is illustrated at every stage of the argument by referring to a specific analysis tool (the Unitary Events method). The conclusions, however, are of a general nature and hold for other analysis techniques. Thorough testing and calibration of analysis tools and the impact of potentially erroneous preprocessing stages are emphasized.
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Larson, Eric, Cyrus P. Billimoria, and Kamal Sen. "A Biologically Plausible Computational Model for Auditory Object Recognition." Journal of Neurophysiology 101, no. 1 (January 2009): 323–31. http://dx.doi.org/10.1152/jn.90664.2008.
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Object recognition is a task of fundamental importance for sensory systems. Although this problem has been intensively investigated in the visual system, relatively little is known about the recognition of complex auditory objects. Recent work has shown that spike trains from individual sensory neurons can be used to discriminate between and recognize stimuli. Multiple groups have developed spike similarity or dissimilarity metrics to quantify the differences between spike trains. Using a nearest-neighbor approach the spike similarity metrics can be used to classify the stimuli into groups used to evoke the spike trains. The nearest prototype spike train to the tested spike train can then be used to identify the stimulus. However, how biological circuits might perform such computations remains unclear. Elucidating this question would facilitate the experimental search for such circuits in biological systems, as well as the design of artificial circuits that can perform such computations. Here we present a biologically plausible model for discrimination inspired by a spike distance metric using a network of integrate-and-fire model neurons coupled to a decision network. We then apply this model to the birdsong system in the context of song discrimination and recognition. We show that the model circuit is effective at recognizing individual songs, based on experimental input data from field L, the avian primary auditory cortex analog. We also compare the performance and robustness of this model to two alternative models of song discrimination: a model based on coincidence detection and a model based on firing rate.
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Reeke, George N., and Allan D. Coop. "Estimating the Temporal Interval Entropy of Neuronal Discharge." Neural Computation 16, no. 5 (May 1, 2004): 941–70. http://dx.doi.org/10.1162/089976604773135050.
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To better understand the role of timing in the function of the nervous system, we have developed a methodology that allows the entropy of neuronal discharge activity to be estimated from a spike train record when it may be assumed that successive interspike intervals are temporally uncorrelated. The so-called interval entropy obtained by this methodology is based on an implicit enumeration of all possible spike trains that are statistically indistinguishable from a given spike train. The interval entropy is calculated from an analytic distribution whose parameters are obtained by maximum likelihood estimation from the interval probability distribution associated with a given spike train. We show that this approach reveals features of neuronal discharge not seen with two alternative methods of entropy estimation. The methodology allows for validation of the obtained data models by calculation of confidence intervals for the parameters of the analytic distribution and the testing of the significance of the fit between the observed and analytic interval distributions by means of Kolmogorov-Smirnov and Anderson-Darling statistics. The method is demonstrated by analysis of two different data sets: simulated spike trains evoked by either Poissonian or near-synchronous pulsed activation of a model cerebellar Purkinje neuron and spike trains obtained by extracellular recording from spontaneously discharging cultured rat hippocampal neurons.
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Cheng, Wen, Ian L. Dryden, David B. Hitchcock, and Huiling Le. "Analysis of spike train data: Classification and Bayesian alignment." Electronic Journal of Statistics 8, no. 2 (2014): 1786–92. http://dx.doi.org/10.1214/14-ejs865c.
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Fotheringhame, David, and Roland Baddeley. "Nonlinear principal components analysis of neuronal spike train data." Biological Cybernetics 77, no. 4 (October 1, 1997): 283–88. http://dx.doi.org/10.1007/s004220050389.
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Lopes-dos-Santos, Vítor, Stefano Panzeri, Christoph Kayser, Mathew E. Diamond, and Rodrigo Quian Quiroga. "Extracting information in spike time patterns with wavelets and information theory." Journal of Neurophysiology 113, no. 3 (February 1, 2015): 1015–33. http://dx.doi.org/10.1152/jn.00380.2014.
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We present a new method to assess the information carried by temporal patterns in spike trains. The method first performs a wavelet decomposition of the spike trains, then uses Shannon information to select a subset of coefficients carrying information, and finally assesses timing information in terms of decoding performance: the ability to identify the presented stimuli from spike train patterns. We show that the method allows: 1) a robust assessment of the information carried by spike time patterns even when this is distributed across multiple time scales and time points; 2) an effective denoising of the raster plots that improves the estimate of stimulus tuning of spike trains; and 3) an assessment of the information carried by temporally coordinated spikes across neurons. Using simulated data, we demonstrate that the Wavelet-Information (WI) method performs better and is more robust to spike time-jitter, background noise, and sample size than well-established approaches, such as principal component analysis, direct estimates of information from digitized spike trains, or a metric-based method. Furthermore, when applied to real spike trains from monkey auditory cortex and from rat barrel cortex, the WI method allows extracting larger amounts of spike timing information. Importantly, the fact that the WI method incorporates multiple time scales makes it robust to the choice of partly arbitrary parameters such as temporal resolution, response window length, number of response features considered, and the number of available trials. These results highlight the potential of the proposed method for accurate and objective assessments of how spike timing encodes information.
