reliability.bib

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@article{SchmandtGalan2012PRE,
	Abstract = {Markov chains provide realistic models of numerous stochastic processes in nature. We demonstrate that in any Markov chain, the change in occupation number in state A is correlated to the change in occupation number in state B if and only if A and B are directly connected. This implies that if we are only interested in state A, fluctuations in B may be replaced with their mean if state B is not directly connected to A, which shortens computing time considerably. We show the accuracy and efficacy of our approximation theoretically and in simulations of stochastic ion-channel gating in neurons.},
	Author = {Schmandt, Nicolaus T and Gal\'{a}n, Roberto F},
	Date-Added = {2013-10-07 22:11:32 +0000},
	Date-Modified = {2013-10-07 22:11:59 +0000},
	Journal = {Phys Rev Lett},
	Journal-Full = {Physical review letters},
	Mesh = {Ion Channel Gating; Markov Chains; Models, Chemical; Models, Neurological; Models, Theoretical; Stochastic Processes},
	Month = {Sep},
	Number = {11},
	Pages = {118101},
	Pmid = {23005678},
	Pst = {ppublish},
	Title = {Stochastic-shielding approximation of {Markov} chains and its application to efficiently simulate random ion-channel gating},
	Volume = {109},
	Year = {2012}}

@article{WangSpencerFellousSejnowski2010Sci,
	Abstract = {Thalamic inputs strongly drive neurons in the primary visual cortex, even though these neurons constitute only approximately 5% of the synapses on layer 4 spiny stellate simple cells. We modeled the feedforward excitatory and inhibitory inputs to these cells based on in vivo recordings in cats, and we found that the reliability of spike transmission increased steeply between 20 and 40 synchronous thalamic inputs in a time window of 5 milliseconds, when the reliability per spike was most energetically efficient. The optimal range of synchronous inputs was influenced by the balance of background excitation and inhibition in the cortex, which could gate the flow of information into the cortex. Ensuring reliable transmission by spike synchrony in small populations of neurons may be a general principle of cortical function.},
	Author = {Wang, Hsi-Ping and Spencer, Donald and Fellous, Jean-Marc and Sejnowski, Terrence J},
	Date-Added = {2013-10-07 21:56:44 +0000},
	Date-Modified = {2013-10-07 21:57:02 +0000},
	Doi = {10.1126/science.1183108},
	Journal = {Science},
	Journal-Full = {Science (New York, N.Y.)},
	Mesh = {Action Potentials; Animals; Cats; Computer Simulation; Geniculate Bodies; Models, Neurological; Neural Inhibition; Neurons; Synapses; Synaptic Transmission; Visual Cortex; Visual Pathways},
	Month = {Apr},
	Number = {5974},
	Pages = {106-9},
	Pmc = {PMC2859205},
	Pmid = {20360111},
	Pst = {ppublish},
	Title = {Synchrony of thalamocortical inputs maximizes cortical reliability},
	Volume = {328},
	Year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1126/science.1183108}}

@article{TaillefumierMagnasco2013PNAS,
	Abstract = {Finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple-looking problem of vast practical importance in physics, biology, chemistry, neuroscience, economics, and industrial engineering. Problems in which the bound to be traversed is itself a fluctuating function of time include widely studied problems in neural coding, such as neuronal integrators with irregular inputs and internal noise. We show that the probability p(t) that a Gauss-Markov process will first exceed the boundary at time t suffers a phase transition as a function of the roughness of the boundary, as measured by its H{\"o}lder exponent H. The critical value occurs when the roughness of the boundary equals the roughness of the process, so for diffusive processes the critical value is Hc = 1/2. For smoother boundaries, H > 1/2, the probability density is a continuous function of time. For rougher boundaries, H < 1/2, the probability is concentrated on a Cantor-like set of zero measure: the probability density becomes divergent, almost everywhere either zero or infinity. The critical point Hc = 1/2 corresponds to a widely studied case in the theory of neural coding, in which the external input integrated by a model neuron is a white-noise process, as in the case of uncorrelated but precisely balanced excitatory and inhibitory inputs. We argue that this transition corresponds to a sharp boundary between rate codes, in which the neural firing probability varies smoothly, and temporal codes, in which the neuron fires at sharply defined times regardless of the intensity of internal noise.},
	Author = {Taillefumier, Thibaud and Magnasco, Marcelo O},
	Date-Added = {2013-10-07 21:52:25 +0000},
	Date-Modified = {2013-10-07 21:52:43 +0000},
	Doi = {10.1073/pnas.1212479110},
	Journal = {Proc Natl Acad Sci U S A},
	Journal-Full = {Proceedings of the National Academy of Sciences of the United States of America},
	Mesh = {Computer Simulation; Diffusion; Models, Biological; Neurons; Stochastic Processes; Synaptic Transmission; Time Factors},
	Month = {Apr},
	Number = {16},
	Pages = {E1438-43},
	Pmc = {PMC3631650},
	Pmid = {23536302},
	Pst = {ppublish},
	Title = {A phase transition in the first passage of a Brownian process through a fluctuating boundary with implications for neural coding},
	Volume = {110},
	Year = {2013},
	Bdsk-Url-1 = {http://dx.doi.org/10.1073/pnas.1212479110}}

@article{GillespieHoughton2011JCompNsci,
	Abstract = {A novel method is presented for calculating the information channel capacity of spike trains. This method works by fitting a χ-distribution to the distribution of distances between responses to the same stimulus: the χ-distribution is the length distribution for a vector of Gaussian variables. The dimension of this vector defines an effective dimension for the noise and by rephrasing the problem in terms of distance based quantities, this allows the channel capacity to be calculated. As an example, the capacity is calculated for a data set recorded from auditory neurons in zebra finch.},
	Author = {Gillespie, James B and Houghton, Conor J},
	Date-Added = {2013-10-07 21:50:11 +0000},
	Date-Modified = {2013-10-07 21:50:30 +0000},
	Doi = {10.1007/s10827-010-0286-8},
	Journal = {J Comput Neurosci},
	Journal-Full = {Journal of computational neuroscience},
	Mesh = {Action Potentials; Animals; Chi-Square Distribution; Electrophysiology; Finches; Information Theory; Models, Neurological; Neurons; Noise; Normal Distribution; Time Factors},
	Month = {Feb},
	Number = {1},
	Pages = {201-9},
	Pmid = {20972614},
	Pst = {ppublish},
	Title = {A metric space approach to the information channel capacity of spike trains},
	Volume = {30},
	Year = {2011},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10827-010-0286-8}}

@article{ErmentroutGalanUrban2008TNsci,
	Abstract = {The brain is noisy. Neurons receive tens of thousands of highly fluctuating inputs and generate spike trains that appear highly irregular. Much of this activity is spontaneous - uncoupled to overt stimuli or motor outputs - leading to questions about the functional impact of this noise. Although noise is most often thought of as disrupting patterned activity and interfering with the encoding of stimuli, recent theoretical and experimental work has shown that noise can play a constructive role - leading to increased reliability or regularity of neuronal firing in single neurons and across populations. These results raise fundamental questions about how noise can influence neural function and computation.},
	Author = {Ermentrout, G Bard and Gal\'{a}n, Roberto F and Urban, Nathaniel N},
	Date-Added = {2013-10-07 21:27:59 +0000},
	Date-Modified = {2013-10-07 21:28:32 +0000},
	Doi = {10.1016/j.tins.2008.06.002},
	Journal = {Trends Neurosci},
	Journal-Full = {Trends in neurosciences},
	Mesh = {Animals; Artifacts; Brain; Cortical Synchronization; Electrophysiology; Humans; Neurons; Reproducibility of Results},
	Month = {Aug},
	Number = {8},
	Pages = {428-34},
	Pmc = {PMC2574942},
	Pmid = {18603311},
	Pst = {ppublish},
	Title = {Reliability, synchrony and noise},
	Volume = {31},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.tins.2008.06.002}}

@article{GalanErmentroutUrban2008JNphys,
	Abstract = {Use of spike timing to encode information requires that neurons respond with high temporal precision and with high reliability. Fast fluctuating stimuli are known to result in highly reproducible spike times across trials, whereas constant stimuli result in variable spike times. Here, we first studied mathematically how spike-time reliability depends on the rapidness of aperiodic stimuli. Then, we tested our theoretical predictions in computer simulations of neuron models (Hodgkin-Huxley and modified quadratic integrate-and-fire), as well as in patch-clamp experiments with real neurons (mitral cells in the olfactory bulb and pyramidal cells in the neocortex). As predicted by our theory, we found that for firing frequencies in the beta/gamma range, spike-time reliability is maximal when the time scale of the input fluctuations (autocorrelation time) is in the range of a few milliseconds (2-5 ms), coinciding with the time scale of fast synapses, and decreases substantially for faster and slower inputs. Finally, we comment how these findings relate to mechanisms causing neuronal synchronization.},
	Author = {Gal{\'a}n, Roberto F and Ermentrout, G Bard and Urban, Nathaniel N},
	Date-Added = {2013-10-07 21:27:47 +0000},
	Date-Modified = {2013-10-07 21:29:05 +0000},
	Doi = {10.1152/jn.00563.2007},
	Journal = {J Neurophysiol},
	Journal-Full = {Journal of neurophysiology},
	Mesh = {Action Potentials; Algorithms; Animals; Computer Simulation; Cortical Synchronization; Mice; Models, Neurological; Neocortex; Neural Pathways; Olfactory Bulb; Organ Culture Techniques; Pyramidal Cells; Reaction Time; Synapses; Synaptic Transmission; Time Factors},
	Month = {Jan},
	Number = {1},
	Pages = {277-83},
	Pmc = {PMC2533711},
	Pmid = {17928562},
	Pst = {ppublish},
	Title = {Optimal time scale for spike-time reliability: theory, simulations, and experiments},
	Volume = {99},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1152/jn.00563.2007}}

@article{RichardsonGerstner2005NeuralComp,
	Abstract = {The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductance-based synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.},
	Author = {Richardson, Magnus J E and Gerstner, Wulfram},
	Date-Added = {2013-03-30 21:04:52 +0000},
	Date-Modified = {2013-03-30 21:05:16 +0000},
	Doi = {10.1162/0899766053429444},
	Journal = {Neural Comput},
	Journal-Full = {Neural computation},
	Mesh = {Action Potentials; Animals; Artifacts; Cell Membrane; Cerebral Cortex; Humans; Ion Channels; Neural Conduction; Neural Networks (Computer); Neural Pathways; Neurons; Normal Distribution; Poisson Distribution; Synaptic Transmission},
	Month = {Apr},
	Number = {4},
	Pages = {923-47},
	Pmid = {15829095},
	Pst = {ppublish},
	Title = {Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance},
	Volume = {17},
	Year = {2005},
	Bdsk-Url-1 = {http://dx.doi.org/10.1162/0899766053429444}}

@article{RichardsonGerstner2006Chaos,
	Abstract = {Neurons in the central nervous system, and in the cortex in particular, are subject to a barrage of pulses from their presynaptic populations. These synaptic pulses are mediated by conductance changes and therefore lead to increases or decreases of the neuronal membrane potential with amplitudes that are dependent on the voltage: synaptic noise is multiplicative. The statistics of the membrane potential are of experimental interest because the measurement of a single subthreshold voltage can be used to probe the activity occurring across the presynaptic population. Though the interpulse interval is not always significantly smaller than the characteristic decay time of the pulses, and so the fluctuations have the nature of shot noise, the majority of results available in the literature have been calculated in the diffusion limit, which is valid for high-rate pulses. Here the effects that multiplicative conductance noise and shot noise have on the voltage fluctuations are examined. It is shown that both these aspects of synaptic drive sculpt high-order features of the subthreshold voltage distribution, such as the skew. It is further shown that the diffusion approximation can only capture the effects arising from the multiplicative conductance noise, predicting a negative voltage skew for excitatory drive. Exact results for the full dynamics are derived from a master-equation approach, predicting positively skewed distributions with long tails in voltage ranges typical for action potential generation. It is argued that, although the skew is a high-order feature of subthreshold voltage distributions, the increased probability of reaching firing threshold suggests a potential role for shot noise in shaping the neuronal transfer function.},
	Author = {Richardson, Magnus J E and Gerstner, Wulfram},
	Date-Added = {2013-03-30 21:04:46 +0000},
	Date-Modified = {2013-03-30 21:06:20 +0000},
	Doi = {10.1063/1.2203409},
	Journal = {Chaos},
	Journal-Full = {Chaos (Woodbury, N.Y.)},
	Mesh = {Action Potentials; Animals; Biological Clocks; Computer Simulation; Differential Threshold; Electric Conductivity; Humans; Membrane Potentials; Models, Neurological; Models, Statistical; Nerve Net; Neurons; Reproducibility of Results; Sensitivity and Specificity; Synaptic Transmission},
	Month = {Jun},
	Number = {2},
	Pages = {026106},
	Pmid = {16822038},
	Pst = {ppublish},
	Title = {Statistics of subthreshold neuronal voltage fluctuations due to conductance-based synaptic shot noise},
	Volume = {16},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2203409}}

@article{PaninskiPillowSimoncelli2004NeuralComp,
	Abstract = {We examine a cascade encoding model for neural response in which a linear filtering stage is followed by a noisy, leaky, integrate-and-fire spike generation mechanism. This model provides a biophysically more realistic alternative to models based on Poisson (memoryless) spike generation, and can effectively reproduce a variety of spiking behaviors seen in vivo. We describe the maximum likelihood estimator for the model parameters, given only extracellular spike train responses (not intracellular voltage data). Specifically, we prove that the log-likelihood function is concave and thus has an essentially unique global maximum that can be found using gradient ascent techniques. We develop an efficient algorithm for computing the maximum likelihood solution, demonstrate the effectiveness of the resulting estimator with numerical simulations, and discuss a method of testing the model's validity using time-rescaling and density evolution techniques.},
	Author = {Paninski, Liam and Pillow, Jonathan W and Simoncelli, Eero P},
	Date-Added = {2013-03-30 04:49:01 +0000},
	Date-Modified = {2013-03-30 04:49:29 +0000},
	Doi = {10.1162/0899766042321797},
	Journal = {Neural Comput},
	Journal-Full = {Neural computation},
	Mesh = {Algorithms; Biophysical Phenomena; Biophysics; Electrophysiology; Likelihood Functions; Membrane Potentials; Models, Neurological; Models, Statistical; Neurons; Nonlinear Dynamics; Poisson Distribution},
	Month = {Dec},
	Number = {12},
	Pages = {2533-61},
	Pmid = {15516273},
	Pst = {ppublish},
	Title = {Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model},
	Volume = {16},
	Year = {2004},
	Bdsk-Url-1 = {http://dx.doi.org/10.1162/0899766042321797}}

@article{Brillinger1988BiolCyb,
	Abstract = {Suppose that a neuron is firing spontaneously or that it is firing under the influence of other neurons. Suppose that the data available are the firing times of the neurons present. An "integrate several inputs and fire" model is developed and studied empirically. For the model a neuron's firing occurs when an internal state variable crosses a random threshold. This conceptual model leads to maximum likelihood estimates of internal quantities, such as the postsynaptic potentials of the measured influencing neurons, the membrane potential, the absolute threshold and also estimates of derived quantities such as the strength-duration curve and the recovery process of the threshold. The model's validity is examined via an estimate of the conditional firing probability. The approach appears useful for estimating biologically meaningful parameters, for examining hypotheses re these parameters, for understanding the connections present in neural networks and for aiding description and classification of neurons and synapses. Analyses are presented for a number of data sets collected for the sea hare, Aplysia californica, by J. P. Segundo. Both excitatory and inhibitory examples are provided. The computations were carried out via the Glim statistical package. An example of a Glim program realizing the work is presented in the Appendix.},
	Author = {Brillinger, D R},
	Date-Added = {2013-03-30 04:42:03 +0000},
	Date-Modified = {2013-03-30 04:42:32 +0000},
	Journal = {Biol Cybern},
	Journal-Full = {Biological cybernetics},
	Mesh = {Animals; Aplysia; Cybernetics; Electrophysiology; Models, Neurological; Models, Theoretical; Nerve Net; Neurons},
	Number = {3},
	Pages = {189-200},
	Pmid = {3179344},
	Pst = {ppublish},
	Title = {Maximum likelihood analysis of spike trains of interacting nerve cells},
	Volume = {59},
	Year = {1988}}

@article{lajoie2012chaos,
	Author = {Lajoie, G. and Lin, K.K. and Shea-Brown, E.},
	Journal = {arXiv preprint arXiv:1209.3051},
	Title = {Chaos and reliability in balanced spiking networks},
	Year = {2012}}

@article{LinSheaBrownYoung2009JCNS,
	Author = {Lin, Kevin K. and Shea-Brown, Eric and Young, Lai-Sang},
	Doi = {10.1007/s10827-008-0133-3},
	Issn = {0929-5313},
	Issue = {1},
	Journal = {Journal of Computational Neuroscience},
	Keywords = {Spike-time reliability; Spiking neural network; Neural oscillator; Theta neuron; Chaos; Stochastic dynamics; Random dynamical systems},
	Language = {English},
	Pages = {135-160},
	Publisher = {Springer US},
	Title = {Spike-time reliability of layered neural oscillator networks},
	Url = {http://dx.doi.org/10.1007/s10827-008-0133-3},
	Volume = {27},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10827-008-0133-3}}

@article{FellousHouwelingModiRaoTiesingaSejnowski2001JNP,
	Abstract = {Pyramidal cells and interneurons in rat prefrontal cortical slices exhibit subthreshold oscillations when depolarized by constant current injection. For both types of neurons, the frequencies of these oscillations for current injection just below spike threshold were 2--10 Hz. Above spike threshold, however, the subthreshold oscillations in pyramidal cells remained low, but the frequency of oscillations in interneurons increased up to 50 Hz. To explore the interaction between these intrinsic oscillations and external inputs, the reliability of spiking in these cortical neurons was studied with sinusoidal current injection over a range of frequencies above and below the intrinsic frequency. Cortical neurons produced 1:1 phase locking for a limited range of driving frequencies for fixed amplitude. For low-input amplitude, 1:1 phase locking was obtained in the 5- to 10-Hz range. For higher-input amplitudes, pyramidal cells phase-locked in the 5- to 20-Hz range, whereas interneurons phase-locked in the 5- to 50-Hz range. For the amplitudes studied here, spike time reliability was always highest during 1:1 phase-locking, between 5 and 20 Hz for pyramidal cells and between 5 and 50 Hz for interneurons. The observed differences in the intrinsic frequency preference between pyramidal cells and interneurons have implications for rhythmogenesis and information transmission between populations of cortical neurons.},
	Author = {Fellous, J M and Houweling, A R and Modi, R H and Rao, R P and Tiesinga, P H and Sejnowski, T J},
	Date-Added = {2013-01-23 04:47:01 +0000},
	Date-Modified = {2013-01-23 04:47:35 +0000},
	Journal = {J Neurophysiol},
	Journal-Full = {Journal of neurophysiology},
	Mesh = {Action Potentials; Animals; Cerebral Cortex; Differential Threshold; Electric Stimulation; Electrophysiology; Interneurons; Oscillometry; Pyramidal Cells; Rats; Rats, Sprague-Dawley; Reaction Time},
	Month = {Apr},
	Number = {4},
	Pages = {1782-7},
	Pmid = {11287500},
	Pst = {ppublish},
	Title = {Frequency dependence of spike timing reliability in cortical pyramidal cells and interneurons},
	Volume = {85},
	Year = {2001}}

@article{HaasWhite2002JNeurophys,
	Abstract = {Electrophysiologically, stellate cells (SCs) from layer II of the medial entorhinal cortex (MEC) are distinguished by intrinsic 4- to 12-Hz subthreshold oscillations. These oscillations are thought to impose a pattern of slow periodic firing that may contribute to the parahippocampal theta rhythm in vivo. Using stimuli with systematically differing frequency content, we examined supra- and subthreshold responses in SCs with the goal of understanding how their distinctive characteristics shape these responses. In reaction to repeated presentations of identical, pseudo-random stimuli, the reliability (repeatability) of the spiking response in SCs depends critically on the frequency content of the stimulus. Reliability is optimal for stimuli with a greater proportion of power in the 4- to 12-Hz range. The simplest mechanistic explanation of these results is that rhythmogenic subthreshold membrane mechanisms resonate with inputs containing significant power in the 4- to 12-Hz band, leading to larger subthreshold excursions and thus enhanced reliability. However, close examination of responses rules out this explanation: SCs do show clear subthreshold resonance (i.e., selective amplification of inputs with particular frequency content) in response to sinusoidal stimuli, while simultaneously showing a lack of subthreshold resonance in response to the pseudo-random stimuli used in reliability experiments. Our results support a model with distinctive input-output relationships under subthreshold and suprathreshold conditions. For suprathreshold stimuli, SC spiking seems to best reflect the amount of input power in the theta (4-12 Hz) frequency band. For subthreshold stimuli, we hypothesize that the magnitude of subthreshold theta-range oscillations in SCs reflects the total power, across all frequencies, of the input.},
	Author = {Haas, Julie S and White, John A},
	Date-Added = {2013-01-22 22:54:16 +0000},
	Date-Modified = {2013-01-22 22:54:47 +0000},
	Doi = {10.1152/jn.00598.2002},
	Journal = {J Neurophysiol},
	Journal-Full = {Journal of neurophysiology},
	Mesh = {Algorithms; Animals; Electric Stimulation; Electrophysiology; Entorhinal Cortex; Membrane Potentials; Neurons; Rats; Rats, Long-Evans; Reproducibility of Results},
	Month = {Nov},
	Number = {5},
	Pages = {2422-9},
	Pmid = {12424283},
	Pst = {ppublish},
	Title = {{Frequency selectivity of layer II stellate cells in the medial entorhinal cortex}},
	Volume = {88},
	Year = {2002},
	Bdsk-Url-1 = {http://dx.doi.org/10.1152/jn.00598.2002}}

