Priestley duality for MV-algebras and beyond

We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions

A non-commutative Priestley duality

We prove that the category of left-handed strongly distributive skew lattices with zero and proper homomorphisms is dually equivalent to a category of sheaves over local Priestley spaces. Our result thus provides a non-commutative version of classical Priestley duality for distributive lattices and generalizes the recent development of Stone duality for skew Boolean algebras. From the point of view of skew lattices, Leech showed early on that any strongly distributive skew lattice can be embedded in the skew lattice of partial functions on some set with the operations being given by restriction and so-called override. Our duality shows that there is a canonical choice for this embedding. Conversely, from the point of view of sheaves over Boolean spaces, our results show that skew lattices correspond to Priestley orders on these spaces and that skew lattice structures are naturally appropriate in any setting involving sheaves over Priestley spaces.Comment: 20 page

Profinite lambda-terms and parametricity

Combining ideas coming from Stone duality and Reynolds parametricity, we formulate in a clean and principled way a notion of profinite lambda-term which, we show, generalizes at every type the traditional notion of profinite word coming from automata theory. We start by defining the Stone space of profinite lambda-terms as a projective limit of finite sets of usual lambda-terms, considered modulo a notion of equivalence based on the finite standard model. One main contribution of the paper is to establish that, somewhat surprisingly, the resulting notion of profinite lambda-term coming from Stone duality lives in perfect harmony with the principles of Reynolds parametricity. In addition, we show that the notion of profinite lambda-term is compositional by constructing a cartesian closed category of profinite lambda-terms, and we establish that the embedding from lambda-terms modulo beta-eta-conversion to profinite lambda-terms is faithful using Statman's finite completeness theorem. Finally, we prove that the traditional Church encoding of finite words into lambda-terms can be extended to profinite words, and leads to a homeomorphism between the space of profinite words and the space of profinite lambda-terms of the corresponding Church type

Deciding Equations in the Time Warp Algebra

Join-preserving maps on the discrete time scale $\omega^+$, referred to as time warps, have been proposed as graded modalities that can be used to quantify the growth of information in the course of program execution. The set of time warps forms a simple distributive involutive residuated lattice -- called the time warp algebra -- that is equipped with residual operations relevant to potential applications. In this paper, we show that although the time warp algebra generates a variety that lacks the finite model property, it nevertheless has a decidable equational theory. We also describe an implementation of a procedure for deciding equations in this algebra, written in the OCaml programming language, that makes use of the Z3 theorem prover

Time Warps, from Algebra to Algorithms

Graded modalities have been proposed in recent work on programming languages as a general framework for refining type systems with intensional properties. In particular, continuous endomaps of the discrete time scale, or time warps, can be used to quantify the growth of information in the course of program execution. Time warps form a complete residuated lattice, with the residuals playing an important role in potential programming applications. In this paper, we study the algebraic structure of time warps, and prove that their equational theory is decidable, a necessary condition for their use in real-world compilers. We also describe how our universal-algebraic proof technique lends itself to a constraint-based implementation, establishing a new link between universal algebra and verification technology.Comment: Submitted to a conferenc

Duality and canonical extensions for stably compact spaces

We construct a canonical extension for strong proximity lattices in order to give an algebraic, point-free description of a finitary duality for stably compact spaces. In this setting not only morphisms, but also objects may have distinct pi- and sigma-extensions.Comment: 29 pages, 1 figur

