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Geometry Aware Compressive Analysis of Human Activities : Application in a Smart Phone PlatformJanuary 2014 (has links)
abstract: Continuous monitoring of sensor data from smart phones to identify human activities and gestures, puts a heavy load on the smart phone's power consumption. In this research study, the non-Euclidean geometry of the rich sensor data obtained from the user's smart phone is utilized to perform compressive analysis and efficient classification of human activities by employing machine learning techniques. We are interested in the generalization of classical tools for signal approximation to newer spaces, such as rotation data, which is best studied in a non-Euclidean setting, and its application to activity analysis. Attributing to the non-linear nature of the rotation data space, which involve a heavy overload on the smart phone's processor and memory as opposed to feature extraction on the Euclidean space, indexing and compaction of the acquired sensor data is performed prior to feature extraction, to reduce CPU overhead and thereby increase the lifetime of the battery with a little loss in recognition accuracy of the activities. The sensor data represented as unit quaternions, is a more intrinsic representation of the orientation of smart phone compared to Euler angles (which suffers from Gimbal lock problem) or the computationally intensive rotation matrices. Classification algorithms are employed to classify these manifold sequences in the non-Euclidean space. By performing customized indexing (using K-means algorithm) of the evolved manifold sequences before feature extraction, considerable energy savings is achieved in terms of smart phone's battery life. / Dissertation/Thesis / M.S. Electrical Engineering 2014
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A posteriori error estimation for non-linear eigenvalue problems for differential operators of second order with focus on 3D vertex singularitiesPester, Cornelia 07 May 2006 (has links) (PDF)
This thesis is concerned with the finite element
analysis and the a posteriori error estimation for
eigenvalue problems for general operator pencils on
two-dimensional manifolds.
A specific application of the presented theory is the
computation of corner singularities.
Engineers use the knowledge of the so-called singularity
exponents to predict the onset and the propagation of
cracks.
All results of this thesis are explained for two model
problems, the Laplace and the linear elasticity problem,
and verified by numerous numerical results.
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Desigualdades universais para autovalores do polidrifting laplaciano em dominios compactos do R^n e S^n / Universal bounds for eigenvalues of the poli-drifting laplaciano operators ìn compact domains in the R^n and S^nPereira, Rosane Gomes 08 March 2016 (has links)
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Previous issue date: 2016-03-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we study eigenvalues of poly-drifting laplacian on compact
Riemannian manifolds with boundary (possibly empty). Here, we bring a
universal inequality for the eigenvalues of the poly-drifting operator on compact
domains in an Euclidean spaceRn. Besides,weintroduce universal inequalities for
eigenvalues of poly-drifting operator on compact domains in a unit n-sphere Sn.
We give an universal inequality for lower order eigenvalues of the poly-drifting
operator inRn and Sn. Moreover, we prove an universal inequality type Ashbaugh
and Benguria for the drifting Laplacian on Riemannian manifold immersed in an
unit sphere or a projective space. Let
be a bounded domain in a n-dimensional
Euclidean space Rn. We study eigenvalues of an eigenvalue problem of a system
of elliptic equations of the drifting laplacian
8>><>>:
L u+ (r(divu)r divu) = ¯ u; in
;
uj@
= 0
Estimates for eigenvalues of the above eigenvalue problem are obtained. Furthermore,
a universal inequality for lower order eigenvalues of the problem is also
derived. / Neste trabalho, estudamos autovalores do polidrifting Laplaciano em variedades
Riemannianas compactas com fronteira (possivelmente vazia). Aqui, trazemos
uma desigualdade universal para autovalores do polidrifting operador em
domínios compactos no espaço Euclidiano Rn. Além disso, introduzimos desigualdades
universais para autovalores do polidrifting operador em domínios
compactos na n-esfera unitária Sn. Fornecemos uma estimativa para autovalores
de ordem inferior do polidrifting operador emRn e Sn. Mais ainda, provamos uma
desigualdade universal do tipo Ashbaugh-Benguria para o drifting Laplacianoem
variedades Riemannianas imersas em uma esfera unitária ou no espaço projetivo.
Seja
um domínio limitado no n-dimensional espaço Euclidiano Rn. Estudamos
autovalores de um problema de autovalores de um sistema de equações elípticas
do drifting Laplaciano
8>><>>:
L u+ (r(divu)r divu) = ¯ u; in
;
uj@
= 0
Estimativas para autovalores do problema de autovalores acima são obtidas. Além
disso, uma desigualdade universal de ordem inferior também é encontrada.
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A posteriori error estimation for non-linear eigenvalue problems for differential operators of second order with focus on 3D vertex singularitiesPester, Cornelia 21 April 2006 (has links)
This thesis is concerned with the finite element
analysis and the a posteriori error estimation for
eigenvalue problems for general operator pencils on
two-dimensional manifolds.
A specific application of the presented theory is the
computation of corner singularities.
Engineers use the knowledge of the so-called singularity
exponents to predict the onset and the propagation of
cracks.
All results of this thesis are explained for two model
problems, the Laplace and the linear elasticity problem,
and verified by numerous numerical results.
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