Studying Algebraic Structures Using Prover9 and Mace4

In this chapter we present a case study, drawn from our research work, on the application of a fully automated theorem prover together with an automatic counter-example generator in the investigation of a class of algebraic structures. We will see that these tools, when combined with human insight and traditional algebraic methods, help us to explore the problem space quickly and effectively. The counter-example generator rapidly rules out many false conjectures, while the theorem prover is often much more efficient than a human being at verifying algebraic identities. The specific tools in our case study are Prover9 and Mace4; the algebraic structures are generalisations of Heyting algebras known as hoops. We will see how this approach helped us to discover new theorems and to find new or improved proofs of known results. We also make some suggestions for how one might deploy these tools to supplement a more conventional approach to teaching algebra.Comment: 21 pages, to appear as Chapter 5 in "Proof Technology in Mathematics Research and Teaching", Mathematics Education in the Digital Era 14, edited by G. Hanna et al. (eds.), published by Springe

Title: will be set by the publisher Editors: will be set by the publisher EAS Publications Series, Vol.?, 2009 THE BEST SITE ON EARTH?

Abstract. We compare the merits of potential observatory sites on the Antarctic Plateau, in regard to the boundary layer, cloud cover, free atmosphere seeing, aurorae, airglow, and precipitable water vapour. We find that (a) all Antarctic sites are likely compromised for optical work by airglow and aurorae; (b) Dome A is the best existing site in almost all respects; (c) there is an even better site (‘Ridge A’) 150kms SW of Dome A; (d) Dome F is a remarkably good site except for aurorae; (e) Dome C probably has the least cloud cover of any of the sites, and might be able to use a predicted ‘OH hole ’ in the Spring. The Antarctic plateau probably contains the best astronomical sites on Earth, but none of the existing bases were situated with astronomy in mind. In Saunders et al.(2009), we use published data and models, and unpublished meteorological and other information, to try to compare the merits of the potential sites. Here, we summarise only the new findings and conclusions. We include boundary layer thickness, cloud cover, auroral emission, airglow, precipitable water vapour, an

Pathways and Management of Phosphorus in urban areas

Due to the finite nature of mineral phosphorus reserves, effective management of anthropogenic phosphorus flows is currently under investigation by the international research community. This article emphasizes the importance of urban phosphorus flows, which are often marginalized due to the greater magnitude of agricultural phosphorus flows. A study on phosphorus flows in Gothenburg, Sweden, points out the potential role of solid waste in nutrient management, as the amounts of phosphorus in solid waste and in wastewater were found to be equal. Importation of food commodities accounts for 50% of the total inflow of phosphorus, and food waste is a major contributor of phosphorus to solid waste. The results suggest that solid waste incineration residues represent a large underestimated sink of phosphorus. Focusing on wastewater as the sole source of recovered phosphorus is not sufficient. The Swedish national goal on phosphorus recycling, which is limited to sewage sludge, targets only a part of the total phosphorus flow that can potentially be recovered. In contrast to previous studies, agricultural flows in Gothenburg were marginal compared to flows related to the urban waste management infrastructure. We emphasize the need for debate on preferable routes for disposal of waste with a high phosphorus content. Both recovery potential and usefulness of the recovered product for agricultural purposes have to be considered. Impacts of five waste management strategies on phosphorus flows were evaluated: incineration of all the waste, comprehensive food waste separation, installation of kitchen grinders, urine diversion, and separation of blackwater and food waste

Bayesian inference reveals positive but subtle effects of experimental fishery closures on marine predator demographics

Global forage-fish landings are increasing, with potentially grave consequences for marine ecosystems. Predators of forage fish may be influenced by this harvest, but the nature of these effects is contentious. Experimental fishery manipulations offer the best solution to quantify population-level impacts, but are rare. We used Bayesian inference to examine changes in chick survival, body condition and population growth rate of endangered African penguins Spheniscus demersus in response to 8 years of alternating time-area closures around two pairs of colonies. Our results demonstrate that fishing closures improved chick survival and condition, after controlling for changing prey availability. However, this effect was inconsistent across sites and years, highlighting the difficultly of assessing management interventions in marine ecosystems. Nevertheless, modelled increases in population growth rates exceeded 1% at one colony; i.e. the threshold considered biologically meaningful by fisheries management in South Africa. Fishing closures evidently can improve the population trend of a forage-fish-dependent predator-we therefore recommend they continue in South Africa and support their application elsewhere. However, detecting demographic gains for mobile marine predators from small no-take zones requires experimental time frames and scales that will often exceed those desired by decision makers

Application of high-dimensional fuzzy <i>k</i>-means cluster analysis to CALIOP/CALIPSO version 4.1 cloud–aerosol discrimination

