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

Plasma interferon-alpha is associated with double-positivity for autoantibodies but is not a predictor of remission in early rheumatoid arthritis-a spin-off study of the NORD-STAR randomized clinical trial

BACKGROUND: The type I interferon (IFN) gene signature is present in a subgroup of patients with early rheumatoid arthritis (RA). Protein levels of IFNα have not been measured in RA and it is unknown whether they associate with clinical characteristics or treatment effect. METHODS: Patients with early untreated RA (n = 347) were randomized to methotrexate combined with prednisone, certolizumab-pegol, abatacept, or tocilizumab. Plasma IFNα protein levels were determined by single molecular array (Simoa) before and 24 weeks after treatment initiation and were related to demographic and clinical factors including clinical disease activity index, disease activity score in 28 joints, swollen and tender joint counts, and patient global assessment. RESULTS: IFNα protein positivity was found in 26% of the patients, and of these, 92% were double-positive for rheumatoid factor (RF) and anti-citrullinated protein antibodies (ACPA). IFNα protein levels were reduced 24 weeks after treatment initiation, and the absolute change was similar irrespective of treatment. IFNα protein positivity was associated neither with disease activity nor with achievement of CDAI remission 24 weeks after randomization. CONCLUSION: IFNα protein positivity is present in a subgroup of patients with early RA and associates with double-positivity for autoantibodies but not with disease activity. Pre-treatment IFNα positivity did not predict remission in any of the treatment arms, suggesting that the IFNα system is distinct from the pathways of TNF, IL-6, and T-cell activation in early RA. A spin-off study of the NORD-STAR randomized clinical trial, NCT01491815 (ClinicalTrials), registered 12/08/2011, https://clinicaltrials.gov/ct2/show/NCT01491815

Androgens and spermatogenesis: lessons from transgenic mouse models

Transgenic mouse models have contributed considerably to our understanding of the cellular and molecular mechanisms by which androgens control spermatogenesis. Cell-selective ablation of the androgen receptor (AR) in Sertoli cells (SC) results in a complete block in meiosis and unambiguously identifies the SC as the main cellular mediator of the effects of androgens on spermatogenesis. This conclusion is corroborated by similar knockouts in other potential testicular target cells. Mutations resulting in diminished expression of the AR or in alleles with increased length of the CAG repeat mimick specific human forms of disturbed fertility that are not accompanied by defects in male sexual development. Transcriptional profiling studies in mice with cell-selective and general knockouts of the AR, searching for androgen-regulated genes relevant to the control of spermatogenesis, have identified many candidate target genes. However, with the exception of Rhox5, the identified subsets of genes show little overlap. Genes related to tubular restructuring, cell junction dynamics, the cytoskeleton, solute transportation and vitamin A metabolism are prominently present. Further research will be needed to decide which of these genes are physiologically relevant and to identify genes that can be used as diagnostic tools or targets to modulate the effects of androgens in spermatogenesis

Effects of age, BMI and sex on the glial cell marker TSPO - a multicentre [C-11]PBR28 HRRT PET study

Purpose The purpose of this study was to investigate the effects of ageing, sex and body mass index (BMI) on translocator protein (TSPO) availability in healthy subjects using positron emission tomography (PET) and the radioligand [C-11]PBR28. Methods [C-11]PBR28 data from 140 healthy volunteers (72 males and 68 females; N = 78 with HAB and N = 62 MAB genotype; age range 19-80 years; BMI range 17.6-36.9) were acquired with High Resolution Research Tomograph at three centres: Karolinska Institutet (N = 53), Turku PET centre (N = 62) and Yale University PET Center (N = 25). The total volume of distribution (V-T) was estimated in global grey matter, frontal, temporal, occipital and parietal cortices, hippocampus and thalamus using multilinear analysis 1. The effects of age, BMI and sex on TSPO availability were investigated using linear mixed effects model, with TSPO genotype and PET centre specified as random intercepts. Results There were significant positive correlations between age and V-T in the frontal and temporal cortex. BMI showed a significant negative correlation with V-T in all regions. Additionally, significant differences between males and females were observed in all regions, with females showing higher V-T. A subgroup analysis revealed a positive correlation between V-T and age in all regions in male subjects, whereas age showed no effect on TSPO levels in female subjects. Conclusion These findings provide evidence that individual biological properties may contribute significantly to the high variation shown in TSPO binding estimates, and suggest that age, BMI and sex can be confounding factors in clinical studies