14,583 research outputs found
Acoustic Space Learning for Sound Source Separation and Localization on Binaural Manifolds
In this paper we address the problems of modeling the acoustic space
generated by a full-spectrum sound source and of using the learned model for
the localization and separation of multiple sources that simultaneously emit
sparse-spectrum sounds. We lay theoretical and methodological grounds in order
to introduce the binaural manifold paradigm. We perform an in-depth study of
the latent low-dimensional structure of the high-dimensional interaural
spectral data, based on a corpus recorded with a human-like audiomotor robot
head. A non-linear dimensionality reduction technique is used to show that
these data lie on a two-dimensional (2D) smooth manifold parameterized by the
motor states of the listener, or equivalently, the sound source directions. We
propose a probabilistic piecewise affine mapping model (PPAM) specifically
designed to deal with high-dimensional data exhibiting an intrinsic piecewise
linear structure. We derive a closed-form expectation-maximization (EM)
procedure for estimating the model parameters, followed by Bayes inversion for
obtaining the full posterior density function of a sound source direction. We
extend this solution to deal with missing data and redundancy in real world
spectrograms, and hence for 2D localization of natural sound sources such as
speech. We further generalize the model to the challenging case of multiple
sound sources and we propose a variational EM framework. The associated
algorithm, referred to as variational EM for source separation and localization
(VESSL) yields a Bayesian estimation of the 2D locations and time-frequency
masks of all the sources. Comparisons of the proposed approach with several
existing methods reveal that the combination of acoustic-space learning with
Bayesian inference enables our method to outperform state-of-the-art methods.Comment: 19 pages, 9 figures, 3 table
Localization of a polymer in random media: Relation to the localization of a quantum particle
In this paper we consider in detail the connection between the problem of a
polymer in a random medium and that of a quantum particle in a random
potential. We are interested in a system of finite volume where the polymer is
known to be {\it localized} inside a low minimum of the potential. We show how
the end-to-end distance of a polymer which is free to move can be obtained from
the density of states of the quantum particle using extreme value statistics.
We give a physical interpretation to the recently discovered one-step
replica-symmetry-breaking solution for the polymer (Phys. Rev. E{\bf 61}, 1729
(2000)) in terms of the statistics of localized tail states. Numerical
solutions of the variational equations for chains of different length are
performed and compared with quenched averages computed directly by using the
eigenfunctions and eigenenergies of the Schr\"odinger equation for a particle
in a one-dimensional random potential. The quantities investigated are the
radius of gyration of a free gaussian chain, its mean square distance from the
origin and the end-to-end distance of a tethered chain. The probability
distribution for the position of the chain is also investigated. The glassiness
of the system is explained and is estimated from the variance of the measured
quantities.Comment: RevTex, 44 pages, 13 figure
Local strong maximal monotonicity and full stability for parametric variational systems
The paper introduces and characterizes new notions of Lipschitzian and
H\"olderian full stability of solutions to general parametric variational
systems described via partial subdifferential and normal cone mappings acting
in Hilbert spaces. These notions, postulated certain quantitative properties of
single-valued localizations of solution maps, are closely related to local
strong maximal monotonicity of associated set-valued mappings. Based on
advanced tools of variational analysis and generalized differentiation, we
derive verifiable characterizations of the local strong maximal monotonicity
and full stability notions under consideration via some positive-definiteness
conditions involving second-order constructions of variational analysis. The
general results obtained are specified for important classes of variational
inequalities and variational conditions in both finite and infinite dimensions
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