Akns Hierarchy, Self-Similarity, String Equations and the Grassmannian

In this paper the Galilean, scaling and translational self--similarity conditions for the AKNS hierarchy are analysed geometrically in terms of the infinite dimensional Grassmannian. The string equations found recently by non--scaling limit analysis of the one--matrix model are shown to correspond to the Galilean self--similarity condition for this hierarchy. We describe, in terms of the initial data for the zero--curvature 1--form of the AKNS hierarchy, the moduli space of these self--similar solutions in the Sato Grassmannian. As a byproduct we characterize the points in the Segal--Wilson Grassmannian corresponding to the Sachs rational solutions of the AKNS equation and to the Nakamura--Hirota rational solutions of the NLS equation. An explicit 1--parameter family of Galilean self--similar solutions of the AKNS equation and the associated solution to the NLS equation is determined.Comment: 25 pages in AMS-LaTe

Drifting Pattern Domains in a Reaction-Diffusion System with Nonlocal Coupling

Drifting pattern domains (DPDs), moving localized patches of traveling waves embedded in a stationary (Turing) pattern background and vice versa, are observed in simulations of a reaction-diffusion model with nonlocal coupling. Within this model, a region of bistability between Turing patterns and traveling waves arises from a codimension-2 Turing-wave bifurcation (TWB). DPDs are found within that region in a substantial distance from the TWB. We investigated the dynamics of single interfaces between Turing and wave patterns. It is found that DPDs exist due to a locking of the interface velocities, which is imposed by the absence of space-time defects near these interfaces.Comment: 4 pages, 4 figure

Automatic learning of gait signatures for people identification

This work targets people identification in video based on the way they walk (i.e. gait). While classical methods typically derive gait signatures from sequences of binary silhouettes, in this work we explore the use of convolutional neural networks (CNN) for learning high-level descriptors from low-level motion features (i.e. optical flow components). We carry out a thorough experimental evaluation of the proposed CNN architecture on the challenging TUM-GAID dataset. The experimental results indicate that using spatio-temporal cuboids of optical flow as input data for CNN allows to obtain state-of-the-art results on the gait task with an image resolution eight times lower than the previously reported results (i.e. 80x60 pixels).Comment: Proof of concept paper. Technical report on the use of ConvNets (CNN) for gait recognition. Data and code: http://www.uco.es/~in1majim/research/cnngaitof.htm

Additional symmetries and solutions of the dispersionless KP hierarchy

The dispersionless KP hierarchy is considered from the point of view of the twistor formalism. A set of explicit additional symmetries is characterized and its action on the solutions of the twistor equations is studied. A method for dealing with the twistor equations by taking advantage of hodograph type equations is proposed. This method is applied for determining the orbits of solutions satisfying reduction constraints of Gelfand--Dikii type under the action of additional symmetries.Comment: 21 page

Evaluation of CNN architectures for gait recognition based on optical flow maps

This work targets people identification in video based on the way they walk (\ie gait) by using deep learning architectures. We explore the use of convolutional neural networks (CNN) for learning high-level descriptors from low-level motion features (\ie optical flow components). The low number of training samples for each subject and the use of a test set containing subjects different from the training ones makes the search of a good CNN architecture a challenging task.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

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