Some Tauberian theorems for Euler and Borel summability

The well-known summability methods of Euler and Borel are studied as mappings from ℓ1 into ℓ1. In this ℓ−ℓ setting, the following Tauberian results are proved: if x is a sequence that is mapped into ℓ1 by the Euler-Knopp method Er with r>0 (or the Borel matrix method) and x satisfies ∑n=0∞|xn−xn+1|n<∞, then x itself is in ℓ1

Some absolutely effective product methods

It is proved that the product method A(C,1), where (C,1) is the Cesàro arithmetic mean matrix, is totally effective under certain conditions concerning the matrix A. This general result is applied to study absolute Nörlund summability of Fourier series and other related series

UtpA and UtpB chaperone nascent pre-ribosomal RNA and U3 snoRNA to initiate eukaryotic ribosome assembly

Early eukaryotic ribosome biogenesis involves large multi-protein complexes, which co-transcriptionally associate with pre-ribosomal RNA to form the small subunit processome. The precise mechanisms by which two of the largest multi-protein complexes—UtpA and UtpB—interact with nascent pre-ribosomal RNA are poorly understood. Here, we combined biochemical and structural biology approaches with ensembles of RNA–protein cross-linking data to elucidate the essential functions of both complexes. We show that UtpA contains a large composite RNA-binding site and captures the 5′ end of pre-ribosomal RNA. UtpB forms an extended structure that binds early pre-ribosomal intermediates in close proximity to architectural sites such as an RNA duplex formed by the 5′ ETS and U3 snoRNA as well as the 3′ boundary of the 18S rRNA. Both complexes therefore act as vital RNA chaperones to initiate eukaryotic ribosome assembly

Whole-body tissue stabilization and selective extractions via tissue-hydrogel hybrids for high-resolution intact circuit mapping and phenotyping

To facilitate fine-scale phenotyping of whole specimens, we describe here a set of tissue fixation-embedding, detergent-clearing and staining protocols that can be used to transform excised organs and whole organisms into optically transparent samples within 1–2 weeks without compromising their cellular architecture or endogenous fluorescence. PACT (passive CLARITY technique) and PARS (perfusion-assisted agent release in situ) use tissue-hydrogel hybrids to stabilize tissue biomolecules during selective lipid extraction, resulting in enhanced clearing efficiency and sample integrity. Furthermore, the macromolecule permeability of PACT- and PARS-processed tissue hybrids supports the diffusion of immunolabels throughout intact tissue, whereas RIMS (refractive index matching solution) grants high-resolution imaging at depth by further reducing light scattering in cleared and uncleared samples alike. These methods are adaptable to difficult-to-image tissues, such as bone (PACT-deCAL), and to magnified single-cell visualization (ePACT). Together, these protocols and solutions enable phenotyping of subcellular components and tracing cellular connectivity in intact biological networks