939 research outputs found
Multiple Meixner-Pollaczek polynomials and the six-vertex model
We study multiple orthogonal polynomials of Meixner-Pollaczek type with
respect to a symmetric system of two orthogonality measures. Our main result is
that the limiting distribution of the zeros of these polynomials is one
component of the solution to a constrained vector equilibrium problem. We also
provide a Rodrigues formula and closed expressions for the recurrence
coefficients. The proof of the main result follows from a connection with the
eigenvalues of block Toeplitz matrices, for which we provide some general
results of independent interest.
The motivation for this paper is the study of a model in statistical
mechanics, the so-called six-vertex model with domain wall boundary conditions,
in a particular regime known as the free fermion line. We show how the multiple
Meixner-Pollaczek polynomials arise in an inhomogeneous version of this model.Comment: 32 pages, 4 figures. References adde
RBF neural net based classifier for the AIRIX accelerator fault diagnosis
The AIRIX facility is a high current linear accelerator (2-3.5kA) used for
flash-radiography at the CEA of Moronvilliers France. The general background of
this study is the diagnosis and the predictive maintenance of AIRIX. We will
present a tool for fault diagnosis and monitoring based on pattern recognition
using artificial neural network. Parameters extracted from the signals recorded
on each shot are used to define a vector to be classified. The principal
component analysis permits us to select the most pertinent information and
reduce the redundancy. A three layer Radial Basis Function (RBF) neural network
is used to classify the states of the accelerator. We initialize the network by
applying an unsupervised fuzzy technique to the training base. This allows us
to determine the number of clusters and real classes, which define the number
of cells on the hidden and output layers of the network. The weights between
the hidden and the output layers, realising the non-convex union of the
clusters, are determined by a least square method. Membership and ambiguity
rejection enable the network to learn unknown failures, and to monitor
accelerator operations to predict future failures. We will present the first
results obtained on the injector.Comment: 3 pages, 4 figures, LINAC'2000 conferenc
Average characteristic polynomials in the two-matrix model
The two-matrix model is defined on pairs of Hermitian matrices of
size by the probability measure where
and are given potential functions and \tau\in\er. We study averages
of products and ratios of characteristic polynomials in the two-matrix model,
where both matrices and may appear in a combined way in both
numerator and denominator. We obtain determinantal expressions for such
averages. The determinants are constructed from several building blocks: the
biorthogonal polynomials and associated to the two-matrix
model; certain transformed functions and \Q_n(v); and finally
Cauchy-type transforms of the four Eynard-Mehta kernels , ,
and . In this way we generalize known results for the
-matrix model. Our results also imply a new proof of the Eynard-Mehta
theorem for correlation functions in the two-matrix model, and they lead to a
generating function for averages of products of traces.Comment: 28 pages, references adde
Passengers information in public transport and privacy: Can anonymous tickets prevent tracking?
Abstract Modern public transportation companies often record large amounts of information. Privacy can be safeguarded by discarding nominal tickets, or introducing anonymization techniques. But is anonymity at all possible when everything is recorded? In this paper we discuss travel information management in the public transport scenario and we present a revealing case study (relative to the city of Cesena, Italy), showing that even anonymous 10-ride bus tickets may betray a user's privacy expectations. We also propose a number of recommendations for the design and management of public transport information systems, aimed at preserving the usersâ privacy, while retaining the useful analysis features enabled by the e-ticketing technology
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