36,824 research outputs found
Nonlinear Hebbian learning as a unifying principle in receptive field formation
The development of sensory receptive fields has been modeled in the past by a
variety of models including normative models such as sparse coding or
independent component analysis and bottom-up models such as spike-timing
dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic
plasticity. Here we show that the above variety of approaches can all be
unified into a single common principle, namely Nonlinear Hebbian Learning. When
Nonlinear Hebbian Learning is applied to natural images, receptive field shapes
were strongly constrained by the input statistics and preprocessing, but
exhibited only modest variation across different choices of nonlinearities in
neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse
network activity are necessary for the development of localized receptive
fields. The analysis of alternative sensory modalities such as auditory models
or V2 development lead to the same conclusions. In all examples, receptive
fields can be predicted a priori by reformulating an abstract model as
nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural
statistics can account for many aspects of receptive field formation across
models and sensory modalities
N-Dark-Dark Solitons in the Generally Coupled Nonlinear Schroedinger Equations
N-dark-dark solitons in the generally coupled integrable NLS equations are
derived by the KP-hierarchy reduction method. These solitons exist when
nonlinearities are all defocusing, or both focusing and defocusing
nonlinearities are mixed. When these solitons collide with each other, energies
in both components of the solitons completely transmit through. This behavior
contrasts collisions of bright-bright solitons in similar systems, where
polarization rotation and soliton reflection can take place. It is also shown
that in the mixed-nonlinearity case, two dark-dark solitons can form a
stationary bound state.Comment: 26 pages, 3 figure
Solitary waves in coupled nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities
Using Lie group theory we construct explicit solitary wave solutions of
coupled nonlinear Schrodinger systems with spatially inhomogeneous
nonlinearities. We present the general theory, use it to construct different
families of explicit solutions and study their linear and dynamical stability
Bright solitons and soliton trains in a fermion-fermion mixture
We use a time-dependent dynamical mean-field-hydrodynamic model to predict
and study bright solitons in a degenerate fermion-fermion mixture in a
quasi-one-dimensional cigar-shaped geometry using variational and numerical
methods. Due to a strong Pauli-blocking repulsion among identical
spin-polarized fermions at short distances there cannot be bright solitons for
repulsive interspecies fermion-fermion interactions. However, stable bright
solitons can be formed for a sufficiently attractive interspecies interaction.
We perform a numerical stability analysis of these solitons and also
demonstrate the formation of soliton trains. These fermionic solitons can be
formed and studied in laboratory with present technology.Comment: 5 pages, 7 figure
MISEP - Linear and Nonlinear ICA Based on Mutual Information
MISEP is a method for linear and nonlinear ICA, that is able to handle a large variety of situations. It is an extension of the well known INFOMAX method, in two directions: (1) handling of nonlinear mixtures, and (2) learning the nonlinearities to be used at the outputs. The method can therefore separate linear and nonlinear mixtures of components with a wide range of statistical distributions.
This paper presents the basis of the MISEP method, as well as experimental results obtained with it. The results illustrate the applicability of the method to various situations, and show that, although the nonlinear blind separation problem is ill-posed, use of regularization allows the problem to be solved when the nonlinear mixture is relatively smooth
Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations
This paper introduces tensorial calculus techniques in the framework of
Proper Orthogonal Decomposition (POD) to reduce the computational complexity of
the reduced nonlinear terms. The resulting method, named tensorial POD, can be
applied to polynomial nonlinearities of any degree . Such nonlinear terms
have an on-line complexity of , where is the
dimension of POD basis, and therefore is independent of full space dimension.
However it is efficient only for quadratic nonlinear terms since for higher
nonlinearities standard POD proves to be less time consuming once the POD basis
dimension is increased. Numerical experiments are carried out with a two
dimensional shallow water equation (SWE) test problem to compare the
performance of tensorial POD, standard POD, and POD/Discrete Empirical
Interpolation Method (DEIM). Numerical results show that tensorial POD
decreases by times the computational cost of the on-line stage of
standard POD for configurations using more than model variables. The
tensorial POD SWE model was only slower than the POD/DEIM SWE model
but the implementation effort is considerably increased. Tensorial calculus was
again employed to construct a new algorithm allowing POD/DEIM shallow water
equation model to compute its off-line stage faster than the standard and
tensorial POD approaches.Comment: 23 pages, 8 figures, 5 table
Stability of solitary-wave solutions of coupled NLS equations with power-type nonlinearities
This paper proves existence and stability results of solitary-wave solutions
to coupled nonlinear Schr\"{o}dinger equations with power-type nonlinearities
arising in several models of modern physics. The existence of solitary waves is
obtained by solving a variational problem subject to two independent
constraints and using the concentration-compactness method. The set of
minimizers is shown to be stable and further information about the structures
of this set are given. The paper extends the results previously obtained by
Cipolatti and Zumpichiatti, Nguyen and Wang, and Ohta
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