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Framelets derived from refinable (vector) functions via the popular oblique extension principle (OEP) are of interest in both theory and applications. Though OEP can increase vanishing moments of framelet generators to improve sparsity, it has a serious shortcoming for scalar framelets: the associated discrete framelet transform is often not compact and deconvolution is unavoidable. On the other hand, in sharp contrast to the extensively studied scalar framelets, OEP-based multiframelets are far from well understood. In this paper, we prove that from any compactly supported refinable vector function having at least two entries, one can always construct through OEP a compactly supported quasi-tight multiframelet such that all framelet generators have the highest possible order of vanishing moments, and its underlying discrete framelet transform is compact and balanced. The key ingredient of our proof is a newly developed normal form of matrix-valued filters, which greatly facilitates the study of multiframelets. [ABSTRACT FROM AUTHOR]

The study of the restricted isometry property (RIP) of corrupted random matrices is particularly important in the field of compressed sensing (CS) with corruptions. If a matrix still satisfies the RIP after that a certain portion of rows are erased, then we say that this matrix has the strong restricted isometry property (SRIP). In the field of compressed sensing, random matrices which satisfy certain moment conditions are of particular interest. Among these matrices, those with entries generated from i.i.d. Gaussian or symmetric Bernoulli random variables are often typically considered. Recent studies have shown that matrices with entries generated from i.i.d. Gaussian random variables satisfy the SRIP under arbitrary erasure of rows with high probability. In this paper, we study the erasure robustness property of Bernoulli random matrices. Our main result shows that with overwhelming probability, the SRIP holds for Bernoulli random matrices. Moreover, our analysis leads to a robust version of the famous Johnson–Lindenstrauss lemma for Bernoulli random matrices. [ABSTRACT FROM AUTHOR]

The aim of this paper is to examine the return connectedness and multiscale spillovers between the Clean Energy Index and the grain commodity market around COVID-19. Using daily data from January 4, 2017 to July 1, 2022, a time-varying parametric vector autoregressive (TVP-VAR) connectedness approach is first used to reveal connectedness patterns before and during COVID-19. We further used Baruník and Křehlík (2018)'s frequency domain spillover method to assess connectedness in different domain horizons. Our results show spillover effects over time and frequency, with COVID-19 significantly affecting the connectedness of the whole system. Dynamic connectedness peaks significantly after sudden bursts of COVID-19, validating the reported uncertainty. We also documented higher spillover levels in the short term than in the medium and long term. In addition, We find that (i) most clean energy indices are positively affected by the COVID-19 outbreak; (ii) the NASDAQ OMX Bio/Clean Fuels Index and NASDAQ OMX Geothermal Index send spillovers to all grain commodities throughout the sample period, while the WilderHill Clean Energy Index and NASDAQ OMX Wind Energy Index indices are the largest recipients of spillovers from other markets regardless of time horizon; (iii) the OMX Bio/Clean Fuels and OMX Geothermal Energy indices dominate spillover shocks to grain commodity markets. This is the first study to analyse the connectedness and time-frequency dynamics of returns in the green energy index and the grain commodity market. These results provide valuable insights to investors and key policymakers, especially at a time of more significant uncertainty. • Examine the return connectedness between the Clean Energy Index and the grain commodity market. • Dynamic connectedness peaks significantly after sudden bursts of COVID-19. • Higher spillover levels in the short term than in the medium and long term. • OMX Bio/Clean Fuels and OMX Geothermal Energy indices dominate spillover shocks to grain commodity markets. [ABSTRACT FROM AUTHOR]

Abstract Owing to the diverse structures and unique characteristics of MOFs, the combination of magnetic particles with porous MOFs is an attractive way for rapid and efficient extraction of organic pollutions from water. In this work, the magnetic porous composites, Fe 3 O 4 -PSS@ZIF-67 (PSS, poly (sodium-p-styrenesulfonate)), were prepared. The obtained composites exhibit core-shell structure, for which the spherical Fe 3 O 4 particles as core are embedded in ZIF-67 shell. The existence of SO 3 − anions on poly (sodium-p-styrenesulfonate) is the key factor for the uniform coating of ZIF-67 on Fe 3 O 4 particles. Poly (sodium-p-styrenesulfonate) providing enough chelating sites (-SO 3 −) for Co2+ which could further coordinate with 2-methylimidazole to form ZIF-67. This work further studied the adsorption property of 2-nitroresorcinol in aqueous solution, using Fe 3 O 4 -PSS@ZIF-67 as adsorbents. The equilibrium adsorption capacity for 2-nitroresorcinol is up to 52.50 mg g−1. The adsorption kinetics were investigated. The mechanism could be attributed to the electrostatic interaction between 2-nitroresorcinol and Fe 3 O 4 -PSS@ZIF-67 composites. Graphical abstract A new magnetic porous composites (Fe 3 O 4 -PSS@ZIF-67) was prepared, for which poly (sodium-p-styrenesulfonate) links the spherical Fe 3 O 4 core and ZIF-67 coating. The composites perform well on nitrophenol from aqueous solution via magnetic separation operation, mainly owing to the porosity of ZIF-67 and the electrostatic interaction between nitrophenol and composites. The combination of magnetic separation with MOFs is attractive way for efficient removal of nitrophenols from waste water. fx1 [ABSTRACT FROM AUTHOR]

Cytoplasmic polyadenylation element binding protein 4 (CPEB4) is a member of CPEB family which is overexpressed in variety of cancers. However, the biological role and regulatory mechanism of CPEB4 in cancers remain unknown. Here, we first investigate the role of CPEB4 in breast cancer progression and metastasis. The expression of CPEB4 is elevated in breast cancer tissues compared with adjacent normal tissues. Furthermore, high expression levels of CPEB4 is associated with tumor metastasis in breast cancer patients. Ectopic expression of CPEB4 dramatically promotes EMT, migration and invasion of breast cancer cells, while silencing CPEB4 expression significantly reduces these events. Mechanically, overexpression of CPEB4 upregulates Vimentin expression and silencing Vimentin expression blocks CPEB4-induced migration and invasion of breast cancer cells. These results implicate the potential role of CPEB4 and Vimentin in breast cancer metastasis, which is further confirmed by the finding that there is a physical interaction between the two proteins. Altogether, our results provide a novel insight into CPEB4 in regulating breast cancer progression and metastasis. [ABSTRACT FROM AUTHOR]

Factorization of matrices of Laurent polynomials plays an important role in mathematics and engineering such as wavelet frame construction and filter bank design. Wavelet frames (a.k.a. framelets) are useful in applications such as signal and image processing. Motivated by the recent development of quasi-tight framelets, we study and characterize generalized spectral factorizations with symmetry for 2 × 2 matrices of Laurent polynomials. Applying our result on generalized matrix spectral factorization, we establish a necessary and sufficient condition for the existence of symmetric quasi-tight framelets with two generators. The proofs of all our main results are constructive and therefore, one can use them as construction algorithms. We provide several examples to illustrate our theoretical results on generalized matrix spectral factorization and quasi-tight framelets with symmetry. [ABSTRACT FROM AUTHOR]

• First publicly available deep learning pipeline to segment the olfactory bulbs (OBs) in sub-millimeter T2-weighted whole-brain MRI. • Rigorous validation in the Rhineland Study - an ongoing large population-based cohort study - in terms of segmentation accuracy, stability and reliability of volume estimates, as well as sensitivity to replicate known OB volume associations (e.g. age effects). • Good generalizability to an unseen heterogeneous independent dataset (the Human Connectome Project). • Robustness even for individuals without apparent OBs, as can be encountered in large cohort studies. The neuroimage analysis community has neglected the automated segmentation of the olfactory bulb (OB) despite its crucial role in olfactory function. The lack of an automatic processing method for the OB can be explained by its challenging properties (small size, location, and poor visibility on traditional MRI scans). Nonetheless, recent advances in MRI acquisition techniques and resolution have allowed raters to generate more reliable manual annotations. Furthermore, the high accuracy of deep learning methods for solving semantic segmentation problems provides us with an option to reliably assess even small structures. In this work, we introduce a novel, fast, and fully automated deep learning pipeline to accurately segment OB tissue on sub-millimeter T2-weighted (T2w) whole-brain MR images. To this end, we designed a three-stage pipeline: (1) Localization of a region containing both OBs using FastSurferCNN , (2) Segmentation of OB tissue within the localized region through four independent AttFastSurferCNN - a novel deep learning architecture with a self-attention mechanism to improve modeling of contextual information, and (3) Ensemble of the predicted label maps. For this work, both OBs were manually annotated in a total of 620 T2w images for training (n=357) and testing. The OB pipeline exhibits high performance in terms of boundary delineation, OB localization, and volume estimation across a wide range of ages in 203 participants of the Rhineland Study (Dice Score (Dice): 0.852, Volume Similarity (VS): 0.910, and Average Hausdorff Distance (AVD): 0.215 m m). Moreover, it also generalizes to scans of an independent dataset never encountered during training, the Human Connectome Project (HCP), with different acquisition parameters and demographics, evaluated in 30 cases at the native 0.7 m m HCP resolution (Dice: 0.738, VS: 0.790, and AVD: 0.340 m m), and the default 0.8 m m pipeline resolution (Dice: 0.782, VS: 0.858, and AVD: 0.268 m m). We extensively validated our pipeline not only with respect to segmentation accuracy but also to known OB volume effects, where it can sensitively replicate age effects (β = − 0.232 , p <. 01). Furthermore, our method can analyze a 3D volume in less than a minute (GPU) in an end-to-end fashion, providing a validated, efficient, and scalable solution for automatically assessing OB volumes. [ABSTRACT FROM AUTHOR]