The Domination Number of Grids

In this paper, we conclude the calculation of the domination number of all $n\times m$ grid graphs. Indeed, we prove Chang's conjecture saying that for every $16\le n\le m$, $\gamma(G_{n,m})=\lfloor\frac{(n+2)(m+2)}{5}\rfloor -4$.Comment: 12 pages, 4 figure

The omnivorous Tyrolean Iceman: colon contents (meat, cereals, pollen, moss and whipworm) and stable isotope analyses

The contents of the colon of the Tyrolean Iceman who lived Ga. 5300 years ago include muscle fibres, cereal remains, a diversity of pollen, and most notably that of the hop hornbeam (Ostrya carpinifolia) retaining cellular contents, as well as a moss leaf (Neckera complanata) and eggs of the parasitic whipworm (Trichuris trichiura). Based almost solely on stable isotope analyses and ignoring the work on the colon contents, two recently published papers on the Iceman's diet draw ill- founded conclusions about vegetarianism and even veganism. Neither the pollen nor the moss is likely to have been deliberately consumed as food by the Iceman. All the available evidence concerning the Iceman's broad-based diet is reviewed and the significance of the colon contents for matters other than assessment of food intake is outlined

An Experimental Platform for Pulsed-Power Driven Magnetic Reconnection

We describe a versatile pulsed-power driven platform for magnetic reconnection experiments, based on exploding wire arrays driven in parallel [Suttle, L. G. et al. PRL, 116, 225001]. This platform produces inherently magnetised plasma flows for the duration of the generator current pulse (250 ns), resulting in a long-lasting reconnection layer. The layer exists for long enough to allow evolution of complex processes such as plasmoid formation and movement to be diagnosed by a suite of high spatial and temporal resolution laser-based diagnostics. We can access a wide range of magnetic reconnection regimes by changing the wire material or moving the electrodes inside the wire arrays. We present results with aluminium and carbon wires, in which the parameters of the inflows and the layer which forms are significantly different. By moving the electrodes inside the wire arrays, we change how strongly the inflows are driven. This enables us to study both symmetric reconnection in a range of different regimes, and asymmetric reconnection.Comment: 14 pages, 9 figures. Version revised to include referee's comments. Submitted to Physics of Plasma

The plastic number and its generalized polynomial

The polynomial $X^{3}-X-1$ has a unique positive root known as plastic number, which is denoted by $\rho$ and is approximately equal to $1.32471795$. In this note we study the zeroes of the generalized polynomial $X^{k}-\sum_{j=0}^{k-2}X^{j}$ for $k\geq 3$ and prove that its unique positive root $\lambda_{k}$ tends to the golden ratio $\phi=\frac{1+\sqrt{5}}{2}$ as $k \to \infty$. We also derive bounds on $\lambda_{k}$ in terms of Fibonacci numbers.Comment: Publisher's pdf versio

Investigation, Development, and Evaluation of Performance Proving for Fault-tolerant Computers

A number of methodologies for verifying systems and computer based tools that assist users in verifying their systems were developed. These tools were applied to verify in part the SIFT ultrareliable aircraft computer. Topics covered included: STP theorem prover; design verification of SIFT; high level language code verification; assembly language level verification; numerical algorithm verification; verification of flight control programs; and verification of hardware logic

Rotations associated with Lorentz boosts

It is possible to associate two angles with two successive non-collinear Lorentz boosts. If one boost is applied after the initial boost, the result is the final boost preceded by a rotation called the Wigner rotation. The other rotation is associated with Wigner's O(3)-like little group. These two angles are shown to be different. However, it is shown that the sum of these two rotation angles is equal to the angle between the initial and final boosts. This relation is studied for both low-speed and high-speed limits. Furthermore, it is noted that the two-by-two matrices which are under the responsibility of other branches of physics can be interpreted in terms of the transformations of the Lorentz group, or vice versa. Classical ray optics is mentioned as a case in point.Comment: LaTeX, 16 Pages, 4 epsfigure

Airborne multiwavelength High Spectral Resolution Lidar (HSRL-2) observations during TCAP 2012 : Vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US

