This article introduces the Special Issue ‘South–South Security Cooperation and the (Re)making of Global Security Governance’. The contributions explore security-driven South–South interactions across the globe, assessing empirical, theoretical, and normative aspects. Our aim is to decentre debates on global security governance, traditionally focused on Northern-led cooperation, and to move beyond simplistic and simplifying assessments of South–South engagements. The Special Issue particularly highlights the ambiguities of South–South security cooperation, including varying degrees of global North involvement and differing interpretations of ‘security’ and ‘South–South’ among the involved actors. The contributions examine the practical outlook, normative consequences, and embeddedness of these cooperations within global hierarchies, and their implications for global security governance. This article sets the stage for this endeavor. Unpacking the categories ‘South’, ‘security’, and ‘cooperation’, we first provide a working definition of South–South security cooperation. Next, we offer a historical perspective, emphasising the role of legacy effects, institutional structures, geopolitical junctures, and international hierarchies in shaping South–South security cooperation. The concluding section presents the contributions to the special issue and discusses the implications of South–South security cooperation for understanding contemporary changes in global security governance.

The time-optimal path following (OPF) problem is to find a time evolution along a prescribed path in task space with shortest time duration. Numerical solution algorithms rely on an algorithm-specific (usually equidistant) sampling of the path parameter. This does not account for the dynamics in joint space, that is, the actual motion of the robot, however. Moreover, a well-known problem is that large joint velocities are obtained when approaching singularities, even for slow task space motions. This can be avoided by a sampling in joint space, where the path parameter is replaced by the arc length. Such discretization in task space leads to an adaptive refinement according to the nonlinear forward kinematics and guarantees bounded joint velocities. The adaptive refinement is also beneficial for the numerical solution of the problem. It is shown that this yields trajectories with improved continuity compared to an equidistant sampling. The OPF is reformulated as a second-order cone programming and solved numerically. The approach is demonstrated for a 6-DOF industrial robot following various paths in task space.

Random constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark examples for algorithms, and they have been harnessed in probabilistic constructions of combinatorial structures with peculiar features. In an important contribution (Krzakala et al. 2007, Proc. Nat. Acad. Sci.), physicists made several predictions on the precise location and nature of phase transitions in random constraint satisfaction problems. Specifically, they predicted that their satisfiability thresholds are quite generally preceded by several other thresholds that have a substantial impact both combinatorially and computationally. These include the condensation phase transition, where long-range correlations between variables emerge, and the reconstruction threshold. In this paper we prove these physics predictions for a broad class of random constraint satisfaction problems. Additionally, we obtain contiguity results that have implications for Bayesian inference tasks, a subject that has received a great deal of interest recently (e.g. Banks et al. 2016, Proc. 29th COLT).

We consider a random graph model that was recently proposed as a model for complex networks by Krioukov et al. (2010). In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are connected if they are at most a certain hyperbolic distance from each other. It has previously been shown that this model has various properties associated with complex networks, including a power-law degree distribution and a strictly positive clustering coefficient. The model is specified using three parameters: the number of nodes N, which we think of as going to infinity, and $\alpha, \nu > 0$, which we think of as constant. Roughly speaking, $\alpha$ controls the power-law exponent of the degree sequence and $\nu$ the average degree. Earlier work of Kiwi and Mitsche (2015) has shown that, when $\alpha \lt 1$ (which corresponds to the exponent of the power law degree sequence being $\lt 3$), the diameter of the largest component is asymptotically almost surely (a.a.s.) at most polylogarithmic in N. Friedrich and Krohmer (2015) showed it was a.a.s. $\Omega(\log N)$ and improved the exponent of the polynomial in $\log N$ in the upper bound. Here we show the maximum diameter over all components is a.a.s. $O(\log N),$ thus giving a bound that is tight up to a multiplicative constant.

The Bundesverfassungsgericht (Federal Constitutional Court) is a constitutional body charged with the task of ensuring that all state institutions, i.e. the legislator as well as the judiciary and executive branches, obey the constitution of the Federal Republic of Germany. Its review standard is the Grundgesetz (Basic Law). Since its foundation in 1951, the Court has helped to secure respect and effectiveness for the free democratic constitutional order. The decisions have far-reaching repercussions, which becomes particularly clear when the Court declares a law unconstitutional. Given the large number of cases handed down every year – at present nearly 5,000 constitutional complaints come before the Federal Constitutional Court annually – it is nearly impossible to give a representative summary of the comprehensive case law. Therefore, the report will concentrate on a selection of four decisions that have drawn the most attention over the course of the years 2005 and 2006.

