A Note on Derivation of Minimal set of Compatibility Classes for Covering

This paper briefly describes the concept of compatibility relation defined on a finite set  and thereby, that of maximal compatibility classes. For a given compatibility relation defined on , not all the maximal compatibles are needed to ensure covering  for . A technique to derive a minimal set of maximal compatibility classes which covers  is proposed and some results obtained. Keywords: Compatibility relation, Maximal compatibility classes, Minimal covering

Observational and genetic associations between cardiorespiratory fitness and cancer: a UK Biobank and international consortia study

Background The association of fitness with cancer risk is not clear. Methods We used Cox proportional hazards models to estimate hazard ratios (HRs) and 95% confidence intervals (CIs) for risk of lung, colorectal, endometrial, breast, and prostate cancer in a subset of UK Biobank participants who completed a submaximal fitness test in 2009-12 (N = 72,572). We also investigated relationships using two-sample Mendelian randomisation (MR), odds ratios (ORs) were estimated using the inverse-variance weighted method. Results After a median of 11 years of follow-up, 4290 cancers of interest were diagnosed. A 3.5 ml O2⋅min−1⋅kg−1 total-body mass increase in fitness (equivalent to 1 metabolic equivalent of task (MET), approximately 0.5 standard deviation (SD)) was associated with lower risks of endometrial (HR = 0.81, 95% CI: 0.73–0.89), colorectal (0.94, 0.90–0.99), and breast cancer (0.96, 0.92–0.99). In MR analyses, a 0.5 SD increase in genetically predicted O2⋅min−1⋅kg−1 fat-free mass was associated with a lower risk of breast cancer (OR = 0.92, 95% CI: 0.86–0.98). After adjusting for adiposity, both the observational and genetic associations were attenuated. Discussion Higher fitness levels may reduce risks of endometrial, colorectal, and breast cancer, though relationships with adiposity are complex and may mediate these relationships. Increasing fitness, including via changes in body composition, may be an effective strategy for cancer prevention

Estimating the Overall Impact of a Change in Agricultural Practices on Atmospheric CO{sub 2}

One option for sequestering carbon in the terrestrial biosphere is to increase the carbon (C) stocks in agricultural soils. There is now an extensive literature on the amount of C that has been lost from soils as a consequence of humans disturbing natural ecosystems, and of the amount of C that might be returned to soils with improved management practices. Improvements in management practices could include efficient use of fertilizers and irrigation water, use of crop rotations, and changing from conventional tillage (CT) to conservation tillage (or, more specifically, to no-till (NT)). The Intergovernmental Panel on Climate Change (IPCC) has estimated that 55 x 10{sup 9} Mg of soil C have been lost, globally, largely as a result of cultivating former grasslands, forests, and wetlands. The IPCC estimated further that 22-29 x 10{sup 9} Mg of C could be returned to existing, world, agricultural soils under improved management regimes. Historical losses of soil organic C (SOC) in the US, due to cultivation, have been estimated to be 1.3 {+-} 0.3 x 10{sup 9} Mg (Kern and Johnson 1993). Kern and Johnson projected that by increasing NT practice in the US from 27% in 1990 to 76%, a total of 0.4 {+-} 0.1 x 10{sup 9} Mg C could be sequestered in the soil during the interval 1990-2020. These studies tend to focus on increasing the C stocks in soils rather than on the overall effect that changes in agricultural practice would have on C stocks in the atmosphere. Changing agricultural practice can impact net CO{sub 2} emissions to the atmosphere in three fundamental ways: (1) it can lead to an increase in the C held in agricultural soils, (2) it can lead to a change in emissions of CO{sub 2} from fossil fuel burning, and (3) it can change agricultural productivity, and hence the amount of cultivated land needed to meet the demand for agricultural products. Changing agricultural practice can also affect the net emissions of other greenhouse gases, such as N{sub 2}O emissions associated with nitrogen (N) fertilizer application. This study focuses on a comprehensive analysis of the first two factors, including N{sub 2}O emissions, and inquires into the balance between C sequestered and the change in C equivalent (C{sub eq}) emissions associated with a change in agricultural practices. N{sub 2}O emissions are converted to C equivalent emissions, based on their time-integrated effect on the global atmospheric energy balance, as suggested by the IPCC (Schimel et al. 1996)

The human carbon budget: An estimate of the spatial distribution of metabolic carbon consumption and release in the United States

Carbon dioxide is taken up by agricultural crops and released soon after during the consumption of agricultural commodities. The global net impact of this process on carbon flux to the atmosphere is negligible, but impact on the spatial distribution of carbon dioxide uptake and release across regions and continents is significant. To estimate the consumption and release of carbon by humans over the landscape, we developed a carbon budget for humans in the United States. The budget was derived from food commodity intake data for the US and from algorithms representing the metabolic processing of carbon by humans. Data on consumption, respiration, and waste of carbon by humans were distributed over the US using geospatial population data with a resolution of ~450 W 450 m. The average adult in the US contains about 21 kg C and consumes about 67 kg C year-1 which is balanced by the annual release of about 59 kg C as expired CO2, 7 kg C as feces and urine, and less than 1 kg C as flatus, sweat, and aromatic compounds. In 2000, an estimated 17.2 Tg C were consumed by the US population and 15.2 Tg C were expired to the atmosphere as CO2. Historically, carbon stock in the US human population has increased between 1790 and 2006 from 0.06 Tg to 5.37 Tg. Displacement and release of total harvested carbon per capita in the US is nearly 12% of per capita fossil fuel emissions. Humans are using, storing, and transporting carbon about the Earths surface. Inclusion of these carbon dynamics in regional carbon budgets can improve our understanding of carbon sources and sinks