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Domain Adaptation by Class Centroid Matching and Local Manifold Self-Learning [article]

Lei Tian, Yongqiang Tang, Liangchen Hu, Zhida Ren, Wensheng Zhang
2020 IEEE Transactions on Image Processing   accepted
In addition to unsupervised domain adaptation, we further extend our method to the semi-supervised scenario including both homogeneous and heterogeneous settings in a direct but elegant way.  ...  Extensive experiments on seven benchmark datasets validate the significant superiority of our proposal in both unsupervised and semi-supervised manners.  ...  Recently, based on Fredholm integral, Wang et al.  ... 
doi:10.1109/tip.2020.3031220 pmid:33079662 arXiv:2003.09391v3 fatcat:xjbrxwmwgvagbedxbdxjrrhhva

Computational Electromagnetism and Acoustics

Ralf Hiptmair, Ronald Hoppe, Patrick Joly, Ulrich Langer
2010 Oberwolfach Reports  
Time domain integral equation methods still enjoy rapid development and much progress was made in their numerical analysis.  ...  Frequency domain integral equation methods continue to receive much attention, with a particular focus on (i) frequency robust matrix compression algorithms through so-called directional schemes or "butterfly  ...  We solved integral equations (13) using the high-order Nyström methods introduced in [1] for a bisinusoidal grating whose height to period ratio equals to 1.  ... 
doi:10.4171/owr/2010/10 fatcat:kckquuef3nandbkembon5szvr4

Computational Electromagnetism and Acoustics

Ralf Hiptmair, Ronald Hoppe, Patrick Joly, Ulrich Langer
2013 Oberwolfach Reports  
Time domain integral equation methods still enjoy rapid development and much progress was made in their numerical analysis.  ...  Frequency domain integral equation methods continue to receive much attention, with a particular focus on (i) frequency robust matrix compression algorithms through so-called directional schemes or "butterfly  ...  We solved integral equations (13) using the high-order Nyström methods introduced in [1] for a bisinusoidal grating whose height to period ratio equals to 1.  ... 
doi:10.4171/owr/2013/03 fatcat:znjejdppnnectpfwz35s5zmiai

Computational Electromagnetism and Acoustics

Ralf Hiptmair, Ronald Hoppe, Patrick Joly, Ulrich Langer
2007 Oberwolfach Reports  
Time domain integral equation methods still enjoy rapid development and much progress was made in their numerical analysis.  ...  Frequency domain integral equation methods continue to receive much attention, with a particular focus on (i) frequency robust matrix compression algorithms through so-called directional schemes or "butterfly  ...  We solved integral equations (13) using the high-order Nyström methods introduced in [1] for a bisinusoidal grating whose height to period ratio equals to 1.  ... 
doi:10.4171/owr/2007/05 fatcat:dx6fpblbjnbwtehcvi4b5iunym

2020 Index IEEE Transactions on Automatic Control Vol. 65

2020 IEEE Transactions on Automatic Control  
Bamieh, B., +, TAC Dec. 2020 5012-5027 Chandrasekhar-Based Maximum Correntropy Kalman Filtering With the Adaptive Kernel Size Selection.  ...  Yang, H., +, TAC Dec. 2020 5376-5383 Difference equations Chandrasekhar-Based Maximum Correntropy Kalman Filtering With the Adaptive Kernel Size Selection.  ...  Linear programming A Decentralized Event-Based Approach for Robust Model Predictive Control.  ... 
doi:10.1109/tac.2020.3046985 fatcat:hfiqhyr7sffqtewdmcwzsrugva

Neural Operator: Learning Maps Between Function Spaces [article]

Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar
2021 arXiv   pre-print
Furthermore, we introduce four classes of operator parameterizations: graph-based operators, low-rank operators, multipole graph-based operators, and Fourier operators and describe efficient algorithms  ...  We formulate the approximation of operators by composition of a class of linear integral operators and nonlinear activation functions, so that the composed operator can approximate complex nonlinear operators  ...  For these reasons, neural networks that build in non-locality via integral operators or spectral domain calculations are natural.  ... 
arXiv:2108.08481v3 fatcat:fpvpnbkogvas5fl36apcia7rnq

2018 Index IEEE Transactions on Automatic Control Vol. 63

2018 IEEE Transactions on Automatic Control  
,TAC June 2018 1828-1834 Fredholm integral equations The Quadratic Regulator Problem and the Riccati Equation for a Process Governed by a Linear Volterra Integrodifferential Equations.  ...  ., +, TAC Oct. 2018 3601-3607 Liveness-Enforcing Supervision in AMS-Oriented HAMGs: An Approach Based on New Characterization of Siphons Using Petri Nets.  ... 
doi:10.1109/tac.2019.2896796 fatcat:bwmqasulnzbwhin5hv4547ypfe

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems [article]

Katiana Kontolati, Dimitrios Loukrezis, Dimitris G. Giovanis, Lohit Vandanapu, Michael D. Shields
2022 arXiv   pre-print
to construct a mapping to quantities of interest via polynomial chaos expansions (PCE).  ...  To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying  ...  Application of the method is dependent on the selection of a positive semi-definite kernel function, of which there are many options.  ... 
arXiv:2202.04648v2 fatcat:xur2ilwqire6xjawbqarc2kv4e

