On the pathwidth of almost semicomplete digraphs

We call a digraph {\em $h$-semicomplete} if each vertex of the digraph has at most $h$ non-neighbors, where a non-neighbor of a vertex $v$ is a vertex $u \neq v$ such that there is no edge between $u$ and $v$ in either direction. This notion generalizes that of semicomplete digraphs which are $0$-semicomplete and tournaments which are semicomplete and have no anti-parallel pairs of edges. Our results in this paper are as follows. (1) We give an algorithm which, given an $h$-semicomplete digraph $G$ on $n$ vertices and a positive integer $k$, in $(h + 2k + 1)^{2k} n^{O(1)}$ time either constructs a path-decomposition of $G$ of width at most $k$ or concludes correctly that the pathwidth of $G$ is larger than $k$. (2) We show that there is a function $f(k, h)$ such that every $h$-semicomplete digraph of pathwidth at least $f(k, h)$ has a semicomplete subgraph of pathwidth at least $k$. One consequence of these results is that the problem of deciding if a fixed digraph $H$ is topologically contained in a given $h$-semicomplete digraph $G$ admits a polynomial-time algorithm for fixed $h$.Comment: 33pages, a shorter version to appear in ESA 201

Theory of stripes in quasi two dimensional rare-earth tritellurides

Even though the rare-earth tritellurides are tetragonal materials with a quasi two dimensional (2D) band structure, they have a "hidden" 1D character. The resultant near-perfect nesting of the Fermi surface leads to the formation of a charge density wave (CDW) state. We show that for this band structure, there are two possible ordered phases: A bidirectional "checkerboard" state would occur if the CDW transition temperature were sufficiently low, whereas a unidirectional "striped" state, consistent with what is observed in experiment, is favored when the transition temperature is higher. This result may also give some insight into why, in more strongly correlated systems, such as the cuprates and nickelates, the observed charge ordered states are generally stripes as opposed to checkerboards.Comment: Added contents and references, changed title and figures. Accepted to PR

Prevalence of cervical disease at age 20 after immunisation with bivalent HPV vaccine at age 12-13 in Scotland: retrospective population study

The manuscript was reviewed by Jo’s Trust, which supports the conclusions. It made the following statement: We think (it has) massive implications for the screening programme, vaccine and also impact on diagnoses in the future. It gives weight for activity to increase vaccine uptake, has implications on screening intervals. The clinically relevant herd protection is very interesting too. It also feeds into our policy calls for a new IT infrastructure (for the screening programme in England) to record and enable invitations based on whether someone has at the vaccine if intervals can be extended. Funding: This study has been undertaken as part of the programme of surveillance of immunisation against human papillomavirus in Scotland, included within the routine work of Health Protection Scotland, a part of the Scottish National Health Service. No funding has been received from industry.Peer reviewedPublisher PD

Inferring effective interactions from the local density of states: application to STM data from Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta}

While the influence of impurities on the local density of states (LDOS) in a metal is notoriously non-local due to interference effects, low order moments of the LDOS in general can be shown to depend only on the local structure of the Hamiltonian. Specifically, we show that an analysis of the spatial variations of these moments permits one to ``work backwards'' from scanning tunneling microscopy (STM) data to infer the local structure of the underlying effective Hamiltonian. Applying this analysis to STM data from the high temperature superconductor, Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, we find that the variations of the electro-chemical potential are remarkably small (i.e., the disorder is, in a sense, weak) but that there are large variations in the local magnitude of the d-wave gap parameter.Comment: 7 pages, 7 figure

THE IMPACT OF ACTIVE LEARNING WITH ADAPTIVE LEARNING SYSTEMS IN GENERAL EDUCATION INFORMATION TECHNOLOGY COURSES

An adaptive learning system is an effective educational tool that meets the individual needs of students, but it is limited in fostering student learning by itself. With active engagement, students learn better than with adaptive learning systems alone. In this study, we investigate the impact of an adaptive learning system with active learning projects on student learning in general education information technology courses. We believe that today\u27s classroom calls for adaptive learning to serve the needs of diverse student populations. Active learning through real-life hands-on learning activities can enhance student learning by allowing them to apply their knowledge to authentic projects. In the classroom, we often find that learning computing with authentic hands-on activities is not only useful, but it contributes to improving student motivation and confidence

Uncertainty rescued: Bohr's complementarity for composite systems

Generalized uncertainty relations may depend not only on the commutator relation of two observables considered, but also on mutual correlations, in particular, on entanglement. The equivalence between the uncertainty relation and Bohr's complementarity thus holds in a much broader sense than anticipated.Comment: Accepted for publication in Phys. Lett.

