81 research outputs found
Steady-state simulation output analysis: MSE-optimal dynamic batch means with parsimonious storage
No full textWe develop theory and methodology to estimate the variance of the sample mean of general steady-state simulation output data, with consideration of statistical efficiency, computational efficiency, and storage requirements. We strive for automatic methods, in that the practitioner needs to provide no algorithmic parameters, including a priori knowledge of the simulation run length. The methodological approach is to batch the output data, without storing individual observations. The batch sizes and the number of batches are increased dynamically as the simulation run length increases. This approach is similar to Dynamic Batch Means (DBM), developed in the author\u27s M.S. thesis, in which batches are combined by collapsing two batches into one with a doubled batch size. In DBM, however, the number of batches does not increase beyond a specified bound. Here, both batch sizes and numbers of batches are dynamically increased with the objective of minimizing the mean squared error (mse) of the variance estimator of the sample mean. We create algorithm DBM-mse, an automatic mse-optimal batching algorithm with parsimonious storage requirements. Our empirical study shows that the storage efficiency obtained costs little in terms of statistical and computational performance. In addition, we study three related topics. First, we correct a conceptual error of Song and Schmeiser concerning the definition of estimator robustness. In particular, we argue that robustness should be based on error in estimating the center of gravity of the data process, not in mse-optimal batch size. Second, we study properties of the center of gravity and construct a new estimator based on the lag-1 autocorrelation of a standardized-time-series area process. Third, we study the relationship between the original data process and the process formed from non-overlapping batch means. The key result is that the product of batch size and center of gravity is a constant, which leads to prebatching variations of existing algorithms
Characteristics and outcomes of SARS-CoV-2 breakthrough infections among double-vaccinated and triple-vaccinated patients with inflammatory rheumatic diseases
No full textObjective To analyse the clinical profile of SARS-CoV-2 breakthrough infections in at least double-vaccinated patients with inflammatory rheumatic diseases (IRDs). Methods Data from the physician-reported German COVID-19-IRD registry collected between February 2021 and July 2022 were analysed. SARS-CoV-2 cases were stratified according to patients’ vaccination status as being not vaccinated, double-vaccinated or triple-vaccinated prior to SARS-CoV-2 infection and descriptively compared. Independent associations between demographic and disease features and outcome of breakthrough infections were estimated by multivariable logistic regression. Results In total, 2314 cases were included in the analysis (unvaccinated n=923, double-vaccinated n=551, triple-vaccinated n=803, quadruple-vaccinated n=37). SARS-CoV-2 infections occurred after a median of 151 (range 14–347) days in patients being double-vaccinated, and after 88 (range 14–270) days in those with a third vaccination. Hospitalisation was required in 15% of unvaccinated, 8% of double-vaccinated and 3% of triple-vaccinated/quadruple-vaccinated patients (p<0.001). Mortality was 2% in unvaccinated, 1.8% in the double-vaccinated and 0.6% in triple-vaccinated patients. Compared with unvaccinated patients, double-vaccinated (OR 0.43, 95% CI 0.29 to 0.62) and triple-vaccinated (OR 0.13, 95% CI 0.08 to 0.21) patients showed a significant lower risk of COVID-19-related hospitalisation. Using multivariable analysis, the third vaccination was significantly associated with a lower risk for COVID-19-related death (OR 0.26; 95% CI 0.01 to 0.73). Conclusions Our cross-sectional data of COVID-19 infections in patients with IRD showed a significant reduction of hospitalisation due to infection in double-vaccinated or triple-vaccinated patients compared with those without vaccination and even a significant reduction of COVID-19-related deaths in triple-vaccinated patients. These data strongly support the beneficial effect of COVID-19 vaccination in patients with IRD. Trial registration number EuDRACT 2020-001958-21.German Society for Rheumatolog
On the Asymptotic Behavior of a Run and Tumble Equation for Bacterial Chemotaxis
No full textWe prove that linear and weakly nonlinear run and tumble equations converge to a unique steady state solution with an exponential rate in a weighted total variation distance. In the linear setting, our result extends the previous results to an arbitary dimension d≥1 while relaxing the assumptions. The main challenge is that even though the equation is a mass-preserving, Boltzmann-type kinetic-transport equation, the classical hypocoercivity methods, e.g., by J. Dolbeault, C. Mouhot, and C. Schmeiser [Trans. Amer. Math. Soc., 367 (2015), pp. 3807–3828], are not applicable for dimension d≥1. We overcome this difficulty by using a probabilistic technique, known as Harris’s theorem. We also introduce a weakly nonlinear model via a nonlocal coupling on the chemoattractant concentration. This toy model serves as an intermediate step between the linear model and the physically more relevant nonlinear models. We build a stationary solution for this equation and provide a hypocoercivity result.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Mathematical Physic