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PETRACCHI, DONATELLA, MICHELE BARBI, SANTI CHILLEMI, ELENI PANTAZELOU, DAVID PIERSON, CHRIS DAMES, LON WILKENS, and FRANK MOSS. "A TEST FOR A BIOLOGICAL SIGNAL ENCODED BY NOISE." International Journal of Bifurcation and Chaos 05, no. 01 (February 1995): 89–100. http://dx.doi.org/10.1142/s0218127495000077.
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We consider here a simple example of stimulated sensory neurons operating under the influence of their own internal noise: the hair mechanoreceptor of the crayfish stimulated by a weak, periodic, hydrodynamic signal. Action potential spike trains from the sensory neuron are recorded and assembled into two objects for analysis: the interspike interval histogram (ISIH) and the cycle histogram of the spike density. A time transformation is carried out on the ISIH’s in order to test the hypothesis that the spike train is basically random and that the probability of coherent spike generation is related to the instantaneous stimulus amplitude. Moreover it is shown that the physiological spike train data can be qualitatively mimicked by an electronic Fitzhugh-Nagumo model, operated in the subcritical mode, driven by noise and a weak periodic signal. A discussion of how the Fitzhugh-Nagumo model is properly operated to mimic noisy data from sensory neurons is included.
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Ghahari, Alireza, Sumit R. Kumar, and Tudor C. Badea. "Identification of Retinal Ganglion Cell Firing Patterns Using Clustering Analysis Supplied with Failure Diagnosis." International Journal of Neural Systems 28, no. 08 (August 26, 2018): 1850008. http://dx.doi.org/10.1142/s0129065718500089.
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An important goal in visual neuroscience is to understand how neuronal population coding in vertebrate retina mediates the broad range of visual functions. Microelectrode arrays interface on isolated retina registers a collective measure of the spiking dynamics of retinal ganglion cells (RGCs) by probing them simultaneously and in large numbers. The recorded data stream is then processed to identify spike trains of individual RGCs by efficient and scalable spike detection and sorting routines. Most spike sorting software packages, available either commercially or as freeware, combine automated steps with judgment calls by the investigator to verify the quality of sorted spikes. This work focused on sorting spikes of RGCs into clusters using an integrated analytical platform for the data recorded during visual stimulation of wild-type mice retinas with whole field stimuli. After spike train detection, we projected each spike onto two feature spaces: a parametric space and a principal components space. We then applied clustering algorithms to sort spikes into separate clusters. To eliminate the need for human intervention, the initial clustering results were submitted to diagnostic tests that evaluated the results to detect the sources of failure in cluster assignment. This failure diagnosis formed a decision logic for diagnosable electrodes to enhance the clustering quality iteratively through rerunning the clustering algorithms. The new clustering results showed that the spike sorting accuracy was improved. Subsequently, the number of active RGCs during each whole field stimulation was found, and the light responsiveness of each RGC was identified. Our approach led to error-resilient spike sorting in both feature extraction methods; however, using parametric features led to less erroneous spike sorting compared to principal components, particularly for low signal-to-noise ratios. As our approach is reliable for retinal signal processing in response to simple visual stimuli, it could be applied to the evaluation of disrupted physiological signaling in retinal neurodegenerative diseases.
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Shimazaki, Hideaki, Shun-ichi Amari, Emery N. Brown, and Sonja Grün. "State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data." PLoS Computational Biology 8, no. 3 (March 8, 2012): e1002385. http://dx.doi.org/10.1371/journal.pcbi.1002385.
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Brillinger, David R. "Nerve Cell Spike Train Data Analysis: A Progression of Technique." Journal of the American Statistical Association 87, no. 418 (June 1992): 260–71. http://dx.doi.org/10.1080/01621459.1992.10475205.
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Huang, Yu, Xiangning Li, Yanling Li, Qingwei Xu, Qiang Lu, and Qian Liu. "An integrative analysis platform for multiple neural spike train data." Journal of Neuroscience Methods 172, no. 2 (July 2008): 303–11. http://dx.doi.org/10.1016/j.jneumeth.2008.04.026.