@article{LyttleFellous2011JNsciMeth,
	Abstract = {An important problem in neuroscience is that of constructing quantitative measures of the similarity between neural spike trains. These measures can be used, for example, to assess the reliability of the response of a single neuron to repeated stimulus presentations, or to uncover relationships in the firing patterns of multiple neurons in a population. While several similarity measures have been proposed, the extent to which they take into account various biologically important spike train features such as bursts of spikes, or periods of inactivity remains poorly understood. Here we compare these measures using tests specifically designed to assess the sensitivity to bursts and silent periods. In addition, we propose two new measures. The first is designed to detect periods of shared silence between spike trains, while the second is designed to emphasize the presence of common bursts. To assist researchers in determining which measure is best suited to their particular data analysis needs, we also show how these measures can be combined and how their parameters can be determined on the basis of physiologically relevant quantities.},
	Author = {Lyttle, David and Fellous, Jean-Marc},
	Date-Added = {2013-01-22 05:40:35 +0000},
	Date-Modified = {2013-01-22 05:40:55 +0000},
	Doi = {10.1016/j.jneumeth.2011.05.005},
	Journal = {J Neurosci Methods},
	Journal-Full = {Journal of neuroscience methods},
	Mesh = {Action Potentials; Algorithms; Computer Simulation; Electrophysiology; Humans; Models, Neurological; Neural Inhibition; Neurophysiology; Reaction Time; Reproducibility of Results; Signal Processing, Computer-Assisted; Time Factors},
	Month = {Aug},
	Number = {2},
	Pages = {296-309},
	Pmid = {21600921},
	Pst = {ppublish},
	Title = {A new similarity measure for spike trains: sensitivity to bursts and periods of inhibition},
	Volume = {199},
	Year = {2011},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jneumeth.2011.05.005}}

@article{ChacronLindnerLongtin2004PRL,
	Author = {Chacron, Maurice J. and Lindner, Benjamin and Longtin, Andr\'e},
	Doi = {10.1103/PhysRevLett.92.080601},
	Issue = {8},
	Journal = {Phys. Rev. Lett.},
	Month = {Feb},
	Numpages = {4},
	Pages = {080601},
	Publisher = {American Physical Society},
	Title = {Noise Shaping by Interval Correlations Increases Information Transfer},
	Url = {http://link.aps.org/doi/10.1103/PhysRevLett.92.080601},
	Volume = {92},
	Year = {2004},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.92.080601},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.92.080601}}

@inbook{LindnerChapterLaingBook2010,
	Author = {Benjamin Lindner},
	Chapter = {1. A brief introduction to some simple stochastic processes},
	Date-Added = {2012-08-01 18:33:21 +0000},
	Date-Modified = {2012-08-01 18:35:00 +0000},
	Publisher = {Oxford University Press},
	Title = {Stochastic Methods in Neuroscience},
	Year = {2010}}

@article{JulicherDierkesLindnerProstMartin2009EPJ,
	Abstract = {A deterministic system that operates in the vicinity of a Hopf bifurcation can be described by a single equation of a complex variable, called the normal form. Proximity to the bifurcation ensures that on the stable side of the bifurcation ( i.e. on the side where a stable fixed point exists), the linear-response function of the system is peaked at the frequency that is characteristic of the oscillatory instability. Fluctuations, which are present in many systems, conceal the Hopf bifurcation and lead to noisy oscillations. Spontaneous hair bundle oscillations by sensory hair cells from the vertebrate ear provide an instructive example of such noisy oscillations. By starting from a simplified description of hair bundle motility based on two degrees of freedom, we discuss the interplay of nonlinearity and noise in the supercritical Hopf normal form. Specifically, we show here that the linear-response function obeys the same functional form as for the noiseless system on the stable side of the bifurcation but with effective, renormalized parameters. Moreover, we demonstrate in specific cases how to relate analytically the parameters of the normal form with added noise to effective parameters. The latter parameters can be measured experimentally in the power spectrum of spontaneous activity and linear-response function to external stimuli. In other cases, numerical solutions were used to determine the effects of noise and nonlinearities on these effective parameters. Finally, we relate our results to experimentally observed spontaneous hair bundle oscillations and responses to periodic stimuli.},
	Affiliation = {Max Planck Institut f{\"u}r Physik komplexer Systeme, Dresden, Germany},
	Author = {J{\"u}licher, F. and Dierkes, K. and Lindner, B. and Prost, J. and Martin, P.},
	Date-Added = {2012-08-01 18:26:27 +0000},
	Date-Modified = {2012-08-01 18:27:09 +0000},
	Issn = {1292-8941},
	Issue = {4},
	Journal = {The European Physical Journal E: Soft Matter and Biological Physics},
	Keyword = {Physics and Astronomy},
	Note = {10.1140/epje/i2009-10487-5},
	Pages = {449-460},
	Publisher = {Springer Berlin / Heidelberg},
	Title = {Spontaneous movements and linear response of a noisy oscillator},
	Url = {http://dx.doi.org/10.1140/epje/i2009-10487-5},
	Volume = {29},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1140/epje/i2009-10487-5}}

@article{KawaiSailerSchimanskyGeierVandenBroeck2004PRE,
	Author = {Kawai, R. and Sailer, X. and Schimansky-Geier, L. and Van den Broeck, C.},
	Date-Added = {2012-08-01 18:19:24 +0000},
	Date-Modified = {2012-08-01 18:19:51 +0000},
	Doi = {10.1103/PhysRevE.69.051104},
	Issue = {5},
	Journal = {Phys. Rev. E},
	Month = {May},
	Numpages = {8},
	Pages = {051104},
	Publisher = {American Physical Society},
	Title = {Macroscopic limit cycle via pure noise-induced phase transitions},
	Url = {http://link.aps.org/doi/10.1103/PhysRevE.69.051104},
	Volume = {69},
	Year = {2004},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.69.051104},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.69.051104}}

@article{HanYimPostnovSosnovtseva1999PRL,
	Author = {Han, Seung Kee and Yim, Tae Gyu and Postnov, D. E. and Sosnovtseva, O. V.},
	Date-Added = {2012-08-01 04:56:02 +0000},
	Date-Modified = {2012-08-01 04:56:29 +0000},
	Doi = {10.1103/PhysRevLett.83.1771},
	Issue = {9},
	Journal = {Phys. Rev. Lett.},
	Month = {Aug},
	Pages = {1771--1774},
	Publisher = {American Physical Society},
	Title = {Interacting Coherence Resonance Oscillators},
	Url = {http://link.aps.org/doi/10.1103/PhysRevLett.83.1771},
	Volume = {83},
	Year = {1999},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.83.1771},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.83.1771}}

@article{TreutleinSchulten1986EBJ,
	Abstract = {The firing pattern of neural pulses often show the following features: the shapes of individual pulses are nearly identical and frequency independent; the firing frequency can vary over a broad range; the time period between pulses shows a stochastic scatter. This behaviour cannot be understood on the basis of a deterministic non-linear dynamic process, e.g. the Bonhoeffer-van der Pol model. We demonstrate in this paper that a noise term added to the Bonhoeffer-van der Pol model can reproduce the firing patterns of neurons very well. For this purpose we have considered the Fokker-Planck equation corresponding to the stochastic Bonhoeffer-van der Pol model. This equation has been solved by a new Monte Carlo algorithm. We demonstrate that the ensuing distribution functions represent only the global characteristics of the underlying force field: lines of zero slope which attract nearby trajectories prove to be the regions of phase space where the distributions concentrate their amplitude. Since there are two such lines the distributions are bimodal representing repeated fluctuations between two lines of zero slope. Even in cases where the deterministic Bonhoeffer-van der Pol model does not show limit cycle behaviour the stochastic system produces a limit cycle. This cycle can be identified with the firing of neural pulses.},
	Author = {Treutlein, H. and Schulten, K.},
	Date-Added = {2012-08-01 04:51:22 +0000},
	Date-Modified = {2012-08-01 04:51:43 +0000},
	Issn = {0175-7571},
	Issue = {6},
	Journal = {European Biophysics Journal},
	Keyword = {Physics and Astronomy},
	Note = {10.1007/BF00265671},
	Pages = {355-365},
	Publisher = {Springer Berlin / Heidelberg},
	Title = {Noise-induced neural impulses},
	Url = {http://dx.doi.org/10.1007/BF00265671},
	Volume = {13},
	Year = {1986},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF00265671}}

@article{TreutleinSchulten1985BBPC,
	Abstract = {The effect of additive noise on the Bonhoeffer-van der Pol (BvP) model is studied. For this purpose we developed a numerical algorithm to solve the pertinent 2-dim. Fokker-Planck equation. The results demonstrate that the global behaviour of the system is determined by certain lines toward which the distribution function is attracted. These lines are also the seeds for the limit cycle in the deterministic system. The noisy BvP model exhibits a limit cycle (oscillations) even when the deterministic system does not. This behaviour may explain the firing pattern of neurons.},
	Author = {Treutlein, Herbert and Schulten, Klaus},
	Date-Added = {2012-08-01 04:48:55 +0000},
	Date-Modified = {2012-08-01 04:49:21 +0000},
	Doi = {10.1002/bbpc.19850890626},
	Issn = {0005-9021},
	Journal = {Berichte der Bunsengesellschaft f{\"u}r physikalische Chemie},
	Keywords = {Biophysical Chemistry, Computer Experiments, Nerve Excitation, Non-linear Phenomena, Stochastic Processes},
	Number = {6},
	Pages = {710--718},
	Publisher = {Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim},
	Title = {Noise Induced Limit Cycles of the Bonhoeffer-Van der Pol Model of Neural Pulses},
	Url = {http://dx.doi.org/10.1002/bbpc.19850890626},
	Volume = {89},
	Year = {1985},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/bbpc.19850890626}}

@article{KurrerSchulten1995PRE,
	Author = {Christian Kurrer and Klaus Schulten},
	Date-Added = {2012-08-01 04:38:21 +0000},
	Date-Modified = {2012-08-01 04:40:30 +0000},
	Journal = {Physical Review E},
	Month = {June},
	Number = {6},
	Pages = {6213-6218},
	Title = {Noise-induced synchronous neuronal oscillations},
	Volume = {51},
	Year = {1995}}

@article{DitlevsenGreenwood2012JMB,
	Abstract = {We show that the stochastic Morris--Lecar neuron, in a neighborhood of its stable point, can be approximated by a two-dimensional Ornstein--Uhlenbeck (OU) modulation of a constant circular motion. The associated radial OU process is an example of a leaky integrate-and-fire (LIF) model prior to firing. A new model constructed from a radial OU process together with a simple firing mechanism based on detailed Morris--Lecar firing statistics reproduces the Morris--Lecar Interspike Interval (ISI) distribution, and has the computational advantages of a LIF. The result justifies the large amount of attention paid to the LIF models.},
	Affiliation = {Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark},
	Author = {Ditlevsen, Susanne and Greenwood, Priscilla},
	Date-Added = {2012-07-25 18:52:13 +0000},
	Date-Modified = {2012-07-25 18:55:00 +0000},
	Issn = {0303-6812},
	Journal = {Journal of Mathematical Biology},
	Keyword = {Mathematics and Statistics},
	Note = {10.1007/s00285-012-0552-7},
	Pages = {1-21},
	Publisher = {Springer Berlin / Heidelberg},
	Title = {The {{Morris}}--{{Lecar}} neuron model embeds a leaky integrate-and-fire model},
	Url = {http://dx.doi.org/10.1007/s00285-012-0552-7},
	Volume = {online first},
	Year = {2012},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00285-012-0552-7}}

@article{OprisanThirumalaiCanavier2003BiophysJ,
	Abstract = {Recordings of the membrane potential from a bursting neuron were used to reconstruct the phase curve for that neuron for a limited set of perturbations. These perturbations were inhibitory synaptic conductance pulses able to shift the membrane potential below the most hyperpolarized level attained in the free running mode. The extraction of the phase resetting curve from such a one-dimensional time series requires reconstruction of the periodic activity in the form of a limit cycle attractor. Resetting was found to have two components. In the first component, if the pulse was applied during a burst, the burst was truncated, and the time until the next burst was shortened in a manner predicted by movement normal to the limit cycle. By movement normal to the limit cycle, we mean a switch between two well-defined solution branches of a relaxation-like oscillator in a hysteretic manner enabled by the existence of a singular dominant slow process (variable). In the second component, the onset of the burst was delayed until the end of the hyperpolarizing pulse. Thus, for the pulse amplitudes we studied, resetting was independent of amplitude but increased linearly with pulse duration. The predicted and the experimental phase resetting curves for a pyloric dilator neuron show satisfactory agreement. The method was applied to only one pulse per cycle, but our results suggest it could easily be generalized to accommodate multiple inputs.},
	Author = {Oprisan, S A and Thirumalai, V and Canavier, C C},
	Date-Added = {2012-07-25 13:56:25 +0000},
	Date-Modified = {2012-07-25 13:56:51 +0000},
	Doi = {10.1016/S0006-3495(03)70019-8},
	Journal = {Biophys J},
	Journal-Full = {Biophysical journal},
	Mesh = {Action Potentials; Adaptation, Physiological; Algorithms; Animals; Computer Simulation; Electric Stimulation; Membrane Potentials; Models, Neurological; Neurons; Nonlinear Dynamics; Oscillometry; Periodicity; Pylorus; Synapses; Synaptic Transmission},
	Month = {May},
	Number = {5},
	Pages = {2919-28},
	Pmc = {PMC1302855},
	Pmid = {12719224},
	Pst = {ppublish},
	Title = {Dynamics from a time series: can we extract the phase resetting curve from a time series?},
	Volume = {84},
	Year = {2003},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0006-3495(03)70019-8}}

@article{SenguptaLaughlinNiven2010PRE,
	Abstract = {The stochastic opening and closing of voltage-gated ion channels produce noise in neurons. The effect of this noise on the neuronal performance has been modeled using either an approximate or Langevin model based on stochastic differential equations or an exact model based on a Markov process model of channel gating. Yet whether the Langevin model accurately reproduces the channel noise produced by the Markov model remains unclear. Here we present a comparison between Langevin and Markov models of channel noise in neurons using single compartment Hodgkin-Huxley models containing either Na+ and K+, or only K+ voltage-gated ion channels. The performance of the Langevin and Markov models was quantified over a range of stimulus statistics, membrane areas, and channel numbers. We find that in comparison to the Markov model, the Langevin model underestimates the noise contributed by voltage-gated ion channels, overestimating information rates for both spiking and nonspiking membranes. Even with increasing numbers of channels, the difference between the two models persists. This suggests that the Langevin model may not be suitable for accurately simulating channel noise in neurons, even in simulations with large numbers of ion channels.},
	Author = {Sengupta, B and Laughlin, S B and Niven, J E},
	Date-Added = {2012-07-25 11:57:22 +0000},
	Date-Modified = {2012-07-25 11:57:46 +0000},
	Journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
	Journal-Full = {Physical review. E, Statistical, nonlinear, and soft matter physics},
	Mesh = {Action Potentials; Algorithms; Animals; Cell Membrane; Computer Simulation; Information Theory; Markov Chains; Models, Neurological; Neurons; Normal Distribution; Potassium Channels, Voltage-Gated; Probability; Sodium Channels; Stochastic Processes},
	Month = {Jan},
	Number = {1 Pt 1},
	Pages = {011918},
	Pmid = {20365410},
	Pst = {ppublish},
	Title = {Comparison of Langevin and Markov channel noise models for neuronal signal generation},
	Volume = {81},
	Year = {2010}}

@article{BrunelHakimRichardson2003PRE,
	Abstract = {Neurons that exhibit a peak at finite frequency in their membrane potential response to oscillatory inputs are widespread in the nervous system. However, the influence of this subthreshold resonance on spiking properties has not yet been thoroughly analyzed. To this end, generalized integrate-and-fire models are introduced that reproduce at the linear level the subthreshold behavior of any given conductance-based model. A detailed analysis is presented of the simplest resonant model of this kind that has two variables: the membrane potential and a supplementary voltage-gated resonant variable. The firing-rate modulation created by a noisy weak oscillatory drive, mimicking an in vivo environment, is computed numerically and analytically when the dynamics of the resonant variable is slow compared to that of the membrane potential. The results show that the firing-rate modulation is shaped by the subthreshold resonance. For weak noise, the firing-rate modulation has a minimum near the preferred subthreshold frequency. For higher noise, such as that prevailing in vivo, the firing-rate modulation peaks near the preferred subthreshold frequency.},
	Author = {Brunel, Nicolas and Hakim, Vincent and Richardson, Magnus J E},
	Date-Added = {2012-07-25 03:06:03 +0000},
	Date-Modified = {2012-07-25 03:07:28 +0000},
	Journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
	Journal-Full = {Physical review. E, Statistical, nonlinear, and soft matter physics},
	Mesh = {Action Potentials; Animals; Biophysical Phenomena; Biophysics; Electrophysiology; Humans; Models, Anatomic; Models, Statistical; Neurons; Time Factors},
	Month = {May},
	Number = {5 Pt 1},
	Pages = {051916},
	Pmid = {12786187},
	Pst = {ppublish},
	Title = {Firing-rate resonance in a generalized integrate-and-fire neuron with subthreshold resonance},
	Volume = {67},
	Year = {2003}}

@article{Longtin1997PRE,
	Author = {Longtin, Andr\'e},
	Doi = {10.1103/PhysRevE.55.868},
	Issue = {1},
	Journal = {Phys. Rev. E},
	Month = {Jan},
	Pages = {868--876},
	Publisher = {American Physical Society},
	Title = {Autonomous stochastic resonance in bursting neurons},
	Url = {http://link.aps.org/doi/10.1103/PhysRevE.55.868},
	Volume = {55},
	Year = {1997},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.55.868},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.55.868}}

@article{LindnerGarcia-OjalvoNeimanSchimansky-Geier2004PhysRep,
	Abstract = {We review the behavior of theoretical models of excitable systems
driven by Gaussian white noise. We focus mainly on those general
properties of such systems that are due to noise, and present several
applications of our findings in biophysics and lasers.

As prototypes of excitable stochastic dynamics we consider the
FitzHugh-Nagumo and the leaky integrate-and-fire model, as well as
cellular automata and phase models. In these systems, taken as
individual units or as networks of globally or locally coupled elements,
we study various phenomena due to noise, such as noise-induced
oscillations, stochastic resonance, stochastic synchronization,
noise-induced phase transitions and noise-induced pulse and spiral
dynamics.

