Spherical orbit closures in simple projective spaces and their normalizations

Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module of finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its closure, then we describe the orbits of X and those of its normalization. If moreover the wonderful completion of G/H is strict, then we give necessary and sufficient combinatorial conditions so that the normalization morphism is a homeomorphism. Such conditions are trivially fulfilled if G is simply laced or if H is a symmetric subgroup.Comment: 24 pages, LaTeX. v4: Final version, to appear in Transformation Groups. Simplified some proofs and corrected minor mistakes, added references. v3: major changes due to a mistake in previous version

A combinatorial smoothness criterion for spherical varieties

We suggest a combinatorial criterion for the smoothness of an arbitrary spherical variety using the classification of multiplicity-free spaces, generalizing an earlier result of Camus for spherical varieties of type $A$.Comment: 14 pages, 2 table

Quantitative adsorbate structure determination under catalytic reaction conditions

Current methods allow quantitative local structure determination of adsorbate geometries on surfaces in ultrahigh vacuum (UHV) but are incompatible with the higher pressures required for a steady-state catalytic reactions. Here we show that photoelectron diffraction can be used to determine the structure of the methoxy and formate reaction intermediates during the steady-state oxidation of methanol over Cu(110) by taking advantage of recent instrumental developments to allow near-ambient pressure x-ray photoelectron spectroscopy. The local methoxy site differs from that under static UHV conditions, attributed to the increased surface mobility and dynamic nature of the surface under reaction conditions

In situ surface coverage analysis of RuO₂-catalysed HCl oxidation reveals the entropic origin of compensation in heterogeneous catalysis

In heterogeneous catalysis, rates with Arrhenius-like temperature dependence are ubiquitous. Compensation phenomena, which arise from the linear correlation between the apparent activation energy and the logarithm of the apparent pre-exponential factor, are also common. Here, we study the origin of compensation and find a similar dependence on the rate-limiting surface coverage term for each Arrhenius parameter. This result is derived from an experimental determination of the surface coverage of oxygen and chlorine species using temporal analysis of products and prompt gamma activation analysis during HCl oxidation to Cl2 on a RuO2 catalyst. It is also substantiated by theory. We find that compensation phenomena appear when the effect on the apparent activation energy caused by changes in surface coverage is balanced out by the entropic configuration contributions of the surface. This result sets a new paradigm in understanding the interplay of compensation effects with the kinetics of heterogeneously catalysed processes

Nanopore direct RNA sequencing maps the complexity of Arabidopsis mRNA processing and m6A modification

Understanding genome organization and gene regulation requires insight into RNA transcription, processing and modification. We adapted nanopore direct RNA sequencing to examine RNA from a wild-type accession of the model plant Arabidopsis thaliana and a mutant defective in mRNA methylation (m6A). Here we show that m6A can be mapped in full-length mRNAs transcriptome-wide and reveal the combinatorial diversity of cap-associated transcription start sites, splicing events, poly(A) site choice and poly(A) tail length. Loss of m6A from 3’ untranslated regions is associated with decreased relative transcript abundance and defective RNA 30 end formation. A functional consequence of disrupted m6A is a lengthening of the circadian period. We conclude that nanopore direct RNA sequencing can reveal the complexity of mRNA processing and modification in full-length single molecule reads. These findings can refine Arabidopsis genome annotation. Further, applying this approach to less well-studied species could transform our understanding of what their genomes encode

Polarizations and Nullcone of Representations of Reductive Groups

The paper starts with the following simple observation. Let V be a representation of a reductive group G, and let f_1,f_2,...,f_n be homogeneous invariant functions. Then the polarizations of f_1,f_2,...,f_n define the nullcone of k 0} h(t) x = 0 for all x in L. This is then applied to many examples. A surprising result is about the group SL(2,C) where almost all representations V have the property that all linear subspaces of the nullcone are annihilated. Again, this has interesting applications to the invariants on several copies. Another result concerns the n-qubits which appear in quantum computing. This is the representation of a product of n copies of $SL_2$ on the n-fold tensor product C^2 otimes C^2 otimes ... otimes C^2. Here we show just the opposite, namely that the polarizations never define the nullcone of several copies if n <= 3. (An earlier version of this paper, distributed in 2002, was split into two parts; the first part with the title ``On the nullcone of representations of reductive groups'' is published in Pacific J. Math. {bf 224} (2006), 119--140.

