Vertex elimination orderings for hereditary graph classes

We provide a general method to prove the existence and compute efficiently elimination orderings in graphs. Our method relies on several tools that were known before, but that were not put together so far: the algorithm LexBFS due to Rose, Tarjan and Lueker, one of its properties discovered by Berry and Bordat, and a local decomposition property of graphs discovered by Maffray, Trotignon and Vu\vskovi\'c. We use this method to prove the existence of elimination orderings in several classes of graphs, and to compute them in linear time. Some of the classes have already been studied, namely even-hole-free graphs, square-theta-free Berge graphs, universally signable graphs and wheel-free graphs. Some other classes are new. It turns out that all the classes that we study in this paper can be defined by excluding some of the so-called Truemper configurations. For several classes of graphs, we obtain directly bounds on the chromatic number, or fast algorithms for the maximum clique problem or the coloring problem

Hall Conductance of a Two-Dimensional Electron Gas in Periodic Lattice with Triangular Antidots

The topic of this contribution is the investigation of quantum states and quantum Hall effect in electron gas subjected to a periodic potential of the lateral lattice. The potential is formed by triangular quantum antidos located on the sites of the square lattice. In a such system the inversion center and the four-fold rotation symmetry are absent. The topological invariants which characterize different magnetic subbands and their Hall conductances are calculated. It is shown that the details of the antidot geometry are crucial for the Hall conductance quantization rule. The critical values of lattice parameters defining the shape of triangular antidots at which the Hall conductance is changed drastically are determined. We demonstrate that the quantum states and Hall conductance quantization law for the triangular antidot lattice differ from the case of the square lattice with cylindrical antidots. As an example, the Hall conductances of magnetic subbands for different antidot geometries are calculated for the case when the number of magnetic flux quanta per unit cell is equal to three.Comment: 6 pages, 5 figure

Low rank perturbations and the spectral statistics of pseudointegrable billiards

We present an efficient method to solve Schr\"odinger's equation for perturbations of low rank. In particular, the method allows to calculate the level counting function with very little numerical effort. To illustrate the power of the method, we calculate the number variance for two pseudointegrable quantum billiards: the barrier billiard and the right triangle billiard (smallest angle $\pi/5$). In this way, we obtain precise estimates for the level compressibility in the semiclassical (high energy) limit. In both cases, our results confirm recent theoretical predictions, based on periodic orbit summation.Comment: 4 page

Classical limit in terms of symbolic dynamics for the quantum baker's map

We derive a simple closed form for the matrix elements of the quantum baker's map that shows that the map is an approximate shift in a symbolic representation based on discrete phase space. We use this result to give a formal proof that the quantum baker's map approaches a classical Bernoulli shift in the limit of a small effective Plank's constant.Comment: 12 pages, LaTex, typos correcte

Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems

We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian depends on quantities which are external to the constraint manifold, such as the external curvature of the constraint manifold, the (Riemannian) curvature of the ambient space, and the constraining potential. In particular, we find the remarkable fact that the twisting of the constraining potential appears as a gauge potential in the constrained Hamiltonian. This gauge potential is an example of geometric phase, closely related to that originally discussed by Berry. The constrained Hamiltonian also contains an effective potential depending on the external curvature of the constraint manifold, the curvature of the ambient space, and the twisting of the constraining potential. The general nature of our analysis allows applications to a wide variety of problems, such as rigid molecules, the evolution of molecular systems along reaction paths, and quantum strip waveguides.Comment: 27 pages with 1 figure, submitted to Phys. Rev.

Acceptability of novel lifelogging technology to determine context of sedentary behaviour in older adults

<strong>Objective:</strong> Lifelogging, using body worn sensors (activity monitors and time lapse photography) has the potential to shed light on the context of sedentary behaviour. The objectives of this study were to examine the acceptability, to older adults, of using lifelogging technology and indicate its usefulness for understanding behaviour.<strong> </strong><strong>Method:</strong> 6 older adults (4 males, mean age: 68yrs) wore the equipment (ActivPAL^TM and Vicon Revue^TM/SenseCam^TM) for 7 consecutive days during free-living activity. The older adults’ perception of the lifelogging technology was assessed through semi-structured interviews, including a brief questionnaire (Likert scale), and reference to the researcher&#39;s diary. <strong>Results:</strong> Older adults in this study found the equipment acceptable to wear and it did not interfere with privacy, safety or create reactivity, but they reported problems with the actual technical functioning of the camera. <strong>Conclusion:</strong> This combination of sensors has good potential to provide lifelogging information on the context of sedentary behaviour

Identifying and prioritising services in European terrestrial and freshwater ecosystems

