20 results for “Scale-free topology”
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The paper introduces a computational framework using Hodge zero-modes to track the geometry of topological features in parameter-dependent data, providing metrics like curvature and holonomy to quanti…
The paper introduces a subgrid marching tetrahedra scheme that accurately recovers complex, intersection-free manifold meshes from tetrahedral grids, overcoming limitations of classic marching methods…
The paper proposes using pseudo-sensitivities, derived from adjoint sensitivity fields, as an optimal conditioning signal in a Bernoulli flow-matching framework to significantly improve the out-of-dis…
The paper presents a novel and significantly faster algorithm for computing the second discrete homology group of a graph by identifying five basic quotient shapes of the 3-cube.
This paper develops a parameterized algorithm for the NP-complete Tree Containment problem, showing it can be solved efficiently based on a structural parameter called scanwidth.
The paper investigates which quantum encodings can be applied directly to classical data point clouds while preserving the topological invariants necessary for topological data analysis (TDA).
This paper presents an algorithmic framework for exhaustively generating and tabulating knot and link diagrams on the thickened torus.
The paper introduces and explores Truly Linear FPT (TLFPT), a complexity class defined by $O(n) + f(k)$, demonstrating that it is a strict subset of standard Linear FPT and providing new algorithms fo…
The paper refutes Steurer's conjecture regarding the existence of large constant-separated sets within families of unit-norm vectors with low average correlation, using high-dimensional expanders to s…
This paper introduces a new variant of the Traveling Salesman Problem where the goal is to find two paths connecting a set of sites while minimizing the Fréchet distance between the two paths.
The paper introduces MetricScenes, a new large-scale, in-the-wild dataset, and demonstrates that fine-tuning existing geometry models on this dataset significantly mitigates the scale-collapse problem…
This paper settles the complexity of three sketching problems in graphs and distributions.
PlanarBench introduces a novel benchmark to test LLM spatial reasoning by requiring them to draw planar graphs as ASCII art from an edge list, finding that edge count is a stronger difficulty predicto…
The paper systematically studies the trade-offs between the number of slopes, bends per edge, and required area for planar drawings of bounded-degree graphs, providing new constructions for high-degre…
The paper introduces an integrated computational toolbox using topological and fractal analysis to quantitatively track microstructural changes during casein gelation, correlating these subtle changes…
Junping Wang, Zhizhong Zhang, Yongqiang Tang, Geng Zheng +4 more
Restructuring the communication topology among robots provides significantly greater performance gains in multi-robot coordination than simply increasing the size of the onboard AI models, given fixed…
OrbitBFT introduces a novel two-stage hierarchical BFT consensus protocol that enables scalable and robust Byzantine Fault-Tolerant coordination for large-scale Low Earth Orbit satellite constellation…
The paper introduces Singularity-aware Adam (S-Adam), a novel optimizer that stabilizes deep learning training in non-smooth loss landscapes by dynamically damping updates based on local geometric ins…
The paper introduces S2MDF, a plug-and-play module that enforces a hard constraint to eliminate interpenetrations in multi-object Signed Distance Field (SDF) representations, significantly improving p…