The Hamiltonian index of a graph and its branch-bonds

Let $G$ be an undirected and loopless finite graph that is not a path. The minimum $m$ such that the iterated line graph $L^m(G)$ is hamiltonian is called the hamiltonian index of $G,$ denoted by $h(G).$ A reduction method to determine the hamiltonian index of a graph $G$ with $h(G)\geq 2$ is given here. With it we will establish a sharp lower bound and a sharp upper bound for $h(G)$, respectively, which improves some known results of P.A. Catlin et al. [J. Graph Theory 14 (1990)] and H.-J. Lai [Discrete Mathematics 69 (1988)]. Examples show that $h(G)$ may reach all integers between the lower bound and the upper bound. \u

The temporal changes in the emission spectrum of Comet 9P/Tempel 1 after Deep Impact

The time dependence of the changes in the emission spectra of Comet 9P/Tempel 1 after Deep Impact are derived and discussed. This was a unique event because for the first time it gave astronomers the opportunity to follow the time history of the formation and decay of O(1S), OH, CN, C2, C3, NH, and NH2. Least squares fits of a modified Haser model with constraints using known rate constants were fit to the observed data. In the case of OH a simple two-step Haser model provides a reasonable fit to the observations. Fitting the emissions from O(1S), CN, C2, C3, NH, and NH2 requires the addition of a delayed component to a regular two or three step Haser model. From this information a picture of the Deep Impact encounter emerges where there is an initial formation of gas and dust, which is responsible for the prompt emission that occurs right after impact. A secondary source of gas starts later after impact when the initial dust has dissipated enough so that solar radiation can reach the surface of freshly exposed material. The implications of this and other results are discussed in terms of the implications on the structure and composition of the comet's nucleus.Comment: Accepted for publication in The Astrophysical Journal; 26 pages including 8 figures and 1 tabl

Solutal Benard-Marangoni Instability as a Growth Mechanism for Single-Walled Carbon Nanotubes

Abstract In the past few years, considerable progress has been achieved in understanding the growth mechanism of single-walled carbon nanotubes (C-SWNTs). Nevertheless, the nucleation of C-SWNTs still remains partially unexplained by these models. A study of the critical synthesis parameters in the plasma torch process and a review of existing growth mechanisms lead us to propose a new growth mechanism for bundles of C-SWNTs, based on the Bénard-Marangoni instability. It is shown that the conditions occurring at the surface of the catalyst nanoparticle (NP) during the growth of the C-SWNTs give rise to the solutal BMI, which in turn results in a pattern of hexagonal convection cells in the liquid layer on the surface of the NP. The vortex ring flow pattern within these cells is then responsible for the structured growth of the C-SWNT bundles. This model highlights the important parameters required to optimize the synthesis of C-SWNTs

Influence of age on ocular biomechanical properties in a canine glaucoma model with ADAMTS10 mutation

<div><p>Soft tissue often displays marked age-associated stiffening. This study aims to investigate how age affects scleral biomechanical properties in a canine glaucoma model with <i>ADAMTS10</i> mutation, whose extracellular matrix is concomitantly influenced by the mutation and an increased mechanical load from an early age. Biomechanical data was acquired from <i>ADAMTS10-</i>mutant dogs (n = 10, 21 to 131 months) and normal dogs (n = 5, 69 to 113 months). Infusion testing was first performed in the whole globes to measure ocular rigidity. After infusion experiments, the corneas were immediately trephined to prepare scleral shells that were mounted on a pressurization chamber to measure strains in the posterior sclera using an inflation testing protocol. Dynamic viscoelastic mechanical testing was then performed on dissected posterior scleral strips and the data were combined with those reported earlier by our group from the same animal model (Palko et al, IOVS 2013). The association between age and scleral biomechanical properties was evaluated using multivariate linear regression. The relationships between scleral properties and the mean and last measured intraocular pressure (IOP) were also evaluated. Our results showed that age was positively associated with complex modulus (p<0.001) and negatively associated with loss tangent (p<0.001) in both the affected and the normal groups, suggesting an increased stiffness and decreased mechanical damping with age. The regression slopes were not different between the groups, although the complex modulus was significantly lower in the affected group (p = 0.041). The posterior circumferential tangential strain was negatively correlated with complex modulus (R = -0.744, p = 0.006) showing consistent mechanical evaluation between the testing methods. Normalized ocular rigidity was negatively correlated with the last IOP in the affected group (p = 0.003). Despite a mutation that affects the extracellular matrix and a chronic IOP elevation in the affected dogs, age-associated scleral stiffening and loss of mechanical damping were still prominent and had a similar rate of change as in the normal dogs.</p></div

