Propagation of epistemic uncertainty in queueing models with unreliable server using chaos expansions

In this paper, we develop a numerical approach based on Chaos expansions to analyze the sensitivity and the propagation of epistemic uncertainty through a queueing systems with breakdowns. Here, the quantity of interest is the stationary distribution of the model, which is a function of uncertain parameters. Polynomial chaos provide an efficient alternative to more traditional Monte Carlo simulations for modelling the propagation of uncertainty arising from those parameters. Furthermore, Polynomial chaos expansion affords a natural framework for computing Sobol' indices. Such indices give reliable information on the relative importance of each uncertain entry parameters. Numerical results show the benefit of using Polynomial Chaos over standard Monte-Carlo simulations, when considering statistical moments and Sobol' indices as output quantities

Robust power series algorithm for epistemic uncertainty propagation in Markov chain models

In this article, we develop a new methodology for integrating epistemic uncertainties into the computation of performance measures of Markov chain models. We developed a power series algorithm that allows for combining perturbation analysis and uncertainty analysis in a joint framework. We characterize statistically several performance measures, given that distribution of the model parameter expressing the uncertainty about the exact parameter value is known. The technical part of the article provides convergence result, bounds for the remainder term of the power series, and bounds for the validity region of the approximation. In the algorithmic part of the article, an efficient implementation of the power series algorithm for propagating epistemic uncertainty in queueing models with breakdowns and repairs is discussed. Several numerical examples are presented to illustrate the performance of the proposed algorithm and are compared with the corresponding Monte Carlo simulations ones

Aerobic exercise inhibits acute lung injury: from mouse to human evidence Exercise reduced lung injury markers in mouse and in cells

Acute respiratory distress syndrome (ARDS) is defined as hypoxemic respiratory failure with intense pulmonary inflammation, involving hyperactivation of endothelial cells and neutrophils. Given the anti-inflammatory effects of aerobic exercise (AE), this study investigated whether AE performed daily for 5 weeks would inhibit extra-pulmonary LPS-induced ARDS. C57Bl/6 mice were distributed into Control, Exercise, LPS and Exercise+ LPS groups. AE was performed on a treadmill for 5x/week for four weeks before LPS administration. 24hours after the final AE physical test, animals received 100ug of LPS intra-peritoneally. In addition, whole blood cell culture, neutrophils and human endothelial cells were pre-incubated with IL-10, an anti-inflammatory cytokine induced by exercise. AE reduced total protein levels (p<0.01) and neutrophil accumulation in bronchoalveolar lavage (BAL) (p<0.01) and lung parenchyma (p<0.01). AE reduced BAL inflammatory cytokines IL-1 beta, IL-6 and GM-CSF (p<0.001), CXCL1/KC, IL-17, TNF-alpha and IGF-1 (p<0.01). Systemically, AE reduced IL-1 beta, IL-6 and IFN-gamma (p<0.001), CXCL1/KC (p<0.01) and TNF-alpha (p<0.05). AE increased IL-10 levels in serum (p<0.001) and BAL (p<0.001). Furthermore, AE increased superoxide dismutase SOD (p<0.01) and decreased superoxide anion accumulation in the lungs (p<0.01). Lastly, pre-incubation with IL-10 significantly reduced LPS-induced activation of whole blood cells, neutrophils and HUVECs, as observed by reduced production of IL-1 beta, IL-6, IL-8 and TNF-alpha. Our data suggest that AE inhibited LPS-induced lung inflammation by attenuating inflammatory cytokines and oxidative stress markers in mice and human cell culture via enhanced IL-10 production.Sao Paulo Research Foundation (FAPESP) [2012/15165-2]Conselho Nacional de Pesquisa e Desenvolvimento (CNPq) [311335-2015-2]Comissao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES) [12804/13-4, 1303/13-9]FAPESP [2013/24076-6, 2014/23196-0, 2012/14604-8, 2012/25435-7, 2012/24880-7]CAPESNove Julho Univ, Sao Paulo, SP, BrazilBrazilian Inst Teaching & Res Pulm & Exercise Imm, Sao Jose Dos Campos, SP, BrazilFed Univ Sao Paulo UNIFESP, Postgrad Program Sci Human Movement & Rehabil, Santos, SP, BrazilUniv Brasil, Sao Paulo, SP, BrazilUniv Sao Paulo, Sch Med, Dept Pathol LIM 59, Sao Paulo, SP, BrazilUniv Fed Lavras UFLA, Sci Dept Hlth, Lavras, MG, BrazilFed Univ Sao Paulo UNIFESP, Campus Sao Paulo, Sao Paulo, SP, BrazilHarbor UCLA Med Ctr, Div Resp & Crit Care Physiol & Med, Los Angeles Biomed Res Inst, Torrance, CA 90509 USAUniv Tubingen, Inst Clin & Expt Transfus Med IKET, Tubingen, GermanyFed Univ Sao Paulo UNIFESP, Postgrad Program Sci Human Movement & Rehabil, Santos, SP, BrazilFed Univ Sao Paulo UNIFESP, Campus Sao Paulo, Sao Paulo, SP, BrazilFAPESP [2012/15165-2]CNPq [311335-2015-2]CAPES [12804/13-4, 1303/13-9]FAPESP [2013/24076-6, 2014/23196-0, 2012/14604-8, 2012/25435-7, 2012/24880-7]Web of Scienc

Statistical Taylor series expansion: An approach for epistemic uncertainty propagation in Markov reliability models

In this paper we develop a new Taylor series expansion method for computing model output metrics under epistemic uncertainty in the model input parameters. Specifically, we compute the expected value and the variance of the stationary distribution associated with Markov reliability models. In the multi-parameter case, our approach allows to analyze the impact of correlation between the uncertainty on the individual parameters the model output metric. In addition, we also approximate true risk by using the Chebyshev’ inequality. Numerical results are presented and compared to the corresponding Monte Carlo simulations ones

PROPAGATION OF EPISTEMIC UNCERTAINTY IN QUEUEING MODELS WITH UNRELIABLE SERVER USING CHAOS EXPANSIONS

International audienceIn this paper, we develop a numerical approach based on Chaos expansions to analyze the sensitivity and the propagation of epistemic uncertainty through a queueing systems with breakdowns. Here, the quantity of interest is the stationary distribution of the model, which is a function of uncertain parameters. Polynomial chaos provide an efficient alternative to more traditional Monte Carlo simulations for modelling the propagation of uncertainty arising from those parameters. Furthermore, Polynomial chaos expansion affords a natural framework for computing Sobol' indices. Such indices give reliable information on the relative importance of each uncertain entry parameters. Numerical results show the benefit of using Polynomial Chaos over standard Monte-Carlo simulations, when considering statistical moments and Sobol' indices as output quantities