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Wu, Wei, Nicholas G. Hatsopoulos, and Anuj Srivastava. "Introduction to neural spike train data for phase-amplitude analysis." Electronic Journal of Statistics 8, no. 2 (2014): 1759–68. http://dx.doi.org/10.1214/14-ejs865.
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‘Atyka Nor Rashid, Fadilla, and Nor Surayahani Suriani. "Spiking neural network classification for spike train analysis of physiotherapy movements." Bulletin of Electrical Engineering and Informatics 9, no. 1 (February 1, 2020): 319–25. http://dx.doi.org/10.11591/eei.v9i1.1868.
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Classifying gesture or movements nowadays become a demanding business as the technologies of sensor rose. This has enchanted many researchers to actively investigated widely within the area of computer vision. Rehabilitation exercises is one of the most popular gestures or movements that being worked by the researchers nowadays. Rehab session usually involves experts that monitored the patients but lacking the experts itself made the session become longer and unproductive. This works adopted a dataset from UI-PRMD that assembled from 10 rehabilitation movements. The data has been encoded into spike trains for spike patterns analysis. Next, we tend to train the spike trains into Spiking Neural Networks and resulting into a promising result. However, in future, this method will be tested with other data to validate the performance, also to enhance the success rate of the accuracy.
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Brown, Samuel P., and Michael S. Thorne. "Viterbi sparse spike detection." GEOPHYSICS 78, no. 4 (July 1, 2013): V157—V169. http://dx.doi.org/10.1190/geo2012-0209.1.
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Accurate interpretation of seismic traveltimes and amplitudes in the exploration and global scales is complicated by the band-limited nature of seismic data. We discovered a stochastic method to reduce a seismic waveform into a most probable constituent spike train. Model waveforms were constructed from a set of candidate spike trains convolved with a source wavelet estimate. For each model waveform, a profile hidden Markov model (HMM) was constructed to represent the waveform as a stochastic generative model with a linear topology corresponding to a sequence of samples. Each match state in the HMM represented a sample in the model waveform, in which the amplitude was represented by a Gaussian distribution. Insert and delete states allowed the underlying source wavelet to dilate or contract, accounting for nonstationarity in the seismic data and errors in the source wavelet estimate. The Gaussian distribution characterizing each sample’s amplitude accounted for random noise. The Viterbi algorithm was employed to simultaneously find the optimal nonlinear alignment between a model waveform and the seismic data and to assign a score to each candidate spike train. The most probable traveltimes and amplitudes were inferred from the alignments of the highest scoring models. The method required no implicit assumptions regarding the distribution of traveltimes and amplitudes; however, in practice, the solution set may be limited to mitigate the nonuniqueness of solutions and to reduce the computational effort. Our analyses found that the method can resolve closely spaced arrivals below traditional resolution limits and that traveltime estimates are robust in the presence of random noise and source wavelet errors. The method was particularly well suited to fine-scale interpretation problems such as thin bed interpretation, tying seismic images to well logs, and the analysis of anomalous waveforms in global seismology.
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Victor, J. D., and K. P. Purpura. "Nature and precision of temporal coding in visual cortex: a metric-space analysis." Journal of Neurophysiology 76, no. 2 (August 1, 1996): 1310–26. http://dx.doi.org/10.1152/jn.1996.76.2.1310.
