Gravity on a 3-brane in 6D Bulk

We study gravity in codimension-2 brane world scenarios with infinite volume extra dimensions. In particular, we consider the case where the brane has non-zero tension. The extra space then is a two-dimensional ``wedge'' with a deficit angle. In such backgrounds we can effectively have the Einstein-Hilbert term on the brane at the classical level if we include higher curvature (Gauss-Bonnet) terms in the bulk. Alternatively, such a term would be generated at the quantum level if the brane matter is not conformal. We study (linearized) gravity in the presence of the Einstein-Hilbert term on the brane in such backgrounds. We find that, just as in the original codimension-2 Dvali-Gabadadze model with a tensionless brane, gravity is almost completely localized on the brane with ultra-light modes penetrating into the bulk.Comment: 16 pages, revtex; references added (to appear in Phys. Lett. B

Fast R Functions for Robust Correlations and Hierarchical Clustering

Many high-throughput biological data analyses require the calculation of large correlation matrices and/or clustering of a large number of objects. The standard R function for calculating Pearson correlation can handle calculations without missing values efficiently, but is inefficient when applied to data sets with a relatively small number of missing data. We present an implementation of Pearson correlation calculation that can lead to substantial speedup on data with relatively small number of missing entries. Further, we parallelize all calculations and thus achieve further speedup on systems where parallel processing is available. A robust correlation measure, the biweight midcorrelation, is implemented in a similar manner and provides comparable speed. The functions cor and bicor for fast Pearson and biweight midcorrelation, respectively, are part of the updated, freely available R package WGCNA. The hierarchical clustering algorithm implemented in R function hclust is an order n3 (n is the number of clustered objects) version of a publicly available clustering algorithm (Murtagh 2012). We present the package flashClust that implements the original algorithm which in practice achieves order approximately n2, leading to substantial time savings when clustering large data sets

A Remark on Smoothing Out Higher Codimension Branes

We discuss some issues arising in studying (linearized) gravity on non-BPS higher codimension branes in an infinite-volume bulk. In particular, such backgrounds are badly singular for codimension-3 and higher delta-function-like branes with non-zero tension. As we discuss in this note, non-trivial issues arise in smoothing out such singularities. Thus, adding higher curvature terms might be necessary in this context.Comment: 8 pages, revtex, a minor misprint corrected (to appear in Mod. Phys. Lett. A

Gravitational Higgs Mechanism

We discuss the gravitational Higgs mechanism in domain wall background solutions that arise in the theory of 5-dimensional Einstein-Hilbert gravity coupled to a scalar field with a non-trivial potential. The scalar fluctuations in such backgrounds can be completely gauged away, and so can be the graviphoton fluctuations. On the other hand, we show that the graviscalar fluctuations do not have normalizable modes. As to the 4-dimensional graviton fluctuations, in the case where the volume of the transverse dimension is finite the massive modes are plane-wave normalizable, while the zero mode is quadratically normalizable. We then discuss the coupling of domain wall gravity to localized 4-dimensional matter. In particular, we point out that this coupling is consistent only if the matter is conformal. This is different from the Randall-Sundrum case as there is a discontinuity in the delta-function-like limit of such a smooth domain wall - the latter breaks diffeomorphisms only spontaneously, while the Randall-Sundrum brane breaks diffeomorphisms explicitly. Finally, at the quantum level both the domain wall as well as the Randall-Sundrum setups suffer from inconsistencies in the coupling between gravity and localized matter, as well as the fact that gravity is generically expected to be delocalized in such backgrounds due to higher curvature terms.Comment: 16 pages, revtex; a minor correctio

On Tunnelling In Two-Throat Warped Reheating

We revisit the energy transfer necessary for the warped reheating scenario in a two-throat geometry. We study KK mode wavefunctions of the full two-throat system in the Randall--Sundrum (RS) approximation and find an interesting subtlety in the calculation of the KK mode tunnelling rate. While wavepacket tunnelling is suppressed unless the Standard Model throat is very long, wavefunctions of modes localized in different throats have a non-zero overlap and energy can be transferred between the throats by interactions between such KK modes. The corresponding decay rates are calculated and found to be faster than the tunnelling rates found in previously published works. However, it turns out that the imaginary parts of the mode frequencies, induced by the decay, slow the decay rates themselves down. The self-consistent decay rate turns out to be given by the plane wave tunnelling rate considered previously in the literature. We then discuss mechanisms that may enhance the energy transfer between the throats over the RS rates. In particular, we study models in which the warp factor changes in the UV region less abruptly than in the RS model, and find that it is easy to build phenomenological models in which the plane wave tunnelling rate, and hence the KK mode interaction rates, are enhanced compared to the standard RS setup.Comment: 27 pages + appendices, 5 figures, latex. v2: Discussion of decay in Section 4 changed: the most dangerous graviton amplitudes are zero, the results are now more positive for the warped reheating scenario; typos fixed, discussion cleaned up. v3:corrections in Section 5 (decay rates slowed down), mild changes of overall conclusion

