891 resultados para science and technology history


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We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

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Thermal transformations of natural calcium oxalate dihydrate known in mineralogy as weddellite have been undertaken using a combination of Raman microscopy and infrared emission spectroscopy. The vibrational spectroscopic data was complimented with high resolution thermogravimetric analysis combined with evolved gas mass spectrometry. TG–MS identified three mass loss steps at 114, 422 and 592 °C. In the first mass loss step water is evolved only, in the second and third steps carbon dioxide is evolved. The combination of Raman microscopy and a thermal stage clearly identifies the changes in the molecular structure with thermal treatment. Weddellite is the phase in the temperature range up to the pre-dehydration temperature of 97 °C. At this temperature, the phase formed is whewellite (calcium oxalate monohydrate) and above 114 °C the phase is the anhydrous calcium oxalate. Above 422 °C, calcium carbonate is formed. Infrared emission spectroscopy shows that this mineral decomposes at around 650 °C. Changes in the position and intensity of the C=O and C---C stretching vibrations in the Raman spectra indicate the temperature range at which these phase changes occur.