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1. We recorded single-unit and multi-unit activity in response to transient presentation of texture and grating patterns at 25 sites within the parafoveal representation of V1, V2, and V3 of two awake monkeys trained to perform a fixation task. In grating experiments, stimuli varied in orientation, spatial frequency, or both. In texture experiments, stimuli varied in contrast, check size, texture type, or pairs of these attributes. 2. To examine the nature and precision of temporal coding, we compared individual responses elicited by each set of stimuli in terms of two families of metrics. One family of metrics, D(spike), was sensitive to the absolute spike time (following stimulus onset). The second family of metrics, D(interval), was sensitive to the pattern of interspike intervals. In each family, the metrics depend on a parameter q, which expresses the precision of temporal coding. For q = 0, both metrics collapse into the "spike count" metric D(Count), which is sensitive to the number of impulses but insensitive to their position in time. 3. Each of these metrics, with values of q ranging from 0 to 512/s, was used to calculate the distance between all pairs of spike trains within each dataset. The extent of stimulus-specific clustering manifest in these pairwise distances was quantified by an information measure. Chance clustering was estimated by applying the same procedure to synthetic data sets in which responses were assigned randomly to the input stimuli. 4. Of the 352 data sets, 170 showed evidence of tuning via the spike count (q = 0) metric, 294 showed evidence of tuning via the spike time metric, 272 showed evidence of tuning via the spike interval metric to the stimulus attribute (contrast, check size, orientation, spatial frequency, or texture type) under study. Across the entire dataset, the information not attributable to chance clustering averaged 0.042 bits for the spike count metric, 0.171 bits for the optimal spike time metric, and 0.107 bits for the optimal spike interval metric. 5. The reciprocal of the optimal cost q serves as a measure of the temporal precision of temporal coding. In V1 and V2, with both metrics, temporal precision was highest for contrast (ca. 10-30 ms) and lowest for texture type (ca. 100 ms). This systematic dependence of q on stimulus attribute provides a possible mechanism for the simultaneous representation of multiple stimulus attributes in one spike train. 6. Our findings are inconsistent with Poisson models of spike trains. Synthetic data sets in which firing rate was governed by a time-dependent Poisson process matched to the observed poststimulus time histogram (PSTH) overestimated clustering induced by D(count) and, for low values of q, D(spike)[q] and D(intervals)[q]. Synthetic data sets constructed from a modified Poisson process, which preserved not only the PSTH but also spike count statistics accounted for the clustering induced by D(count) but underestimated the clustering induced by D(spike)[q] and D(interval)[q].
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Patriarca, Mirco, Laura M. Sangalli, Piercesare Secchi, and Simone Vantini. "Analysis of spike train data: An application of $k$-mean alignment." Electronic Journal of Statistics 8, no. 2 (2014): 1769–75. http://dx.doi.org/10.1214/14-ejs865a.
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LONGTIN, ANDRÉ. "NONLINEAR FORECASTING OF SPIKE TRAINS FROM SENSORY NEURONS." International Journal of Bifurcation and Chaos 03, no. 03 (June 1993): 651–61. http://dx.doi.org/10.1142/s0218127493000556.
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The sequence of firing times of a neuron can be viewed as a point process. The problem of spike train analysis is to infer the underlying neural dynamics from this point process when, for example, one does not have access to a state variable such as intracellular voltage. Traditional analyses of spike trains have focussed to a large extent on fitting the parameters of a model stochastic point process to the data, such as the intensity of a homogeneous Poisson point process. This paper shows how methods from nonlinear time series analysis can be used to gain knowledge about correlations between the spiking events recorded from periodically driven sensory neurons. Results on nonlinear forecastability of these spike trains are compared to those on data sets derived from the original data set and satisfying an appropriately chosen null hypothesis. While no predictability, linear or nonlinear, is revealed by our analysis of the raw data using local linear predictors, it appears that there is some predictability in the successive phases (rather than intervals) at which the neurons fire.
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Rogers, Robert F., Jacob D. Runyan, A. Ganesh Vaidyanathan, and James S. Schwaber. "Information Theoretic Analysis of Pulmonary Stretch Receptor Spike Trains." Journal of Neurophysiology 85, no. 1 (January 1, 2001): 448–61. http://dx.doi.org/10.1152/jn.2001.85.1.448.
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Primary afferent neurons transduce physical, continuous stimuli into discrete spike trains. Investigators have long been interested in interpreting the meaning of the number or pattern of action potentials in attempts to decode the spike train back into stimulus parameters. Pulmonary stretch receptors (PSRs) are visceral mechanoreceptors that respond to deformation of the lungs and pulmonary tree. They provide the brain stem with feedback that is used by cardiorespiratory control circuits. In anesthetized, paralyzed, artificially ventilated rabbits, we recorded the action potential trains of individual PSRs while continuously manipulating ventilator rate and volume. We describe an information theoretic-based analytical method for evaluating continuous stimulus and spike train data that is of general applicability to any continuous, dynamic system. After adjusting spike times for conduction velocity, we used a sliding window to discretize the stimulus (average tracheal pressure) and response (number of spikes), and constructed co-occurrence matrices. We systematically varied the number of categories into which the stimulus and response were evenly divided at 26 different sliding window widths (5, 10, 20, 30, … , 230, 240, 250 ms). Using the probability distributions defined by the co-occurrence matrices, we estimated associated stimulus, response, joint, and conditional entropies, from which we calculated information transmitted as a fraction of the maximum possible, as well as encoding and decoding efficiencies. We found that, in general, information increases rapidly as the sliding window width increases from 5 to ∼50 ms and then saturates as observation time increases. In addition, the information measures suggest that individual PSRs transmit more “when” than “what” type of information about the stimulus, based on the finding that the maximum information at a given window width was obtained when the stimulus was divided into just a few (usually <6) categories. Our results indicate that PSRs provide quite reliable information about tracheal pressure, with each PSR conveying about 31% of the maximum possible information about the dynamic stimulus, given our analytical parameters. When the stimulus and response are divided into more categories, slightly less information is transmitted, and this quantity also saturates as a function of observation time. We consider and discuss the importance of information contained in window widths on the time scales of an excitatory postsynaptic potential and Hering-Breuer reflex central delay.
