Simplicial Chern-Weil theory for coherent analytic sheaves, part I

In "Chern classes for coherent sheaves", H.I. Green constructs Chern classes in de Rham cohomology of coherent analytic sheaves, but in a way that is directly amenable to being abstractified to give us a theory of simplicial connections, as well as a simplicial version of Chern-Weil theory. We construct here a formal $(\infty,1)$-categorical framework into which we can place Green's work, as well as a more general idea as to what exactly a simplicial connection should be. The result will be the ability to work with generalised invariant polynomials (which will be introduced in the sequel to this paper) evaluated at the curvature of so-called admissible simplicial connections to get explicit \v{C}ech representatives in de Rham cohomology of characteristic classes of coherent analytic sheaves.Comment: 45 page

Markov models to estimate and describe survival time and experience in cohorts with high euthanasia frequency

Unique to survival analysis of veterinary clinical data is classification of observations from euthanized animals. The first study highlighted limitations of Kaplan-Meier product limit analysis (KM) of veterinary clinical data. Three data sets with different outcome proportions (alive, lost-to-follow-up, dead due to disease, dead due to other, euthanized due to disease, euthanized due to other) were used. Different classifications of observations from euthanized animals caused inconsistent conclusions of significant differences between strata within data sets. At times, ranking of median survival time estimates for strata was reversed. The KM was found inappropriate to evaluate observations from euthanized animals. This finding, coupled with restriction of KM to two-state description of disease (alive to outcome), prompted exploration of an alternate analysis method. Markov models allow modeling of multiple health states and outcomes. A 5-state, time-homogeneous, Markov chain was used for a cohort of 64 dogs with generalized lymphoma. The model contained two transient (WELL, TOXIC) and three absorbing (DEAD, EUTHANASIA, LOST-TO-FOLLOWUP) states. The transition probability matrix (P) was used to iterate future transitions and survival probabilities. Matrix solution and Monte Carlo simulation were used to estimate survival time. Estimates appeared reliable. Markov modeling was extended for comparison of vaccine-associated sarcoma progression after treatment in a cohort of 294 cats. For a 5-state model, transition probabilities derived from exponential transformation of incidence rates were used to construct P for each treatment - NONE (no surgery), SX (surgery) and SX+RAD (surgery and radiation). Monte Carlo estimates of durations in transient states and expected survival showed SX+RAD prolonged expected survival significantly longer than SX than NONE. Commitment to repeated treatment with surgery and radiation did prolong expected survival of cats with vaccine-associated sarcoma. Assumptions of Markov modeling did not appear prohibitive for analysis of veterinary clinical data and further exploration is warranted

Comparison of the use of sodium carbonate (washing soda crystals) and apomorphine for inducing emesis in dogs

Objective: To describe the use of sodium carbonate and apomorphine in a historical cohort of dogs, compare the occurrence of emesis and report any adverse effects recorded. Methods: This historical, observational study included information from medical records of dogs that received an emetic agent. The occurrence of emesis with apomorphine or sodium carbonate was calculated and the association between emesis and agent was explored, with the odds ratio and 95% confidence interval (CI) reported. A non-inferiority analysis of the occurrence of emesis for sodium carbonate was performed against an equivalence range of ±7% of the estimated occurrence of emesis with apomorphine. Owners were emailed a short survey about their dog's health after their visit to the hospital for induced emesis. Results: Records for 787 dogs seen from January 2007 to December 2013 were included. For apomorphine, 382/392 dogs showed emesis (97%, 95% CI 95–100%). For sodium carbonate, 320/395 dogs showed emesis (81%, 95% CI 77–85%), which fell below the equivalence range for apomorphine (97 ± 7%, 90–100%) and was considered inferior. The odds ratio of emesis with apomorphine to sodium carbonate was 9.0 (95% CI 4.6–17.6). Of 18 responses to the survey, 5 reported abnormalities after emesis (3 with sodium carbonate, 2 with apomorphine). Conclusion: The occurrence of emesis with sodium carbonate was high but inferior to apomorphine. However, the advantages of sodium carbonate, including less expense and ease of accession compared with apomorphine, make it a viable choice in emergency medicine

Hyperspectral Analysis of Oil and Oil-Impacted Soils for Remote Sensing Purposes

While conventional multispectral sensors record the radiometric signal only at a handful of wavelengths, hyperspectral sensors measure the reflected solar signal at hundreds contiguous and narrow wavelength bands, spanning from the visible to the infrared. Hyperspectral images provide ample spectral information to identify and distinguish between spectrally similar (but unique) materials, providing the ability to make proper distinctions among materials with only subtle signature differences. Hyperspectral images show hence potentiality for proper discrimination between oil slicks and other natural phenomena (look-alike); and even for proper distinctions between oil types. Additionally they can give indications on oil volume. At present, many airborne hyperspectral sensors are available to collect data, but only two civil spaceborn hyperspectral sensors exist as technology demonstrator: the Hyperion sensor on NASA’s EO-1 satellite and the CHRIS sensor on the European Space Agency’s PROBA satellite. Consequently, the concrete opportunity to use spaceborn hyperspectral remote sensing for operational oil spill monitoring is yet not available. Nevertheless, it is clear that the future of satellite hyperspectral remote sensing of oil pollution in the marine/coastal environment is very promising. In order to correctly interpret the hyperspectral data, the retrieved spectral signatures must be correlated to specific materials. Therefore specific spectral libraries, containing the spectral signature of the materials to be detected, must be built up. This requires that highly accurate reflected light measurements of samples of the investigated material must be performed in the lab or in the field. Accurate measurements of the spectral reflectance of several samples of oil-contaminated soils have been performed in the laboratory, in the 400-2500 nm wavelength range. Samples of the oils spilt from the Erika and the Prestige tankers during the major accidents of 1999 and 2002 were also collected and analyzed in the same spectral range, using a portable spectrophotometer. All measurements showed the typical absorption features of hydrocarbon-bearing substances: the two absorption peaks centered at 1732 and 2310 nm.JRC.G.3-Agricultur

A diagrammatic view of differential equations in physics

Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm mathematical footing, while also systematizing a broadly applicable framework to reason formally about systems of equations and their solutions. Our main mathematical tools are category-theoretic diagrams, which are well known, and morphisms between diagrams, which have been less appreciated. As an application of the diagrammatic framework, we show how complex, multiphysical systems can be modularly constructed from basic physical principles. A wealth of examples, drawn from electromagnetism, transport phenomena, fluid mechanics, and other fields, is included.Comment: 69 page