Simultaneous Graph Embeddings with Fixed Edges

We study the problem of simultaneously embedding several graphs on the same vertex set in such a way that edges common to two or more graphs are represented by the same curve. This problem is known as simultaneously embedding graphs with fixed edges. We show that this problem is closely related to the weak realizability problem: Can a graph be drawn such that all edge crossings occur in a given set of edge pairs? By exploiting this relationship we can explain why the simultaneous embedding problem is challenging, both from a computational and a combinatorial point of view. More precisely, we prove that simultaneously embedding graphs with fixed edges is NP-complete even for three planar graphs. For two planar graphs the complexity status is still open

Simultaneous Graph Embeddings with Fixed Edges

We study the problem of simultaneously embedding several graphs on the same vertex set in such a way that edges common to two or more graphs are represented by the same curve. This problem is known as simultaneously embedding graphs with fixed edges. We show that this problem is closely related to the weak realizability problem: Can a graph be drawn such that all edge crossings occur in a given set of edge pairs? By exploiting this relationship we can explain why the simultaneous embedding problem is challenging, both from a computational and a combinatorial point of view. More precisely, we prove that simultaneously embedding graphs with fixed edges is NP-complete even for three planar graphs. For two planar graphs the complexity status is still open

Row-switched states in two-dimensional underdamped Josephson junction arrays

When magnetic flux moves across layered or granular superconductor structures, the passage of vortices can take place along channels which develop finite voltage, while the rest of the material remains in the zero-voltage state. We present analytical studies of an example of such mixed dynamics: the row-switched (RS) states in underdamped two-dimensional Josephson arrays, driven by a uniform DC current under external magnetic field but neglecting self-fields. The governing equations are cast into a compact differential-algebraic system which describes the dynamics of an assembly of Josephson oscillators coupled through the mesh current. We carry out a formal perturbation expansion, and obtain the DC and AC spatial distributions of the junction phases and induced circulating currents. We also estimate the interval of the driving current in which a given RS state is stable. All these analytical predictions compare well with our numerics. We then combine these results to deduce the parameter region (in the damping coefficient versus magnetic field plane) where RS states can exist.Comment: latex, 48 pages, 15 figs using psfi

Physiological correlates of intellectual function in children with sickle cell disease: hypoxemia, hyperaemia and brain infarction

Lowered intelligence relative to controls is evident by mid-childhood in children with sickle cell disease. There is consensus that brain infarct contributes to this deficit, but the subtle lowering of IQ in children with normal MRI scans might be accounted for by chronic systemic complications leading to insufficient oxygen delivery to the brain. We investigated the relationship between daytime oxyhaemoglobin saturation (SpO2), cerebral blood flow velocity (CBFV) and intellectual function (IQ) using path-analysis in 30 adolescents with sickle cell disease (mean age 17.4 years, SD 4.2). Initial analyses revealed that the association between SpO2 and Full Scale IQ (FSIQ) was fully mediated by increased CBFV, whereby SpO2 was negatively correlated with CBFV and CBFV was negatively correlated with FSIQ, i.e. decreases in oxygen saturation are associated with increases in velocity, and increased velocity is associated with lowered IQ scores. The mediated relationship suggests that lowered IQ may be a function of abnormal oxygen delivery to the brain. Further analyses showed that the association between CBFV and IQ was significant for verbal but not for performance IQ. The pathophysiology characteristic of SCD can interfere with brain function and constrain intellectual development, even in the absence of an infarct. This supports the hypothesis that lowered intellectual function is partly explained by chronic hypoxia, and has wider implications for our understanding of SCD pathophysiology

Unfractionated Heparin and New Heparin Analogues from Ascidians (Chordate-Tunicate) Ameliorate Colitis in Rats*

The anti-inflammatory effect of mammalian heparin analogues, named dermatan sulfate and heparin, isolated from the ascidian Styela plicata was accessed in a TNBS-induced colitis model in rats. Subcutaneous administration of the invertebrate compounds during a 7-day period drastically reduced inflammation as observed by the normalization of the macroscopic and histological characteristics of the colon. At the molecular level, a decrease in the production of TNF-α, TGF-β, and VEGF was observed, as well as a reduction of NF-κB and MAPK kinase activation. At the cellular level, the heparin analogues attenuated lymphocyte and macrophage recruitment and epithelial cell apoptosis. A drastic reduction in collagen-mediated fibrosis was also observed. No hemorrhagic events were observed after glycan treatment. These results strongly indicate the potential therapeutic use of these compounds for the treatment of colonic inflammation with a lower risk of hemorrhage when compared with mammalian heparin