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Lu, Xiaosun, and J. S. Marron. "Analysis of spike train data: Comparison between the real and the simulated data." Electronic Journal of Statistics 8, no. 2 (2014): 1793–96. http://dx.doi.org/10.1214/14-ejs865d.
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Schneider, Gaby. "Messages of Oscillatory Correlograms: A Spike Train Model." Neural Computation 20, no. 5 (May 2008): 1211–38. http://dx.doi.org/10.1162/neco.2007.12-06-424.
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Oscillatory correlograms are widely used to study neuronal activity that shows a joint periodic rhythm. In most cases, the statistical analysis of cross-correlation histograms (CCH) features is based on the null model of independent processes, and the resulting conclusions about the underlying processes remain qualitative. Therefore, we propose a spike train model for synchronous oscillatory firing activity that directly links characteristics of the CCH to parameters of the underlying processes. The model focuses particularly on asymmetric central peaks, which differ in slope and width on the two sides. Asymmetric peaks can be associated with phase offsets in the (sub-) millisecond range. These spatiotemporal firing patterns can be highly consistent across units yet invisible in the underlying processes. The proposed model includes a single temporal parameter that accounts for this peak asymmetry. The model provides approaches for the analysis of oscillatory correlograms, taking into account dependencies and nonstationarities in the underlying processes. In particular, the auto- and the cross-correlogram can be investigated in a joint analysis because they depend on the same spike train parameters. Particular temporal interactions such as the degree to which different units synchronize in a common oscillatory rhythm can also be investigated. The analysis is demonstrated by application to a simulated data set.
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Rasch, Malte J., Arthur Gretton, Yusuke Murayama, Wolfgang Maass, and Nikos K. Logothetis. "Inferring Spike Trains From Local Field Potentials." Journal of Neurophysiology 99, no. 3 (March 2008): 1461–76. http://dx.doi.org/10.1152/jn.00919.2007.
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We investigated whether it is possible to infer spike trains solely on the basis of the underlying local field potentials (LFPs). Using support vector machines and linear regression models, we found that in the primary visual cortex (V1) of monkeys, spikes can indeed be inferred from LFPs, at least with moderate success. Although there is a considerable degree of variation across electrodes, the low-frequency structure in spike trains (in the 100-ms range) can be inferred with reasonable accuracy, whereas exact spike positions are not reliably predicted. Two kinds of features of the LFP are exploited for prediction: the frequency power of bands in the high γ-range (40–90 Hz) and information contained in low-frequency oscillations (<10 Hz), where both phase and power modulations are informative. Information analysis revealed that both features code (mainly) independent aspects of the spike-to-LFP relationship, with the low-frequency LFP phase coding for temporally clustered spiking activity. Although both features and prediction quality are similar during seminatural movie stimuli and spontaneous activity, prediction performance during spontaneous activity degrades much more slowly with increasing electrode distance. The general trend of data obtained with anesthetized animals is qualitatively mirrored in that of a more limited data set recorded in V1 of non-anesthetized monkeys. In contrast to the cortical field potentials, thalamic LFPs (e.g., LFPs derived from recordings in the dorsal lateral geniculate nucleus) hold no useful information for predicting spiking activity.
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Lehky, Sidney R. "Decoding Poisson Spike Trains by Gaussian Filtering." Neural Computation 22, no. 5 (May 2010): 1245–71. http://dx.doi.org/10.1162/neco.2009.07-08-823.