Ecosystems are multifunctional and provide humanity with a broad array of vital services. Effective management of services requires an improved evidence base, identifying the role of ecosystems in delivering multiple services, which can assist policy-makers in maintaining them. Here, information from the literature and scientific experts was used to systematically document the importance of services and identify trends in their use and status over time for the main terrestrial and freshwater ecosystems in Europe. The results from this review show that intensively managed ecosystems contribute mostly to vital provisioning services (e.g. agro-ecosystems provide food via crops and livestock, and forests provide wood), while semi-natural ecosystems (e.g. grasslands and mountains) are key contributors of genetic resources and cultural services (e.g. aesthetic values and sense of place). The most recent European trends in human use of services show increases in demand for crops from agro-ecosystems, timber from forests, water flow regulation from rivers, wetlands and mountains, and recreation and ecotourism in most ecosystems, but decreases in livestock production, freshwater capture fisheries, wild foods and virtually all services associated with ecosystems which have considerably decreased in area (e.g. semi-natural grasslands). The condition of the majority of services show either a degraded or mixed status across Europe with the exception of recent enhancements in timber production in forests and mountains, freshwater provision, water/erosion/natural hazard regulation and recreation/ecotourism in mountains, and climate regulation in forests. Key gaps in knowledge were evident for certain services across all ecosystems, including the provision of biochemicals and natural medicines, genetic resources and the regulating services of seed dispersal, pest/disease regulation and invasion resistance

Forest continuity and conservation value in Western Europe

Long forest continuity has often been linked with high conservation value in western European Quercus and Fagus woodlands, but this assumption of long continuity has rarely been tested. Birks discussed the antiquity of bryophyte-rich Quercus woodland in western United Kingdom, presenting evidence that the modern plant communities developed during the late Holocene influenced by human activities. We use pollen data from forest hollows to show that the modern communities within ancient woodlands are all significantly influenced by recent human disturbance. A short period of deforestation in Johnny’s Wood, Cumbria, UK dates from the late 19th century and is not of Viking age as previously thought. The brief opening of the forest is associated with the local loss of Tilia cordata and Taxus baccata, but a rich bryophyte community exists today. Rich lichen floras of high conservation interest growing on Fagus sylvatica in south-western Sweden occur despite a recent history of human disturbance and local immigration of Fagus as recently as the 9th century ad. Wistman’s Wood, Cornwall, UK had a diverse tree flora until the 11th century ad and then experienced heavy browsing and grazing until ad 1850, after which time the present Quercus woodland developed with its associated flora of high conservation value. Most western European forests today have long and diverse histories of anthropogenic disturbance and current conservation values incorporate both natural and cultural features. Pollen studies with high spatial resolution demonstrate that simple temporal concepts like ‘natural baselines’ and the continuity of forest cover underestimate the complexity of the past. Long forest continuity may be of importance for the local survival of higher plants, but for the insects, fungi, lichens and bryophytes that are so valued in contemporary European temperate and boreal forests, habitat diversity maintained by dynamic processes would appear to be of greater significance

Wideband THz time domain spectroscopy based on optical rectification and electro-optic sampling

We present an analytical model describing the full electromagnetic propagation in a THz time-domain spectroscopy (THz-TDS) system, from the THz pulses via Optical Rectification to the detection via Electro Optic-Sampling. While several investigations deal singularly with the many elements that constitute a THz-TDS, in our work we pay particular attention to the modelling of the time-frequency behaviour of all the stages which compose the experimental set-up. Therefore, our model considers the following main aspects: (i) pump beam focusing into the generation crystal; (ii) phase-matching inside both the generation and detection crystals; (iii) chromatic dispersion and absorption inside the crystals; (iv) Fabry-Perot effect; (v) diffraction outside, i.e. along the propagation, (vi) focalization and overlapping between THz and probe beams, (vii) electro-optic sampling. In order to validate our model, we report on the comparison between the simulations and the experimental data obtained from the same set-up, showing their good agreement

Implementation of ultrasonic sensing for high resolution measurement of binary gas mixture fractions

We describe an ultrasonic instrument for continuous real-time analysis of the fractional mixture of a binary gas system. The instrument is particularly well suited to measurement of leaks of a high molecular weight gas into a system that is nominally composed of a single gas. Sensitivity &#60; 5 × 10−5 is demonstrated to leaks of octaflouropropane (C3F8) coolant into nitrogen during a long duration (18 month) continuous study. The sensitivity of the described measurement system is shown to depend on the difference in molecular masses of the two gases in the mixture. The impact of temperature and pressure variances on the accuracy of the measurement is analysed. Practical considerations for the implementation and deployment of long term, in situ ultrasonic leak detection systems are also described. Although development of the described systems was motivated by the requirements of an evaporative fluorocarbon cooling system, the instrument is applicable to the detection of leaks of many other gases and to processes requiring continuous knowledge of particular binary gas mixture fractions