IRIS Uni Torinohttps://iris.unito.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Mon, 24 Jan 2022 18:07:59 GMT2022-01-24T18:07:59Z10301Dependencies between spike times of a couple of neurons modeled via a two-dimensional LIF modelhttp://hdl.handle.net/2318/81723Titolo: Dependencies between spike times of a couple of neurons modeled via a two-dimensional LIF model
Abstract: There exists a large literature on the Stein’s model. However, the largest part of these studies performs a diﬀusion limit on Stein’s equation to get a mathematically tractable stochastic process. Use of these continuous processes has allowed the discovery of various neuronal features
that are hidden in the original Stein’s model, for instance the stochastic resonance.
In this work, we consider a diﬀusion limit of two or more neuronal dynamics governed by Stein’s model to describe dependencies between their spike times. For this reason, we separate the PSPs impinging on each neuron into two groups, one with the PSPs coming from a common
network and the other one with those typical of the speciﬁc neuron.
We study the diﬀusion limit of these equations, superimposing a common threshold S and we describe the interspike intervals as ﬁrst passage times of the bidimensional diﬀusion processes through the boundary. The introduced dependency between the two Stein’s processes is maintained in the diﬀusion limit.
The aim of this work is to relate the introduced dependencies on the processes with those
obtained on the spike times of the two neurons, through their joint law.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/2318/817232010-01-01T00:00:00ZEstimation of information measures in coupled diffusion neuronal modelshttp://hdl.handle.net/2318/92739Titolo: Estimation of information measures in coupled diffusion neuronal models
Abstract: Estimation of the mutual information between ISI's can be a useful tool to characterize dependencies in small neuronal networks. We introduce here a method to compute the mutual information of coupled model neurons by employing the copula function describing the dependence between the spiking distributions.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/2318/927392011-01-01T00:00:00ZStochastic processes for modeling and evaluating atomic clock behaviourhttp://hdl.handle.net/2318/20622Titolo: Stochastic processes for modeling and evaluating atomic clock behaviour
Abstract: The behavior of the atomic clocks is typically studied considering their phase and frequency error with respect to an ideal clock. This quantity is known to be well modeled by a stochastic process. We presented and study the problem of the first passage time of the stochastic processes across two fixed constant barriers. This topic is also known as survival probability between two absorbing barriers and it can be studied by means of the infinitesimal generator. We present the application of these results to atomic clocks modelling, in particular to the prediction of their errors and to the evaluation of the probability that the clock error exceeds the limit of permissible error a certain time after synchronization. This aspect has an interesting application in the frame of the Mutual Recognition Arrangement where it may be important not only demonstrating that two standards are “equivalent”, but also evaluating how long such equivalence can last.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/2318/206222004-01-01T00:00:00ZMultidimensional Bridges with application to the Integrated Brownian Motionhttp://hdl.handle.net/2318/20976Titolo: Multidimensional Bridges with application to the Integrated Brownian Motion
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/2318/209762006-01-01T00:00:00ZA Monte Carlo Method for the Simulation of First Passage Time of Diffusion Processes.http://hdl.handle.net/2318/60250Titolo: A Monte Carlo Method for the Simulation of First Passage Time of Diffusion Processes.