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The temporal waveform of neural activity is commonly estimated by low-pass filtering spike train data through convolution with a gaussian kernel. However, the criteria for selecting the gaussian width σ are not well understood. Given an ensemble of Poisson spike trains generated by an instantaneous firing rate function λ(t), the problem was to recover an optimal estimate of λ(t) by gaussian filtering. We provide equations describing the optimal value of σ using an error minimization criterion and examine how the optimal σ varies within a parameter space defining the statistics of inhomogeneous Poisson spike trains. The process was studied both analytically and through simulations. The rate functions λ(t) were randomly generated, with the three parameters defining spike statistics being the mean of λ(t), the variance of λ(t), and the exponent α of the Fourier amplitude spectrum 1/fα of λ(t). The value of σopt followed a power law as a function of the pooled mean interspike interval I, σopt = aIb, where a was inversely related to the coefficient of variation CV of λ(t), and b was inversely related to the Fourier spectrum exponent α. Besides applications for data analysis, optimal recovery of an analog signal waveform λ(t) from spike trains may also be useful in understanding neural signal processing in vivo.
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Berger, T. W., J. L. Eriksson, D. A. Ciarolla, and R. J. Sclabassi. "Nonlinear systems analysis of the hippocampal perforant path-dentate projection. III. Comparison of random train and paired impulse stimulation." Journal of Neurophysiology 60, no. 3 (September 1, 1988): 1095–109. http://dx.doi.org/10.1152/jn.1988.60.3.1095.
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1. The transformational properties of the network of hippocampal neurons activated monosynaptically and polysynaptically by electrical stimulation of the perforant path were analyzed using random impulse train and paired impulse stimuli. In response to both types of input, the amplitudes of granule cell population spikes evoked in the dentate gyrus were used as the measure of network output. The random stimulus train consisted of a series of 4,064 electrical impulses, with interimpulse intervals determined by a Poisson distribution; the mean interimpulse interval of the train was 500 ms, and the range was 1-5,000 ms. Paired impulse stimuli consisted of pairs of impulses separated by 10-1,200 ms; impulses pairs were delivered once every 20 s. The procedures were applied to both anesthetized and chronically implanted, unanesthetized preparations. 2. Nonlinear systems analysis of population spike responses evoked during random train stimulation revealed that dentate granule cell output to any impulse was highly dependent on the interval since a prior impulse. Data from anesthetized animals showed that population spike amplitudes were markedly suppressed in response to intervals less than 50 ms, facilitated in response to intervals of approximately 100 ms, suppressed slightly in response to intervals of 300-700 ms, and unaffected by intervals greater than 700 ms. Data from unanesthetized animals showed similar results except that facilitation rather than suppression of spike amplitude was observed in response to intervals of 300-700 ms, and could extend to intervals as great as 1,000 ms. 3. The results of paired impulse stimulation applied to the same preparations also showed that granule cell response was highly dependent on interimpulse interval. However, nonlinearities observed with paired impulse stimulation differed from those revealed by a random impulse signal. Compared to results of random train stimulation, a paired impulse format produced greater magnitude spike suppression in response to short interimpulse intervals (e.g., 10-20 ms), maximum facilitation in response to shorter interstimulus intervals (50 ms rather than 100 ms), greater magnitude spike facilitation, and greater suppression in response to intervals greater than or equal to 300 ms. Furthermore, there were virtually no differences in the nonlinearities of granule cell response recorded from anesthetized and unanesthetized animals when a paired impulse format was used, whereas several differences were observed with random train stimuli. 4.(ABSTRACT TRUNCATED AT 400 WORDS)
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Tezuka, Taro, and Christophe Claramunt. "Kernel Analysis for Estimating the Connectivity of a Network with Event Sequences." Journal of Artificial Intelligence and Soft Computing Research 7, no. 1 (January 1, 2017): 17–31. http://dx.doi.org/10.1515/jaiscr-2017-0002.
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AbstractEstimating the connectivity of a network from events observed at each node has many applications. One prominent example is found in neuroscience, where spike trains (sequences of action potentials) are observed at each neuron, but the way in which these neurons are connected is unknown. This paper introduces a novel method for estimating connections between nodes using a similarity measure between sequences of event times. Specifically, a normalized positive definite kernel defined on spike trains was used. The proposed method was evaluated using synthetic and real data, by comparing with methods using transfer entropy and the Victor-Purpura distance. Synthetic data was generated using CERM (Coupled Escape-Rate Model), a model that generates various spike trains. Real data recorded from the visual cortex of an anaesthetized cat was analyzed as well. The results showed that the proposed method provides an effective way of estimating the connectivity of a network when the time sequences of events are the only available information.
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Panzeri, Stefano, Riccardo Senatore, Marcelo A. Montemurro, and Rasmus S. Petersen. "Correcting for the Sampling Bias Problem in Spike Train Information Measures." Journal of Neurophysiology 98, no. 3 (September 2007): 1064–72. http://dx.doi.org/10.1152/jn.00559.2007.