© Author(s) 2014. This work is distributed under the Creative Commons Attribution 3.0 License.We present measurements acquired by the world's first airborne 3 backscatter (β) + 2 extinction (α) High Spectral Resolution Lidar (HSRL-2). HSRL-2 measures particle backscatter coefficients at 355, 532, and 1064 nm, and particle extinction coefficients at 355 and 532 nm. The instrument has been developed by the NASA Langley Research Center. The instrument was operated during Phase 1 of the Department of Energy (DOE) Two-Column Aerosol Project (TCAP) in July 2012. We observed pollution outflow from the northeastern coast of the US out over the western Atlantic Ocean. Lidar ratios were 50-60 sr at 355 nm and 60-70 sr at 532 nm. Extinction-related Ångström exponents were on average 1.2-1.7, indicating comparably small particles. Our novel automated, unsupervised data inversion algorithm retrieved particle effective radii of approximately 0.2 μm, which is in agreement with the large Ångström exponents. We find good agreement with particle size parameters obtained from coincident in situ measurements carried out with the DOE Gulfstream-1 aircraft.Peer reviewedFinal Published versio

‘O sibling, where art thou?’ – a review of avian sibling recognition with respect to the mammalian literature

Avian literature on sibling recognition is rare compared to that developed by mammalian researchers. We compare avian and mammalian research on sibling recognition to identify why avian work is rare, how approaches differ and what avian and mammalian researchers can learn from each other. Three factors: (1) biological differences between birds and mammals, (2) conceptual biases and (3) practical constraints, appear to influence our current understanding. Avian research focuses on colonial species because sibling recognition is considered adaptive where ‘mixing potential’ of dependent young is high; research on a wider range of species, breeding systems and ecological conditions is now needed. Studies of acoustic recognition cues dominate avian literature; other types of cues (e.g. visual, olfactory) deserve further attention. The effect of gender on avian sibling recognition has yet to be investigated; mammalian work shows that gender can have important influences. Most importantly, many researchers assume that birds recognise siblings through ‘direct familiarisation’ (commonly known as associative learning or familiarity); future experiments should also incorporate tests for ‘indirect familiarisation’ (commonly known as phenotype matching). If direct familiarisation proves crucial, avian research should investigate how periods of separation influence sibling discrimination. Mammalian researchers typically interpret sibling recognition in broad functional terms (nepotism, optimal outbreeding); some avian researchers more successfully identify specific and testable adaptive explanations, with greater relevance to natural contexts. We end by reporting exciting discoveries from recent studies of avian sibling recognition that inspire further interest in this topic

Effectiveness of multifaceted educational programme to reduce antibiotic dispensing in primary care: practice based randomised controlled trial

Objective: To evaluate the effectiveness and costs of a multifaceted flexible educational programme aimed at reducing antibiotic dispensing at the practice level in primary care.<p></p> Design: Randomised controlled trial with general practices as the unit of randomisation and analysis. Clinicians and researchers were blinded to group allocation until after randomisation.<p></p> Setting: 68 general practices with about 480 000 patients in Wales, United Kingdom.<p></p> Participants: 34 practices were randomised to receive the educational programme and 34 practices to be controls. 139 clinicians from the intervention practices and 124 from control practices had agreed to participate before randomisation. Practice level data covering all the clinicians in the 68 practices were analysed.<p></p> Interventions: Intervention practices followed the Stemming the Tide of Antibiotic Resistance (STAR) educational programme, which included a practice based seminar reflecting on the practices’ own dispensing and resistance data, online educational elements, and practising consulting skills in routine care. Control practices provided usual care.<p></p> Main outcome measures: Total numbers of oral antibiotic items dispensed for all causes per 1000 practice patients in the year after the intervention, adjusted for the previous year’s dispensing. Secondary outcomes included reconsultations, admissions to hospital for selected causes, and costs.<p></p> Results: The rate of oral antibiotic dispensing (items per 1000 registered patients) decreased by 14.1 in the intervention group but increased by 12.1 in the control group, a net difference of 26.1. After adjustment for baseline dispensing rate, this amounted to a 4.2% (95% confidence interval 0.6% to 7.7%) reduction in total oral antibiotic dispensing for the year in the intervention group relative to the control group (P=0.02). Reductions were found for all classes of antibiotics other than penicillinase-resistant penicillins but were largest and significant individually for phenoxymethylpenicillins (penicillin V) (7.3%, 0.4% to 13.7%) and macrolides (7.7%, 1.1% to 13.8%). There were no significant differences between intervention and control practices in the number of admissions to hospital or in reconsultations for a respiratory tract infection within seven days of an index consultation. The mean cost of the programme was £2923 (€3491, $4572) per practice (SD £1187). There was a 5.5% reduction in the cost of dispensed antibiotics in the intervention group compared with the control group (−0.4% to 11.4%), equivalent to a reduction of about £830 a year for an average intervention practice.<p></p> Conclusion: The STAR educational programme led to reductions in all cause oral antibiotic dispensing over the subsequent year with no significant change in admissions to hospital, reconsultations, or costs