We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2D quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic underlying classical dynamics, and for each case the limiting distribution is universal (system independent). Thus, a new criterion for quantum chaos is provided b...

The paper 'Evaluation Metrics for Biostatistical and Epidemiological Collaborations' of Rubio et al. represents an important initial advance in the evaluation of biostatistics, epidemiology, and research design (BERD). The authors present a sensible three-domain model (collaboration with investigators, application of BERD-related methods, and discovery of new BERD methodologies), rightly acknow...

This section looks back on a ground-breaking contribution to public health, reproduces an extract of the original text and adds a commentary on its significance from a modern perspective. To complement the theme of this month’s issue, John R Williams looks at the Declaration of Helsinki and how it has evolved over time. The original declaration is reproduced here in full with permission of the ...

Architects are enthusiastic about "bioinformed design" as occupant well-being is a primary measure of architectural success. However, architects are also under mounting pressure to create more sustainable buildings. Scientists have a critical opportunity to make the emerging field of microbiology of the built environment more relevant and applicable to real-world design problems by addressing h...

Human self-consciousness depends on the metarepresentation of mental and bodily states as one's own mental and bodily states. First-person-perspective taking is not sufficient, but necessary for human self-consciousness. To assign a first-person-perspective is to center one's own multimodal experiential space upon one's own body, thus operating in an egocentric reference frame. The brain region...

We generalize the results of [AS], finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each the lift of a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots cannot possess totally geodesic Seifert surfaces by giving bounds on the width invariant in the presence of s...

We prove the hyperbolicity of the complement of five lines in general position in an almost complex projective plane, answering a question by S. Ivashkovich.

The main results of this article are small time heat comparison results for two points in two manifolds with characteristic functions as initial temperature distributions (Theorems 1 and 2). These results are based on the geometric concepts of (essential) distance from the complement and spherical area function. We also discuss some other geometric results about the heat development and illustr...

In this paper, we obtain some formulas for compound matrices of generalized Schur complements of matrices. Further, we give some Löwner partial orders for compound matrices of Schur complements of positive semidefinite Hermitian matrices, and obtain some estimates for eigenvalues of Schur complements of sums of positive semidefinite Hermitian matrices.