Potential long-term associations between repetitive negative thinking and mother-infant interactions have received little attention. The current longitudinal study including N = 62 mother-infant dyads investigated both maternal and infant behavior in face-to-face interactions as a function of pre- and postnatal maternal repetitive negative thinking when infants were aged around 4 months. We hypothesised that mothers with a strong tendency to engage in repetitive negative thinking would react less contingently to their infants’ behavior compared to mothers with a weak tendency to engage in repetitive negative thinking. Furthermore, we hypothesised that infants of mothers high in repetitive negative thinking would differ from infants of mothers low in repetitive negative thinking in their reactions in the still-face task. Contrary to expectations, there was no difference in maternal contingency between mothers high versus low in repetitive negative thinking. However, infant behavior in the still-face task differed as a function of maternal repetitive negative thinking status. Specifically, infants of mothers high in repetitive negative thinking spent more time with object/environment engagement than infants of mothers who were low in repetitive negative thinking, and they also protested less frequently. These findings are discussed in terms of their relevance for the intergenerational transmission of mental disorders.

In this paper we study the treewidth of the random geometric graph, obtained by dropping n points onto the square [0,√n]2 and connecting pairs of points by an edge if their distance is at most r=r(n). We prove a conjecture of Mitsche and Perarnau (2014) stating that, with probability going to 1 as n→∞, the treewidth of the random geometric graph is 𝜣(r√n) when lim inf r>r c, where r c is the critical radius for the appearance of the giant component. The proof makes use of a comparison to standard bond percolation and with a little bit of extra work we are also able to show that, with probability tending to 1 as k→∞, the treewidth of the graph we obtain by retaining each edge of the k×k grid with probability p is 𝜣(k) if p>½ and 𝜣(√log k) if p<½.

Multidimensional effects are essential for the success of the neutrino-driven explosion mechanism of core-collapse supernovae. Although astrophysical phenomena in nature involve three spatial dimensions, the huge computational demands still allow only for a few self-consistent, three-dimensional (3D) simulations focusing on specific aspects of the explosion physics, whereas systematic studies of larger sets of progenitor models or detailed investigations of different explosion parameters are restricted to the axisymmetric (2D) modeling approach at the moment. Employing state-of-the-art neutrino physics, we present the results of self-consistent core-collapse supernova simulations performed with the Prometheus-Vertex code in 2D and 3D. The 2D study of 18 successfully exploding pre-supernova models in the range of 11 to 28 solar masses shows the progenitor dependence of the explosion dynamics: if the progenitor exhibits a pronounced decline of the density at the Si/Si-O composition shell interface, the rapid drop of the mass-accretion rate at the time the interface arrives at the shock induces a steep reduction of the accretion ram pressure. This causes a strong shock expansion supported by neutrino heating and thus favors an early explosion. In case of a more gradually decreasing accretion rate, it takes longer for the neutrino heating to overcome the accretion ram pressure and explosions set in later. By considering the effects of turbulent pressure in the gain layer, we derive a generalized condition for the critical neutrino luminosity that captures the explosion behavior of all models very well. We show that this concept can also be extended to describe the effects of rotation as well as the behavior of recent 3D simulations and that the conditions necessary for the onset of explosion can be defined in a similar way.

We present the first successful simulations of neutrino-driven supernova explosions in three dimensions (3D) using the Vertex-Prometheus code including sophisticated energy-dependent neutrino transport. The simulated models of 9.6 and 20 solar-mass iron-core stars demonstrate that successful explosions can be obtained in self-consistent 3D simulations, where previous models have failed. New insights into the supernova mechanism can be gained from these explosions. The first 3D model (Melson et al. 2015a) explodes at the same time but more energetically than its axially symmetric (2D) counterpart. Turbulent energy cascading reduces the kinetic energy dissipation in the cooling layer and therefore suppresses neutrino cooling. The consequent inward shift of the gain radius increases the gain layer mass, whose recombination energy provides the surplus for the explosion energy.

The second explosion (Melson et al. 2015b) is obtained through a moderate reduction of the neutral-current neutrino opacity motivated by strange-quark contributions to the nucleon spin. A corresponding reference model without these corrections failed, which demonstrates how close current 3D models are to explosion. The strangeness adjustment is meant as a prototype for remaining neutrino opacity uncertainties.

We study the limiting behavior of the discrete spectra associated to the principal congruence subgroups of a reductive group over a number field. While this problem is well understood in the cocompact case (i.e., when the group is anisotropic modulo the center), we treat groups of unbounded rank. For the groups $\text{GL}(n)$ and $\text{SL}(n)$ we show that the suitably normalized spectra converge to the Plancherel measure (the limit multiplicity property). For general reductive groups we obtain a substantial reduction of the problem. Our main tool is the recent refinement of the spectral side of Arthur’s trace formula obtained in [Finis, Lapid, and Müller, Ann. of Math. (2) 174(1) (2011), 173–195; Finis and Lapid, Ann. of Math. (2) 174(1) (2011), 197–223], which allows us to show that for $\text{GL}(n)$ and $\text{SL}(n)$ the contribution of the continuous spectrum is negligible in the limit.