Our approach is based on stochastic differential equations and their corresponding Fokker-Planck equations, treated by both analytical calculations and/or numerical simulations. We calculate and/or measure the rate and diffusion coefficient of the excitation process, as well as spectral quantities like power spectra and degree of coherence. Combined with a multiparametric bifurcation analysis of the corresponding cumulant equations, these approaches provide a comprehensive picture of the multifaceted dynamical behaviour of noisy excitable systems.},
	Author = {B. Lindner and J. Garc\'{i}a-Ojalvo and A. Neiman and L. Schimansky-Geier},
	Date-Modified = {2012-07-21 12:08:31 -0400},
	Doi = {10.1016/j.physrep.2003.10.015},
	Issn = {0370-1573},
	Journal = {Physics Reports},
	Keywords = {Ion-channel clusters},
	Number = {6},
	Pages = {321 - 424},
	Title = {Effects of noise in excitable systems},
	Url = {http://www.sciencedirect.com/science/article/pii/S0370157303004228},
	Volume = {392},
	Year = {2004},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0370157303004228},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.physrep.2003.10.015}}

@article{LindnerSchimansky-Geier2000PRE,
	Abstract = {The subject of our study is a two-state dynamics driven by Gaussian white noise and a weak harmonic signal. The system resulting from a piecewise linear FizHugh-Nagumo model in the case of perfect time scale separation between fast and slow variables shows either bistable, excitable, or oscillatory behavior. Its output spectra as well as the spectral power amplification of the signal can be calculated for arbitrary noise strength and frequency, allowing characterization of the coherence resonance in the bistable and excitable regimes as well as quantification of nonadiabatic resonances with respect to the external signal in all regimes.},
	Author = {Lindner and Schimansky-Geier},
	Date-Added = {2012-07-21 11:50:50 -0400},
	Date-Modified = {2012-07-21 11:51:37 -0400},
	Journal = {Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics},
	Journal-Full = {Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
	Month = {Jun},
	Number = {6 Pt A},
	Pages = {6103-10},
	Pmid = {11088283},
	Pst = {ppublish},
	Title = {Coherence and stochastic resonance in a two-state system},
	Volume = {61},
	Year = {2000}}

@article{LindnerSchimanskyGeier1999PRE,
	Abstract = {We consider the FitzHugh-Nagumo system under the influence of white Gaussian noise in the excitable regime. We present an analytical approximation in the limit of fast activator time scale. Marginal probability densities of a reduced system and dynamical quantities such as the pulse rate are found and the mean interspike interval and its relative standard deviation are investigated. The latter quantities allow a quantitative description of the phenomenon of coherence resonance, as comparisons with simulations show.},
	Author = {Lindner, B and Schimansky-Geier, L},
	Date-Added = {2012-07-21 11:50:43 -0400},
	Date-Modified = {2012-08-01 04:25:10 +0000},
	Journal = {Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics},
	Journal-Full = {Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
	Mesh = {Action Potentials; Computer Simulation; Neurons; Noise; Probability; Stochastic Processes; Time Factors},
	Month = {Dec},
	Number = {6 Pt B},
	Pages = {7270-6},
	Pmid = {11970671},
	Pst = {ppublish},
	Title = {Analytical approach to the stochastic FitzHugh-Nagumo system and coherence resonance},
	Volume = {60},
	Year = {1999}}

@article{RotsteinOppermanWhiteKopell2006JCN,
	Abstract = {Medial entorhinal cortex layer II stellate cells display subthreshold oscillations (STOs). We study a single compartment biophysical model of such cells which qualitatively reproduces these STOs. We argue that in the subthreshold interval (STI) the seven-dimensional model can be reduced to a three-dimensional system of equations with well differentiated times scales. Using dynamical systems arguments we provide a mechanism for generations of STOs. This mechanism is based on the "canard structure," in which relevant trajectories stay close to repelling manifolds for a significant interval of time. We also show that the transition from subthreshold oscillatory activity to spiking ("canard explosion") is controlled in the STI by the same structure. A similar mechanism is invoked to explain why noise increases the robustness of the STO regime. Taking advantage of the reduction of the dimensionality of the full stellate cell system, we propose a nonlinear artificially spiking (NAS) model in which the STI reduced system is supplemented with a threshold for spiking and a reset voltage. We show that the synchronization properties in networks made up of the NAS cells are similar to those of networks using the full stellate cell models.},
	Author = {Rotstein, Horacio G and Oppermann, Tim and White, John A and Kopell, Nancy},
	Date-Added = {2011-10-17 15:49:12 -0400},
	Date-Modified = {2011-10-17 15:49:47 -0400},
	Doi = {10.1007/s10827-006-8096-8},
	Journal = {J Comput Neurosci},
	Journal-Full = {Journal of computational neuroscience},
	Mesh = {Action Potentials; Animals; Biological Clocks; Entorhinal Cortex; Models, Biological; Neuroglia; Nonlinear Dynamics},
	Month = {Dec},
	Number = {3},
	Pages = {271-92},
	Pmid = {16927211},
	Pst = {ppublish},
	Title = {The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells},
	Volume = {21},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10827-006-8096-8}}

@article{ChatterjeeRobert2001JARO,
	Abstract = {Cochlear implants restore auditory sensitivity to the profoundly hearing-impaired by means of electrical stimulation of residual auditory nerve fibers. Sensorineural hearing loss results in a loss of spontaneous activity among the remaining auditory neurons and is accompanied by a reduction in the normal stochastic nature of neural firing in response to electric stimulation. It has been hypothesized that the natural stochasticity of the neural response is important for auditory signal processing and that introducing some optimal amount of noise into the stimulus may improve auditory perception through the implant. In this article we show that, for soft but audible stimuli, an optimal amount of "prosthetic" noise significantly improves sensitivity to envelope modulation in cochlear implant listeners. A nonmonotonic function relates modulation sensitivity and noise level, suggesting the presence of stochastic resonance.},
	Affiliation = {Department of Auditory Implants and Perception, House Ear Institute, Los Angeles, CA 90057, USA US},
	Author = {Chatterjee, Monita and Robert, Mark E.},
	Date-Added = {2011-07-26 10:40:31 -0400},
	Date-Modified = {2011-07-26 10:41:01 -0400},
	Issn = {1525-3961},
	Issue = {2},
	Journal = {Journal of the Association for Research in Otolaryngology},
	Keyword = {Medicine},
	Note = {10.1007/s101620010079},
	Pages = {159-171},
	Publisher = {Springer New York},
	Title = {Noise Enhances Modulation Sensitivity in Cochlear Implant Listeners: Stochastic Resonance in a Prosthetic Sensory System?},
	Url = {http://dx.doi.org/10.1007/s101620010079},
	Volume = {2},
	Year = {2001},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s101620010079}}

@article{RubinsteinWilsonFinleyAbbas1999HearingRsch,
	Author = {J. T. Rubinstein and B. S. Wilson and C. C. Finley and P. J. Abbas},
	Doi = {DOI: 10.1016/S0378-5955(98)00185-3},
	Issn = {0378-5955},
	Journal = {Hearing Research},
	Keywords = {Auditory nerve},
	Number = {1-2},
	Pages = {108 - 118},
	Title = {Pseudospontaneous activity: stochastic independence of auditory nerve fibers with electrical stimulation},
	Url = {http://www.sciencedirect.com/science/article/pii/S0378595598001853},
	Volume = {127},
	Year = {1999},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0378595598001853},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/S0378-5955(98)00185-3}}

@article{AbouzeidErmentrout:2009:PRE,
	Abstract = {The phase-resetting curve (PRC) describes the response of a neural oscillator to small perturbations in membrane potential. Its usefulness for predicting the dynamics of weakly coupled deterministic networks has been well characterized. However, the inputs to real neurons may often be more accurately described as barrages of synaptic noise. Effective connectivity between cells may thus arise in the form of correlations between the noisy input streams. We use constrained optimization and perturbation methods to prove that the PRC shape determines susceptibility to synchrony among otherwise uncoupled noise-driven neural oscillators. PRCs can be placed into two general categories: type-I PRCs are non-negative, while type-II PRCs have a large negative region. Here we show that oscillators with type-II PRCs receiving common noisy input synchronize more readily than those with type-I PRCs.},
	Author = {Abouzeid, Aushra and Ermentrout, Bard},
	Date-Added = {2011-07-22 00:38:04 -0400},
	Date-Modified = {2011-07-23 16:54:18 -0400},
	Journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
	Journal-Full = {Physical review. E, Statistical, nonlinear, and soft matter physics},
	Mesh = {Brain; Models, Biological; Neurons; Stochastic Processes},
	Month = {Jul},
	Number = {1 Pt 1},
	Pages = {011911},
	Pmid = {19658733},
	Pst = {ppublish},
	Title = {{Type-II phase resetting curve is optimal for stochastic synchrony}},
	Volume = {80},
	Year = {2009}}

@article{LinShea-BrownYoung2009JNonlinSci,
	Affiliation = {University of Arizona Department of Mathematics Tucson AZ USA},
	Author = {Lin, Kevin and Shea-Brown, Eric and Young, Lai-Sang},
	Date-Added = {2011-07-22 00:36:26 -0400},
	Date-Modified = {2011-07-22 00:36:48 -0400},
	Issn = {0938-8974},
	Issue = {5},
	Journal = {Journal of Nonlinear Science},
	Keyword = {Mathematics and Statistics},
	Note = {10.1007/s00332-009-9042-5},
	Pages = {497-545},
	Publisher = {Springer New York},
	Title = {Reliability of Coupled Oscillators},
	Url = {http://dx.doi.org/10.1007/s00332-009-9042-5},
	Volume = {19},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00332-009-9042-5}}

@article{Galan2007Neurocomputing,
	Author = {Roberto F. Gal\'{a}n and G. Bard Ermentrout and Nathaniel N. Urban},
	Date-Modified = {2013-10-07 21:27:19 +0000},
	Doi = {DOI: 10.1016/j.neucom.2006.10.075},
	Issn = {0925-2312},
	Journal = {Neurocomputing},
	Keywords = {Synchrony},
	Note = {Computational Neuroscience: Trends in Research 2007, Computational Neuroscience 2006},
	Number = {10-12},
	Pages = {2102-2106},
	Title = {Reliability and stochastic synchronization in type {I} vs. type {II} neural oscillators},
	Url = {http://www.sciencedirect.com/science/article/pii/S0925231206004413},
	Volume = {70},
	Year = {2007},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0925231206004413},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.neucom.2006.10.075}}

@article{DoironRinzelReyes:2006:PRE,
	Abstract = {We study a stochastic synchronization of spiking activity in feedforward networks of integrate-and-fire model neurons. A stochastic mean field analysis shows that synchronization occurs only when the network size is sufficiently small. This gives evidence that the dynamics, and hence processing, of finite size populations can be drastically different from that observed in the infinite size limit. Our results agree with experimentally observed synchrony in cortical networks, and further strengthen the link between synchrony and propagation in cortical systems.},
	Author = {Doiron, Brent and Rinzel, John and Reyes, Alex},
	Date-Added = {2011-07-22 00:24:22 -0400},
	Date-Modified = {2011-07-22 00:28:22 -0400},
	Journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
	Journal-Full = {Physical review. E, Statistical, nonlinear, and soft matter physics},
	Mesh = {Action Potentials; Algorithms; Computer Simulation; Models, Neurological; Nerve Net; Neurons; Stochastic Processes},
	Month = {Sep},
	Number = {3 Pt 1},
	Pages = {030903},
	Pmid = {17025585},
	Pst = {ppublish},
	Title = {Stochastic synchronization in finite size spiking networks},
	Volume = {74},
	Year = {2006}}

@article{MarellaErmentrout:2008:PRE,
	Abstract = {We describe the relationship between the shape of the phase-resetting curve (PRC) and the degree of stochastic synchronization observed between a pair of uncoupled general oscillators receiving partially correlated Poisson inputs in addition to inputs from independent sources. We use perturbation methods to derive an expression relating the shape of the PRC to the probability density function (PDF) of the phase difference between the oscillators. We compute various measures of the degree of synchrony and cross correlation from the PDF's and use the same to compare and contrast differently shaped PRCs, with respect to their ability to undergo stochastic synchronization. Since the shape of the PRC depends on underlying dynamical details of the oscillator system, we utilize the results obtained from the analysis of general oscillator systems to study specific models of neuronal oscillators. It is shown that the degree of stochastic synchronization is controlled both by the firing rate of the neuron and the membership of the PRC (type I or type II). It is also shown that the circular variance for the integrate and fire neuron and the generalized order parameter for a hippocampal interneuron model have a nonlinear relationship to the input correlation.},
	Author = {Marella, Sashi and Ermentrout, G Bard},
	Date-Added = {2011-07-22 00:23:23 -0400},
	Date-Modified = {2011-07-23 16:55:16 -0400},
	Journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
	Journal-Full = {Physical review. E, Statistical, nonlinear, and soft matter physics},
	Mesh = {Animals; Biological Clocks; Computer Simulation; Cortical Synchronization; Hippocampus; Humans; Interneurons; Models, Neurological; Monte Carlo Method; Neurons; Poisson Distribution; Stochastic Processes; Time Factors},
	Month = {Apr},
	Number = {4 Pt 1},
	Pages = {041918},
	Pmid = {18517667},
	Pst = {ppublish},
	Title = {{Class-II neurons display a higher degree of stochastic synchronization than class-I neurons}},
	Volume = {77},
	Year = {2008}}

@article{Medvedev2010PhysLettA,
	Author = {Georgi S. Medvedev},
	Date-Added = {2011-07-10 18:13:54 -0400},
	Date-Modified = {2011-07-10 18:16:08 -0400},
	Journal = {Physics Letters A},
	Month = {19 Feb},
	Pages = {1712--1720},
	Title = {Synchronization of coupled stochastic limit cycle oscillators},
	Volume = {374},
	Year = {2010}}

@article{CarlsonLanger:1989:PRL,
	Author = {Carlson and Langer},
	Date-Added = {2011-07-10 18:04:23 -0400},
	Date-Modified = {2011-07-10 18:04:36 -0400},
	Journal = {Phys Rev Lett},
	Journal-Full = {Physical review letters},
	Month = {May},
	Number = {22},
	Pages = {2632-2635},
	Pmid = {10040041},
	Pst = {ppublish},
	Title = {Properties of earthquakes generated by fault dynamics},
	Volume = {62},
	Year = {1989}}

@article{ItohTainaka1994:PhysLettA,
	Author = {Yoshiaki Itoh and Kei-ichi Tainaka},
	Date-Added = {2011-07-10 17:57:40 -0400},
	Date-Modified = {2011-07-10 17:59:22 -0400},
	Journal = {Physics Letters A},
	Month = {6 June},
	Pages = {37-42},
	Title = {Stochastic limit cycle with power-law spectrum},
	Volume = {189},
	Year = {1994}}

@book{PikovskyRosenblumKurths2001,
	Author = {Arkady Pikovsky and Michael Rosenblum and J\"{u}rgen Kurths},
	Date-Added = {2011-07-10 17:35:27 -0400},
	Date-Modified = {2011-07-10 17:36:58 -0400},
	Publisher = {Cambridge University Press},
	Title = {Synchronization: a universal concept in nonlinear sciences},
	Year = {2001}}

@book{Kuramoto1984,
	Address = {Berlin},
	Author = {Yoshiki Kuramoto},
	Date-Added = {2011-07-10 17:34:07 -0400},
	Date-Modified = {2011-07-10 17:35:14 -0400},
	Publisher = {Springer-Verlag},
	Title = {Chemical Oscillations, Waves, and Turbulence},
	Year = {1984}}

@book{Kuramoto2003,
	Address = {31 East 2nd Street, Mineola, N.Y.~11501},
	Author = {Yoshiki Kuramoto},
	Date-Added = {2011-07-10 17:27:37 -0400},
	Date-Modified = {2011-07-10 17:30:53 -0400},
	Publisher = {Dover Publications, Inc.},
	Title = {Chemical Oscillations, Waves, and Turbulence},
	Year = {2003}}

@inbook{Yoshimura2010RevNonlinDynChapter,
	Author = {Kazuyuki Yoshimura},
	Chapter = {3. Phase Reduction of Stochastic Limit-Cycle Oscillators},
	Date-Added = {2011-07-10 17:18:22 -0400},
	Date-Modified = {2011-07-10 17:20:49 -0400},
	Publisher = {Wiley-VCH Verlag GmbH \& Co.},
	Title = {Reviews of Nonlinear Dynamics and Complexity},
	Volume = {3},
	Year = {2010}}

@article{XiaoHouXin:2008:JChemPhys,
	Abstract = {Entropy production along a trajectory in the stochastic irreversible Brusselator model of chemical oscillating reactions is discussed. Particular attention is paid to a parameter region near the deterministic supercritical Hopf bifurcation. In the stationary state, detailed fluctuation theorem holds due to the reversibility in the state space, which is verified by direct simulations via Gillespie's algorithm [J. Comput. Phys. 22, 403 (1976); J. Phys. Chem. 81, 2340 (1977)]. In addition, we have considered how the entropy production along a noisy limit cycle depends on the system size. Interestingly, in the large system size limit, the entropy production approaches a constant value when the control parameter stays at the deterministic steady state region, while it increases linearly in the deterministic oscillatory region. Such simulation results can be well understood by a stochastic normal form analysis.},
	Author = {Xiao, Tie Jun and Hou, Zhonghuai and Xin, Houwen},
	Date-Added = {2011-07-10 16:29:34 -0400},
	Date-Modified = {2011-07-10 16:41:15 -0400},
	Doi = {10.1063/1.2978179},
	Journal = {J Chem Phys},
	Journal-Full = {The Journal of chemical physics},
	Month = {Sep},
	Number = {11},
	Pages = {114506},
	Pmid = {19044968},
	Pst = {ppublish},
	Title = {Entropy production and fluctuation theorem along a stochastic limit cycle},
	Volume = {129},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2978179}}

@article{YoshimuraArai:2008:PRL,
	Abstract = {We point out that for an oscillator subjected to noise the conventional phase equation is not a proper approximation even for weak noise. We present a phase reduction method valid for an oscillator subjected to weak white Gaussian noise. Numerical evidence demonstrates that the phase equation properly approximates dynamics of the original oscillator. Moreover, we show that, in general, noise causes a shift of the oscillator frequency and discuss its effects on entrainment.},
	Author = {Yoshimura, Kazuyuki and Arai, Kenichi},
	Date-Added = {2011-07-10 16:28:53 -0400},
	Date-Modified = {2011-07-10 16:32:56 -0400},
	Journal = {Phys Rev Lett},
	Journal-Full = {Physical review letters},
	Month = {Oct},
	Number = {15},
	Pages = {154101},
	Pmid = {18999602},
	Pst = {ppublish},
	Title = {Phase reduction of stochastic limit cycle oscillators},
	Volume = {101},
	Year = {2008}}

@article{KooijmanGrasmanKooi:2007:MathBiosci,
	Abstract = {We study the effects of random feeding, growing and dying in a closed nutrient-limited producer/consumer system, in which nutrient is fully conserved, not only in the mean, but, most importantly, also across random events. More specifically, we relate these random effects to the closest deterministic models, and evaluate the importance of the various times scales that are involved. These stochastic models differ from deterministic ones not only in stochasticity, but they also have more details that involve shorter times scales. We tried to separate the effects of more detail from that of stochasticity. The producers have (nutrient) reserve and (body) structure, and so a variable chemical composition. The consumers have only structure, so a constant chemical composition. The conversion efficiency from producer to consumer, therefore, varies. The consumers use reserve and structure of the producers as complementary compounds, following the rules of Dynamic Energy Budget theory. Consumers die at constant specific rate and decompose instantaneously. Stochasticity is incorporated in the behaviour of the consumers, where the switches to handling and searching, as well as dying are Poissonian point events. We show that the stochastic model has one parameter more than the deterministic formulation without time scale separation for conversions between searching and handling consumers, which itself has one parameter more than the deterministic formulation with time scale separation for these conversions. These extra parameters are the contributions of a single individual producer and consumer to their densities, and the ratio of the two, respectively. The tendency to oscillate increases with the number of parameters. The focus bifurcation point has more relevance for the asymptotic behaviour of the stochastic model than the Hopf bifurcation point, since a randomly perturbed damped oscillation exhibits a behaviour similar to that of the stochastic limit cycle particularly near this bifurcation point. For total nutrient values below the focus bifurcation point, the system gradually becomes more confined to the direct neighbourhood of the isocline for which the producers do not change.},
	Author = {Kooijman, S A L M and Grasman, J and Kooi, B W},
	Date-Added = {2011-07-10 16:28:22 -0400},
	Date-Modified = {2011-07-10 17:12:14 -0400},
	Doi = {10.1016/j.mbs.2007.05.010},
	Journal = {Math Biosci},
	Journal-Full = {Mathematical biosciences},
	Mesh = {Biomass; Computer Simulation; Food; Models, Biological; Monte Carlo Method; Nonlinear Dynamics; Population Dynamics; Stochastic Processes},
	Month = {Dec},
	Number = {2},
	Pages = {378-94},
	Pmid = {17659307},
	Pst = {ppublish},
	Title = {A new class of non-linear stochastic population models with mass conservation},
	Volume = {210},
	Year = {2007},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.mbs.2007.05.010}}

