527 research outputs found
Matlab codes for "Convex relaxation of discrete vector-valued optimization problems"
No full textvectormultibang
===============
This repository contains Matlab codes accompanying the paper [Convex relaxation of discrete vector-valued optimization problems](https://doi.org/10.1137/21M1426237) ([arXiv preprint](http://arxiv.org/abs/2108.10077)) by [Christian Clason](https://homepage.uni-graz.at/c.clason), Carla Tameling, and [Benedikt Wirth](https://www.uni-muenster.de/AMM/num/wirth/people/Wirth/index.html).
Contents
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##### directory `bloch`
contains the test scripts for the example concerning optimal control of the Bloch equation using discrete control vectors (run `test_bloch.m`)
##### directory `elasticity`
contains the test scripts for the example concerning optimal control of the equations of linearized elasticity (run `test_elasticity.m`)
##### directory `mbtransport`
contains the test scripts for the example concerning multimaterial branched transport (run `test_branchedTransport.m`)
If you find this approach useful, you can cite the paper as
@article{vectormultibang,
author = {Clason, Christian and Tameling, Carla and Wirth, Benedikt},
title = {Convex relaxation of discrete vector-valued optimization problems},
journal = {SIAM Review},
volume = {63},
number = {4},
year = {2021},
doi = {10.1137/21M1426237
Dynamic models of Wasserstein-1-type unbalanced transport
No full textWe consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which transport costs are proportional to transport distance. For those models we derive an equivalent, computationally more efficient static formulation, we perform a detailed analysis of the model optimizers and the associated optimal mass change and transport, and we examine which static models are generated by a corresponding equivalent dynamic one. Alongside we discuss thoroughly how the employed model formulations relate to other formulations found in the literature.</jats:p
SupplementaryMaterial_WirthWentura_revised_compressed – Supplemental material for Attentional bias to threat in the general population is contingent on target competition, not on attentional control settings
No full textSupplemental material, SupplementaryMaterial_WirthWentura_revised_compressed for Attentional bias to threat in the general population is contingent on target competition, not on attentional control settings by Benedikt Emanuel Wirth and Dirk Wentura in Quarterly Journal of Experimental Psychology</p
A Continuum Mechanical Approach to Geodesics in Shape Space
No full text1 online resource (PDF, 38 pages, includes illustrations)Wirth, Benedikt; Bar, Leah; Rumpf, Martin; Sapiro, Guillermo. (2010). A Continuum Mechanical Approach to Geodesics in Shape Space. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/180741
Dynamic Cell Imaging in PET With Optimal Transport Regularization
No full textWe propose a novel dynamic image reconstruction method from PET listmode data that could be particularly suited to tracking single or small numbers of cells. In contrast to conventional PET reconstruction our method combines the information from all detected events not only to reconstruct the dynamic evolution of the radionuclide distribution, but also to improve the reconstruction at each single time point by enforcing temporal consistency. This is achieved via optimal transport regularization where in principle, among all possible temporally evolving radionuclide distributions consistent with the PET measurement, the one is chosen with least kinetic motion energy. The reconstruction is found by convex optimization so that there is no dependence on the initialization of the method. We study its behaviour on simulated data of a human PET system and demonstrate its robustness even in settings with very low radioactivity. In contrast to previously reported cell tracking algorithms, our technique is oblivious to the number of tracked cells. Without any additional complexity one or multiple cells can be reconstructed, and the model automatically determines the number of particles. For instance, four radiolabelled cells moving at a velocity of 3.1 mm/s and a PET recorded count rate of 1.1 cps (for each cell) could be simultaneously tracked with a tracking accuracy of 5.3 mm inside a simulated human body
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