Complete subvarieties of moduli spaces and the Prym map

We prove that in characteristic p>0 the locus of stable curves of p-rank at most f is pure of codimension g-f in the moduli space of stable curves. Then we consider the Prym map and analyze it using tautological classes. We study the locus of curves with an etale double cover of p-rank 0 in some detail. In particular, in genus 2 we obtain a formula for the number of such curves. We end with several examples illustrating our formula.Comment: 20 pages, 1 figure. Final version, to appear in J. Reine Angew. Mat

Covariants of binary sextics and vector-valued Siegel modular forms of genus two

We extend Igusa's description of the relation between invariants of binary sextics and Siegel modular forms of degree two to a relation between covariants and vector-valued Siegel modular forms of degree two. We show how this relation can be used to effectively calculate the Fourier expansions of Siegel modular forms of degree two.Comment: 19 page

Controlling colloidal phase transitions with critical Casimir forces

The critical Casimir effect provides a thermodynamic analogue of the well-known quantum mechanical Casimir effect. It acts between two surfaces immersed in a critical binary liquid mixture, and results from the confinement of concentration fluctuations of the solvent. Unlike the quantum mechanical effect, the magnitude and range of this attraction can be adjusted with temperature via the solvent correlation length, thus offering new opportunities for the assembly of nano and micron-scale structures. Here, we demonstrate the active assembly control of equilibrium phases using critical Casimir forces. We guide colloidal particles into analogues of molecular liquid and solid phases via exquisite control over their interactions. By measuring the critical Casimir particle pair potential directly from density fluctuations in the colloidal gas, we obtain insight into liquefaction at small scales: We apply the Van der Waals model of molecular liquefaction and show that the colloidal gas-liquid condensation is accurately described by the Van der Waals theory, even on the scale of a few particles. These results open up new possibilities in the active assembly control of micro and nanostructures

Covariants of binary sextics and modular forms of degree 2 with character

We use covariants of binary sextics to describe the structure of modules of scalar-valued or vector-valued Siegel modular forms of degree 2 with character, over the ring of scalar-valued Siegel modular forms of even weight. For a modular form defined by a covariant we express the order of vanishing along the locus of products of elliptic curves in terms of the covariant.Comment: 18 page

The Euler characteristic of local systems on the moduli of curves and abelian varieties of genus three

We show how to calculate the Euler characteristic of a local system associated to an irreducible representation of the symplectic group of genus 3 on the moduli space of curves of genus 3 and the moduli space of principally polarized abelian varieties of dimension 3

Clinical Value of Multiomics-Based Biomarker Signatures in Inflammatory Bowel Diseases:Challenges and Opportunities

Inflammatory bowel diseases (IBD), encompassing Crohn's disease (CD) and ulcerative colitis (UC), are complex and heterogeneous diseases characterized by a multifactorial etiology, therefore demanding a multimodal approach to disentangle the main pathophysiological components driving disease onset and progression. Adoption of a systems biology approach is increasingly advocated with the advent of multi-omics profiling technologies, aiming to improve disease classification, to identify disease biomarkers and to accelerate drug discovery for patients with IBD. However, clinical translation of multi-omics-derived biomarker signatures is lagging behind, since there are several obstacles that need to be addressed in order to realize clinically useful signatures. Multi-omics integration and IBD-specific identification of molecular networks, standardization and clearly defined outcomes, strategies to tackle cohort heterogeneity, and external validation of multi-omics-based signatures are critical aspects. While striving for personalized medicine in IBD, careful consideration of these aspects is however needed to adequately match biomarker targets (e.g. the gut microbiome, immunity or oxidative stress) with their corresponding utilities (e.g. early disease detection, endoscopic and clinical outcome). Theory-driven disease classifications and predictions are still governing clinical practice, while this could be improved by adopting an unbiased, data-driven approach relying on molecular data structures integrated with patient and disease characteristics. In the foreseeable future, the main challenge will lie in the complexity and impracticality of implementing multi-omics-based signatures into clinical practice. Still, this could be achieved by developing easy-to-use, robust and cost-effective tools incorporating omics-derived predictive signatures and through the design and execution of prospective, longitudinal, biomarker-stratified clinical trials

Pirfenidone Inhibits Cell Proliferation and Collagen I Production of Primary Human Intestinal Fibroblasts

Intestinal fibrosis is a common complication of inflammatory bowel disease. So far, there is no safe and effective drug for intestinal fibrosis. Pirfenidone is an anti-fibrotic compound available for the treatment of idiopathic pulmonary fibrosis. Here, we explored the anti-proliferative and anti-fibrotic properties of pirfenidone on primary human intestinal fibroblasts (p-hIFs). p-hIFs were cultured in the absence and presence of pirfenidone. Cell proliferation was measured by a real-time cell analyzer (xCELLigence) and BrdU incorporation. Cell motility was monitored by live cell imaging. Cytotoxicity and cell viability were analyzed by Sytox green, Caspase-3 and Water Soluble Tetrazolium Salt-1 (WST-1) assays. Gene expression of fibrosis markers was determined by quantitative reverse transcription PCR (RT-qPCR). The mammalian target of rapamycin (mTOR) signaling was analyzed by Western blotting and type I collagen protein expression additionally by immunofluorescence microscopy. Pirfenidone dose-dependently inhibited p-hIF proliferation and motility, without inducing cell death. Pirfenidone suppressed mRNA levels of genes that contribute to extracellular matrix production, as well as basal and TGF-beta 1-induced collagen I protein production, which was associated with inhibition of the rapamycin-sensitive mTOR/p70S6K pathway in p-hIFs. Thus, pirfenidone inhibits the proliferation of intestinal fibroblasts and suppresses collagen I production through the TGF-beta 1/mTOR/p70S6K signaling pathway, which might be a novel and safe anti-fibrotic strategy to treat intestinal fibrosis