Entanglement demonstration on board a nano-satellite

Global quantum networks for secure communication can be realized using large fleets of satellites distributing entangled photon pairs between ground-based nodes. Because the cost of a satellite depends on its size, the smallest satellites will be most cost-effective. This Letter describes a miniaturized, polarization entangled, photon-pair source operating on board a nano-satellite. The source violates Bell’s inequality with a Clauser–Horne–Shimony–Holt parameter of 2.60±0.06. This source can be combined with optical link technologies to enable future quantum communication nano-satellite missions

SpooQy-1: The First Nano-Satellite to Demonstrate Quantum Entanglement in Space

SpooQy-1 is a 3-unit nanosatellite that was launched into a Low Earth Orbit from the International Space Station on the 17th of June 2019. The spacecraft hosts a scientific payload capable of producing entangled photon-pairs and measuring their polarization in orthogonal bases to perform a Bell test. Since launch, SpooQy-1 has routinely demonstrated the generation and detection of polarization entangled photon-pairs in Space, something that has previously only been demonstrated by the 630kg Micius mission by the Chinese Academy of Sciences. The measured entanglement correlations can violate Bell\u27s inequality with a CHSH parameter value of 2.60±0.06, over operating temperatures of 16 °C to 21.5 °C. These results demonstrate that quantum entanglement can be generated in space on highly resource-constrained platforms. A follow-on 12U mission, developed in partnership with RAL space,will build on this to demonstrate space-to-ground entanglement distribution, which is required for space-based nodes to support global quantum communication networks

Mucin Variable Number Tandem Repeat Polymorphisms and Severity of Cystic Fibrosis Lung Disease: Significant Association with MUC5AC

Variability in cystic fibrosis (CF) lung disease is partially due to non-CFTR genetic modifiers. Mucin genes are very polymorphic, and mucins play a key role in the pathogenesis of CF lung disease; therefore, mucin genes are strong candidates as genetic modifiers. DNA from CF patients recruited for extremes of lung phenotype was analyzed by Southern blot or PCR to define variable number tandem repeat (VNTR) length polymorphisms for MUC1, MUC2, MUC5AC, and MUC7. VNTR length polymorphisms were tested for association with lung disease severity and for linkage disequilibrium (LD) with flanking single nucleotide polymorphisms (SNPs). No strong associations were found for MUC1, MUC2, or MUC7. A significant association was found between the overall distribution of MUC5AC VNTR length and CF lung disease severity (p = 0.025; n = 468 patients); plus, there was robust association of the specific 6.4 kb HinfI VNTR fragment with severity of lung disease (p = 6.2 x 10(-4) after Bonferroni correction). There was strong LD between MUC5AC VNTR length modes and flanking SNPs. The severity-associated 6.4 kb VNTR allele of MUC5AC was confirmed to be genetically distinct from the 6.3 kb allele, as it showed significantly stronger association with nearby SNPs. These data provide detailed respiratory mucin gene VNTR allele distributions in CF patients. Our data also show a novel link between the MUC5AC 6.4 kb VNTR allele and severity of CF lung disease. The LD pattern with surrounding SNPs suggests that the 6.4 kb allele contains, or is linked to, important functional genetic variation

Genome Reference and Sequence Variation in the Large Repetitive Central Exon of Human MUC5AC

Despite modern sequencing efforts, the difficulty in assembly of highly repetitive sequences has prevented resolution of human genome gaps, including some in the coding regions of genes with important biological functions. One such gene, MUC5AC, encodes a large, secreted mucin, which is one of the two major secreted mucins in human airways. The MUC5AC region contains a gap in the human genome reference (hg19) across the large, highly repetitive, and complex central exon. This exon is predicted to contain imperfect tandem repeat sequences and multiple conserved cysteine-rich (CysD) domains. To resolve the MUC5AC genomic gap, we used high-fidelity long PCR followed by single molecule real-time (SMRT) sequencing. This technology yielded long sequence reads and robust coverage that allowed for de novo sequence assembly spanning the entire repetitive region. Furthermore, we used SMRT sequencing of PCR amplicons covering the central exon to identify genetic variation in four individuals. The results demonstrated the presence of segmental duplications of CysD domains, insertions/deletions (indels) of tandem repeats, and single nucleotide variants. Additional studies demonstrated that one of the identified tandem repeat insertions is tagged by nonexonic single nucleotide polymorphisms. Taken together, these data illustrate the successful utility of SMRT sequencing long reads for de novo assembly of large repetitive sequences to fill the gaps in the human genome. Characterization of the MUC5AC gene and the sequence variation in the central exon will facilitate genetic and functional studies for this critical airway mucin

Nudel and FAK as Antagonizing Strength Modulators of Nascent Adhesions through Paxillin

Competition for binding to the cellular protein paxillin by the proteins Nudel and focal adhesion kinase is important for the proper regulation of cell adhesion and migration