Minimum-weight triangulation is NP-hard

A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum-weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem is NP-hard. We use a reduction from PLANAR-1-IN-3-SAT. The correct working of the gadgets is established with computer assistance, using dynamic programming on polygonal faces, as well as the beta-skeleton heuristic to certify that certain edges belong to the minimum-weight triangulation.Comment: 45 pages (including a technical appendix of 13 pages), 28 figures. This revision contains a few improvements in the expositio

COVID-19 lockdowns highlight a risk of increasing ozone pollution in European urban areas

In March 2020, non-pharmaceutical intervention measures in the form of lockdowns were applied across Europe to urgently reduce the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus which causes the COVID-19 disease. The aggressive curtailing of the European economy had widespread impacts on the atmospheric composition, particularly for nitrogen dioxide (NO2) and ozone (O3). To investigate these changes, we analyse data from 246 ambient air pollution monitoring sites in 102 urban areas and 34 countries in Europe between February and July 2020. Counterfactual, businessas-usual air quality time series are created using machinelearning models to account for natural weather variability. Across Europe, we estimate that NO2 concentrations were 34 % and 32 % lower than expected for respective traffic and urban background locations, whereas O3 was 30 % and 21 % higher (in the same respective environments) at the point of maximum restriction on mobility. To put the 2020 changes into context, average NO2 trends since 2010 were calculated, and the changes experienced across European urban areas in 2020 was equivalent to 7.6 years of average NO2 reduction (or concentrations which might be anticipated in 2028). Despite NO2 concentrations decreasing by approximately a third, total oxidant (Ox) changed little, suggesting that the reductions in NO2 were substituted by increases in O3. The lockdown period demonstrated that the expected future reductions in NO2 in European urban areas are likely to lead to widespread increases in urban O3 pollution unless additional mitigation measures are introduced

Spatially and temporally resolved measurements of NOxfluxes by airborne eddy covariance over Greater London

Flux measurements of nitrogen oxides (NOx) were made over London using airborne eddy covariance from a low-flying aircraft. Seven low-altitude flights were conducted over Greater London, performing multiple overpasses across the city during eight days in July 2014. NOx fluxes across the Greater London region (GLR) exhibited high heterogeneity and strong diurnal variability, with central areas responsible for the highest emission rates (20-30mgm-2h-1). Other high-emission areas included the M25 orbital motorway. The complexity of London's emission characteristics makes it challenging to pinpoint single emissions sources definitively using airborne measurements. Multiple sources, including road transport and residential, commercial and industrial combustion sources, are all likely to contribute to measured fluxes. Measured flux estimates were compared to scaled National Atmospheric Emissions Inventory (NAEI) estimates, accounting for monthly, daily and hourly variability. Significant differences were found between the flux-driven emissions and the NAEI estimates across Greater London, with measured values up to 2 times higher in Central London than those predicted by the inventory. To overcome the limitations of using the national inventory to contextualise measured fluxes, we used physics-guided flux data fusion to train environmental response functions (ERFs) between measured flux and environmental drivers (meteorological and surface). The aim was to generate time-of-day emission surfaces using calculated ERF relationships for the entire GLR; 98% spatial coverage was achieved across the GLR at 400m2 spatial resolution. All flight leg projections showed substantial heterogeneity across the domain, with high emissions emanating from Central London and major road infrastructure. The diurnal emission structure of the GLR was also investigated, through ERF, with the morning rush hour distinguished from lower emissions during the early afternoon. Overall, the integration of airborne fluxes with an ERF-driven strategy enabled the first independent generation of surface NOx emissions, at high resolution using an eddy-covariance approach, for an entire city region

