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1,284 results on '"Parallel transport"'

108. Improving EEG-based decoding of the locus of auditory attention through domain adaptation .

Author

Wilroth J, Bernhardsson B, Heskebeck F, Skoglund MA, Bergeling C, and Alickovic E

Subjects
Humans, Acoustic Stimulation methods, Noise, Attention, Electroencephalography methods, Speech Perception
Abstract

Objective. This paper presents a novel domain adaptation (DA) framework to enhance the accuracy of electroencephalography (EEG)-based auditory attention classification, specifically for classifying the direction (left or right) of attended speech. The framework aims to improve the performances for subjects with initially low classification accuracy, overcoming challenges posed by instrumental and human factors. Limited dataset size, variations in EEG data quality due to factors such as noise, electrode misplacement or subjects, and the need for generalization across different trials, conditions and subjects necessitate the use of DA methods. By leveraging DA methods, the framework can learn from one EEG dataset and adapt to another, potentially resulting in more reliable and robust classification models. Approach. This paper focuses on investigating a DA method, based on parallel transport, for addressing the auditory attention classification problem. The EEG data utilized in this study originates from an experiment where subjects were instructed to selectively attend to one of the two spatially separated voices presented simultaneously. Main results. Significant improvement in classification accuracy was observed when poor data from one subject was transported to the domain of good data from different subjects, as compared to the baseline. The mean classification accuracy for subjects with poor data increased from 45.84% to 67.92%. Specifically, the highest achieved classification accuracy from one subject reached 83.33%, a substantial increase from the baseline accuracy of 43.33%. Significance. The findings of our study demonstrate the improved classification performances achieved through the implementation of DA methods. This brings us a step closer to leveraging EEG in neuro-steered hearing devices., (Creative Commons Attribution license.)

Published
2023
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112. Multi-directional geodesic neural networks via equivariant convolution.

Author

Poulenard, Adrien and Ovsjanikov, Maks

Subjects
ARTIFICIAL neural networks, DEEP learning, MATHEMATICAL convolutions, GEODESICS, IMAGE segmentation
Abstract

We propose a novel approach for performing convolution of signals on curved surfaces and show its utility in a variety of geometric deep learning applications. Key to our construction is the notion of directional functions defined on the surface, which extend the classic real-valued signals and which can be naturally convolved with with real-valued template functions. As a result, rather than trying to fix a canonical orientation or only keeping the maximal response across all alignments of a 2D template at every point of the surface, as done in previous works, we show how information across all rotations can be kept across different layers of the neural network. Our construction, which we call multi-directional geodesic convolution, or directional convolution for short, allows, in particular, to propagate and relate directional information across layers and thus different regions on the shape. We first define directional convolution in the continuous setting, prove its key properties and then show how it can be implemented in practice, for shapes represented as triangle meshes. We evaluate directional convolution in a wide variety of learning scenarios ranging from classification of signals on surfaces, to shape segmentation and shape matching, where we show a significant improvement over several baselines. [ABSTRACT FROM AUTHOR]

Published
2018
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113. A FANNING SCHEME FOR THE PARALLEL TRANSPORT ALONG GEODESICS ON RIEMANNIAN MANIFOLDS.

Author

LOUIS, MAXIME, CHARLIER, BENJAMIN, JUSSELIN, PAUL, PAL, SUSOVAN, and DURRLEMAN, STANLEY

Subjects
*NUMERICAL analysis, *PARTIAL differential equations, *GEODESIC equation, *APPROXIMATION theory, *DIFFERENTIAL equations
Abstract

Parallel transport on Riemannian manifolds allows one to connect tangent spaces at different points in an isometric way and is therefore of importance in many contexts, such as statistics on manifolds. The existing methods for computing parallel transport require either the computation of Riemannian logarithms, such as Schild's ladder, or the Christoffel symbols. The logarithm is rarely given in closed form, and therefore expensive to compute, whereas the Christoffel symbols are in general hard and costly to compute. From an identity between parallel transport and Jacobi fields, we propose a numerical scheme to approximate parallel transport along a geodesic. We find and prove an optimal convergence rate for the scheme, which is equivalent to Schild's ladders. We investigate potential variations of the scheme and give experimental results on the Euclidean 2-sphere and on the manifold of symmetric positive definite matrices. [ABSTRACT FROM AUTHOR]

Published
2018
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118. General Features of Spacetime

Author

de Monvel, Anne Boutet, editor, Kaiser, Gerald, editor, Berenstein, C., editor, Berry, M., editor, Blanchard, P., editor, Eastwood, M., editor, Fokas, A. S., editor, Sternheimer, D., editor, Tracy, C., editor, and Sharan, Pankaj

Published
2009
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119. Discrete Dynamics: Gauge Invariance and Quantization

Author

Kornyak, Vladimir V., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Gerdt, Vladimir P., editor, Mayr, Ernst W., editor, and Vorozhtsov, Evgenii V., editor

Published
2009
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120. Displacement interpolation

Author

Villani, Cédric, Berger, M., editor, Eckmann, B., editor, de la Harpe, P., editor, Hirzebruch, F., editor, Hitchin, N., editor, Hörmander, L., editor, Kupiainen, A., editor, Lebeau, G., editor, Ratner, M., editor, Serre, D., editor, Sinai, Ya. G., editor, Sloane, N. J. A., editor, Vershik, A. M., editor, Waldschmidt, M., editor, and Villani, Cédric

Published
2009
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123. Expectation Values and Vacuum Currents of Quantum Fields

Author

Vilkovisky, G. A., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, B.-G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gasperini, Maurizio, editor, and Maharana, Jnan, editor

Published
2008
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124. Emergent Behaviors of Cucker–Smale Flocks on Riemannian Manifolds