Star Formation in Disk Galaxies. II. The Effect of Star Formation and Photoelectric Heating on the Formation and Evolution of Giant Molecular Clouds

We investigate the effect of star formation and diffuse photoelectric heating on the properties of giant molecular clouds (GMCs) formed in high resolution (~< 10 pc) global (~ 20 kpc) simulations of isolated Milky Way-type galaxy disks. The clouds are formed through gravitational fragmentation and structures with densities n_H>=100cm^-3 are identified as GMCs. Between 1000-1500 clouds are created in the simulations with masses M > 10^5 Msolar and 180-240 with masses M > 10^6 Msolar in agreement with estimates of the Milky Way's population. We find that the effect of photoelectric heating is to suppress the fragmentation of the ISM, resulting in a filamentary structure in the warm gas surrounding clouds. This environment suppresses the formation of a retrograde rotating cloud population, with 88% of the clouds rotating prograde with respect to the galaxy after 300 Myr. The diffuse heating also reduces the initial star formation rate, slowing the conversation of gas into stars. We therefore conclude that the interstellar environment plays an important role in the GMCs evolution. Our clouds live between 0-20 Myr with a high infant mortality (t' < 3 Myr) due to cloud mergers and star formation. Other properties, including distributions of mass, size and surface density agree well with observations. Collisions between our clouds are common, occurring at a rate of ~1/4 of the orbital period. It is not clear whether such collisions trigger or suppress star formation at our current resolution. Our star formation rate is a factor of 10 higher than observations in local galaxies. This is likely due to the absence of localized feedback in our models.Comment: 25 pages. 18 figures. Accepted for publication in Ap

Resilient High Catalytic Performance of Platinum Nanocatalysts with Porous Graphene Envelope.

Despite the innumerable developments of nanosized and well dispersed noble metal catalysts, the degradation of metal nanoparticle catalysts has proven to be a significant obstacle for the commercialization of the hydrogen fuel cell. Here, the formation of Pt nanoparticle catalysts with a porous graphene envelope has been achieved using a single step low temperature vaporization process. While these Pt-Gr core-shell nanoparticles possess superior resilience to degradation, it comes at the cost of degraded overall catalyst efficacy. However, it is possible to combat this lower overall performance through inclusion of low concentrations of nitrogen precursor in the initial stage of single-step synthesis, inhibiting the formation of complete graphene shells, as verified by atomic resolution aberration-corrected transmission electron microscopy (AC-TEM) imaging. The resultant porous graphene encapsulated Pt catalysts are found to have both the high peak performance of the bare Pt nanoparticle catalysts and the increased resilience of the fully shielded Pt-Gr core-shells, with the optimal N-doped Pt-Gr yielding a peak efficiency of 87% compared to bare Pt, and maintaining 90% of its catalytic activity after extended potential cycling. The nitrogen treated Pt-Gr core-shells thus act as an effective substitute catalyst for conventional bare Pt nanoparticles, maintaining their catalytic performance over prolonged use

Finite size effects on the Poynting-Robertson effect: a fully general relativistic treatment

Ever since the first discovery of Poynting and Robertson, the radiation source has been treated as merely a point. Even in a very few studies where the size of the source has been taken into account, the treatment of the problem remained largely non-relativistic. In the present work, we address the issue of the finite size effects on the Poynting-Robertson effect in a fully relativistic manner for the first time. As a result, the emergence and the characteristic of the critical point/suspension orbit can be studied in a systematic and detailed manner.Comment: 11pages, 3figure

Randomised controlled feasibility trial of an evidence-informed behavioural intervention for obese adults with additional risk factors

Peer reviewedPublisher PD