Abstract: A reliable Monte Carlo method for the evaluation of first passage times of diffusion processes through boundaries is proposed. A nested algorithm that simulates the first passage time of a suitable tied-down process is introduced to account for undetected crossings that may occur inside each discretization interval of the stochastic differential equation associated to the diffusion. A detailed analysis of the performances of the algorithm is then carried on both via analytical proofs and by means of some numerical examples. The advantages of the new method with respect to a previously proposed numerical-simulative method for the evaluation of first passage times are discussed. Analytical results on the distribution of tied-down diffusion processes are proved in order to provide a theoretical justification of the Monte Carlo method.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/2318/602502001-01-01T00:00:00ZStochastic leaky integrate and fire neuronal model: examples of its application to neuronal coding studyhttp://hdl.handle.net/2318/13929Titolo: Stochastic leaky integrate and fire neuronal model: examples of its application to neuronal coding study
Abstract: Mathematical models help the analysis of experimental data and the understanding of observed features. Two examples are discussed with reference to neuronal modeling to suggest different applications of stochastic leaky integrate and fire models. The first one allows to explain the existence of preferential spiking times while the second suggests a classification method for simultaneous recorded data.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/2318/139292005-01-01T00:00:00ZOn the relationship between interspikes interval distribution and boundary shape in the Ornstein-Uhlenbeck neuronal modelhttp://hdl.handle.net/2318/19752Titolo: On the relationship between interspikes interval distribution and boundary shape in the Ornstein-Uhlenbeck neuronal model
Abstract: The reliabilityof the use of FPTs through the boundaries of an OU process to model interspikes intervals (ISIs) is investigated by means of a new method inspired to an algorithm that solves the inverse FPT proble. The boundary shape corresponding to experimental ISI is determined when the underthreshold membrane potential behavior is modeled via an OU process with parameters estimated from the data. The values are finally compared with the constant value characterizing the model.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/2318/197522003-01-01T00:00:00ZThreshold shape corresponding to a gamma firing distribution in an Ornstein-Uhlenbeck neuronal modelhttp://hdl.handle.net/2318/45948Titolo: Threshold shape corresponding to a gamma firing distribution in an Ornstein-Uhlenbeck neuronal model
Abstract: We introduce two numerical methods to determine the shape of a time dependent boundary for the Ornstein-Uhlenbeck process that corresponds to an assigned first passage time probability density function. The application of these methods to the stochastic leaky integrate and fire neuronal model allows to check the reliability of specified densities as approximation of the interspike interval distribution. The cases of the Gamma and of the inverse Gaussian
densities are discussed.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/2318/459482003-01-01T00:00:00ZOptimum signal in a diffusion leaky integrate and fire neuronal modelhttp://hdl.handle.net/2318/10776Titolo: Optimum signal in a diffusion leaky integrate and fire neuronal model
Abstract: An optimum signal in the Ornstein–Uhlenbeck neuronal model is determined on the basis of interspike interval data. Two criteria are proposed for this purpose. The first, the classical one, is based on searching for maxima of the slope of the frequency transfer function. The second one uses maximum of the Fisher information, which is, under certain conditions, the inverse variance of the best possible estimator. The Fisher information is further normalized with respect to the time required to make the observation on which the signal estimation is performed. Three variants of the model are investigated. Beside the basic one, we use the version obtained by inclusion of the refractory period. Finally, we investigate such a version of the model in which signal and the input parameter of the model are in a nonlinear relationship. The results show that despite qualitative similarity between the criteria, there is substantial quantitative difference. As a common feature, we found that in the Ornstein–Uhlenbeck model with increasing noise the optimum signal decreases and the coding range gets broader.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/2318/107762007-01-01T00:00:00ZJoint distribution of first exit times of a two dimensional Wiener process with jumps with application to a pair of coupled neuronshttp://hdl.handle.net/2318/137977Titolo: Joint distribution of first exit times of a two dimensional Wiener process with jumps with application to a pair of coupled neurons
Abstract: Motivated by a neuronal modeling problem, a bivariate Wiener process with two independent components is considered. Each component evolves independently until one of them reaches a threshold value.
If the ﬁrst component crosses the threshold value, it is reset while the dynamics of the other component
remains unchanged. But, if this happens to the second component, the ﬁrst one has a jump of constant
amplitude; the second component is then reset to its starting value and its evolution restarts. Both processes evolve once again until one of them reaches again its boundary. In this work, the coupling of the
ﬁrst exit times of the two connected processes is studied.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/2318/1379772013-01-01T00:00:00Z