Indices of pseudodifferential operators on open manifolds [article]

Alexander Engel
2014 arXiv   pre-print
We give a simple definition of uniform K-theory for all metric spaces and in the case of manifolds of bounded geometry we give an interpretation via vector bundles of bounded geometry over the manifold  ...  Though this reasoning only works if A is Fredholm and if the domain of integration is compact, we may use it to define "averaged analytic indices": if M is non-compact but the integral kernel of the projection  ...  the local index theorem using the heat kernel method.  ... 
arXiv:1410.8030v1 fatcat:ysqmqxqekbfafmdkwbj3lchmz4

The Yang-Mills Gradient Flow and Loop Spaces of Compact Lie Groups [article]

Jan Swoboda
2012 arXiv   pre-print
The resulting Morse homology is compared to the heat flow homology of the space Ω G of based loops in the compact Lie group G.  ...  Acknowledgements This work is based on the author's PhD thesis [18] . He would like to express his gratitude to his advisor D. A. Salamon for his support while working on this project.  ...  However, it is easy to see that dF(u) is Fredholm if and only if this property holds for D u , and that the Fredholm indices are related via the formula ind dF(u) = ind D u + dim C − + dim C + .  ... 
arXiv:1104.5514v3 fatcat:44m263ocljflbfwzkdxvcbdd4i

The Yang–Mills gradient flow and loop spaces of compact Lie groups

Jan Swoboda
2017 Journal für die Reine und Angewandte Mathematik  
Acknowledgements This work is based on the author's PhD thesis [18] . He would like to express his gratitude to his advisor D. A. Salamon for his support while working on this project.  ...  However, it is easy to see that dF(u) is Fredholm if and only if this property holds for D u , and that the Fredholm indices are related via the formula ind dF(u) = ind D u + dim C − + dim C + .  ...  Step 1 The statement on surjectivity and the kernel is true in the case p = 2. The operator H A + δ with domain as in (18) is an unbounded self-adjoint operator on the Hilbert space H, cf.  ... 
doi:10.1515/crelle-2014-0091 fatcat:nu2rt2v5dzdf7pckm3bqoeuq2u

Legendrian contact homology and topological entropy [article]

Marcelo R. R. Alves
2017 arXiv   pre-print
Let (M, ker λ F ) be the contact manifold associated with the hypertight contact form λ F obtained via the integral Foulon-Hasselblat surgery on the Legendrian L σ ⊂ T 1 S, where σ is a separating geodesic  ...  An interesting feature of this result (and also of a result in [45] ) is that it gives a method of proving the existence of many Reeb orbits of a Reeb flow which is not based on the use of a contact topological  ... 
arXiv:1410.3381v5 fatcat:vzaei4jhurfabmfi7c76fu35pu

Eliakim Hastings Moores "General Analysis"

Reinhard Siegmund-Schultze
1998 Archive for History of Exact Sciences  
This was the case with the papers Hildebrandt 1912 and Root 1914 , which are based on doctoral dissertations supervised by Moore in Chicago.  ...  Without any difficulty whatever I showed how all five could be reduced to the classical Fredholm Theory. I wonder if the situation is not the same in many domains which are abstractly treated.  ...  2 but also on the notion of uniformity relative to a scale." 169 This quotation which summarizes here a rather lengthy argument in Moore and Chittenden, makes it clear that Moore had not succeeded in basing  ... 
doi:10.1007/s004070050010 fatcat:3zlemcwzuzdplp54stdvc5yc5a

The International Conference MATHEMATICAL AND COMPUTATIONAL MODELLING IN SCIENCE AND TECHNOLOGY

Amar Debbouche, Juan J. Nieto, Anatoly Yagola
2017 Journal of Computational and Applied Mathematics  
Semi-empirical calculations using PM3, PM6, ONIOM2 (B3LYP/6-31G : PM3) and ONIOM2 (B3LYP/6-31G : PM6) methods, in vacuum and in water were performed.  ...  called factorial methods.  ...  For this purpose an approach based on the fusion of four methods of supervised classifications (Support Vector Machine, Maximum Likelihood, Neural Net and Spectral Angle Mapper).  ... 
doi:10.1016/j.cam.2016.08.013 fatcat:mcmx2fnpkbeztpweuwk6ugyluu

Stochastic turbulence modeling in RANS simulations via Multilevel Monte Carlo

Prashant Kumar, Martin Schmelzer, Richard P. Dwight
2020 Computers & Fluids  
For two fundamental flows, we show that the MLMC method based on a hierarchy of meshes is asymptotically faster than plain Monte Carlo.  ...  The first approach is based on global perturbation of the baseline eddy viscosity field using a lognormal random field.  ...  covariance kernel C ( x 1 , x 2 ), obtained from the solution of the Fredholm integral, D C( x 1 , x 2 ) ( x 1 ) d x 1 = λ ( x 2 ) . (13) The sum in (12) represents an infinite dimensional uncertain  ... 
doi:10.1016/j.compfluid.2019.104420 fatcat:2hqv2nyfqje3plpolpudammpha
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