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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]

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]