Unusual square roots in the ghost-free theory of massive gravity

A crucial building block of the ghost free massive gravity is the square root function of a matrix. This is a problematic entity from the viewpoint of existence and uniqueness properties. We accurately describe the freedom of choosing a square root of a (non-degenerate) matrix. It has discrete and (in special cases) continuous parts. When continuous freedom is present, the usual perturbation theory in terms of matrices can be critically ill defined for some choices of the square root. We consider the new formulation of massive and bimetric gravity which deals directly with eigenvalues (in disguise of elementary symmetric polynomials) instead of matrices. It allows for a meaningful discussion of perturbation theory in such cases, even though certain non-analytic features arise.Comment: 24 pages; minor changes, final versio

Diagonal finite volume matrix elements in the sinh-Gordon model

Using the fermionic basis we conjecture exact expressions for diagonal finite volume matrix elements of exponential operators and their descendants in the sinh-Gordon theory. Our expressions sum up the LeClair-Mussardo type infinite series generalized by Pozsgay for excited state expectation values. We checked our formulae against the Liouville three-point functions for small, while against Pozsgay's expansion for large volumes and found complete agreement.Comment: 19 pages, 1 figur

Isolation-Aware Timing Analysis and Design Space Exploration for Predictable and Composable Many-Core Systems

Composable many-core systems enable the independent development and analysis of applications which will be executed on a shared platform where the mix of concurrently executed applications may change dynamically at run time. For each individual application, an off-line DSE is performed to compute several mapping alternatives on the platform, offering Pareto-optimal trade-offs in terms of real-time guarantees, resource usage, etc. At run time, one mapping is then chosen to launch the application on demand. In this context, to enable an independent analysis of each individual application at design time, so-called inter-application isolation schemes are applied which specify temporal/spatial isolation policies between applications. State-of-the-art composable many-core systems are developed based on a fixed isolation scheme that is exclusively applied to every resource in every mapping of every application and use a timing analysis tailored to that isolation scheme to derive timing guarantees for each mapping. A fixed isolation scheme, however, heavily restricts the explored space of solutions and can, therefore, lead to suboptimality. Lifting this restriction necessitates a timing analysis that is applicable to mappings with an arbitrary mix of isolation schemes on different resources. To address this issue, in this paper, we (a) present an isolation-aware timing analysis that - unlike existing analyses - can handle multiple isolation schemes in combination within one mapping and delivers safe yet tight timing bounds by identifying and excluding interference scenarios that can never happen under the given combination of isolation schemes. Based on the timing analysis, we (b) present a DSE which explores the choices of isolation scheme per resource within each mapping and uses the proposed timing analysis for timing verification. Experimental results demonstrate that, for a variety of real-time applications and many-core platforms, the proposed approach achieves an improvement of up to 67% in the quality of delivered mappings compared to approaches based on a fixed isolation scheme

Dark matter production and reheating via direct inflaton couplings : collective effects

We study scalar dark matter production and reheating via renormalizable inflaton couplings, which include both quartic and trilinear interactions. These processes often depend crucially on collective effects such as resonances, backreaction and rescattering of the produced particles. To take them into account, we perform lattice simulations and map out parameter space producing the correct (non-thermal) dark matter density. We find that the inflaton-dark matter system can reach a quasi-equilibrium state during preheating already at very small couplings, in which case the dark matter abundance becomes independent of the inflaton-dark matter coupling and is described by a universal formula. Dark matter is readily overproduced and even tiny values of the direct inflaton couplings can be sufficient to get the right composition of the Universe, which reaffirms their importance in cosmology.Peer reviewe