Statistical properties of spike trains: Universal and stimulus-dependent aspects

Brenner, Naama; Agam, Oded; Bialek, William; Steveninck, Rob de Ruyter van

doi:10.1103/physreve.66.031907

Cited by 18 publications

(16 citation statements)

References 26 publications

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“…As shown by our data, responses of receptor neurons may allow an even simpler framework with a clear separation between external stimulus and stimulus-independent cell dynamics (see also Brenner et al 2002;Johnson 1996). For the investigated auditory receptors, the cell dynamics are captured by a renewal process under constant stimulation so that each neuron can be characterized by one unique recovery function w(t Ϫ t last ).…”

Section: Discussionmentioning

confidence: 87%

Spike-Train Variability of Auditory Neurons In Vivo: Dynamic Responses Follow Predictions From Constant Stimuli

Schaette¹,

Gollisch²,

Herz³

2005

Journal of Neurophysiology

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Schaette, Roland, Tim Gollisch, and Andreas V. M. Herz. Spike-train variability of auditory neurons in vivo: dynamic responses follow predictions from constant stimuli. J Neurophysiol 93: 3270 -3281, 2005. First published February 2, 2005 doi:10.1152/jn.00758.2004. Reliable accounts of the variability observed in neural spike trains are a prerequisite for the proper interpretation of neural dynamics and coding principles. Models that accurately describe neural variability over a wide range of stimulation and response patterns are therefore highly desirable, especially if they can explain this variability in terms of basic neural observables and parameters such as firing rate and refractory period. In this work, we analyze the response variability recorded in vivo from locust auditory receptor neurons under acoustic stimulation. In agreement with results from other systems, our data suggest that neural refractoriness has a strong influence on spike-train variability. We therefore explore a stochastic model of spike generation that includes refractoriness through a recovery function. Because our experimental data are consistent with a renewal process, the recovery function can be derived from a single interspike-interval histogram obtained under constant stimulation. The resulting description yields quantitatively accurate predictions of the response variability over the whole range of firing rates for constant-intensity as well as amplitude-modulated sound stimuli. Model parameters obtained from constant stimulation can be used to predict the variability in response to dynamic stimuli. These results demonstrate that key ingredients of the stochastic response dynamics of a sensory neuron are faithfully captured by a simple stochastic model framework. I N T R O D U C T I O NSensory neurons provide an animal with the primary representation of its environment and internal state. Any computation and behavioral decision has to be based on this representation. Yet even under controlled laboratory conditions, repeated stimulus presentations often lead to a considerable trial-to-trial variability of neural responses. This is particularly true for cortical neurons, which typically discharge with high variability under in vivo conditions (Buracas et al. 1998;Holt et al. 1996;Shadlen and Newsome 1998;Stevens and Zador 1998). As expected for Poisson-like random processes, coefficients of variation near unity and spike-count variances equal to or even above the mean count have been found (Softky and Koch 1993;Teich et al. 1996).On the other hand, neural response characteristics depend sensitively on the temporal features of the stimulus pattern (Mainen and Sejnowski 1995), which is of special importance for sensory neurons receiving highly structured dynamic stimuli (de Ruyter van Kara et al. 2000;Machens et al. 2001;Warzecha et al. 2000). Indeed, for appropriate inputs, individual spikes can be highly reliable and precisely timed (Berry et al. 1997;Reinagel and Reid 2002), resulting in spike-count variances far below the mea...

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Section: Discussionmentioning

confidence: 87%

Spike-Train Variability of Auditory Neurons In Vivo: Dynamic Responses Follow Predictions From Constant Stimuli

Schaette¹,

Gollisch²,

Herz³

2005

Journal of Neurophysiology

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“…Analytical approaches using this trick have been largely limited to the case of exponentially correlated noise (for an exception, see (Bauermeister et al 2013)), that can be mimicked by an Ornstein-Uhlenbeck process (one additional degree of freedom). Using perturbation techniques (small or large correlation time or small noise intensity) approximations have been worked out for the firing rate (Brunel and Sergi 1998;Moreno-Bote and Parga 2004;Alijani and Richardson 2011), the spike train's auto-correlation (Brenner et al 2002;Moreno-Bote and Parga 2006), the ISI density (Lindner 2004;Schwalger and SchimanskyGeier 2008) and ISI correlations (Lindner 2004), and the dynamical response (Brunel et al 2001;Alijani and Presynaptic spike trains have temporal structure, e.g. due to refractoriness, bursting, or rate modulations, which is expressed by non-flat power spectra S kk (f ), k = 1, .…”

