Some Results On Convex Greedy Embedding Conjecture for 3-Connected Planar Graphs

A greedy embedding of a graph $G = (V,E)$ into a metric space $(X,d)$ is a function $x : V(G) \to X$ such that in the embedding for every pair of non-adjacent vertices $x(s), x(t)$ there exists another vertex $x(u)$ adjacent to $x(s)$ which is closer to $x(t)$ than $x(s)$. This notion of greedy embedding was defined by Papadimitriou and Ratajczak (Theor. Comput. Sci. 2005), where authors conjectured that every 3-connected planar graph has a greedy embedding (possibly planar and convex) in the Euclidean plane. Recently, greedy embedding conjecture has been proved by Leighton and Moitra (FOCS 2008). However, their algorithm do not result in a drawing that is planar and convex for all 3-connected planar graph in the Euclidean plane. In this work we consider the planar convex greedy embedding conjecture and make some progress. We derive a new characterization of planar convex greedy embedding that given a 3-connected planar graph $G = (V,E)$, an embedding x: V \to \bbbr^2 of $G$ is a planar convex greedy embedding if and only if, in the embedding $x$, weight of the maximum weight spanning tree ($T$) and weight of the minimum weight spanning tree (\func{MST}) satisfies \WT(T)/\WT(\func{MST}) \leq (\card{V}-1)^{1 - \delta}, for some $0 < \delta \leq 1$.Comment: 19 pages, A short version of this paper has been accepted for presentation in FCT 2009 - 17th International Symposium on Fundamentals of Computation Theor

Admission C – reactive protein after acute ischemic stroke is associated with stroke severity and mortality: The 'Bergen stroke study'

<p>Abstract</p> <p>Background</p> <p>There is growing evidence that inflammation plays an important role in atherogenesis. Previous studies show that C-reactive protein (CRP), an inflammatory marker, is associated with stroke outcomes and future vascular events. It is not clear whether this is due a direct dose-response effect or rather an epiphenomenon. We studied the effect of CRP measured within 24 hours after stroke onset on functional outcome, mortality and future vascular events.</p> <p>Methods</p> <p>We prospectively studied 498 patients with ischemic stroke who were admitted within 24 hours after the onset of symptoms. CRP and NIH stroke scale (NIHSS) were measured at the time of admission. Short-term functional outcome was measured by modified Rankin scale (mRS) and Barthel ADL index (BI) 7 days after admission. Patients were followed for up to 2.5 years for long-term mortality and future vascular events data.</p> <p>Results</p> <p>The median CRP at admission was 3 mg/L. High CRP was associated with high NIHSS (p = 0.01) and high long-term mortality (p < 0.0001). After adjusting for confounding variables, high CRP remained to be associated with high NIHSS (p = 0.02) and high long-term mortality (p = 0.002). High CRP was associated with poor short-term functional outcomes (mRS > 3; BI < 95) (p = 0.01; p = 0.03). However, the association was not significant after adjusting for confounding variables including stroke severity (p = 0.98; p = 0.88). High CRP was not associated with future vascular events (p = 0.98).</p> <p>Conclusion</p> <p>Admission CRP is associated with stroke severity and long-term mortality when measured at least 24 hours after onset. There is a crude association between high CRP and short-term functional outcome which is likely secondary to stroke severity. CRP is an independent predictor of long-term mortality after ischemic stroke.</p

On vertex coloring without monochromatic triangles

We study a certain relaxation of the classic vertex coloring problem, namely, a coloring of vertices of undirected, simple graphs, such that there are no monochromatic triangles. We give the first classification of the problem in terms of classic and parametrized algorithms. Several computational complexity results are also presented, which improve on the previous results found in the literature. We propose the new structural parameter for undirected, simple graphs -- the triangle-free chromatic number $\chi_3$. We bound $\chi_3$ by other known structural parameters. We also present two classes of graphs with interesting coloring properties, that play pivotal role in proving useful observation about our problem. We give/ask several conjectures/questions throughout this paper to encourage new research in the area of graph coloring.Comment: Extended abstrac

