On elliptic factors in real endoscopic transfer I

This paper is concerned with the structure of packets of representations and some refinements that are helpful in endoscopic transfer for real groups. It includes results on the structure and transfer of packets of limits of discrete series representations. It also reinterprets the Adams-Johnson transfer of certain nontempered representations via spectral analogues of the Langlands-Shelstad factors, thereby providing structure and transfer compatible with the associated transfer of orbital integrals. The results come from two simple tools introduced here. The first concerns a family of splittings of the algebraic group G under consideration; such a splitting is based on a fundamental maximal torus of G rather than a maximally split maximal torus. The second concerns a family of Levi groups attached to the dual data of a Langlands or an Arthur parameter for the group G. The introduced splittings provide explicit realizations of these Levi groups. The tools also apply to maps on stable conjugacy classes associated with the transfer of orbital integrals. In particular, they allow for a simpler version of the definitions of Kottwitz-Shelstad for twisted endoscopic transfer in certain critical cases. The paper prepares for spectral factors in twisted endoscopic transfer that are compatible in a certain sense with the standard factors discussed here. This compatibility is needed for Arthur's global theory. The twisted factors themselves will be defined in a separate paper.Comment: 48 pages, to appear in Progress in Mathematics, Volume 312, Birkha\"user. Also renumbering to match that of submitted versio

Hydraulic Conditions Required to Move Unanchored Residue Materials

Hydraulic conditions required to initiate movement of unanchored residue materials are identified in the present study. Selected amounts of corn, cotton, pine needles, sorghum, soybean, sunflower, and wheat residue are placed in a flume on a sand surface, and flow is then introduced at the top of the flume in progressive increments. The discharge rate and flow velocity necessary to cause residue movement are determined. The ratio of critical flow depth to residue diameter, critical Reynolds number, critical shear stress, dimensionless shear stress, and boundary Reynolds number are calculated from hydraulic measurements. Regression equations are developed to relate dimensionless shear stress to boundary Reynolds number and residue diameter. Boundary Reynolds number, in turn, is related to residue diameter and cover. Close agreement is found between predicted and actual parameter values obtained from the regression relations. The regression equations can be used to estimate the beginning of motion for other residue materials if residue diameter and cover are known

The Discriminant of an Algebraic Torus

For a torus T defined over a global field K, we revisit an analytic class number formula obtained by Shyr in the 1970's as a generalization of Dirichlet's class number formula. We prove a local-global presentation of the quasi-discriminant of T, which enters into this formula, in terms of cocharacters of T. This presentation can serve as a more natural definition of this invariant.Comment: 17 page

On a Conjecture of Rapoport and Zink

In their book Rapoport and Zink constructed rigid analytic period spaces $F^{wa}$ for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of $p$-divisible groups to some of these period spaces. They conjectured the existence of an \'etale bijective morphism $F^a \to F^{wa}$ of rigid analytic spaces and of a universal local system of $Q_p$-vector spaces on $F^a$. For Hodge-Tate weights $n-1$ and $n$ we construct in this article an intrinsic Berkovich open subspace $F^0$ of $F^{wa}$ and the universal local system on $F^0$. We conjecture that the rigid-analytic space associated with $F^0$ is the maximal possible $F^a$, and that $F^0$ is connected. We give evidence for these conjectures and we show that for those period spaces possessing PEL period morphisms, $F^0$ equals the image of the period morphism. Then our local system is the rational Tate module of the universal $p$-divisible group and enjoys additional functoriality properties. We show that only in exceptional cases $F^0$ equals all of $F^{wa}$ and when the Shimura group is $GL_n$ we determine all these cases.Comment: v2: 48 pages; many new results added, v3: final version that will appear in Inventiones Mathematica

Myoglobin for Detection of High-Risk Patients with Acute Myocarditis

There is an unmet need for accurate and practical screening to detect myocarditis. We sought to test the hypothesis that the extent of acute myocarditis, measured by late gadolinium enhancement (LGE) on cardiac magnetic resonance imaging (CMR), can be estimated based on routine blood markers. A total of 44 patients were diagnosed with acute myocarditis and included in this study. There was strong correlation between myoglobin and LGE (rs = 0.73 [95% CI 0.51; 0.87], p < 0.001), while correlation was weak between LGE and TnT-hs (rs = 0.37 [95% CI 0.09; 0.61], p = 0.01). Receiver operating curve (ROC) analysis determined myoglobin ≥ 87 μg/L as cutoff to identify myocarditis (92% sensitivity, 80% specificity). The data were reproduced in an established model of coxsackievirus B3 myocarditis in mice (n = 26). These data suggest that myoglobin is an accurate marker of acute myocarditis. Graphical Abstract Receiver operating curve analysis determined myoglobin ≥ 87 μg/L as cutoff to identify myocarditis and these data were reproduced in an established model of coxsackievirus B3 myocarditis in mice: CMRI, cardiac magnetic resonance imaging; Mb, myoglobin; LGE, late gadolinium enhancement; ROC, receiver operating curve analysis

Tissue-specific regulatory network extractor (TS-REX): a database and software resource for the tissue and cell type-specific investigation of transcription factor-gene networks

The prediction of transcription factor binding sites in genomic sequences is in principle very useful to identify upstream regulatory factors. However, when applying this concept to genomes of multicellular organisms such as mammals, one has to deal with a large number of false positive predictions since many transcription factor genes are only expressed in specific tissues or cell types. We developed TS-REX, a database/software system that supports the analysis of tissue and cell type-specific transcription factor-gene networks based on expressed sequence tag abundance of transcription factor-encoding genes in UniGene EST libraries. The use of expression levels of transcription factor-encoding genes according to hierarchical anatomical classifications covering different tissues and cell types makes it possible to filter out irrelevant binding site predictions and to identify candidates of potential functional importance for further experimental testing. TS-REX covers ESTs from H. sapiens and M. musculus, and allows the characterization of both presence and specificity of transcription factors in user-specified tissues or cell types. The software allows users to interactively visualize transcription factor-gene networks, as well as to export data for further processing. TS-REX was applied to predict regulators of Polycomb group genes in six human tumor tissues and in human embryonic stem cells

Mutations in PINK1 and Parkin Impair Ubiquitination of Mitofusins in Human Fibroblasts

PINK1 and Parkin mutations cause recessive Parkinson's disease (PD). In Drosophila and SH-SY5Y cells, Parkin is recruited by PINK1 to damaged mitochondria, where it ubiquitinates Mitofusins and consequently promotes mitochondrial fission and mitophagy