Computations of height 22 higher Real KK-theory spectra at prime 22

We completely compute the $G$-homotopy fixed point spectral sequences at prime $2$ for the height $2$ Lubin-Tate theory $E_2$, in the case of finite subgroups $G$ of the Morava stabilizer group for $G=Q_8,SD_{16},G_{24},$ and $G_{48}$. Our computation uses recently developed equivariant techniques since Hill-Hopkins-Ravenel. We also compute the $(*-\sigma_i)$-graded $Q_8$- and $SD_{16}$-homotopy fixed point spectral sequences where $\sigma_i$ is a non-trivial one dimensional $Q_8$-representation.Comment: 48 pages, comments welcome

F-theory and linear sigma models

We present an explicit method for translating between the linear sigma model and the spectral cover description of SU(r) stable bundles over an elliptically fibered Calabi-Yau manifold. We use this to investigate the 4-dimensional duality between (0,2) heterotic and F-theory compactifications. We indirectly find that much interesting heterotic information must be contained in the `spectral bundle' and in its dual description as a gauge theory on multiple F-theory 7-branes. A by-product of these efforts is a method for analyzing semistability and the splitting type of vector bundles over an elliptic curve given as the sheaf cohomology of a monad.Comment: 40 pages, no figures; minor cosmetic reorganization of section 4; reference [6] update

Breaking the curse of dimensionality in regression

Models with many signals, high-dimensional models, often impose structures on the signal strengths. The common assumption is that only a few signals are strong and most of the signals are zero or close (collectively) to zero. However, such a requirement might not be valid in many real-life applications. In this article, we are interested in conducting large-scale inference in models that might have signals of mixed strengths. The key challenge is that the signals that are not under testing might be collectively non-negligible (although individually small) and cannot be accurately learned. This article develops a new class of tests that arise from a moment matching formulation. A virtue of these moment-matching statistics is their ability to borrow strength across features, adapt to the sparsity size and exert adjustment for testing growing number of hypothesis. GRoup-level Inference of Parameter, GRIP, test harvests effective sparsity structures with hypothesis formulation for an efficient multiple testing procedure. Simulated data showcase that GRIPs error control is far better than the alternative methods. We develop a minimax theory, demonstrating optimality of GRIP for a broad range of models, including those where the model is a mixture of a sparse and high-dimensional dense signals.Comment: 51 page

Occurrence of L-iduronic acid and putative D-glucuronyl C5-epimerases in prokaryotes

Glycosaminoglycans (GAGs) are polysaccharides that are typically present in a wide diversity of animal tissue. Most common GAGs are well-characterized and pharmaceutical applications exist for many of these compounds, e.g. heparin and hyaluronan. In addition, also bacterial glycosaminoglycan-like structures exist. Some of these bacterial GAGs have been characterized, but until now no bacterial GAG has been found that possesses the modifications that are characteristic for many of the animal GAGs such as sulfation and C5-epimerization. Nevertheless, the latter conversion may also occur in bacterial and archaeal GAGs, as some prokaryotic polysaccharides have been demonstrated to contain L-iduronic acid. However, experimental evidence for the enzymatic synthesis of L-iduronic acid in prokaryotes is as yet lacking. We therefore performed an in silico screen for D-glucuronyl C5-epimerases in prokaryotes. Multiple candidate C5-epimerases were found, suggesting that many more microorganisms are likely to exist possessing an L-iduronic acid residue as constituent of their cell wall polysaccharides

The Escherichia coli Serogroup O1 and O2 Lipopolysaccharides Are Encoded by Multiple O-antigen Gene Clusters

Escherichia coli strains belonging to serogroups O1 and O2 are frequently associated with human infections, especially extra-intestinal infections such as bloodstream infections or urinary tract infections. These strains can be associated with a large array of flagellar antigens. Because of their frequency and clinical importance, a reliable detection of E. coli O1 and O2 strains and also the frequently associated K1 capsule is important for diagnosis and source attribution of E. coli infections in humans and animals. By sequencing the O-antigen clusters of various O1 and O2 strains we showed that the serogroups O1 and O2 are encoded by different sets of O-antigen encoding genes and identified potentially new O-groups. We developed qPCR- assays to detect the various O1 and O2 variants and the K1-encoding gene. These qPCR assays proved to be 100% sensitive and 100% specific and could be valuable tools for the investigations of zoonotic and food-borne infection of humans with O1 and O2 extra-intestinal (ExPEC) or Shiga toxin-producing E. coli (STEC) strains