相关论文: Some Notes on Geometric Interpretation of Holding-…
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…
Plenoptic cameras usually sacrifice the spatial resolution of their SAIs to acquire geometry information from different viewpoints. Several methods have been proposed to mitigate such spatio-angular trade-off, but seldom make use of the…
Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. In this paper, we develop…
Geometry problem-solving remains a significant challenge for Large Multimodal Models (LMMs), requiring not only global shape recognition but also attention to intricate local relationships related to geometric theory. To address this, we…
Smooth autonomous dynamical systems modeled by ordinary differential equations (ODEs) cannot robustly and globally stabilize a point in compact, boundaryless manifolds. This obstruction, which is topological in nature, implies that…
Recent NeRF methods on large-scale scenes have underlined the importance of scene decomposition for scalable NeRFs. Although achieving reasonable scalability, there are several critical problems remaining unexplored, i.e., learnable…
Mechanistic interpretability seeks to reverse-engineer neural network computations into human-understandable algorithms, yet extracting sparse computational circuits from billion-parameter language models remains challenging due to…
High definition (HD) maps have demonstrated their essential roles in enabling full autonomy, especially in complex urban scenarios. As a crucial layer of the HD map, lane-level maps are particularly useful: they contain geometrical and…
In this work, we introduce a novel computational framework for solving the two-dimensional Hele-Shaw free boundary problem with surface tension. The moving boundary is represented by point clouds, eliminating the need for a global…
We consider the method of mappings for performing shape optimization for unsteady fluid-structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes…
One of the strategies to detect the pose and shape of unknown objects is their geometric modeling, consisting on fitting known geometric entities. Classical geometric modeling fits simple shapes such as spheres or cylinders, but often those…
Collision detection is essential to virtually all robotics applications. However, traditional geometric collision detection methods generally require pre-existing workspace geometry representations; thus, they are unable to infer the…
We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…
Design patterns are elegant and well-tested solutions to recurrent software development problems. They are the result of software developers dealing with problems that frequently occur, solving them in the same or a slightly adapted way. A…
We propose a method to determine the smoothness of sufficiently flat solutions of one phase Hele-Shaw problems. The novelty is the observation that under a flatness assumption the free boundary --represented by the hodograph transform of…
In the context of the optimization of rotating electric machines, many different objective functions are of interest and considering this during the optimization is of crucial importance. While evolutionary algorithms can provide a Pareto…
We propose a new algorithm for finding an unknown number of geometric models, e.g., homographies. The problem is formalized as finding dominant model instances progressively without forming crisp point-to-model assignments. Dominant…
Aiming for higher-level scene understanding, this work presents a neural network approach that takes a road-layout map in bird's-eye-view as input, and predicts a human-interpretable graph that represents the road's topological layout. Our…
Metropolis nested sampling evolves a Markov chain from a current livepoint and accepts new points along the chain according to a version of the Metropolis acceptance ratio modified to satisfy the likelihood constraint, characteristic of…
We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensional algebra over a field can be obtained by…