@article{Burke+dePaor:2004:BiolCyb,
	Abstract = {We present an empirical model of the electroencephalogram (EEG) signal based on the construction of a stochastic limit cycle oscillator using Ito calculus. This formulation, where the noise influences actually interact with the dynamics, is substantially different from the usual definition of measurement noise. Analysis of model data is compared with actual EEG data using both traditional methods and modern techniques from nonlinear time series analysis. The model demonstrates visually displayed patterns and statistics that are similar to actual EEG data. In addition, the nonlinear mechanisms underlying the dynamics of the model do not manifest themselves in nonlinear time series analysis, paralleling the situation with real, non-pathological EEG data. This modeling exercise suggests that the EEG is optimally described by stochastic limit cycle behavior.},
	Author = {Burke, D P and de Paor, A M},
	Date-Added = {2011-07-10 16:27:52 -0400},
	Date-Modified = {2011-07-21 23:25:53 -0400},
	Doi = {10.1007/s00422-004-0509-z},
	Journal = {Biol Cybern},
	Journal-Full = {Biological cybernetics},
	Mesh = {Algorithms; Brain; Electroencephalography; Humans; Models, Neurological; Oscillometry; Stochastic Processes},
	Month = {Oct},
	Number = {4},
	Pages = {221-30},
	Pmid = {15378376},
	Pst = {ppublish},
	Title = {A stochastic limit cycle oscillator model of the {EEG}},
	Volume = {91},
	Year = {2004},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00422-004-0509-z}}

@article{HernandezValdesVila:1996:Neurorpt,
	Abstract = {Many reports based upon correlation dimension studies have suggested the chaotic nature of electroencephalographic spike and wave activity (SW). Another study found no evidence for this, showing that surrogate stochastic data generated from SW have the same dynamical properties as the original data. The present paper explicitly models SW as the output of a non-linear stochastic system. Non-linear non-parametric kernel autoregression is used to show that the attractor of this system may be a limit cycle. The addition of system noise originates a simulated time series with the same interspike interval variability originally hypothesized as chaotic. Tests performed on the correlation dimension obtained from the original data as well as from both linear and non-linear surrogates show that the noise-perturbed limit cycle model achieves the best fit to the original data. We conclude that SW is likely to be a form of stochastic disturbed limit cycle behaviour rather than chaos.},
	Author = {Hern{\'a}ndez, J L and Vald{\'e}s, P A and Vila, P},
	Date-Added = {2011-07-10 16:27:44 -0400},
	Date-Modified = {2011-07-10 17:02:47 -0400},
	Journal = {Neuroreport},
	Journal-Full = {Neuroreport},
	Mesh = {Animals; Electroencephalography; Humans; Models, Neurological; Regression Analysis; Statistics, Nonparametric; Stochastic Processes; Time Factors},
	Month = {Sep},
	Number = {13},
	Pages = {2246-50},
	Pmid = {8930998},
	Pst = {ppublish},
	Title = {EEG spike and wave modelled by a stochastic limit cycle},
	Volume = {7},
	Year = {1996}}

@article{Renshaw:1994:IMA-J-Math-Appl-Med-Biol,
	Abstract = {Although the study of chaotic and periodic phenomena began as recently as the 1960s, its subsequent development during the past few years has been extremely rapid in terms of both theory and practical application. The purpose of this paper is therefore to present an overview which will enable researchers with little prior knowledge to assess the relevance and potential application of nonlinear systems to problems in medicine and biology. Deterministic dynamic behaviour is examined through discrete logistic-type equations; stochastic behaviour is studied by superimposing an appropriate birth-death structure. Analysis of a variety of insect data sets shows that periodic and chaotic structures do indeed feature in natural populations; the classic Nicholson's blowfly data are viewed from both stochastic limit-cycle and deterministic chaos standpoints. Determination of the attractor dimension can be an invaluable aid to the understanding of biological and medical phenomena, and convincing examples include phase-space comparisons between healthy and sick humans for both EEG and ECG records.},
	Author = {Renshaw, E},
	Date-Added = {2011-07-10 16:27:39 -0400},
	Date-Modified = {2011-07-10 17:04:53 -0400},
	Journal = {IMA J Math Appl Med Biol},
	Journal-Full = {IMA journal of mathematics applied in medicine and biology},
	Mesh = {Animals; Biometry; Insects; Mathematics; Nonlinear Dynamics; Population Dynamics; Stochastic Processes},
	Number = {1},
	Pages = {17-44},
	Pmid = {8057039},
	Pst = {ppublish},
	Title = {Chaos in biometry},
	Volume = {11},
	Year = {1994}}

@article{ErmentroutBeverlinTroyerNetoff:2011:JCNS,
	Abstract = {Phase resetting curves (PRCs) provide a measure of the sensitivity of oscillators to perturbations. In a noisy environment, these curves are themselves very noisy. Using perturbation theory, we compute the mean and the variance for PRCs for arbitrary limit cycle oscillators when the noise is small. Phase resetting curves and phase dependent variance are fit to experimental data and the variance is computed using an ad-hoc method. The theoretical curves of this phase dependent method match both simulations and experimental data significantly better than an ad-hoc method. A dual cell network simulation is compared to predictions using the analytical phase dependent variance estimation presented in this paper. We also discuss how entrainment of a neuron to a periodic pulse depends on the noise amplitude.},
	Author = {Ermentrout, G Bard and Beverlin, 2nd, Bryce and Troyer, Todd and Netoff, Theoden I},
	Date-Added = {2011-07-09 23:55:10 -0400},
	Date-Modified = {2011-07-09 23:56:04 -0400},
	Doi = {10.1007/s10827-010-0305-9},
	Journal = {J Comput Neurosci},
	Journal-Full = {Journal of computational neuroscience},
	Month = {Jan},
	Pmid = {21207126},
	Pst = {aheadofprint},
	Title = {The variance of phase-resetting curves},
	Year = {2011},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10827-010-0305-9}}

@article{TiesingaFellousSejnowski:2008:NatRevNsci,
	Abstract = {A train of action potentials (a spike train) can carry information in both the average firing rate and the pattern of spikes in the train. But can such a spike-pattern code be supported by cortical circuits? Neurons in vitro produce a spike pattern in response to the injection of a fluctuating current. However, cortical neurons in vivo are modulated by local oscillatory neuronal activity and by top-down inputs. In a cortical circuit, precise spike patterns thus reflect the interaction between internally generated activity and sensory information encoded by input spike trains. We review the evidence for precise and reliable spike timing in the cortex and discuss its computational role.},
	Author = {Tiesinga, Paul and Fellous, Jean-Marc and Sejnowski, Terrence J},
	Date-Added = {2011-02-07 23:06:27 -0500},
	Date-Modified = {2011-02-07 23:06:54 -0500},
	Doi = {10.1038/nrn2315},
	Journal = {Nat Rev Neurosci},
	Journal-Full = {Nature reviews. Neuroscience},
	Mesh = {Action Potentials; Animals; Biological Clocks; Humans; Neurons; Reaction Time; Synaptic Transmission; Time Factors; Visual Cortex; Visual Pathways; Visual Perception},
	Month = {Feb},
	Number = {2},
	Pages = {97-107},
	Pmc = {PMC2868969},
	Pmid = {18200026},
	Pst = {ppublish},
	Title = {Regulation of spike timing in visual cortical circuits},
	Volume = {9},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nrn2315}}

@article{Tanabe:1999kx,
	Abstract = {It is known that coupling can enhance the response of noisy bistable devices to weak periodic modulation. This work examines whether a similar phenomenon occurs in the active rotator model for excitable systems. We study the dynamics of assemblies of weakly periodically modulated active rotators. The addition of noise to these brings about a number of behaviors that have no counterpart in networks of bistable systems. The analysis of the dynamics of the solution of the Fokker-Planck equation of active rotator networks shows that these new behaviors are similar to generic responses of periodically forced autonomous oscillators. This is because noise alone, in the absence of other inputs, can regularize the dynamics of single active rotators through coherence resonance, and lead to regular synchronous activity at the level of networks. We argue that similar phenomena take place in a broad class of excitable systems.},
	Author = {Tanabe, S and Shimokawa, T and Sato, S and Pakdaman, K},
	Date-Added = {2011-01-15 16:25:36 -0500},
	Date-Modified = {2011-01-15 16:25:36 -0500},
	Journal = {Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics},
	Journal-Full = {Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
	Mesh = {Acoustic Stimulation; Excitatory Postsynaptic Potentials; Models, Biological; Nervous System; Noise; Nonlinear Dynamics; Oscillometry; Synaptic Transmission},
	Month = {Aug},
	Number = {2 Pt B},
	Pages = {2182-5},
	Pmid = {11970012},
	Pst = {ppublish},
	Title = {Response of coupled noisy excitable systems to weak stimulation},
	Volume = {60},
	Year = {1999}}

@article{Shimokawa:1999uq,
	Abstract = {Leaky integrate-and-fire neuron models display stochastic resonance-like behavior when stimulated by subthreshold periodic signal and noise. Previous works have shown that matching between the time scales of the noise induced discharges and the modulation period can account for this phenomenon at low modulation amplitudes, but not large subthreshold modulation amplitude. In order to examine the discharge patterns of the model in this regime, we introduce a method for the computation of the power spectral density of the discharge train. Using this method, we clarify the role of the distribution of the input phase at discharge times. Finally, we argue that for large subthreshold inputs, mean discharge frequency locking accounts for the enhanced response.},
	Author = {Shimokawa, T and Pakdaman, K and Sato, S},
	Date-Added = {2011-01-15 16:25:35 -0500},
	Date-Modified = {2011-01-15 16:25:35 -0500},
	Journal = {Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics},
	Journal-Full = {Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
	Mesh = {Animals; Biophysical Phenomena; Biophysics; Models, Statistical; Nerve Net; Neurons; Stochastic Processes},
	Month = {Jul},
	Number = {1},
	Pages = {R33-6},
	Pmid = {11969874},
	Pst = {ppublish},
	Title = {Mean discharge frequency locking in the response of a noisy neuron model to subthreshold periodic stimulation},
	Volume = {60},
	Year = {1999}}

@article{Lindner:2004:JStatPhys,
	Author = {Benjamin Lindner},
	Date-Added = {2010-01-15 19:55:33 -0500},
	Date-Modified = {2010-01-15 19:57:30 -0500},
	Journal = {Journal of Statistical Physics},
	Month = {Nov},
	Number = {3-4},
	Pages = {703-737},
	Title = {Moments of the First Passage Time Under External Driving},
	Volume = {117},
	Year = {2004}}

@article{Glass+Graves+Petrillo+Mackey:1980:JThBiol,
	Author = {Glass, L and Graves, C and Petrillo, G A and Mackey, M C},
	Date-Added = {2010-01-15 19:48:40 -0500},
	Date-Modified = {2010-01-15 19:49:11 -0500},
	Journal = {J Theor Biol},
	Journal-Full = {Journal of theoretical biology},
	Mesh = {Action Potentials; Animals; Cats; Models, Neurological; Periodicity; Phrenic Nerve; Respiration},
	Month = {Oct},
	Number = {3},
	Pages = {455-75},
	Pmid = {7218820},
	Title = {Unstable dynamics of a periodically driven oscillator in the presence of noise},
	Volume = {86},
	Year = {1980}}

@article{Glass:1979fk,
	Author = {Glass, L and Mackey, M C},
	Date-Added = {2010-01-15 19:48:38 -0500},
	Date-Modified = {2010-01-15 19:48:38 -0500},
	Journal = {Ann N Y Acad Sci},
	Journal-Full = {Annals of the New York Academy of Sciences},
	Mesh = {Adult; Arrhythmias, Cardiac; Hematologic Diseases; Hematopoiesis; Humans; Infant, Newborn; Male; Mathematics; Models, Biological; Periodicity; Respiration; Respiratory Tract Diseases},
	Pages = {214-35},
	Pmid = {288317},
	Title = {Pathological conditions resulting from instabilities in physiological control systems},
	Volume = {316},
	Year = {1979}}

@article{NesseNegroBressloff2008PRL,
	Abstract = {We investigate oscillation regularity of a noise-driven system modeled with a slow after-hyperpolarizing adaptation current (AHP) composed of multiple-exponential relaxation time scales. Sufficiently separated slow and fast AHP time scales (biphasic decay) cause a peak in oscillation irregularity for intermediate input currents I, with relatively regular oscillations for small and large currents. An analytic formulation of the system as a stochastic escape problem establishes that the phenomena is distinct from standard forms of coherence resonance. Our results explain data on the oscillation regularity of the pre-B{\"o}tzinger complex, a neural oscillator responsible for inspiratory breathing rhythm generation in mammals.},
	Author = {Nesse, William H and Negro, Christopher A Del and Bressloff, Paul C},
	Date-Added = {2010-01-04 06:10:17 -0500},
	Date-Modified = {2012-08-01 17:11:43 +0000},
	Journal = {Phys Rev Lett},
	Journal-Full = {Physical review letters},
	Mesh = {Biological Clocks; Models, Neurological; Monte Carlo Method; Neurons; Noise; Stochastic Processes},
	Month = {Aug},
	Number = {8},
	Pages = {088101},
	Pmid = {18764664},
	Title = {Oscillation regularity in noise-driven excitable systems with multi-time-scale adaptation},
	Volume = {101},
	Year = {2008}}

@article{NesseBorisyukBressloff2008JCN,
	Abstract = {We study an excitatory all-to-all coupled network of N spiking neurons with synaptically filtered background noise and slow activity-dependent hyperpolarization currents. Such a system exhibits noise-induced burst oscillations over a range of values of the noise strength (variance) and level of cell excitability. Since both of these quantities depend on the rate of background synaptic inputs, we show how noise can provide a mechanism for increasing the robustness of rhythmic bursting and the range of burst frequencies. By exploiting a separation of time scales we also show how the system dynamics can be reduced to low-dimensional mean field equations in the limit N --> infinity. Analysis of the bifurcation structure of the mean field equations provides insights into the dynamical mechanisms for initiating and terminating the bursts.},
	Author = {Nesse, William H and Borisyuk, Alla and Bressloff, Paul C},
	Date-Added = {2010-01-04 06:09:37 -0500},
	Date-Modified = {2012-08-01 17:12:42 +0000},
	Doi = {10.1007/s10827-008-0081-y},
	Journal = {J Comput Neurosci},
	Journal-Full = {Journal of computational neuroscience},
	Mesh = {Action Potentials; Adaptation, Physiological; Animals; Calcium; Feedback; Models, Neurological; Nerve Net; Neurons; Nonlinear Dynamics; Numerical Analysis, Computer-Assisted; Periodicity; Synapses},
	Month = {Oct},
	Number = {2},
	Pages = {317-33},
	Pmid = {18427966},
	Title = {Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation},
	Volume = {25},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10827-008-0081-y}}

@article{NesseClarkBressloff2007PRE,
	Abstract = {We present a phase model of a repetitively firing neuron possessing a phase-dependent stochastic response to periodic inhibition. We analyze the dynamics in terms of a stochastic phase map and determine the invariant phase distribution. We use the latter to compute both the distribution of interspike intervals (ISIs) and the stochastic winding number (mean firing rate) as a function of the input frequency. We show that only low-order phase locking persists in the presence of weak phase dependence, and is characterized statistically by a multimodal ISI distribution and a nonmonotonic variation in the stochastic winding number as a function of input frequency.},
	Author = {Nesse, William H and Clark, Gregory A and Bressloff, Paul C},
	Date-Added = {2010-01-04 06:08:46 -0500},
	Date-Modified = {2010-01-04 06:12:05 -0500},
	Journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
	Journal-Full = {Physical review. E, Statistical, nonlinear, and soft matter physics},
	Mesh = {Action Potentials; Biological Clocks; Computer Simulation; Feedback; Models, Neurological; Nerve Net; Neural Inhibition; Periodicity; Stochastic Processes; Synaptic Transmission},
	Month = {Mar},
	Number = {3 Pt 1},
	Pages = {031912},
	Pmid = {17500731},
	Title = {Spike patterning of a stochastic phase model neuron given periodic inhibition},
	Volume = {75},
	Year = {2007}}

@article{Pakdaman2001PRE,
	Author = {K. Pakdaman},
	Date-Added = {2009-11-09 08:44:59 -0500},
	Date-Modified = {2009-11-09 08:46:43 -0500},
	Journal = {Physical Review E},
	Number = {4},
	Pages = {041907 1-5},
	Title = {Periodically forced leaky integrate-and-fire model},
	Volume = {63},
	Year = {2001}}

@article{Shimokawa+Pakdaman+Takahata+Tanabe+Sato:2000:BiolCyb,
	Author = {T. Shimokawa and K. Pakdaman and T. Takahata and S. Tanabe and S. Sato},
	Date-Added = {2009-11-09 08:41:50 -0500},
	Date-Modified = {2009-11-09 08:44:07 -0500},
	Journal = {Biological Cybernetics},
	Pages = {327-340},
	Title = {A first-passage-time analysis of the periodically forced noisy leaky integrate-and-fire model},
	Volume = {83},
	Year = {2000}}

@article{Brunel+vanRossum:2007BiolCyb,
	Abstract = {Exactly 100 years ago, Louis Lapicque published a paper on the excitability of nerves that is often cited in the context of integrate-and-fire neurons. We discuss Lapicque's contributions along with a translation of the original publication.},
	Author = {Brunel, Nicolas and van Rossum, Mark C W},
	Date-Added = {2009-11-07 10:47:42 -0500},
	Date-Modified = {2009-11-07 10:48:01 -0500},
	Doi = {10.1007/s00422-007-0190-0},
	Journal = {Biol Cybern},
	Journal-Full = {Biological cybernetics},
	Mesh = {Action Potentials; Animals; Anura; Electric Stimulation; Electrophysiology; History, 19th Century; History, 20th Century; Neurons},
	Month = {Dec},
	Number = {5-6},
	Pages = {337-9},
	Pmid = {17968583},
	Title = {Lapicque's 1907 paper: from frogs to integrate-and-fire},
	Volume = {97},
	Year = {2007},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00422-007-0190-0}}

@article{Abbott:1999:RRB,
	Author = {Abbott, L F},
	Date = {1999 Nov 15-Dec},
	Date-Added = {2009-11-07 10:45:00 -0500},
	Date-Modified = {2009-11-07 10:45:36 -0500},
	Journal = {Brain Res Bull},
	Journal-Full = {Brain research bulletin},
	Mesh = {Electrophysiology; History, 20th Century; Models, Neurological; Neurons; Neurosciences},
	Number = {5-6},
	Pages = {303-4},
	Pmid = {10643408},
	Title = {Lapicque's introduction of the integrate-and-fire model neuron (1907)},
	Volume = {50},
	Year = {1999}}

@article{Fries+Reynolds+Rorie+Desimone:2001:Science,
	Abstract = {In crowded visual scenes, attention is needed to select relevant stimuli. To study the underlying mechanisms, we recorded neurons in cortical area V4 while macaque monkeys attended to behaviorally relevant stimuli and ignored distracters. Neurons activated by the attended stimulus showed increased gamma-frequency (35 to 90 hertz) synchronization but reduced low-frequency (<17 hertz) synchronization compared with neurons at nearby V4 sites activated by distracters. Because postsynaptic integration times are short, these localized changes in synchronization may serve to amplify behaviorally relevant signals in the cortex.},
	Author = {Fries, P and Reynolds, J H and Rorie, A E and Desimone, R},
	Date-Added = {2009-11-05 16:06:58 -0500},
	Date-Modified = {2009-11-05 16:07:28 -0500},
	Doi = {10.1126/science.291.5508.1560},
	Journal = {Science},
	Journal-Full = {Science (New York, N.Y.)},
	Mesh = {Action Potentials; Animals; Attention; Cues; Electrophysiology; Fixation, Ocular; Macaca; Neurons; Photic Stimulation; Visual Cortex; Visual Perception},
	Month = {Feb},
	Number = {5508},
	Pages = {1560-3},
	Pmid = {11222864},
	Title = {Modulation of oscillatory neuronal synchronization by selective visual attention},
	Volume = {291},
	Year = {2001},
	Bdsk-Url-1 = {http://dx.doi.org/10.1126/science.291.5508.1560}}

