A role for cryptochromes in sleep regulation

Background  

The cryptochrome 1 and 2 genes (cry1 and cry2) are necessary for the generation of circadian rhythms, as mice lacking both of these genes (cry1,2 ^-/-) lack circadian rhythms. We studied sleep in cry1,2 ^-/- mice under baseline conditions as well as under conditions of constant darkness and enforced wakefulness to determine whether cryptochromes influence sleep regulatory processes.     

An approximation condition and extremal quasiconformal extensions

The possibility that the extremal dilatation of quasiconformal extensions from the circle is determined by quadrilaterals with vertices on the circle is related to an approximation question for holomorphic functions. This allows an alternative demonstration of a result of Anderson and Hinkkanen.

     

Integration in the GHP formalism I: A coordinate approach with applications to twisting type N spaces

The compacted spin coefficient (ghp) formalism is clearly more concise and efficient than the older Newman-Penrose formalism. Yet few people use it when integration of the field equations is involved, Held being the notable exception. However, to most workers in the field, Held's approach seems far removed from the usual Newman-Unti (nu) type integration procedure. This paper and a subsequent one are concerned with integration within theghp formalism. In this first paper we develop aghp coordinate-style integration procedure modelled closely on thenu procedure whereas in the second paper we present aghp operator-style integration procedure along the lines suggested by Held. For simplicity of illustration we restrict the discussion to algebraically special vacuum spacetimes. We show clearly the similarities and differences between the two approaches, and compare their respective efficiencies. To deal with a concrete example, we illustrate the two methods by once more considering the problem of twisting typeN vacuum solutions to Einstein's field equations. TheGhp approach enables us to have a comprehensive overview of this much discussed problem and gain new insight into the relationship between various results derived in a number of different formalisms.     

Loans,ordering and shortage costs in start-ups: a dynamic stochastic decision approach

Start-up companies are a vital ingredient in the success of a globalised networked world economy. We believe that such companies are interested in maximising the chance of surviving in the long term. We present a Markov decision model to analyse survival probabilities of start-up manufacturing companies. Our model examines the implications of their operating decisions, in particular how their inventory strategy is influenced by purchasing, shortage, transportation and ordering costs, as well as loans to the firm. It is shown that although the start-up company should be more conservative in its component purchasing strategy than if it were a well-established company it should not be too conservative. Nor is its strategy monotone in the amount of capital available.     

Relative homological algebra in the category of quasi-coherent sheaves

In this paper, we prove the existence of a flat cover and of a cotorsion envelope for any quasi-coherent sheaf over a scheme (X,O_X). Indeed we prove something more general. We define what it is understood by the category of quasi-coherent R-modules, where R is a representation by rings of a quiver Q, and we prove the existence of a flat cover and a cotorsion envelope for quasi-coherent R-modules. Then we use the fact that the category of quasi-coherent sheaves on (X,O_X) is equivalent to the category of quasi-coherent R-modules for some Q and R to get our result.     

Further Development and Validation of the Teaching Science as Inquiry (TSI) Instrument

The purpose of this study was to further develop and validate the Teaching Science as Inquiry (TSI) Instrument, an instrument designed to measure the self‐efficacy beliefs of preservice teachers in regards to the teaching of science as inquiry. Based on the validation processes and the associated data analysis, the TSI demonstrates continued content and construct validity with high internal reliability when used with prospective elementary science teachers.