This study applies fuzzy k-means (FKM) cluster analyses to a subset of the parameters reported in the CALIPSO lidar level 2 data products in order to classify the layers detected as either clouds or aerosols. The results obtained are used to assess the reliability of the cloud–aerosol discrimination (CAD) scores reported in the version 4.1 release of the CALIPSO data products. FKM is an unsupervised learning algorithm, whereas the CALIPSO operational CAD algorithm (COCA) takes a highly supervised approach. Despite these substantial computational and architectural differences, our statistical analyses show that the FKM classifications agree with the COCA classifications for more than 94&thinsp;% of the cases in the troposphere. This high degree of similarity is achieved because the lidar-measured signatures of the majority of the clouds and the aerosols are naturally distinct, and hence objective methods can independently and effectively separate the two classes in most cases. Classification differences most often occur in complex scenes (e.g., evaporating water cloud filaments embedded in dense aerosol) or when observing diffuse features that occur only intermittently (e.g., volcanic ash in the tropical tropopause layer). The two methods examined in this study establish overall classification correctness boundaries due to their differing algorithm uncertainties. In addition to comparing the outputs from the two algorithms, analysis of sampling, data training, performance measurements, fuzzy linear discriminants, defuzzification, error propagation, and key parameters in feature type discrimination with the FKM method are further discussed in order to better understand the utility and limits of the application of clustering algorithms to space lidar measurements. In general, we find that both FKM and COCA classification uncertainties are only minimally affected by noise in the CALIPSO measurements, though both algorithms can be challenged by especially complex scenes containing mixtures of discrete layer types. Our analysis results show that attenuated backscatter and color ratio are the driving factors that separate water clouds from aerosols; backscatter intensity, depolarization, and mid-layer altitude are most useful in discriminating between aerosols and ice clouds; and the joint distribution of backscatter intensity and depolarization ratio is critically important for distinguishing ice clouds from water clouds.</p

The status and conservation of Cape Gannets Morus capensis

This is the author accepted manuscript. The final version is available from Taylor & Francis via the DOI in this recordThe Cape Gannet Morus capensis is one of several seabird species that are endemic to the Benguela upwelling ecosystem (BUS), whose populations recently decreased leading to unfavourable Red List classifications. Application of JARA, a Bayesian state-space tool for IUCN Red List assessment, to updated information on areas occupied by and nest densities of breeding Cape Gannets at their six colonies suggested the species should be classified as Vulnerable. However, the rate of decrease of Cape Gannets in their most recent generation exceeded that of the previous generation, primarily as a result of large decreases at Bird Island, Lambert’s Bay, and Malgas Island off South Africa’s west coast. Since the 1960s, there has been an ongoing redistribution of the species from northwest to southeast so that c. 70% of the species now occurs at Bird Island, Algoa Bay, on the eastern border of the BUS. Recruitment rather than adult survival may be limiting the present population, although information on demographic parameters and mortality in fisheries is lacking for colonies in the northern BUS. Major present threats to the species include a substantially decreased availability of their preferred prey in the west, heavy mortality of eggs, chicks and fledglings at and around colonies inflicted by Cape Fur Seals Arctocephalus pusillus and other seabirds, substantial disturbance at colonies caused by Cape Fur Seals attacking adults ashore, oiling and disease

A method for finding new sets of axioms for classes of semigroups

We introduce a general technique for finding sets of axioms for a given class of semigroups. To illustrate the technique, we provide new sets of defining axioms for groups of exponent n, bands, and semilattices

Bounding global aerosol radiative forcing of climate change

Aerosols interact with radiation and clouds. Substantial progress made over the past 40 years in observing, understanding, and modeling these processes helped quantify the imbalance in the Earth's radiation budget caused by anthropogenic aerosols, called aerosol radiative forcing, but uncertainties remain large. This review provides a new range of aerosol radiative forcing over the industrial era based on multiple, traceable, and arguable lines of evidence, including modeling approaches, theoretical considerations, and observations. Improved understanding of aerosol absorption and the causes of trends in surface radiative fluxes constrain the forcing from aerosol-radiation interactions. A robust theoretical foundation and convincing evidence constrain the forcing caused by aerosol-driven increases in liquid cloud droplet number concentration. However, the influence of anthropogenic aerosols on cloud liquid water content and cloud fraction is less clear, and the influence on mixed-phase and ice clouds remains poorly constrained. Observed changes in surface temperature and radiative fluxes provide additional constraints. These multiple lines of evidence lead to a 68% confidence interval for the total aerosol effective radiative forcing of -1.6 to -0.6 W m−2, or -2.0 to -0.4 W m−2 with a 90% likelihood. Those intervals are of similar width to the last Intergovernmental Panel on Climate Change assessment but shifted toward more negative values. The uncertainty will narrow in the future by continuing to critically combine multiple lines of evidence, especially those addressing industrial-era changes in aerosol sources and aerosol effects on liquid cloud amount and on ice clouds

The Importance of Equity Finance for R&D Activity – Are There Differences Between Young and Old Companies?

This paper analyzes the importance of equity finance for the R&D activity of small and medium-sized enterprises. We use information on almost 6000 German SMEs from a company survey. Using the intensity of banking competition at the district level as instrument to control for endogeneity, we find that a higher equity ratio is conducive to more R&D for young but not for old companies. Equity may be a constraining factor for young companies which have to rely on the original equity investment of their owners since they have not yet accumulated retained earnings and can relay less on outside financing. The positive influence is found for R&D intensity but not for the decision whether to perform R&D. Equity financing is therefore especially important for the most innovative, young companies