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A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, ...
This interdisciplinary work combines the use of shape- and size-defined Pd nanocrystals (cubes of 10 and 18 nm, and octahedra of 37 nm) with in situ techniques and DFT calculations to unravel the dynamic phenomena with respect to Pd reconstruction taking p ...
Exact nonadiabatic quantum evolution preserves many geometric properties of the molecular Hilbert space. In the first paper of this series ["Paper I," S. Choi and J. Vaníček, J. Chem. Phys. 150, 204112 (2019)], we presented numerical integrators of arbitra ...
This dissertation develops geometric variational models for different inverse problems in imaging that are ill-posed, designing at the same time efficient numerical algorithms to compute their solutions. Variational methods solve inverse problems by the fo ...
We show that the Flaschka map, originally introduced to analyze the dynamics of the integrable Toda lattice system, is the inverse of a momentum map. We discuss the geometrical setting of the map and apply it to the generalized Toda lattice systems on semi ...
Earthquakes cause severe damage to masonry structures due to inertial forces acting in the normal direction to the plane of the walls. The out-of-plane behavior of masonry walls is complex and depends on several parameters, such as material and geometric p ...
Metal-organic frameworks (MOFs), a class of porous materials, are of particular interest in gas storage and separation applications due largely to their high internal surface areas and tunable structures. MOF-5 is perhaps the archetypal MOF; in particular, ...
Geometric integrators of the Schrödinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement but, unfortunately, is restricted to systems whose Hamiltonian ...
Automatically extracting linear structures from images is a fundamental low-level vision problem with numerous applications in different domains. Centerline detection and radial estimation are the first crucial steps in most Computer Vision pipelines aimin ...
The goal of this paper is to analyze the geometric properties of deep neural network image classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision boundary. ...