Methods for extremes of functional data

2018 Fall.Includes bibliographical references.Motivated by the problem of extreme behavior of functional data, we develop statistical theory at the nexus of functional data analysis (FDA) and extreme value theory (EVT). A fundamental technique of functional data analysis is to replace infinite dimensional curves with finite dimensional representations in terms of functional principal components (FPCs). The coefficients of these projections, called the scores, encode the shapes of the curves. Therefore, the study of the extreme behavior of functional time series can be transformed to the study on functional principal component scores. We first derive two tests of significance of the slope function using functional principal components and their empirical counterparts (EFPC's). Applied to tropical storm data, these tests show a significant trend in the annual pattern of upper wind speed levels of hurricanes. Then we establish sufficient conditions under which the asymptotic extreme behavior of the multivariate estimated scores is the same as that of the population scores. We clarify these issues, including the rate of convergence, for Gaussian functions and for more general functional time series whose projections are in the Gumbel domain of attraction. Finally, we derive the asymptotic distribution of the sample covariance operator and of the sample functional principal components for functions which are regularly varying and whose fourth moment does not exist. The new theory is applied to establish the consistency of the regression operator in a functional linear model, with such errors

Effects of Sijunzi decoction and Yupingfeng powder on expression of janus kinase-signal transducer and activator of transcription signal pathway in the brain of spleen-deficiency model rats

AbstractObjectiveTo observe the influence of Sijunzi decoction and Yupingfeng powder on the expression of the relevant DNAs of janus kinase (JAK)-signal transducer and activator of transcription (STAT) signal pathway of the brain in spleen-deficiency model rats.MethodsEighty male Wistar rats of sanitary degree were divided randomly into four groups: normal group, model group, treatment group 1, treatment group 2. Besides the rats in the normal group, all the rats in other 3 groups were prepared as spleen deficiency model. The treatment group 1 were treated with Sijunzi decoction and the treatment group 2 were treated with Yupingfeng powder. After treatment for 6 weeks, perfusion was given and the brain was taken for detection of the expression of the relevant DNAs of JAK-STAT signal pathway of the brain in SD rats by gene chip method.ResultsSpleen deficiency could lead to increase expression of JAK1, STAT1 and Interleukin 4 (IL-4) in the brain, but the decrease expression of Suppressor of cytokine signaling 1 (SOCS1), prolactin receptor (PRLR) and binding protein 3 (GATA 3). Sijunzi decoction could increase expression of STAT3, Prolactin (PRL) and GATA3, but decrease expression of JAK1, STAT, STAT4, Interleukin 10 receptor, alpha (IL10RA), Coagulation factor II (F2), PRLR, MAD homolog 3 (SMAD3) and IL-4. Yupingfeng powder could decrease expression of JAK1, STAT1, STAT4, SOCS4_ predicted, Epidermal growth factor receptor (EGFR), PRLR, High mobility group AT-hook 1 (HMGA10), IL-4.ConclusionSijunzi decoction and Yupingfeng powder can improve immune function of the rat through influencing the genetic expression of JAK-STAT signal pathway

Mechanical Tuning of Thermal Transport in a Molecular Junction

Understanding and controlling heat transport in molecular junctions would provide new routes to design nanoscale coupled electronic and phononic devices. Using first principles full quantum calculations, we tune thermal conductance of a molecular junction by mechanically compressing and extending a short alkane chain connected to graphene leads. We find that the thermal conductance of the compressed junction drops by half in comparison to the extended junction, making it possible to turn on and off the heat current. The low conductance of the off state does not vary by further approaching the leads and stems from the suppression of the transmission of the in--plane transverse and longitudinal channels. Furthermore, we show that misalignment of the leads does not reduce the conductance ratio. These results also contribute to the general understanding of thermal transport in molecular junctions.Comment: 12 pages, 6 figure

Expectile-based conditional tail moments with covariates

Expectile, as the minimizer of an asymmetric quadratic loss function, is a coherent risk measure and is helpful to use more information about the distribution of the considered risk. In this paper, we propose a new risk measure by replacing quantiles by expectiles, called expectile-based conditional tail moment, and focus on the estimation of this new risk measure as the conditional survival function of the risk, given the risk exceeding the expectile and given a value of the covariates, is heavy tail. Under some regular conditions, asymptotic properties of this new estimator are considered. The extrapolated estimation of the conditional tail moments is also investigated. These results are illustrated both on simulated data and on a real insurance data.Comment: 17 pages, 7 figure