Search results for " function"
showing 10 items of 9395 documents
Cutting rules and positivity in finite temperature many-body theory
2022
Abstract For a given diagrammatic approximation in many-body perturbation theory it is not guaranteed that positive observables, such as the density or the spectral function, retain their positivity. For zero-temperature systems we developed a method [2014 Phys. Rev. B 90 115134] based on so-called cutting rules for Feynman diagrams that enforces these properties diagrammatically, thus solving the problem of negative spectral densities observed for various vertex approximations. In this work we extend this method to systems at finite temperature by formulating the cutting rules in terms of retarded N-point functions, thereby simplifying earlier approaches and simultaneously solving the issu…
A Random Field Approach to Transect Counts of Wildlife Populations
1991
Line transect counting of a wildlife population is considered a sampling from a planar marked point process, where the marks describe the detectability of the animals. Sampling properties of transect counts and a new density estimator are derived from a counting process, which is a shot-noise field induced by the marked point process. A general formula for the sampling variance of a transect is derived and applied to compare five common types of transects. Some stereological connections of transect sampling and density estimators are shown.
Role of sub- and super-Poisson noise sources in population dynamics
2020
In this paper we present a study on pulse noise sources characterized by sub- and super-Poisson statistics. We make a comparison with their uncorrelated counterpart. i.e. pulse noise with Poisson statistics, while showing that the correlation properties of sub- and super-Poisson noise sources can be efficiently applied to population dynamics. Specifically, we consider a termite population, described by a Langevin equation in the presence of a pulse noise source, and we study its dynamics and stability properties for two models. The first one describes a population of several colonies in a new territory with adverse environmental conditions. The second one considers the development of a sing…
Existence, uniqueness and Malliavin differentiability of Lévy-driven BSDEs with locally Lipschitz driver
2019
We investigate conditions for solvability and Malliavin differentiability of backward stochastic differential equations driven by a L\'evy process. In particular, we are interested in generators which satisfy a locally Lipschitz condition in the $Z$ and $U$ variable. This includes settings of linear, quadratic and exponential growths in those variables. Extending an idea of Cheridito and Nam to the jump setting and applying comparison theorems for L\'evy-driven BSDEs, we show existence, uniqueness, boundedness and Malliavin differentiability of a solution. The pivotal assumption to obtain these results is a boundedness condition on the terminal value $\xi$ and its Malliavin derivative $D\xi…
Bayesian longitudinal models for paediatric kidney transplant recipients
2015
Chronic kidney disease is a progressive loss of renal function which results in the inability of the kidneys to properly filter waste from the blood. Renal function is usually estimated by the glomerular filtration rate (eGFR), which decreases with the worsening of the disease. Bayesian longitudinal models with covariates, random effects, serial correlation and measurement error are discussed to analyse the progression of eGFR in first transplanted children taken from a study in Valencia, Spain.
Test of the Latent Dimension of a Spatial Blind Source Separation Model
2024
We assume a spatial blind source separation model in which the observed multivariate spatial data is a linear mixture of latent spatially uncorrelated random fields containing a number of pure white noise components. We propose a test on the number of white noise components and obtain the asymptotic distribution of its statistic for a general domain. We also demonstrate how computations can be facilitated in the case of gridded observation locations. Based on this test, we obtain a consistent estimator of the true dimension. Simulation studies and an environmental application in the Supplemental Material demonstrate that our test is at least comparable to and often outperforms bootstrap-bas…
Spectral characteristics of steady-state Lévy flights in confinement potential profiles
2016
The steady-state correlation characteristics of superdiffusion in the form of Levy flights in one-dimensional confinement potential profiles are investigated both theoretically and numerically. Specifically, for Cauchy stable noise we calculate the steady-state probability density function for an infinitely deep rectangular potential well and for a symmetric steep potential well of the type U(x)∞x2m. For these potential profiles and arbitrary Levy index α, we obtain the asymptotic expression of the spectral power density.
Probabilistic response of linear structures equipped with nonlinear damper devices (PIS method)
2008
Passive control introducing energy absorbing devices into the structure has received considerable attention in recent years. Unfortunately the constitutive law of viscous fluid dampers is highly nonlinear, and even supposing that the structure behaves linearly, the whole system has inherent nonlinear properties. Usually the analysis is performed by a stochastic linearization technique (SLT) determining a linear system equivalent to the nonlinear one, in a statistical sense. In this paper the effect of the non-Gaussianity of the response due to the inherent nonlinearity of the damper device will be studied in detail via the Path Integral Solution (PIS) method. A systematic study is conducted…
Anomalous diffusion and nonlinear relaxation phenomena in stochastic models of interdisciplinary physics
2020
The study of nonlinear dynamical systems in the presence of both Gaussian and non-Gaussian noise sources is the topic of this research work. In particular, after shortly present new theoretical results for statistical characteristics in the framework of Markovian theory, we analyse four different physical systems in the presence of Levy noise source. (a) The residence time problem of a particle subject to a non-Gaussian noise source in arbitrary potential profile was analyzed and the exact analytical results for the statistical characteristics of the residence time for anomalous diffusion in the form of Levy flights in fully unstable potential profile was obtained. Noise enhanced stability …
Gaia DR2 reveals a star formation burst in the disc 2-3 Gyr ago
2019
We use Gaia DR2 magnitudes, colours and parallaxes for stars with G<12 to explore a 15-dimensional space that includes simultaneously the initial mass function (IMF) and a non-parametric star formation history (SFH) for the Galactic disc. This inference is performed by combining the Besancon Galaxy Model fast approximate simulations (BGM FASt) and an approximate Bayesian computation algorithm. We find in Gaia DR2 data an imprint of a star formation burst 2-3 Gyr ago, in the Galactic thin disc domain, and a present star formation rate (SFR) of about 1 Msun. Our results show a decreasing trend of the SFR from 9-10 Gyr to 6-7 Gyr ago. This is consistent with the cosmological star formation …