On the Six-dimensional Kerr Theorem and Twistor Equation

The Kerr theorem is revisited as part of the twistor program in six dimensions. The relationship between pure spinors and integrable 3-planes is investigated. The real condition for Lorentzian spacetimes is seen to induce a projective property in the space of solutions, reminiscent of the quaternionic structure of the 6-dimensional Lorentz group. The twistor equation (or Killing spinor equations generically) also has an interpretation as integrable null planes and a family of Einstein spacetimes with this property are presented in the Kerr-Schild fashion.Comment: JHEP style, 19 pages, minor corrections. Matches printed versio

Signature of a Cosmic String Wake at z=3z=3

In this paper, we describe the results of N-body simulation runs, which include a cosmic string wake of tension $G\mu= 4 \times 10^{-8}$ on top of the usual $\Lambda CDM$ fluctuations. To obtain a higher resolution of the wake in the simulations compared to previous work, we insert the effects of the string wake at a lower redshift and perform the simulations in a smaller volume. A curvelet analysis of the wake and no-wake maps is applied, indicating that the presence of a wake can be extracted at a three-sigma confidence level from maps of the two-dimensional dark matter projection down to a redshift of $z=3$.Comment: 8 pages, 6 figures; We have improved the analysis and results. The text now agrees with the published versio

Isomonodromy, Painlev\'e Transcendents and Scattering off of Black Holes

We apply the method of isomonodromy to study the scattering of a generic Kerr-NUT-(A)dS black hole. For generic values of the charges, the problem is related to the connection problem of the Painlev\'e VI transcendent. We review a few facts about Painlev\'e VI, Garnier systems and the Hamiltonian structure of flat connections in the Riemann sphere. We then outline a method for computing the scattering amplitudes based on Hamilton-Jacobi structure of Painlev\'e, and discuss the implications of the generic result to black hole complementarity.Comment: 40 pages, 4 figures, JHEP styl

The web of federal crimes in Brazil: topology, weaknesses, and control

Law enforcement and intelligence agencies worldwide struggle to find effective ways to fight and control organized crime. However, illegal networks operate outside the law and much of the data collected is classified. Therefore, little is known about criminal networks structure, topological weaknesses, and control. In this contribution we present a unique criminal network of federal crimes in Brazil. We study its structure, its response to different attack strategies, and its controllability. Surprisingly, the network composed of multiple crimes of federal jurisdiction has a giant component, enclosing more than a half of all its edges. This component shows some typical social network characteristics, such as small-worldness and high clustering coefficient, however it is much "darker" than common social networks, having low levels of edge density and network efficiency. On the other side, it has a very high modularity value, $Q=0.96$. Comparing multiple attack strategies, we show that it is possible to disrupt the giant component of the network by removing only $2\%$ of its edges or nodes, according to a module-based prescription, precisely due to its high modularity. Finally, we show that the component is controllable, in the sense of the exact network control theory, by getting access to $20\%$ of the driver nodes.Comment: 9 pages, 5 figure