The Geometry of Warped Product Singularities

In this article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.Comment: 14 page

The Friedmann-Lemaitre-Robertson-Walker Big Bang singularities are well behaved

We show that the Big Bang singularity of the Friedmann-Lemaitre-Robertson-Walker model does not raise major problems to General Relativity. We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang. The physical interpretation of the fields used is discussed. These results follow from our research on singular semi-Riemannian geometry and singular General Relativity.Comment: 10 pages, 5 figure

Short-range nuclear effects on axion emissivities by nucleon-nucleon bremsstrahlung

The rates of axion emission by nucleon-nucleon (NN) bremsstrahlung are reconsidered by taking into account the NN short range correlations. The analytical formulas for the neutron-neutron (nn), proton-proton (pp) and neutron-proton (np) processes with the inclusion of the full momentum dependence of an one- and two- pion exchange nuclear potentials, in the non-degenerate limit, are explicitly given. We find that the two-pion exchange (short range) effects can give a significant contribution to the emission rates, and are temperature dependent. Other short range nuclear effects like effective nucleon mass, polarization effects and use of correlated wave functions, are discused as well. The trend of all these nuclear effects is to diminish the corresponding axion emission rates. Further, we estimate that the values of the emission rates calculated with the inclusion of all these effects can differ from the corresponding ones derived with constant nuclear matrix elements by a factor of $\sim 24$. This leads to an uncertainty factor of $\sim 4.9$ when extracting bounds of the axion parametersComment: 11 pages, 4 figure

Reducing Congestion Effects by Multipath Routing in Wireless Networks

We propose a solution to improve fairness and increasethroughput in wireless networks with location information.Our approach consists of a multipath routing protocol, BiasedGeographical Routing (BGR), and two congestion controlalgorithms, In-Network Packet Scatter (IPS) and End-to-EndPacket Scatter (EPS), which leverage BGR to avoid the congestedareas of the network. BGR achieves good performancewhile incurring a communication overhead of just 1 byte perdata packet, and has a computational complexity similar togreedy geographic routing. IPS alleviates transient congestion bysplitting traffic immediately before the congested areas. In contrast,EPS alleviates long term congestion by splitting the flow atthe source, and performing rate control. EPS selects the pathsdynamically, and uses a less aggressive congestion controlmechanism on non-greedy paths to improve energy efficiency.Simulation and experimental results show that our solutionachieves its objectives. Extensive ns-2 simulations show that oursolution improves both fairness and throughput as compared tosingle path greedy routing. Our solution reduces the variance ofthroughput across all flows by 35%, reduction which is mainlyachieved by increasing throughput of long-range flows witharound 70%. Furthermore, overall network throughput increasesby approximately 10%. Experimental results on a 50-node testbed are consistent with our simulation results, suggestingthat BGR is effective in practice

A New Approach for Guaranteed State Estimation by Zonotopes

18th World CongressThe International Federation of Automatic ControlMilano (Italy) August 28 - September 2This paper proposes a methodology for guaranteed state estimation of linear discrete-time systems in the presence of bounded disturbances and noises. This aims at computing an outer approximation of the state estimation domain represented by a zonotope. A new criterion is used to reduce the size of the zonotope at each sample time. An illustrative example is analyzed in order to highlight the advantages of the proposed algorithm

Solar System Constraints on Gauss-Bonnet Dark Energy

Quadratic curvature Gauss-Bonnet gravity may be the solution to the dark energy problem, but a large coupling strength is required. This can lead to conflict with laboratory and planetary tests of Newton's law, as well as light bending. The corresponding constraints are derived. If applied directly to cosmological scales, the resulting bound on the density fraction is |Omega_GB| < 3.6 x 10^-32.Comment: 4 pages, PASCOS-07 conference proceeding