TY - JOUR A1 - von Kleist, Max A1 - Schütte, Christof A1 - Zhang, Wei T1 - Statistical analysis of the first passage path ensemble of jump processes JF - Journal of Statistical Physics N2 - The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas. Y1 - 2018 U6 - https://doi.org/10.1007/s10955-017-1949-x VL - 170 SP - 809 EP - 843 ER - TY - JOUR A1 - Schmitt, Kira A1 - Titschack, Jürgen A1 - Baum, Daniel T1 - CoDA: Interactive Segmentation and Morphological Analysis of Dendroid Structures Exemplified on Stony Cold-Water Corals JF - IEEE Transactions on Visualization and Computer Graphics Y1 - 2026 U6 - https://doi.org/10.1109/TVCG.2026.3656066 ER - TY - JOUR A1 - Ngokingha Tchouto, Mireille A1 - Mehl, Julia A1 - Khomeijani Farahani, Saeed A1 - Baum, Daniel A1 - Duda, Georg T1 - Novel image registration approach for combining 2D Osterix and collagen bundles images with 3D µCT JF - Journal of Bone and Mineral Research Y1 - 2026 U6 - https://doi.org/10.1093/jbmrpl/ziag009 VL - 10 IS - 3 ER - TY - CHAP A1 - Sengupta, Agniva A1 - Kuş, Dilara A1 - Li, Jianning A1 - Zachow, Stefan T1 - Globally Optimal Pose from Orthographic Silhouettes N2 - We solve the problem of determining the pose of known shapes in R^3 from their unoccluded silhouettes. The pose is determined up to global optimality using a simple yet under-explored property of the area-of-silhouette: its continuity w.r.t trajectories in the rotation space. The proposed method utilises pre-computed silhouette-signatures, modelled as a response surface of the area-of-silhouettes. Querying this silhouette-signature response surface for pose estimation leads to a strong branching of the rotation search space, making resolution-guided candidate search feasible. Additionally, we utilise the aspect ratio of 2D ellipses fitted to projected silhouettes as an auxiliary global shape signature to accelerate the pose search. This combined strategy forms the first method to efficiently estimate globally optimal pose from just the silhouettes, without being guided by correspondences, for any shape, irrespective of its convexity and genus. We validate our method on synthetic and real examples, demonstrating significantly improved accuracy against comparable approaches. Y1 - 2026 ER - TY - CHAP A1 - Sunkara, Vikram A1 - Rostami, Atefe A1 - von Tycowicz, Christoph A1 - Schütte, Christof T1 - Stop throwing away your Decoder; extract the learnt local coordinate system using Latent-XAI T2 - The 4th World Conference on Explainable Artificial Intelligence (XAI-2026) Y1 - 2026 ER - TY - CHAP A1 - Stokke, Jo Andersson A1 - Bergmann, Ronny A1 - Hanik, Martin A1 - von Tycowicz, Christoph T1 - p-Laplacians for Manifold-valued Hypergraphs T2 - Geometric Science of Information. GSI 2025 N2 - Hypergraphs extend traditional graphs by enabling the representation of N-ary relationships through higher-order edges. Akin to a common approach of deriving graph Laplacians, we define function spaces and corresponding symmetric products on the nodes and edges to derive hypergraph Laplacians. While this has been done before for Euclidean features, this work generalizes previous hypergraph Laplacian approaches to accommodate manifold-valued hypergraphs for many commonly encountered manifolds. Y1 - 2025 U6 - https://doi.org/10.1007/978-3-032-03924-8_17 VL - 16035 ER - TY - JOUR A1 - Navayazdani, Esfandiar T1 - Ridge Regression on Riemannian Manifolds for Time-Series Prediction JF - Information Geometry Y1 - 2026 ER -