Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration

We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type $\operatorname{SL}_n$ and $\operatorname{PGL}_n$. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore we prove for $d$ coprime to $n$, that the number of rank $n$ Higgs bundles of degree $d$ over a fixed curve defined over a finite field, is independent of $d$. This proves a conjecture by Mozgovoy--Schiffman in the coprime case.Comment: Various part of the article have been revise

Arithmetic and metric aspects of open de Rham spaces

In this paper we determine the motivic class---in particular, the weight polynomial and conjecturally the Poincar\'e polynomial---of the open de Rham space, defined and studied by Boalch, of certain moduli of irregular meromorphic connections on the trivial bundle on $\mathbb{P}^1$. The computation is by motivic Fourier transform. We show that the result satisfies the purity conjecture, that is, it agrees with the pure part of the conjectured mixed Hodge polynomial of the corresponding wild character variety. We also identify the open de Rham spaces with quiver varieties with multiplicities of Yamakawa and Geiss--Leclerc--Schr\"oer. We finish with constructing natural complete hyperk\"ahler metrics on them, which in the $4$-dimensional cases are expected to be of type ALF.Comment: 69 page

Correction of high amounts of astigmatism through orthokeratology. A case report

AbstractThe purpose of this case report is to introduce a method for a successful treatment of high astigmatism with a new orthokeratology design, called FOKX (Falco Kontaktlinsen, Switzerland). This novel toric orthokeratology contact lens design, the fitting approach and the performance of FOKX lenses will be illustrated in the form of a case report. Correcting astigmatism with orthokeratology offers a new perspective for all patients suffering astigmatism

Evaluation der Doppelseite Wissen in 20 Minuten : Wahrnehmung von Wissenschaftskommunikation bei Jugendlichen

SchlussberichtDas IAM führte an der Professur Journalistik für die Stiftung Mercator Schweiz und die Gebert Rüf Stiftung eine Evaluation der Wissensseiten in 20 Minuten durch. Bei den Wissensseiten handelt sich um Doppelseiten, die jeden Freitag in 20 Minuten publiziert werden und bezwecken, die Wissenschaft näher an die Jugendlichen zu bringen. Die Seiten werden von den beiden Stiftungen finanziert und von scitec media produziert. Im Rahmen der Evaluation wurde eine Inhaltsananlyse, Interviews und eine Fokusgruppe durchgeführt zur Doppelseite Wissen, deren Inhalte, Rezeption und Akzeptanz und zu scientainment generell

Geometric stabilisation via p-adic integration

In this article we give a new proof of Ng\^o's Geometric Stabilisation Theorem, which implies the Fundamental Lemma. This is a statement which relates the cohomology of Hitchin fibres for a quasi-split reductive group scheme $G$ to the cohomology of Hitchin fibres for the endoscopy groups $H_{\kappa}$. Our proof avoids the Decomposition and Support Theorem, instead the argument is based on results for $p$-adic integration on coarse moduli spaces of Deligne-Mumford stacks. Along the way we establish a description of the inertia stack of the (anisotropic) moduli stack of $G$-Higgs bundles in terms of endoscopic data, and extend duality for generic Hitchin fibres of Langlands dual group schemes to the quasi-split case.Comment: 49 page

Investigation of ventricular cerebrospinal fluid flow phase differences between the foramina of Monro and the aqueduct of Sylvius

In this paper, phase contrast magnetic resonance flow measurements of the foramina of Monro and the aqueduct of Sylvius of seven healthy volunteers are presented. Peak volume flow rates are of the order of 150 mm3/s for the aqueduct of Sylvius and for the foramina of Monro. The temporal shift between these volume flows is analyzed with a high-resolution cross-correlation scheme which reveals high subject-specific phase differences. Repeated measurements show the invariability of the phase differences over time for each volunteer. The phase differences as a fraction of one period range from -0.0537 to 0.0820. A mathematical model of the pressure dynamics is presented. The model features one lumped compartment per ventricle. The driving force of the cerebrospinal fluid is modeled through pulsating choroid plexus. The model includes variations of the distribution of the choroid plexus between the ventricles. The proposed model is able to reproduce the measured phase differences with a very small (5%) variation of the distribution of the choroid plexus between the ventricles and, therefore, supports the theory that the choroid plexus drives the cerebrospinal fluid motio

NanoPET imaging of [18F]fluoromisonidazole uptake in experimental mouse tumours

Purpose: The purpose of this study was to assess the potential and utility of ultra-high-resolution hypoxia imaging in various murine tumour models using the established hypoxia PET tracer [18F]fluoromisonidazole ([18F]FMISO). Methods: [18F]FMISO PET imaging was performed with the dedicated small-animal PET scanner NanoPET (Oxford Positron Systems) and ten different human tumour xenografts in nude mice as well as B16 melanoma tumours in syngeneic Balb/c mice. For comparison, [18F]fluorodeoxyglucose ([18F]FDG) PET scans were also performed in the mice bearing human tumour xenografts. Results: In 10 out of 11 experimental tumour models, [18F]FMISO PET imaging allowed clear-cut visualisation of the tumours. Inter- and intratumoural heterogeneity of tracer uptake was evident. In addition to average TMRR (tumour-to-muscle retention ratio including all voxels in a volume of interest (VOI)), the parameters TMRR75% and TMRR5 (tumour-to-muscle retention ratio including voxels of 75% or more of the maximum radioactivity in a VOI and the five hottest pixels, respectively) also served as measures for quantifying the heterogeneous [18F]FMISO uptake in the tumours. The variability observed in [18F]FMISO uptake was related neither to tumour size nor to the injected mass of the radiotracer. The pattern of normoxic and hypoxic regions within the human tumour xenografts, however, correlated with glucose metabolism as revealed by comparison of [18F]FDG and [18F]FMISO images. Conclusion: This study demonstrates the feasibility and utility of [18F]FMISO for imaging murine tumour models using NanoPE

