The Waldschmidt constant for squarefree monomial ideals

Given a squarefree monomial ideal $I \subseteq R =k[x_1,\ldots,x_n]$, we show that $\widehat\alpha(I)$, the Waldschmidt constant of $I$, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of $I$. By applying results from fractional graph theory, we can then express $\widehat\alpha(I)$ in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of $I$. Moreover, expressing $\widehat\alpha(I)$ as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on $\widehat\alpha(I)$, thus verifying a conjecture of Cooper-Embree-H\`a-Hoefel for monomial ideals in the squarefree case. As an application, we compute the Waldschmidt constant and the resurgence for some families of squarefree monomial ideals. For example, we determine both constants for unions of general linear subspaces of $\mathbb{P}^n$ with few components compared to $n$, and we find the Waldschmidt constant for the Stanley-Reisner ideal of a uniform matroid.Comment: 26 pages. This project was started at the Mathematisches Forschungsinstitut Oberwolfach (MFO) as part of the mini-workshop "Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems" held in February 2015. Comments are welcome. Revised version corrects some typos, updates the references, and clarifies some hypotheses. To appear in the Journal of Algebraic Combinatoric

Postnatal mental health and mothers' processing of infant emotion: an eye-tracking study

BACKGROUND: Postnatal mental illnesses are associated with less maternal sensitivity. Differences in how mothers with and without mental illness process infant emotions could explain this. People with mental illness in non-perinatal populations show certain processing patterns when viewing emotional faces, but it is not clear whether these patterns are present in mothers. OBJECTIVE: Compared to mothers without affective symptoms (anxiety, depression and post-traumatic stress). Task 1 aimed to identify whether mothers with affective symptoms show an attentional bias towards negative infant faces; and Task 2 aimed to identify whether mothers with affective symptoms look less at infants' eyes compared to eyes and mouth. DESIGN: An experimental design was used in two tasks to answer the research objective. METHODS: Mothers with affective symptoms (n = 23) and without affective symptoms (n = 47) had their eye movements tracked whilst: Task 1, viewing pairs of infant faces; and Task 2, viewing morphed infant faces. RESULTS: In Task 1 mothers with affective symptoms were more likely to fixate first on neutral faces when the choice was between negative and neutral. In Task 2, no differences were found between groups. CONCLUSIONS: The findings from Task 1 are unexpected given previous research. More research is needed to identify potential explanations for this

High Resolution Spectroscopy of the Pulsating White Dwarf G29-38

We present the analysis of time-resolved, high resolution spectra of the cool white dwarf pulsator, G29-38. From measuring the Doppler shifts of the H-alpha core, we detect velocity changes as large as 16.5 km/s and conclude that they are due to the horizontal motions associated with the g-mode pulsations on the star. We detect seven pulsation modes from the velocity time-series and identify the same modes in the flux variations. We discuss the properties of these modes and use the advantage of having both velocity and flux measurements of the pulsations to test the convective driving theory proposed for DAV stars. Our data show limited agreement with the expected relationships between the amplitude and phases of the velocity and flux modes. Unexpectedly, the velocity curve shows evidence for harmonic distortion, in the form of a peak in the Fourier transform whose frequency is the exact sum of the two largest frequencies. Combination frequencies are a characteristic feature of the Fourier transforms of light curves of G29-38, but before now have not been detected in the velocities, nor does published theory predict that they should exist. We compare our velocity combination frequency to combination frequencies found in the analysis of light curves of G29-38, and discuss what might account for the existence of velocity combinations with the properties we observe. We also use our high-resolution spectra to determine if either rotation or pulsation can explain the truncated shape observed for the DAV star's line core. We are able to eliminate both mechanisms: the average spectrum does not fit the rotationally broadened model and the time-series of spectra provides proof that the pulsations do not significantly truncate the line.Comment: 24 pages, 9 figures, Accepted for publication in ApJ (June

Effectiveness of Ledipasvir/Sofosbuvir with/without Ribavarin in Liver Transplant Recipients with Hepatitis C.

