1,721,017 research outputs found
Un percorso con il metodo Monte Carlo
No full textThe Monte Carlo method is useful. As proof of this statement, there is
its use in various scientific fields: physical sciences, engineering, statistical,
financial, and computing: physical, engineering, statistical,
financial and computing sciences. In addition, there are also numerous
examples of application of the method in areas that are not quantitative.
The Monte Carlo method is also interesting. The idea is to obtain
a more thorough knowledge about the characteristics of a system,
simply by observing its "simulation" obtained through random sampling.
This approach is powerful, flexible and very direct. This approach
is powerful, flexible and very direct. On the other hand, in
many circumstances, it is the easiest way to get the quantity of interest
and sometimes it is also the only walkable way. In this article, we propose
to follow this idea in a teaching perspective: contextualize probabilistic
concepts through simulation of a simple mathematical model
that allows changes and generalizations
Il test chi-quadrato per un dado ... malfatto
No full textIn questo articolo si intende presentare un semplice contesto aleatorio, il lancio di un dado, con il quale introdurre gli studenti alla costruzione di modelli matematici la cui validazione avviene attraverso l’utilizzo del test chi-quadrato. In tale fase, oltre alla necessità della messa a punto di programmi di calcolo per la costruzione del grafico di funzioni, si evidenziano difficoltà di tipo analitico superabili mediante l’utilizzo di procedure numeriche atte a determinare un’approssimazione del minimo assunto da una funzione di una o due variabili
A Note on the Sum of Uniform Random Variables
No full textAn inductive procedure is used to obtain distributions and probability densities for the sum of independent, non equally uniform random variables. Some known results are then shown to follow immediately as special cases. Under the assumption of equally uniform random variables some new formulas are obtained for probabilities and means related to . Finally, some new recursive formulas involving distributions are derived
On the evaluation of firing densities for periodically driven neuron models
No full textThe leaky integrate-and-fire model for neuronal spiking events driven by a periodic stimulus is studied by using the Fokker–Planck formulation. To this purpose, an essential use is made of the asymptotic behavior of the first-passage-time probability density function of a time homogeneous diffusion process through an asymptotically periodic threshold. Numerical comparisons with some recently published results derived by a different approach are performed. Use of a new asymptotic approximation is then made in order to design a numerical algorithm of predictor–corrector type to solve the integral equation in the unknown first-passage-time probability density function. Such algorithm, characterized by a reduced (linear) computation time, is seen to provide a high computation accuracy. Finally, it is shown that such an approach yields excellent approximations to the firing probability density function for a wide range of parameters, including the case of high stimulus frequencies
On myosin II dynamics
No full textOn the grounds of a set of data obtained in single molecule experiments on actomyosin dynamics under external applied loads, we postulate a joint mechanism consisting of a thermal component coupled with a deterministic unit-step, as invoked by the "lever-arm" theory, are simultaneously acting in determining myosin dynamics
On certain approximations to firing rate for a periodically driven neuron model
No full textIn Schindler et al. (2005) an approximation of the instantaneous firing rate is obtained within a non stationary Leaky Integrate-and-Fire (LIF) neuron model whose dynamics is described by a Langevin equation with an oscillating drift. The purpose of the present paper is to exploit a space-time transformation to be led to the standard LIF model. We are able to point out the ranges of validity of an exponential approximation to p.d.f. of the first-passage-time as frequency, stimulus amplitude and diffusion constant are made to vary
A Simple Algorithm to Generate Firing Times for Leaky Integrate-and-Fire Neuronal Model
No full textA method to generate first passage times for a class of stochastic processes is proposed. It does not require construction of the trajectories as usually needed in simulation studies, but is based on an integral equation whose unknown quantity is the probability density function of the studied first passage times and on the application of the hazard rate method. The proposed procedure is particularly efficient in the case of the Ornstein-Uhlenbeck process, which is important for modeling spiking neuronal activity
Gauss-Diffusion Processes for Modeling the Dynamics of a Couple of Interacting Neurons
No full textWith the aim to describe the interaction between a couple of neurons a stochastic model is proposed and formalized. In such a model, maintaining statements of the Leaky Integrate-and-Fire framework, we include a random component in the synaptic current, whose role is to modify the equilibrium point of the membrane potential of one of the two neurons and when a spike of the other one occurs it is turned on. The initial and after spike reset positions do not allow to identify the inter-spike intervals with the corresponding first passage times. However, we are able to apply some well-known results for the first passage time problem for the Ornstein-Uhlenbeck process in order to obtain (i) an approximation of the probability density function of the inter-spike intervals in one-way-type interaction and (ii) an approximation of the tail of the probability density function of the inter-spike intervals in the mutual interaction. Such an approximation is admissible for small instantaneous firing rates of both neurons
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