We address the problem of forecasting high-dimensional functional time series through a two-fold dimension reduction procedure. The difficulty of forecasting high-dimensional functional time series lies in the curse of dimensionality. In this paper, we propose a novel method to solve this problem. Dynamic functional principal component analysis is first applied to reduce each functional time series to a vector. We then use the factor model as a further dimension reduction technique so that only a small number of latent factors are preserved. Classic time series models can be used to forecast the factors and conditional forecasts of the functions can be constructed. Asymptotic properties of the approximated functions are established, including both estimation error and forecast error. The proposed method is easy to implement especially when the dimension of the functional time series is large. We show the superiority of our approach by both simulation studies and an application to Japanese age-specific mortality rates.
A versatile experimental approach is described to achieve very high sensitivity analysis of peptides by capillary electrophoresis-mass spectrometry with sheath flow configuration based on optimization of field-amplified sample injection. Compared to traditional hydrodynamic injection methods, signal enhancement in terms of detection sensitivity of the bioanalytes by more than 3000-fold can be achieved. The effects of injection conditions, composition of the acid and organic solvent in the sample solution, length of the water plug, sample injection time, and voltage on the efficiency of the sample stacking have been systematically investigated, with peptides in the low-nanomolar (10(-9) M) range readily detected under the optimized conditions. Linearity of the established stacking method was found to be excellent over 2 orders of magnitude of concentration. The method was further evaluated for the analysis of low concentration bioactive peptide mixtures and tryptic digests of proteins. A distinguishing feature of the described approach is that it can be employed directly for the analysis of low-abundance protein fragments generated by enzymatic digestion and a reversed-phase-based sample-desalting procedure. Thus, rapid identification of protein fragments as low-abundance analytes can be achieved with this new approach by comparison of the actual tandem mass spectra of selected peptides with the predicted fragmentation patterns using online database searching algorithms.
This paper proposes a new statistic to test independence between two high dimensional random vectors X : p 1 × 1 and Y : p 2 × 1. The proposed statistic is based on the sum of regularized sample canonical correlation coefficients of X and Y. The asymptotic distribution of the statistic under the null hypothesis is established as a corollary of general central limit theorems (CLT) for the linear statistics of classical and regularized sample canonical correlation coefficients when p 1 and p 2 are both comparable to the sample size n. As applications of the developed independence test, various types of dependent structures, such as factor models, ARCH models and a general uncorrelated but dependent case, etc., are investigated by simulations. As an empirical application, cross-sectional dependence of daily stock returns of companies between different sections in the New York Stock Exchange (NYSE) is detected by the proposed test.
The oxidative N-demethylation of tropane alkaloids to their nortropane derivatives has been investigated using H 2 O 2 and an iron(III) tetraamido macrocycle (Fe III -TAML) catalyst. The yields of the nortropanes were found to be dependent on the amount of H 2 O 2 used in the reaction, the catalyst loading, the nature of the organic co-solvent and the type of tropine substrate. N-Hydroxy-nortropane, N-formyl-nortropane and tropane-N-oxide derivatives were identified as by-products of the reaction. After screening various reaction conditions, the optimised conditions were applied to the N-demethylation of atropine and scopolamine at preparative scales and the desired products, noratropine and norscopolamine, obtained following one pot reactions in good yields and high purity without the need for any chromatographic purification steps. Fig. 1 Structures of several naturally occurring (1-3) and semi-synthetic (4-7) tropane alkaloids. † Electronic supplementary information (ESI) available. See
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