Three dimensional, axisymmetric cusps without chaos

We construct three dimensional axisymmetric, cuspy density distributions, whose potentials are of St\"ackel form in parabolic coordinates. As in Sridhar and Touma (1997), a black hole of arbitrary mass may be added at the centre, without destroying the St\"ackel form of the potentials. The construction uses a classic method, originally due to Kuzmin (1956), which is here extended to parabolic coordinates. The models are highly oblate, and the cusps are "weak", with the density, $\rho \propto 1/r^k$, where $0<k<1$.Comment: 5 pages, 2 figures, submitted to MNRA

Stellar Dynamics around Black Holes in Galactic Nuclei

We classify orbits of stars that are bound to central black holes in galactic nuclei. The stars move under the combined gravitational influences of the black hole and the central star cluster. Within the sphere of influence of the black hole, the orbital periods of the stars are much shorter than the periods of precession. We average over the orbital motion and end up with a simpler problem and an extra integral of motion: the product of the black hole mass and the semimajor axis of the orbit. Thus the black hole enforces some degree of regularity in its neighborhood. Well within the sphere of influence, (i) planar, as well as three dimensional, axisymmetric configurations-both of which could be lopsided-are integrable, (ii) fully three dimensional clusters with no spatial symmetry whatsover must have semi-regular dynamics with two integrals of motion. Similar considerations apply to stellar orbits when the black hole grows adiabatically. We introduce a family of planar, non-axisymmetric potential perturbations, and study the orbital structure for the harmonic case in some detail. In the centered potentials there are essentially two main families of orbits: the familiar loops and lenses, which were discussed in Sridhar and Touma (1997, MNRAS, 287, L1-L4). We study the effect of lopsidedness, and identify a family of loop orbits, whose orientation reinforces the lopsidedness, an encouraging sign for the construction of self-consistent models of eccentric, discs around black holes, such as in M31 and NGC 4486B.Comment: to appear in MNRAS, 10 pages, latex, 20 POstScript figure

A Path to Implement Precision Child Health Cardiovascular Medicine.

Congenital heart defects (CHDs) affect approximately 1% of live births and are a major source of childhood morbidity and mortality even in countries with advanced healthcare systems. Along with phenotypic heterogeneity, the underlying etiology of CHDs is multifactorial, involving genetic, epigenetic, and/or environmental contributors. Clear dissection of the underlying mechanism is a powerful step to establish individualized therapies. However, the majority of CHDs are yet to be clearly diagnosed for the underlying genetic and environmental factors, and even less with effective therapies. Although the survival rate for CHDs is steadily improving, there is still a significant unmet need for refining diagnostic precision and establishing targeted therapies to optimize life quality and to minimize future complications. In particular, proper identification of disease associated genetic variants in humans has been challenging, and this greatly impedes our ability to delineate gene-environment interactions that contribute to the pathogenesis of CHDs. Implementing a systematic multileveled approach can establish a continuum from phenotypic characterization in the clinic to molecular dissection using combined next-generation sequencing platforms and validation studies in suitable models at the bench. Key elements necessary to advance the field are: first, proper delineation of the phenotypic spectrum of CHDs; second, defining the molecular genotype/phenotype by combining whole-exome sequencing and transcriptome analysis; third, integration of phenotypic, genotypic, and molecular datasets to identify molecular network contributing to CHDs; fourth, generation of relevant disease models and multileveled experimental investigations. In order to achieve all these goals, access to high-quality biological specimens from well-defined patient cohorts is a crucial step. Therefore, establishing a CHD BioCore is an essential infrastructure and a critical step on the path toward precision child health cardiovascular medicine