Frame properties of systems arising via iterated actions of operators

Motivated by recent progress in dynamical sampling we prove that every frame which is norm-bounded below can be represented as a finite union of sequences ${\{{(T_j)}^n{\phi }_j\}}_{n=0}^{\infty },j=1,\dots ,J$ for some bounded operators $T_j$ and elements ${\phi }_j$ in the underlying Hilbert space. The result is optimal, in the sense that it turns out to be problematic to replace the collection of generators ${\phi }_1,\dots ,{\phi }_J$ by a singleton: indeed, for linearly independent frames we prove that we can represent the frame in terms of just one system ${\{T^n\phi \}}_{n=0}^{\infty }$, but unfortunately this representation often forces the operator T to be unbounded. Several examples illustrate the connection of the results to typical frames like Gabor frames and wavelet frames, as well as generic constructions in arbitrary separable Hilbert spaces.     

Change points in heavy‐tailed multivariate time series: Methods using precision matrices

We propose two robust data‐driven techniques for detecting network structure change points between heavy‐tailed multivariate time series for situations where both the placement and number of change points are unknown. The first technique utilizes the graphical lasso method to estimate the change points, whereas the second technique utilizes the tlasso method. The techniques not only locate the change points but also estimate an undirected graph (or precision matrix) representing the relationship between the time series within each interval created by pairs of adjacent change points. An inference procedure on the edges is used in the graphs to effectively remove false‐positive edges, which are caused by the data deviating from normality. The techniques are compared using simulated multivariate t‐distributed (heavy‐tailed) time series data and the best method is applied to two financial returns data sets of stocks and indices. The results illustrate the method's ability to determine how the dependence structure of the returns changes over time. This information could potentially be used as a tool for portfolio optimization.     

Effect of quality control on the proliferation of the extract from Taraxacum mongolicum Hand.‐Mazz. in Lactobacillus plantarum

In recent years, the fingerprint of high‐performance liquid chromatography has been extensively applied in the identification and quality control of traditional Chinese medicine. It can be a potential protocol for assessing the authenticity, stability and consistency of traditional Chinese medicine and guaranteeing the expected biological activity. In this paper, a method using high‐performance liquid chromatography to identify and control the quality of the extract of Taraxacum mongolicum Hand.‐Mazz. (TME) was established. With this method, the correlation coefficients of the similarity of 10 batches were ≥0.994. The TME displayed a steady proliferative effect in Lactobacillus plantarum. In brief, this study successfully built a reliable, simple and efficient method to control and confirm the quality and the stability of biological activity of the TME.     

A-posteriori KAM theory with optimal estimates for partially integrable systems

In this paper we present a-posteriori KAM results for existence of d-dimensional isotropic invariant tori for n-DOF Hamiltonian systems with additional $n?d$ independent first integrals in involution. We carry out a covariant formulation that does not require the use of action-angle variables nor symplectic reduction techniques. The main advantage is that we overcome the curse of dimensionality avoiding the practical shortcomings produced by the use of reduced coordinates, which may cause difficulties and underperformance when quantifying the hypotheses of the KAM theorem in such reduced coordinates. The results include ordinary and (generalized) iso-energetic KAM theorems. The approach is suitable to perform numerical computations and computer assisted proofs.     

Intermolecular interactions between natural humic substances and tricyclic antidepressants

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Trimetallic NiCoM catalysts (M = Mn,Fe, Cu) for methane conversion into synthesis gas

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