Fourth order indirect integration method for black hole perturbations: even modes

On the basis of a recently proposed strategy of finite element integration in time domain for partial differential equations with a singular source term, we present a fourth order algorithm for non-rotating black hole perturbations in the Regge-Wheeler gauge. Herein, we address even perturbations induced by a particle plunging in. The forward time value at the upper node of the $(r^*,t)$ grid cell is obtained by an algebraic sum of i) the preceding node values of the same cell, ii) analytic expressions, related to the jump conditions on the wave function and its derivatives, iii) the values of the wave function at adjacent cells. In this approach, the numerical integration does not deal with the source and potential terms directly, for cells crossed by the particle world line. This scheme has also been applied to circular and eccentric orbits and it will be object of a forthcoming publication.Comment: This series of papers deals with EMRI for LISA. With the respect to the v1 version, the algorithm has been improved; convergence tests and references have been added; v2 is composed by 23 pages, and 6 figures. Paper accepted by Class. Quantum Gravity for the special issue on Theory Meets Data Analysis at Comparable and Extreme Mass Ratios (Capra and NRDA) at Perimeier Institute in June 201

The Univariate Marginal Distribution Algorithm Copes Well With Deception and Epistasis

In their recent work, Lehre and Nguyen (FOGA 2019) show that the univariate marginal distribution algorithm (UMDA) needs time exponential in the parent populations size to optimize the DeceptiveLeadingBlocks (DLB) problem. They conclude from this result that univariate EDAs have difficulties with deception and epistasis. In this work, we show that this negative finding is caused by an unfortunate choice of the parameters of the UMDA. When the population sizes are chosen large enough to prevent genetic drift, then the UMDA optimizes the DLB problem with high probability with at most $\lambda(\frac{n}{2} + 2 e \ln n)$ fitness evaluations. Since an offspring population size $\lambda$ of order $n \log n$ can prevent genetic drift, the UMDA can solve the DLB problem with $O(n^2 \log n)$ fitness evaluations. In contrast, for classic evolutionary algorithms no better run time guarantee than $O(n^3)$ is known (which we prove to be tight for the ${(1+1)}$ EA), so our result rather suggests that the UMDA can cope well with deception and epistatis. From a broader perspective, our result shows that the UMDA can cope better with local optima than evolutionary algorithms; such a result was previously known only for the compact genetic algorithm. Together with the lower bound of Lehre and Nguyen, our result for the first time rigorously proves that running EDAs in the regime with genetic drift can lead to drastic performance losses

Evolutionary design of a full-envelope full-authority flight control system for an unstable high-performance aircraft

The use of an evolutionary algorithm in the framework of H1 control theory is being considered as a means for synthesizing controller gains that minimize a weighted combination of the infinite norm of the sensitivity function (for disturbance attenuation requirements) and complementary sensitivity function (for robust stability requirements) at the same time. The case study deals with a complete full-authority longitudinal control system for an unstable high-performance jet aircraft featuring (i) a stability and control augmentation system and (ii) autopilot functions (speed and altitude hold). Constraints on closed-loop response are enforced, that representing typical requirements on airplane handling qualities, that makes the control law synthesis process more demanding. Gain scheduling is required, in order to obtain satisfactory performance over the whole flight envelope, so that the synthesis is performed at different reference trim conditions, for several values of the dynamic pressure, used as the scheduling parameter. Nonetheless, the dynamic behaviour of the aircraft may exhibit significant variations when flying at different altitudes, even for the same value of the dynamic pressure, so that a trade-off is required between different feasible controllers synthesized at different altitudes for a given equivalent airspeed. A multiobjective search is thus considered for the determination of the best suited solution to be introduced in the scheduling of the control law. The obtained results are then tested on a longitudinal non-linear model of the aircraft

Extreme objects with arbitrary large mass, or density, and arbitrary size

We consider a generalization of the interior Schwarzschild solution that we match to the exterior one to build global C^1 models that can have arbitrary large mass, or density, with arbitrary size. This is possible because of a new insight into the problem of localizing the center of symmetry of the models and the use of principal transformations to understand the structure of space.Comment: 20 pages, 6 figures. Fixed one reference. Added a new equatio

