Retrieving information from a noisy "knowledge network"

We address the problem of retrieving information from a noisy version of the ``knowledge networks'' introduced by Maslov and Zhang. We map this problem onto a disordered statistical mechanics model, which opens the door to many analytical and numerical approaches. We give the replica symmetric solution, compare with numerical simulations, and finally discuss an application to real datas from the United States Senate.Comment: 10 pages, 4 figures. Writing of the last section improved; version accepted in JSTA

Super Quantum Mechanics in the Integral Form Formalism

We reformulate Super Quantum Mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of Picture Changing Operators (PCO). In this way we retrieve component and superspace actions, and prove their equivalence. The PCO are closed integral forms, and can be interpreted as super Poincar\'e duals of bosonic submanifolds embedded into a supermanifold.. We use them to construct Lagrangians that are top integral forms, and therefore can be integrated on the whole supermanifold. The $D=1, ~N=1$ and the $D=1,~ N=2$ cases are studied, in a flat and in a curved supermanifold. In this formalism we also consider coupling with gauge fields, Hilbert space of quantum states and observables.Comment: 41 pages, no figures. Use birkjour.cls. Minor misprints, moved appendix A and B in the main text. Version to be published in Annales H. Poincar\'

The Geometry of Supermanifolds and New Supersymmetric Actions

We construct the Hodge dual for supermanifolds by means of the Grassmannian Fourier transform of superforms. In the case of supermanifolds it is known that the superforms are not sufficient to construct a consistent integration theory and that the integral forms are needed. They are distribution-like forms which can be integrated on supermanifolds as a top form can be integrated on a conventional manifold. In our construction of the Hodge dual of superforms they arise naturally. The compatibility between Hodge duality and supersymmetry is exploited and applied to several examples. We define the irreducible representations of supersymmetry in terms of integral and superforms in a new way which can be easily generalised to several models in different dimensions. The construction of supersymmetric actions based on the Hodge duality is presented and new supersymmetric actions with higher derivative terms are found. These terms are required by the invertibility of the Hodge operator.Comment: LateX2e, 51 pages. Corrected some further misprint

Yang-Mills and Born-Infeld actions on finite group spaces

Discretized nonabelian gauge theories living on finite group spaces G are defined by means of a geometric action \int Tr F\wedge *F . This technique is extended to obtain a discrete version of the Born-Infeld action.Comment: Talk presented at GROUP24, Paris, July 2002. LaTeX, 4 pages, IOP style

Advancing Shannon entropy for measuring diversity in systems

From economic inequality and species diversity to power laws and the analysis of multiple trends and trajectories, diversity within systems is a major issue for science. Part of the challenge is measuring it. Shannon entropy H has been used to re-think diversity within probability distributions, based on the notion of information. However, there are two major limitations to Shannon's approach. First, it cannot be used to compare diversity distributions that have different levels of scale. Second, it cannot be used to compare parts of diversity distributions to the whole. To address these limitations, we introduce a re-normalization of probability distributions based on the notion of case-based entropy Cc as a function of the cumulative probability c. Given a probability density p(x), Cc measures the diversity of the distribution up to a cumulative probability of c, by computing the length or support of an equivalent uniform distribution that has the same Shannon information as the conditional distribution of ^pc(x) up to cumulative probability c. We illustrate the utility of our approach by re-normalizing and comparing three well-known energy distributions in physics, namely, the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distributions for energy of sub-atomic particles. The comparison shows that Cc is a vast improvement over H as it provides a scale-free comparison of these diversity distributions and also allows for a comparison between parts of these diversity distributions

RR Lyrae Stars in NGC 6388 and NGC 6441: A New Oosterhoff Group?

NGC 6388 and NGC 6441 are anomalies among Galactic globular clusters in that they cannot be readily place into either Oosterhoff group I or Oosterhoff group II despite their significant numbers of RR Lyrae variables. The mean pulsation periods, , of their RRab variables, at 0.71 d and 0.76 d, respectively, are even larger than for Oosterhoff II clusters. Moreover, Oosterhoff II clusters are very metal-poor, whereas NGC 6388 and NGC 6441 are the most metal-rich globular clusters known to contain RR Lyrae stars. The location of the NGC 6388 and NGC 6441 RRab variables in the period-amplitude diagram implies that the RR Lyrae stars in those two clusters are brighter than expected for their metallicities. Our results therefore indicate that a universal relationship may not exist between the luminosity and the metallicity of RR Lyrae variables.Comment: Four pages, three figures. ApJ (Letters), in pres

Self-Adaptation and Secure Information Flow in Multiparty Structured Communications: A Unified Perspective

We present initial results on a comprehensive model of structured communications, in which self- adaptation and security concerns are jointly addressed. More specifically, we propose a model of self-adaptive, multiparty communications with secure information flow guarantees. In this model, security violations occur when processes attempt to read or write messages of inappropriate security levels within directed exchanges. Such violations trigger adaptation mechanisms that prevent the violations to occur and/or to propagate their effect in the choreography. Our model is equipped with local and global mechanisms for reacting to security violations; type soundness results ensure that global protocols are still correctly executed, while the system adapts itself to preserve security.Comment: In Proceedings BEAT 2014, arXiv:1408.556