Search results for " Process"

Hysteretic Systems Subjected to Delta Correlated Input

1994

The paper deals with the evaluation of the probabilistic response of a single degree of freedom elastic-perfectly plastic system subjected to a delta correlated input process. The probabilistic characterisation of the response is here obtained by considering the accumulated plastic deformations as a compound homogeneous Poisson process independent of the external input. In this case the former can be considered as an external noise acting on the linear system. A closed form solution is also obtained and the analytic expression is compared with the customary Monte-Carlo method.

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 Homogeneous Poisson Point Process

2008

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.

Saddle index properties, singular topology, and its relation to thermodynamic singularities for aϕ4mean-field model

2004

We investigate the potential energy surface of a ${\ensuremath{\phi}}^{4}$ model with infinite range interactions. All stationary points can be uniquely characterized by three real numbers ${\ensuremath{\alpha}}_{+},{\ensuremath{\alpha}}_{0},{\ensuremath{\alpha}}_{\ensuremath{-}}$ with ${\ensuremath{\alpha}}_{+}+{\ensuremath{\alpha}}_{0}+{\ensuremath{\alpha}}_{\ensuremath{-}}=1$, provided that the interaction strength $\ensuremath{\mu}$ is smaller than a critical value. The saddle index ${n}_{s}$ is equal to ${\ensuremath{\alpha}}_{0}$ and its distribution function has a maximum at ${n}_{s}^{\mathrm{max}}=1∕3$. The density $p(e)$ of stationary points with energy per particle $e$, as well as…

The Complex WKB Method

2019

In this chapter we shall study the exponential growth and asymptotic expansions of exact solutions of second-order differential equations in the semi-classical limit. As an application, we establish a Bohr-Sommerfeld quantization condition for Schrodinger operators with real-analytic complex-valued potentials.

Robust H<inf>∞</inf> control of Markovian jump systems with mixed time delays

2010

In this paper, the problem of stability analysis and control synthesis for Markovian jump linear systems with time delays and norm-bounded uncertainties is studied. The model under consideration consists of different time-invariant discrete, neutral and distributed delays. Delay-dependent sufficient conditions for the design of a mode-dependent delayed state feedback H ∞ control are given in terms of linear matrix inequalities (LMIs). A controller which guarantees stochastic stability and a prescribed level of H ∞ performance for the closed-loop system is then developed. A Lyapunov-Krasovskii functional (LKF) method underlies the control design. A numerical example with simulation results i…

Surface Nanophysics: Macro-, Meso-, Micro- and Nano-approaches

2017

The surface factor is very important for manipulating objects at a nanoscale. Thermodynamic behaviour is observed from the classical point of view, and conditional division into macro-, meso-, micro- and nano-approaches is presented. Processes of physical and chemical adsorption on the surface are presented from the energy and structure aspects. The occurrence of electronic states of the surface is presented from the classical point of view in comparison with molecular electronic states. One of the most important non-invasive optical methods to investigate nanoparticles is the surface plasmon resonance (SPR), which is quite useful for practical detection of nanoparticles in the surrounding …

Sensitivity analysis of Gaussian processes for oceanic chlorophyll prediction

2015

Gaussian Process Regression (GPR) for machine learning has lately been successfully introduced for chlorophyll content mapping from remotely sensed data. The method provides a fast, stable and accurate prediction of biophysical parameters. However, since GPR is a non-linear kernel regression method, the relevance of the features are not accessible. In this paper, we introduce a probabilistic approach for feature sensitivity analysis (SA) of the GPR in order to reveal the relative importance of the features (bands) being used in the regression process. We evaluated the SA on GPR ocean chlorophyll content prediction. The method revealed the importance of the spectral bands, thus allowing the …

Representation of Stationary Multivariate Gaussian Processes Fractional Differential Approach

2011

In this paper, the fractional spectral moments method (H-FSM) is used to generate stationary Gaussian multivariate processes with assigned power spectral density matrix. To this aim, firstly the N-variate process is expressed as sum of N fully coherent normal random vectors, and then, the representation in terms of HFSM is used.