Semi-invariants of symmetric quivers of finite type

Let $(Q,\sigma)$ be a symmetric quiver, where $Q=(Q_0,Q_1)$ is a finite quiver without oriented cycles and $\sigma$ is a contravariant involution on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form on a representation $V$ of $Q$. We shall call the representation orthogonal if is symmetric and symplectic if $$ is skew-symmetric. Moreover we can define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. For symmetric quivers of finite type, we prove that the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type $c^V$ and, in the case when matrix defining $c^V$ is skew-symmetric, by the Pfaffians $pf^V$

Physical Controls on Carbonate Intraclasts: Modern Flat Pebbles From Great Salt Lake, Utah

In carbonate‐forming environments, authigenic minerals can cement surface sediments into centimeter‐sized intraclasts that are later reworked into “flat‐pebble” or “edgewise” conglomerates. Flat‐pebble conglomerates comprise only a small portion of facies in modern marine environments but are common in ancient strata, implying that seafloor cements were more widespread in the past. Flat‐pebble conglomerates nearly disappeared after the Ordovician radiation, yet it is unclear if this decline was due to changing seawater chemistry or if increased infaunalization and bioturbation simply worked to break down nascent clasts. We discovered a process analog that produces flat‐pebble conglomerates around the Great Salt Lake, Utah, USA, and studied these facies using field observations, wave models, satellite imagery, petrography, and microanalytic chemical data. Clasts were sourced from wave‐rippled grainstone that cemented in situ in offshore environments. Lake floor cements formed under aragonite saturation states that are lower than modern marine settings, suggesting that physical processes are at least as important as chemical ones. Results from our wave models showed that coarse sediments near the field site experience quiescent periods of up to 6 months between suspension events, allowing isopachous cements to form. Using a simple mathematical framework, we show that the main difference between Great Salt Lake and modern, low‐energy marine settings is that the latter has enough bioturbating organisms to break up clasts. Observations from Great Salt Lake demonstrate how geologic trends in flat‐pebble abundance could largely reflect changes in total infaunal biomass and ecology without requiring regional‐to‐global changes in seawater chemistry

Density-functional theory of inhomogeneous electron systems in thin quantum wires

Motivated by current interest in strongly correlated quasi-one-dimensional (1D) Luttinger liquids subject to axial confinement, we present a novel density-functional study of few-electron systems confined by power-low external potentials inside a short portion of a thin quantum wire. The theory employs the 1D homogeneous Coulomb liquid as the reference system for a Kohn-Sham treatment and transfers the Luttinger ground-state correlations to the inhomogeneous electron system by means of a suitable local-density approximation (LDA) to the exchange-correlation energy functional. We show that such 1D-adapted LDA is appropriate for fluid-like states at weak coupling, but fails to account for the transition to a ``Wigner molecules'' regime of electron localization as observed in thin quantum wires at very strong coupling. A detailed analyzes is given for the two-electron problem under axial harmonic confinement.Comment: 8 pages, 7 figures, submitte

A 2-year prospective study of patient-relevant outcomes in patients operated on for knee osteoarthritis with tibial osteotomy

