A position and orientation measurement method is investigated by adopting a camera calibrated by the projection geometry of the skew-symmetric Plücker matrices of 3D lines. The relationship between the Plücker matrices of the dual 3D lines and the 2D projective lines is provided in two vertical world coordinate planes. The transform matrix is generated from the projections of the 3D lines. The ...

Genotypic correlations and regressions can be estimated from multiallelic data sets either by weighting the allelic effects additively or by specifically weighting the genotypic interactions. Both methods can be extended to multiple loci, but they do not fully take into account the joint segregation patterns at the loci. These genotypic statistics have a great importance in sociobiological cont...

We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with a finite spectrum. Our result extends the Schur-Horn theorem from a finite dimensional setting to an infinite dimensional Hilbert space, analogous to Kadison’s theorem for orthogonal projections [17, 18], and the second author’s result for operators with three point spectrum [16].

In this paper, we study the pro-Σ fundamental groups of configuration spaces, where Σ is either the set of all prime numbers or a set consisting of a single prime number. In particular, we show, via two somewhat distinct approaches, that, in many cases, the “fiber subgroups” of such fundamental groups arising from the various natural projections of a configuration space to lower-dimensional con...

Evidence-based parenting interventions have been developed and evaluated largely with mothers. This study examined practitioner reports of rates of father attendance, barriers to engagement, organizational support for father-inclusive practice, participation in training in father engagement, and competencies in working with fathers. It also explored predictors of practitioner competence and rat...

This paper makes three contributions: (1) the paper provides a better understanding of online behavior by showing the main drivers of Internet portal choice, (2) the rich data allow for a deeper understanding of brand substitution patterns than previously possible and (3) the paper introduces a wider statistics community to a new data opportunity and a recently developed method.

Many crucial results of the asymptotic theory of symmetric convex bodies were extended to the non-symmetric case in recent years. That led to the conjecture that for every n-dimensional convex body K there exists a projection P of rank k, proportional to n, such that PK is almost symmetric. We prove that the conjecture does not hold. More precisely, we construct an n-dimensional convex body K s...

We prove that AW*-algebras are determined by their projections, their symmetries, and the action of the latter on the former. We introduce active lattices, which are formed from these three ingredients. More generally, we prove that the category of AW*-algebras is equivalent to a full subcategory of active lattices. Crucial ingredients are an equivalence between the category of piecewise AW*-al...

Every commuting set of normal matrices with entries in an AW*algebra can be simultaneously diagonalized. To establish this, a dimension theory for properly infinite projections in AW*-algebras is developed. As a consequence, passing to matrix rings is a functor on the category of AW*-

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