Found 95 Documents (Results 1–95)
The dance of neurons: exploring nonlinear dynamics in brain networks. (English) Zbl 07900556
Reviewer: Nikolay Kyurkchiev (Plovdiv)
Interacting systems of infinite spiking neurons with weights beyond uniform summability. (English) Zbl 1537.60127
The steady state and response to a periodic stimulation of the firing rate for a theta neuron with correlated noise. (English) Zbl 1518.92030
Dynamical response of autaptic Izhikevich neuron disturbed by Gaussian white noise. (English) Zbl 1518.92029
Damped oscillations of the probability of random events followed by absolute refractory period: exact analytical results. (English) Zbl 1498.60395
MSC:
60K40
Emergence of stochastic resonance in a two-compartment hippocampal pyramidal neuron model. (English) Zbl 1494.92011
Invariance of Poisson point processes by moment identities with statistical applications. (English) Zbl 1499.60157
Ugolini, Stefania (ed.) et al., Geometry and invariance in stochastic dynamics. Selected papers based on the presentations at the the conference on random transformations and invariance in stochastic dynamics, Verona, Italy, March 25–29, 2019. Cham: Springer. Springer Proc. Math. Stat. 378, 247-265 (2021).
Random neural network methods and deep learning. (English) Zbl 1493.68335
Reviewer: Arzu Ahmadova (Essen)
Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach. (English) Zbl 1480.92038
Synchronization and pattern formation in a memristive diffusive neuron model. (English) Zbl 1471.92078
Modified log-Sobolev inequality for a compact pure jump Markov process with degenerate jumps. (English) Zbl 1434.60300
Local asymptotic normality for shape and periodicity of a signal in the drift of a degenerate diffusion with internal variables. (English) Zbl 1454.62093
Reviewer: Joseph Melamed (Los Angeles)
Synchronization of stochastic mean field networks of Hodgkin-Huxley neurons with noisy channels. (English) Zbl 1415.60085
Reviewer: Utkir A. Rozikov (Tashkent)
Detection of sub-threshold periodic signal by multiplicative and additive cross-correlated sine-Wiener noises in the Fitzhugh-Nagumo neuron. (English) Zbl 1514.92022
Stability of stochastic semigroups and applications to Stein’s neuronal model. (English) Zbl 1517.47080
Mixed stimulus-induced mode selection in neural activity driven by high and low frequency current under electromagnetic radiation. (English) Zbl 1377.92019
A stochastic differential equation model of a neuronal activity driven by Poisson inputs. (English) Zbl 1374.60078
Output stream of leaky integrate-and-fire neuron without diffusion approximation. (English) Zbl 1364.82046
The effect of positive interspike interval correlations on neuronal information transmission. (English) Zbl 1348.93241
Spatio-temporal dynamics of a cylindrical neuron subject to a stochastic noise. (English) Zbl 1334.60125
Ergodicity for a stochastic Hodgkin-Huxley model driven by Ornstein-Uhlenbeck type input. (English. French summary) Zbl 1335.60091
Activity of excitatory neuron with delayed feedback stimulated with Poisson stream is non-Markov. (English) Zbl 1339.60053
Multiscale piecewise deterministic Markov process in infinite dimension: central limit theorem and Langevin approximation. (English) Zbl 1320.60014
Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods. (English) Zbl 1454.62246
A note on the first passage time of diffusions with holding and jumping boundary. (English) Zbl 1296.60217
MSC:
60J60
A note on the analysis of asymptotic mean-square stability properties for systems of linear stochastic delay differential equations. (English) Zbl 1390.34228
Averaging for a fully coupled piecewise-deterministic Markov process in infinite dimensions. (English) Zbl 1276.60023
Reviewer: Martin Riedler (Wien)
Asymptotic expansion and central limit theorem for multiscale piecewise-deterministic Markov processes. (English) Zbl 1261.60031
An exact stochastic hybrid model of excitable membranes including spatio-temporal evolution. (English) Zbl 1284.92038
A discrete time neural network model with spiking neurons. II: Dynamics with noise. (English) Zbl 1230.92012
Data assimilation using a GPU accelerated path integral Monte Carlo approach. (English) Zbl 1231.65013
A lower bound for the first passage time density of the suprathreshold Ornstein-Uhlenbeck process. (English) Zbl 1242.60086
Reviewer: Gabriel V. Orman (Braşov)
Neural coherence and stochastic resonance. (English) Zbl 1352.92031
Laing, Carlo (ed.) et al., Stochastic methods in neuroscience. Oxford: Oxford University Press (ISBN 978-0-19-923507-0/hbk). 94-123 (2010).
The power spectral density of the conditional Markov pulse process. (English. Russian original) Zbl 1220.92014
Mosc. Univ. Phys. Bull. 65, No. 5, 372-377 (2010); translation from Vest. Mosk. Univ., Ser. III 2010, No. 5, 38-42 (2010).