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Information Theory enables the quantification of how much information a neuronal response carries about external stimuli and is hence a natural analytic framework for studying neural coding. The main difficulty in its practical application to spike train analysis is that estimates of neuronal information from experimental data are prone to a systematic error (called “bias”). This bias is an inevitable consequence of the limited number of stimulus-response samples that it is possible to record in a real experiment. In this paper, we first explain the origin and the implications of the bias problem in spike train analysis. We then review and evaluate some recent general-purpose methods to correct for sampling bias: the Panzeri-Treves, Quadratic Extrapolation, Best Universal Bound, Nemenman-Shafee-Bialek procedures, and a recently proposed shuffling bias reduction procedure. Finally, we make practical recommendations for the accurate computation of information from spike trains. Our main recommendation is to estimate information using the shuffling bias reduction procedure in combination with one of the other four general purpose bias reduction procedures mentioned in the preceding text. This provides information estimates with acceptable variance and which are unbiased even when the number of trials per stimulus is as small as the number of possible discrete neuronal responses.
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Brown, Emery N., Robert E. Kass, and Partha P. Mitra. "Multiple neural spike train data analysis: state-of-the-art and future challenges." Nature Neuroscience 7, no. 5 (April 27, 2004): 456–61. http://dx.doi.org/10.1038/nn1228.
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Myers, S. F., H. H. Salem, and J. A. Kaltenbach. "Efferent Neurons and Vestibular Cross Talk in the Frog." Journal of Neurophysiology 77, no. 4 (April 1, 1997): 2061–70. http://dx.doi.org/10.1152/jn.1997.77.4.2061.
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Myers, S. F., H. H. Salem, and J. A. Kaltenbach. Efferent neurons and vestibular cross talk in the frog. J. Neurophysiol. 77: 2061–2070, 1997. A galvanic stimulus (30- to 120-s, 0.3-mA constant current pulse) was used to depolarize the spike-generating region of horizontal and anterior canal afferent neurons. The galvanically induced spike activity from these neurons served as a driving input to the efferent vestibular system in the bullfrog. Efferent-mediated effects were assessed by intracellular recordings of posterior canal afferent spike activity, either ipsilateral or contralateral to the driving stimulus. Ipsilateral to the driving stimulus, efferent-mediated spike rate changes occurred in 62 (39%) of 158 posterior canal afferent neurons. Ipsilateral efferent-mediated effects were overwhelmingly excitatory (92%). Of responding units, 3% were inhibited during stimulus application and 5% showed mixed responses involving 3–20 s of inhibition followed by facilitation. Contralateral to the driving stimulus, efferent-mediated spike rate changes occurred in 18 (23%) of 77 posterior canal afferent neurons. Contralateral efferent-mediated effects were overwhelmingly inhibitory (95%). Only one unit was facilitated during stimulation and no mixed responses to contralateral stimulation were observed. Analysis of the coefficient of variation in interspike intervals (CV) before and during stimulation showed no significant efferent-mediated effects on spike train noise. Comparisons of resting spike rates between units showing efferent-mediated effects and those that did not were in general agreement with previous studies. Responding units had a lower mean spike rate (6.8 ± 0.70 spikes/s, mean ± SE) than did nonresponding units (10.7 ± 0.42 spikes/s, mean ± SE; P < 0.001; 2-tailed t-test of log-normalized data). Comparison between groups in the regularity of their resting spike rates, as quantified by CV, showed considerable overlap. When responding and nonresponding units with similar resting spike rates were compared, responding units had more irregular resting spike rates than did nonresponding units ( P < 0.004; 2-tailed, paired t-test). In most cases (77%) the temporal pattern and general shapes of efferent-mediated responses mirrored the driving input of the galvanically activated afferent neurons. The other 23% of efferent-mediated responses exhibited a marked adaptation of the response. Adapting and nonadapting units were not significantly different in their mean resting spike rates or in the regularity of their resting spike rates.
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Hu, Meng, Wu Li, and Hualou Liang. "A Copula-Based Granger Causality Measure for the Analysis of Neural Spike Train Data." IEEE/ACM Transactions on Computational Biology and Bioinformatics 15, no. 2 (March 1, 2018): 562–69. http://dx.doi.org/10.1109/tcbb.2014.2388311.
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Meng, Liang, Mark A. Kramer, Steven J. Middleton, Miles A. Whittington, and Uri T. Eden. "A Unified Approach to Linking Experimental, Statistical and Computational Analysis of Spike Train Data." PLoS ONE 9, no. 1 (January 17, 2014): e85269. http://dx.doi.org/10.1371/journal.pone.0085269.
