20,640 research outputs found
Computing maximum cliques in -EPG graphs
EPG graphs, introduced by Golumbic et al. in 2009, are edge-intersection
graphs of paths on an orthogonal grid. The class -EPG is the subclass of
EPG graphs where the path on the grid associated to each vertex has at most
bends. Epstein et al. showed in 2013 that computing a maximum clique in
-EPG graphs is polynomial. As remarked in [Heldt et al., 2014], when the
number of bends is at least , the class contains -interval graphs for
which computing a maximum clique is an NP-hard problem. The complexity status
of the Maximum Clique problem remains open for and -EPG graphs. In
this paper, we show that we can compute a maximum clique in polynomial time in
-EPG graphs given a representation of the graph.
Moreover, we show that a simple counting argument provides a
-approximation for the coloring problem on -EPG graphs without
knowing the representation of the graph. It generalizes a result of [Epstein et
al, 2013] on -EPG graphs (where the representation was needed)
Polarization and readout of coupled single spins in diamond
We study the coupling of a single nitrogen-vacancy center in diamond to a
nearby single nitrogen defect at room temperature. The magnetic dipolar
coupling leads to a splitting in the electron spin resonance frequency of the
nitrogen-vacancy center, allowing readout of the state of a single nitrogen
electron spin. At magnetic fields where the spin splitting of the two centers
is the same we observe a strong polarization of the nitrogen electron spin. The
amount of polarization can be controlled by the optical excitation power. We
combine the polarization and the readout in time-resolved pump-probe
measurements to determine the spin relaxation time of a single nitrogen
electron spin. Finally, we discuss indications for hyperfine-induced
polarization of the nitrogen nuclear spin
Abstract Tensor Systems as Monoidal Categories
The primary contribution of this paper is to give a formal, categorical
treatment to Penrose's abstract tensor notation, in the context of traced
symmetric monoidal categories. To do so, we introduce a typed, sum-free version
of an abstract tensor system and demonstrate the construction of its associated
category. We then show that the associated category of the free abstract tensor
system is in fact the free traced symmetric monoidal category on a monoidal
signature. A notable consequence of this result is a simple proof for the
soundness and completeness of the diagrammatic language for traced symmetric
monoidal categories.Comment: Dedicated to Joachim Lambek on the occasion of his 90th birthda
Oesophageal ulceration in HIV-infected patients
Objective. To determine the aetiology of oesophageal ulceration in HIV-infected patients. Design. A retrospective clinical, endoscopic and histopathological analysis of patients with confirmed HIV infection and an oesophageal ulcer diagnosed on endoscopy. Setting. A tertiary referral, gastrointestinal clinic in Cape Town. Results. Fifty-one patients with HIV infection and oesophageal ulceration were seen from January 2001 to December 2007. Median CD4 count was 26 cells/µl. Mean age was 35.5 years. Sixty per cent of patients were female. Forty-nine per cent of oesophageal ulcers were idiopathic while 23% were caused by cytomegalovirus infection. The remainder were due to miscellaneous causes. Conclusion. A surprisingly small number of patients with HIV associated oesophageal ulceration were seen during the study period. This may reflect local referral practices or the fact that patients with severe immunosuppression succumb before developing oesophageal ulcers. As in other series, idiopathic oesophageal ulcers and cytomegalovirus ulcers made up the majority of cases. Correct biopsy technique and appropriate histological and microbiological investigations are associated with improved diagnostic yield in these patients
Factors Affecting the Corporate Decision-Making Process of Air Transport Manufacturers
Fuel economy is a pivotal question influencing the future sale and utilization of commercial aircraft. The NASA Aircraft Energy Efficiency (ACEE) Program Office has a program intended to accelerate the readiness of advanced technologies for energy efficient aircraft. Because the decision to develop a new airframe or engine is a major financial hazard for manufacturers, it is important to know what factors influence the decision making process. A method is described for identifying and ranking individuals and organizations involved at each stage of commercial air transport development, and the barriers that must be overcome in adopting new technologies
Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity
In the framework of perturbative algebraic quantum field theory a local
construction of interacting fields in terms of retarded products is performed,
based on earlier work of Steinmann. In our formalism the entries of the
retarded products are local functionals of the off shell classical fields, and
we prove that the interacting fields depend only on the action and not on terms
in the Lagrangian which are total derivatives, thus providing a proof of
Stora's 'Action Ward Identity'. The theory depends on free parameters which
flow under the renormalization group. This flow can be derived in our local
framework independently of the infrared behavior, as was first established by
Hollands and Wald. We explicitly compute non-trivial examples for the
renormalization of the interaction and the field.Comment: 76 pages, to appear in Rev. Math. Phy
A note on the algebraic growth rate of Poincar\'e series for Kleinian groups
In this note we employ infinite ergodic theory to derive estimates for the
algebraic growth rate of the Poincar\'e series for a Kleinian group at its
critical exponent of convergence.Comment: 8 page
Vacuum polarization around stars: nonlocal approximation
We compute the vacuum polarization associated with quantum massless fields
around stars with spherical symmetry. The nonlocal contribution to the vacuum
polarization is dominant in the weak field limit, and induces quantum
corrections to the exterior metric that depend on the inner structure of the
star. It also violates the null energy conditions. We argue that similar
results also hold in the low energy limit of quantum gravity. Previous
calculations of the vacuum polarization in spherically symmetric spacetimes,
based on local approximations, are not adequate for newtonian stars.Comment: 8 pages, no figure
EPG-representations with small grid-size
In an EPG-representation of a graph each vertex is represented by a path
in the rectangular grid, and is an edge in if and only if the paths
representing an share a grid-edge. Requiring paths representing edges
to be x-monotone or, even stronger, both x- and y-monotone gives rise to three
natural variants of EPG-representations, one where edges have no monotonicity
requirements and two with the aforementioned monotonicity requirements. The
focus of this paper is understanding how small a grid can be achieved for such
EPG-representations with respect to various graph parameters.
We show that there are -edge graphs that require a grid of area
in any variant of EPG-representations. Similarly there are
pathwidth- graphs that require height and area in
any variant of EPG-representations. We prove a matching upper bound of
area for all pathwidth- graphs in the strongest model, the one where edges
are required to be both x- and y-monotone. Thus in this strongest model, the
result implies, for example, , and area bounds
for bounded pathwidth graphs, bounded treewidth graphs and all classes of
graphs that exclude a fixed minor, respectively. For the model with no
restrictions on the monotonicity of the edges, stronger results can be achieved
for some graph classes, for example an area bound for bounded treewidth
graphs and bound for graphs of bounded genus.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
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