A platform approach for the production of Hand, Foot, Mouth Disease vaccines

Hand, Foot and Mouth Disease (HFMD) is an endemic childhood disease in Southeast Asia, with substantial disease burden affecting millions of children each year. Occasionally the central nervous system is involved causing serious and sometimes fatal neurological complications. HFMD outbreaks are also observed outside the Asia-Pacific countries. HFMD can be caused by multiple enteroviruses of which the best known virus is EVA71. However, also other enteroviruses such as CVA6, CVA10 and CVA16 can cause the disease. Inactivated EVA71 vaccines are registered in China, but in order to prevent all HFMD cases, multivalent vaccines are warranted. Intravacc is developing an HFMD combination vaccine. Here we used our rescue platform to generate the starting materials required for vaccine production. Infectious clones from EVA71_B4, EVA71_C4, CVA6, CVA10 and CVA16 were constructed and the corresponding enteroviruses were rescued. Virus seeds were produced on Vero cells in animal component free medium. Rescued enteroviruses could efficiently replicate, resulting in seed lots with high viral titers. This rescue platform has the major advantage that clinical isolates are not required to obtain the starting material to produce a vaccine, thus mitigating the risk that other, unwanted, viruses are also present. Next to that, the virus source is pre-designed, controlled and well documented. Please click Download on the upper right corner to see the full abstract

Finding Disjoint Paths on Directed Acyclic Graphs

Given k+1 pairs of vertices (s_1,s_2),(u_1,v_1),...,(u_k,v_k) of a directed acyclic graph, we show that a modified version of a data structure of Suurballe and Tarjan can output, for each pair (u_l,v_l) with 1<=l<=k, a tuple (s_1,t_1,s_2,t_2) with {t_1,t_2}={u_l,v_l} in constant time such that there are two disjoint paths p_1, from s_1 to t_1, and p_2, from s_2 to t_2, if such a tuple exists. Disjoint can mean vertex- as well as edge-disjoint. As an application we show that the presented data structure can be used to improve the previous best known running time O(mn) for the so called 2-disjoint paths problem on directed acyclic graphs to O(m(log(n)/log(2+m/n))+n*log³(n)). In this problem, given four vertices s_1, s_2, t_1, and t_2, we want to construct two disjoint paths p_1, from s_1 to t_1, and p_2, from s_2 to t_2, if such paths exist

Third generation vaccine for world eradication of poliomyelitis

Great efforts have been undertaken by the World Health Organization to achieve eradication of poliomyelitis, a paralytic disease. At present, two different vaccines are available: inactivated polio vaccine (IPV) developed by Salk based on chemical inactivation of the virus and oral polio vaccine (OPV) developed by Sabin based on live attenuated virus strains. The risks associated with IPV concern the safety of the production process as it is based on highly virulent wild type strains, and in contrast, the OPV risks are associated with the reversibility of the attenuated viruses to a transmissible paralytic form. There is therefore a need for a new generation polio vaccines capable to overcome outbreaks and manufacturing risks. With the evolution of molecular virology of Sabin vaccine strains, it is now possible to design extremely genetically stable and hyperattenuated strains without the associated reversion risks. Sabin poliovirus strains were therefore genetically modified giving rise to the third generation of polio vaccine strains [1, 2]. In the present work we have explored the possibility of using the already well-established IPV production process, developed at our site [3] and integrated worldwide [4] for the production and manufacturing of third generation of IPV strains. Specifically, we have produced third generation vaccines in animal component free medium and at 50-L pilot scale. The product obtained did show acceptable yields and was immunogenic in rats. Together, our results indicate that the third generation vaccine strains produced under the flexible platform process are potential candidates which provide increased biosafety during manufacturing which is necessary after polio eradication. In addition, the flexibility and scalability of the process constitute a platform for the production of a large range of vaccines worldwide. 1. Knowlson, S., et al., New Strains Intended for the Production of Inactivated Polio Vaccine at Low-Containment After Eradication. PLoS Pathog, 2015. 11(12): p. e1005316. 2. Macadam, A.J., et al., Rational design of genetically stable, live-attenuated poliovirus vaccines of all three serotypes: relevance to poliomyelitis eradication. J Virol, 2006. 80(17): p. 8653-63. 3. Thomassen, Y.E., et al., Scale-down of the inactivated polio vaccine production process. Biotechnol Bioeng, 2013. 110(5): p. 1354-65. 4. Wezel, v., Monolayer growth systems: Homogeneous unit processes. Spier, R. E. and Griffiths, J. B., eds., 1985: p. 266-281