Background and Aims: Recurrent infection of hepatitis C virus (HCV) in liver transplant (LT) recipients is universal and associated with significant morbidity and mortality. Methods: We retrospectively evaluated the safety and efficacy of ledipasvir/sofosbuvir with and without ribavirin in LT recipients with recurrent genotype 1 hepatitis C. Results: Eighty-five LT recipients were treated for recurrent HCV with ledipasvir/sofosbuvirwith and without ribavirin for 12 or 24 weeks. The mean (± standard deviation [SD]) time from LT to treatment initiation was 68 (±71) months. The mean (± SD) age of the cohort was 63 (±8.6) years old. Most recipients were male (70%). Baseline alanine transaminase, total bilirubin, and HCV ribonucleic acid (RNA) values (± SD) were 76.8 (±126) mg/dL, 0.8 (±1.3) U/L, and 8,010,421.9 (±12,420,985) IU/mL, respectively. Five of 43 recipients who were treated with ribavirin required drug cessation due to side effects, with 4 of those being anemia complications. No recipient discontinued the ledipasvir/sofosbuvir. Eighty-one percent of recipients had undetectable viral levels at 4 weeks after starting therapy, and all recipients had complete viral suppression at the end of therapy. The sustained viral response at 12 weeks after completion of therapy was 94%. Conclusion : Ledipasvir and sofosbuvir with and without ribavirin therapy is an effective and well-tolerated interferon-free treatment for recurrent HCV infection after LT. Anemia is not uncommon in LT recipients receiving ribavirin

The Distribution, Excitation and Formation of Cometary Molecules: Methanol, Methyl Cyanide and Ethylene Glycol

We present an interferometric and single dish study of small organic species toward Comets C/1995 O1 (Hale-Bopp) and C/2002 T7 (LINEAR) using the BIMA interferometer at 3 mm and the ARO 12m telescope at 2 mm. For Comet Hale-Bopp, both the single-dish and interferometer observations of CH3OH indicate an excitation temperature of 105+/-5 K and an average production rate ratio Q(CH3OH)/Q(H2O)~1.3% at ~1 AU. Additionally, the aperture synthesis observations of CH3OH suggest a distribution well described by a spherical outflow and no evidence of significant extended emission. Single-dish observations of CH3CN in Comet Hale-Bopp indicate an excitation temperature of 200+/-10 K and a production rate ratio of Q(CH3CN)/Q(H2O)~0.017% at ~1 AU. The non-detection of a previously claimed transition of cometary (CH2OH)2 toward Comet Hale-Bopp with the 12m telescope indicates a compact distribution of emission, D<9'' (<8500 km). For the single-dish observations of Comet T7 LINEAR, we find an excitation temperature of CH3OH of 35+/-5 K and a CH3OH production rate ratio of Q(CH3OH)/Q(H2O)~1.5% at ~0.3 AU. Our data support current chemical models that CH3OH, CH3CN and (CH2OH)2 are parent nuclear species distributed into the coma via direct sublimation off cometary ices from the nucleus with no evidence of significant production in the outer coma.Comment: accepted for publication in Ap

Zermelo Navigation and a Speed Limit to Quantum Information Processing

We use a specific geometric method to determine speed limits to the implementation of quantum gates in controlled quantum systems that have a specific class of constrained control functions. We achieve this by applying a recent theorem of Shen, which provides a connection between time optimal navigation on Riemannian manifolds and the geodesics of a certain Finsler metric of Randers type. We use the lengths of these geodesics to derive the optimal implementation times (under the assumption of constant control fields) for an arbitrary quantum operation (on a finite dimensional Hilbert space), and explicitly calculate the result for the case of a controlled single spin system in a magnetic field, and a swap gate in a Heisenberg spin chain

On the trace of the antipode and higher indicators

We introduce two kinds of gauge invariants for any finite-dimensional Hopf algebra H. When H is semisimple over C, these invariants are respectively, the trace of the map induced by the antipode on the endomorphism ring of a self-dual simple module, and the higher Frobenius-Schur indicators of the regular representation. We further study the values of these higher indicators in the context of complex semisimple quasi-Hopf algebras H. We prove that these indicators are non-negative provided the module category over H is modular, and that for a prime p, the p-th indicator is equal to 1 if, and only if, p is a factor of dim H. As an application, we show the existence of a non-trivial self-dual simple H-module with bounded dimension which is determined by the value of the second indicator.Comment: additional references, fixed some typos, minor additions including a questions and some remark