Spectrum of Exponentially Weighted Covariance Matrices
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The local physical properties - such as shape and flexibility - of the DNA double-helix is today widely believed to be influenced by nucleic acid sequence in a non-trivial way. Furthermore, there is strong evidence that these properties play a role in many ...
We study the statistical mechanics and the equilibrium dynamics of a system of classical Heisenberg spins with frustrated interactions on a d -dimensional simple hypercubic lattice, in the limit of infinite dimensionality d -> infinity . In the analysis we ...
New materials for electrochemical energy storage and conversion are the key to the electrification and sustainable development of our modern societies. Molecular modelling based on the principles of quantum mechanics and statistical mechanics as well as em ...
Predictions of relative stabilities of (competing) molecular crystals are of great technological relevance, most notably for the pharmaceutical industry. However, they present a long-standing challenge for modeling, as often minuscule free energy differenc ...
In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges, but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows for the generation of graphs with extens ...
Atomistic simulations are a bottom up approach that predict properties
of materials by modelling the quantum mechanical behaviour of all electrons
and nuclei present in a system. These simulations, however, routinely assume
nuclei to be classical particles ...
Simulation-based optimization models are widely applied to find optimal operating conditions of processes. Often, computational challenges arise from model complexity, making the generation of reliable design solutions difficult. We propose an algorithm fo ...
We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...
We revisit the statistical mechanics of charge fluctuations in capacitors. In constant-potential classical molecular simulations, the atomic charges of electrode atoms are treated as additional degrees of freedom which evolve in time so as to satisfy the c ...