Investigations of solutions of Einstein's field equations close to lambda-Taub-NUT

We present investigations of a class of solutions of Einstein's field equations close to the family of lambda-Taub-NUT spacetimes. The studies are done using a numerical code introduced by the author elsewhere. One of the main technical complication is due to the S3-topology of the Cauchy surfaces. Complementing these numerical results with heuristic arguments, we are able to yield some first insights into the strong cosmic censorship issue and the conjectures by Belinskii, Khalatnikov, and Lifschitz in this class of spacetimes. In particular, the current investigations suggest that strong cosmic censorship holds in this class. We further identify open issues in our current approach and point to future research projects.Comment: 24 pages, 12 figures, uses psfrag and hyperref; replaced with published version, only minor corrections of typos and reference

Smooth Gowdy symmetric generalized Taub-NUT solutions

We study a class of S3 Gowdy vacuum models with a regular past Cauchy horizon which we call smooth Gowdy symmetric generalized Taub-NUT solutions. In particular, we prove existence of such solutions by formulating a singular initial value problem with asymptotic data on the past Cauchy horizon. The result of our investigations is that a future Cauchy horizon exists for generic asymptotic data. Moreover, we derive an explicit expression for the metric on the future Cauchy horizon in terms of the asymptotic data on the past horizon. This complements earlier results about S2xS1 Gowdy models.Comment: 56 pages, 1 figure. The new version contains a detailed explanation of the Fuchsian method on the 2-spher

Simple Max-Min Ant Systems and the Optimization of Linear Pseudo-Boolean Functions

With this paper, we contribute to the understanding of ant colony optimization (ACO) algorithms by formally analyzing their runtime behavior. We study simple MAX-MIN ant systems on the class of linear pseudo-Boolean functions defined on binary strings of length 'n'. Our investigations point out how the progress according to function values is stored in pheromone. We provide a general upper bound of O((n^3 \log n)/ \rho) for two ACO variants on all linear functions, where (\rho) determines the pheromone update strength. Furthermore, we show improved bounds for two well-known linear pseudo-Boolean functions called OneMax and BinVal and give additional insights using an experimental study.Comment: 19 pages, 2 figure

Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes

We set up the singular initial value problem for quasilinear hyperbolic Fuchsian systems of first order and establish an existence and uniqueness theory for this problem with smooth data and smooth coefficients (and with even lower regularity). We apply this theory in order to show the existence of smooth (generally not analytic) T2-symmetric solutions to the vacuum Einstein equations, which exhibit AVTD (asymptotically velocity term dominated) behavior in the neighborhood of their singularities and are polarized or half-polarized.Comment: 78 page

An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs. This integral representation is a suitable starting point for a detailed analysis of the long-time dynamics of scalar waves in the Kerr geometry.Comment: 41 pages, 4 figures, minor correction

Spectroscopic study of the F1Σg+^1\Sigma_g^+ outer well state in H2_2, HD and D2_2

Two-photon UV-photolysis of hydrogen sulfide molecules is applied to produce hydrogen molecules in highly excited vibrational levels in the \X\ electronic ground state, up to the dissociation energy and into the quasibound region. Photolysis precursors H$_2$S, HDS and D$_2$S are used to produce vibrationally hot H$_2$, HD and D$_2$. The wave function density at large internuclear separation is excited via two-photon transitions in the \F\ - \X\ system to probe ro-vibrational levels in the first excited \F\ outer well state of \emph{gerade} symmetry. Combining with accurate knowledge of the \X($v,J$) levels from advanced ab initio calculations, energies of rovibrational levels in the \F\ state are determined. For the H$_2$ isotopologue a three-laser scheme is employed yielding level energies at accuracies of $4 \times 10^{-3}$ \wn\ for F($v=0,J$) up to $J=21$ and for some low $J$ values of F($v=1$). A two-laser scheme was applied to determine level energies in H$_2$ for F($v=0-4$) levels as well as for various F levels in HD and D$_2$, also up to large rotational quantum numbers. The latter measurements in the two-laser scheme are performed at lower resolution and the accuracy is strongly limited to 0.5 \wn\ by ac-Stark effects. For H$_2$ a new quasibound resonance ($v=6$, $J=23$) is detected through the Q(23) and O(23) transitions in the F0-X6 band. The experimental results on F($v,J$) level energies are compared with previously reported theoretical results from multi-channel quantum-defect calculations as well as with results from newly performed nonadiabatic quantum calculations

How social contexts affect cognition: mentalizing interferes with sense of agency during voluntary action

Living in complex social structures, humans have evolved a unique aptitude for mentalizing: trying to understand and predict the behaviour of others. To date, little is known about how mentalizing interacts with other cognitive processes. “Sense of agency” refers to the feeling of control over the outcomes of one's actions, providing a precursor of responsibility. Here, we test a model of how social context influences this key feature of human action, even when action outcomes are not specifically social. We propose that in social contexts, sense of agency is affected by the requirement to mentalize, increasing the complexity of individual decision-making. We test this hypothesis by comparing two situations, in which participants could either consider potential actions of another person (another participant acting to influence the task), or potential failures of a causal mechanism (a mechanical device breaking down and thereby influencing the task). For relatively good outcomes, we find an agency-reducing effect of external influence only in the social condition, suggesting that the presence of another intentional agent has a unique influence on the cognitive processes underlying one's own voluntary action. In a second experiment, we show that the presence of another potential agent reduces sense of agency both in a context of varying financial gains or of losses. This clearly dissociates social modulation of sense of agency from classical self-serving bias. Previous work primarily focused on social facilitation of human cognition. However, when people must incorporate potential actions of others into their decision-making, we show that the resulting socio-cognitive processes reduce the individuals' feelings of control