5,337 research outputs found
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 and the
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
Stripe ordering and two-gap model for underdoped cuprates
The evidence of edge-gaps around the M-points in the metallic state of
underdoped cuprates has triggered a very active debate on their origin. We
first consider the possibility that this spectroscopic feature results from a
quasi-static charge ordering taking place in the underdoped regime. It comes
out that to explain the coexistence of gaps and arcs on the Fermi surface the
charge modulation should be in an eggbox form. In the lack of evidences for
that, we then investigate the local pairing induced by charge-stripe
fluctuations. A proper description of the strong anisotropy of both the
interactions and the Fermi velocities requires a two-gap model for pairing. We
find that a gap due to incoherent pairing forms near the M-points, while
coherence is established by the stiffness of the pairing near the nodal points.
The model allows for a continuos evolution from a pure BCS pairing (over- and
optimally doped regime) to a mixed boson-fermion model (heavily underdoped
regime).Comment: 4 pages, Proceedings of M2S-HTS
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
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