Subjective and objective performance evaluation

We study executive compensation in an environment in which firms compete offering contingent contracts to managers with private information about their ability. We ask whether equilibrium executive compensation depends on subjective evaluations, i.e., on assessments made by the firm which are based on noncontractible information. We also allow for objective (i.e., contractible) performance measures and we depart from the rest of the literature on the topic by assuming that subjective evaluations are made before the uncertainty on the objective performance measures is resolved. We find that even in this case, equilibrium contracts ignore subjective evaluations regardless of their informativeness

HyperANF: Approximating the Neighbourhood Function of Very Large Graphs on a Budget

The neighbourhood function N(t) of a graph G gives, for each t, the number of pairs of nodes such that y is reachable from x in less that t hops. The neighbourhood function provides a wealth of information about the graph (e.g., it easily allows one to compute its diameter), but it is very expensive to compute it exactly. Recently, the ANF algorithm (approximate neighbourhood function) has been proposed with the purpose of approximating NG(t) on large graphs. We describe a breakthrough improvement over ANF in terms of speed and scalability. Our algorithm, called HyperANF, uses the new HyperLogLog counters and combines them efficiently through broadword programming; our implementation uses overdecomposition to exploit multi-core parallelism. With HyperANF, for the first time we can compute in a few hours the neighbourhood function of graphs with billions of nodes with a small error and good confidence using a standard workstation. Then, we turn to the study of the distribution of the shortest paths between reachable nodes (that can be efficiently approximated by means of HyperANF), and discover the surprising fact that its index of dispersion provides a clear-cut characterisation of proper social networks vs. web graphs. We thus propose the spid (Shortest-Paths Index of Dispersion) of a graph as a new, informative statistics that is able to discriminate between the above two types of graphs. We believe this is the first proposal of a significant new non-local structural index for complex networks whose computation is highly scalable

What form of relative performance evaluation?

We study relative performance evaluation in executive compensation when executives have private information about their ability. We assume that the joint distribution of an individual firm’s profit and market movements depends on the ability of the executive that runs the firm. In the equilibrium of the executive labor market, compensation schemes exploit this fact to sort executives of di ?erent abilities. This implies that executive compensation is increasing in own performance, but may also be increasing in industry performance-a sharp departure from standard relative performance evaluation. This result provides an explanation for the scarcity of relative performance considerations in executive compensation documented by the empirical literature.Executive compensation, relative performance evaluation

All AdS_7 solutions of type II supergravity

In M-theory, the only AdS_7 supersymmetric solutions are AdS_7 x S^4 and its orbifolds. In this paper, we find and classify new supersymmetric solutions of the type AdS_7 x M_3 in type II supergravity. While in IIB none exist, in IIA with Romans mass (which does not lift to M-theory) there are many new ones. We use a pure spinor approach reminiscent of generalized complex geometry. Without the need for any Ansatz, the system determines uniquely the form of the metric and fluxes, up to solving a system of ODEs. Namely, the metric on M_3 is that of an S^2 fibered over an interval; this is consistent with the Sp(1) R-symmetry of the holographically dual (1,0) theory. By including D8 brane sources, one can numerically obtain regular solutions, where topologically M_3 = S^3.Comment: 45 pages, 4 figures. v2: solution with single D8 added; references added; minor correction

Layered Label Propagation: A MultiResolution Coordinate-Free Ordering for Compressing Social Networks

We continue the line of research on graph compression started with WebGraph, but we move our focus to the compression of social networks in a proper sense (e.g., LiveJournal): the approaches that have been used for a long time to compress web graphs rely on a specific ordering of the nodes (lexicographical URL ordering) whose extension to general social networks is not trivial. In this paper, we propose a solution that mixes clusterings and orders, and devise a new algorithm, called Layered Label Propagation, that builds on previous work on scalable clustering and can be used to reorder very large graphs (billions of nodes). Our implementation uses overdecomposition to perform aggressively on multi-core architecture, making it possible to reorder graphs of more than 600 millions nodes in a few hours. Experiments performed on a wide array of web graphs and social networks show that combining the order produced by the proposed algorithm with the WebGraph compression framework provides a major increase in compression with respect to all currently known techniques, both on web graphs and on social networks. These improvements make it possible to analyse in main memory significantly larger graphs

Noiseless Linear Amplification and Quantum Channels

The employ of a noiseless linear amplifier (NLA) has been proven as a useful tool for mitigating imperfections in quantum channels. Its analysis is usually conducted within specific frameworks, for which the set of input states for a given protocol is fixed. Here we obtain a more general description by showing that a noisy and lossy Gaussian channel followed by a NLA has a general description in terms of effective channels. This has the advantage of offering a simpler mathematical description, best suitable for mixed states, both Gaussian and non-Gaussian. We investigate the main properties of this effective system, and illustrate its potential by applying it to loss compensation and reduction of phase uncertainty.Comment: 8 pages, 3 figure

Use of ANTARES and IceCube data to constrain a single power-law neutrino flux

We perform the first statistical combined analysis of the diffuse neutrino flux observed by ANTARES (nine-year) and IceCube (six-year) by assuming a single astrophysical power-law flux. The combined analysis reduces by a few percent the best-fit values for the flux normalization and the spectral index. Both data samples show an excess in the same energy range (40--200 TeV), suggesting the presence of a second component. We perform a goodness-of-fit test to scrutinize the null assumption of a single power-law, scanning different values for the spectral index. The addition of the ANTARES data reduces the $p$-value by a factor 2$\div$3. In particular, a single power-law component in the neutrino flux with the spectral index deduced by the six-year up-going muon neutrinos of IceCube is disfavored with a $p$-value smaller than $10^{-2}$.Comment: 6 pages, 4 figures. Version published in AP