Automorphy lifting for residually reducible-adic Galois representations, II

We revisit the paper [Automorphy lifting for residually reducible$l$-adic Galois representations, J. Amer. Math. Soc. 28 (2015), 785–870] by the third author. We prove new automorphy lifting theorems for residually reducible Galois representations of unitary type in which the residual representation is permitted to have an arbitrary number of irreducible constituents.This work was partially conducted during the period that J.T. served as a Clay Research Fellow. J.T.’s work received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714405). J.T. would like to thank Lue Pan for pointing out an error in [Tho15], which is addressed here in §3.1 below. P.A. was supported by Simons Foundation Collaboration Grant 527275 and NSF grant DMS- 1902155

Altered brain connectivity in sudden unexpected death in epilepsy (SUDEP) revealed using resting-state fMRI.

The circumstances surrounding SUDEP suggest autonomic or respiratory collapse, implying central failure of regulation or recovery. Characterisation of the communication among brain areas mediating such processes may shed light on mechanisms and noninvasively indicate risk. We used rs-fMRI to examine network properties among brain structures in people with epilepsy who suffered SUDEP (n = 8) over an 8-year follow-up period, compared with matched high- and low-risk subjects (n = 16/group) who did not suffer SUDEP during that period, and a group of healthy controls (n = 16). Network analysis was employed to explore connectivity within a 'regulatory-subnetwork' of brain regions involved in autonomic and respiratory regulation, and over the whole-brain. Modularity, the extent of network organization into separate modules, was significantly reduced in the regulatory-subnetwork, and the whole-brain, in SUDEP and high-risk. Increased participation, a local measure of inter-modular belonging, was evident in SUDEP and high-risk groups, particularly among thalamic structures. The medial prefrontal thalamus was increased in SUDEP compared with all other control groups, including high-risk. Patterns of hub topology were similar in SUDEP and high-risk, but were more extensive in low-risk patients, who displayed greater hub prevalence and a radical reorganization of hubs in the subnetwork. SUDEP is associated with reduced functional organization among cortical and sub-cortical brain regions mediating autonomic and respiratory regulation. Living high-risk subjects demonstrated similar patterns, suggesting such network measures may provide prospective risk-indicating value, though a crucial difference between SUDEP and high-risk was altered connectivity of the medial thalamus in SUDEP, which was also elevated compared with all sub-groups. Disturbed thalamic connectivity may reflect a potential non-invasive marker of elevated SUDEP risk

Photoacoustic wavefront shaping with a long coherence length laser

Photoacoustic (PA) wavefront shaping (WS; PAWS) could allow focusing light deep in biological tissue. This could enable increasing the penetration depth of biomedical optical techniques including PA imaging. However, focussing at depth requires a light source of long coherence length (CL), presenting a challenge because the CLs of typical PA excitation lasers are short. To address this challenge, we developed a PAWS system based on an externally modulated external cavity laser with a long CL. The system was demonstrated by focussing light through rigid scattering media using both PAWS and optical WS. PAWS enabled focussing through diffusers with 8 × enhancements, while all-optical WS enabled focussing through various scattering media including a 5.8 mm thick tissue phantom. By enabling PAWS with increased coherence, the system could facilitate exploring the practical depth limits of PAWS, paving the way to focussing light deep in tissue

Mitotic instability in triploid and tetraploid one-year-old eastern oyster, Crassostrea virginica, assessed by cytogenetic and flow cytometry techniques

For commercial oyster aquaculture, triploidy has significant advantages. To produce triploids, the principal technology uses diploid x tetraploid crosses. The development of tetraploid brood stock for this purpose has been successful, but as more is understood about tetraploids, it seems clear that chromosome instability is a principal feature in oysters. This paper is a continuation of work to investigate chromosome instability in polyploid Crassostrea virginica. We established families between tetraploids-apparently stable (non-mosaic) and unstable (mosaic)-and normal reference diploids, creating triploid groups, as well as tetraploids between mosaic and non-mosaic tetraploids. Chromosome loss was about the same for triploid juveniles produced from either mosaic or non-mosaic tetraploids or from either male or female tetraploids. However, there was a statistically significant difference in chromosome loss in tetraploid juveniles produced from mosaic versus non-mosaic parents, with mosaics producing more unstable progeny. These results confirm that chromosome instability, as manifested in mosaic tetraploids, is of little concern for producing triploids, but it is clearly problematic for tetraploid breeding. Concordance between the results from cytogenetics and flow cytometry was also tested for the first time in oysters, by assessing the ploidy of individuals using both techniques. Results between the two were non-concordant

Comparing Social Science and Computer Science Workflow Processes for Studying Group Interactions

In this article, a team of authors from the Geeks and Groupies workshop, in Leiden, the Netherlands, compare prototypical approaches to studying group interaction in social science and computer science disciplines, which we call workflows. To help social and computer science scholars understand and manage these differences, we organize workflow into three major stages: research design, data collection, and analysis. For each stage, we offer a brief overview on how scholars from each discipline work. We then compare those approaches and identify potential synergies and challenges. We conclude our article by discussing potential directions for more integrated and mutually beneficial collaboration that go beyond the producer–consumer model

5-Cyclo­hexyl-2-(3-fluoro­phen­yl)-3-methyl­sulfinyl-1-benzofuran

In the title compound, C21H21FO2S, the cyclo­hexyl ring adopts a chair conformation. The 3-fluoro­phenyl ring makes a dihedral angle of 38.38 (6)° with the mean plane [r.m.s. deviation = 0.010 (1) Å] of the benzofuran fragment. In the crystal, mol­ecules are linked by weak C—H⋯O hydrogen bonds