Author

Doheon Kim, Seung-Yeal Ha, and Franz Wilhelm Schloder

Subjects
0209 industrial biotechnology, Pure mathematics, Parallel transport, Euclidean space, 02 engineering and technology, Electronic mail, Computer Science Applications, Covariant derivative, symbols.namesake, 020901 industrial engineering & automation, Unit circle, Control and Systems Engineering, Poincaré conjecture, symbols, Mathematics::Differential Geometry, Electrical and Electronic Engineering, Unit (ring theory), Energy functional, Mathematics
Abstract

In this article, we present a new Cucker–Smale model on smooth Riemannian manifolds using the concepts of covariant derivative and parallel transport, and we also study its emergent dynamics under an a priori assumption on the energy functional. For Euclidean space, our proposed model coincides with the original Cucker–Smale model. As concrete examples, we consider three Riemannian manifolds: the unit 2-sphere, the unit circle, and the Poincare half-plane, and provide explicit reductions from the proposed general model to aforementioned manifolds via explicit formulas for the covariant derivative and parallel transport.

Published
2021
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125. Purely Infinitesimal Geometry (Excerpt)

Author

Weyl, Hermann, Cohen, Robert S., editor, Renn, Jürgen, editor, Gavroglu, Kostas, editor, Janssen, Michel, editor, Norton, John D., editor, Sauer, Tilman, editor, and Stachel, John, editor

Published
2007
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129. Intrinsic Control Designs for Abstract Machines

Author

Fuentes, Robert, Hicks, Gregory, Osborne, Jason, Thoma, M., editor, Morari, M., editor, Allgüwer, F., editor, Fleming, P., editor, Kokotovic, P., editor, Kurzhanski, A.B., editor, Kwakernaak, H., editor, Rantzer, A., editor, Tsitsiklis, J.N., editor, Bullo, Francesco, editor, and Fujimoto, Kenji, editor

Published
2007
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130. Imaging Brain Activation Streams from Optical Flow Computation on 2-Riemannian Manifolds

Author

Lefèvre, Julien, Obozinski, Guillaume, Baillet, Sylvain, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Rangan, C. Pandu, editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Karssemeijer, Nico, editor, and Lelieveldt, Boudewijn, editor

Published
2007
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134. Geometry of Riemann Spaces

Author

Börner, G., editor, Burkert, A., editor, Burton, W. B., editor, Dopita, M. A., editor, Eckart, A., editor, Encrenaz, T., editor, Leibundgut, B., editor, Lequeux, J., editor, Maeder, A., editor, Trimble, V., editor, and Hoyng, Peter

Published
2006
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135. Fermi-Walker Transport

Author

Börner, G., editor, Burkert, A., editor, Burton, W. B., editor, Dopita, M. A., editor, Eckart, A., editor, Encrenaz, T., editor, Leibundgut, B., editor, Lequeux, J., editor, Maeder, A., editor, Trimble, V., editor, and Hoyng, Peter

Published
2006
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136. Geodesics Between 3D Closed Curves Using Path-Straightening

Author

Klassen, Eric, Srivastava, Anuj, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Dough, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Leonardis, Aleš, editor, Bischof, Horst, editor, and Pinz, Axel, editor

Published
2006
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137. Subspace Estimation Using Projection Based M-Estimators over Grassmann Manifolds

Author

Subbarao, Raghav, Meer, Peter, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Dough, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Leonardis, Aleš, editor, Bischof, Horst, editor, and Pinz, Axel, editor

Published
2006
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145. Smooth 2-Group Extensions and Symmetries of Bundle Gerbes

Author

Lukas Müller, Severin Bunk, and Richard J. Szabo

Subjects
Mathematics - Differential Geometry, High Energy Physics - Theory, Bundle gerbe, Pure mathematics, String group, FOS: Physical sciences, Gerbe, 01 natural sciences, 0103 physical sciences, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, 0101 mathematics, Mathematical Physics, Mathematics, Parallel transport, 010308 nuclear & particles physics, 010102 general mathematics, Connection (principal bundle), Lie group, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Differential Geometry (math.DG), High Energy Physics - Theory (hep-th), Associated bundle, Bundle
Abstract

We study bundle gerbes on manifolds $M$ that carry an action of a connected Lie group $G$. We show that these data give rise to a smooth 2-group extension of $G$ by the smooth 2-group of hermitean line bundles on $M$. This 2-group extension classifies equivariant structures on the bundle gerbe, and its non-triviality poses an obstruction to the existence of equivariant structures. We present a new global approach to the parallel transport of a bundle gerbe with connection, and use it to give an alternative construction of this smooth 2-group extension in terms of a homotopy-coherent version of the associated bundle construction. We apply our results to give new descriptions of nonassociative magnetic translations in quantum mechanics and the Faddeev-Mickelsson-Shatashvili anomaly in quantum field theory. We also propose a definition of smooth string 2-group models within our geometric framework. Starting from a basic gerbe on a compact simply-connected Lie group $G$, we prove that the smooth 2-group extensions of $G$ arising from our construction provide new models for the string group of $G$., Comment: 79 pages, 2 figures; v2: minor corrections, comments and references added; Final version to be published in Communications in Mathematical Physics

Published
2021
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146. More Mathematics

Author

Hehl, Friedrich W., Obukhov, Yuri N., de Monvel, Anne Boutet, editor, Kaiser, Gerald, editor, Hehl, Friedrich W., and Obukhov, Yuri N.

Published
2003
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147. Lorentzian Comments on Stokes Parameters

Author

Morales, Juan Antonio, Navarro, Emilio, Beig, R., editor, Englert, B. -G., editor, Frisch, U., editor, Hänggi, P., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, v Löhneysen, H., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Fernández-Jambrina, Leonardo, editor, and González-Romero, Luis Manuel, editor

Published
2003
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