On negative flows of the AKNS hierarchy and a class of deformations of bihamiltonian structure of hydrodynamic type

A deformation parameter of a bihamiltonian structure of hydrodynamic type is shown to parameterize different extensions of the AKNS hierarchy to include negative flows. This construction establishes a purely algebraic link between, on the one hand, two realizations of the first negative flow of the AKNS model and, on the other, two-component generalizations of Camassa-Holm and Dym type equations. The two-component generalizations of Camassa-Holm and Dym type equations can be obtained from the negative order Hamiltonians constructed from the Lenard relations recursively applied on the Casimir of the first Poisson bracket of hydrodynamic type. The positive order Hamiltonians, which follow from Lenard scheme applied on the Casimir of the second Poisson bracket of hydrodynamic type, are shown to coincide with the Hamiltonians of the AKNS model. The AKNS Hamiltonians give rise to charges conserved with respect to equations of motion of two-component Camassa-Holm and two-component Dym type equations.Comment: 20 pages, Late

Vertex Operators and Soliton Solutions of Affine Toda Model with U(2) Symmetry

The symmetry structure of non-abelian affine Toda model based on the coset $SL(3)/SL(2)\otimes U(1)$ is studied. It is shown that the model possess non-abelian Noether symmetry closing into a q-deformed $SL(2)\otimes U(1)$ algebra. Specific two vertex soliton solutions are constructed.Comment: 17 pages, latex, misprints corrected, version to appear in J.Phys

Exact static soliton solutions of 3+1 dimensional integrable theory with nonzero Hopf numbers

In this paper we construct explicitly an infinite number of Hopfions (static, soliton solutions with non-zero Hopf topological charges) within the recently proposed 3+1-dimensional, integrable and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are constructed explicitly in terms of the toroidal coordinates and shown to have a form of linked closed vortices.Comment: LaTeX, 7 pg

The complex Sine-Gordon equation as a symmetry flow of the AKNS Hierarchy

It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the ``negative'' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and the vector Nonlinear Schrodinger equations appear as lowest negative and second positive flows within the extended hierarchy. This is fully analogous to the well-known connection between the sine-Gordon and mKdV equations within the extended mKdV hierarchy. A general formalism for a Toda-like symmetry occupying the ``negative'' sector of sl(N) constrained KP hierarchy and giving rise to the negative Borel sl(N) loop algebra is indicated.Comment: 8 pages, LaTeX, typos corrected, references update

Transcranial direct current stimulation over multiple days improves learning and maintenance of a novel vocabulary

Introduction: Recently, growing interest emerged in the enhancement of human potential by means of non-invasive brain stimulation. In particular, anodal transcranial direct current stimulation (atDCS) has been shown to exert beneficial effects on motor and higher cognitive functions. However, the majority of transcranial direct current stimulation (tDCS) studies have assessed effects of single stimulation sessions that are mediated by transient neural modulation. Studies assessing the impact of multiple stimulation sessions on learning that may induce long-lasting behavioural and neural changes are scarce and have not yet been accomplished in the language domain in healthy individuals

Myosin II activity regulates vinculin recruitment to focal adhesions through FAK-mediated paxillin phosphorylation

© The Authors, 2010. This article is distributed under the terms of the Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License. The definitive version was published in Journal of Cell Biology 188 (2010): 877-890, doi:10.1083/jcb.200906012.Focal adhesions (FAs) are mechanosensitive adhesion and signaling complexes that grow and change composition in response to myosin II–mediated cytoskeletal tension in a process known as FA maturation. To understand tension-mediated FA maturation, we sought to identify proteins that are recruited to FAs in a myosin II–dependent manner and to examine the mechanism for their myosin II–sensitive FA association. We find that FA recruitment of both the cytoskeletal adapter protein vinculin and the tyrosine kinase FA kinase (FAK) are myosin II and extracellular matrix (ECM) stiffness dependent. Myosin II activity promotes FAK/Src-mediated phosphorylation of paxillin on tyrosines 31 and 118 and vinculin association with paxillin. We show that phosphomimic mutations of paxillin can specifically induce the recruitment of vinculin to adhesions independent of myosin II activity. These results reveal an important role for paxillin in adhesion mechanosensing via myosin II–mediated FAK phosphorylation of paxillin that promotes vinculin FA recruitment to reinforce the cytoskeletal ECM linkage and drive FA maturation.This work was supported by NHLBI (C.M. Waterman and A.M. Pasapera; and grant HL093156 to D.D. Schlaepfer) and the Burroughs Wellcome Fund (E. Rericha)