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Correction: Accelerated affine-invariant convergence rates of the Frank-Wolfe algorithm with open-loop step-sizes
No full textSource code and simulation results: Hidden resonances in non-Hermitian systems with scattering thresholds
No full textFunctional models from limited data: a parametric and multimodal approach to anatomy and 3D kinematics of feeding in basking sharks (Cetorhinus maximus)
No full textIntegrating Agent-Based and Compartmental Models for Infectious Disease Modeling: A Novel Hybrid Approach
No full textThis study investigates the spatial integration of agent-based models (ABMs) and compartmental models for infectious disease modeling, presenting a novel hybrid approach and examining its implications. ABMs offer detailed insights by simulating interactions and decisions among individuals but are computationally expensive for large populations. Compartmental models capture population-level dynamics more efficiently but lack granular detail. We developed a hybrid model that aims to balance the granularity of ABMs with the computational efficiency of compartmental models, offering a more nuanced understanding of disease spread in diverse scenarios, including large populations. This model spatially couples discrete and continuous populations by integrating an ordinary differential equation model with a spatially explicit ABM. Our key objectives were to systematically assess the consistency of disease dynamics and the computational efficiency across various configurations. For this, we evaluated two experimental scenarios and varied the influence of each sub-model via spatial distribution. In the first, the ABM component modeled a homogeneous population; in the second, it simulated a heterogeneous population with landscape-driven movement. Results show that the hybrid model can significantly reduce computational costs but is sensitive to between-model differences, highlighting the importance of model equivalence in hybrid approaches. The code is available at: git.zib.de/ibostanc/hybrid_abm_ode
A GPU accelerated variant of Schroeppel-Shamir's algorithm for solving the market split problem
No full textThe market split problem (MSP), introduced by Cornuéjols and Dawande (1998), is a challenging binary optimization problem that performs poorly on state-of-the-art linear programming-based branch-and-cut solvers. We present a novel algorithm for solving the feasibility version of this problem, derived from Schroeppel–Shamir's algorithm for the one-dimensional subset sum problem. Our approach is based on exhaustively enumerating one-dimensional solutions of MSP and utilizing GPUs to evaluate candidate solutions across the entire problem. The resulting hybrid CPU-GPU implementation efficiently solves instances with up to 10 constraints and 90 variables. We demonstrate the algorithm's performance on benchmark problems, solving instances of size (9, 80) in less than fifteen minutes and (10, 90) in up to one day
Uncertainty Visualization for Biomolecular Structures: An Empirical Evaluation
No full textUncertainty is an intrinsic property of almost all data, regardless of the data being measured, simulated, or generated. It can significantly influence the results and reliability of subsequent analysis steps. Clearly communicating uncertainties is crucial for informed decision-making and understanding, especially in biomolecular data, where uncertainty is often difficult to infer. Uncertainty visualization (UV) is a powerful tool for this purpose. However, previously proposed UV methods lack sufficient empirical evaluation. We collected and categorized visualization methods for portraying positional uncertainty in biomolecular structures. We then organized the methods into metaphorical groups and extracted nine representatives: color, clouds, ensemble, hulls, sausages, contours, texture, waves, and noise. We assessed their strengths and weaknesses in a twofold approach: expert assessments with six domain experts and three perceptual evaluations involving 1,756 participants. Through the expert assessments, we aimed to highlight the advantages and limitations of the individual methods for the application domain and discussed areas for necessary improvements. Through the perceptual evaluation, we investigated whether the visualizations are intuitively associated with uncertainty and whether the directionality of the mapping is perceived as intended. We also assessed the accuracy
of inferring uncertainty values from the visualizations. Based on our results, we judged the appropriateness of the metaphors for encoding uncertainty and suggest further areas for improvement
Camera Pose in SfT and NRSfM under Isometric and Weaker Deformation Models
No full textCamera pose is a very natural concept in 3D vision in the rigid setting. It is however much more difficult
to work with in deformable settings. Consequently, numerous deformable reconstruction methods simply ignore
camera pose. We analyse the concept of pose in deformable settings and prove that it is unconstrained with the
existing formulations, properly justifying the existing pose-less methods reconstructing structure only. We explain
this result intuitively by the impossibility to define an intrinsic coordinate frame to a general deforming object. The
proposed analysis uses the isometric deformation model and extends to the weaker models including conformality
and equiareality. We propose a novel prior to rescue camera pose estimation in deformable settings, which attributes
the deforming object’s dominant rigid-body motion to the camera. We show that adding this prior to any existing
formulation fully constrains camera pose and leads to elegant two-step solution methods, involving deformable
structure reconstruction using a base method in the first step, and absolute orientation or Procrustes analysis in
the second step. We derive the proposed approach for the template-based and template-less settings, respectively
implemented using Shape-from-Template (SfT) and Non-Rigid Structure-from-Motion (NRSfM) as base methods,
and validate them experimentally, showing that the computed pose is qualitatively and quantitatively plausible
Convex Solutions to SfT and NRSfM under Algebraic Deformation Models
No full textWe present nonlinear formulations to Shape-from-Template (SfT) and Non-Rigid Structure-from-Motion (NRSfM) faithfully exploiting the isometric, conformal and equiareal deformation models. Existing work uses relaxations such as inextensibility or requires knowing the optic flow field around the correspondences, an impractical assumption. In contrast, the proposed formulations only require point correspondences and resolve all ambiguities using the notions of maximal depth and maximal isometry heuristics. We propose solution methods using Semi-Definite Programming (SDP) for all formulations. We show that straightforward SDP models conflict with the usual maximal depth heuristic and propose an adapted opposite-depth parameterisation demonstrating a lesser relaxation gap. Experimental results on many real-world benchmark datasets demonstrate superior accuracy over existing methods