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Related Articles from SNS
Differentiable 3D Triangle-Triangle Intersection Energy
arXiv:2606.06511v1 Announce Type: new Abstract: Obtaining intersection-freeness or global injectivity is important in computer graphics. However, it is challenging, especially for the non-oriented deformation primitives.
Quantum Algorithms for Triangle Cut Sparsification
arXiv:2606.06287v2 Announce Type: replace-cross Abstract: Triangles capture higher-order structures in graphs and are fundamental to applications such as clustering and network analysis. To enable efficient use of such structures at scale, we study the problem of triangle cut sparsification, which aims to reduce the graph size while approximately preserving triangle counts across every cut. We investigate quantum algorithms for this problem, using triangle listing as our main technical...
Quantum Algorithms for Triangle Cut Sparsification
arXiv:2606.06287v1 Announce Type: cross Abstract: Triangles capture higher-order structures in graphs and are fundamental to applications such as clustering and network analysis. To enable efficient use of such structures at scale, we study the problem of \emph{triangle cut sparsification}, which aims to reduce the graph size while approximately preserving triangle counts across every cut. We investigate \emph{quantum algorithms} for this problem, using triangle listing as our main technical...
Triangle Splatting SLAM
Announce Type: new Abstract: We present a dense RGB-D SLAM system using differentiable triangles as the 3D map representation. While 3D Gaussian Splatting has emerged as the leading method for novel-view synthesis, triangles remain the standard primitive for traditional rendering hardware, game engines, and downstream tasks requiring explicit geometry such as simulation, collision, and editing. Recent offline methods have demonstrated that an unstructured 'triangle soup' can be optimised...
Characterization and chromatic number of triangle-free graphs with diameter 2
arXiv:2606.03267v1 Announce Type: cross Abstract: In this paper, we consider triangle-free graphs with diameter 2. If a triangle-free graph $G$ with diameter 2 is not isomorphic to a star, then the radius of $G$ is also 2, where such a graph is also called a $2$-self-centered graph. [A characterization for 2-self-centered graphs, Discuss.
Publishing Below-Threshold Triangle Counts under Local Weight Differential Privacy
arXiv:2601.01710v3 Announce Type: replace Abstract: We propose an algorithm for counting below-threshold triangles in weighted graphs under local weight differential privacy. While prior work has largely focused on unweighted graphs, edge weights are intrinsic to many real-world networks. We consider the setting in which the graph topology is publicly known and privacy is required only for the contribution of an individual to incident edge weights, capturing practical scenarios such as road...
Stable Triangle Projections for Variable-Degree Tetrahedral Spaces and Uniform IPDG Preconditioning
Announce Type: new Abstract: The main ingredient of this paper is an edge-local variable-degree projection on a triangle that is uniformly stable in both L2 and H1. We use this two-dimensional operator in two tetrahedral constructions. First, on a reference tetrahedron, we build an H1-stable projection from a high order polynomial space onto a variable-degree space whose degrees are prescribed independently on edges, faces, and in the volume.
Distributed Triangle and Simplex Enumeration in Hypergraphs
Announce Type: replace Abstract: In the last decade, subgraph detection and enumeration have emerged as central problems in distributed graph algorithms. This is largely due to the problems' theoretical challenges and practical applications. In this paper, we initiate the systematic study of distributed sub-hypergraph enumeration in hypergraphs.
Mastermind of nanny love triangle murders defiantly rips sentencing as judge condemns 'evil' plot
The Virginia man convicted of killing his wife and another man to hide his affair with the family’s Brazilian au pair will spend the rest of his days behind bars after he was sentenced Friday to life in prison without the possibility of parole. Brendan Banfield, a former IRS law enforcement officer, was found guilty earlier this year on two counts of aggravated murder, one count of using a firearm in committing a crime and child endangerment stemming from the 2023 murders of Christine...
Painting the growing season in the Maize Triangle
Radar data from an agricultural area in South Africa, shown in a vivid color palette, reveal crop types and how they changed during the Southern Hemisphere's growing season.