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A mathematical description of the refractoriness period in neuronal diffusion modeling is given and its moments are explicitly obtained in a form that is suitable for quantitative evaluations. ... Then, for the Wiener, Ornstein-Uhlenbeck and Feller neuronal models, an analysis of the features exhibited by the mean and variance of the first passage time and of refractoriness period is performed. ... Acknowledgement Work performed within a joint cooperation agreement between Japan Science and Technology Corporation (JST) and Università di Napoli Federico II, under partial support by INdAM (G.N.C.S) ...arXiv:math/0305106v1 fatcat:5pkpu66dnrhabmvrmbse6op24y
Application of Wiener nonlinear analysis to these data yielded a predictive model of the facilitating postsynaptic potential. ... The model shows that facilitation changes both the timecourse and the magnitude of the early synaptic potential. The facilitated response has a longer duration than the unfacilitated response. ... INTRODUCTION The generality of the Wiener method of nonlinear analysis makes it an attractive approach to an integrative neuronal model. ...doi:10.1085/jgp.73.6.747 pmid:225406 pmcid:PMC2215203 fatcat:ha5naxydmrbjbgctzi3uy3cnxm
These models are variants of the general Wiener-Bose model, adapted to this problem as to represent the nonlinear dynamics of neural signal transformation using a set of parallel filters (neuron modes) ... This paper addresses this issue at the level of neural units (neurons) using nonparametric nonlinear dynamic models. ... If this general Wiener-Bose model is followed by a threshold-trigger TT (shown in Fig. 8 ) then we have the general model for Wiener systems with spike outputs. ...doi:10.1109/10.16445 pmid:2646209 fatcat:o5sx6d7cazgudlpmzi4rxxbpzm
At the end of the trial, a decoder based on the mixture-of-Poissons model correctly decoded about three times as many trials as expected by chance, compared with approximately twice as many as expected ... We demonstrate that data from neurons in primary visual cortex are well fit by a mixture of Poisson processes; in this special case, our computations are substantially faster. ... Kass and Ventura (2001) model firing probability as a product of time from stimulus onset and a refractory term depending on the time of the last spike (i.e., an inhomogeneous Poisson process with a refractory ...doi:10.1523/jneurosci.23-06-02394.2003 pmid:12657699 fatcat:4payjjaqsbawvhgmyjkcxnwvii
The Journal of Neuroscience
(i.e., with a flat PSTH) for all stimuli. ... A similar effect can be observed in surrogate data generated to match the spike count distribution seen in one of the neurons from the experiment with 16 stimuli but with spikes equally likely at any time ...
The Journal of Neuroscience
Proc Natl Acad Sci USA 94:5411-5416. (1998) Refractoriness and neural precision. ... Shoham S, Paninski L, Fellows MR, Hatsopoulos NG, Donoghue JP, Nor- mann RA (2005) Statistical encoding model for a primary motor corti- cal brain-machine interface. ...
During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. ... This review is divided in two parts: Derivation of the models with the list of the available closed forms expressions for their characterization; Presentation of the existing mathematical and statistical ... This study allows to introduce the refractoriness of the neuron in a quite natural way. ...arXiv:1101.5539v1 fatcat:su4ek3saznhebjbnux7qmh76la
a new test, the "Wiener process test", is proposed. ... After an elementary derivation of the "time transformation", mapping a counting process onto a homogeneous Poisson process with rate one, a brief review of Ogata's goodness of fit tests is presented and ... (CNRS) and by a CNRS GDR grant (Système Multi-éléctrodes et traitement du signal appliqués à l'étude des réseaux de Neurones). ...arXiv:0909.2785v1 fatcat:qmzx4a3b4zfghij2rwd3j43bki
The Journal of Neuroscience
Hunter IW, Korenberg MJ (1986) The identification of nonlinear bio- logical systems: Wiener and Hammerstein cascade models. Biol Cybern 55:135-144. ... The refractory period is commonly thought to limit the performance of a neuron, but this view is tied to a preconception about how the cell conveys its signal. ...
A systematic reduction of the neuronal dynamics of type I models [i.e., neurons with a smooth frequency-current curve (Hodgkin 1948)] in the limit of very low firing rates yields a canonical type I model ... Keat and colleagues (2001) have shown that a phenomenological model of neuronal activity can predict every spike of lateral geniculate nucleus (LGN) neurons with a millisecond precision. ... Integration restarts after an absolute refractory period of 2 ms with a time constant of 0.1 ms. ...doi:10.1152/jn.00190.2004 pmid:15277599 fatcat:6v4gakhedngn5ljllxhp37wi2a
Reliably decoding neuronal responses requires knowing what aspects of neuronal responses are stimulus related, and which aspects act as noise. ... refractory period by multiplying the order statistic by a refractory function. ... et al., 1998; Wiener and Richmond, 1999) . ...doi:10.1016/s0303-2647(02)00087-4 pmid:12459310 fatcat:36vobegh4fb5bojhaigzvjjxea
A good approximation to the integrate-and-"re model with di!usive noise can be obtained using a noisy threshold model. ... This allows the response of a population of noisy neurons to a current transient to be described using a linear "lter. ... The neuron may now be tested with a &signal', a small pulse that generates a PSP. ...doi:10.1016/s0925-2312(00)00156-9 fatcat:prro4usun5fnnf77hav5r2ojiq
A number of variations of the model are discussed, together with the relationship with the Hodgkin-Huxley neuron model and the comparison with electrophysiological data. ... The integrate-and-fire neuron model has become established as a canonical model for the description of spiking neurons because it is capable of being analyzed mathematically while at the same time being ... Acknowledgements The author thanks Hamish Meffin and David Grayden for a critical reading of the manuscript and detailed comments. ...doi:10.1007/s00422-006-0068-6 pmid:16622699 fatcat:ruhoi6xlojhdfcscvbicfnrfze
Being able to estimate neuronal responses in a particular brain region is fundamental for many models of functional integration and connectivity in the brain. ... BDSs comprise a stochastic bilinear neurodynamical model specified in discrete-time and a set of linear convolution kernels for the hemodynamics. ... In fact, a Dynamic Causal Modelling analysis of this data  , which allows for both neuronal and hemodynamic refractoriness, concluded that both effects were present. ...doi:10.1098/rstb.2005.1642 pmid:16087442 pmcid:PMC1854926 fatcat:lrduecxj35c23h4cq7maznqkmy
Lecture Notes in Computer Science
near-Poisson range to one associated with regular firing. ... modelling as an approximation to more biophysically based models. ... By contrast, mean (ISI) for the HH model shows a much weaker correlation with r of lower slope; i.e. inhibitory input has a much greater impact on the firing rate of the I&F neuron than the HH neuron. ...doi:10.1007/bfb0098174 fatcat:2soxlrkgz5e6pidaolv4gwa3cq
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