707 research outputs found
The multiplicities of the equivariant index of twisted Dirac operators
In this note, we give a geometric expression for the multiplicities of the
equivariant index of a Dirac operator twisted by a line bundle.Comment: 8 page
Kirillov's orbit method: the case of discrete series representations
Let V be an Harish-Chandra discrete series representation of a real
semi-simple Lie group G' and let G be a semi-simple subgroup of G'. In this
paper, we give a geometric expression of the G-multiplicities in V when the
representation V is supposed to be G-admissible
Spectral Asymmetry, Zeta Functions and the Noncommutative Residue
In this paper we study the spectral asymmetry of (possibly nonselfadjoint)
elliptic PsiDO's in terms of the difference of zeta functions coming from
different cuttings. Refining previous formulas of Wodzicki in the case of odd
class elliptic PsiDO's, our main results have several consequence concerning
the local independence with respect to the cutting, the regularity at integer
points of eta functions and a geometric expression for the spectral asymmetry
of Dirac operators which, in particular, yields a new spectral interpretation
of the Einstein-Hilbert action in gravity.Comment: v8: final version. To appear in Int. Math. J., 22 page
Minimal area submanifolds in AdS x compact
We describe the asymptotic behavior of minimal area submanifolds in product
spacetimes of an asymptotically hyperbolic space times a compact internal
manifold. In particular, we find that unlike the case of a minimal area
submanifold just in an asymptotically hyperbolic space, the internal part of
the boundary submanifold is constrained to be itself a minimal area
submanifold. For applications to holography, this tells us what are the allowed
"flavor branes" that can be added to a holographic field theory. We also give a
compact geometric expression for the spectrum of operator dimensions associated
with the slipping modes of the submanifold in the internal space. We illustrate
our results with several examples, including some that haven't appeared in the
literature before.Comment: 24 pages, no figure
Equivariant Dirac operators and differentiable geometric invariant theory
International audienceIn this paper, we give a geometric expression for the multiplicities of the equivariant index of a spin-c Dirac operator
Invariant four-variable automorphic kernel functions
Let be a number field, let be its ring of adeles, and let
. Previously the author
provided an absolutely convergent geometric expression for the four variable
kernel function where the sum is over isomorphism classes of cuspidal
automorphic representations of . Here
is the typical kernel function representing the action of a test
function on the space of the cuspidal automorphic representation . In this
paper we show how to use ideas from the circle method to provide an alternate
expansion for the four variable kernel function that is visibly invariant under
the natural action of .Comment: The formula in this version is more explicit and simpler than the
previous versio
Geometric Expression Invariant 3D Face Recognition using Statistical Discriminant Models
Currently there is no complete face recognition system that is invariant to all facial expressions.
Although humans find it easy to identify and recognise faces regardless of changes in illumination,
pose and expression, producing a computer system with a similar capability has proved to
be particularly di cult. Three dimensional face models are geometric in nature and therefore
have the advantage of being invariant to head pose and lighting. However they are still susceptible
to facial expressions. This can be seen in the decrease in the recognition results using
principal component analysis when expressions are added to a data set.
In order to achieve expression-invariant face recognition systems, we have employed a tensor
algebra framework to represent 3D face data with facial expressions in a parsimonious
space. Face variation factors are organised in particular subject and facial expression modes.
We manipulate this using single value decomposition on sub-tensors representing one variation
mode. This framework possesses the ability to deal with the shortcomings of PCA in less constrained
environments and still preserves the integrity of the 3D data. The results show improved
recognition rates for faces and facial expressions, even recognising high intensity expressions
that are not in the training datasets.
We have determined, experimentally, a set of anatomical landmarks that best describe facial
expression e ectively. We found that the best placement of landmarks to distinguish di erent
facial expressions are in areas around the prominent features, such as the cheeks and eyebrows.
Recognition results using landmark-based face recognition could be improved with better placement.
We looked into the possibility of achieving expression-invariant face recognition by reconstructing
and manipulating realistic facial expressions. We proposed a tensor-based statistical
discriminant analysis method to reconstruct facial expressions and in particular to neutralise
facial expressions. The results of the synthesised facial expressions are visually more realistic
than facial expressions generated using conventional active shape modelling (ASM). We
then used reconstructed neutral faces in the sub-tensor framework for recognition purposes.
The recognition results showed slight improvement. Besides biometric recognition, this novel
tensor-based synthesis approach could be used in computer games and real-time animation
applications
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