Crop Updates 2008 - Farming Systems

This session covers thirty nine papers from different authors: PLENARY 1. Developments in grain end use, Dr John de Majnik, New Grain Products, GRDC, Mr Paul Meibusch, New Farm Products and Services, GRDC, Mr Vince Logan, New Products Executive Manager, GRDC PRESENTATIONS 2. Global warming potential of wheat production in Western Australia: A life cycle assessment, Louise Barton1, Wahid Biswas2 and Daniel Carter3, 1School of Earth & Geographical Sciences, The University of Western Australia, 2Centre of Excellence in Cleaner Production, Division of Science and Engineering, Curtin University of Technology, 3Department of Agriculture and Food 3. How much fuel does your farm use for different farm operations? Nicolyn Short1, Jodie Bowling1, Glen Riethmuller1, James Fisher2 and Moin Salam1, 1Department of Agriculture and Food, 2Muresk Institute, Curtin University of Technology 4. Poor soil water storage and soil constraints are common in WA cropping soils, Stephen Davies, Jim Dixon, Dennis Van Gool and Alison Slade, Department of Agriculture and Food, Bob Gilkes, School of Earth and Geographical Sciences, University of Western Australia 5. Developing potential adaptations to climate change for low rainfall farming system using economic analysis tool. STEP, Megan Abrahams, Caroline Peek, Dennis Van Gool, Daniel Gardiner and Kari-Lee Falconer, Department of Agriculture and Food 6. What soil limitations affect the profitability of claying on non-wetting sandplain soils? David Hall1, Jeremy Lemon1, Harvey Jones1, Yvette Oliver2 and Tania Butler1, 1Department of Agriculture and Food, 2CSIRO Div Sustainable Ecology, Perth 7. Farming systems adapting to a variable climate; Two case studies, Kari-Lee Falconer, Department of Agriculture and Food 8. Importance of accounting for variation in crop yield potential when making fertiliser decisions, Michael Robertson and Yvette Oliver, CSIRO Sustainable Ecosystems, Floreat 9. Soil acidity is a widespread problem across the Avon River Basin, Stephen Carr1, Chris Gazey2, David York1 and Joel Andrew1, 1Precision SoilTech, 2Department of Agriculture and Food 10. The use of soil testing kits and ion-selective electrodes for the analysis of plant available nutrients in Western Australian soils, Michael Simeoni and Bob Gilkes School of Earth and Geographical Sciences, University of Western Australia 11. Redlegged earth mite resistance and integrated strategies for their control in Western Australia, Mangano G. Peter and Micic Svetlana, Department of Agriculture and Food 12. The economics of treating soil pH (liming), Chris Gazey, Steve Davies, Dave Gartner and Adam Clune, Department of Agriculture and Food, 13. Health benefits – A future differentiator for high value grains, Matthew Morell, Theme Leader, CSIRO Food Futures Flagship 14. Carbon in Sustralian cropping soils – We need to be realistic, Alan Umbers (M Rur Sc), GRDC/DAFF Sustainable Industries Initiative Project 15. AGWEST® Bartolo bladder clover (Trifolium spumosum) − a low cost annual pasture legume for the wheat/sheep zone, Angelo Loi, Brad Nutt and Clinton Revell, Department of Agriculture and Food 16. Maximising the value of point based soil sampling: Monitering trends in soil pH through time, Joel Andrew1, David York1, Stephen Carr1 and Chris Gazey2, 1Precision SoilTech, 2Department of Agriculture and Food 17. Improved crop root growth and productivity with deep ripping and deep placed lime, Stephen Davies1, Geoff Kew2*, Chris Gazey1, David Gartner1 and Adam Clune1, 1Department of Agriculture and Food, 2School of Earth and Geographical Sciences University of Western Australia, *Presenting author 18. The role of pastures in hosting Root Lesion Nematode (RLN, Pratylenchus neglectus), Vivien Vanstone, Ali Bhatti and Ming Pei You, Department of Agriculture and Food 19. To rip or not to rip. When does it pay? Imma Farre, Bill Bowden and Stephen Davies, Department of Agriculture and Food 20. Can yield be predicted from remotely sensed data, Henry Smolinski, Jane Speijers and John Bruce, Department of Agriculture and Food 21. Rotations for profit, David McCarthy and Gary Lang, Facey Group, Wickepin, WA 22. Rewriting rules for the new cropping economics, David Rees, Consultant, Albany 23. Reducing business risk in Binnu! – A case study, Rob Grima, Department of Agriculture and Food 24. Does improved ewe management offer grain farmers much extra profit? John Young, Farming Systems Analysis Service, Ross Kingwell, Department of Agriculture and Food, and UWA, Chris Oldham, Department of Agriculture and Food RESEARCH HIGHLIGHTS 25. Crop establishment and productivity with improved root zone drainage, Dr Derk Bakker, Research Officer, Department of Agriculture and Food 26. Will wheat production in Western Australia be more risky in the future? Imma Farre and Ian Foster, Department of Agriculture and Food PAPERS 27. Building farmers’ adaptive capacity to manage seasonal variability and climate change, David Beard, Department of Agriculture and Food 28. Precision placement increases crop phosphorus uptake under variable rainfall: Simulation studies, Wen Chen1 2, Richard Bell1, Bill Bowden2, Ross Brennan2, Art Diggle2 and Reg Lunt2, 1School of Environmental Science, Murdoch University, 2Department of Agriculture and Food 29. What is the role of grain legumes on red soil farms? Rob Grima, Department of Agriculture and Food 30. Fertiliser placement influences plant growth and seed yield of grain crops at different locations of WA, Qifu Ma1, Zed Rengel1, Bill Bowden2, Ross Brennan2, Reg Lunt2 and Tim Hilder2, 1Soil Science & Plant Nutrition, University of Western Australia, 2Department of Agriculture and Food 31. A review of pest and disease occurrences for 2007, Peter Mangano and Dusty Severtson, Department of Agriculture and Food 32. Effect of stocking rates on grain yield and quality of wheat in Western Australia in 2007, Shahajahan Miyan, Sam Clune, Barb Sage and Tenielle Martin, Department of Agriculture and Food 33. Storing grain is not ‘set and forget’ management, Chris Newman, Department of Agriculture and Food 34. Improving understanding of soil plant available water capacity (PAWC): The WA soil water database (APSoil), Yvette Oliver, Neal Dalgliesh and Michael Robertson, CSIRO Sustainable Ecosystems 35. The impact of management decisions in drought on a low rainfall northern wheatbelt farm, Caroline Peek and Andrew Blake, Department of Agriculture and Food 37. Cullen – A native pasture legume shows promise for the low-medium rainfall cropping zone, Megan Ryan, Richard Bennett, Tim Colmer, Daniel Real, Jiayin Pang, Lori Kroiss, Dion Nicol and Tammy Edmonds-Tibbett, School of Plant Biology, The University of Western Australia and Future Farm Industries CRC 38. Climate risk management tools – useful, or just another gadget? Lisa Sherriff, Kari-Lee Falconer, Daniel Gardiner and Ron McTaggart Department of Agriculture and Food 39. Benefits of crop rotation for management of Root Lesion Nematode (RLN, Pratylenchus neglectus), Vivien Vanstone, Sean Kelly and Helen Hunter, Department of Agriculture and Foo

Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study

Background Early death after cancer surgery is higher in low-income and middle-income countries (LMICs) compared with in high-income countries, yet the impact of facility characteristics on early postoperative outcomes is unknown. The aim of this study was to examine the association between hospital infrastructure, resource availability, and processes on early outcomes after cancer surgery worldwide.Methods A multimethods analysis was performed as part of the GlobalSurg 3 study-a multicentre, international, prospective cohort study of patients who had surgery for breast, colorectal, or gastric cancer. The primary outcomes were 30-day mortality and 30-day major complication rates. Potentially beneficial hospital facilities were identified by variable selection to select those associated with 30-day mortality. Adjusted outcomes were determined using generalised estimating equations to account for patient characteristics and country-income group, with population stratification by hospital.Findings Between April 1, 2018, and April 23, 2019, facility-level data were collected for 9685 patients across 238 hospitals in 66 countries (91 hospitals in 20 high-income countries; 57 hospitals in 19 upper-middle-income countries; and 90 hospitals in 27 low-income to lower-middle-income countries). The availability of five hospital facilities was inversely associated with mortality: ultrasound, CT scanner, critical care unit, opioid analgesia, and oncologist. After adjustment for case-mix and country income group, hospitals with three or fewer of these facilities (62 hospitals, 1294 patients) had higher mortality compared with those with four or five (adjusted odds ratio [OR] 3.85 [95% CI 2.58-5.75]; p<0.0001), with excess mortality predominantly explained by a limited capacity to rescue following the development of major complications (63.0% vs 82.7%; OR 0.35 [0.23-0.53]; p<0.0001). Across LMICs, improvements in hospital facilities would prevent one to three deaths for every 100 patients undergoing surgery for cancer.Interpretation Hospitals with higher levels of infrastructure and resources have better outcomes after cancer surgery, independent of country income. Without urgent strengthening of hospital infrastructure and resources, the reductions in cancer-associated mortality associated with improved access will not be realised

Impact of infection on proteome-wide glycosylation revealed by distinct signatures for bacterial and viral pathogens

Mechanisms of infection and pathogenesis have predominantly been studied based on differential gene or protein expression. Less is known about posttranslational modifications, which are essential for protein functional diversity. We applied an innovative glycoproteomics method to study the systemic proteome-wide glycosylation in response to infection. The protein site-specific glycosylation was characterized in plasma derived from well-defined controls and patients. We found 3862 unique features, of which we identified 463 distinct intact glycopeptides, that could be mapped to more than 30 different proteins. Statistical analyses were used to derive a glycopeptide signature that enabled significant differentiation between patients with a bacterial or viral infection. Furthermore, supported by a machine learning algorithm, we demonstrated the ability to identify the causative pathogens based on the distinctive host blood plasma glycopeptide signatures. These results illustrate that glycoproteomics holds enormous potential as an innovative approach to improve the interpretation of relevant biological changes in response to infection