Identifying reliable traits across laboratory mouse exploration arenas: A meta-analysis

This study is a meta-analysis of 367 mice from a collection of behaviour neuroscience and behaviour genetic studies run in the same lab in Zurich, Switzerland. We employed correlation-based statistics to confirm and quantify consistencies in behaviour across the testing environments. All 367 mice ran exactly the same behavioural arenas: the light/dark box, the null maze, the open field arena, an emergence task and finally an object exploration task. We analysed consistency of three movement types across those arenas (resting, scanning, progressing), and their relative preference for three zones of the arenas (home, transition, exploration). Results were that 5/6 measures showed strong individual-differences consistency across the tests. Mean inter-arena correlations for these five measures ranged from +.12 to +.53. Unrotated principal component factor analysis (UPCFA) and Cronbach’s alpha measures showed these traits to be reliable and substantial (32-63% of variance across the five arenas). UPCFA loadings then indicate which tasks give the best information about these cross-task traits. One measure (that of time spent in “intermediate” zones) was not reliable across arenas. Conclusions centre on the use of individual differences research and behavioural batteries to revise understandings of what measures in one task predict for behaviour in others. Developing better behaviour measures also makes sound scientific and ethical sense

Representation fields for commutative orders

A representation field for a non-maximal order \Ha in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of \Ha. Not every non-maximal order has a representation field. In this work we prove that every commutative order has a representation field and give a formula for it. The main result is proved for central simple algebras over arbitrary global fields.Comment: Annales de l'institut Fourier, vol 61, 201

Roots of unity in definite quaternion orders

A commutative order in a quaternion algebra is called selective if it is embeds into some, but not all, the maximal orders in the algebra. It is known that a given quadratic order over a number field can be selective in at most one indefinite quaternion algebra. Here we prove that the order generated by a cubic root of unity is selective for any definite quaternion algebra over the rationals with a type number 3 or larger. The proof extends to a few other closely related orders