Related papers: Over the Rainbow: Numerical Relativity beyond Scri…

Special relativity theory is generalized to two or more ``maximal'' signalling speeds. This framework is discussed in three contexts: (i) as a scenario for superluminal signalling and motion, (ii) as the possibility of two or more ``light''…

We report on a systematic study of the dynamics of gravitational waves in full 3D numerical relativity. We find that there exists an interesting regime in the parameter space of the wave configurations: a near-linear regime in which the…

We review the motivations for the search of stochastic backgrounds of gravitational waves and we compare the experimental sensitivities that can be reached in the near future with the existing bounds and with the theoretical predictions.

We discuss a gauge choice which allows us to avoid the introduction of artificial timelike outer boundaries in numerical studies of test fields based on a 3+1 decomposition of asymptotically flat background spacetimes. The main idea is to…

Expander graphs are widely used in communication problems and construction of error correcting codes. In such graphs, information gets through very quickly. Typically, it is not true for social or biological networks, though we may find a…

We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on…

We provide an upper bound on the uniform exponent of approximation to a triple (xi, xi^2, xi^3) by rational numbers with the same denominator, valid for any transcendental real number xi. This upper bound refines a previous result of…

Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…

Let X be a projective cubic hypersurface of dimension 11 or more, which is defined over the rationals. In this paper it is shown that X contains rational points provided that the cubic form defining X can be written as the sum of two forms…

In numerical relativity, spacetimes involving compact strongly gravitating objects are constructed as numerical solutions of Einstein's equations. Success of such a process strongly depends on the availability of appropriate coordinates,…

The Shape From Shading is one of a computer vision field. It studies the 3D reconstruction of an object from a single grayscale image. The difficulty of this field can be expressed in the local ambiguity (convex / concave). J.Shi and Q.Zhu…

In this short note we review some known results on the structure and regularity of spaces with lower Ricci curvature bounds. We present some known and new open questions about next steps.

This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving…

Motivated by the first detection of gravitational waves, this dissertation develops analytical, numerical, and data analysis techniques to address persistent blind spots in our understanding of gravity. Beginning with asymptotically flat…

The aim of this talk is to provide non-experts with a brief and elementary introduction on the field of extra dimensions. The main motivation for extra dimensions relies on the more fundamental string theories that predict ten (or eleven)…

Let $(X,D)$ be a pair where $X$ is a projective variety. We study in detail how the behavior of rational curves on $X$ as well as the positivity of $-(K_X+D)$ and $D$ influence the behavior of rational curves on $D$. In particular we give…

Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…

Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…

The definition of natural modes for confined structures is one of the central problems in physics, as in nuclear physics, astrophysics, etc. The main problem is due to the boundary conditions, when they are such to push out the problem from…

We study bounds arising from the analyticity and unitarity of scattering amplitudes in the context of effective field theories with massless particles. We provide an approach that only uses dispersion relations away from the forward limit.…