Velocity, energy and helicity of vortex knots and unknots

In this paper we determine the velocity, the energy and estimate writhe and twist helicity contributions of vortex filaments in the shape of torus knots and unknots (toroidal and poloidal coils) in a perfect fluid. Calculations are performed by numerical integration of the Biot-Savart law. Vortex complexity is parametrized by the winding number $w$, given by the ratio of the number of meridian wraps to that of the longitudinal wraps. We find that for $w<1$ vortex knots and toroidal coils move faster and carry more energy than a reference vortex ring of same size and circulation, whereas for $w>1$ knots and poloidal coils have approximately same speed and energy of the reference vortex ring. Helicity is dominated by the writhe contribution. Finally, we confirm the stabilizing effect of the Biot-Savart law for all knots and unknots tested, that are found to be structurally stable over a distance of several diameters. Our results also apply to quantized vortices in superfluid $^4$He.Comment: 17 pages, 8 figures, 2 table

Polycyclic Aromatic Hydrocarbon Size Tracers

We examine the dependence of polycyclic aromatic hydrocarbon (PAH) band intensity ratios as a function of the average number of carbon atoms and assess their effectiveness as tracers for PAH size, utilising the data, models, and tools provided by the NASA Ames PAH Infrared Spectroscopic Database. To achieve this, we used spectra from mixtures of PAHs of different ionisation fractions, following a size distribution. Our work, congruent with earlier findings, shows that band ratios that include the 3.3 ${\mu}$m PAH band provide the best PAH size tracers for small-to-intermediate sized PAHs. In addition, we find that band ratios that include the sum of the 15-20 ${\mu}$m PAH features (I$_{\Sigma_{15-20}}$) and the 6.2 or 7.7 ${\mu}$m bands also serve as good tracers for PAH size in the case of small-to-intermediate sized PAHs, for objects under a similar PAH size distribution as with the presented models. For different PAH size distributions, the application of a scaling factor to the I$_{6.2}$/I$_{\Sigma_{15-20}}$ ratio can provide estimates for the size of the small-to-intermediate PAH population within sources. Employment of the I$_{6.2}$/I$_{\Sigma_{15-20}}$ and I$_{7.7}$/I$_{\Sigma_{15-20}}$ ratios can be of particular interest for JWST observations limited only to $\sim$ 5-28 ${\mu}$m MIRI(-MRS) coverage.Comment: 8 pages, 5 figures; Accepted for publication in MNRA

Deep Learning for the Generation of Heuristics in Answer Set Programming: A Case Study of Graph Coloring

Answer Set Programming (ASP) is a well-established declarative AI formalism for knowledge representation and reasoning. ASP systems were successfully applied to both industrial and academic problems. Nonetheless, their performance can be improved by embedding domain-specific heuristics into their solving process. However, the development of domain-specific heuristics often requires both a deep knowledge of the domain at hand and a good understanding of the fundamental working principles of the ASP solvers. In this paper, we investigate the use of deep learning techniques to automatically generate domain-specific heuristics for ASP solvers targeting the well-known graph coloring problem. Empirical results show that the idea is promising: the performance of the ASP solver wasp can be improved

Pregnant women voice their concerns and birth expectations during the COVID-19 pandemic in Italy.

Background In March 2020, COVID-19 was declared to be a pandemic. While data suggests that COVID-19 is not associated with significant adverse health outcomes for pregnant women and newborns, the psychological impact on pregnant women is likely to be high. Aim The aim was to explore the psychological impact of the COVID-19 pandemic on Italian pregnant women, especially regarding concerns and birth expectations. Methods A cross-sectional online survey of pregnant women in Italy was conducted. Responses were analysed for all women and segregated into two groups depending on previous experience of pregnancy loss. Analysis of open text responses examined expectations and concerns before and after the onset of the pandemic. Findings Two hundred pregnant women responded to the first wave of the survey. Most (n = 157, 78.5%) had other children and 100 (50.0%) had a previous history of perinatal loss. ‘Joy’ was the most prevalent emotion expressed before COVID-19 (126, 63.0% before vs 34, 17.0% after; p < 0.05); fear was the most prevalent after (15, 7.5% before vs 98, 49.0% after; p < 0.05). Positive constructs were prevalent before COVID-19, while negative ones were dominant after (p < 0.05). Across the country, women were concerned about COVID-19 and a history of psychological disorders was significantly associated with higher concerns (p < 0.05). A previous pregnancy loss did not influence women’s concerns. Conclusions Women’s expectations and concerns regarding childbirth changed significantly as a result of the COVID-19 pandemic in Italy. Women with a history of psychological disorders need particular attention as they seem to experience higher levels of concern

The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra

We investigate closed ideals in the Grassmann algebra serving as bases of Lie-invariant geometric objects studied before by E. Cartan. Especially, the E. Cartan theory is enlarged for Lax integrable nonlinear dynamical systems to be treated in the frame work of the Wahlquist Estabrook prolongation structures on jet-manifolds and Cartan-Ehresmann connection theory on fibered spaces. General structure of integrable one-forms augmenting the two-forms associated with a closed ideal in the Grassmann algebra is studied in great detail. An effective Maurer-Cartan one-forms construction is suggested that is very useful for applications. As an example of application the developed Lie-invariant geometric object theory for the Burgers nonlinear dynamical system is considered having given rise to finding an explicit form of the associated Lax type representation