On the n-th row of the graded Betti table of an n-dimensional toric variety

We prove an explicit formula for the first non-zero entry in the n-th row of the graded Betti table of an n-dimensional projective toric variety associated to a normal polytope with at least one interior lattice point. This applies to Veronese embeddings of projective space where we prove a special case of a conjecture of Ein and Lazarsfeld. We also prove an explicit formula for the entire n-th row when the interior of the polytope is one-dimensional. All results are valid over an arbitrary field k.Comment: 20 pages, 9 figure

Revealing the correlation between real-space structure and chiral magnetic order at the atomic scale

We image simultaneously the geometric, electronic and magnetic structure of a buckled iron bilayer film that exhibits chiral magnetic order. We achieve this by combining spin-polarized scanning tunneling microscopy and magnetic exchange force microscopy (SPEX), to independently characterize the geometric as well as the electronic and magnetic structure of non-flat surfaces. This new SPEX imaging technique reveals the geometric height corrugation of the reconstruction lines resulting from strong strain relaxation in the bilayer, enabling the decomposition of the real-space from the eletronic structure at the atomic level, and the correlation with the resultant spin spiral ground state. By additionally utilizing adatom manipulation, we reveal the chiral magnetic ground state of portions of the unit cell that were not previously imaged with SP-STM alone. Using density functional theory (DFT), we investigate the structural and electronic properties of the reconstructed bilayer and identify the favorable stoichiometry regime in agreement with our experimental result

Doping effects on charge density instability in non-centrosymmetric PbxTaSe2

We report on the investigation of vibrational and electronic properties of the Pb doped dichalcogenide PbxTaSe2 using Raman scattering experiments. We observe a marked variation of the main vibrational modes with Pb concentration x. The concentration dependence of the vibrational modes resembles the dependence of the vibrational modes in TaSe2 on the number of crystallographic layers along the c axis direction [1]. The temperature and polarization dependence of Raman spectra of PbxTaSe2 revealed additional broad modes in the low frequency regime which are discussed in context of remnant charge density wave, induced disorder, or PbSe phase formed in the interface of Pb and TaSe2 layers.Comment: 14 page

Electronic energy transfer ionization in naphthalene–CO 2 clusters reveals excited states of dry ice

Electronic energy relaxation and transfer shapes the photochemistry in molecules and materials that are exposed to UV radiation in areas ranging from astrochemistry to biology. The interaction between CO2 and polycyclic aromatic hydrocarbons (PAHs) specifically, is of paramount interest in astrochemically relevant ices, the transition to renewable energy and the development of green chemistry. We investigate the vacuum UV excitation of the naphthalene-CO2 complex and observe excited states of CO2 through a newly identified molecular electronic energy transfer ionization mechanism. We evaluate the spectral development upon cluster growth with time-dependent density functional theory and show that the photoionization spectrum of naphthalene-CO2 closely resembles the photon-stimulated desorption spectrum of CO2 ice. The molecular electronic energy transfer ionization mechanism may affect the energy redistribution and charge balance in the interstellar medium significantly and therefore we discuss its implications for astrochemical models

Sex-specific-differences in cardiovascular risk in type-1-diabetes : a cross sectional study

Background: Little is known about the impact of sex-specific differences in the management of type 1 diabetes (T1DM). Thus, we evaluated the influence of gender on risk factors, complications, clinical care and adherence in patients with T1DM. Methods: In a cross-sectional study, sex-specific disparities in glycaemic control, cardiovascular risk factors, diabetic complications, concomitant medication use and adherence to treatment recommendations were evaluated in 225 consecutive patients (45.3% women) who were comparable with respect to age, diabetes duration, and body mass index. Results: Although women with T1DM had a higher total cholesterol than men, triglycerides were higher in obese men and males with HbA1c>7% than in their female counterparts. No sex differences were observed in glycaemic control and in micro- or macrovascular complications. However, the subgroup analysis showed that nephropathy was more common in obese men, hyperlipidaemic women and all hypertensive patients, whereas peripheral neuropathy was more common in hyperlipidaemic women. Retinopathy was found more frequently in women with HbA1c>7%, obese men and in both sexes with a long duration of diabetes. The multivariate analysis revealed that microvascular complications were associated with the duration of disease and BMI in both sexes and with hyperlipidaemia in males. The overall adherence to interventions according to the guidelines was higher in men than in women. This adherence was concerned particularly with co-medication in patients diagnosed with hypertension, aspirin prescription in elderly patients and the achievement of target lipid levels following the prescription of statins. Conclusions: Our data showed sex differences in lipids and overweight in patients with T1DM. Although glycaemic control and the frequency of diabetic complications were comparable between the sexes, the overall adherence to guidelines, particularly with respect to the prescription of statins and aspirin, was lower in women than in men

Photon-counting detector computed tomography in cardiac imaging

Photon-counting detector computed tomography (PCD-CT) has emerged as a revolutionary technology in CT imaging. PCD-CT offers significant advancements over conventional energy-integrating detector CT, including increased spatial resolution, artefact reduction and inherent spectral imaging capabilities. In cardiac imaging, PCD-CT can offer a more accurate assessment of coronary artery disease, plaque characterisation and the in-stent lumen. Additionally, it might improve the visualisation of myocardial fibrosis through qualitative late enhancement imaging and quantitative extracellular volume measurements. The use of PCD-CT in cardiac imaging holds significant potential, positioning itself as a valuable modality that could serve as a one-stop-shop by integrating both angiography and tissue characterisation into a single examination. Despite its potential, large-scale clinical trials, standardisation of protocols and cost-effectiveness considerations are required for its broader integration into clinical practice. This narrative review provides an overview of the current literature on PCD-CT regarding the possibilities and limitations of cardiac imaging.</p