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Dedicated to the memory of Leonid R. Volevič. In this paper, we combine results on extensions of operators with recent results on the relation between the M-function and the spectrum, to examine the spectral behaviour of boundary value problems. M-functions are defined for general closed extensions, and associated with realisations of elliptic operators. In(More)
Accurately identifying duplicate records between multiple data sources is a persistent problem that continues to plague organizations and researchers alike. Small inconsistencies between records can prevent detection between two otherwise identical records. In this paper, we present a new probabilistic h-gram (hash gram) record matching technique by(More)
— Metaheuristics such as Estimation of Distribution Algorithms and the Cross-Entropy method use probabilistic modelling and inference to generate candidate solutions in optimization problems. The model fitting task in this class of algorithms has largely been carried out to date based on maximum likelihood. An alternative approach that is prevalent in(More)
Starting with an adjoint pair of operators, under suitable abstract versions of standard PDE hypotheses, we consider the Weyl M-function of extensions of the operators. The extensions are determined by abstract boundary conditions and we establish results on the relationship between the M-function as an analytic function of a spectral parameter and the(More)
Ray Solomonoff invented the notion of universal induction featuring an aptly termed " universal " prior probability function over all possible computable environments [9]. The essential property of this prior was its ability to dominate all other such priors. Later, Levin introduced another construction — a mixture of all possible priors or " universal(More)
The nature of the stable phase of iron in the Earth's solid inner core is still highly controversial. Laboratory experiments suggest the possibility of an uncharacterized phase transformation in iron at core conditions and seismological observations have indicated the possible presence of complex, inner-core layering. Theoretical studies currently suggest(More)
Keywords: iron sulfide phase transformation magnetic property high pressure first principles calculation evolutionary crystal structure prediction Iron sulfide (FeS) was investigated using first-principles calculations up to a pressure of 400 GPa. A number of new phase transitions were found. An antiferromagnetic MnP-type structure, FeS II, was confirmed to(More)
The cementite phase of Fe 3 C has been studied by high-resolution neutron powder diffraction at 4.2 K and at 20 K intervals between 20 and 600 K. The crystal structure remains orthorhombic (Pnma) throughout, with the fractional coordinates of all atoms varying only slightly (the magnetic structure of the ferromagnetic phase could not be determined). The(More)