Integrable Quasiclassical Deformations of Algebraic Curves

A general scheme for determining and studying integrable deformations of algebraic curves is presented. The method is illustrated with the analysis of the hyperelliptic case. An associated multi-Hamiltonian hierarchy of systems of hydrodynamic type is characterized.Comment: 28 pages, no figure

Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations

A class of nonlinear problems on the plane, described by nonlinear inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described by Hamilton-Jacobi type equations associated with hierarchies of dispersionless integrable systems. These hierarchies are constructed by applying the quasiclassical $\bar{\partial}$-dressing method.Comment: 30 pages, tcilate

Hydrodynamic reductions and solutions of a universal hierarchy

The diagonal hydrodynamic reductions of a hierarchy of integrable hydrodynamic chains are explicitly characterized. Their compatibility with previously introduced reductions of differential type is analyzed and their associated class of hodograph solutions is discussed.Comment: 19 page

dbar-approach to the dispersionless KP hierarchy

The dispersionless limit of the scalar nonlocal dbar-problem is derived. It is given by a special class of nonlinear first-order equations. A quasi-classical version of the dbar-dressing method is presented. It is shown that the algebraic formulation of dispersionless hierarchies can be expressed in terms of properties of Beltrami tupe equations. The universal Whitham hierarchy and, in particular, the dispersionless KP hierarchy turn out to be rings of symmetries for the quasi-classical dbar-problem.Comment: 13 pages, LaTex 24.9K

On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

Assessing HRTF preprocessing methods for Ambisonics rendering through perceptual models

Binaural rendering of Ambisonics signals is a common way to reproduce spatial audio content. Processing Ambisonics signals at low spatial orders is desirable in order to reduce complexity, although it may degrade the perceived quality, in part due to the mismatch that occurs when a low-order Ambisonics signal is paired with a spatially dense head-related transfer function (HRTF). In order to alleviate this issue, the HRTF may be preprocessed so its spatial order is reduced. Several preprocessing methods have been proposed, but they have not been thoroughly compared yet. In this study, nine HRTF preprocessing methods were used to render anechoic binaural signals from Ambisonics representations of orders 1 to 44, and these were compared through perceptual hearing models in terms of localisation performance, externalisation and speech reception. This assessment was supported by numerical analyses of HRTF interpolation errors, interaural differences, perceptually-relevant spectral differences, and loudness stability. Models predicted that the binaural renderings’ accuracy increased with spatial order, as expected. A notable effect of the preprocessing method was observed: whereas all methods performed similarly at the highest spatial orders, some were considerably better at lower orders. A newly proposed method, BiMagLS, displayed the best performance overall and is recommended for the rendering of bilateral Ambisonics signals. The results, which were in line with previous literature, indirectly validate the perceptual models’ ability to predict listeners’ responses in a consistent and explicable manner

L1CAM binds ErbB receptors through Ig-like domains coupling cell adhesion and neuregulin signalling.

During nervous system development different cell-to-cell communication mechanisms operate in parallel guiding migrating neurons and growing axons to generate complex arrays of neural circuits. How such a system works in coordination is not well understood. Cross-regulatory interactions between different signalling pathways and redundancy between them can increase precision and fidelity of guidance systems. Immunoglobulin superfamily proteins of the NCAM and L1 families couple specific substrate recognition and cell adhesion with the activation of receptor tyrosine kinases. Thus it has been shown that L1CAM-mediated cell adhesion promotes the activation of the EGFR (erbB1) from Drosophila to humans. Here we explore the specificity of the molecular interaction between L1CAM and the erbB receptor family. We show that L1CAM binds physically erbB receptors in both heterologous systems and the mammalian developing brain. Different Ig-like domains located in the extracellular part of L1CAM can support this interaction. Interestingly, binding of L1CAM to erbB enhances its response to neuregulins. During development this may synergize with the activation of erbB receptors through L1CAM homophilic interactions, conferring diffusible neuregulins specificity for cells or axons that interact with the substrate through L1CAM