相关论文: TriCCo -- a cubulation-based method for computing …

Grid clustering algorithms are valued for their efficiency in large-scale data analysis but face persistent limitations: parameter sensitivity, loss of structural detail at coarse resolutions, and misclassifications of edge or bridge cells…

Spatial correlations of the cubic 3-torus topology are analysed using the Planck 2013 data. The spatial-correlation method for detecting multiply connected spaces is based on the fact that positions on the cosmic microwave background (CMB)…

InteGriTy is a software package that performs topological analysis following AIM approach on electron densities given on 3D grids. Use of tricubic interpolation is made to get the density, its gradient and hessian matrix at any required…

Cluster identification tasks occur in a multitude of contexts in physics and engineering such as, for instance, cluster algorithms for simulating spin models, percolation simulations, segmentation problems in image processing, or network…

TriCG is a short-recurrence iterative method recently introduced by Montoison and Orban [SIAM J. Sci. Comput., 43 (2021), pp. A2502--A2525] for solving symmetric quasi-definite (SQD) linear systems. TriCG takes advantage of the inherent…

Hypergraphs, which use hyperedges to capture groupwise interactions among different entities, have gained increasing attention recently for their versatility in effectively modeling real-world networks. In this paper, we study the problem…

We present an algorithm for finding a perfect matching in a $3$-edge-connected cubic graph that intersects every $3$-edge cut in exactly one edge. Specifically, we propose an algorithm with a time complexity of $O(n \log^4 n)$, which…

Lagrangian coherent structures (LCS) in fluid flows appear as co-dimension one ridges of the finite time Lyapunov exponent (FTLE) field. In three- dimensions this means two-dimensional ridges. A fast algorithm is presented here to locate…

In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…

A connected graph is 4-connected if it contains at least five vertices and removing any three of them does not disconnect it. A frequent preprocessing step in graph drawing is to decompose a plane graph into its 4-connected components and…

Counting and finding triangles in graphs is often used in real-world analytics to characterize cohesiveness and identify communities in graphs. In this paper, we propose the novel concept of a cover-edge set that can be used to find…

DBSCAN is a fundamental spatial clustering algorithm with numerous practical applications. However, a bottleneck of the algorithm is in the worst case, the run time complexity is $O(n^2)$. To address this limitation, we propose a new…

Differentially private triangle counting in graphs is essential for analyzing connection patterns and calculating clustering coefficients while protecting sensitive individual information. Previous works have relied on either central or…

We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid…

TriCloudEdge is a scalable three-tier cloud continuum that integrates far-edge devices, intermediate edge nodes, and central cloud services, working in parallel as a unified solution. At the far edge, ultra-low-cost microcontrollers can…

A new kind of overset grid, named Yin-Yang grid, for spherical geometry is proposed. The Yin-Yang grid is composed of two identical component grids that are combined in a complemental way to cover a spherical surface with partial overlap on…

Simulations of many rigid bodies colliding with each other sometimes yield particularly interesting results if the colliding objects differ significantly in size and are non-spherical. The most expensive part within such a simulation code…

Tight triangulations are exotic, but highly regular objects in combinatorial topology. A triangulation is tight if all its piecewise linear embeddings into a Euclidean space are as convex as allowed by the topology of the underlying…

Sudoku puzzles are now popular among people in many countries across the world with simple constraints that no repeated digits in each row, each column, or each block. In this paper, we demonstrate that the Sudoku configuration provides us…

The enumeration of shortest paths in cubic grid is presented herein, which could have importance in image processing and also in the network sciences. The cubic grid considers three neighborhoods - namely, 6-, 18- and 26-neighborhood…