@article{Vierling-Claassen+Siekmeier+Stufflebeam+Kopell:2008:JNPhys,
	Abstract = {The disorganized symptoms of schizophrenia, including severely disordered thought patterns, may be indicative of a problem with the construction and maintenance of cell assemblies during sensory processing and attention. The gamma and beta frequency bands (15-70 Hz) are believed relevant to such processing. This paper addresses the results of an experimental examination of the cortical response of 12 schizophrenia patients and 12 control subjects when presented with auditory click-train stimuli in the gamma/beta frequency band during measurement using magnetoencephalography (MEG), as well as earlier work by Kwon et al. These data indicate that control subjects show an increased 40-Hz response to both 20- and 40-Hz stimulation as compared with patients, whereas schizophrenic subjects show a preference for 20-Hz response to the same driving frequencies. In this work, two computational models of the auditory cortex are constructed based on postmortem studies that indicate cortical interneurons in schizophrenic subjects have decreased GAT-1 (a GABA transporter) and GAD(67) (1 of 2 enzymes responsible for GABA synthesis). The models transition from control to schizophrenic frequency response when an extended inhibitory decay time is introduced; this change captures a possible effect of these GABA alterations. Modeling gamma/beta range auditory entrainment in schizophrenia provides insight into how biophysical mechanisms can impact cognitive function. In addition, the study of dynamics that underlie auditory entrainment in schizophrenia may contribute to the understanding of how gamma and beta rhythms impact cognition in general.},
	Author = {Vierling-Claassen, Dorea and Siekmeier, Peter and Stufflebeam, Steven and Kopell, Nancy},
	Date-Added = {2009-11-05 16:03:21 -0500},
	Date-Modified = {2009-11-05 16:04:17 -0500},
	Doi = {10.1152/jn.00870.2007},
	Journal = {J Neurophysiol},
	Journal-Full = {Journal of neurophysiology},
	Mesh = {Acoustic Stimulation; Adolescent; Adult; Algorithms; Auditory Cortex; Auditory Perception; Beta Rhythm; Computer Simulation; Electroencephalography; Evoked Potentials; Excitatory Postsynaptic Potentials; GABA Plasma Membrane Transport Proteins; Glutamate Decarboxylase; Humans; Interneurons; Magnetoencephalography; Male; Middle Aged; Models, Neurological; Neural Networks (Computer); Psychiatric Status Rating Scales; Schizophrenia; Schizophrenic Psychology; gamma-Aminobutyric Acid},
	Month = {May},
	Number = {5},
	Pages = {2656-71},
	Pmid = {18287555},
	Title = {Modeling GABA alterations in schizophrenia: a link between impaired inhibition and altered gamma and beta range auditory entrainment},
	Volume = {99},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1152/jn.00870.2007}}

@article{Ullah+Cressman+Barreto+Schiff:2009:JCNS,
	Abstract = {In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. We seek to study these dynamics with respect to the following compartments: neurons, glia, and extracellular space. We are particularly interested in the slower time-scale dynamics that determine overall excitability, and set the stage for transient episodes of persistent oscillations, working memory, or seizures. In this second of two companion papers, we present an ionic current network model composed of populations of Hodgkin-Huxley type excitatory and inhibitory neurons embedded within extracellular space and glia, in order to investigate the role of micro-environmental ionic dynamics on the stability of persistent activity. We show that these networks reproduce seizure-like activity if glial cells fail to maintain the proper micro-environmental conditions surrounding neurons, and produce several experimentally testable predictions. Our work suggests that the stability of persistent states to perturbation is set by glial activity, and that how the response to such perturbations decays or grows may be a critical factor in a variety of disparate transient phenomena such as working memory, burst firing in neonatal brain or spinal cord, up states, seizures, and cortical oscillations.},
	Author = {Ullah, Ghanim and Cressman, Jr, John R and Barreto, Ernest and Schiff, Steven J},
	Date-Added = {2009-11-05 15:57:12 -0500},
	Date-Modified = {2009-11-05 15:58:28 -0500},
	Doi = {10.1007/s10827-008-0130-6},
	Journal = {J Comput Neurosci},
	Journal-Full = {Journal of computational neuroscience},
	Mesh = {Algorithms; Membrane Potentials; Models, Neurological; Neuroglia; Neurons; Potassium; Seizures; Sodium; Sodium-Potassium-Exchanging ATPase},
	Month = {Apr},
	Number = {2},
	Pages = {171-83},
	Pmid = {19083088},
	Title = {The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states. II. Network and glial dynamics},
	Volume = {26},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10827-008-0130-6}}

@article{Cressman+Ullah+Ziburkus+Schiff+Barreto:2009:JCNS,
	Abstract = {In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. In this first paper, we construct a mathematical model consisting of a single conductance-based neuron together with intra- and extracellular ion concentration dynamics. We formulate a reduction of this model that permits a detailed bifurcation analysis, and show that the reduced model is a reasonable approximation of the full model. We find that competition between intrinsic neuronal currents, sodium-potassium pumps, glia, and diffusion can produce very slow and large-amplitude oscillations in ion concentrations similar to what is seen physiologically in seizures. Using the reduced model, we identify the dynamical mechanisms that give rise to these phenomena. These models reveal several experimentally testable predictions. Our work emphasizes the critical role of ion concentration homeostasis in the proper functioning of neurons, and points to important fundamental processes that may underlie pathological states such as epilepsy.},
	Author = {Cressman, Jr, John R and Ullah, Ghanim and Ziburkus, Jokubas and Schiff, Steven J and Barreto, Ernest},
	Date-Added = {2009-11-05 15:57:12 -0500},
	Date-Modified = {2009-11-05 15:58:28 -0500},
	Doi = {10.1007/s10827-008-0132-4},
	Journal = {J Comput Neurosci},
	Journal-Full = {Journal of computational neuroscience},
	Mesh = {Algorithms; Diffusion; Membrane Potentials; Models, Neurological; Neuroglia; Neurons; Potassium; Seizures; Sodium; Sodium-Potassium-Exchanging ATPase},
	Month = {Apr},
	Number = {2},
	Pages = {159-70},
	Pmid = {19169801},
	Title = {The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics},
	Volume = {26},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10827-008-0132-4}}

@article{IsomuraEtAlBuzsaki:2006:Neuron,
	Abstract = {Brain systems communicate by means of neuronal oscillations at multiple temporal and spatial scales. In anesthetized rats, we find that neocortical "slow" oscillation engages neurons in prefrontal, somatosensory, entorhinal, and subicular cortices into synchronous transitions between UP and DOWN states, with a corresponding bimodal distribution of their membrane potential. The membrane potential of hippocampal granule cells and CA3 and CA1 pyramidal cells lacked bimodality, yet it was influenced by the slow oscillation in a region-specific manner. Furthermore, in both anesthetized and naturally sleeping rats, the cortical UP states resulted in increased activity of dentate and most CA1 neurons, as well as the highest probability of ripple events. Yet, the CA3-CA1 network could self-organize into gamma bursts and occasional ripples during the DOWN state. Thus, neo/paleocortical and hippocampal networks periodically reset, self-organize, and temporally coordinate their cell assemblies via the slow oscillation.},
	Author = {Isomura, Yoshikazu and Sirota, Anton and Ozen, Simal and Montgomery, Sean and Mizuseki, Kenji and Henze, Darrell A and Buzs{\'a}ki, Gy{\"o}rgy},
	Date-Added = {2009-11-05 15:55:33 -0500},
	Date-Modified = {2009-11-05 15:55:59 -0500},
	Doi = {10.1016/j.neuron.2006.10.023},
	Journal = {Neuron},
	Journal-Full = {Neuron},
	Mesh = {Anesthesia; Animals; Data Interpretation, Statistical; Electrophysiology; Entorhinal Cortex; Extracellular Matrix; Hippocampus; Male; Membrane Potentials; Neocortex; Nerve Net; Neurons; Rats; Rats, Sprague-Dawley; Sleep},
	Month = {Dec},
	Number = {5},
	Pages = {871-82},
	Pmid = {17145507},
	Title = {Integration and segregation of activity in entorhinal-hippocampal subregions by neocortical slow oscillations},
	Volume = {52},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.neuron.2006.10.023}}

@article{Smith:1991,
	Abstract = {The location of neurons generating the rhythm of breathing in mammals is unknown. By microsection of the neonatal rat brainstem in vitro, a limited region of the ventral medulla (the pre-B{\"o}tzinger Complex) that contains neurons essential for rhythmogenesis was identified. Rhythm generation was eliminated by removal of only this region. Medullary slices containing the pre-B{\"o}tzinger Complex generated respiratory-related oscillations similar to those generated by the whole brainstem in vitro, and neurons with voltage-dependent pacemaker-like properties were identified in this region. Thus, the respiratory rhythm in the mammalian neonatal nervous system may result from a population of conditional bursting pacemaker neurons in the pre-B{\"o}tzinger Complex.},
	Author = {Smith, J C and Ellenberger, H H and Ballanyi, K and Richter, D W and Feldman, J L},
	Date-Added = {2009-11-05 15:47:48 -0500},
	Date-Modified = {2009-11-05 15:48:02 -0500},
	Journal = {Science},
	Journal-Full = {Science (New York, N.Y.)},
	Mesh = {6-Cyano-7-nitroquinoxaline-2,3-dione; Activity Cycles; Animals; Animals, Newborn; Evoked Potentials; Mammals; Medulla Oblongata; Neurons; Quinoxalines; Rats; Respiration},
	Month = {Nov},
	Number = {5032},
	Pages = {726-9},
	Pmid = {1683005},
	Title = {Pre-B{\"o}tzinger complex: a brainstem region that may generate respiratory rhythm in mammals},
	Volume = {254},
	Year = {1991}}

@article{Sejnowski+Paulsen:2006:JNsci,
	Author = {Sejnowski, Terrence J and Paulsen, Ole},
	Date-Added = {2009-11-05 15:18:20 -0500},
	Date-Modified = {2009-11-05 15:18:41 -0500},
	Doi = {10.1523/JNEUROSCI.3737-05d.2006},
	Journal = {J Neurosci},
	Journal-Full = {The Journal of neuroscience : the official journal of the Society for Neuroscience},
	Mesh = {Animals; Brain; Hippocampus; Humans; Learning; Memory; Models, Neurological; Nerve Net; Oscillometry; Reproducibility of Results},
	Month = {Feb},
	Number = {6},
	Pages = {1673-6},
	Pmid = {16467514},
	Title = {Network oscillations: emerging computational principles},
	Volume = {26},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1523/JNEUROSCI.3737-05d.2006}}

@article{Tiesinga+Sejnowski:2009:Neuron,
	Abstract = {The response of a neuron to sensory stimuli can only give correlational support for functional hypotheses. To experimentally test causal function, the neural activity needs to be manipulated in a cell-type-specific as well as spatially and temporally precise way. We review recent optogenetic experiments on parvalbumin-positive cortical interneurons that link modeling studies of synchronization to experimental studies on attentional modulation of gamma oscillations in primates.},
	Author = {Tiesinga, Paul and Sejnowski, Terrence J},
	Date-Added = {2009-11-05 15:04:13 -0500},
	Date-Modified = {2009-11-05 15:04:46 -0500},
	Doi = {10.1016/j.neuron.2009.09.009},
	Journal = {Neuron},
	Journal-Full = {Neuron},
	Mesh = {Animals; Attention; Biological Clocks; Cerebral Cortex; Humans; Interneurons; Models, Neurological; Nerve Net; Neural Inhibition; Neural Pathways; Space Perception},
	Month = {Sep},
	Number = {6},
	Pages = {727-32},
	Pmid = {19778503},
	Title = {Cortical enlightenment: are attentional gamma oscillations driven by ING or PING?},
	Volume = {63},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.neuron.2009.09.009}}

@article{Glass:2001:Nature,
	Abstract = {Complex bodily rhythms are ubiquitous in living organisms. These rhythms arise from stochastic, nonlinear biological mechanisms interacting with a fluctuating environment. Disease often leads to alterations from normal to pathological rhythm. Fundamental questions concerning the dynamics of these rhythmic processes abound. For example, what is the origin of physiological rhythms? How do the rhythms interact with each other and the external environment? Can we decode the fluctuations in physiological rhythms to better diagnose human disease? And can we develop better methods to control pathological rhythms? Mathematical and physical techniques combined with physiological and medical studies are addressing these questions and are transforming our understanding of the rhythms of life.},
	Author = {Glass, L},
	Date-Added = {2009-10-22 23:46:51 -0400},
	Date-Modified = {2009-10-22 23:47:07 -0400},
	Doi = {10.1038/35065745},
	Journal = {Nature},
	Journal-Full = {Nature},
	Mesh = {Models, Biological; Nonlinear Dynamics; Oscillometry; Periodicity; Physiology; Stochastic Processes; Systems Theory},
	Month = {Mar},
	Number = {6825},
	Pages = {277-84},
	Pmid = {11258383},
	Title = {Synchronization and rhythmic processes in physiology},
	Volume = {410},
	Year = {2001},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/35065745}}

@article{Glass+Mackey:1979:JMathBiol,
	Abstract = {A mathematical model is presented for phase locking of a biological oscillator to a sinusoidal stimulus. Analytical, numerical and topological considerations are used to discuss the patterns of phase locking as a function of amplitude of the sinusoidal stimulus and the relative frequencies of the osillator and the sinusoidal stimulus. The sorts of experimental data which are needed to make comparisons between theory and experiment are discussed.},
	Author = {Glass, L and Mackey, M C},
	Date-Added = {2009-10-22 23:44:13 -0400},
	Date-Modified = {2009-10-22 23:44:37 -0400},
	Journal = {J Math Biol},
	Journal-Full = {Journal of mathematical biology},
	Mesh = {Biological Clocks; Mathematics; Models, Biological; Periodicity; Time Factors},
	Month = {May},
	Number = {4},
	Pages = {339-52},
	Pmid = {469413},
	Title = {A simple model for phase locking of biological oscillators},
	Volume = {7},
	Year = {1979}}

@article{Lewis:1992lk,
	Abstract = {In a previous study (Lewis et al., 1990), the response of the respiratory rhythm to a perturbing stimulus was investigated using two different stimulus protocols: phase resetting and fixed-delay stimulation. The first protocol consists of measuring the effects of perturbing an oscillator at different phases of the cycle on the duration of the perturbed cycle. The resulting phase response curves (PRCs) can be used to characterize the properties of the oscillator (Winfree, 1980). A second protocol, fixed-delay stimulation, involves perturbing an oscillator at a fixed latency from the onset of the cycle, repeated every n-th cycle. If a single stimulus produces an effect that lasts longer than a single cycle, complicated responses can be expected from fixed-delay stimulation (Lewis et al., 1987). A simple three-phase model for respiratory rhythm generation based on a hypothesis by Richter and coworkers (1982, 1983, 1986) was investigated in the context of these experimental studies. Phase resetting and fixed-delay stimulation protocols were simulated in the model. PRCs of the model resemble those obtained experimentally: a phase-dependent prolongation or shortening of the inspiratory phase depending on the stimulus magnitude, and a slight prolongation of the expiratory phase. Stimuli delivered to the model repetitively during successive inspiratory periods at a fixed-delay produced various combinations of shortened and prolonged cycles, similar to those observed in the experiments. However, the marked increases in cycle duration observed in the experiments during, as well as after, stimulation were not evident in the model. These comparisons suggest that (1) PRCs may not be an adequate way to evaluate certain models of rhythmogenesis, and (2) to improve the present simplified formulation of the three-phase model of the respiratory oscillator, time-varying stimulus dependent effects should be incorporated.},
	Author = {Lewis, J E and Glass, L and Bachoo, M and Polosa, C},
	Date-Added = {2009-10-22 23:42:11 -0400},
	Date-Modified = {2009-10-22 23:42:11 -0400},
	Journal = {J Theor Biol},
	Journal-Full = {Journal of theoretical biology},
	Mesh = {Animals; Lung; Models, Biological; Respiration},
	Month = {Dec},
	Number = {4},
	Pages = {491-506},
	Pmid = {1296101},
	Title = {Phase resetting and fixed-delay stimulation of a simple model of respiratory rhythm generation},
	Volume = {159},
	Year = {1992}}

@article{Zeng:1992vm,
	Abstract = {The topological properties of the phase resetting of biological oscillators by an isolated stimulus delivered at various phases of the cycle depend on whether the stimulus is "weak" or "strong." When multiple stimuli are delivered to the oscillator, the response to stimulation also depends on the time between the stimuli, and the rate at which the oscillator returns to an underlying limit cycle attractor. If the time between two consecutive "weak" stimuli is sufficiently short, the effects produced by the pair of stimuli may be characteristic of a single "strong" stimulus. These results are demonstrated in a model experimental system, spontaneously beating aggregates of cells derived from embryonic chick heart, and are illustrated by consideration of a simple theoretical model of nonlinear oscillators, the Poincar{\'e} oscillator.},
	Author = {Zeng, W and Glass, L and Shrier, A},
	Date-Added = {2009-10-22 23:41:52 -0400},
	Date-Modified = {2009-10-22 23:41:52 -0400},
	Journal = {J Biol Rhythms},
	Journal-Full = {Journal of biological rhythms},
	Mesh = {Animals; Biological Clocks; Chick Embryo; Electric Stimulation; Heart; Models, Biological; Oscillometry},
	Number = {2},
	Pages = {89-104},
	Pmid = {1611132},
	Title = {The topology of phase response curves induced by single and paired stimuli in spontaneously oscillating chick heart cell aggregates},
	Volume = {7},
	Year = {1992}}

@article{Mackey:1977cy,
	Abstract = {First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions. These results are discussed in relation to dynamical respiratory and hematopoietic diseases.},
	Author = {Mackey, M C and Glass, L},
	Date-Added = {2009-10-22 23:41:17 -0400},
	Date-Modified = {2009-10-22 23:41:17 -0400},
	Journal = {Science},
	Journal-Full = {Science (New York, N.Y.)},
	Mesh = {Cheyne-Stokes Respiration; Hematopoiesis; Leukemia, Myeloid; Models, Biological; Periodicity; Respiration},
	Month = {Jul},
	Number = {4300},
	Pages = {287-9},
	Pmid = {267326},
	Title = {Oscillation and chaos in physiological control systems},
	Volume = {197},
	Year = {1977}}

@article{Zeng:1990hh,
	Abstract = {The effects of periodic stimulation of spontaneously beating aggregates of chick atrial heart cells are considered. Provided the effects of a single stimulus do not change the properties of the oscillation, and that the oscillation is re-established rapidly following a stimulus, this system can be modeled by one-dimensional finite difference equations. These equations employ experimentally generated phase resetting data that describe the effects of a single isolated stimulus at different phases of the oscillation. A complete analysis of the predicted dynamics is given over a broad range of stimulation frequencies and amplitudes. Prominent features of the dynamics include phase locking, bistability, chaos, and disappearance of Arnold tongues at large stimulation amplitudes. The fine details of the bifurcations are sensitive to properties of the phase resetting curves, and consequently, the observed bifurcations are not expected to be "universal" for larger stimulation amplitudes. Experimental traces show many correspondences with theoretical computations.},
	Author = {Zeng, W Z and Courtemanche, M and Sehn, L and Shrier, A and Glass, L},
	Date-Added = {2009-10-22 23:41:11 -0400},
	Date-Modified = {2009-10-22 23:41:11 -0400},
	Journal = {J Theor Biol},
	Journal-Full = {Journal of theoretical biology},
	Mesh = {Animals; Biological Clocks; Chick Embryo; Electric Stimulation; Heart Atria; Models, Biological},
	Month = {Jul},
	Number = {2},
	Pages = {225-44},
	Pmid = {2402157},
	Title = {Theoretical computation of phase locking in embryonic atrial heart cell aggregates},
	Volume = {145},
	Year = {1990}}

@article{Glass:1984ag,
	Abstract = {The effects of perturbing an on-going biological oscillation with a single brief stimulus are considered. If the time from some observable event before the stimulus to the next event after the stimulus is plotted as a function of the phase of the stimulus, then there may be discontinuities in this plot. The discontinuities reflect the size of the stimulus and the topological properties of the biological oscillation. The implications for experiments are discussed.},
	Author = {Glass, L and Winfree, A T},
	Date-Added = {2009-10-22 23:41:07 -0400},
	Date-Modified = {2009-10-22 23:41:07 -0400},
	Journal = {Am J Physiol},
	Journal-Full = {The American journal of physiology},
	Mesh = {Animals; Models, Biological; Terminology as Topic},
	Month = {Feb},
	Number = {2 Pt 2},
	Pages = {R251-8},
	Pmid = {6696148},
	Title = {Discontinuities in phase-resetting experiments},
	Volume = {246},
	Year = {1984}}

@article{Guevara:1981ou,
	Abstract = {The spontaneous rhythmic activity of aggregates of embryonic chick heart cells was perturbed by the injection of single current pulses and periodic trains of current pulses. The regular and irregular dynamics produced by periodic stimulation were predicted theoretically from a mathematical analysis of the response to single pulses. Period-doubling bifurcations, in which the period of a regular oscillation doubles, were predicted theoretically and observed experimentally.},
	Author = {Guevara, M R and Glass, L and Shrier, A},
	Date-Added = {2009-10-22 23:40:26 -0400},
	Date-Modified = {2009-10-22 23:40:26 -0400},
	Journal = {Science},
	Journal-Full = {Science (New York, N.Y.)},
	Mesh = {Animals; Cells, Cultured; Chick Embryo; Electric Stimulation; Heart; Membrane Potentials; Models, Biological; Myocardial Contraction; Periodicity},
	Month = {Dec},
	Number = {4527},
	Pages = {1350-3},
	Pmid = {7313693},
	Title = {Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells},
	Volume = {214},
	Year = {1981}}

