Search results for "Statistica"
showing 10 items of 5969 documents
Assessing Transfer Entropy in cardiovascular and respiratory time series: A VARFI approach
2021
In the study of complex biomedical systems represented by multivariate stochastic processes, such as the cardiovascular and respiratory systems, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. Recently, the quantification of multiscale complexity based on linear parametric models, incorporating autoregressive coefficients and fractional integration, encompassing short term dynamics and long-range correlations, was extended to multivariate time series. Within this Vector AutoRegressive Fractionally Integrated (VARFI) framework formalized for Gaussian processes, in this work we propose to estimate the Transfer Entropy, or equivalently G…
The Poisson Point Process
2020
Poisson point processes can be used as a cornerstone in the construction of very different stochastic objects such as, for example, infinitely divisible distributions, Markov processes with complex dynamics, objects of stochastic geometry and so forth.
Thermodynamics: Classical Framework
2016
This chapter starts with a summary of the thermodynamic potentials and the relationships between them which are obtained from Legendre transformation. This is followed by an excursion to some important global properties of materials such as specific heat, expansion coefficients and others. The thermodynamic relations provide the basis for a discussion of continuous changes of state which are illustrated by the Joule-Thomson effect and the Van der Waals gas. These are models which are more realistic than the ideal gas. The discussion of Carnot cycles leads to and illustrates the second and third laws of thermodynamics. The chapter closes with a discussion of entropy as a concave function of …
On the autocorrelation function of Rice processes for unsymmetrical doppler power spectral densities
2010
In this paper, we derive an analytical expression for the ACF of Rice processes in the general case of unsymmetrical Doppler power spectral densities. This expression, which is obtained based on the multidimensional Gaussian distribution approach, is shown to cover the ACF of Rayleigh processes as a special case. Various numerical examples are presented to illustrate the impact of the channel parameters on the ACF. Computer simulations, considering the von Mises distribution for the angle of arrivals, are also performed to check the validity of the analytical result. Finally, the analysis of the covariance spectrum is addressed.
A New Family of Deformations of Darboux-Pöschl-Teller Potentials
2004
The aim of this Letter is to present a new family of integrable functional-difference deformations of the Schrodinger equation with Darboux–Poschl–Teller potentials. The related potentials are labeled by two integers m and n, and also depend on a deformation parameter h. When h→ 0 the classical Darboux–Poschl–Teller model is recovered.
Non-linear systems under parametric alpha-stable LÉVY WHITE NOISES
2005
In this study stochastic analysis of nonlinear dynamical systems under a-stable, multiplicative white noise has been performed. Analysis has been conducted by means of the Ito rule extended to the case of α-stable noises. In this context the order of increments of Levy process has been evaluated and differential equations ruling the evolutions of statistical moments of either parametrically and external dynamical systems have been obtained. The extended Ito rule has also been used to yield the differential equation ruling the evolution of the characteristic function for parametrically excited dynamical systems. The Fourier transform of the characteristic function, namely the probability den…
Self-regulation mechanism of an ecosystem in a non-Gaussian fluctuation regime
1996
We study a dynamical model for an ecological network of many interacting species. We consider a Malthus-Verhulst type of self-regulation mechanism. In the framework of the mean field theory we study the nonlinear relaxation in three different cases: (a) towards the equilibrium state, (b) towards the absorbing barrier, (c) at the critical point. We obtain asymptotic behavior in all different cases for the time average of the process. The dynamical behavior of the system, in the limit of infinitely many interacting species, is investigated in the stability and instability conditions and theoretical results are compared with numerical simulations. \textcopyright{} 1996 The American Physical So…
Convergence of Measures
2020
One focus of probability theory is distributions that are the result of an interplay of a large number of random impacts. Often a useful approximation can be obtained by taking a limit of such distributions, for example, a limit where the number of impacts goes to infinity. With the Poisson distribution, we have encountered such a limit distribution that occurs as the number of very rare events when the number of possibilities goes to infinity (see Theorem 3.7). In many cases, it is necessary to rescale the original distributions in order to capture the behavior of the essential fluctuations, e.g., in the central limit theorem. While these theorems work with real random variables, we will a…
Regional differences in Italian students' performance: a simulation model
2017
This work presents the first results of a research project seeking to build a simulation model able to reproduce the differences of Italian students’ performance at regional level. A preliminary qualitative cause-and-effect model defines the main variable involved in the inter-generational skill formation processes, as well as their interplay with the job market context and the triggering of motivational forces for new skill acquisition. Such model was designed according to a system dynamics perspective, considered suitable for capturing the interrelatedness of key variables and for providing useful simulation tools to conduct and communicate future scenario analyses. Keywords: regional…
How many longitudinal covariate measurements are needed for risk prediction?
2014
Abstract Objective In epidemiologic follow-up studies, many key covariates, such as smoking, use of medication, blood pressure, and cholesterol, are time varying. Because of practical and financial limitations, time-varying covariates cannot be measured continuously, but only at certain prespecified time points. We study how the number of these longitudinal measurements can be chosen cost-efficiently by evaluating the usefulness of the measurements for risk prediction. Study Design and Setting The usefulness is addressed by measuring the improvement in model discrimination between models using different amounts of longitudinal information. We use simulated follow-up data and the data from t…