The Rise Times of High and Low Redshift Type Ia Supernovae are Consistent

We present a self-consistent comparison of the rise times for low- and high-redshift Type Ia supernovae. Following previous studies, the early light curve is modeled using a t-squared law, which is then mated with a modified Leibundgut template light curve. The best-fit t-squared law is determined for ensemble samples of low- and high-redshift supernovae by fitting simultaneously for all light curve parameters for all supernovae in each sample. Our method fully accounts for the non-negligible covariance amongst the light curve fitting parameters, which previous analyses have neglected. Contrary to Riess et al. (1999), we find fair to good agreement between the rise times of the low- and high-redshift Type Ia supernovae. The uncertainty in the rise time of the high-redshift Type Ia supernovae is presently quite large (roughly +/- 1.2 days statistical), making any search for evidence of evolution based on a comparison of rise times premature. Furthermore, systematic effects on rise time determinations from the high-redshift observations, due to the form of the late-time light curve and the manner in which the light curves of these supernovae were sampled, can bias the high-redshift rise time determinations by up to +3.6/-1.9 days under extreme situations. The peak brightnesses - used for cosmology - do not suffer any significant bias, nor any significant increase in uncertainty.Comment: 18 pages, 4 figures, Accepted for publication in the Astronomical Journal. Also available at http://www.lbl.gov/~nugent/papers.html Typos were corrected and a few sentences were added for improved clarit

The unusual afterglow of GRB 980326: evidence for the gamma-ray burst/supernova connection

Cosmic gamma-ray bursts (GRBs) have been firmly established as one of the most powerful phenomena in the Universe, releasing electromagnetic energy approaching the rest-mass energy of a neutron star in a few seconds. The two currently popular models for GRB progenitors are the coalescence of two compact objects (such as neutron stars or black holes) or collapse of a massive star. An unavoidable consequence of the latter model is that a bright supernovae should accompany the GRB. The emission from this supernova competes with the much brighter afterglow produced by the relativistic shock that gives rise to the GRB itself. Here we present evidence for an unusual light curve for GRB 980326 based on new optical observations. The transient brightened ~3 weeks after the burst to a flux sixty times larger than that extrapolated from the rapid decay seen at early time. Furthermore, the spectrum changed dramatically and became extremely red. We argue that the new source is the underlying supernova. If our hypothesis is true then this would be the first evidence for a supernova connection with GRBs at cosmological distances. We suggest that GRBs with long durations are associated with death of massive stars.Comment: Submitted to Nature (restricted embargo). Sixteen pages of TeX. Uses macros reforder.tex, citmac.tex and psfig.sty (included). Three Postscript figure

Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices

We study the Steiner Tree problem, in which a set of terminal vertices needs to be connected in the cheapest possible way in an edge-weighted graph. This problem has been extensively studied from the viewpoint of approximation and also parametrization. In particular, on one hand Steiner Tree is known to be APX-hard, and W[2]-hard on the other, if parameterized by the number of non-terminals (Steiner vertices) in the optimum solution. In contrast to this we give an efficient parameterized approximation scheme (EPAS), which circumvents both hardness results. Moreover, our methods imply the existence of a polynomial size approximate kernelization scheme (PSAKS) for the considered parameter. We further study the parameterized approximability of other variants of Steiner Tree, such as Directed Steiner Tree and Steiner Forest. For neither of these an EPAS is likely to exist for the studied parameter: for Steiner Forest an easy observation shows that the problem is APX-hard, even if the input graph contains no Steiner vertices. For Directed Steiner Tree we prove that computing a constant approximation for this parameter is W[1]-hard. Nevertheless, we show that an EPAS exists for Unweighted Directed Steiner Tree. Also we prove that there is an EPAS and a PSAKS for Steiner Forest if in addition to the number of Steiner vertices, the number of connected components of an optimal solution is considered to be a parameter

Filtering of spin currents based on ballistic ring

Quantum interference effects in rings provide suitable means for controlling spin at mesoscopic scales. Here we apply such a control mechanism to the spin-dependent transport in a ballistic quasi one dimensional ring patterned in two dimensional electron gases (2DEGs). The study is essentially based on the {\it natural} spin-orbit (SO) interactions, one arising from the laterally confining electric field {($\beta$ term) and the other due to to the quantum-well potential that confines electrons in the 2DEG (conventional Rashba SO interaction or $\alpha$ term).} We focus on single-channel transport and solve analytically the spin polarization of the current. As an important consequence of the presence of spin splitting, we find the occurrence of spin dependent current oscillations. We analyze %the effects of disorder by discussing the transport in the presence of one non-magnetic obstacle in the ring. We demonstrate that a spin polarized current can be induced when an unpolarized charge current is injected in the ring, by focusing on the central role that the presence of the obstacle plays.Comment: 9 pages, 7 figures, PACS numbers: 72.25.-b, 72.20.My, 73.50.Jt, accepted for publication in J. Phys. - Cond. Ma