TY  - JOUR
A1  - Hüper, Knut
A1  - Silva Leite, Fátima
T1  - Endpoint geodesic formulas on Graßmannians applied to interpolation problems
JF  - Mathematics
N2  - Simple closed formulas for endpoint geodesics on Graßmann manifolds are presented. In addition to realizing the shortest distance between two points, geodesics are also essential tools to generate more sophisticated curves that solve higher order interpolation problems on manifolds. This will be illustrated with the geometric de Casteljau construction offering an excellent alternative to the variational approach which gives rise to Riemannian polynomials and splines.
KW  - Graßmannians
KW  - Lie group actions
KW  - rotations
KW  - reflections
KW  - endpoint geodesics
KW  - de Casteljau Algorithm
KW  - MSC: 53C22
KW  - MSC: 53C35
KW  - MSC: 14M15
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-327016
SN  - 2227-7390
VL  - 11
IS  - 16
ER  - 
TY  - JOUR
A1  - Kaltdorf, Martin
A1  - Breitenbach, Tim
A1  - Karl, Stefan
A1  - Fuchs, Maximilian
A1  - Kessie, David Komla
A1  - Psota, Eric
A1  - Prelog, Martina
A1  - Sarukhanyan, Edita
A1  - Ebert, Regina
A1  - Jakob, Franz
A1  - Dandekar, Gudrun
A1  - Naseem, Muhammad
A1  - Liang, Chunguang
A1  - Dandekar, Thomas
T1  - Software JimenaE allows efficient dynamic simulations of Boolean networks, centrality and system state analysis
JF  - Scientific Reports
N2  - The signal modelling framework JimenaE simulates dynamically Boolean networks. In contrast to SQUAD, there is systematic and not just heuristic calculation of all system states. These specific features are not present in CellNetAnalyzer and BoolNet. JimenaE is an expert extension of Jimena, with new optimized code, network conversion into different formats, rapid convergence both for system state calculation as well as for all three network centralities. It allows higher accuracy in determining network states and allows to dissect networks and identification of network control type and amount for each protein with high accuracy. Biological examples demonstrate this: (i) High plasticity of mesenchymal stromal cells for differentiation into chondrocytes, osteoblasts and adipocytes and differentiation-specific network control focusses on wnt-, TGF-beta and PPAR-gamma signaling. JimenaE allows to study individual proteins, removal or adding interactions (or autocrine loops) and accurately quantifies effects as well as number of system states. (ii) Dynamical modelling of cell–cell interactions of plant Arapidopsis thaliana against Pseudomonas syringae DC3000: We analyze for the first time the pathogen perspective and its interaction with the host. We next provide a detailed analysis on how plant hormonal regulation stimulates specific proteins and who and which protein has which type and amount of network control including a detailed heatmap of the A.thaliana response distinguishing between two states of the immune response. (iii) In an immune response network of dendritic cells confronted with Aspergillus fumigatus, JimenaE calculates now accurately the specific values for centralities and protein-specific network control including chemokine and pattern recognition receptors.
KW  - cellular signalling networks
KW  - computer modelling
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-313303
VL  - 13
ER  -