Fluid limit theorems for stochastic hybrid systems with application to neuron models. (English) Zbl 1232.60019
Reviewer: Marius Iosifescu (Bucureşti)
Statistical approach in search for optimal signal in simple olfactory neuronal models. (English) Zbl 1143.92006
On the classification of experimental data modeled via a stochastic leaky integrate and fire model through boundary values. (English) Zbl 1334.92080
Comment on “Characterization of subthreshold voltage fluctuations in neuronal membranes,” by M. Rudolph and A. Destexhe. (English) Zbl 1121.92014
A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. (English) Zbl 1161.92315
A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties. (English) Zbl 1161.92314
A stochastic model and a functional central limit theorem for information processing in large systems of neurons. (English) Zbl 1094.92016
An extended analytic expression for the membrane potential distribution of conductance-based synaptic noise. (English) Zbl 1072.92010
Information coding and oscillatory activity in synfire neural networks with and without inhibitory coupling. (English) Zbl 1095.92014
A population density approach that facilitates large-scale modeling of neural networks: extension to slow inhibitory synapses. (English) Zbl 1052.92016
Gaussian process approach to spiking neurons for inhomogeneous Poisson inputs. (English) Zbl 0984.92006
Stability results for a general class of interacting point processes dynamics, and applications. (English) Zbl 0944.60053
Reviewer: B.Maslowski (Praha)
Analytical and simulation results for stochastic Fitzhugh-Nagumo neurons and neural networks. (English) Zbl 0896.92009
The effect of a refractory period on the power spectrum of neuronal discharge. (English) Zbl 0829.92006
Coupled Hodgkin Huxley neurons with stochastic synaptic inputs. (English) Zbl 0902.92006
Bertrand, J. (ed.) et al., Modern group theoretical methods in physics. Proceedings of the conference in honour of Guy Rideau on the occasion of his retirement, Paris, France, January 1995. Dordrecht: Kluwer Academic Publishers. Math. Phys. Stud. 18, 233-242 (1995).
Analysis of some stochastic neural models. (English) Zbl 0861.92009
Caballero, M. E. (ed.) et al., 3rd symposium on probability and stochastic processes. Proceedings, Hermosillo, Mexico, March 7–11, 1994. To the memory of Diego Bricio Hernández. Hermosillo: Sociedad Matemática Mexicana. Aportaciones Mat., Notas Invest. 11, 157-169 (1994).
Single effective neuron: Dendritic coupling effects and stochastic resonance. (English) Zbl 0789.92005
A correlated point process arising from integral density modulation of a renewal process. (English) Zbl 0780.60046
Interval distribution of a stationary point process. (English) Zbl 0769.60096
Reviewer: V.Schmidt (Ulm)
Applications of thinning processes. (English) Zbl 0769.60041
Reviewer: V.V.Kalashnikov (Moskva)
A stochastic model of an artificial neuron. (English) Zbl 0732.60120
MSC:
60K99
A limit theorem and asymptotical statistical characteristics for a selective interaction model of a single neuron. (English) Zbl 0756.92008
Stochastic processes and their applications, Proc. Symp. Honour Prof. S. K. Srinivasan, Bombay/India 1990, Lect. Notes Econ. Math. Syst. 370, 127-133 (1991).
Infinite dimensional stochastic differential equations with applications. (English) Zbl 0818.60048
Kasprzak, Wacław (ed.) et al., Proceedings of the 1989 COSMEX meeting on stochastic methods in experimental sciences, held in Szklarska Poreba, Poland, 8-14 September, 1989. Singapore: World Scientific. 227-238 (1990).
Diffusion approximation and first-passage-time problem for a model neuron. III: A birth-and-death process approach. (English) Zbl 0641.92008
Note on the Ornstein-Uhlenbeck process model for stochastic activity of a single neuron. (English) Zbl 0618.92004
Stochastic methods in biology, Proc. Workshop, Nagoya/Jap. 1985, Lect. Notes Biomath. 70, 146-156 (1987).
System identification based on point processes and correlation densities. I: The nonrefractory neuron model. (English) Zbl 0613.92013
Reviewer: P.Lánský
A model of neurons with pacemaker behavior receiving strong synaptic input. (English) Zbl 0549.92008
Reviewer: T.Kostova-Vassilevska
On the diffusion approximation to a discontinuous model for a single neuron. (English) Zbl 0526.92009
Contributions to statistics, Essays in Hon. of N. L. Johnson, 247-258 (1983).
Diffusion approximation and first passage time problem for a model neuron. II. Outline of a computation method. (English) Zbl 0525.92006
Diffusion approximations and computational problems for single neurons’ activity. (English) Zbl 0508.92010
Competition and cooperation in neural nets, Proc. U.S.-Jap. Semin., Kyoto 1982, Lect. Notes Biomath. 45, 142-154 (1982).
Models for neural discharge which lead to Markov renewal equations for probability density. (English) Zbl 0446.92006
Stochastic constancy, variability and adaptation of spike generation: Performance of a giant neuron in the visual system of the fly. (English) Zbl 0434.92005
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