@misc{NavaYazdaniHegevonTycowiczetal.2018, author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and von Tycowicz, Christoph and Sullivan, T. J.}, title = {A Shape Trajectories Approach to Longitudinal Statistical Analysis}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69759}, year = {2018}, abstract = {For Kendall's shape space we determine analytically Jacobi fields and parallel transport, and compute geodesic regression. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and reduce the computational expense by several orders of magnitude. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As application example we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative. Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data only.}, language = {en} } @misc{WeberQuer2015, author = {Weber, Marcus and Quer, Jannes}, title = {Estimating exit rates in rare event dynamical systems via extrapolation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56622}, year = {2015}, abstract = {In this article we present a new idea for approximating exit rates for diffusion processes living in a craggy landscape. We are especially interested in the exit rates of a process living in a metastable regions. Due to the fact that Monte Carlo simulations perform quite poor and are very computational expensive in this setting we create several similar situations with a smoothed potential. For this we introduce a new parameter \$\lambda \in [0,1]\$ (\$\lambda = 1\$ very smoothed potential, \$\lambda=0\$ original potential) into the potential which controls the influence the smoothing. We then sample the exit rate for different parameters \$\lambda\$ the exit rate from a given region. Due to the fact that \$\lambda\$ is connected to the exit rate we can use this dependency to approximate the real exit rate. The method can be seen as something between hyperdynamics and temperature accelerated MC.}, language = {en} }