Section: Introductionmentioning

confidence: 99%

Statistical structure of neural spiking under non-Poissonian or other non-white stimulation

2015

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Nerve cells in the brain generate sequences of action potentials with a complex statistics. Theoretical attempts to understand this statistics were largely limited to the case of a temporally uncorrelated input (Poissonian shot noise) from the neurons in the surrounding network. However, the stimulation from thousands of other neurons has various sorts of temporal structure. Firstly, input spike trains are temporally correlated because their firing rates can carry complex signals and because of cell-intrinsic properties like neural refractoriness, bursting, or adaptation. Secondly, at the connections between neurons, the synapses, usagedependent changes in the synaptic weight (short-term plasticity) further shape the correlation structure of the effective input to the cell. From the theoretical side, it is poorly understood how these correlated stimuli, socalled colored noise, affect the spike train statistics. In particular, no standard method exists to solve the associated first-passage-time problem for the interspikeinterval statistics with an arbitrarily colored noise. Assuming that input fluctuations are weaker than the mean neuronal drive, we derive simple formulas for the essential interspike-interval statistics for a canon- ical model of a tonically firing neuron subjected to arbitrarily correlated input from the network. We verify our theory by numerical simulations for three paradigmatic situations that lead to input correlations: (i) ratecoded naturalistic stimuli in presynaptic spike trains; (ii) presynaptic refractoriness or bursting; (iii) synaptic short-term plasticity. In all cases, we find severe effects on interval statistics. Our results provide a framework for the interpretation of firing statistics measured in vivo in the brain.

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“…Mutual information can be interpreted as a measure of how much information two studied systems exchange or two studied stochastic processes or data sets share. Due to these characteristics mutual information is suitable for many applications, and has been used successfully particularly enhance the understanding of the development and functioning of the brain in neuroscience [48][49][50], to characterise [51,52] and model various complex and chaotic systems [53][54][55], and also to quantify the information capacity of a communication system [56]. Additionally mutual information provides a convenient way to identify the most relevant variables with which to describe the behaviour of a complex system [57], which is of paramount importance in modelling those systems, and indeed to the methodology of this paper.…”

Section: Introductionmentioning

confidence: 99%

Networks in financial markets based on the mutual information rate

Fiedor

2014

Phys. Rev. E

117

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In the last years efforts in econophysics have been shifted to study how network theory can facilitate understanding of complex financial markets. Main part of these efforts is the study of correlation-based hierarchical networks. This is somewhat surprising as the underlying assumptions of research looking at financial markets is that they behave chaotically. In fact it's common for econophysicists to estimate maximal Lyapunov exponent for log returns of a given financial asset to confirm that prices behave chaotically. Chaotic behaviour is only displayed by dynamical systems which are either non-linear or infinite-dimensional. Therefore it seems that non-linearity is an important part of financial markets, which is proved by numerous studies confirming financial markets display significant non-linear behaviour, yet network theory is used to study them using almost exclusively correlations and partial correlations, which are inherently dealing with linear dependencies only. In this paper we introduce a way to incorporate non-linear dynamics and dependencies into hierarchical networks to study financial markets using mutual information and its dynamical extension: the mutual information rate. We estimate it using multidimensional Lempel-Ziv complexity and then convert it into an Euclidean metric in order to find appropriate topological structure of networks modelling financial markets. We show that this approach leads to different results than correlation-based approach used in most studies, on the basis of 15 biggest companies listed on Warsaw Stock Exchange in the period of 2009-2012 and 91 companies listed on NYSE100 between 2003 and 2013, using minimal spanning trees and planar maximally filtered graphs.

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Statistical properties of spike trains: Universal and stimulus-dependent aspects

Cited by 18 publications

References 26 publications

Spike-Train Variability of Auditory Neurons In Vivo: Dynamic Responses Follow Predictions From Constant Stimuli

Spike-Train Variability of Auditory Neurons In Vivo: Dynamic Responses Follow Predictions From Constant Stimuli

Statistical structure of neural spiking under non-Poissonian or other non-white stimulation

Networks in financial markets based on the mutual information rate

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