<jats:p>This paper presents a spectral calculus for computing the spectra of causal Lorentz invariant Borel complex measures on Minkowski space, thereby enabling one to compute their densities with respect to Lebesque measure. The spectra of certain elementary convolutions involving Feynman propagators of scalar particles are computed. It is proved that the convolution of arbitrary causal Lorentz invariant Borel complex measures exists and the product of such measures exists in a wide class of cases. Techniques for their computation in terms of their spectral representation are presented.</jats:p>

<jats:p>Accurate air quality modelling is an essential tool, both for strategic assessment (regulation development for emission controls) and for short-term forecasting (enabling warnings to be issued to protect vulnerable members of society when the pollution levels are predicted to be high). Model intercomparison studies are a valuable support to this work, being useful for identifying any issues with air quality models, and benchmarking their performance against international standards, thereby increasing confidence in their predictions. This paper presents the results of a comparison study of six chemical transport models which have been used to simulate short-term hourly to 24 hourly concentrations of fine particulate matter less than and equal to 2.5 µm in diameter (PM2.5) and ozone (O3) for Sydney, Australia. Model performance was evaluated by comparison to air quality measurements made at 16 locations for O3 and 5 locations for PM2.5, during three time periods that coincided with major atmospheric composition measurement campaigns in the region. These major campaigns included daytime measurements of PM2.5 composition, and so model performance for particulate sulfate (SO42−), nitrate (NO3−), ammonium (NH4+) and elemental carbon (EC) was evaluated at one site per modelling period. Domain-wide performance of the models for hourly O3 was good, with models meeting benchmark criteria and reproducing the observed O3 production regime (based on the O3/NOx indicator) at 80% or more of the sites. Nevertheless, model performance was worse at high (and low) O3 percentiles. Domain-wide model performance for 24 h average PM2.5 was more variable, with a general tendency for the models to under-predict PM2.5 concentrations during the summer and over-predict PM2.5 concentrations in the autumn. The modelling intercomparison exercise has led to improvements in the implementation of these models for Sydney and has increased confidence in their skill at reproducing observed atmospheric composition.</jats:p>

<jats:p>In this paper, we investigate how systemic errors due to random sampling impact on automated algorithm selection for bound-constrained, single-objective, continuous black-box optimization. We construct a machine learning-based algorithm selector, which uses exploratory landscape analysis features as inputs. We test the accuracy of the recommendations experimentally using resampling techniques and the hold-one-instance-out and hold-one-problem-out validation methods. The results demonstrate that the selector remains accurate even with sampling noise, although not without trade-offs.</jats:p>

We propose a new formulation of Hall polynomials in terms of honeycombs, which were previously introduced in the context of the Littlewood–Richardson rule. We prove a Pieri rule and associativity for our honeycomb formula, thus showing equality with Hall polynomials. Our proofs are linear algebraic in nature, extending nontrivially the corresponding bijective results for ordinary Littlewood–Richardson coefficients

Vibrational modes of higher order in micromachined resonators exhibit low damping in liquid environments, which facilitates accurate sensing even in highly viscous liquids. A steady increment in mode order, however, results in sound dissipation effects at a critical mode number n , which drastically increases damping in the system. Basic understanding in the emerging of sound dissipation in micromachined resonators is therefore of utmost importance, when an application of higher mode orders is targeted. For that reason, we experimentally investigated in this paper the appearance of sound dissipation in higher order non-conventional vibrational modes in MEMS plate resonators in liquids. The results are compared to those of an analytical model and of finite element method analyses. Micromechanical piezoelectric resonators were fabricated and characterized in sample fluids with a dynamic viscosity μ ranging from 1 to 5 mPa s and density values ρ ranging from 0.774 up to 0.835 kg l . Quality factors up to 333 are obtained for the eighth mode order in model solution with a dynamic viscosity of 1 mPa s. By monitoring the resonance and damping characteristics as a function of mode order, sound dissipation effects occur, observed by the detection of increased damping, starting at mode number n = 8, which is in good agreement to the predictions of an analytical model and to finite element method simulations. At the critical mode number n , a reduction in quality factor up to 50% is measured. The results show a direct correlation of n and the density of the fluid, which agrees to theory. The lowest value of 8 for n is obtained in a sample liquid with the lowest density value of 0.774 kg l , followed by n = 9 in a sample liquid with ρ = 0.782 kg l and n = 10 in a sample liquid with ρ = 0.835 kg l . These findings are of particular interest for sensing applications in low dense liquids, as sound dissipation effects emerge even at lower mode numbers. crit fluid fluid crit crit crit crit fluid crit fluid -1 -1 -1 -1

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>Entanglement entropy of quantum fields in gravitational settings is a topic of growing importance. This entropy of entanglement is conventionally computed relative to Cauchy hypersurfaces where it is possible via a partial tracing to associate a reduced density matrix to the spacelike region of interest. In recent years Sorkin has proposed an alternative, manifestly covariant, formulation of entropy in terms of the spacetime two-point correlation function. This formulation, developed for a Gaussian scalar field theory, is explicitly spacetime in nature and evades some of the possible non-covariance issues faced by the conventional formulation. In this paper we take the first steps towards extending Sorkin’s entropy to non-Gaussian theories where Wick’s theorem no longer holds and one would expect higher correlators to contribute. We consider quartic perturbations away from the Gaussian case and find that to first order in perturbation theory, the entropy formula derived by Sorkin continues to hold but with the two-point correlators replaced by their perturbation-corrected counterparts. We then show that our results continue to hold for arbitrary perturbations (of both bosonic and fermionic theories). This is a non-trivial and, to our knowledge, novel result. Furthermore we also derive closed-form formulas of the entanglement entropy for arbitrary perturbations at first and second order. Our work also suggests avenues for further extensions to generic interacting theories.</jats:p>

<jats:p>Figure 5b of the paper [1] contained a misinterpretation in the comparison between the reported new ATLAS measurement of the process <jats:italic>pp → Xp</jats:italic> and previously published CMS data [2]. The ATLAS measurement corresponds to cases where either proton dissociates.</jats:p>

<jats:p>Two additions impacting tables 3 and 4 in ref. [1] are presented in the following. No significant impact is found for other results or figures in ref. [1].</jats:p>