LCD vs. E-ink: An Analysis of the Reading Behavior

Electronic books (e-book) are an interesting option compared to classic paper books. Most e-reading devices of the first generation were based on e-ink technology. With the appearance of the Apple iPad on the market, TFT-LCDs became important in the field of e-reading. Both technologies have advantages and disadvantages but the question remains whether one or the other technology is better for reading. In the present study we analyzed and compared reading behavior when reading on e-inkreader (e-ink displays) and on tablets (TFT-LCDs) as measured by eye-tracking. The results suggest that the reading behavior on tablets is indeed very similar to the reading behavior on e-ink-reader. Participants showed no difference in fixation duration. Significant differences in reading speed and in the proportion of regressive saccades suggest that tablets, under special artificial light conditions, may even provide better legibility

High sugar intake exacerbates cardiac reperfusion injury in perinatal taurine depleted adult rats

Perinatal taurine depletion and high sugar diets blunted baroreflex function and heightens sympathetic nerve activity in adult rats. Cardiac ischemia/reperfusion also produces these disorders and taurine treatment appears to improve these effects. This study tests the hypothesis that perinatal taurine exposure predisposes recovery from reperfusion injury in rats on either a basal or high sugar diet. Female Sprague-Dawley rats were fed normal rat chow with 3% beta-alanine (taurine depletion, TD), 3% taurine (taurine supplementation, TS) or water alone (control, C) from conception to weaning. Male offspring were fed normal rat chow and water containing 5% glucose (G) or water alone (W) throughout the experiment. At 7-8 weeks of age, all rats were anesthetized and their trachea clamped until cardiac arrest occurred and mean arterial pressure fell below 60 mm Hg. The clamp was immediately released and cardiopulmonary resuscitation was performed with cardiac function returning within 4 min. Twenty-four hours later, arterial pressure, heart rate, and baroreflex function were measured in conscious and one day later in anesthetized conditions. Basic blood chemistry and circulating markers of cardiac injury were also measured. Baroreflex sensitivity was depressed moderately in CG and TDW, and severely in TDG. TSW displayed increased baroreflex and high sugar intake returned it to CW. Sympathetic nerve activity increased and parasympathetic decreased in TDW but not TSW and these effects were exacerbated sharply in TDG and slightly in TSG. Arterial pressure and heart rate increased in all groups but to a lesser degree in TDG. Plasma aspartate aminotransferase increased in all groups except TSW, but the increase was nearly 3X greater in TDG vs. any other group. Creatine kinase-MB increased in all groups except TSG and was far greater in TD than other groups. Troponin-T and brain natriuretic peptide were greatly increased in TDG compared to all other groups. Thus, perinatal taurine depletion increases injury from cardiac ischemia/reperfusion, and in adult rats on a high sugar diet, these effects are greatly exacerbated

Adult renal function is modified by perinatal taurine status in conscious male rats

Perinatal taurine exposure influences renal function in adult female offspring. This study tests the hypothesis that prenatal rather than postnatal taurine exposure alters renal function in adult conscious male rats. Female Sprague Dawley rats were fed normal rat chow and tap water alone (Control), tap water containing 3% β-alanine (taurine depletion, TD) or tap water containing 3% taurine (taurine supplementation, TS) either from conception until delivery (fetal period; TDF or TSF) or from delivery until weaning (lactation period; TDL or TSL). After weaning, male offspring were fed with the normal rat chow and tap water ad libitum. At 7-8 weeks of age, renal function was studied in conscious, restrained rats. Mean arterial pressures were slightly higher in rats receiving taurine supplementation during either the fetal or lactation periods (compared to Control and TD groups), but heart rates were not significantly different among groups. Effective renal blood flows were lower in TDF, TDL, and TSF rats (TDF 4.6±0.8 ml/min/g kidney weight (KW), TDL 3.0±0.9 ml/min/g KW, and TSF 2.8±0.7 ml/min/g KW) than in TSL (7.7±0.9 ml/min/g KW) or Control rats (7.3±1.6 ml/min/g KW). These differences were correlated with significant increases in renal vascular resistance in TDF, TDL, and TSF groups compared to TSL and Control rats. In contrast, glomerular filtration rates were not significantly different among groups. Although basal water and sodium excretion were slightly lower in TDL and TSF rats compared to other groups, their diuretic and natriuretic responses to an acute saline load were not different from Control. The present data indicate that in adult male rats, both perinatal supplementation and depletion of taurine can alter renal hemodynamics, and these effects are differentially time-dependent