BACKGROUND: Tibial osteotomy is a treatment for younger and/or physically active patients suffering from uni-compartmental knee osteoarthritis. The open wedge osteotomy by the hemicallotasis technique includes the use of external fixation. The use of external fixation has several advantages, as early mobilization and the opportunity for optimal correction. However, the hemicallotasis technique has also been described as a cumbersome procedure for the patient. The aim of this study was to prospectively evaluate patient-relevant outcomes during the first 2 post-operative years. Especially the treatment period, during which external fixation was used, was closely monitored. METHODS: In an uncontrolled study, fifty-eight consecutive patients, 30 men and 28 women (mean age 54 years) were operated on by the hemicallotasis technique were evaluated with the patient-relevant outcome measure Knee injury and Osteoarthritis Outcome Score (KOOS) preoperatively, during the treatment with external fixation, one week after removal of the external fixation, at 6 months, and at one and two years postoperatively. RESULTS: At the 2-year postoperative follow-up, all subscales of the KOOS were improved (p < 0.001), mostly in pain (41–80 on a 0–100 worst to best scale) and knee-related quality of life (21–61 on a 0–100 worst to best scale), compared to the preoperative status. Significant improvements in pain and other symptoms, function of daily life and quality of life were seen already during the treatment period (mean 98 ± 18 days) with the external fixation. More demanding functions such as kneeling, squatting, jumping and running, were improved first after extraction of the external fixation device and the pins. CONCLUSION: Tibial osteotomy by the hemicallotasis technique yields large improvement in self-rated pain, function and quality of life, which persists over two years. Surprisingly, large improvements occurred already during the immediate post-operative period when the external fixation was still used

Physical Controls on Carbonate Intraclasts: Modern Flat Pebbles From Great Salt Lake, Utah

In carbonate‐forming environments, authigenic minerals can cement surface sediments into centimeter‐sized intraclasts that are later reworked into “flat‐pebble” or “edgewise” conglomerates. Flat‐pebble conglomerates comprise only a small portion of facies in modern marine environments but are common in ancient strata, implying that seafloor cements were more widespread in the past. Flat‐pebble conglomerates nearly disappeared after the Ordovician radiation, yet it is unclear if this decline was due to changing seawater chemistry or if increased infaunalization and bioturbation simply worked to break down nascent clasts. We discovered a process analog that produces flat‐pebble conglomerates around the Great Salt Lake, Utah, USA, and studied these facies using field observations, wave models, satellite imagery, petrography, and microanalytic chemical data. Clasts were sourced from wave‐rippled grainstone that cemented in situ in offshore environments. Lake floor cements formed under aragonite saturation states that are lower than modern marine settings, suggesting that physical processes are at least as important as chemical ones. Results from our wave models showed that coarse sediments near the field site experience quiescent periods of up to 6 months between suspension events, allowing isopachous cements to form. Using a simple mathematical framework, we show that the main difference between Great Salt Lake and modern, low‐energy marine settings is that the latter has enough bioturbating organisms to break up clasts. Observations from Great Salt Lake demonstrate how geologic trends in flat‐pebble abundance could largely reflect changes in total infaunal biomass and ecology without requiring regional‐to‐global changes in seawater chemistry

Single crystal diamond membranes for nanoelectronics

© 2018 The Royal Society of Chemistry. Single crystal, nanoscale diamond membranes are highly sought after for a variety of applications including nanophotonics, nanoelectronics and quantum information science. However, so far, the availability of conductive diamond membranes has remained an unreachable goal. In this work we present a complete nanofabrication methodology for engineering high aspect ratio, electrically active single crystal diamond membranes. The membranes have large lateral directions, exceeding ∼500 × 500 μm2 and are only several hundreds of nanometers thick. We further realize vertical single crystal p-n junctions made from the diamond membranes that exhibit onset voltages of ∼10 V and a current of several mA. Moreover, we deterministically introduce optically active color centers into the membranes, and demonstrate for the first time a single crystal nanoscale diamond LED. The robust and scalable approach to engineer the electrically active single crystal diamond membranes offers new pathways for advanced nanophotonic, nanoelectronic and optomechanical devices employing diamond

Zero-one Schubert polynomials

We prove that if σ∈Sm is a pattern of w∈Sn, then we can express the Schubert polynomial w as a monomial times σ (in reindexed variables) plus a polynomial with nonnegative coefficients. This implies that the set of permutations whose Schubert polynomials have all their coefficients equal to either 0 or 1 is closed under pattern containment. Using Magyar's orthodontia, we characterize this class by a list of twelve avoided patterns. We also give other equivalent conditions on w being zero-one. In this case, the Schubert polynomial w is equal to the integer point transform of a generalized permutahedron