186,857 research outputs found
Diffusion approximation and first–passage–time problem for a model neuron. III. A birth–and–death process approach
No full textA stochastic model for single neuron's activity is constructed as the continuous limit of a birth-and-death process in the presence of a reversal hyperpolarization potential. The resulting process is a one dimensional diffusion with linear drift and infinitesimal variance, somewhat different from that proposed by Lansky and Lanska in a previous paper. A detailed study is performed for both the discrete process and its continuous approximation. In particular, the neuronal firing time problem is discussed and the moments of the firing time are explicitly obtained. Use of a new computation method is then made to obtain the firing p.d.f.. The behaviour of mean, variance and coefficient of variation of the firing time and of its p.d.f. is analysed to pinpoint the role played by the parameters of the model. A mathematical description of the return process for this neuronal diffusion model is finally provided to obtain closed form expressions for the asymptotic moments and steady state p.d.f. of the neuron's membrane potential
Diffusion models and neural activity
No full textNeuronal interspike intervals can be characterized in terms of the first-passage time probability density of stochastic diffusion processes under steady state and periodic stimulation. The Wiener and Ornstein–Uhlenbeck models, and models with multiplicative noise, can be used to elucidate neuronal activity
Diffusion models and neural activity
No full textNeuronal interspike intervals can be characterized in terms of the first-passage time probability density of stochastic diffusion processes under steady state and periodic stimulation. The Wiener and Ornstein–Uhlenbeck models, and models with multiplicative noise, can be used to elucidate neuronal activity
An outline of some one-dimensional diffusion neuronal models
No full textStochastic neuronal models with restricted hyperpolarization due to the existence of inhibitory reversal potential are presented. The study focuses on models of diffusion type far which the mathematical theory is the most developed one. The introduction of the inhibitory reversal potential into the models causes that the infinitesimal variance is no more constant. The role of parameters in the models is considered
An outline of some one-dimensional diffusion neuronal models
No full textStochastic neuronal models with restricted hyperpolarization due to the existence of inhibitory reversal potential are presented. The study focuses on models of diffusion type far which the mathematical theory is the most developed one. The introduction of the inhibitory reversal potential into the models causes that the infinitesimal variance is no more constant. The role of parameters in the models is considered
Estimating input parameters from intracellular recordings in the Feller neuronal model
No full textWe study the estimation of the input parameters in a Feller neuronal model from a trajectory of the membrane potential sampled at discrete times. These input parameters are identified with the drift and the infinitesimal variance of the underlying stochastic diffusion process with multiplicative noise. The state space of the process is restricted from below by an inaccessible boundary. Further, the model is characterized by the presence of an absorbing threshold, the first hitting of which determines the length of each trajectory and which constrains the state space from above. We compare, both in the presence and in the absence of the absorbing threshold, the efficiency of different known estimators. In addition, we propose an estimator for the drift term, which is proved to be more efficient than the others, at least in the explored range of the parameters. The presence of the threshold makes the estimates of the drift term biased, and two methods to correct it are proposed
Inhibition enhances the coherence in the Jacobi neuronal model
No full textThe output signal is examined for the Jacobi neuronal model which is characterized by input-dependent multiplicative noise. The dependence of the noise on the rate of inhibition turns out to be of primary importance to observe maxima both in the output firing rate and in the diffusion coefficient of the spike count and, simultaneously, a minimum in the coefficient of variation (Fano factor). Moreover, we observe that an increment of the rate of inhibition can increase the degree of coherence computed from the power spectrum. This means that inhibition can enhance the coherence and thus the information transmission between the input and the output in this neuronal model. Finally, we stress that the firing rate, the coefficient of variation and the diffusion coefficient of the spike count cannot be used as the only indicator of coherence resonance without considering the power spectrum
The Jacobi diffusion process as a neuronal model
No full textThe Jacobi process is a stochastic diffusion characterized by a linear drift and a special form of multiplicative noise which keeps the process confined between two boundaries. One example of such a process can be obtained as the diffusion limit of the Stein's model of membrane depolarization which includes both excitatory and inhibitory reversal potentials. The reversal potentials create the two boundaries between which the process is confined. Solving the first-passage-time problem for the Jacobi process, we found closed-form expressions for mean, variance, and third moment that are easy to implement numerically. The first two moments are used here to determine the role played by the parameters of the neuronal model; namely, the effect of multiplicative noise on the output of the Jacobi neuronal model with input-dependent parameters is examined in detail and compared with the properties of the generic Jacobi diffusion. It appears that the dependence of the model parameters on the rate of inhibition turns out to be of primary importance to observe a change in the slope of the response curves. This dependence also affects the variability of the output as reflected by the coefficient of variation. It often takes values larger than one, and it is not always a monotonic function in dependency on the rate of excitation
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