A note on spherically symmetric naked singularities in general dimension

We discuss generalizations of the recent theorem by Dafermos (hep-th/0403033) forbidding a certain class of naked singularities in the spherical collapse of a scalar field. Employing techniques similar to the ones Dafermos used, we consider extending the theorem (1) to higher dimensions, (2) by including more general matter represented by a stress-energy tensor satisfying certain assumptions, and (3) by replacing the spherical geometry by a toroidal or higher genus (locally hyperbolic) one. We show that the extension to higher dimensions and a more general topology is straightforward; on the other hand, replacing the scalar field by a more general matter content forces us to shrink the class of naked singularities we are able to exclude. We then show that the most common matter theories (scalar field interacting with a non-abelian gauge field and a perfect fluid satisfying certain conditions) obey the assumptions of our weaker theorem, and we end by commenting on the applicability of our results to the five-dimensional AdS scenarii considered recently in the literature.Comment: 16 pages, no figures, typos fixe

A Remark on Non-conformal Non-supersymmetric Theories with Vanishing Vacuum Energy Density

We discuss non-conformal non-supersymmetric large N gauge theories with vanishing vacuum energy density to all orders in perturbation theory. These gauge theories can be obtained via a field theory limit of Type IIB D3-branes embedded in orbifolded space-times. We also discuss gravity in this setup.Comment: 13 pages, revtex; a minor change in wordin

Does the Tachyon Matter?

We study time-dependent solutions of Einstein-Maxwell gravity in four dimensions coupled to tachyon matter--the Dirac-Born-Infeld Lagrangian that provides an effective description of a decaying tachyon on an unstable D-brane in string theory. Asymptotically, the solutions are similar to the recently studied space-like brane solutions and carry S-brane charge. They do not break the Lorentzian R-symmetry. We study the tachyon matter as a probe in such a background and analyze its backreaction. For early/late times, the tachyon field has a constant energy density and vanishing pressure as in flat space. On the other hand, at intermediate times, the energy density of the tachyon diverges and produces a space-like curvature singularity.Comment: 15 pages, 1 figure, v2: refs added, v3: two more refs adde

Integrated genomics and proteomics define huntingtin CAG length-dependent networks in mice.

To gain insight into how mutant huntingtin (mHtt) CAG repeat length modifies Huntington's disease (HD) pathogenesis, we profiled mRNA in over 600 brain and peripheral tissue samples from HD knock-in mice with increasing CAG repeat lengths. We found repeat length-dependent transcriptional signatures to be prominent in the striatum, less so in cortex, and minimal in the liver. Coexpression network analyses revealed 13 striatal and 5 cortical modules that correlated highly with CAG length and age, and that were preserved in HD models and sometimes in patients. Top striatal modules implicated mHtt CAG length and age in graded impairment in the expression of identity genes for striatal medium spiny neurons and in dysregulation of cyclic AMP signaling, cell death and protocadherin genes. We used proteomics to confirm 790 genes and 5 striatal modules with CAG length-dependent dysregulation at the protein level, and validated 22 striatal module genes as modifiers of mHtt toxicities in vivo

Is human blood a good surrogate for brain tissue in transcriptional studies?

Abstract Background Since human brain tissue is often unavailable for transcriptional profiling studies, blood expression data is frequently used as a substitute. The underlying hypothesis in such studies is that genes expressed in brain tissue leave a transcriptional footprint in blood. We tested this hypothesis by relating three human brain expression data sets (from cortex, cerebellum and caudate nucleus) to two large human blood expression data sets (comprised of 1463 individuals). Results We found mean expression levels were weakly correlated between the brain and blood data (r range: [0.24,0.32]). Further, we tested whether co-expression relationships were preserved between the three brain regions and blood. Only a handful of brain co-expression modules showed strong evidence of preservation and these modules could be combined into a single large blood module. We also identified highly connected intramodular "hub" genes inside preserved modules. These preserved intramodular hub genes had the following properties: first, their expression levels tended to be significantly more heritable than those from non-preserved intramodular hub genes (p < 10-90); second, they had highly significant positive correlations with the following cluster of differentiation genes: CD58, CD47, CD48, CD53 and CD164; third, a significant number of them were known to be involved in infection mechanisms, post-transcriptional and post-translational modification and other basic processes. Conclusions Overall, we find transcriptome organization is poorly preserved between brain and blood. However, the subset of preserved co-expression relationships characterized here may aid future efforts to identify blood biomarkers for neurological and neuropsychiatric diseases when brain tissue samples are unavailable