High-order gauge-invariant perturbations of a spherical spacetime

We complete the formulation of a general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbations. We present a general algorithm to construct these invariants and provide explicit formulas for the case of second-order metric perturbations. We show that the well-known problem of lack of invariance for the first-order perturbations with l=0,1 propagates to increasing values of l for perturbations of higher order, owing to mode coupling. We also discuss in which circumstances it is possible to construct the invariants

Evaluation of tree-based routing Ethernet

Tree-based Routing (TRE) revisits Tree-based Routing Architecture for Irregular Networks (TRAIN)—a forwarding scheme based on a spanning tree that was extended to use some shortcut links.We propose its adaptation to Ethernet, using a new type of hierarchical Ethernet addresses and a procedure to assign them to bridges. We show that compared to RSTP, TRE offers improved throughput. The impact of transient loops in TRE is lower compared to the application of the classical shortest path routing protocols to Ethernet. Finally, TRE is self-configuring and its forwarding process is simpler and more efficient than in standard Ethernet and shortest path routing proposals.Publicad

Hierarchical Up/Down Routing Architecture for Ethernet backbones and campus networks

We describe a new layer two distributed and scalable routing architecture. It uses an automatic hierarchical node identifier assignment mechanism associated to the rapid spanning tree protocol. Enhanced up/down mechanisms are used to prohibit some turns at nodes to break cycles, instead of blocking links like the spannning tree protocol does. The protocol performance is similar or better than other turn prohibition algorithms recently proposed with lower complexity O(Nd) and better scalability. Simulations show that the fraction of prohibited turns over random networks is less than 0.2. The effect of root bridge election on the performance of the protocol is limited both in the random and regular networks studied. The use of hierarchical, tree-descriptive addresses simplifies the routing, and avoids the need of all nodes having a global knowleddge of the network topology. Routing frames through the hierarchical tree at very high speed is possible by progressive decoding of frame destination address, without routing tables or port address learning. Coexistence with standard bridges is achieved using combined devices: bridges that forward the frames having global destination MAC addresses as standard bridges and frames with local MAC frames with the proposed protocol.Publicad

Second and higher-order perturbations of a spherical spacetime

The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory. The GS harmonics are generalized to an arbitrary number of indices on the unit sphere and a formula is given for their products. The formalism is optimized for its implementation in a computer algebra system, something that becomes essential in practice given the size and complexity of the equations. All evolution equations for the second-order perturbations, as well as the conservation equations for the energy-momentum tensor at this perturbation order, are given in covariant form, in Regge-Wheeler gauge.Comment: Accepted for publication in Physical Review

Improving the statistical detection of regulated genes from microarray data using intensity-based variance estimation

BACKGROUND: Gene microarray technology provides the ability to study the regulation of thousands of genes simultaneously, but its potential is limited without an estimate of the statistical significance of the observed changes in gene expression. Due to the large number of genes being tested and the comparatively small number of array replicates (e.g., N = 3), standard statistical methods such as the Student's t-test fail to produce reliable results. Two other statistical approaches commonly used to improve significance estimates are a penalized t-test and a Z-test using intensity-dependent variance estimates. RESULTS: The performance of these approaches is compared using a dataset of 23 replicates, and a new implementation of the Z-test is introduced that pools together variance estimates of genes with similar minimum intensity. Significance estimates based on 3 replicate arrays are calculated using each statistical technique, and their accuracy is evaluated by comparing them to a reliable estimate based on the remaining 20 replicates. The reproducibility of each test statistic is evaluated by applying it to multiple, independent sets of 3 replicate arrays. Two implementations of a Z-test using intensity-dependent variance produce more reproducible results than two implementations of a penalized t-test. Furthermore, the minimum intensity-based Z-statistic demonstrates higher accuracy and higher or equal precision than all other statistical techniques tested. CONCLUSION: An intensity-based variance estimation technique provides one simple, effective approach that can improve p-value estimates for differentially regulated genes derived from replicated microarray datasets. Implementations of the Z-test algorithms are available at

Space of solutions of the Ashtekar-Olmedo-Singh effective black hole model

We consider a general choice of integration constants in the resolution of the dynamical equations derived from a recently proposed effective model that describes black hole spacetimes in the context of loop quantum cosmology. The interest of our analysis is twofold. On the one hand, it allows for a study of the entire space of solutions of the model, which is absent in the literature and is fundamental for understanding the relation with any underlying quantum theory. On the other hand, choices of integration constants that generalize the type of solutions considered so far may lead to exotic behaviors in the effective black hole geometry, as well as modified thermodynamical properties. With these motivations in mind, we discuss the interior and exterior geometries, and present the conditions that a satisfactory matching at the horizons imposes. Then, we turn our attention to the Hawking temperature associated with the black horizon of the model, which we find to be affected by the freedom of choice of integration constants. Finally, we briefly comment on the asymptotic structure of the general solution and compare different notions of mass.Comment: 11 pages, accepted for publication in Physical Review