Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models

[EN] In this paper, we deal with computational uncertainty quantification for stochastic models with one random input parameter. The goal of the paper is twofold: First, to approximate the set of probability density functions of the solution stochastic process, and second, to show the capability of our theoretical findings to deal with some important epidemiological models. The approximations are constructed in terms of a polynomial evaluated at the random input parameter, by means of generalized polynomial chaos expansions and the stochastic Galerkin projection technique. The probability density function of the aforementioned univariate polynomial is computed via the random variable transformation method, by taking into account the domains where the polynomial is strictly monotone. The algebraic/exponential convergence of the Galerkin projections gives rapid convergence of these density functions. The examples are based on fundamental epidemiological models formulated via linear and nonlinear differential and difference equations, where one of the input parameters is assumed to be a random variable.This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. The author Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.Calatayud-Gregori, J.; Chen-Charpentier, BM.; Cortés, J.; Jornet-Sanz, M. (2019). Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models. Symmetry (Basel). 11(1):1-28. https://doi.org/10.3390/sym11010043S128111Strand, J. . (1970). Random ordinary differential equations. Journal of Differential Equations, 7(3), 538-553. doi:10.1016/0022-0396(70)90100-2Bharucha-Reid, A. T. (1964). 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Earthworm management in tropical agroecosystems

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Control of membrane barrier during bacterial type-III protein secretion

Type-III secretion systems (T3SSs) of the bacterial flagellum and the evolutionarily related injectisome are capable of translocating proteins with a remarkable speed of several thousand amino acids per second. Here, we investigate how T3SSs are able to transport proteins at such a high rate while preventing the leakage of small molecules. Our mutational and evolutionary analyses demonstrate that an ensemble of conserved methionine residues at the cytoplasmic side of the T3SS channel create a deformable gasket (M-gasket) around fast-moving substrates undergoing export. The unique physicochemical features of the M-gasket are crucial to preserve the membrane barrier, to accommodate local conformational changes during active secretion, and to maintain stability of the secretion pore in cooperation with a plug domain (R-plug) and a network of salt-bridges. The conservation of the M-gasket, R-plug, and salt-bridge network suggests a universal mechanism by which the membrane integrity is maintained during high-speed protein translocation in all T3SSs.Peer Reviewe

Cassava processing wastewater as a platform for third generation biodiesel production

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Study of Tau-pair Production in Photon-Photon Collisions at LEP and Limits on the Anomalous Electromagnetic Moments of the Tau Lepton

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Energy dependence of Cronin momentum in saturation model for p+Ap+A and A+AA+A collisions

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Search for composite and exotic fermions at LEP 2

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Impact of lopinavir/ritonavir use on antiretroviral resistance in recent clinical practice

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Search for lightest neutralino and stau pair production in light gravitino scenarios with stau NLSP

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