Sources of non-methane hydrocarbons in surface air in Delhi, India

Rapid economic growth and development have exacerbated air quality problems across India, driven by many poorly understood pollution sources and understanding their relative importance remains critical to characterising the key drivers of air pollution. A comprehensive suite of measurements of 90 non-methane hydrocarbons (NMHCs) (C2–C14), including 12 speciated monoterpenes and higher molecular weight monoaromatics, were made at an urban site in Old Delhi during the pre-monsoon (28-May to 05-Jun 2018) and post-monsoon (11 to 27-Oct 2018) seasons using dual-channel gas chromatography (DC-GC-FID) and two-dimensional gas chromatography (GC×GC-FID). Significantly higher mixing ratios of NMHCs were measured during the post-monsoon campaign, with a mean night-time enhancement of around 6. Like with NOx and CO, strong diurnal profiles were observed for all NMHCs, except isoprene, with very high NMHC mixing ratios between 35–1485 ppbv. The sum of mixing ratios of benzene, toluene, ethylbenzene and xylenes (BTEX) routinely exceeded 100 ppbv at night during the post-monsoon period, with a maximum measured mixing ratio of monoaromatic species of 370 ppbv. The mixing ratio of highly reactive monoterpenes peaked at around 6 ppbv in the post-monsoon campaign and correlated strongly with anthropogenic NMHCs, suggesting a strong non-biogenic source in Delhi. A detailed source apportionment study was conducted which included regression analysis to CO, acetylene and other NMHCs, hierarchical cluster analysis, EPA UNMIX 6.0, principal component analysis/absolute principal component scores (PCA/APCS) and comparison with NMHC ratios (benzene/toluene and i-/n-pentane) in ambient samples to liquid and solid fuels. These analyses suggested the primary source of anthropogenic NMHCs in Delhi was from traffic emissions (petrol and diesel), with average mixing ratio contributions from Unmix and PCA/APCS models of 38% from petrol, 14% from diesel and 32% from liquified petroleum gas (LPG) with a smaller contribution (16%) from solid fuel combustion. Detailed consideration of the underlying meteorology during the campaigns showed that the extreme night-time mixing ratios of NMHCs during the post-monsoon campaign were the result of emissions into a very shallow and stagnant boundary layer. The results of this study suggest that despite widespread open burning in India, traffic-related petrol and diesel emissions remain the key drivers of gas-phase urban air pollution in Delhi

Modern microwave methods in solid state inorganic materials chemistry: from fundamentals to manufacturing

No abstract available

Res Medica, Autumn 1961, Volume 3, Number 1

TABLE OF CONTENTSPERFUSION: Professor W.A. MackeyABDOMINAL CRISES 1: I.S.R. Sinclair, F.R.C.S.FIBRINOLYSIS AND OCCLUSIVE VASCULAR DISEASE: J.D. Cash, B.Sc., M.B., CH.B.RES MEDICATHE UNBORN CHILD: Professor C.S. RussellTHE USE OF CONTROLS IN THE ASSESSMENT OF CLINICAL EVIDENCE: C.V. Ruckley, M.B., CH.B."THE SLIMY MUD OF WORDS":H.C. Drysdale, M.B., CH.B.THE HARVEIAN ORATION, 1961: Dr. J.K. Slater, O.B.E., M.D.MELANCHOLIA: E.B. Ritson, M.B., CH.B

Biogenic and anthropogenic sources of isoprene and monoterpenes and their secondary organic aerosol in Delhi, India

Isoprene and monoterpene emissions to the atmosphere are generally dominated by biogenic sources. The oxidation of these compounds can lead to the production of secondary organic aerosol; however the impact of this chemistry in polluted urban settings has been poorly studied. Isoprene and monoterpenes can form secondary organic aerosol (SOA) heterogeneously via anthropogenic–biogenic interactions, resulting in the formation of organosulfate (OS) and nitrooxy-organosulfate (NOS) species. Delhi, India, is one of the most polluted cities in the world, but little is known about the emissions of biogenic volatile organic compounds (VOCs) or the sources of SOA. As part of the DELHI-FLUX project, gas-phase mixing ratios of isoprene and speciated monoterpenes were measured during pre- and post-monsoon measurement campaigns in central Delhi. Nocturnal mixing ratios of the VOCs were substantially higher during the post-monsoon (isoprene: (0.65±0.43) ppbv; limonene: (0.59±0.11) ppbv; α-pinene: (0.13±0.12) ppbv) than the pre-monsoon (isoprene: (0.13±0.18) ppbv; limonene: 0.011±0.025 (ppbv); α-pinene: 0.033±0.009) period. At night, isoprene and monoterpene concentrations correlated strongly with CO during the post-monsoon period. Filter samples of particulate matter less than 2.5 µm in diameter (PM2.5) were collected and the OS and NOS content analysed using ultra-high-performance liquid chromatography tandem mass spectrometry (UHPLC-MS2). Inorganic sulfate was shown to facilitate the formation of isoprene OS species across both campaigns. Sulfate contained within OS and NOS species was shown to contribute significantly to the sulfate signal measured via AMS. Strong nocturnal enhancements of NOS species were observed across both campaigns. The total concentration of OS and NOS species contributed an average of (2.0±0.9) % and (1.8±1.4) % to the total oxidized organic aerosol and up to a maximum of 4.2 % and 6.6 % across the pre- and post-monsoon periods, respectively. Overall, this study provides the first molecular-level measurements of SOA derived from isoprene and monoterpene in Delhi and demonstrates that both biogenic and anthropogenic sources of these compounds can be important in urban areas.</p