A note on palindromic δ\delta-vectors for certain rational polytopes

Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart $\delta$-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact.Comment: 4 page

Few smooth d-polytopes with n lattice points

We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result

Statistical Variation in the Embodied Carbon of Concrete Mixtures

This study presents a refined calculation of the embodied carbon of concrete mixtures via life cycle assessment (LCA) with an explicit focus on three innovations. First, probability distributions that represent process-related variability in the embodied carbon of concrete are calculated using a variety of life cycle inventory data sources. Second, the traditional concrete LCA system boundary (i.e., cradle-to-gate) is expanded to incorporate and analyze estimates of in situ carbon sequestration via concrete carbonation. Third, we analyze the impact of different transportation scenarios on the utility of using fly ash to reduce the embodied carbon of concrete. We use these data to heuristically determine the breakeven transportation distance for fly ash via trucking to be 2655 km for domestic sources of fly ash. However, when fly ash is imported from international sources, reductions to embodied carbon attributed to fly ash replacement can be negligible. The calculated breakeven maritime shipping distance for fly ash equals 15,110 km&mdash;beyond which, the anticipated embodied carbon reductions due to fly ash use in concrete are compromised due to transportation. The advancements described herein enable improved scenario-based decision-making for understanding, quantifying, and reducing the embodied carbon of concrete mixtures. In addition, the results highlight the importance of accounting for international transportation of fly ash in LCAs, especially given that domestic sources of quality fly ash are expected to continue to decline and imports are expected to increase in many parts of the world over the next few decades. &nbsp;</p

Hilbert Series, Machine Learning, and Applications to Physics

We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ${\sim}1$ mean absolute error, whilst classifiers predict dimension and Gorenstein index to $>90\%$ accuracy with ${\sim}0.5\%$ standard error. Binary random forest classifiers managed to distinguish whether the underlying HS describes a complete intersection with high accuracies exceeding $95\%$. Neural networks (NNs) exhibited success identifying HS from a Gorenstein ring to the same order of accuracy, whilst generation of 'fake' HS proved trivial for NNs to distinguish from those associated to the three-dimensional Fano varieties considered

A novel method for the absolute fluorescence yield measurement by AIRFLY

One of the goals of the AIRFLY (AIR FLuorescence Yield) experiment is to measure the absolute fluorescence yield induced by electrons in air to better than 10% precision. We introduce a new technique for measurement of the absolute fluorescence yield of the 337 nm line that has the advantage of reducing the systematic uncertainty due to the detector calibration. The principle is to compare the measured fluorescence yield to a well known process - the Cerenkov emission. Preliminary measurements taken in the BFT (Beam Test Facility) in Frascati, Italy with 350 MeV electrons are presented. Beam tests in the Argonne Wakefield Accelerator at the Argonne National Laboratory, USA with 14 MeV electrons have also shown that this technique can be applied at lower energies.Comment: presented at the 5th Fluorescence Workshop, El Escorial - Madrid, Spain, 16 - 20 September 200

Temperature and Humidity Dependence of Air Fluorescence Yield measured by AIRFLY

The fluorescence detection of ultra high energy cosmic rays requires a detailed knowledge of the fluorescence light emission from nitrogen molecules over a wide range of atmospheric parameters, corresponding to altitudes typical of the cosmic ray shower development in the atmosphere. We have studied the temperature and humidity dependence of the fluorescence light spectrum excited by MeV electrons in air. Results for the 313.6 nm, 337.1 nm, 353.7 nm and 391.4 nm bands are reported in this paper. We found that the temperature and humidity dependence of the quenching process changes the fluorescence yield by a sizeable amount (up to 20%) and its effect must be included for a precise estimation of the energy of ultra high energy cosmic rays.Comment: presented at the 5th Fluorescence Workshop, El Escorial - Madrid, Spain, 16 - 20 September 2007, to appear in Nuclear Instruments and Methods

Wastewater monitoring for detection of public health markers during the COVID-19 pandemic: Near-source monitoring of schools in England over an academic year