@article{Glass:1993uv,
	Abstract = {A variety of mathematical methods have been developed to characterize complex rhythms that are observed in physiological systems. These methods include classical techniques such as the mean, standard deviation, and power spectrum, as well as newer methods suggested by nonlinear dynamics including the dimension, Lyapunov number, and entropy. This paper reviews the various ways in which these measures have been applied to analyze physiological dynamics with emphasis on the potential advantages and pitfalls of the various approaches. We conclude that these methods may be useful to help characterize complex time series, but only rarely is it possible to use these methods to establish deterministic chaos in a given time series.},
	Author = {Glass, L and Kaplan, D},
	Date-Added = {2009-10-22 23:38:33 -0400},
	Date-Modified = {2009-10-22 23:38:33 -0400},
	Journal = {Med Prog Technol},
	Journal-Full = {Medical progress through technology},
	Mesh = {Animals; Artifacts; Data Interpretation, Statistical; Feedback; Humans; Mathematics; Nonlinear Dynamics; Periodicity; Physiology; Research Design; Signal Processing, Computer-Assisted; Stochastic Processes; Time Factors},
	Number = {3},
	Pages = {115-28},
	Pmid = {8127277},
	Title = {Time series analysis of complex dynamics in physiology and medicine},
	Volume = {19},
	Year = {1993}}

@article{Courtemanche:1990fd,
	Author = {Courtemanche, M and Glass, L and Rosengarten, M D},
	Date-Added = {2009-10-22 23:38:07 -0400},
	Date-Modified = {2009-10-22 23:38:07 -0400},
	Journal = {Ann N Y Acad Sci},
	Journal-Full = {Annals of the New York Academy of Sciences},
	Mesh = {Arrhythmias, Cardiac; Heart Ventricles; Humans; Models, Cardiovascular},
	Pages = {178-89},
	Pmid = {2197920},
	Title = {Modeling ventricular parasystole},
	Volume = {591},
	Year = {1990}}

@article{Milton:1989kr,
	Author = {Milton, J G and Longtin, A and Beuter, A and Mackey, M C and Glass, L},
	Date-Added = {2009-10-22 23:38:00 -0400},
	Date-Modified = {2009-10-22 23:38:00 -0400},
	Journal = {J Theor Biol},
	Journal-Full = {Journal of theoretical biology},
	Mesh = {Algorithms; Animals; Electrophysiology; Feedback; Humans; Models, Neurological; Nervous System Diseases; Neural Pathways; Psychomotor Performance; Reflex, Pupillary; Time Factors},
	Month = {May},
	Number = {2},
	Pages = {129-47},
	Pmid = {2691758},
	Title = {Complex dynamics and bifurcations in neurology},
	Volume = {138},
	Year = {1989}}

@article{Glass:1990un,
	Author = {Glass, L and Zeng, W Z},
	Date-Added = {2009-10-22 23:37:55 -0400},
	Date-Modified = {2009-10-22 23:37:55 -0400},
	Journal = {Ann N Y Acad Sci},
	Journal-Full = {Annals of the New York Academy of Sciences},
	Mesh = {Action Potentials; Animals; Electric Stimulation; Electrophysiology; Heart Conduction System; Humans; Models, Cardiovascular; Periodicity; Reference Values},
	Pages = {316-27},
	Pmid = {2197927},
	Title = {Complex bifurcations and chaos in simple theoretical models of cardiac oscillations},
	Volume = {591},
	Year = {1990}}

@article{Rescigno:1978kt,
	Author = {Rescigno, A},
	Date-Added = {2009-10-22 17:06:15 -0400},
	Date-Modified = {2009-10-22 17:06:15 -0400},
	Journal = {Bull Math Biol},
	Journal-Full = {Bulletin of mathematical biology},
	Mesh = {Mathematics; Models, Neurological; Neural Conduction; Neurons; Periodicity; Synaptic Transmission},
	Number = {6},
	Pages = {807-21},
	Pmid = {217472},
	Title = {On phase locking of pulse encoders},
	Volume = {40},
	Year = {1978}}

@article{Gerstein+Mandelbrot:1964:BPJ,
	Abstract = {Quantitative methods for the study of the statistical properties of spontaneously occurring spike trains from single neurons have recently been presented. Such measurements suggest a number of descriptive mathematical models. One of these, based on a random walk towards an absorbing barrier, can describe a wide range of neuronal activity in terms of two parameters. These parameters are readily associated with known physiological mechanisms.},
	Author = {GERSTEIN, G L and MANDELBROT, B},
	Date-Added = {2009-10-22 14:32:52 -0400},
	Date-Modified = {2009-10-22 14:33:40 -0400},
	Journal = {Biophys J},
	Journal-Full = {Biophysical journal},
	Keywords = {ELECTROPHYSIOLOGY; EXPERIMENTAL LAB STUDY; NEURONS},
	Mesh = {Electrophysiology; Neurons; Research},
	Month = {Jan},
	Pages = {41-68},
	Pmid = {14104072},
	Title = {RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON},
	Volume = {4},
	Year = {1964}}

@article{Zhurov+Brezina:2006:JNSci,
	Abstract = {The accessory radula closer (ARC) muscle of Aplysia has long been studied as a typical "slow" muscle, one that would be assumed to respond only to the overall, integrated spike rate of its motor neurons, B15 and B16. The precise timing of the individual spikes should not much matter. However, but real B15 and B16 spike patterns recorded in vivo show great variability that extends down to the timing of individual spikes. By replaying these real as well as artificially constructed spike patterns into ARC muscles in vitro, we examined the consequences of this spike-level variability for contraction. Replaying the same pattern several times reproduces precisely the same contraction shape: the B15/B16-ARC neuromuscular transform is deterministic. However, varying the timing of the spikes produces very different contraction shapes and amplitudes. The transform in fact operates at an interface between "fast" and "slow" regimens. It is fast enough that the timing of individual spikes greatly influences the detailed contraction shape. At the same time, slow integration of the spike pattern through the nonlinear transform allows the variable spike timing to determine also the overall contraction amplitude. Indeed, the variability appears to be necessary to maintain the contraction amplitude at a robust level. This phenomenon is tuned by neuromodulators that tune the speed and nonlinearity of the transform. Thus, the variable timing of individual spikes does matter, in at least two, functionally significant ways, in this "slow" neuromuscular system.},
	Author = {Zhurov, Yuriy and Brezina, Vladimir},
	Date-Added = {2009-10-22 14:28:36 -0400},
	Date-Modified = {2009-10-22 14:29:04 -0400},
	Doi = {10.1523/JNEUROSCI.5277-05.2006},
	Journal = {J Neurosci},
	Journal-Full = {The Journal of neuroscience : the official journal of the Society for Neuroscience},
	Mesh = {Action Potentials; Animals; Aplysia; Motor Neurons; Muscle Contraction; Muscles; Reaction Time},
	Month = {Jun},
	Number = {26},
	Pages = {7056-70},
	Pmid = {16807335},
	Title = {Variability of motor neuron spike timing maintains and shapes contractions of the accessory radula closer muscle of Aplysia},
	Volume = {26},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1523/JNEUROSCI.5277-05.2006}}

@article{Lum:2005gm,
	Abstract = {Variability in nervous systems is often taken to be merely "noise." Yet in some cases it may play a positive, active role in the production of behavior. The central pattern generator (CPG) that drives the consummatory feeding behaviors of Aplysia generates large, quasi-random variability in the parameters of the feeding motor programs from one cycle to the next; the variability then propagates through the firing patterns of the motor neurons to the contractions of the feeding muscles. We have proposed that, when the animal is faced with a new, imperfectly known feeding task in each cycle, the variability implements a trial-and-error search through the space of possible feeding movements. Although this strategy will not be successful in every cycle, over many cycles it may be the optimal strategy for feeding in an uncertain and changing environment. To play this role, however, the variability must actually appear in the feeding movements and, presumably, in the functional performance of the feeding behavior. Here we have tested this critical prediction. We have developed a technique to measure, in intact, freely feeding animals, the performance of Aplysia swallowing behavior, by continuously recording with a length transducer the movement of the seaweed strip being swallowed. Simultaneously, we have recorded with implanted electrodes activity at each of the internal levels, the CPG, motor neurons, and muscles, of the feeding neuromusculature. Statistical analysis of a large data set of these recordings suggests that functional performance is not determined strongly by one or a few parameters of the internal activity, but weakly by many. Most important, the internal variability does emerge in the behavior and its functional performance. Even when the animal is swallowing a long, perfectly regular seaweed strip, remarkably, the length swallowed from cycle to cycle is extremely variable, as variable as the parameters of the activity of the CPG, motor neurons, and muscles.},
	Author = {Lum, Cecilia S and Zhurov, Yuriy and Cropper, Elizabeth C and Weiss, Klaudiusz R and Brezina, Vladimir},
	Date-Added = {2009-10-22 14:28:35 -0400},
	Date-Modified = {2009-10-22 14:28:35 -0400},
	Doi = {10.1152/jn.00280.2005},
	Journal = {J Neurophysiol},
	Journal-Full = {Journal of neurophysiology},
	Mesh = {Action Potentials; Activity Cycles; Animals; Aplysia; Behavior, Animal; Deglutition; Electric Stimulation; Feeding Behavior; Ganglia, Invertebrate; Motor Neurons; Muscles; Reaction Time},
	Month = {Oct},
	Number = {4},
	Pages = {2427-46},
	Pmid = {15944235},
	Title = {Variability of swallowing performance in intact, freely feeding aplysia},
	Volume = {94},
	Year = {2005},
	Bdsk-Url-1 = {http://dx.doi.org/10.1152/jn.00280.2005}}

@article{Zhurov:2005yr,
	Abstract = {Like other complex behaviors, the cyclical, rhythmic consummatory feeding behaviors of Aplysia-biting, swallowing, and rejection of unsuitable food-are produced by a complex neuromuscular system: the animal's buccal mass, with numerous pairs of antagonistic muscles, controlled by the firing of numerous motor neurons, all driven by the motor programs of a central pattern generator (CPG) in the buccal ganglia. In such a complex neuromuscular system, it has always been assumed that the activities of the various components must necessarily be tightly coupled and coordinated if successful functional behavior is to be produced. However, we have recently found that the CPG generates extremely variable motor programs from one cycle to the next, and so very variable motor neuron firing patterns and contractions of individual muscles. Here we show that this variability extends even to higher-level parameters of the operation of the neuromuscular system such as the coordination between entire antagonistic subsystems within the buccal neuromusculature. In motor programs elicited by stimulation of the esophageal nerve, we have studied the relationship between the contractions of the accessory radula closer (ARC) muscle, and the firing patterns of its motor neurons B15 and B16, with those of its antagonist, the radula opener (I7) muscle, and its motor neuron B48. There are two separate B15/B16-ARC subsystems, one on each side of the animal, and these are indeed very tightly coupled. Tight coupling can, therefore, be achieved in this neuromuscular system where required. Yet there is essentially no coupling at all between the contractions of the ARC muscles and those of the antagonistic radula opener muscle. We interpret this result in terms of a hypothesis that ascribes a higher-order benefit to such loose coupling in the neuromusculature. The variability, emerging in the successive feeding movements made by the animal, diversifies the range of movements and thereby implements a trial-and-error search through the space of movements that might be successful, an optimal strategy for the animal in an unknown, rapidly changing feeding environment.},
	Author = {Zhurov, Yuriy and Weiss, Klaudiusz R and Brezina, Vladimir},
	Date-Added = {2009-10-22 14:28:33 -0400},
	Date-Modified = {2009-10-22 14:28:33 -0400},
	Doi = {10.1152/jn.01336.2004},
	Journal = {J Neurophysiol},
	Journal-Full = {Journal of neurophysiology},
	Mesh = {Action Potentials; Animals; Aplysia; Electric Stimulation; Evoked Potentials, Motor; Feeding Behavior; Ganglia, Invertebrate; Models, Biological; Motor Neurons; Muscle Contraction; Neuromuscular Junction; Neurons, Afferent},
	Month = {Jul},
	Number = {1},
	Pages = {531-49},
	Pmid = {15917315},
	Title = {Tight or loose coupling between components of the feeding neuromusculature of Aplysia?},
	Volume = {94},
	Year = {2005},
	Bdsk-Url-1 = {http://dx.doi.org/10.1152/jn.01336.2004}}

@article{Horn:2004jc,
	Abstract = {Aplysia consummatory feeding behavior, a rhythmic cycling of biting, swallowing, and rejection movements, is often said to be stereotyped. Yet closer examination shows that cycles of the behavior are very variable. Here we have quantified and analyzed the variability at several complementary levels in the neuromuscular system. In reduced preparations, we recorded the motor programs produced by the central pattern generator, firing of the motor neurons B15 and B16, and contractions of the accessory radula closer (ARC) muscle while repetitive programs were elicited by stimulation of the esophageal nerve. In other similar experiments, we recorded firing of motor neuron B48 and contractions of the radula opener muscle. In intact animals, we implanted electrodes to record nerve or ARC muscle activity while the animals swallowed controlled strips of seaweed or fed freely. In all cases, we found large variability in all parameters examined. Some of this variability reflected systematic, slow, history-dependent changes in the character of the central motor programs. Even when these trends were factored out, however, by focusing only on the differences between successive cycles, considerable variability remained. This variability was apparently random. Nevertheless, it too was the product of central history dependency because regularizing merely the high-level timing of the programs also regularized many of the downstream neuromuscular parameters. Central motor program variability thus appears directly in the behavior. With regard to the production of functional behavior in any one cycle, the large variability may indicate broad tolerances in the operation of the neuromuscular system. Alternatively, some cycles of the behavior may be dysfunctional. Overall, the variability may be part of an optimal strategy of trial, error, and stabilization that the CNS adopts in an uncertain environment.},
	Author = {Horn, Charles C and Zhurov, Yuriy and Orekhova, Irina V and Proekt, Alex and Kupfermann, Irving and Weiss, Klaudiusz R and Brezina, Vladimir},
	Date-Added = {2009-10-22 14:28:30 -0400},
	Date-Modified = {2009-10-22 14:28:30 -0400},
	Doi = {10.1152/jn.01190.2003},
	Journal = {J Neurophysiol},
	Journal-Full = {Journal of neurophysiology},
	Mesh = {Action Potentials; Animals; Aplysia; Electric Stimulation; Feeding Behavior; Ganglia, Invertebrate; Muscle Contraction; Neuromuscular Junction},
	Month = {Jul},
	Number = {1},
	Pages = {157-80},
	Pmid = {14985412},
	Title = {Cycle-to-cycle variability of neuromuscular activity in Aplysia feeding behavior},
	Volume = {92},
	Year = {2004},
	Bdsk-Url-1 = {http://dx.doi.org/10.1152/jn.01190.2003}}

@article{Grossberg:2008ti,
	Abstract = {How does the brain make decisions? Speed and accuracy of perceptual decisions covary with certainty in the input, and correlate with the rate of evidence accumulation in parietal and frontal cortical "decision neurons". A biophysically realistic model of interactions within and between Retina/LGN and cortical areas V1, MT, MST, and LIP, gated by basal ganglia, simulates dynamic properties of decision-making in response to ambiguous visual motion stimuli used by Newsome, Shadlen, and colleagues in their neurophysiological experiments. The model clarifies how brain circuits that solve the aperture problem interact with a recurrent competitive network with self-normalizing choice properties to carry out probabilistic decisions in real time. Some scientists claim that perception and decision-making can be described using Bayesian inference or related general statistical ideas, that estimate the optimal interpretation of the stimulus given priors and likelihoods. However, such concepts do not propose the neocortical mechanisms that enable perception, and make decisions. The present model explains behavioral and neurophysiological decision-making data without an appeal to Bayesian concepts and, unlike other existing models of these data, generates perceptual representations and choice dynamics in response to the experimental visual stimuli. Quantitative model simulations include the time course of LIP neuronal dynamics, as well as behavioral accuracy and reaction time properties, during both correct and error trials at different levels of input ambiguity in both fixed duration and reaction time tasks. Model MT/MST interactions compute the global direction of random dot motion stimuli, while model LIP computes the stochastic perceptual decision that leads to a saccadic eye movement.},
	Author = {Grossberg, Stephen and Pilly, Praveen K},
	Date-Added = {2009-10-22 14:26:39 -0400},
	Date-Modified = {2009-10-22 14:26:39 -0400},
	Doi = {10.1016/j.visres.2008.02.019},
	Journal = {Vision Res},
	Journal-Full = {Vision research},
	Mesh = {Animals; Computer Simulation; Decision Making; Discrimination (Psychology); Humans; Models, Neurological; Motion Perception; Neurons; Psychophysics; Reaction Time; Saccades; Visual Cortex; Visual Pathways},
	Month = {Jun},
	Number = {12},
	Pages = {1345-73},
	Pmid = {18452967},
	Title = {Temporal dynamics of decision-making during motion perception in the visual cortex},
	Volume = {48},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.visres.2008.02.019}}

@article{Shadlen:2001ug,
	Abstract = {We recorded the activity of single neurons in the posterior parietal cortex (area LIP) of two rhesus monkeys while they discriminated the direction of motion in random-dot visual stimuli. The visual task was similar to a motion discrimination task that has been used in previous investigations of motion-sensitive regions of the extrastriate cortex. The monkeys were trained to decide whether the direction of motion was toward one of two choice targets that appeared on either side of the random-dot stimulus. At the end of the trial, the monkeys reported their direction judgment by making an eye movement to the appropriate target. We studied neurons in LIP that exhibited spatially selective persistent activity during delayed saccadic eye movement tasks. These neurons are thought to carry high-level signals appropriate for identifying salient visual targets and for guiding saccadic eye movements. We arranged the motion discrimination task so that one of the choice targets was in the LIP neuron's response field (RF) while the other target was positioned well away from the RF. During motion viewing, neurons in LIP altered their firing rate in a manner that predicted the saccadic eye movement that the monkey would make at the end of the trial. The activity thus predicted the monkey's judgment of motion direction. This predictive activity began early in the motion-viewing period and became increasingly reliable as the monkey viewed the random-dot motion. The neural activity predicted the monkey's direction judgment on both easy and difficult trials (strong and weak motion), whether or not the judgment was correct. In addition, the timing and magnitude of the response was affected by the strength of the motion signal in the stimulus. When the direction of motion was toward the RF, stronger motion led to larger neural responses earlier in the motion-viewing period. When motion was away from the RF, stronger motion led to greater suppression of ongoing activity. Thus the activity of single neurons in area LIP reflects both the direction of an impending gaze shift and the quality of the sensory information that instructs such a response. The time course of the neural response suggests that LIP accumulates sensory signals relevant to the selection of a target for an eye movement.},
	Author = {Shadlen, M N and Newsome, W T},
	Date-Added = {2009-10-22 14:26:35 -0400},
	Date-Modified = {2009-10-22 14:26:35 -0400},
	Journal = {J Neurophysiol},
	Journal-Full = {Journal of neurophysiology},
	Mesh = {Action Potentials; Animals; Discrimination (Psychology); Electrophysiology; Female; Linear Models; Macaca mulatta; Male; Motion Perception; Motor Neurons; Neurons, Afferent; Parietal Lobe; Photic Stimulation; Psychophysics; Saccades},
	Month = {Oct},
	Number = {4},
	Pages = {1916-36},
	Pmid = {11600651},
	Title = {Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey},
	Volume = {86},
	Year = {2001}}

@article{Shadlen+Newsome:1998:JNSci,
	Abstract = {Cortical neurons exhibit tremendous variability in the number and temporal distribution of spikes in their discharge patterns. Furthermore, this variability appears to be conserved over large regions of the cerebral cortex, suggesting that it is neither reduced nor expanded from stage to stage within a processing pathway. To investigate the principles underlying such statistical homogeneity, we have analyzed a model of synaptic integration incorporating a highly simplified integrate and fire mechanism with decay. We analyzed a "high-input regime" in which neurons receive hundreds of excitatory synaptic inputs during each interspike interval. To produce a graded response in this regime, the neuron must balance excitation with inhibition. We find that a simple integrate and fire mechanism with balanced excitation and inhibition produces a highly variable interspike interval, consistent with experimental data. Detailed information about the temporal pattern of synaptic inputs cannot be recovered from the pattern of output spikes, and we infer that cortical neurons are unlikely to transmit information in the temporal pattern of spike discharge. Rather, we suggest that quantities are represented as rate codes in ensembles of 50-100 neurons. These column-like ensembles tolerate large fractions of common synaptic input and yet covary only weakly in their spike discharge. We find that an ensemble of 100 neurons provides a reliable estimate of rate in just one interspike interval (10-50 msec). Finally, we derived an expression for the variance of the neural spike count that leads to a stable propagation of signal and noise in networks of neurons-that is, conditions that do not impose an accumulation or diminution of noise. The solution implies that single neurons perform simple algebra resembling averaging, and that more sophisticated computations arise by virtue of the anatomical convergence of novel combinations of inputs to the cortical column from external sources.},
	Author = {Shadlen, M N and Newsome, W T},
	Date-Added = {2009-10-22 14:26:28 -0400},
	Date-Modified = {2009-10-22 14:27:31 -0400},
	Journal = {J Neurosci},
	Journal-Full = {The Journal of neuroscience : the official journal of the Society for Neuroscience},
	Mesh = {Action Potentials; Animals; Cerebral Cortex; Data Interpretation, Statistical; Electrophysiology; Higher Nervous Activity; Information Theory; Interneurons; Macaca mulatta; Mental Processes; Models, Neurological; Neural Pathways; Reaction Time},
	Month = {May},
	Number = {10},
	Pages = {3870-96},
	Pmid = {9570816},
	Title = {The variable discharge of cortical neurons: implications for connectivity, computation, and information coding},
	Volume = {18},
	Year = {1998}}