Estimators of the variance of the sample mean: Quadratic forms, optimal batch sizes, and linear combinations
No full textA classical problem of stochastic simulation is how to estimate the variance of point estimators, the prototype problem being the sample mean from a steady-state autocorrelated process. A variety of estimators for the variance of the sample mean exist, all designed to provide robustness to violations of assumptions, small variance, and reasonable computing requirements. No estimator seems to dominate the others in terms of the statistical properties for all covariance-stationary processes and for all sample sizes. Obtaining good estimators of the variance of the sample mean for all covariance-stationary processes is the primary motivation of the author\u27s dissertation research. The research encompasses three areas: (1) The investigation of some desirable properties of the class of quadratic-form estimators and the derivation of quadratic-form coefficients for some well-known estimators. (2) The investigation of optimal batch sizes and the derivation of an explicit formula for the asymptotic optimal batch size as a function of sample size, estimator type, and the center of gravity of the nonnegative autocorrelations of the data type. (3) The creation of estimators with smaller variance or mean squared error by using linear combinations of known estimators
Metaanalyse und systematischer Review zur Arthritis bei Patienten mit systemischer Sklerodermie
No full textDie systemische Sklerodermie gehört zu den Kollagenosen und ist gekennzeichnet durch eineVerdickung der Dermis sowie durch eine Beteiligung innerer Organe. Im Weiteren stellenBeschwerden der peripheren Gelenke eine typische Manifestation der SSc dar, wobeientzündliche Gelenkmanifestationen und deren Häufigkeit kontrovers diskutiert werden. DiePrävalenz einer entzündlichen Gelenkmanifestation und deren Schwere sind bisher nurunzureichend geklärt. Aus diesem Grund erfolgte als Grundlage dieser Arbeit dieDurchführung eines systematischen Reviews und einer Metaanalyse zur Evaluation derHäufigkeit einer arthritischen Manifestation der SSc.Das Literatur Online-Portal PubMed wurde nach Studien zur Arthritis bei SSc durchsucht.Die Suche wurde mit Fachbegriffen (z.B. Sklerodermie, systemische Sklerose, Arthritis,Hand- und Fußbeteiligung) in verschiedenen Kombinationen durchgeführt. Originalartikel,die nicht in englischer Sprache verfasst wurden und Artikel, deren Thema sich nicht mit derArthritis in Zusammenhang mit SSc befasste, wurden ausgeschlossen. Eingeschlossen wurdenPublikationen in denen die untersuchten Patientenkohorten entsprechend der ACR oderLeRoy Kriterien eingeschlossen wurden und in denen die Arthritis nach klinischen undradiologischen Gesichtspunkten untersucht wurde. Die Arbeiten wurden von zweiunabhängigen Untersuchern gelesen und bewertet.Basierend auf dem Random-effect Modell wurde in einer Metaanalyse von sieben Arbeiteneine Prävalenz 26 % (95 % KI[16.7, 36.1]) nach radiologischen und eine Prävalenz von 23 %(95% KI[14.9, 30.9]) nach klinischen Gesichtspunkten ermittelt. Interessant ist, dass keinUnterschied im Auftreten einer peripheren Arthritis nach radiologischen (OR=1.1, 95%KI[0.47,2.57]) oder klinischen (OR= 1.11, 95% KI[0.6,2.05]) Gesichtspunkten in derSubtypenanalyse der lcSSc gegenüber der dcSSc errechnet werden konnte.Die systematische Untersuchung der bis dato publizierten Arbeiten zur peripherenGelenkbeteiligung bei SSc machen deutlich, dass die von den Patienten beklagtenGelenkbeschwerden nicht alleine über eine Arthrose oder Veränderungen der Dermis zuerklären sind. Vielmehr muss differentialdiagnostisch auch eine arthritische Genese derBeschwerden bedacht werden. Nach den hier vorgelegten Daten ist die Prävalenz für eineArthritis bei SSc höher einzuschätzen als die einer PAH.Systemic sclerosis (SSc) is a connective tissue disease characterised by excessive thickeningof the dermis and in addition affection of internal organs. During the clinical course of diseasemany patients experience a musculoskeletal involvement; however, true arthritis is describedas a very rare manifestation in textbooks. Currently, the frequency and severity ofinflammatory joint disorders are insufficiently recorded and evaluated. Therefore thisassignment represents a metaanalysis (and systematic review) in which the frequency ofmanifestation of peripheral arthritis in SSc patients was determined based on clinical andradiological data.A systematic literature search using PubMed was performed to find studies on arthritis in SScpatients. The search terms were sclerodema, systemic sclerosis, arthritis, inflammatory jointdisease, hand involvement, foot involvement and musculoskeletal findings in variouscombinations. Original