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Wu, Wei, and Anuj Srivastava. "Analysis of spike train data: Alignment and comparisons using the extended Fisher-Rao metric." Electronic Journal of Statistics 8, no. 2 (2014): 1776–85. http://dx.doi.org/10.1214/14-ejs865b.
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Hadjipantelis, Pantelis Z., John A. D. Aston, Hans-Georg Müller, and John Moriarty. "Analysis of spike train data: A multivariate mixed effects model for phase and amplitude." Electronic Journal of Statistics 8, no. 2 (2014): 1797–807. http://dx.doi.org/10.1214/14-ejs865e.
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Kociuba, Wanda, Wieslaw Mądry, Aneta Kramek, Krzysztof Ukalski, and Marcin Studnicki. "Multtvariate diversity of Polish winter triticale cultivars for spike and other traits." Plant Breeding and Seed Science 62, no. 1 (January 1, 2010): 31–42. http://dx.doi.org/10.2478/v10129-011-0003-4.
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Multtvariate diversity of Polish winter triticale cultivars for spike and other traits The objective of the present study was to determine the extent and pattern of genotypic diversity for six spike quantitative characters and two other traits in 36 winter triticale cultivars released in Poland, to classify the cultivars into similarity groups (clusters) and to identify those traits, among the studied ones, which mostly discriminated distinguished groups of cultivars. The 36 cultivars, released in the period from 1982 to 1999, were evaluated across three years 2002-2004 at the Experimental Field Station in Czesławice near Nałęczów, Poland. The experiments were carried out on the brown soil with loess subsoil. In each year the one-replicated experimental design was used with 2 m2 plots, rows 20 cm apart, and dense sowing using about 2 cm spacing of seeds. Analyses of variance for each trait data according to the random model (both cultivars and years were assumed to be random factors) were done. To classify and characterize genotypic diversity of the cultivars for the eight traits, the pattern analysis was used. It involved both cluster analysis using Ward's procedure with a measure of the multivariate similarity among cultivars being Squared Euclidean Distance and canonical variate analysis (CVA) on the basis of cultivar BLUPs for the original traits. Quite different groups of cultivars for the studied traits were found, specially one group was substantially distanced to the others. As it was shown by CVA, spike length and number of spikelets per spike as negatively correlated with number of grains per spikelet in the studied set of the cultivars relatively largest contributed to overall differentiation of the distinguished eight groups and then, these traits best discriminated among the eight cultivar groups in the term of Mahalanobis distance for the considered traits. The 1000 grain weight and grain protein content much less contributed to overall discrimination of the cultivar groups than the previous four traits. The most important agronomic traits characterizing productivity of the spike grain weight and its two components, e.g. number of grains per spikelet and number of grains per spike had least discriminating power for the groups of cultivars. Grain yield per unit area of cereals is a result of spike grain yield and the number of spikes per unit area. In these studies of winter triticale cultivar diversity only grain spike yield and its components were included. Thus, the presented study are a primary evaluating of phenotypic diversity in the cultivars. The further study on the cultivar diversity evaluation for grain yield per unit area and its components is necessary.
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Brockmeier, Austin J., John S. Choi, Evan G. Kriminger, Joseph T. Francis, and Jose C. Principe. "Neural Decoding with Kernel-Based Metric Learning." Neural Computation 26, no. 6 (June 2014): 1080–107. http://dx.doi.org/10.1162/neco_a_00591.
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In studies of the nervous system, the choice of metric for the neural responses is a pivotal assumption. For instance, a well-suited distance metric enables us to gauge the similarity of neural responses to various stimuli and assess the variability of responses to a repeated stimulus—exploratory steps in understanding how the stimuli are encoded neurally. Here we introduce an approach where the metric is tuned for a particular neural decoding task. Neural spike train metrics have been used to quantify the information content carried by the timing of action potentials. While a number of metrics for individual neurons exist, a method to optimally combine single-neuron metrics into multineuron, or population-based, metrics is lacking. We pose the problem of optimizing multineuron metrics and other metrics using centered alignment, a kernel-based dependence measure. The approach is demonstrated on invasively recorded neural data consisting of both spike trains and local field potentials. The experimental paradigm consists of decoding the location of tactile stimulation on the forepaws of anesthetized rats. We show that the optimized metrics highlight the distinguishing dimensions of the neural response, significantly increase the decoding accuracy, and improve nonlinear dimensionality reduction methods for exploratory neural analysis.