@article{Shadlen:1996sr,
	Abstract = {We have documented previously a close relationship between neuronal activity in the middle temporal visual area (MT or V5) and behavioral judgments of motion (Newsome et al., 1989; Salzman et al., 1990; Britten et al., 1992; Britten et al., 1996). We have now used numerical simulations to try to understand how neural signals in area MT support psychophysical decisions. We developed a model that pools neuronal responses drawn from our physiological data set and compares average responses in different pools to produce psychophysical decisions. The structure of the model allows us to assess the relationship between "neuronal" input signals and simulated psychophysical performance using the same methods we have applied to real experimental data. We sought to reconcile three experimental observations: psychophysical performance (threshold sensitivity to motion stimuli embedded in noise), a trial-by-trial covariation between the neural response and the monkey's choices, and a modest correlation between pairs of MT neurons in their variable responses to identical visual stimuli. Our results can be most accurately simulated if psychophysical decisions are based on pools of at least 100 weakly correlated sensory neurons. The neurons composing the pools must include a broader range of sensitivities than we encountered in our MT recordings, presumably because of the inclusion of neurons whose optimal stimulus is different from the one being discriminated. Central sources of noise degrade the signal-to-noise ratio of the pooled signal, but this degradation is relatively small compared with the noise typically carried by single cortical neurons. This suggests that our monkeys base near-threshold psychophysical judgments on signals carried by populations of weakly interacting neurons; these populations include many neurons that are not tuned optimally for the particular stimuli being discriminated.},
	Author = {Shadlen, M N and Britten, K H and Newsome, W T and Movshon, J A},
	Date-Added = {2009-10-22 14:25:38 -0400},
	Date-Modified = {2009-10-22 14:25:38 -0400},
	Journal = {J Neurosci},
	Journal-Full = {The Journal of neuroscience : the official journal of the Society for Neuroscience},
	Mesh = {Animals; Behavior, Animal; Macaca mulatta; Models, Neurological; Neuronal Plasticity; Statistics as Topic; Visual Cortex; Visual Perception},
	Month = {Feb},
	Number = {4},
	Pages = {1486-510},
	Pmid = {8778300},
	Title = {A computational analysis of the relationship between neuronal and behavioral responses to visual motion},
	Volume = {16},
	Year = {1996}}

@article{Shadlen:1996tf,
	Abstract = {The primate visual system offers unprecedented opportunities for investigating the neural basis of cognition. Even the simplest visual discrimination task requires processing of sensory signals, formation of a decision, and orchestration of a motor response. With our extensive knowledge of the primate visual and oculomotor systems as a base, it is now possible to investigate the neural basis of simple visual decisions that link sensation to action. Here we describe an initial study of neural responses in the lateral intraparietal area (LIP) of the cerebral cortex while alert monkeys discriminated the direction of motion in a visual display. A subset of LIP neurons carried high-level signals that may comprise a neural correlate of the decision process in our task. These signals are neither sensory nor motor in the strictest sense; rather they appear to reflect integration of sensory signals toward a decision appropriate for guiding movement. If this ultimately proves to be the case, several fascinating issues in cognitive neuroscience will be brought under rigorous physiological scrutiny.},
	Author = {Shadlen, M N and Newsome, W T},
	Date-Added = {2009-10-22 14:25:32 -0400},
	Date-Modified = {2009-10-22 14:25:32 -0400},
	Journal = {Proc Natl Acad Sci U S A},
	Journal-Full = {Proceedings of the National Academy of Sciences of the United States of America},
	Mesh = {Animals; Decision Making; Discrimination (Psychology); Higher Nervous Activity; Macaca mulatta; Motion Perception; Neurons; Neurophysiology; Parietal Lobe; Saccades},
	Month = {Jan},
	Number = {2},
	Pages = {628-33},
	Pmid = {8570606},
	Title = {Motion perception: seeing and deciding},
	Volume = {93},
	Year = {1996}}

@article{Britten:1996tn,
	Abstract = {We have previously documented the exquisite motion sensitivity of neurons in extrastriate area MT by studying the relationship between their responses and the direction and strength of visual motion signals delivered to their receptive fields. These results suggested that MT neurons might provide the signals supporting behavioral choice in visual discrimination tasks. To approach this question from another direction, we have now studied the relationship between the discharge of MT neurons and behavioral choice, independently of the effects of visual stimulation. We found that trial-to-trial variability in neuronal signals was correlated with the choices the monkey made. Therefore, when a directionally selective neuron in area MT fires more vigorously, the monkey is more likely to make a decision in favor of the preferred direction of the cell. The magnitude of the relationship was modest, on average, but was highly significant across a sample of 299 cells from four monkeys. The relationship was present for all stimuli (including those without a net motion signal), and for all but the weakest responses. The relationship was reduced or eliminated when the demands of the task were changed so that the directional signal carried by the cell was less informative. The relationship was evident within 50 ms of response onset, and persisted throughout the stimulus presentation. On average, neurons that were more sensitive to weak motion signals had a stronger relationship to behavior than those that were less sensitive. These observations are consistent with the idea that neuronal signals in MT are used by the monkey to determine the direction of stimulus motion. The modest relationship between behavioral choice and the discharge of any one neuron, and the prevalence of the relationship across the population, make it likely that signals from many neurons are pooled to form the data on which behavioral choices are based.},
	Author = {Britten, K H and Newsome, W T and Shadlen, M N and Celebrini, S and Movshon, J A},
	Date = {1996 Jan-Feb},
	Date-Added = {2009-10-22 14:25:29 -0400},
	Date-Modified = {2009-10-22 14:25:29 -0400},
	Journal = {Vis Neurosci},
	Journal-Full = {Visual neuroscience},
	Mesh = {Animals; Choice Behavior; Discrimination (Psychology); Female; Macaca mulatta; Male; Neurons; Photic Stimulation; Probability; Reproducibility of Results; Visual Cortex; Visual Perception},
	Number = {1},
	Pages = {87-100},
	Pmid = {8730992},
	Title = {A relationship between behavioral choice and the visual responses of neurons in macaque MT},
	Volume = {13},
	Year = {1996}}

@article{Shadlen:1995iq,
	Author = {Shadlen, M N and Newsome, W T},
	Date-Added = {2009-10-22 14:25:23 -0400},
	Date-Modified = {2009-10-22 14:25:23 -0400},
	Journal = {Curr Opin Neurobiol},
	Journal-Full = {Current opinion in neurobiology},
	Mesh = {Animals; Cerebral Cortex; Electrophysiology; Evoked Potentials; Humans; Models, Neurological; Neurons},
	Month = {Apr},
	Number = {2},
	Pages = {248-50},
	Pmid = {7620314},
	Title = {Is there a signal in the noise?},
	Volume = {5},
	Year = {1995}}

@article{Shadlen:1994ft,
	Abstract = {Cortical circuitry must facilitate information transfer in accordance with a neural code. In this article we examine two candidate neural codes: information is represented in the spike rate of neurons, or information is represented in the precise timing of individual spikes. These codes can be distinguished by examining the physiological basis of the highly irregular interspike intervals typically observed in cerebral cortex. Recent advances in our understanding of cortical microcircuitry suggest that the timing of neuronal spikes conveys little, if any, information. The cortex is likely to propagate a noisy rate code through redundant, patchy interconnections.},
	Author = {Shadlen, M N and Newsome, W T},
	Date-Added = {2009-10-22 14:24:58 -0400},
	Date-Modified = {2009-10-22 14:24:58 -0400},
	Journal = {Curr Opin Neurobiol},
	Journal-Full = {Current opinion in neurobiology},
	Mesh = {Action Potentials; Animals; Cerebral Cortex; Humans; Neural Pathways; Neurons; Synapses},
	Month = {Aug},
	Number = {4},
	Pages = {569-79},
	Pmid = {7812147},
	Title = {Noise, neural codes and cortical organization},
	Volume = {4},
	Year = {1994}}

@article{Zohary:1994zi,
	Abstract = {Single neurons can signal subtle changes in the sensory environment with surprising fidelity, often matching the perceptual sensitivity of trained psychophysical observers. This similarity poses an intriguing puzzle: why is psychophysical sensitivity not greater than that of single neurons? Pooling responses across neurons should average out noise in the activity of single cells, leading to substantially improved psychophysical performance. If, however, noise is correlated among these neurons, the beneficial effects of pooling would be diminished. To assess correlation within a pool, the responses of pairs of neurons were recorded simultaneously during repeated stimulus presentations. We report here that the observed covariation in spike count was relatively weak, the correlation coefficient averaging 0.12. A theoretical analysis revealed, however, that weak correlation can limit substantially the signalling capacity of the pool. In addition, theory suggests a relationship between neuronal responses and psychophysical decisions which may prove useful for identifying cell populations underlying specific perceptual capacities.},
	Author = {Zohary, E and Shadlen, M N and Newsome, W T},
	Date-Added = {2009-10-22 14:24:54 -0400},
	Date-Modified = {2009-10-22 14:24:54 -0400},
	Doi = {10.1038/370140a0},
	Journal = {Nature},
	Journal-Full = {Nature},
	Mesh = {Action Potentials; Animals; Discrimination (Psychology); Fixation, Ocular; Macaca mulatta; Mathematics; Neurons, Afferent; Psychomotor Performance; Temporal Lobe; Visual Pathways; Visual Perception},
	Month = {Jul},
	Number = {6485},
	Pages = {140-3},
	Pmid = {8022482},
	Title = {Correlated neuronal discharge rate and its implications for psychophysical performance},
	Volume = {370},
	Year = {1994},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/370140a0}}

@article{Britten:1993ce,
	Abstract = {Dynamic random-dot stimuli have been widely used to explore central mechanisms of motion processing. We have measured the responses of neurons in area MT of the alert monkey while we varied the strength and direction of the motion signal in such displays. The strength of motion is controlled by the proportion of spatiotemporally correlated dots, which we term the correlation of the stimulus. For many MT cells, responses varied approximately linearly with stimulus correlation. When they occurred, nonlinearities were equally likely to be either positively or negatively accelerated. We also explored the relationship between response magnitude and response variance for these cells and found, in general agreement with other investigators, that this relationship conforms to a power law with an exponent slightly greater than 1. The variance of the cells' discharge is little influenced by the trial-to-trial fluctuations inherent in our stochastic display, and is therefore likely to be of neural origin. Linear responses to these stochastic motion stimuli are predicted by simple, low-level motion models incorporating sensors having relatively broad spatial and temporal frequency tuning.},
	Author = {Britten, K H and Shadlen, M N and Newsome, W T and Movshon, J A},
	Date = {1993 Nov-Dec},
	Date-Added = {2009-10-22 14:24:45 -0400},
	Date-Modified = {2009-10-22 14:24:45 -0400},
	Journal = {Vis Neurosci},
	Journal-Full = {Visual neuroscience},
	Mesh = {Animals; Female; Light; Macaca mulatta; Male; Microelectrodes; Motion Perception; Neurons; Sensory Thresholds; Visual Cortex},
	Number = {6},
	Pages = {1157-69},
	Pmid = {8257671},
	Title = {Responses of neurons in macaque MT to stochastic motion signals},
	Volume = {10},
	Year = {1993}}

@article{Britten:1992xv,
	Abstract = {We compared the ability of psychophysical observers and single cortical neurons to discriminate weak motion signals in a stochastic visual display. All data were obtained from rhesus monkeys trained to perform a direction discrimination task near psychophysical threshold. The conditions for such a comparison were ideal in that both psychophysical and physiological data were obtained in the same animals, on the same sets of trials, and using the same visual display. In addition, the psychophysical task was tailored in each experiment to the physiological properties of the neuron under study; the visual display was matched to each neuron's preference for size, speed, and direction of motion. Under these conditions, the sensitivity of most MT neurons was very similar to the psychophysical sensitivity of the animal observers. In fact, the responses of single neurons typically provided a satisfactory account of both absolute psychophysical threshold and the shape of the psychometric function relating performance to the strength of the motion signal. Thus, psychophysical decisions in our task are likely to be based upon a relatively small number of neural signals. These signals could be carried by a small number of neurons if the responses of the pooled neurons are statistically independent. Alternatively, the signals may be carried by a much larger pool of neurons if their responses are partially intercorrelated.},
	Author = {Britten, K H and Shadlen, M N and Newsome, W T and Movshon, J A},
	Date-Added = {2009-10-22 14:24:39 -0400},
	Date-Modified = {2009-10-22 14:24:39 -0400},
	Journal = {J Neurosci},
	Journal-Full = {The Journal of neuroscience : the official journal of the Society for Neuroscience},
	Mesh = {Animals; Discrimination (Psychology); Eye Movements; Female; Macaca mulatta; Male; Mathematics; Models, Neurological; Motion Perception; Neurons; Psychometrics; Visual Cortex},
	Month = {Dec},
	Number = {12},
	Pages = {4745-65},
	Pmid = {1464765},
	Title = {The analysis of visual motion: a comparison of neuronal and psychophysical performance},
	Volume = {12},
	Year = {1992}}

@article{Knoblauch:2005rp,
	Abstract = {The response of a cortical neuron to a stimulus can show a very large variability when repeatedly stimulated by exactly the same stimulus. This has been quantified in terms of inter-spike-interval (ISI) statistics by several researchers (e.g., [Softky, W., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13(1), 334-350.]). The common view is that this variability reflects noisy information processing based on redundant representation in large neuron populations. This view has been challenged by the idea that the apparent noise inherent in brain activity that is not strictly related or temporally coupled to the experiment could be functionally significant. In this work we examine the ISI statistics and discuss these views in a recently published model of interacting cortical areas [Knoblauch, A., Palm, G., 2002. Scene segmentation by spike synchronization in reciprocally connected visual areas. I. Local effects of cortical feedback. Biol. Cybernet. 87(3), 151-167.]. From the results of further single neuron simulations we can isolate temporally modulated synaptic input as a main contributor for high ISI variability in our model and possibly in real neurons. In contrast to alternative mechanisms, our model suggests a function of the temporal modulations for short-term binding and segmentation of figures from background. Moreover, we show that temporally modulated inputs lead to ISI statistics which fit better to the neurophysiological data than alternative mechanisms.},
	Author = {Knoblauch, Andreas and Palm, G{\"u}nther},
	Date = {2005 Jan-Mar},
	Date-Added = {2009-10-22 14:17:21 -0400},
	Date-Modified = {2009-10-22 14:17:21 -0400},
	Doi = {10.1016/j.biosystems.2004.09.007},
	Journal = {Biosystems},
	Journal-Full = {Bio Systems},
	Mesh = {Action Potentials; Brain; Models, Biological; Neurons},
	Number = {1-3},
	Pages = {83-90},
	Pmid = {15649592},
	Title = {What is signal and what is noise in the brain?},
	Volume = {79},
	Year = {2005},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.biosystems.2004.09.007}}

@article{Christodoulou+Bugmann:2000:Biosystems,
	Abstract = {The effect of inhibition on the firing variability is examined in this paper using the biologically-inspired temporal noisy-leaky integrator (TNLI) neuron model. The TNLI incorporates hyperpolarising inhibition with negative current pulses of controlled shapes and it also separates dendritic from somatic integration. The firing variability is observed by looking at the coefficient of variation (C(V)) (standard deviation/mean interspike interval) as a function of the mean interspike interval of firing (delta tM) and by comparing the results with the theoretical curve for random spike trains, as well as looking at the interspike interval (ISI) histogram distributions. The results show that with 80\% inhibition, firing at high rates (up to 200 Hz) is nearly consistent with a Poisson-type variability, which complies with the analysis of cortical neuron firing recordings by Softky and Koch [1993, J. Neurosci. 13(1) 334-530]. We also demonstrate that the mechanism by which inhibition increases the C(V) values is by introducing more short intervals in the firing pattern as indicated by a small initial hump at the beginning of the ISI histogram distribution. The use of stochastic inputs and the separation of the dendritic and somatic integration which we model in TNLI, also affect the high firing, near Poisson-type (explained in the paper) variability produced. We have also found that partial dendritic reset increases slightly the firing variability especially at short ISIs.},
	Author = {Christodoulou, C and Bugmann, G},
	Date = {2000 Oct-Dec},
	Date-Added = {2009-10-22 14:17:20 -0400},
	Date-Modified = {2009-10-22 14:18:05 -0400},
	Journal = {Biosystems},
	Journal-Full = {Bio Systems},
	Mesh = {Neurons; Poisson Distribution},
	Number = {1-3},
	Pages = {41-8},
	Pmid = {11164629},
	Title = {Near Poisson-type firing produced by concurrent excitation and inhibition},
	Volume = {58},
	Year = {2000}}

@article{Shinomoto:1999fd,
	Abstract = {Cortical neurons of behaving animals generate irregular spike sequences. Recently, there has been a heated discussion about the origin of this irregularity. Softky and Koch (1993) pointed out the inability of standard single-neuron models to reproduce the irregularity of the observed spike sequences when the model parameters are chosen within a certain range that they consider to be plausible. Shadlen and Newsome (1994), on the other hand, demonstrated that a standard leaky integrate-and-fire model can reproduce the irregularity if the inhibition is balanced with the excitation. Motivated by this discussion, we attempted to determine whether the Ornstein-Uhlenbeck process, which is naturally derived from the leaky integration assumption, can in fact reproduce higher-order statistics of biological data. For this purpose, we consider actual neuronal spike sequences recorded from the monkey prefrontal cortex to calculate the higher-order statistics of the interspike intervals. Consistency of the data with the model is examined on the basis of the coefficient of variation and the skewness coefficient, which are, respectively, a measure of the spiking irregularity and a measure of the asymmetry of the interval distribution. It is found that the biological data are not consistent with the model if the model time constant assumes a value within a certain range believed to cover all reasonable values. This fact suggests that the leaky integrate-and-fire model with the assumption of uncorrelated inputs is not adequate to account for the spiking in at least some cortical neurons.},
	Author = {Shinomoto, S and Sakai, Y and Funahashi, S},
	Date-Added = {2009-10-22 14:17:20 -0400},
	Date-Modified = {2009-10-22 14:17:20 -0400},
	Journal = {Neural Comput},
	Journal-Full = {Neural computation},
	Mesh = {Action Potentials; Animals; Models, Statistical; Neurons; Prefrontal Cortex; Reproducibility of Results},
	Month = {May},
	Number = {4},
	Pages = {935-51},
	Pmid = {10226190},
	Title = {The Ornstein-Uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex},
	Volume = {11},
	Year = {1999}}

@article{Troyer:1997vp,
	Abstract = {To understand the interspike interval (ISI) variability displayed by visual cortical neurons (Softky \& Koch, 1993), it is critical to examine the dynamics of their neuronal integration, as well as the variability in their synaptic input current. Most previous models have focused on the latter factor. We match a simple integrate-and-fire model to the experimentally measured integrative properties of cortical regular spiking cells (McCormick, Connors, Lighthall, \& Prince, 1985). After setting RC parameters, the post-spike voltage reset is set to match experimental measurements of neuronal gain (obtained from in vitro plots of firing frequency versus injected current). Examination of the resulting model leads to an intuitive picture of neuronal integration that unifies the seemingly contradictory 1/square root of N and random walk pictures that have previously been proposed. When ISIs are dominated by postspike recovery, 1/square root of N arguments hold and spiking is regular; after the "memory" of the last spike becomes negligible, spike threshold crossing is caused by input variance around a steady state and spiking is Poisson. In integrate-and-fire neurons matched to cortical cell physiology, steady-state behavior is predominant, and ISIs are highly variable at all physiological firing rates and for a wide range of inhibitory and excitatory inputs.},
	Author = {Troyer, T W and Miller, K D},
	Date-Added = {2009-10-22 14:17:19 -0400},
	Date-Modified = {2009-10-22 14:17:19 -0400},
	Journal = {Neural Comput},
	Journal-Full = {Neural computation},
	Mesh = {Animals; Computer Simulation; Electric Conductivity; Models, Neurological; Neurons; Poisson Distribution; Synapses; Visual Cortex},
	Month = {Jul},
	Number = {5},
	Pages = {971-83},
	Pmid = {9188190},
	Title = {Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell},
	Volume = {9},
	Year = {1997}}