First Steps Towards a Runtime Analysis When Starting with a Good Solution

International audienc

Holonomy in the Schwarzschild-Droste Geometry

Parallel transport of vectors in curved spacetimes generally results in a deficit angle between the directions of the initial and final vectors. We examine such holonomy in the Schwarzschild-Droste geometry and find a number of interesting features that are not widely known. For example, parallel transport around circular orbits results in a quantized band structure of holonomy invariance. We also examine radial holonomy and extend the analysis to spinors and to the Reissner-Nordstr\"om metric, where we find qualitatively different behavior for the extremal ($Q = M$) case. Our calculations provide a toolbox that will hopefully be useful in the investigation of quantum parallel transport in Hilbert-fibered spacetimes.Comment: 18 Latex pages, 3 figures. Second replacement. This version as published in CQG with some misprints correcte

On the Effect of Connectedness for Biobjective Multiple and Long Path Problems

Recently, the property of connectedness has been claimed to give a strong motivation on the design of local search techniques for multiobjective combinatorial optimization (MOCO). Indeed, when connectedness holds, a basic Pareto local search, initialized with at least one non-dominated solution, allows to identify the efficient set exhaustively. However, this becomes quickly infeasible in practice as the number of efficient solutions typically grows exponentially with the instance size. As a consequence, we generally have to deal with a limited-size approximation, where a good sample set has to be found. In this paper, we propose the biobjective multiple and long path problems to show experimentally that, on the first problems, even if the efficient set is connected, a local search may be outperformed by a simple evolutionary algorithm in the sampling of the efficient set. At the opposite, on the second problems, a local search algorithm may successfully approximate a disconnected efficient set. Then, we argue that connectedness is not the single property to study for the design of local search heuristics for MOCO. This work opens new discussions on a proper definition of the multiobjective fitness landscape.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome : Italy (2011

Trends and emissions of six perfluorocarbons in the Northern Hemisphere and Southern Hemisphere

Perfluorocarbons (PFCs) are potent greenhouse gases with global warming potentials up to several thousand times greater than CO2 on a 100-year time horizon. The lack of any significant sinks for PFCs means that they have long atmospheric lifetimes of the order of thousands of years. Anthropogenic production is thought to be the only source for most PFCs. Here we report an update on the global atmospheric abundances of the following PFCs, most of which have for the first time been analytically separated according to their isomers: c-octafluorobutane (c-C4F8), n-decafluorobutane (n-C4F10), n-dodecafluoropentane (n-C5F12), n-tetradecafluorohexane (n-C6F14), and n-hexadecafluoroheptane (n-C7F16). Additionally, we report the first data set on the atmospheric mixing ratios of perfluoro-2-methylpentane (i-C6F14). The existence and significance of PFC isomers have not been reported before, due to the analytical challenges of separating them. The time series spans a period from 1978 to the present. Several data sets are used to investigate temporal and spatial trends of these PFCs: time series of air samples collected at Cape Grim, Australia, from 1978 to the start of 2018; a time series of air samples collected between July 2015 and April 2017 at Tacolneston, UK; and intensive campaign-based sampling collections from Taiwan. Although the remote “background” Southern Hemispheric Cape Grim time series indicates that recent growth rates of most of these PFCs are lower than in the 1990s, we continue to see significantly increasing mixing ratios that are between 6 % and 27 % higher by the end of 2017 compared to abundances measured in 2010. Air samples from Tacolneston show a positive offset in PFC mixing ratios compared to the Southern Hemisphere baseline. The highest mixing ratios and variability are seen in air samples from Taiwan, which is therefore likely situated much closer to PFC sources, confirming predominantly Northern Hemispheric emissions for most PFCs. Even though these PFCs occur in the atmosphere at levels of parts per trillion molar or less, their total cumulative global emissions translate into 833 million metric tonnes of CO2 equivalent by the end of 2017, 23 % of which has been emitted since 2010. Almost two-thirds of the CO2 equivalent emissions within the last decade are attributable to c-C4F8, which currently also has the highest emission rates that continue to grow. Sources of all PFCs covered in this work remain poorly constrained and reported emissions in global databases do not account for the abundances found in the atmosphere

Distributed Synthesis in Continuous Time

We introduce a formalism modelling communication of distributed agents strictly in continuous-time. Within this framework, we study the problem of synthesising local strategies for individual agents such that a specified set of goal states is reached, or reached with at least a given probability. The flow of time is modelled explicitly based on continuous-time randomness, with two natural implications: First, the non-determinism stemming from interleaving disappears. Second, when we restrict to a subclass of non-urgent models, the quantitative value problem for two players can be solved in EXPTIME. Indeed, the explicit continuous time enables players to communicate their states by delaying synchronisation (which is unrestricted for non-urgent models). In general, the problems are undecidable already for two players in the quantitative case and three players in the qualitative case. The qualitative undecidability is shown by a reduction to decentralized POMDPs for which we provide the strongest (and rather surprising) undecidability result so far