Search results for "probability density function"
showing 10 items of 183 documents
Statistical Analysis of Biological Models with Uncertainty
2020
In this contribution relevant biological models, based on random differential equations, are studied. For the sake of generality, we assume that the initial condition and the biological model parameters are dependent random variables with arbitrary probability distributions. We present a general methodology that enables us to provide a full probabilistic description of the solution stochastic process for each stochastic model. The statistical analysis is performed through the calculation of the first probability function by applying the random variable transformation technique. From the first probability density function, we can calculate any one-dimensional moment of the solution, includin…
Ideal and physical barrier problems for non-linear systems driven by normal and Poissonian white noise via path integral method
2016
Abstract In this paper, the probability density evolution of Markov processes is analyzed for a class of barrier problems specified in terms of certain boundary conditions. The standard case of computing the probability density of the response is associated with natural boundary conditions, and the first passage problem is associated with absorbing boundaries. In contrast, herein we consider the more general case of partially reflecting boundaries and the effect of these boundaries on the probability density of the response. In fact, both standard cases can be considered special cases of the general problem. We provide solutions by means of the path integral method for half- and single-degr…
MuTE: a MATLAB toolbox to compare established and novel estimators of the multivariate transfer entropy.
2014
A challenge for physiologists and neuroscientists is to map information transfer between components of the systems that they study at different scales, in order to derive important knowledge on structure and function from the analysis of the recorded dynamics. The components of physiological networks often interact in a nonlinear way and through mechanisms which are in general not completely known. It is then safer that the method of choice for analyzing these interactions does not rely on any model or assumption on the nature of the data and their interactions. Transfer entropy has emerged as a powerful tool to quantify directed dynamical interactions. In this paper we compare different ap…
LCRT: A ToA Based Mobile Terminal Localization Algorithm in NLOS Environment
2009
©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Article also available from publisher: http://dx.doi.org/10.1109/VETECS.2009.5073644 Non line-of-sight (NLOS) propagation in range measurement is a key problem for mobile terminal localization. This paper proposes a low computational residual test (LCRT) algorithm that can identify the number of line-of-sight (LOS) transmissions and reduce the computational com…
Laplace’s Method of Integration in the Path Integral Approach for the Probabilistic Response of Nonlinear Systems
2020
In this paper the response of nonlinear systems under stationary Gaussian white noise excitation is studied. The Path Integral (PI) approach, generally employed for evaluating the response Probability Density Function (PDF) of systems in short time steps based on the Chapman-Kolmogorov equation, is here used in conjunction with the Laplace’s method of integration. This yields an approximate analytical solution of the integral involved in the Chapman-Kolmogorov equation. Further, in this manner the repetitive integrations, generally required in the conventional numerical implementation of the procedure, can be circumvented. Application to a nonlinear system is considered, and pertinent compa…
The Regression Tsetlin Machine: A Tsetlin Machine for Continuous Output Problems
2019
The recently introduced Tsetlin Machine (TM) has provided competitive pattern classification accuracy in several benchmarks, composing patterns with easy-to-interpret conjunctive clauses in propositional logic. In this paper, we go beyond pattern classification by introducing a new type of TMs, namely, the Regression Tsetlin Machine (RTM). In all brevity, we modify the inner inference mechanism of the TM so that input patterns are transformed into a single continuous output, rather than to distinct categories. We achieve this by: (1) using the conjunctive clauses of the TM to capture arbitrarily complex patterns; (2) mapping these patterns to a continuous output through a novel voting and n…
A novel method based on augmented Markov vector process for the time-variant extreme value distribution of stochastic dynamical systems enforced by P…
2020
Abstract The probability density function (PDF) of the time-variant extreme value process for structural responses is of great importance. Poisson white noise excitation occurs widely in practical engineering problems. The extreme value distribution of the response of systems excited by Poisson white noise processes is still not yet readily available. For this purpose, in the present paper, a novel method based on the augmented Markov vector process for the PDF of the time-variant extreme value process for a Poisson white noise driven dynamical system is proposed. Specifically, the augmented Markov vector (AMV) process is constructed by combining the extreme value process and its underlying…
Extreme Statistics in Raman Fiber Amplifiers: From Analytical Description to Experiments
2011
International audience; In this work, we investigate the emergence of rare and intense events during the Raman fiber amplification of a continuous wave. We highlight how dispersive properties and pump depletion can strongly influence the statistical properties of the amplified signal and its optical spectrum. Under certain conditions, the probability density functions of the amplified signal are calculated analytically and compared with the results of the numerical simulations. The conclusions are qualitatively validated by experiments carried out at telecommunication wavelengths.
Rates, polarizations, and asymmetries in charmless vector-vector B meson decays
2003
With a sample of approximately 89 million BBbar pairs collected with the BABAR detector, we perform a search for B meson decays into pairs of charmless vector mesons (phi, rho, and K*). We measure the branching fractions, determine the degree of longitudinal polarization, and search for CP violation asymmetries in the processes B->phiK*+, B->phiK*0, B->rho0K*+, and B->rho0rho+. We also set an upper limit on the branching fraction for the decay B->rho0rho0.
Stochastic ship roll motion via path integral method
2010
ABSTRACTThe response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple …