On prisms, M\"obius ladders and the cycle space of dense graphs

For a graph X, let f_0(X) denote its number of vertices, d(X) its minimum degree and Z_1(X;Z/2) its cycle space in the standard graph-theoretical sense (i.e. 1-dimensional cycle group in the sense of simplicial homology theory with Z/2-coefficients). Call a graph Hamilton-generated if and only if the set of all Hamilton circuits is a Z/2-generating system for Z_1(X;Z/2). The main purpose of this paper is to prove the following: for every s > 0 there exists n_0 such that for every graph X with f_0(X) >= n_0 vertices, (1) if d(X) >= (1/2 + s) f_0(X) and f_0(X) is odd, then X is Hamilton-generated, (2) if d(X) >= (1/2 + s) f_0(X) and f_0(X) is even, then the set of all Hamilton circuits of X generates a codimension-one subspace of Z_1(X;Z/2), and the set of all circuits of X having length either f_0(X)-1 or f_0(X) generates all of Z_1(X;Z/2), (3) if d(X) >= (1/4 + s) f_0(X) and X is square bipartite, then X is Hamilton-generated. All these degree-conditions are essentially best-possible. The implications in (1) and (2) give an asymptotic affirmative answer to a special case of an open conjecture which according to [European J. Combin. 4 (1983), no. 3, p. 246] originates with A. Bondy.Comment: 33 pages; 5 figure

SN 2016iet: The Pulsational or Pair Instability Explosion of a Low Metallicity Massive CO Core Embedded in a Dense Hydrogen-Poor Circumstellar Medium

We present optical photometry and spectroscopy of SN 2016iet, an unprecedented Type I supernova (SN) at $z=0.0676$ with no obvious analog in the existing literature. The peculiar light curve has two roughly equal brightness peaks ($\approx -19$ mag) separated by 100 days, and a subsequent slow decline by 5 mag in 650 rest-frame days. The spectra are dominated by emission lines of calcium and oxygen, with a width of only $3400$ km s$^{-1}$, superposed on a strong blue continuum in the first year, and with a large ratio of $L_{\rm [Ca\,II]}/L_{\rm [O\,I]}\approx 4$ at late times. There is no clear evidence for hydrogen or helium associated with the SN at any phase. We model the light curves with several potential energy sources: radioactive decay, central engine, and circumstellar medium (CSM) interaction. Regardless of the model, the inferred progenitor mass near the end of its life (i.e., CO core mass) is $\gtrsim 55$ M$_\odot$ and up to $120$ M$_\odot$, placing the event in the regime of pulsational pair instability supernovae (PPISNe) or pair instability supernovae (PISNe). The models of CSM interaction provide the most consistent explanation for the light curves and spectra, and require a CSM mass of $\approx 35$ M$_\odot$ ejected in the final decade before explosion. We further find that SN 2016iet is located at an unusually large offset ($16.5$ kpc) from its low metallicity dwarf host galaxy ($Z\approx 0.1$ Z$_\odot$, $M\approx 10^{8.5}$ M$_\odot$), supporting the PPISN/PISN interpretation. In the final spectrum, we detect narrow H$\alpha$ emission at the SN location, likely due to a dim underlying galaxy host or an H II region. Despite the overall consistency of the SN and its unusual environment with PPISNe and PISNe, we find that the inferred properties of SN\,2016iet challenge existing models of such events.Comment: 26 Pages, 17 Figures, Submitted to Ap

Access to Life-Saving Medicines and Intellectual Property Rights: An Ethical Assessment

© 2011 Cambridge University Press. Online edition of the journal is available at http://journals.cambridge.org/action/displayJournal?jid=CQHDying before one’s time has been a prominent theme in classic literature and poetry. Catherine Linton’s youthful death in Wuthering Heights leaves behind a bereft Heathcliff and generations of mourning readers. The author herself, Emily Brontë, died young from tuberculosis. John Keats’ Ode on Melancholy captures the transitory beauty of 19th century human lives too often ravished by early death. Keats also died of tuberculosis, aged 25. “The bloom, whose petals nipped before they blew, died on the promise of the fruit” is how Percy Bysshe Shelley expressed his grief over Keats’ death. Emily Dickinson wrote So Has a Daisy Vanished, being driven into depression by the early loss of loved ones from typhoid and tuberculosis

