22 research outputs found
A counter-example to a recent version of the Penrose conjecture
By considering suitable axially symmetric slices on the Kruskal spacetime, we
construct counterexamples to a recent version of the Penrose inequality in
terms of so-called generalized apparent horizons.Comment: 12 pages. Appendix added with technical details. To appear in
Classical and Quantum Gravit
Nonexistence of Generalized Apparent Horizons in Minkowski Space
We establish a Positive Mass Theorem for initial data sets of the Einstein
equations having generalized trapped surface boundary. In particular we answer
a question posed by R. Wald concerning the existence of generalized apparent
horizons in Minkowski space
On the Penrose Inequality for Charged Black Holes
In arXiv:0905.2622v1 and arXiv:0910.4785v1, Bray and Khuri outlined an
approach to prove the Penrose inequality for general initial data sets of the
Einstein equations. In this paper we extend this approach so that it may be
applied to a charged version of the Penrose inequality. Moreover, assuming that
the initial data is time symmetric, we prove the rigidity statement in the case
of equality for the charged Penrose inequality, a result which seems to be
absent from the literature. A new quasi-local mass, tailored to charged initial
data sets is also introduced, and used in the proof.Comment: 19 pages; final versio
Existence, Regularity, and Properties of Generalized Apparent Horizons
We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the
existence of the outermost generalized apparent horizon in an initial data set
and that it is outer area minimizing.Comment: 16 pages, thoroughly revised, no major changes, to appear in Comm.
Math. Phy
Geometric inequalities for axially symmetric black holes
A geometric inequality in General Relativity relates quantities that have
both a physical interpretation and a geometrical definition. It is well known
that the parameters that characterize the Kerr-Newman black hole satisfy
several important geometric inequalities. Remarkably enough, some of these
inequalities also hold for dynamical black holes. This kind of inequalities
play an important role in the characterization of the gravitational collapse,
they are closed related with the cosmic censorship conjecture. Axially
symmetric black holes are the natural candidates to study these inequalities
because the quasi-local angular momentum is well defined for them. We review
recent results in this subject and we also describe the main ideas behind the
proofs. Finally, a list of relevant open problem is presented.Comment: 65 pages, 5 figures. Review article, to appear in Class. Quantum
Grav. as Topical Review. Improved presentation, minor corrections, references
updat
Identification of critical paralog groups with indispensable roles in the regulation of signaling flow
Extensive cross-talk between signaling pathways is required to integrate the myriad of extracellular signal combinations at the cellular level. Gene duplication events may lead to the emergence of novel functions, leaving groups of similar genes - termed paralogs - in the genome. To distinguish critical paralog groups (CPGs) from other paralogs in human signaling networks, we developed a signaling network-based method using cross-talk annotation and tissue-specific signaling flow analysis. 75 CPGs were found with higher degree, betweenness centrality, closeness, and ‘bowtieness’ when compared to other paralogs or other proteins in the signaling network. CPGs had higher diversity in all these measures, with more varied biological functions and more specific post-transcriptional regulation than non-critical paralog groups (non-CPG). Using TGF-beta, Notch and MAPK pathways as examples, SMAD2/3, NOTCH1/2/3 and MEK3/6-p38 CPGs were found to regulate the signaling flow of their respective pathways. Additionally, CPGs showed a higher mutation rate in both inherited diseases and cancer, and were enriched in drug targets. In conclusion, the results revealed two distinct types of paralog groups in the signaling network: CPGs and non-CPGs. Thus highlighting the importance of CPGs as compared to non-CPGs in drug discovery and disease pathogenesis