20,713 research outputs found
Parametrization of the Driven Betatron Oscillation
An AC dipole is a magnet which produces a sinusoidally oscillating dipole
field and excites coherent transverse beam motion in a synchrotron. By
observing this coherent motion, the optical parameters can be directly measured
at the beam position monitor locations. The driven oscillation induced by an AC
dipole will generate a phase space ellipse which differs from that of the free
oscillation. If not properly accounted for, this difference can lead to a
misinterpretation of the actual optical parameters, for instance, of 6% or more
in the cases of the Tevatron, RHIC, or LHC. The effect of an AC dipole on the
linear optics parameters is identical to that of a thin lens quadrupole. By
introducing a new amplitude function to describe this new phase space ellipse,
the motion produced by an AC dipole becomes easier to interpret. Beam position
data taken under the influence of an AC dipole, with this new interpretation in
mind, can lead to more precise measurements of the normal Courant-Snyder
parameters. This new parameterization of the driven motion is presented and is
used to interpret data taken in the FNAL Tevatron using an AC dipole.Comment: 8 pages, 8 figures, and 1 tabl
Special symplectic Lie groups and hypersymplectic Lie groups
A special symplectic Lie group is a triple such that
is a finite-dimensional real Lie group and is a left invariant
symplectic form on which is parallel with respect to a left invariant
affine structure . In this paper starting from a special symplectic Lie
group we show how to ``deform" the standard Lie group structure on the
(co)tangent bundle through the left invariant affine structure such
that the resulting Lie group admits families of left invariant hypersymplectic
structures and thus becomes a hypersymplectic Lie group. We consider the affine
cotangent extension problem and then introduce notions of post-affine structure
and post-left-symmetric algebra which is the underlying algebraic structure of
a special symplectic Lie algebra. Furthermore, we give a kind of double
extensions of special symplectic Lie groups in terms of post-left-symmetric
algebras.Comment: 32 page
High-Dimensional Inference with the generalized Hopfield Model: Principal Component Analysis and Corrections
We consider the problem of inferring the interactions between a set of N
binary variables from the knowledge of their frequencies and pairwise
correlations. The inference framework is based on the Hopfield model, a special
case of the Ising model where the interaction matrix is defined through a set
of patterns in the variable space, and is of rank much smaller than N. We show
that Maximum Lik elihood inference is deeply related to Principal Component
Analysis when the amp litude of the pattern components, xi, is negligible
compared to N^1/2. Using techniques from statistical mechanics, we calculate
the corrections to the patterns to the first order in xi/N^1/2. We stress that
it is important to generalize the Hopfield model and include both attractive
and repulsive patterns, to correctly infer networks with sparse and strong
interactions. We present a simple geometrical criterion to decide how many
attractive and repulsive patterns should be considered as a function of the
sampling noise. We moreover discuss how many sampled configurations are
required for a good inference, as a function of the system size, N and of the
amplitude, xi. The inference approach is illustrated on synthetic and
biological data.Comment: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
(2011) to appea
A Random Matrix Approach to VARMA Processes
We apply random matrix theory to derive spectral density of large sample
covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2)
processes. In particular, we consider a limit where the number of random
variables N and the number of consecutive time measurements T are large but the
ratio N/T is fixed. In this regime the underlying random matrices are
asymptotically equivalent to Free Random Variables (FRV). We apply the FRV
calculus to calculate the eigenvalue density of the sample covariance for
several VARMA-type processes. We explicitly solve the VARMA(1,1) case and
demonstrate a perfect agreement between the analytical result and the spectra
obtained by Monte Carlo simulations. The proposed method is purely algebraic
and can be easily generalized to q1>1 and q2>1.Comment: 16 pages, 6 figures, submitted to New Journal of Physic
A silent speech system based on permanent magnet articulography and direct synthesis
In this paper we present a silent speech interface (SSI) system aimed at restoring speech communication for individuals who have lost their voice due to laryngectomy or diseases affecting the vocal folds. In the proposed system, articulatory data captured from the lips and tongue using permanent magnet articulography (PMA) are converted into audible speech using a speaker-dependent transformation learned from simultaneous recordings of PMA and audio signals acquired before laryngectomy. The transformation is represented using a mixture of factor analysers, which is a generative model that allows us to efficiently model non-linear behaviour and perform dimensionality reduction at the same time. The learned transformation is then deployed during normal usage of the SSI to restore the acoustic speech signal associated with the captured PMA data. The proposed system is evaluated using objective quality measures and listening tests on two databases containing PMA and audio recordings for normal speakers. Results show that it is possible to reconstruct speech from articulator movements captured by an unobtrusive technique without an intermediate recognition step. The SSI is capable of producing speech of sufficient intelligibility and naturalness that the speaker is clearly identifiable, but problems remain in scaling up the process to function consistently for phonetically rich vocabularies
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