Background Schools are high-risk settings for infectious disease transmission. Wastewater monitoring for infectious diseases has been used to identify and mitigate outbreaks in many near-source settings during the COVID-19 pandemic, including universities and hospitals but less is known about the technology when applied for school health protection. This study aimed to implement a wastewater surveillance system to detect SARS-CoV-2 and other public health markers from wastewater in schools in England. Methods A total of 855 wastewater samples were collected from 16 schools (10 primary, 5 secondary and 1 post-16 and further education) over 10 months of school term time. Wastewater was analysed for SARS-CoV-2 genomic copies of N1 and E genes by RT-qPCR. A subset of wastewater samples was sent for genomic sequencing, enabling determination of the presence of SARS-CoV-2 and emergence of variant(s) contributing to COVID-19 infections within schools. In total, >280 microbial pathogens and >1200 AMR genes were screened using RT-qPCR and metagenomics to consider the utility of these additional targets to further inform on health threats within the schools. Results We report on wastewater-based surveillance for COVID-19 within English primary, secondary and further education schools over a full academic year (October 2020 to July 2021). The highest positivity rate (80.4%) was observed in the week commencing 30th November 2020 during the emergence of the Alpha variant, indicating most schools contained people who were shedding the virus. There was high SARS-CoV-2 amplicon concentration (up to 9.2x106 GC/L) detected over the summer term (8th June - 6th July 2021) during Delta variant prevalence. The summer increase of SARS-CoV-2 in school wastewater was reflected in age-specific clinical COVID-19 cases. Alpha variant and Delta variant were identified in the wastewater by sequencing of samples collected from December to March and June to July, respectively. Lead/lag analysis between SARS-CoV-2 concentrations in school and WWTP data sets show a maximum correlation between the two-time series when school data are lagged by two weeks. Furthermore, wastewater sample enrichment coupled with metagenomic sequencing and rapid informatics enabled the detection of other clinically relevant viral and bacterial pathogens and AMR. Conclusions Passive wastewater monitoring surveillance in schools can identify cases of COVID-19. Samples can be sequenced to monitor for emerging and current variants of concern at the resolution of school catchments. Wastewater based monitoring for SARS-CoV-2 is a useful tool for SARS-CoV-2 passive surveillance and could be applied for case identification and containment, and mitigation in schools and other congregate settings with high risks of transmission. Wastewater monitoring enables public health authorities to develop targeted prevention and education programmes for hygiene measures within undertested communities across a broad range of use cases

Including adaptation and mitigation responses to climate change in a multiobjective evolutionary algorithm framework for urban water supply systems incorporating GHG emissions

Cities around the world are increasingly involved in climate action and mitigating greenhouse gas (GHG) emissions. However, in the context of responding to climate pressures in the water sector, very few studies have investigated the impacts of changing water use on GHG emissions, even though water resource adaptation often requires greater energy use. Consequently, reducing GHG emissions, and thus focusing on both mitigation and adaptation responses to climate change in planning and managing urban water supply systems, is necessary. Furthermore, the minimization of GHG emissions is likely to conflict with other objectives. Thus, applying a multiobjective evolutionary algorithm (MOEA), which can evolve an approximation of entire trade-off (Pareto) fronts of multiple objectives in a single run, would be beneficial. Consequently, the main aim of this paper is to incorporate GHG emissions into a MOEA framework to take into consideration both adaptation and mitigation responses to climate change for a city’s water supply system. The approach is applied to a case study based on Adelaide’s southern water supply system to demonstrate the framework’s practical management implications. Results indicate that trade-offs exist between GHG emissions and risk-based performance, as well as GHG emissions and economic cost. Solutions containing rainwater tanks are expensive, while GHG emissions greatly increase with increased desalinated water supply. Consequently, while desalination plants may be good adaptation options to climate change due to their climate-independence, rainwater may be a better mitigation response, albeit more expensive.F. L. Paton, H. R. Maier, and G. C. Dand