Career
- 2013-date: University Lecturer, DAMTP, University of Cambridge, UK
- 2012-date: Royal Society University Research Fellow, University of Cambridge, UKĀ
- 2012: Marie Curie Fellow, University of Vienna Austria
- 2009 -2012: Junior Research Fellow, University of Cambridge, Homerton College UK
- 2008 -2009: Von Karman Instructor, California Institute of Technology, USA
Research
Anders is a member of the Department of Applied Mathematics and Theoretical Physics and head of the Applied Functional and Harmonic Analysis research group. His current research interests include but are not limited to Functional Analysis (applied), operator/ Spectral Theory, Compressed Sensing, Mathematical Signal Processing, Sampling Theory, Compressed Sensing, Mathematical Signal Processing, Sampling Theory, Computational Harmonic Analysis, Inverse problems, Medical Imaging, Geometric Intergration, Numerical Analysis, C*- algebras.
Selected Publications
- A. C. Hansen, On the Solvability Complexity Index, the n-Pseudospectrum and Approximations of Spectra of Operators, J. Amer. Math. Soc. 24, no. 1, 81-124
- A. C. Hansen, On the approximation of Spectra of linear operators on Hilbert spaces, J. Funct. Anal. 254 no.8, 2092--2126
- A. C. Hansen, Infinite dimensional numerical linear algebra; theory and applications, Proc. R. Soc. Lond. Ser. A. 466, no.2124, 3539-3559
- B. Adcock, A. C. Hansen, Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon, Appl. Comput. Harmon. Anal. 32, no.3, 357-388
Publications
The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem.
– Proceedings of the National Academy of Sciences of the United States of America
(2022)
119,
e2107151119
(doi: 10.1073/pnas.2107151119)
Can stable and accurate neural networks be computed? - On the barriers of deep learning and Smale's 18th problem.
– Proceedings of the National Academy of Sciences of the United States of America
(2022)
abs/2101.08286,
ARTN e2107151119
(doi: 10.1073/pnas.2107151119)
Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling
– Applied and Computational Harmonic Analysis
(2021)
55,
1
(doi: 10.1016/j.acha.2021.04.001)
Deep Learning: What Could Go Wrong?
– SIAM News
(2021)
Deep Learning: What Could Go Wrong?
– SIAM News
(2021)
Non-uniform Recovery Guarantees for Binary Measurements and Infinite-Dimensional Compressed Sensing
– Journal of Fourier Analysis and Applications
(2021)
27,
14
(doi: 10.1007/s00041-021-09813-6)
On structure and optimisation in computational harmonic analysis - The key aspects in sparse regularisation
(2021)
168,
125
(doi: 10.1007/978-3-030-61887-2_6)
On instabilities of deep learning in image reconstruction and the potential costs of AI
– Proceedings of the National Academy of Sciences of the United States of America
(2020)
117,
30088
(doi: 10.1073/pnas.1907377117)
Compressed sensing MRI with variable density averaging (CS-VDA) outperforms full sampling at low SNR.
– Physics in Medicine and Biology
(2020)
65,
045004
(doi: 10.1088/1361-6560/ab63b7)
The foundations of spectral computations via the Solvability Complexity
Index hierarchy
(2019)
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