Monotone Discretizations for Elliptic Second Order Partial Differential Equations - Data of Reference Curves

This is the data to following monograph: Gabriel R. Barrenechea, Volker John, Petr Knobloch (eds), "Monotone Discretizations for Elliptic Second Order Partial Differential Equations", Springer Series in Computational Mathematics, Springer Nature. This monograph contains the first comprehensive presentation of monotone discretization for elliptic boundary value problems. All currently available relevant methods are studied in detail. Besides monotonicity or the satisfaction of discrete maximum principles, other properties of these methods, in particular their error analysis are discussed. Many concepts and techniques from the numerical analysis are explained. Numerical examples illustrate the behavior of many methods and numerical comparisons are presented. Here, the data of the reference curves used in the numerical simulations are provided

Utilizing anatomical information for signal detection in functional magnetic resonance imaging - Data

This is p-value data from a multi-subject program comprehension study mapped onto anatomical labels (APARC). The data can be used to reproduce the figures in the accompanying publication

Matlab code to solve state and control constrained linear quadratic Mean-Field Games

This repository provides a Matlab code to approximate a state and control constrained linear quadratic Mean-Field Game. This code was developed with Matlab version R2023a in the context of the Ph.D. thesis of Mike Theiß. The theoretical background can be found in the thesis with the name "First Order Mean-Field Games and Mean-Field Optimal Control with State and Control Constraints", which is available at the bibliography of the Humboldt University

ACID: A Comprehensive Toolbox for Image Processing and Modeling of Brain, Spinal Cord, and Ex Vivo Diffusion MRI Data - Software

Diffusion MRI (dMRI) has become a crucial imaging technique in the field of neuroscience, with a growing number of clinical applications. Although most studies still focus on the brain, there is a growing interest in utilizing dMRI to investigate the healthy or injured spinal cord. The past decade has also seen the development of biophysical models that link MR-based diffusion measures to underlying microscopic tissue characteristics, which necessitates validation through ex vivo dMRI measurements. Building upon 13 years of research and development, we present an open-source, MATLAB-based academic software toolkit dubbed ACID: A Comprehensive Toolbox for Image Processing and Modeling of Brain, Spinal Cord, and Ex Vivo Diffusion MRI Data. ACID is an extension to the Statistical Parametric Mapping (SPM) software, designed to process and model dMRI data of the brain, spinal cord, and ex vivo specimens by incorporating state-of-the-art artifact correction tools, diffusion and kurtosis tensor imaging, and biophysical models that enable the estimation of microstructural properties in white matter. Additionally, the software includes an array of linear and non-linear fitting algorithms for accurate diffusion parameter estimation. By adhering to the Brain Imaging Data Structure (BIDS) data organization principles, ACID facilitates standardized analysis, ensures compatibility with other BIDS-compliant software, and aligns with the growing availability of large databases utilizing the BIDS format. Furthermore, being integrated into the popular SPM framework, ACID benefits from a wide range of segmentation, spatial processing, and statistical analysis tools as well as a large and growing number of SPM extensions. As such, this comprehensive toolbox covers the entire processing chain from raw DICOM data to group-level statistics, all within a single software package

Sharp-interface problem of the Ohta--Kawasaki model for symmetric diblock copolymers

The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding sharp-interface limit using matched asymptotic expansions, and show that the limiting process leads to a Hele-Shaw type moving interface problem. The numerical treatment of the sharp-interface limit is more complicated due to the stiffness of the equations. To address this problem, we present a boundary integral formulation corresponding to a sharp interface limit of the Ohta-Kawasaki model. Starting with the governing equations defined on separate phase domains, we develop boundary integral equations valid for multi-connected domains in a 2D plane. For numerical simplicity we assume our problem is driven by a uniform Dirichlet condition on a circular far-field boundary. The integral formulation of the problem involves both double- and single-layer potentials due to the modified boundary condition. In particular, our formulation allows one to compute the nonlinear dynamics of a non-equilibrium system and pattern formation of an equilibrating system. Numerical tests on an evolving slightly perturbed circular interface (separating the two phases) are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient and spectrally accurate in space

The power of first-order smooth optimization for black-box non-smooth problems

Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration complexity, and propose a generic approach that, based on optimal first-order methods, allows to obtain in a black-box fashion new zeroth-order algorithms for non-smooth convex optimization problems. Our approach not only leads to optimal oracle complexity, but also allows to obtain iteration complexity similar to first-order methods, which, in turn, allows to exploit parallel computations to accelerate the convergence of our algorithms. We also elaborate on extensions for stochastic optimization problems, saddle-point problems, and distributed optimization

Nonlinear Wasserstein distributionally robust optimal control

This paper presents a novel approach to addressing the distributionally robust nonlinear model predictive control (DRNMPC) problem. Current literature primarily focuses on the static Wasserstein distributionally robust optimal control problem with a prespecified ambiguity set of uncertain system states. Although a few studies have tackled the dynamic setting, a practical algorithm remains elusive. To bridge this gap, we introduce an DRNMPC scheme that dynamically controls the propagation of ambiguity, based on the constrained iterative linear quadratic regulator. The theoretical results are also provided to characterize the stochastic error reachable sets under ambiguity. We evaluate the effectiveness of our proposed iterative DRMPC algorithm by comparing the closed-loop performance of feedback and open-loop on a mass-spring system. Finally, we demonstrate in numerical experiments that our algorithm controls the propagated Wasserstein ambiguity

Data-driven Regularization and Quantitative Imaging

oai:archive.wias-berlin.de:wias_mods_0000757