Improved test of Lorentz Invariance in Electrodynamics using Rotating Cryogenic Sapphire Oscillators

We present new results from our test of Lorentz invariance, which compares two orthogonal cryogenic sapphire microwave oscillators rotating in the lab. We have now acquired over 1 year of data, allowing us to avoid the short data set approximation (less than 1 year) that assumes no cancelation occurs between the $\tilde{\kappa}_{e-}$ and $\tilde{\kappa}_{o+}$ parameters from the photon sector of the standard model extension. Thus, we are able to place independent limits on all eight $\tilde{\kappa}_{e-}$ and $\tilde{\kappa}_{o+}$ parameters. Our results represents up to a factor of 10 improvement over previous non rotating measurements (which independently constrained 7 parameters), and is a slight improvement (except for $\tilde{\kappa}_{e-}^{ZZ}$) over results from previous rotating experiments that assumed the short data set approximation. Also, an analysis in the Robertson-Mansouri-Sexl framework allows us to place a new limit on the isotropy parameter $P_{MM}=\delta-\beta+{1/2}$ of $9.4(8.1)\times10^{-11}$, an improvement of a factor of 2.Comment: Accepted for publication in Phys. Rev.

Seeking the Goal in the Process, the Process for the Goal: Organizational Learning in a Public Sector Change Project

This paper describes how a combination of process modelling and goal modelling techniques has been used to facilitate organizational learning. The case study comes from the public sector in the UK. The modelling techniques have helped users to rationalise about the existing processes and then to design how they would like the process to work. The paper describes how the users have been able to confront the complex issues involved. The experience suggests that the combination of the modelling techniques is important to the learning experience of the users involved

Coordinated circadian timing through the integration of local inputs in Arabidopsis thaliana.

Individual plant cells have a genetic circuit, the circadian clock, that times key processes to the day-night cycle. These clocks are aligned to the day-night cycle by multiple environmental signals that vary across the plant. How does the plant integrate clock rhythms, both within and between organs, to ensure coordinated timing? To address this question, we examined the clock at the sub-tissue level across Arabidopsis thaliana seedlings under multiple environmental conditions and genetic backgrounds. Our results show that the clock runs at different speeds (periods) in each organ, which causes the clock to peak at different times across the plant in both constant environmental conditions and light-dark (LD) cycles. Closer examination reveals that spatial waves of clock gene expression propagate both within and between organs. Using a combination of modeling and experiment, we reveal that these spatial waves are the result of the period differences between organs and local coupling, rather than long-distance signaling. With further experiments we show that the endogenous period differences, and thus the spatial waves, can be generated by the organ specificity of inputs into the clock. We demonstrate this by modulating periods using light and metabolic signals, as well as with genetic perturbations. Our results reveal that plant clocks can be set locally by organ-specific inputs but coordinated globally via spatial waves of clock gene expression

Host brood traits, independent of adult behaviours, reduce Varroa destructor mite reproduction in resistant honeybee populations.

The ectoparasitic mite Varroa destructor is an invasive species of Western honey bees (Apis mellifera) and the largest pathogenic threat to their health world-wide. Its successful invasion and expansion is related to its ability to exploit the worker brood for reproduction, which results in an exponential population growth rate in the new host. With invasion of the mite, wild honeybee populations have been nearly eradicated from Europe and North America, and the survival of managed honeybee populations relies on mite population control treatments. However, there are a few documented honeybee populations surviving extended periods without control treatments due to adapted host traits that directly impact Varroa mite fitness. The aim of this study was to investigate if Varroa mite reproductive success was affected by traits of adult bee behaviours or by traits of the worker brood, in three mite-resistant honey bee populations from Sweden, France and Norway. The mite's reproductive success was measured and compared in broods that were either exposed to, or excluded from, adult bee access. Mite-resistant bee populations were also compared with a local mite-susceptible population, as a control group. Our results show that mite reproductive success rates and mite fecundity in the three mite-resistant populations were significantly different from the control population, with the French and Swedish populations having significantly lower reproductive rates than the Norwegian population. When comparing mite reproduction in exposed or excluded brood treatments, no differences were observed, regardless of population. This result clearly demonstrates that Varroa mite reproductive success can be suppressed by traits of the brood, independent of adult worker bees