|Dr. Miguel Del Alamo
I enjoy learning mathematics for its own sake, but I typically also have concrete applications in mind.
During my bachelor and master studies I worked on PDEs, writing my Master's thesis on the analysis of semilinear wave equations via Young measures.
In my PhD I have mainly worked on nonparametric statistics, analysing variational estimators defined by total variation penalties and multiscale constraints. I proved that these estimators are minimax optimal for estimating functions of bounded variation in any dimension. Before that, no method was known to be minimax optimal for bounded variation functions in dimension d>1. The theoretical analysis relies strongly on harmonic analysis, and the efficient computational implementation uses techniques from nonsmooth optimization.
I'm currently interested in the theoretical analysis of optimization methods, and in the properties of deep neural networks applied to statistical problems.
I have mentored Bachelor and Master students in the following topics:
I have also worked on the following applied projects:
Summer semester 2018:
Mathematical Statistics II, Exercises. Topics: confidence intervals, hypothesis testing.
Summer semester 2017:
Mathematical Statistics IV, Exercises. Topics: nonparametric regression.
Winter semester 2016/2017:
Mathematical Statistics III, Exercises. Topics: multiple testing, nonparametric regression.
Total variation multiscale estimators for linear inverse problemsM. del Álamo, and A. Munk
arxiv preprint - To appear in Information and Inference
Frame-constrained Total Variation Regularization for White Noise RegressionM. del Álamo, H. Li, and A. Munk
arxiv preprint - To appear in The Annals of Statistics
The molecular contribution function in RESOLFT nanoscopy
L. Frahm, J. Keller-Findeisen, P. Alt, S. Schnorrenberg, M. del Alamo Ruiz, T. Aspelmeier, A. Munk, S. Jakobs, S. Hell
Editors' Pick in Optics Express 27(15), 21956-21987 (2019)
Strong Coupling between Mechanical Modes in a Nanotube ResonatorA. Eichler, M. del Álamo Ruiz, J. A. Plaza, and A. Bachtold
Physical Review Letters 109, 025503 – Published 11 July 2012
Multiscale Total Variation Estimators for Regression and Inverse ProblemsPredicate: Summa cum laude. 2019 pdf