Towards a meaningful prudential supervision dialogue in the Euro area?

In the context of the introduction of the Single Supervisory Mechanism ( SSM) as part of the European Banking Union, the European Central Bank ( ECB) has been assigned specific supervisory tasks relating to credit institutions established primarily in the euro area. One particularly remarkable feature of this new legislation, notably when compared with the monetary policy tasks of the ECB, is the introduction of an explicit accountability framework with a particular focus on the relationship between the ECB and the European Parliament. It is this relationship, and mainly the so-called supervisory dialogue, that form the focal point of this contribution, which offers an assessment of the legal framework, as well as of the actual practice in these first years of the existence of the SSM, against a clearly defined notion of accountability. With regard to the actual practice, the contribution focuses on the exchanges between the chair of the ECB’s main decision-preparing body on SSM matters, i.e. the Supervisory Board, and the European Parliament’s Committee on Economic and Monetary Affairs

Binary Neutron Stars with Generic Spin, Eccentricity, Mass ratio, and Compactness - Quasi-equilibrium Sequences and First Evolutions

Information about the last stages of a binary neutron star inspiral and the final merger can be extracted from quasi-equilibrium configurations and dynamical evolutions. In this article, we construct quasi-equilibrium configurations for different spins, eccentricities, mass ratios, compactnesses, and equations of state. For this purpose we employ the SGRID code, which allows us to construct such data in previously inaccessible regions of the parameter space. In particular, we consider spinning neutron stars in isolation and in binary systems; we incorporate new methods to produce highly eccentric and eccentricity reduced data; we present the possibility of computing data for significantly unequal-mass binaries; and we create equal-mass binaries with individual compactness up to 0.23. As a proof of principle, we explore the dynamical evolution of three new configurations. First, we simulate a $q=2.06$ mass ratio which is the highest mass ratio for a binary neutron star evolved in numerical relativity to date. We find that mass transfer from the companion star sets in a few revolutions before merger and a rest mass of $\sim10^{-2}M_\odot$ is transferred between the two stars. This configuration also ejects a large amount of material during merger, imparting a substantial kick to the remnant. Second, we simulate the first merger of a precessing binary neutron star. We present the dominant modes of the gravitational waves for the precessing simulation, where a clear imprint of the precession is visible in the (2,1) mode. Finally, we quantify the effect of an eccentricity reduction procedure on the gravitational waveform. The procedure improves the waveform quality and should be employed in future precision studies, but also other errors, notably truncation errors, need to be reduced in order for the improvement due to eccentricity reduction to be effective. [abridged]Comment: (37pages, 26 figures

SUBARU and e-Merlin observations of NGC3718. Diaries of an SMBH recoil?

NGC3718 is a LINER $L1.9$ galaxy, lying at a distance of about $\sim 17.4$ Mpc away from earth and its similarities with NGC5128 often award it the name "northern Centaurus A". We use high angular resolution ($\sim100$ mas) e-Merlin radio and SUBARU NIR ($\sim170$ mas) data, to take a detailed view of the processes taking place in its central region. In order to preserve some objectivity in our interpretation, we combine our results with literature values and findings from previous studies. Our NIR maps suggest, on one hand, that towards the stellar bulge there are no large scale absorption phenomena caused by the apparent dust lane and, on the other, that there is a significant (local) contribution from hot ($\sim1000$ K) dust to the nuclear NIR emission. The position where this takes place appears to be closer to the offset compact radio emission from our e-Merlin $6$ cm map, lying offset by $\sim4.25$ pc from the center of the underlying stellar bulge. The shape of the radio map suggests the presence of one (or possibly two, forming an X-shape) bipolar structure(s) $\sim1$ ($\sim0.6$) arcsec across, which combined with the balance between the gas and the stellar velocity dispersions and the presence of hard X-ray emission, point towards effects expected by AGN feedback. We also argue that NGC3718 has a "core" in its surface brightness profile, despite the fact that it is a gas-rich galaxy and we discuss its mixed photometric and spectroscopic characteristics. The latter combined with the observed spatial and radio offsets, the relative redshift between the broad and the narrow $H{\mathrm{\alpha}}$ line, the limited star formation activity and AGN feedback, strongly imply the existence of an SMBH recoil. Finally, we discuss a possible interpretation, that could naturally incorporate all these findings into one physically consistent picture.Comment: 18 pages, 18 figures, 3 tables, accepted for publications in A&

Use of a Strongly Nonlinear Gambier Equation for the Construction of Exact Closed Form Solutions of Nonlinear ODEs

We establish an analytical method leading to a more general form of the exact solution of a nonlinear ODE of the second order due to Gambier. The treatment is based on the introduction and determination of a new function, by means of which the solution of the original equation is expressed. This treatment is applied to another nonlinear equation, subjected to the same general class as that of Gambier, by constructing step by step an appropriate analytical technique. The developed procedure yields a general exact closed form solution of this equation, valid for specific values of the parameters involved and containing two arbitrary (free) parameters evaluated by the relevant initial conditions. We finally verify this technique by applying it to two specific sets of parameter values of the equation under consideration

Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems

Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind ((Ab-1) equations). Based on the results of a previous work, concerning a closed-form solution of a general (Ab-1) equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of which only first integrals (in closed or parametric form) have been obtained so far. Two-dimensional autonomous systems of differential equations of the first order, equivalent to the considered herein autonomous forms, are constructed and solved by means of the developed analysis

Cooperative games with overlapping coalitions

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions—or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure

Complexity of Strong Implementability

We consider the question of implementability of a social choice function in a classical setting where the preferences of finitely many selfish individuals with private information have to be aggregated towards a social choice. This is one of the central questions in mechanism design. If the concept of weak implementation is considered, the Revelation Principle states that one can restrict attention to truthful implementations and direct revelation mechanisms, which implies that implementability of a social choice function is easy to check. For the concept of strong implementation, however, the Revelation Principle becomes invalid, and the complexity of deciding whether a given social choice function is strongly implementable has been open so far. In this paper, we show by using methods from polyhedral theory that strong implementability of a social choice function can be decided in polynomial space and that each of the payments needed for strong implementation can always be chosen to be of polynomial encoding length. Moreover, we show that strong implementability of a social choice function involving only a single selfish individual can be decided in polynomial time via linear programming

Undominated Groves Mechanisms

The family of Groves mechanisms, which includes the well-known VCG mechanism (also known as the Clarke mechanism), is a family of efficient and strategy-proof mechanisms. Unfortunately, the Groves mechanisms are generally not budget balanced. That is, under such mechanisms, payments may flow into or out of the system of the agents, resulting in deficits or reduced utilities for the agents. We consider the following problem: within the family of Groves mechanisms, we want to identify mechanisms that give the agents the highest utilities, under the constraint that these mechanisms must never incur deficits. We adopt a prior-free approach. We introduce two general measures for comparing mechanisms in prior-free settings. We say that a non-deficit Groves mechanism M in- dividually dominates another non-deficit Groves mechanism M′ if for every type profile, every agent’s utility under M is no less than that under M′, and this holds with strict inequality for at least one type profile and one agent. We say that a non-deficit Groves mechanism M collectively dominates another non-deficit Groves mechanism M′ if for every type profile, the agents’ total utility under M is no less than that under M′, and this holds with strict inequality for at least one type profile. The above definitions induce two partial orders on non-deficit Groves mechanisms. We study the maximal elements corresponding to these two partial orders, which we call the individually undominated mechanisms and the collectively undominated mechanisms, respectively