743 research outputs found
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
-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
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