452 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
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
String Equations for the Unitary Matrix Model and the Periodic Flag Manifold
The periodic flag manifold (in the Sato Grassmannian context) description of
the modified Korteweg--de Vries hierarchy is used to analyse the translational
and scaling self--similar solutions of this hierarchy. These solutions are
characterized by the string equations appearing in the double scaling limit of
the symmetric unitary matrix model with boundary terms. The moduli space is a
double covering of the moduli space in the Sato Grassmannian for the
corresponding self--similar solutions of the Korteweg--de Vries hierarchy, i.e.
of stable 2D quantum gravity. The potential modified Korteweg--de Vries
hierarchy, which can be described in terms of a line bundle over the periodic
flag manifold, and its self--similar solutions corresponds to the symmetric
unitary matrix model. Now, the moduli space is in one--to--one correspondence
with a subset of codimension one of the moduli space in the Sato Grassmannian
corresponding to self--similar solutions of the Korteweg--de Vries hierarchy.Comment: 21 pages in LaTeX-AMSTe
Non-degenerate solutions of universal Whitham hierarchy
The notion of non-degenerate solutions for the dispersionless Toda hierarchy
is generalized to the universal Whitham hierarchy of genus zero with
marked points. These solutions are characterized by a Riemann-Hilbert problem
(generalized string equations) with respect to two-dimensional canonical
transformations, and may be thought of as a kind of general solutions of the
hierarchy. The Riemann-Hilbert problem contains arbitrary functions
, , which play the role of generating functions of
two-dimensional canonical transformations. The solution of the Riemann-Hilbert
problem is described by period maps on the space of -tuples
of conformal maps from disks of the
Riemann sphere and their complements to the Riemann sphere. The period maps are
defined by an infinite number of contour integrals that generalize the notion
of harmonic moments. The -function (free energy) of these solutions is also
shown to have a contour integral representation.Comment: latex2e, using amsmath, amssym and amsthm packages, 32 pages, no
figur
Time representation in reinforcement learning models of the basal ganglia
Reinforcement learning (RL) models have been influential in understanding many aspects of basal ganglia function, from reward prediction to action selection. Time plays an important role in these models, but there is still no theoretical consensus about what kind of time representation is used by the basal ganglia. We review several theoretical accounts and their supporting evidence. We then discuss the relationship between RL models and the timing mechanisms that have been attributed to the basal ganglia. We hypothesize that a single computational system may underlie both RL and interval timingâthe perception of duration in the range of seconds to hours. This hypothesis, which extends earlier models by incorporating a time-sensitive action selection mechanism, may have important implications for understanding disorders like Parkinson's disease in which both decision making and timing are impaired
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
On integration of some classes of dimensional nonlinear Partial Differential Equations
The paper represents the method for construction of the families of
particular solutions to some new classes of dimensional nonlinear
Partial Differential Equations (PDE). Method is based on the specific link
between algebraic matrix equations and PDE. Admittable solutions depend on
arbitrary functions of variables.Comment: 6 page
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