articles not written in English and articles which were not dealing witharthritis in SSc patients were excluded from the study. Articles were included in which theexamined cohorts correspond to the ACR- or LeRoy criteria for SSc and arthritis wasdiagnosed based on clinical and/ or radiological data. All manuscripts were read and reviewedby two independent investigators.In a metaanalysis of 7 studies a prevalence of 26 % (95 % CI[16.7, 36.1]) for radiologicallydetectable arthritis in SSc patients was found based on the random-effect model. For clinicalarthritis, the prevalence was calculated to be 23 % (95% CI[14.9, 30.9]). Of interest, nodifference in the occurence of arthritis in diffuse and limited SSc was observed radiologically(OR=1.1, 95% CI [0.47,2.57]) or clinically (OR= 1.11, 95% CI [0.6,2.05]).The screening of recent publications reveals that an involvement of peripheral joints in SScpatients cannot be explained solely by destructive changes or alterations of the dermis and theconnective tissue. Rather a true arthritis has to be recognized as a possible organmanifestation of SSc. Finally it is pointed out that the occurrence of true arthritis in SSc isfound more frequent than the manifestation of PAH
Kinetic Boundary Layers and Fluid-Kinetic Coupling in Semiconductors
No full text. The semiconductor Boltzmann equation with elastic collisions as the dominating scattering effects is considered. For the corresponding fluid limit, the spherical harmonics expansion model, kinetic boundary layers are analyzed and higher order accurate boundary conditions are constructed. In a further step, boundary value problems for the energy transport model and the drift-diffusion model are derived. As an application, interface conditions for the fluid-kinetic coupling in a domain decomposition approach are presented. Key words: Semiconductor Boltzmann equation, spherical harmonics expansion model, energy transport model, drift-diffusion model, domain decomposition, Milne problem. AMS subject classification: 35Q20, 76P05, 82A70, 78A35 Acknowledgements: The work of the second author has been supported by the Austrian Fonds zur Forderung der wissenschaftlichen Forschung under grant Nr. P11308-MAT. It has been carried out during a visit of the second author at Univ. Paul Sabatier, T..
Properties of batch means from stationary ARMA time series
No full textThe batch means process arising from an arbitrary autoregressive moving-average (ARMA) process time series is derived. As side results, the variance and correlation structures of the batch means process as functions of the batch size and parameters of the original process are obtained. Except for the first-order ARMA process, for which a closed-form expression is obtained, the parameters of the batch-means process are determined numerically. Keywords: Monte Carlo method; Simulation. (Author)Naval Postgraduate School, Monterey, CAhttp://archive.org/details/propertiesofbatc00kan
Relaxation Time Approximation for Electron-Phonon Interaction in Semiconductors
No full text. A Boltzmann equation for semiconductors is considered. Physical assumptions include the parabolic band approximation and a new relaxation time model for electron-phonon interaction. Thermal equilibrium distributions for this scattering mechanism are products of Maxwellian distributions with periodic functions of the energy, where the period is the energy of a phonon. The hydrodynamic limit is considered and a drift-diffusion model is derived by formal asymptotic methods. Key words: Semiconductors, Boltzmann equation, drift-diffusion limit AMS subject classification: 82A70, 78A35 Acknowledgements: The work of the first author has been supported by the "Human Capital and Mobility"-Project No. ERBCHRXCT 930413 entitled "Nonlinear Spatial-Temporal Structures in Semiconductors, Fluids and Oscillator Ensembles" funded by the E.U. and by the DFG-Project Ma 1662/1-1. The work of the second author has been supported by the Austrian "Fonds zur Forderung der wissenschaftlichen Forschung" under..
Kinetic Boundary Layers and Fluid-Kinetic Coupling in Semiconductors
No full text. The semiconductor Boltzmann equation with elastic collisions as the dominating scattering effects is considered. For the corresponding fluid limit, the spherical harmonics expansion model, kinetic boundary layers are analyzed and higher order accurate boundary conditions are constructed. In a further step, boundary value problems for the energy transport model and the drift-diffusion model are derived. As an application, interface conditions for the fluid-kinetic coupling in a domain decomposition approach are presented. Key words: Semiconductor Boltzmann equation, spherical harmonics expansion model, energy transport model, drift-diffusion model, domain decomposition, Milne problem. AMS subject classification: 35Q20, 76P05, 82A70, 78A35 Acknowledgements: This work has been supported by the TMR-network No. ERB FMBX CT97 0157 on "Asymptotic Methods in Kinetic Theory". The second author also acknowledges support by the Austrian Science Foundation through grant No. P11308-MAT. 1 MIP..
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