Separation index of graphs and stacked 2-spheres

In 1987, Kalai proved that stacked spheres of dimension $d\geq 3$ are characterised by the fact that they attain equality in Barnette's celebrated Lower Bound Theorem. This result does not extend to dimension $d=2$. In this article, we give a characterisation of stacked $2$-spheres using what we call the {\em separation index}. Namely, we show that the separation index of a triangulated $2$-sphere is maximal if and only if it is stacked. In addition, we prove that, amongst all $n$-vertex triangulated $2$-spheres, the separation index is {\em minimised} by some $n$-vertex flag sphere for $n\geq 6$. Furthermore, we apply this characterisation of stacked $2$-spheres to settle the outstanding $3$-dimensional case of the Lutz-Sulanke-Swartz conjecture that "tight-neighbourly triangulated manifolds are tight". For dimension $d\geq 4$, the conjecture has already been proved by Effenberger following a result of Novik and Swartz.Comment: Some typos corrected, to appear in "Journal of Combinatorial Theory A

Trapping and sorting active particles: motility-induced condensation & smectic defects

We present an experimental realization of the collective trapping phase transition [Kaiser et al., PRL 108, 268307 (2012)], using motile polar granular rods in the presence of a V-shaped obstacle. We offer a theory of this transition based on the interplay of motility-induced condensation and liquid-crystalline ordering and show that trapping occurs when persistent influx overcomes the collective expulsion of smectic defect structures. In agreement with the theory, our experiments find that a trap fills to the brim when the trap angle $\theta$ is below a threshold $\theta_c$, while all particles escape for $\theta > \theta_c$. Our simulations support a further prediction, that $\theta_c$ goes down with increasing rotational noise. We exploit the sensitivity of trapping to the persistence of directed motion to sort particles based on the statistical properties of their activityComment: 6 pages, 5 figures, for supplementary mpg files, see "https://www.dropbox.com/sh/3cmswfoysdn0sb6/AACpEp-G3768B6Y62nDFj_Hea?dl=0". This paper supersedes our earlier version arXiv:1603.08535 and contains substantial new results including revised theoretical treatmen

TGFβ1 orchestrates renal fibrosis following Escherichia coli pyelonephritis

Renal scarring after pyelonephritis is linked to long-term health risks for hypertension and chronic kidney disease. Androgen exposure increases susceptibility to, and severity of, uropathogenic Escherichia coli (UPEC) pyelonephritis and resultant scarring in both male and female mice, while anti-androgen therapy is protective against severe urinary tract infection (UTI) in these models. This work employed androgenized female C57BL/6 mice to elucidate the molecular mechanisms of post-infectious renal fibrosis and to determine how these pathways are altered by the presence of androgens. We found that elevated circulating testosterone levels primed the kidney for fibrosis by increasing local production of TGFβ1 before the initiation of UTI, altering the ratio of transcription factors Smad2 and Smad3 and increasing the presence of mesenchymal stem cell (MSC)-like cells and Gli1 + activated myofibroblasts, the cells primarily responsible for deposition of scar components. Increased production of TGFβ1 and aberrations in Smad2:Smad3 were maintained throughout the course of infection in the presence of androgen, correlating with renal scarring that was not observed in non-androgenized female mice. Pharmacologic inhibition of TGFβ1 signaling blunted myofibroblast activation. We conclude that renal fibrosis after pyelonephritis is exacerbated by the presence of androgens and involves activation of the TGFβ1 signaling cascade, leading to increases in cortical populations of MSC-like cells and the Gli1 + activated myofibroblasts that are responsible for scarring

Aortic arch tortuosity with PHACE syndrome : a rare case scenario

PHACE syndrome is a rare neurocutaneous disorder characterised by an association of infantile haemangiomas with structural anomalies of brain, cerebral vasculature, eye, aorta and chest wall.1 Coarctation of aorta (COA) is most the common cardiac anomaly reported in PHACE syndrome. COA or interrupted aortic arch in PHACE is unique and complex both in location and character compared to the typical coarctation anatomy. Arterial tortuosity of the cerebral vasculature has been well described in literature in PHACE syndrome. We present a rare case of tortuous aortic arch continuing as descending aorta in an infant with PHACE syndrome.peer-reviewe

Fault-tolerant onboard digital information switching and routing for communications satellites

The NASA Lewis Research Center is developing an information-switching processor for future meshed very-small-aperture terminal (VSAT) communications satellites. The information-switching processor will switch and route baseband user data onboard the VSAT satellite to connect thousands of Earth terminals. Fault tolerance is a critical issue in developing information-switching processor circuitry that will provide and maintain reliable communications services. In parallel with the conceptual development of the meshed VSAT satellite network architecture, NASA designed and built a simple test bed for developing and demonstrating baseband switch architectures and fault-tolerance techniques. The meshed VSAT architecture and the switching demonstration test bed are described, and the initial switching architecture and the fault-tolerance techniques that were developed and tested are discussed