@article{Holt+Softky+Koch+Douglas:1996:JNPhys,
	Abstract = {1. In neocortical slices, the majority of neurons fire quite regularly in response to constant current injections. But neurons in the intact animal fire irregularly in response to constant current injection as well as to visual stimuli. 2. To quantify this observation, we developed a new measure of variability, which compares only adjacent interspike intervals and is therefore less sensitive to rate variations than existing measures such as the coefficient of variation of interspike intervals. 3. We find that the variability of firing is much higher in cells of primary visual cortex in the anesthetized cat than in slice. The response to current injected from an intracellular electrode in vivo is also variable, but slightly more regular and less bursty than in response to visual stimuli. 4. Using a new technique for analyzing the variability of integrate-and-fire neurons, we prove that this behavior is consistent with a simple integrate-and-fire model receiving a large amount of synaptic background activity, but not with a noisy spiking mechanism.},
	Author = {Holt, G R and Softky, W R and Koch, C and Douglas, R J},
	Date-Added = {2009-10-22 14:17:19 -0400},
	Date-Modified = {2009-10-22 14:19:40 -0400},
	Journal = {J Neurophysiol},
	Journal-Full = {Journal of neurophysiology},
	Mesh = {Animals; Cats; Electric Stimulation; Electrodes, Implanted; Electrophysiology; Microelectrodes; Neurons; Photic Stimulation; Refractory Period, Electrophysiological; Visual Cortex},
	Month = {May},
	Number = {5},
	Pages = {1806-14},
	Pmid = {8734581},
	Title = {Comparison of discharge variability in vitro and in vivo in cat visual cortex neurons},
	Volume = {75},
	Year = {1996}}

@article{Softky+Koch:1993:JNSci,
	Abstract = {How random is the discharge pattern of cortical neurons? We examined recordings from primary visual cortex (V1; Knierim and Van Essen, 1992) and extrastriate cortex (MT; Newsome et al., 1989a) of awake, behaving macaque monkey and compared them to analytical predictions. For nonbursting cells firing at sustained rates up to 300 Hz, we evaluated two indices of firing variability: the ratio of the variance to the mean for the number of action potentials evoked by a constant stimulus, and the rate-normalized coefficient of variation (Cv) of the interspike interval distribution. Firing in virtually all V1 and MT neurons was nearly consistent with a completely random process (e.g., Cv approximately 1). We tried to model this high variability by small, independent, and random EPSPs converging onto a leaky integrate-and-fire neuron (Knight, 1972). Both this and related models predicted very low firing variability (Cv << 1) for realistic EPSP depolarizations and membrane time constants. We also simulated a biophysically very detailed compartmental model of an anatomically reconstructed and physiologically characterized layer V cat pyramidal cell (Douglas et al., 1991) with passive dendrites and active soma. If independent, excitatory synaptic input fired the model cell at the high rates observed in monkey, the Cv and the variability in the number of spikes were both very low, in agreement with the integrate-and-fire models but in strong disagreement with the majority of our monkey data. The simulated cell only produced highly variable firing when Hodgkin-Huxley-like currents (INa and very strong IDR) were placed on distal dendrites. Now the simulated neuron acted more as a millisecond-resolution detector of dendritic spike coincidences than as a temporal integrator. We argue that neurons that act as temporal integrators over many synaptic inputs must fire very regularly. Only in the presence of either fast and strong dendritic nonlinearities or strong synchronization among individual synaptic events will the degree of predicted variability approach that of real cortical neurons.},
	Author = {Softky, W R and Koch, C},
	Date-Added = {2009-10-22 14:17:18 -0400},
	Date-Modified = {2009-10-22 14:21:46 -0400},
	Journal = {J Neurosci},
	Journal-Full = {The Journal of neuroscience : the official journal of the Society for Neuroscience},
	Mesh = {Action Potentials; Animals; Computer Simulation; Dendrites; Humans; Models, Neurological; Neurons; Random Allocation; Reaction Time; Synapses; Visual Cortex},
	Month = {Jan},
	Number = {1},
	Pages = {334-50},
	Pmid = {8423479},
	Title = {The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs},
	Volume = {13},
	Year = {1993}}

@article{Coombes1999PhysLettA,
	Author = {S. Coombes},
	Date-Added = {2009-07-03 13:06:35 -0400},
	Date-Modified = {2009-07-03 13:08:04 -0400},
	Journal = {Physics Letters A},
	Pages = {49-57},
	Title = {Liapunov Exponents and Mode-locked Solutions for Integrate-and-fire Dynamical Systems},
	Volume = {255},
	Year = {1999}}

@article{Hunter+Milton:2003:JNeurophys,
	Abstract = {The spike-time reliability of motoneurons in the Aplysia buccal motor ganglion was studied as a function of the frequency content and the relative amplitude of the fluctuations in the neuronal input, calculated as the coefficient of variation (CV). Measurements of spike-time reliability to sinusoidal and aperiodic inputs, as well as simulations of a noisy leaky integrate-and-fire neuron stimulated by spike trains drawn from a periodically modulated process, demonstrate that there are three qualitatively different CV-dependent mechanisms that determine reliability: noise-dominated (CV < 0.05 for Aplysia motoneurons) where spike timing is unreliable regardless of frequency content; resonance-dominated (CV approximately 0.05-0.25) where reliability is reduced by removal of input frequencies equal to motoneuron firing rate; and amplitude-dominated (CV >0.35) where reliability depends on input frequencies greater than motoneuron firing rate. In the resonance-dominated regime, changes in the activity of the presynaptic inhibitory interneuron B4/5 alter motoneuron spike-time reliability. The increases or decreases in reliability occur coincident with small changes in motoneuron spiking rate due to changes in interneuron activity. Injection of a hyperpolarizing current into the motoneuron reproduces the interneuron-induced changes in reliability. The rate-dependent changes in reliability can be understood from the phase-locking properties of regularly spiking motoneurons to periodic inputs. Our observations demonstrate that the ability of a neuron to support a spike-time code can be actively controlled by varying the properties of the neuron and its input.},
	Address = {Department of Neurology, University of Chicago, Chicago, Illinois 60615, USA.},
	Author = {Hunter, John D and Milton, John G},
	Crdt = {2003/03/14 04:00},
	Da = {20030704},
	Date = {2003 Jul},
	Date-Added = {2009-07-03 12:56:14 -0400},
	Date-Modified = {2009-07-03 12:56:42 -0400},
	Dcom = {20030912},
	Dep = {20030312},
	Doi = {10.1152/jn.00074.2003},
	Edat = {2003/03/14 04:00},
	Issn = {0022-3077 (Print)},
	Jid = {0375404},
	Journal = {J Neurophysiol},
	Jt = {Journal of neurophysiology},
	Language = {eng},
	Lr = {20061115},
	Mh = {*Action Potentials; Animals; Aplysia; Interneurons; Motor Neurons/*physiology; Neural Inhibition; Poisson Distribution; Reproducibility of Results; Synaptic Transmission},
	Mhda = {2003/09/13 05:00},
	Month = {Jul},
	Number = {1},
	Own = {NLM},
	Pages = {387--394},
	Phst = {2003/03/12 {$[$}aheadofprint{$]$}},
	Pii = {00074.2003},
	Pl = {United States},
	Pmid = {12634276},
	Pst = {ppublish},
	Pt = {Journal Article; Research Support, Non-U.S. Gov't; Research Support, U.S. Gov't, P.H.S.},
	Sb = {IM},
	Source = {J Neurophysiol. 2003 Jul;90(1):387-94. Epub 2003 Mar 12.},
	Status = {MEDLINE},
	Title = {Amplitude and frequency dependence of spike timing: implications for dynamic regulation.},
	Volume = {90},
	Year = {2003},
	Bdsk-Url-1 = {http://dx.doi.org/10.1152/jn.00074.2003}}

@article{Tuckwell+Wan:1984:JApplProb,
	Author = {Henry C. Tuckwell and Frederic Y.M. Wan},
	Date-Added = {2009-07-03 11:56:25 -0400},
	Date-Modified = {2009-07-03 11:57:38 -0400},
	Journal = {J. Appl. Prob.},
	Pages = {695-709},
	Title = {First-Passage Time of Markov Processes to Moving Barriers},
	Volume = {21},
	Year = {1984}}

@article{Wan+Tuckwell:1979:BiolCyb,
	Abstract = {The depolarization of passive nerve cylinder or dendritic tree in the equivalent cylinder representation is assumed to satisfy the cable equation. We consider in detail the effects of white noise current injection at a given location for the case of sealed end boundary conditions and for an initial resting state. The depolarization at a point is a Gaussian random process but is not Markovian. Expression (infinite series) are obtained for the expectation, variance, spatial and temporal covariances of the depolarization. We examine the steady state expectation and variance and investigate how these are approached in time over the whole neuronal surface. We consider the relative contributions of various terms in the series for the expectation and variance of the depolarization at x = 0 (soma, trigger zone, recording electrode) for various positions of the input process. It is found that different numbers of terms must be taken to obtain a reasonable approximation depending on whether the stimulus is at proximal, central or distal parts of the dendritic tree. We consider briefly the interspike time problem and see in an approximate way how spatial effects are important in determining the mean time between impulses.},
	Author = {Wan, F Y and Tuckwell, H C},
	Crdt = {1979/06/29 00:00},
	Da = {19790917},
	Date = {1979 Jun 29},
	Date-Added = {2009-07-03 11:50:59 -0400},
	Date-Modified = {2009-07-03 11:54:48 -0400},
	Dcom = {19790917},
	Edat = {1979/06/29},
	Issn = {0340-1200 (Print)},
	Jid = {7502533},
	Journal = {Biol Cybern},
	Jt = {Biological cybernetics},
	Language = {eng},
	Lr = {20061115},
	Mh = {Action Potentials; Animals; Axons/physiology; Cats; Cell Membrane/physiology; Dendrites/*physiology; *Membrane Potentials; *Models, Neurological; Motor Neurons/physiology; Neural Conduction; Neurons/*physiology; Synapses/physiology},
	Mhda = {1979/06/29 00:01},
	Month = {Jun},
	Number = {1},
	Own = {NLM},
	Pages = {39--55},
	Pl = {GERMANY, WEST},
	Pmid = {454708},
	Pst = {ppublish},
	Pt = {Comparative Study; Journal Article},
	Sb = {IM},
	Status = {MEDLINE},
	Title = {The response of a spatially distributed neuron to white noise current injection.},
	Volume = {33},
	Year = {1979}}

@article{Tuckwell:1980:JTB,
	Author = {Tuckwell, H C and Wan, F Y},
	Crdt = {1980/11/21 00:00},
	Da = {19810720},
	Date = {1980 Nov 21},
	Date-Added = {2009-07-03 11:50:56 -0400},
	Date-Modified = {2009-07-03 11:53:19 -0400},
	Dcom = {19810720},
	Edat = {1980/11/21},
	Issn = {0022-5193 (Print)},
	Jid = {0376342},
	Journal = {J Theor Biol},
	Jt = {Journal of theoretical biology},
	Language = {eng},
	Lr = {20061115},
	Mh = {Action Potentials; Animals; Cell Membrane/physiology; Electric Stimulation; Membrane Potentials; *Models, Neurological; Neurons/*physiology},
	Mhda = {1980/11/21 00:01},
	Month = {Nov},
	Number = {2},
	Own = {NLM},
	Pages = {275--295},
	Pii = {0022-5193(80)90361-6},
	Pl = {ENGLAND},
	Pmid = {7230847},
	Pst = {ppublish},
	Pt = {Journal Article; Research Support, Non-U.S. Gov't},
	Sb = {IM},
	Source = {J Theor Biol. 1980 Nov 21;87(2):275-95.},
	Status = {MEDLINE},
	Title = {The response of a nerve cylinder to spatially distributed white noise inputs.},
	Volume = {87},
	Year = {1980}}

@article{Tuckwell+Wan+Wong:1984:BiolCyb,
	Abstract = {The firing time of a cable model neuron in response to white noise current injection is investigated with various methods. The Fourier decomposition of the depolarization leads to partial differential equations for the moments of the firing time. These are solved by perturbation and numerical methods, and the results obtained are in excellent agreement with those obtained by Monte Carlo simulation. The convergence of the random Fourier series is found to be very slow for small times so that when the firing time is small it is more efficient to simulate the solution of the stochastic cable equation directly using the two different representations of the Green's function, one which converges rapidly for small times and the other which converges rapidly for large times. The shape of the interspike interval density is found to depend strongly on input position. The various shapes obtained for different input positions resemble those for real neurons. The coefficient of variation of the interspike interval decreases monotonically as the distance between the input and trigger zone increases. A diffusion approximation for a nerve cell receiving Poisson input is considered and input/output frequency relations obtained for different input sites. The cases of multiple trigger zones and multiple input sites are briefly discussed.},
	Author = {Tuckwell, H C and Wan, F Y and Wong, Y S},
	Crdt = {1984/01/01 00:00},
	Da = {19840524},
	Date = {1984},
	Date-Added = {2009-07-03 11:50:52 -0400},
	Date-Modified = {2009-07-03 11:53:41 -0400},
	Dcom = {19840524},
	Edat = {1984/01/01},
	Issn = {0340-1200 (Print)},
	Jid = {7502533},
	Journal = {Biol Cybern},
	Jt = {Biological cybernetics},
	Language = {eng},
	Lr = {20061115},
	Mh = {Action Potentials; Mathematics; *Models, Neurological; Neurons/*physiology},
	Mhda = {1984/01/01 00:01},
	Number = {3},
	Own = {NLM},
	Pages = {155--167},
	Pl = {GERMANY, WEST},
	Pmid = {6704439},
	Pst = {ppublish},
	Pt = {Journal Article; Research Support, Non-U.S. Gov't},
	Sb = {IM},
	Source = {Biol Cybern. 1984;49(3):155-67.},
	Status = {MEDLINE},
	Title = {The interspike interval of a cable model neuron with white noise input.},
	Volume = {49},
	Year = {1984}}

@article{Smith:1992:JTB,
	Abstract = {The Ornstein-Uhlenbeck process with a constant forcing function has often been used as a model for the subthreshold membrane potential of a neuron. The mean, variance and coefficient of variation of the first passage time to a constant threshold are examined for this model in the limit of small synaptic noise and low thresholds. A comparison is made between the asymptotic results of Wan & Tuckwell, who used perturbation analysis, and several computationally simpler approximation methods. A generalization of Stein's method gives an overestimate of the mean interval while an approximation by a Wiener process with linear drift gives an underestimate of the mean interval. These bounds are simple to calculate and can be used as a prelude to a more detailed perturbation analysis.},
	Address = {Department of Statistics, North Carolina State University, Raleigh 27695-8203.},
	Author = {Smith, C E},
	Crdt = {1992/02/07 00:00},
	Da = {19920702},
	Date = {1992 Feb 7},
	Date-Added = {2009-07-03 11:50:46 -0400},
	Date-Modified = {2009-07-03 11:53:07 -0400},
	Dcom = {19920702},
	Edat = {1992/02/07},
	Issn = {0022-5193 (Print)},
	Jid = {0376342},
	Journal = {J Theor Biol},
	Jt = {Journal of theoretical biology},
	Language = {eng},
	Lr = {20061115},
	Mh = {Animals; Mathematics; Membrane Potentials/physiology; *Models, Neurological; Neurons/*physiology; Synapses/physiology},
	Mhda = {1992/02/07 00:01},
	Month = {Feb},
	Number = {3},
	Own = {NLM},
	Pages = {271--275},
	Pl = {ENGLAND},
	Pmid = {1593893},
	Pst = {ppublish},
	Pt = {Comparative Study; Journal Article; Research Support, U.S. Gov't, Non-P.H.S.},
	Sb = {IM},
	Source = {J Theor Biol. 1992 Feb 7;154(3):271-5.},
	Status = {MEDLINE},
	Title = {A note on neuronal firing and input variability.},
	Volume = {154},
	Year = {1992}}

@article{Tuckwell+Wan+Rospars:2002:BiolCyb,
	Abstract = {We consider a spatial neuron model in which the membrane potential satisfies a linear cable equation with an input current which is a dynamical random process of the Ornstein-Uhlenbeck (OU) type. This form of current may represent an approximation to that resulting from the random opening and closing of ion channels on a neuron's surface or to randomly occurring synaptic input currents with exponential decay. We compare the results for the case of an OU input with those for a purely white-noise-driven cable model. The statistical properties, including mean, variance and covariance of the voltage response to an OU process input in the absence of a threshold are determined analytically. The mean and the variance are calculated as a function of time for various synaptic input locations and for values of the ratio of the time constant of decay of the input current to the time constant of decay of the membrane voltage in the physiological range for real neurons. The limiting case of a white-noise input current is obtained as the correlation time of the OU process approaches zero. The results obtained with an OU input current can be substantially different from those in the white-noise case. Using simulation of the terms in the series representation for the solution, we estimate the interspike interval distribution for various parameter values, and determine the effects of the introduction of correlation in the synaptic input stochastic process.},
	Address = {Department of Mathematics, University of California, Irvine 92697, USA. tuckwell@b3e.jussieu.fr},
	Author = {Tuckwell, Henry C and Wan, Frederic Y M and Rospars, Jean-Pierre},
	Crdt = {2002/03/26 10:00},
	Da = {20020322},
	Date = {2002 Feb},
	Date-Added = {2009-07-03 11:50:37 -0400},
	Date-Modified = {2009-07-03 11:54:07 -0400},
	Dcom = {20020903},
	Edat = {2002/03/26 10:00},
	Issn = {0340-1200 (Print)},
	Jid = {7502533},
	Journal = {Biol Cybern},
	Jt = {Biological cybernetics},
	Language = {eng},
	Mh = {Action Potentials/*physiology; *Models, Neurological; Neurons/*physiology; Stochastic Processes; Synapses/physiology},
	Mhda = {2002/09/11 10:01},
	Month = {Feb},
	Number = {2},
	Own = {NLM},
	Pages = {137--145},
	Pl = {Germany},
	Pmid = {11911115},
	Pst = {ppublish},
	Pt = {Journal Article},
	Sb = {IM},
	Source = {Biol Cybern. 2002 Feb;86(2):137-45.},
	Status = {MEDLINE},
	Title = {A spatial stochastic neuronal model with Ornstein-Uhlenbeck input current.},
	Volume = {86},
	Year = {2002}}

@article{Tuckwell+Rodriguez+Wan:2003:NeuralComp,
	Abstract = {We present for the first time an analytical approach for determining the time of firing of multicomponent nonlinear stochastic neuronal models. We apply the theory of first exit times for Markov processes to the Fitzhugh-Nagumo system with a constant mean gaussian white noise input, representing stochastic excitation and inhibition. Partial differential equations are obtained for the moments of the time to first spike. The observation that the recovery variable barely changes in the prespike trajectory leads to an accurate one-dimensional approximation. For the moments of the time to reach threshold, this leads to ordinary differential equations that may be easily solved. Several analytical approaches are explored that involve perturbation expansions for large and small values of the noise parameter. For ranges of the parameters appropriate for these asymptotic methods, the perturbation solutions are used to establish the validity of the one-dimensional approximation for both small and large values of the noise parameter. Additional verification is obtained with the excellent agreement between the mean and variance of the firing time found by numerical solution of the differential equations for the one-dimensional approximation and those obtained by simulation of the solutions of the model stochastic differential equations. Such agreement extends to intermediate values of the noise parameter. For the mean time to threshold, we find maxima at small noise values that constitute a form of stochastic resonance. We also investigate the dependence of the mean firing time on the initial values of the voltage and recovery variables when the input current has zero mean.},
	Address = {Department of Mathematics, University of California, Irvine, CA 92697, USA. tuckwell@b3e.jussieu.fr},
	Author = {Tuckwell, Henry C and Rodriguez, Roger and Wan, Frederic Y M},
	Crdt = {2003/02/20 04:00},
	Da = {20030219},
	Date = {2003 Jan},
	Date-Added = {2009-07-03 11:50:31 -0400},
	Date-Modified = {2009-07-03 11:54:30 -0400},
	Dcom = {20030312},
	Doi = {10.1162/089976603321043739},
	Edat = {2003/02/20 04:00},
	Issn = {0899-7667 (Print)},
	Jid = {9426182},
	Journal = {Neural Comput},
	Jt = {Neural computation},
	Language = {eng},
	Lr = {20061115},
	Mh = {*Models, Neurological; Neurons/*physiology; Stochastic Processes; Synaptic Transmission/*physiology},
	Mhda = {2003/03/13 04:00},
	Month = {Jan},
	Number = {1},
	Own = {NLM},
	Pages = {143--159},
	Pl = {United States},
	Pmid = {12590823},
	Pst = {ppublish},
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